benchmarks

Smooth extreme eigenvalue function for tensors

.gitignore

@@ -214,6 +214,7 @@ miniapps/adjoint/adjoint_advection_diffusion
 
 miniapps/dfem/dfem-minimal-surface
 miniapps/dfem/dfem-minimal-surface-output
+miniapps/dfem/dfem-hyperelasticity_energy
 
 miniapps/electromagnetics/volta
 miniapps/electromagnetics/tesla

CHANGELOG

@@ -44,6 +44,9 @@ Discretization improvements
 - Added methods to estimate function extremum using piecewise linear bounds plus
   recursive subdivision.
 
+- Added class VectorQuadratureSpace that represents a vector (multi-component)
+  version of the scalar (single-component) class QuadratureSpaceBase.
+
 - Extend FindPointsGSLIB to support surface meshes.
 
 - Added support for complex-valued mixed bilinear forms via the new classes
@@ -53,16 +56,6 @@ Discretization improvements
   ComplexHypreParMatrix::GetSystemMatrix, which previously assumed equal
   trial and test spaces.
 
-- Added FiniteElementSpace::GetBoundaryLoopEdgeDofs to extract the edge DOFs on
-  the perimeter loop of a set of boundary elements, with a ParFiniteElementSpace
-  overload that reconciles the selection across processor boundaries so the
-  result is partition invariant. This is useful for imposing boundary conditions
-  on boundary edge DOFs.
-
-- Added a MaxAbs reduction to GroupCommunicator that selects the signed value of
-  largest magnitude across a group, keeping its sign. Equal-magnitude ties
-  resolve deterministically to the positive value.
-
 Meshing improvements
 --------------------
 - Added support for nonuniform anisotropic mesh refinement on parallel quad/hex
@@ -89,11 +82,6 @@ Linear and nonlinear solvers
   PRefinement multigrid methods for problems posed on trace spaces (see e.g. the
   DPG miniapps).
 
-- Added new class MultiVector: an array of Vectors of different sizes where each
-  Vector can be allocated independently. Also, added associated methods in class
-  Operator: MultMV, MultTransposeMV, and GetGradientMV, that use MultiVector
-  objects for input and/or output parameters. [PR #5249]
-
 GPU computing
 -------------
 - Improved partial assembly for VectorDivergenceIntegrator with shared-memory
@@ -107,22 +95,6 @@ GPU computing
 
 - Added device assembly support for 3D H(curl) VectorFEDomainLFIntegrator.
 
-- Added partial assembly support for MixedScalarWeakGradientIntegrator.
-
-- Added partial assembly support for MixedDotProductIntegrator.
-
-- Added partial assembly support for MixedScalarCrossProductIntegrator.
-
-- Added partial assembly support for MixedScalarWeakCrossProductIntegrator.
-
-- Added partial assembly support for MixedVectorGradientIntegrator for H1->RT.
-
-- Added support for device partial assembly CurlInterpolator.
-  This supports 2D and 3D variants:
-    2D H1 (out-of-plane) to RT (in-plane)
-    2D ND (in-plane) to Integral L2 (out-of-plane)
-    3D ND to RT
-
 - Added NVIDIA cuDSS library interface. Implementation examples have been
   added to ex1 and ex1p. See https://developer.nvidia.com/cudss for more
   details. Supported versions >= 0.6.0.
@@ -135,9 +107,6 @@ GPU computing
 - Added support for FiniteElement::MapType::INTEGRAL spaces to
   QuadratureInterpolator.
 
-- Added support for FiniteElement::MapType::INTEGRAL spaces to
-  MixedScalarCurlIntegrator.
-
 New and updated examples and miniapps
 -------------------------------------
 - The Lorentz miniapp (in miniapps/electromagnetics) has been updated to
@@ -152,20 +121,6 @@ Miscellaneous
   using the new method ApplyDofSigns() in class ParFiniteElementSpace: the
   method will return immediately if no sign flips are needed.
 
-- Added support for coefficient-weighted LOR transfer in
-  L2ProjectionGridTransfer. The transfer conserves the weighted mass, for
-  example when transferring velocity while conserving density-weighted momentum.
-  This is illustrated in the lor-transfer and plor-transfer miniapps.
-
-- Added support for saving DataCollection output on the node-local storage,
-  instead of requiring that the filesystem is shared among all the ranks.
-
-API changes
------------
-- Removed ProjectGrad from 2D RT elements. Users should use ProjectCurl instead.
-  This also fixes a bug where ProjectCurl was returning the negative curl,
-  identical to ProjectGrad.
-
 
 Version 4.9, released on Dec 11, 2025
 =====================================

CMakeLists.txt

@@ -88,9 +88,18 @@ if (MFEM_USE_STRUMPACK OR MFEM_USE_MUMPS)
   # Just needed to find the MPI_Fortran libraries to link with
   set(XSDK_ENABLE_Fortran ON)
 endif()
-# RAJA requires C++20:
-if ((MFEM_USE_UMPIRE OR MFEM_USE_RAJA) AND ("${CMAKE_CXX_STANDARD}" LESS "20"))
-  set(CMAKE_CXX_STANDARD 20 CACHE STRING "C++ standard to use." FORCE)
+# Ginkgo requires C++17:
+if ((MFEM_USE_GINKGO) AND ("${CMAKE_CXX_STANDARD}" LESS "17"))
+  set(CMAKE_CXX_STANDARD 17 CACHE STRING "C++ standard to use." FORCE)
+# Google Benchmark, SUNDIALS, STRUMPACK, Tribol, RAJA and Umpire require C++14:
+elseif ((MFEM_USE_BENCHMARK OR
+         MFEM_USE_SUNDIALS OR
+         MFEM_USE_STRUMPACK OR
+         MFEM_USE_TRIBOL OR
+         MFEM_USE_RAJA OR
+         MFEM_USE_UMPIRE) AND
+    ("${CMAKE_CXX_STANDARD}" LESS "14"))
+  set(CMAKE_CXX_STANDARD 14 CACHE STRING "C++ standard to use." FORCE)
 endif()
 
 # Include xSDK default CMake file.
@@ -175,6 +184,45 @@ if (MFEM_USE_CUDA)
    set(CMAKE_CUDA_EXTENSIONS OFF CACHE BOOL "Enable CUDA standard extensions.")
    set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS}")
    find_package(CUDAToolkit REQUIRED)
+   if(CMAKE_CUDA_COMPILER_ID STREQUAL "Clang")
+     set(_real_fatbinary "${CMAKE_CUDA_FATBINARY}")
+     set(_fatbinary_wrapper
+       "${CMAKE_BINARY_DIR}/cmake-fatbinary-cuda13")
+
+     file(WRITE "${_fatbinary_wrapper}"
+"#!/usr/bin/env bash
+real_fatbinary=\"${_real_fatbinary}\"
+"
+[=[
+translated=()
+
+for argument in "$@"; do
+  case "$argument" in
+    -im=profile=sm_*,file=*)
+      value=${argument#-im=profile=sm_}
+      architecture=${value%%,*}
+      filename=${value#*,file=}
+      translated+=(
+        "--image3=kind=elf,sm=${architecture},file=${filename}"
+      )
+      ;;
+    *)
+      translated+=("$argument")
+      ;;
+  esac
+done
+
+exec "$real_fatbinary" "${translated[@]}"
+]=])
+
+    file(CHMOD "${_fatbinary_wrapper}"
+    PERMISSIONS
+      OWNER_READ OWNER_WRITE OWNER_EXECUTE
+      GROUP_READ GROUP_EXECUTE
+      WORLD_READ WORLD_EXECUTE)
+
+    set(CMAKE_CUDA_FATBINARY "${_fatbinary_wrapper}")
+endif()
    set(CUSPARSE_FOUND TRUE)
    set(CUBLAS_FOUND TRUE)
    # Initialize CUSPARSE_LIBRARIES and CUBLAS_LIBRARIES:
@@ -599,6 +647,13 @@ if (MFEM_USE_ENZYME)
     set(ENZYME_INCLUDE_DIRS ${ENZYME_DIR}/include)
 endif()
 
+if (MFEM_USE_PROTEUS)
+    enable_language(C)
+    find_package(proteus REQUIRED PATHS "${PROTEUS_DIR}")
+    message(STATUS "${PROTEUS_DIR}/include")
+    include_directories("${PROTEUS_DIR}/include")
+endif()
+
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
   if (APPLE)
@@ -735,6 +790,16 @@ mfem_add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
 target_compile_features(mfem PUBLIC cxx_std_${CMAKE_CXX_STANDARD})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
 target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES} ${TPL_TARGETS})
+
+if (MFEM_USE_PROTEUS)
+    add_library(ClangProteusFlags INTERFACE IMPORTED)
+    set_target_properties(ClangProteusFlags PROPERTIES
+        INTERFACE_COMPILE_OPTIONS "-fpass-plugin=$<TARGET_FILE:ProteusPass>"
+    )
+    target_link_libraries(mfem PUBLIC ClangProteusFlags)
+    target_link_libraries(mfem PUBLIC proteus)
+endif()
+
 if (TPL_TARGETS)
   add_dependencies(mfem ${TPL_TARGETS})
 endif()
@@ -742,7 +807,7 @@ if (MINGW)
   target_link_libraries(mfem PRIVATE ws2_32)
 endif()
 if (MSVC)
-  target_compile_options(mfem PUBLIC "/wd4819")
+  target_compile_options(mfem PUBLIC "/wd4819" "/bigobj")
 endif()
 message(STATUS "TPL_INCLUDE_DIRS = ${TPL_INCLUDE_DIRS}")
 target_include_directories(mfem
@@ -771,7 +836,7 @@ set_target_properties(mfem PROPERTIES SOVERSION "${mfem_VERSION}")
 # If building out-of-source, define MFEM_CONFIG_FILE to point to the config file
 # inside the build directory.
 if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
-  target_compile_definitions(mfem PRIVATE
+  target_compile_definitions(mfem PUBLIC
     "MFEM_CONFIG_FILE=\"${PROJECT_BINARY_DIR}/config/_config.hpp\"")
 endif()
 
@@ -831,16 +896,15 @@ if (MFEM_ENABLE_TESTING)
   add_mfem_target(${MFEM_ALL_TESTS_TARGET_NAME} OFF)
   add_subdirectory(tests EXCLUDE_FROM_ALL)
 
-  if (MFEM_USE_BENCHMARK)
-    # Create a target for all benchmarks and, optionally, enable it.
-    set(MFEM_ALL_BENCHMARKS_TARGET_NAME benchmarks)
-    add_mfem_target(${MFEM_ALL_BENCHMARKS_TARGET_NAME}
-                    ${MFEM_ENABLE_BENCHMARKS})
-    if (MFEM_ENABLE_BENCHMARKS)
-      add_subdirectory(tests/benchmarks) #install benchmarks if enabled
-    else()
-      add_subdirectory(tests/benchmarks EXCLUDE_FROM_ALL)
-    endif()
+  # Create a target for all benchmarks and, optionally, enable it. Some simple
+  # timer-based benchmarks in tests/benchmarks do not require Google Benchmark.
+  set(MFEM_ALL_BENCHMARKS_TARGET_NAME benchmarks)
+  add_mfem_target(${MFEM_ALL_BENCHMARKS_TARGET_NAME}
+                  ${MFEM_ENABLE_BENCHMARKS})
+  if (MFEM_ENABLE_BENCHMARKS)
+    add_subdirectory(tests/benchmarks) #install benchmarks if enabled
+  else()
+    add_subdirectory(tests/benchmarks EXCLUDE_FROM_ALL)
   endif()
 endif()
 
@@ -1020,6 +1084,7 @@ install(EXPORT ${PROJECT_NAME_UC}Targets
 install(DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/data
   DESTINATION ${MFEM_INSTALL_DIR} OPTIONAL)
 
+
 #-------------------------------------------------------------------------------
 # Create 'config.mk' from 'config.mk.in' for the build and install locations and
 # define install rules for 'config.mk' and 'test.mk'

config/config.hpp

@@ -18,9 +18,9 @@
 #define MFEM_CONFIG_HPP
 
 #ifdef MFEM_CONFIG_FILE
-#include MFEM_CONFIG_FILE
+#include MFEM_CONFIG_FILE // IWYU pragma: export
 #else
-#include "_config.hpp"
+#include "_config.hpp" // IWYU pragma: export
 #endif
 
 #include <cstdint>

config/defaults.mk

@@ -28,8 +28,11 @@ MPICXX = mpicxx
 BASE_FLAGS  = -std=c++17
 OPTIM_FLAGS = -O3 $(BASE_FLAGS)
 
-# The variable WARNING_FLAGS depends on which compiler is used, and is defined
-# later in this file.
+# Shadow warnings for clang only; GCC's -Wshadow flags more.
+SHADOW_WARNING_FLAG = $(if $(findstring clang,\
+ $(shell $(MFEM_HOST_CXX) --version 2>/dev/null)),-Wshadow,)
+WARNING_FLAGS = -pedantic -Wall $(SHADOW_WARNING_FLAG)
+
 DEBUG_FLAGS = $(strip -g $(addprefix $(XCOMPILER),$(WARNING_FLAGS)) $(BASE_FLAGS))
 
 # Prefixes for passing flags to the compiler and linker when using CXX or MPICXX
@@ -49,10 +52,6 @@ SHARED = NO
 #
 # If you set MFEM_USE_ENZYME=YES, must use CUDA_CXX=clang++
 CUDA_CXX = nvcc
-# CUDA compute capability used during compilation, e.g. sm_60. Multiple
-# architectures can be requested as a comma-separated list, e.g. sm_70,sm_80.
-# A single value may also be one of the nvcc special values "all",
-# "all-major", or "native".
 CUDA_ARCH = sm_60
 # Base CUDA install directory, only needed if building with clang+cuda:
 # The default setting is:
@@ -61,23 +60,11 @@ CUDA_ARCH = sm_60
 # 3. Use /usr/local/cuda
 CUDA_DIR = $(or $(CUDA_HOME),$(patsubst %/,%,$(dir \
  $(patsubst %/,%,$(dir $(shell command -v nvcc))))),/usr/local/cuda)
-# Derive nvcc/clang architecture flags from CUDA_ARCH. A comma-separated list
-# expands into one -gencode / --cuda-gpu-arch flag per architecture; otherwise
-# use the -arch / --cuda-gpu-arch shorthand.
-MFEM_COMMA := ,
-CUDA_ARCH_NUMS = $(patsubst sm_%,%,$(subst $(MFEM_COMMA), ,$(CUDA_ARCH)))
-NVCC_ARCH_FLAGS = $(strip $(if $(findstring $(MFEM_COMMA),$(CUDA_ARCH)),\
- $(foreach arch,$(CUDA_ARCH_NUMS),\
- -gencode arch=compute_$(arch)$(MFEM_COMMA)code=sm_$(arch)),\
- -arch=$(CUDA_ARCH)))
-CLANG_ARCH_FLAGS = $(strip $(if $(findstring $(MFEM_COMMA),$(CUDA_ARCH)),\
- $(foreach arch,$(CUDA_ARCH_NUMS),--cuda-gpu-arch=sm_$(arch)),\
- --cuda-gpu-arch=$(CUDA_ARCH)))
 # flags for clang+cuda
-CLANG_CUDA_FLAGS = -xcuda --cuda-path=$(CUDA_DIR) $(CLANG_ARCH_FLAGS)
+CLANG_CUDA_FLAGS = -xcuda --cuda-path=$(CUDA_DIR) --cuda-gpu-arch=$(CUDA_ARCH)
 # flags for nvcc
 NVCC_FLAGS = -x=cu --expt-extended-lambda --expt-relaxed-constexpr \
- $(NVCC_ARCH_FLAGS) -isystem "$(CUDA_DIR)/include"
+ -arch=$(CUDA_ARCH) -isystem "$(CUDA_DIR)/include"
 # Prefixes for passing flags to the host compiler and linker when using
 # CUDA_CXX=nvcc
 CUDA_XCOMPILER = -Xcompiler=
@@ -395,7 +382,7 @@ CUDSS_LIBRARY_DIR = $(CUDSS_DIR)/lib
 CUDSS_OPT         = -I$(CUDSS_INCLUDE_DIR)
 CUDSS_LIB         = \
  $(XLINKER)-rpath,$(CUDSS_LIBRARY_DIR) -L$(CUDSS_LIBRARY_DIR) -lcudss
-# The cuDSS communication and threading libraries.
+# The cuDSS communication and threading libraries. 
 MFEM_CUDSS_COMM_LIB = $(abspath $(wildcard $(or $(CUDSS_COMM_LIB),\
    $(subst @MFEM_DIR@,$(MFEM_DIR), $(CUDSS_LIBRARY_DIR)/libcudss_commlayer_openmpi.so))))
 MFEM_CUDSS_THREADING_LIB = $(abspath $(wildcard $(or $(CUDSS_THREADING_LIB),\
@@ -678,15 +665,3 @@ VERBOSE = NO
 
 # Optional build tag
 MFEM_BUILD_TAG = $(shell uname -snm)
-
-# Enable -pedantic flag only for gcc or clang. nvcc complains with -pedantic
-# because of line directives.
-PEDANTIC_FLAG = $(if \
-   $(findstring NVIDIA,$(shell $(MFEM_CXX) --version 2>&1)),, \
-   $(if $(or \
-      $(findstring gcc version,$(shell $(MFEM_CXX) -v 2>&1)), \
-      $(findstring clang version,$(shell $(MFEM_CXX) -v 2>&1))),-pedantic,))
-# Enable shadow warnings for clang only; GCC's -Wshadow flags more.
-SHADOW_WARNING_FLAG = $(if $(findstring clang,\
- $(shell $(MFEM_HOST_CXX) --version 2>/dev/null)),-Wshadow,)
-WARNING_FLAGS = $(PEDANTIC_FLAG) -Wall $(SHADOW_WARNING_FLAG)

data/nested_cubes.geo

@@ -1,131 +0,0 @@
-// Define the cube sizes
-L_outer = 1.0;
-L_inner = 0.5;
-
-// Set mesh size and algorithm
-mesh_size = 0.4;
-Mesh.Algorithm3D = 1; // Delaunay algorithm for 3D mesh
-Mesh.CharacteristicLengthFactor = 1.0;
-Mesh.MshFileVersion = 2.2;
-
-// Define center point for concentric cubes
-cx = 0.5;
-cy = 0.5;
-cz = 0.5;
-
-// Define the points (vertices of the outer cube)
-Point(1) = {cx-L_outer/2, cy-L_outer/2, cz-L_outer/2, mesh_size};
-Point(2) = {cx+L_outer/2, cy-L_outer/2, cz-L_outer/2, mesh_size};
-Point(3) = {cx+L_outer/2, cy+L_outer/2, cz-L_outer/2, mesh_size};
-Point(4) = {cx-L_outer/2, cy+L_outer/2, cz-L_outer/2, mesh_size};
-Point(5) = {cx-L_outer/2, cy-L_outer/2, cz+L_outer/2, mesh_size};
-Point(6) = {cx+L_outer/2, cy-L_outer/2, cz+L_outer/2, mesh_size};
-Point(7) = {cx+L_outer/2, cy+L_outer/2, cz+L_outer/2, mesh_size};
-Point(8) = {cx-L_outer/2, cy+L_outer/2, cz+L_outer/2, mesh_size};
-
-// Define the points (vertices of the inner cube)
-Point(9) = {cx-L_inner/2, cy-L_inner/2, cz-L_inner/2, mesh_size};
-Point(10) = {cx+L_inner/2, cy-L_inner/2, cz-L_inner/2, mesh_size};
-Point(11) = {cx+L_inner/2, cy+L_inner/2, cz-L_inner/2, mesh_size};
-Point(12) = {cx-L_inner/2, cy+L_inner/2, cz-L_inner/2, mesh_size};
-Point(13) = {cx-L_inner/2, cy-L_inner/2, cz+L_inner/2, mesh_size};
-Point(14) = {cx+L_inner/2, cy-L_inner/2, cz+L_inner/2, mesh_size};
-Point(15) = {cx+L_inner/2, cy+L_inner/2, cz+L_inner/2, mesh_size};
-Point(16) = {cx-L_inner/2, cy+L_inner/2, cz+L_inner/2, mesh_size};
-
-// Define the lines (edges of the outer cube)
-Line(1) = {1, 2};
-Line(2) = {2, 3};
-Line(3) = {3, 4};
-Line(4) = {4, 1};
-Line(5) = {5, 6};
-Line(6) = {6, 7};
-Line(7) = {7, 8};
-Line(8) = {8, 5};
-Line(9) = {1, 5};
-Line(10) = {2, 6};
-Line(11) = {3, 7};
-Line(12) = {4, 8};
-
-// Define the lines (edges of the inner cube)
-Line(13) = {9, 10};
-Line(14) = {10, 11};
-Line(15) = {11, 12};
-Line(16) = {12, 9};
-Line(17) = {13, 14};
-Line(18) = {14, 15};
-Line(19) = {15, 16};
-Line(20) = {16, 13};
-Line(21) = {9, 13};
-Line(22) = {10, 14};
-Line(23) = {11, 15};
-Line(24) = {12, 16};
-
-// Define the surfaces (faces of the outer cube)
-Line Loop(1) = {1, 2, 3, 4};
-Plane Surface(1) = {1};
-
-Line Loop(2) = {5, 6, 7, 8};
-Plane Surface(2) = {2};
-
-Line Loop(3) = {9, 5, -10, -1};
-Plane Surface(3) = {3};
-
-Line Loop(4) = {10, 6, -11, -2};
-Plane Surface(4) = {4};
-
-Line Loop(5) = {11, 7, -12, -3};
-Plane Surface(5) = {5};
-
-Line Loop(6) = {12, 8, -9, -4};
-Plane Surface(6) = {6};
-
-// Define the surfaces (faces of the inner cube)
-Line Loop(7) = {13, 14, 15, 16};
-Plane Surface(7) = {7};
-
-Line Loop(8) = {17, 18, 19, 20};
-Plane Surface(8) = {8};
-
-Line Loop(9) = {21, 17, -22, -13};
-Plane Surface(9) = {9};
-
-Line Loop(10) = {22, 18, -23, -14};
-Plane Surface(10) = {10};
-
-Line Loop(11) = {23, 19, -24, -15};
-Plane Surface(11) = {11};
-
-Line Loop(12) = {24, 20, -21, -16};
-Plane Surface(12) = {12};
-
-// Define the volumes
-Surface Loop(1) = {1, 2, 3, 4, 5, 6};
-Surface Loop(2) = {7, 8, 9, 10, 11, 12};
-Volume(1) = {1, 2}; // Outer volume with inner hole
-Volume(2) = {2};    // Inner volume
-
-// Assign physical groups
-Physical Volume(1) = {1}; // Outer volume
-Physical Volume(2) = {2}; // Inner volume
-
-// Outer cube surfaces
-Physical Surface(1) = {1}; // Outer bottom
-Physical Surface(2) = {2}; // Outer top
-Physical Surface(3) = {3}; // Outer front
-Physical Surface(4) = {4}; // Outer right
-Physical Surface(5) = {5}; // Outer back
-Physical Surface(6) = {6}; // Outer left
-
-// Inner cube surfaces
-Physical Surface(7) = {7};  // Inner bottom (-xy)
-Physical Surface(8) = {8};  // Inner top (+xy)
-Physical Surface(9) = {9};  // Inner front (-xz)
-Physical Surface(10) = {10}; // Inner right (+yz)
-Physical Surface(11) = {11}; // Inner back (+xz)
-Physical Surface(12) = {12}; // Inner left (-yz)
-
-// Mesh control
-Mesh.OptimizeNetgen = 1;
-Mesh.Optimize = 1;
-Mesh.ElementOrder = 1;

data/nested_cubes.msh

@@ -1,907 +0,0 @@
-$MeshFormat
-2.2 0 8
-$EndMeshFormat
-$Nodes
-138
-1 0 0 0
-2 1 0 0
-3 1 1 0
-4 0 1 0
-5 0 0 1
-6 1 0 1
-7 1 1 1
-8 0 1 1
-9 0.25 0.25 0.25
-10 0.75 0.25 0.25
-11 0.75 0.75 0.25
-12 0.25 0.75 0.25
-13 0.25 0.25 0.75
-14 0.75 0.25 0.75
-15 0.75 0.75 0.75
-16 0.25 0.75 0.75
-17 0.3333333333325025 0 0
-18 0.6666666666657889 0 0
-19 1 0.3333333333325025 0
-20 1 0.6666666666657889 0
-21 0.6666666666675911 1 0
-22 0.3333333333347203 1 0
-23 0 0.6666666666675911 0
-24 0 0.3333333333347203 0
-25 0.3333333333325025 0 1
-26 0.6666666666657889 0 1
-27 1 0.3333333333325025 1
-28 1 0.6666666666657889 1
-29 0.6666666666675911 1 1
-30 0.3333333333347203 1 1
-31 0 0.6666666666675911 1
-32 0 0.3333333333347203 1
-33 0 0 0.3333333333325025
-34 0 0 0.6666666666657889
-35 1 0 0.3333333333325025
-36 1 0 0.6666666666657889
-37 1 1 0.3333333333325025
-38 1 1 0.6666666666657889
-39 0 1 0.3333333333325025
-40 0 1 0.6666666666657889
-41 0.5000000000003468 0.25 0.25
-42 0.75 0.5000000000003468 0.25
-43 0.5000000000013763 0.75 0.25
-44 0.25 0.5000000000013763 0.25
-45 0.5000000000003468 0.25 0.75
-46 0.75 0.5000000000003468 0.75
-47 0.5000000000013763 0.75 0.75
-48 0.25 0.5000000000013763 0.75
-49 0.25 0.25 0.5000000000003468
-50 0.75 0.25 0.5000000000003468
-51 0.75 0.75 0.5000000000003468
-52 0.25 0.75 0.5000000000003468
-53 0.7113248654055673 0.4999999999991457 0
-54 0.2886751345942123 0.5000000000011557 0
-55 0.5000000000006117 0.7525600817161773 0
-56 0.4999999999993867 0.2474399182839603 0
-57 0.2423197548524782 0.7576802451481532 0
-58 0.757680245147464 0.2423197548520695 0
-59 0.2423197548507857 0.2423197548513912 0
-60 0.7576802451491019 0.7576802451486099 0
-61 0.7113248654055673 0.4999999999991457 1
-62 0.2886751345942123 0.5000000000011557 1
-63 0.5000000000006117 0.7525600817161773 1
-64 0.4999999999993867 0.2474399182839603 1
-65 0.2423197548524782 0.7576802451481532 1
-66 0.757680245147464 0.2423197548520695 1
-67 0.2423197548507857 0.2423197548513912 1
-68 0.7576802451491019 0.7576802451486099 1
-69 0.4999999999993203 0 0.301447615129799
-70 0.4999999999992795 0 0.7028666213189801
-71 0.7525600817158393 0 0.5007190394076877
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-570 4 2 1 1 48 105 62 106
-571 4 2 1 1 91 43 12 22
-572 4 2 1 1 91 43 22 85
-573 4 2 1 1 93 12 23 98
-574 4 2 1 1 93 23 12 44
-575 4 2 1 1 46 81 116 15
-576 4 2 1 1 46 116 81 78
-577 4 2 1 1 92 47 120 15
-578 4 2 1 1 120 47 92 86
-579 4 2 1 1 46 82 115 78
-580 4 2 1 1 46 115 82 14
-581 4 2 1 1 73 45 112 70
-582 4 2 1 1 73 112 45 14
-583 4 2 1 1 99 44 9 24
-584 4 2 1 1 99 44 24 93
-585 4 2 1 1 84 42 113 77
-586 4 2 1 1 84 113 42 10
-587 4 2 1 1 76 41 109 69
-588 4 2 1 1 109 41 76 9
-589 4 2 1 1 42 83 114 77
-590 4 2 1 1 42 114 83 11
-591 4 2 2 2 135 13 122 131
-592 4 2 2 2 132 138 125 110
-593 4 2 2 2 138 108 125 106
-594 4 2 2 2 136 108 125 137
-595 4 2 2 2 110 138 125 131
-596 4 2 2 2 136 107 134 125
-597 4 2 2 2 122 135 131 125
-598 4 2 2 2 13 49 122 131
-599 4 2 2 2 136 108 137 46
-600 4 2 2 2 110 138 131 111
-601 4 2 2 2 132 138 110 112
-602 4 2 2 2 106 107 108 125
-603 4 2 2 2 138 112 137 45
-604 4 2 2 2 104 127 125 128
-605 4 2 2 2 113 115 114 125
-606 4 2 2 2 131 122 125 121
-607 4 2 2 2 112 45 14 137
-608 4 2 2 2 110 131 125 130
-609 4 2 2 2 115 116 114 125
-610 4 2 2 2 132 138 112 137
-611 4 2 2 2 50 137 115 132
-612 4 2 2 2 104 127 128 42
-613 4 2 2 2 105 134 125 133
-614 4 2 2 2 129 120 51 119
-615 4 2 2 2 104 130 128 125
-616 4 2 2 2 105 134 133 47
-617 4 2 2 2 135 106 138 125
-618 4 2 2 2 106 105 107 125
-619 4 2 2 2 138 108 106 45
-620 4 2 2 2 104 130 125 102
-621 4 2 2 2 104 127 42 103
-622 4 2 2 2 109 131 49 111
-623 4 2 2 2 106 135 48 105
-624 4 2 2 2 126 101 43 125
-625 4 2 2 2 138 137 125 108
-626 4 2 2 2 104 127 103 125
-627 4 2 2 2 116 114 129 51
-628 4 2 2 2 136 108 46 107
-629 4 2 2 2 136 108 107 125
-630 4 2 2 2 52 124 123 125
-631 4 2 2 2 132 112 110 50
-632 4 2 2 2 44 121 125 123
-633 4 2 2 2 131 122 121 49
-634 4 2 2 2 105 134 47 107
-635 4 2 2 2 106 13 135 138
-636 4 2 2 2 52 133 125 118
-637 4 2 2 2 103 43 101 125
-638 4 2 2 2 117 43 119 125
-639 4 2 2 2 105 134 107 125
-640 4 2 2 2 137 115 132 125
-641 4 2 2 2 50 137 132 112
-642 4 2 2 2 106 135 105 125
-643 4 2 2 2 102 101 44 125
-644 4 2 2 2 104 130 102 41
-645 4 2 2 2 138 45 13 111
-646 4 2 2 2 131 138 135 13
-647 4 2 2 2 138 112 45 111
-648 4 2 2 2 131 138 13 111
-649 4 2 2 2 107 134 15 136
-650 4 2 2 2 118 52 117 125
-651 4 2 2 2 101 126 12 44
-652 4 2 2 2 104 130 41 128
-653 4 2 2 2 138 137 108 45
-654 4 2 2 2 133 118 16 47
-655 4 2 2 2 44 101 126 125
-656 4 2 2 2 133 134 118 47
-657 4 2 2 2 133 134 125 118
-658 4 2 2 2 124 122 123 125
-659 4 2 2 2 129 118 119 125
-660 4 2 2 2 102 104 103 125
-661 4 2 2 2 135 48 13 106
-662 4 2 2 2 123 122 121 125
-663 4 2 2 2 103 127 43 125
-664 4 2 2 2 106 45 13 138
-665 4 2 2 2 103 11 127 42
-666 4 2 2 2 127 51 129 114
-667 4 2 2 2 13 49 131 111
-668 4 2 2 2 137 108 14 46
-669 4 2 2 2 15 47 134 107
-670 4 2 2 2 10 41 128 104
-671 4 2 2 2 16 118 133 52
-672 4 2 2 2 46 107 15 136
-673 4 2 2 2 41 102 9 130
-674 4 2 2 2 128 50 132 110
-675 4 2 2 2 10 41 110 128
-676 4 2 2 2 50 137 112 14
-677 4 2 2 2 130 102 9 44
-678 4 2 2 2 105 133 16 47
-679 4 2 2 2 127 11 103 43
-680 4 2 2 2 128 130 41 110
-681 4 2 2 2 116 134 15 51
-682 4 2 2 2 137 45 14 108
-683 4 2 2 2 12 126 101 43
-684 4 2 2 2 133 48 135 105
-685 4 2 2 2 128 42 10 104
-686 4 2 2 2 131 9 109 49
-687 4 2 2 2 118 117 119 125
-688 4 2 2 2 102 103 101 125
-689 4 2 2 2 129 118 125 134
-690 4 2 2 2 125 129 116 114
-691 4 2 2 2 117 126 43 125
-692 4 2 2 2 126 117 12 52
-693 4 2 2 2 52 126 117 125
-694 4 2 2 2 12 117 126 43
-695 4 2 2 2 127 51 114 11
-696 4 2 2 2 114 129 127 125
-697 4 2 2 2 127 119 43 125
-698 4 2 2 2 119 11 127 43
-699 4 2 2 2 127 113 114 125
-700 4 2 2 2 127 113 42 114
-701 4 2 2 2 128 130 110 125
-702 4 2 2 2 15 47 120 134
-703 4 2 2 2 127 11 114 42
-704 4 2 2 2 120 47 118 134
-705 4 2 2 2 44 130 102 125
-706 4 2 2 2 44 126 12 123
-707 4 2 2 2 123 44 126 125
-708 4 2 2 2 129 118 134 120
-709 4 2 2 2 110 132 128 125
-710 4 2 2 2 128 127 125 113
-711 4 2 2 2 128 127 113 42
-712 4 2 2 2 128 50 110 10
-713 4 2 2 2 113 42 10 128
-714 4 2 2 2 129 134 125 116
-715 4 2 2 2 127 51 11 119
-716 4 2 2 2 129 134 116 51
-717 4 2 2 2 127 51 119 129
-718 4 2 2 2 129 119 127 125
-719 4 2 2 2 110 131 130 109
-720 4 2 2 2 109 130 9 131
-721 4 2 2 2 121 130 9 44
-722 4 2 2 2 122 48 13 135
-723 4 2 2 2 44 121 130 125
-724 4 2 2 2 110 138 111 112
-725 4 2 2 2 131 138 125 135
-726 4 2 2 2 115 137 14 46
-727 4 2 2 2 126 52 12 123
-728 4 2 2 2 123 126 52 125
-729 4 2 2 2 50 137 14 115
-730 4 2 2 2 136 137 115 46
-731 4 2 2 2 121 9 131 49
-732 4 2 2 2 121 131 130 125
-733 4 2 2 2 131 130 9 121
-734 4 2 2 2 113 132 115 125
-735 4 2 2 2 113 50 115 132
-736 4 2 2 2 128 50 10 113
-737 4 2 2 2 132 113 128 125
-738 4 2 2 2 128 50 113 132
-739 4 2 2 2 133 105 135 125
-740 4 2 2 2 52 124 125 133
-741 4 2 2 2 133 48 105 16
-742 4 2 2 2 16 133 124 52
-743 4 2 2 2 136 137 125 115
-744 4 2 2 2 132 138 137 125
-745 4 2 2 2 41 130 9 109
-746 4 2 2 2 134 120 15 51
-747 4 2 2 2 129 118 120 119
-748 4 2 2 2 129 120 134 51
-749 4 2 2 2 135 122 124 125
-750 4 2 2 2 135 48 124 122
-751 4 2 2 2 133 48 16 124
-752 4 2 2 2 133 135 124 125
-753 4 2 2 2 133 48 124 135
-754 4 2 2 2 116 136 134 125
-755 4 2 2 2 115 136 116 125
-756 4 2 2 2 46 115 136 116
-757 4 2 2 2 136 134 15 116
-758 4 2 2 2 46 136 15 116
-759 4 2 2 2 109 41 130 110
-760 4 2 2 2 110 131 109 111
-$EndElements

data/square_in_square.geo

@@ -1,77 +0,0 @@
-// Square-in-square 2D geometry for MFEM
-// Creates concentric squares with different material attributes
-
-// Define the square sizes
-L_outer = 2.0;
-L_inner = 0.5;
-
-// Set mesh size and algorithm
-mesh_size = 1.0;
-Mesh.Algorithm = 6; // Frontal-Delaunay for 2D triangular mesh
-Mesh.CharacteristicLengthFactor = 1.0;
-Mesh.MshFileVersion = 2.2;
-
-// Define center point for concentric squares
-cx = 0.0;
-cy = 0.0;
-
-// Define the points (vertices of the outer square)
-Point(1) = {cx-L_outer/2, cy-L_outer/2, 0, mesh_size}; // bottom-left outer
-Point(2) = {cx+L_outer/2, cy-L_outer/2, 0, mesh_size}; // bottom-right outer
-Point(3) = {cx+L_outer/2, cy+L_outer/2, 0, mesh_size}; // top-right outer
-Point(4) = {cx-L_outer/2, cy+L_outer/2, 0, mesh_size}; // top-left outer
-
-// Define the points (vertices of the inner square)
-Point(5) = {cx-L_inner/2, cy-L_inner/2, 0, mesh_size}; // bottom-left inner
-Point(6) = {cx+L_inner/2, cy-L_inner/2, 0, mesh_size}; // bottom-right inner
-Point(7) = {cx+L_inner/2, cy+L_inner/2, 0, mesh_size}; // top-right inner
-Point(8) = {cx-L_inner/2, cy+L_inner/2, 0, mesh_size}; // top-left inner
-
-// Define the lines (edges of the outer square)
-Line(1) = {1, 2}; // bottom edge
-Line(2) = {2, 3}; // right edge
-Line(3) = {3, 4}; // top edge
-Line(4) = {4, 1}; // left edge
-
-// Define the lines (edges of the inner square)
-Line(5) = {5, 6}; // bottom edge
-Line(6) = {6, 7}; // right edge
-Line(7) = {7, 8}; // top edge
-Line(8) = {8, 5}; // left edge
-
-// Define the surfaces
-// Outer square boundary
-Line Loop(1) = {1, 2, 3, 4};
-
-// Inner square boundary (hole in the outer region)
-Line Loop(2) = {5, 6, 7, 8};
-
-// Define the surface areas
-// Outer region (annular region between squares)
-Plane Surface(1) = {1, 2}; // Outer loop minus inner loop (creates hole)
-
-// Inner region (solid inner square)
-Plane Surface(2) = {2}; // Inner loop only
-
-// Assign physical groups for materials
-Physical Surface(1) = {1}; // Outer material (annular region)
-Physical Surface(2) = {2}; // Inner material (solid square)
-
-// Physical lines for boundary conditions
-// Outer square boundary edges
-Physical Line(1) = {1}; // outer bottom
-Physical Line(2) = {2}; // outer right
-Physical Line(3) = {3}; // outer top
-Physical Line(4) = {4}; // outer left
-
-// Inner square boundary edges
-Physical Line(5) = {5}; // inner bottom
-Physical Line(6) = {6}; // inner right
-Physical Line(7) = {7}; // inner top
-Physical Line(8) = {8}; // inner left
-
-// Mesh control for quality
-Mesh.OptimizeNetgen = 1;
-Mesh.Optimize = 1;
-Mesh.ElementOrder = 1;
-Mesh.RecombineAll = 0; // Keep triangular elements (don't recombine to quads)

data/square_in_square.msh

@@ -1,50 +0,0 @@
-$MeshFormat
-2.2 0 8
-$EndMeshFormat
-$Nodes
-13
-1 -1 -1 0
-2 1 -1 0
-3 1 1 0
-4 -1 1 0
-5 -0.25 -0.25 0
-6 0.25 -0.25 0
-7 0.25 0.25 0
-8 -0.25 0.25 0
-9 -2.752797989558076e-12 -1 0
-10 1 -2.752797989558076e-12 0
-11 2.752797989558076e-12 1 0
-12 -1 2.752797989558076e-12 0
-13 0 0 0
-$EndNodes
-$Elements
-28
-1 1 2 1 1 1 9
-2 1 2 1 1 9 2
-3 1 2 2 2 2 10
-4 1 2 2 2 10 3
-5 1 2 3 3 3 11
-6 1 2 3 3 11 4
-7 1 2 4 4 4 12
-8 1 2 4 4 12 1
-9 1 2 5 5 5 6
-10 1 2 6 6 6 7
-11 1 2 7 7 7 8
-12 1 2 8 8 8 5
-13 2 2 1 1 6 5 9
-14 2 2 1 1 5 8 12
-15 2 2 1 1 7 6 10
-16 2 2 1 1 8 7 11
-17 2 2 1 1 9 5 1
-18 2 2 1 1 5 12 1
-19 2 2 1 1 6 9 2
-20 2 2 1 1 10 6 2
-21 2 2 1 1 7 10 3
-22 2 2 1 1 11 7 3
-23 2 2 1 1 8 11 4
-24 2 2 1 1 8 4 12
-25 2 2 2 2 5 6 13
-26 2 2 2 2 8 5 13
-27 2 2 2 2 6 7 13
-28 2 2 2 2 7 8 13
-$EndElements

doc/CodeDocumentation.conf.in

@@ -1083,8 +1083,7 @@ EXCLUDE_PATTERNS       =
 # ANamespace::AClass, ANamespace::*Test
 
 EXCLUDE_SYMBOLS        = mfem::internal \
-                         mfem::kernels::internal \
-                         mfem::future::detail
+                         mfem::kernels::internal
 
 # The EXAMPLE_PATH tag can be used to specify one or more files or directories
 # that contain example code fragments that are included (see the \include

examples/CMakeLists.txt

@@ -47,6 +47,7 @@ list(APPEND ALL_EXE_SRCS
   ex39.cpp
   ex40.cpp
   ex41.cpp
+  # jitplayground.cpp
   )
 
 if (MFEM_USE_MPI)

examples/jitplayground.cpp

@@ -0,0 +1,548 @@
+#include <mfem.hpp>
+
+#ifdef MFEM_USE_PROTEUS
+
+#include "../fem/dfem/util.hpp"
+
+#include <proteus/CppJitModule.h>
+
+#include "jitplayground.hpp"
+
+#include <algorithm>
+#include <array>
+#include <cctype>
+#include <cmath>
+#include <fstream>
+#include <initializer_list>
+#include <iostream>
+#include <memory>
+#include <sstream>
+#include <string>
+#include <string_view>
+#include <type_traits>
+#include <unordered_map>
+#include <unordered_set>
+#include <utility>
+#include <vector>
+
+namespace util
+{
+constexpr std::string_view Dirname(std::string_view path)
+{
+   const size_t last_sep = path.find_last_of("/\\");
+   if (last_sep == std::string_view::npos) { return {}; }
+   return path.substr(0, last_sep);
+}
+
+constexpr std::string_view thisFileDir = Dirname(__FILE__);
+}
+
+template <typename T>
+static std::string TypeNameString()
+{
+   return std::string(mfem::future::get_type_name<T>());
+}
+
+template <typename Tuple, size_t... Is>
+static auto ParamTypeStringsImpl(std::index_sequence<Is...>)
+{
+   return std::array<std::string, sizeof...(Is)>
+   {
+      TypeNameString<std::remove_reference_t<decltype(mfem::future::get<Is>(std::declval<Tuple&>()))>>()...
+   };
+}
+
+template <typename Tuple>
+static auto ParamTypeStrings()
+{
+   return ParamTypeStringsImpl<Tuple>(
+             std::make_index_sequence<mfem::future::tuple_size<Tuple>::value> {});
+}
+
+static std::string_view Trim(std::string_view s)
+{
+   size_t begin = 0;
+   while (begin < s.size() && std::isspace(static_cast<unsigned char>(s[begin])))
+   {
+      ++begin;
+   }
+   size_t end = s.size();
+   while (end > begin &&
+          std::isspace(static_cast<unsigned char>(s[end - 1])))
+   {
+      --end;
+   }
+   return s.substr(begin, end - begin);
+}
+
+static bool IsValidIdentifier(std::string_view s)
+{
+   if (s.empty()) { return false; }
+   const unsigned char c0 = static_cast<unsigned char>(s[0]);
+   if (!(std::isalpha(c0) || c0 == '_')) { return false; }
+   for (size_t i = 1; i < s.size(); ++i)
+   {
+      const unsigned char c = static_cast<unsigned char>(s[i]);
+      if (!(std::isalnum(c) || c == '_')) { return false; }
+   }
+   return true;
+}
+
+static bool ParseJitDirective(std::string_view line,
+                              std::string &type,
+                              std::string &var,
+                              std::string &kind)
+{
+   const size_t jit_pos = line.find("$JIT");
+   if (jit_pos == std::string_view::npos) { return false; }
+
+   const size_t open = line.find('[', jit_pos);
+   const size_t close = line.find(']', jit_pos);
+   MFEM_VERIFY(open != std::string_view::npos &&
+               close != std::string_view::npos &&
+               close > open,
+               "malformed $JIT directive (expected brackets): " << line);
+
+   const std::string_view payload = line.substr(open + 1, close - open - 1);
+   const size_t comma1 = payload.find(',');
+   const size_t comma2 = (comma1 == std::string_view::npos)
+                         ? std::string_view::npos
+                         : payload.find(',', comma1 + 1);
+   MFEM_VERIFY(comma1 != std::string_view::npos &&
+               comma2 != std::string_view::npos,
+               "malformed $JIT directive (expected 3 comma-separated fields): "
+               << line);
+
+   const std::string_view f0 = Trim(payload.substr(0, comma1));
+   const std::string_view f1 = Trim(payload.substr(comma1 + 1,
+                                                   comma2 - comma1 - 1));
+   const std::string_view f2 = Trim(payload.substr(comma2 + 1));
+   MFEM_VERIFY(!f0.empty() && !f1.empty() && !f2.empty(),
+               "malformed $JIT directive (empty field): " << line);
+
+   type.assign(f0);
+   var.assign(f1);
+   kind.assign(f2);
+   return true;
+}
+
+static std::string ReadFileOrEmpty(const std::string &fn)
+{
+   std::ifstream file(fn);
+   if (!file.is_open())
+   {
+      std::cerr << "could not open file " << fn << "\n";
+      return {};
+   }
+   std::stringstream buffer;
+   buffer << file.rdbuf();
+   return buffer.str();
+}
+
+static std::vector<std::string> ExtractJitVarNames(const std::string
+                                                   &kernel_code)
+{
+   std::stringstream ss(kernel_code);
+   std::string line;
+   std::vector<std::string> var_names;
+   std::unordered_set<std::string> seen_vars;
+
+   while (std::getline(ss, line))
+   {
+      std::string type, var, kind;
+      if (ParseJitDirective(line, type, var, kind))
+      {
+         MFEM_VERIFY(IsValidIdentifier(var),
+                     "$JIT variable must be a valid identifier: " << var);
+         MFEM_VERIFY(seen_vars.insert(var).second,
+                     "duplicate $JIT variable name: " << var);
+         var_names.push_back(var);
+      }
+   }
+   return var_names;
+}
+
+static std::string RewriteKernelForJit(std::string kernel_code,
+                                       const std::vector<std::string> &jit_values)
+{
+   std::stringstream ss(kernel_code);
+   std::string line;
+
+   std::string out;
+   out.reserve(kernel_code.size() + 128);
+
+   bool have_pending = false;
+   size_t pending_index = 0;
+   std::string pending_type;
+   std::string pending_var;
+   std::unordered_set<std::string> seen_vars;
+
+   while (std::getline(ss, line))
+   {
+      line.push_back('\n');
+
+      if (have_pending)
+      {
+         MFEM_VERIFY(pending_index < jit_values.size(),
+                     "not enough JIT values provided");
+         const size_t indent_end = line.find_first_not_of(" \t");
+         const std::string indent =
+            (indent_end == std::string::npos) ? std::string() :
+            line.substr(0, indent_end);
+         out += indent + "const " + pending_type + " " + pending_var + " = " +
+                jit_values[pending_index] + ";\n";
+         have_pending = false;
+         ++pending_index;
+         continue;
+      }
+
+      std::string type, var, kind;
+      if (ParseJitDirective(line, type, var, kind))
+      {
+         MFEM_VERIFY(IsValidIdentifier(var),
+                     "$JIT variable must be a valid identifier: " << var);
+         MFEM_VERIFY(kind == "generic",
+                     "unsupported $JIT kind: " << kind);
+         MFEM_VERIFY(seen_vars.insert(var).second,
+                     "duplicate $JIT variable name: " << var);
+
+         pending_type = std::move(type);
+         pending_var = std::move(var);
+         have_pending = true;
+         continue; // drop directive line
+      }
+
+      out += line;
+   }
+
+   MFEM_VERIFY(!have_pending,
+               "$JIT directive must annotate a following line");
+   MFEM_VERIFY(jit_values.size() == pending_index,
+               "JIT value count must match number of $JIT directives");
+   return out;
+}
+
+static std::string GeneratedOutputPath(std::string_view original_path)
+{
+   const size_t last_sep = original_path.find_last_of("/\\");
+   const size_t dot = original_path.find_last_of('.');
+   const bool dot_in_filename =
+      (dot != std::string_view::npos) &&
+      (last_sep == std::string_view::npos || dot > last_sep);
+
+   const std::string_view base =
+      dot_in_filename ? original_path.substr(0, dot) : original_path;
+   return std::string(base) + "_generated.hpp";
+}
+
+static void WriteFileOrWarn(const std::string &path,
+                            const std::string &contents)
+{
+   std::ofstream out(path);
+   if (!out.is_open())
+   {
+      std::cerr << "could not write generated file " << path << "\n";
+      return;
+   }
+   out << contents;
+}
+
+class JitQFunction
+{
+public:
+   template <typename ImplT, size_t N>
+   JitQFunction(ImplT, const std::string &fn,
+                const std::array<bool, N> &activity_map)
+   {
+      using qf_signature = typename
+                           mfem::future::get_function_signature<
+                           decltype(&ImplT::operator())>::type;
+      using qf_param_ts = typename qf_signature::parameter_ts;
+      constexpr size_t nparams = mfem::future::tuple_size<qf_param_ts>::value;
+      static_assert(N == nparams, "activity_map size must match qfunc arity");
+
+      this->fn = fn;
+      this->nparams = nparams;
+      this->activity_map.reserve(N);
+      for (size_t i = 0; i < N; ++i)
+      {
+         this->activity_map.push_back(activity_map[i]);
+      }
+      {
+         const auto param_types_arr = ParamTypeStrings<qf_param_ts>();
+         this->param_types.assign(param_types_arr.begin(), param_types_arr.end());
+      }
+      this->return_type = TypeNameString<typename qf_signature::return_t>();
+      this->return_is_void = std::is_same_v<typename qf_signature::return_t, void>;
+      this->impl_type_name = TypeNameString<ImplT>();
+      this->jit_var_names = ExtractJitVarNames(ReadFileOrEmpty(fn));
+   }
+
+   template <typename ReturnT, typename... Args>
+   ReturnT run(std::string_view name,
+               std::initializer_list<std::pair<std::string_view, std::string_view>> jit_values,
+               Args&&... args)
+   {
+      auto ordered_values = MatchJitValues(jit_values);
+      auto &mod = GetOrCreateModule(ordered_values);
+      auto &instance = mod.instantiate(std::string(name), std::string());
+      return instance.template run<ReturnT>(std::forward<Args>(args)...);
+   }
+
+   template <typename ReturnT, typename... Args>
+   ReturnT run_primal(
+      std::initializer_list<std::pair<std::string_view, std::string_view>> jit_values,
+      Args&&... args)
+   {
+      return run<ReturnT>(qfunc_name, jit_values,
+                          std::forward<Args>(args)...);
+   }
+
+   template <typename ReturnT, typename... Args>
+   ReturnT run_derivative(
+      std::initializer_list<std::pair<std::string_view, std::string_view>> jit_values,
+      Args&&... args)
+   {
+      return run<ReturnT>(qfunc_name + "_fwddiff", jit_values,
+                          std::forward<Args>(args)...);
+   }
+
+private:
+   std::vector<std::string_view> MatchJitValues(
+      std::initializer_list<std::pair<std::string_view, std::string_view>>
+      named_values) const
+   {
+      std::unordered_map<std::string_view, std::string_view> value_map;
+      for (const auto &[name, value] : named_values)
+      {
+         value_map[name] = value;
+      }
+
+      std::vector<std::string_view> ordered_values;
+      ordered_values.reserve(jit_var_names.size());
+      for (const auto &var_name : jit_var_names)
+      {
+         auto it = value_map.find(var_name);
+         MFEM_VERIFY(it != value_map.end(),
+                     "missing JIT value for variable: " << var_name);
+         ordered_values.push_back(it->second);
+      }
+
+      MFEM_VERIFY(ordered_values.size() == named_values.size(),
+                  "provided " << named_values.size() << " JIT values but expected "
+                  << jit_var_names.size());
+      return ordered_values;
+   }
+
+
+   std::string BuildModuleCode(const std::vector<std::string> &jit_values) const
+   {
+      std::string module_code =
+         RewriteKernelForJit(ReadFileOrEmpty(fn), jit_values);
+      module_code += "\n\n";
+      module_code += "// --- generated ---\n";
+      module_code +=
+         "template <typename return_type, typename... Args>\n"
+         "return_type __enzyme_fwddiff(Args...);\n"
+         "\n"
+         "extern int enzyme_const;\n"
+         "extern int enzyme_dup;\n"
+         "\n";
+
+      // Generate a primal wrapper with the requested symbol name, so the kernel
+      // header can just define the qfunc as a functor.
+      //
+      // Note: Proteus instantiates entrypoints via `qfunc_wrapper<>(...)` even
+      // when there are no user template args, so keep the wrapper itself a
+      // template (with a default parameter) while still doing literal `$JIT`
+      // replacements in the kernel code.
+      module_code += "template <typename = void>\n";
+      module_code += return_type + " " +
+                     std::string(qfunc_name) + "(";
+      bool first = true;
+      for (size_t i = 0; i < nparams; ++i)
+      {
+         if (!first) { module_code += ", "; }
+         first = false;
+         module_code += param_types[i] + " Arg" + std::to_string(i);
+      }
+      module_code += ")\n";
+      module_code += "{\n";
+      module_code += "   " + impl_type_name + " qf;\n";
+      if (return_is_void)
+      {
+         module_code += "   ";
+      }
+      else
+      {
+         module_code += "   return ";
+      }
+      module_code += "qf(";
+      for (size_t i = 0; i < nparams; ++i)
+      {
+         if (i) { module_code += ", "; }
+         module_code += "Arg" + std::to_string(i);
+      }
+      module_code += ");\n";
+      module_code += "}\n\n";
+
+      module_code += "template <typename = void>\n";
+      module_code += return_type + " " +
+                     std::string(qfunc_name) + "_fwddiff(";
+
+      first = true;
+      for (size_t i = 0; i < nparams; ++i)
+      {
+         if (!first) { module_code += ", "; }
+         first = false;
+         module_code += param_types[i] + " Arg" + std::to_string(i);
+         if (activity_map[i])
+         {
+            module_code += ", " + param_types[i] + " dArg" + std::to_string(i);
+         }
+      }
+      module_code += ")\n";
+      module_code += "{\n";
+      if (return_is_void)
+      {
+         module_code += "   __enzyme_fwddiff<void>(\n";
+      }
+      else
+      {
+         module_code += "   return __enzyme_fwddiff<" +
+                        return_type + ">(\n";
+      }
+      module_code += "      (void*)" + std::string(qfunc_name) + "<>";
+      module_code += ",\n";
+      for (size_t i = 0; i < nparams; ++i)
+      {
+         if (activity_map[i])
+         {
+            module_code += "      enzyme_dup, Arg" + std::to_string(i) +
+                           ", dArg" + std::to_string(i);
+         }
+         else
+         {
+            module_code += "      enzyme_const, Arg" + std::to_string(i);
+         }
+         module_code += (i + 1 == nparams) ? ");\n" : ",\n";
+      }
+      module_code += "}\n";
+
+      WriteFileOrWarn(GeneratedOutputPath(fn), module_code);
+      return module_code;
+   }
+
+   proteus::CppJitModule &GetOrCreateModule(
+      const std::vector<std::string_view> &jit_values)
+   {
+      std::string key;
+      for (const auto &val : jit_values)
+      {
+         if (!key.empty()) { key += ","; }
+         key += val;
+      }
+
+      auto it = modules.find(key);
+      if (it != modules.end())
+      {
+         return *it->second;
+      }
+
+      std::vector<std::string> values(jit_values.begin(), jit_values.end());
+      std::string code = BuildModuleCode(values);
+      auto mod = std::make_unique<proteus::CppJitModule>("host", code,
+                                                         DefaultExtraArgs());
+      auto [inserted, ok] = modules.emplace(key, std::move(mod));
+      MFEM_VERIFY(ok, "failed to cache JIT module");
+      return *inserted->second;
+   }
+
+   static std::vector<std::string> DefaultExtraArgs()
+   {
+      return {"-fplugin=/Users/andrej1/local/enzyme/lib/ClangEnzyme-20.dylib"};
+   }
+
+   std::string qfunc_name = "qfunc_wrapper";
+   std::string fn;
+   size_t nparams = 0;
+   std::vector<bool> activity_map;
+   std::vector<std::string> param_types;
+   std::string return_type;
+   bool return_is_void = false;
+   std::string impl_type_name;
+   std::vector<std::string> jit_var_names;
+   std::unordered_map<std::string, std::unique_ptr<proteus::CppJitModule>> modules;
+};
+
+int main()
+{
+   const size_t N = 4;
+   const size_t M = 5;
+   const double A = 123.4;
+
+   std::vector<double> X(N);
+   std::vector<double> Y(N);
+   for (size_t i = 0; i < N; ++i)
+   {
+      X[i] = static_cast<double>(i + 1);
+      Y[i] = static_cast<double>(N - i);
+   }
+
+   // // >>> user interface calls
+   // const std::string kernel_path = std::string(util::thisFileDir) +
+   //                                 "/jitplayground.hpp";
+   // JitQFunction qf(daxpy_op{}, kernel_path, std::array{false, true, false});
+   // // <<< user interface calls
+
+   // // this will happen internally in dFEM
+
+   daxpy_op op;
+   printf("\n\nfunction call\n");
+   op(&A, X.data(), Y.data(), &N);
+
+   // reset X for the derivative test
+   for (size_t i = 0; i < N; ++i)
+   {
+      X[i] = static_cast<double>(i + 1);
+      Y[i] = static_cast<double>(N - i);
+   }
+
+   std::vector<double> dX(N, 1.0);
+   printf("\n\nforward diff call\n");
+   daxpy_op_fwddiff(&A, X.data(), dX.data(), Y.data(), &N);
+
+   std::vector<double> dX_manual(N, A);
+
+   printf("\n\nderivative checks\n");
+   std::cout << "dX: ";
+   for (size_t i = 0; i < N; ++i)
+   {
+      std::cout << dX[i] << (i + 1 == N ? '\n' : ' ');
+   }
+
+   std::cout << "dX_manual: ";
+   for (size_t i = 0; i < N; ++i)
+   {
+      std::cout << dX_manual[i] << (i + 1 == N ? '\n' : ' ');
+   }
+
+   double max_abs_err = 0.0;
+   for (size_t i = 0; i < N; ++i)
+   {
+      max_abs_err = std::max(max_abs_err, std::abs(dX[i] - dX_manual[i]));
+   }
+   std::cout << "max |dX - dX_manual| = " << max_abs_err << "\n";
+
+   return 0;
+}
+
+#else
+
+int main()
+{
+   std::cerr << "Proteus is required to run this example.\n";
+   return EXIT_FAILURE;
+}
+
+#endif // MFEM_USE_PROTEUS

examples/jitplayground.hpp

@@ -0,0 +1,58 @@
+#pragma once
+
+#include <cstddef>
+#include <vector>
+#include <type_traits>
+
+#include "proteus/JitInterface.h"
+
+struct daxpy_op
+{
+   void operator()(
+      const double *a,
+      double *x,
+      const double *y,
+      const size_t *N) const
+   {
+      const size_t n = *N;
+      auto lam = [=, n = proteus::jit_variable(n)]
+                 () __attribute__((annotate("jit")))
+      {
+         printf("N = %zu\n", n);
+         for (size_t i = 0; i < n; ++i)
+         {
+            printf("x[%zu] = %f, y[%zu] = %f\n", i, x[i], i, y[i]);
+            x[i] = *a * x[i] + y[i];
+            printf("updated x[%zu] = %f\n", i, x[i]);
+         }
+      };
+
+      proteus::register_lambda(lam);
+
+      lam();
+   }
+};
+
+template <typename return_type, typename... Args>
+return_type __enzyme_fwddiff(Args...);
+
+extern int enzyme_const;
+extern int enzyme_dup;
+
+void daxpy_op_wrapper(const double * Arg0, double * Arg1,
+                      const double * Arg2, const size_t *Arg3)
+{
+   daxpy_op qf;
+   qf(Arg0, Arg1, Arg2, Arg3);
+}
+
+void daxpy_op_fwddiff(const double * Arg0, double * Arg1,
+                      double * dArg1, const double * Arg2, const size_t *Arg3)
+{
+   __enzyme_fwddiff<void>(
+      (void*)daxpy_op_wrapper,
+      enzyme_const, Arg0,
+      enzyme_dup, Arg1, dArg1,
+      enzyme_const, Arg2,
+      enzyme_const, Arg3);
+}

fem/CMakeLists.txt

@@ -67,6 +67,7 @@ set(SRCS
   dgmassinv.cpp
   doftrans.cpp
   dfem/doperator.cpp
+  dfem/backends/local_qf/kernels.cpp
   eltrans.cpp
   batchitrans.cpp
   estimators.cpp
@@ -123,6 +124,11 @@ set(SRCS
   qinterp/eval_hdiv.cpp
   qinterp/grad_by_nodes.cpp
   qinterp/grad_by_vdim.cpp
+  qinterp/grad_transpose.cpp
+  qinterp/grad_transpose_by_nodes.cpp
+  qinterp/grad_transpose_by_vdim.cpp
+  qinterp/eval_transpose.cpp
+  qinterp/eval_transpose_by_vdim.cpp
   qspace.cpp
   quadinterpolator.cpp
   quadinterpolator_face.cpp
@@ -219,13 +225,32 @@ set(HDRS
   dgmassinv_kernels.hpp
   doftrans.hpp
   dfem/doperator.hpp
+  dfem/fielddescriptor.hpp
   dfem/fieldoperator.hpp
-  dfem/integrate.hpp
+  dfem/integrator_ctx.hpp
   dfem/parameterspace.hpp
-  dfem/qfunction_apply.hpp
-  dfem/qfunction_transform.hpp
+  dfem/tensor_functions.hpp
   dfem/tuple.hpp
   dfem/util.hpp
+  dfem/backends/util.hpp
+  dfem/backends/global_qf/action.hpp
+  dfem/backends/global_qf/derivative_action.hpp
+  dfem/backends/global_qf/derivative_apply.hpp
+  dfem/backends/global_qf/derivative_apply_transpose.hpp
+  dfem/backends/global_qf/derivative_setup.hpp
+  dfem/backends/global_qf/prelude.hpp
+  dfem/backends/local_qf/action.hpp
+  dfem/backends/local_qf/derivative_action.hpp
+  dfem/backends/local_qf/derivative_apply.hpp
+  dfem/backends/local_qf/derivative_apply_transpose.hpp
+  dfem/backends/local_qf/derivative_assemble.hpp
+  dfem/backends/local_qf/derivative_assemble_diagonal.hpp
+  dfem/backends/local_qf/derivative_setup.hpp
+  dfem/backends/local_qf/kernels.hpp
+  dfem/backends/local_qf/kernels_ho.hpp
+  dfem/backends/local_qf/kernels_lo.hpp
+  dfem/backends/local_qf/prelude.hpp
+  dfem/backends/local_qf/util.hpp
   eltrans.hpp
   estimators.hpp
   fe.hpp
@@ -290,8 +315,10 @@ set(HDRS
   qfunction.hpp
   qinterp/det.hpp
   qinterp/eval.hpp
+  qinterp/eval_transpose.hpp
   qinterp/eval_hdiv.hpp
   qinterp/grad.hpp
+  qinterp/grad_transpose.hpp
   qspace.hpp
   quadinterpolator.hpp
   quadinterpolator_face.hpp
@@ -326,36 +353,36 @@ set(HDRS
   )
 
 if (MFEM_USE_SIDRE)
-  list(APPEND SRCS sidredatacollection.cpp)
-  list(APPEND HDRS sidredatacollection.hpp)
+    list(APPEND SRCS sidredatacollection.cpp)
+    list(APPEND HDRS sidredatacollection.hpp)
 endif()
 
 if (MFEM_USE_CONDUIT)
-  list(APPEND SRCS conduitdatacollection.cpp)
-  list(APPEND HDRS conduitdatacollection.hpp)
+    list(APPEND SRCS conduitdatacollection.cpp)
+    list(APPEND HDRS conduitdatacollection.hpp)
 endif()
 
 if (MFEM_USE_ADIOS2)
-  list(APPEND SRCS adios2datacollection.cpp)
-  list(APPEND HDRS adios2datacollection.hpp)
+    list(APPEND SRCS adios2datacollection.cpp)
+    list(APPEND HDRS adios2datacollection.hpp)
 endif()
 
 if (MFEM_USE_FMS)
-  list(APPEND SRCS fmsdatacollection.cpp fmsconvert.cpp)
-  list(APPEND HDRS fmsdatacollection.hpp fmsconvert.hpp)
+    list(APPEND SRCS fmsdatacollection.cpp fmsconvert.cpp)
+    list(APPEND HDRS fmsdatacollection.hpp fmsconvert.hpp)
 endif()
 
 if (MFEM_USE_MPI)
-  list(APPEND SRCS
+    list(APPEND SRCS
     pbilinearform.cpp
     pfespace.cpp
     pgridfunc.cpp
     plinearform.cpp
     pnonlinearform.cpp
     prestriction.cpp)
-  # If this list (HDRS -> HEADERS) is used for install, we probably want the
-  # headers added all the time.
-  list(APPEND HDRS
+    # If this list (HDRS -> HEADERS) is used for install, we probably want the
+    # headers added all the time.
+    list(APPEND HDRS
     pbilinearform.hpp
     pfespace.hpp
     pgridfunc.hpp

fem/bilinearform.cpp

@@ -1255,31 +1255,6 @@ void BilinearForm::Mult(const Vector &x, Vector &y) const
    }
 }
 
-void BilinearForm::AddMult(const Vector &x, Vector &y, const real_t a) const
-{
-   if (ext)
-   {
-      ext->AddMult(x, y, a);
-   }
-   else
-   {
-      mat->AddMult(x, y, a);
-   }
-}
-
-void BilinearForm::AddMultTranspose(const Vector &x, Vector &y,
-                                    const real_t a) const
-{
-   if (ext)
-   {
-      ext->AddMultTranspose(x, y, a);
-   }
-   else
-   {
-      mat->AddMultTranspose(x, y, a);
-   }
-}
-
 void BilinearForm::MultTranspose(const Vector & x, Vector & y) const
 {
    if (ext)

fem/bilinearform.hpp

@@ -307,8 +307,8 @@ public:
    { mat->Mult(x, y); mat_e->AddMult(x, y); }
 
    /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   void AddMult(const Vector &x, Vector &y,
-                const real_t a = 1.0) const override;
+   void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const override
+   { mat -> AddMult (x, y, a); }
 
    /** @brief Add the original uneliminated matrix vector multiple to a vector.
        The original matrix is $ M + Me $ so we have:
@@ -318,7 +318,8 @@ public:
 
    /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
    void AddMultTranspose(const Vector & x, Vector & y,
-                         const real_t a = 1.0) const override;
+                         const real_t a = 1.0) const override
+   { mat->AddMultTranspose(x, y, a); }
 
    /** @brief Add the original uneliminated matrix transpose vector
        multiple to a vector. The original matrix is $ M + M_e $

fem/bilinearform_ext.cpp

@@ -1997,11 +1997,7 @@ void PADiscreteLinearOperatorExtension::Assemble()
    }
    else
    {
-      const L2ElementRestriction* l2_elem_restrict =
-         dynamic_cast<const L2ElementRestriction*>(elem_restrict_test);
-      MFEM_VERIFY(l2_elem_restrict,
-                  "A real ElementRestriction is required in this setting!");
-      test_multiplicity = 1.0;
+      mfem_error("A real ElementRestriction is required in this setting!");
    }
 
    auto tm = test_multiplicity.ReadWrite();
@@ -2040,13 +2036,7 @@ void PADiscreteLinearOperatorExtension::AddMult(
    }
    else
    {
-      const L2ElementRestriction* l2_elem_restrict =
-         dynamic_cast<const L2ElementRestriction*>(elem_restrict_test);
-      MFEM_VERIFY(l2_elem_restrict,
-                  "In this setting you need a real ElementRestriction!");
-      tempY.SetSize(y.Size());
-      l2_elem_restrict->MultTranspose(localTest, tempY);
-      y += tempY;
+      mfem_error("In this setting you need a real ElementRestriction!");
    }
 }
 

fem/coefficient.hpp

@@ -1055,8 +1055,7 @@ public:
 
 typedef VectorCoefficient DiagonalMatrixCoefficient;
 
-/** Base class for matrix-valued coefficients that optionally depend on time
-    and space. */
+/// Base class for Matrix Coefficients that optionally depend on time and space.
 class MatrixCoefficient
 {
 protected:
@@ -1103,9 +1102,6 @@ public:
    /// the quadrature points. The matrix will be transposed or not according to
    /// the boolean argument @a transpose.
    ///
-   /// The stored entries use the same row/column convention as `Eval()`,
-   /// unless `transpose == true`, in which case `K^T` is stored instead.
-   ///
    /// The @a vdim of the QuadratureFunction should be equal to the height times
    /// the width of the matrix.
    virtual void Project(QuadratureFunction &qf, bool transpose=false);

fem/complex_fem.cpp

@@ -588,38 +588,6 @@ SesquilinearForm::AssembleComplexSparseMatrix()
                                   false, false, conv);
 }
 
-void
-SesquilinearForm::BuildComplexOperator(OperatorHandle &A_r,
-                                       OperatorHandle &A_i,
-                                       OperatorHandle &A) const
-{
-   // A = A_r + i A_i
-   A.Clear();
-   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
-       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
-   {
-      ComplexSparseMatrix * A_sp =
-         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
-                                 A_i.As<SparseMatrix>(),
-                                 A_r.OwnsOperator(),
-                                 A_i.OwnsOperator(),
-                                 conv);
-      A.Reset<ComplexSparseMatrix>(A_sp, true);
-   }
-   else
-   {
-      ComplexOperator * A_op =
-         new ComplexOperator(A_r.Ptr(),
-                             A_i.Ptr(),
-                             A_r.OwnsOperator(),
-                             A_i.OwnsOperator(),
-                             conv);
-      A.Reset<ComplexOperator>(A_op, true);
-   }
-   A_r.SetOperatorOwner(false);
-   A_i.SetOperatorOwner(false);
-}
-
 void
 SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                                    Vector &x, Vector &b,
@@ -748,7 +716,31 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
    B_r.SyncAliasMemory(B);
    B_i.SyncAliasMemory(B);
 
-   BuildComplexOperator(A_r, A_i, A);
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
+   {
+      ComplexSparseMatrix * A_sp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_sp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.Ptr(),
+                             A_i.Ptr(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -785,7 +777,31 @@ SesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
       }
    }
 
-   BuildComplexOperator(A_r, A_i, A);
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
+   {
+      ComplexSparseMatrix * A_sp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_sp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.Ptr(),
+                             A_i.Ptr(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -1877,81 +1893,6 @@ ParSesquilinearForm::ParallelAssemble()
                                     true, true, conv);
 }
 
-void
-ParSesquilinearForm::BuildComplexOperator(OperatorHandle &A_r,
-                                          OperatorHandle &A_i,
-                                          OperatorHandle &A) const
-{
-   // A = A_r + i A_i
-   A.Clear();
-   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
-       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
-   {
-      ComplexHypreParMatrix * A_hyp =
-         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
-                                   A_i.As<HypreParMatrix>(),
-                                   A_r.OwnsOperator(),
-                                   A_i.OwnsOperator(),
-                                   conv);
-      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
-   }
-   else
-   {
-      ComplexOperator * A_op =
-         new ComplexOperator(A_r.As<Operator>(),
-                             A_i.As<Operator>(),
-                             A_r.OwnsOperator(),
-                             A_i.OwnsOperator(),
-                             conv);
-      A.Reset<ComplexOperator>(A_op, true);
-   }
-   A_r.SetOperatorOwner(false);
-   A_i.SetOperatorOwner(false);
-}
-
-namespace
-{
-struct ZeroDiagonalHypreKernel
-{
-   const int *ess_tdof_list;
-   const HYPRE_Int *diag_i;
-   real_t *diag_data;
-
-   void MFEM_HOST_DEVICE operator()(int k) const
-   {
-      const int j = ess_tdof_list[k];
-      diag_data[diag_i[j]] = 0.0;
-   }
-};
-}
-
-void
-ParSesquilinearForm::SetImaginaryEssentialDiagonalToZero(
-   const Array<int> &ess_tdof_list, OperatorHandle &A)
-{
-   if (A.Type() == Operator::Hypre_ParCSR)
-   {
-      const int n = ess_tdof_list.Size();
-      HypreParMatrix *Ah;
-      A.Get(Ah);
-      hypre_ParCSRMatrix *Aih = *Ah;
-      Ah->HypreReadWrite();
-      const int *d_ess_tdof_list =
-         ess_tdof_list.GetMemory().Read(GetHypreForallMemoryClass(), n);
-      HYPRE_Int *d_diag_i = Aih->diag->i;
-      real_t *d_diag_data = Aih->diag->data;
-      mfem::hypre_forall(n, ZeroDiagonalHypreKernel
-      {
-         d_ess_tdof_list, d_diag_i, d_diag_data
-      });
-   }
-   else
-   {
-      A.As<ConstrainedOperator>()->SetDiagonalPolicy
-      (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
-   }
-}
-
 void
 ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                                       Vector &x, Vector &b,
@@ -2052,7 +1993,27 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
       });
       // Modify off-diagonal blocks (imaginary parts of the matrix) to conform
       // with standard essential BC treatment
-      SetImaginaryEssentialDiagonalToZero(ess_tdof_list, A_i);
+      if (A_i.Type() == Operator::Hypre_ParCSR)
+      {
+         HypreParMatrix * Ah;
+         A_i.Get(Ah);
+         hypre_ParCSRMatrix *Aih = *Ah;
+         Ah->HypreReadWrite();
+         const int *d_ess_tdof_list =
+            ess_tdof_list.GetMemory().Read(GetHypreForallMemoryClass(), n);
+         HYPRE_Int *d_diag_i = Aih->diag->i;
+         real_t *d_diag_data = Aih->diag->data;
+         mfem::hypre_forall(n, [=] MFEM_HOST_DEVICE (int k)
+         {
+            const int j = d_ess_tdof_list[k];
+            d_diag_data[d_diag_i[j]] = 0.0;
+         });
+      }
+      else
+      {
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
    }
 
    if (conv == ComplexOperator::BLOCK_SYMMETRIC)
@@ -2071,7 +2032,31 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
    B_r.SyncAliasMemory(B);
    B_i.SyncAliasMemory(B);
 
-   BuildComplexOperator(A_r, A_i, A);
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
+   {
+      ComplexHypreParMatrix * A_hyp =
+         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
+                                   A_i.As<HypreParMatrix>(),
+                                   A_r.OwnsOperator(),
+                                   A_i.OwnsOperator(),
+                                   conv);
+      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.As<Operator>(),
+                             A_i.As<Operator>(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -2096,10 +2081,50 @@ ParSesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
    {
       // Modify off-diagonal blocks (imaginary parts of the matrix) to conform
       // with standard essential BC treatment
-      SetImaginaryEssentialDiagonalToZero(ess_tdof_list, A_i);
+      if ( A_i.Type() == Operator::Hypre_ParCSR )
+      {
+         int n = ess_tdof_list.Size();
+         HypreParMatrix * Ah;
+         A_i.Get(Ah);
+         hypre_ParCSRMatrix * Aih = *Ah;
+         for (int k = 0; k < n; k++)
+         {
+            int j = ess_tdof_list[k];
+            Aih->diag->data[Aih->diag->i[j]] = 0.0;
+         }
+      }
+      else
+      {
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
    }
 
-   BuildComplexOperator(A_r, A_i, A);
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
+   {
+      ComplexHypreParMatrix * A_hyp =
+         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
+                                   A_i.As<HypreParMatrix>(),
+                                   A_r.OwnsOperator(),
+                                   A_i.OwnsOperator(),
+                                   conv);
+      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.As<Operator>(),
+                             A_i.As<Operator>(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void

fem/complex_fem.hpp

@@ -392,9 +392,6 @@ private:
    bool RealInteg();
    bool ImagInteg();
 
-   void BuildComplexOperator(OperatorHandle &A_r, OperatorHandle &A_i,
-                             OperatorHandle &A) const;
-
 public:
    SesquilinearForm(FiniteElementSpace *fes,
                     ComplexOperator::Convention
@@ -989,12 +986,6 @@ private:
    bool RealInteg();
    bool ImagInteg();
 
-   void SetImaginaryEssentialDiagonalToZero(
-      const Array<int> &ess_tdof_list, OperatorHandle &A);
-
-   void BuildComplexOperator(OperatorHandle &A_r, OperatorHandle &A_i,
-                             OperatorHandle &A) const;
-
 public:
    ParSesquilinearForm(ParFiniteElementSpace *pf,
                        ComplexOperator::Convention

fem/datacollection.cpp

@@ -38,24 +38,9 @@ int DataCollection::create_directory(const std::string &dir_name,
    // create directories recursively
    const char path_delim = '/';
    std::string::size_type pos = 0;
-   int err_flag = 0;
+   int err_flag;
 #ifdef MFEM_USE_MPI
    const ParMesh *pmesh = dynamic_cast<const ParMesh*>(mesh);
-   // In addition to the global root, let the lowest rank on each shared-memory
-   // node create the directory too, so that node-local (non-shared) filesystems
-   // get it on every node rather than only where the global root lives. On a
-   // shared filesystem the extra mkdir() hits EEXIST and is tolerated below.
-   bool node_root = true;
-   if (pmesh)
-   {
-      MPI_Comm node_comm;
-      MPI_Comm_split_type(pmesh->GetComm(), MPI_COMM_TYPE_SHARED, myid,
-                          MPI_INFO_NULL, &node_comm);
-      int node_rank;
-      MPI_Comm_rank(node_comm, &node_rank);
-      node_root = (node_rank == 0);
-      MPI_Comm_free(&node_comm);
-   }
 #endif
 
    do
@@ -67,7 +52,7 @@ int DataCollection::create_directory(const std::string &dir_name,
       err_flag = mkdir(subdir.c_str(), 0777);
       err_flag = (err_flag && (errno != EEXIST)) ? 1 : 0;
 #else
-      if (node_root || pmesh == NULL)
+      if (myid == 0 || pmesh == NULL)
       {
          err_flag = mkdir(subdir.c_str(), 0777);
          err_flag = (err_flag && (errno != EEXIST)) ? 1 : 0;
@@ -79,8 +64,7 @@ int DataCollection::create_directory(const std::string &dir_name,
 #ifdef MFEM_USE_MPI
    if (pmesh)
    {
-      MPI_Allreduce(MPI_IN_PLACE, &err_flag, 1, MPI_INT, MPI_MAX,
-                    pmesh->GetComm());
+      MPI_Bcast(&err_flag, 1, MPI_INT, 0, pmesh->GetComm());
    }
 #endif
 

fem/dfem/assemble.hpp

@@ -1,403 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-
-namespace mfem::future
-{
-
-/// @brief Assemble element matrix for three dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_t3d(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& q1d,
-   const int& td1d)
-{
-   constexpr int dimension = 3;
-
-   // [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, num_qp]
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-
-   // [num_test_dof, ...]
-   const auto num_test_dof = A.GetShape()[0];
-
-   for (int Jx = 0; Jx < td1d; Jx++)
-   {
-      for (int Jy = 0; Jy < td1d; Jy++)
-      {
-         for (int Jz = 0; Jz < td1d; Jz++)
-         {
-            const int J = Jx + td1d * (Jy + td1d * Jz);
-
-            for (int j = 0; j < trial_vdim; j++)
-            {
-               for (int tv = 0; tv < test_vdim; tv++)
-               {
-                  for (int tod = 0; tod < test_op_dim; tod++)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-                              fhat(tv, tod, q) = 0.0;
-                           }
-                        }
-                     }
-                  }
-               }
-
-               // MSVC lambda capture workaround
-               [[maybe_unused]] const auto& inputs_ref = inputs;
-
-               int m_offset = 0;
-               for_constexpr<num_inputs>([&](auto s)
-               {
-                  using fop_t = std::decay_t<decltype(get<s>(inputs_ref))>;
-
-                  const int trial_op_dim = static_cast<int>(itod(static_cast<int>(s)));
-                  if (trial_op_dim == 0)
-                  {
-                     // This is inside a lambda so we have to return
-                     // instead of idiomatic 'continue'.
-                     return;
-                  }
-
-                  auto& B = input_dtqmaps[s].B;
-                  auto& G = input_dtqmaps[s].G;
-
-                  if constexpr (is_value_fop<fop_t>::value)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-
-                              for (int m = 0; m < trial_op_dim; m++)
-                              {
-                                 for (int i = 0; i < test_vdim; i++)
-                                 {
-                                    for (int k = 0; k < test_op_dim; k++)
-                                    {
-                                       const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                       fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy) * B(qz, 0, Jz);
-                                    }
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-                  else if constexpr (is_gradient_fop<fop_t>::value)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-                              for (int m = 0; m < trial_op_dim; m++)
-                              {
-                                 for (int i = 0; i < test_vdim; i++)
-                                 {
-                                    for (int k = 0; k < test_op_dim; k++)
-                                    {
-                                       const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                       if (m == 0)
-                                       {
-                                          fhat(i, k, q) += f * G(qx, 0, Jx) * B(qy, 0, Jy) * B(qz, 0, Jz);
-                                       }
-                                       else if (m == 1)
-                                       {
-                                          fhat(i, k, q) += f * B(qx, 0, Jx) * G(qy, 0, Jy) * B(qz, 0, Jz);
-                                       }
-                                       else if (m == 2)
-                                       {
-                                          fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy) * G(qz, 0, Jz);
-                                       }
-                                    }
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-                  else
-                  {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-                     MFEM_ABORT("sum factorized sparse matrix assemble routine "
-                                "not implemented for field operator");
-#endif
-                  }
-                  MFEM_SYNC_THREAD;
-                  m_offset += trial_op_dim;
-               });
-
-               auto bvtfhat = Reshape(&A(0, 0, J, j), num_test_dof, test_vdim);
-               map_quadrature_data_to_fields(bvtfhat, fhat, output, output_dtqmap,
-                                             scratch_shmem, dimension, true);
-            }
-         }
-      }
-   }
-}
-
-/// @brief Assemble element matrix for two dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_t2d(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& q1d,
-   const int& td1d)
-{
-   constexpr int dimension = 2;
-
-   // [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, num_qp]
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-
-   // [num_test_dof, ...]
-   const auto num_test_dof = A.GetShape()[0];
-
-   for (int Jx = 0; Jx < td1d; Jx++)
-   {
-      for (int Jy = 0; Jy < td1d; Jy++)
-      {
-         const int J = Jy + Jx * td1d;
-
-         for (int j = 0; j < trial_vdim; j++)
-         {
-            for (int tv = 0; tv < test_vdim; tv++)
-            {
-               for (int tod = 0; tod < test_op_dim; tod++)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        fhat(tv, tod, q) = 0.0;
-                     }
-                  }
-               }
-            }
-
-            // MSVC lambda capture workaround
-            [[maybe_unused]] const auto& inputs_ref = inputs;
-
-            int m_offset = 0;
-            for_constexpr<num_inputs>([&](auto s)
-            {
-               using fop_t = std::decay_t<decltype(get<s>(inputs_ref))>;
-
-               const int trial_op_dim = static_cast<int>(itod(static_cast<int>(s)));
-               if (trial_op_dim == 0)
-               {
-                  // This is inside a lambda so we have to return
-                  // instead of idiomatic 'continue'.
-                  return;
-               }
-
-               auto& B = input_dtqmaps[s].B;
-               auto& G = input_dtqmaps[s].G;
-
-               if constexpr (is_value_fop<fop_t>::value)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        for (int m = 0; m < trial_op_dim; m++)
-                        {
-                           for (int i = 0; i < test_vdim; i++)
-                           {
-                              for (int k = 0; k < test_op_dim; k++)
-                              {
-                                 const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                 fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy);
-                              }
-                           }
-                        }
-                     }
-                  }
-               }
-               else if constexpr (is_gradient_fop<fop_t>::value)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        for (int m = 0; m < trial_op_dim; m++)
-                        {
-                           for (int i = 0; i < test_vdim; i++)
-                           {
-                              for (int k = 0; k < test_op_dim; k++)
-                              {
-                                 const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                 if (m == 0)
-                                 {
-                                    fhat(i, k, q) += f * B(qx, 0, Jx) * G(qy, 0, Jy);
-                                 }
-                                 else
-                                 {
-                                    fhat(i, k, q) += f * G(qx, 0, Jx) * B(qy, 0, Jy);
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-               }
-               else
-               {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-                  MFEM_ABORT("sum factorized sparse matrix assemble routine "
-                             "not implemented for field operator");
-#endif
-               }
-               MFEM_SYNC_THREAD;
-               m_offset += trial_op_dim;
-            });
-
-            auto bvtfhat = Reshape(&A(0, 0, J, j), num_test_dof, test_vdim);
-            map_quadrature_data_to_fields(bvtfhat, fhat, output, output_dtqmap,
-                                          scratch_shmem, dimension, true);
-         }
-      }
-   }
-}
-
-/// @brief Assemble element matrix for two or three dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param dimension The spatial dimension.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-/// @param use_sum_factorization Indicator if sum factorization is used.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_naive(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& dimension,
-   const int& q1d,
-   const int& td1d,
-   const bool& use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 2)
-      {
-         assemble_element_mat_t2d(A, fhat, qpdc, itod, inputs, output,
-                                  input_dtqmaps, output_dtqmap, scratch_shmem, q1d, td1d);
-      }
-      else if (dimension == 3)
-      {
-         assemble_element_mat_t3d(A, fhat, qpdc, itod, inputs, output,
-                                  input_dtqmaps, output_dtqmap, scratch_shmem, q1d, td1d);
-      }
-   }
-   else
-   {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-      MFEM_ABORT("element matrix assemble not implemented for non tensor "
-                 "product basis");
-#endif
-   }
-}
-
-} // namespace mfem::future

fem/dfem/backends/global_qf/action.hpp

@@ -0,0 +1,122 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../util.hpp"
+#include "../../integrator_ctx.hpp"
+
+#include <utility>
+
+namespace mfem::future
+{
+
+namespace GlobalQFImpl
+{
+
+template<
+   typename qfunc_t,
+   typename inputs_t,
+   typename outputs_t,
+   size_t ninputs = tuple_size<inputs_t>::value,
+   size_t noutputs = tuple_size<outputs_t>::value>
+struct Action
+{
+   Action(
+      IntegratorContext ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs) :
+      ctx(ctx),
+      qfunc(qfunc),
+      inputs(inputs),
+      outputs(outputs)
+   {
+      create_fop_to_fd(inputs, ctx.infds, input_to_infd);
+      create_fop_to_fd(outputs, ctx.outfds, output_to_outfd);
+
+      check_consistency(inputs, input_to_infd, ctx.infds);
+      check_consistency(outputs, output_to_outfd, ctx.outfds);
+
+      create_fieldbases(inputs, input_to_infd, ctx.infds, ctx.ir, input_bases);
+      create_fieldbases(outputs, output_to_outfd, ctx.outfds, ctx.ir, output_bases);
+
+      create_qlayouts(inputs, ctx.in_qlayouts, input_qlayouts);
+      create_qlayouts(outputs, ctx.out_qlayouts, output_qlayouts);
+
+      const int nqp = ctx.ir.GetNPoints();
+      gnqp = nqp * ctx.nentities;
+
+      // prepare xq and yq BlockVectors
+      xq_offsets.SetSize(ninputs + 1);
+      xq_offsets[0] = 0;
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         const auto input = get<i>(inputs);
+         xq_offsets[i + 1] = nqp * input.size_on_qp * ctx.nentities;
+      });
+      xq_offsets.PartialSum();
+      InitBlockVector(xq, xq_offsets);
+
+      yq_offsets.SetSize(noutputs + 1);
+      yq_offsets[0] = 0;
+      constexpr_for<0, noutputs>([&](auto i)
+      {
+         const auto output = get<i>(outputs);
+         yq_offsets[i + 1] = nqp * output.size_on_qp * ctx.nentities;
+      });
+      yq_offsets.PartialSum();
+      InitBlockVector(yq, yq_offsets);
+   }
+
+   void operator()(
+      const std::vector<Vector *> &xe,
+      std::vector<Vector *> &ye) const
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      // E -> Q
+      interpolate(input_to_infd, input_bases, xe, xq);
+
+      // Q -> Q
+      static_assert(
+         detail::supports_tensor_array_qfunc<qfunc_t, inputs_t, outputs_t>::value,
+         "qfunc signature not supported by default backend Action");
+
+      detail::call_qfunc(
+         qfunc, xq, yq, gnqp, input_qlayouts, output_qlayouts,
+         std::make_index_sequence<ninputs> {},
+         std::make_index_sequence<noutputs> {});
+
+      // Q -> E
+      integrate(output_to_outfd, output_bases, yq, ye);
+   }
+
+   IntegratorContext ctx;
+   qfunc_t qfunc;
+   inputs_t inputs;
+   outputs_t outputs;
+
+   std::array<size_t, ninputs> input_to_infd;
+   std::array<size_t, noutputs> output_to_outfd;
+
+   std::array<FieldBasis, ninputs> input_bases;
+   std::array<FieldBasis, noutputs> output_bases;
+
+   std::array<std::vector<int>, ninputs>  input_qlayouts;
+   std::array<std::vector<int>, noutputs> output_qlayouts;
+
+   int gnqp = 0;
+   Array<int> xq_offsets, yq_offsets;
+   mutable BlockVector xq, yq;
+};
+
+}
+}

fem/dfem/backends/global_qf/derivative_action.hpp

@@ -0,0 +1,180 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "../util.hpp"
+#include <utility>
+
+namespace mfem::future::GlobalQFImpl
+{
+
+template<
+   int derivative_id,
+   typename qfunc_t,
+   typename inputs_t,
+   typename outputs_t,
+   size_t ninputs = tuple_size<inputs_t>::value,
+   size_t noutputs = tuple_size<outputs_t>::value>
+struct DerivativeAction
+{
+   using qfunc_shadow_t = detail::qfunc_shadow_t<qfunc_t>;
+
+   DerivativeAction(
+      IntegratorContext ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs):
+      ctx(ctx), qfunc(qfunc),
+      qfunc_shadow(detail::MakeQFunctionShadowStorage(this->qfunc)),
+      inputs(inputs), outputs(outputs)
+   {
+      create_fop_to_fd(inputs, ctx.infds, input_to_infd);
+      create_fop_to_fd(outputs, ctx.outfds, output_to_outfd);
+
+      check_consistency(inputs, input_to_infd, ctx.infds);
+      check_consistency(outputs, output_to_outfd, ctx.outfds);
+
+      create_fieldbases(inputs, input_to_infd, ctx.infds, ctx.ir, input_bases);
+      create_fieldbases(
+         outputs, output_to_outfd, ctx.outfds, ctx.ir, output_bases);
+
+      create_qlayouts(inputs, ctx.in_qlayouts, input_qlayouts);
+      create_qlayouts(outputs, ctx.out_qlayouts, output_qlayouts);
+
+      const int nqp = ctx.ir.GetNPoints();
+      gnqp = nqp * ctx.nentities;
+
+      xq_offsets.SetSize(ninputs + 1);
+      xq_offsets[0] = 0;
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         const auto input = get<i>(inputs);
+         xq_offsets[i + 1] = nqp * input.size_on_qp * ctx.nentities;
+      });
+      xq_offsets.PartialSum();
+      InitBlockVector(xq, xq_offsets);
+
+      yq_offsets.SetSize(noutputs + 1);
+      yq_offsets[0] = 0;
+      constexpr_for<0, noutputs>([&](auto i)
+      {
+         const auto output = get<i>(outputs);
+         yq_offsets[i + 1] = nqp * output.size_on_qp * ctx.nentities;
+      });
+      yq_offsets.PartialSum();
+      InitBlockVector(yq, yq_offsets);
+
+      // Shadow blocks use the same offsets as xq so tensor_array views
+      shadow_xq_offsets.SetSize(xq_offsets.Size());
+      shadow_xq_offsets = xq_offsets;
+      InitBlockVector(shadow_xq, shadow_xq_offsets);
+
+      dof_ordering = ElementDofOrdering::LEXICOGRAPHIC;
+
+      const size_t direction_fd_idx = FindIdx(derivative_id, ctx.infds);
+      MFEM_ASSERT(direction_fd_idx != SIZE_MAX,
+                  "derivative direction field not found in infds");
+      direction_fd = ctx.infds[direction_fd_idx];
+   }
+
+   void operator()(
+      const std::vector<Vector *> &xe,
+      const Vector *de,
+      std::vector<Vector *> &ye)
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      // E -> Q
+      interpolate(input_to_infd, input_bases, xe, xq);
+
+      constexpr auto input_active =
+         detail::make_activity_map<derivative_id>(inputs_t{});
+
+      MFEM_ASSERT(de != nullptr, "derivative direction vector is null");
+      restriction(direction_fd, direction_rcache, *de, direction_e,
+                  dof_ordering);
+
+      shadow_xq = 0.0;
+      shadow_xq.SyncToBlocks();
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         if (!input_active[i]) { return; }
+         input_bases[i].forward(direction_e, shadow_xq.GetBlock(i));
+      });
+
+      static_assert(detail::supports_tensor_array_qfunc<qfunc_t,
+                    inputs_t,
+                    outputs_t>::value,
+                    "qfunc signature not supported by default backend Action");
+
+      // Q -> Q
+      yq = 0.0;
+      yq.SyncToBlocks();
+      if constexpr (detail::qfunc_uses_scratch_v<qfunc_t>)
+      {
+         detail::fwddiff<derivative_id, qfunc_t, qfunc_shadow_t, inputs_t,
+                outputs_t>(
+                   qfunc,
+                   qfunc_shadow,
+                   xq,
+                   shadow_xq,
+                   yq,
+                   gnqp,
+                   input_qlayouts,
+                   output_qlayouts,
+                   std::make_index_sequence<ninputs> {},
+                   std::make_index_sequence<noutputs> {});
+      }
+      else
+      {
+         detail::fwddiff<derivative_id, qfunc_t, inputs_t, outputs_t>(
+            qfunc,
+            xq,
+            shadow_xq,
+            yq,
+            gnqp,
+            input_qlayouts,
+            output_qlayouts,
+            std::make_index_sequence<ninputs> {},
+            std::make_index_sequence<noutputs> {});
+      }
+
+      // Q -> E
+      integrate(output_to_outfd, output_bases, yq, ye);
+   }
+
+   IntegratorContext ctx;
+   qfunc_t qfunc;
+   qfunc_shadow_t qfunc_shadow;
+   inputs_t inputs;
+   outputs_t outputs;
+
+   std::array<size_t, ninputs> input_to_infd;
+   std::array<size_t, noutputs> output_to_outfd;
+
+   std::array<FieldBasis, ninputs> input_bases;
+   std::array<FieldBasis, noutputs> output_bases;
+
+   std::array<std::vector<int>, ninputs> input_qlayouts;
+   std::array<std::vector<int>, noutputs> output_qlayouts;
+
+   int gnqp = 0;
+   Array<int> xq_offsets, shadow_xq_offsets, yq_offsets;
+   mutable BlockVector xq, shadow_xq, yq;
+
+   FieldDescriptor direction_fd;
+   ElementDofOrdering dof_ordering = ElementDofOrdering::LEXICOGRAPHIC;
+   mutable Vector direction_e;
+   mutable RestrictionCache<Entity::Element> direction_rcache;
+};
+
+} // namespace mfem::future::GlobalQFImpl

fem/dfem/backends/global_qf/derivative_apply.hpp

@@ -0,0 +1,242 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "../util.hpp"
+
+#include <array>
+#include <utility>
+#include <vector>
+
+namespace mfem::future::GlobalQFImpl
+{
+
+// Q-function-shape-agnostic cached forward apply (J·v)
+template<
+   int derivative_id,
+   typename inputs_t,
+   typename outputs_t>
+struct DerivativeApply
+{
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+
+   DerivativeApply(
+      IntegratorContext ctx,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache):
+      ctx(ctx), inputs(std::move(inputs)), outputs(std::move(outputs)),
+      qp_cache(qp_cache)
+   {
+      create_fop_to_fd(this->inputs, ctx.infds, input_to_infd);
+      create_fop_to_fd(this->outputs, ctx.outfds, output_to_outfd);
+
+      check_consistency(this->inputs, input_to_infd, ctx.infds);
+      check_consistency(this->outputs, output_to_outfd, ctx.outfds);
+
+      create_fieldbases(
+         this->inputs, input_to_infd, ctx.infds, ctx.ir, input_bases);
+      create_fieldbases(
+         this->outputs, output_to_outfd, ctx.outfds, ctx.ir, output_bases);
+
+      const int nqp = ctx.ir.GetNPoints();
+      const int ne = ctx.nentities;
+      num_qp = nqp;
+      gnqp = nqp * ne;
+
+      // Precompute Q-space BlockVector layouts
+      dir_q_offsets.SetSize(n_inputs + 1);
+      dir_q_offsets[0] = 0;
+      constexpr_for<0, n_inputs>([&](auto i)
+      {
+         dir_q_offsets[i + 1] =
+            dir_q_offsets[i] + get<i>(this->inputs).size_on_qp * nqp * ne;
+      });
+      InitBlockVector(dir_q_local, dir_q_offsets);
+
+      result_q_offsets.SetSize(n_outputs + 1);
+      result_q_offsets[0] = 0;
+      constexpr_for<0, n_outputs>([&](auto i)
+      {
+         result_q_offsets[i + 1] =
+            result_q_offsets[i] + get<i>(this->outputs).size_on_qp * nqp * ne;
+      });
+      InitBlockVector(result_q_local, result_q_offsets);
+
+      // Cache layout metadata (must match DerivativeSetup)
+      residual_size_on_qp = 0;
+      trial_vdim = 0;
+      total_trial_op_dim = 0;
+
+      constexpr auto activity =
+         detail::make_activity_map<derivative_id>(inputs_t{});
+
+      constexpr_for<0, n_inputs>([&](auto i)
+      {
+         if (!activity[i]) { return; }
+         const auto &fop = get<i>(this->inputs);
+         trial_vdim = fop.vdim;
+         total_trial_op_dim += fop.size_on_qp / fop.vdim;
+      });
+
+      constexpr_for<0, n_outputs>([&](auto i)
+      { residual_size_on_qp += get<i>(this->outputs).size_on_qp; });
+      residual_size_on_qp *= trial_vdim * total_trial_op_dim;
+   }
+
+   void operator()(
+      const std::vector<Vector *> & /*xe*/,
+      const Vector *direction_l,
+      std::vector<Vector *> &ye) const
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      MFEM_ASSERT(direction_l != nullptr,
+                  "Global DerivativeApply: direction vector is null");
+
+      // Re-zero pre-allocated Q temporaries
+      dir_q_local = 0.0;
+      dir_q_local.SyncToBlocks();
+      result_q_local = 0.0;
+      result_q_local.SyncToBlocks();
+
+      // Restrict trial direction from the derivative field
+      size_t in_fd = SIZE_MAX;
+      constexpr_for<0, n_inputs>([&](auto i)
+      {
+         if (get<i>(inputs).GetFieldId() == derivative_id)
+         {
+            in_fd = input_to_infd[i.value];
+         }
+      });
+      MFEM_ASSERT(in_fd != SIZE_MAX,
+                  "DerivativeApply: derivative field not found among inputs");
+
+      const auto &fd = ctx.infds[in_fd];
+
+      Vector dir_e;
+      restriction(fd, direction_rcache, *direction_l, dir_e,
+                  ElementDofOrdering::LEXICOGRAPHIC);
+
+      // Forward the trial direction into active input Q block
+      constexpr_for<0, n_inputs>([&](auto s)
+      {
+         if (get<s>(inputs).GetFieldId() != derivative_id) { return; }
+         input_bases[s.value].forward(dir_e, dir_q_local.GetBlock(s.value));
+      });
+
+      const real_t *cache_ptr = qp_cache.Read();
+      const int res_sz = residual_size_on_qp;
+      const int gnqp_local = gnqp;
+      const int num_qp_local = num_qp;
+      const int trial_vdim_local = trial_vdim;
+      const int total_trial_op_dim_local = total_trial_op_dim;
+
+      constexpr_for<0, n_outputs>([&](auto o)
+      {
+         const int tv_o = get<o>(outputs).vdim;
+         const int to_o = get<o>(outputs).size_on_qp / tv_o;
+         const int out_base = [&]
+         {
+            int off = 0;
+            constexpr_for<0, o.value>([&](auto prev)
+            { off += get<prev>(outputs).size_on_qp; });
+            return off;
+         }();
+
+         real_t *res_o = result_q_local.GetBlock(o.value).ReadWrite();
+
+         int m_offset = 0;
+         constexpr_for<0, n_inputs>([&](auto s)
+         {
+            if (get<s>(inputs).GetFieldId() != derivative_id) { return; }
+
+            const int tv = get<s>(inputs).vdim;
+            const int to = get<s>(inputs).size_on_qp / tv;
+            const real_t *dir_s = dir_q_local.GetBlock(s.value).Read();
+
+            mfem::forall(gnqp_local, [=] MFEM_HOST_DEVICE(int gq)
+            {
+               // Cache is (q, cache_idx, e): adjacent threads (adjacent gq)
+               // read adjacent addresses for a fixed cache_idx.
+               const int cache_base =
+                  (gq % num_qp_local) +
+                  num_qp_local * res_sz * (gq / num_qp_local);
+
+               for (int j = 0; j < tv; ++j)
+               {
+                  for (int m = 0; m < to; ++m)
+                  {
+                     const real_t v = dir_s[(j * to + m) + (tv * to) * gq];
+                     const int m_global = m + m_offset;
+
+                     for (int i = 0; i < tv_o; ++i)
+                     {
+                        for (int k = 0; k < to_o; ++k)
+                        {
+                           const int out_comp = out_base + i * to_o + k;
+
+                           const int cache_idx =
+                              out_comp * trial_vdim_local * total_trial_op_dim_local +
+                              j * total_trial_op_dim_local + m_global;
+
+                           const real_t c =
+                              cache_ptr[cache_base + num_qp_local * cache_idx];
+                           res_o[(i * to_o + k) + (tv_o * to_o) * gq] += c * v;
+                        }
+                     }
+                  }
+               }
+            });
+            m_offset += to;
+         });
+      });
+
+      result_q_local.SyncToBlocks();
+
+      // Map result Q back to output fields
+      constexpr_for<0, n_outputs>([&](auto o)
+      {
+         const size_t out_fd = output_to_outfd[o.value];
+         output_bases[o.value].transpose(result_q_local.GetBlock(o.value),
+                                         *ye[out_fd]);
+      });
+   }
+
+private:
+   IntegratorContext ctx;
+   inputs_t inputs;
+   outputs_t outputs;
+   const Vector &qp_cache;
+
+   std::array<size_t, n_inputs> input_to_infd;
+   std::array<size_t, n_outputs> output_to_outfd;
+
+   std::array<FieldBasis, n_inputs> input_bases;
+   std::array<FieldBasis, n_outputs> output_bases;
+
+   int gnqp = 0;
+   int num_qp = 0;
+
+   Array<int> dir_q_offsets;
+   Array<int> result_q_offsets;
+   mutable BlockVector dir_q_local;
+   mutable BlockVector result_q_local;
+   mutable RestrictionCache<Entity::Element> direction_rcache;
+
+   int residual_size_on_qp = 0;
+   int trial_vdim = 0;
+   int total_trial_op_dim = 0;
+};
+
+} // namespace mfem::future::GlobalQFImpl

fem/dfem/backends/global_qf/derivative_apply_transpose.hpp

@@ -0,0 +1,260 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "../util.hpp"
+
+#include <array>
+#include <utility>
+#include <vector>
+
+namespace mfem::future::GlobalQFImpl
+{
+
+// Q-function-shape-agnostic cached transpose apply (Jᵀ·w)
+template<
+   int derivative_id,
+   typename qfunc_t,
+   typename inputs_t,
+   typename outputs_t>
+struct DerivativeApplyTranspose
+{
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+
+   DerivativeApplyTranspose(
+      IntegratorContext ctx,
+      qfunc_t /*qfunc*/,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache):
+      ctx(ctx), inputs(std::move(inputs)), outputs(std::move(outputs)),
+      qp_cache(qp_cache), dir_out_l(n_outputs), dir_out_e(n_outputs)
+   {
+      create_fop_to_fd(this->inputs, ctx.infds, input_to_infd);
+      create_fop_to_fd(this->outputs, ctx.outfds, output_to_outfd);
+
+      check_consistency(this->inputs, input_to_infd, ctx.infds);
+      check_consistency(this->outputs, output_to_outfd, ctx.outfds);
+
+      create_fieldbases(
+         this->inputs, input_to_infd, ctx.infds, ctx.ir, input_bases);
+      create_fieldbases(
+         this->outputs, output_to_outfd, ctx.outfds, ctx.ir, output_bases);
+
+      const int nqp = ctx.ir.GetNPoints();
+      const int ne = ctx.nentities;
+      num_qp = nqp;
+      gnqp = nqp * ne;
+
+      // Precompute Q-space BlockVector layouts
+      dir_q_offsets.SetSize(n_outputs + 1);
+      dir_q_offsets[0] = 0;
+      constexpr_for<0, n_outputs>([&](auto i)
+      {
+         dir_q_offsets[i + 1] =
+            dir_q_offsets[i] + get<i>(this->outputs).size_on_qp * nqp * ne;
+      });
+      InitBlockVector(dir_q_local, dir_q_offsets);
+
+      result_q_offsets.SetSize(n_inputs + 1);
+      result_q_offsets[0] = 0;
+      constexpr_for<0, n_inputs>([&](auto i)
+      {
+         result_q_offsets[i + 1] =
+            result_q_offsets[i] + get<i>(this->inputs).size_on_qp * nqp * ne;
+      });
+      InitBlockVector(result_q_local, result_q_offsets);
+
+      // Cache layout metadata
+      residual_size_on_qp = 0;
+      trial_vdim = 0;
+      total_trial_op_dim = 0;
+
+      constexpr auto activity =
+         detail::make_activity_map<derivative_id>(inputs_t{});
+
+      constexpr_for<0, n_inputs>([&](auto i)
+      {
+         if (!activity[i]) { return; }
+         const auto &fop = get<i>(this->inputs);
+         trial_vdim = fop.vdim;
+         total_trial_op_dim += fop.size_on_qp / fop.vdim;
+      });
+
+      constexpr_for<0, n_outputs>([&](auto i)
+      { residual_size_on_qp += get<i>(this->outputs).size_on_qp; });
+      residual_size_on_qp *= trial_vdim * total_trial_op_dim;
+   }
+
+   void operator()(
+      const std::vector<Vector *> & /*xe*/,
+      const Vector *direction_l,
+      std::vector<Vector *> &ye) const
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      MFEM_ASSERT(direction_l != nullptr,
+                  "Global DerivativeApplyTranspose: direction vector is null");
+
+      // Re-zero the pre-allocated Q temporaries
+      dir_q_local = 0.0;
+      result_q_local = 0.0;
+      dir_q_local.SyncToBlocks();
+      result_q_local.SyncToBlocks();
+
+      // Bring test cotangent to quadrature points
+      pull_output_cotangents_to_q(direction_l, dir_q_local);
+
+      // Contract qp_cache with test directions at quadrature points
+      const real_t *cache_ptr = qp_cache.Read();
+      const int res_sz = residual_size_on_qp;
+      const int gnqp_local = gnqp;
+      const int num_qp_local = num_qp;
+      const int trial_vdim_local = trial_vdim;
+      const int total_trial_op_dim_local = total_trial_op_dim;
+
+      constexpr_for<0, n_outputs>([&](auto o)
+      {
+         const int tv_o = get<o>(outputs).vdim;
+         const int to_o = get<o>(outputs).size_on_qp / tv_o;
+         const int out_base = [&]
+         {
+            int off = 0;
+            constexpr_for<0, o.value>([&](auto prev)
+            { off += get<prev>(outputs).size_on_qp; });
+            return off;
+         }();
+
+         const int size_o = get<o>(outputs).size_on_qp;
+         const real_t *dir_o = dir_q_local.GetBlock(o.value).Read();
+
+         int m_offset = 0;
+         constexpr_for<0, n_inputs>([&](auto s)
+         {
+            if (get<s>(inputs).GetFieldId() != derivative_id) { return; }
+
+            const int size_s = get<s>(inputs).size_on_qp;
+            const int to_s = size_s / trial_vdim_local;
+            real_t *res_s = result_q_local.GetBlock(s.value).ReadWrite();
+
+            mfem::forall(gnqp_local, [=] MFEM_HOST_DEVICE(int gq)
+            {
+               // Cache is (q, cache_idx, e): adjacent threads (adjacent gq)
+               // read adjacent addresses for a fixed cache_idx.
+               const int cache_base =
+                  (gq % num_qp_local) +
+                  num_qp_local * res_sz * (gq / num_qp_local);
+
+               for (int i = 0; i < tv_o; ++i)
+               {
+                  for (int k = 0; k < to_o; ++k)
+                  {
+                     const int out_comp = out_base + i * to_o + k;
+                     const real_t w = dir_o[(i * to_o + k) + size_o * gq];
+
+                     for (int j = 0; j < trial_vdim_local; ++j)
+                     {
+                        for (int m = 0; m < to_s; ++m)
+                        {
+                           const int m_global = m + m_offset;
+                           const int cache_idx =
+                              out_comp * trial_vdim_local * total_trial_op_dim_local +
+                              j * total_trial_op_dim_local + m_global;
+
+                           const real_t c =
+                              cache_ptr[cache_base + num_qp_local * cache_idx];
+                           res_s[(j * to_s + m) + size_s * gq] += c * w;
+                        }
+                     }
+                  }
+               }
+            });
+            m_offset += to_s;
+         });
+      });
+
+      // Map result Q back to the trial (input) fields
+      constexpr_for<0, n_inputs>([&](auto s)
+      {
+         if (get<s>(inputs).GetFieldId() != derivative_id) { return; }
+
+         const size_t in_fd = input_to_infd[s.value];
+         input_bases[s.value].transpose(
+            result_q_local.GetBlock(s.value), *ye[in_fd]);
+      });
+   }
+
+private:
+   IntegratorContext ctx;
+   inputs_t inputs;
+   outputs_t outputs;
+   const Vector &qp_cache;
+
+   std::array<size_t, n_inputs> input_to_infd;
+   std::array<size_t, n_outputs> output_to_outfd;
+
+   std::array<FieldBasis, n_inputs> input_bases;
+   std::array<FieldBasis, n_outputs> output_bases;
+
+   int gnqp = 0;
+   int num_qp = 0;
+
+   // Pre-allocated Q-space temporaries
+   Array<int> dir_q_offsets;
+   Array<int> result_q_offsets;
+   mutable BlockVector dir_q_local;
+   mutable BlockVector result_q_local;
+
+   // Pre-allocated owning storage for output cotangent temporaries
+   mutable std::array<Vector, n_outputs> dir_out_l_owned;
+   mutable std::array<Vector, n_outputs> dir_out_e_owned;
+   mutable std::vector<Vector *> dir_out_l;
+   mutable std::vector<Vector *> dir_out_e;
+   mutable RestrictionCache<Entity::Element> out_rcache;
+
+   int residual_size_on_qp = 0;
+   int trial_vdim = 0;
+   int total_trial_op_dim = 0;
+
+   /// Pull output cotangents from L-space into the pre-allocated Q BlockVector
+   void pull_output_cotangents_to_q(const Vector *direction_l,
+                                    BlockVector &dir_q) const
+   {
+      int l_offset = 0;
+      constexpr_for<0, n_outputs>([&](auto i)
+      {
+         const size_t outfd = output_to_outfd[i];
+         const auto &fd = ctx.outfds[outfd];
+         const int l_size = GetVSize(fd);
+
+         dir_out_l_owned[i] =
+            Vector(*const_cast<Vector *>(direction_l), l_offset, l_size);
+         dir_out_e_owned[i].SetSize(0);
+         dir_out_e_owned[i].UseDevice(true);
+
+         dir_out_l[i] = &dir_out_l_owned[i];
+         dir_out_e[i] = &dir_out_e_owned[i];
+         l_offset += l_size;
+      });
+
+      restriction(ctx.outfds, out_rcache, dir_out_l, dir_out_e);
+
+      constexpr_for<0, n_outputs>([&](auto i)
+      {
+         output_bases[i.value].forward(*dir_out_e[i], dir_q.GetBlock(i.value));
+      });
+      dir_q.SyncToBlocks();
+   }
+};
+
+} // namespace mfem::future::GlobalQFImpl

fem/dfem/backends/global_qf/derivative_setup.hpp

@@ -0,0 +1,244 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "../util.hpp"
+#include <utility>
+
+namespace mfem::future::GlobalQFImpl
+{
+
+template<
+   int derivative_id,
+   typename qfunc_t,
+   typename inputs_t,
+   typename outputs_t,
+   size_t ninputs = tuple_size<inputs_t>::value,
+   size_t noutputs = tuple_size<outputs_t>::value>
+struct DerivativeSetup
+{
+   using qfunc_shadow_t = detail::qfunc_shadow_t<qfunc_t>;
+
+   DerivativeSetup(
+      IntegratorContext ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      Vector &qp_cache) :
+      ctx(ctx),
+      qfunc(qfunc),
+      qfunc_shadow(detail::MakeQFunctionShadowStorage(this->qfunc)),
+      inputs(inputs),
+      outputs(outputs),
+      qp_cache(qp_cache)
+   {
+      create_fop_to_fd(inputs, ctx.infds, input_to_infd);
+      create_fop_to_fd(outputs, ctx.outfds, output_to_outfd);
+
+      check_consistency(inputs, input_to_infd, ctx.infds);
+      check_consistency(outputs, output_to_outfd, ctx.outfds);
+
+      create_fieldbases(inputs, input_to_infd, ctx.infds, ctx.ir, input_bases);
+      create_fieldbases(outputs, output_to_outfd, ctx.outfds, ctx.ir, output_bases);
+
+      create_qlayouts(inputs, ctx.in_qlayouts, input_qlayouts);
+      create_qlayouts(outputs, ctx.out_qlayouts, output_qlayouts);
+
+      const int nqp = ctx.ir.GetNPoints();
+      num_qp = nqp;
+      nentities = ctx.nentities;
+      gnqp = nqp * nentities;
+
+      xq_offsets.SetSize(ninputs + 1);
+      xq_offsets[0] = 0;
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         xq_offsets[i + 1] = nqp * get<i>(inputs).size_on_qp * nentities;
+      });
+      xq_offsets.PartialSum();
+      InitBlockVector(xq, xq_offsets);
+
+      shadow_xq_offsets.SetSize(xq_offsets.Size());
+      shadow_xq_offsets = xq_offsets;
+      InitBlockVector(shadow_xq, shadow_xq_offsets);
+
+      yq_offsets.SetSize(noutputs + 1);
+      yq_offsets[0] = 0;
+      constexpr_for<0, noutputs>([&](auto o)
+      {
+         yq_offsets[o + 1] = nqp * get<o>(outputs).size_on_qp * nentities;
+      });
+      yq_offsets.PartialSum();
+      InitBlockVector(yq, yq_offsets);
+
+      total_out_size_on_qp = 0;
+      constexpr_for<0, noutputs>([&](auto o)
+      {
+         total_out_size_on_qp += get<o>(outputs).size_on_qp;
+         out_vdim[o] = get<o>(outputs).vdim;
+         out_op_dim[o] = get<o>(outputs).size_on_qp / get<o>(outputs).vdim;
+      });
+
+      activity_map = detail::make_activity_map<derivative_id>(inputs_t {});
+
+      trial_vdim = 0;
+      total_trial_op_dim = 0;
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         if (!activity_map[i]) { return; }
+         const auto inp = get<i>(inputs);
+         trial_vdim = inp.vdim;
+         total_trial_op_dim += inp.size_on_qp / inp.vdim;
+      });
+
+      constexpr_for<0, ninputs>([&](auto i)
+      {
+         input_size_on_qp_arr[i] = get<i>(inputs).size_on_qp;
+      });
+
+      residual_size_on_qp = total_out_size_on_qp * trial_vdim * total_trial_op_dim;
+      qp_cache.SetSize(residual_size_on_qp * num_qp * nentities);
+      qp_cache.UseDevice(true);
+   }
+
+   void operator()(const std::vector<Vector *> &xe)
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      interpolate(input_to_infd, input_bases, xe, xq);
+
+      const int gnqp_local = gnqp;
+      const int num_qp_local = num_qp;
+      const int trial_vdim_local = trial_vdim;
+      const int total_trial_op_dim_local = total_trial_op_dim;
+      const int residual_size_local = residual_size_on_qp;
+
+      for (int j = 0; j < trial_vdim; j++)
+      {
+         int m_offset = 0;
+         constexpr_for<0, ninputs>([&](auto s)
+         {
+            if (!activity_map[s]) { return; }
+
+            const int input_vdim_s  = get<s>(inputs).vdim;
+            const int input_size_s  = input_size_on_qp_arr[s];
+            const int trial_op_dim_s = input_size_s / input_vdim_s;
+
+            for (int m = 0; m < trial_op_dim_s; m++)
+            {
+               shadow_xq = 0.0;
+               shadow_xq.SyncToBlocks();
+
+               // Set component (j + input_vdim_s * m) to 1 at all QPs
+               const int c_shadow = j + input_vdim_s * m;
+               real_t *shadow_ptr = shadow_xq.GetBlock(s.value).ReadWrite();
+               mfem::forall(gnqp_local, [=] MFEM_HOST_DEVICE(int gq)
+               {
+                  shadow_ptr[c_shadow + input_size_s * gq] = 1.0;
+               });
+
+               yq = 0.0;
+               yq.SyncToBlocks();
+
+               if constexpr (detail::qfunc_uses_scratch_v<qfunc_t>)
+               {
+                  detail::fwddiff<derivative_id, qfunc_t, qfunc_shadow_t,
+                         inputs_t, outputs_t>(
+                            qfunc, qfunc_shadow, xq, shadow_xq, yq, gnqp,
+                            input_qlayouts, output_qlayouts,
+                            std::make_index_sequence<ninputs> {},
+                            std::make_index_sequence<noutputs> {});
+               }
+               else
+               {
+                  detail::fwddiff<derivative_id, qfunc_t, inputs_t, outputs_t>(
+                     qfunc, xq, shadow_xq, yq, gnqp,
+                     input_qlayouts, output_qlayouts,
+                     std::make_index_sequence<ninputs> {},
+                     std::make_index_sequence<noutputs> {});
+               }
+
+               real_t *cache_d = qp_cache.ReadWrite();
+
+               // Write yq into the cache column
+               const int m_global = m + m_offset;
+               const int j_cur    = j;
+               int out_offset = 0;
+               constexpr_for<0, noutputs>([&](auto o)
+               {
+                  const int test_vdim_o   = out_vdim[o];
+                  const int test_op_dim_o = out_op_dim[o];
+                  const int yq_out_size   = test_vdim_o * test_op_dim_o;
+                  const int out_offset_o  = out_offset;
+                  const real_t *yq_d      = yq.GetBlock(o.value).Read();
+
+                  // The cache is (q, cache_idx, e) with the quadrature index
+                  // fastest, so gq is the fastest-varying thread index to keep
+                  // the stores coalesced.
+                  mfem::forall(gnqp_local * yq_out_size, [=] MFEM_HOST_DEVICE(int idx)
+                  {
+                     const int gq       = idx % gnqp_local;
+                     const int c_out    = idx / gnqp_local;
+                     const int q        = gq % num_qp_local;
+                     const int entity   = gq / num_qp_local;
+                     const int out_comp = out_offset_o + c_out;
+                     const int cache_idx =
+                        out_comp * trial_vdim_local * total_trial_op_dim_local +
+                        j_cur * total_trial_op_dim_local +
+                        m_global;
+                     cache_d[q + num_qp_local *
+                               (cache_idx + residual_size_local * entity)] =
+                                yq_d[c_out + yq_out_size * gq];
+                  });
+                  out_offset += yq_out_size;
+               });
+            }
+            m_offset += trial_op_dim_s;
+         });
+      }
+   }
+
+   IntegratorContext ctx;
+   qfunc_t qfunc;
+   qfunc_shadow_t qfunc_shadow;
+   inputs_t inputs;
+   outputs_t outputs;
+   Vector &qp_cache;
+
+   std::array<size_t, ninputs> input_to_infd;
+   std::array<size_t, noutputs> output_to_outfd;
+
+   std::array<FieldBasis, ninputs> input_bases;
+   std::array<FieldBasis, noutputs> output_bases;
+
+   std::array<std::vector<int>, ninputs>  input_qlayouts;
+   std::array<std::vector<int>, noutputs> output_qlayouts;
+
+   int gnqp = 0;
+   int num_qp = 0;
+   int nentities = 0;
+
+   Array<int> xq_offsets, shadow_xq_offsets, yq_offsets;
+   mutable BlockVector xq, shadow_xq, yq;
+
+   int total_out_size_on_qp = 0;
+   int trial_vdim = 0;
+   int total_trial_op_dim = 0;
+   int residual_size_on_qp = 0;
+
+   std::array<int, noutputs> out_vdim {};
+   std::array<int, noutputs> out_op_dim {};
+   std::array<int, ninputs>  input_size_on_qp_arr {};
+   std::array<bool, ninputs> activity_map {};
+};
+
+} // namespace mfem::future::GlobalQFImpl

fem/dfem/backends/global_qf/prelude.hpp

@@ -0,0 +1,219 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "action.hpp"
+#include "derivative_action.hpp"
+#include "derivative_setup.hpp"
+
+#include "derivative_apply_transpose.hpp"
+
+#include "../local_qf/derivative_apply.hpp"
+#include "../local_qf/derivative_assemble.hpp"
+#include "../local_qf/derivative_assemble_diagonal.hpp"
+
+#include "../scratch_bank.hpp"
+
+namespace mfem::future
+{
+
+namespace detail
+{
+
+template <typename T>
+struct LocalQFShapeArg
+{
+   using type = std::remove_const_t<T>&;
+};
+
+template <typename scalar_t, int ndims, int... tensor_sizes>
+struct LocalQFShapeArg<tensor_ndarray<scalar_t, ndims, tensor_sizes...>>
+{
+   using scalar_type = std::remove_const_t<scalar_t>;
+   using type = std::conditional_t<
+                sizeof...(tensor_sizes) == 0,
+                scalar_type,
+                tensor<scalar_type, tensor_sizes...>>&;
+};
+
+template <typename scalar_t, int... tensor_sizes>
+struct LocalQFShapeArg<tensor<scalar_t, tensor_sizes...>>
+{
+   using scalar_type = std::remove_const_t<scalar_t>;
+   using type = std::conditional_t<
+                sizeof...(tensor_sizes) == 0,
+                scalar_type,
+                tensor<scalar_type, tensor_sizes...>>&;
+};
+
+template <typename qf_param_ts>
+struct LocalQFShapeFunction;
+
+template <typename... qf_param_ts>
+struct LocalQFShapeFunction<tuple<qf_param_ts...>>
+{
+   void operator()(
+      typename LocalQFShapeArg<qf_param_decay_t<qf_param_ts>>::type...) const;
+};
+
+template <typename qfunc_t>
+using LocalQFShapeFunctionFor = LocalQFShapeFunction<
+                                typename get_function_signature<qfunc_t>::type::parameter_ts>;
+
+} // namespace detail
+
+struct GlobalQFBackend
+{
+   /**
+    * @brief Make an action for a global Q-function.
+    *
+    * @param ctx The integrator context.
+    * @param args The arguments to the action.
+    * @return The action.
+    */
+   template<
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeAction(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs)
+   {
+      return GlobalQFImpl::Action(ctx, qfunc, inputs, outputs);
+   }
+
+   /**
+    * @brief Make a derivative action for a global Q-function.
+    *
+    * @tparam derivative_id The id of the derivative.
+    * @param ctx The integrator context.
+    * @param args The arguments to the derivative action.
+    * @return The derivative action.
+    */
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeAction(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs)
+   {
+      return GlobalQFImpl::DerivativeAction<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs);
+   }
+
+   /**
+    * @brief Make a derivative setup for a global Q-function.
+    *
+    * @tparam derivative_id The id of the derivative.
+    * @param ctx The integrator context.
+    * @param args The arguments to the derivative setup.
+    * @return The derivative setup.
+    */
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeSetup(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      Vector &qp_cache)
+   {
+      return GlobalQFImpl::DerivativeSetup<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeApply(
+      const IntegratorContext &ctx,
+      const qfunc_t & /*qfunc*/,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeApply<
+             derivative_id,
+             detail::LocalQFShapeFunctionFor<qfunc_t>,
+             inputs_t,
+             outputs_t>(ctx,
+                        detail::LocalQFShapeFunctionFor<qfunc_t> {},
+                        inputs,
+                        outputs,
+                        qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeApplyTranspose(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return GlobalQFImpl::DerivativeApplyTranspose<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeAssemble(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeAssemble<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   auto static MakeDerivativeAssembleDiagonal(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeAssembleDiagonal<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs, qp_cache);
+   }
+};
+
+} // namespace mfem::future

fem/dfem/backends/local_qf/action.hpp

@@ -0,0 +1,658 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../fieldoperator.hpp"
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include "../../integrator_ctx.hpp"
+#include "../util.hpp"
+
+#include <utility>
+
+namespace mfem::future::LocalQFImpl
+{
+
+template <typename outputs_t, typename index_seq>
+struct action_outputs_direct_impl;
+
+template <typename outputs_t, std::size_t... Is>
+struct action_outputs_direct_impl<outputs_t, std::index_sequence<Is...>>
+{
+   static constexpr bool value =
+      ((is_identity_fop_v<tuple_element_t<Is, outputs_t>> ||
+        is_functionalvalue_fop_v<tuple_element_t<Is, outputs_t>>) && ...);
+};
+
+template <typename outputs_t>
+constexpr bool action_outputs_direct_v = action_outputs_direct_impl<outputs_t,
+               std::make_index_sequence<tuple_size<outputs_t>::value>>::value;
+
+template <typename qfunc_t, typename inputs_t, typename outputs_t,
+          typename index_seq>
+struct action_outputs_direct_value_impl;
+
+template <typename qfunc_t, typename inputs_t, typename outputs_t,
+          std::size_t... Is>
+struct action_outputs_direct_value_impl<qfunc_t, inputs_t, outputs_t,
+          std::index_sequence<Is...>>
+{
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr bool value =
+      ((is_identity_fop_v<tuple_element_t<Is, outputs_t>> ||
+        is_functionalvalue_fop_v<tuple_element_t<Is, outputs_t>>) && ...)
+      && ((!qf_param_uses_dual_v<
+           typename qf_param_slot<qfunc_t, n_inputs + Is>::qf_decay_param_t>)
+          && ...);
+};
+
+template <typename qfunc_t, typename inputs_t, typename outputs_t>
+constexpr bool action_outputs_direct_value_v =
+   action_outputs_direct_value_impl<qfunc_t, inputs_t, outputs_t,
+   std::make_index_sequence<tuple_size<outputs_t>::value>>::value;
+
+template<typename qfunc_t, typename inputs_t, typename outputs_t>
+class Action
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   using qf_signature = typename get_function_signature<qfunc_t>::type;
+   using qf_param_ts = typename qf_signature::parameter_ts;
+   using args_tuple_t = decay_tuple<qf_param_ts>;
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+   static_assert(n_inputs + n_outputs == tuple_size<qf_param_ts>::value,
+                 "LocalQF: q-function arity must match inputs + outputs");
+
+   template<typename backend_t, std::size_t I, typename RArgs, typename InXEs>
+   static MFEM_HOST_DEVICE decltype(auto) direct_input_arg(
+      RArgs &rargs,
+      const InXEs &in_XE,
+      const int qx,
+      const int qy,
+      const int qz,
+      const int e)
+   {
+      const auto &XE = in_XE[I];
+      using FOP = tuple_element_t<I, inputs_t>;
+      using ARG = typename qf_param_slot<qfunc_t, I>::qf_reg_param_t;
+      if constexpr (is_identity_fop_v<FOP>)
+      {
+         using DT = typename qf_param_slot<qfunc_t, I>::qf_decay_param_t;
+         if constexpr (qf_param_uses_dual_v<DT>)
+         {
+            return backend_t::template identity_qp_pull_dual<DT>(
+               false, XE, XE, qx, qy, qz, e);
+         }
+         else
+         {
+            return as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+         }
+      }
+      else if constexpr (is_weight_fop_v<FOP>)
+      {
+         return XE(qx, qy, qz, 0, 0);
+      }
+      else if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+      {
+         return backend_t::template qp_pull<ARG>(get<I>(rargs), qx, qy, qz);
+      }
+      else
+      {
+         static_assert(false, "Unsupported");
+      }
+   }
+
+   template<std::size_t I, typename OutYEs>
+   static MFEM_HOST_DEVICE decltype(auto) direct_output_arg(
+      const OutYEs &out_YE,
+      const int qx,
+      const int qy,
+      const int qz,
+      const int e)
+   {
+      constexpr size_t o = n_inputs + I;
+      const auto &YE = out_YE[I];
+      using DT = typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+      using ARG = typename qf_param_slot<qfunc_t, o>::qf_reg_param_t;
+      if constexpr (std::is_same_v<DT, real_t>)
+      {
+         return YE(0, qx, qy, qz, e);
+      }
+      else
+      {
+         return as_tensor<ARG>(&YE(0, qx, qy, qz, e));
+      }
+   }
+
+   template<typename backend_t, typename RArgs, typename InXEs, typename OutYEs,
+            std::size_t... InIs, std::size_t... OutIs>
+   static MFEM_HOST_DEVICE void call_qfunc_direct(
+      const qfunc_t &qfunc,
+      RArgs &rargs,
+      const InXEs &in_XE,
+      const OutYEs &out_YE,
+      const int qx,
+      const int qy,
+      const int qz,
+      const int e,
+      std::index_sequence<InIs...>,
+      std::index_sequence<OutIs...>)
+   {
+      qfunc(direct_input_arg<backend_t, InIs>(rargs, in_XE, qx, qy, qz, e)...,
+            direct_output_arg<OutIs>(out_YE, qx, qy, qz, e)...);
+   }
+
+   const qfunc_t qfunc;
+   const inputs_t inputs;
+   const outputs_t outputs;
+   const IntegratorContext ctx;
+   const std::vector<const DofToQuad *> dtqs;
+   // inputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_inputs> input_dtq;
+   const std::array<size_t, n_inputs> input_idx; // input to field
+   const std::array<const real_t *, n_inputs> input_B, input_G;
+   const std::array<int, n_inputs> input_d1d, input_q1d, input_vdim;
+   // outputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_outputs> output_dtq;
+   const std::array<size_t, n_outputs> output_idx; // output to field
+   const std::array<const real_t *, n_outputs> output_B, output_G;
+   const std::array<int, n_outputs> output_d1d, output_q1d, output_vdim;
+   // other constants
+   const int dim, ne, nq, q1d;
+
+public:
+   ////////////////////////////////////////////////////////
+   Action() = delete;
+
+   Action(IntegratorContext ctx,
+          qfunc_t qfunc,
+          inputs_t inputs,
+          outputs_t outputs):
+      qfunc(std::move(qfunc)), inputs(inputs), outputs(outputs), ctx(ctx),
+      dtqs(make_dtqs(ctx)),
+      // inputs: dtq, idx, B, G, d1d, q1d, vdim
+      input_dtq(create_dtq_maps<Entity::Element>(
+                   inputs,
+                   dtqs,
+                   create_union_field_map_for_dtq(ctx, inputs),
+                   ctx.unionfds,
+                   ctx.ir)),
+      input_idx(create_input_vector_map(ctx, inputs)),
+      input_B(get_B(input_dtq)), input_G(get_G(input_dtq)),
+      input_d1d(get_D1D(input_dtq)), input_q1d(get_Q1D(input_dtq)),
+      input_vdim(get_vdim(inputs)),
+      // outputs: dtq, idx, B, G, d1d, q1d, vdim
+      output_dtq(create_dtq_maps<Entity::Element>(
+                    outputs,
+                    dtqs,
+                    create_union_field_map_for_dtq(ctx, outputs),
+                    ctx.unionfds,
+                    ctx.ir)),
+      output_idx(create_output_vector_map(ctx, outputs)),
+      output_B(get_B(output_dtq)), output_G(get_G(output_dtq)),
+      output_d1d(get_D1D(output_dtq)), output_q1d(get_Q1D(output_dtq)),
+      output_vdim(get_vdim(outputs)),
+      // other constants
+      dim(ctx.mesh.Dimension()), ne(ctx.nentities), nq(ctx.ir.GetNPoints()),
+      q1d(tensor_1d_size(nq, dim))
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+   }
+
+   template<typename Backend>
+   void run_kernels(const std::vector<Vector *> &xe,
+                    std::vector<Vector *> &ye) const
+   {
+      Backend::Run(dim,
+                   q1d,
+                   // arguments
+                   ctx,
+                   qfunc,
+                   // inputs
+                   input_idx,
+                   input_B,
+                   input_G,
+                   input_vdim,
+                   input_d1d,
+                   input_q1d,
+                   // outputs
+                   output_idx,
+                   output_B,
+                   output_G,
+                   output_vdim,
+                   output_d1d,
+                   output_q1d,
+                   // input and output vectors
+                   xe,
+                   ye,
+                   // fallback arguments
+                   dim,
+                   q1d);
+   }
+
+   void operator()(const std::vector<Vector *> &xe,
+                   std::vector<Vector *> &ye) const
+   {
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<ActionLO>(xe, ye);
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<ActionHO>(xe, ye);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+   }
+
+   ////////////////////////////////////////////////////////
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void
+   action_callback(const IntegratorContext &ctx,
+                   const qfunc_t &qfunc,
+                   // inputs: idx, B, G, vdim, d1d, q1d
+                   const std::array<size_t, n_inputs> &in_idx,
+                   const std::array<const real_t *, n_inputs> in_B,
+                   const std::array<const real_t *, n_inputs> in_G,
+                   const std::array<int, n_inputs> &in_vdim,
+                   const std::array<int, n_inputs> &in_d1d,
+                   const std::array<int, n_inputs> &in_q1d,
+                   // outputs: idx, B, G, vdim, d1d, q1d
+                   const std::array<size_t, n_outputs> &out_idx,
+                   const std::array<const real_t *, n_outputs> out_B,
+                   const std::array<const real_t *, n_outputs> out_G,
+                   const std::array<int, n_outputs> &out_vdim,
+                   const std::array<int, n_outputs> &out_d1d,
+                   const std::array<int, n_outputs> &out_q1d,
+                   const std::vector<Vector *> &xe,
+                   std::vector<Vector *> &ye,
+                   // fallback arguments
+                   const int dim,
+                   const int q1d)
+   {
+      if (ctx.attr.Size() == 0) { return; }
+      MFEM_CONTRACT_VAR(dim);
+      MFEM_ASSERT(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+
+      static constexpr auto B2D = backend_t::DIM == 2;
+      static constexpr auto MQ1 = T_Q1D ? T_Q1D : backend_t::Q1D;
+      static constexpr auto MTPB = backend_t::MAX_THREADS_PER_BLOCK();
+
+      const int ne = ctx.nentities;
+
+      constexpr auto k_dim = [](const int k) { return k * k * (B2D ? 1 : k); };
+
+      // --------------------------------------------------
+      // INPUTS: XE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = in_idx[i];
+         const int d = in_d1d[i], q = in_q1d[i], v = in_vdim[i];
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else if constexpr (is_weight_fop_v<FOP>)
+         {
+            MFEM_VERIFY(ctx.ir.GetNPoints() == k_dim(q1d),
+                        "tensor-product IR expected");
+            in_XE[i] = Reshape(
+                          ctx.ir.GetWeights().Read(), q1d, q1d, B2D ? 1 : q1d, 1, 1);
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      // --------------------------------------------------
+      // OUTPUTS: YE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, real_t>, n_outputs> out_YE;
+      for_constexpr<n_outputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = out_idx[i];
+         const int d = out_d1d[i], q = out_q1d[i], v = out_vdim[i];
+         using FOP = tuple_element_t<i, outputs_t>;
+         if constexpr (is_gradient_fop_v<FOP> || is_value_fop_v<FOP>)
+         {
+            MFEM_ASSERT(ye[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP> || is_functionalvalue_fop_v<FOP>)
+         {
+            MFEM_ASSERT(ye[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else
+         {
+            static_assert(false, "Unsupported FieldOperator");
+         }
+      });
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      dfem::forall<MTPB>(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         // -----------------------------------------------
+         // Inputs and outputs argument registers
+         // -----------------------------------------------
+         action_args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> rargs;
+
+         // -----------------------------------------------
+         // Shared memory
+         // -----------------------------------------------
+         MFEM_SHARED typename backend_t::Shared smem;
+
+         // -----------------------------------------------
+         // Load inputs
+         // -----------------------------------------------
+         for_constexpr<n_inputs>([&](auto ic)
+         {
+            constexpr size_t i = ic.value;
+            const auto &XE = in_XE[i];
+            const int d = in_d1d[i], q = in_q1d[i], Q1D = q1d;
+            ;
+            const real_t *B = in_B[i], *G = in_G[i];
+            auto &rarg = get<i>(rargs);
+            using FOP = tuple_element_t<i, inputs_t>;
+            if constexpr (is_value_fop<FOP>::value)
+            {
+               backend_t::LoadValue(smem, e, d, q, Q1D, B, XE, rarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               using XE_t = decltype(XE);
+               using rarg_t = decltype(rarg);
+               using qf_param_t =
+                  typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+               constexpr auto RNK = qf_param_slot<qfunc_t, i>::extents.size();
+               backend_t::template LoadGradient<RNK, rarg_t, XE_t, qf_param_t>(
+                  smem, e, d, q, q1d, B, G, XE, rarg);
+            }
+            else if constexpr (is_weight_fop_v<FOP> || is_identity_fop_v<FOP>)
+            {
+               // qp values are read directly from in_XE / IR
+            }
+            else
+            {
+               static_assert(false, "Unsupported");
+            }
+         });
+
+         // -----------------------------------------------
+         // Evaluate the quadrature function
+         // Warning: no 'DIRECT' on the 'Z' direction,
+         // as one backend may need to iterate over it.
+         // -----------------------------------------------
+         MFEM_FOREACH_THREAD(qz, z, (B2D ? 1 : q1d))
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+               {
+                  if constexpr (action_outputs_direct_value_v<qfunc_t, inputs_t,
+                                outputs_t>)
+                  {
+                     call_qfunc_direct<backend_t>(
+                        qfunc, rargs, in_XE, out_YE, qx, qy, qz, e,
+                        std::make_index_sequence<n_inputs> {},
+                        std::make_index_sequence<n_outputs> {});
+                  }
+                  else
+                  {
+                     args_tuple_t qargs;
+
+                     // --------------------------------------
+                     // Pulling arguments from registers to qargs tuple
+                     // --------------------------------------
+                     for_constexpr<n_inputs>([&](auto ic)
+                     {
+                        constexpr size_t i = ic.value;
+                        auto &qarg = get<i>(qargs);
+                        const auto &XE = in_XE[i];
+                        using FOP = tuple_element_t<i, inputs_t>;
+                        using ARG =
+                           typename qf_param_slot<qfunc_t, i>::qf_reg_param_t;
+                        if constexpr (is_identity_fop_v<FOP>)
+                        {
+                           using DT =
+                              typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+                           if constexpr (qf_param_uses_dual_v<DT>)
+                           {
+                              qarg = backend_t::template identity_qp_pull_dual<DT>(
+                                 false, XE, XE, qx, qy, qz, e);
+                           }
+                           else
+                           {
+                              qarg = as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+                           }
+                        }
+                        else if constexpr (is_weight_fop_v<FOP>)
+                        {
+                           qarg = XE(qx, qy, qz, 0, 0);
+                        }
+                        else if constexpr (is_value_fop_v<FOP> ||
+                                           is_gradient_fop_v<FOP>)
+                        {
+                           qarg = backend_t::template qp_pull<ARG>(
+                              get<i>(rargs), qx, qy, qz);
+                        }
+                        else
+                        {
+                           static_assert(false, "Unsupported");
+                        }
+                     });
+
+                     // --------------------------------------
+                     // Call the quadrature function
+                     // --------------------------------------
+                     call_qfunc_no_move(qfunc, qargs);
+
+                     // --------------------------------------
+                     // Pushing arguments from qargs tuple to registers
+                     // --------------------------------------
+                     for_constexpr<n_outputs>([&](auto ic)
+                     {
+                        constexpr size_t i = ic.value, o = n_inputs + i;
+                        const auto &qarg = get<o>(qargs);
+                        const auto &YE = out_YE[i];
+                        using FOP = tuple_element_t<i, outputs_t>;
+                        using ARG =
+                           typename qf_param_slot<qfunc_t, o>::qf_reg_param_t;
+                        if constexpr (is_identity_fop_v<FOP> ||
+                                      is_functionalvalue_fop_v<FOP>)
+                        {
+                           using DT =
+                              typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+                           if constexpr (qf_param_uses_dual_v<DT>)
+                           {
+                              backend_t::identity_qp_write_value(
+                                 YE, qx, qy, qz, e, qarg);
+                           }
+                           else
+                           {
+                              as_tensor<ARG>(&YE(0, qx, qy, qz, e)) = qarg;
+                           }
+                        }
+                        else if constexpr (is_value_fop_v<FOP> ||
+                                           is_gradient_fop_v<FOP>)
+                        {
+                           auto &rarg = get<o>(rargs);
+                           backend_t::template qp_push<ARG>(
+                              rarg, qx, qy, qz, qarg);
+                        }
+                        else
+                        {
+                           static_assert(false, "Unsupported");
+                        }
+                     });
+                  }
+               }
+            }
+         }
+         if constexpr (!action_outputs_direct_v<outputs_t>)
+         {
+            MFEM_SYNC_THREAD;
+         }
+
+         // -----------------------------------------------
+         // Integrate outputs
+         // -----------------------------------------------
+         if constexpr (!action_outputs_direct_v<outputs_t>)
+         {
+            for_constexpr<n_outputs>([&](auto ic)
+            {
+               constexpr size_t i = ic.value, o = n_inputs + i;
+               const int d = out_d1d[i], q = out_q1d[i], Q1D = q1d;
+               const auto B = out_B[i], G = out_G[i];
+               const auto &YE = out_YE[i];
+               auto &rarg = get<o>(rargs);
+               using FOP = tuple_element_t<i, outputs_t>;
+               if constexpr (is_value_fop_v<FOP>)
+               {
+                  backend_t::WriteValue(smem, e, d, q, q1d, B, YE, rarg);
+               }
+               else if constexpr (is_gradient_fop_v<FOP>)
+               {
+                  using YE_t = decltype(YE);
+                  using rarg_t = decltype(rarg);
+                  // Both the rank and the extents have to come from the output
+                  // parameter slot o, not from the output index i.
+                  using qf_param_t =
+                     typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+                  constexpr auto RNK = qf_param_slot<qfunc_t, o>::extents.size();
+                  backend_t::template WriteGradient<RNK, rarg_t, YE_t, qf_param_t>(
+                     smem, e, d, q, Q1D, B, G, YE, rarg);
+               }
+               else if constexpr (is_identity_fop_v<FOP> ||
+                                  is_functionalvalue_fop_v<FOP>)
+               {
+                  // nothing to do
+               }
+               else
+               {
+                  static_assert(false, "Unsupported");
+               }
+            });
+         }
+      },
+      ne,
+      backend_t::thread_blocks(compute_kernel_thread_1d<inputs_t, outputs_t>(
+                                  q1d, in_d1d, out_d1d)),
+      0,
+      nullptr);
+   }
+   using KernelType = decltype(&Action::action_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(ActionLO, KernelType, (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(ActionHO, KernelType, (int, int) );
+};
+
+// Low Order kernels
+template<typename qfunc_t, typename inputs_t, typename outputs_t>
+template<int DIM, int Q1D>
+inline typename Action<qfunc_t, inputs_t, outputs_t>::KernelType
+Action<qfunc_t, inputs_t, outputs_t>::ActionLO::Kernel()
+{
+   static_assert(Q1D <= LocalQFLOBackend<DIM>::MQ1);
+   using action_t = Action<qfunc_t, inputs_t, outputs_t>;
+   if constexpr (DIM == 3 && Q1D == LocalQFLOBackendMQ1() &&
+                 action_outputs_direct_value_v<qfunc_t, inputs_t, outputs_t>)
+   {
+      return action_t::template action_callback<LocalQFLOBackend<DIM, Q1D, Q1D / 2>>;
+   }
+   else
+   {
+      return action_t::template action_callback<LocalQFLOBackend<DIM, Q1D>>;
+   }
+}
+
+// Low Order fallback
+template<typename qfunc_t, typename inputs_t, typename outputs_t>
+inline typename Action<qfunc_t, inputs_t, outputs_t>::KernelType
+Action<qfunc_t, inputs_t, outputs_t>::ActionLO::Fallback(int dim, int q1d)
+{
+   using action_t = Action<qfunc_t, inputs_t, outputs_t>;
+   using ActionLO = typename action_t::ActionLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<ActionLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<ActionLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+// High Order kernels
+template<typename qfunc_t, typename inputs_t, typename outputs_t>
+template<int DIM, int Q1D>
+inline typename Action<qfunc_t, inputs_t, outputs_t>::KernelType
+Action<qfunc_t, inputs_t, outputs_t>::ActionHO::Kernel()
+{
+   using action_t = Action<qfunc_t, inputs_t, outputs_t>;
+   return action_t::template action_callback<LocalQFHOBackend<DIM>, Q1D>;
+}
+
+// High Order fallback
+template<typename qfunc_t, typename inputs_t, typename outputs_t>
+inline typename Action<qfunc_t, inputs_t, outputs_t>::KernelType
+Action<qfunc_t, inputs_t, outputs_t>::ActionHO::Fallback(int dim, int q1d)
+{
+   using action_t = Action<qfunc_t, inputs_t, outputs_t>;
+   using ActionHO = typename action_t::ActionHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<ActionHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<ActionHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_action.hpp

@@ -0,0 +1,926 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include "../util.hpp"
+
+namespace mfem::future::LocalQFImpl
+{
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeAction
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   using qf_signature = typename get_function_signature<qfunc_t>::type;
+   using qf_param_ts = typename qf_signature::parameter_ts;
+   using args_tuple_t = decay_tuple<qf_param_ts>;
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+   static_assert(n_inputs + n_outputs == tuple_size<qf_param_ts>::value,
+                 "LocalQF: q-function arity must match inputs + outputs");
+
+   /// Which inputs carry a tangent, i.e. are attached to the field being
+   /// differentiated against. This is a property of `inputs_t` and
+   /// `derivative_id` alone, so it is available at compile time: it decides the
+   /// Enzyme activity of every q-function parameter, which loads the tangent
+   /// pass has to do, and how large the shadow register bank has to be. The
+   /// runtime `input_is_dependent` below holds the same values and is kept for
+   /// the host-side sizing checks.
+   static constexpr auto input_activity =
+      mfem::future::detail::make_activity_map <
+   static_cast<std::size_t>(derivative_id) > (inputs_t {});
+   static_assert(input_activity.size() == n_inputs);
+
+   /// Shadow register bank: only the active input slots are materialized.
+   template <typename backend_t, int MQ1, std::size_t... Is>
+   static auto shadow_bank_type(std::index_sequence<Is...>)
+#ifdef MFEM_USE_ENZYME
+   -> masked_input_args_reg_t<backend_t, qfunc_t, MQ1, input_activity[Is]...>;
+#else
+   // The dual-number path pulls through every input slot unconditionally.
+   -> input_args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1>;
+#endif
+
+   template <typename backend_t, int MQ1>
+   using shadow_bank_t = decltype(shadow_bank_type<backend_t, MQ1>(
+   std::make_index_sequence<n_inputs> {}));
+
+   /// Per-quadrature-point shadow argument tuple. Only the active inputs and
+   /// the outputs are materialized where supported; the rest are `enzyme_const`
+   /// and their shadow slots are never addressed. This is the innermost live
+   /// state of the kernel, and on device it shares a per-thread register budget
+   /// capped by the launch bounds, so the dead slots are worth removing
+   /// explicitly rather than hoping the optimizer splits the tuple.
+#ifdef _MSC_VER
+   using shadow_args_t = args_tuple_t;
+#else
+   template <std::size_t... Is>
+   static auto shadow_tuple_type(std::index_sequence<Is...>)
+   -> masked_args_tuple_t < args_tuple_t,
+   (Is<n_inputs ? input_activity[Is] : true)... >;
+
+   using shadow_args_t = decltype(shadow_tuple_type(
+   std::make_index_sequence<n_inputs + n_outputs> {}));
+#endif
+
+#ifdef MFEM_USE_ENZYME
+   /// Forward-mode call with the activity of every q-function parameter fixed
+   /// at compile time. Outputs are always active; inputs follow
+   /// `input_activity`, so an inactive input (the mesh nodes and the quadrature
+   /// weight, for a derivative w.r.t. the trial field) is marked `enzyme_const`
+   /// rather than dup'd with a zero tangent. Without this Enzyme differentiates
+   /// everything those inputs feed - for a diffusion q-function the whole
+   /// inv(J) / det(J) chain - to produce a tangent that is structurally zero.
+   // `qf_t` is deduced because the kernel captures the q-function by value into
+   // a const lambda, so it arrives here as `const qfunc_t`.
+   template <typename qf_t, std::size_t... Is>
+   MFEM_FUTURE_ALWAYS_INLINE
+   MFEM_HOST_DEVICE static void call_fwddiff(qf_t &qfunc,
+                                             args_tuple_t &primal_args,
+                                             shadow_args_t &shadow_args,
+                                             std::index_sequence<Is...>)
+   {
+      mfem::future::call_enzyme_fwddiff_active <
+      (Is < n_inputs ? input_activity[Is] : true)... > (
+         qfunc, primal_args, shadow_args);
+   }
+#endif
+
+   qfunc_t qfunc;
+   const inputs_t inputs;
+   const outputs_t outputs;
+   const IntegratorContext ctx;
+   const std::vector<const DofToQuad *> dtqs;
+   // inputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_inputs> input_dtq;
+   const std::array<size_t, n_inputs> input_idx;
+   const std::array<const real_t *, n_inputs> input_B, input_G;
+   const std::array<int, n_inputs> input_d1d, input_q1d, input_vdim;
+   // outputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_outputs> output_dtq;
+   const std::array<size_t, n_outputs> output_idx;
+   const std::array<const real_t *, n_outputs> output_B, output_G;
+   const std::array<int, n_outputs> output_d1d, output_q1d, output_vdim;
+   // other constants
+   const int dim, ne, nq, q1d;
+
+   std::array<bool, n_inputs> input_is_dependent;
+   FieldDescriptor direction_fd;
+   mutable Vector direction_e;
+   mutable RestrictionCache<Entity::Element> direction_rcache;
+
+public:
+   //////////////////////////////////////////////////////////////////
+   DerivativeAction() = delete;
+
+   DerivativeAction(IntegratorContext ctx,
+                    qfunc_t qfunc,
+                    inputs_t inputs,
+                    outputs_t outputs):
+      qfunc(std::move(qfunc)), inputs(inputs), outputs(outputs), ctx(ctx),
+      dtqs(make_dtqs(ctx)),
+      // inputs: dtq, idx, B, G, d1d, q1d, vdim
+      input_dtq(create_dtq_maps<Entity::Element>(
+                   inputs,
+                   dtqs,
+                   create_union_field_map_for_dtq(ctx, inputs),
+                   ctx.unionfds,
+                   ctx.ir)),
+      input_idx(create_input_vector_map(ctx, inputs)),
+      input_B(get_B(input_dtq)), input_G(get_G(input_dtq)),
+      input_d1d(get_D1D(input_dtq)), input_q1d(get_Q1D(input_dtq)),
+      input_vdim(get_vdim(inputs)),
+      // outputs: dtq, idx, B, G, d1d, q1d, vdim
+      output_dtq(create_dtq_maps<Entity::Element>(
+                    outputs,
+                    dtqs,
+                    create_union_field_map_for_dtq(ctx, outputs),
+                    ctx.unionfds,
+                    ctx.ir)),
+      output_idx(create_output_vector_map(ctx, outputs)),
+      output_B(get_B(output_dtq)), output_G(get_G(output_dtq)),
+      output_d1d(get_D1D(output_dtq)), output_q1d(get_Q1D(output_dtq)),
+      output_vdim(get_vdim(outputs)),
+      // other constants
+      dim(ctx.mesh.Dimension()), ne(ctx.nentities), nq(ctx.ir.GetNPoints()),
+      q1d(tensor_1d_size(nq, dim))
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+
+      // Determine which inputs are dependent on the derivative direction
+      auto dependency_map = make_dependency_map(inputs);
+      auto it = dependency_map.find(derivative_id);
+      MFEM_ASSERT(it != dependency_map.end(),
+                  "Derivative ID not found in dependency map");
+      input_is_dependent = it->second;
+
+      // Find direction field index
+      int direction_field_idx = -1;
+      for (size_t uf = 0; uf < nfields; uf++)
+      {
+         if (static_cast<int>(ctx.unionfds[uf].id) == derivative_id)
+         {
+            direction_field_idx = static_cast<int>(uf);
+            break;
+         }
+      }
+      MFEM_ASSERT(
+         direction_field_idx != -1,
+         "LocalQFBackend: derivative direction field not found in unionfds");
+      direction_fd = ctx.unionfds[static_cast<size_t>(direction_field_idx)];
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename Backend>
+   void run_kernels(const std::vector<Vector *> &xe,
+                    std::vector<Vector *> &ye)
+   {
+      Backend::Run(dim,
+                   q1d,
+                   // arguments
+                   ctx,
+                   qfunc,
+                   // inputs
+                   input_idx,
+                   input_B,
+                   input_G,
+                   input_vdim,
+                   input_d1d,
+                   input_q1d,
+                   // outputs
+                   output_idx,
+                   output_B,
+                   output_G,
+                   output_vdim,
+                   output_d1d,
+                   output_q1d,
+                   // input and output vectors
+                   xe,
+                   ye,
+                   input_is_dependent,
+                   direction_e,
+                   // fallback arguments
+                   dim,
+                   q1d);
+   }
+
+   //////////////////////////////////////////////////////////////////
+   void operator()(const std::vector<Vector *> &xe,
+                   const Vector *direction_l,
+                   std::vector<Vector *> &ye)
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      MFEM_ASSERT(direction_l != nullptr,
+                  "LocalQF DerivativeAction: direction vector is null");
+
+      restriction(direction_fd,
+                  direction_rcache,
+                  *direction_l,
+                  direction_e,
+                  ElementDofOrdering::LEXICOGRAPHIC);
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<DerivativeActionLO>(xe, ye);
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<DerivativeActionHO>(xe, ye);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+   }
+
+
+   template<typename backend_t, int T_Q1D>
+   struct DerivativeActionKernelData
+   {
+      qfunc_t qfunc;
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE;
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE_dir;
+      std::array<DeviceTensor<3 + 1 + 1, real_t>, n_outputs> out_YE;
+      std::array<const real_t *, n_inputs> in_B;
+      std::array<const real_t *, n_inputs> in_G;
+      std::array<int, n_inputs> in_d1d;
+      std::array<int, n_inputs> in_q1d;
+      std::array<const real_t *, n_outputs> out_B;
+      std::array<const real_t *, n_outputs> out_G;
+      std::array<int, n_outputs> out_d1d;
+      std::array<int, n_outputs> out_q1d;
+      std::array<bool, n_inputs> input_dep;
+      const int *d_attr;
+      bool has_attr;
+      const int *d_elem_attr;
+      int q1d;
+   };
+
+   template<typename backend_t, int T_Q1D>
+   MFEM_FUTURE_ALWAYS_INLINE MFEM_HOST_DEVICE static void
+   derivative_action_kernel_body(
+      const DerivativeActionKernelData<backend_t, T_Q1D> &data, const int e)
+   {
+      static constexpr auto B2D = backend_t::DIM == 2;
+      static constexpr auto MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+      auto &qfunc = data.qfunc;
+      const auto &in_XE = data.in_XE;
+      const auto &in_XE_dir = data.in_XE_dir;
+      const auto &out_YE = data.out_YE;
+      const auto &in_B = data.in_B;
+      const auto &in_G = data.in_G;
+      const auto &in_d1d = data.in_d1d;
+      const auto &in_q1d = data.in_q1d;
+      const auto &out_B = data.out_B;
+      const auto &out_G = data.out_G;
+      const auto &out_d1d = data.out_d1d;
+      const auto &out_q1d = data.out_q1d;
+      const auto &input_dep = data.input_dep;
+      MFEM_CONTRACT_VAR(input_dep);
+      const auto d_attr = data.d_attr;
+      const bool has_attr = data.has_attr;
+      const auto d_elem_attr = data.d_elem_attr;
+      const int q1d = data.q1d;
+      if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+      // -----------------------------------------------
+      // Inputs and outputs argument registers
+      // -----------------------------------------------
+      args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> rargs;
+      shadow_bank_t<backend_t, MQ1> sargs; // shadow, active inputs only
+
+      // -----------------------------------------------
+      // Shared memory
+      // -----------------------------------------------
+      MFEM_SHARED typename backend_t::Shared smem;
+
+      // -----------------------------------------------
+      // Load primal inputs (rargs)
+      // -----------------------------------------------
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const auto &XE = in_XE[i];
+         const int d = in_d1d[i], q = in_q1d[i], Q1D = q1d;
+         const real_t *B = in_B[i], *G = in_G[i];
+         auto &rarg = get<i>(rargs);
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (is_value_fop<FOP>::value)
+         {
+            backend_t::LoadValue(smem, e, d, q, Q1D, B, XE, rarg);
+         }
+         else if constexpr (is_gradient_fop_v<FOP>)
+         {
+            constexpr auto RNK = qf_param_slot<qfunc_t, i>::extents.size();
+            using FieldParamT =
+               typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+            backend_t::template LoadGradient<RNK,
+                                             decltype(rarg),
+                                             decltype(XE),
+                                             FieldParamT>(
+                                                smem, e, d, q, Q1D, B, G, XE, rarg);
+         }
+         else if constexpr (is_weight_fop_v<FOP> || is_identity_fop_v<FOP>)
+         {
+            // qp values are read directly from in_XE / IR
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      // -----------------------------------------------
+      // Load tangent directions (sargs)
+      // -----------------------------------------------
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (input_activity[i] &&
+                       (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>))
+         {
+            const auto &XE = in_XE_dir[i];
+            const int d = in_d1d[i], q = in_q1d[i], Q1D = q1d;
+            const real_t *B = in_B[i], *G = in_G[i];
+            auto &sarg = get<i>(sargs); // shadow argument register
+            if constexpr (is_value_fop_v<FOP>)
+            {
+               backend_t::LoadValue(smem, e, d, q, Q1D, B, XE, sarg);
+            }
+            else
+            {
+               constexpr auto RNK = qf_param_slot<qfunc_t, i>::extents.size();
+               using FieldParamT =
+                  typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+               backend_t::template LoadGradient<RNK,
+                                                decltype(sarg),
+                                                decltype(XE),
+                                                FieldParamT>(
+                                                   smem, e, d, q, Q1D, B, G, XE, sarg);
+            }
+         }
+         else
+         {
+            // Inactive input, or an input read straight from quadrature
+            // point data (weight / identity): nothing to interpolate.
+            static_assert(!input_activity[i] || is_weight_fop_v<FOP> ||
+                          is_identity_fop_v<FOP>, "Unsupported");
+         }
+      });
+
+      // -----------------------------------------------
+      // Evaluate the quadrature function
+      // Warning: no 'DIRECT' on the 'Z' direction,
+      // as one backend may need to iterate over it.
+      // -----------------------------------------------
+      MFEM_FOREACH_THREAD(qz, z, (B2D ? 1 : q1d))
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+            {
+#ifdef MFEM_USE_ENZYME
+               args_tuple_t primal_args {};
+               shadow_args_t shadow_args {};
+
+               // --------------------------------------
+               // Pulling arguments from registers to primal and shadow
+               // tuples
+               // --------------------------------------
+               for_constexpr<n_inputs>([&](auto ic)
+               {
+                  constexpr size_t i = ic.value;
+                  auto &parg = get<i>(primal_args);
+                  auto &targ = get<i>(shadow_args);
+                  const auto &XE = in_XE[i];
+                  const auto &XEd = in_XE_dir[i];
+                  using FOP = tuple_element_t<i, inputs_t>;
+                  using ARG =
+                     typename qf_param_slot<qfunc_t, i>::qf_reg_param_t;
+                  MFEM_CONTRACT_VAR(targ);
+                  MFEM_CONTRACT_VAR(XEd);
+                  if constexpr (is_identity_fop_v<FOP>)
+                  {
+                     parg = as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+                     if constexpr (input_activity[i])
+                     {
+                        targ = as_tensor<ARG>(&XEd(0, qx, qy, qz, e));
+                     }
+                  }
+                  else if constexpr (is_weight_fop_v<FOP>)
+                  {
+                     parg = XE(qx, qy, qz, 0, 0);
+                  }
+                  else if constexpr (is_value_fop_v<FOP> ||
+                                     is_gradient_fop_v<FOP>)
+                  {
+                     parg = backend_t::template qp_pull<ARG>(
+                        get<i>(rargs), qx, qy, qz);
+                     if constexpr (input_activity[i])
+                     {
+                        targ = backend_t::template qp_pull<ARG>(
+                           get<i>(sargs), qx, qy, qz);
+                     }
+                  }
+                  else
+                  {
+                     static_assert(false, "Unsupported");
+                  }
+               });
+
+               // --------------------------------------
+               // Call the quadrature function. Inactive inputs are
+               // enzyme_const, so their shadow slots are never read and are
+               // deliberately left unset above.
+               // --------------------------------------
+               call_fwddiff(qfunc, primal_args, shadow_args,
+                            std::make_index_sequence<n_inputs + n_outputs> {});
+
+               // --------------------------------------
+               // Pushing arguments from enzyme_shadow tuple to registers
+               // --------------------------------------
+               for_constexpr<n_outputs>([&](auto ic)
+               {
+                  constexpr size_t i = ic.value, o = n_inputs + i;
+                  const auto &qout = get<o>(shadow_args);
+                  auto &YE = out_YE[i];
+                  using FOP = tuple_element_t<i, outputs_t>;
+                  using ARG =
+                     typename qf_param_slot<qfunc_t, o>::qf_reg_param_t;
+                  if constexpr (is_identity_fop_v<FOP>)
+                  {
+                     as_tensor<ARG>(&YE(0, qx, qy, qz, e)) = qout;
+                  }
+                  else if constexpr (is_value_fop_v<FOP> ||
+                                     is_gradient_fop_v<FOP>)
+                  {
+                     auto &rarg = get<o>(rargs);
+                     backend_t::template qp_push_tangent<ARG>(
+                        rarg, qx, qy, qz, qout);
+                  }
+                  else
+                  {
+                     static_assert(false, "Unsupported");
+                  }
+               });
+#else  // MFEM_USE_ENZYME
+               args_tuple_t qargs;
+
+               // --------------------------------------
+               // Pulling arguments from registers to qargs tuple
+               // --------------------------------------
+               for_constexpr<n_inputs>([&](auto ic)
+               {
+                  constexpr size_t i = ic.value;
+                  auto &qarg = get<i>(qargs);
+                  const auto &XE = in_XE[i];
+                  const auto &XEd = in_XE_dir[i];
+                  using FOP = tuple_element_t<i, inputs_t>;
+                  using ARG =
+                     typename qf_param_slot<qfunc_t, i>::qf_reg_param_t;
+                  if constexpr (is_identity_fop_v<FOP>)
+                  {
+                     using DT =
+                        typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+                     if constexpr (qf_param_uses_dual_v<DT>)
+                     {
+                        qarg = backend_t::template identity_qp_pull_dual<DT>(
+                           input_dep[i], XE, XEd, qx, qy, qz, e);
+                     }
+                     else
+                     {
+                        qarg = as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+                     }
+                  }
+                  else if constexpr (is_weight_fop_v<FOP>)
+                  {
+                     qarg = XE(qx, qy, qz, 0, 0);
+                  }
+                  else if constexpr (is_value_fop_v<FOP> ||
+                                     is_gradient_fop_v<FOP>)
+                  {
+                     qarg = backend_t::template qp_pull_directional<ARG>(
+                        get<i>(rargs),
+                        get<i>(sargs),
+                        qx,
+                        qy,
+                        qz,
+                        input_dep[i]);
+                  }
+                  else
+                  {
+                     static_assert(false, "Unsupported");
+                  }
+               });
+
+               // --------------------------------------
+               // Call the quadrature function
+               // --------------------------------------
+               call_qfunc_no_move(qfunc, qargs);
+
+               // --------------------------------------
+               // Pushing arguments from qargs tuple to registers
+               // --------------------------------------
+               for_constexpr<n_outputs>([&](auto ic)
+               {
+                  constexpr size_t i = ic.value, o = n_inputs + i;
+                  const auto &qarg = get<o>(qargs);
+                  const auto &YE = out_YE[i];
+                  using FOP = tuple_element_t<i, outputs_t>;
+                  using ARG =
+                     typename qf_param_slot<qfunc_t, o>::qf_reg_param_t;
+                  if constexpr (is_identity_fop_v<FOP>)
+                  {
+                     using DT =
+                        typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+                     if constexpr (qf_param_uses_dual_v<DT>)
+                     {
+                        backend_t::identity_qp_write_tangent(
+                           YE, qx, qy, qz, e, qarg);
+                     }
+                     else
+                     {
+                        as_tensor<ARG>(&YE(0, qx, qy, qz, e)) = qarg;
+                     }
+                  }
+                  else if constexpr (is_value_fop_v<FOP> ||
+                                     is_gradient_fop_v<FOP>)
+                  {
+                     auto &rarg = get<o>(rargs);
+                     backend_t::template qp_push_tangent<ARG>(
+                        rarg, qx, qy, qz, qarg);
+                  }
+                  else
+                  {
+                     static_assert(false, "Unsupported");
+                  }
+               });
+#endif // MFEM_USE_ENZYME
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      // -----------------------------------------------
+      // Integrate outputs
+      // -----------------------------------------------
+      for_constexpr<n_outputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value, o = n_inputs + i;
+         const int d = out_d1d[i], q = out_q1d[i];
+         const auto B = out_B[i], G = out_G[i];
+         auto &YE = out_YE[i];
+         auto &rarg = get<o>(rargs);
+         using FOP = tuple_element_t<i, outputs_t>;
+         if constexpr (is_value_fop_v<FOP>)
+         {
+            backend_t::WriteValue(smem, e, d, q, q1d, B, YE, rarg);
+         }
+         else if constexpr (is_gradient_fop_v<FOP>)
+         {
+            using YE_t = decltype(YE);
+            using rarg_t = decltype(rarg);
+            using qf_param_t =
+               typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+            constexpr auto RNK = qf_param_slot<qfunc_t, o>::extents.size();
+            backend_t::template WriteGradient<RNK, rarg_t, YE_t, qf_param_t>(
+               smem, e, d, q, q1d, B, G, YE, rarg);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            // nothing to do
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+   }
+
+   template<typename backend_t, int T_Q1D>
+   struct DerivativeActionKernelBody
+   {
+      MFEM_FUTURE_ALWAYS_INLINE MFEM_HOST_DEVICE static void run(
+         const DerivativeActionKernelData<backend_t, T_Q1D> &data, const int e)
+      {
+         derivative_action_kernel_body<backend_t, T_Q1D>(data, e);
+      }
+   };
+
+   //////////////////////////////////////////////////////////////////
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void
+   derivative_action_callback(const IntegratorContext &ctx,
+                              qfunc_t &qfunc,
+                              // inputs: idx, B, G, vdim, d1d, q1d
+                              const std::array<size_t, n_inputs> &in_idx,
+                              const std::array<const real_t *, n_inputs> in_B,
+                              const std::array<const real_t *, n_inputs> in_G,
+                              const std::array<int, n_inputs> &in_vdim,
+                              const std::array<int, n_inputs> &in_d1d,
+                              const std::array<int, n_inputs> &in_q1d,
+                              // outputs: idx, B, G, vdim, d1d, q1d
+                              const std::array<size_t, n_outputs> &out_idx,
+                              const std::array<const real_t *, n_outputs> out_B,
+                              const std::array<const real_t *, n_outputs> out_G,
+                              const std::array<int, n_outputs> &out_vdim,
+                              const std::array<int, n_outputs> &out_d1d,
+                              const std::array<int, n_outputs> &out_q1d,
+                              const std::vector<Vector *> &xe,
+                              std::vector<Vector *> &ye,
+                              const std::array<bool, n_inputs> &input_dep,
+                              const Vector &direction_e,
+                              // fallback arguments
+                              const int dim,
+                              const int q1d)
+   {
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      // Dependency is resolved at compile time through `input_activity`; the
+      // runtime array is only carried for the non-Enzyme dual-number path.
+      MFEM_CONTRACT_VAR(input_dep);
+
+      if (ctx.attr.Size() == 0) { return; }
+
+      static constexpr auto B2D = backend_t::DIM == 2;
+
+      const int ne = ctx.nentities;
+
+      constexpr auto k_dim = [](const int k) { return k * k * (B2D ? 1 : k); };
+
+      // --------------------------------------------------
+      // INPUTS: XE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = in_idx[i];
+         const int d = in_d1d[i], q = in_q1d[i], v = in_vdim[i];
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else if constexpr (is_weight_fop_v<FOP>)
+         {
+            MFEM_VERIFY(ctx.ir.GetNPoints() == k_dim(q1d),
+                        "tensor-product IR expected");
+            in_XE[i] = Reshape(
+                          ctx.ir.GetWeights().Read(), q1d, q1d, B2D ? 1 : q1d, 1, 1);
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      const auto d_direction = direction_e.Read();
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE_dir;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = in_idx[i];
+         const int d = in_d1d[i], q = in_q1d[i], v = in_vdim[i];
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            if constexpr (input_activity[i])
+            {
+               MFEM_ASSERT(direction_e.Size() == xe[k]->Size(),
+                           "direction E-vector size mismatch for input " << i);
+               in_XE_dir[i] = Reshape(d_direction, d, d, B2D ? 1 : d, v, ne);
+            }
+            else
+            {
+               in_XE_dir[i] = in_XE[i];
+            }
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            if constexpr (input_activity[i])
+            {
+               MFEM_VERIFY(direction_e.Size() == xe[k]->Size(),
+                           "direction E-vector size mismatch (identity input) "
+                           << i);
+               in_XE_dir[i] = Reshape(d_direction, v, q, q, B2D ? 1 : q, ne);
+            }
+            else
+            {
+               in_XE_dir[i] = in_XE[i];
+            }
+         }
+         else if constexpr (is_weight_fop_v<FOP>) { in_XE_dir[i] = in_XE[i]; }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      // --------------------------------------------------
+      // OUTPUTS: YE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, real_t>, n_outputs> out_YE;
+      for_constexpr<n_outputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = out_idx[i];
+         const int d = out_d1d[i], q = out_q1d[i], v = out_vdim[i];
+         using FOP = tuple_element_t<i, outputs_t>;
+         if constexpr (is_gradient_fop_v<FOP> || is_value_fop_v<FOP>)
+         {
+            MFEM_ASSERT(ye[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            MFEM_ASSERT(ye[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else
+         {
+            static_assert(false, "Unsupported FieldOperator");
+         }
+      });
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      DerivativeActionKernelData<backend_t, T_Q1D> data
+      {
+         qfunc,
+         in_XE,
+         in_XE_dir,
+         out_YE,
+         in_B,
+         in_G,
+         in_d1d,
+         in_q1d,
+         out_B,
+         out_G,
+         out_d1d,
+         out_q1d,
+         input_dep,
+         d_attr,
+         has_attr,
+         d_elem_attr,
+         q1d
+      };
+
+      const auto blocks = backend_t::thread_blocks(
+                             compute_kernel_thread_1d<inputs_t, outputs_t>(q1d, in_d1d, out_d1d));
+
+      if (Device::Allows(Backend::CUDA_MASK) ||
+          Device::Allows(Backend::HIP_MASK))
+      {
+         dfem::forall_data<backend_t::MAX_THREADS_PER_BLOCK(),
+              DerivativeActionKernelBody<backend_t, T_Q1D>>(
+                 data, ne, blocks);
+      }
+      else if (Device::Allows(Backend::CPU_MASK))
+      {
+         for (int e = 0; e < ne; e++)
+         {
+            derivative_action_kernel_body<backend_t, T_Q1D>(data, e);
+         }
+      }
+      else
+      {
+         MFEM_ABORT("no compute backend available");
+      }
+   }
+
+   using DerivativeKernelType =
+      decltype(&DerivativeAction::derivative_action_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeActionLO,
+                                     DerivativeKernelType,
+                                     (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeActionHO,
+                                     DerivativeKernelType,
+                                     (int, int) );
+};
+
+// Low Order kernels
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeKernelType
+DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeActionLO::Kernel()
+{
+   static_assert((DIM == 2 || DIM == 3) && Q1D <= 8);
+   using derivative_action_t =
+      DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return derivative_action_t::template derivative_action_callback<
+             LocalQFLOBackend<DIM, Q1D>>;
+}
+
+// Low Order fallback
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeKernelType
+DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeActionLO::Fallback(int dim, int q1d)
+{
+   using derivative_action_t =
+      DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeActionLO =
+      typename derivative_action_t::DerivativeActionLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<DerivativeActionLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<DerivativeActionLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+// High Order kernels
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeKernelType
+DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeActionHO::Kernel()
+{
+   using derivative_action_t =
+      DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return derivative_action_t::
+          template derivative_action_callback<LocalQFHOBackend<DIM>, Q1D>;
+}
+
+// High Order fallback
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeKernelType
+DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeActionHO::Fallback(int dim, int q1d)
+{
+   using derivative_action_t =
+      DerivativeAction<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeActionHO = typename derivative_action_t::DerivativeActionHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeActionHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeActionHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_apply.hpp

@@ -0,0 +1,738 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include <array>
+
+namespace mfem::future::LocalQFImpl
+{
+
+// Cached Jacobian apply: J·v from qp_cache filled by DerivativeSetup
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeApply
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   using qf_signature = typename get_function_signature<qfunc_t>::type;
+   using qf_param_ts = typename qf_signature::parameter_ts;
+   using args_tuple_t = decay_tuple<qf_param_ts>;
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+   static_assert(n_inputs + n_outputs == tuple_size<qf_param_ts>::value,
+                 "LocalQF: q-function arity must match inputs + outputs");
+
+   const inputs_t inputs;
+   const outputs_t outputs;
+   const IntegratorContext ctx;
+   const Vector &qp_cache;
+   const std::vector<const DofToQuad *> dtqs;
+   // inputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_inputs> input_dtq;
+   const std::array<size_t, n_inputs> input_idx;
+   const std::array<const real_t *, n_inputs> input_B, input_G;
+   const std::array<int, n_inputs> input_d1d, input_q1d, input_vdim;
+   // outputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_outputs> output_dtq;
+   const std::array<size_t, n_outputs> output_idx;
+   const std::array<const real_t *, n_outputs> output_B, output_G;
+   const std::array<int, n_outputs> output_d1d, output_q1d, output_vdim;
+   // Jacobian cache metadata
+   const std::array<bool, n_inputs> input_is_dependent;
+   const std::array<int, n_inputs> input_size_on_qp;
+   const std::array<int, n_outputs> out_op_dim;
+   const std::array<int, n_outputs> out_offsets;
+   const int output_size_on_qp;
+   const int trial_vdim;
+   const int total_trial_op_dim;
+   const int residual_size_on_qp;
+   // other constants
+   const int dim, ne, nq, q1d;
+   FieldDescriptor direction_fd;
+   mutable Vector direction_e;
+   mutable RestrictionCache<Entity::Element> direction_rcache;
+
+   template <std::size_t slot>
+   static constexpr int ParamRank()
+   {
+      using param_t = typename qf_param_slot<qfunc_t, slot>::qf_decay_param_t;
+      return qf_param_shape<param_t>::rank;
+   }
+
+   template <std::size_t slot, int dim_idx>
+   static constexpr int ParamExtent()
+   {
+      using param_t = typename qf_param_slot<qfunc_t, slot>::qf_decay_param_t;
+      return qf_param_shape<param_t>::extents[dim_idx];
+   }
+
+   template <typename fop_t, std::size_t slot>
+   static constexpr int StaticVDim()
+   {
+      constexpr int rank = ParamRank<slot>();
+      if constexpr (is_gradient_fop_v<fop_t>)
+      {
+         if constexpr (rank <= 1) { return 1; }
+         else { return ParamExtent<slot, 0>(); }
+      }
+      else
+      {
+         if constexpr (rank == 0) { return 1; }
+         else { return ParamExtent<slot, 0>(); }
+      }
+   }
+
+   template <typename fop_t, std::size_t slot>
+   static constexpr int StaticOpDim()
+   {
+      constexpr int rank = ParamRank<slot>();
+      if constexpr (is_gradient_fop_v<fop_t>)
+      {
+         if constexpr (rank == 0) { return 1; }
+         else if constexpr (rank == 1) { return ParamExtent<slot, 0>(); }
+         else { return ParamExtent<slot, 1>(); }
+      }
+      else
+      {
+         if constexpr (rank <= 1) { return 1; }
+         else { return ParamExtent<slot, 1>(); }
+      }
+   }
+
+   template <std::size_t input_slot>
+   static constexpr bool StaticInputDep()
+   {
+      using fop_t = tuple_element_t<input_slot, inputs_t>;
+      return fop_t::GetFieldId() == derivative_id;
+   }
+
+   template <std::size_t input_slot>
+   static constexpr int StaticInputVDim()
+   {
+      using fop_t = tuple_element_t<input_slot, inputs_t>;
+      return StaticVDim<fop_t, input_slot>();
+   }
+
+   template <std::size_t input_slot>
+   static constexpr int StaticInputOpDim()
+   {
+      using fop_t = tuple_element_t<input_slot, inputs_t>;
+      return StaticOpDim<fop_t, input_slot>();
+   }
+
+   template <std::size_t output_slot>
+   static constexpr int StaticOutputVDim()
+   {
+      using fop_t = tuple_element_t<output_slot, outputs_t>;
+      return StaticVDim<fop_t, n_inputs + output_slot>();
+   }
+
+   template <std::size_t output_slot>
+   static constexpr int StaticOutputOpDim()
+   {
+      using fop_t = tuple_element_t<output_slot, outputs_t>;
+      return StaticOpDim<fop_t, n_inputs + output_slot>();
+   }
+
+   template <std::size_t output_slot>
+   static constexpr int StaticOutputOffset()
+   {
+      int offset = 0;
+      for_constexpr<output_slot>([&](auto oc)
+      {
+         constexpr size_t o = oc.value;
+         offset += StaticOutputVDim<o>() * StaticOutputOpDim<o>();
+      });
+      return offset;
+   }
+
+   template <std::size_t input_slot>
+   static constexpr int StaticInputOpOffset()
+   {
+      int offset = 0;
+      for_constexpr<input_slot>([&](auto sc)
+      {
+         constexpr size_t s = sc.value;
+         if constexpr (StaticInputDep<s>()) { offset += StaticInputOpDim<s>(); }
+      });
+      return offset;
+   }
+
+   static constexpr int StaticTrialVDim()
+   {
+      int vdim = 1;
+      for_constexpr<n_inputs>([&](auto sc)
+      {
+         constexpr size_t s = sc.value;
+         if constexpr (StaticInputDep<s>()) { vdim = StaticInputVDim<s>(); }
+      });
+      return vdim;
+   }
+
+   static constexpr int StaticTotalTrialOpDim()
+   {
+      int op_dim = 0;
+      for_constexpr<n_inputs>([&](auto sc)
+      {
+         constexpr size_t s = sc.value;
+         if constexpr (StaticInputDep<s>()) { op_dim += StaticInputOpDim<s>(); }
+      });
+      return op_dim;
+   }
+
+public:
+   DerivativeApply() = delete;
+
+   DerivativeApply(IntegratorContext ctx,
+                   qfunc_t /*qfunc*/,
+                   inputs_t inputs,
+                   outputs_t outputs,
+                   const Vector &qp_cache_in):
+      inputs(inputs), outputs(outputs), ctx(ctx), qp_cache(qp_cache_in),
+      dtqs(make_dtqs(ctx)), input_dtq(create_dtq_maps<Entity::Element>(
+                                         inputs,
+                                         dtqs,
+                                         create_union_field_map_for_dtq(ctx, inputs),
+                                         ctx.unionfds,
+                                         ctx.ir)),
+      input_idx(create_input_vector_map(ctx, inputs)),
+      input_B(get_B(input_dtq)), input_G(get_G(input_dtq)),
+      input_d1d(get_D1D(input_dtq)), input_q1d(get_Q1D(input_dtq)),
+      input_vdim(get_vdim(inputs)),
+      output_dtq(create_dtq_maps<Entity::Element>(
+                    outputs,
+                    dtqs,
+                    create_union_field_map_for_dtq(ctx, outputs),
+                    ctx.unionfds,
+                    ctx.ir)),
+      output_idx(create_output_vector_map(ctx, outputs)),
+      output_B(get_B(output_dtq)), output_G(get_G(output_dtq)),
+      output_d1d(get_D1D(output_dtq)), output_q1d(get_Q1D(output_dtq)),
+      output_vdim(get_vdim(outputs)),
+      input_is_dependent(compute_input_is_dependent(inputs, derivative_id)),
+      input_size_on_qp(
+         get_input_size_on_qp(inputs, std::make_index_sequence<n_inputs> {})),
+                           out_op_dim(compute_out_op_dim(outputs)),
+                           out_offsets(compute_out_offsets(output_vdim, out_op_dim)),
+                           output_size_on_qp(
+                              [&]
+   {
+      int s = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      { s += get<o>(outputs).size_on_qp; });
+      return s;
+   }()),
+   trial_vdim(compute_trial_vdim(inputs, derivative_id)),
+   total_trial_op_dim(compute_total_trial_op_dim(
+                         inputs, input_is_dependent, input_size_on_qp)),
+   residual_size_on_qp(output_size_on_qp * trial_vdim * total_trial_op_dim),
+   dim(ctx.mesh.Dimension()), ne(ctx.nentities), nq(ctx.ir.GetNPoints()),
+   q1d(tensor_1d_size(nq, dim))
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+
+      int direction_field_idx = -1;
+      for (size_t uf = 0; uf < nfields; uf++)
+      {
+         if (static_cast<int>(ctx.unionfds[uf].id) == derivative_id)
+         {
+            direction_field_idx = static_cast<int>(uf);
+            break;
+         }
+      }
+      MFEM_ASSERT(direction_field_idx != -1,
+                  "DerivativeApply: derivative direction field not found");
+
+      direction_fd = ctx.unionfds[static_cast<size_t>(direction_field_idx)];
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename Backend>
+   void run_kernels(std::vector<Vector *> &ye) const
+   {
+      Backend::Run(dim,
+                   q1d,
+                   ctx,
+                   qp_cache,
+                   // inputs
+                   input_idx,
+                   input_B,
+                   input_G,
+                   input_vdim,
+                   input_d1d,
+                   input_q1d,
+                   input_size_on_qp,
+                   input_is_dependent,
+                   // outputs
+                   output_idx,
+                   output_B,
+                   output_G,
+                   output_vdim,
+                   output_d1d,
+                   output_q1d,
+                   out_op_dim,
+                   out_offsets,
+                   trial_vdim,
+                   total_trial_op_dim,
+                   residual_size_on_qp,
+                   output_size_on_qp,
+                   direction_e,
+                   ye,
+                   // fallback arguments
+                   dim,
+                   q1d);
+   }
+
+   //////////////////////////////////////////////////////////////////
+   void operator()(const std::vector<Vector *> &,
+                   const Vector *direction_l,
+                   std::vector<Vector *> &ye) const
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      MFEM_ASSERT(direction_l != nullptr,
+                  "LocalQF DerivativeApply: direction vector is null");
+
+      restriction(direction_fd,
+                  direction_rcache,
+                  *direction_l,
+                  direction_e,
+                  ElementDofOrdering::LEXICOGRAPHIC);
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<DerivativeApplyLO>(ye);
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<DerivativeApplyHO>(ye);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void
+   derivative_apply_callback(const IntegratorContext &ctx,
+                             const Vector &qp_cache,
+                             // inputs: idx, B, G, vdim, d1d, q1d
+                             const std::array<size_t, n_inputs> & /*in_idx*/,
+                             const std::array<const real_t *, n_inputs> in_B,
+                             const std::array<const real_t *, n_inputs> in_G,
+                             const std::array<int, n_inputs> &in_vdim,
+                             const std::array<int, n_inputs> &in_d1d,
+                             const std::array<int, n_inputs> &in_q1d,
+                             const std::array<int, n_inputs> &in_size_on_qp,
+                             const std::array<bool, n_inputs> &input_dep,
+                             // outputs: idx, B, G, vdim, d1d, q1d
+                             const std::array<size_t, n_outputs> &out_idx,
+                             const std::array<const real_t *, n_outputs> out_B,
+                             const std::array<const real_t *, n_outputs> out_G,
+                             const std::array<int, n_outputs> &out_vdim,
+                             const std::array<int, n_outputs> &out_d1d,
+                             const std::array<int, n_outputs> &out_q1d,
+                             const std::array<int, n_outputs> &out_op_dim,
+                             const std::array<int, n_outputs> &out_offsets,
+                             const int trial_vdim,
+                             const int total_trial_op_dim,
+                             const int residual_size_on_qp,
+                             const int output_size_on_qp,
+                             const Vector &direction_e,
+                             std::vector<Vector *> &ye,
+                             // fallback arguments
+                             const int dim,
+                             const int q1d)
+   {
+      MFEM_CONTRACT_VAR(input_dep);
+      MFEM_CONTRACT_VAR(in_size_on_qp);
+      MFEM_CONTRACT_VAR(out_vdim);
+      MFEM_CONTRACT_VAR(out_op_dim);
+      MFEM_CONTRACT_VAR(out_offsets);
+      MFEM_CONTRACT_VAR(trial_vdim);
+      MFEM_CONTRACT_VAR(total_trial_op_dim);
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      if (ctx.attr.Size() == 0) { return; }
+
+      static constexpr auto B2D = backend_t::DIM == 2;
+      static constexpr auto MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+      static constexpr auto MTPB = backend_t::MAX_THREADS_PER_BLOCK();
+
+      const int ne = ctx.nentities;
+      const int nq = ctx.ir.GetNPoints();
+      MFEM_CONTRACT_VAR(output_size_on_qp);
+
+      constexpr auto k_dim = [](const int k) { return k * k * (B2D ? 1 : k); };
+
+      // --------------------------------------------------
+      // DIRECTION (trial): XE_dir for the dependent inputs
+      // --------------------------------------------------
+      const auto d_direction = direction_e.Read();
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE_dir;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const int d = in_d1d[i], q = in_q1d[i], v = in_vdim[i];
+         using FOP = tuple_element_t<i, inputs_t>;
+         if (!input_dep[i]) { return; }
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            in_XE_dir[i] = Reshape(d_direction, d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            in_XE_dir[i] = Reshape(d_direction, v, q, q, B2D ? 1 : q, ne);
+         }
+         else if constexpr (is_weight_fop_v<FOP>) { /* never a direction */ }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      // --------------------------------------------------
+      // OUTPUTS: YE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, real_t>, n_outputs> out_YE;
+      for_constexpr<n_outputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = out_idx[i];
+         const int d = out_d1d[i], q = out_q1d[i], v = out_vdim[i];
+         using FOP = tuple_element_t<i, outputs_t>;
+         if constexpr (is_gradient_fop_v<FOP> || is_value_fop_v<FOP>)
+         {
+            MFEM_VERIFY(ye[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            MFEM_VERIFY(ye[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            out_YE[i] = Reshape(ye[k]->ReadWrite(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else
+         {
+            static_assert(false, "Unsupported FieldOperator");
+         }
+      });
+
+      auto cache_tensor = DeviceTensor<3, const real_t>(
+                             qp_cache.Read(), nq, residual_size_on_qp, ne);
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      dfem::forall<MTPB>(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         // -----------------------------------------------
+         // Output integration registers, trial direction (shadow) registers
+         // and shared memory. `rargs` only ever holds test-function data, so
+         // it is an output-only bank: slot `o` is q-function parameter
+         // `n_inputs + o`.
+         // -----------------------------------------------
+         output_args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> rargs;
+         input_args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> sargs;
+         MFEM_SHARED typename backend_t::Shared smem;
+
+         // -----------------------------------------------
+         // Load trial direction (sargs) for the dependent inputs
+         // -----------------------------------------------
+         for_constexpr<n_inputs>([&](auto ic)
+         {
+            constexpr size_t i = ic.value;
+            if constexpr (!StaticInputDep<i>()) { return; }
+            const auto &XE = in_XE_dir[i];
+            const int d = in_d1d[i], q = in_q1d[i], Q1D = q1d;
+            const real_t *B = in_B[i], *G = in_G[i];
+            auto &sarg = get<i>(sargs);
+            using FOP = tuple_element_t<i, inputs_t>;
+            if constexpr (is_value_fop<FOP>::value)
+            {
+               backend_t::LoadValue(smem, e, d, q, Q1D, B, XE, sarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               constexpr auto RNK = qf_param_slot<qfunc_t, i>::extents.size();
+               using FieldParamT =
+                  typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+               backend_t::template LoadGradient<RNK,
+                                                decltype(sarg),
+                                                decltype(XE),
+                                                FieldParamT>(
+                                                   smem, e, d, q, Q1D, B, G, XE, sarg);
+            }
+            else if constexpr (is_identity_fop_v<FOP> || is_weight_fop_v<FOP>)
+            {
+               // identity read at qp; weight is never a trial direction
+            }
+            else
+            {
+               static_assert(false, "Unsupported");
+            }
+         });
+         MFEM_SYNC_THREAD;
+
+         // -----------------------------------------------
+         // Contract the cached Jacobian with the trial direction at each
+         // quadrature point and push the result into the test registers.
+         // -----------------------------------------------
+         MFEM_FOREACH_THREAD(qz, z, (B2D ? 1 : q1d))
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+               {
+                  const int q = qx + q1d * (qy + q1d * qz);
+
+                  // The trial direction at this quadrature point is the same
+                  // for every test row (i, k), so pull each dependent input
+                  // slot out of the register bank once, here, instead of once
+                  // per row inside the contraction below.
+                  args_tuple_t dvecs {};
+                  for_constexpr<n_inputs>([&](auto sc)
+                  {
+                     constexpr size_t s = sc.value;
+                     if constexpr (StaticInputDep<s>())
+                     {
+                        using SARG =
+                           typename qf_param_slot<qfunc_t, s>::qf_reg_param_t;
+                        get<s>(dvecs) = backend_t::template qp_pull<SARG>(
+                           get<s>(sargs), qx, qy, qz);
+                     }
+                  });
+
+                  for_constexpr<n_outputs>([&](auto oc)
+                  {
+                     constexpr size_t o = oc.value, ao = n_inputs + o;
+                     using FOP = tuple_element_t<o, outputs_t>;
+                     using ARG =
+                        typename qf_param_slot<qfunc_t, ao>::qf_reg_param_t;
+                     constexpr int tv = StaticOutputVDim<o>();
+                     constexpr int to = StaticOutputOpDim<o>();
+                     constexpr int offset_o = StaticOutputOffset<o>();
+                     constexpr int trial_vdim_ct = StaticTrialVDim();
+                     constexpr int total_trial_op_dim_ct = StaticTotalTrialOpDim();
+
+                     ARG fhat{};
+                     MFEM_UNROLL(tv)
+                     for (int i = 0; i < tv; i++)
+                     {
+                        MFEM_UNROLL(to)
+                        for (int k = 0; k < to; k++)
+                        {
+                           const int row = offset_o + i * to + k;
+                           const int cache_row =
+                              row * trial_vdim_ct * total_trial_op_dim_ct;
+                           real_t sum = 0.0;
+                           for_constexpr<n_inputs>([&](auto sc)
+                           {
+                              constexpr size_t s = sc.value;
+                              if constexpr (StaticInputDep<s>())
+                              {
+                                 constexpr int op_dim_s = StaticInputOpDim<s>();
+                                 constexpr int m_offset = StaticInputOpOffset<s>();
+                                 const auto &dvec = get<s>(dvecs);
+                                 MFEM_UNROLL(trial_vdim_ct)
+                                 for (int j = 0; j < trial_vdim_ct; j++)
+                                 {
+                                    MFEM_UNROLL(op_dim_s)
+                                    for (int m = 0; m < op_dim_s; m++)
+                                    {
+                                       const int cache_idx =
+                                          cache_row + j * total_trial_op_dim_ct +
+                                          (m + m_offset);
+                                       sum += cache_tensor(q, cache_idx, e) *
+                                              qf_value_at(dvec, j, m);
+                                    }
+                                 }
+                              }
+                           });
+                           qf_set_value_at(fhat, i, k, sum);
+                        }
+                     }
+
+                     auto &YE = out_YE[o];
+                     if constexpr (is_identity_fop_v<FOP>)
+                     {
+                        MFEM_UNROLL(tv)
+                        for (int i = 0; i < tv; i++)
+                        {
+                           MFEM_UNROLL(to)
+                           for (int k = 0; k < to; k++)
+                           {
+                              YE(i + tv * k, qx, qy, qz, e) =
+                                 qf_value_at(fhat, i, k);
+                           }
+                        }
+                     }
+                     else
+                     {
+                        backend_t::template qp_push<ARG>(
+                           get<o>(rargs), qx, qy, qz, fhat);
+                     }
+                  });
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // -----------------------------------------------
+         // Integrate value / gradient outputs to the test dofs
+         // -----------------------------------------------
+         for_constexpr<n_outputs>([&](auto ic)
+         {
+            constexpr size_t i = ic.value, o = n_inputs + i;
+            const int d = out_d1d[i], q = out_q1d[i], Q1D = q1d;
+            const auto B = out_B[i], G = out_G[i];
+            auto &YE = out_YE[i];
+            auto &rarg = get<i>(rargs);
+            using FOP = tuple_element_t<i, outputs_t>;
+            if constexpr (is_value_fop_v<FOP>)
+            {
+               backend_t::WriteValue(smem, e, d, q, Q1D, B, YE, rarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               using YE_t = decltype(YE);
+               using rarg_t = decltype(rarg);
+               using qf_param_t =
+                  typename qf_param_slot<qfunc_t, o>::qf_decay_param_t;
+               constexpr auto RNK = qf_param_slot<qfunc_t, o>::extents.size();
+               backend_t::template WriteGradient<RNK, rarg_t, YE_t, qf_param_t>(
+                  smem, e, d, q, Q1D, B, G, YE, rarg);
+            }
+            else if constexpr (is_identity_fop_v<FOP>) { /* written at qp */ }
+            else
+            {
+               static_assert(false, "Unsupported");
+            }
+         });
+      },
+      ne,
+      backend_t::thread_blocks(compute_kernel_thread_1d<inputs_t, outputs_t>(
+                                  q1d, in_d1d, out_d1d)),
+      0,
+      nullptr);
+   }
+
+   using ApplyKernelType =
+      decltype(&DerivativeApply::derivative_apply_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeApplyLO,
+                                     ApplyKernelType,
+                                     (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeApplyHO,
+                                     ApplyKernelType,
+                                     (int, int) );
+};
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+ApplyKernelType
+DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeApplyLO::Kernel()
+{
+   static_assert((DIM == 2 || DIM == 3) && Q1D <= 8);
+   using apply_t = DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return apply_t::template derivative_apply_callback<
+             LocalQFLOBackend<DIM, Q1D>>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+ApplyKernelType
+DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeApplyLO::Fallback(int dim, int q1d)
+{
+   using apply_t = DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeApplyLO = typename apply_t::DerivativeApplyLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<DerivativeApplyLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<DerivativeApplyLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+ApplyKernelType
+DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeApplyHO::Kernel()
+{
+   using apply_t = DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return apply_t::template derivative_apply_callback<LocalQFHOBackend<DIM>,
+                                                      Q1D>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+ApplyKernelType
+DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeApplyHO::Fallback(int dim, int q1d)
+{
+   using apply_t = DerivativeApply<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeApplyHO = typename apply_t::DerivativeApplyHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeApplyHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeApplyHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_apply_transpose.hpp

@@ -0,0 +1,637 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include <array>
+
+namespace mfem::future::LocalQFImpl
+{
+
+// Cached transposed Jacobian apply: Jᵀ·w from the qp_cache
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeApplyTranspose
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   using qf_signature = typename get_function_signature<qfunc_t>::type;
+   using qf_param_ts = typename qf_signature::parameter_ts;
+   using args_tuple_t = decay_tuple<qf_param_ts>;
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+   static_assert(n_inputs + n_outputs == tuple_size<qf_param_ts>::value,
+                 "LocalQF: q-function arity must match inputs + outputs");
+
+   // Input tuple slot referencing the derivative field (compile-time)
+   static constexpr size_t deriv_input_idx_ct = []() constexpr
+   {
+      size_t idx = SIZE_MAX;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         using FOP = tuple_element_t<i, inputs_t>;
+         if (FOP::GetFieldId() == derivative_id) { idx = i; }
+      });
+      return idx;
+   }();
+   static_assert(deriv_input_idx_ct < n_inputs,
+                 "DerivativeApplyTranspose: derivative input slot not found");
+
+   const inputs_t inputs;
+   const outputs_t outputs;
+   const IntegratorContext ctx;
+   const Vector &qp_cache; // Jacobian cache from DerivativeSetup
+   const std::vector<const DofToQuad *> dtqs;
+   // inputs: dtq, B, G, d1d, q1d, vdim (trial / derivative fields)
+   const std::array<DofToQuadMap, n_inputs> input_dtq;
+   const std::array<const real_t *, n_inputs> input_B, input_G;
+   const std::array<int, n_inputs> input_d1d, input_q1d, input_vdim;
+   // outputs: dtq, idx, B, G, d1d, q1d, vdim (test / cotangent fields)
+   const std::array<DofToQuadMap, n_outputs> output_dtq;
+   const std::array<size_t, n_outputs> output_idx;
+   const std::array<const real_t *, n_outputs> output_B, output_G;
+   const std::array<int, n_outputs> output_d1d, output_q1d, output_vdim;
+   // Jacobian cache metadata
+   const std::array<bool, n_inputs> input_is_dependent;
+   const std::array<int, n_inputs> input_size_on_qp;
+   const std::array<int, n_outputs> out_op_dim;
+   const std::array<int, n_outputs> out_offsets;
+   const int output_size_on_qp;
+   const int trial_vdim;
+   const int total_trial_op_dim;
+   const int residual_size_on_qp;
+   // other constants
+   const int dim, ne, nq, q1d;
+   const size_t deriv_infd_idx; // index of the derivative field in ye
+   // output cotangent restriction workspace (blocked by element)
+   std::array<int, n_outputs> out_elem_dof_size;
+   mutable Vector dir_out_e;
+   /// One restriction cache per output field, resolved on first use.
+   mutable std::array<RestrictionCache<Entity::Element>, n_outputs>
+   out_rcaches;
+
+public:
+   //////////////////////////////////////////////////////////////////
+   DerivativeApplyTranspose() = delete;
+
+   DerivativeApplyTranspose(IntegratorContext ctx,
+                            qfunc_t /*qfunc*/,
+                            inputs_t inputs,
+                            outputs_t outputs,
+                            const Vector &qp_cache):
+      inputs(inputs), outputs(outputs), ctx(ctx), qp_cache(qp_cache),
+      dtqs(make_dtqs(ctx)), input_dtq(create_dtq_maps<Entity::Element>(
+                                         inputs,
+                                         dtqs,
+                                         create_union_field_map_for_dtq(ctx, inputs),
+                                         ctx.unionfds,
+                                         ctx.ir)),
+      input_B(get_B(input_dtq)), input_G(get_G(input_dtq)),
+      input_d1d(get_D1D(input_dtq)), input_q1d(get_Q1D(input_dtq)),
+      input_vdim(get_vdim(inputs)),
+      output_dtq(create_dtq_maps<Entity::Element>(
+                    outputs,
+                    dtqs,
+                    create_union_field_map_for_dtq(ctx, outputs),
+                    ctx.unionfds,
+                    ctx.ir)),
+      output_idx(create_output_vector_map(ctx, outputs)),
+      output_B(get_B(output_dtq)), output_G(get_G(output_dtq)),
+      output_d1d(get_D1D(output_dtq)), output_q1d(get_Q1D(output_dtq)),
+      output_vdim(get_vdim(outputs)),
+      input_is_dependent(compute_input_is_dependent(inputs, derivative_id)),
+      input_size_on_qp(
+         get_input_size_on_qp(inputs, std::make_index_sequence<n_inputs> {})),
+                           out_op_dim(compute_out_op_dim(outputs)),
+                           out_offsets(compute_out_offsets(output_vdim, out_op_dim)),
+                           output_size_on_qp(
+                              [&]
+   {
+      int s = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      { s += get<o>(outputs).size_on_qp; });
+      return s;
+   }()),
+   trial_vdim(compute_trial_vdim(inputs, derivative_id)),
+   total_trial_op_dim(compute_total_trial_op_dim(
+                         inputs, input_is_dependent, input_size_on_qp)),
+   residual_size_on_qp(output_size_on_qp * trial_vdim * total_trial_op_dim),
+   dim(ctx.mesh.Dimension()), ne(ctx.nentities), nq(ctx.ir.GetNPoints()),
+   q1d(tensor_1d_size(nq, dim)),
+   deriv_infd_idx(find_infd_index(ctx, derivative_id)), out_elem_dof_size{}
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+      MFEM_ASSERT(
+         deriv_infd_idx != SIZE_MAX,
+         "DerivativeApplyTranspose: derivative field not found in infds");
+
+      // Size the workspace that holds the output cotangent(s) in element
+      // layout.
+      int total_dir_e_size = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      {
+         const int elem_sz = compute_element_dof_sz(
+            ctx.outfds[output_idx[o]], ne, ElementDofOrdering::LEXICOGRAPHIC);
+         out_elem_dof_size[o] = elem_sz;
+         total_dir_e_size += elem_sz;
+      });
+      dir_out_e.SetSize(total_dir_e_size * ne);
+      dir_out_e.UseDevice(true);
+      dir_out_e.Read();
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename Backend>
+   void run_kernels(std::vector<Vector *> &ye) const
+   {
+      Backend::Run(dim,
+                   q1d,
+                   ctx,
+                   qp_cache,
+                   dir_out_e,
+                   // inputs (integration target metadata)
+                   input_B,
+                   input_G,
+                   input_vdim,
+                   input_d1d,
+                   input_q1d,
+                   input_size_on_qp,
+                   input_is_dependent,
+                   // outputs (direction interpolation metadata)
+                   output_B,
+                   output_G,
+                   output_vdim,
+                   output_d1d,
+                   output_q1d,
+                   out_op_dim,
+                   out_offsets,
+                   trial_vdim,
+                   total_trial_op_dim,
+                   residual_size_on_qp,
+                   output_size_on_qp,
+                   deriv_infd_idx,
+                   ye,
+                   // fallback arguments
+                   dim,
+                   q1d);
+   }
+
+   //////////////////////////////////////////////////////////////////
+   void operator()(const std::vector<Vector *> & /*xe*/,
+                   const Vector *direction_l,
+                   std::vector<Vector *> &ye) const
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      MFEM_ASSERT(direction_l != nullptr,
+                  "LocalQF DerivativeApplyTranspose: direction vector is null");
+
+      // Restrict output cotangent from L-vectors into element layout
+      // (dir_out_e).
+      int l_offset = 0;
+      int e_offset = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      {
+         const size_t outfd = output_idx[o];
+         const auto &fd = ctx.outfds[outfd];
+         const int l_size = GetVSize(fd);
+         Vector dir_o_l(*const_cast<Vector *>(direction_l), l_offset, l_size);
+         dir_o_l.UseDevice(true);
+         const int elem_sz = out_elem_dof_size[o];
+         Vector dir_o_e(dir_out_e, e_offset, elem_sz * ne);
+         dir_o_e.UseDevice(true);
+         restriction(fd, out_rcaches[o], dir_o_l, dir_o_e,
+                     ElementDofOrdering::LEXICOGRAPHIC);
+         l_offset += l_size;
+         e_offset += elem_sz * ne;
+      });
+
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<DerivativeApplyTransposeLO>(ye);
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<DerivativeApplyTransposeHO>(ye);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void derivative_apply_transpose_callback(
+      const IntegratorContext &ctx,
+      const Vector &qp_cache,
+      const Vector &dir_e, // restricted, concatenated output cotangents
+      // inputs (integration target metadata)
+      const std::array<const real_t *, n_inputs> in_B,
+      const std::array<const real_t *, n_inputs> in_G,
+      const std::array<int, n_inputs> &in_vdim,
+      const std::array<int, n_inputs> &in_d1d,
+      const std::array<int, n_inputs> &in_q1d,
+      const std::array<int, n_inputs> &in_size_on_qp,
+      const std::array<bool, n_inputs> &input_dep,
+      // outputs (direction interpolation metadata)
+      const std::array<const real_t *, n_outputs> out_B,
+      const std::array<const real_t *, n_outputs> out_G,
+      const std::array<int, n_outputs> &out_vdim,
+      const std::array<int, n_outputs> &out_d1d,
+      const std::array<int, n_outputs> &out_q1d,
+      const std::array<int, n_outputs> &out_op_dim,
+      const std::array<int, n_outputs> &out_offsets,
+      const int trial_vdim,
+      const int total_trial_op_dim,
+      const int residual_size_on_qp,
+      const int output_size_on_qp,
+      const size_t deriv_infd_idx,
+      std::vector<Vector *> &ye,
+      // fallback arguments
+      const int dim,
+      const int q1d)
+   {
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      if (ctx.attr.Size() == 0) { return; }
+
+      static constexpr auto B2D = backend_t::DIM == 2;
+      static constexpr auto MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+      static constexpr auto MTPB = backend_t::MAX_THREADS_PER_BLOCK();
+
+      const int ne = ctx.nentities;
+      const int nq = ctx.ir.GetNPoints();
+      MFEM_CONTRACT_VAR(output_size_on_qp);
+      MFEM_CONTRACT_VAR(in_q1d);
+
+      constexpr auto k_dim = [](const int k) { return k * k * (B2D ? 1 : k); };
+
+      // --------------------------------------------------
+      // DIRECTION (test cotangent): out_XE_dir, concatenated per output
+      // --------------------------------------------------
+      const auto d_dir = dir_e.Read();
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_outputs> out_XE_dir;
+      int e_offset = 0;
+      for_constexpr<n_outputs>([&](auto oc)
+      {
+         constexpr size_t o = oc.value;
+         const int d = out_d1d[o], q = out_q1d[o], v = out_vdim[o];
+         using FOP = tuple_element_t<o, outputs_t>;
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            out_XE_dir[o] = Reshape(d_dir + e_offset, d, d, B2D ? 1 : d, v, ne);
+            e_offset += k_dim(d) * v * ne;
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            out_XE_dir[o] = Reshape(d_dir + e_offset, v, q, q, B2D ? 1 : q, ne);
+            e_offset += k_dim(q) * v * ne;
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      // --------------------------------------------------
+      // DERIVATIVE TRIAL FIELD: ye_XE (accumulates Jᵀ w)
+      // --------------------------------------------------
+      const int d_in = in_d1d[deriv_input_idx_ct];
+      const int v_in = in_vdim[deriv_input_idx_ct];
+      auto ye_XE = Reshape(
+                      ye[deriv_infd_idx]->ReadWrite(), d_in, d_in, B2D ? 1 : d_in, v_in, ne);
+
+      auto cache_tensor = DeviceTensor<3, const real_t>(
+                             qp_cache.Read(), nq, residual_size_on_qp, ne);
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      dfem::forall<MTPB>(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         // -----------------------------------------------
+         // Output cotangent (direction) registers live in the output slots;
+         // the trial integration data is pushed into the input slots.
+         // -----------------------------------------------
+         args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> rargs;
+         MFEM_SHARED typename backend_t::Shared smem;
+
+         // -----------------------------------------------
+         // Interpolate the test cotangent to quadrature points (output slots)
+         // -----------------------------------------------
+         for_constexpr<n_outputs>([&](auto oc)
+         {
+            constexpr size_t o = oc.value, ao = n_inputs + o;
+            using FOP = tuple_element_t<o, outputs_t>;
+            const auto &XE = out_XE_dir[o];
+            const int d = out_d1d[o], q = out_q1d[o], Q1D = q1d;
+            const real_t *B = out_B[o], *G = out_G[o];
+            auto &oarg = get<ao>(rargs);
+            if constexpr (is_value_fop_v<FOP>)
+            {
+               backend_t::LoadValue(smem, e, d, q, Q1D, B, XE, oarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               constexpr auto RNK = qf_param_slot<qfunc_t, ao>::extents.size();
+               using FieldParamT =
+                  typename qf_param_slot<qfunc_t, ao>::qf_decay_param_t;
+               backend_t::template LoadGradient<RNK,
+                                                decltype(oarg),
+                                                decltype(XE),
+                                                FieldParamT>(
+                                                   smem, e, d, q, Q1D, B, G, XE, oarg);
+            }
+            else if constexpr (is_identity_fop_v<FOP>)
+            {
+               // identity cotangent is read directly at qp from out_XE_dir
+            }
+            else
+            {
+               static_assert(false, "Unsupported");
+            }
+         });
+         MFEM_SYNC_THREAD;
+
+         // -----------------------------------------------
+         // Contract the transposed cached Jacobian with the test cotangent at
+         // each quadrature point and push the trial result into the dependent
+         // input registers.
+         // -----------------------------------------------
+         MFEM_FOREACH_THREAD(qz, z, (B2D ? 1 : q1d))
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+               {
+                  const int q = qx + q1d * (qy + q1d * qz);
+
+                  // The test cotangent at this quadrature point is the same
+                  // for every trial column (j, m), so pull each interpolated
+                  // output slot out of the register bank once, here, instead
+                  // of once per column inside the contraction below. Identity
+                  // outputs have no register bank and are read from
+                  // out_XE_dir at the point of use.
+                  args_tuple_t wvecs {};
+                  for_constexpr<n_outputs>([&](auto oc)
+                  {
+                     constexpr size_t o = oc.value, ao = n_inputs + o;
+                     using OFOP = tuple_element_t<o, outputs_t>;
+                     if constexpr (is_value_fop_v<OFOP> ||
+                                   is_gradient_fop_v<OFOP>)
+                     {
+                        using OARG =
+                           typename qf_param_slot<qfunc_t, ao>::qf_reg_param_t;
+                        get<ao>(wvecs) = backend_t::template qp_pull<OARG>(
+                           get<ao>(rargs), qx, qy, qz);
+                     }
+                  });
+
+                  int m_offset = 0;
+                  for_constexpr<n_inputs>([&](auto sc)
+                  {
+                     constexpr size_t s = sc.value;
+                     if (!input_dep[s]) { return; }
+                     using SARG =
+                        typename qf_param_slot<qfunc_t, s>::qf_reg_param_t;
+                     const int vdim_s = in_vdim[s];
+                     const int op_dim_s = in_size_on_qp[s] / vdim_s;
+
+                     SARG fhat{};
+                     for (int j = 0; j < trial_vdim; j++)
+                     {
+                        for (int m = 0; m < op_dim_s; m++)
+                        {
+                           const int col =
+                              j * total_trial_op_dim + (m + m_offset);
+                           real_t sum = 0.0;
+                           for_constexpr<n_outputs>([&](auto oc)
+                           {
+                              constexpr size_t o = oc.value, ao = n_inputs + o;
+                              using OFOP = tuple_element_t<o, outputs_t>;
+                              const int tv = out_vdim[o], to = out_op_dim[o];
+                              const auto offset_o = out_offsets[o];
+                              const auto &cache = cache_tensor;
+                              if constexpr (is_value_fop_v<OFOP> ||
+                                            is_gradient_fop_v<OFOP>)
+                              {
+                                 const auto &wvec = get<ao>(wvecs);
+                                 for (int i = 0; i < tv; i++)
+                                 {
+                                    for (int k = 0; k < to; k++)
+                                    {
+                                       const int row = offset_o + i * to + k;
+                                       const int cache_idx =
+                                          row * trial_vdim *
+                                          total_trial_op_dim +
+                                          col;
+                                       sum += cache(q, cache_idx, e) *
+                                              qf_value_at(wvec, i, k);
+                                    }
+                                 }
+                              }
+                              else if constexpr (is_identity_fop_v<OFOP>)
+                              {
+                                 const auto &XEo = out_XE_dir[o];
+                                 for (int i = 0; i < tv; i++)
+                                 {
+                                    for (int k = 0; k < to; k++)
+                                    {
+                                       const int row = offset_o + i * to + k;
+                                       const int cache_idx =
+                                          row * trial_vdim *
+                                          total_trial_op_dim +
+                                          col;
+                                       sum += cache(q, cache_idx, e) *
+                                              XEo(i + tv * k, qx, qy, qz, e);
+                                    }
+                                 }
+                              }
+                           });
+                           qf_set_value_at(fhat, j, m, sum);
+                        }
+                     }
+                     backend_t::template qp_push<SARG>(
+                        get<s>(rargs), qx, qy, qz, fhat);
+                     m_offset += op_dim_s;
+                  });
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // -----------------------------------------------
+         // Integrate the trial result into the derivative field dofs. Multiple
+         // dependent input slots (e.g. value and gradient of the same field)
+         // accumulate into ye_XE via the writers' '+=' semantics.
+         // -----------------------------------------------
+         for_constexpr<n_inputs>([&](auto sc)
+         {
+            constexpr size_t s = sc.value;
+            if (!input_dep[s]) { return; }
+            using FOP = tuple_element_t<s, inputs_t>;
+            const int d = in_d1d[s], q = in_q1d[s], Q1D = q1d;
+            const real_t *B = in_B[s], *G = in_G[s];
+            auto &sarg = get<s>(rargs);
+            auto &YE = ye_XE;
+            if constexpr (is_value_fop_v<FOP>)
+            {
+               backend_t::WriteValue(smem, e, d, q, Q1D, B, YE, sarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               using YE_t = decltype(YE);
+               using rarg_t = decltype(sarg);
+               using qf_param_t =
+                  typename qf_param_slot<qfunc_t, s>::qf_decay_param_t;
+               constexpr auto RNK = qf_param_slot<qfunc_t, s>::extents.size();
+               backend_t::template WriteGradient<RNK, rarg_t, YE_t, qf_param_t>(
+                  smem, e, d, q, Q1D, B, G, YE, sarg);
+            }
+            else
+            {
+               // identity / weight derivative targets are not produced here
+            }
+         });
+      },
+      ne,
+      backend_t::thread_blocks(compute_kernel_thread_1d<inputs_t, outputs_t>(
+                                  q1d, in_d1d, out_d1d)),
+      0,
+      nullptr);
+   }
+
+   using TransposeKernelType =
+      decltype(&DerivativeApplyTranspose::
+               derivative_apply_transpose_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeApplyTransposeLO,
+                                     TransposeKernelType,
+                                     (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeApplyTransposeHO,
+                                     TransposeKernelType,
+                                     (int, int) );
+};
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeApplyTranspose<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::TransposeKernelType
+       DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeApplyTransposeLO::Kernel()
+{
+   static_assert((DIM == 2 || DIM == 3) && Q1D <= 8);
+   using transpose_t =
+      DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return transpose_t::template derivative_apply_transpose_callback<
+             LocalQFLOBackend<DIM, Q1D>>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeApplyTranspose<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::TransposeKernelType
+       DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeApplyTransposeLO::Fallback(int dim, int q1d)
+{
+   using transpose_t =
+      DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeApplyTransposeLO =
+      typename transpose_t::DerivativeApplyTransposeLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<DerivativeApplyTransposeLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<DerivativeApplyTransposeLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeApplyTranspose<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::TransposeKernelType
+       DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeApplyTransposeHO::Kernel()
+{
+   using transpose_t =
+      DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return transpose_t::
+          template derivative_apply_transpose_callback<LocalQFHOBackend<DIM>, Q1D>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeApplyTranspose<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::TransposeKernelType
+       DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeApplyTransposeHO::Fallback(int dim, int q1d)
+{
+   using transpose_t =
+      DerivativeApplyTranspose<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeApplyTransposeHO =
+      typename transpose_t::DerivativeApplyTransposeHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeApplyTransposeHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeApplyTransposeHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_assemble.hpp

@@ -0,0 +1,987 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "../../../kernels.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include <array>
+#include <type_traits>
+
+namespace ker = mfem::kernels::internal;
+
+namespace mfem::future::LocalQFImpl
+{
+
+namespace detail
+{
+
+template<int DIM>
+MFEM_HOST_DEVICE inline int tensor_idx(int x, int y, int z, int N)
+{
+   static_assert(DIM == 2 || DIM == 3);
+   if constexpr (DIM == 2) { assert(z == 0); }
+   return x + N * (y + N * z);
+}
+
+template<int DIM>
+MFEM_HOST_DEVICE inline real_t
+trial_basis_weight_value(const DeviceTensor<3, const real_t> &B,
+                         const int qx,
+                         const int qy,
+                         const int qz,
+                         const int Jx,
+                         const int Jy,
+                         const int Jz)
+{
+   static_assert(DIM == 2 || DIM == 3);
+   return B(qx, 0, Jx) * B(qy, 0, Jy) * ((DIM == 3) ? B(qz, 0, Jz) : 1.0);
+}
+
+template<int DIM>
+MFEM_HOST_DEVICE inline real_t
+trial_basis_weight_gradient(const DeviceTensor<3, const real_t> &B,
+                            const DeviceTensor<3, const real_t> &G,
+                            const int m,
+                            const int qx,
+                            const int qy,
+                            const int qz,
+                            const int Jx,
+                            const int Jy,
+                            const int Jz)
+{
+   const auto Gx = G(qx, 0, Jx), Gy = G(qy, 0, Jy);
+   const auto Bx = B(qx, 0, Jx), By = B(qy, 0, Jy);
+   if constexpr (DIM == 2)
+   {
+      MFEM_CONTRACT_VAR(qz & Jz);
+      return (m == 0) ? Gx * By : Bx * Gy;
+   }
+   else
+   {
+      const auto Bz = B(qz, 0, Jz), Gz = G(qz, 0, Jz);
+      return (m == 0)   ? Gx * By * Bz
+             : (m == 1) ? Bx * Gy * Bz
+             : (m == 2) ? Bx * By * Gz
+             : (assert(false), 0.0);
+   }
+}
+
+template<int DIM, int MQ1, typename Shared, typename output_t>
+MFEM_HOST_DEVICE void
+map_quadrature_data_to_fields(DeviceTensor<2, real_t> &y,
+                              const DeviceTensor<3, real_t> &f,
+                              const output_t &output,
+                              const DofToQuadMap &dtq,
+                              Shared &s,
+                              const int tv_dof = -1)
+{
+   using output_fop_t = std::decay_t<output_t>;
+   const auto B = dtq.B, G = dtq.G;
+   const bool f_slab = (tv_dof >= 0);
+   const int vdim = output.vdim;
+   const int vd_begin = f_slab ? tv_dof : 0;
+   const int vd_end = f_slab ? tv_dof + 1 : vdim;
+
+   if constexpr (is_value_fop_v<output_fop_t>)
+   {
+      const auto [q1d, unused, d1d] = B.GetShape();
+      MFEM_CONTRACT_VAR(unused);
+      const int test_dim = output.size_on_qp / vdim;
+      MFEM_CONTRACT_VAR(test_dim);
+      const int f_vdim = f_slab ? 1 : vdim;
+
+      if constexpr (DIM == 2)
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_vdim, test_dim, q1d, q1d);
+         auto yd = Reshape(&y(0, 0), d1d, d1d, vdim);
+         ker::LoadMatrix(d1d, q1d, B, s.B);
+         ker::s_regs2d_t<MQ1> r_qp, Y;
+         for (int vd = vd_begin; vd < vd_end; vd++)
+         {
+            const int fi = f_slab ? 0 : vd;
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qx, x, q1d)
+            { r_qp[qy][qx] = fqp(fi, 0, qx, qy); }
+            MFEM_SYNC_THREAD;
+            ker::Eval2d<MQ1, true>(d1d, q1d, s.M, s.B, r_qp, Y);
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            MFEM_FOREACH_THREAD(dx, x, d1d) { yd(dx, dy, vd) += Y[dy][dx]; }
+            MFEM_SYNC_THREAD;
+         }
+      }
+      else
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_vdim, test_dim, q1d, q1d, q1d);
+         auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
+         ker::LoadMatrix(d1d, q1d, B, s.B);
+         ker::s_regs3d_t<MQ1> f_qp, Y;
+         for (int vd = vd_begin; vd < vd_end; vd++)
+         {
+            const int fi = f_slab ? 0 : vd;
+            for (int qz = 0; qz < q1d; qz++)
+            {
+               MFEM_FOREACH_THREAD(qy, y, q1d)
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               { f_qp[qz][qy][qx] = fqp(fi, 0, qx, qy, qz); }
+            }
+            MFEM_SYNC_THREAD;
+            ker::Eval3d<MQ1, true>(d1d, q1d, s.M, s.B, f_qp, Y);
+            for (int dz = 0; dz < d1d; dz++)
+            {
+               MFEM_FOREACH_THREAD(dy, y, d1d)
+               MFEM_FOREACH_THREAD(dx, x, d1d)
+               { yd(dx, dy, dz, vd) += Y[dz][dy][dx]; }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   }
+   else if constexpr (is_gradient_fop_v<output_fop_t>)
+   {
+      const auto [q1d, unused, d1d] = G.GetShape();
+      MFEM_CONTRACT_VAR(unused);
+      const int test_dim = output.size_on_qp / vdim;
+      const int f_vdim = f_slab ? 1 : vdim;
+
+      if constexpr (DIM == 2)
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_vdim, test_dim, q1d, q1d);
+         auto yd = Reshape(&y(0, 0), d1d, d1d, vdim);
+         ker::LoadMatrix(d1d, q1d, B, s.B);
+         ker::LoadMatrix(d1d, q1d, G, s.G);
+         ker::vd_regs2d_t<1, DIM, MQ1> X, Y;
+         for (int vd = vd_begin; vd < vd_end; vd++)
+         {
+            const int fi = f_slab ? 0 : vd;
+            MFEM_FOREACH_THREAD(qx, x, q1d)
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            for (int k = 0; k < DIM; k++)
+            {
+               X[0][k][qy][qx] = fqp(fi, k, qx, qy);
+            }
+            MFEM_SYNC_THREAD;
+            ker::Grad2d<1, DIM, MQ1, true>(d1d, q1d, s.M, s.B, s.G, X, Y);
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            MFEM_FOREACH_THREAD(dx, x, d1d)
+            {
+               real_t u = 0.0;
+               for (int k = 0; k < DIM; k++) { u += Y[0][k][dy][dx]; }
+               yd(dx, dy, vd) += u;
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+      else
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_vdim, test_dim, q1d, q1d, q1d);
+         auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
+         ker::LoadMatrix(d1d, q1d, B, s.B);
+         ker::LoadMatrix(d1d, q1d, G, s.G);
+         ker::vd_regs3d_t<1, DIM, MQ1> X, Y;
+         for (int vd = vd_begin; vd < vd_end; vd++)
+         {
+            const int fi = f_slab ? 0 : vd;
+            for (int qz = 0; qz < q1d; qz++)
+            {
+               MFEM_FOREACH_THREAD(qy, y, q1d)
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               for (int k = 0; k < DIM; k++)
+               {
+                  X[0][k][qz][qy][qx] = fqp(fi, k, qx, qy, qz);
+               }
+            }
+            MFEM_SYNC_THREAD;
+            ker::Grad3d<1, DIM, MQ1, true>(d1d, q1d, s.M, s.B, s.G, X, Y);
+            for (int dz = 0; dz < d1d; dz++)
+            {
+               MFEM_FOREACH_THREAD(dy, y, d1d)
+               MFEM_FOREACH_THREAD(dx, x, d1d)
+               {
+                  real_t u = 0.0;
+                  for (int k = 0; k < DIM; k++) { u += Y[0][k][dz][dy][dx]; }
+                  yd(dx, dy, dz, vd) += u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   }
+   else if constexpr (is_identity_fop_v<output_fop_t>)
+   {
+      const auto [q1d, unused, d1d] = B.GetShape();
+      MFEM_CONTRACT_VAR(unused);
+      MFEM_CONTRACT_VAR(d1d);
+
+      const int f_sq = f_slab ? 1 : output.size_on_qp;
+      const int sq_begin = f_slab ? tv_dof : 0;
+      const int sq_end = f_slab ? tv_dof + 1 : output.size_on_qp;
+
+      if constexpr (DIM == 2)
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_sq, q1d, q1d);
+         auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d, q1d);
+         for (int sq = sq_begin; sq < sq_end; sq++)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qx, x, q1d)
+            {
+               int qz = 0;
+               MFEM_CONTRACT_VAR(qz);
+               yqp(sq, qx, qy) = fqp(0, qx, qy);
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+      else
+      {
+         const auto fqp = Reshape(&f(0, 0, 0), f_sq, q1d, q1d, q1d);
+         auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d, q1d, q1d);
+         for (int sq = sq_begin; sq < sq_end; sq++)
+         {
+            for (int qz = 0; qz < q1d; qz++)
+            {
+               MFEM_FOREACH_THREAD(qy, y, q1d)
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               { yqp(sq, qx, qy, qz) = fqp(0, qx, qy, qz); }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   }
+   else
+   {
+      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
+                        " for this field descriptor with sum factorization on"
+                        " tensor product elements");
+   }
+}
+
+template<int DIM,
+         int MQ1,
+         typename Shared,
+         typename input_fop_ts,
+         std::size_t n_inputs,
+         typename output_fop_t>
+MFEM_HOST_DEVICE void assemble_element_mat_sumfact(
+   const DeviceTensor<5, real_t> &Ae,
+   const DeviceTensor<5, const real_t> &qpdc,
+   const int e,
+   const DeviceTensor<1, const real_t> &itod,
+   const input_fop_ts &inputs,
+   const output_fop_t &output,
+   const std::array<DofToQuadMap, n_inputs> &input_dtq_maps,
+   const DofToQuadMap &output_dtq,
+   const int row_offset,
+   const int test_vdim,
+   const int test_op_dim,
+   const int q1d,
+   const int num_trial_dof_1d,
+   real_t *fhat_storage,
+   Shared &smem)
+{
+   static constexpr int MQN = (DIM == 2) ? MQ1 * MQ1 : MQ1 * MQ1 * MQ1;
+   // Slab must hold full (test_vdim, test_op_dim, nq) fhat.
+   // It is allocated by the caller, and is shared by every output, so it must be
+   // Before, declaring it here allocated one slab per output and the device
+   // kernel ran out of shared memory once an integrator had more outputs.
+   static constexpr int FHAT_SLAB_MAX = MQN * 4;
+
+   static constexpr bool grad_out = is_gradient_fop_v<output_fop_t>;
+   static constexpr bool ident_out = is_identity_fop_v<output_fop_t>;
+
+   // qpdc shape: (nq, total_trial_op_dim, trial_vdim, output_size_on_qp, ne),
+   // where output_size_on_qp spans every output FieldOperator (multi-output mode).
+   // The rows of  one output start at @a row_offset and are laid out as
+   // i * test_op_dim + k, matching how DerivativeSetup writes the cache.
+   const int trial_vdim = qpdc.GetShape()[2];
+   const int num_test_dof = Ae.GetShape()[0];
+   const int nq = qpdc.GetShape()[0];
+   const int size_on_qp = output.size_on_qp;
+
+#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
+   MFEM_VERIFY(test_op_dim <= DIM,
+               "DerivativeAssemble: test_op_dim exceeds spatial DIM");
+   MFEM_VERIFY(test_op_dim * nq <= FHAT_SLAB_MAX,
+               "DerivativeAssemble: fhat slab exceeds capacity");
+#endif
+
+   const auto &inputs_ref = inputs;
+
+   // Iterate quadrature points using the thread-block mapping
+   const auto foreach_qp = [&](auto &&body)
+   {
+      if constexpr (DIM == 2)
+      {
+         MFEM_FOREACH_THREAD(qx, x, q1d)
+         MFEM_FOREACH_THREAD(qy, y, q1d) { body(qx, qy, 0); }
+      }
+      else
+      {
+         for (int qz = 0; qz < q1d; qz++)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qx, x, q1d) { body(qx, qy, qz); }
+         }
+      }
+   };
+
+   const auto zero_slab = [&](const int n_comp)
+   {
+      foreach_qp([&](const int qx, const int qy, const int qz)
+      {
+         const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+         for (int k = 0; k < n_comp; k++) { fhat_storage[k * nq + q] = 0.0; }
+      });
+      MFEM_SYNC_THREAD;
+   };
+
+   const auto accumulate_tv = [&](const int Jx,
+                                  const int Jy,
+                                  const int Jz,
+                                  const int j,
+                                  const int tv,
+                                  const int tod_only = -1)
+   {
+      int m_offset = 0;
+      for_constexpr<n_inputs>([&](auto inp)
+      {
+         using fop_t = std::decay_t<decltype(get<inp>(inputs_ref))>;
+
+         const int trial_op_dim = static_cast<int>(itod(static_cast<int>(inp)));
+         if (trial_op_dim == 0) { return; }
+
+         const auto &B = input_dtq_maps[inp].B;
+         const auto &G = input_dtq_maps[inp].G;
+
+         if constexpr (is_value_fop<fop_t>::value)
+         {
+            foreach_qp([&](const int qx, const int qy, const int qz)
+            {
+               const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+               const real_t w =
+                  trial_basis_weight_value<DIM>(B, qx, qy, qz, Jx, Jy, Jz);
+               for (int m = 0; m < trial_op_dim; m++)
+               {
+                  for (int k = 0; k < test_op_dim; k++)
+                  {
+                     if (tod_only >= 0 && k != tod_only) { continue; }
+                     const real_t f = qpdc(q, m + m_offset, j, row_offset + tv * test_op_dim + k, e);
+                     if constexpr (grad_out && !ident_out)
+                     {
+                        fhat_storage[k * nq + q] += f * w;
+                     }
+                     else
+                     {
+                        fhat_storage[q] += f * w;
+                     }
+                  }
+               }
+            });
+         }
+         else if constexpr (is_gradient_fop<fop_t>::value)
+         {
+            foreach_qp([&](const int qx, const int qy, const int qz)
+            {
+               const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+               for (int m = 0; m < trial_op_dim; m++)
+               {
+                  const real_t w = trial_basis_weight_gradient<DIM>(
+                                      B, G, m, qx, qy, qz, Jx, Jy, Jz);
+                  for (int k = 0; k < test_op_dim; k++)
+                  {
+                     if (tod_only >= 0 && k != tod_only) { continue; }
+                     const real_t f = qpdc(q, m + m_offset, j, row_offset + tv * test_op_dim + k, e);
+                     if constexpr (grad_out && !ident_out)
+                     {
+                        fhat_storage[k * nq + q] += f * w;
+                     }
+                     else
+                     {
+                        fhat_storage[q] += f * w;
+                     }
+                  }
+               }
+            });
+         }
+         else
+         {
+            MFEM_ABORT_KERNEL("sum factorized sparse matrix assemble routine "
+                              "not implemented for field operator");
+         }
+         MFEM_SYNC_THREAD;
+         m_offset += trial_op_dim;
+      });
+   };
+
+   for (int Jz = 0; Jz < ((DIM == 2) ? 1 : num_trial_dof_1d); Jz++)
+   {
+      for (int Jy = 0; Jy < num_trial_dof_1d; Jy++)
+      {
+         for (int Jx = 0; Jx < num_trial_dof_1d; Jx++)
+         {
+            const int J = tensor_idx<DIM>(Jx, Jy, Jz, num_trial_dof_1d);
+            for (int j = 0; j < trial_vdim; j++)
+            {
+               auto bvtfhat =
+                  Reshape(&Ae(0, 0, J, j, e), num_test_dof, test_vdim);
+               const int fhat_size = test_vdim * test_op_dim * nq;
+
+               if (fhat_size <= FHAT_SLAB_MAX)
+               {
+                  auto fhat =
+                     Reshape(&fhat_storage[0], test_vdim, test_op_dim, nq);
+                  for (int tv = 0; tv < test_vdim; tv++)
+                  {
+                     for (int tod = 0; tod < test_op_dim; tod++)
+                     {
+                        foreach_qp([&](const int qx, const int qy, const int qz)
+                        {
+                           const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+                           fhat(tv, tod, q) = 0.0;
+                        });
+                     }
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  int m_offset = 0;
+                  for_constexpr<n_inputs>([&](auto inp)
+                  {
+                     using fop_t = std::decay_t<decltype(get<inp>(inputs_ref))>;
+
+                     const int trial_op_dim =
+                        static_cast<int>(itod(static_cast<int>(inp)));
+                     if (trial_op_dim == 0) { return; }
+
+                     const auto &B = input_dtq_maps[inp].B;
+                     const auto &G = input_dtq_maps[inp].G;
+
+                     if constexpr (is_value_fop<fop_t>::value)
+                     {
+                        foreach_qp([&](const int qx, const int qy, const int qz)
+                        {
+                           const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+                           const real_t w = trial_basis_weight_value<DIM>(
+                                               B, qx, qy, qz, Jx, Jy, Jz);
+                           for (int m = 0; m < trial_op_dim; m++)
+                           {
+                              for (int i = 0; i < test_vdim; i++)
+                              {
+                                 for (int k = 0; k < test_op_dim; k++)
+                                 {
+                                    const real_t f =
+                                       qpdc(q, m + m_offset, j, row_offset + i * test_op_dim + k, e);
+                                    fhat(i, k, q) += f * w;
+                                 }
+                              }
+                           }
+                        });
+                     }
+                     else if constexpr (is_gradient_fop<fop_t>::value)
+                     {
+                        foreach_qp([&](const int qx, const int qy, const int qz)
+                        {
+                           const int q = tensor_idx<DIM>(qx, qy, qz, q1d);
+                           for (int m = 0; m < trial_op_dim; m++)
+                           {
+                              const real_t w = trial_basis_weight_gradient<DIM>(
+                                                  B, G, m, qx, qy, qz, Jx, Jy, Jz);
+                              for (int i = 0; i < test_vdim; i++)
+                              {
+                                 for (int k = 0; k < test_op_dim; k++)
+                                 {
+                                    const real_t f =
+                                       qpdc(q, m + m_offset, j, row_offset + i * test_op_dim + k, e);
+                                    fhat(i, k, q) += f * w;
+                                 }
+                              }
+                           }
+                        });
+                     }
+                     else
+                     {
+                        MFEM_ABORT_KERNEL(
+                           "sum factorized sparse matrix assemble routine "
+                           "not implemented for field operator");
+                     }
+                     MFEM_SYNC_THREAD;
+                     m_offset += trial_op_dim;
+                  });
+                  map_quadrature_data_to_fields<DIM, MQ1>(
+                     bvtfhat, fhat, output, output_dtq, smem);
+               }
+               else if constexpr (ident_out)
+               {
+                  for (int sq = 0; sq < size_on_qp; sq++)
+                  {
+                     const int tv = sq / test_op_dim;
+                     const int tod = sq % test_op_dim;
+                     zero_slab(1);
+                     accumulate_tv(Jx, Jy, Jz, j, tv, tod);
+                     auto f_slab = Reshape(&fhat_storage[0], 1, 1, nq);
+                     map_quadrature_data_to_fields<DIM, MQ1>(
+                        bvtfhat, f_slab, output, output_dtq, smem, sq);
+                  }
+               }
+               else if constexpr (grad_out)
+               {
+                  for (int tv = 0; tv < test_vdim; tv++)
+                  {
+                     zero_slab(test_op_dim);
+                     accumulate_tv(Jx, Jy, Jz, j, tv);
+                     auto f_slab =
+                        Reshape(&fhat_storage[0], 1, test_op_dim, nq);
+                     map_quadrature_data_to_fields<DIM, MQ1>(
+                        bvtfhat, f_slab, output, output_dtq, smem, tv);
+                  }
+               }
+               else
+               {
+                  for (int tv = 0; tv < test_vdim; tv++)
+                  {
+                     zero_slab(1);
+                     accumulate_tv(Jx, Jy, Jz, j, tv);
+                     auto f_slab = Reshape(&fhat_storage[0], 1, 1, nq);
+                     map_quadrature_data_to_fields<DIM, MQ1>(
+                        bvtfhat, f_slab, output, output_dtq, smem, tv);
+                  }
+               }
+            }
+         }
+      }
+   }
+}
+
+} // namespace detail
+
+// ────────────────────────────────────────────────────────────────────────────
+// Assemble sparse Jacobian from cached quadrature derivatives (tensor 2D/3D)
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeAssemble
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+
+   const IntegratorContext ctx;
+   const Vector &qp_cache;
+   inputs_t inputs;
+   outputs_t outputs;
+   const bool use_sum_factorization;
+   const std::vector<const DofToQuad *> dtqs;
+   const std::array<DofToQuadMap, n_inputs> input_dtq_maps;
+   const std::array<DofToQuadMap, n_outputs> output_dtq_maps;
+   const std::array<bool, n_inputs> input_is_dependent;
+   const size_t trial_field_uf;
+   const size_t test_field_uf;
+   const ParFiniteElementSpace *test_fes;
+   const ParFiniteElementSpace *trial_fes;
+   const int test_vdim;
+   /// Per-output row geometry of the quadrature point cache. DerivativeSetup
+   /// lays that cache out over every output FieldOperator, so reading it needs
+   /// all of them.
+   const std::array<int, n_outputs> out_vdim;
+   const std::array<int, n_outputs> out_op_dim;
+   const std::array<int, n_outputs> out_offsets;
+   const int output_size_on_qp;
+   const int num_test_dof;
+   const int trial_vdim;
+   const int trial_op_dim;
+   const int num_trial_dof;
+   const int dim, ne, nq, q1d;
+   const int num_trial_dof_1d;
+   const int total_trial_op_dim;
+   mutable Vector inputs_trial_op_dim;
+   mutable Vector Ae_mem;
+
+public:
+   DerivativeAssemble() = delete;
+
+   DerivativeAssemble(IntegratorContext ctx_in,
+                      qfunc_t /*qfunc*/,
+                      inputs_t inputs_in,
+                      outputs_t outputs_in,
+                      const Vector &qp_cache_in):
+      ctx(ctx_in), qp_cache(qp_cache_in), inputs(inputs_in),
+      outputs(outputs_in), use_sum_factorization(
+         [&]
+   {
+      const Element::Type etype =
+         Element::TypeFromGeometry(ctx_in.mesh.GetTypicalElementGeometry());
+      return (etype == Element::QUADRILATERAL || etype == Element::HEXAHEDRON);
+   }()),
+   dtqs(
+      [&]
+   {
+      const DofToQuad::Mode dtq_mode = use_sum_factorization
+      ? DofToQuad::Mode::TENSOR
+      : DofToQuad::Mode::FULL;
+      std::vector<const DofToQuad *> maps;
+      maps.reserve(ctx_in.unionfds.size());
+      for (const auto &field : ctx_in.unionfds)
+      {
+         maps.emplace_back(
+            GetDofToQuad<Entity::Element>(field, ctx_in.ir, dtq_mode));
+      }
+      return maps;
+   }()),
+   input_dtq_maps(create_dtq_maps<Entity::Element>(
+                     inputs,
+                     dtqs,
+                     create_union_field_map_for_dtq(ctx_in, inputs),
+                     ctx_in.unionfds,
+                     ctx_in.ir)),
+   output_dtq_maps(create_dtq_maps<Entity::Element>(
+                      outputs,
+                      dtqs,
+                      create_union_field_map_for_dtq(ctx_in, outputs),
+                      ctx_in.unionfds,
+                      ctx_in.ir)),
+   input_is_dependent(compute_input_is_dependent(inputs, derivative_id)),
+   trial_field_uf(find_union_field_index(ctx_in, derivative_id)),
+   test_field_uf(
+      find_union_field_index(ctx_in, get<0>(outputs).GetFieldId())),
+   test_fes(
+      [&]
+   {
+      const auto *fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[test_field_uf].data);
+      MFEM_ASSERT(fes != nullptr && *fes != nullptr,
+                  "LocalQFBackend: test space is not a ParFiniteElementSpace");
+      return *fes;
+   }()),
+   trial_fes(
+      [&]
+   {
+      const auto *fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[trial_field_uf].data);
+      MFEM_ASSERT(fes != nullptr && *fes != nullptr,
+                  "LocalQFBackend: trial space is not a ParFiniteElementSpace");
+      return *fes;
+   }()),
+   // All outputs are attached to the same test field, so vdim is common to
+   // them; only the operator dimension differs, and that lives in out_op_dim.
+   test_vdim(get<0>(outputs).vdim),
+   out_vdim(get_vdim(outputs)),
+   out_op_dim(compute_out_op_dim(outputs)),
+   out_offsets(compute_out_offsets(out_vdim, out_op_dim)),
+   output_size_on_qp(
+      [&]
+   {
+      int s = 0;
+      for_constexpr<n_outputs>([&](auto o) { s += get<o>(outputs).size_on_qp; });
+      return s;
+   }()),
+   num_test_dof(test_fes->GetFE(0)->GetDof()),
+   trial_vdim(compute_trial_vdim(inputs, derivative_id)), trial_op_dim(
+      [&]
+   {
+      int top = 0;
+      for_constexpr<n_inputs>([&](auto i)
+      {
+         if (get<i>(inputs).GetFieldId() == derivative_id)
+         {
+            top = get<i>(inputs).size_on_qp / get<i>(inputs).vdim;
+         }
+      });
+      return top;
+   }()),
+   num_trial_dof(trial_fes->GetFE(0)->GetDof()),
+   dim(ctx_in.mesh.Dimension()), ne(ctx_in.nentities),
+   nq(ctx_in.ir.GetNPoints()), q1d(tensor_1d_size(nq, dim)),
+   num_trial_dof_1d(tensor_1d_size(num_trial_dof, dim)), total_trial_op_dim(
+      [&]
+   {
+      const auto in_qp_sizes =
+      get_input_size_on_qp(inputs, std::make_index_sequence<n_inputs>{});
+      return compute_total_trial_op_dim(
+         inputs, input_is_dependent, in_qp_sizes);
+   }()),
+   inputs_trial_op_dim(), Ae_mem()
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+      MFEM_ASSERT(trial_field_uf != SIZE_MAX,
+                  "DerivativeAssemble: trial field not found in unionfds");
+      MFEM_ASSERT(test_field_uf != SIZE_MAX,
+                  "DerivativeAssemble: test field not found in unionfds");
+
+      MFEM_ASSERT(trial_vdim > 0,
+                  "LocalQFBackend: could not determine trial vdim");
+      MFEM_ASSERT(total_trial_op_dim > 0,
+                  "LocalQFBackend: no dependent inputs found");
+
+      inputs_trial_op_dim.UseDevice(true);
+      inputs_trial_op_dim.SetSize(n_inputs);
+      auto inputs_trial_op_dim_host = inputs_trial_op_dim.HostWrite();
+      for_constexpr<n_inputs>([&](auto i)
+      {
+         inputs_trial_op_dim_host[i] =
+            input_is_dependent[i]
+            ? get<i>(inputs).size_on_qp / get<i>(inputs).vdim
+            : 0;
+      });
+
+      const int elem_mat_size =
+         num_test_dof * test_vdim * num_trial_dof * trial_vdim;
+      Ae_mem.SetSize(elem_mat_size * ne, Device::GetDeviceMemoryType());
+      Ae_mem.UseDevice(true);
+      Ae_mem = 0.0;
+   }
+
+   void operator()(SparseMatrix *&A) const
+   {
+      // Every output is contracted into one element matrix Ae, sized from the
+      // test space of get<0>(outputs), and filled through a single test
+      // ElementRestriction.
+      //
+      // WIP:
+      // This takes care of single-field, multiple-outputs case.
+      // For a multiple fields case, outputs on a second field would need a second
+      // matrix -- the derivative then eould be a block column with one row block per
+      // test space.
+      //
+      // For now we just add a check that all outputs are attached to the same test field, and abort if not.
+      for_constexpr<n_outputs>([&](auto o)
+      {
+         MFEM_VERIFY(get<o>(outputs).GetFieldId() == get<0>(outputs).GetFieldId(),
+                     "DerivativeAssemble: every output FieldOperator has to be "
+                     "attached to the same test field; assembling outputs that "
+                     "span several fields is not supported");
+      });
+
+      if (ctx.attr.Size() == 0) { return; }
+
+      if (!(use_sum_factorization && (dim == 2 || dim == 3)))
+      {
+         MFEM_ABORT("DerivativeAssemble optimized path is implemented "
+                    "for tensor-product 2D/3D elements only");
+      }
+
+      DerivativeAssembleHO::Run(dim,
+                                q1d,
+                                ctx,
+                                qp_cache,
+                                Ae_mem,
+                                inputs,
+                                outputs,
+                                input_dtq_maps,
+                                output_dtq_maps,
+                                out_vdim,
+                                out_op_dim,
+                                out_offsets,
+                                output_size_on_qp,
+                                inputs_trial_op_dim,
+                                test_vdim,
+                                num_test_dof,
+                                num_trial_dof,
+                                num_trial_dof_1d,
+                                trial_vdim,
+                                total_trial_op_dim,
+                                nq,
+                                ne,
+                                q1d,
+                                dim);
+
+      A = new SparseMatrix;
+      A->OverrideSize(test_fes->GetVSize(), trial_fes->GetVSize());
+
+      const auto *test_restr = dynamic_cast<const ElementRestriction *>(
+                                  test_fes->GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC));
+      const auto *trial_restr = dynamic_cast<const ElementRestriction *>(
+                                   trial_fes->GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC));
+      MFEM_VERIFY(test_restr != nullptr && trial_restr != nullptr,
+                  "DerivativeAssemble SparseMatrix assembly requires "
+                  "H1/conforming ElementRestriction spaces");
+
+      test_restr->FillSparseMatrix(Ae_mem, *A, *trial_restr);
+   }
+
+   template<typename backend_t = LocalQFHOBackend<3>, int T_Q1D = 0>
+   static void derivative_assemble_callback(
+      const IntegratorContext &ctx,
+      const Vector &qp_cache,
+      Vector &Ae_mem,
+      const inputs_t &inputs,
+      const outputs_t &outputs,
+      const std::array<DofToQuadMap, n_inputs> &input_dtq_maps,
+      const std::array<DofToQuadMap, n_outputs> &output_dtq_maps,
+      const std::array<int, n_outputs> &out_vdim,
+      const std::array<int, n_outputs> &out_op_dim,
+      const std::array<int, n_outputs> &out_offsets,
+      const int output_size_on_qp,
+      const Vector &inputs_trial_op_dim,
+      const int test_vdim,
+      const int num_test_dof,
+      const int num_trial_dof,
+      const int num_trial_dof_1d,
+      const int trial_vdim,
+      const int total_trial_op_dim,
+      const int nq,
+      const int ne,
+      const int q1d,
+      const int dim)
+   {
+      static constexpr int DIM = backend_t::DIM;
+      static constexpr int MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+      static constexpr int MNQ = (DIM == 2) ? MQ1 * MQ1 : MQ1 * MQ1 * MQ1;
+
+      MFEM_VERIFY(dim == DIM,
+                  "DerivativeAssemble: mesh dim does not match backend");
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      MFEM_VERIFY(q1d <= MQ1, "q1d exceeds backend MQ1 limit");
+      MFEM_VERIFY(nq <= MNQ,
+                  "DerivativeAssemble: nq exceeds backend quadrature capacity");
+      for_constexpr<n_outputs>([&](auto o)
+      {
+         MFEM_VERIFY(out_op_dim[o] <= DIM,
+                     "DerivativeAssemble: test_op_dim exceeds spatial DIM");
+      });
+      if (ctx.attr.Size() == 0) { return; }
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      const auto qpdc = Reshape(qp_cache.Read(),
+                                nq,
+                                total_trial_op_dim,
+                                trial_vdim,
+                                output_size_on_qp,
+                                ne);
+      const auto itod = Reshape(inputs_trial_op_dim.Read(), n_inputs);
+
+      auto Ae = Reshape(Ae_mem.ReadWrite(),
+                        num_test_dof,
+                        test_vdim,
+                        num_trial_dof,
+                        trial_vdim,
+                        ne);
+
+      dfem::forall(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         static constexpr int DIM = backend_t::DIM;
+         static constexpr int MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+
+         static constexpr int MQN = (DIM == 2) ? MQ1 * MQ1 : MQ1 * MQ1 * MQ1;
+         static constexpr int fhat_slab_size = MQN * 4;
+
+         MFEM_SHARED typename backend_t::Shared s;
+         // One slab shared by every output. Declaring it inside the templated
+         // per-output kernel allocates one per output instead, and static
+         // shared memory is summed across instantiations on device.
+         MFEM_SHARED real_t fhat_storage[fhat_slab_size];
+
+         // Each output contributes its own rows of the cache, contracted
+         // against its own test basis operation; map_quadrature_data_to_fields
+         // accumulates, so the element matrix is the sum over outputs for the
+         // same field.
+         for_constexpr<n_outputs>([&](auto o)
+         {
+            using output_fop_t = std::decay_t<decltype(get<o>(outputs))>;
+
+            if constexpr (!is_identity_fop_v<output_fop_t>)
+            {
+               // The outputs share fhat_storage, so one has to be done with it
+               // before the next zeroes it.
+               MFEM_SYNC_THREAD;
+               detail::assemble_element_mat_sumfact<DIM, MQ1>(Ae,
+                                                              qpdc,
+                                                              e,
+                                                              itod,
+                                                              inputs,
+                                                              get<o>(outputs),
+                                                              input_dtq_maps,
+                                                              output_dtq_maps[o],
+                                                              out_offsets[o],
+                                                              out_vdim[o],
+                                                              out_op_dim[o],
+                                                              q1d,
+                                                              num_trial_dof_1d,
+                                                              fhat_storage,
+                                                              s);
+            }
+         });
+      },
+      ne,
+      backend_t::thread_blocks(q1d),
+      0,
+      nullptr);
+   }
+
+   using AssembleKernelType =
+      decltype(&DerivativeAssemble::derivative_assemble_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeAssembleHO,
+                                     AssembleKernelType,
+                                     (int, int));
+};
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline
+typename DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>::
+AssembleKernelType
+DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeAssembleHO::Kernel()
+{
+   static_assert(DIM == 2 || DIM == 3);
+   using assemble_t =
+      DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return assemble_t::template derivative_assemble_callback<
+             LocalQFHOBackend<DIM, Q1D>>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline
+typename DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>::
+AssembleKernelType
+DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeAssembleHO::Fallback(int dim, int q1d)
+{
+   using assemble_t =
+      DerivativeAssemble<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeAssembleHO = typename assemble_t::DerivativeAssembleHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeAssembleHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeAssembleHO, 3, 8>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_assemble_diagonal.hpp

@@ -0,0 +1,540 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include <array>
+
+namespace mfem::future::LocalQFImpl
+{
+
+// Assemble diagonal of cached Jacobian (square trial == test, tensor 2D/3D)
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeAssembleDiagonal
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+
+   const IntegratorContext ctx;
+   const Vector &qp_cache;
+   inputs_t inputs;
+   outputs_t outputs;
+   const bool use_sum_factorization;
+   const std::vector<const DofToQuad *> dtqs;
+   const std::array<DofToQuadMap, n_inputs> input_dtq_maps;
+   const std::array<DofToQuadMap, n_outputs> output_dtq_maps;
+   const std::array<bool, n_inputs> input_is_dependent;
+   const size_t trial_field_uf;
+   const size_t test_field_uf;
+   const bool is_square;
+   const int test_vdim;
+   const std::array<int, n_outputs> out_vdim;
+   const std::array<int, n_outputs> out_op_dim;
+   const std::array<int, n_outputs> out_offsets;
+   const int output_size_on_qp;
+   const int num_test_dof;
+   const int num_test_dof_1d;
+   const int trial_vdim;
+   const int total_trial_op_dim;
+   const int num_trial_dof_1d;
+   const int residual_size_on_qp;
+   const int dim, ne, nq, q1d;
+   const std::array<int, n_inputs> inputs_trial_op_dim;
+   mutable Vector Ye_mem;
+
+public:
+   DerivativeAssembleDiagonal() = delete;
+
+   DerivativeAssembleDiagonal(IntegratorContext ctx_in,
+                              qfunc_t /*qfunc*/,
+                              inputs_t inputs_in,
+                              outputs_t outputs_in,
+                              const Vector &qp_cache_in):
+      ctx(ctx_in), qp_cache(qp_cache_in), inputs(inputs_in),
+      outputs(outputs_in), use_sum_factorization(
+         [&]
+   {
+      const Element::Type etype =
+         Element::TypeFromGeometry(ctx_in.mesh.GetTypicalElementGeometry());
+      return (etype == Element::QUADRILATERAL || etype == Element::HEXAHEDRON);
+   }()),
+   dtqs(
+      [&]
+   {
+      const DofToQuad::Mode dtq_mode = use_sum_factorization
+      ? DofToQuad::Mode::TENSOR
+      : DofToQuad::Mode::FULL;
+      std::vector<const DofToQuad *> maps;
+      maps.reserve(ctx_in.unionfds.size());
+      for (const auto &field : ctx_in.unionfds)
+      {
+         maps.emplace_back(
+            GetDofToQuad<Entity::Element>(field, ctx_in.ir, dtq_mode));
+      }
+      return maps;
+   }()),
+   input_dtq_maps(create_dtq_maps<Entity::Element>(
+                     inputs,
+                     dtqs,
+                     create_union_field_map_for_dtq(ctx_in, inputs),
+                     ctx_in.unionfds,
+                     ctx_in.ir)),
+   output_dtq_maps(create_dtq_maps<Entity::Element>(
+                      outputs,
+                      dtqs,
+                      create_union_field_map_for_dtq(ctx_in, outputs),
+                      ctx_in.unionfds,
+                      ctx_in.ir)),
+   input_is_dependent(compute_input_is_dependent(inputs, derivative_id)),
+   trial_field_uf(find_union_field_index(ctx_in, derivative_id)),
+   test_field_uf(
+      find_union_field_index(ctx_in, get<0>(outputs).GetFieldId())),
+   is_square(
+      [&]
+   {
+      const auto *test_fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[test_field_uf].data);
+      const auto *trial_fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[trial_field_uf].data);
+      return test_fes && trial_fes && *test_fes && *trial_fes &&
+      (*test_fes == *trial_fes);
+   }()),
+   test_vdim(get<0>(outputs).vdim),
+   out_vdim(get_vdim(outputs_in)),
+   out_op_dim(compute_out_op_dim(outputs_in)),
+   out_offsets(compute_out_offsets(out_vdim, out_op_dim)),
+   output_size_on_qp(
+      [&]
+   {
+      int s = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      { s += get<o>(outputs_in).size_on_qp; });
+      return s;
+   }()), num_test_dof(
+      [&]
+   {
+      const auto *test_fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[test_field_uf].data);
+      MFEM_ASSERT(test_fes != nullptr && *test_fes != nullptr,
+                  "LocalQFBackend: test space is not a ParFiniteElementSpace");
+      return (*test_fes)->GetFE(0)->GetDof();
+   }()),
+   num_test_dof_1d(tensor_1d_size(num_test_dof, ctx_in.mesh.Dimension())),
+   trial_vdim(compute_trial_vdim(inputs, derivative_id)), total_trial_op_dim(
+      [&]
+   {
+      const auto input_size_on_qp =
+      get_input_size_on_qp(inputs, std::make_index_sequence<n_inputs>{});
+      return compute_total_trial_op_dim(
+         inputs, input_is_dependent, input_size_on_qp);
+   }()),
+   num_trial_dof_1d(
+      [&]
+   {
+      const auto *trial_fes = std::get_if<const ParFiniteElementSpace *>(
+         &ctx_in.unionfds[trial_field_uf].data);
+      MFEM_ASSERT(trial_fes != nullptr && *trial_fes != nullptr,
+                  "LocalQFBackend: trial space is not a ParFiniteElementSpace");
+      const int num_trial_dof = (*trial_fes)->GetFE(0)->GetDof();
+      return tensor_1d_size(num_trial_dof, ctx_in.mesh.Dimension());
+   }()),
+   residual_size_on_qp(output_size_on_qp * trial_vdim * total_trial_op_dim),
+   dim(ctx_in.mesh.Dimension()), ne(ctx_in.nentities),
+   nq(ctx_in.ir.GetNPoints()), q1d(tensor_1d_size(nq, dim)),
+   inputs_trial_op_dim(
+      [&]
+   {
+      std::array<int, n_inputs> itod{};
+      for_constexpr<n_inputs>([&](auto i)
+      {
+         itod[i] = input_is_dependent[i]
+                   ? get<i>(inputs).size_on_qp / get<i>(inputs).vdim
+                   : 0;
+      });
+      return itod;
+   }()),
+   Ye_mem()
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+      MFEM_ASSERT(
+         trial_field_uf != SIZE_MAX,
+         "DerivativeAssembleDiagonal: trial field not found in unionfds");
+      MFEM_ASSERT(
+         test_field_uf != SIZE_MAX,
+         "DerivativeAssembleDiagonal: test field not found in unionfds");
+      MFEM_ASSERT(trial_vdim > 0,
+                  "LocalQFBackend: could not determine trial vdim");
+      MFEM_ASSERT(total_trial_op_dim > 0,
+                  "LocalQFBackend: no dependent inputs found");
+      for_constexpr<n_outputs>([&](auto o)
+      {
+         MFEM_CONTRACT_VAR(o);
+         MFEM_ASSERT(out_vdim[o] == test_vdim,
+                     "DerivativeAssembleDiagonal: all outputs must share the "
+                     "test field vdim");
+      });
+
+      if (is_square)
+      {
+         Ye_mem.SetSize(num_test_dof * test_vdim * ne);
+         Ye_mem.UseDevice(true);
+      }
+   }
+
+   template<typename Backend>
+   void run_kernels() const
+   {
+      Backend::Run(dim,
+                   q1d,
+                   ctx,
+                   qp_cache,
+                   Ye_mem,
+                   inputs,
+                   outputs,
+                   output_dtq_maps,
+                   input_dtq_maps,
+                   test_vdim,
+                   out_op_dim,
+                   out_offsets,
+                   output_size_on_qp,
+                   num_test_dof,
+                   num_test_dof_1d,
+                   trial_vdim,
+                   total_trial_op_dim,
+                   residual_size_on_qp,
+                   inputs_trial_op_dim,
+                   nq,
+                   ne,
+                   q1d,
+                   dim);
+   }
+
+   void operator()(Vector &diag_e) const
+   {
+      if (!is_square) { return; }
+      if (ctx.attr.Size() == 0) { return; }
+
+      if (!(use_sum_factorization && (dim == 2 || dim == 3)))
+      {
+         MFEM_ABORT("DerivativeAssembleDiagonal optimized path is implemented "
+                    "for tensor-product 2D/3D elements only");
+      }
+      MFEM_VERIFY(num_test_dof_1d == num_trial_dof_1d,
+                  "DerivativeAssembleDiagonal requires matching tensor dofs");
+      MFEM_VERIFY(num_test_dof_1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+      MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+      Ye_mem = 0.0;
+
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<DerivativeAssembleDiagonalLO>();
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<DerivativeAssembleDiagonalHO>();
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+
+      diag_e += Ye_mem;
+   }
+
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void derivative_assemble_diagonal_callback(
+      const IntegratorContext &ctx,
+      const Vector &qp_cache,
+      Vector &Ye_mem,
+      const inputs_t &inputs,
+      const outputs_t &outputs,
+      const std::array<DofToQuadMap, n_outputs> &output_dtq_maps,
+      const std::array<DofToQuadMap, n_inputs> &input_dtq_maps,
+      const int test_vdim,
+      const std::array<int, n_outputs> &out_op_dim,
+      const std::array<int, n_outputs> &out_offsets,
+      const int output_size_on_qp,
+      const int num_test_dof,
+      const int num_test_dof_1d,
+      const int trial_vdim,
+      const int total_trial_op_dim,
+      const int residual_size_on_qp,
+      const std::array<int, n_inputs> &inputs_trial_op_dim,
+      const int nq,
+      const int ne,
+      const int q1d,
+      const int dim)
+   {
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      if (ctx.attr.Size() == 0) { return; }
+
+      static constexpr bool B2D = backend_t::DIM == 2;
+      static constexpr int MTPB = backend_t::MAX_THREADS_PER_BLOCK();
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      auto cache_tensor = DeviceTensor<3, const real_t>(
+                             qp_cache.Read(), nq, residual_size_on_qp, ne);
+      const int num_dofs_per_elem = num_test_dof * test_vdim;
+      auto Ye = Reshape(Ye_mem.ReadWrite(), num_dofs_per_elem, ne);
+
+      dfem::forall<MTPB>(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         // The cache is written with the quadrature index fastest, then the
+         // trial op index, then the (test vdim, test op) rows of all outputs
+         // stacked via out_offsets.
+         auto qpdc = Reshape(&cache_tensor(0, 0, e),
+                             nq,
+                             total_trial_op_dim,
+                             trial_vdim,
+                             output_size_on_qp);
+
+         // Backend-owned shared scratch for the sum-factorized contraction.
+         MFEM_SHARED typename backend_t::Shared s_diag;
+         const int nz_dof = B2D ? 1 : num_test_dof_1d;
+
+         for (int vd = 0; vd < test_vdim; vd++)
+         {
+            auto Y = Reshape(&Ye(vd * num_test_dof, e),
+                             num_test_dof_1d,
+                             num_test_dof_1d,
+                             nz_dof);
+
+            MFEM_FOREACH_THREAD(dz_t, z, nz_dof)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dy_t, y, num_test_dof_1d)
+               {
+                  MFEM_FOREACH_THREAD_DIRECT(dx_t, x, num_test_dof_1d)
+                  { Y(dx_t, dy_t, dz_t) = 0.0; }
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            // Accumulate every (output o, test op k, dependent input s,
+            // trial op m) block of the cached Jacobian into the diagonal via
+            // the backend driver.
+            for_constexpr<n_outputs>([&](auto o)
+            {
+               using test_fop_t = std::decay_t<decltype(get<o>(outputs))>;
+               const auto &out_dtq = output_dtq_maps[o];
+               const int test_op_dim = out_op_dim[static_cast<int>(o)];
+
+               // Test-basis factor along a spatial axis
+               const auto eval_test =
+                  [&](const int k, const int axis, const int q, const int d)
+               {
+                  const auto &B = out_dtq.B;
+                  const auto &G = out_dtq.G;
+                  if constexpr (is_value_fop<test_fop_t>::value)
+                  {
+                     return (k == 0) ? B(q, 0, d) : 0.0;
+                  }
+                  else if constexpr (is_gradient_fop<test_fop_t>::value)
+                  {
+                     return (k == axis) ? G(q, 0, d) : B(q, 0, d);
+                  }
+                  else
+                  {
+                     return 0.0;
+                  }
+               };
+
+               for (int k = 0; k < test_op_dim; k++)
+               {
+                  const int row =
+                     out_offsets[static_cast<int>(o)] + vd * test_op_dim + k;
+                  int m_offset = 0;
+                  for_constexpr<n_inputs>([&](auto s)
+                  {
+                     using fop_t = std::decay_t<decltype(get<s>(inputs))>;
+                     const int trial_op_dim =
+                        inputs_trial_op_dim[static_cast<int>(s)];
+                     if (trial_op_dim == 0) { return; }
+
+                     const auto &in_dtq = input_dtq_maps[s];
+                     const auto eval_input =
+                        [&](const int m, const int axis, const int q,
+                            const int d)
+                     {
+                        if constexpr (is_value_fop<fop_t>::value)
+                        {
+                           return (m == 0) ? in_dtq.B(q, 0, d) : 0.0;
+                        }
+                        else if constexpr (is_gradient_fop<fop_t>::value)
+                        {
+                           return (m == axis) ? in_dtq.G(q, 0, d)
+                                  : in_dtq.B(q, 0, d);
+                        }
+                        else
+                        {
+                           return 0.0;
+                        }
+                     };
+
+                     for (int m = 0; m < trial_op_dim; m++)
+                     {
+                        const int col = m_offset + m;
+                        backend_t::DiagContract(
+                           s_diag,
+                           num_test_dof_1d,
+                           q1d,
+                           nz_dof,
+                           [&](int axis, int q, int d)
+                        { return eval_test(k, axis, q, d); },
+                        [&](int axis, int q, int d)
+                        { return eval_input(m, axis, q, d); },
+                        [&](int q) { return qpdc(q, col, vd, row); },
+                        [&](int dx, int dy, int dz, real_t u)
+                        { Y(dx, dy, dz) += u; });
+                     }
+                     m_offset += trial_op_dim;
+                  });
+               }
+            });
+         }
+      },
+      ne,
+      backend_t::thread_blocks(std::max(q1d, num_test_dof_1d)),
+      0,
+      nullptr);
+   }
+
+   using DiagonalKernelType =
+      decltype(&DerivativeAssembleDiagonal::
+               derivative_assemble_diagonal_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeAssembleDiagonalLO,
+                                     DiagonalKernelType,
+                                     (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeAssembleDiagonalHO,
+                                     DiagonalKernelType,
+                                     (int, int) );
+};
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeAssembleDiagonal<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::DiagonalKernelType
+       DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeAssembleDiagonalLO::Kernel()
+{
+   static_assert((DIM == 2 || DIM == 3) && Q1D <= 8);
+   using diag_t =
+      DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return diag_t::template derivative_assemble_diagonal_callback<
+             LocalQFLOBackend<DIM, Q1D>>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeAssembleDiagonal<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::DiagonalKernelType
+       DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeAssembleDiagonalLO::Fallback(int dim, int q1d)
+{
+   using diag_t =
+      DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeAssembleDiagonalLO =
+      typename diag_t::DerivativeAssembleDiagonalLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<DerivativeAssembleDiagonalLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<DerivativeAssembleDiagonalLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeAssembleDiagonal<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::DiagonalKernelType
+       DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeAssembleDiagonalHO::Kernel()
+{
+   using diag_t =
+      DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return diag_t::template derivative_assemble_diagonal_callback<
+             LocalQFHOBackend<DIM>,
+             Q1D>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeAssembleDiagonal<derivative_id,
+       qfunc_t,
+       inputs_t,
+       outputs_t>::DiagonalKernelType
+       DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>::
+       DerivativeAssembleDiagonalHO::Fallback(int dim, int q1d)
+{
+   using diag_t =
+      DerivativeAssembleDiagonal<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeAssembleDiagonalHO =
+      typename diag_t::DerivativeAssembleDiagonalHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeAssembleDiagonalHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeAssembleDiagonalHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/derivative_setup.hpp

@@ -0,0 +1,600 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+
+#include "kernels.hpp"
+#include "util.hpp"
+
+#include <array>
+
+namespace mfem::future::LocalQFImpl
+{
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+class DerivativeSetup
+{
+   static constexpr auto inout_tuple =
+   merge_mfem_tuples_as_empty_std_tuple(inputs_t {}, outputs_t{});
+   static constexpr auto filtered_inout_tuple = filter_fields(inout_tuple);
+   static constexpr size_t nfields =
+      count_unique_field_ids(filtered_inout_tuple);
+
+   using qf_signature = typename get_function_signature<qfunc_t>::type;
+   using qf_param_ts = typename qf_signature::parameter_ts;
+   using args_tuple_t = decay_tuple<qf_param_ts>;
+
+   static constexpr std::size_t n_inputs = tuple_size<inputs_t>::value;
+   static constexpr std::size_t n_outputs = tuple_size<outputs_t>::value;
+   static_assert(n_inputs + n_outputs == tuple_size<qf_param_ts>::value,
+                 "LocalQF: q-function arity must match inputs + outputs");
+
+   qfunc_t qfunc;
+   const inputs_t inputs;
+   const outputs_t outputs;
+   const IntegratorContext ctx;
+   Vector &qp_cache;
+   const std::vector<const DofToQuad *> dtqs;
+   // inputs: dtq, idx, B, G, d1d, q1d, vdim
+   const std::array<DofToQuadMap, n_inputs> input_dtq;
+   const std::array<size_t, n_inputs> input_idx;
+   const std::array<const real_t *, n_inputs> input_B, input_G;
+   const std::array<int, n_inputs> input_d1d, input_q1d, input_vdim;
+   // Jacobian cache metadata
+   const std::array<bool, n_inputs> input_is_dependent;
+   const std::array<int, n_inputs> input_size_on_qp;
+   const std::array<int, n_outputs> out_vdim;
+   const std::array<int, n_outputs> out_op_dim;
+   const std::array<int, n_outputs> out_offsets;
+   const int output_size_on_qp;
+   const int trial_vdim;
+   const int total_trial_op_dim;
+   const int residual_size_on_qp;
+   // other constants
+   const int dim, ne, nq, q1d;
+
+public:
+   //////////////////////////////////////////////////////////////////
+   DerivativeSetup() = delete;
+
+   DerivativeSetup(IntegratorContext ctx,
+                   qfunc_t qfunc,
+                   inputs_t inputs,
+                   outputs_t outputs,
+                   Vector &qp_cache):
+      qfunc(std::move(qfunc)), inputs(inputs), outputs(outputs), ctx(ctx),
+      qp_cache(qp_cache), dtqs(make_dtqs(ctx)),
+      input_dtq(create_dtq_maps<Entity::Element>(
+                   inputs,
+                   dtqs,
+                   create_union_field_map_for_dtq(ctx, inputs),
+                   ctx.unionfds,
+                   ctx.ir)),
+      input_idx(create_input_vector_map(ctx, inputs)),
+      input_B(get_B(input_dtq)), input_G(get_G(input_dtq)),
+      input_d1d(get_D1D(input_dtq)), input_q1d(get_Q1D(input_dtq)),
+      input_vdim(get_vdim(inputs)),
+      input_is_dependent(compute_input_is_dependent(inputs, derivative_id)),
+      input_size_on_qp(
+         get_input_size_on_qp(inputs, std::make_index_sequence<n_inputs> {})),
+                           out_vdim(get_vdim(outputs)), out_op_dim(compute_out_op_dim(outputs)),
+                           out_offsets(compute_out_offsets(out_vdim, out_op_dim)), output_size_on_qp(
+                              [&]
+   {
+      int s = 0;
+      for_constexpr<n_outputs>([&](auto o)
+      { s += get<o>(outputs).size_on_qp; });
+      return s;
+   }()),
+   trial_vdim(compute_trial_vdim(inputs, derivative_id)),
+   total_trial_op_dim(compute_total_trial_op_dim(
+                         inputs, input_is_dependent, input_size_on_qp)),
+   residual_size_on_qp(output_size_on_qp * trial_vdim * total_trial_op_dim),
+   dim(ctx.mesh.Dimension()), ne(ctx.nentities), nq(ctx.ir.GetNPoints()),
+   q1d(tensor_1d_size(nq, dim))
+   {
+      MFEM_ASSERT(ctx.unionfds.size() == nfields,
+                  "LocalQFBackend: unionfds size mismatch");
+
+      qp_cache.SetSize(ne * nq * residual_size_on_qp);
+      qp_cache.UseDevice(true);
+   }
+
+   //////////////////////////////////////////////////////////////////
+   void operator()(const std::vector<Vector *> &xe)
+   {
+      if (ctx.attr.Size() == 0) { return; }
+
+      // Quadrature index is fastest-varying so that adjacent threads (one per
+      // quadrature point) touch adjacent addresses.
+      auto cache_tensor = DeviceTensor<3, real_t>(
+                             qp_cache.ReadWrite(), nq, residual_size_on_qp, ne);
+
+      if (q1d <= LocalQFLOBackendMQ1())
+      {
+         run_kernels<DerivativeSetupLO>(xe, cache_tensor);
+      }
+      else if (q1d <= LocalQFHOBackendMQ1())
+      {
+         run_kernels<DerivativeSetupHO>(xe, cache_tensor);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported quadrature order for LocalQF backend");
+      }
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename Backend>
+   void run_kernels(const std::vector<Vector *> &xe,
+                    DeviceTensor<3, real_t> &cache_tensor)
+   {
+      Backend::Run(dim,
+                   q1d,
+                   ctx,
+                   qfunc,
+                   // inputs
+                   input_idx,
+                   input_B,
+                   input_G,
+                   input_vdim,
+                   input_d1d,
+                   input_q1d,
+                   input_size_on_qp,
+                   input_is_dependent,
+                   // outputs / cache metadata
+                   out_vdim,
+                   out_op_dim,
+                   out_offsets,
+                   trial_vdim,
+                   total_trial_op_dim,
+                   residual_size_on_qp,
+                   // vectors
+                   xe,
+                   cache_tensor,
+                   // fallback arguments
+                   dim,
+                   q1d);
+   }
+
+   //////////////////////////////////////////////////////////////////
+   /// Zeroes the q-function *output* slots of an argument tuple.
+   ///
+   /// The argument tuple is built once per quadrature point and reused for
+   /// every trial seed. The q-function writes through its output parameters,
+   /// so those slots have to be restored before each call to give every seed
+   /// the same starting state a freshly value-initialized tuple would.
+   static MFEM_HOST_DEVICE inline void reset_output_args(args_tuple_t &args)
+   {
+      for_constexpr<n_outputs>([&](auto oc)
+      {
+         constexpr size_t ao = n_inputs + oc.value;
+         auto &oarg = get<ao>(args);
+         oarg = std::remove_reference_t<decltype(oarg)> {};
+      });
+   }
+
+   //////////////////////////////////////////////////////////////////
+   template<typename backend_t = LocalQFLOBackend<3>, int T_Q1D = 0>
+   static void
+   derivative_setup_callback(const IntegratorContext &ctx,
+                             qfunc_t &qfunc,
+                             // inputs: idx, B, G, vdim, d1d, q1d
+                             const std::array<size_t, n_inputs> &in_idx,
+                             const std::array<const real_t *, n_inputs> in_B,
+                             const std::array<const real_t *, n_inputs> in_G,
+                             const std::array<int, n_inputs> &in_vdim,
+                             const std::array<int, n_inputs> &in_d1d,
+                             const std::array<int, n_inputs> &in_q1d,
+                             const std::array<int, n_inputs> &in_size_on_qp,
+                             const std::array<bool, n_inputs> &input_dep,
+                             // outputs / cache metadata
+                             const std::array<int, n_outputs> &out_vdim,
+                             const std::array<int, n_outputs> &out_op_dim,
+                             const std::array<int, n_outputs> &out_offsets,
+                             const int trial_vdim,
+                             const int total_trial_op_dim,
+                             const int residual_size_on_qp,
+                             const std::vector<Vector *> &xe,
+                             DeviceTensor<3, real_t> &cache_tensor,
+                             // fallback arguments
+                             const int dim,
+                             const int q1d)
+   {
+      MFEM_VERIFY(dim == ctx.mesh.Dimension(), "Dimension mismatch");
+      if (ctx.attr.Size() == 0) { return; }
+
+      static constexpr auto B2D = backend_t::DIM == 2;
+      static constexpr auto MQ1 = T_Q1D ? T_Q1D : backend_t::MQ1;
+      static constexpr auto MTPB = backend_t::MAX_THREADS_PER_BLOCK();
+
+      const int ne = ctx.nentities;
+      MFEM_CONTRACT_VAR(residual_size_on_qp);
+
+      constexpr auto k_dim = [](const int k) { return k * k * (B2D ? 1 : k); };
+
+      // --------------------------------------------------
+      // INPUTS: XE, 3(max DIM) + 1(VDIM) + 1(number of elements)
+      // --------------------------------------------------
+      std::array<DeviceTensor<3 + 1 + 1, const real_t>, n_inputs> in_XE;
+      for_constexpr<n_inputs>([&](auto ic)
+      {
+         constexpr size_t i = ic.value;
+         const size_t k = in_idx[i];
+         const int d = in_d1d[i], q = in_q1d[i], v = in_vdim[i];
+         using FOP = tuple_element_t<i, inputs_t>;
+         if constexpr (is_value_fop_v<FOP> || is_gradient_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(d) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), d, d, B2D ? 1 : d, v, ne);
+         }
+         else if constexpr (is_identity_fop_v<FOP>)
+         {
+            MFEM_VERIFY(xe[k]->Size() == k_dim(q) * v * ne, "Size mismatch");
+            in_XE[i] = Reshape(xe[k]->Read(), v, q, q, B2D ? 1 : q, ne);
+         }
+         else if constexpr (is_weight_fop_v<FOP>)
+         {
+            MFEM_VERIFY(ctx.ir.GetNPoints() == k_dim(q1d),
+                        "tensor-product IR expected");
+            in_XE[i] = Reshape(
+                          ctx.ir.GetWeights().Read(), q1d, q1d, B2D ? 1 : q1d, 1, 1);
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      });
+
+      const auto d_attr = ctx.attr.Read();
+      const bool has_attr = ctx.attr.Size() > 0;
+      const auto d_elem_attr = ctx.elem_attr->Read();
+
+      dfem::forall<MTPB>(
+         [=] MFEM_HOST_DEVICE(const int e, void *)
+      {
+         if (has_attr && !d_attr[d_elem_attr[e] - 1]) { return; }
+
+         // -----------------------------------------------
+         // Inputs argument registers + shared memory
+         // -----------------------------------------------
+         input_args_reg_t<backend_t, qfunc_t, inputs_t, outputs_t, MQ1> rargs;
+         MFEM_SHARED typename backend_t::Shared smem;
+
+         // -----------------------------------------------
+         // Load primal inputs (rargs) once for this element
+         // -----------------------------------------------
+         for_constexpr<n_inputs>([&](auto ic)
+         {
+            constexpr size_t i = ic.value;
+            const auto &XE = in_XE[i];
+            const int d = in_d1d[i], q = in_q1d[i], Q1D = q1d;
+            const real_t *B = in_B[i], *G = in_G[i];
+            auto &rarg = get<i>(rargs);
+            using XE_t = decltype(XE);
+            using rarg_t = decltype(rarg);
+            using FOP = tuple_element_t<i, inputs_t>;
+            if constexpr (is_value_fop<FOP>::value)
+            {
+               backend_t::template LoadValue<rarg_t, XE_t>(
+                  smem, e, d, q, Q1D, B, XE, rarg);
+            }
+            else if constexpr (is_gradient_fop_v<FOP>)
+            {
+               constexpr auto RNK = qf_param_slot<qfunc_t, i>::extents.size();
+               using FieldParamT =
+                  typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+               backend_t::template LoadGradient<RNK, rarg_t, XE_t, FieldParamT>(
+                  smem, e, d, q, q1d, B, G, XE, rarg);
+            }
+            else if constexpr (is_weight_fop_v<FOP> || is_identity_fop_v<FOP>)
+            {
+               // qp values are read directly from in_XE / IR
+            }
+            else
+            {
+               static_assert(false, "Unsupported");
+            }
+         });
+         MFEM_SYNC_THREAD;
+
+         // -----------------------------------------------
+         // Build the primal arguments once per quadrature point, then, for
+         // each trial seed (j, dependent input s, m), differentiate the
+         // q-function with a unit tangent and store the result row in the
+         // cache. Nothing in the primal pull depends on the seed, so the
+         // thread loop is the outermost one here. The seed loops only touch
+         // per-thread state, hence no barrier inside them.
+         // Warning: no 'DIRECT' on the 'Z' direction,
+         // as one backend may need to iterate over it.
+         // -----------------------------------------------
+         MFEM_FOREACH_THREAD(qz, z, (B2D ? 1 : q1d))
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+               {
+                  const int q = qx + q1d * (qy + q1d * qz);
+#ifdef MFEM_USE_ENZYME
+                  args_tuple_t primal_args {};
+                  for_constexpr<n_inputs>([&](auto ic)
+                  {
+                     constexpr size_t i = ic.value;
+                     auto &parg = get<i>(primal_args);
+                     const auto &XE = in_XE[i];
+                     using FOP = tuple_element_t<i, inputs_t>;
+                     using ARG =
+                        typename qf_param_slot<qfunc_t, i>::qf_reg_param_t;
+                     if constexpr (is_identity_fop_v<FOP>)
+                     {
+                        parg = as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+                     }
+                     else if constexpr (is_weight_fop_v<FOP>)
+                     {
+                        parg = XE(qx, qy, qz, 0, 0);
+                     }
+                     else if constexpr (is_value_fop_v<FOP> ||
+                                        is_gradient_fop_v<FOP>)
+                     {
+                        parg = backend_t::template qp_pull<ARG>(
+                           get<i>(rargs), qx, qy, qz);
+                     }
+                     else
+                     {
+                        static_assert(false, "Unsupported");
+                     }
+                  });
+
+                  for (int j = 0; j < trial_vdim; j++)
+                  {
+                     int m_offset = 0;
+                     for_constexpr<n_inputs>([&](auto sc)
+                     {
+                        constexpr size_t s = sc.value;
+                        if (!input_dep[s]) { return; }
+
+                        const int vdim_s = in_vdim[s];
+                        const int op_dim_s = in_size_on_qp[s] / vdim_s;
+
+                        for (int m = 0; m < op_dim_s; m++)
+                        {
+                           const int col_m = m + m_offset;
+
+                           // Enzyme writes through the output slots of the
+                           // primal tuple, so they are reset per seed.
+                           reset_output_args(primal_args);
+
+                           args_tuple_t shadow_args {};
+                           qf_set_value_at(get<s>(shadow_args), j, m, 1.0);
+
+                           call_enzyme_fwddiff(qfunc, primal_args, shadow_args);
+
+                           for_constexpr<n_outputs>([&](auto oc)
+                           {
+                              constexpr size_t o = oc.value, ao = n_inputs + o;
+                              const auto &tangent = get<ao>(shadow_args);
+                              const int tv = out_vdim[o], to = out_op_dim[o];
+                              for (int i = 0; i < tv; i++)
+                              {
+                                 for (int k = 0; k < to; k++)
+                                 {
+                                    const int row = out_offsets[o] + i * to + k;
+                                    const int cache_idx =
+                                       row * trial_vdim * total_trial_op_dim +
+                                       j * total_trial_op_dim + col_m;
+                                    cache_tensor(q, cache_idx, e) =
+                                       qf_value_at(tangent, i, k);
+                                 }
+                              }
+                           });
+                        }
+                        m_offset += op_dim_s;
+                     });
+                  }
+#else  // MFEM_USE_ENZYME
+                  args_tuple_t qargs {};
+                  for_constexpr<n_inputs>([&](auto ic)
+                  {
+                     constexpr size_t i = ic.value;
+                     auto &qarg = get<i>(qargs);
+                     const auto &XE = in_XE[i];
+                     using FOP = tuple_element_t<i, inputs_t>;
+                     using ARG =
+                        typename qf_param_slot<qfunc_t, i>::qf_reg_param_t;
+                     if constexpr (is_identity_fop_v<FOP>)
+                     {
+                        using DT =
+                           typename qf_param_slot<qfunc_t, i>::qf_decay_param_t;
+                        if constexpr (qf_param_uses_dual_v<DT>)
+                        {
+                           qarg = backend_t::template identity_qp_pull_dual<DT>(
+                              false, XE, XE, qx, qy, qz, e);
+                        }
+                        else
+                        {
+                           qarg = as_tensor<ARG>(&XE(0, qx, qy, qz, e));
+                        }
+                     }
+                     else if constexpr (is_weight_fop_v<FOP>)
+                     {
+                        qarg = XE(qx, qy, qz, 0, 0);
+                     }
+                     else if constexpr (is_value_fop_v<FOP> ||
+                                        is_gradient_fop_v<FOP>)
+                     {
+                        qarg = backend_t::template qp_pull<ARG>(
+                           get<i>(rargs), qx, qy, qz);
+                     }
+                     else
+                     {
+                        static_assert(false, "Unsupported");
+                     }
+                  });
+
+                  for (int j = 0; j < trial_vdim; j++)
+                  {
+                     int m_offset = 0;
+                     for_constexpr<n_inputs>([&](auto sc)
+                     {
+                        constexpr size_t s = sc.value;
+                        if (!input_dep[s]) { return; }
+
+                        const int vdim_s = in_vdim[s];
+                        const int op_dim_s = in_size_on_qp[s] / vdim_s;
+
+                        for (int m = 0; m < op_dim_s; m++)
+                        {
+                           const int col_m = m + m_offset;
+
+                           // The q-function writes through the output slots,
+                           // so they are reset per seed.
+                           reset_output_args(qargs);
+
+                           qf_set_gradient_at(get<s>(qargs), j, m, 1.0);
+
+                           call_qfunc_no_move(qfunc, qargs);
+
+                           for_constexpr<n_outputs>([&](auto oc)
+                           {
+                              constexpr size_t o = oc.value, ao = n_inputs + o;
+                              const auto &tangent = get<ao>(qargs);
+                              const int tv = out_vdim[o], to = out_op_dim[o];
+                              for (int i = 0; i < tv; i++)
+                              {
+                                 for (int k = 0; k < to; k++)
+                                 {
+                                    const int row = out_offsets[o] + i * to + k;
+                                    const int cache_idx =
+                                       row * trial_vdim * total_trial_op_dim +
+                                       j * total_trial_op_dim + col_m;
+                                    cache_tensor(q, cache_idx, e) =
+                                       qf_gradient_at(tangent, i, k);
+                                 }
+                              }
+                           });
+
+                           // Clear the seed so the next direction starts from
+                           // the pristine (zero-tangent) primal state.
+                           qf_set_gradient_at(get<s>(qargs), j, m, 0.0);
+                        }
+                        m_offset += op_dim_s;
+                     });
+                  }
+#endif // MFEM_USE_ENZYME
+               }
+            }
+         }
+      },
+      ne,
+      backend_t::thread_blocks(
+         compute_kernel_thread_1d<inputs_t>(q1d, in_d1d)),
+      0,
+      nullptr);
+   }
+
+   using SetupKernelType =
+      decltype(&DerivativeSetup::derivative_setup_callback<>);
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeSetupLO,
+                                     SetupKernelType,
+                                     (int, int) );
+   MFEM_REGISTER_KERNELS_HEADER_ONLY(DerivativeSetupHO,
+                                     SetupKernelType,
+                                     (int, int) );
+};
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+SetupKernelType
+DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeSetupLO::Kernel()
+{
+   static_assert((DIM == 2 || DIM == 3) && Q1D <= 8);
+   using setup_t = DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return setup_t::template derivative_setup_callback<
+             LocalQFLOBackend<DIM, Q1D>>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+SetupKernelType
+DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeSetupLO::Fallback(int dim, int q1d)
+{
+   using setup_t = DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeSetupLO = typename setup_t::DerivativeSetupLO;
+   if (dim == 2)
+   {
+      return DispatchLOKernelByQ1D<DerivativeSetupLO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchLOKernelByQ1D<DerivativeSetupLO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+template<int DIM, int Q1D>
+inline typename DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+SetupKernelType
+DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeSetupHO::Kernel()
+{
+   using setup_t = DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   return setup_t::template derivative_setup_callback<LocalQFHOBackend<DIM>,
+                                                      Q1D>;
+}
+
+template<int derivative_id,
+         typename qfunc_t,
+         typename inputs_t,
+         typename outputs_t>
+inline typename DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+SetupKernelType
+DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>::
+DerivativeSetupHO::Fallback(int dim, int q1d)
+{
+   using setup_t = DerivativeSetup<derivative_id, qfunc_t, inputs_t, outputs_t>;
+   using DerivativeSetupHO = typename setup_t::DerivativeSetupHO;
+   if (dim == 2)
+   {
+      return DispatchHOKernelByQ1D<DerivativeSetupHO, 2>(q1d);
+   }
+   else if (dim == 3)
+   {
+      return DispatchHOKernelByQ1D<DerivativeSetupHO, 3>(q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+      return nullptr;
+   }
+}
+
+} // namespace mfem::future::LocalQFImpl

fem/dfem/backends/local_qf/fwddiff_transformer.hpp

@@ -0,0 +1,277 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../util.hpp"
+
+#ifdef MFEM_USE_ENZYME
+
+namespace mfem::future
+{
+
+template <typename T> struct function_traits;
+
+template <typename R, typename C, typename... Args>
+struct function_traits<R (C::*)(Args...) const>
+{
+   using primal_return_type = R;
+   using args_tuple = std::tuple<Args...>;
+   static constexpr size_t arity = sizeof...(Args);
+};
+
+// Component count and writable counterpart of a per-point argument, which
+// is either a tensor or a plain scalar.
+template <typename Arg> struct qp_traits
+{
+   static_assert(std::is_arithmetic_v<Arg>,
+                 "per-point arguments must be tensors or scalars");
+   using view_type = Arg;
+   static constexpr int components = 1;
+};
+
+template <typename T, int... Sizes> struct qp_traits<tensor<T, Sizes...>>
+{
+   using view_type = tensor<std::remove_const_t<T>, Sizes...>;
+   static constexpr int components = (Sizes * ... * 1);
+};
+
+// Generic FwdDiff: computes the full gradient of a pointwise qfunction at a
+// single quadrature point.
+//
+// active_input is the index of the argument to differentiate with respect
+// to; active_output is the index of the (scalar) output argument whose
+// derivative is taken.
+//
+// operator()(args...) takes the qfunction's arguments, except that the
+// active output position receives the *gradient*, shaped like the active
+// input (d(output)/d(input component)).
+//
+// Per input component d, one enzyme fwddiff call with the one-hot seed e_d
+// in the input tangent yields gradient entry d, i.e. grad_components enzyme
+// calls per point. The output tangent is not pre-zeroed, so the qfunction
+// must fully write its output (tangent stores overwrite).
+//
+// operator() is MFEM_HOST_DEVICE, stateless and allocation-free, so it is
+// callable inside a GPU kernel: seed, primal scratch and tangent all live
+// on the stack.
+template <typename Func, size_t active_input, size_t active_output>
+struct FwdDiff
+{
+   using traits = function_traits<decltype(&Func::operator())>;
+   using args_tuple = typename traits::args_tuple;
+   static constexpr size_t arity = traits::arity;
+
+   static_assert(std::is_void_v<typename traits::primal_return_type>,
+                 "FwdDiff only supports primal functions with void return type");
+   static_assert(active_input < arity && active_output < arity,
+                 "active argument indices must be within the function arity");
+   static_assert(active_input != active_output,
+                 "active input and output must be different arguments");
+
+   using input_type =
+      std::decay_t<std::tuple_element_t<active_input, args_tuple>>;
+   using output_type =
+      std::decay_t<std::tuple_element_t<active_output, args_tuple>>;
+
+   using grad_type = typename qp_traits<input_type>::view_type;
+   using output_view = typename qp_traits<output_type>::view_type;
+
+   static constexpr int grad_components = qp_traits<input_type>::components;
+
+   static_assert(qp_traits<output_type>::components == 1,
+                 "gradient output requires a scalar output");
+
+   // Signature of the differentiated qfunction: the primal arguments, with
+   // the Active output slot receiving the (writable) gradient instead.
+   // Exposed through create_function_signature below so that
+   // DifferentiableOperator can deduce the parameter types, which it cannot
+   // do from the variadic operator().
+   template <size_t I>
+   using qf_arg_t = std::conditional_t<I == active_output, grad_type &,
+         std::tuple_element_t<I, args_tuple>>;
+
+   template <size_t... Is>
+   static FunctionSignature<void(qf_arg_t<Is>...)>
+   signature_impl(std::index_sequence<Is...>);
+
+   using signature =
+      decltype(signature_impl(std::make_index_sequence<arity> {}));
+
+   // d-th scalar of a per-point argument in flat row-major order, regardless
+   // of rank, built on the native operator[] (tensor has no flat-index
+   // accessor; flatten() returns a copy, so it cannot be written through).
+   MFEM_HOST_DEVICE static double &component(double &t, int) { return t; }
+
+   template <typename T, int n0, int... n>
+   MFEM_HOST_DEVICE static T &component(tensor<T, n0, n...> &t, int d)
+   {
+      if constexpr (sizeof...(n) == 0)
+      {
+         return t[d];
+      }
+      else
+      {
+         constexpr int stride = (n * ... * 1);
+         return component(t[d / stride], d % stride);
+      }
+   }
+
+   // Plain function with the qfunction's exact (reference) signature, so it
+   // can be handed to Enzyme as a function pointer; references are pointers
+   // to Enzyme, so primal arguments and shadows are passed by address below.
+   template <size_t... Is>
+   MFEM_HOST_DEVICE static void
+   static_call(std::tuple_element_t<Is, args_tuple>... args)
+   {
+      Func{}(args...);
+   }
+
+   template <size_t... Is>
+   static constexpr auto fn_ptr(std::index_sequence<Is...>)
+   {
+      return &static_call<Is...>;
+   }
+   static constexpr auto fn()
+   {
+      return fn_ptr(std::make_index_sequence<arity> {});
+   }
+
+   // Writable, zero-initialized scratch with the shape of argument I, used
+   // as its enzyme shadow.
+   template <size_t I>
+   using shadow_t = typename qp_traits<
+                    std::decay_t<std::tuple_element_t<I, args_tuple>>>::view_type;
+
+   template <size_t... Is>
+   MFEM_HOST_DEVICE static auto make_shadows(std::index_sequence<Is...>)
+   {
+      return mfem::future::make_tuple(shadow_t<Is> {}...);
+   }
+
+   template <typename Shadows, size_t... Is>
+   MFEM_HOST_DEVICE static auto make_shadow_ptrs(Shadows &shadows,
+                                                 std::index_sequence<Is...>)
+   {
+      return mfem::future::make_tuple(&mfem::future::get<int(Is)>(shadows)...);
+   }
+
+   // The caller's argument pointers, except the active output slot, which
+   // points to scalar scratch: the caller's slot holds the gradient, while
+   // the primal function writes its scalar output there.
+   template <size_t I, typename Ptrs>
+   MFEM_HOST_DEVICE static auto primal_ptr(Ptrs &ptrs, output_view &primal)
+   {
+      if constexpr (I == active_output) { return &primal; }
+      else { return mfem::future::get<int(I)>(ptrs); }
+   }
+
+   template <typename Ptrs, size_t... Is>
+   MFEM_HOST_DEVICE static auto make_primal_ptrs(Ptrs &ptrs,
+                                                 output_view &primal,
+                                                 std::index_sequence<Is...>)
+   {
+      return mfem::future::make_tuple(primal_ptr<Is>(ptrs, primal)...);
+   }
+
+   // Single flat enzyme call. The activity markers must appear directly in
+   // the __enzyme_fwddiff argument list — Enzyme cannot trace markers that
+   // were forwarded through function parameters (e.g. at -O0, where nothing
+   // is inlined). Every argument is therefore enzyme_dup'd in one sticky
+   // group; Const arguments simply carry a zero tangent, which is equivalent
+   // to marking them enzyme_const.
+   //
+   // always_inline is load-bearing: when FwdDiff is itself differentiated
+   // (second derivatives, forward-over-forward), Enzyme only recognizes this
+   // nested __enzyme_fwddiff call if it sits at most one call level below
+   // the function handed to the outer __enzyme_fwddiff. Without inlining
+   // (-O0) it sits two levels down (wrapper -> operator() -> call_enzyme)
+   // and the outer pass treats it as a regular call: the activity marker
+   // ints then receive undef shadows, which misaligns the argument pairing
+   // (observed as "cannot compute with global variable that doesn't have
+   // marked shadow global" at compile time or null-shadow segfaults at
+   // runtime). The always-inliner runs even at -O0, hoisting this call into
+   // operator() where the nested handling applies.
+   template <typename PrimalPtrs, typename ShadowPtrs, size_t... Is>
+   MFEM_FUTURE_ALWAYS_INLINE
+   MFEM_HOST_DEVICE static void call_enzyme(PrimalPtrs &primal_ptrs,
+                                            ShadowPtrs &shadow_ptrs,
+                                            std::index_sequence<Is...>)
+   {
+      __enzyme_fwddiff<void>(fn(), enzyme_dup,
+                             mfem::future::get<int(Is)>(primal_ptrs)...,
+                             enzyme_interleave,
+                             mfem::future::get<int(Is)>(shadow_ptrs)...,
+                             enzyme_runtime_activity);
+   }
+
+   template <typename... Args>
+   MFEM_HOST_DEVICE void operator()(Args &&...args) const
+   {
+      static_assert(sizeof...(Args) == arity, "Wrong number of arguments");
+      auto ptrs = mfem::future::make_tuple(&args...);
+
+      auto &grad = *mfem::future::get<int(active_output)>(ptrs);
+      static_assert(std::is_same_v<std::decay_t<decltype(grad)>, grad_type>,
+                    "gradient argument must be shaped like the Active input "
+                    "(with writable scalars)");
+
+      constexpr auto seq = std::make_index_sequence<arity> {};
+
+      output_view primal{};
+      auto primal_ptrs = make_primal_ptrs(ptrs, primal, seq);
+
+      auto shadows = make_shadows(seq);
+      auto shadow_ptrs = make_shadow_ptrs(shadows, seq);
+      auto &seed = mfem::future::get<int(active_input)>(shadows);
+      auto &tangent = mfem::future::get<int(active_output)>(shadows);
+
+      // One enzyme call per input component d: seed e_d in the input tangent
+      // and read gradient entry d off the output tangent.
+      for (int d = 0; d < grad_components; d++)
+      {
+         component(seed, d) = 1.0;
+         call_enzyme(primal_ptrs, shadow_ptrs, seq);
+         component(grad, d) = component(tangent, 0);
+         component(seed, d) = 0.0;
+      }
+   }
+
+   static void print() { print_impl(std::make_index_sequence<arity> {}); }
+
+   template <size_t... Is> static void print_impl(std::index_sequence<Is...>)
+   {
+      mfem::out << "for d in [0, " << grad_components
+                << "): __enzyme_fwddiff<void>(fptr, enzyme_dup";
+      ((mfem::out << ", "
+        << get_type_name<std::tuple_element_t<Is, args_tuple>>()),
+       ...);
+      mfem::out << ", enzyme_interleave";
+      (([&]
+      {
+         if constexpr (Is == active_input) { mfem::out << ", e_d seed"; }
+         else if constexpr (Is == active_output) { mfem::out << ", tangent out"; }
+         else { mfem::out << ", zero tangent"; }
+      }()),
+      ...);
+      mfem::out << ")\n";
+   }
+};
+
+template <typename Func, size_t active_input, size_t active_output>
+struct create_function_signature<FwdDiff<Func, active_input, active_output>>
+{
+   using type =
+      typename FwdDiff<Func, active_input, active_output>::signature;
+};
+
+} // namespace mfem::future
+
+#endif // MFEM_USE_ENZYME

fem/dfem/backends/local_qf/kernels.cpp

@@ -0,0 +1,83 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+// Explicit instantiation of the local Q-function backend device code
+
+#include "../../../../config/config.hpp"
+
+#ifdef MFEM_USE_MPI
+
+#include "kernels.hpp"
+
+namespace mfem::future
+{
+
+// ────────────────────────────────────────────────────────────────────────────
+// Low-order backends instantiations for (DIM, Q1D)
+// ────────────────────────────────────────────────────────────────────────────
+template struct lo_ker_backend<2, 2>;
+template struct lo_ker_backend<2, 3>;
+template struct lo_ker_backend<2, 4>;
+template struct lo_ker_backend<2, 5>;
+template struct lo_ker_backend<2, 6>;
+template struct lo_ker_backend<2, 7>;
+template struct lo_ker_backend<2, 8>;
+
+template struct lo_ker_backend<3, 2>;
+template struct lo_ker_backend<3, 3>;
+template struct lo_ker_backend<3, 4>;
+template struct lo_ker_backend<3, 5>;
+template struct lo_ker_backend<3, 6>;
+template struct lo_ker_backend<3, 7>;
+template struct lo_ker_backend<3, 8>;
+
+template struct LocalQFLOBackend<2, 2>;
+template struct LocalQFLOBackend<2, 3>;
+template struct LocalQFLOBackend<2, 4>;
+template struct LocalQFLOBackend<2, 5>;
+template struct LocalQFLOBackend<2, 6>;
+template struct LocalQFLOBackend<2, 7>;
+template struct LocalQFLOBackend<2, 8>;
+
+template struct LocalQFLOBackend<3, 2>;
+template struct LocalQFLOBackend<3, 3>;
+template struct LocalQFLOBackend<3, 4>;
+template struct LocalQFLOBackend<3, 5>;
+template struct LocalQFLOBackend<3, 6>;
+template struct LocalQFLOBackend<3, 7>;
+template struct LocalQFLOBackend<3, 8>;
+
+// ────────────────────────────────────────────────────────────────────────────
+// High-order backends instantiations for (DIM, Q1D)
+// ────────────────────────────────────────────────────────────────────────────
+template struct ho_ker_backend<2, 8>;
+template struct ho_ker_backend<2, 10>;
+template struct ho_ker_backend<2, 12>;
+template struct ho_ker_backend<2, 16>;
+
+template struct ho_ker_backend<3, 8>;
+template struct ho_ker_backend<3, 10>;
+template struct ho_ker_backend<3, 12>;
+template struct ho_ker_backend<3, 16>;
+
+template struct LocalQFHOBackend<2, 8>;
+template struct LocalQFHOBackend<2, 10>;
+template struct LocalQFHOBackend<2, 12>;
+template struct LocalQFHOBackend<2, 16>;
+
+template struct LocalQFHOBackend<3, 8>;
+template struct LocalQFHOBackend<3, 10>;
+template struct LocalQFHOBackend<3, 12>;
+template struct LocalQFHOBackend<3, 16>;
+
+} // namespace mfem::future
+
+#endif // MFEM_USE_MPI

fem/dfem/backends/local_qf/kernels.hpp

@@ -0,0 +1,77 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "kernels_lo.hpp" // IWYU pragma: export
+#include "kernels_ho.hpp" // IWYU pragma: export
+
+namespace mfem::future
+{
+
+// ────────────────────────────────────────────────────────────────────────────
+// Low-order backends instantiations for (DIM, Q1D)
+// ────────────────────────────────────────────────────────────────────────────
+extern template struct lo_ker_backend<2, 2>;
+extern template struct lo_ker_backend<2, 3>;
+extern template struct lo_ker_backend<2, 4>;
+extern template struct lo_ker_backend<2, 5>;
+extern template struct lo_ker_backend<2, 6>;
+extern template struct lo_ker_backend<2, 7>;
+extern template struct lo_ker_backend<2, 8>;
+
+extern template struct lo_ker_backend<3, 2>;
+extern template struct lo_ker_backend<3, 3>;
+extern template struct lo_ker_backend<3, 4>;
+extern template struct lo_ker_backend<3, 5>;
+extern template struct lo_ker_backend<3, 6>;
+extern template struct lo_ker_backend<3, 7>;
+extern template struct lo_ker_backend<3, 8>;
+
+extern template struct LocalQFLOBackend<2, 2>;
+extern template struct LocalQFLOBackend<2, 3>;
+extern template struct LocalQFLOBackend<2, 4>;
+extern template struct LocalQFLOBackend<2, 5>;
+extern template struct LocalQFLOBackend<2, 6>;
+extern template struct LocalQFLOBackend<2, 7>;
+extern template struct LocalQFLOBackend<2, 8>;
+
+extern template struct LocalQFLOBackend<3, 2>;
+extern template struct LocalQFLOBackend<3, 3>;
+extern template struct LocalQFLOBackend<3, 4>;
+extern template struct LocalQFLOBackend<3, 5>;
+extern template struct LocalQFLOBackend<3, 6>;
+extern template struct LocalQFLOBackend<3, 7>;
+extern template struct LocalQFLOBackend<3, 8>;
+
+// ────────────────────────────────────────────────────────────────────────────
+// High-order backends instantiations for (DIM, Q1D)
+// ────────────────────────────────────────────────────────────────────────────
+extern template struct ho_ker_backend<2, 8>;
+extern template struct ho_ker_backend<2, 10>;
+extern template struct ho_ker_backend<2, 12>;
+extern template struct ho_ker_backend<2, 16>;
+
+extern template struct ho_ker_backend<3, 8>;
+extern template struct ho_ker_backend<3, 10>;
+extern template struct ho_ker_backend<3, 12>;
+extern template struct ho_ker_backend<3, 16>;
+
+extern template struct LocalQFHOBackend<2, 8>;
+extern template struct LocalQFHOBackend<2, 10>;
+extern template struct LocalQFHOBackend<2, 12>;
+extern template struct LocalQFHOBackend<2, 16>;
+
+extern template struct LocalQFHOBackend<3, 8>;
+extern template struct LocalQFHOBackend<3, 10>;
+extern template struct LocalQFHOBackend<3, 12>;
+extern template struct LocalQFHOBackend<3, 16>;
+
+} // namespace mfem::future

fem/dfem/backends/local_qf/kernels_ho.hpp

@@ -0,0 +1,803 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../../kernels.hpp"
+namespace ker = mfem::kernels::internal;
+
+#include "../../util.hpp" // for ThreadBlocks
+#include "util.hpp"
+
+namespace mfem::future
+{
+
+// ────────────────────────────────────────────────────────────────────────────
+inline constexpr int LocalQFHOBackendMQ1() { return 16; }
+
+// ────────────────────────────────────────────────────────────────────────────
+/// Register type for one HO q-function parameter
+template<typename KerOps, typename T, int rank = qf_param_shape<T>::rank>
+struct ho_qreg;
+
+template<typename KerOps, typename T>
+struct ho_qreg<KerOps, T, 0>
+{
+   using type = typename KerOps::template val_reg_t<1>;
+};
+
+template<typename KerOps, typename T>
+struct ho_qreg<KerOps, T, 1>
+{
+   static constexpr int e0 = qf_param_shape<T>::extents[0];
+   using type = typename KerOps::template val_reg_t<e0>;
+};
+
+template<typename KerOps, typename T>
+struct ho_qreg<KerOps, T, 2>
+{
+   static constexpr int VDIM = qf_param_shape<T>::extents[0];
+   static constexpr int SDIM = qf_param_shape<T>::extents[1];
+   using type = typename KerOps::template del_reg_t<VDIM, SDIM>;
+};
+
+template<typename KerOps, typename T>
+using ho_qreg_t = typename ho_qreg<KerOps, T>::type;
+
+// ────────────────────────────────────────────────────────────────────────────
+namespace hok
+{
+
+/// Load one quadrature-point value
+template<int DIM, typename T, typename Reg>
+MFEM_HOST_DEVICE inline auto load_at(Reg &reg, int qx, int qy, int qz)
+{
+   static_assert(DIM == 2 || DIM == 3);
+   constexpr int RNK = qf_param_shape<T>::rank;
+   if constexpr (DIM == 2)
+   {
+      MFEM_CONTRACT_VAR(qz);
+      if constexpr (RNK == 0) { return T{ reg(0, qy, qx) }; }
+      else if constexpr (RNK == 1)
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         T t{};
+         MFEM_UNROLL(e0)
+         for (int dd = 0; dd < e0; ++dd) { t(dd) = reg(dd, qy, qx); }
+         return t;
+      }
+      else
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         constexpr int e1 = qf_param_shape<T>::extents[1];
+         T t;
+         MFEM_UNROLL(e0)
+         for (int i = 0; i < e0; ++i)
+         {
+            MFEM_UNROLL(e1)
+            for (int j = 0; j < e1; ++j) { t(i, j) = reg(i, j, qy, qx); }
+         }
+         return t;
+      }
+   }
+   else
+   {
+      if constexpr (RNK == 0) { return T{ reg(0, qz, qy, qx) }; }
+      else if constexpr (RNK == 1)
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         T t{};
+         MFEM_UNROLL(e0)
+         for (int dd = 0; dd < e0; ++dd) { t(dd) = reg(dd, qz, qy, qx); }
+         return t;
+      }
+      else
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         constexpr int e1 = qf_param_shape<T>::extents[1];
+         T t;
+         MFEM_UNROLL(e0)
+         for (int i = 0; i < e0; ++i)
+         {
+            MFEM_UNROLL(e1)
+            for (int j = 0; j < e1; ++j) { t(i, j) = reg(i, j, qz, qy, qx); }
+         }
+         return t;
+      }
+   }
+}
+
+template<bool tangent, typename U>
+MFEM_HOST_DEVICE inline auto qp_store(const U &v)
+{
+   if constexpr (tangent) { return qf_store_gradient(v); }
+   else
+   {
+      return qf_store_value(v);
+   }
+}
+
+// Store primal value or dual tangent at one quadrature point
+template<int DIM, typename T, typename Reg, bool tangent>
+MFEM_HOST_DEVICE inline void
+store_at(Reg &reg, int qx, int qy, int qz, const T &out)
+{
+   static_assert(DIM == 2 || DIM == 3);
+   constexpr int RNK = qf_param_shape<T>::rank;
+   if constexpr (DIM == 2)
+   {
+      MFEM_CONTRACT_VAR(qz);
+      if constexpr (RNK == 0) { reg(0, qy, qx) = qp_store<tangent>(out); }
+      else if constexpr (RNK == 1)
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         MFEM_UNROLL(e0)
+         for (int dd = 0; dd < e0; ++dd)
+         {
+            reg(dd, qy, qx) = qp_store<tangent>(out(dd));
+         }
+      }
+      else
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         constexpr int e1 = qf_param_shape<T>::extents[1];
+         MFEM_UNROLL(e0)
+         for (int i = 0; i < e0; ++i)
+         {
+            MFEM_UNROLL(e1)
+            for (int j = 0; j < e1; ++j)
+            {
+               reg(i, j, qy, qx) = qp_store<tangent>(out(i, j));
+            }
+         }
+      }
+   }
+   else
+   {
+      if constexpr (RNK == 0) { reg(0, qz, qy, qx) = qp_store<tangent>(out); }
+      else if constexpr (RNK == 1)
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         MFEM_UNROLL(e0)
+         for (int dd = 0; dd < e0; ++dd)
+         {
+            reg(dd, qz, qy, qx) = qp_store<tangent>(out(dd));
+         }
+      }
+      else
+      {
+         constexpr int e0 = qf_param_shape<T>::extents[0];
+         constexpr int e1 = qf_param_shape<T>::extents[1];
+         MFEM_UNROLL(e0)
+         for (int i = 0; i < e0; ++i)
+         {
+            MFEM_UNROLL(e1)
+            for (int j = 0; j < e1; ++j)
+            {
+               reg(i, j, qz, qy, qx) = qp_store<tangent>(out(i, j));
+            }
+         }
+      }
+   }
+}
+
+// Pull primal/tangent pair into a dual q-function argument
+template<int DIM, typename T, typename Reg>
+MFEM_HOST_DEVICE inline auto
+pull_directional(Reg &preg, Reg &sreg, int qx, int qy, int qz, bool dependent)
+{
+   if constexpr (!qf_param_uses_dual_v<T>)
+   {
+      return load_at<DIM, T>(preg, qx, qy, qz);
+   }
+   else
+   {
+      if (!dependent) { return load_at<DIM, T>(preg, qx, qy, qz); }
+      constexpr int RNK = qf_param_shape<T>::rank;
+      if constexpr (DIM == 2)
+      {
+         MFEM_CONTRACT_VAR(qz);
+         if constexpr (RNK == 0)
+         {
+            return T{ preg(0, qy, qx), sreg(0, qy, qx) };
+         }
+         else if constexpr (RNK == 1)
+         {
+            constexpr int e0 = qf_param_shape<T>::extents[0];
+            T t{};
+            MFEM_UNROLL(e0)
+            for (int dd = 0; dd < e0; ++dd)
+            {
+               t(dd) = { preg(dd, qy, qx), sreg(dd, qy, qx) };
+            }
+            return t;
+         }
+         else
+         {
+            constexpr int e0 = qf_param_shape<T>::extents[0];
+            constexpr int e1 = qf_param_shape<T>::extents[1];
+            T t;
+            MFEM_UNROLL(e0)
+            for (int i = 0; i < e0; ++i)
+            {
+               MFEM_UNROLL(e1)
+               for (int j = 0; j < e1; ++j)
+               {
+                  t(i, j) = { preg(i, j, qy, qx), sreg(i, j, qy, qx) };
+               }
+            }
+            return t;
+         }
+      }
+      else
+      {
+         if constexpr (RNK == 0)
+         {
+            return T{ preg(0, qz, qy, qx), sreg(0, qz, qy, qx) };
+         }
+         else if constexpr (RNK == 1)
+         {
+            constexpr int e0 = qf_param_shape<T>::extents[0];
+            T t{};
+            MFEM_UNROLL(e0)
+            for (int dd = 0; dd < e0; ++dd)
+            {
+               t(dd) = { preg(dd, qz, qy, qx), sreg(dd, qz, qy, qx) };
+            }
+            return t;
+         }
+         else
+         {
+            constexpr int e0 = qf_param_shape<T>::extents[0];
+            constexpr int e1 = qf_param_shape<T>::extents[1];
+            T t;
+            MFEM_UNROLL(e0)
+            for (int i = 0; i < e0; ++i)
+            {
+               MFEM_UNROLL(e1)
+               for (int j = 0; j < e1; ++j)
+               {
+                  t(i, j) = { preg(i, j, qz, qy, qx), sreg(i, j, qz, qy, qx) };
+               }
+            }
+            return t;
+         }
+      }
+   }
+}
+
+} // namespace hok
+
+// ────────────────────────────────────────────────────────────────────────────
+/// HO tensor-product kernels
+template<int T_DIM, int MQ1>
+struct ho_ker_backend
+{
+   static constexpr int DIM = T_DIM;
+   static_assert(DIM == 2 || DIM == 3);
+
+   template<int VDIM>
+   using val_reg_t = std::conditional_t<(DIM == 2),
+         ker::v_regs2d_t<VDIM, MQ1>,
+         ker::v_regs3d_t<VDIM, MQ1>>;
+
+   template<int VDIM, int SDIM>
+   using del_reg_t = std::conditional_t<(DIM == 2),
+         ker::vd_regs2d_t<VDIM, SDIM, MQ1>,
+         ker::vd_regs3d_t<VDIM, SDIM, MQ1>>;
+
+   struct Shared
+   {
+      real_t M[MQ1][MQ1], B[MQ1][MQ1], G[MQ1][MQ1];
+   };
+
+   template<typename XE_t, typename Dofs>
+   static MFEM_HOST_DEVICE void
+   load_dofs(const int e, const int d, const XE_t &XE, Dofs &dofs)
+   {
+      if constexpr (DIM == 2) { ker::LoadDofs2d(e, d, XE, dofs); }
+      else
+      {
+         ker::LoadDofs3d(e, d, XE, dofs);
+      }
+   }
+
+   template<int VDIM, int SDIM, typename XE_t, typename Dofs>
+   static MFEM_HOST_DEVICE void
+   load_grad_dofs(const int e, const int d, const XE_t &XE, Dofs &dofs)
+   {
+      static_assert(SDIM == DIM, "gradient spatial dim must match kernel DIM");
+      load_dofs(e, d, XE, dofs);
+   }
+
+   template<typename Smem, typename Dofs, typename ArgReg>
+   static MFEM_HOST_DEVICE void
+   eval_value(const int d, const int q, Smem &s, Dofs &dofs, ArgReg &rarg)
+   {
+      if constexpr (DIM == 2) { ker::Eval2d(d, q, s.M, s.B, dofs, rarg); }
+      else
+      {
+         ker::Eval3d(d, q, s.M, s.B, dofs, rarg);
+      }
+   }
+
+   template<int VDIM, int SDIM, typename Smem, typename Dofs, typename ArgReg>
+   static MFEM_HOST_DEVICE void
+   grad(const int d, const int q, Smem &s, Dofs &dofs, ArgReg &rarg)
+   {
+      static_assert(SDIM == DIM, "gradient spatial dim must match kernel DIM");
+      if constexpr (DIM == 2) { ker::Grad2d(d, q, s.M, s.B, s.G, dofs, rarg); }
+      else
+      {
+         ker::Grad3d(d, q, s.M, s.B, s.G, dofs, rarg);
+      }
+   }
+
+   template<typename Smem, typename Dofs, typename ArgReg, typename YE_t>
+   static MFEM_HOST_DEVICE void write_value(const int d,
+                                            const int q,
+                                            const int e,
+                                            Smem &s,
+                                            ArgReg &rarg,
+                                            Dofs &dofs,
+                                            YE_t &YE)
+   {
+      if constexpr (DIM == 2)
+      {
+         ker::EvalTranspose2d(d, q, s.M, s.B, rarg, dofs);
+         ker::WriteDofs2d(e, d, dofs, YE);
+      }
+      else
+      {
+         ker::EvalTranspose3d(d, q, s.M, s.B, rarg, dofs);
+         ker::WriteDofs3d(e, d, dofs, YE);
+      }
+   }
+
+   template<typename Smem, typename Dofs, typename ArgReg, typename YE_t>
+   static MFEM_HOST_DEVICE void write_gradient_2d(const int d,
+                                                  const int q,
+                                                  const int e,
+                                                  Smem &s,
+                                                  ArgReg &rarg,
+                                                  Dofs &dofs,
+                                                  YE_t &YE)
+   {
+      ker::GradTranspose2d(d, q, s.M, s.B, s.G, rarg, dofs);
+      ker::WriteDofs2d(e, d, dofs, YE);
+   }
+
+   template<typename Smem, typename Dofs, typename ArgReg, typename YE_t>
+   static MFEM_HOST_DEVICE void write_gradient_3d(const int d,
+                                                  const int q,
+                                                  const int e,
+                                                  Smem &s,
+                                                  ArgReg &rarg,
+                                                  Dofs &dofs,
+                                                  YE_t &YE)
+   {
+      ker::GradTranspose3d(d, q, s.M, s.B, s.G, rarg, dofs);
+      ker::WriteDofs3d(e, d, dofs, YE);
+   }
+
+   template<int VDIM,
+            int SDIM,
+            typename Smem,
+            typename Dofs,
+            typename ArgReg,
+            typename YE_t>
+   static MFEM_HOST_DEVICE void write_gradient(const int d,
+                                               const int q,
+                                               const int e,
+                                               Smem &s,
+                                               ArgReg &rarg,
+                                               Dofs &dofs,
+                                               YE_t &YE)
+   {
+      static_assert(SDIM == DIM, "gradient spatial dim must match kernel DIM");
+      if constexpr (DIM == 2) { write_gradient_2d(d, q, e, s, rarg, dofs, YE); }
+      else
+      {
+         write_gradient_3d(d, q, e, s, rarg, dofs, YE);
+      }
+   }
+};
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int T_DIM, int T_Q1D = LocalQFHOBackendMQ1()>
+struct LocalQFHOBackend
+{
+   // ─────────────────────────────────────────────────────
+   static constexpr int DIM = T_DIM, MQ1 = T_Q1D, Q1D = T_Q1D;
+   static_assert(DIM == 2 || DIM == 3);
+
+   // ─────────────────────────────────────────────────────
+   static inline ThreadBlocks thread_blocks(const int q1d)
+   {
+      MFEM_ASSERT(q1d <= Q1D, "q1d must be <= " << Q1D);
+      return { q1d, q1d, 1 };
+   }
+
+   // ─────────────────────────────────────────────────────
+   static inline constexpr int MAX_THREADS_PER_BLOCK() { return Q1D * Q1D; }
+
+   // ─────────────────────────────────────────────────────
+   using backend_t = ho_ker_backend<DIM, Q1D>;
+
+   // ─────────────────────────────────────────────────────
+   using Shared = typename backend_t::Shared;
+
+   // ─────────────────────────────────────────────────────
+   template<typename WT, typename WI, typename Cache, typename AddY>
+   static MFEM_HOST_DEVICE inline void DiagContract(Shared &s,
+                                                    const int num_dof_1d,
+                                                    const int q1d,
+                                                    const int nz_dof,
+                                                    WT wt,
+                                                    WI wi,
+                                                    Cache cache,
+                                                    AddY add_y)
+   {
+      MFEM_CONTRACT_VAR(nz_dof);
+      const int nqz = (DIM == 3) ? q1d : 1;
+      const int ndz = (DIM == 3) ? num_dof_1d : 1;
+
+      ker::s_regs3d_t<MQ1> rz, ry;
+      auto &smem = s.M;
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+         {
+            for (int dz = 0; dz < ndz; dz++)
+            {
+               real_t u = 0.0;
+               for (int qz = 0; qz < nqz; qz++)
+               {
+                  const int q = qx + (qy + qz * q1d) * q1d;
+                  const real_t wz =
+                     (DIM == 3) ? (wt(2, qz, dz) * wi(2, qz, dz)) : real_t(1);
+                  u += wz * cache(q);
+               }
+               rz[dz][qy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      for (int dz = 0; dz < ndz; dz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+            { smem[qy][qx] = rz[dz][qy][qx]; }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, num_dof_1d)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+            {
+               real_t u = 0.0;
+               for (int qy = 0; qy < q1d; qy++)
+               {
+                  u += wt(1, qy, dy) * wi(1, qy, dy) * smem[qy][qx];
+               }
+               ry[dz][dy][qx] = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+
+      for (int dz = 0; dz < ndz; dz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, num_dof_1d)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+            { smem[dy][qx] = ry[dz][dy][qx]; }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, num_dof_1d)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, num_dof_1d)
+            {
+               real_t u = 0.0;
+               for (int qx = 0; qx < q1d; qx++)
+               {
+                  u += wt(0, qx, dx) * wi(0, qx, dx) * smem[dy][qx];
+               }
+               add_y(dx, dy, dz, u);
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename T>
+   using QReg = ho_qreg_t<backend_t, T>;
+
+   // ─────────────────────────────────────────────────────
+   template<typename ArgRegT, typename XE_T>
+   static inline MFEM_HOST_DEVICE void LoadValue(Shared &s,
+                                                 const int e,
+                                                 const int d,
+                                                 const int q,
+                                                 const int,
+                                                 const real_t *B,
+                                                 const XE_T &XE,
+                                                 ArgRegT &rarg)
+   {
+      ker::LoadMatrix(d, q, B, s.B);
+      std::remove_reference_t<ArgRegT> dofs;
+      backend_t::load_dofs(e, d, XE, dofs);
+      backend_t::eval_value(d, q, s, dofs, rarg);
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<int RNK,
+            typename ArgRegT,
+            typename XE_T,
+            typename FieldParamT = ArgRegT>
+   static inline MFEM_HOST_DEVICE void LoadGradient(Shared &s,
+                                                    const int e,
+                                                    const int d,
+                                                    const int q,
+                                                    const int,
+                                                    const real_t *B,
+                                                    const real_t *G,
+                                                    const XE_T &XE,
+                                                    ArgRegT &rarg)
+   {
+      ker::LoadMatrix(d, q, B, s.B);
+      ker::LoadMatrix(d, q, G, s.G);
+      static_assert(RNK == 1 || RNK == 2);
+      static constexpr int VDIM =
+         (RNK == 1) ? 1 : qf_param_shape<FieldParamT>::extents[0];
+      static constexpr int SDIM = (RNK == 1)
+                                  ? qf_param_shape<FieldParamT>::extents[0]
+                                  : qf_param_shape<FieldParamT>::extents[1];
+      if constexpr (SDIM == DIM)
+      {
+         typename backend_t::template del_reg_t<VDIM, SDIM> dofs;
+         if constexpr (RNK == 1) { backend_t::load_dofs(e, d, XE, dofs); }
+         else
+         {
+            backend_t::template load_grad_dofs<VDIM, SDIM>(e, d, XE, dofs);
+         }
+         backend_t::template grad<VDIM, SDIM>(d, q, s, dofs, rarg);
+      }
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename T>
+   static MFEM_HOST_DEVICE inline auto
+   qp_pull(QReg<T> &reg, int qx, int qy, int qz)
+   { return hok::load_at<DIM, T>(reg, qx, qy, qz); }
+
+   // ─────────────────────────────────────────────────────
+   template<typename T>
+   static MFEM_HOST_DEVICE inline auto qp_pull_directional(
+      QReg<T> &preg, QReg<T> &sreg, int qx, int qy, int qz, bool dependent)
+   { return hok::pull_directional<DIM, T>(preg, sreg, qx, qy, qz, dependent); }
+
+   // ─────────────────────────────────────────────────────
+   template<typename DT, typename XE_T>
+   static MFEM_HOST_DEVICE inline DT identity_qp_pull_dual(bool dependent,
+                                                           const XE_T &XP,
+                                                           const XE_T &XD,
+                                                           int qx,
+                                                           int qy,
+                                                           int qz,
+                                                           int e)
+   {
+      constexpr int RNK = qf_param_shape<DT>::rank;
+      if constexpr (RNK == 0)
+      {
+         DT t{};
+         t.value = XP(0, qx, qy, qz, e);
+         t.gradient = dependent ? XD(0, qx, qy, qz, e) : 0.0;
+         return t;
+      }
+      else if constexpr (RNK == 1)
+      {
+         constexpr int e0 = qf_param_shape<DT>::extents[0];
+         DT t{};
+         MFEM_UNROLL(e0)
+         for (int dd = 0; dd < e0; ++dd)
+         {
+            t(dd).value = XP(dd, qx, qy, qz, e);
+            t(dd).gradient = dependent ? XD(dd, qx, qy, qz, e) : 0.0;
+         }
+         return t;
+      }
+      else if constexpr (RNK == 2)
+      {
+         constexpr int e0 = qf_param_shape<DT>::extents[0];
+         constexpr int e1 = qf_param_shape<DT>::extents[1];
+         DT t{};
+         MFEM_UNROLL(e0)
+         for (int i = 0; i < e0; ++i)
+         {
+            MFEM_UNROLL(e1)
+            for (int j = 0; j < e1; ++j)
+            {
+               t(i, j).value = XP(i + e0 * j, qx, qy, qz, e);
+               t(i, j).gradient =
+                  dependent ? XD(i + e0 * j, qx, qy, qz, e) : 0.0;
+            }
+         }
+         return t;
+      }
+      else
+      {
+         static_assert(false, "Unsupported");
+      }
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename T>
+   static MFEM_HOST_DEVICE inline void
+   qp_push(QReg<T> &reg, int qx, int qy, int qz, const T &out)
+   { hok::store_at<DIM, T, decltype(reg), false>(reg, qx, qy, qz, out); }
+
+   // ─────────────────────────────────────────────────────
+   template<typename T>
+   static MFEM_HOST_DEVICE inline void
+   qp_push_tangent(QReg<T> &reg, int qx, int qy, int qz, const T &out)
+   {
+      hok::store_at<DIM, T, decltype(reg), qf_param_uses_dual_v<T>>(
+                                                                    reg, qx, qy, qz, out);
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename DT, typename YE_T>
+   static MFEM_HOST_DEVICE inline void identity_qp_write_value(
+      YE_T &YE, int qx, int qy, int qz, int e, const DT &qout)
+   {
+      constexpr int RNK = qf_param_shape<DT>::rank;
+      if constexpr (qf_param_uses_dual_v<DT>)
+      {
+         if constexpr (RNK == 0)
+         {
+            YE(0, qx, qy, qz, e) = qf_store_value(qout);
+         }
+         else if constexpr (RNK == 1)
+         {
+            constexpr int e0 = qf_param_shape<DT>::extents[0];
+            MFEM_UNROLL(e0)
+            for (int dd = 0; dd < e0; ++dd)
+            {
+               YE(dd, qx, qy, qz, e) = qf_store_value(qout(dd));
+            }
+         }
+         else if constexpr (RNK == 2)
+         {
+            constexpr int e0 = qf_param_shape<DT>::extents[0];
+            constexpr int e1 = qf_param_shape<DT>::extents[1];
+            MFEM_UNROLL(e0)
+            for (int i = 0; i < e0; ++i)
+            {
+               MFEM_UNROLL(e1)
+               for (int j = 0; j < e1; ++j)
+               {
+                  YE(i + e0 * j, qx, qy, qz, e) = qf_store_value(qout(i, j));
+               }
+            }
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      }
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename DT, typename YE_T>
+   static MFEM_HOST_DEVICE inline void identity_qp_write_tangent(
+      YE_T &YE, int qx, int qy, int qz, int e, const DT &qout)
+   {
+      constexpr int RNK = qf_param_shape<DT>::rank;
+      if constexpr (qf_param_uses_dual_v<DT>)
+      {
+         if constexpr (RNK == 0)
+         {
+            YE(0, qx, qy, qz, e) = qf_store_gradient(qout);
+         }
+         else if constexpr (RNK == 1)
+         {
+            constexpr int e0 = qf_param_shape<DT>::extents[0];
+            MFEM_UNROLL(e0)
+            for (int dd = 0; dd < e0; ++dd)
+            {
+               YE(dd, qx, qy, qz, e) = qf_store_gradient(qout(dd));
+            }
+         }
+         else if constexpr (RNK == 2)
+         {
+            constexpr int e0 = qf_param_shape<DT>::extents[0];
+            constexpr int e1 = qf_param_shape<DT>::extents[1];
+            MFEM_UNROLL(e0)
+            for (int i = 0; i < e0; ++i)
+            {
+               MFEM_UNROLL(e1)
+               for (int j = 0; j < e1; ++j)
+               {
+                  YE(i + e0 * j, qx, qy, qz, e) = qf_store_gradient(qout(i, j));
+               }
+            }
+         }
+         else
+         {
+            static_assert(false, "Unsupported");
+         }
+      }
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<typename ArgRegT, typename YE_T>
+   static inline MFEM_HOST_DEVICE void WriteValue(Shared &s,
+                                                  const int e,
+                                                  const int d,
+                                                  const int q,
+                                                  const int,
+                                                  const real_t *B,
+                                                  YE_T &YE,
+                                                  ArgRegT &rarg)
+   {
+      ker::LoadMatrix(d, q, B, s.B);
+      std::remove_reference_t<ArgRegT> dofs;
+      backend_t::write_value(d, q, e, s, rarg, dofs, YE);
+   }
+
+   // ─────────────────────────────────────────────────────
+   template<int RNK,
+            typename ArgRegT,
+            typename YE_T,
+            typename FieldParamT = ArgRegT>
+   static inline MFEM_HOST_DEVICE void WriteGradient(Shared &s,
+                                                     const int e,
+                                                     const int d,
+                                                     const int q,
+                                                     const int,
+                                                     const real_t *B,
+                                                     const real_t *G,
+                                                     YE_T &YE,
+                                                     ArgRegT &rarg)
+   {
+      ker::LoadMatrix(d, q, B, s.B);
+      ker::LoadMatrix(d, q, G, s.G);
+      static_assert(RNK == 1 || RNK == 2);
+      static constexpr int VDIM =
+         (RNK == 1) ? 1 : qf_param_shape<FieldParamT>::extents[0];
+      static constexpr int SDIM = (RNK == 1)
+                                  ? qf_param_shape<FieldParamT>::extents[0]
+                                  : qf_param_shape<FieldParamT>::extents[1];
+      if constexpr (SDIM == DIM)
+      {
+         typename backend_t::template del_reg_t<VDIM, SDIM> dofs;
+         backend_t::template write_gradient<VDIM, SDIM>(
+            d, q, e, s, rarg, dofs, YE);
+      }
+   }
+};
+
+/// @brief Dispatch to a compile-time HO kernel with MQ1 >= runtime @a q1d.
+template <typename HOKernelTable, int DIM, int MQ1 = LocalQFHOBackendMQ1()>
+inline typename HOKernelTable::KernelSignature
+DispatchHOKernelByQ1D(int q1d)
+{
+   MFEM_VERIFY(q1d >= 2 && q1d <= MQ1,
+               "Unsupported HO quadrature order: " << q1d);
+   return HOKernelTable::template Kernel<DIM, MQ1>();
+}
+
+} // namespace mfem::future

fem/dfem/backends/local_qf/prelude.hpp

@@ -0,0 +1,242 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../../integrator_ctx.hpp"
+#include "action.hpp"
+#include "derivative_action.hpp"
+#include "derivative_setup.hpp"
+#include "derivative_apply.hpp"
+#include "derivative_assemble.hpp"
+#include "derivative_assemble_diagonal.hpp"
+#include "derivative_apply_transpose.hpp"
+
+namespace mfem::future
+{
+
+struct LocalQFBackend
+{
+   /**
+    * @brief Make an action for a local Q-function backend.
+    *
+    * @param ctx The integrator context.
+    * @param args The arguments to the action.
+    * @return The action.
+    */
+   template<typename qfunc_t, typename inputs_t, typename outputs_t>
+   static auto MakeAction(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs)
+   {
+      return LocalQFImpl::Action<qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs);
+   }
+
+   /**
+    * @brief Make a derivative action for a local Q-function backend.
+    *
+    * @tparam derivative_id The id of the derivative.
+    * @param ctx The integrator context.
+    * @param args The arguments to the derivative action.
+    * @return The derivative action.
+    */
+   template<int id, typename qfunc_t, typename inputs_t, typename outputs_t>
+   static auto MakeDerivativeAction(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs)
+   {
+      return LocalQFImpl::DerivativeAction<id, qfunc_t, inputs_t, outputs_t>(
+                ctx, qfunc, inputs, outputs);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   static auto MakeDerivativeSetup(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeSetup<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(ctx, qfunc, inputs,
+                                                          outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   static auto MakeDerivativeApply(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeApply<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(ctx, qfunc, inputs,
+                                                          outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   static auto MakeDerivativeApplyTranspose(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeApplyTranspose<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(ctx, qfunc, inputs,
+                                                          outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   static auto MakeDerivativeAssemble(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeAssemble<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(ctx, qfunc, inputs,
+                                                          outputs, qp_cache);
+   }
+
+   template<
+      int derivative_id,
+      typename qfunc_t,
+      typename inputs_t,
+      typename outputs_t>
+   static auto MakeDerivativeAssembleDiagonal(
+      const IntegratorContext &ctx,
+      const qfunc_t &qfunc,
+      inputs_t inputs,
+      outputs_t outputs,
+      const Vector &qp_cache)
+   {
+      return LocalQFImpl::DerivativeAssembleDiagonal<
+             derivative_id, qfunc_t, inputs_t, outputs_t>(ctx, qfunc, inputs,
+                                                          outputs, qp_cache);
+   }
+};
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, typename QT, typename IT, typename OT>
+inline void AddAction()
+{
+   using ker = LocalQFImpl::Action<QT, IT, OT>;
+   if constexpr (Q1D <= 8)
+   {
+      ker::ActionLO::template Specialization<DIM, Q1D>::Add();
+   }
+   else
+   {
+      ker::ActionHO::template Specialization<DIM, Q1D>::Add();
+   }
+}
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, int DID, typename QT, typename IT, typename OT>
+inline void AddDerivativeAction()
+{
+   using ker = LocalQFImpl::DerivativeAction<DID, QT, IT, OT>;
+   if constexpr (Q1D <= 8)
+   {
+      ker::DerivativeActionLO::template Specialization<DIM, Q1D>::Add();
+   }
+   else
+   {
+      ker::DerivativeActionHO::template Specialization<DIM, Q1D>::Add();
+   }
+}
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, int DID, typename QT, typename IT, typename OT>
+inline void AddDerivativeSetup()
+{
+   using ker = LocalQFImpl::DerivativeSetup<DID, QT, IT, OT>;
+   if constexpr (Q1D <= 8)
+   {
+      ker::DerivativeSetupLO::template Specialization<DIM, Q1D>::Add();
+   }
+   else
+   {
+      ker::DerivativeSetupHO::template Specialization<DIM, Q1D>::Add();
+   }
+}
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, int DID, typename QT, typename IT, typename OT>
+inline void AddDerivativeApply()
+{
+   using ker = LocalQFImpl::DerivativeApply<DID, QT, IT, OT>;
+   if constexpr (Q1D <= 8)
+   {
+      ker::DerivativeApplyLO::template Specialization<DIM, Q1D>::Add();
+   }
+   else
+   {
+      ker::DerivativeApplyHO::template Specialization<DIM, Q1D>::Add();
+   }
+}
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, int DID, typename QT, typename IT, typename OT>
+inline void AddDerivativeApplyTranspose()
+{
+   using ker = LocalQFImpl::DerivativeApplyTranspose<DID, QT, IT, OT>;
+   if constexpr (Q1D <= 8)
+   {
+      ker::DerivativeApplyTransposeLO::template Specialization<DIM, Q1D>::Add();
+   }
+   else
+   {
+      ker::DerivativeApplyTransposeHO::template Specialization<DIM, Q1D>::Add();
+   }
+}
+
+// ────────────────────────────────────────────────────────────────────────────
+template<int DIM, int Q1D, typename QT, typename IT, typename OT,
+         typename derivative_ids_t = std::index_sequence<>>
+inline void AddLocalSpecializations()
+{
+   AddAction<DIM, Q1D, QT, IT, OT>();
+
+   for_constexpr([&](auto i)
+   {
+      using derivative_id = decltype(i);
+      AddDerivativeAction<DIM, Q1D, derivative_id::value, QT, IT, OT>();
+      AddDerivativeSetup<DIM, Q1D, derivative_id::value, QT, IT, OT>();
+      AddDerivativeApply<DIM, Q1D, derivative_id::value, QT, IT, OT>();
+      AddDerivativeApplyTranspose<DIM, Q1D, derivative_id::value, QT, IT, OT>();
+   }, derivative_ids_t{});
+}
+
+}

fem/dfem/backends/local_qf/revdiff_transformer.hpp

@@ -0,0 +1,606 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../util.hpp"
+#include "util.hpp"
+#include "../../util.hpp"
+
+namespace mfem::future
+{
+
+template <typename T> struct function_traits;
+
+template <typename R, typename C, typename... Args>
+struct function_traits<R (C::*)(Args...) const>
+{
+   using primal_return_type = R;
+   using args_tuple = tuple<Args...>;
+   static constexpr size_t arity = sizeof...(Args);
+};
+
+/// Scalar-level view of a per-point argument: the plain value type it stores
+/// and the dual type used to carry a first-order tangent alongside it.
+template <typename T>
+struct qp_scalar_traits
+{
+   using view_type = T;
+   using dual_type = dual<T, T>;
+};
+
+template <typename V, typename G>
+struct qp_scalar_traits<dual<V, G>>
+{
+   using view_type = V;
+   using dual_type = dual<V, G>;
+};
+
+// Component count and writable counterpart of a per-point argument, which
+// is either a tensor or a plain scalar. `view_type` keeps the argument's own
+// scalar type; `dual_type` is the same shape with a dual scalar, used for the
+// gradient blocks of the native dual-number backend.
+template <typename Arg> struct qp_traits
+{
+   static_assert(std::is_arithmetic_v<Arg> || is_dual_number<Arg>::value,
+                 "per-point arguments must be tensors or scalars");
+   using scalar_type = std::remove_const_t<Arg>;
+   using view_type = scalar_type;
+   using dual_type = typename qp_scalar_traits<scalar_type>::dual_type;
+   static constexpr int components = 1;
+};
+
+template <typename T, int... Sizes> struct qp_traits<tensor<T, Sizes...>>
+{
+   using scalar_type = std::remove_const_t<T>;
+   using view_type = tensor<scalar_type, Sizes...>;
+   using dual_type =
+      tensor<typename qp_scalar_traits<scalar_type>::dual_type, Sizes...>;
+   static constexpr int components = (Sizes * ... * 1);
+};
+
+template <typename... T1s, typename... T2s>
+constexpr tuple<T1s..., T2s...> concat_tuples(tuple<T1s...>, tuple<T2s...>);
+
+///////////////////////////////////////////////////////////////////////////////
+/// Nested ("hyper") dual utilities, used for second derivatives on the native
+/// dual-number backend.
+///
+/// A second derivative taken with plain duals would have to reuse the single
+/// gradient slot that already carries the incoming direction. Lifting the
+/// scalar to `dual<dual<V,G>, dual<V,G>>` adds a second, independent slot:
+///
+///   dual(a, b) -> ((a, c), (b, d))
+///
+/// `a`/`b` stay the incoming primal/direction, `c` is seeded per component and
+/// `d` returns the second-order result.
+template <typename T>
+struct make_nested_qp_type
+{
+   using type = T;
+};
+
+template <typename V, typename G>
+struct make_nested_qp_type<dual<V, G>>
+{
+   using type = dual<dual<V, G>, dual<V, G>>;
+};
+
+template <typename S, int... Sizes>
+struct make_nested_qp_type<tensor<S, Sizes...>>
+{
+   using type = tensor<typename make_nested_qp_type<S>::type, Sizes...>;
+};
+
+template <typename T>
+using make_nested_qp_type_t = typename make_nested_qp_type<T>::type;
+
+using native_dual_t = typename qp_scalar_traits<real_t>::dual_type;
+using nested_native_dual_t = make_nested_qp_type_t<native_dual_t>;
+
+/// Rebinds a q-function's scalar template parameter so its arguments are
+/// nested duals. Only the leading scalar parameter is rebound; any remaining
+/// non-type parameters (e.g. `dim`) are carried through unchanged. This
+/// requires q-functions of the form `QFunc<scalar_t>` or `QFunc<scalar_t,
+/// Params...>`; `supported` reports whether that shape was matched, so callers
+/// can fail with a readable static_assert.
+template <typename qfunc_t, typename nested_scalar_t, typename = void>
+struct rebind_qfunc_scalar
+{
+   static constexpr bool supported = false;
+};
+
+template <template <typename> class qfunc_template_t,
+          typename old_scalar_t,
+          typename nested_scalar_t>
+struct rebind_qfunc_scalar<qfunc_template_t<old_scalar_t>, nested_scalar_t>
+{
+   static constexpr bool supported = true;
+   using type = qfunc_template_t<nested_scalar_t>;
+};
+
+template <template <typename, auto...> class qfunc_template_t,
+          typename old_scalar_t,
+          auto... Params,
+          typename nested_scalar_t>
+struct rebind_qfunc_scalar<qfunc_template_t<old_scalar_t, Params...>,
+          nested_scalar_t,
+       std::enable_if_t<(sizeof...(Params) > 0)>>
+       {
+          static constexpr bool supported = true;
+          using type = qfunc_template_t<nested_scalar_t, Params...>;
+       };
+
+template <typename qfunc_t, typename nested_scalar_t>
+using rebind_qfunc_scalar_t =
+   typename rebind_qfunc_scalar<qfunc_t, nested_scalar_t>::type;
+
+/// Copies a q-function argument into its nested-dual counterpart, mapping
+/// dual(a, b) -> ((a, 0), (b, 0)). The inner gradients stay zero; the caller
+/// seeds one of them per component.
+template <typename Dst, typename Src>
+MFEM_HOST_DEVICE void lift_to_nested_arg(const Src &src, Dst &dst)
+{
+   using dst_t = std::decay_t<Dst>;
+   constexpr bool dst_uses_dual = is_dual_number<dst_t>::value ||
+                                  qf_param_uses_dual_v<dst_t> ||
+                                  is_nested_dual_number<dst_t>::value ||
+                                  qf_param_uses_nested_dual_v<dst_t>;
+   if constexpr (dst_uses_dual)
+   {
+      constexpr int ncomp = qp_traits<dst_t>::components;
+      for (int component = 0; component < ncomp; component++)
+      {
+         qf_set_flat_value(dst, component, qf_flat_value(src, component));
+         qf_set_flat_gradient(dst, component, qf_flat_gradient(src, component));
+      }
+   }
+   else
+   {
+      // Destination carries no derivative slots: a plain copy is the lift.
+      dst = src;
+   }
+}
+
+// RevDiff: computes the full gradient of a pointwise qfunction at a single
+// quadrature point using one Enzyme reverse-mode (autodiff) call.
+//
+// operator()(args...) takes all qfunction input primals followed by one
+// writable gradient output per Active input (same shape as that input).
+// The qfunction's own output is not passed; Enzyme writes it to stack
+// scratch (enzyme_dupnoneed).
+//
+// A single __enzyme_autodiff call with the output adjoint seeded to 1
+// yields all gradient blocks simultaneously — O(1) calls per point
+// regardless of input size, vs O(ncomp) for forward mode.
+//
+// operator() is MFEM_HOST_DEVICE and allocation-free.
+//
+// Without Enzyme the same interface is served by a forward-mode dual-number
+// fallback (`call_dual_rev`), which seeds one component at a time. `mode`
+// selects what that fallback is being asked for: `Eval` is the plain gradient,
+// `Derivative` is a gradient taken inside an outer derivative, which lifts the
+// q-function to nested duals so seeding does not clobber the outer direction.
+// With Enzyme both modes use the single reverse-mode call and `mode` is inert.
+enum class RevDiffDualMode
+{
+   Eval,
+   Derivative
+};
+
+// Number of Active inputs and their argument indices, in ascending order.
+// A qfunction may have several Active inputs at once: e.g. a field's value
+// u and its gradient dudx both feed the output and both must be
+// differentiated (the chain-rule contraction with the value/gradient shape
+// functions then happens at the FE-operator level). We produce one gradient
+// block, d(output)/d(input), per Active input — each computed with the other
+// Active inputs frozen, so they come out as isolated partials.
+template <typename activity_t, size_t num_inputs, size_t... Is>
+constexpr size_t count_active_inputs(std::index_sequence<Is...>)
+{
+   return ((Is < num_inputs && qf_param_is_active_v<activity_t, Is>
+            ? size_t{1} : size_t{0}) + ...);
+}
+
+template <typename activity_t, size_t num_inputs, size_t num_active,
+          size_t... Is>
+constexpr std::array<size_t, num_active>
+collect_active_inputs(std::index_sequence<Is...>)
+{
+   std::array<size_t, num_active> idx{};
+   size_t j = 0;
+   (((Is < num_inputs && qf_param_is_active_v<activity_t, Is>)
+     ? (idx[j++] = Is) : size_t{0}), ...);
+   return idx;
+}
+
+template <typename Func, typename InputActivityTuple,
+          typename OutputActivityTuple,
+          RevDiffDualMode mode = RevDiffDualMode::Eval>
+struct RevDiff
+{
+   using traits = function_traits<decltype(&Func::operator())>;
+   using args_tuple = typename traits::args_tuple;
+   using activity =
+      decltype(concat_tuples(InputActivityTuple{}, OutputActivityTuple{}));
+   static constexpr size_t arity = traits::arity;
+   static constexpr size_t num_inputs = tuple_size<InputActivityTuple>::value;
+
+   static_assert(std::is_void_v<typename traits::primal_return_type>,
+                 "RevDiff only supports primal functions with void return type");
+   static_assert(tuple_size<activity>::value == arity,
+                 "Number of input and output activity tags must match function "
+                 "arity");
+
+   static constexpr size_t num_active_inputs =
+      count_active_inputs<activity, num_inputs>(
+         std::make_index_sequence<arity> {});
+
+   static constexpr auto active_inputs =
+      collect_active_inputs<activity, num_inputs, num_active_inputs>(
+   std::make_index_sequence<arity> {});
+
+   // Slot index of argument I in the active_inputs array (compile-time).
+   template <size_t I>
+   static constexpr size_t slot_of()
+   {
+      for (size_t s = 0; s < num_active_inputs; s++)
+         if (active_inputs[s] == I) { return s; }
+      return num_active_inputs;
+   }
+
+   static constexpr size_t active_output =
+      find_single_active_qparam<activity, num_inputs, arity>();
+   static_assert(active_output < arity,
+                 "gradient mode requires exactly one Active output");
+   static_assert(num_active_inputs >= 1,
+                 "gradient mode requires at least one Active input");
+   static_assert(tuple_size<OutputActivityTuple>::value == 1,
+                 "gradient mode requires exactly one (scalar) output");
+
+   using output_type =
+      std::decay_t<tuple_element_t<active_output, args_tuple>>;
+
+   using output_view = typename qp_traits<output_type>::view_type;
+
+   static_assert(qp_traits<output_type>::components == 1,
+                 "gradient output requires a scalar output");
+
+   template <size_t I>
+   using primal_arg_t = tuple_element_t<I, args_tuple>;
+
+   // True when reverse mode is served by the dual-number fallback rather than
+   // Enzyme. Everything below that widens a type to a dual is gated on this, so
+   // an Enzyme build sees exactly the types it saw before nested duals existed.
+#ifdef MFEM_USE_ENZYME
+   static constexpr bool native_dual_backend = false;
+#else
+   static constexpr bool native_dual_backend = true;
+#endif
+
+   static constexpr bool use_native_dual_derivative =
+      native_dual_backend && (mode == RevDiffDualMode::Derivative);
+
+   // Under the native-dual second-derivative path the active primals arrive
+   // carrying the outer direction, so they must be dual-typed.
+   template <size_t I>
+   using derivative_arg_t =
+      std::conditional_t<use_native_dual_derivative &&
+      qf_param_is_active_v<activity, I>,
+      typename qp_traits<std::decay_t<tuple_element_t<I, args_tuple>>>::dual_type,
+      primal_arg_t<I>>;
+
+   template <size_t S>
+   using active_arg_decay_t =
+      std::decay_t<tuple_element_t<active_inputs[S], args_tuple>>;
+
+   template <size_t S>
+   static constexpr bool active_arg_uses_dual()
+   {
+      return native_dual_backend &&
+             (is_dual_number<active_arg_decay_t<S>>::value ||
+              qf_param_uses_dual_v<active_arg_decay_t<S>>);
+   }
+
+   // A gradient block mirrors its active input's shape. It needs a dual scalar
+   // whenever the fallback has to return a value and a tangent through it.
+   template <size_t S>
+   using grad_arg_t =
+      std::conditional_t<use_native_dual_derivative || active_arg_uses_dual<S>(),
+      typename qp_traits<active_arg_decay_t<S>>::dual_type,
+      typename qp_traits<active_arg_decay_t<S>>::view_type>
+      &;
+
+   template <typename qfunc_type>
+   using qfunc_args_tuple_t =
+      decay_tuple<typename function_traits<decltype(&qfunc_type::operator())>::args_tuple>;
+
+   template <size_t... Is, size_t... Ss>
+   static FunctionSignature<void(derivative_arg_t<Is>..., grad_arg_t<Ss>...)>
+   signature_impl(std::index_sequence<Is...>, std::index_sequence<Ss...>);
+
+   using signature = decltype(signature_impl(std::make_index_sequence<num_inputs> {},
+                                             std::make_index_sequence<num_active_inputs> {}));
+
+   Func func {};
+
+   RevDiff() = default;
+   MFEM_HOST_DEVICE explicit RevDiff(const Func &func_) : func(func_) { }
+
+   // Plain function with the qfunction's exact (reference) signature, plus the
+   // configured qfunction instance, so it can be handed to Enzyme as a function
+   // pointer without default-constructing away runtime qfunction state.
+   template <size_t... Is>
+   MFEM_HOST_DEVICE static MFEM_FUTURE_ALWAYS_INLINE void
+   static_call(Func *func, tuple_element_t<Is, args_tuple>... args)
+   {
+      (*func)(args...);
+   }
+
+   template <size_t... Is>
+   static constexpr auto fn_ptr(std::index_sequence<Is...>)
+   {
+      return &static_call<Is...>;
+   }
+   static constexpr auto fn()
+   {
+      return fn_ptr(std::make_index_sequence<arity> {});
+   }
+
+   // Load primal inputs from the pointer tuple into a local qargs copy. Dual
+   // gradient parts are implicitly zero because qargs is value-initialized.
+   template <typename QArgs, typename AllPtrs, size_t... Is>
+   MFEM_HOST_DEVICE static MFEM_FUTURE_ALWAYS_INLINE void load_qargs(
+      QArgs &qargs, AllPtrs &ptrs, std::index_sequence<Is...>)
+   {
+      ((mfem::future::get<int(Is)>(qargs) =
+           *mfem::future::get<int(Is)>(ptrs)), ...);
+   }
+
+   template <typename QArgs, typename AllPtrs, size_t... Is>
+   MFEM_HOST_DEVICE static MFEM_FUTURE_ALWAYS_INLINE void
+   lift_qargs_to_nested_dual(QArgs &qargs, AllPtrs &ptrs,
+                             std::index_sequence<Is...>)
+   {
+      (lift_to_nested_arg(*mfem::future::get<int(Is)>(ptrs),
+                          mfem::future::get<Is>(qargs)), ...);
+   }
+
+   // The nested-dual q-function is a *different* type — its scalar template
+   // parameter is rebound — so a configured instance cannot simply be copied
+   // over. Runtime q-function state must still survive, or the second
+   // derivative would silently be taken of a differently-parameterised energy.
+   //
+   // Three cases, in order:
+   //   * the rebound type converts from this one: use that conversion;
+   //   * no state at all: nothing to carry;
+   //   * same size and trivially copyable: none of the members depend on the
+   //     rebound scalar, so the two are layout-identical and the state copies
+   //     over bytewise. A member that *did* depend on the scalar would change
+   //     the size and land in the static_assert below instead.
+   template <typename nested_func_t>
+   MFEM_HOST_DEVICE MFEM_FUTURE_ALWAYS_INLINE nested_func_t
+   make_nested_func() const
+   {
+      if constexpr (std::is_constructible_v<nested_func_t, const Func &>)
+      {
+         return nested_func_t(func);
+      }
+      else if constexpr (std::is_empty_v<Func>)
+      {
+         return nested_func_t {};
+      }
+      else
+      {
+         static_assert(std::is_trivially_copyable_v<Func> &&
+                       std::is_trivially_copyable_v<nested_func_t> &&
+                       sizeof(Func) == sizeof(nested_func_t),
+                       "second derivatives on the native dual backend rebind "
+                       "the q-function's scalar type; a q-function whose state "
+                       "depends on that scalar must be constructible from its "
+                       "rebound form");
+         nested_func_t nested {};
+         const auto *src = reinterpret_cast<const unsigned char *>(&func);
+         auto *dst = reinterpret_cast<unsigned char *>(&nested);
+         for (size_t b = 0; b < sizeof(Func); b++) { dst[b] = src[b]; }
+         return nested;
+      }
+   }
+
+   // Seed the s-th Active input one component at a time and read the resulting
+   // gradient block back out. This is the forward-mode dual-number stand-in for
+   // one reverse-mode call: O(ncomp) evaluations instead of O(1).
+   template <size_t S, typename AllPtrs>
+   MFEM_HOST_DEVICE MFEM_FUTURE_ALWAYS_INLINE void seed_active_input(
+      AllPtrs &ptrs) const
+   {
+      constexpr size_t input_idx = active_inputs[S];
+      using active_arg_t = std::decay_t<tuple_element_t<input_idx, args_tuple>>;
+      constexpr int ncomp = qp_traits<active_arg_t>::components;
+
+      for (int component = 0; component < ncomp; component++)
+      {
+         if constexpr (mode == RevDiffDualMode::Eval)
+         {
+            // Fresh value-initialized qargs: primals loaded below, all dual
+            // gradient parts start at zero, so no explicit clear is needed.
+            qfunc_args_tuple_t<Func> qargs {};
+            load_qargs(qargs, ptrs, std::make_index_sequence<num_inputs> {});
+
+            auto &grad = *mfem::future::get<num_inputs + S>(ptrs);
+
+            qf_set_flat_gradient(mfem::future::get<input_idx>(qargs), component,
+                                 1.0);
+
+            call_qfunc_no_move(func, qargs);
+
+            auto &out = mfem::future::get<active_output>(qargs);
+
+            qf_set_flat_value(grad, component, qf_flat_gradient(out, 0));
+         }
+         else
+         {
+            // Lift the incoming dual (a, b) to ((a, c), (b, d)): b is the outer
+            // Hessian-action direction, c is this loop's component seed. After
+            // evaluating E the nested output holds ((E, dE/dx_i), (E'[b],
+            // H_i[b])), and we hand dfem back (dE/dx_i, H_i[b]).
+            static_assert(rebind_qfunc_scalar<Func, nested_native_dual_t>::supported,
+                          "RevDiff native-dual derivative mode requires "
+                          "q-function types of the form QFunc<scalar_t> so they "
+                          "can be rebound to nested dual scalars");
+            using nested_func_t = rebind_qfunc_scalar_t<Func, nested_native_dual_t>;
+            qfunc_args_tuple_t<nested_func_t> nested_qargs {};
+
+            lift_qargs_to_nested_dual(nested_qargs, ptrs,
+                                      std::make_index_sequence<num_inputs> {});
+
+            qf_set_flat_value_gradient(
+               mfem::future::get<input_idx>(nested_qargs), component, 1.0);
+
+            call_qfunc_no_move(make_nested_func<nested_func_t>(), nested_qargs);
+
+            auto &out = mfem::future::get<active_output>(nested_qargs);
+            auto &grad = *mfem::future::get<num_inputs + S>(ptrs);
+
+            qf_set_flat_value(grad, component, qf_flat_value_gradient(out, 0));
+            qf_set_flat_gradient(grad, component,
+                                 qf_flat_gradient_gradient(out, 0));
+         }
+      }
+   }
+
+   // Dual-number fallback for the whole reverse-mode call: one seeded sweep per
+   // Active input.
+   template <typename AllPtrs>
+   MFEM_HOST_DEVICE MFEM_FUTURE_ALWAYS_INLINE void call_dual_rev(
+      AllPtrs &ptrs) const
+   {
+      for_constexpr<num_active_inputs>([&](auto s)
+      {
+         seed_active_input<decltype(s)::value>(ptrs);
+      });
+   }
+
+#ifdef MFEM_USE_ENZYME
+   // Recursive builder of the per-argument reverse-mode enzyme call.
+   template <size_t I = 0, typename AllPtrs, typename... Built>
+   MFEM_HOST_DEVICE MFEM_FUTURE_ALWAYS_INLINE void
+   call_enzyme_rev(AllPtrs &ptrs, output_view &scratch, output_view &adjoint,
+                   Built... built) const
+   {
+      if constexpr (I == arity)
+      {
+         __enzyme_autodiff<void>(fn(), enzyme_const, const_cast<Func *>(&func),
+                                 built...);
+      }
+      else if constexpr (I == active_output)
+      {
+         // Output: primal written to scratch (unused), adjoint seeded to 1.
+         call_enzyme_rev<I + 1>(ptrs, scratch, adjoint, built...,
+                                enzyme_dupnoneed, &scratch, &adjoint);
+      }
+      else if constexpr (qf_param_is_active_v<activity, I>)
+      {
+         // Active input: gradient accumulates into its grad-output slot.
+         call_enzyme_rev<I + 1>(
+            ptrs, scratch, adjoint, built..., enzyme_dup,
+            mfem::future::get<int(I)>(ptrs),
+            mfem::future::get<int(num_inputs + slot_of<I>())>(ptrs));
+      }
+      else
+      {
+         // Const input: primal only, no shadow.
+         call_enzyme_rev<I + 1>(ptrs, scratch, adjoint, built...,
+                                enzyme_const, mfem::future::get<int(I)>(ptrs));
+      }
+   }
+#endif // MFEM_USE_ENZYME
+
+   // Zero all gradient outputs before the enzyme call (Enzyme accumulates).
+   template <typename AllPtrs, size_t... Ss>
+   MFEM_HOST_DEVICE static
+   MFEM_FUTURE_ALWAYS_INLINE void zero_grads(
+      AllPtrs &ptrs,
+      std::index_sequence<Ss...>)
+   {
+      ((*mfem::future::get<int(num_inputs + Ss)>(ptrs) =
+           std::decay_t<decltype(*mfem::future::get<int(num_inputs + Ss)>(ptrs))> {}),
+       ...);
+   }
+
+   // Called once per quadrature point. Arguments are, in order:
+   //   * the primal value of every qfunction input (active and const), then
+   //   * one gradient output per Active input (ascending index order), each
+   //     shaped like its Active input.
+   // The qfunction's own output slot is not passed; Enzyme writes it to stack
+   // scratch (enzyme_dupnoneed). A single __enzyme_autodiff call yields all
+   // gradient blocks simultaneously.
+   template <typename... Args>
+   MFEM_HOST_DEVICE MFEM_FUTURE_ALWAYS_INLINE void operator()(
+      Args &&...args) const
+   {
+      static_assert(sizeof...(Args) == num_inputs + num_active_inputs,
+                    "expected one primal per input plus one gradient output per "
+                    "Active input");
+      auto ptrs = mfem::future::make_tuple(&args...);
+      zero_grads(ptrs, std::make_index_sequence<num_active_inputs> {});
+#ifdef MFEM_USE_ENZYME
+      output_view out_scratch {};
+      output_view out_adjoint{1.0}; // seed: d(output)/d(output) = 1
+      call_enzyme_rev(ptrs, out_scratch, out_adjoint);
+#else
+      call_dual_rev(ptrs);
+#endif
+   }
+
+   static MFEM_FUTURE_ALWAYS_INLINE void print() { print_impl(std::make_index_sequence<arity> {}); }
+
+   template <size_t... Is> static MFEM_FUTURE_ALWAYS_INLINE void print_impl(
+      std::index_sequence<Is...>)
+   {
+      mfem::out << "__enzyme_autodiff<void>(fptr";
+      (([&]
+      {
+         auto name = get_type_name<tuple_element_t<Is, args_tuple>>();
+         if constexpr (Is == active_output)
+            mfem::out << ", enzyme_dupnoneed, " << name << ", adjoint=1";
+         else if constexpr (qf_param_is_active_v<activity, Is>)
+            mfem::out << ", enzyme_dup, " << name << ", grad out";
+         else
+         {
+            mfem::out << ", enzyme_const, " << name;
+         }
+      }()),
+      ...);
+      mfem::out << ")\n";
+   }
+};
+
+template <typename Func, typename InputActivityTuple,
+          typename OutputActivityTuple, RevDiffDualMode mode>
+struct create_function_signature<RevDiff<Func, InputActivityTuple,
+          OutputActivityTuple, mode>>
+{
+   using type = typename
+                RevDiff<Func, InputActivityTuple, OutputActivityTuple, mode>::signature;
+};
+
+/// Builds the reverse-mode transform of @a f, differentiating the inputs marked
+/// Active in @a activity_t.
+///
+/// A factory rather than a plain declaration of a RevDiff variable for compatibility with MSVC.
+template <typename activity_t, RevDiffDualMode mode = RevDiffDualMode::Eval,
+          typename func_t>
+auto make_revdiff(const func_t &f)
+{
+   return RevDiff<func_t, activity_t, tuple<Active>, mode>(f);
+}
+
+} // namespace mfem::future

fem/dfem/backends/scratch_bank.hpp

@@ -0,0 +1,327 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+#include "../../../general/error.hpp"
+#include "../../../linalg/vector.hpp"
+#include "../tuple.hpp"
+#include <initializer_list>
+#include <memory>
+#include <type_traits>
+#include <utility>
+#include <vector>
+
+namespace mfem::future
+{
+// Scratch storage and q-function shadow helpers for dFEM backends. The bank
+// supports two scratch kinds:
+// - quadrature-point scratch: real_t buffers sized as NQ * components_per_qp,
+// - global scratch: one tuple of qfunction-local temporaries, independent of
+//   NQ, used for values such as flags, scalars, or small Vector workspaces.
+//
+// @a scalar_t is the scalar the owning q-function uses at a quadrature point.
+// With Enzyme this is real_t and the tangent lives in a separate shadow bank.
+// Without Enzyme the q-function is evaluated on native duals, which carry the
+// tangent inside the value itself; the bank then widens its backing storage
+// accordingly so that a scratch entry can round-trip a dual without dropping
+// the gradient. Backing storage stays a real_t Vector in both cases, so the
+// device and shadow plumbing is unchanged.
+template <typename scalar_t, typename... GlobalScratchTypes>
+struct ScratchBank
+{
+   static_assert(sizeof(scalar_t) % sizeof(real_t) == 0,
+                 "scratch scalar must be a whole number of real_t");
+
+   /// Number of real_t needed to back one scalar_t scratch entry.
+   static constexpr int scalar_size = sizeof(scalar_t) / sizeof(real_t);
+
+
+   //=================================
+   ///<--- Global scratch utilities.
+   //=================================
+
+   using GlobalScratchTuple = tuple<GlobalScratchTypes...>;
+
+   template <typename T>
+   static T MakeGlobalScratchShadow(const T &)
+   {
+      return T {};
+   }
+
+   static Vector MakeGlobalScratchShadow(const Vector &primal)
+   {
+      Vector shadow(primal.Size());
+      shadow.UseDevice(true);
+      shadow = 0.0;
+      return shadow;
+   }
+
+   template <typename Tuple, size_t... Is>
+   static auto MakeGlobalScratchShadowTuple(const Tuple &primal,
+                                            std::index_sequence<Is...>)
+   {
+      return make_tuple(MakeGlobalScratchShadow(get<Is>(primal))...);
+   }
+
+   template <typename Tuple>
+   static auto MakeGlobalScratchShadowTuple(const Tuple &primal)
+   {
+      return MakeGlobalScratchShadowTuple(
+                primal, std::make_index_sequence<tuple_size<Tuple>::value> {});
+   }
+
+
+   //===========================
+   ///<--- Scratch objects
+   //===========================
+
+   mutable GlobalScratchTuple global;
+
+   int nq = 0;
+   std::vector<int> components;
+   std::vector<int> sizes;
+   std::vector<std::shared_ptr<Vector>> owned;
+   std::vector<real_t *> ptrs;
+
+
+   //===========================
+   ///<--- Setter methods
+   //===========================
+
+   void SetScratch(const int nq_,
+                   std::initializer_list<int> components_per_qp = {1})
+   {
+      SetScratch(nq_, std::vector<int>(components_per_qp));
+   }
+
+   void SetScratch(const int nq_, const std::vector<int> &components_per_qp)
+   {
+      nq = nq_;
+      components.clear();
+      sizes.clear();
+      owned.clear();
+      ptrs.clear();
+      for (int component_count : components_per_qp)
+      {
+         AddScratch(component_count);
+      }
+   }
+
+   void AddScratch(const int components_per_qp = 1)
+   {
+      MFEM_VERIFY(nq > 0, "SetScratch must be called before AddScratch");
+      MFEM_VERIFY(components_per_qp > 0,
+                  "scratch components per quadrature point must be positive");
+      owned.push_back(std::make_shared<Vector>());
+      Vector &scratch = *owned.back();
+      const int size = components_per_qp * nq * scalar_size;
+      scratch.SetSize(size);
+      scratch.UseDevice(true);
+      scratch = 0.0;
+      components.push_back(components_per_qp);
+      sizes.push_back(scratch.Size());
+      ptrs.push_back(scratch.ReadWrite());
+   }
+
+   void SetGlobalScratch(const GlobalScratchTuple &global_)
+   {
+      global = global_;
+   }
+
+
+   //===========================
+   ///<--- Getter methods
+   //===========================
+
+   /// Scratch buffer @a i viewed as the q-function's scalar type.
+   scalar_t *GetScratchPointer(const int i) const
+   {
+      return reinterpret_cast<scalar_t *>(ptrs[i]);
+   }
+
+   scalar_t *operator[](const int i) const { return GetScratchPointer(i); }
+
+   /// Raw real_t backing storage of scratch buffer @a i. Its size is
+   /// scalar_size times the number of scalar_t entries.
+   Vector &GetScratchVector(const int i) const { return *owned[i]; }
+
+   template <int I>
+   auto &GetGlobalScratch() const
+   {
+      return get<I>(global);
+   }
+
+
+   //===========================
+   ///<--- Utils methods
+   //===========================
+
+   void CloneScratchLayoutTo(ScratchBank &shadow) const
+   {
+      shadow.SetScratch(nq, components);
+      shadow.SetGlobalScratch(MakeGlobalScratchShadowTuple(global));
+   }
+
+   int Size() const { return static_cast<int>(ptrs.size()); }
+};
+
+// Shared base for Q-functions that use ScratchBank. Under Enzyme a matching
+// scratch shadow is created for forward differentiation; with native duals the
+// tangent rides along in the scratch entry and no shadow is created.
+template <typename scalar_t, typename... GlobalScratchTypes>
+struct QFWithScratch
+{
+   using GlobalScratchTuple = tuple<GlobalScratchTypes...>;
+   using ScratchScalar = scalar_t;
+
+   /// Number of real_t backing one scratch entry; see ScratchBank.
+   static constexpr int scalar_size =
+      ScratchBank<scalar_t, GlobalScratchTypes...>::scalar_size;
+
+   int nq = 0;
+   ScratchBank<scalar_t, GlobalScratchTypes...> scratch;
+
+   void SetScratch(const int nq_,
+                   std::initializer_list<int> components_per_qp = {1})
+   {
+      nq = nq_;
+      scratch.SetScratch(nq, components_per_qp);
+   }
+
+   void SetScratch(const int nq_, const std::vector<int> &components_per_qp)
+   {
+      nq = nq_;
+      scratch.SetScratch(nq, components_per_qp);
+   }
+
+   void SetScratch(const int nq_, const int num_scratch_elem,
+                   const int components_per_qp = 1)
+   {
+      nq = nq_;
+      scratch.SetScratch(nq,
+                         std::vector<int>(num_scratch_elem, components_per_qp));
+   }
+
+   void SetGlobalScratch(const GlobalScratchTuple &global_scratch_)
+   {
+      scratch.SetGlobalScratch(global_scratch_);
+   }
+
+   Vector &GetScratchVector(const int i) const
+   {
+      return scratch.GetScratchVector(i);
+   }
+
+   scalar_t *GetScratchPointer(const int i) const
+   {
+      return scratch.GetScratchPointer(i);
+   }
+
+   template <int I>
+   auto &GetGlobalScratch() const
+   {
+      return scratch.template GetGlobalScratch<I>();
+   }
+
+   void CloneScratchLayoutTo(QFWithScratch &shadow) const
+   {
+      shadow.nq = nq;
+      scratch.CloneScratchLayoutTo(shadow.scratch);
+   }
+
+   QFWithScratch CreateShadow() const
+   {
+      QFWithScratch shadow;
+      CloneScratchLayoutTo(shadow);
+      return shadow;
+   }
+};
+
+/// Q-function base with quadrature-point scratch only. @a scalar_t is the
+/// scalar the q-function signature uses (real_t under Enzyme, dual otherwise).
+template <typename scalar_t = real_t>
+using QFWithScratchType = QFWithScratch<scalar_t>;
+
+/// Q-function base with quadrature-point scratch and a global scratch tuple.
+template <typename scalar_t = real_t>
+using QFWithGlobalScratchType =
+   QFWithScratch<scalar_t, bool, real_t, Vector>;
+
+namespace detail
+{
+
+template <typename T>
+struct qfunc_uses_scratch
+{
+private:
+   template <typename scalar_t, typename... GlobalScratchTypes>
+   static std::true_type Test(
+      const QFWithScratch<scalar_t, GlobalScratchTypes...> *);
+
+   static std::false_type Test(...);
+
+public:
+   static constexpr bool value = decltype(Test(
+                                             static_cast<std::remove_cv_t<std::remove_reference_t<T>> *>(nullptr)))::value;
+};
+
+template <typename T>
+inline constexpr bool qfunc_uses_scratch_v =
+   qfunc_uses_scratch<T>::value;
+
+struct unused_qfunc_shadow { };
+
+// A separate shadow scratch bank only exists for Enzyme, which writes tangents
+// into shadow memory. The native dual fallback carries the tangent inside the
+// scratch entry itself (see ScratchBank::scalar_size), so a shadow bank would
+// be allocated and never read; it is dropped entirely there.
+template <typename T>
+inline constexpr bool qfunc_needs_shadow_v =
+#ifdef MFEM_USE_ENZYME
+   qfunc_uses_scratch_v<T>;
+#else
+   false;
+#endif
+
+template <typename qfunc_t, bool needs_shadow>
+struct qfunc_shadow_type
+{
+   using type = unused_qfunc_shadow;
+};
+
+template <typename qfunc_t>
+struct qfunc_shadow_type<qfunc_t, true>
+{
+   using type = decltype(std::declval<const qfunc_t &>().CreateShadow());
+};
+
+template <typename qfunc_t>
+using qfunc_shadow_t = typename qfunc_shadow_type<qfunc_t,
+      qfunc_needs_shadow_v<qfunc_t>>::type;
+
+// Create a persistent q-function shadow if one is needed, otherwise return an empty struct.
+template <typename qfunc_t>
+inline qfunc_shadow_t<qfunc_t> MakeQFunctionShadowStorage(
+   const qfunc_t &qfunc)
+{
+   if constexpr (qfunc_needs_shadow_v<qfunc_t>)
+   {
+      return qfunc.CreateShadow();
+   }
+   else
+   {
+      MFEM_CONTRACT_VAR(qfunc);
+      return {};
+   }
+}
+
+} // namespace detail
+
+}

fem/dfem/doperator.cpp

@@ -11,92 +11,366 @@
 
 #include "doperator.hpp"
 
+#include <algorithm>
+
 #ifdef MFEM_USE_MPI
 
 using namespace mfem;
 using namespace mfem::future;
 
-void DifferentiableOperator::SetParameters(std::vector<Vector *> p) const
+namespace
 {
-   MFEM_ASSERT(parameters.size() == p.size(),
-               "number of parameters doesn't match descriptors");
-   for (size_t i = 0; i < parameters.size(); i++)
+int GetTotalTrueVSize(const std::vector<FieldDescriptor> &fds)
+{
+   int size = 0;
+   for (const auto &fd : fds)
    {
-      p[i]->Read();
-      parameters_l[i] = *p[i];
+      size += mfem::future::GetTrueVSize(fd);
    }
+   return size;
+}
+
+template <typename map_t>
+const typename map_t::mapped_type &FindOrDefault(
+   const map_t &map, const typename map_t::key_type &id,
+   const typename map_t::mapped_type &fallback)
+{
+   const auto it = map.find(id);
+   return it == map.end() ? fallback : it->second;
+}
+
+template <typename map_t>
+typename map_t::mapped_type FindOrEmpty(
+   const map_t &map, const typename map_t::key_type &id)
+{
+   const auto it = map.find(id);
+   return it == map.end() ? typename map_t::mapped_type{} : it->second;
+}
+
+const std::vector<derivative_action_t> &SelectActionCallbacks(
+   const std::vector<derivative_action_t> &direct_actions,
+   const DerivativeActionMap &cached_actions,
+   size_t derivative_id,
+   bool use_cached_setup)
+{
+   if (use_cached_setup)
+   {
+      const auto it_apply = cached_actions.find(derivative_id);
+      if (it_apply != cached_actions.end() && !it_apply->second.empty())
+      {
+         return it_apply->second;
+      }
+   }
+
+   return direct_actions;
+}
+
+struct DerivativeCallbackSet
+{
+   const DerivativeActionMap &actions;
+   const DerivativeActionMap &cached_actions;
+   const DerivativeActionMap &transpose_actions;
+   const DerivativeFieldMap &outfds;
+   const SparseAssemblyMap &assemble_sparse;
+   const HypreAssemblyMap &assemble_hypre;
+   const DiagonalAssemblyMap &assemble_diagonal;
+   const DerivativeSetupMap &setup;
+   const char *missing_action_message;
+};
+
+struct SecondDerivativeCallbackSet
+{
+   const SecondDerivativeActionMap &actions;
+   const SecondDerivativeActionMap &cached_actions;
+   const SecondDerivativeActionMap &transpose_actions;
+   const SecondDerivativeFieldMap &outfds;
+   const SecondSparseAssemblyMap &assemble_sparse;
+   const SecondHypreAssemblyMap &assemble_hypre;
+   const SecondDiagonalAssemblyMap &assemble_diagonal;
+   const SecondDerivativeSetupMap &setup;
+   const char *missing_action_message;
+};
+
+template <typename vector_t>
+std::shared_ptr<DerivativeOperator> MakeStatefulDerivativeOperator(
+   size_t derivative_id,
+   const vector_t &x,
+   const std::vector<FieldDescriptor> &infds,
+   const std::vector<FieldDescriptor> &default_outfds,
+   const DerivativeCallbackSet &callbacks,
+   bool use_cached_setup,
+   bool lvector_mode,
+   bool functional_gradient = false)
+{
+   const auto it_action = callbacks.actions.find(derivative_id);
+   MFEM_ASSERT(it_action != callbacks.actions.end(),
+               callbacks.missing_action_message << derivative_id);
+
+   const size_t dfidx = FindIdx(derivative_id, infds);
+   const auto &doutfds =
+      FindOrDefault(callbacks.outfds, derivative_id, default_outfds);
+   const auto &mult_callbacks =
+      SelectActionCallbacks(it_action->second, callbacks.cached_actions,
+                            derivative_id, use_cached_setup);
+
+   return std::make_shared<DerivativeOperator>(
+             GetTotalTrueVSize(doutfds),
+             GetTrueVSize(infds[dfidx]),
+             mult_callbacks,
+             FindOrEmpty(callbacks.transpose_actions, derivative_id),
+             infds[dfidx],
+             x,
+             infds,
+             doutfds,
+             FindOrEmpty(callbacks.assemble_sparse, derivative_id),
+             FindOrEmpty(callbacks.assemble_hypre, derivative_id),
+             FindOrEmpty(callbacks.assemble_diagonal, derivative_id),
+             FindOrEmpty(callbacks.setup, derivative_id),
+             lvector_mode,
+             functional_gradient);
+}
+
+const std::vector<derivative_action_t> &SelectSecondDerivativeActionCallbacks(
+   const std::vector<derivative_action_t> &direct_actions,
+   const SecondDerivativeActionMap &cached_actions,
+   second_derivative_key_t derivative_key,
+   bool use_cached_setup)
+{
+   if (use_cached_setup)
+   {
+      const auto it_apply = cached_actions.find(derivative_key);
+      if (it_apply != cached_actions.end() && !it_apply->second.empty())
+      {
+         return it_apply->second;
+      }
+   }
+
+   return direct_actions;
+}
+
+template <typename vector_t>
+std::shared_ptr<DerivativeOperator> MakeStatefulSecondDerivativeOperator(
+   size_t gradient_id,
+   size_t direction_id,
+   const vector_t &x,
+   const std::vector<FieldDescriptor> &infds,
+   const std::vector<FieldDescriptor> &default_outfds,
+   const SecondDerivativeCallbackSet &callbacks,
+   bool use_cached_setup,
+   bool lvector_mode)
+{
+   const second_derivative_key_t derivative_key{gradient_id, direction_id};
+   const auto it_action = callbacks.actions.find(derivative_key);
+   MFEM_ASSERT(it_action != callbacks.actions.end(),
+               callbacks.missing_action_message << "(" << gradient_id << ", "
+               << direction_id << ")");
+
+   const size_t dfidx = FindIdx(direction_id, infds);
+   const auto &doutfds =
+      FindOrDefault(callbacks.outfds, derivative_key, default_outfds);
+   const auto &mult_callbacks =
+      SelectSecondDerivativeActionCallbacks(
+         it_action->second, callbacks.cached_actions, derivative_key,
+         use_cached_setup);
+
+   return std::make_shared<DerivativeOperator>(
+             GetTotalTrueVSize(doutfds),
+             GetTrueVSize(infds[dfidx]),
+             mult_callbacks,
+             FindOrEmpty(callbacks.transpose_actions, derivative_key),
+             infds[dfidx],
+             x,
+             infds,
+             doutfds,
+             FindOrEmpty(callbacks.assemble_sparse, derivative_key),
+             FindOrEmpty(callbacks.assemble_hypre, derivative_key),
+             FindOrEmpty(callbacks.assemble_diagonal, derivative_key),
+             FindOrEmpty(callbacks.setup, derivative_key),
+             lvector_mode);
+}
 }
 
 DifferentiableOperator::DifferentiableOperator(
-   const std::vector<FieldDescriptor> &solutions,
-   const std::vector<FieldDescriptor> &parameters,
+   const std::vector<FieldDescriptor> &infds,
+   const std::vector<FieldDescriptor> &outfds,
    const ParMesh &mesh) :
+   Operator(),
    mesh(mesh),
-   solutions(solutions),
-   parameters(parameters)
+   infds(infds),
+   outfds(outfds)
 {
-   fields.resize(solutions.size() + parameters.size());
-   fields_e.resize(fields.size());
-   solutions_l.resize(solutions.size());
-   parameters_l.resize(parameters.size());
+   unionfds.clear();
+   unionfds.insert(unionfds.end(), infds.begin(), infds.end());
+   unionfds.insert(unionfds.end(), outfds.begin(), outfds.end());
+   std::sort(unionfds.begin(), unionfds.end());
+   auto last = std::unique(unionfds.begin(), unionfds.end());
+   unionfds.erase(last, unionfds.end());
 
-   for (size_t i = 0; i < solutions.size(); i++)
+   infields_l.resize(infds.size());
+   for (size_t i = 0; i < infds.size(); i++)
    {
-      fields[i] = solutions[i];
+      infields_l[i] = new Vector(GetVSize(infds[i]));
    }
 
-   for (size_t i = 0; i < parameters.size(); i++)
-   {
-      fields[i + solutions.size()] = parameters[i];
-   }
+   infields_e.resize(infds.size());
 }
 
-
-void FDJacobian::Mult(const Vector &v, Vector &y) const
+void DifferentiableOperator::SetMultLevel(MultLevel level)
 {
-   // See [1] for choice of eps.
-   //
-   // [1] Woodward, C.S., Gardner, D.J. and Evans, K.J., 2015. On the use of
-   // finite difference matrix-vector products in Newton-Krylov solvers for
-   // implicit climate dynamics with spectral elements. Procedia Computer
-   // Science, 51, pp.2036-2045.
-   real_t eps;
-   if (fixed_eps > 0.0)
-   {
-      eps = fixed_eps;
-   }
-   else
-   {
-      const real_t vnorm_local = v.Norml2();
-      real_t vnorm;
-      MPI_Allreduce(&vnorm_local, &vnorm, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
-                    MPI_COMM_WORLD);
-      eps = lambda * (lambda + xnorm / vnorm);
-   }
+   mult_level = level;
+}
 
-   // x + eps * v
-   {
-      const auto d_v = v.Read();
-      const auto d_x = x.Read();
-      auto d_xpev = xpev.Write();
-      mfem::forall(x.Size(), [=] MFEM_HOST_DEVICE (int i)
-      {
-         d_xpev[i] = d_x[i] + eps * d_v[i];
-      });
-   }
+void DifferentiableOperator::Mult(const Vector &x, Vector &y) const
+{
+   MFEM_ASSERT(!action_callbacks.empty(),
+               "no integrators have been set");
 
-   // y = f(x + eps * v)
-   op.Mult(xpev, y);
+   MFEM_ASSERT(dynamic_cast<const BlockVector*>(&x),
+               "x needs to be a BlockVector");
 
-   // y = (f(x + eps * v) - f(x)) / eps
+   MFEM_ASSERT(dynamic_cast<const BlockVector*>(&y),
+               "y needs to be a BlockVector");
+
+   const auto &bx = static_cast<const BlockVector &>(x);
+   auto &by = static_cast<BlockVector &>(y);
+
+   Mult(bx, by);
+}
+
+void DifferentiableOperator::DisableTensorProductStructure(bool disable)
+{
+   use_tensor_product_structure = !disable;
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetDerivative(
+   size_t derivative_id, const Vector &x)
+{
+   return MakeStatefulDerivativeOperator(
+             derivative_id, x, infds, outfds,
    {
-      const auto d_f = f.Read();
-      auto d_y = y.ReadWrite();
-      mfem::forall(f.Size(), [=] MFEM_HOST_DEVICE (int i)
-      {
-         d_y[i] = (d_y[i] - d_f[i]) / eps;
-      });
-   }
+      derivative_action_callbacks,
+      derivative_apply_callbacks,
+      daction_transpose_callbacks,
+      derivative_outfds,
+      assemble_derivative_sparsematrix_callbacks,
+      assemble_derivative_hypreparmatrix_callbacks,
+      assemble_diagonal_callbacks,
+      derivative_setup_callbacks,
+      "no derivative action has been found for ID "
+   },
+   true,
+   mult_level == MultLevel::LVECTOR,
+   IsFunctionalDerivative(derivative_id));
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetDerivative(
+   size_t derivative_id, const MultiVector &x, const bool use_cached_setup)
+{
+   return MakeStatefulDerivativeOperator(
+             derivative_id, x, infds, outfds,
+   {
+      derivative_action_callbacks,
+      derivative_apply_callbacks,
+      daction_transpose_callbacks,
+      derivative_outfds,
+      assemble_derivative_sparsematrix_callbacks,
+      assemble_derivative_hypreparmatrix_callbacks,
+      assemble_diagonal_callbacks,
+      derivative_setup_callbacks,
+      "no derivative action has been found for ID "
+   },
+   use_cached_setup,
+   mult_level == MultLevel::LVECTOR,
+   IsFunctionalDerivative(derivative_id));
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetDerivative(
+   size_t derivative_id)
+{
+   MFEM_ASSERT(HasFunctionalIntegrator(),
+               "stateless GetDerivative is available only for functionals");
+
+   const auto it_action = derivative_action_callbacks.find(derivative_id);
+   MFEM_ASSERT(it_action != derivative_action_callbacks.end(),
+               "no derivative action has been found for ID " << derivative_id);
+
+   const size_t dfidx = FindIdx(derivative_id, infds);
+   const auto &doutfds =
+      FindOrDefault(derivative_outfds, derivative_id, outfds);
+
+   return std::make_shared<DerivativeOperator>(
+             GetTotalTrueVSize(doutfds),
+             GetTrueVSize(infds[dfidx]),
+             it_action->second,
+             infds,
+             doutfds);
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetSecondDerivative(
+   size_t derivative_id, const Vector &x)
+{
+   return GetSecondDerivative(derivative_id, derivative_id, x);
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetSecondDerivative(
+   size_t gradient_id, size_t direction_id, const Vector &x)
+{
+   MFEM_ASSERT(HasFunctionalIntegrator(),
+               "second derivatives are available only for functionals");
+
+   return MakeStatefulSecondDerivativeOperator(
+             gradient_id, direction_id, x, infds, outfds,
+   {
+      second_derivative_action_callbacks,
+      second_derivative_apply_callbacks,
+      second_daction_transpose_callbacks,
+      second_derivative_outfds,
+      assemble_second_derivative_sparsematrix_callbacks,
+      assemble_second_derivative_hypreparmatrix_callbacks,
+      assemble_second_derivative_diagonal_callbacks,
+      second_derivative_setup_callbacks,
+      "no second derivative action has been found for ID "
+   },
+   false,
+   mult_level == MultLevel::LVECTOR);
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetSecondDerivative(
+   size_t derivative_id, const MultiVector &x, const bool use_cached_setup)
+{
+   return GetSecondDerivative(derivative_id, derivative_id, x, use_cached_setup);
+}
+
+std::shared_ptr<DerivativeOperator> DifferentiableOperator::GetSecondDerivative(
+   size_t gradient_id, size_t direction_id, const MultiVector &x,
+   const bool use_cached_setup)
+{
+   MFEM_ASSERT(HasFunctionalIntegrator(),
+               "second derivatives are available only for functionals");
+
+   return MakeStatefulSecondDerivativeOperator(
+             gradient_id, direction_id, x, infds, outfds,
+   {
+      second_derivative_action_callbacks,
+      second_derivative_apply_callbacks,
+      second_daction_transpose_callbacks,
+      second_derivative_outfds,
+      assemble_second_derivative_sparsematrix_callbacks,
+      assemble_second_derivative_hypreparmatrix_callbacks,
+      assemble_second_derivative_diagonal_callbacks,
+      second_derivative_setup_callbacks,
+      "no second derivative action has been found for ID "
+   },
+   use_cached_setup,
+   mult_level == MultLevel::LVECTOR);
+}
+
+bool DifferentiableOperator::HasSecondDerivative(size_t gradient_id,
+                                                 size_t direction_id) const
+{
+   const second_derivative_key_t derivative_key{gradient_id, direction_id};
+   const auto it = second_derivative_action_callbacks.find(derivative_key);
+   return it != second_derivative_action_callbacks.end() && !it->second.empty();
 }
 
 #endif // MFEM_USE_MPI

fem/dfem/fielddescriptor.hpp

@@ -0,0 +1,64 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include "../fespace.hpp"
+#include "../qspace.hpp"
+#include "parameterspace.hpp"
+
+namespace mfem::future
+{
+
+/// @brief FieldDescriptor struct
+///
+/// This struct is used to store information about a field.
+struct FieldDescriptor
+{
+   using data_variant_t =
+      std::variant<const FiniteElementSpace *,
+      const ParFiniteElementSpace *,
+      const VectorQuadratureSpace *,
+      const ParameterSpace *>;
+
+   /// Field ID
+   std::size_t id;
+
+   /// Field variant
+   data_variant_t data;
+
+   /// Default constructor
+   FieldDescriptor() :
+      id(SIZE_MAX), data(data_variant_t{}) {}
+
+   /// Constructor
+   template <typename T>
+   FieldDescriptor(std::size_t field_id, const T* v) :
+      id(field_id), data(v) {}
+
+   bool operator==(const FieldDescriptor& other) const
+   {
+      return id == other.id;
+   }
+
+   bool operator<(const FieldDescriptor& other) const
+   {
+      return id < other.id;
+   }
+
+   friend void swap(FieldDescriptor& a, FieldDescriptor& b)
+   {
+      using std::swap;
+      swap(a.id, b.id);
+      swap(a.data, b.data);
+   }
+};
+
+}

fem/dfem/fieldoperator.hpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 #pragma once
 
+#include <ostream>
 #include <type_traits>
 
 namespace mfem::future
@@ -74,6 +75,15 @@ struct is_identity_fop : std::false_type {};
 template <int FIELD_ID>
 struct is_identity_fop<Identity<FIELD_ID>> : std::true_type {};
 
+template <typename T>
+constexpr bool is_identity_fop_v = is_identity_fop<T>::value;
+
+template <int FIELD_ID>
+inline std::ostream& operator<<(std::ostream& out, Identity<FIELD_ID>)
+{
+   return out << "Identity<" << FIELD_ID << ">";
+}
+
 /// @brief Weight FieldOperator.
 ///
 /// This FieldOperator is used to signal that this field contains the quadrature
@@ -90,6 +100,14 @@ struct is_weight_fop : std::false_type {};
 template <>
 struct is_weight_fop<Weight> : std::true_type {};
 
+template <typename T>
+constexpr bool is_weight_fop_v = is_weight_fop<T>::value;
+
+inline std::ostream& operator<<(std::ostream& out, Weight)
+{
+   return out << "Weight";
+}
+
 /// @brief Value FieldOperator.
 ///
 /// This FieldOperator is used to signal that the field contains the
@@ -101,11 +119,20 @@ public:
    constexpr Value() : FieldOperator<FIELD_ID>() {};
 };
 
-template< typename T >
+template <typename T>
 struct is_value_fop : std::false_type {};
 
+template <int T>
+struct is_value_fop<Value<T>> : std::true_type {};
+
+template <typename T>
+constexpr bool is_value_fop_v = is_value_fop<T>::value;
+
 template <int FIELD_ID>
-struct is_value_fop<Value<FIELD_ID>> : std::true_type {};
+inline std::ostream& operator<<(std::ostream& out, Value<FIELD_ID>)
+{
+   return out << "Value<" << FIELD_ID << ">";
+}
 
 /// @brief Gradient FieldOperator.
 ///
@@ -124,6 +151,15 @@ struct is_gradient_fop : std::false_type {};
 template <int FIELD_ID>
 struct is_gradient_fop<Gradient<FIELD_ID>> : std::true_type {};
 
+template <typename T>
+constexpr bool is_gradient_fop_v = is_gradient_fop<T>::value;
+
+template <int FIELD_ID>
+inline std::ostream& operator<<(std::ostream& out, Gradient<FIELD_ID>)
+{
+   return out << "Gradient<" << FIELD_ID << ">";
+}
+
 /// @brief Sum FieldOperator.
 ///
 /// This FieldOperator is commonly used to signal that an output of a quadrature
@@ -141,4 +177,39 @@ struct is_sum_fop : std::false_type {};
 template <int FIELD_ID>
 struct is_sum_fop<Sum<FIELD_ID>> : std::true_type {};
 
+template <typename T>
+constexpr bool is_sum_fop_v = is_sum_fop<T>::value;
+
+template <int FIELD_ID>
+inline std::ostream& operator<<(std::ostream& out, Sum<FIELD_ID>)
+{
+   return out << "Sum<" << FIELD_ID << ">";
+}
+
+/// @brief FunctionalValue FieldOperator.
+///
+/// This FieldOperator is commonly used to signal that an output of a quadrature
+/// function should be summed.
+template <int FIELD_ID = -1>
+class FunctionalValue : public FieldOperator<FIELD_ID>
+{
+public:
+   constexpr FunctionalValue() : FieldOperator<FIELD_ID>() {};
+};
+
+template< typename T >
+struct is_functionalvalue_fop : std::false_type {};
+
+template <int FIELD_ID>
+struct is_functionalvalue_fop<FunctionalValue<FIELD_ID>> : std::true_type {};
+
+template <typename T>
+constexpr bool is_functionalvalue_fop_v = is_functionalvalue_fop<T>::value;
+
+template <int FIELD_ID>
+inline std::ostream& operator<<(std::ostream& out, FunctionalValue<FIELD_ID>)
+{
+   return out << "FunctionalValue<" << FIELD_ID << ">";
+}
+
 } // namespace mfem::future

fem/dfem/integrate.hpp

@@ -1,536 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-
-namespace mfem::future
-{
-
-template <typename output_t>
-MFEM_HOST_DEVICE
-void map_quadrature_data_to_fields_impl(
-   DeviceTensor<2, real_t> &y,
-   const DeviceTensor<3, real_t> &f,
-   const output_t &output,
-   const DofToQuadMap &dtq)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   // assuming the quadrature point residual has to "play nice with
-   // the test function"
-   if constexpr (is_value_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [num_qp, cdim, num_dof] = B.GetShape();
-      const int vdim = output.vdim > 0 ? output.vdim : cdim ;
-      for (int dof = 0; dof < num_dof; dof++)
-      {
-         for (int vd = 0; vd < vdim; vd++)
-         {
-            real_t acc = 0.0;
-            for (int qp = 0; qp < num_qp; qp++)
-            {
-               acc += B(qp, 0, dof) * f(vd, 0, qp);
-            }
-            y(dof, vd) += acc;
-         }
-      }
-   }
-   else if constexpr (
-      is_gradient_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [num_qp, dim, num_dof] = G.GetShape();
-      const int vdim = output.vdim;
-      for (int dof = 0; dof < num_dof; dof++)
-      {
-         for (int vd = 0; vd < vdim; vd++)
-         {
-            real_t acc = 0.0;
-            for (int d = 0; d < dim; d++)
-            {
-               for (int qp = 0; qp < num_qp; qp++)
-               {
-                  acc += G(qp, d, dof) * f(vd, d, qp);
-               }
-            }
-            y(dof, vd) += acc;
-         }
-      }
-   }
-   else if constexpr (is_sum_fop<std::decay_t<output_t>>::value)
-   {
-      // This is the "integral over all quadrature points type" applying
-      // B = 1 s.t. B^T * C \in R^1.
-      const auto [num_qp, unused, unused1] = B.GetShape();
-      auto cc = Reshape(&f(0, 0, 0), num_qp);
-      for (int i = 0; i < num_qp; i++)
-      {
-         y(0, 0) += cc(i);
-      }
-   }
-   else if constexpr (is_identity_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [num_qp, unused, num_dof] = B.GetShape();
-      const auto vdim = output.vdim;
-      auto cc = Reshape(&f(0, 0, 0), num_qp * vdim);
-      auto yy = Reshape(&y(0, 0), num_qp * vdim);
-      for (int i = 0; i < num_qp * vdim; i++)
-      {
-         yy(i) = cc(i);
-      }
-   }
-   else
-   {
-      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
-                        " for this field descriptor");
-   }
-}
-
-template <typename output_t>
-MFEM_HOST_DEVICE
-void map_quadrature_data_to_fields_tensor_impl_1d(
-   DeviceTensor<2, real_t> &y,
-   const DeviceTensor<3, real_t> &f,
-   const output_t &output,
-   const DofToQuadMap &dtq,
-   std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, vdim);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dx, x, d1d)
-         {
-            real_t acc = 0.0;
-            for (int qx = 0; qx < q1d; qx++)
-            {
-               acc += fqp(vd, 0, qx) * B(qx, 0, dx);
-            }
-            yd(dx, vd) = acc;
-         }
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (is_gradient_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = G.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, vdim);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dx, x, d1d)
-         {
-            real_t acc = 0.0;
-            for (int qx = 0; qx < q1d; qx++)
-            {
-               acc += fqp(vd, 0, qx) * G(qx, 0, dx);
-            }
-            yd(dx, vd) = acc;
-         }
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (is_identity_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      auto fqp = Reshape(&f(0, 0, 0), output.size_on_qp, q1d);
-      auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d);
-
-      for (int sq = 0; sq < output.size_on_qp; sq++)
-      {
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            yqp(sq, qx) = fqp(sq, qx);
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else
-   {
-      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
-                        "for this field descriptor with sum factorization on"
-                        " tensor product elements");
-   }
-}
-
-template <typename output_t>
-MFEM_HOST_DEVICE
-void map_quadrature_data_to_fields_tensor_impl_2d(
-   DeviceTensor<2, real_t> &y,
-   const DeviceTensor<3, real_t> &f,
-   const output_t &output,
-   const DofToQuadMap &dtq,
-   std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, d1d, vdim);
-
-      auto s0 = Reshape(&scratch_mem[0](0), q1d, d1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               real_t acc = 0.0;
-               for (int qx = 0; qx < q1d; qx++)
-               {
-                  acc += fqp(vd, 0, qx, qy) * B(qx, 0, dx);
-               }
-               s0(qy, dx) = acc;
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               real_t acc = 0.0;
-               for (int qy = 0; qy < q1d; qy++)
-               {
-                  acc += s0(qy, dx) * B(qy, 0, dy);
-               }
-               yd(dx, dy, vd) += acc;
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (is_gradient_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = G.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, d1d, vdim);
-
-      auto s0 = Reshape(&scratch_mem[0](0), q1d, d1d);
-      auto s1 = Reshape(&scratch_mem[1](0), q1d, d1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               real_t uv[2] = {0.0, 0.0};
-               for (int qx = 0; qx < q1d; qx++)
-               {
-                  uv[0] += fqp(vd, 0, qx, qy) * G(qx, 0, dx);
-                  uv[1] += fqp(vd, 1, qx, qy) * B(qx, 0, dx);
-               }
-               s0(qy, dx) = uv[0];
-               s1(qy, dx) = uv[1];
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               real_t uv[2] = {0.0, 0.0};
-               for (int qy = 0; qy < q1d; qy++)
-               {
-                  uv[0] += s0(qy, dx) * B(qy, 0, dy);
-                  uv[1] += s1(qy, dx) * G(qy, 0, dy);
-               }
-               yd(dx, dy, vd) += uv[0] + uv[1];
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (is_identity_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-
-      // // TODO: Check if this is the right fix for all cases
-      // auto fqp = Reshape(&f(0, 0, 0), output.size_on_qp, q1d);
-      // auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d);
-      // for (int sq = 0; sq < output.size_on_qp; sq++)
-      // {
-      //    MFEM_FOREACH_THREAD(qx, x, q1d)
-      //    {
-      //       yqp(sq, qx) = fqp(sq, qx);
-      //    }
-      //    MFEM_SYNC_THREAD;
-      // }
-
-      auto fqp = Reshape(&f(0, 0, 0), output.size_on_qp, q1d, q1d);
-      auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d, q1d);
-
-      for (int sq = 0; sq < output.size_on_qp; sq++)
-      {
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               yqp(sq, qx, qy) = fqp(sq, qx, qy);
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else
-   {
-      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
-                        " for this field descriptor with sum factorization on"
-                        " tensor product elements");
-   }
-}
-
-template <typename output_t>
-MFEM_HOST_DEVICE
-void map_quadrature_data_to_fields_tensor_impl_3d(
-   DeviceTensor<2, real_t> &y,
-   const DeviceTensor<3, real_t> &f,
-   const output_t &output,
-   const DofToQuadMap &dtq,
-   std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
-
-      auto s0 = Reshape(&scratch_mem[0](0), q1d, q1d, d1d);
-      auto s1 = Reshape(&scratch_mem[1](0), q1d, d1d, d1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               MFEM_FOREACH_THREAD(qz, z, q1d)
-               {
-                  real_t acc = 0.0;
-                  for (int qx = 0; qx < q1d; qx++)
-                  {
-                     acc += fqp(vd, 0, qx, qy, qz) * B(qx, 0, dx);
-                  }
-                  s0(qz, qy, dx) = acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               MFEM_FOREACH_THREAD(qz, z, q1d)
-               {
-                  real_t acc = 0.0;
-                  for (int qy = 0; qy < q1d; qy++)
-                  {
-                     acc += s0(qz, qy, dx) * B(qy, 0, dy);
-                  }
-                  s1(qz, dy, dx) = acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(dx, x, d1d)
-            {
-               MFEM_FOREACH_THREAD(dz, z, d1d)
-               {
-                  real_t acc = 0.0;
-                  for (int qz = 0; qz < q1d; qz++)
-                  {
-                     acc += s1(qz, dy, dx) * B(qz, 0, dz);
-                  }
-                  yd(dx, dy, dz, vd) += acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (is_gradient_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = G.GetShape();
-      const int vdim = output.vdim;
-      const int test_dim = output.size_on_qp / vdim;
-      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d, q1d);
-      auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
-
-      auto s0 = Reshape(&scratch_mem[0](0), q1d, q1d, d1d);
-      auto s1 = Reshape(&scratch_mem[1](0), q1d, q1d, d1d);
-      auto s2 = Reshape(&scratch_mem[2](0), q1d, q1d, d1d);
-      auto s3 = Reshape(&scratch_mem[3](0), q1d, d1d, d1d);
-      auto s4 = Reshape(&scratch_mem[4](0), q1d, d1d, d1d);
-      auto s5 = Reshape(&scratch_mem[5](0), q1d, d1d, d1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qz, z, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD(dx, x, d1d)
-               {
-                  real_t uvw[3] = {0.0, 0.0, 0.0};
-                  for (int qx = 0; qx < q1d; qx++)
-                  {
-                     uvw[0] += fqp(vd, 0, qx, qy, qz) * G(qx, 0, dx);
-                     uvw[1] += fqp(vd, 1, qx, qy, qz) * B(qx, 0, dx);
-                     uvw[2] += fqp(vd, 2, qx, qy, qz) * B(qx, 0, dx);
-                  }
-                  s0(qz, qy, dx) = uvw[0];
-                  s1(qz, qy, dx) = uvw[1];
-                  s2(qz, qy, dx) = uvw[2];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(qz, z, q1d)
-         {
-            MFEM_FOREACH_THREAD(dy, y, d1d)
-            {
-               MFEM_FOREACH_THREAD(dx, x, d1d)
-               {
-                  real_t uvw[3] = {0.0, 0.0, 0.0};
-                  for (int qy = 0; qy < q1d; qy++)
-                  {
-                     uvw[0] += s0(qz, qy, dx) * B(qy, 0, dy);
-                     uvw[1] += s1(qz, qy, dx) * G(qy, 0, dy);
-                     uvw[2] += s2(qz, qy, dx) * B(qy, 0, dy);
-                  }
-                  s3(qz, dy, dx) = uvw[0];
-                  s4(qz, dy, dx) = uvw[1];
-                  s5(qz, dy, dx) = uvw[2];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dz, z, d1d)
-         {
-            MFEM_FOREACH_THREAD(dy, y, d1d)
-            {
-               MFEM_FOREACH_THREAD(dx, x, d1d)
-               {
-                  real_t uvw[3] = {0.0, 0.0, 0.0};
-                  for (int qz = 0; qz < q1d; qz++)
-                  {
-                     uvw[0] += s3(qz, dy, dx) * B(qz, 0, dz);
-                     uvw[1] += s4(qz, dy, dx) * B(qz, 0, dz);
-                     uvw[2] += s5(qz, dy, dx) * G(qz, 0, dz);
-                  }
-                  yd(dx, dy, dz, vd) += uvw[0] + uvw[1] + uvw[2];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (is_identity_fop<std::decay_t<output_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      auto fqp = Reshape(&f(0, 0, 0), output.size_on_qp, q1d, q1d, q1d);
-      auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d, q1d, q1d);
-
-      for (int sq = 0; sq < output.size_on_qp; sq++)
-      {
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD(qz, z, q1d)
-               {
-                  yqp(sq, qx, qy, qz) = fqp(sq, qx, qy, qz);
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else
-   {
-      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
-                        " for this field descriptor with sum factorization on"
-                        " tensor product elements");
-   }
-}
-
-template <typename output_t>
-MFEM_HOST_DEVICE
-void map_quadrature_data_to_fields(
-   DeviceTensor<2, real_t> &y,
-   const DeviceTensor<3, real_t> &f,
-   const output_t &output,
-   const DofToQuadMap &dtq,
-   std::array<DeviceTensor<1>, 6> &scratch_mem,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         map_quadrature_data_to_fields_tensor_impl_1d(y, f, output, dtq, scratch_mem);
-      }
-      else if (dimension == 2)
-      {
-         map_quadrature_data_to_fields_tensor_impl_2d(y, f, output, dtq, scratch_mem);
-      }
-      else if (dimension == 3)
-      {
-         map_quadrature_data_to_fields_tensor_impl_3d(y, f, output, dtq, scratch_mem);
-      }
-      else { MFEM_ABORT_KERNEL("dimension not supported"); }
-   }
-   else
-   {
-      map_quadrature_data_to_fields_impl(y, f, output, dtq);
-   }
-}
-
-} // namespace mfem::future

fem/dfem/integrator_ctx.hpp

@@ -0,0 +1,37 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+#pragma once
+
+#include <typeindex>
+#include <unordered_map>
+#include <vector>
+
+#include "../../general/array.hpp"
+#include "fielddescriptor.hpp"
+
+namespace mfem::future
+{
+
+struct IntegratorContext
+{
+   const ParMesh &mesh;
+   const Array<int> *elem_attr;
+   Array<int> attr;
+   const int nentities;
+   const std::vector<FieldDescriptor> &infds;
+   const std::vector<FieldDescriptor> &outfds;
+   const std::vector<FieldDescriptor> &unionfds;
+   const IntegrationRule &ir;
+   std::unordered_map<std::type_index, std::vector<int>> &in_qlayouts;
+   std::unordered_map<std::type_index, std::vector<int>> &out_qlayouts;
+};
+
+}

fem/dfem/interpolate.hpp

@@ -1,678 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-
-namespace mfem::future
-{
-
-template <typename field_operator_t>
-MFEM_HOST_DEVICE inline
-void map_field_to_quadrature_data_tensor_product_3d(
-   DeviceTensor<2> &field_qp,
-   const DofToQuadMap &dtq,
-   const DeviceTensor<1> &field_e,
-   const field_operator_t &input,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<field_operator_t>>::value)
-   {
-      auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const auto field = Reshape(&field_e[0], d1d, d1d, d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, q1d, q1d, q1d);
-      auto s0 = Reshape(&scratch_mem[0](0), d1d, d1d, q1d);
-      auto s1 = Reshape(&scratch_mem[1](0), d1d, q1d, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dz, z, d1d)
-         {
-            MFEM_FOREACH_THREAD(dy, y, d1d)
-            {
-               MFEM_FOREACH_THREAD(qx, x, q1d)
-               {
-                  real_t acc = 0.0;
-                  for (int dx = 0; dx < d1d; dx++)
-                  {
-                     acc += B(qx, 0, dx) * field(dx, dy, dz, vd);
-                  }
-                  s0(dz, dy, qx) = acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dz, z, d1d)
-         {
-            MFEM_FOREACH_THREAD(qx, x, q1d)
-            {
-               MFEM_FOREACH_THREAD(qy, y, q1d)
-               {
-                  real_t acc = 0.0;
-                  for (int dy = 0; dy < d1d; dy++)
-                  {
-                     acc += s0(dz, dy, qx) * B(qy, 0, dy);
-                  }
-                  s1(dz, qy, qx) = acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(qz, z, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD(qx, x, q1d)
-               {
-                  real_t acc = 0.0;
-                  for (int dz = 0; dz < d1d; dz++)
-                  {
-                     acc += s1(dz, qy, qx) * B(qz, 0, dz);
-                  }
-                  fqp(vd, qx, qy, qz) = acc;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (
-      is_gradient_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const int dim = input.dim;
-      const auto field = Reshape(&field_e[0], d1d, d1d, d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, dim, q1d, q1d, q1d);
-
-      auto s0 = Reshape(&scratch_mem[0](0), d1d, d1d, q1d);
-      auto s1 = Reshape(&scratch_mem[1](0), d1d, d1d, q1d);
-      auto s2 = Reshape(&scratch_mem[2](0), d1d, q1d, q1d);
-      auto s3 = Reshape(&scratch_mem[3](0), d1d, q1d, q1d);
-      auto s4 = Reshape(&scratch_mem[4](0), d1d, q1d, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dz, z, d1d)
-         {
-            MFEM_FOREACH_THREAD(dy, y, d1d)
-            {
-               MFEM_FOREACH_THREAD(qx, x, q1d)
-               {
-                  real_t uv[2] = {0.0, 0.0};
-                  for (int dx = 0; dx < d1d; dx++)
-                  {
-                     const real_t f = field(dx, dy, dz, vd);
-                     uv[0] += f * B(qx, 0, dx);
-                     uv[1] += f * G(qx, 0, dx);
-                  }
-                  s0(dz, dy, qx) = uv[0];
-                  s1(dz, dy, qx) = uv[1];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(dz, z, d1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD(qx, x, q1d)
-               {
-                  real_t uvw[3] = {0.0, 0.0, 0.0};
-                  for (int dy = 0; dy < d1d; dy++)
-                  {
-                     const real_t s0i = s0(dz, dy, qx);
-                     uvw[0] += s1(dz, dy, qx) * B(qy, 0, dy);
-                     uvw[1] += s0i * G(qy, 0, dy);
-                     uvw[2] += s0i * B(qy, 0, dy);
-                  }
-                  s2(dz, qy, qx) = uvw[0];
-                  s3(dz, qy, qx) = uvw[1];
-                  s4(dz, qy, qx) = uvw[2];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(qz, z, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD(qx, x, q1d)
-               {
-                  real_t uvw[3] = {0.0, 0.0, 0.0};
-                  for (int dz = 0; dz < d1d; dz++)
-                  {
-                     uvw[0] += s2(dz, qy, qx) * B(qz, 0, dz);
-                     uvw[1] += s3(dz, qy, qx) * B(qz, 0, dz);
-                     uvw[2] += s4(dz, qy, qx) * G(qz, 0, dz);
-                  }
-                  fqp(vd, 0, qx, qy, qz) = uvw[0];
-                  fqp(vd, 1, qx, qy, qz) = uvw[1];
-                  fqp(vd, 2, qx, qy, qz) = uvw[2];
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   // TODO: Create separate function for clarity
-   else if constexpr (
-      std::is_same_v<std::decay_t<field_operator_t>, Weight>)
-   {
-      const int num_qp = integration_weights.GetShape()[0];
-      // TODO: eeek
-      const int q1d = (int)floor(std::pow(num_qp, 1.0/input.dim) + 0.5);
-      auto w = Reshape(&integration_weights[0], q1d, q1d, q1d);
-      auto f = Reshape(&field_qp[0], q1d, q1d, q1d);
-      MFEM_FOREACH_THREAD(qx, x, q1d)
-      {
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            MFEM_FOREACH_THREAD(qz, z, q1d)
-            {
-               f(qx, qy, qz) = w(qx, qy, qz);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (is_identity_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const int q1d = B.GetShape()[0];
-      auto field = Reshape(&field_e[0], input.size_on_qp, q1d * q1d * q1d);
-      field_qp = field;
-   }
-   else
-   {
-      static_assert(dfem::always_false<std::decay_t<field_operator_t>>,
-                    "can't map field to quadrature data");
-   }
-}
-
-template <typename field_operator_t>
-MFEM_HOST_DEVICE inline
-void map_field_to_quadrature_data_tensor_product_2d(
-   DeviceTensor<2> &field_qp,
-   const DofToQuadMap &dtq,
-   const DeviceTensor<1> &field_e,
-   const field_operator_t &input,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<field_operator_t>>::value)
-   {
-      auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const auto field = Reshape(&field_e[0], d1d, d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, q1d, q1d);
-      auto s0 = Reshape(&scratch_mem[0](0), d1d, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(qx, x, q1d)
-            {
-               real_t acc = 0.0;
-               for (int dx = 0; dx < d1d; dx++)
-               {
-                  acc += B(qx, 0, dx) * field(dx, dy, vd);
-               }
-               s0(dy, qx) = acc;
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD(qy, y, q1d)
-            {
-               real_t acc = 0.0;
-               for (int dy = 0; dy < d1d; dy++)
-               {
-                  acc += s0(dy, qx) * B(qy, 0, dy);
-               }
-               fqp(vd, qx, qy) = acc;
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   else if constexpr (
-      is_gradient_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const int dim = input.dim;
-      const auto field = Reshape(&field_e[0], d1d, d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, dim, q1d, q1d);
-
-      auto s0 = Reshape(&scratch_mem[0](0), d1d, q1d);
-      auto s1 = Reshape(&scratch_mem[1](0), d1d, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(dy, y, d1d)
-         {
-            MFEM_FOREACH_THREAD(qx, x, q1d)
-            {
-               real_t uv[2] = {0.0, 0.0};
-               for (int dx = 0; dx < d1d; dx++)
-               {
-                  const real_t f = field(dx, dy, vd);
-                  uv[0] += f * B(qx, 0, dx);
-                  uv[1] += f * G(qx, 0, dx);
-               }
-               s0(dy, qx) = uv[0];
-               s1(dy, qx) = uv[1];
-            }
-         }
-         MFEM_SYNC_THREAD;
-
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            MFEM_FOREACH_THREAD(qx, x, q1d)
-            {
-               real_t uv[2] = {0.0, 0.0};
-               for (int dy = 0; dy < d1d; dy++)
-               {
-                  const real_t s0i = s0(dy, qx);
-                  uv[0] += s1(dy, qx) * B(qy, 0, dy);
-                  uv[1] += s0i * G(qy, 0, dy);
-               }
-               fqp(vd, 0, qx, qy) = uv[0];
-               fqp(vd, 1, qx, qy) = uv[1];
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   // TODO: Create separate function for clarity
-   else if constexpr (
-      std::is_same_v<std::decay_t<field_operator_t>, Weight>)
-   {
-      const int num_qp = integration_weights.GetShape()[0];
-      // TODO: eeek
-      const int q1d = (int)floor(std::pow(num_qp, 1.0/input.dim) + 0.5);
-      auto w = Reshape(&integration_weights[0], q1d, q1d);
-      auto f = Reshape(&field_qp[0], q1d, q1d);
-      MFEM_FOREACH_THREAD(qx, x, q1d)
-      {
-         MFEM_FOREACH_THREAD(qy, y, q1d)
-         {
-            f(qx, qy) = w(qx, qy);
-         }
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (is_identity_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const int q1d = B.GetShape()[0];
-      auto field = Reshape(&field_e[0], input.size_on_qp, q1d * q1d);
-      field_qp = field;
-   }
-   else
-   {
-      static_assert(dfem::always_false<std::decay_t<field_operator_t>>,
-                    "can't map field to quadrature data");
-   }
-}
-
-
-template <typename field_operator_t>
-MFEM_HOST_DEVICE inline
-void map_field_to_quadrature_data_tensor_product_1d(
-   DeviceTensor<2> &field_qp,
-   const DofToQuadMap &dtq,
-   const DeviceTensor<1> &field_e,
-   const field_operator_t &input,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-
-   if constexpr (is_value_fop<std::decay_t<field_operator_t>>::value)
-   {
-      auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const auto field = Reshape(&field_e[0], d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            real_t acc = 0.0;
-            for (int dx = 0; dx < d1d; dx++)
-            {
-               acc += B(qx, 0, dx) * field(dx, vd);
-            }
-            fqp(vd, qx) = acc;
-         }
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (
-      is_gradient_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const auto [q1d, unused, d1d] = B.GetShape();
-      const int vdim = input.vdim;
-      const int dim = input.dim;
-      const auto field = Reshape(&field_e[0], d1d, vdim);
-      auto fqp = Reshape(&field_qp[0], vdim, dim, q1d);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         MFEM_FOREACH_THREAD(qx, x, q1d)
-         {
-            real_t acc = 0.0;
-            for (int dx = 0; dx < d1d; dx++)
-            {
-               acc += G(qx, 0, dx) * field(dx, vd);
-            }
-            fqp(vd, 0, qx) = acc;
-         }
-         MFEM_SYNC_THREAD;
-      }
-   }
-   // TODO: Create separate function for clarity
-   else if constexpr (
-      std::is_same_v<std::decay_t<field_operator_t>, Weight>)
-   {
-      const int num_qp = integration_weights.GetShape()[0];
-      // TODO: eeek
-      const int q1d = (int)floor(std::pow(num_qp, 1.0/input.dim) + 0.5);
-      auto w = Reshape(&integration_weights[0], q1d);
-      auto f = Reshape(&field_qp[0], q1d);
-      MFEM_FOREACH_THREAD(qx, x, q1d)
-      {
-         f(qx) = w(qx);
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else if constexpr (is_identity_fop<std::decay_t<field_operator_t>>::value)
-   {
-      const int q1d = B.GetShape()[0];
-      auto field = Reshape(&field_e[0], input.size_on_qp, q1d);
-      field_qp = field;
-   }
-   else
-   {
-      static_assert(dfem::always_false<std::decay_t<field_operator_t>>,
-                    "can't map field to quadrature data");
-   }
-}
-
-template <typename field_operator_t>
-MFEM_HOST_DEVICE
-void map_field_to_quadrature_data(
-   DeviceTensor<2> field_qp,
-   const DofToQuadMap &dtq,
-   const DeviceTensor<1> &field_e,
-   const field_operator_t &input,
-   const DeviceTensor<1, const real_t> &integration_weights)
-{
-   [[maybe_unused]] auto B = dtq.B;
-   [[maybe_unused]] auto G = dtq.G;
-   if constexpr (is_value_fop<field_operator_t>::value)
-   {
-      auto [num_qp, dim, num_dof] = B.GetShape();
-      const int vdim = input.vdim;
-      const auto field = Reshape(&field_e(0), num_dof, vdim);
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         for (int qp = 0; qp < num_qp; qp++)
-         {
-            real_t acc = 0.0;
-            for (int dof = 0; dof < num_dof; dof++)
-            {
-               acc += B(qp, 0, dof) * field(dof, vd);
-            }
-            field_qp(vd, qp) = acc;
-         }
-      }
-   }
-   else if constexpr (is_gradient_fop<field_operator_t>::value)
-   {
-      const auto [num_qp, dim, num_dof] = G.GetShape();
-      const int vdim = input.vdim;
-      const auto field = Reshape(&field_e(0), num_dof, vdim);
-
-      auto f = Reshape(&field_qp[0], vdim, dim, num_qp);
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         for (int qp = 0; qp < num_qp; qp++)
-         {
-            for (int d = 0; d < dim; d++)
-            {
-               real_t acc = 0.0;
-               for (int dof = 0; dof < num_dof; dof++)
-               {
-                  acc += G(qp, d, dof) * field(dof, vd);
-               }
-               f(vd, d, qp) = acc;
-            }
-         }
-      }
-   }
-   else if constexpr (std::is_same_v<field_operator_t, Weight>)
-   {
-      const int num_qp = integration_weights.GetShape()[0];
-      auto f = Reshape(&field_qp[0], num_qp);
-      for (int qp = 0; qp < num_qp; qp++)
-      {
-         f(qp) = integration_weights(qp);
-      }
-   }
-   else if constexpr (is_identity_fop<field_operator_t>::value)
-   {
-      auto [num_qp, unused, num_dof] = B.GetShape();
-      const int size_on_qp = input.size_on_qp;
-      const auto field = Reshape(&field_e[0], size_on_qp * num_qp);
-      auto f = Reshape(&field_qp[0], size_on_qp * num_qp);
-      for (int i = 0; i < size_on_qp * num_qp; i++)
-      {
-         f(i) = field(i);
-      }
-   }
-   else
-   {
-      static_assert(dfem::always_false<field_operator_t>,
-                    "can't map field to quadrature data");
-
-   }
-}
-
-template <typename field_operator_ts, size_t num_inputs, size_t num_fields>
-MFEM_HOST_DEVICE inline
-void map_fields_to_quadrature_data(
-   std::array<DeviceTensor<2>, num_inputs> &fields_qp,
-   const std::array<DeviceTensor<1>, num_fields> &fields_e,
-   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
-   const std::array<size_t, num_inputs> &input_to_field,
-   const field_operator_ts &fops,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem,
-   const int &dimension,
-   const bool &use_sum_factorization = false)
-{
-   // When the input_to_field map returns -1, this means the requested input
-   // is the integration weight. Weights don't have a user defined field
-   // attached to them and we create a dummy field which is not accessed
-   // inside the functions it is passed to.
-   const auto dummy_field_weight = DeviceTensor<1>(nullptr, 0);
-   for_constexpr<num_inputs>([&](auto i)
-   {
-      const DeviceTensor<1> &field_e =
-         (input_to_field[i] == SIZE_MAX) ? dummy_field_weight :
-         fields_e[input_to_field[i]];
-
-      if (use_sum_factorization)
-      {
-         if (dimension == 1)
-         {
-            map_field_to_quadrature_data_tensor_product_1d(
-               fields_qp[i], dtqmaps[i], field_e, get<i>(fops),
-               integration_weights, scratch_mem);
-         }
-         else if (dimension == 2)
-         {
-            map_field_to_quadrature_data_tensor_product_2d(
-               fields_qp[i], dtqmaps[i], field_e, get<i>(fops),
-               integration_weights, scratch_mem);
-         }
-         else if (dimension == 3)
-         {
-            map_field_to_quadrature_data_tensor_product_3d(
-               fields_qp[i], dtqmaps[i], field_e, get<i>(fops),
-               integration_weights, scratch_mem);
-         }
-         else
-         {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-            MFEM_ABORT("unsupported dimension");
-#endif
-         }
-      }
-      else
-      {
-         map_field_to_quadrature_data(
-            fields_qp[i], dtqmaps[i], field_e, get<i>(fops),
-            integration_weights);
-      }
-   });
-}
-
-template <typename field_operator_t>
-MFEM_HOST_DEVICE
-void map_field_to_quadrature_data_conditional(
-   DeviceTensor<2> &field_qp,
-   const DeviceTensor<1> &field_e,
-   const DofToQuadMap &dtqmap,
-   field_operator_t &fop,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem,
-   const bool &condition,
-   const int &dimension,
-   const bool &use_sum_factorization = false)
-{
-   if (condition)
-   {
-      if (use_sum_factorization)
-      {
-         if (dimension == 1)
-         {
-            map_field_to_quadrature_data_tensor_product_1d(
-               field_qp, dtqmap, field_e, fop, integration_weights, scratch_mem);
-
-         }
-         else if (dimension == 2)
-         {
-            map_field_to_quadrature_data_tensor_product_2d(
-               field_qp, dtqmap, field_e, fop, integration_weights, scratch_mem);
-         }
-         else if (dimension == 3)
-         {
-            map_field_to_quadrature_data_tensor_product_3d(
-               field_qp, dtqmap, field_e, fop, integration_weights, scratch_mem);
-         }
-      }
-      else
-      {
-         map_field_to_quadrature_data(
-            field_qp, dtqmap, field_e, fop, integration_weights);
-      }
-   }
-}
-
-template <size_t num_fields, size_t num_inputs, typename field_operator_ts>
-MFEM_HOST_DEVICE
-void map_fields_to_quadrature_data_conditional(
-   std::array<DeviceTensor<2>, num_inputs> &fields_qp,
-   const std::array<DeviceTensor<1, const real_t>, num_fields> &fields_e,
-   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
-   field_operator_ts fops,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem,
-   const std::array<bool, num_inputs> &conditions,
-   const bool &use_sum_factorization = false)
-{
-   for_constexpr<num_inputs>([&](auto i)
-   {
-      map_field_to_quadrature_data_conditional(
-         fields_qp[i], fields_e[i], dtqmaps[i], get<i>(fops), integration_weights,
-         scratch_mem, conditions[i], use_sum_factorization);
-   });
-}
-
-template <size_t num_inputs, typename field_operator_ts>
-MFEM_HOST_DEVICE
-void map_direction_to_quadrature_data_conditional(
-   std::array<DeviceTensor<2>, num_inputs> &directions_qp,
-   const DeviceTensor<1> &direction_e,
-   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
-   field_operator_ts fops,
-   const DeviceTensor<1, const real_t> &integration_weights,
-   const std::array<DeviceTensor<1>, 6> &scratch_mem,
-   const std::array<bool, num_inputs> &conditions,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   for_constexpr<num_inputs>([&](auto i)
-   {
-      if (conditions[i])
-      {
-         if (use_sum_factorization)
-         {
-            if (dimension == 1)
-            {
-               map_field_to_quadrature_data_tensor_product_1d(
-                  directions_qp[i], dtqmaps[i], direction_e, get<i>(fops),
-                  integration_weights, scratch_mem);
-            }
-            else if (dimension == 2)
-            {
-               map_field_to_quadrature_data_tensor_product_2d(
-                  directions_qp[i], dtqmaps[i], direction_e, get<i>(fops),
-                  integration_weights, scratch_mem);
-            }
-            else if (dimension == 3)
-            {
-               map_field_to_quadrature_data_tensor_product_3d(
-                  directions_qp[i], dtqmaps[i], direction_e, get<i>(fops),
-                  integration_weights, scratch_mem);
-            }
-         }
-         else
-         {
-            map_field_to_quadrature_data(
-               directions_qp[i], dtqmaps[i], direction_e, get<i>(fops),
-               integration_weights);
-         }
-      }
-   });
-}
-
-}

fem/dfem/parameterspace.hpp

@@ -20,7 +20,7 @@ namespace mfem::future
 class ParameterSpace
 {
 public:
-   ParameterSpace(int vdim = 1) : vdim(vdim) {}
+   ParameterSpace(int vdim = 1) : vdim(vdim) { dtq.FE = nullptr; dtq.IntRule = nullptr; }
 
    /// @brief Get vector dimension at each point
    ///
@@ -43,7 +43,7 @@ public:
    /// Get spatial dimension
    ///
    /// returns always 1.
-   int Dimension() const
+   constexpr int Dimension() const
    {
       return 1;
    }
@@ -65,7 +65,7 @@ public:
    /// It should not be used by a user.
    ///
    /// returns identity by default that is lazy evaluated.
-   virtual const Operator* GetElementRestriction(ElementDofOrdering o) const
+   virtual const Operator* GetElementRestriction(ElementDofOrdering) const
    {
       if (!elem_restr)
       {
@@ -74,11 +74,14 @@ public:
       return elem_restr.get();
    }
 
+   virtual const Operator* GetB() const = 0;
+
+   virtual const Operator* GetBt() const = 0;
+
 protected:
    int vdim;
    DofToQuad dtq;
-   mutable std::unique_ptr<Operator> prolongation;
-   mutable std::unique_ptr<Operator> elem_restr;
+   mutable std::unique_ptr<Operator> prolongation, elem_restr, B, Bt;
 };
 
 /// @brief Uniform parameter space

fem/dfem/qfunction_apply.hpp

@@ -1,619 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-#include "qfunction_transform.hpp"
-
-namespace mfem::future
-{
-
-/// @brief Call a qfunction with the given parameters.
-///
-/// @param qfunc the qfunction to call.
-/// @param input_shmem the input shared memory.
-/// @param residual_shmem the residual shared memory.
-/// @param rs_qp the size of the residual.
-/// @param num_qp the number of quadrature points.
-/// @param q1d the number of quadrature points in 1D.
-/// @param dimension the spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-/// @tparam qf_param_ts the tuple type of the qfunction parameters.
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   DeviceTensor<2> &residual_shmem,
-   const int &rs_qp,
-   const int &num_qp,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            auto qf_args = decay_tuple<qf_param_ts> {};
-            auto r = Reshape(&residual_shmem(0, q), rs_qp);
-            apply_kernel(r, qfunc, qf_args, input_shmem, q);
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               auto qf_args = decay_tuple<qf_param_ts> {};
-               auto r = Reshape(&residual_shmem(0, q), rs_qp);
-               apply_kernel(r, qfunc, qf_args, input_shmem, q);
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  auto qf_args = decay_tuple<qf_param_ts> {};
-                  auto r = Reshape(&residual_shmem(0, q), rs_qp);
-                  apply_kernel(r, qfunc, qf_args, input_shmem, q);
-               }
-            }
-         }
-      }
-      else
-      {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-         MFEM_ABORT("unsupported dimension for sum factorization");
-#endif
-      }
-      MFEM_SYNC_THREAD;
-   }
-   else
-   {
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         auto qf_args = decay_tuple<qf_param_ts> {};
-         auto r = Reshape(&residual_shmem(0, q), rs_qp);
-         apply_kernel(r, qfunc, qf_args, input_shmem, q);
-      }
-   }
-}
-
-/// @brief Call a qfunction with the given parameters and
-/// compute it's derivative action.
-///
-/// @param qfunc the qfunction to call.
-/// @param input_shmem the input shared memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param residual_shmem the residual shared memory.
-/// @param das_qp the size of the derivative action.
-/// @param num_qp the number of quadrature points.
-/// @param q1d the number of quadrature points in 1D.
-/// @param dimension the spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-/// @tparam qf_param_ts the tuple type of the qfunction parameters.
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction_derivative_action(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   DeviceTensor<2> &residual_shmem,
-   const int &das_qp,
-   const int &num_qp,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            auto r = Reshape(&residual_shmem(0, q), das_qp);
-            auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-            auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-            apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                        shadow_shmem, q);
-#else
-            apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               auto r = Reshape(&residual_shmem(0, q), das_qp);
-               auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-               auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-               apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                           shadow_shmem, q);
-#else
-               apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  auto r = Reshape(&residual_shmem(0, q), das_qp);
-                  auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-                  auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-                  apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                              shadow_shmem, q);
-#else
-                  apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-               }
-            }
-         }
-      }
-      else
-      {
-         MFEM_ABORT_KERNEL("unsupported dimension");
-      }
-   }
-   else
-   {
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         auto r = Reshape(&residual_shmem(0, q), das_qp);
-         auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-         auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-         apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                     shadow_shmem, q);
-#else
-         apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-      }
-   }
-   MFEM_SYNC_THREAD;
-}
-
-namespace detail
-{
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction_derivative(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   DeviceTensor<2> &residual_shmem,
-   DeviceTensor<5> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &das_qp,
-   const int &q)
-{
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-   const int num_qp = qpdc.GetShape()[4];
-   const size_t num_inputs = itod.GetShape()[0];
-
-   for (int j = 0; j < trial_vdim; j++)
-   {
-      int m_offset = 0;
-      for (size_t s = 0; s < num_inputs; s++)
-      {
-         const int trial_op_dim = static_cast<int>(itod(s));
-         if (trial_op_dim == 0)
-         {
-            continue;
-         }
-
-         auto d_qp = Reshape(&(shadow_shmem[s])[0], trial_vdim, trial_op_dim, num_qp);
-         for (int m = 0; m < trial_op_dim; m++)
-         {
-            d_qp(j, m, q) = 1.0;
-
-            auto r = Reshape(&residual_shmem(0, q), das_qp);
-            auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-            auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-            apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                        shadow_shmem, q);
-#else
-            apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-            d_qp(j, m, q) = 0.0;
-
-            auto f = Reshape(&r(0), test_vdim, test_op_dim);
-            for (int i = 0; i < test_vdim; i++)
-            {
-               for (int k = 0; k < test_op_dim; k++)
-               {
-                  qpdc(i, k, j, m + m_offset, q) = f(i, k);
-               }
-            }
-         }
-         m_offset += trial_op_dim;
-      }
-   }
-}
-}
-
-/// @brief Call a qfunction with the given parameters and
-/// compute it's derivative represented by the Jacobian on
-/// each quadrature point.
-///
-/// @param qfunc the qfunction to call.
-/// @param input_shmem the input shared memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param residual_shmem the residual shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param das_qp the size of the derivative action.
-/// @param q1d the number of quadrature points in 1D.
-/// @param dimension the spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-/// @tparam qf_param_ts the tuple type of the qfunction parameters.
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction_derivative(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   DeviceTensor<2> &residual_shmem,
-   DeviceTensor<5> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &das_qp,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            detail::call_qfunction_derivative<qf_param_ts>(
-               qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               detail::call_qfunction_derivative<qf_param_ts>(
-                  qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  detail::call_qfunction_derivative<qf_param_ts>(
-                     qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-               }
-            }
-         }
-      }
-      else
-      {
-         MFEM_ABORT_KERNEL("unsupported dimension");
-      }
-   }
-   else
-   {
-      const int num_qp = qpdc.GetShape()[4];
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         detail::call_qfunction_derivative<qf_param_ts>(
-            qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-      }
-   }
-   MFEM_SYNC_THREAD;
-}
-
-namespace detail
-{
-
-/// @brief Apply the quadrature point data cache (qpdc) to a vector
-/// (usually a direction) on quadrature point q.
-///
-/// The qpdc consists of compatible data to be used for integration with a test
-/// operator, e.g. Jacobians of a linearization from a FE operation with a trial
-/// function including integration weights and necessesary transformations.
-///
-/// @param fhat the qpdc applied to a vector in shadow_memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param q the current quadrature point index.
-template <size_t num_fields>
-MFEM_HOST_DEVICE inline
-void apply_qpdc(
-   DeviceTensor<3> &fhat,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   const DeviceTensor<5, const real_t> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &q)
-{
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-   const int num_qp = qpdc.GetShape()[4];
-   const size_t num_inputs = itod.GetShape()[0];
-
-   for (int i = 0; i < test_vdim; i++)
-   {
-      for (int k = 0; k < test_op_dim; k++)
-      {
-         real_t sum = 0.0;
-         int m_offset = 0;
-         for (size_t s = 0; s < num_inputs; s++)
-         {
-            const int trial_op_dim = static_cast<int>(itod(s));
-            if (trial_op_dim == 0)
-            {
-               continue;
-            }
-            const auto d_qp =
-               Reshape(&(shadow_shmem[s])[0], trial_vdim, trial_op_dim, num_qp);
-            for (int j = 0; j < trial_vdim; j++)
-            {
-               for (int m = 0; m < trial_op_dim; m++)
-               {
-                  sum += qpdc(i, k, j, m + m_offset, q) * d_qp(j, m, q);
-               }
-            }
-            m_offset += trial_op_dim;
-         }
-         fhat(i, k, q) = sum;
-      }
-   }
-}
-}
-
-/// @brief Apply the quadrature point data cache (qpdc) to a vector
-/// (usually a direction).
-///
-/// The qpdc consists of compatible data to be used for integration with a test
-/// operator, e.g. Jacobians of a linearization from a FE operation with a trial
-/// function including integration weights and necessesary transformations.
-///
-/// @param fhat the qpdc applied to a vector in shadow_memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param q1d number of quadrature points in 1D.
-/// @param dimension spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-template <size_t num_fields>
-MFEM_HOST_DEVICE inline
-void apply_qpdc(
-   DeviceTensor<3> &fhat,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   const DeviceTensor<5, const real_t> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-               }
-            }
-         }
-      }
-      else
-      {
-         MFEM_ABORT_KERNEL("unsupported dimension");
-      }
-   }
-   else
-   {
-      const int num_qp = qpdc.GetShape()[4];
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-      }
-   }
-}
-
-template <typename qfunc_t, typename args_ts, size_t num_args>
-MFEM_HOST_DEVICE inline
-void apply_kernel(
-   DeviceTensor<1, real_t> &f_qp,
-   const qfunc_t &qfunc,
-   args_ts &args,
-   const std::array<DeviceTensor<2>, num_args> &u,
-   int qp)
-{
-   process_qf_args(u, args, qp);
-   process_qf_result(f_qp, get<0>(apply(qfunc, args)));
-}
-
-template <typename qfunc_t, typename arg_ts, size_t num_args>
-MFEM_HOST_DEVICE inline
-void apply_kernel_native_dual(
-   DeviceTensor<1, real_t> &f_qp,
-   const qfunc_t &qfunc,
-   arg_ts &args,
-   const std::array<DeviceTensor<2>, num_args> &u,
-   const std::array<DeviceTensor<2>, num_args> &v,
-   const int &qp_idx)
-{
-   process_qf_args(u, v, args, qp_idx);
-   auto r = get<0>(apply(qfunc, args));
-   process_derivative_from_native_dual(f_qp, r);
-}
-
-#ifdef MFEM_USE_ENZYME
-
-template <typename func_t, typename... arg_ts>
-MFEM_HOST_DEVICE inline
-auto qfunction_wrapper(const func_t &f, arg_ts &&...args)
-{
-   return f(args...);
-}
-
-// Version for active function arguments only
-//
-// This is an Enzyme regression and can be removed in later versions.
-template <typename qfunc_t, typename arg_ts, std::size_t... Is,
-          typename inactive_arg_ts>
-MFEM_HOST_DEVICE inline
-auto fwddiff_apply_enzyme_indexed(qfunc_t &qfunc, arg_ts &&args,
-                                  arg_ts &&shadow_args,
-                                  std::index_sequence<Is...>,
-                                  inactive_arg_ts &&inactive_args,
-                                  std::index_sequence<>)
-{
-   using qf_return_t = typename create_function_signature<
-                       decltype(&qfunc_t::operator())>::type::return_t;
-   return __enzyme_fwddiff<qf_return_t>(
-             qfunction_wrapper<qfunc_t, decltype(get<Is>(args))...>, enzyme_const,
-             (void *)&qfunc, enzyme_dup, &get<Is>(args)..., enzyme_interleave,
-             &get<Is>(shadow_args)...);
-}
-
-// Interleave function arguments for enzyme
-template <typename qfunc_t, typename arg_ts, std::size_t... Is,
-          typename inactive_arg_ts, std::size_t... Js>
-MFEM_HOST_DEVICE inline
-auto fwddiff_apply_enzyme_indexed(qfunc_t &qfunc, arg_ts &&args,
-                                  arg_ts &&shadow_args,
-                                  std::index_sequence<Is...>,
-                                  inactive_arg_ts &&inactive_args,
-                                  std::index_sequence<Js...>)
-{
-   using qf_return_t = typename create_function_signature<
-                       decltype(&qfunc_t::operator())>::type::return_t;
-   return __enzyme_fwddiff<qf_return_t>(
-             qfunction_wrapper<qfunc_t, decltype(get<Is>(args))...,
-             decltype(get<Js>(inactive_args))...>,
-             enzyme_const, (void *)&qfunc, enzyme_dup, &get<Is>(args)...,
-             enzyme_const, &get<Js>(inactive_args)..., enzyme_interleave,
-             &get<Is>(shadow_args)...);
-}
-
-template <typename qfunc_t, typename arg_ts, typename inactive_arg_ts>
-MFEM_HOST_DEVICE inline
-auto fwddiff_apply_enzyme(qfunc_t &qfunc, arg_ts &&args,
-                          arg_ts &&shadow_args,
-                          inactive_arg_ts &&inactive_args)
-{
-   auto arg_indices = std::make_index_sequence<
-                      tuple_size<std::remove_reference_t<arg_ts>>::value> {};
-
-   auto inactive_arg_indices = std::make_index_sequence<
-                               tuple_size<std::remove_reference_t<inactive_arg_ts>>::value> {};
-
-   return fwddiff_apply_enzyme_indexed(qfunc, args, shadow_args, arg_indices,
-                                       inactive_args, inactive_arg_indices);
-}
-
-template <typename qfunc_t, typename arg_ts, size_t num_args>
-MFEM_HOST_DEVICE inline
-void apply_kernel_fwddiff_enzyme(
-   DeviceTensor<1, real_t> &f_qp,
-   qfunc_t &qfunc,
-   arg_ts &args,
-   arg_ts &shadow_args,
-   const std::array<DeviceTensor<2>, num_args> &u,
-   const std::array<DeviceTensor<2>, num_args> &v,
-   int qp_idx)
-{
-   process_qf_args(u, args, qp_idx);
-   process_qf_args(v, shadow_args, qp_idx);
-   process_qf_result(f_qp,
-                     get<0>(fwddiff_apply_enzyme(qfunc, args, shadow_args, tuple<> {})));
-}
-#endif // MFEM_USE_ENZYME
-
-} // namespace mfem::future

fem/dfem/qfunction_transform.hpp

@@ -1,346 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-#include "../../linalg/tensor.hpp"
-
-namespace mfem::future
-{
-
-template <typename T0, typename T1, typename T2>
-MFEM_HOST_DEVICE
-void process_qf_arg(const T0 &, const T1 &, T2 &)
-{
-   static_assert(dfem::always_false<T0, T1, T2>,
-                 "process_qf_arg not implemented for arg type");
-}
-
-template <typename T>
-MFEM_HOST_DEVICE
-void process_qf_arg(
-   const DeviceTensor<1, T> &u,
-   const DeviceTensor<1, T> &v,
-   T &arg)
-{
-   arg = u(0);
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   tensor<dual<T, T>, n, m> &arg)
-{
-   for (int i = 0; i < m; i++)
-   {
-      for (int j = 0; j < n; j++)
-      {
-         arg(j, i).value = u((i * n) + j);
-      }
-   }
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   dual<T, T> &arg)
-{
-   arg.value = u(0);
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   const DeviceTensor<1> &v,
-   dual<T, T> &arg)
-{
-   arg.value = u(0);
-   arg.gradient = v(0);
-}
-
-template <typename T, int n>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   const DeviceTensor<1> &v,
-   tensor<dual<T, T>, n> &arg)
-{
-   for (int i = 0; i < n; i++)
-   {
-      arg(i).value = u(i);
-      arg(i).gradient = v(i);
-   }
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   const DeviceTensor<1> &v,
-   tensor<dual<T, T>, n, m> &arg)
-{
-   for (int i = 0; i < m; i++)
-   {
-      for (int j = 0; j < n; j++)
-      {
-         arg(j, i).value = u((i * n) + j);
-         arg(j, i).gradient = v((i * n) + j);
-      }
-   }
-}
-
-template <typename T, int n>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const tensor<dual<T, T>, n> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      r(i) = x(i).value;
-   }
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const tensor<dual<T, T>, n, m> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      for (size_t j = 0; j < m; j++)
-      {
-         r(i + n * j) = x(i, j).value;
-      }
-   }
-}
-
-template <typename arg_type>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<2> &u,
-   const DeviceTensor<2> &v,
-   arg_type &arg,
-   const int &qp)
-{
-   const auto u_qp = Reshape(&u(0, qp), u.GetShape()[0]);
-   const auto v_qp = Reshape(&v(0, qp), v.GetShape()[0]);
-   process_qf_arg(u_qp, v_qp, arg);
-}
-
-template <size_t num_fields, typename qf_args>
-MFEM_HOST_DEVICE inline
-void process_qf_args(
-   const std::array<DeviceTensor<2>, num_fields> &u,
-   const std::array<DeviceTensor<2>, num_fields> &v,
-   qf_args &args,
-   const int &qp)
-{
-   for_constexpr<tuple_size<qf_args>::value>([&](auto i)
-   {
-      process_qf_arg(u[i], v[i], get<i>(args), qp);
-   });
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_derivative_from_native_dual(
-   DeviceTensor<1, T> &r,
-   const tensor<dual<T, T>, n, m> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      for (size_t j = 0; j < m; j++)
-      {
-         r(i + n * j) = x(i, j).gradient;
-      }
-   }
-}
-
-template <typename T, int n>
-MFEM_HOST_DEVICE inline
-void process_derivative_from_native_dual(
-   DeviceTensor<1, T> &r,
-   const tensor<dual<T, T>, n> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      r(i) = x(i).gradient;
-   }
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_derivative_from_native_dual(
-   DeviceTensor<1, T> &r,
-   const dual<T, T> &x)
-{
-   r(0) = x.gradient;
-}
-
-template <typename T0, typename T1>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(const T0 &, T1 &)
-{
-   static_assert(dfem::always_false<T0, T1>,
-                 "process_qf_arg not implemented for arg type");
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1, T> &u,
-   T &arg)
-{
-   arg = u(0);
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1, T> &u,
-   tensor<T> &arg)
-{
-   arg(0) = u(0);
-}
-
-template <typename T, int n>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   tensor<T, n> &arg)
-{
-   for (int i = 0; i < n; i++)
-   {
-      arg(i) = u(i);
-   }
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1> &u,
-   tensor<T, n, m> &arg)
-{
-   for (int i = 0; i < m; i++)
-   {
-      for (int j = 0; j < n; j++)
-      {
-         arg(j, i) = u((i * n) + j);
-      }
-   }
-}
-
-template <typename arg_type>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(const DeviceTensor<2> &u, arg_type &arg, int qp)
-{
-   const auto u_qp = Reshape(&u(0, qp), u.GetShape()[0]);
-   process_qf_arg(u_qp, arg);
-}
-
-template <size_t num_fields, typename qf_args>
-MFEM_HOST_DEVICE inline
-void process_qf_args(
-   const std::array<DeviceTensor<2>, num_fields> &u,
-   qf_args &args,
-   const int &qp)
-{
-   for_constexpr<tuple_size<qf_args>::value>([&](auto i)
-   {
-      process_qf_arg(u[i], get<i>(args), qp);
-   });
-}
-
-template <typename T0, typename T1>
-MFEM_HOST_DEVICE inline
-Vector process_qf_result(T0, T1)
-{
-   static_assert(dfem::always_false<T0, T1>,
-                 "process_qf_result not implemented for result type");
-   return Vector{};
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const T &x)
-{
-   r(0) = x;
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1> &r,
-   const dual<T, T> &x)
-{
-   r(0) = x.value;
-}
-
-template <typename T>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const tensor<T> &x)
-{
-   r(0) = x(0);
-}
-
-template <typename T, int n>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const tensor<T, n> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      r(i) = x(i);
-   }
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_result(
-   DeviceTensor<1, T> &r,
-   const tensor<T, n, m> &x)
-{
-   for (size_t i = 0; i < n; i++)
-   {
-      for (size_t j = 0; j < m; j++)
-      {
-         r(i + n * j) = x(i, j);
-      }
-   }
-}
-
-template <typename T, int n, int m>
-MFEM_HOST_DEVICE inline
-void process_qf_arg(
-   const DeviceTensor<1, T> &u,
-   const DeviceTensor<1, T> &v,
-   tensor<T, n, m> &arg)
-{
-   for (int i = 0; i < m; i++)
-   {
-      for (int j = 0; j < n; j++)
-      {
-         arg(j, i) = u((i * n) + j);
-      }
-   }
-}
-
-} // namespace mfem::future

fem/dfem/tensor_functions.hpp

@@ -0,0 +1,264 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+/**
+ * @file tensor_functions.hpp
+ *
+ * @brief Differentiable functions of tensors
+ */
+
+#pragma once
+
+#include <cmath>
+
+#include "../../linalg/dual.hpp"
+#include "../../linalg/tensor.hpp"
+#include "tuple.hpp"
+#include "util.hpp"
+
+// Force-inline every tensor operation under clang
+#if defined(__clang__)
+#pragma clang attribute push (__attribute__((always_inline)), apply_to = function)
+#endif
+
+namespace mfem
+{
+namespace future
+{
+
+/**
+ * @brief Differentiable approximation of maximum eigenvale of a symmetric tensor
+ *
+ * Estimates the maximum eigenvalue using
+ * $$
+ *     smooth_max_eigenvalue(A) = \frac{1}{\beta} \log\Big( \mathrm{tr}\big(\exp(\beta A) \big) \Big)
+ * $$
+ * which is equivalent to using the log-sum-exp function on the eigenvalues of A.
+ *
+ * @param A The input tensor
+ * @param beta Sharpness parameter. Must be > 0. Larger values makes the approximation sharper.
+ * @return Approximate maximum eigenvalue of A
+ */
+template <int n> MFEM_HOST_DEVICE
+real_t smooth_max_eigenvalue_symm(const tensor<real_t, n, n>& A, real_t beta)
+{
+   auto [lambda, V] = eig_symm(A);
+   real_t lambda_max = lambda[n - 1];
+   real_t sum = 0;
+   for (int i = 0; i < n - 1; i++)
+   {
+      sum += std::exp(beta*(lambda[i] - lambda_max));
+   }
+   return lambda_max + std::log1p(sum)/beta;
+}
+
+/**
+ * @brief Differentiable approximation of minimum eigenvale of a symmetric tensor
+ *
+ * Estimates the minimum eigenvalue using
+ * $$
+ *     smooth_min_eigenvalue(A) = -\frac{1}{\beta} \log\Big( \mathrm{tr}\big(\exp(-\beta A) \big) \Big)
+ * $$
+ * which is equivalent to using the negated log-sum-exp function on the eigenvalues of -A.
+ *
+ * @param A The input tensor
+ * @param beta Sharpness parameter. Must be > 0. Larger values makes the approximation sharper.
+ * @return Approximate minimum eigenvalue of A
+ */
+template <int n> MFEM_HOST_DEVICE
+real_t smooth_min_eigenvalue_symm(const tensor<real_t, n, n>& A, real_t beta)
+{
+   return -smooth_max_eigenvalue_symm<n>(-A, beta);
+}
+
+#ifdef MFEM_USE_ENZYME
+
+namespace detail
+{
+
+// Custom forward-mode derivative rule for Enzyme
+template<int n> MFEM_HOST_DEVICE
+dual<real_t, real_t> smooth_max_eigenvalue_symm_fwddiff(
+   const tensor<real_t, n, n>& A, const tensor<real_t, n, n>& A_dot, real_t beta,
+   real_t beta_dot)
+{
+   auto [lambda, V] = eig_symm(A);
+   real_t lambda_max = lambda[n - 1];
+   real_t sum = 0;
+   tensor<real_t, n> eg;
+   tensor<real_t, n> lambda_shifted;
+   for (int i = 0; i < n; i++)
+   {
+      lambda_shifted[i] = lambda[i] - lambda_max;
+      eg[i] = std::exp(beta*lambda_shifted[i]);
+      if (i != n - 1) { sum += eg[i]; }
+   }
+   real_t value = lambda_max + std::log1p(sum)/beta;
+
+   real_t Z = sum + 1.0;
+   real_t derivative{};
+   for (int mu = 0; mu < n; mu++)
+   {
+      real_t w_mu = eg[mu]/Z;
+      for (int i = 0; i < n; i++)
+      {
+         for (int j = 0; j < n; j++)
+         {
+            derivative += w_mu*V[i][mu]*V[j][mu]*A_dot[i][j];
+         }
+      }
+   }
+   derivative += (lambda_max - value + dot(eg, lambda_shifted)/Z)/beta * beta_dot;
+   return {value, derivative};
+}
+
+// Types and functions for Enzyme custom reverse mode derivative
+template <int n>
+struct SmoothMaxEigenvalueSymmTape
+{
+   tensor<real_t, n> lambda;
+   tensor<real_t, n, n> V;
+   tensor<real_t, n> eg;
+   real_t sum;
+   real_t logZ;
+};
+
+template <int n>
+struct SmoothMaxEigenvalueSymmAugmentedReturn
+{
+   void* tape;
+   real_t value;
+};
+
+template <int n> MFEM_HOST_DEVICE
+SmoothMaxEigenvalueSymmAugmentedReturn<n>
+smooth_max_eigenvalue_symm_aug(const tensor<real_t, n, n>* A,
+                               tensor<real_t, n, n>* A_bar,
+                               real_t beta)
+{
+   (void)A_bar; // accumulated in reverse pass
+
+   auto [lambda, V] = eig_symm(*A);
+   const real_t lambda_max = lambda[n - 1];
+
+   tensor<real_t, n> eg;
+   real_t sum = 0;
+   for (int i = 0; i < n; i++)
+   {
+      eg[i] = std::exp(beta*(lambda[i] - lambda_max));
+      if (i != n - 1) { sum += eg[i]; }
+   }
+
+   const real_t logZ = std::log1p(sum);
+   const real_t value = lambda_max + logZ/beta;
+
+   auto* tape = static_cast<SmoothMaxEigenvalueSymmTape<n>*>(
+                   std::malloc(sizeof(SmoothMaxEigenvalueSymmTape<n>)));
+   if (tape)
+   {
+      tape->lambda = lambda;
+      tape->V = V;
+      tape->eg = eg;
+      tape->sum = sum;
+      tape->logZ = logZ;
+   }
+
+   return {static_cast<void*>(tape), value};
+}
+
+template <int n> MFEM_HOST_DEVICE
+real_t smooth_max_eigenvalue_symm_rev(const tensor<real_t, n, n>* A,
+                                      tensor<real_t, n, n>* A_bar,
+                                      real_t beta,
+                                      real_t out_bar,
+                                      void* tape_ptr)
+{
+   (void)A; // all needed info is on the tape
+
+   const auto* tape = static_cast<const SmoothMaxEigenvalueSymmTape<n>*>(tape_ptr);
+   if (!tape)
+   {
+      return 0.0;
+   }
+
+   const real_t Z = tape->sum + 1.0;
+
+   // d/dA = Σ_mu w_mu v_mu v_mu^T, where w_mu = eg[mu]/Z
+   for (int mu = 0; mu < n; mu++)
+   {
+      const real_t w_mu = tape->eg[mu] / Z;
+      for (int i = 0; i < n; i++)
+      {
+         for (int j = 0; j < n; j++)
+         {
+            (*A_bar)[i][j] += out_bar * w_mu * tape->V[i][mu] * tape->V[j][mu];
+         }
+      }
+   }
+
+   // d/dβ = -(log Z)/β^2 + (1/(β Z)) Σ_{i<n-1} exp(β(λ_i-λ_max)) (λ_i-λ_max)
+   real_t dZ_dBeta = 0.0;
+   const real_t& lambda_max = tape->lambda[n - 1];
+   for (int i = 0; i < n - 1; i++)
+   {
+      dZ_dBeta += tape->eg[i] * (tape->lambda[i] - lambda_max);
+   }
+
+   const real_t beta2 = beta * beta;
+   const real_t d_value_dBeta = -(tape->logZ)/beta2 + dZ_dBeta/(beta * Z);
+
+   std::free(const_cast<SmoothMaxEigenvalueSymmTape<n>*>(tape));
+
+   return out_bar * d_value_dBeta;
+}
+
+} // namespace detail
+
+// Register custom derivatives (forward mode) with Enzyme
+__attribute__((used))
+void* __enzyme_register_derivative_smooth_max_eigenvalue_symm_2d[] =
+{
+   reinterpret_cast<void*>(smooth_max_eigenvalue_symm<2>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_fwddiff<2>)
+};
+
+__attribute__((used))
+void* __enzyme_register_derivative_smooth_max_eigenvalue_symm_3d[] =
+{
+   reinterpret_cast<void*>(smooth_max_eigenvalue_symm<3>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_fwddiff<3>)
+};
+
+// Register custom gradients (combined reverse mode) with Enzyme
+__attribute__((used))
+void* __enzyme_register_gradient_smooth_max_eigenvalue_symm_2d[] =
+{
+   reinterpret_cast<void*>(smooth_max_eigenvalue_symm<2>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_aug<2>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_rev<2>)
+};
+
+__attribute__((used))
+void* __enzyme_register_gradient_smooth_max_eigenvalue_symm_3d[] =
+{
+   reinterpret_cast<void*>(smooth_max_eigenvalue_symm<3>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_aug<3>),
+   reinterpret_cast<void*>(detail::smooth_max_eigenvalue_symm_rev<3>)
+};
+
+#endif // MFEM_USE_ENZYME
+
+} // namespace future
+} // namespace mfem
+
+#if defined(__clang__)
+#pragma clang attribute pop
+#endif

fem/dfem/tuple.hpp

@@ -16,6 +16,24 @@
 #include <type_traits>
 #include <tuple>
 
+// Define a portable unreachable macro
+#if defined(__GNUC__) || defined(__clang__)
+#if defined(__CUDACC_VER_MAJOR__)
+#if __CUDACC_VER_MAJOR__ <= 11 && __CUDACC_VER_MINOR__ < 3
+// nvcc didn't add __builtin_unreachable() until cuda 11.3
+#define MFEM_UNREACHABLE()
+#else
+// nvcc >= 11.3
+#define MFEM_UNREACHABLE() __builtin_unreachable()
+#endif
+#else
+// host-only version
+#define MFEM_UNREACHABLE() __builtin_unreachable()
+#endif
+#elif defined(_MSC_VER)
+#define MFEM_UNREACHABLE() __assume(0)
+#endif
+
 namespace mfem::future
 {
 
@@ -23,31 +41,10 @@ namespace mfem::future
 template <typename... T>
 struct tuple;
 
-// Implementation detail: storage using multiple inheritance from tuple_leaf,
-// which lets the tuple be defined for an arbitrary number of elements.
-// Structured bindings come from the std::tuple_size / std::tuple_element / get
-// specializations at the bottom of this file, not from the layout.
+// Implementation detail: storage using multiple inheritance from tuple_leaf
+// to support structured bindings
 namespace detail
 {
-/**
- * @brief Trait that is true when @a U is a single argument that is (a reference
- * to) @a Self
- *
- * A variadic constructor taking @c "U&&..." is a better match than the copy
- * constructor for a non-const lvalue of its own type; this is used to constrain
- * it out of those overload sets.
- */
-template <typename Self, typename... U>
-struct is_self_arg : std::false_type {};
-
-/// @overload
-template <typename Self, typename U>
-struct is_self_arg<Self, U> : std::is_same<Self, std::decay_t<U>> {};
-
-/// SFINAE guard enabling a constructor for every @a U except @a Self itself
-template <typename Self, typename... U>
-using disable_if_self_t = std::enable_if_t<!is_self_arg<Self, U...>::value>;
-
 /**
  * @brief A single tuple element storage
  * @tparam I The index of this element in the tuple
@@ -62,7 +59,7 @@ struct tuple_leaf
    MFEM_HOST_DEVICE constexpr tuple_leaf() = default;
 
    /// Construct from value
-   template <typename U, typename = disable_if_self_t<tuple_leaf, U>>
+   template <typename U>
    MFEM_HOST_DEVICE constexpr explicit tuple_leaf(U&& v) :
       value(std::forward<U>(v)) {}
 };
@@ -72,9 +69,8 @@ struct tuple_leaf
  * @tparam Indices Index sequence for tuple elements
  * @tparam T The types stored in the tuple
  *
- * This uses multiple inheritance from tuple_leaf base classes so that a single
- * definition covers any number of elements, while keeping the storage layout
- * (and the trivial copyability that device kernels rely on) of a plain struct.
+ * This uses multiple inheritance from tuple_leaf base classes to enable
+ * structured bindings while maintaining efficient storage.
  */
 template <typename Indices, typename... T>
 struct tuple_impl;
@@ -89,61 +85,19 @@ struct tuple_impl<std::index_sequence<I...>, T...> : tuple_leaf<I, T>...
    /**
     * @brief Construct from values
     * @param args The values to store in the tuple
-    *
-    * @note the arguments are perfectly forwarded, so that constructing a tuple
-    * from lvalues costs exactly one copy per element (taking them by value
-    * would add a copy plus a move).
     */
-   template <typename... U, typename = disable_if_self_t<tuple_impl, U...>>
    MFEM_HOST_DEVICE
-   constexpr explicit tuple_impl(U&&... args)
-      : tuple_leaf<I, T>(std::forward<U>(args))... {}
+   constexpr explicit tuple_impl(T... args)
+      : tuple_leaf<I, T>(std::forward<T>(args))... {}
    };
-
-/**
- * @brief Element-wise constructibility check, only instantiated once the
- * argument list is known to have the right length
- * @tparam Viable whether the arity and self-argument checks have passed
- * @tparam Tuple the @p tuple being constructed
- * @tparam U the constructor argument types
- */
-template <bool Viable, typename Tuple, typename... U>
-struct is_constructible_from : std::false_type {};
-
-/// @overload
-template <typename... T, typename... U>
-struct is_constructible_from<true, tuple<T...>, U...>
-: std::bool_constant<(std::is_constructible_v<T, U&&> && ...)> {};
-
-/**
- * @brief Trait that is true when @a Tuple can be constructed element-wise from
- * the argument list @a U
- * @tparam Tuple the @p tuple being constructed
- * @tparam U the constructor argument types
- */
-template <typename Tuple, typename... U>
-struct is_elementwise_constructible : std::false_type {};
-
-/// @overload
-template <typename... T, typename... U>
-struct is_elementwise_constructible<tuple<T...>, U...>
-   : is_constructible_from<sizeof...(U) == sizeof...(T) && sizeof...(U) != 0 &&
-  !is_self_arg<tuple<T...>, U...>::value, tuple<T...>, U...> {};
-
-/// SFINAE guard for the element-wise constructor of @p tuple
-template <typename Tuple, typename... U>
-using enable_elementwise_t =
-   std::enable_if_t<is_elementwise_constructible<Tuple, U...>::value>;
-}  // namespace detail
+}
 
 /**
  * @tparam T the types stored in the tuple
  * @brief This is a class that mimics most of std::tuple's interface,
- * except that it is usable in CUDA kernels and admits some arithmetic operator
- * overloads.
+ * except that it is usable in CUDA kernels and admits some arithmetic operator overloads.
  *
- * See https://en.cppreference.com/w/cpp/utility/tuple for more information
- * about std::tuple.
+ * see https://en.cppreference.com/w/cpp/utility/tuple for more information about std::tuple
  */
 template <typename... T>
 struct tuple : detail::tuple_impl<std::index_sequence_for<T...>, T...>
@@ -157,16 +111,9 @@ struct tuple : detail::tuple_impl<std::index_sequence_for<T...>, T...>
    /**
     * @brief Construct tuple from values
     * @param args The values to store
-    *
-    * @note this constructor is deliberately *not* explicit, so that the
-    * copy-list-initialization forms that worked when @p tuple was an aggregate
-    * (@c "tuple<A,B> t = {a,b};", @c "return {a,b};", passing @c "{a,b}" to a
-    * function) keep working.
     */
-   template <typename... U,
-             typename = detail::enable_elementwise_t<tuple, U...>>
    MFEM_HOST_DEVICE
-   constexpr tuple(U&&... args) : base_type(std::forward<U>(args)...) {}
+   constexpr explicit tuple(T... args) : base_type(std::forward<T>(args)...) {}
 
    /// Copy constructor
    MFEM_HOST_DEVICE
@@ -222,8 +169,10 @@ template <class... Types>
 struct tuple_size;
 
 template <class... Types>
-struct tuple_size<tuple<Types...> >
-: std::integral_constant<std::size_t, sizeof...(Types)> {};
+struct tuple_size<tuple<Types...>> :
+                                std::integral_constant<std::size_t, sizeof...(Types)>
+{
+};
 
 /**
  * @brief a struct used to determine the type at index I of a tuple
@@ -239,8 +188,10 @@ struct tuple_element;
 // recursive case
 /// @overload
 template <size_t I, class Head, class... Tail>
-struct tuple_element<I, tuple<Head, Tail...> >
-   : tuple_element<I - 1, tuple<Tail...>> {};
+struct tuple_element<I, tuple<Head, Tail...>> : tuple_element<I - 1,
+                                              tuple<Tail...>>
+{
+};
 
 // base case
 /// @overload
@@ -250,20 +201,19 @@ struct tuple_element<0, tuple<Head, Tail...>>
    using type = Head;  ///< the type at the specified index
 };
 
-namespace detail
-{
+/// @brief Type alias mirroring std::tuple_element_t for mfem::future::tuple
+template <size_t I, class T>
+using tuple_element_t = typename tuple_element<I, T>::type;
+
 /**
  * @brief Get implementation for tuple_leaf - non-const lvalue reference
  * @tparam I the index of the tuple element
  * @tparam T the type of the tuple element
  * @param leaf the tuple_leaf containing the value
  * @return reference to the value
- *
- * @note @a T is deduced from the (unique) @p tuple_leaf base class of the
- * argument, so callers only have to supply the index @a I.
  */
 template <size_t I, typename T>
-MFEM_HOST_DEVICE constexpr T& get_impl(tuple_leaf<I, T>& leaf)
+MFEM_HOST_DEVICE constexpr T& get_impl(detail::tuple_leaf<I, T>& leaf)
 {
    return leaf.value;
 }
@@ -276,7 +226,8 @@ MFEM_HOST_DEVICE constexpr T& get_impl(tuple_leaf<I, T>& leaf)
  * @return const reference to the value
  */
 template <size_t I, typename T>
-MFEM_HOST_DEVICE constexpr const T& get_impl(const tuple_leaf<I, T>& leaf)
+MFEM_HOST_DEVICE constexpr const T& get_impl(const detail::tuple_leaf<I, T>&
+                                             leaf)
 {
    return leaf.value;
 }
@@ -289,7 +240,7 @@ MFEM_HOST_DEVICE constexpr const T& get_impl(const tuple_leaf<I, T>& leaf)
  * @return rvalue reference to the value
  */
 template <size_t I, typename T>
-MFEM_HOST_DEVICE constexpr T&& get_impl(tuple_leaf<I, T>&& leaf)
+MFEM_HOST_DEVICE constexpr T&& get_impl(detail::tuple_leaf<I, T>&& leaf)
 {
    return static_cast<T&&>(leaf.value);
 }
@@ -302,11 +253,11 @@ MFEM_HOST_DEVICE constexpr T&& get_impl(tuple_leaf<I, T>&& leaf)
  * @return const rvalue reference to the value
  */
 template <size_t I, typename T>
-MFEM_HOST_DEVICE constexpr const T&& get_impl(const tuple_leaf<I, T>&& leaf)
+MFEM_HOST_DEVICE constexpr const T&& get_impl(const detail::tuple_leaf<I, T>&&
+                                              leaf)
 {
    return static_cast<const T&&>(leaf.value);
 }
-}  // namespace detail
 
 /**
  * @tparam I the tuple index to access
@@ -318,7 +269,9 @@ template <size_t I, typename... T>
 MFEM_HOST_DEVICE constexpr auto& get(tuple<T...>& t)
 {
    static_assert(I < sizeof...(T), "Tuple index out of bounds");
-   return detail::get_impl<I>(t);
+   using elem_type = typename tuple_element<I, tuple<T...>>::type;
+   using leaf_type = detail::tuple_leaf<I, elem_type>;
+   return get_impl<I>(static_cast<leaf_type&>(t));
 }
 
 /**
@@ -331,7 +284,9 @@ template <size_t I, typename... T>
 MFEM_HOST_DEVICE constexpr const auto& get(const tuple<T...>& t)
 {
    static_assert(I < sizeof...(T), "Tuple index out of bounds");
-   return detail::get_impl<I>(t);
+   using elem_type = typename tuple_element<I, tuple<T...>>::type;
+   using leaf_type = detail::tuple_leaf<I, elem_type>;
+   return get_impl<I>(static_cast<const leaf_type&>(t));
 }
 
 /**
@@ -344,7 +299,9 @@ template <size_t I, typename... T>
 MFEM_HOST_DEVICE constexpr auto&& get(tuple<T...>&& t)
 {
    static_assert(I < sizeof...(T), "Tuple index out of bounds");
-   return detail::get_impl<I>(std::move(t));
+   using elem_type = typename tuple_element<I, tuple<T...>>::type;
+   using leaf_type = detail::tuple_leaf<I, elem_type>;
+   return get_impl<I>(static_cast<leaf_type&&>(t));
 }
 
 /**
@@ -357,15 +314,15 @@ template <size_t I, typename... T>
 MFEM_HOST_DEVICE constexpr const auto&& get(const tuple<T...>&& t)
 {
    static_assert(I < sizeof...(T), "Tuple index out of bounds");
-   return detail::get_impl<I>(std::move(t));
+   using elem_type = typename tuple_element<I, tuple<T...>>::type;
+   using leaf_type = detail::tuple_leaf<I, elem_type>;
+   return get_impl<I>(static_cast<const leaf_type&&>(t));
 }
 
 /**
- * @brief a function intended to be used for extracting the ith type from a
- * tuple.
+ * @brief a function intended to be used for extracting the ith type from a tuple.
  *
- * @note type<i>(my_tuple) returns a value, whereas get<i>(my_tuple) returns a
- * reference
+ * @note type<i>(my_tuple) returns a value, whereas get<i>(my_tuple) returns a reference
  *
  * @tparam I the index of the tuple to query
  * @tparam T the types stored in the tuple
@@ -379,8 +336,6 @@ MFEM_HOST_DEVICE constexpr auto type(const tuple<T...>& t)
    return get<I>(t);
 }
 
-namespace detail
-{
 /**
  * @brief Helper for applying binary operations element-wise
  *
@@ -402,7 +357,6 @@ MFEM_HOST_DEVICE constexpr auto apply_op_helper(
 {
    return tuple{op(get<I>(x), get<I>(y))...};
 }
-} // namespace detail
 
 /**
  * @tparam S the types stored in the tuple x
@@ -416,8 +370,7 @@ MFEM_HOST_DEVICE constexpr auto operator+(const tuple<S...>& x,
                                           const tuple<T...>& y)
 {
    static_assert(sizeof...(S) == sizeof...(T), "tuples must have same size");
-   return detail::apply_op_helper(x, y,
-   [](const auto& a, const auto& b) { return a + b; },
+   return apply_op_helper(x, y, [](auto a, auto b) { return a + b; },
    std::make_index_sequence<sizeof...(S)> {});
 }
 
@@ -433,8 +386,7 @@ MFEM_HOST_DEVICE constexpr auto operator-(const tuple<S...>& x,
                                           const tuple<T...>& y)
 {
    static_assert(sizeof...(S) == sizeof...(T), "tuples must have same size");
-   return detail::apply_op_helper(x, y,
-   [](const auto& a, const auto& b) { return a - b; },
+   return apply_op_helper(x, y, [](auto a, auto b) { return a - b; },
    std::make_index_sequence<sizeof...(S)> {});
 }
 
@@ -443,16 +395,14 @@ MFEM_HOST_DEVICE constexpr auto operator-(const tuple<S...>& x,
  * @tparam T the types stored in the tuple y
  * @param x a tuple of values
  * @param y a tuple of values
- * @brief return a tuple of values defined by elementwise multiplication of x
- * and y
+ * @brief return a tuple of values defined by elementwise multiplication of x and y
  */
 template <typename... S, typename... T>
 MFEM_HOST_DEVICE constexpr auto operator*(const tuple<S...>& x,
                                           const tuple<T...>& y)
 {
    static_assert(sizeof...(S) == sizeof...(T), "tuples must have same size");
-   return detail::apply_op_helper(x, y,
-   [](const auto& a, const auto& b) { return a * b; },
+   return apply_op_helper(x, y, [](auto a, auto b) { return a * b; },
    std::make_index_sequence<sizeof...(S)> {});
 }
 
@@ -468,13 +418,10 @@ MFEM_HOST_DEVICE constexpr auto operator/(const tuple<S...>& x,
                                           const tuple<T...>& y)
 {
    static_assert(sizeof...(S) == sizeof...(T), "tuples must have same size");
-   return detail::apply_op_helper(x, y,
-   [](const auto& a, const auto& b) { return a / b; },
+   return apply_op_helper(x, y, [](auto a, auto b) { return a / b; },
    std::make_index_sequence<sizeof...(S)> {});
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the += operator of tuples
  *
@@ -491,7 +438,6 @@ MFEM_HOST_DEVICE constexpr void inplace_add_helper(
 {
    ((get<I>(x) += get<I>(y)), ...);
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuples x and y
@@ -500,15 +446,12 @@ MFEM_HOST_DEVICE constexpr void inplace_add_helper(
  * @brief add values contained in y, to the tuple x
  */
 template <typename... T>
-MFEM_HOST_DEVICE constexpr tuple<T...>& operator+=(tuple<T...>& x,
-                                                   const tuple<T...>& y)
+MFEM_HOST_DEVICE constexpr auto operator+=(tuple<T...>& x, const tuple<T...>& y)
 {
-   detail::inplace_add_helper(x, y, std::make_index_sequence<sizeof...(T)> {});
+   inplace_add_helper(x, y, std::make_index_sequence<sizeof...(T)> {});
    return x;
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the -= operator of tuples
  *
@@ -525,7 +468,6 @@ MFEM_HOST_DEVICE constexpr void inplace_sub_helper(
 {
    ((get<I>(x) -= get<I>(y)), ...);
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuples x and y
@@ -534,15 +476,12 @@ MFEM_HOST_DEVICE constexpr void inplace_sub_helper(
  * @brief subtract values contained in y from the tuple x
  */
 template <typename... T>
-MFEM_HOST_DEVICE constexpr tuple<T...>& operator-=(tuple<T...>& x,
-                                                   const tuple<T...>& y)
+MFEM_HOST_DEVICE constexpr auto operator-=(tuple<T...>& x, const tuple<T...>& y)
 {
-   detail::inplace_sub_helper(x, y, std::make_index_sequence<sizeof...(T)> {});
+   inplace_sub_helper(x, y, std::make_index_sequence<sizeof...(T)> {});
    return x;
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the unary - operator of tuples
  *
@@ -558,23 +497,18 @@ MFEM_HOST_DEVICE constexpr auto unary_minus_helper(
 {
    return tuple{-get<I>(x)...};
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuple x
  * @param x a tuple of values
- * @brief return a tuple of values defined by applying the unary minus operator
- * to each element of x
+ * @brief return a tuple of values defined by applying the unary minus operator to each element of x
  */
 template <typename... T>
 MFEM_HOST_DEVICE constexpr auto operator-(const tuple<T...>& x)
 {
-   return detail::unary_minus_helper(
-             x, std::make_index_sequence<sizeof...(T)> {});
+   return unary_minus_helper(x, std::make_index_sequence<sizeof...(T)> {});
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the * operator of tuples with scalar
  *
@@ -584,15 +518,14 @@ namespace detail
  * @param x tuple of values
  * @return the returned tuple product
  */
-template <typename scalar_t, typename... T, size_t... I>
+template <typename... T, size_t... I>
 MFEM_HOST_DEVICE constexpr auto scalar_mult_helper(
-   scalar_t a,
+   real_t a,
    const tuple<T...>& x,
    std::index_sequence<I...>)
 {
    return tuple{a * get<I>(x)...};
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuple
@@ -600,11 +533,10 @@ MFEM_HOST_DEVICE constexpr auto scalar_mult_helper(
  * @param x the tuple object
  * @brief multiply each component of x by the value a on the left
  */
-template <typename scalar_t, typename... T>
-MFEM_HOST_DEVICE constexpr auto operator*(scalar_t a, const tuple<T...>& x)
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator*(real_t a, const tuple<T...>& x)
 {
-   return detail::scalar_mult_helper(
-             a, x, std::make_index_sequence<sizeof...(T)> {});
+   return scalar_mult_helper(a, x, std::make_index_sequence<sizeof...(T)> {});
 }
 
 /**
@@ -613,14 +545,12 @@ MFEM_HOST_DEVICE constexpr auto operator*(scalar_t a, const tuple<T...>& x)
  * @param a a scaling factor
  * @brief multiply each component of x by the value a on the right
  */
-template <typename scalar_t, typename... T>
-MFEM_HOST_DEVICE constexpr auto operator*(const tuple<T...>& x, scalar_t a)
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator*(const tuple<T...>& x, real_t a)
 {
    return a * x;
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the / operator of tuples with scalar denominator
  *
@@ -630,15 +560,14 @@ namespace detail
  * @param a the constant denominator
  * @return the returned tuple ratio
  */
-template <typename scalar_t, typename... T, size_t... I>
+template <typename... T, size_t... I>
 MFEM_HOST_DEVICE constexpr auto scalar_div_helper(
    const tuple<T...>& x,
-   scalar_t a,
+   real_t a,
    std::index_sequence<I...>)
 {
    return tuple{get<I>(x) / a...};
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuple x
@@ -646,15 +575,12 @@ MFEM_HOST_DEVICE constexpr auto scalar_div_helper(
  * @param a a denominator
  * @brief return a tuple of values defined by elementwise division of x by a
  */
-template <typename scalar_t, typename... T>
-MFEM_HOST_DEVICE constexpr auto operator/(const tuple<T...>& x, scalar_t a)
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator/(const tuple<T...>& x, real_t a)
 {
-   return detail::scalar_div_helper(
-             x, a, std::make_index_sequence<sizeof...(T)> {});
+   return scalar_div_helper(x, a, std::make_index_sequence<sizeof...(T)> {});
 }
 
-namespace detail
-{
 /**
  * @brief A helper function for the / operator with scalar numerator
  *
@@ -664,15 +590,14 @@ namespace detail
  * @param x tuple of values
  * @return the returned tuple ratio
  */
-template <typename scalar_t, typename... T, size_t... I>
+template <typename... T, size_t... I>
 MFEM_HOST_DEVICE constexpr auto scalar_div_inv_helper(
-   scalar_t a,
+   real_t a,
    const tuple<T...>& x,
    std::index_sequence<I...>)
 {
    return tuple{a / get<I>(x)...};
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuple x
@@ -680,15 +605,12 @@ MFEM_HOST_DEVICE constexpr auto scalar_div_inv_helper(
  * @param x a tuple of denominator values
  * @brief return a tuple of values defined by division of a by the elements of x
  */
-template <typename scalar_t, typename... T>
-MFEM_HOST_DEVICE constexpr auto operator/(scalar_t a, const tuple<T...>& x)
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator/(real_t a, const tuple<T...>& x)
 {
-   return detail::scalar_div_inv_helper(
-             a, x, std::make_index_sequence<sizeof...(T)> {});
+   return scalar_div_inv_helper(a, x, std::make_index_sequence<sizeof...(T)> {});
 }
 
-namespace detail
-{
 /**
  * @tparam T the types stored in the tuple
  * @tparam I a list of indices used to access each element of the tuple
@@ -705,7 +627,6 @@ auto& print_helper(std::ostream& out, const tuple<T...>& t,
    out << "}";
    return out;
 }
-} // namespace detail
 
 /**
  * @tparam T the types stored in the tuple
@@ -716,12 +637,9 @@ auto& print_helper(std::ostream& out, const tuple<T...>& t,
 template <typename... T>
 auto& operator<<(std::ostream& out, const tuple<T...>& t)
 {
-   return detail::print_helper(
-             out, t, std::make_index_sequence<sizeof...(T)> {});
+   return print_helper(out, t, std::make_index_sequence<sizeof...(T)> {});
 }
 
-namespace detail
-{
 /**
  * @brief A helper to apply a lambda to a tuple
  *
@@ -738,27 +656,23 @@ MFEM_HOST_DEVICE auto apply_helper(F&& f, tuple<T...>& args,
 {
    return std::forward<F>(f)(get<I>(args)...);
 }
-} // namespace detail
 
 /**
  * @tparam F a callable type
  * @tparam T the types of arguments to be passed in to f
  * @param f the callable object
  * @param args a tuple of arguments
- * @brief a way of passing an n-tuple to a function that expects n separate
- * arguments
+ * @brief a way of passing an n-tuple to a function that expects n separate arguments
  *
- * For example, foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz)).
+ *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
  */
 template <typename F, typename... T>
 MFEM_HOST_DEVICE auto apply(F&& f, tuple<T...>& args)
 {
-   return detail::apply_helper(std::forward<F>(f), args,
-                               std::make_index_sequence<sizeof...(T)> {});
+   return apply_helper(std::forward<F>(f), args,
+                       std::make_index_sequence<sizeof...(T)> {});
 }
 
-namespace detail
-{
 /**
  * @overload
  */
@@ -768,23 +682,21 @@ MFEM_HOST_DEVICE auto apply_helper(F&& f, const tuple<T...>& args,
 {
    return std::forward<F>(f)(get<I>(args)...);
 }
-} // namespace detail
 
 /**
  * @tparam F a callable type
  * @tparam T the types of arguments to be passed in to f
  * @param f the callable object
  * @param args a tuple of arguments
- * @brief a way of passing an n-tuple to a function that expects n separate
- * arguments
+ * @brief a way of passing an n-tuple to a function that expects n separate arguments
  *
- * For example, foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz)).
+ *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
  */
 template <typename F, typename... T>
 MFEM_HOST_DEVICE auto apply(F&& f, const tuple<T...>& args)
 {
-   return detail::apply_helper(std::forward<F>(f), args,
-                               std::make_index_sequence<sizeof...(T)> {});
+   return apply_helper(std::forward<F>(f), args,
+                       std::make_index_sequence<sizeof...(T)> {});
 }
 
 /**
@@ -802,8 +714,7 @@ struct is_tuple<tuple<T...>> : std::true_type
 };
 
 /**
- * @brief Trait for checking if a type if a @p mfem::tuple containing only
- * @p mfem::tuple
+ * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
  */
 template <typename T>
 struct is_tuple_of_tuples : std::false_type
@@ -811,8 +722,7 @@ struct is_tuple_of_tuples : std::false_type
 };
 
 /**
- * @brief Trait for checking if a type if a @p mfem::tuple containing only
- * @p mfem::tuple
+ * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
  */
 template <typename... T>
 struct is_tuple_of_tuples<tuple<T...>>
@@ -842,8 +752,8 @@ namespace std
  * @tparam T The types in the mfem::future::tuple
  */
 template <typename... T>
-struct tuple_size<mfem::future::tuple<T...> >
-: integral_constant<size_t, sizeof...(T)> {};
+struct tuple_size<mfem::future::tuple<T...>>
+                                          : integral_constant<size_t, sizeof...(T)> {};
 
 /**
  * @brief Specialization of std::tuple_element for mfem::future::tuple
@@ -856,4 +766,20 @@ struct tuple_element<I, mfem::future::tuple<T...>>
    using type = typename
                 mfem::future::tuple_element<I, mfem::future::tuple<T...>>::type;
 };
-} // namespace std
+
+template <size_t I, typename... T>
+constexpr decltype(auto) get(mfem::future::tuple<T...>& t) noexcept
+{ return mfem::future::get<I>(t); }
+
+template <size_t I, typename... T>
+constexpr decltype(auto) get(const mfem::future::tuple<T...>& t) noexcept
+{ return mfem::future::get<I>(t); }
+
+template <size_t I, typename... T>
+constexpr decltype(auto) get(mfem::future::tuple<T...>&& t) noexcept
+{ return mfem::future::get<I>(std::move(t)); }
+
+template <size_t I, typename... T>
+constexpr decltype(auto) get(const mfem::future::tuple<T...>&& t) noexcept
+{ return mfem::future::get<I>(std::move(t)); }
+}

fem/fe/fe_base.cpp

@@ -1316,14 +1316,13 @@ void VectorFiniteElement::Project_RT(
    }
 }
 
-void VectorFiniteElement::ProjectCurl2D_RT(
+void VectorFiniteElement::ProjectGrad_RT(
    const real_t *nk, const Array<int> &d2n, const FiniteElement &fe,
    ElementTransformation &Trans, DenseMatrix &grad) const
 {
-   // 2D "ProjectCurl_RT"
    if (dim != 2)
    {
-      mfem_error("VectorFiniteElement::ProjectCurl2D_RT works only in 2D!");
+      mfem_error("VectorFiniteElement::ProjectGrad_RT works only in 2D!");
    }
 
    DenseMatrix dshape(fe.GetDof(), fe.GetDim());
@@ -1334,8 +1333,8 @@ void VectorFiniteElement::ProjectCurl2D_RT(
    for (int k = 0; k < dof; k++)
    {
       fe.CalcDShape(Nodes.IntPoint(k), dshape);
-      tk[0] = -nk[d2n[k]*dim+1];
-      tk[1] = nk[d2n[k]*dim];
+      tk[0] = nk[d2n[k]*dim+1];
+      tk[1] = -nk[d2n[k]*dim];
       dshape.Mult(tk, grad_k);
       for (int j = 0; j < grad_k.Size(); j++)
       {
@@ -1382,7 +1381,7 @@ void VectorFiniteElement::ProjectCurl_ND(
    }
 }
 
-void VectorFiniteElement::ProjectCurl3D_RT(
+void VectorFiniteElement::ProjectCurl_RT(
    const real_t *nk, const Array<int> &d2n, const FiniteElement &fe,
    ElementTransformation &Trans, DenseMatrix &curl) const
 {

fem/fe/fe_base.hpp

@@ -957,11 +957,10 @@ protected:
                    const FiniteElement &fe, ElementTransformation &Trans,
                    DenseMatrix &I) const;
 
-   // Input is a scalar representing the Z (out of plane) component, Output is
-   // the X-Y (in-plane) RT curl
-   void ProjectCurl2D_RT(const real_t *nk, const Array<int> &d2n,
-                         const FiniteElement &fe, ElementTransformation &Trans,
-                         DenseMatrix &grad) const;
+   // rotated gradient in 2D
+   void ProjectGrad_RT(const real_t *nk, const Array<int> &d2n,
+                       const FiniteElement &fe, ElementTransformation &Trans,
+                       DenseMatrix &grad) const;
 
    // Compute the curl as a discrete operator from ND FE (fe) to ND FE (this).
    // The natural FE for the range is RT, so this is an approximation.
@@ -969,9 +968,9 @@ protected:
                        const FiniteElement &fe, ElementTransformation &Trans,
                        DenseMatrix &curl) const;
 
-   void ProjectCurl3D_RT(const real_t *nk, const Array<int> &d2n,
-                         const FiniteElement &fe, ElementTransformation &Trans,
-                         DenseMatrix &curl) const;
+   void ProjectCurl_RT(const real_t *nk, const Array<int> &d2n,
+                       const FiniteElement &fe, ElementTransformation &Trans,
+                       DenseMatrix &curl) const;
 
    /** @brief Project a vector coefficient onto the ND basis functions
        @param tk    Edge tangent vectors for this element type
@@ -1447,8 +1446,6 @@ public:
                                 dof2quad_array_open);
    }
 
-   const Poly_1D::Basis &GetOpenBasis1D() const { return obasis1d; }
-
    virtual ~VectorTensorFiniteElement();
 };
 

fem/fe/fe_rt.hpp

@@ -73,11 +73,16 @@ public:
    void Project(const FiniteElement &fe, ElementTransformation &Trans,
                 DenseMatrix &I) const override
    { Project_RT(nk, dof2nk, fe, Trans, I); }
+   // Gradient + rotation = Curl: H1 -> H(div)
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
+   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
    // Curl = Gradient + rotation: H1 -> H(div)
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl2D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
 
    void GetFaceMap(const int face_id, Array<int> &face_map) const override;
 
@@ -143,7 +148,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 
    /// @brief Return the mapping from lexicographically ordered face DOFs to
    /// lexicographically ordered element DOFs corresponding to local face
@@ -205,11 +210,16 @@ public:
    void Project(const FiniteElement &fe, ElementTransformation &Trans,
                 DenseMatrix &I) const override
    { Project_RT(nk, dof2nk, fe, Trans, I); }
+   // Gradient + rotation = Curl: H1 -> H(div)
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
+   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
    // Curl = Gradient + rotation: H1 -> H(div)
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl2D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 
@@ -264,7 +274,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 class RT_WedgeElement : public VectorFiniteElement
@@ -322,7 +332,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 /** Arbitrary order H(Div) basis functions defined on pyramid-shaped elements
@@ -418,7 +428,7 @@ public:
    virtual void ProjectCurl(const FiniteElement &fe,
                             ElementTransformation &Trans,
                             DenseMatrix &curl) const
-   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 
    void CalcRawVShape(const IntegrationPoint &ip,
                       DenseMatrix &shape) const;

fem/fem.hpp

@@ -52,7 +52,7 @@
 #include "bounds.hpp"
 #include "particleset.hpp"
 
-#include "dfem/doperator.hpp"
+// #include "dfem/doperator.hpp"
 
 #ifdef MFEM_USE_MPI
 #include "pfespace.hpp"

fem/fespace.cpp

@@ -22,8 +22,6 @@
 #include <algorithm>
 #include <cmath>
 #include <cstdarg>
-#include <unordered_map>
-#include <unordered_set>
 
 using namespace std;
 
@@ -4529,210 +4527,6 @@ void FiniteElementSpace
    }
 }
 
-void FiniteElementSpace::GetBoundaryLoopEdgeDofs(
-   const Array<int> &boundary_element_indices,
-   Array<int> &boundary_edge_dofs,
-   Array<int> *dof_edges,
-   Array<int> *dof_boundary_elements) const
-{
-   MFEM_VERIFY(mesh->Dimension() >= 2,
-               "GetBoundaryLoopEdgeDofs requires 2D or 3D meshes to find edge objects");
-
-   boundary_edge_dofs.SetSize(0);
-   if (dof_edges) { dof_edges->SetSize(0); }
-   if (dof_boundary_elements) { dof_boundary_elements->SetSize(0); }
-
-   // A DOF that appears in exactly one selected boundary element lies on the
-   // bounding loop; one appearing in two or more is interior to the boundary
-   // region and is dropped. Count occurrences of each DOF (using scratch maps,
-   // exposed only as parallel-indexed Array<int> below) and record, on first
-   // sight, the local edge and boundary element carrying it.
-   //
-   // The count is over GetEdgeDofs, which returns endpoint vertex DOFs as well
-   // as edge-interior DOFs (relevant for collections such as ND_R2D that carry
-   // vertex DOFs). Edge-interior DOFs occur once per edge, so the count mainly
-   // resolves vertex DOFs: a vertex shared by several elements is interior and
-   // dropped, while a genuine loop-corner (open-curve endpoint) vertex is kept.
-   // This is why we count GetEdgeDofs rather than collecting GetEdgeInteriorDofs,
-   // which would omit the endpoint vertex DOFs the method is documented to keep.
-   // The 3D removal criterion (any edge in two or more faces) matches the
-   // parallel version rather than a parity toggle.
-   std::unordered_map<int, int> dof_count, dof_edge, dof_belem;
-   Array<int> edge_dofs, edges, edge_orientations;
-
-   const int dim = mesh->Dimension();
-   for (int i = 0; i < boundary_element_indices.Size(); ++i)
-   {
-      const int boundary_element_idx = boundary_element_indices[i];
-      std::unordered_set<int> boundary_element_dofs;
-
-      if (dim == 3)
-      {
-         // Boundary elements are 2D faces; extract their 1D edges.
-         int face_index, face_orientation;
-         mesh->GetBdrElementFace(boundary_element_idx, &face_index,
-                                 &face_orientation);
-         mesh->GetFaceEdges(face_index, edges, edge_orientations);
-      }
-      else
-      {
-         // Boundary elements are 1D segments, each being a single edge.
-         mesh->GetBdrElementEdges(boundary_element_idx, edges, edge_orientations);
-         MFEM_VERIFY(edges.Size() == 1,
-                     "2D boundary element should have exactly one edge");
-      }
-
-      for (int j = 0; j < edges.Size(); ++j)
-      {
-         GetEdgeDofs(edges[j], edge_dofs);
-         for (int k = 0; k < edge_dofs.Size(); ++k)
-         {
-            const int dof = edge_dofs[k];
-            // Count each DOF once per boundary element and record metadata the
-            // first time it is seen, so H1 DOFs shared by multiple edges of the
-            // same element are not double counted.
-            if (boundary_element_dofs.insert(dof).second &&
-                dof_count[dof]++ == 0)
-            {
-               dof_edge[dof] = edges[j];
-               dof_belem[dof] = boundary_element_idx;
-            }
-         }
-      }
-   }
-
-   // Emit the DOFs seen in exactly one selected boundary element, in a
-   // deterministic (increasing DOF index) order shared by all output arrays.
-   std::vector<int> kept;
-   kept.reserve(dof_count.size());
-   for (const auto &[dof, count] : dof_count)
-   {
-      if (count == 1) { kept.push_back(dof); }
-   }
-   std::sort(kept.begin(), kept.end());
-
-   boundary_edge_dofs.Reserve(static_cast<int>(kept.size()));
-   if (dof_edges) { dof_edges->Reserve(static_cast<int>(kept.size())); }
-   if (dof_boundary_elements)
-   {
-      dof_boundary_elements->Reserve(static_cast<int>(kept.size()));
-   }
-   for (int dof : kept)
-   {
-      boundary_edge_dofs.Append(dof);
-      if (dof_edges) { dof_edges->Append(dof_edge[dof]); }
-      if (dof_boundary_elements) { dof_boundary_elements->Append(dof_belem[dof]); }
-   }
-}
-
-void FiniteElementSpace::GetBoundaryElementsByAttribute(
-   const Array<int> &bdr_attrs,
-   std::vector<Array<int>> &attr_to_elements)
-{
-   // One (initially empty) list of boundary elements per requested attribute,
-   // indexed to match bdr_attrs.
-   attr_to_elements.assign(bdr_attrs.Size(), Array<int>());
-
-   // Map attribute value -> position in bdr_attrs for quick lookup.
-   std::unordered_map<int, int> attr_to_index;
-   for (int i = 0; i < bdr_attrs.Size(); ++i)
-   {
-      attr_to_index[bdr_attrs[i]] = i;
-   }
-
-   // Bucket boundary elements by their attribute.
-   for (int i = 0; i < mesh->GetNBE(); ++i)
-   {
-      int attr = mesh->GetBdrElement(i)->GetAttribute();
-      auto it = attr_to_index.find(attr);
-      if (it != attr_to_index.end())
-      {
-         attr_to_elements[it->second].Append(i);
-      }
-   }
-}
-
-void FiniteElementSpace::GetBoundaryElementsByAttribute(int bdr_attr,
-                                                        Array<int> &boundary_elements)
-{
-   boundary_elements.SetSize(0);
-
-   for (int i = 0; i < mesh->GetNBE(); ++i)
-   {
-      if (mesh->GetBdrElement(i)->GetAttribute() == bdr_attr)
-      {
-         boundary_elements.Append(i);
-      }
-   }
-}
-
-void FiniteElementSpace::ComputeLoopEdgeOrientations(
-   const Array<int> &dof_edges,
-   const Array<int> &dof_boundary_elements,
-   const Vector &loop_normal,
-   Array<int> &dof_orientations) const
-{
-   MFEM_VERIFY(dof_edges.Size() == dof_boundary_elements.Size(),
-               "dof_edges and dof_boundary_elements must be parallel-indexed");
-
-   const int ndof = dof_edges.Size();
-   dof_orientations.SetSize(ndof);
-
-   Array<int> edge_verts, bdr_elem_verts;
-   Vector edge_vec(3), to_edge_vec(3), cross_product(3);
-   for (int i = 0; i < ndof; i++)
-   {
-      const int edge_id = dof_edges[i];
-      const int bdr_elem_idx = dof_boundary_elements[i];
-
-      // Get edge vertices
-      mesh->GetEdgeVertices(edge_id, edge_verts);
-
-      const real_t *v0 = mesh->GetVertex(edge_verts[0]);
-      const real_t *v1 = mesh->GetVertex(edge_verts[1]);
-
-      // Get boundary element vertices
-      mesh->GetBdrElement(bdr_elem_idx)->GetVertices(bdr_elem_verts);
-
-      // Find the third vertex (not part of the edge)
-      int third_vertex = -1;
-      for (int j = 0; j < bdr_elem_verts.Size(); j++)
-      {
-         int v = bdr_elem_verts[j];
-         if (v != edge_verts[0] && v != edge_verts[1])
-         {
-            third_vertex = v;
-            break;
-         }
-      }
-
-      if (third_vertex == -1)
-      {
-         MFEM_ABORT("Boundary element " << bdr_elem_idx << " has only 2 vertices, "
-                    "but 3D boundary elements must have at least 3 vertices");
-      }
-
-      const real_t *v2 = mesh->GetVertex(third_vertex);
-
-      // Edge vector
-      for (int j = 0; j < 3; j++) { edge_vec[j] = v1[j] - v0[j]; }
-
-      // Vector from third vertex to edge (use edge midpoint)
-      for (int j = 0; j < 3; j++)
-      {
-         real_t edge_midpoint = (v0[j] + v1[j]) * 0.5;
-         to_edge_vec[j] = edge_midpoint - v2[j];
-      }
-
-      // Cross product: to_edge × edge
-      to_edge_vec.cross3D(edge_vec, cross_product);
-
-      // Check alignment with loop normal
-      real_t dot_product = cross_product * loop_normal;
-      dof_orientations[i] = (dot_product > 0) ? 1 : -1;
-   }
-}
-
 FiniteElementCollection *FiniteElementSpace::Load(Mesh *m, std::istream &input)
 {
    string buff;

fem/fespace.hpp

@@ -22,7 +22,6 @@
 #include "restriction.hpp"
 #include <iostream>
 #include <unordered_map>
-#include <vector>
 
 namespace mfem
 {
@@ -1390,80 +1389,6 @@ public:
    virtual void GetExteriorTrueDofs(Array<int> &exterior_dofs,
                                     int component = -1) const;
 
-   /** @brief Extract the edge degrees of freedom of a boundary "loop".
-
-       Here a "loop" is the set of boundary edges bounding the region covered by
-       @a boundary_element_indices: in 3D the outer edges of a patch of boundary
-       faces, in 2D the boundary segments themselves. An edge that is shared by
-       two (or more) of the selected boundary elements is interior to that region
-       rather than on its bounding loop, so its DOFs are excluded from the result.
-       This exclusion of interior DOFs is the defining feature of the method.
-
-       The three output arrays share a single indexing: for each valid index @a i,
-       @a dof_edges[i] and @a dof_boundary_elements[i] describe the DOF
-       @a boundary_edge_dofs[i].
-
-       @param[in]  boundary_element_indices Boundary element indices spanning a
-                   boundary surface (3D) or curve (2D).
-       @param[out] boundary_edge_dofs Local DOF indices on the boundary loop.
-       @param[out] dof_edges Optional; local edge index carrying each DOF.
-       @param[out] dof_boundary_elements Optional; a boundary element containing
-                   each DOF.
-
-       @note In 3D the edge DOFs are extracted from the 1D edges of the 2D
-       boundary faces; in 2D they come directly from the 1D boundary segments, so
-       @a dof_edges then holds the boundary element (segment) edge indices.
-       @note This method uses GetEdgeDofs internally, which returns both vertex and
-       edge DOFs. Standard Nédélec elements (ND_FECollection) have no vertex DOFs,
-       so only genuine edge DOFs appear. Collections that carry vertex DOFs (e.g.
-       ND_R2D_FECollection) additionally contribute the vertex DOFs at loop
-       endpoints.
-       @note This is the serial version. For parallel meshes, use the parallel
-       version in ParFiniteElementSpace which handles processor boundaries
-       correctly.
-       @note Requires a 2D or 3D mesh to identify edge objects. The method will
-       assert if called on 1D meshes.
-       @note Only supports conforming meshes; non-conforming meshes are not
-       supported. */
-   void GetBoundaryLoopEdgeDofs(const Array<int> &boundary_element_indices,
-                                Array<int> &boundary_edge_dofs,
-                                Array<int> *dof_edges = nullptr,
-                                Array<int> *dof_boundary_elements = nullptr) const;
-
-   /** @brief Get boundary elements grouped by attribute.
-
-       For each attribute in @a bdr_attrs, collect the indices of all boundary
-       elements carrying that attribute. The result is indexed to match
-       @a bdr_attrs: @a attr_to_elements[i] holds the boundary elements with
-       attribute @a bdr_attrs[i]. */
-   void GetBoundaryElementsByAttribute(
-      const Array<int> &bdr_attrs,
-      std::vector<Array<int>> &attr_to_elements);
-
-   /** @brief Get all boundary elements with a specific attribute. */
-   void GetBoundaryElementsByAttribute(int bdr_attr,
-                                       Array<int> &boundary_elements);
-
-   /** @brief Compute edge orientations relative to a boundary loop direction.
-
-       For each boundary-loop DOF described by @a dof_edges and
-       @a dof_boundary_elements (see GetBoundaryLoopEdgeDofs), determine whether
-       the carrying edge is
-       traversed in the direction consistent with @a loop_normal, following the
-       right-hand rule. Intended for 3D meshes.
-
-       @param[in]  dof_edges Local edge index of each DOF (parallel-indexed with
-                   the boundary_edge_dofs output of GetBoundaryLoopEdgeDofs).
-       @param[in]  dof_boundary_elements A boundary element containing each DOF,
-                   using the same indexing as @a dof_edges.
-       @param[in]  loop_normal Normal vector defining the loop orientation.
-       @param[out] dof_orientations Orientation (+1 or -1) for each DOF, using the
-                   same indexing as @a dof_edges. */
-   void ComputeLoopEdgeOrientations(const Array<int> &dof_edges,
-                                    const Array<int> &dof_boundary_elements,
-                                    const Vector &loop_normal,
-                                    Array<int> &dof_orientations) const;
-
    /// Convert a Boolean marker array to a list containing all marked indices.
    static void MarkerToList(const Array<int> &marker, Array<int> &list);
 

fem/gslib.cpp

@@ -556,7 +556,7 @@ void obboxsurf_calc_3(Vector &bb,
    gslib::lagrange_fun *const lag = gslib::gll_lag_setup(work, n);
    lag(I0, work, n, 1, 0);
 
-   for (int ie = 0; (unsigned)ie < nel; ie++,x+=n2,y+=n2,z+=n2)
+   for (int ie = 0; ie < nel; ie++,x+=n2,y+=n2,z+=n2)
    {
       struct gslib::dbl_range ab[3];
       struct gslib::dbl_range tb[3];
@@ -780,7 +780,7 @@ void obboxedge_calc_2(Vector &bb,
    gslib::lagrange_fun *const lag = gslib::gll_lag_setup(work, nr);
    lag(I0r, work, nr,1, 0);
 
-   for (int ie = 0; (unsigned)ie < nel; ie++,x+=nr,y+=nr)
+   for (int ie = 0; ie < nel; ie++,x+=nr,y+=nr)
    {
       double x0[2], A[4];
       struct gslib::dbl_range ab[2], tb[2];
@@ -892,7 +892,7 @@ void obboxedge_calc_3(Vector &bb,
    gslib::lagrange_fun *const lag = gslib::gll_lag_setup(work, nr);
    lag(I0r, work, nr, 1, 0);
 
-   for (int ie = 0; (unsigned)ie < nel; ie++,x+=nr,y+=nr,z+=nr)
+   for (int ie = 0; ie < nel; ie++,x+=nr,y+=nr,z+=nr)
    {
       double x0[3], A[9], Ai[9];
       struct gslib::dbl_range ab[3], tb[3];
@@ -4518,7 +4518,7 @@ Mesh* FindPointsGSLIB::GetBoundingBoxMesh(int type)
    int eidx = 0;
    if (myid == save_rank)
    {
-      for (int p = 0; (unsigned)p < gsl_comm->np; p++)
+      for (int p = 0; p < gsl_comm->np; p++)
       {
          if (static_cast<unsigned int>(p) != save_rank)
          {

fem/integ/bilininteg_convection_pa.cpp

@@ -178,8 +178,6 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    // Assumes tensor-product elements
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
-   MFEM_VERIFY(el.GetMapType() == FiniteElement::VALUE,
-               "Only value map type currently supported");
    ElementTransformation &Trans = *mesh->GetTypicalElementTransformation();
    const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, Trans);
    if (DeviceCanUseCeed())

fem/integ/bilininteg_hcurl_kernels.cpp

@@ -785,23 +785,6 @@ void PAHcurlL2Setup2D(const int Q1D,
    });
 }
 
-void PAHcurlL2IntSetup2D(const int Q1D, const int NE, const Array<real_t> &w,
-                         Vector &coeff, const Vector &detJ, Vector &op)
-{
-   const int NQ = Q1D*Q1D;
-   auto W = w.Read();
-   auto C = Reshape(coeff.Read(), NQ, NE);
-   auto J = Reshape(detJ.Read(), NQ, NE);
-   auto y = Reshape(op.Write(), NQ, NE);
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int q = 0; q < NQ; ++q)
-      {
-         y(q,e) = W[q] * C(q,e) / J(q,e);
-      }
-   });
-}
-
 void PAHcurlL2Setup3D(const int NQ,
                       const int coeffDim,
                       const int NE,

fem/integ/bilininteg_hcurl_kernels.hpp

@@ -1889,17 +1889,13 @@ inline void SmemPACurlCurlApply3D(const int d1d,
    ForallWrap<3>(true, NE, device_kernel, host_kernel, Q1D, Q1D, Q1D);
 }
 
-// PA H(curl)-L2 value Assemble 2D kernel
+// PA H(curl)-L2 Assemble 2D kernel
 void PAHcurlL2Setup2D(const int Q1D,
                       const int NE,
                       const Array<real_t> &w,
                       Vector &coeff,
                       Vector &op);
 
-// PA H(curl)-L2 integral Assemble 2D kernel
-void PAHcurlL2IntSetup2D(const int Q1D, const int NE, const Array<real_t> &w,
-                         Vector &coeff, const Vector &detJ, Vector &op);
-
 // PA H(curl)-L2 Assemble 3D kernel
 void PAHcurlL2Setup3D(const int NQ,
                       const int coeffDim,

fem/integ/bilininteg_hcurlhdiv_kernels.hpp

@@ -864,656 +864,8 @@ inline void PAHcurlHdivApplyTranspose3D(const int d1d,
    }); // end of element loop
 }
 
-namespace curlinterp
-{
-constexpr int NBZ3D(int ndof_o, int nquad_o, int mdq)
-{
-   if (ndof_o <= 0 || nquad_o <= 0)
-   {
-      return 1;
-   }
-   int ndof_c = ndof_o + 1;
-   int nquad_c = nquad_o + 1;
-   // z dimension is capped at 64 on nvidia and amd gpus
-   int tmp =
-      std::min((128 + mdq * mdq * (mdq - 1) - 1) / (mdq * mdq * (mdq - 1)), 64);
-   int smem_req =
-      sizeof(mfem::real_t) *
-      ((3 * ndof_c * ndof_c * ndof_o + 2 * 2 * mdq * mdq * mdq) * tmp +
-       ndof_c * nquad_o + ndof_c * nquad_c + ndof_o * nquad_o);
-   // assume GPU has at least 48k shared memory
-   return std::max(std::min(tmp, (48 * 1024 + smem_req - 1) / smem_req), 1);
-}
-}
-
-template <int T_NDOF_O, int T_NQUAD_O>
-void CurlInterpolatorApply3DSmem(const int ne, const int ndof_o,
-                                 const int nquad_o, const Vector &pa,
-                                 const Vector &x_, Vector &y_)
-{
-   constexpr int mnd_o = T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
-   constexpr int mnq_o =
-      T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
-   constexpr int mndq = std::max(mnd_o + 1, mnq_o + 1);
-   constexpr int tbatch = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, mndq);
-   MFEM_VERIFY(ndof_o <= mnd_o, "Error: H(curl) order larger than supported");
-   MFEM_VERIFY(nquad_o <= mnq_o, "Error: H(div) order larger than supported");
-   int mnq = std::max(ndof_o + 1, nquad_o + 1);
-   auto pa_data = pa.Read();
-   auto x_d = x_.Read();
-   auto y_d = y_.ReadWrite();
-   mfem::forall_2D_batch<mndq * mndq * (mndq - 1) * tbatch>(
-      ne, mnq * mnq * (mnq - 1), 1, tbatch, [=] MFEM_HOST_DEVICE(int e)
-   {
-      constexpr int MND_O =
-         T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
-      constexpr int MNQ_O =
-         T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
-      constexpr int MNDQ = std::max(MND_O + 1, MNQ_O + 1);
-#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
-      constexpr int nbz = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, MNDQ);
-      int tidz = MFEM_THREAD_ID(z);
-      // Make mnq a local variable since capturing would result in different
-      // captures between host/device versions, and spuriously fails
-      int mnq = std::max(ndof_o + 1, nquad_o + 1);
-#else
-      constexpr int nbz = 1;
-      constexpr int tidz = 0;
-#endif
-      const int NDOF_O = T_NDOF_O ? T_NDOF_O : ndof_o;
-      const int NQUAD_O = T_NQUAD_O ? T_NQUAD_O : nquad_o;
-      const int NDOF_C = NDOF_O + 1;
-      const int NQUAD_C = NQUAD_O + 1;
-      MFEM_SHARED real_t
-      sBG[(MND_O + 1) * MNQ_O + (MND_O + 1) * (MNQ_O + 1) + MND_O * MNQ_O];
-      auto X_ = Reshape(x_d, 3 * NDOF_C * NDOF_C * NDOF_O, ne);
-      auto Y = Reshape(y_d, 3 * NQUAD_C * NQUAD_O * NQUAD_O, ne);
-      auto Gco = Reshape(sBG, NQUAD_O, NDOF_C);
-      auto Bcc = Reshape(sBG + NDOF_C * NQUAD_O, NQUAD_C, NDOF_C);
-      auto Boo =
-         Reshape(sBG + NDOF_C * NQUAD_O + NDOF_C * NQUAD_C, NQUAD_O, NDOF_O);
-      MFEM_SHARED real_t X[3][nbz][MND_O * (MND_O + 1) * (MND_O + 1)];
-      MFEM_SHARED real_t sm0[nbz * 2 * MNDQ * MNDQ * MNDQ];
-      MFEM_SHARED real_t sm1[nbz * 2 * MNDQ * MNDQ * MNDQ];
-
-      // shapes of buffers always use MNDQ to mitigate shared memory bank
-      // conflicts
-      real_t(*DDQ)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
-      real_t(*DQQ)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm1);
-      real_t(*QQQ)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
-      const int offset = NDOF_O * NDOF_C * NDOF_C;
-      const int offsetq = NQUAD_C * NQUAD_O * NQUAD_O;
-      MFEM_FOREACH_THREAD_DIRECT(ix, x, offset)
-      {
-         for (int dim = 0; dim < 3; ++dim)
-         {
-            X[dim][tidz][ix] = X_(ix + dim * offset, e);
-         }
-      }
-      // load basis functions data
-      if (tidz == 0)
-      {
-         auto npts = NDOF_C * NQUAD_O + NDOF_C * NQUAD_C + NDOF_O * NQUAD_O;
-         MFEM_FOREACH_THREAD(ix, x, npts) { sBG[ix] = pa_data[ix]; }
-      }
-      MFEM_SYNC_THREAD;
-
-      // x: Vz Bcc Gco Boo - Vy Bcc Boo Gco
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_C, NDOF_C,
-                                           NDOF_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_C; ++dx)
-         {
-            u += X[2][tidz][dx + (dy + dz * NDOF_C) * NDOF_C] * Bcc(qx, dx);
-         }
-         DDQ[0][tidz][dz][dy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_C, NDOF_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_C; ++dx)
-         {
-            u += X[1][tidz][dx + (dy + dz * NDOF_O) * NDOF_C] * Bcc(qx, dx);
-         }
-         DDQ[1][tidz][dz][dy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_C, NQUAD_O,
-                                           NDOF_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_C; ++dy)
-         {
-            u += DDQ[0][tidz][dz][dy][qx] * Gco(qy, dy);
-         }
-         DQQ[0][tidz][dz][qy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_C, NQUAD_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_O; ++dy)
-         {
-            u += DDQ[1][tidz][dz][dy][qx] * Boo(qy, dy);
-         }
-         DQQ[1][tidz][dz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_C, NQUAD_O,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_O; ++dz)
-         {
-            u += DQQ[0][tidz][dz][qy][qx] * Boo(qz, dz);
-         }
-         QQQ[0][tidz][qz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_C, NQUAD_O,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_C; ++dz)
-         {
-            u += DQQ[1][tidz][dz][qy][qx] * Gco(qz, dz);
-         }
-         Y(qx + (qy + qz * NQUAD_O) * NQUAD_C, e) =
-            QQQ[0][tidz][qz][qy][qx] - u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // y: Vx Boo Bcc Gco - Vz Gco Bcc Boo
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
-                                           NDOF_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_O; ++dx)
-         {
-            u += X[0][tidz][dx + (dy + dz * NDOF_C) * NDOF_O] * Boo(qx, dx);
-         }
-         DDQ[0][tidz][dz][dy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
-                                           NDOF_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_C; ++dx)
-         {
-            u += X[2][tidz][dx + (dy + dz * NDOF_C) * NDOF_C] * Gco(qx, dx);
-         }
-         DDQ[1][tidz][dz][dy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_C,
-                                           NDOF_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_C; ++dy)
-         {
-            u += DDQ[0][tidz][dz][dy][qx] * Bcc(qy, dy);
-         }
-         DQQ[0][tidz][dz][qy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_C,
-                                           NDOF_O, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_C; ++dy)
-         {
-            u += DDQ[1][tidz][dz][dy][qx] * Bcc(qy, dy);
-         }
-         DQQ[1][tidz][dz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_C; ++dz)
-         {
-            u += DQQ[0][tidz][dz][qy][qx] * Gco(qz, dz);
-         }
-         QQQ[0][tidz][qz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_O; ++dz)
-         {
-            u += DQQ[1][tidz][dz][qy][qx] * Boo(qz, dz);
-         }
-         Y(qx + (qy + qz * NQUAD_C) * NQUAD_O + offsetq, e) =
-            QQQ[0][tidz][qz][qy][qx] - u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // z: Vy Gco Boo Bcc - Vx Boo Gco Bcc
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_C; ++dx)
-         {
-            u += X[1][tidz][dx + (dy + dz * NDOF_O) * NDOF_C] * Gco(qx, dx);
-         }
-         DDQ[0][tidz][dz][dy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
-                                           NDOF_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int dx = 0; dx < NDOF_O; ++dx)
-         {
-            u += X[0][tidz][dx + (dy + dz * NDOF_C) * NDOF_O] * Boo(qx, dx);
-         }
-         DDQ[1][tidz][dz][dy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_O; ++dy)
-         {
-            u += DDQ[0][tidz][dz][dy][qx] * Boo(qy, dy);
-         }
-         DQQ[0][tidz][dz][qy][qx] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dy = 0; dy < NDOF_C; ++dy)
-         {
-            u += DDQ[1][tidz][dz][dy][qx] * Gco(qy, dy);
-         }
-         DQQ[1][tidz][dz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_O,
-                                           NQUAD_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_C; ++dz)
-         {
-            u += DQQ[0][tidz][dz][qy][qx] * Bcc(qz, dz);
-         }
-         QQQ[0][tidz][qz][qy][qx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_O,
-                                           NQUAD_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int dz = 0; dz < NDOF_C; ++dz)
-         {
-            u += DQQ[1][tidz][dz][qy][qx] * Bcc(qz, dz);
-         }
-         Y(qx + (qy + qz * NQUAD_O) * NQUAD_O + 2 * offsetq, e) =
-            QQQ[0][tidz][qz][qy][qx] - u;
-      }
-      MFEM_SYNC_THREAD;
-   });
-}
-
-template <int T_NDOF_O, int T_NQUAD_O>
-void CurlInterpolatorTApply3DSmem(const int ne, const int ndof_o,
-                                  const int nquad_o, const Vector &pa,
-                                  const Vector &x_, Vector &y_)
-{
-   constexpr int mnd_o = T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
-   constexpr int mnq_o =
-      T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
-   constexpr int mndq = std::max(mnd_o + 1, mnq_o + 1);
-   constexpr int tbatch = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, mndq);
-   MFEM_VERIFY(ndof_o <= mnd_o, "Error: H(curl) order larger than supported");
-   MFEM_VERIFY(nquad_o <= mnq_o, "Error: H(div) order larger than supported");
-   int mnq = std::max(ndof_o + 1, nquad_o + 1);
-   auto pa_data = pa.Read();
-   auto x_d = x_.Read();
-   auto y_d = y_.ReadWrite();
-   mfem::forall_2D_batch<mndq * mndq * (mndq - 1) * tbatch>(
-      ne, mnq * mnq * (mnq - 1), 1, tbatch, [=] MFEM_HOST_DEVICE(int e)
-   {
-      constexpr int MND_O =
-         T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
-      constexpr int MNQ_O =
-         T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
-      constexpr int MNDQ = std::max(MND_O + 1, MNQ_O + 1);
-#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
-      constexpr int nbz = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, MNDQ);
-      int tidz = MFEM_THREAD_ID(z);
-      // Make mnq a local variable since capturing would result in different
-      // captures between host/device versions, and spuriously fails
-      int mnq = std::max(ndof_o + 1, nquad_o + 1);
-#else
-      constexpr int nbz = 1;
-      constexpr int tidz = 0;
-#endif
-      const int NDOF_O = T_NDOF_O ? T_NDOF_O : ndof_o;
-      const int NQUAD_O = T_NQUAD_O ? T_NQUAD_O : nquad_o;
-      const int NDOF_C = NDOF_O + 1;
-      const int NQUAD_C = NQUAD_O + 1;
-      MFEM_SHARED real_t
-      sBG[(MND_O + 1) * MNQ_O + (MND_O + 1) * (MNQ_O + 1) + MND_O * MNQ_O];
-      auto X_ = Reshape(x_d, 3 * NQUAD_C * NQUAD_O * NQUAD_O, ne);
-      auto Y = Reshape(y_d, 3 * NDOF_C * NDOF_C * NDOF_O, ne);
-      auto Gco = Reshape(sBG, NQUAD_O, NDOF_C);
-      auto Bcc = Reshape(sBG + NDOF_C * NQUAD_O, NQUAD_C, NDOF_C);
-      auto Boo =
-         Reshape(sBG + NDOF_C * NQUAD_O + NDOF_C * NQUAD_C, NQUAD_O, NDOF_O);
-      MFEM_SHARED real_t X[3][nbz][MNQ_O * MNQ_O * (MNQ_O + 1)];
-      MFEM_SHARED real_t sm0[nbz * 2 * MNDQ * MNDQ * MNDQ];
-      MFEM_SHARED real_t sm1[nbz * 2 * MNDQ * MNDQ * MNDQ];
-
-      // shapes of buffers always use MNDQ to mitigate shared memory bank
-      // conflicts
-      real_t(*QQD)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
-      real_t(*QDD)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm1);
-      real_t(*DDD)[nbz][MNDQ][MNDQ][MNDQ] =
-         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
-      const int offset = NDOF_O * NDOF_C * NDOF_C;
-      const int offsetq = NQUAD_C * NQUAD_O * NQUAD_O;
-      MFEM_FOREACH_THREAD_DIRECT(ix, x, offsetq)
-      {
-         for (int dim = 0; dim < 3; ++dim)
-         {
-            X[dim][tidz][ix] = X_(ix + dim * offsetq, e);
-         }
-      }
-      // load basis functions data
-      if (tidz == 0)
-      {
-         auto npts = NDOF_C * NQUAD_O + NDOF_C * NQUAD_C + NDOF_O * NQUAD_O;
-         MFEM_FOREACH_THREAD(ix, x, npts) { sBG[ix] = pa_data[ix]; }
-      }
-      MFEM_SYNC_THREAD;
-
-      // x: Vy Boo Bcc Gco - Vz Boo Gco Bcc
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
-                                           NQUAD_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_O; ++qz)
-         {
-            u += X[1][tidz][qx + (qy + qz * NQUAD_C) * NQUAD_O] * Gco(qz, dz);
-         }
-         QQD[0][tidz][qy][qx][dz] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_C; ++qz)
-         {
-            u += X[2][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_O] * Bcc(qz, dz);
-         }
-         QQD[1][tidz][qy][qx][dz] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_C; ++qy)
-         {
-            u += QQD[0][tidz][qy][qx][dz] * Bcc(qy, dy);
-         }
-         QDD[0][tidz][qx][dz][dy] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_O; ++qy)
-         {
-            u += QQD[1][tidz][qy][qx][dz] * Gco(qy, dy);
-         }
-         QDD[1][tidz][qx][dz][dy] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_O, NDOF_C,
-                                           NDOF_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_O; ++qx)
-         {
-            u += QDD[0][tidz][qx][dz][dy] * Boo(qx, dx);
-         }
-         DDD[0][tidz][dz][dy][dx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_O, NDOF_C,
-                                           NDOF_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_O; ++qx)
-         {
-            u += QDD[1][tidz][qx][dz][dy] * Boo(qx, dx);
-         }
-         Y(dx + (dy + dz * NDOF_C) * NDOF_O, e) =
-            DDD[0][tidz][dz][dy][dx] - u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // y: Vz Gco Boo Bcc - Vx Bcc Boo Gco
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_C; ++qz)
-         {
-            u += X[2][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_O] * Bcc(qz, dz);
-         }
-         QQD[0][tidz][qy][qx][dz] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_O; ++qz)
-         {
-            u += X[0][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_C] * Gco(qz, dz);
-         }
-         QQD[1][tidz][qy][qx][dz] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_O, NDOF_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_O; ++qy)
-         {
-            u += QQD[0][tidz][qy][qx][dz] * Boo(qy, dy);
-         }
-         QDD[0][tidz][qx][dz][dy] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_O, NDOF_C,
-                                           NQUAD_C, mnq - 1, mnq, mnq)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_O; ++qy)
-         {
-            u += QQD[1][tidz][qy][qx][dz] * Boo(qy, dy);
-         }
-         QDD[1][tidz][qx][dz][dy] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_O; ++qx)
-         {
-            u += QDD[0][tidz][qx][dz][dy] * Gco(qx, dx);
-         }
-         DDD[0][tidz][dz][dy][dx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_O,
-                                           NDOF_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_C; ++qx)
-         {
-            u += QDD[1][tidz][qx][dz][dy] * Bcc(qx, dx);
-         }
-         Y(dx + (dy + dz * NDOF_O) * NDOF_C + offset, e) =
-            DDD[0][tidz][dz][dy][dx] - u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // z: Vx Bcc Gco Boo - Vy Gco Bcc Boo
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_O, NQUAD_C,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_O; ++qz)
-         {
-            u += X[0][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_C] * Boo(qz, dz);
-         }
-         QQD[0][tidz][qy][qx][dz] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_O, NQUAD_O,
-                                           NQUAD_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int qz = 0; qz < NQUAD_O; ++qz)
-         {
-            u += X[1][tidz][qx + (qy + qz * NQUAD_C) * NQUAD_O] * Boo(qz, dz);
-         }
-         QQD[1][tidz][qy][qx][dz] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_O,
-                                           NQUAD_C, mnq, mnq - 1, mnq)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_O; ++qy)
-         {
-            u += QQD[0][tidz][qy][qx][dz] * Gco(qy, dy);
-         }
-         QDD[0][tidz][qx][dz][dy] = u;
-      }
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_O,
-                                           NQUAD_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qy = 0; qy < NQUAD_C; ++qy)
-         {
-            u += QQD[1][tidz][qy][qx][dz] * Bcc(qy, dy);
-         }
-         QDD[1][tidz][qx][dz][dy] = u;
-      }
-      MFEM_SYNC_THREAD;
-
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_C,
-                                           NDOF_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_C; ++qx)
-         {
-            u += QDD[0][tidz][qx][dz][dy] * Bcc(qx, dx);
-         }
-         DDD[0][tidz][dz][dy][dx] = u;
-      }
-      MFEM_SYNC_THREAD;
-      // threads assigned to mitigate bank conflicts
-      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_C,
-                                           NDOF_O, mnq, mnq, mnq - 1)
-      {
-         real_t u = 0;
-         for (int qx = 0; qx < NQUAD_O; ++qx)
-         {
-            u += QDD[1][tidz][qx][dz][dy] * Gco(qx, dx);
-         }
-         Y(dx + (dy + dz * NDOF_C) * NDOF_C + 2 * offset, e) =
-            DDD[0][tidz][dz][dy][dx] - u;
-      }
-      MFEM_SYNC_THREAD;
-   });
-}
-
 } // namespace internal
 
-template <int DIM, int NDOF_O, int NQUAD_O>
-CurlInterpolator::ApplyKernelType
-CurlInterpolator::ApplyPAKernels::Kernel()
-{
-   if constexpr (DIM == 3)
-   {
-      return internal::CurlInterpolatorApply3DSmem<NDOF_O, NQUAD_O>;
-   }
-   MFEM_ABORT("Bad dimension!");
-}
-
-template <int DIM, int NDOF_O, int NQUAD_O>
-CurlInterpolator::ApplyKernelType
-CurlInterpolator::ApplyTPAKernels::Kernel()
-{
-   if constexpr (DIM == 3)
-   {
-      return internal::CurlInterpolatorTApply3DSmem<NDOF_O, NQUAD_O>;
-   }
-   MFEM_ABORT("Bad dimension!");
-}
-
 } // namespace mfem
 
 /// \endcond DO_NOT_DOCUMENT

fem/integ/bilininteg_interp_pa.cpp

@@ -14,218 +14,9 @@
 #include "../gridfunc.hpp"
 #include "../qfunction.hpp"
 
-#include "bilininteg_hcurlhdiv_kernels.hpp"
-
 namespace mfem
 {
 
-namespace
-{
-
-void PAHcurlApplyCurl2D(const int c_dofs1D,
-                        const int o_dofs1D,
-                        const int NE,
-                        const Array<real_t> &Bo_,
-                        const Array<real_t> &Gc_,
-                        const Vector &x_,
-                        Vector &y_)
-{
-   auto Bo = Reshape(Bo_.Read(), o_dofs1D, o_dofs1D);
-   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
-   auto X = Reshape(x_.Read(), 2 * c_dofs1D * o_dofs1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), o_dofs1D, o_dofs1D, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int iy = 0; iy < c_dofs1D; ++iy)
-      {
-         for (int ix = 0; ix < o_dofs1D; ++ix)
-         {
-            const real_t xv = X(ix + iy * o_dofs1D, e);
-            for (int oy = 0; oy < o_dofs1D; ++oy)
-            {
-               const real_t gy = Gc(oy, iy);
-               for (int ox = 0; ox < o_dofs1D; ++ox)
-               {
-                  Y(ox, oy, e) -= Bo(ox, ix) * gy * xv;
-               }
-            }
-         }
-      }
-
-      const int y_nd = c_dofs1D * o_dofs1D;
-      for (int iy = 0; iy < o_dofs1D; ++iy)
-      {
-         for (int ix = 0; ix < c_dofs1D; ++ix)
-         {
-            const real_t xv = X(y_nd + ix + iy * c_dofs1D, e);
-            for (int oy = 0; oy < o_dofs1D; ++oy)
-            {
-               const real_t by = Bo(oy, iy);
-               for (int ox = 0; ox < o_dofs1D; ++ox)
-               {
-                  Y(ox, oy, e) += Gc(ox, ix) * by * xv;
-               }
-            }
-         }
-      }
-   });
-}
-
-void PAHcurlApplyCurlTranspose2D(const int c_dofs1D,
-                                 const int o_dofs1D,
-                                 const int NE,
-                                 const Array<real_t> &Bo_,
-                                 const Array<real_t> &Gc_,
-                                 const Vector &x_,
-                                 Vector &y_)
-{
-   auto Bo = Reshape(Bo_.Read(), o_dofs1D, o_dofs1D);
-   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
-   auto X = Reshape(x_.Read(), o_dofs1D, o_dofs1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), 2 * c_dofs1D * o_dofs1D, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int dy = 0; dy < c_dofs1D; ++dy)
-      {
-         for (int dx = 0; dx < o_dofs1D; ++dx)
-         {
-            real_t sum = 0.0;
-            for (int oy = 0; oy < o_dofs1D; ++oy)
-            {
-               const real_t gy = Gc(oy, dy);
-               for (int ox = 0; ox < o_dofs1D; ++ox)
-               {
-                  sum -= Bo(ox, dx) * gy * X(ox, oy, e);
-               }
-            }
-            Y(dx + dy * o_dofs1D, e) += sum;
-         }
-      }
-
-      const int y_nd = c_dofs1D * o_dofs1D;
-      for (int dy = 0; dy < o_dofs1D; ++dy)
-      {
-         for (int dx = 0; dx < c_dofs1D; ++dx)
-         {
-            real_t sum = 0.0;
-            for (int oy = 0; oy < o_dofs1D; ++oy)
-            {
-               const real_t by = Bo(oy, dy);
-               for (int ox = 0; ox < o_dofs1D; ++ox)
-               {
-                  sum += Gc(ox, dx) * by * X(ox, oy, e);
-               }
-            }
-            Y(y_nd + dx + dy * c_dofs1D, e) += sum;
-         }
-      }
-   });
-}
-
-void PAHdivApplyCurl2D(const int c_dofs1D,
-                       const int o_dofs1D,
-                       const int NE,
-                       const Array<real_t> &Bc_,
-                       const Array<real_t> &Gc_,
-                       const Vector &x_,
-                       Vector &y_)
-{
-   auto Bc = Reshape(Bc_.Read(), c_dofs1D, c_dofs1D);
-   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
-   auto X = Reshape(x_.Read(), c_dofs1D, c_dofs1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), 2 * c_dofs1D * o_dofs1D, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int iy = 0; iy < c_dofs1D; ++iy)
-      {
-         for (int ix = 0; ix < c_dofs1D; ++ix)
-         {
-            const real_t xv = X(ix, iy, e);
-            for (int oy = 0; oy < o_dofs1D; ++oy)
-            {
-               const real_t gy = Gc(oy, iy);
-               for (int ox = 0; ox < c_dofs1D; ++ox)
-               {
-                  Y(ox + oy * c_dofs1D, e) += Bc(ox, ix) * gy * xv;
-               }
-            }
-         }
-      }
-
-      const int y_nd = c_dofs1D * o_dofs1D;
-      for (int iy = 0; iy < c_dofs1D; ++iy)
-      {
-         for (int ix = 0; ix < c_dofs1D; ++ix)
-         {
-            const real_t xv = X(ix, iy, e);
-            for (int oy = 0; oy < c_dofs1D; ++oy)
-            {
-               const real_t by = Bc(oy, iy);
-               for (int ox = 0; ox < o_dofs1D; ++ox)
-               {
-                  Y(y_nd + ox + oy * o_dofs1D, e) -= Gc(ox, ix) * by * xv;
-               }
-            }
-         }
-      }
-   });
-}
-
-void PAHdivApplyCurlTranspose2D(const int c_dofs1D,
-                                const int o_dofs1D,
-                                const int NE,
-                                const Array<real_t> &Bc_,
-                                const Array<real_t> &Gc_,
-                                const Vector &x_,
-                                Vector &y_)
-{
-   auto Bc = Reshape(Bc_.Read(), c_dofs1D, c_dofs1D);
-   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
-   auto X = Reshape(x_.Read(), 2 * c_dofs1D * o_dofs1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), c_dofs1D, c_dofs1D, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int dy = 0; dy < o_dofs1D; ++dy)
-      {
-         for (int dx = 0; dx < c_dofs1D; ++dx)
-         {
-            const real_t xv = X(dx + dy * c_dofs1D, e);
-            for (int iy = 0; iy < c_dofs1D; ++iy)
-            {
-               const real_t gy = Gc(dy, iy);
-               for (int ix = 0; ix < c_dofs1D; ++ix)
-               {
-                  Y(ix, iy, e) += Bc(dx, ix) * gy * xv;
-               }
-            }
-         }
-      }
-
-      const int y_nd = c_dofs1D * o_dofs1D;
-      for (int dy = 0; dy < c_dofs1D; ++dy)
-      {
-         for (int dx = 0; dx < o_dofs1D; ++dx)
-         {
-            const real_t xv = X(y_nd + dx + dy * o_dofs1D, e);
-            for (int iy = 0; iy < c_dofs1D; ++iy)
-            {
-               const real_t by = Bc(dy, iy);
-               for (int ix = 0; ix < c_dofs1D; ++ix)
-               {
-                  Y(ix, iy, e) -= Gc(dx, ix) * by * xv;
-               }
-            }
-         }
-      }
-   });
-}
-
-}
-
 // Apply to x corresponding to DOFs in H^1 (domain) the (topological) gradient
 // to get a dof in H(curl) (range). You can think of the range as the "test" space
 // and the domain as the "trial" space, but there's no integration.
@@ -2159,266 +1950,4 @@ void IdentityInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
    }
 }
 
-void CurlInterpolator::AssemblePA(const FiniteElementSpace &dom_fes,
-                                  const FiniteElementSpace &ran_fes)
-{
-   Mesh *mesh = dom_fes.GetMesh();
-   dim = mesh->Dimension();
-   ne = dom_fes.GetNE();
-   pa_mode_2d = 0;
-   MFEM_VERIFY(ne == ran_fes.GetNE(),
-               "Different meshes for domain and range spaces");
-
-   if (dim == 2)
-   {
-      pa_data.SetSize(0);
-      const FiniteElement *dom_fel = dom_fes.GetTypicalFE();
-      const FiniteElement *ran_fel = ran_fes.GetTypicalFE();
-      const bool hcurl_to_scalar =
-         dynamic_cast<const VectorTensorFiniteElement*>(dom_fel) != NULL &&
-         dom_fel->GetDerivType() == FiniteElement::CURL &&
-         dynamic_cast<const TensorBasisElement*>(ran_fel) != NULL &&
-         ran_fel->GetRangeType() == FiniteElement::SCALAR;
-      const bool scalar_to_hdiv =
-         dynamic_cast<const TensorBasisElement*>(dom_fel) != NULL &&
-         dom_fel->GetRangeType() == FiniteElement::SCALAR &&
-         dynamic_cast<const VectorTensorFiniteElement*>(ran_fel) != NULL &&
-         ran_fel->GetDerivType() == FiniteElement::DIV;
-
-      MFEM_VERIFY(hcurl_to_scalar || scalar_to_hdiv,
-                  "2D CurlInterpolator PA supports H(curl)->scalar and scalar->H(div) only.");
-
-      int closed_basis_type = -1;
-      int open_basis_type = -1;
-      if (hcurl_to_scalar)
-      {
-         const auto *trial_fec = dynamic_cast<const ND_FECollection*>(dom_fes.FEColl());
-         const auto *range_fec = dynamic_cast<const L2_FECollection*>(ran_fes.FEColl());
-         MFEM_VERIFY(trial_fec != NULL, "H(curl) domain must use ND_FECollection.");
-         MFEM_VERIFY(range_fec != NULL, "Scalar range must use L2_FECollection.");
-         MFEM_VERIFY(ran_fel->GetMapType() == FiniteElement::INTEGRAL,
-                     "2D H(curl)->scalar CurlInterpolator PA supports integral-map scalar range spaces only.");
-         closed_basis_type = trial_fec->GetClosedBasisType();
-         open_basis_type = trial_fec->GetOpenBasisType();
-         MFEM_VERIFY(range_fec->GetBasisType() == open_basis_type,
-                     "Domain/range open basis types do not match.");
-         pa_mode_2d = 1;
-      }
-      else
-      {
-         const auto *trial_fec = dynamic_cast<const H1_FECollection*>(dom_fes.FEColl());
-         const auto *range_fec = dynamic_cast<const RT_FECollection*>(ran_fes.FEColl());
-         MFEM_VERIFY(trial_fec != NULL, "Scalar domain must use H1_FECollection.");
-         MFEM_VERIFY(range_fec != NULL, "H(div) range must use RT_FECollection.");
-         closed_basis_type = trial_fec->GetBasisType();
-         open_basis_type = range_fec->GetOpenBasisType();
-         MFEM_VERIFY(range_fec->GetClosedBasisType() == closed_basis_type,
-                     "Domain/range closed basis types do not match.");
-         pa_mode_2d = 2;
-      }
-
-      const int order = hcurl_to_scalar
-                        ? dynamic_cast<const VectorTensorFiniteElement*>(dom_fel)->GetOrder()
-                        : dynamic_cast<const NodalTensorFiniteElement*>(dom_fel)->GetOrder();
-      c_dofs1D = order + 1;
-      o_dofs1D = order;
-
-      closed_dofquad_fe.reset(new H1_SegmentElement(order, closed_basis_type));
-      open_dofquad_fe.reset(new L2_SegmentElement(order - 1, open_basis_type));
-
-      mfem::QuadratureFunctions1D qf1d;
-      mfem::IntegrationRule closed_ir;
-      closed_ir.SetSize(c_dofs1D);
-      qf1d.GaussLobatto(c_dofs1D, &closed_ir);
-
-      mfem::IntegrationRule open_ir;
-      open_ir.SetSize(o_dofs1D);
-      qf1d.GaussLegendre(o_dofs1D, &open_ir);
-
-      maps_C_C = &closed_dofquad_fe->GetDofToQuad(closed_ir, DofToQuad::TENSOR);
-      maps_O_C = &closed_dofquad_fe->GetDofToQuad(open_ir, DofToQuad::TENSOR);
-      maps_O_O = &open_dofquad_fe->GetDofToQuad(open_ir, DofToQuad::TENSOR);
-
-      MFEM_VERIFY(maps_C_C->ndof == c_dofs1D && maps_C_C->nqpt == c_dofs1D, "");
-      MFEM_VERIFY(maps_O_C->ndof == c_dofs1D && maps_O_C->nqpt == o_dofs1D, "");
-      MFEM_VERIFY(maps_O_O->ndof == o_dofs1D && maps_O_O->nqpt == o_dofs1D, "");
-      return;
-   }
-
-   closed_dofquad_fe.reset();
-   open_dofquad_fe.reset();
-   maps_C_C = nullptr;
-   maps_O_C = nullptr;
-   maps_O_O = nullptr;
-
-   const VectorTensorFiniteElement *dom_el =
-      dynamic_cast<const VectorTensorFiniteElement *>(dom_fes.GetTypicalFE());
-   const VectorTensorFiniteElement *ran_el =
-      dynamic_cast<const VectorTensorFiniteElement *>(ran_fes.GetTypicalFE());
-   MFEM_VERIFY(dom_el != NULL, "Only VectorTensorFiniteElement is supported!");
-   MFEM_VERIFY(ran_el != NULL, "Only VectorTensorFiniteElement is supported!");
-   MFEM_VERIFY(dom_el->GetDerivType() == FiniteElement::CURL,
-               "Domain space must be H(curl)");
-   MFEM_VERIFY(ran_el->GetDerivType() == FiniteElement::DIV,
-               "Range space must be H(div)");
-
-   const int dims = dom_el->GetDim();
-   MFEM_VERIFY(dims == 3, "");
-
-   ndof_o = dom_el->GetOrder();
-   int ndof_c = ndof_o + 1;
-   nquad_o = ran_el->GetOrder();
-   int nquad_c = nquad_o + 1;
-
-   // extract the tensor product range dof locations
-   std::vector<real_t> qc(nquad_c);
-   std::vector<real_t> qo(nquad_o);
-   {
-      const IntegrationRule &ran_nodes = ran_el->GetNodes();
-      const Array<int> &quad_map = ran_el->GetDofMap();
-      for (int i = 0; i < nquad_c; ++i)
-      {
-         int idx = UnsignIndex(quad_map[i]);
-         qc[i] = ran_nodes.IntPoint(idx).x;
-      }
-      int offset = ndof_c * ndof_o * ndof_o;
-      for (int i = 0; i < nquad_o; ++i)
-      {
-         int idx = UnsignIndex(quad_map[i + offset]);
-         qo[i] = ran_nodes.IntPoint(idx).x;
-      }
-   }
-
-   // evaluate closed/open 1D basis (and their derivatives) at closed and
-   // open quads
-   // storage order: GCO, BCC, BOO
-   pa_data.SetSize(ndof_c * nquad_o + ndof_c * nquad_c + ndof_o * nquad_o);
-   auto ptr = pa_data.HostWrite();
-   auto &cbasis1d = dom_el->GetBasis1D();
-   auto &obasis1d = dom_el->GetOpenBasis1D();
-   Vector b, g;
-   b.SetSize(ndof_c);
-   g.SetSize(ndof_c);
-   for (int j = 0; j < nquad_o; ++j)
-   {
-      cbasis1d.Eval(qo[j], b, g);
-      for (int i = 0; i < ndof_c; ++i)
-      {
-         ptr[j + i * nquad_o] = g[i];
-      }
-   }
-   ptr += nquad_o * ndof_c;
-
-   for (int j = 0; j < nquad_c; ++j)
-   {
-      cbasis1d.Eval(qc[j], b);
-      for (int i = 0; i < ndof_c; ++i)
-      {
-         ptr[j + i * nquad_c] = b[i];
-      }
-   }
-   ptr += ndof_c * nquad_c;
-
-   b.SetSize(ndof_o);
-   for (int j = 0; j < nquad_o; ++j)
-   {
-      obasis1d.Eval(qo[j], b);
-      for (int i = 0; i < ndof_o; ++i)
-      {
-         ptr[j + i * nquad_o] = b[i];
-      }
-   }
-}
-
-CurlInterpolator::Kernels::Kernels()
-{
-   CurlInterpolator::AddSpecialization<3, 1, 1>();
-   CurlInterpolator::AddSpecialization<3, 2, 2>();
-   CurlInterpolator::AddSpecialization<3, 3, 3>();
-   CurlInterpolator::AddSpecialization<3, 4, 4>();
-   CurlInterpolator::AddSpecialization<3, 5, 5>();
-}
-
-CurlInterpolator::CurlInterpolator() { static Kernels kernels{}; }
-
-void CurlInterpolator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (dim == 2)
-   {
-      MFEM_VERIFY(maps_C_C != nullptr && maps_O_C != nullptr,
-                  "2D CurlInterpolator PA data is not assembled.");
-      if (pa_mode_2d == 1)
-      {
-         MFEM_VERIFY(maps_O_O != nullptr,
-                     "2D CurlInterpolator scalar curl map is not assembled.");
-         PAHcurlApplyCurl2D(c_dofs1D, o_dofs1D, ne, maps_O_O->B, maps_O_C->G,
-                            x, y);
-      }
-      else if (pa_mode_2d == 2)
-      {
-         PAHdivApplyCurl2D(c_dofs1D, o_dofs1D, ne, maps_C_C->B, maps_O_C->G,
-                           x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unsupported 2D CurlInterpolator mode.");
-      }
-      return;
-   }
-
-   ApplyPAKernels::Run(dim, ndof_o, nquad_o, ne, ndof_o, nquad_o, pa_data, x, y);
-}
-
-void CurlInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
-{
-   if (dim == 2)
-   {
-      MFEM_VERIFY(maps_C_C != nullptr && maps_O_C != nullptr,
-                  "2D CurlInterpolator PA data is not assembled.");
-      if (pa_mode_2d == 1)
-      {
-         MFEM_VERIFY(maps_O_O != nullptr,
-                     "2D CurlInterpolator scalar curl map is not assembled.");
-         PAHcurlApplyCurlTranspose2D(c_dofs1D, o_dofs1D, ne, maps_O_O->B,
-                                     maps_O_C->G, x, y);
-      }
-      else if (pa_mode_2d == 2)
-      {
-         PAHdivApplyCurlTranspose2D(c_dofs1D, o_dofs1D, ne, maps_C_C->B,
-                                    maps_O_C->G, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unsupported 2D CurlInterpolator mode.");
-      }
-      return;
-   }
-
-   ApplyTPAKernels::Run(dim, ndof_o, nquad_o, ne, ndof_o, nquad_o, pa_data, x, y);
-}
-
-/// \cond DO_NOT_DOCUMENT
-
-CurlInterpolator::ApplyKernelType
-CurlInterpolator::ApplyPAKernels::Fallback(int DIM, int, int)
-{
-   if (DIM == 3)
-   {
-      return internal::CurlInterpolatorApply3DSmem<0, 0>;
-   }
-   MFEM_ABORT("Bad dimension!");
-}
-
-CurlInterpolator::ApplyKernelType
-CurlInterpolator::ApplyTPAKernels::Fallback(int DIM, int, int)
-{
-   if (DIM == 3)
-   {
-      return internal::CurlInterpolatorTApply3DSmem<0, 0>;
-   }
-   MFEM_ABORT("Bad dimension!");
-}
-
-/// \endcond DO_NOT_DOCUMENT
-
 } // namespace mfem

fem/integ/bilininteg_vecmass_pa.cpp

@@ -22,8 +22,6 @@ void VectorMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
-   MFEM_VERIFY(el.GetMapType() == FiniteElement::VALUE,
-               "Only value map type supported");
    ElementTransformation &Trans = *mesh->GetTypicalElementTransformation();
    const auto *ir = IntRule ? IntRule : &MassIntegrator::GetRule(el, el, Trans);
 

fem/kernel_dispatch.hpp

@@ -48,7 +48,11 @@ namespace mfem
 
 #define MFEM_REGISTER_KERNELS(KernelName, KernelType, ...)                     \
    MFEM_EXPAND(MFEM_EXPAND(MFEM_REGISTER_KERNELS_N(__VA_ARGS__,2,1,))          \
-      (KernelName,KernelType,__VA_ARGS__))
+      (MFEM_EXPORT, KernelName, KernelType, __VA_ARGS__))
+
+#define MFEM_REGISTER_KERNELS_HEADER_ONLY(KernelName, KernelType, ...)         \
+   MFEM_EXPAND(MFEM_EXPAND(MFEM_REGISTER_KERNELS_N(__VA_ARGS__,2,1,))          \
+      (, KernelName, KernelType, __VA_ARGS__))
 
 #define MFEM_REGISTER_KERNELS_N(_1, _2, N, ...) MFEM_REGISTER_KERNELS_##N
 
@@ -58,19 +62,19 @@ namespace mfem
 
 // Version of MFEM_REGISTER_KERNELS without any "optional" (non-dispatch)
 // parameters.
-#define MFEM_REGISTER_KERNELS_1(KernelName, KernelType, Params)                \
-   MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, (), Params)
+#define MFEM_REGISTER_KERNELS_1(ExportMacro, KernelName, KernelType, Params)   \
+   MFEM_REGISTER_KERNELS_(ExportMacro, KernelName, KernelType, Params, (), Params)
 
 // Version of MFEM_REGISTER_KERNELS with optional (non-dispatch)
 // parameters (e.g. NBZ).
-#define MFEM_REGISTER_KERNELS_2(KernelName, KernelType, Params, OptParams)     \
-   MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, OptParams,           \
+#define MFEM_REGISTER_KERNELS_2(ExportMacro, KernelName, KernelType, Params, OptParams) \
+   MFEM_REGISTER_KERNELS_(ExportMacro, KernelName, KernelType, Params, OptParams,       \
                           (MFEM_PARAM_LIST Params, MFEM_PARAM_LIST OptParams))
 
 // P1 are the parameters, P2 are the optional (non-dispatch parameters), and P3
 // is the concatenation of P1 and P2. We need to pass it as a separate argument
 // to avoid a trailing comma in the case that P2 is empty.
-#define MFEM_REGISTER_KERNELS_(KernelName, KernelType, P1, P2, P3)             \
+#define MFEM_REGISTER_KERNELS_(ExportMacro, KernelName, KernelType, P1, P2, P3) \
   class KernelName                                                             \
       : public ::mfem::KernelDispatchTable<                                    \
             KernelName, KernelType,                                            \
@@ -80,8 +84,8 @@ namespace mfem
     const char *kernel_name = MFEM_KERNEL_NAME(KernelName);                    \
     using KernelSignature = KernelType;                                        \
     template <MFEM_PARAM_LIST P3> static KernelSignature Kernel();             \
-    static MFEM_EXPORT KernelSignature Fallback(MFEM_PARAM_LIST P1);           \
-    static MFEM_EXPORT KernelName &Get() {                                     \
+    static ExportMacro KernelSignature Fallback(MFEM_PARAM_LIST P1);           \
+    static ExportMacro KernelName &Get() {                                     \
       static KernelName table;                                                 \
       return table;                                                            \
     }                                                                          \

fem/lor/lor_ams.cpp

@@ -94,10 +94,10 @@ void BatchedLOR_AMS::Form2DEdgeToVertex_RT(Array<int> &edge2vert)
          const int iv0 = ix + iy*op1;
          const int iv1 = ix1 + iy1*op1;
 
-         // 2D curl (dy, -dx), so flip the sign for the second
-         // component (c == 1).
-         e2v(0, iedge) = (c == 0) ? iv0 : iv1;
-         e2v(1, iedge) = (c == 0) ? iv1 : iv0;
+         // Rotated gradient in 2D (-dy, dx), so flip the sign for the first
+         // component (c == 0).
+         e2v(0, iedge) = (c == 1) ? iv0 : iv1;
+         e2v(1, iedge) = (c == 1) ? iv1 : iv0;
       }
    }
 }

fem/lor/lor_batched.cpp

@@ -142,6 +142,8 @@ static MFEM_HOST_DEVICE int GetAndIncrementNnzIndex(const int i_L, int* I)
 
 int BatchedLORAssembly::FillI(SparseMatrix &A) const
 {
+   static constexpr int Max = 16;
+
    const int nvdof = fes_ho.GetVSize();
 
    const int ndof_per_el = fes_ho.GetTypicalFE()->GetDof();
@@ -163,8 +165,6 @@ int BatchedLORAssembly::FillI(SparseMatrix &A) const
    const auto K = dof_glob2loc_offsets_.Read();
    const auto map = Reshape(sparse_mapping.Read(), nnz_per_row, ndof_per_el);
 
-   Array<int> ij_elts(dof_glob2loc_.Size() * 2);
-   auto d_ij_elts = Reshape(ij_elts.Write(), dof_glob2loc_.Size(), 2);
 
    auto I = A.WriteI();
 
@@ -176,10 +176,10 @@ int BatchedLORAssembly::FillI(SparseMatrix &A) const
       const int sii = el_dof_lex(ii_el, iel_ho);
       const int ii = (sii >= 0) ? sii : -1 -sii;
       // Get number and list of elements containing this DOF
+      int i_elts[Max];
       const int i_offset = K[ii];
       const int i_next_offset = K[ii+1];
       const int i_ne = i_next_offset - i_offset;
-      int *i_elts = &d_ij_elts(i_offset, 0);
       for (int e_i = 0; e_i < i_ne; ++e_i)
       {
          const int si_E = dof_glob2loc[i_offset+e_i]; // signed
@@ -202,7 +202,7 @@ int BatchedLORAssembly::FillI(SparseMatrix &A) const
          }
          else // assembly required
          {
-            int *j_elts = &d_ij_elts(j_offset, 1);
+            int j_elts[Max];
             for (int e_j = 0; e_j < j_ne; ++e_j)
             {
                const int sj_E = dof_glob2loc[j_offset+e_j]; // signed
@@ -269,8 +269,7 @@ void BatchedLORAssembly::FillJAndData(SparseMatrix &A) const
       mfem::forall(nvdof + 1, [=] MFEM_HOST_DEVICE (int i) { I[i] = I2[i]; });
    }
 
-   Array<int> ij_B_el(dof_glob2loc_.Size() * 4);
-   auto d_ij_B_el = Reshape(ij_B_el.Write(), dof_glob2loc_.Size(), 4);
+   static constexpr int Max = 16;
 
    mfem::forall(ndof_per_el*nel_ho, [=] MFEM_HOST_DEVICE (int i)
    {
@@ -280,13 +279,11 @@ void BatchedLORAssembly::FillJAndData(SparseMatrix &A) const
       const int sii = el_dof_lex(ii_el, iel_ho); // signed
       const int ii = (sii >= 0) ? sii : -1 - sii;
       // Get number and list of elements containing this DOF
+      int i_elts[Max];
+      int i_B[Max];
       const int i_offset = K[ii];
       const int i_next_offset = K[ii+1];
       const int i_ne = i_next_offset - i_offset;
-
-      int *i_elts = &d_ij_B_el(i_offset, 0);
-      int *i_B = &d_ij_B_el(i_offset, 1);
-
       for (int e_i = 0; e_i < i_ne; ++e_i)
       {
          const int si_E = dof_glob2loc[i_offset+e_i]; // signed
@@ -315,8 +312,8 @@ void BatchedLORAssembly::FillJAndData(SparseMatrix &A) const
          }
          else // assembly required
          {
-            int *j_elts = &d_ij_B_el(j_offset, 2);
-            int *j_B = &d_ij_B_el(j_offset, 3);
+            int j_elts[Max];
+            int j_B[Max];
             for (int e_j = 0; e_j < j_ne; ++e_j)
             {
                const int sj_E = dof_glob2loc[j_offset+e_j]; // signed

fem/nonlinearform.hpp

@@ -224,6 +224,9 @@ public:
    /** @see GetGradient(const Vector &) */
    Operator &GetGradient(const Vector &x, bool finalize) const;
 
+   /// Suppress a warning about hiding overloaded virtual function.
+   using Operator::GetGradient;
+
    /// Update the NonlinearForm to propagate updates of the associated FE space.
    /** After calling this method, the essential boundary conditions need to be
        set again. */

fem/pfespace.cpp

@@ -26,8 +26,6 @@
 
 #include <limits>
 #include <list>
-#include <unordered_map>
-#include <unordered_set>
 
 namespace mfem
 {
@@ -1287,342 +1285,6 @@ void ParFiniteElementSpace::GetExteriorVDofs(Array<int> &ext_dofs,
    Synchronize(ext_dofs);
 }
 
-void ParFiniteElementSpace::GetBoundaryLoopEdgeDofs(
-   const Array<int> &boundary_element_indices,
-   Array<int> &ess_tdof_list,
-   Array<int> &boundary_edge_dofs_out,
-   Array<int> *ldof_marker,
-   Array<int> *dof_edges,
-   Array<int> *dof_boundary_elements,
-   Array<int> *ess_edge_list)
-{
-   MFEM_VERIFY(!pmesh->Nonconforming(),
-               "GetBoundaryLoopEdgeDofs does not support nonconforming meshes");
-   MFEM_VERIFY(pmesh->Dimension() >= 2,
-               "GetBoundaryLoopEdgeDofs requires 2D or 3D meshes to find 1D edge objects");
-
-   // Call the serial version, then rebuild scratch maps/set from the returned
-   // arrays for the O(1) lookups the parallel reconciliation below needs.
-   Array<int> loc_dofs, loc_edges, loc_belems;
-   FiniteElementSpace::GetBoundaryLoopEdgeDofs(boundary_element_indices, loc_dofs,
-                                               &loc_edges, &loc_belems);
-
-   std::unordered_set<int> boundary_edge_dofs;
-   std::unordered_map<int, int> dof_to_edge_map;
-   std::unordered_map<int, int> dof_to_boundary_element;
-   boundary_edge_dofs.reserve(loc_dofs.Size());
-   dof_to_edge_map.reserve(loc_dofs.Size());
-   dof_to_boundary_element.reserve(loc_dofs.Size());
-   for (int i = 0; i < loc_dofs.Size(); i++)
-   {
-      const int dof = loc_dofs[i];
-      boundary_edge_dofs.insert(dof);
-      dof_to_edge_map[dof] = loc_edges[i];
-      dof_to_boundary_element[dof] = loc_belems[i];
-   }
-
-   // Parallel processing: Build edge sharing lookup table
-   std::unordered_map<int, int> edge_to_group_size;
-   int num_groups = pmesh->GetNGroups();
-
-   int total_shared_edges = 0;
-   for (int group = 1; group < num_groups; group++)
-   {
-      total_shared_edges += pmesh->GroupNEdges(group);
-   }
-   edge_to_group_size.reserve(total_shared_edges);
-
-   for (int group = 1; group < num_groups; group++)
-   {
-      int group_size = pmesh->gtopo.GetGroupSize(group);
-      int num_edges_in_group = pmesh->GroupNEdges(group);
-
-      for (int i = 0; i < num_edges_in_group; i++)
-      {
-         edge_to_group_size.emplace(pmesh->GroupEdge(group, i), group_size);
-      }
-   }
-
-   // Get global indices
-   Array<HYPRE_BigInt> global_edge_indices;
-   pmesh->GetGlobalEdgeIndices(global_edge_indices);
-
-   // Handle dimension-specific boundary element relationships
-   Array<HYPRE_BigInt> global_face_indices;
-   std::unordered_map<int, int> boundary_element_to_companion;
-   std::unordered_set<int> dofs_to_remove;
-
-   const int dim = pmesh->Dimension();
-   if (dim == 3)
-   {
-      // In 3D: boundary elements are faces, we track which face each boundary element is
-      pmesh->GetGlobalFaceIndices(global_face_indices);
-      for (int boundary_element_idx : boundary_element_indices)
-      {
-         int face_index, face_orientation;
-         pmesh->GetBdrElementFace(boundary_element_idx, &face_index, &face_orientation);
-         boundary_element_to_companion[boundary_element_idx] = face_index;
-      }
-
-      std::vector<HYPRE_BigInt> local_data;
-      local_data.reserve(boundary_edge_dofs.size() * 2);
-
-      std::unordered_set<int> processed_edges;
-      processed_edges.reserve(boundary_edge_dofs.size());
-
-      for (const auto& [dof, local_edge] : dof_to_edge_map)
-      {
-         // Skip if already processed this edge
-         if (!processed_edges.insert(local_edge).second) { continue; }
-
-         // Check if edge is shared (fast lookup)
-         auto it = edge_to_group_size.find(local_edge);
-         if (it != edge_to_group_size.end() && it->second > 1)
-         {
-            // Get boundary element and companion index directly from pre-computed map
-            int boundary_element_idx = dof_to_boundary_element[dof];
-            int companion_index = boundary_element_to_companion[boundary_element_idx];
-
-            // Store edge-face pair for 3D artificial boundary detection
-            local_data.push_back(global_edge_indices[local_edge]);
-            local_data.push_back(global_face_indices[companion_index]);
-         }
-      }
-
-      // MPI communication for 3D artificial boundary detection
-      int num_procs = pmesh->GetNRanks();
-      int local_size = local_data.size();
-
-      std::vector<int> mpi_arrays(num_procs * 4);
-      int* all_sizes = mpi_arrays.data();
-      int* displs = all_sizes + num_procs;
-      int* byte_sizes = displs + num_procs;
-      int* byte_displs = byte_sizes + num_procs;
-
-      MPI_Allgather(&local_size, 1, MPI_INT, all_sizes, 1, MPI_INT, pmesh->GetComm());
-
-      int total_size = 0;
-      constexpr int hypre_size = sizeof(HYPRE_BigInt);
-      for (int i = 0; i < num_procs; i++)
-      {
-         displs[i] = total_size;
-         byte_displs[i] = total_size * hypre_size;
-         total_size += all_sizes[i];
-         byte_sizes[i] = all_sizes[i] * hypre_size;
-      }
-
-      if (total_size > 0)
-      {
-         std::vector<HYPRE_BigInt> all_data(total_size);
-         MPI_Allgatherv(local_data.data(), local_size * hypre_size, MPI_BYTE,
-                        all_data.data(), byte_sizes, byte_displs, MPI_BYTE, pmesh->GetComm());
-
-         // Build global-to-local edge mapping
-         std::unordered_map<HYPRE_BigInt, int> global_to_local_edge;
-         global_to_local_edge.reserve(global_edge_indices.Size());
-         for (int i = 0; i < global_edge_indices.Size(); ++i)
-         {
-            global_to_local_edge[global_edge_indices[i]] = i;
-         }
-
-         // Process collected data to find edges in multiple faces (artificial boundaries)
-         std::unordered_map<HYPRE_BigInt, std::unordered_set<HYPRE_BigInt>>edge_to_faces;
-         edge_to_faces.reserve(total_size / 2);
-
-         for (size_t i = 0; i < all_data.size(); i += 2)
-         {
-            edge_to_faces[all_data[i]].insert(all_data[i + 1]);
-         }
-
-         // Mark DOFs from artificial edges for removal
-         dofs_to_remove.reserve(local_data.size() / 4);
-
-         for (size_t i = 0; i < local_data.size(); i += 2)
-         {
-            HYPRE_BigInt global_edge_id = local_data[i];
-
-            // If this edge appears in 2+ distinct faces, it's artificial
-            if (edge_to_faces[global_edge_id].size() >= 2)
-            {
-               int local_edge = global_to_local_edge[global_edge_id];
-               Array<int> local_edge_dofs;
-               GetEdgeDofs(local_edge, local_edge_dofs);
-
-               // Mark boundary DOFs of this edge for removal
-               for (int k = 0; k < local_edge_dofs.Size(); ++k)
-               {
-                  int dof = local_edge_dofs[k];
-                  if (boundary_edge_dofs.count(dof))
-                  {
-                     dofs_to_remove.insert(dof);
-                  }
-               }
-            }
-         }
-      }
-   }
-   else if (dim == 2)
-   {
-      // In 2D the boundary elements are themselves the edges, so there are no
-      // artificial boundary edges to detect. However, for collections with
-      // vertex DOFs (e.g. ND_R2D), a vertex shared by two boundary segments is
-      // interior to the boundary curve and must be dropped. The serial code
-      // does this by erasing a DOF on its second occurrence, which only sees
-      // the occurrences local to this rank. When the two segments meeting at a
-      // vertex live on different ranks, each rank sees a single occurrence and
-      // wrongly keeps the DOF. Reconcile the occurrence parity across each
-      // sharing group: membership in boundary_edge_dofs is the local parity,
-      // and the parities sum (mod 2) to the global occurrence parity.
-      Array<int> boundary_dof_count(GetVSize());
-      boundary_dof_count = 0;
-      for (const int dof : boundary_edge_dofs)
-      {
-         boundary_dof_count[dof] = 1;
-      }
-
-      // implement allreduce(+) as reduce(+) + broadcast
-      gcomm->Reduce<int>(boundary_dof_count, GroupCommunicator::Sum);
-      gcomm->Bcast(boundary_dof_count);
-
-      for (const int dof : boundary_edge_dofs)
-      {
-         if (boundary_dof_count[dof] % 2 == 0)
-         {
-            dofs_to_remove.insert(dof);
-         }
-      }
-   }
-
-   // Remove artificial DOFs
-   for (int dof : dofs_to_remove)
-   {
-      boundary_edge_dofs.erase(dof);
-      dof_to_edge_map.erase(dof);
-      dof_to_boundary_element.erase(dof);
-   }
-
-   // Convert to true DOFs and output
-   ess_tdof_list.SetSize(0);
-   ess_tdof_list.Reserve(boundary_edge_dofs.size());
-   if (ess_edge_list)
-   {
-      // Reset as well, so that it stays in correspondence with ess_tdof_list
-      // when the same output array is reused across calls.
-      ess_edge_list->SetSize(0);
-      ess_edge_list->Reserve(boundary_edge_dofs.size());
-   }
-   // Marker of the boundary edge DOFs. Always computed locally because the
-   // parallel reconciliation below needs it; only copied to the caller's output
-   // if requested (see the ldof_marker parameter).
-   Array<int> local_ldof_marker(GetVSize());
-   local_ldof_marker = 0;
-
-   for (int dof : boundary_edge_dofs)
-   {
-      local_ldof_marker[dof] = 1; // Mark all boundary edge dofs
-   }
-
-   // Make sure that a selected shared DOF is marked on every rank of its
-   // sharing group, including ranks holding none of the selected boundary
-   // elements. Only the group master owns the corresponding true DOF, so
-   // without this the true DOF would be emitted by no rank at all: the
-   // non-master ranks get -1 from GetLocalTDofNumber(), while the master may
-   // not have selected the DOF locally.
-   Synchronize(local_ldof_marker);
-
-   // A DOF marked only through the synchronization above has no local
-   // dof_to_edge_map entry, but the shared edge carrying it is still present in
-   // the local mesh. Build the missing DOF -> edge entries from the shared
-   // edges of the groups, so that ess_edge_list stays in correspondence with
-   // ess_tdof_list. Note that a vertex DOF is not associated with a unique
-   // edge, so it is only resolved when it is an interior DOF of an edge.
-   std::unordered_map<int, int> shared_dof_to_edge;
-   Array<int> shared_edge_dofs;
-   for (int group = 1; group < num_groups; group++)
-   {
-      const int num_edges_in_group = pmesh->GroupNEdges(group);
-      for (int i = 0; i < num_edges_in_group; i++)
-      {
-         const int edge = pmesh->GroupEdge(group, i);
-         GetEdgeInteriorDofs(edge, shared_edge_dofs);
-         for (int k = 0; k < shared_edge_dofs.Size(); k++)
-         {
-            shared_dof_to_edge.emplace(shared_edge_dofs[k], edge);
-         }
-      }
-   }
-
-   // Build parallel arrays for DOFs and corresponding edges
-   std::vector<std::pair<int, int>> tdof_edge_pairs;
-   tdof_edge_pairs.reserve(boundary_edge_dofs.size());
-
-   for (int dof = 0; dof < local_ldof_marker.Size(); dof++)
-   {
-      if (!local_ldof_marker[dof]) { continue; }
-
-      const int tdof = GetLocalTDofNumber(dof);
-      if (tdof < 0) { continue; } // tdof == -1 means not owned by this rank
-
-      int edge = -1;
-      auto it = dof_to_edge_map.find(dof);
-      if (it != dof_to_edge_map.end())
-      {
-         edge = it->second;
-      }
-      else
-      {
-         auto shared_it = shared_dof_to_edge.find(dof);
-         if (shared_it != shared_dof_to_edge.end())
-         {
-            edge = shared_it->second;
-         }
-      }
-      tdof_edge_pairs.push_back({tdof, edge});
-   }
-
-   // Sort by true DOF index to maintain consistent ordering
-   std::sort(tdof_edge_pairs.begin(), tdof_edge_pairs.end());
-
-   // Extract sorted true DOFs and edges
-   for (const auto& pair : tdof_edge_pairs)
-   {
-      ess_tdof_list.Append(pair.first);
-      if (ess_edge_list)
-      {
-         ess_edge_list->Append(pair.second);
-      }
-   }
-
-   // Emit the local boundary-loop DOFs in a deterministic (increasing DOF
-   // index) order shared by all output arrays.
-   std::vector<int> kept(boundary_edge_dofs.begin(), boundary_edge_dofs.end());
-   std::sort(kept.begin(), kept.end());
-
-   boundary_edge_dofs_out.SetSize(0);
-   boundary_edge_dofs_out.Reserve(static_cast<int>(kept.size()));
-   if (dof_edges)
-   {
-      dof_edges->SetSize(0);
-      dof_edges->Reserve(static_cast<int>(kept.size()));
-   }
-   if (dof_boundary_elements)
-   {
-      dof_boundary_elements->SetSize(0);
-      dof_boundary_elements->Reserve(static_cast<int>(kept.size()));
-   }
-   for (int dof : kept)
-   {
-      boundary_edge_dofs_out.Append(dof);
-      if (dof_edges) { dof_edges->Append(dof_to_edge_map[dof]); }
-      if (dof_boundary_elements)
-      {
-         dof_boundary_elements->Append(dof_to_boundary_element[dof]);
-      }
-   }
-
-   if (ldof_marker) { ldof_marker->Swap(local_ldof_marker); }
-}
-
 void ParFiniteElementSpace::GetExteriorTrueDofs(Array<int> &ext_tdof_list,
                                                 int component) const
 {

fem/pfespace.hpp

@@ -460,41 +460,6 @@ public:
    void GetExteriorTrueDofs(Array<int> &ext_tdof_list,
                             int component = -1) const override;
 
-   /** @brief Extract the edge degrees of freedom of a boundary "loop" on a
-       parallel mesh (see the serial FiniteElementSpace::GetBoundaryLoopEdgeDofs
-       for the definition of a loop). This version removes the artificial
-       boundary edges that appear at processor boundaries, so the selected DOFs
-       are independent of the mesh partitioning.
-
-       As in the serial version, the @a boundary_edge_dofs_out, @a dof_edges and
-       @a dof_boundary_elements outputs share a single indexing describing the
-       same local DOF at each position.
-
-       Requirements:
-       - Mesh must be conforming (no hanging nodes)
-       - Mesh dimension must be >= 2
-       @param[in]  boundary_element_indices Array of boundary element indices.
-       @param[out] ess_tdof_list Essential true DOF indices, sorted ascending.
-       @param[out] boundary_edge_dofs_out Local boundary-loop DOF indices.
-       @param[out] ldof_marker Optional; marker of the boundary edge DOFs,
-                   derivable from @a boundary_edge_dofs_out via ListToMarker().
-       @param[out] dof_edges Optional; local edge index of each DOF.
-       @param[out] dof_boundary_elements Optional; a boundary element containing
-                   each DOF.
-       @param[out] ess_edge_list Optional array of edge indices, in one-to-one
-                                 correspondence with @a ess_tdof_list. An entry
-                                 is -1 when the true DOF is owned by this rank
-                                 but no local edge can be associated with it,
-                                 which can happen for a shared vertex DOF whose
-                                 boundary elements are all on other ranks. */
-   void GetBoundaryLoopEdgeDofs(const Array<int> &boundary_element_indices,
-                                Array<int> &ess_tdof_list,
-                                Array<int> &boundary_edge_dofs_out,
-                                Array<int> *ldof_marker = nullptr,
-                                Array<int> *dof_edges = nullptr,
-                                Array<int> *dof_boundary_elements = nullptr,
-                                Array<int> *ess_edge_list = nullptr);
-
    /** If the given ldof is owned by the current processor, return its local
        tdof number, otherwise return -1 */
    int GetLocalTDofNumber(int ldof) const;

fem/qfunction.hpp

@@ -79,6 +79,27 @@ public:
       Vector::operator=(orig);
    }
 
+   /** @brief Construct a QuadratureFunction on the given
+       VectorQuadratureSpace, @a vqspace.
+
+       After construction, the QuadratureFunction does not need the
+       VectorQuadratureSpace object. Instead, it uses directly its underlying
+       QuadratureSpaceBase object. */
+   QuadratureFunction(VectorQuadratureSpace &vqspace)
+      : QuadratureFunction(*vqspace.GetSpace(), vqspace.GetVDim())
+   { }
+
+   /** @brief Construct a QuadratureFunction on the given
+       VectorQuadratureSpace, @a vqspace, with the given MemoryType, @a mt, used
+       for the underlying Vector object.
+
+       After construction, the QuadratureFunction does not need the
+       VectorQuadratureSpace object. Instead, it uses directly its underlying
+       QuadratureSpaceBase object. */
+   QuadratureFunction(VectorQuadratureSpace &vqspace, MemoryType mt)
+      : QuadratureFunction(*vqspace.GetSpace(), mt, vqspace.GetVDim())
+   { }
+
    /// Read a QuadratureFunction from the stream @a in.
    /** The QuadratureFunction assumes ownership of the read QuadratureSpace. */
    QuadratureFunction(Mesh *mesh, std::istream &in);

fem/qinterp/eval_transpose.cpp

@@ -0,0 +1,44 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../quadinterpolator.hpp"
+#include "eval_transpose.hpp"
+
+namespace mfem
+{
+
+/// @cond Suppress_Doxygen_warnings
+
+QuadratureInterpolator::TensorEvalTransposeKernelType
+QuadratureInterpolator::TensorEvalTransposeKernels::Fallback(
+   int DIM, QVectorLayout Q_LAYOUT, int, int, int)
+{
+   using namespace internal::quadrature_interpolator;
+
+   if (Q_LAYOUT == QVectorLayout::byNODES)
+   {
+      if (DIM == 1) { return ValuesTranspose1D<QVectorLayout::byNODES>; }
+      else if (DIM == 2) { return ValuesTranspose2D<QVectorLayout::byNODES>; }
+      else if (DIM == 3) { return ValuesTranspose3D<QVectorLayout::byNODES>; }
+   }
+   else
+   {
+      if (DIM == 1) { return ValuesTranspose1D<QVectorLayout::byVDIM>; }
+      else if (DIM == 2) { return ValuesTranspose2D<QVectorLayout::byVDIM>; }
+      else if (DIM == 3) { return ValuesTranspose3D<QVectorLayout::byVDIM>; }
+   }
+   MFEM_ABORT("Invalid dimension");
+   return nullptr;
+}
+
+/// @endcond
+
+} // namespace mfem

fem/qinterp/eval_transpose.hpp

@@ -0,0 +1,304 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#pragma once
+
+#include "../quadinterpolator.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../../linalg/kernels.hpp"
+#include "../kernels.hpp"
+
+namespace mfem
+{
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+template<QVectorLayout Q_LAYOUT>
+static void ValuesTranspose1D(const int NE,
+                              const real_t *b_,
+                              const real_t *q_,
+                              real_t *e_,
+                              const int vdim,
+                              const int d1d,
+                              const int q1d)
+{
+   const auto b = Reshape(b_, q1d, d1d);
+   const auto qd = Q_LAYOUT == QVectorLayout::byNODES ?
+                   Reshape(q_, q1d, vdim, NE) :
+                   Reshape(q_, vdim, q1d, NE);
+   auto e = Reshape(e_, d1d, vdim, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int el)
+   {
+      for (int c = 0; c < vdim; c++)
+      {
+         for (int d = 0; d < d1d; d++)
+         {
+            real_t u = 0.0;
+            for (int q = 0; q < q1d; q++)
+            {
+               const real_t qval = Q_LAYOUT == QVectorLayout::byVDIM ?
+                                   qd(c, q, el) : qd(q, c, el);
+               u += b(q, d) * qval;
+            }
+            e(d, c, el) += u;
+         }
+      }
+   });
+}
+
+template<QVectorLayout Q_LAYOUT,
+         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
+         int T_NBZ = 1>
+static void ValuesTranspose2D(const int NE,
+                              const real_t *b_,
+                              const real_t *q_,
+                              real_t *e_,
+                              const int vdim = 0,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+
+   const auto b = Reshape(b_, Q1D, D1D);
+   const auto q = Q_LAYOUT == QVectorLayout::byNODES ?
+                  Reshape(q_, Q1D, Q1D, VDIM, NE) :
+                  Reshape(q_, VDIM, Q1D, Q1D, NE);
+   auto e = Reshape(e_, D1D, D1D, VDIM, NE);
+
+   mfem::forall_2D_batch(NE, D1D, D1D, NBZ, [=] MFEM_HOST_DEVICE (int el)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      const int tidz = MFEM_THREAD_ID(z);
+
+      MFEM_SHARED real_t sB[MQ1*MD1];
+      MFEM_SHARED real_t sm0[NBZ][MDQ*MDQ];
+      MFEM_SHARED real_t sm1[NBZ][MDQ*MDQ];
+
+      kernels::internal::LoadB<MD1,MQ1>(D1D,Q1D,b,sB);
+
+      ConstDeviceMatrix B(sB, D1D, Q1D);
+      DeviceMatrix QQ(sm0[tidz], MQ1, MQ1);
+      DeviceMatrix DQ(sm1[tidz], MD1, MQ1);
+      DeviceMatrix DD(sm0[tidz], MD1, MD1);
+
+      for (int c = 0; c < VDIM; c++)
+      {
+         // Load Q data
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               QQ(qx,qy) = Q_LAYOUT == QVectorLayout::byVDIM ?
+                           q(c,qx,qy,el) : q(qx,qy,c,el);
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Transpose in y: QQ -> DQ (apply B^T in y-direction)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               real_t u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += B(dy,qy) * QQ(qx,qy);
+               }
+               DQ(dy,qx) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Transpose in x: DQ -> DD (apply B^T in x-direction)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               real_t u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += B(dx,qx) * DQ(dy,qx);
+               }
+               DD(dx,dy) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Store result
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               e(dx,dy,c,el) += DD(dx,dy);
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+template<QVectorLayout Q_LAYOUT,
+         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0>
+static void ValuesTranspose3D(const int NE,
+                              const real_t *b_,
+                              const real_t *q_,
+                              real_t *e_,
+                              const int vdim = 0,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+
+   const auto b = Reshape(b_, Q1D, D1D);
+   const auto q = Q_LAYOUT == QVectorLayout::byNODES ?
+                  Reshape(q_, Q1D, Q1D, Q1D, VDIM, NE) :
+                  Reshape(q_, VDIM, Q1D, Q1D, Q1D, NE);
+   auto e = Reshape(e_, D1D, D1D, D1D, VDIM, NE);
+
+   mfem::forall_3D(NE, D1D, D1D, D1D, [=] MFEM_HOST_DEVICE (int el)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_INTERP_1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_INTERP_1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+
+      MFEM_SHARED real_t sB[MQ1*MD1];
+      MFEM_SHARED real_t sm0[MDQ*MDQ*MDQ];
+      MFEM_SHARED real_t sm1[MDQ*MDQ*MDQ];
+
+      kernels::internal::LoadB<MD1,MQ1>(D1D,Q1D,b,sB);
+
+      ConstDeviceMatrix B(sB, D1D, Q1D);
+      DeviceCube QQQ(sm0, MQ1, MQ1, MQ1);
+      DeviceCube DQQ(sm1, MD1, MQ1, MQ1);
+      DeviceCube DDQ(sm0, MD1, MD1, MQ1);
+      DeviceCube DDD(sm1, MD1, MD1, MD1);
+
+      for (int c = 0; c < VDIM; c++)
+      {
+         // Load Q data
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  QQQ(qx,qy,qz) = Q_LAYOUT == QVectorLayout::byVDIM ?
+                                  q(c,qx,qy,qz,el) : q(qx,qy,qz,c,el);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Transpose in z
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u += B(dz,qz) * QQQ(qx,qy,qz);
+                  }
+                  DQQ(dz,qx,qy) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Transpose in y
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     u += B(dy,qy) * DQQ(dz,qx,qy);
+                  }
+                  DDQ(dz,dy,qx) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Transpose in x
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     u += B(dx,qx) * DDQ(dz,dy,qx);
+                  }
+                  DDD(dx,dy,dz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  e(dx,dy,dz,c,el) += DDD(dx,dy,dz);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+} // namespace quadrature_interpolator
+} // namespace internal
+
+/// \cond DO_NOT_DOCUMENT
+
+template<int DIM, QVectorLayout Q_LAYOUT,
+         int VDIM, int D1D, int Q1D, int NBZ>
+QuadratureInterpolator::TensorEvalTransposeKernelType
+QuadratureInterpolator::TensorEvalTransposeKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::ValuesTranspose1D<Q_LAYOUT>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::ValuesTranspose2D<Q_LAYOUT, VDIM, D1D, Q1D, NBZ>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::ValuesTranspose3D<Q_LAYOUT, VDIM, D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/qinterp/eval_transpose_by_vdim.cpp

@@ -0,0 +1,61 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../quadinterpolator.hpp"
+#include "eval_transpose.hpp"
+
+namespace mfem
+{
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+void InitEvalTransposeByVDimKernels()
+{
+   using k = QuadratureInterpolator::TensorEvalTransposeKernels;
+   constexpr auto L = QVectorLayout::byVDIM;
+
+   // 2D
+   k::Specialization<2,L,1,2,4>::Opt<8>::Add();
+   k::Specialization<2,L,1,3,6>::Opt<4>::Add();
+   k::Specialization<2,L,1,4,8>::Opt<2>::Add();
+
+   k::Specialization<2,L,2,2,4>::Opt<8>::Add();
+   k::Specialization<2,L,2,3,4>::Opt<8>::Add();
+   k::Specialization<2,L,2,3,6>::Opt<4>::Add();
+   k::Specialization<2,L,2,4,6>::Opt<2>::Add();
+   k::Specialization<2,L,2,4,8>::Opt<2>::Add();
+
+   // 3D
+   k::Specialization<3,L,1,2,4>::Opt<1>::Add();
+   k::Specialization<3,L,1,3,6>::Opt<1>::Add();
+   k::Specialization<3,L,1,4,8>::Opt<1>::Add();
+   k::Specialization<3,L,3,2,4>::Opt<1>::Add();
+   k::Specialization<3,L,3,3,6>::Opt<1>::Add();
+   k::Specialization<3,L,3,4,8>::Opt<1>::Add();
+
+   k::Specialization<3,L,3,2,2>::Opt<1>::Add();
+   k::Specialization<3,L,3,3,3>::Opt<1>::Add();
+   k::Specialization<3,L,3,4,4>::Opt<1>::Add();
+   k::Specialization<3,L,3,5,5>::Opt<1>::Add();
+   k::Specialization<3,L,3,6,6>::Opt<1>::Add();
+   k::Specialization<3,L,3,7,7>::Opt<1>::Add();
+   k::Specialization<3,L,3,8,8>::Opt<1>::Add();
+   k::Specialization<3,L,3,9,9>::Opt<1>::Add();
+
+   k::Specialization<3,L,3,4,6>::Opt<1>::Add();
+   k::Specialization<3,L,3,3,4>::Opt<1>::Add();
+}
+
+} // namespace quadrature_interpolator
+} // namespace internal
+} // namespace mfem

fem/qinterp/grad_transpose.cpp

@@ -0,0 +1,62 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../quadinterpolator.hpp"
+#include "grad_transpose.hpp"
+
+namespace mfem
+{
+
+/// @cond Suppress_Doxygen_warnings
+
+QuadratureInterpolator::GradTransposeKernelType
+QuadratureInterpolator::GradTransposeKernels::Fallback(
+   int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int, int, int)
+{
+   using namespace internal::quadrature_interpolator;
+
+   if (Q_LAYOUT == QVectorLayout::byNODES)
+   {
+      if (GRAD_PHYS)
+      {
+         if (DIM == 1) { return DerivativesTranspose1D<QVectorLayout::byNODES, true>; }
+         else if (DIM == 2) { return DerivativesTranspose2D<QVectorLayout::byNODES, true>; }
+         else if (DIM == 3) { return DerivativesTranspose3D<QVectorLayout::byNODES, true>; }
+      }
+      else
+      {
+         if (DIM == 1) { return DerivativesTranspose1D<QVectorLayout::byNODES, false>; }
+         else if (DIM == 2) { return DerivativesTranspose2D<QVectorLayout::byNODES, false>; }
+         else if (DIM == 3) { return DerivativesTranspose3D<QVectorLayout::byNODES, false>; }
+      }
+   }
+   else
+   {
+      if (GRAD_PHYS)
+      {
+         if (DIM == 1) { return DerivativesTranspose1D<QVectorLayout::byVDIM, true>; }
+         else if (DIM == 2) { return DerivativesTranspose2D<QVectorLayout::byVDIM, true>; }
+         else if (DIM == 3) { return DerivativesTranspose3D<QVectorLayout::byVDIM, true>; }
+      }
+      else
+      {
+         if (DIM == 1) { return DerivativesTranspose1D<QVectorLayout::byVDIM, false>; }
+         else if (DIM == 2) { return DerivativesTranspose2D<QVectorLayout::byVDIM, false>; }
+         else if (DIM == 3) { return DerivativesTranspose3D<QVectorLayout::byVDIM, false>; }
+      }
+   }
+   MFEM_ABORT("Invalid dimension");
+   return nullptr;
+}
+
+/// @endcond
+
+} // namespace mfem

fem/qinterp/grad_transpose.hpp

@@ -0,0 +1,741 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#pragma once
+
+#include "../quadinterpolator.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../../linalg/kernels.hpp"
+#include "../kernels.hpp"
+
+namespace mfem
+{
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+// Transpose gradient operation: integrate against shape function derivatives
+// This is the adjoint of the Derivatives operation
+
+template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS>
+static void DerivativesTranspose1D(const int NE,
+                                   const real_t *b_,
+                                   const real_t *g_,
+                                   const real_t *j_,
+                                   const real_t *q_,
+                                   real_t *e_,
+                                   const int sdim,
+                                   const int vdim,
+                                   const int d1d,
+                                   const int q1d)
+{
+   MFEM_CONTRACT_VAR(b_);
+   const int SDIM = GRAD_PHYS ? sdim : 1;
+   const auto g = Reshape(g_, q1d, d1d);
+   const auto j = Reshape(j_, q1d, SDIM, NE);
+   const auto q = Q_LAYOUT == QVectorLayout::byNODES ?
+                  Reshape(q_, q1d, vdim, SDIM, NE):
+                  Reshape(q_, vdim, SDIM, q1d, NE);
+   auto e = Reshape(e_, d1d, vdim, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int el)
+   {
+      for (int c = 0; c < vdim; c++)
+      {
+         for (int d = 0; d < d1d; d++)
+         {
+            real_t u = 0.0;
+            for (int qx = 0; qx < q1d; qx++)
+            {
+               // Load gradient from q-vector
+               real_t dq[3] = {0.0, 0.0, 0.0};
+               for (int s = 0; s < SDIM; ++s)
+               {
+                  if (Q_LAYOUT == QVectorLayout::byVDIM)  { dq[s] = q(c, s, qx, el); }
+                  if (Q_LAYOUT == QVectorLayout::byNODES) { dq[s] = q(qx, c, s, el); }
+               }
+
+               // Apply inverse Jacobian transpose (adjoint of physical gradient)
+               real_t du = dq[0];
+               if (GRAD_PHYS)
+               {
+                  if (SDIM == 1) { du = dq[0] / j(qx, 0, el); }
+                  else if (SDIM == 2)
+                  {
+                     const real_t Jloc[2] = {j(qx,0,el), j(qx,1,el)};
+                     real_t Jinv[3];
+                     kernels::CalcLeftInverse<2,1>(Jloc, Jinv);
+                     du = Jinv[0]*dq[0] + Jinv[1]*dq[1];
+                  }
+                  else // SDIM == 3
+                  {
+                     const real_t Jloc[3] = {j(qx,0,el), j(qx,1,el), j(qx,2,el)};
+                     real_t Jinv[3];
+                     kernels::CalcLeftInverse<3,1>(Jloc, Jinv);
+                     du = Jinv[0]*dq[0] + Jinv[1]*dq[1] + Jinv[2]*dq[2];
+                  }
+               }
+
+               // Accumulate contribution (transpose of G matrix)
+               u += g(qx, d) * du;
+            }
+            e(d, c, el) += u;
+         }
+      }
+   });
+}
+
+template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS,
+         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
+         int T_NBZ = 1>
+static void DerivativesTranspose2D(const int NE,
+                                   const real_t *b_,
+                                   const real_t *g_,
+                                   const real_t *j_,
+                                   const real_t *q_,
+                                   real_t *e_,
+                                   const int sdim = 2,
+                                   const int vdim = 0,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   const int SDIM = GRAD_PHYS ? sdim : 2;
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+
+   const auto b = Reshape(b_, Q1D, D1D);
+   const auto g = Reshape(g_, Q1D, D1D);
+   const auto j = Reshape(j_, Q1D, Q1D, SDIM, 2, NE);
+   const auto q = Q_LAYOUT == QVectorLayout::byNODES ?
+                  Reshape(q_, Q1D, Q1D, VDIM, SDIM, NE):
+                  Reshape(q_, VDIM, SDIM, Q1D, Q1D, NE);
+   auto e = Reshape(e_, D1D, D1D, VDIM, NE);
+
+   mfem::forall_2D_batch(NE, D1D, D1D, NBZ, [=] MFEM_HOST_DEVICE (int el)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      const int tidz = MFEM_THREAD_ID(z);
+
+      MFEM_SHARED real_t BG[2][MQ1*MD1];
+      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,b,g,BG);
+      DeviceMatrix B(BG[0], D1D, Q1D);
+      DeviceMatrix G(BG[1], D1D, Q1D);
+
+      MFEM_SHARED real_t sm0[NBZ][MDQ*MDQ];
+      MFEM_SHARED real_t sm1[NBZ][MDQ*MDQ];
+
+      DeviceMatrix QQ(sm0[tidz], MQ1, MQ1);
+      DeviceMatrix DQ0(sm1[tidz], MD1, MQ1);
+      DeviceMatrix DQ1(sm1[tidz], MD1, MQ1);  // Reuse sm1 after DQ0 is done
+      DeviceMatrix DD(sm0[tidz], MD1, MD1);   // Reuse sm0 after QQ is done
+
+      for (int c = 0; c < VDIM; c++)
+      {
+         // Load Q data and apply inverse Jacobian
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               // Load gradient components
+               real_t dq[3] = {0.0, 0.0, 0.0};
+               for (int d = 0; d < SDIM; ++d)
+               {
+                  if (Q_LAYOUT == QVectorLayout::byVDIM) { dq[d] = q(c, d, qx, qy, el); }
+                  else { dq[d] = q(qx, qy, c, d, el); }
+               }
+
+               // Apply inverse Jacobian transpose (adjoint of physical gradient)
+               real_t du[2] = {dq[0], dq[1]};
+               if (GRAD_PHYS)
+               {
+                  if (SDIM == 2)
+                  {
+                     real_t Jloc[4], Jinv[4];
+                     Jloc[0] = j(qx,qy,0,0,el);
+                     Jloc[1] = j(qx,qy,1,0,el);
+                     Jloc[2] = j(qx,qy,0,1,el);
+                     Jloc[3] = j(qx,qy,1,1,el);
+                     kernels::CalcInverse<2>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[2]*dq[1];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[3]*dq[1];
+                     du[0] = U;
+                     du[1] = V;
+                  }
+                  else // SDIM == 3
+                  {
+                     real_t Jloc[6], Jinv[6];
+                     Jloc[0] = j(qx,qy,0,0,el);
+                     Jloc[1] = j(qx,qy,1,0,el);
+                     Jloc[2] = j(qx,qy,2,0,el);
+                     Jloc[3] = j(qx,qy,0,1,el);
+                     Jloc[4] = j(qx,qy,1,1,el);
+                     Jloc[5] = j(qx,qy,2,1,el);
+                     kernels::CalcLeftInverse<3,2>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[2]*dq[1] + Jinv[4]*dq[2];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[3]*dq[1] + Jinv[5]*dq[2];
+                     du[0] = U;
+                     du[1] = V;
+                  }
+               }
+               QQ(qx, qy) = du[0];  // Store du/dx component
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in y-direction: QQ -> DQ0
+         // (Transpose of d/dx which uses DQ1(dy,qx)*B(dy,qy))
+         // Must produce DQ0(dy,qx) to match forward's DQ1 indexing
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               real_t u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += B(dy,qy) * QQ(qx,qy);
+               }
+               DQ0(dy,qx) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply G^T in x-direction: DQ0 -> DD
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               real_t u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += G(dx,qx) * DQ0(dy,qx);
+               }
+               DD(dx,dy) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Accumulate to output
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               e(dx,dy,c,el) += DD(dx,dy);
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Now process du/dy component
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               // Load gradient components
+               real_t dq[3] = {0.0, 0.0, 0.0};
+               for (int d = 0; d < SDIM; ++d)
+               {
+                  if (Q_LAYOUT == QVectorLayout::byVDIM) { dq[d] = q(c, d, qx, qy, el); }
+                  else { dq[d] = q(qx, qy, c, d, el); }
+               }
+
+               // Apply inverse Jacobian transpose
+               real_t du[2] = {dq[0], dq[1]};
+               if (GRAD_PHYS)
+               {
+                  if (SDIM == 2)
+                  {
+                     real_t Jloc[4], Jinv[4];
+                     Jloc[0] = j(qx,qy,0,0,el);
+                     Jloc[1] = j(qx,qy,1,0,el);
+                     Jloc[2] = j(qx,qy,0,1,el);
+                     Jloc[3] = j(qx,qy,1,1,el);
+                     kernels::CalcInverse<2>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[2]*dq[1];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[3]*dq[1];
+                     du[0] = U;
+                     du[1] = V;
+                  }
+                  else // SDIM == 3
+                  {
+                     real_t Jloc[6], Jinv[6];
+                     Jloc[0] = j(qx,qy,0,0,el);
+                     Jloc[1] = j(qx,qy,1,0,el);
+                     Jloc[2] = j(qx,qy,2,0,el);
+                     Jloc[3] = j(qx,qy,0,1,el);
+                     Jloc[4] = j(qx,qy,1,1,el);
+                     Jloc[5] = j(qx,qy,2,1,el);
+                     kernels::CalcLeftInverse<3,2>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[2]*dq[1] + Jinv[4]*dq[2];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[3]*dq[1] + Jinv[5]*dq[2];
+                     du[0] = U;
+                     du[1] = V;
+                  }
+               }
+               QQ(qx, qy) = du[1];  // Store du/dy component
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply G^T in y-direction: QQ -> DQ1
+         // (Transpose of d/dy which uses DQ0(dy,qx)*G(dy,qy))
+         // Must produce DQ1(dy,qx) to match forward's DQ0 indexing
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               real_t u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += G(dy,qy) * QQ(qx,qy);
+               }
+               DQ1(dy,qx) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in x-direction: DQ1 -> DD
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               real_t u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += B(dx,qx) * DQ1(dy,qx);
+               }
+               DD(dx,dy) = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Accumulate to output
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               e(dx,dy,c,el) += DD(dx,dy);
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS,
+         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0>
+static void DerivativesTranspose3D(const int NE,
+                                   const real_t *b_,
+                                   const real_t *g_,
+                                   const real_t *j_,
+                                   const real_t *q_,    // q_der
+                                   real_t *e_,          // e_vec
+                                   const int sdim = 3,
+                                   const int vdim = 0,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+
+   const auto b = Reshape(b_, Q1D, D1D);
+   const auto g = Reshape(g_, Q1D, D1D);
+   const auto j = Reshape(j_, Q1D, Q1D, Q1D, 3, 3, NE);
+   const auto q = Q_LAYOUT == QVectorLayout::byNODES ?
+                  Reshape(q_, Q1D, Q1D, Q1D, VDIM, 3, NE):
+                  Reshape(q_, VDIM, 3, Q1D, Q1D, Q1D, NE);
+   auto e = Reshape(e_, D1D, D1D, D1D, VDIM, NE);
+
+   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int el)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_INTERP_1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_INTERP_1D;
+
+      MFEM_SHARED real_t BG[2][MQ1*MD1];
+      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,b,g,BG);
+      DeviceMatrix B(BG[0], D1D, Q1D);
+      DeviceMatrix G(BG[1], D1D, Q1D);
+
+      MFEM_SHARED real_t sm0[1][MQ1*MQ1*MQ1];
+      MFEM_SHARED real_t sm1[1][MQ1*MQ1*MQ1];
+      DeviceCube QQQ(sm0[0], MQ1, MQ1, MQ1);
+      DeviceCube DQQ(sm1[0], MD1, MQ1, MQ1);
+      DeviceCube DDQ(sm0[0], MD1, MD1, MQ1);
+      DeviceCube DDD(sm1[0], MD1, MD1, MD1);
+
+      for (int c = 0; c < VDIM; c++)
+      {
+         // Process du/dx component
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t dq[3];
+                  if (Q_LAYOUT == QVectorLayout::byVDIM)
+                  {
+                     dq[0] = q(c,0,qx,qy,qz,el);
+                     dq[1] = q(c,1,qx,qy,qz,el);
+                     dq[2] = q(c,2,qx,qy,qz,el);
+                  }
+                  else
+                  {
+                     dq[0] = q(qx,qy,qz,c,0,el);
+                     dq[1] = q(qx,qy,qz,c,1,el);
+                     dq[2] = q(qx,qy,qz,c,2,el);
+                  }
+
+                  real_t du[3] = {dq[0], dq[1], dq[2]};
+                  if (GRAD_PHYS)
+                  {
+                     real_t Jloc[9], Jinv[9];
+                     for (int col = 0; col < 3; col++)
+                     {
+                        for (int row = 0; row < 3; row++)
+                        {
+                           Jloc[row+3*col] = j(qx,qy,qz,row,col,el);
+                        }
+                     }
+                     kernels::CalcInverse<3>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[3]*dq[1] + Jinv[6]*dq[2];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[4]*dq[1] + Jinv[7]*dq[2];
+                     const real_t W = Jinv[2]*dq[0] + Jinv[5]*dq[1] + Jinv[8]*dq[2];
+                     du[0] = U; du[1] = V; du[2] = W;
+                  }
+                  QQQ(qx,qy,qz) = du[0];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply G^T in x: QQQ -> DQQ (transpose of G⊗B⊗B)
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     u += G(dx,qx) * QQQ(qx,qy,qz);
+                  }
+                  DQQ(dx,qy,qz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in y: DQQ -> DDQ
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     u += B(dy,qy) * DQQ(dx,qy,qz);
+                  }
+                  DDQ(dx,dy,qz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in z: DDQ -> DDD
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u += B(dz,qz) * DDQ(dx,dy,qz);
+                  }
+                  DDD(dx,dy,dz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Accumulate result
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  e(dx,dy,dz,c,el) += DDD(dx,dy,dz);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Process du/dy component
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t dq[3];
+                  if (Q_LAYOUT == QVectorLayout::byVDIM)
+                  {
+                     dq[0] = q(c,0,qx,qy,qz,el);
+                     dq[1] = q(c,1,qx,qy,qz,el);
+                     dq[2] = q(c,2,qx,qy,qz,el);
+                  }
+                  else
+                  {
+                     dq[0] = q(qx,qy,qz,c,0,el);
+                     dq[1] = q(qx,qy,qz,c,1,el);
+                     dq[2] = q(qx,qy,qz,c,2,el);
+                  }
+
+                  real_t du[3] = {dq[0], dq[1], dq[2]};
+                  if (GRAD_PHYS)
+                  {
+                     real_t Jloc[9], Jinv[9];
+                     for (int col = 0; col < 3; col++)
+                     {
+                        for (int row = 0; row < 3; row++)
+                        {
+                           Jloc[row+3*col] = j(qx,qy,qz,row,col,el);
+                        }
+                     }
+                     kernels::CalcInverse<3>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[3]*dq[1] + Jinv[6]*dq[2];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[4]*dq[1] + Jinv[7]*dq[2];
+                     const real_t W = Jinv[2]*dq[0] + Jinv[5]*dq[1] + Jinv[8]*dq[2];
+                     du[0] = U; du[1] = V; du[2] = W;
+                  }
+                  QQQ(qx,qy,qz) = du[1];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in x: QQQ -> DQQ (transpose of B⊗G⊗B)
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     u += B(dx,qx) * QQQ(qx,qy,qz);
+                  }
+                  DQQ(dx,qy,qz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply G^T in y: DQQ -> DDQ
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     u += G(dy,qy) * DQQ(dx,qy,qz);
+                  }
+                  DDQ(dx,dy,qz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in z: DDQ -> DDD
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u += B(dz,qz) * DDQ(dx,dy,qz);
+                  }
+                  DDD(dx,dy,dz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Accumulate result
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  e(dx,dy,dz,c,el) += DDD(dx,dy,dz);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Process du/dz component
+         MFEM_FOREACH_THREAD(qz,z,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t dq[3];
+                  if (Q_LAYOUT == QVectorLayout::byVDIM)
+                  {
+                     dq[0] = q(c,0,qx,qy,qz,el);
+                     dq[1] = q(c,1,qx,qy,qz,el);
+                     dq[2] = q(c,2,qx,qy,qz,el);
+                  }
+                  else
+                  {
+                     dq[0] = q(qx,qy,qz,c,0,el);
+                     dq[1] = q(qx,qy,qz,c,1,el);
+                     dq[2] = q(qx,qy,qz,c,2,el);
+                  }
+
+                  real_t du[3] = {dq[0], dq[1], dq[2]};
+                  if (GRAD_PHYS)
+                  {
+                     real_t Jloc[9], Jinv[9];
+                     for (int col = 0; col < 3; col++)
+                     {
+                        for (int row = 0; row < 3; row++)
+                        {
+                           Jloc[row+3*col] = j(qx,qy,qz,row,col,el);
+                        }
+                     }
+                     kernels::CalcInverse<3>(Jloc, Jinv);
+                     const real_t U = Jinv[0]*dq[0] + Jinv[3]*dq[1] + Jinv[6]*dq[2];
+                     const real_t V = Jinv[1]*dq[0] + Jinv[4]*dq[1] + Jinv[7]*dq[2];
+                     const real_t W = Jinv[2]*dq[0] + Jinv[5]*dq[1] + Jinv[8]*dq[2];
+                     du[0] = U; du[1] = V; du[2] = W;
+                  }
+                  QQQ(qx,qy,qz) = du[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply G^T in z: QQQ -> DQQ (transpose of B⊗B⊗G)
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u += G(dz,qz) * QQQ(qx,qy,qz);
+                  }
+                  DQQ(dz,qy,qx) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in y: DQQ -> DDQ
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(qx,x,Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     u += B(dy,qy) * DQQ(dz,qy,qx);
+                  }
+                  DDQ(dz,dy,qx) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Apply B^T in x: DDQ -> DDD
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     u += B(dx,qx) * DDQ(dz,dy,qx);
+                  }
+                  DDD(dx,dy,dz) = u;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Accumulate result
+         MFEM_FOREACH_THREAD(dz,z,D1D)
+         {
+            MFEM_FOREACH_THREAD(dy,y,D1D)
+            {
+               MFEM_FOREACH_THREAD(dx,x,D1D)
+               {
+                  e(dx,dy,dz,c,el) += DDD(dx,dy,dz);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+} // namespace quadrature_interpolator
+} // namespace internal
+
+/// \cond DO_NOT_DOCUMENT
+
+template<int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int VDIM, int D1D,
+         int Q1D, int NBZ>
+QuadratureInterpolator::GradTransposeKernelType
+QuadratureInterpolator::GradTransposeKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::DerivativesTranspose1D<Q_LAYOUT, GRAD_PHYS>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::DerivativesTranspose2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D, NBZ>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::DerivativesTranspose3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/qinterp/grad_transpose_by_nodes.cpp

@@ -0,0 +1,50 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../quadinterpolator.hpp"
+#include "grad_transpose.hpp"
+
+namespace mfem
+{
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+template <bool P>
+void InitGradTransposeByNodesKernels()
+{
+   using k = QuadratureInterpolator::GradTransposeKernels;
+   constexpr auto L = QVectorLayout::byNODES;
+   // 2D
+   k::Specialization<2,L,P,1,3,4>::template Opt<8>::Add();
+   k::Specialization<2,L,P,1,4,6>::template Opt<4>::Add();
+   k::Specialization<2,L,P,1,5,8>::template Opt<2>::Add();
+
+   k::Specialization<2,L,P,2,3,3>::template Opt<8>::Add();
+   k::Specialization<2,L,P,2,3,4>::template Opt<8>::Add();
+   k::Specialization<2,L,P,2,4,6>::template Opt<4>::Add();
+   k::Specialization<2,L,P,2,5,8>::template Opt<2>::Add();
+   // 3D
+   k::Specialization<3,L,P,1,3,4>::Add();
+   k::Specialization<3,L,P,1,4,6>::Add();
+   k::Specialization<3,L,P,1,5,8>::Add();
+   k::Specialization<3,L,P,3,3,4>::Add();
+   k::Specialization<3,L,P,3,4,6>::Add();
+   k::Specialization<3,L,P,3,5,8>::Add();
+}
+
+template void InitGradTransposeByNodesKernels<false>();
+template void InitGradTransposeByNodesKernels<true>();
+
+} // namespace quadrature_interpolator
+} // namespace internal
+} // namespace mfem

fem/qinterp/grad_transpose_by_vdim.cpp

@@ -0,0 +1,50 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../quadinterpolator.hpp"
+#include "grad_transpose.hpp"
+
+namespace mfem
+{
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+template <bool P>
+void InitGradTransposeByVDimKernels()
+{
+   using k = QuadratureInterpolator::GradTransposeKernels;
+   constexpr auto L = QVectorLayout::byVDIM;
+   // 2D
+   k::Specialization<2,L,P,1,3,4>::template Opt<8>::Add();
+   k::Specialization<2,L,P,1,4,6>::template Opt<4>::Add();
+   k::Specialization<2,L,P,1,5,8>::template Opt<2>::Add();
+
+   k::Specialization<2,L,P,2,3,3>::template Opt<8>::Add();
+   k::Specialization<2,L,P,2,3,4>::template Opt<8>::Add();
+   k::Specialization<2,L,P,2,4,6>::template Opt<4>::Add();
+   k::Specialization<2,L,P,2,5,8>::template Opt<2>::Add();
+   // 3D
+   k::Specialization<3,L,P,1,3,4>::Add();
+   k::Specialization<3,L,P,1,4,6>::Add();
+   k::Specialization<3,L,P,1,5,8>::Add();
+   k::Specialization<3,L,P,3,3,4>::Add();
+   k::Specialization<3,L,P,3,4,6>::Add();
+   k::Specialization<3,L,P,3,5,8>::Add();
+}
+
+template void InitGradTransposeByVDimKernels<false>();
+template void InitGradTransposeByVDimKernels<true>();
+
+} // namespace quadrature_interpolator
+} // namespace internal
+} // namespace mfem

fem/qspace.hpp

@@ -27,7 +27,11 @@ enum class QSpaceOffsetStorage
 
 /// Abstract base class for QuadratureSpace and FaceQuadratureSpace.
 /** This class represents the storage layout for QuadratureFunction%s, that may
-    be defined either on mesh elements or mesh faces. */
+    be defined either on mesh elements or mesh faces.
+
+    This class represents the layout for a single scalar value at each
+    quadrature point. Use class VectorQuadratureSpace to represent a space with
+    multiple (vector) values at each quadrature point. */
 class QuadratureSpaceBase
 {
 protected:
@@ -158,8 +162,62 @@ public:
    virtual ~QuadratureSpaceBase() { }
 };
 
+/// Vector version of the scalar class QuadratureSpaceBase.
+class VectorQuadratureSpace
+{
+protected:
+   /// Points to an external object provided during construction. Not owned.
+   QuadratureSpaceBase *qspace;
+   /// Vector dimension.
+   int vdim;
+
+public:
+   /** @brief Construct a VectorQuadratureSpace on the given
+       QuadratureSpaceBase, @a qspace_, with the given vector dimension,
+       @a vdim_.
+
+       The VectorQuadratureSpace does not assume ownership of the
+       QuadratureSpaceBase, @a qspace_. */
+   VectorQuadratureSpace(QuadratureSpaceBase &qspace_, int vdim_)
+      : qspace(&qspace_),
+        vdim(vdim_)
+   { }
+
+   /// Copy constructor: default.
+   VectorQuadratureSpace(const VectorQuadratureSpace &) = default;
+
+   /// Copy assignment: default.
+   VectorQuadratureSpace &operator=(const VectorQuadratureSpace &) = default;
+
+   /// Move construction is not allowed.
+   VectorQuadratureSpace(VectorQuadratureSpace &&) = delete;
+
+   /// Move assignment is not allowed.
+   VectorQuadratureSpace &operator=(VectorQuadratureSpace &&) = delete;
+
+   /// Destructor: default.
+   ~VectorQuadratureSpace() = default;
+
+   /// Get the associated scalar QuadratureSpaceBase object.
+   QuadratureSpaceBase *GetSpace() { return qspace; }
+
+   /// Get the associated scalar QuadratureSpaceBase object (const version).
+   const QuadratureSpaceBase *GetSpace() const { return qspace; }
+
+   /// Get the vector dimension.
+   int GetVDim() const { return vdim; }
+
+   /** @brief Get the total size (on this MPI-rank in parallel) of the
+       VectorQuadratureSpace. */
+   int GetVSize() const { return qspace->GetSize() * vdim; }
+};
+
 /// Class representing the storage layout of a QuadratureFunction.
-/** Multiple QuadratureFunction%s can share the same QuadratureSpace. */
+/** Multiple QuadratureFunction%s can share the same QuadratureSpace.
+
+    This class represents the layout for a single scalar value at each
+    quadrature point. Use class VectorQuadratureSpace to represent a space with
+    multiple (vector) values at each quadrature point. */
 class QuadratureSpace : public QuadratureSpaceBase
 {
 protected:
@@ -209,7 +267,11 @@ public:
 
 /// Class representing the storage layout of a FaceQuadratureFunction.
 /** FaceQuadratureSpace is defined on either the interior or boundary faces
-    of a mesh, depending on the provided FaceType. */
+    of a mesh, depending on the provided FaceType.
+
+    This class represents the layout for a single scalar value at each
+    quadrature point. Use class VectorQuadratureSpace to represent a space with
+    multiple (vector) values at each quadrature point. */
 class FaceQuadratureSpace : public QuadratureSpaceBase
 {
    FaceType face_type; ///< Is the space defined on interior or boundary faces?

fem/quadinterpolator.cpp

@@ -11,6 +11,7 @@
 
 #include "quadinterpolator.hpp"
 #include "qinterp/grad.hpp"
+#include "qinterp/grad_transpose.hpp"
 #include "qinterp/eval.hpp"
 #include "qspace.hpp"
 #include "../general/forall.hpp"
@@ -30,7 +31,10 @@ void InitEvalKernels();
 void InitDetKernels();
 template <bool P> void InitGradByNodesKernels();
 template <bool P> void InitGradByVDimKernels();
+template <bool P> void InitGradTransposeByNodesKernels();
+template <bool P> void InitGradTransposeByVDimKernels();
 void InitTensorEvalHDivKernels();
+void InitEvalTransposeByVDimKernels();
 struct Kernels
 {
    Kernels()
@@ -45,12 +49,19 @@ struct Kernels
       // Phys grad kernels
       InitGradByNodesKernels<true>();
       InitGradByVDimKernels<true>();
+      // Non-phys grad transpose kernels
+      InitGradTransposeByNodesKernels<false>();
+      InitGradTransposeByVDimKernels<false>();
+      // Phys grad transpose kernels
+      InitGradTransposeByNodesKernels<true>();
+      InitGradTransposeByVDimKernels<true>();
       // Determinants
       InitDetKernels();
       // Non-tensor
       InitEvalKernels();
       // Tensor (quad,hex) H(div)
       InitTensorEvalHDivKernels();
+      InitEvalTransposeByVDimKernels();
    }
 };
 }
@@ -408,16 +419,59 @@ void QuadratureInterpolator::MultHDiv(const Vector &e_vec,
    MFEM_CONTRACT_VAR(q_div);
 }
 
-void QuadratureInterpolator::MultTranspose(unsigned eval_flags,
-                                           const Vector &q_val,
-                                           const Vector &q_der,
-                                           Vector &e_vec) const
+void QuadratureInterpolator::AddMultTranspose(unsigned eval_flags,
+                                              const Vector &q_val,
+                                              const Vector &q_der,
+                                              Vector &e_vec) const
 {
-   MFEM_CONTRACT_VAR(eval_flags);
-   MFEM_CONTRACT_VAR(q_val);
-   MFEM_CONTRACT_VAR(q_der);
-   MFEM_CONTRACT_VAR(e_vec);
-   MFEM_ABORT("this method is not implemented yet");
+   const int ne = fespace->GetNE();
+   if (ne == 0) { return; }
+   const FiniteElement *fe = fespace->GetFE(0);
+   const int vdim = fespace->GetVDim();
+   const int sdim = fespace->GetMesh()->SpaceDimension();
+
+   const bool use_tensor_eval =
+      use_tensor_products &&
+      dynamic_cast<const TensorBasisElement*>(fe) != nullptr;
+   const IntegrationRule *ir =
+      IntRule ? IntRule : &qspace->GetElementIntRule(0);
+   const DofToQuad::Mode mode =
+      use_tensor_eval ? DofToQuad::TENSOR : DofToQuad::FULL;
+   const DofToQuad &maps = fe->GetDofToQuad(*ir, mode);
+   const int dim = maps.FE->GetDim();
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+
+   const GeometricFactors *geom = nullptr;
+   if (eval_flags & PHYSICAL_DERIVATIVES)
+   {
+      const int jacobians = GeometricFactors::JACOBIANS;
+      geom = fespace->GetMesh()->GetGeometricFactors(*ir, jacobians);
+   }
+
+   if (use_tensor_eval)
+   {
+      if (eval_flags & (VALUES | PHYSICAL_VALUES))
+      {
+         TensorEvalTransposeKernels::Run(dim, q_layout, vdim, nd, nq, ne,
+                                         maps.B.Read(), q_val.Read(),
+                                         e_vec.ReadWrite(), vdim, nd, nq);
+      }
+      if (eval_flags & (DERIVATIVES | PHYSICAL_DERIVATIVES))
+      {
+         const bool phys = (eval_flags & PHYSICAL_DERIVATIVES);
+         const real_t *J = phys ? geom->J.Read() : nullptr;
+         const int s_dim = phys ? sdim : dim;
+         GradTransposeKernels::Run(dim, q_layout, phys, vdim, nd, nq, ne,
+                                   maps.B.Read(), maps.G.Read(), J,
+                                   q_der.Read(), e_vec.ReadWrite(),
+                                   s_dim, vdim, nd, nq);
+      }
+   }
+   else
+   {
+      MFEM_ABORT("Non-tensor MultTranspose not yet implemented");
+   }
 }
 
 void QuadratureInterpolator::Values(const Vector &e_vec,

fem/quadinterpolator.hpp

@@ -156,8 +156,8 @@ public:
    void Determinants(const Vector &e_vec, Vector &q_det) const;
 
    /// Perform the transpose operation of Mult(). (TODO)
-   void MultTranspose(unsigned eval_flags, const Vector &q_val,
-                      const Vector &q_der, Vector &e_vec) const;
+   void AddMultTranspose(unsigned eval_flags, const Vector &q_val,
+                         const Vector &q_der, Vector &e_vec) const;
 
    /// @brief Returns true if the given finite element space is supported by
    /// QuadratureInterpolator.
@@ -204,6 +204,13 @@ public:
    using TensorEvalHDivKernelType =
       void(*)(const int, const real_t *, const real_t *, const real_t *,
               const real_t *, real_t *, const int, const int);
+   using TensorEvalTransposeKernelType = void(*)(const int, const real_t *,
+                                                 const real_t *,
+                                                 real_t *, const int, const int, const int);
+   using GradTransposeKernelType = void(*)(const int, const real_t *,
+                                           const real_t *, const real_t *,
+                                           const real_t *, real_t *,
+                                           const int, const int, const int, const int);
 
    // value-type mapping
    MFEM_REGISTER_KERNELS(TensorEvalKernels, TensorEvalKernelType,
@@ -222,6 +229,10 @@ public:
 
    MFEM_REGISTER_KERNELS(TensorEvalHDivKernels, TensorEvalHDivKernelType,
                          (int, QVectorLayout, unsigned, int, int));
+   MFEM_REGISTER_KERNELS(TensorEvalTransposeKernels, TensorEvalTransposeKernelType,
+                         (int, QVectorLayout, int, int, int), (int));
+   MFEM_REGISTER_KERNELS(GradTransposeKernels, GradTransposeKernelType,
+                         (int, QVectorLayout, bool, int, int, int), (int));
 
    /// Adds specializations for TensorEvalKernels
    template <int DIM, QVectorLayout Q_LAYOUT, int VDIM, int D1D, int Q1D,

fem/restriction.cpp

@@ -299,6 +299,17 @@ void ElementRestriction::FillSparseMatrix(const Vector &mat_ea,
    FillJAndData(mat_ea, mat);
 }
 
+void ElementRestriction::FillSparseMatrix(
+   const Vector &mat_ea, SparseMatrix &mat,
+   const ElementRestriction &trial_restr) const
+{
+   mat.GetMemoryI().New(mat.Height()+1, mat.GetMemoryI().GetMemoryType());
+   const int nnz = FillI(mat, trial_restr);
+   mat.GetMemoryJ().New(nnz, mat.GetMemoryJ().GetMemoryType());
+   mat.GetMemoryData().New(nnz, mat.GetMemoryData().GetMemoryType());
+   FillJAndData(mat_ea, mat, trial_restr);
+}
+
 static MFEM_HOST_DEVICE int GetMinElt(const int *my_elts, const int nbElts,
                                       const int *nbr_elts, const int nbrNbElts)
 {
@@ -328,6 +339,23 @@ static MFEM_HOST_DEVICE int GetAndIncrementNnzIndex(const int i_L, int* I)
    return ind;
 }
 
+static MFEM_HOST_DEVICE int DofToVDof(const int dof, const int c,
+                                      const int ndofs, const int vdim,
+                                      const bool byvdim)
+{
+   return byvdim ? dof*vdim + c : c*ndofs + dof;
+}
+
+static MFEM_HOST_DEVICE int SignedIndexAbs(const int i)
+{
+   return (i >= 0) ? i : -1 - i;
+}
+
+static MFEM_HOST_DEVICE int SignedIndexSign(const int i)
+{
+   return (i >= 0) ? 1 : -1;
+}
+
 int ElementRestriction::FillI(SparseMatrix &mat) const
 {
    const int all_dofs = ndofs;
@@ -405,6 +433,98 @@ int ElementRestriction::FillI(SparseMatrix &mat) const
    return h_I[nTdofs];
 }
 
+int ElementRestriction::FillI(SparseMatrix &mat,
+                              const ElementRestriction &trial_restr) const
+{
+   MFEM_VERIFY(ne == trial_restr.ne,
+               "ElementRestriction::FillI: test/trial NE mismatch");
+   const int test_all_dofs = ndofs;
+   const int test_vd = vdim;
+   const int trial_vd = trial_restr.vdim;
+   const int test_elt_dofs = dof;
+   const int trial_elt_dofs = trial_restr.dof;
+   const bool test_byvdim = byvdim;
+   auto I = mat.ReadWriteI();
+   auto test_offsets = offsets.Read();
+   auto test_indices = indices.Read();
+   auto test_gather_map = gather_map.Read();
+   auto trial_offsets = trial_restr.offsets.Read();
+   auto trial_indices = trial_restr.indices.Read();
+   auto trial_gather_map = trial_restr.gather_map.Read();
+
+   Array<int> test_elts(indices.Size());
+   Array<int> trial_elts(trial_restr.indices.Size());
+   auto d_test_elts = test_elts.Write();
+   auto d_trial_elts = trial_elts.Write();
+
+   mfem::forall(test_vd*test_all_dofs+1, [=] MFEM_HOST_DEVICE (int i_L)
+   {
+      I[i_L] = 0;
+   });
+   mfem::forall(ne*test_elt_dofs*test_vd, [=] MFEM_HOST_DEVICE (int iE)
+   {
+      const int e = iE/(test_elt_dofs*test_vd);
+      const int it = iE%(test_elt_dofs*test_vd);
+      const int i = it%test_elt_dofs;
+      const int test_c = it/test_elt_dofs;
+
+      const int i_gm = e*test_elt_dofs + i;
+      const int i_dof = SignedIndexAbs(test_gather_map[i_gm]);
+      const int i_L = DofToVDof(i_dof, test_c, test_all_dofs, test_vd,
+                                test_byvdim);
+      const int i_offset = test_offsets[i_dof];
+      const int i_next_offset = test_offsets[i_dof+1];
+      const int i_nbElts = i_next_offset - i_offset;
+
+      int *i_elts = &d_test_elts[i_offset];
+      for (int e_i = 0; e_i < i_nbElts; ++e_i)
+      {
+         const int i_loc = SignedIndexAbs(test_indices[i_offset+e_i]);
+         i_elts[e_i] = i_loc/test_elt_dofs;
+      }
+      for (int trial_c = 0; trial_c < trial_vd; ++trial_c)
+      {
+         MFEM_CONTRACT_VAR(trial_c);
+         for (int j = 0; j < trial_elt_dofs; j++)
+         {
+            const int j_gm = e*trial_elt_dofs + j;
+            const int j_dof = SignedIndexAbs(trial_gather_map[j_gm]);
+            const int j_offset = trial_offsets[j_dof];
+            const int j_next_offset = trial_offsets[j_dof+1];
+            const int j_nbElts = j_next_offset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1)
+            {
+               GetAndIncrementNnzIndex(i_L, I);
+            }
+            else
+            {
+               int *j_elts = &d_trial_elts[j_offset];
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_loc = SignedIndexAbs(trial_indices[j_offset+e_j]);
+                  j_elts[e_j] = j_loc/trial_elt_dofs;
+               }
+               const int min_e = GetMinElt(i_elts, i_nbElts,
+                                           j_elts, j_nbElts);
+               if (e == min_e) { GetAndIncrementNnzIndex(i_L, I); }
+            }
+         }
+      }
+   });
+
+   auto h_I = mat.HostReadWriteI();
+   const int nTdofs = test_vd*test_all_dofs;
+   int sum = 0;
+   for (int i = 0; i < nTdofs; i++)
+   {
+      const int nnz = h_I[i];
+      h_I[i] = sum;
+      sum += nnz;
+   }
+   h_I[nTdofs] = sum;
+   return h_I[nTdofs];
+}
+
 void ElementRestriction::FillJAndData(const Vector &ea_data,
                                       SparseMatrix &mat) const
 {
@@ -501,6 +621,135 @@ void ElementRestriction::FillJAndData(const Vector &ea_data,
    h_I[0] = 0;
 }
 
+void ElementRestriction::FillJAndData(
+   const Vector &ea_data, SparseMatrix &mat,
+   const ElementRestriction &trial_restr) const
+{
+   MFEM_VERIFY(ne == trial_restr.ne,
+               "ElementRestriction::FillJAndData: test/trial NE mismatch");
+   const int test_all_dofs = ndofs;
+   const int trial_all_dofs = trial_restr.ndofs;
+   const int test_vd = vdim;
+   const int trial_vd = trial_restr.vdim;
+   const int test_elt_dofs = dof;
+   const int trial_elt_dofs = trial_restr.dof;
+   const bool test_byvdim = byvdim;
+   const bool trial_byvdim = trial_restr.byvdim;
+   auto I = mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto test_offsets = offsets.Read();
+   auto test_indices = indices.Read();
+   auto test_gather_map = gather_map.Read();
+   auto trial_offsets = trial_restr.offsets.Read();
+   auto trial_indices = trial_restr.indices.Read();
+   auto trial_gather_map = trial_restr.gather_map.Read();
+   auto mat_ea = Reshape(ea_data.Read(), test_elt_dofs, test_vd,
+                         trial_elt_dofs, trial_vd, ne);
+
+   Array<int> test_el(indices.Size() * 3);
+   Array<int> trial_el(trial_restr.indices.Size() * 3);
+   auto d_test_el = Reshape(test_el.Write(), indices.Size(), 3);
+   auto d_trial_el = Reshape(trial_el.Write(), trial_restr.indices.Size(), 3);
+
+   mfem::forall(ne*test_elt_dofs*test_vd, [=] MFEM_HOST_DEVICE (int iE)
+   {
+      const int e = iE/(test_elt_dofs*test_vd);
+      const int it = iE%(test_elt_dofs*test_vd);
+      const int i = it%test_elt_dofs;
+      const int test_c = it/test_elt_dofs;
+
+      const int i_gm = e*test_elt_dofs + i;
+      const int i_gm_s = test_gather_map[i_gm];
+      const int i_dof = SignedIndexAbs(i_gm_s);
+      const int i_sgn = SignedIndexSign(i_gm_s);
+      const int i_L = DofToVDof(i_dof, test_c, test_all_dofs, test_vd,
+                                test_byvdim);
+      const int i_offset = test_offsets[i_dof];
+      const int i_next_offset = test_offsets[i_dof+1];
+      const int i_nbElts = i_next_offset - i_offset;
+
+      int *i_elts = &d_test_el(i_offset, 0);
+      int *i_B = &d_test_el(i_offset, 1);
+      int *i_sgns = &d_test_el(i_offset, 2);
+      for (int e_i = 0; e_i < i_nbElts; ++e_i)
+      {
+         const int i_idx_s = test_indices[i_offset+e_i];
+         const int i_idx = SignedIndexAbs(i_idx_s);
+         i_elts[e_i] = i_idx/test_elt_dofs;
+         i_B[e_i] = i_idx%test_elt_dofs;
+         i_sgns[e_i] = SignedIndexSign(i_idx_s);
+      }
+      for (int trial_c = 0; trial_c < trial_vd; ++trial_c)
+      {
+         for (int j = 0; j < trial_elt_dofs; j++)
+         {
+            const int j_gm = e*trial_elt_dofs + j;
+            const int j_gm_s = trial_gather_map[j_gm];
+            const int j_dof = SignedIndexAbs(j_gm_s);
+            const int j_sgn = SignedIndexSign(j_gm_s);
+            const int j_L = DofToVDof(j_dof, trial_c, trial_all_dofs,
+                                      trial_vd, trial_byvdim);
+            const int j_offset = trial_offsets[j_dof];
+            const int j_next_offset = trial_offsets[j_dof+1];
+            const int j_nbElts = j_next_offset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1)
+            {
+               const int nnz = GetAndIncrementNnzIndex(i_L, I);
+               J[nnz] = j_L;
+               Data[nnz] = i_sgn*j_sgn*mat_ea(i, test_c, j, trial_c, e);
+            }
+            else
+            {
+               int *j_elts = &d_trial_el(j_offset, 0);
+               int *j_B = &d_trial_el(j_offset, 1);
+               int *j_sgns = &d_trial_el(j_offset, 2);
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_idx_s = trial_indices[j_offset+e_j];
+                  const int j_idx = SignedIndexAbs(j_idx_s);
+                  j_elts[e_j] = j_idx/trial_elt_dofs;
+                  j_B[e_j] = j_idx%trial_elt_dofs;
+                  j_sgns[e_j] = SignedIndexSign(j_idx_s);
+               }
+               const int min_e = GetMinElt(i_elts, i_nbElts,
+                                           j_elts, j_nbElts);
+               if (e == min_e)
+               {
+                  real_t val = 0.0;
+                  for (int k = 0; k < i_nbElts; k++)
+                  {
+                     const int e_i = i_elts[k];
+                     const int i_Bloc = i_B[k];
+                     for (int l = 0; l < j_nbElts; l++)
+                     {
+                        const int e_j = j_elts[l];
+                        const int j_Bloc = j_B[l];
+                        if (e_i == e_j)
+                        {
+                           val += i_sgns[k]*j_sgns[l]*
+                                  mat_ea(i_Bloc, test_c, j_Bloc, trial_c, e_i);
+                        }
+                     }
+                  }
+                  const int nnz = GetAndIncrementNnzIndex(i_L, I);
+                  J[nnz] = j_L;
+                  Data[nnz] = val;
+               }
+            }
+         }
+      }
+   });
+
+   auto h_I = mat.HostReadWriteI();
+   const int size = test_vd*test_all_dofs;
+   for (int i = 0; i < size; i++)
+   {
+      h_I[size-i] = h_I[size-(i+1)];
+   }
+   h_I[0] = 0;
+}
+
 L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
    : ne(fes.GetNE()),
      vdim(fes.GetVDim()),

fem/restriction.hpp

@@ -87,12 +87,25 @@ public:
    /// Fill a Sparse Matrix with Element Matrices.
    void FillSparseMatrix(const Vector &mat_ea, SparseMatrix &mat) const;
 
+   /** Fill a SparseMatrix with element matrices for this (test) restriction and
+       the given trial restriction. The element matrix layout is
+       test_dof x test_vdim x trial_dof x trial_vdim x ne. */
+   void FillSparseMatrix(const Vector &mat_ea, SparseMatrix &mat,
+                         const ElementRestriction &trial_restr) const;
+
    /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
        given by this ElementRestriction. */
    int FillI(SparseMatrix &mat) const;
+   /** Fill the I array for this (test) and the given trial restriction. */
+   int FillI(SparseMatrix &mat, const ElementRestriction &trial_restr) const;
    /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
        pattern given by this ElementRestriction, and the values of ea_data. */
    void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
+   /** Fill the J and Data arrays for this (test) and the given trial
+       restriction, using element matrix layout
+       test_dof x test_vdim x trial_dof x trial_vdim x ne. */
+   void FillJAndData(const Vector &ea_data, SparseMatrix &mat,
+                     const ElementRestriction &trial_restr) const;
    /// @private Not part of the public interface (device kernel limitation).
    ///
    /// Performs either MultTranspose or AddMultTranspose depending on the

fem/transfer.cpp

@@ -231,11 +231,9 @@ const Operator &InterpolationGridTransfer::BackwardOperator()
 
 L2ProjectionGridTransfer::L2Projection::L2Projection(
    const FiniteElementSpace &fes_ho_, const FiniteElementSpace &fes_lor_,
-   CoefficientWithOrder coeff_ho_, CoefficientWithOrder coeff_lor_,
    MemoryType d_mt_)
    : Operator(fes_lor_.GetVSize(), fes_ho_.GetVSize()),
-     fes_ho(fes_ho_), fes_lor(fes_lor_), coeff_ho(coeff_ho_),
-     coeff_lor(coeff_lor_), d_mt(d_mt_)
+     fes_ho(fes_ho_), fes_lor(fes_lor_), d_mt(d_mt_)
 { }
 
 void L2ProjectionGridTransfer::L2Projection::BuildHo2Lor(
@@ -265,13 +263,12 @@ void L2ProjectionGridTransfer::L2Projection::ElemMixedMass(
    IntegrationPointTransformation& ip_tr,
    DenseMatrix& M_mixed_el) const
 {
-   int order = fe_lor.GetOrder() + fe_ho.GetOrder() + tr_lor->OrderW() +
-               coeff_ho.order;
-   const IntegrationRule &ir = IntRules.Get(geom, order);
+   int order = fe_lor.GetOrder() + fe_ho.GetOrder() + tr_lor->OrderW();
+   const IntegrationRule* ir = &IntRules.Get(geom, order);
    M_mixed_el = 0.0;
-   for (int i = 0; i < ir.GetNPoints(); i++)
+   for (int i = 0; i < ir->GetNPoints(); i++)
    {
-      const IntegrationPoint& ip_lor = ir.IntPoint(i);
+      const IntegrationPoint& ip_lor = ir->IntPoint(i);
       IntegrationPoint ip_ho;
       ip_tr.Transform(ip_lor, ip_ho);
       Vector shape_lor(fe_lor.GetDof());
@@ -287,23 +284,23 @@ void L2ProjectionGridTransfer::L2Projection::ElemMixedMass(
       {
          w *= tr_lor->Weight();
       }
-      if (coeff_ho)
-      {
-         w *= coeff_ho.coeff->Eval(*tr_ho, ip_ho);
-      }
       shape_lor *= w;
       AddMultVWt(shape_lor, shape_ho, M_mixed_el);
    }
 }
 
-void L2ProjectionGridTransfer::L2Projection::ElemMixedEvaluation(
-   Geometry::Type geom, const FiniteElement& fe_ho, const FiniteElement& fe_lor,
-   IntegrationPointTransformation& ip_tr, const IntegrationRule& ir,
+void L2ProjectionGridTransfer::L2Projection::ElemMixedMass(
+   Geometry::Type geom, const FiniteElement& fe_ho,
+   const FiniteElement& fe_lor, ElementTransformation* el_tr,
+   IntegrationPointTransformation& ip_tr,
    DenseMatrix& B_L, DenseMatrix& B_H) const
 {
-   for (int i = 0; i < ir.GetNPoints(); i++)
+   int order = fe_lor.GetOrder() + fe_ho.GetOrder() + el_tr->OrderW();
+   const IntegrationRule* ir = &IntRules.Get(geom, order);
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
    {
-      const IntegrationPoint& ip_lor = ir.IntPoint(i);
+      const IntegrationPoint& ip_lor = ir->IntPoint(i);
       IntegrationPoint ip_ho;
 
       // maps integration point ip_lor -> ip_ho
@@ -323,6 +320,7 @@ void L2ProjectionGridTransfer::L2Projection::ElemMixedEvaluation(
          B_H(i, j) = shape_ho(j);
       }
    }
+
 }
 
 void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
@@ -330,11 +328,10 @@ void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
    const FiniteElementSpace& fes_lor_ea,
    Vector &M_LH, MemoryType d_mt_)
 {
-   Mesh &mesh_ho = *fes_ho_ea.GetMesh();
-   Mesh &mesh_lor = *fes_lor_ea.GetMesh();
-
-   const int nel_ho = mesh_ho.GetNE();
-   const int nel_lor = mesh_lor.GetNE();
+   Mesh* mesh_ho = fes_ho_ea.GetMesh();
+   Mesh* mesh_lor = fes_lor_ea.GetMesh();
+   int nel_ho = mesh_ho->GetNE();
+   int nel_lor = mesh_lor->GetNE();
 
    if (nel_ho == 0)
    {
@@ -342,11 +339,11 @@ void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
       return;
    }
 
-   const CoarseFineTransformations& cf_tr = mesh_lor.GetRefinementTransforms();
+   const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();
 
    int nref_max = 0;
    Array<Geometry::Type> geoms;
-   mesh_ho.GetGeometries(mesh_ho.Dimension(), geoms);
+   mesh_ho->GetGeometries(mesh_ho->Dimension(), geoms);
    for (int ig = 0; ig < geoms.Size(); ++ig)
    {
       Geometry::Type geom = geoms[ig];
@@ -363,226 +360,130 @@ void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
    {
       // Assume all HO elements are LOR in the same way
       const int iho = 0;
-      Array<int> lor_els;
-      ho2lor.GetRow(iho, lor_els);
-      const int nref = ho2lor.RowSize(iho);
-      MFEM_VERIFY(nel_ho*nref == nel_lor, "we expect nel_ho*nref == nel_lor");
-
-      Geometry::Type geom = mesh_ho.GetElementBaseGeometry(iho);
-
-      emb_tr.SetIdentityTransformation(geom);
-      const DenseTensor &pmats = cf_tr.point_matrices[geom];
-
-      const FiniteElement &fe_ho = *fes_ho_ea.GetFE(iho);
-      const FiniteElement &fe_lor = *fes_lor_ea.GetFE(lor_els[0]);
-
-      // Allocate space for DenseTensors
-      ElementTransformation &el_tr = *mesh_lor.GetTypicalElementTransformation();
-      const int order = fe_lor.GetOrder() + fe_ho.GetOrder() + el_tr.OrderW()
-                        + coeff_ho.order;
-      const IntegrationRule &ir_ea = IntRules.Get(geom, order);
-      const int qPts = ir_ea.GetNPoints();
-
-      // Containers for the basis functions sampled at quadrature points
-      B_L.SetSize(qPts, fe_lor.GetDof(), nref, d_mt);
-      B_H.SetSize(qPts, fe_ho.GetDof(), nref, d_mt);
-      D.SetSize(qPts, nref, nel_ho, d_mt);
-
-      const GeometricFactors *geo_facts =
-         mesh_lor.GetGeometricFactors(ir_ea, GeometricFactors::DETERMINANTS);
-
-      Vector coeff_vec(qPts*nel_lor);
-      coeff_vec.UseDevice(true);
-
-      const int dim = mesh_ho.Dimension();
-      const int nq1d = (int)floor(pow(ir_ea.Size(), 1.0/dim) + 0.5);
-      const int nref_1d = (int)floor(pow(nref, 1.0/dim) + 0.5);
-
-      if (!coeff_ho)
       {
-         coeff_vec = 1.0;
-      }
-      else if (UsesTensorBasis(fes_ho) &&
-               nq1d*nref_1d <= DeviceDofQuadLimits::Get().MAX_Q1D)
-      {
-         // Fast coefficient evaluation for tensor-product case. We create a
-         // "composite" quadrature rule in the high-order element that is the
-         // union of the quadrature rules within each of the low-order-refined
-         // subelements.
-         //
-         // NOTE: if the integration rule order is high and there are many LOR
-         // subelements, this can create a very big quadrature rule. That is
-         // why we need to check that we do not exceed MAX_Q1D. If we do, then
-         // we fall back on the slower "legacy" evaluation.
+         Array<int> lor_els;
+         ho2lor.GetRow(iho, lor_els);
+         int nref = ho2lor.RowSize(iho);
 
-         // Construct the composite rule as a tensor-product of the 1D LOR rule.
-         IntegrationRule ir_ho = [&]()
+         Geometry::Type geom = mesh_ho->GetElementBaseGeometry(iho);
+         const FiniteElement &fe_ho = *fes_ho_ea.GetFE(iho);
+         const FiniteElement &fe_lor = *fes_lor_ea.GetFE(lor_els[0]);
+
+         // Allocate space for DenseTensors
+         ElementTransformation *el_tr = fes_lor_ea.GetElementTransformation(0);
+         int order = fe_lor.GetOrder() + fe_ho.GetOrder() + el_tr->OrderW();
+         const IntegrationRule* ir_ea = &IntRules.Get(geom, order);
+         int qPts = ir_ea->GetNPoints();
+
+         // Containers for the basis functions sampled at quadrature points
+         B_L.SetSize(qPts, fe_lor.GetDof(), nref, d_mt);
+         B_H.SetSize(qPts, fe_ho.GetDof(), nref, d_mt);
+         D.SetSize(qPts, nref, nel_ho, d_mt);
+
+         const GeometricFactors *geo_facts =
+            mesh_lor->GetGeometricFactors(*ir_ea, GeometricFactors::DETERMINANTS);
+
+         MFEM_ASSERT(nel_ho*nref == nel_lor, "we expect nel_ho*nref == nel_lor");
+
+         // Setup data at quadrature points
+         // TODO add support for user coefficient
+         const auto W = Reshape(ir_ea->GetWeights().Read(), qPts);
+         const auto J = Reshape(geo_facts->detJ.Read(), qPts, nel_lor);
+         const auto d_D = Reshape(D.Write(), qPts, nref, nel_ho);
+
+         mfem::forall(qPts * nref * nel_ho, [=] MFEM_HOST_DEVICE (int tid)
          {
-            IntegrationRule ir_ho_1d(nq1d * nref_1d);
-            for (int iref = 0; iref < nref_1d; ++iref)
-            {
-               const real_t a = pmats(cf_tr.embeddings[iref].matrix)(0,0);
-               const real_t b = pmats(cf_tr.embeddings[iref].matrix)(0,1);
-               for (int iq = 0; iq < nq1d; ++iq)
-               {
-                  ir_ho_1d[iq + iref*nq1d].x = a + ir_ea[iq].x*(b - a);
-               }
-            }
-            if (dim == 1) { return ir_ho_1d; }
-            else if (dim == 2) { return IntegrationRule(ir_ho_1d, ir_ho_1d); }
-            else { return IntegrationRule(ir_ho_1d, ir_ho_1d, ir_ho_1d); }
-         }();
+            const int q    = tid % qPts;
+            const int iref = (tid / qPts) % nref;
+            const int iho  = (tid / (qPts * nref)) % nel_ho;
 
-         // Project the high-order coefficient on the high-order composite rule.
-         QuadratureSpace qs(mesh_ho, ir_ho);
-         CoefficientVector coeff_vec_ho(*coeff_ho.coeff, qs);
+            const int lo_el_id = iref + nref*iho;
+            const real_t detJ = J(q, lo_el_id);
 
-         // Permute the coefficient values to the expected LOR ordering.
-         const int nq_ho = ir_ho.Size();
-         const auto d_Q_ho = Reshape(coeff_vec_ho.Read(), nq_ho, nel_ho);
-         const auto d_Q = Reshape(coeff_vec.Write(), qPts, nel_lor);
+            d_D(q, iref, iho) = W(q) * detJ;
 
-         mfem::forall(nq_ho * nel_ho, [=] MFEM_HOST_DEVICE (int ii)
-         {
-            const int e_ho = ii / nq_ho;
-            const int iq_ho = ii % nq_ho;
-
-            int iq_tensor = iq_ho;
-            int iq_lor = 0;
-            int iref = 0;
-            int iq_stride = 1;
-            int iref_stride = 1;
-            const int nq_ho_1d = nq1d*nref_1d;
-            for (int d = 0; d < dim; ++d)
-            {
-               const int iq_ho_1d = iq_tensor % nq_ho_1d;
-               iq_tensor /= nq_ho_1d;
-
-               iq_lor += (iq_ho_1d % nq1d)*iq_stride;
-               iref += (iq_ho_1d / nq1d)*iref_stride;
-               iq_stride *= nq1d;
-               iref_stride *= nref_1d;
-            }
-            const int e_lor = iref + e_ho*nref;
-
-            d_Q(iq_lor, e_lor) = d_Q_ho(iq_ho, e_ho);
          });
-      }
-      else
-      {
-         // Legacy/fallback coefficient evaluation for non-tensor-product cases
-         // or when the number of quadrature points is too large for the device
-         // kernels.
-         IntegrationPoint ip_ho;
-         for (int e_ho = 0; e_ho < nel_ho; ++e_ho)
+
+         emb_tr.SetIdentityTransformation(geom);
+         const DenseTensor &pmats = cf_tr.point_matrices[geom];
+
+         // Collect the basis functions
+         for (int iref = 0; iref < nref; ++iref)
          {
-            ElementTransformation &ho_tr = *mesh_ho.GetElementTransformation(e_ho);
-            for (int iref = 0; iref < nref; ++iref)
-            {
-               const int e_lor = iref + e_ho*nref;
-               emb_tr.SetPointMat(pmats(cf_tr.embeddings[e_lor].matrix));
+            int ilor = lor_els[iref];
+            // Now assemble the block-row of the mixed mass matrix associated
+            // with integrating HO functions against LOR functions on the LOR
+            // sub-element.
 
-               for (int iq = 0; iq < qPts; ++iq)
-               {
-                  const IntegrationPoint &ip_lor = ir_ea[iq];
-                  ip_tr.Transform(ip_lor, ip_ho);
-                  ho_tr.SetIntPoint(&ip_ho);
-                  coeff_vec[iq + e_lor*qPts] = coeff_ho.coeff->Eval(ho_tr, ip_ho);
-               }
-            }
-         }
+            // Create the transformation that embeds the fine low-order element
+            // within the coarse high-order element in reference space
+            emb_tr.SetPointMat(pmats(cf_tr.embeddings[ilor].matrix));
+
+            DenseMatrix &b_lo = B_L(ilor);
+            DenseMatrix &b_ho = B_H(ilor);
+
+            ElemMixedMass(geom, fe_ho, fe_lor, el_tr, ip_tr, b_lo, b_ho);
+
+         } // loop over subcells of ho element
+         // end of quadrature point setup
       }
 
-      // Setup data at quadrature points
-      const auto W = Reshape(ir_ea.GetWeights().Read(), qPts);
-      const auto J = Reshape(geo_facts->detJ.Read(), qPts, nel_lor);
-      const auto d_D = Reshape(D.Write(), qPts, nref, nel_ho);
-      const auto d_Q = Reshape(coeff_vec.Read(), qPts, nel_lor);
-
-      mfem::forall(qPts * nref * nel_ho, [=] MFEM_HOST_DEVICE (int tid)
-      {
-         const int q    = tid % qPts;
-         const int iref = (tid / qPts) % nref;
-         const int iho  = (tid / (qPts * nref)) % nel_ho;
-
-         const int lo_el_id = iref + nref*iho;
-         const real_t detJ = J(q, lo_el_id);
-
-         d_D(q, iref, iho) = W(q) * d_Q(q, lo_el_id) * detJ;
-      });
-
-      // Collect the basis functions
-      for (int iref = 0; iref < nref; ++iref)
-      {
-         int ilor = lor_els[iref];
-         // Now assemble the block-row of the mixed mass matrix associated
-         // with integrating HO functions against LOR functions on the LOR
-         // sub-element.
-
-         // Create the transformation that embeds the fine low-order element
-         // within the coarse high-order element in reference space
-         emb_tr.SetPointMat(pmats(cf_tr.embeddings[ilor].matrix));
-
-         DenseMatrix &b_lo = B_L(ilor);
-         DenseMatrix &b_ho = B_H(ilor);
-
-         ElemMixedEvaluation(geom, fe_ho, fe_lor, ip_tr, ir_ea, b_lo, b_ho);
-      } // loop over subcells of ho element
-      // end of quadrature point setup
    } // completed setup of basis function and quadrature point
 
    // Assemble mixed mass matrix
-   int iho = 0;
-   Array<int> lor_els;
-   ho2lor.GetRow(iho, lor_els);
-   int nref = ho2lor.RowSize(iho);
-
-   const FiniteElement &fe_ho = *fes_ho_ea.GetFE(iho);
-   const FiniteElement &fe_lor = *fes_lor_ea.GetFE(lor_els[0]);
-   const int ndof_ho = fe_ho.GetDof();
-   const int ndof_lor = fe_lor.GetDof();
-
-   const int qPts = D.SizeI();
-
-   M_LH.SetSize(ndof_lor*ndof_ho*nref*nel_ho, d_mt);
-
-   // Rows x columns
-   // Recall MFEM is column major
-   // rows x columns is inverted  - matrix is ndof_lor x ndof_ho
-   auto v_M_LH = Reshape(M_LH.Write(), ndof_lor, ndof_ho, nref,
-                         nel_ho);
-
-   const int fe_ho_ndof = fe_ho.GetDof();
-   const int fe_lor_ndof = fe_lor.GetDof();
-
-   auto d_B_L = Reshape(B_L.Read(), qPts, fe_lor_ndof, nref);
-   auto d_B_H = Reshape(B_H.Read(), qPts, fe_ho_ndof, nref);
-   auto d_D   = Reshape(D.Read(), qPts, nref, nel_ho);
-
-   mfem::forall(fe_ho_ndof*nref*nel_ho, [=] MFEM_HOST_DEVICE (int idx)
    {
-      const int bh = idx % fe_ho_ndof;
-      const int iref = (idx / fe_ho_ndof) % nref;
-      const int iho = idx / fe_ho_ndof / nref;
-      // (B_lo_dofs x Q) x (Q x B_ho_dofs)
-      for (int bl = 0; bl < fe_lor_ndof; ++bl)
+      int iho = 0;
+      Array<int> lor_els;
+      ho2lor.GetRow(iho, lor_els);
+      int nref = ho2lor.RowSize(iho);
+
+      const FiniteElement &fe_ho = *fes_ho_ea.GetFE(iho);
+      const FiniteElement &fe_lor = *fes_lor_ea.GetFE(lor_els[0]);
+      const int ndof_ho = fe_ho.GetDof();
+      const int ndof_lor = fe_lor.GetDof();
+
+      const int qPts = D.SizeI();
+
+      M_LH.SetSize(ndof_lor*ndof_ho*nref*nel_ho, d_mt);
+
+      // Rows x columns
+      // Recall MFEM is column major
+      // rows x columns is inverted  - matrix is ndof_lor x ndof_ho
+      auto v_M_LH = Reshape(M_LH.Write(), ndof_lor, ndof_ho, nref,
+                            nel_ho);
+
+      const int fe_ho_ndof = fe_ho.GetDof();
+      const int fe_lor_ndof = fe_lor.GetDof();
+
+      auto d_B_L = Reshape(B_L.Read(), qPts, fe_lor_ndof, nref);
+      auto d_B_H = Reshape(B_H.Read(), qPts, fe_ho_ndof, nref);
+      auto d_D   = Reshape(D.Read(), qPts, nref, nel_ho);
+
+      mfem::forall(fe_ho_ndof*nref*nel_ho, [=] MFEM_HOST_DEVICE (int idx)
       {
-         real_t dot = 0.0;
-         for (int qi=0; qi<qPts; ++qi)
+         const int bh = idx % fe_ho_ndof;
+         const int iref = (idx / fe_ho_ndof) % nref;
+         const int iho = idx / fe_ho_ndof / nref;
+         // (B_lo_dofs x Q) x (Q x B_ho_dofs)
+         for (int bl = 0; bl < fe_lor_ndof; ++bl)
          {
-            dot += d_B_L(qi, bl, iref) *  d_D(qi, iref, iho) * d_B_H(qi, bh, iref);
+            real_t dot = 0.0;
+            for (int qi=0; qi<qPts; ++qi)
+            {
+               dot += d_B_L(qi, bl, iref) *  d_D(qi, iref, iho) * d_B_H(qi, bh, iref);
+            }
+            // column major storage
+            v_M_LH(bl, bh, iref, iho) = dot;
          }
-         // column major storage
-         v_M_LH(bl, bh, iref, iho) = dot;
-      }
-   });
+      });
+   } // end of mixed assembly mass matrix
 }
 
 L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space
 (const FiniteElementSpace &fes_ho_, const FiniteElementSpace &fes_lor_,
- CoefficientWithOrder coeff_ho_, CoefficientWithOrder coeff_lor_,
  const bool use_ea_, MemoryType d_mt_)
-   : L2Projection(fes_ho_, fes_lor_, coeff_ho_, coeff_lor_, d_mt_), use_ea(use_ea_)
+   : L2Projection(fes_ho_, fes_lor_, d_mt_),
+     use_ea(use_ea_)
 {
    if (use_ea)
    {
@@ -658,11 +559,7 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space
       DenseMatrix Minv_lor(ndof_lor*nref, ndof_lor*nref);
       DenseMatrix M_mixed(ndof_lor*nref, ndof_ho);
 
-      MassIntegrator mi = [&]()
-      {
-         return coeff_lor ? MassIntegrator(*coeff_lor.coeff) : MassIntegrator();
-      }();
-
+      MassIntegrator mi;
       DenseMatrix M_lor_el(ndof_lor, ndof_lor);
       DenseMatrixInverse Minv_lor_el(&M_lor_el);
       DenseMatrix M_lor(ndof_lor*nref, ndof_lor*nref);
@@ -680,10 +577,6 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space
          // Assemble the low-order refined mass matrix and invert locally
          int ilor = lor_els[iref];
          ElementTransformation *tr_lor = fes_lor.GetElementTransformation(ilor);
-
-         const int order = 2*fe_lor.GetOrder() + tr_lor->OrderW() + coeff_lor.order;
-         mi.SetIntegrationRule(IntRules.Get(geom, order));
-
          mi.AssembleElementMatrix(fe_lor, *tr_lor, M_lor_el);
          M_lor.CopyMN(M_lor_el, iref*ndof_lor, iref*ndof_lor);
          Minv_lor_el.Factor();
@@ -775,22 +668,25 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAL2ProjectionL2Space()
    // Need to compute M_L
    // Note: Using user-inputted M_LH IntegrationRule ir
    // (higher order than needed) in order to re-use coeff
-   MassIntegrator mi = [&]()
-   {
-      return coeff_lor ? MassIntegrator(*coeff_lor.coeff) : MassIntegrator();
-   }();
-
-   const int order = 2*fes_lor.GetMaxElementOrder()
-                     + mesh_lor->GetTypicalElementTransformation()->OrderW()
-                     + coeff_lor.order;
-   mi.SetIntegrationRule(
-      IntRules.Get(mesh_lor->GetTypicalElementGeometry(), order));
+   MassIntegrator mi;
 
    Vector M_ea_lor;
-   const int ndof_lor = fes_lor.GetTypicalFE()->GetDof();
-   const int ndof_ho = fes_ho.GetTypicalFE()->GetDof();
-   const int nref = ho2lor.RowSize(0);
-   M_ea_lor.SetSize(ndof_lor*ndof_lor*nel_lor, d_mt);
+   int ndof_lor;
+   int ndof_ho;
+   int nref;
+   {
+      int iho = 0;
+      Array<int> lor_els;
+      ho2lor.GetRow(iho, lor_els);
+      nref = ho2lor.RowSize(iho);
+
+      const FiniteElement &fe_ho = *fes_ho.GetFE(iho);
+      const FiniteElement &fe_lor = *fes_lor.GetFE(lor_els[0]);
+      ndof_ho = fe_ho.GetDof();
+      ndof_lor = fe_lor.GetDof();
+
+      M_ea_lor.SetSize(ndof_lor*ndof_lor*nel_lor, d_mt);
+   }
 
    const bool add = false;
    mi.AssembleEA(fes_lor, M_ea_lor, add);
@@ -1136,9 +1032,8 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAProlongateTranspose(
 
 L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
    const FiniteElementSpace& fes_ho_, const FiniteElementSpace& fes_lor_,
-   CoefficientWithOrder coeff_ho_, CoefficientWithOrder coeff_lor_,
    const bool use_ea_, MemoryType d_mt_)
-   : L2Projection(fes_ho_, fes_lor_, coeff_ho_, coeff_lor_, d_mt_),
+   : L2Projection(fes_ho_, fes_lor_, d_mt_),
      use_ea(use_ea_)
 {
 
@@ -1197,9 +1092,8 @@ L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
 
 L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
    const ParFiniteElementSpace& pfes_ho, const ParFiniteElementSpace& pfes_lor,
-   CoefficientWithOrder coeff_ho_, CoefficientWithOrder coeff_lor_,
    const bool use_ea_, MemoryType d_mt_)
-   : L2Projection(pfes_ho, pfes_lor, coeff_ho_, coeff_lor_, d_mt_),
+   : L2Projection(pfes_ho, pfes_lor, d_mt_),
      use_ea(use_ea_), pcg(pfes_ho.GetComm())
 {
 
@@ -1271,12 +1165,12 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::SetupPCG()
 
 void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
 {
-   Mesh &mesh_ho = *fes_ho.GetMesh();
-   Mesh &mesh_lor = *fes_lor.GetMesh();
-   const int nel_ho = mesh_ho.GetNE();
-   const int nel_lor = mesh_lor.GetNE();
-   const int ndof_ho = fes_ho.GetNDofs();
-   const int ndof_lor = fes_lor.GetNDofs();
+   Mesh* mesh_ho = fes_ho.GetMesh();
+   Mesh* mesh_lor = fes_lor.GetMesh();
+   int nel_ho = mesh_ho->GetNE();
+   int nel_lor = mesh_lor->GetNE();
+   int ndof_ho = fes_ho.GetNDofs();
+   int ndof_lor = fes_lor.GetNDofs();
 
    // If the local mesh is empty, skip all computations
    if (nel_ho == 0)
@@ -1284,11 +1178,11 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
       return;
    }
 
-   const CoarseFineTransformations& cf_tr = mesh_lor.GetRefinementTransforms();
+   const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();
 
    int nref_max = 0;
    Array<Geometry::Type> geoms;
-   mesh_ho.GetGeometries(mesh_ho.Dimension(), geoms);
+   mesh_ho->GetGeometries(mesh_ho->Dimension(), geoms);
    for (int ig = 0; ig < geoms.Size(); ++ig)
    {
       Geometry::Type geom = geoms[ig];
@@ -1311,8 +1205,7 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
 
    BilinearForm Mho(fes_ho_scalar.get());
    Mho.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   Mho.AddDomainIntegrator(coeff_ho ? new MassIntegrator(*coeff_ho.coeff)
-                           : new MassIntegrator);
+   Mho.AddDomainIntegrator(new MassIntegrator);
    Mho.Assemble();
 
    // Processor local lumped Mass
@@ -1322,16 +1215,7 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
 
    BilinearForm Mlor(fes_lor_scalar.get());
    Mlor.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   {
-      MassIntegrator *mi = coeff_lor ? new MassIntegrator(*coeff_lor.coeff)
-                           : new MassIntegrator;
-      const int order = 2*fes_lor.GetMaxElementOrder()
-                        + mesh_lor.GetTypicalElementTransformation()->OrderW()
-                        + coeff_lor.order;
-      mi->SetIntegrationRule(
-         IntRules.Get(mesh_lor.GetTypicalElementGeometry(), order));
-      Mlor.AddDomainIntegrator(mi);
-   }
+   Mlor.AddDomainIntegrator(new MassIntegrator);
    Mlor.Assemble();
 
    Vector ones_lor(Mlor.Width()); ones_lor = 1.0;
@@ -1344,14 +1228,15 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
    MixedMassEA(fes_ho, fes_lor, M_LH_ea, d_mt);
 
    // Set ownership
-   M_LH.reset(new H1SpaceMixedMassOperator(fes_ho_scalar.get(),
-                                           fes_lor_scalar.get(),
-                                           &ho2lor,
-                                           &M_LH_ea));
+   M_LH_local_op = new H1SpaceMixedMassOperator(fes_ho_scalar.get(),
+                                                fes_lor_scalar.get(),
+                                                &ho2lor,
+                                                &M_LH_ea);
 
    ML_inv_vea.reset(new H1SpaceLumpedMassOperator(fes_ho_scalar.get(),
                                                   fes_lor_scalar.get(),
                                                   ML_inv_ea));
+   M_LH.reset(M_LH_local_op);
    R.reset(new ProductOperator(ML_inv_vea.get(), M_LH.get(), false,
                                false));
 
@@ -1368,18 +1253,18 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space()
 void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space
 (const ParFiniteElementSpace& pfes_ho, const ParFiniteElementSpace& pfes_lor)
 {
-   Mesh &mesh_ho = *pfes_ho.GetParMesh();
-   Mesh &mesh_lor = *pfes_lor.GetParMesh();
-   int nel_ho = mesh_ho.GetNE();
-   int nel_lor = mesh_lor.GetNE();
+   Mesh* mesh_ho = pfes_ho.GetParMesh();
+   Mesh* mesh_lor = pfes_lor.GetParMesh();
+   int nel_ho = mesh_ho->GetNE();
+   int nel_lor = mesh_lor->GetNE();
    int ndof_ho = pfes_ho.GetNDofs();
    int ndof_lor = pfes_lor.GetNDofs();
 
-   const CoarseFineTransformations& cf_tr = mesh_lor.GetRefinementTransforms();
+   const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();
 
    int nref_max = 0;
    Array<Geometry::Type> geoms;
-   mesh_ho.GetGeometries(mesh_ho.Dimension(), geoms);
+   mesh_ho->GetGeometries(mesh_ho->Dimension(), geoms);
    for (int ig = 0; ig < geoms.Size(); ++ig)
    {
       Geometry::Type geom = geoms[ig];
@@ -1402,8 +1287,7 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space
 
    ParBilinearForm pMho(pfes_ho_scalar.get());
    pMho.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   pMho.AddDomainIntegrator(coeff_ho ? new MassIntegrator(*coeff_ho.coeff)
-                            : new MassIntegrator);
+   pMho.AddDomainIntegrator(new MassIntegrator);
    pMho.Assemble();
 
    // Processor local lumped Mass
@@ -1413,16 +1297,7 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space
 
    ParBilinearForm pMlor(pfes_lor_scalar.get());
    pMlor.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   {
-      MassIntegrator *mi = coeff_lor ? new MassIntegrator(*coeff_lor.coeff)
-                           : new MassIntegrator;
-      const int order = 2*fes_lor.GetMaxElementOrder()
-                        + mesh_lor.GetTypicalElementTransformation()->OrderW()
-                        + coeff_lor.order;
-      mi->SetIntegrationRule(
-         IntRules.Get(mesh_lor.GetTypicalElementGeometry(), order));
-      pMlor.AddDomainIntegrator(mi);
-   }
+   pMlor.AddDomainIntegrator(new MassIntegrator);
    pMlor.Assemble();
 
    Vector ones_lor(pMlor.Width()); ones_lor = 1.0;
@@ -1695,7 +1570,7 @@ std::unique_ptr<SparseMatrix>>
          int ilor = lor_els[iref];
          ElementTransformation* el_tr = fes_lor.GetElementTransformation(ilor);
 
-         int order = 2 * fe_lor.GetOrder() + el_tr->OrderW() + coeff_lor.order;
+         int order = 2 * fe_lor.GetOrder() + el_tr->OrderW();
          const IntegrationRule* ir = &IntRules.Get(geom, order);
          ML_el = 0.0;
          for (int i = 0; i < ir->GetNPoints(); ++i)
@@ -1703,13 +1578,7 @@ std::unique_ptr<SparseMatrix>>
             const IntegrationPoint& ip_lor = ir->IntPoint(i);
             fe_lor.CalcShape(ip_lor, shape_lor);
             el_tr->SetIntPoint(&ip_lor);
-            real_t w = ip_lor.weight;
-            if (coeff_lor)
-            {
-               w *= coeff_lor.coeff->Eval(*el_tr, ip_lor);
-            }
-            shape_lor *= el_tr->Weight() * w;
-            ML_el += shape_lor;
+            ML_el += (shape_lor *= (el_tr->Weight() * ip_lor.weight));
          }
          fes_lor.GetElementDofs(ilor, dofs_lor);
          ML_inv.AddElementVector(dofs_lor, ML_el);
@@ -2155,8 +2024,8 @@ void L2ProjectionGridTransfer::BuildF()
    {
       if (!Parallel())
       {
-         F = new L2ProjectionH1Space(
-            dom_fes, ran_fes, coeff_ho, coeff_lor, use_ea, d_mt);
+         F = new L2ProjectionH1Space(dom_fes, ran_fes,
+                                     use_ea, d_mt);
       }
       else
       {
@@ -2165,15 +2034,15 @@ void L2ProjectionGridTransfer::BuildF()
             static_cast<mfem::ParFiniteElementSpace&>(dom_fes);
          const mfem::ParFiniteElementSpace& ran_pfes =
             static_cast<mfem::ParFiniteElementSpace&>(ran_fes);
-         F = new L2ProjectionH1Space(
-            dom_pfes, ran_pfes, coeff_ho, coeff_lor, use_ea, d_mt);
+         F = new L2ProjectionH1Space(dom_pfes, ran_pfes,
+                                     use_ea, d_mt);
 #endif
       }
    }
    else
    {
-      F = new L2ProjectionL2Space(
-         dom_fes, ran_fes, coeff_ho, coeff_lor, use_ea, d_mt);
+      F = new L2ProjectionL2Space(dom_fes, ran_fes,
+                                  use_ea, d_mt);
    }
 }
 

fem/transfer.hpp

@@ -19,8 +19,6 @@
 #include "pfespace.hpp"
 #endif
 
-#include <cstddef>
-
 namespace mfem
 {
 
@@ -164,18 +162,6 @@ public:
 };
 
 
-struct CoefficientWithOrder
-{
-   Coefficient *coeff;
-   int order;
-   CoefficientWithOrder() : coeff(nullptr), order(0) { }
-   CoefficientWithOrder(std::nullptr_t) : coeff(nullptr), order(0) { }
-   CoefficientWithOrder(Coefficient &coeff_) : coeff(&coeff_), order(1) { }
-   CoefficientWithOrder(Coefficient &coeff_, int order_)
-      : coeff(&coeff_), order(order_) { }
-   operator bool() const { return coeff != nullptr; }
-};
-
 /** @brief Transfer data in L2 and H1 finite element spaces between a coarse
     mesh and an embedded refined mesh using L2 projection. */
 /** The forward, coarse-to-fine, transfer uses L2 projection. The backward,
@@ -221,8 +207,6 @@ public:
    protected:
       const FiniteElementSpace& fes_ho;
       const FiniteElementSpace& fes_lor;
-      CoefficientWithOrder coeff_ho;
-      CoefficientWithOrder coeff_lor;
 
       MemoryType d_mt;
       Array<int> offsets;
@@ -230,15 +214,8 @@ public:
 
       L2Projection(const FiniteElementSpace& fes_ho_,
                    const FiniteElementSpace& fes_lor_,
-                   CoefficientWithOrder coeff_ho_,
-                   CoefficientWithOrder coeff_lor_,
                    MemoryType d_mt_ = Device::GetHostMemoryType());
 
-      L2Projection(const FiniteElementSpace& fes_ho_,
-                   const FiniteElementSpace& fes_lor_,
-                   MemoryType d_mt_ = Device::GetHostMemoryType())
-         : L2Projection(fes_ho_, fes_lor_, nullptr, nullptr, d_mt_) { }
-
       void BuildHo2Lor(int nel_ho, int nel_lor,
                        const CoarseFineTransformations& cf_tr);
 
@@ -248,11 +225,11 @@ public:
                          IntegrationPointTransformation& ip_tr,
                          DenseMatrix& M_mixed_el) const;
 
-      void ElemMixedEvaluation(Geometry::Type geom, const FiniteElement& fe_ho,
-                               const FiniteElement& fe_lor,
-                               IntegrationPointTransformation& ip_tr,
-                               const IntegrationRule& ir,
-                               DenseMatrix& B_L, DenseMatrix& B_H) const;
+      void ElemMixedMass(Geometry::Type geom, const FiniteElement& fe_ho,
+                         const FiniteElement& fe_lor,
+                         ElementTransformation* el_tr,
+                         IntegrationPointTransformation& ip_tr,
+                         DenseMatrix& B_L, DenseMatrix& B_H) const;
    public:
       /* Returns the Mixed Mass M_LH via device element assembly by building the
       basis functions and data at the quadrature points. */
@@ -310,17 +287,9 @@ public:
    public:
       L2ProjectionL2Space(const FiniteElementSpace& fes_ho_,
                           const FiniteElementSpace& fes_lor_,
-                          CoefficientWithOrder coeff_ho_,
-                          CoefficientWithOrder coeff_lor_,
                           const bool use_ea_,
                           MemoryType d_mt_ = Device::GetHostMemoryType());
 
-      L2ProjectionL2Space(const FiniteElementSpace& fes_ho_,
-                          const FiniteElementSpace& fes_lor_,
-                          const bool use_ea_,
-                          MemoryType d_mt_ = Device::GetHostMemoryType())
-         : L2ProjectionL2Space(fes_ho_, fes_lor_, nullptr, nullptr, use_ea_, d_mt_) { }
-
       /*Same as above but assembles and stores R_ea, P_ea */
       void EAL2ProjectionL2Space();
 
@@ -387,30 +356,13 @@ public:
    public:
       L2ProjectionH1Space(const FiniteElementSpace &fes_ho_,
                           const FiniteElementSpace &fes_lor_,
-                          CoefficientWithOrder coeff_ho_,
-                          CoefficientWithOrder coeff_lor_,
                           const bool use_ea_,
                           MemoryType d_mt_ = Device::GetHostMemoryType());
-
-      L2ProjectionH1Space(const FiniteElementSpace& fes_ho_,
-                          const FiniteElementSpace& fes_lor_,
-                          const bool use_ea_,
-                          MemoryType d_mt_ = Device::GetHostMemoryType())
-         : L2ProjectionH1Space(fes_ho_, fes_lor_, nullptr, nullptr, use_ea_, d_mt_) { }
-
 #ifdef MFEM_USE_MPI
       L2ProjectionH1Space(const ParFiniteElementSpace &pfes_ho_,
                           const ParFiniteElementSpace &pfes_lor_,
-                          CoefficientWithOrder coeff_ho_,
-                          CoefficientWithOrder coeff_lor_,
                           const bool use_ea_,
                           MemoryType d_mt_ = Device::GetHostMemoryType());
-
-      L2ProjectionH1Space(const ParFiniteElementSpace& fes_ho_,
-                          const ParFiniteElementSpace& fes_lor_,
-                          const bool use_ea_,
-                          MemoryType d_mt_ = Device::GetHostMemoryType())
-         : L2ProjectionH1Space(fes_ho_, fes_lor_, nullptr, nullptr, use_ea_, d_mt_) { }
 #endif
       /// Same as above but assembles action of R through 4 parts:
       ///   ( )  inv( lumped(M_L) ), which is a diagonal matrix (essentially a vector)
@@ -556,38 +508,18 @@ public:
       virtual ~L2Prolongation() { }
    };
 
-   /// Coefficient for the mixed L2 inner product.
-   CoefficientWithOrder coeff_ho;
-   /// Coefficient for the low-order L2 inner product.
-   CoefficientWithOrder coeff_lor;
    L2Projection   *F; ///< Forward, coarse-to-fine, operator
    L2Prolongation *B; ///< Backward, fine-to-coarse, operator
    bool force_l2_space;
 
 public:
-   /// Construct the unweighted L2 projection grid transfer.
    L2ProjectionGridTransfer(FiniteElementSpace &coarse_fes_,
                             FiniteElementSpace &fine_fes_,
                             bool force_l2_space_ = false,
                             MemoryType d_mt_ = Device::GetHostMemoryType()) // move to method
       : GridTransfer(coarse_fes_, fine_fes_),
-        coeff_ho(nullptr), coeff_lor(nullptr), F(nullptr), B(nullptr),
-        force_l2_space(force_l2_space_) { }
-
-   /// @brief Construct the weighted L2 projection grid transfer.
-   ///
-   /// The low-order inner product is weighted by @a coeff_lor, and the mixed
-   /// inner product is weighted by @a coeff_ho.
-   L2ProjectionGridTransfer(FiniteElementSpace &coarse_fes_,
-                            FiniteElementSpace &fine_fes_,
-                            CoefficientWithOrder coeff_ho_,
-                            CoefficientWithOrder coeff_lor_,
-                            bool force_l2_space_ = false,
-                            MemoryType d_mt_ = Device::GetHostMemoryType()) // move to method
-      : GridTransfer(coarse_fes_, fine_fes_),
-        coeff_ho(coeff_ho_), coeff_lor(coeff_lor_), F(nullptr), B(nullptr),
-        force_l2_space(force_l2_space_) { }
-
+        F(NULL), B(NULL), force_l2_space(force_l2_space_)
+   { }
    virtual ~L2ProjectionGridTransfer();
 
    const Operator &ForwardOperator() override;
@@ -595,7 +527,6 @@ public:
    const Operator &BackwardOperator() override;
 
    bool SupportsBackwardsOperator() const override;
-
 private:
    void BuildF();
 };

general/backends.hpp

@@ -14,7 +14,7 @@
 
 #include "../config/config.hpp"
 
-#if defined(MFEM_USE_CUDA)
+#if defined(MFEM_USE_CUDA) && defined(__CUDACC__)
 #include <cusparse.h>
 #include <library_types.h>
 #include <cuda_runtime.h>
@@ -22,7 +22,7 @@
 #endif
 #include "cuda.hpp"
 
-#if defined(MFEM_USE_HIP)
+#if defined(MFEM_USE_HIP) && defined(__HIP__)
 #include <hip/hip_runtime.h>
 #endif
 #include "hip.hpp"
@@ -45,17 +45,15 @@
 #endif
 
 #if !defined(MFEM_USE_CUDA_OR_HIP)
-// MFEM_DEVICE_SYNC is made available for debugging purposes
-#define MFEM_DEVICE_SYNC
-// MFEM_STREAM_SYNC is used for UVM and MPI GPU-Aware kernels
-#define MFEM_STREAM_SYNC
-#endif
-
-#if !defined(MFEM_USE_CUDA_OR_HIP_LANG)
+constexpr bool mfem_use_gpu = false;
 #define MFEM_DEVICE
 #define MFEM_HOST
 #define MFEM_LAMBDA
 // #define MFEM_HOST_DEVICE // defined in config/config.hpp
+// MFEM_DEVICE_SYNC is made available for debugging purposes
+#define MFEM_DEVICE_SYNC
+// MFEM_STREAM_SYNC is used for UVM and MPI GPU-Aware kernels
+#define MFEM_STREAM_SYNC
 #define MFEM_LAUNCH_BOUNDS(...)
 #endif
 
@@ -128,23 +126,4 @@ MFEM_HOST_DEVICE T AtomicAdd(T &add, const T val)
 #endif
 }
 
-namespace mfem::internal
-{
-
-#if defined(MFEM_USE_CUDA_OR_HIP) && !defined(MFEM_USE_CUDA_OR_HIP_LANG)
-static constexpr bool can_compile_kernels = false;
-#else
-static constexpr bool can_compile_kernels = true;
-#endif
-
-template <bool can_compile_kernels = can_compile_kernels>
-void RequireKernelCompilation()
-{
-   static_assert(
-      can_compile_kernels,
-      "The calling function needs to be compiled with CUDA/HIP language!");
-}
-
-}
-
 #endif // MFEM_BACKENDS_HPP

general/communication.cpp

@@ -1108,126 +1108,6 @@ void GroupCommunicator::ReduceEnd(T *ldata, int layout,
    num_requests = 0;
 }
 
-template <class T>
-void GroupCommunicator::ReduceMarked(T *ldata, const Array<int> &marker,
-                                     int layout,
-                                     void (*Op)(OpData<T>)) const
-{
-   if (comm_lock == 0) { return; }
-   // The above also handles the case (group_buf_size == 0).
-   MFEM_VERIFY(comm_lock == 2, "object is NOT locked for Reduce");
-
-   switch (mode)
-   {
-      case byGroup: // ***** Communication by groups *****
-      {
-         OpData<T> opd;
-         opd.ldata = ldata;
-         Array<int> group_num_req(group_ldof.Size());
-         for (int gr = 1; gr < group_ldof.Size(); gr++)
-         {
-            group_num_req[gr] =
-               gtopo.IAmMaster(gr) ? gtopo.GetGroupSize(gr)-1 : 0;
-         }
-         int idx;
-         while (MPI_Waitany(num_requests, requests, &idx, MPI_STATUS_IGNORE),
-                idx != MPI_UNDEFINED)
-         {
-            int gr = request_marker[idx];
-            if (gr == -1) { continue; } // skip send requests
-
-            // Delay the processing of a group until all receive requests, for
-            // that group, are done:
-            if ((--group_num_req[gr]) != 0) { continue; }
-
-            opd.nldofs = group_ldof.RowSize(gr);
-            // groups without dofs are skipped, so here nldofs > 0.
-
-            opd.buf = (T *)group_buf.GetData() + buf_offsets[gr];
-            opd.ldofs = (layout == 0) ?
-                        group_ldof.GetRow(gr) : group_ltdof.GetRow(gr);
-            opd.nb = gtopo.GetGroupSize(gr)-1;
-
-            // Apply operation only to marked DOFs. The receive buffer is
-            // neighbor-major with stride opd.nldofs, i.e. the contributions to
-            // DOF i are buf[j*opd.nldofs + i] for j = 0 ... opd.nb-1. Setting
-            // nldofs = 1 for a single DOF changes that stride to 1, so the
-            // strided values must first be gathered into a contiguous buffer.
-            Array<T> single_buf(opd.nb);
-            for (int i = 0; i < opd.nldofs; i++)
-            {
-               if (marker[opd.ldofs[i]])
-               {
-                  for (int j = 0; j < opd.nb; j++)
-                  {
-                     single_buf[j] = opd.buf[j*opd.nldofs + i];
-                  }
-
-                  // Create a temporary OpData with just this one DOF
-                  OpData<T> single_opd;
-                  single_opd.ldata = ldata;
-                  single_opd.buf = single_buf.GetData();
-                  single_opd.ldofs = opd.ldofs + i;
-                  single_opd.nldofs = 1;
-                  single_opd.nb = opd.nb;
-
-                  // Apply the operation
-                  Op(single_opd);
-               }
-            }
-         }
-         break;
-      }
-
-      case byNeighbor: // ***** Communication by neighbors *****
-      {
-         MPI_Waitall(num_requests, requests, MPI_STATUSES_IGNORE);
-
-         for (int nbr = 1; nbr < nbr_send_groups.Size(); nbr++)
-         {
-            // In Reduce operation: send_groups <--> recv_groups
-            const int num_recv_groups = nbr_send_groups.RowSize(nbr);
-            if (num_recv_groups > 0)
-            {
-               const int *grp_list = nbr_send_groups.GetRow(nbr);
-               const T *buf = (T*)group_buf.GetData() + buf_offsets[nbr];
-               for (int i = 0; i < num_recv_groups; i++)
-               {
-                  // Custom version of ReduceGroupFromBuffer that checks marker
-                  int gr = grp_list[i];
-                  const int *ldofs = (layout == 0) ?
-                                     group_ldof.GetRow(gr) : group_ltdof.GetRow(gr);
-                  const int nldofs = group_ldof.RowSize(gr);
-
-                  for (int j = 0; j < nldofs; j++)
-                  {
-                     if (marker[ldofs[j]])
-                     {
-                        // Create a temporary OpData with just this one DOF
-                        OpData<T> opd;
-                        opd.ldata = ldata;
-                        opd.buf = const_cast<T*>(buf) + j;
-                        opd.ldofs = ldofs + j;
-                        opd.nldofs = 1;
-                        opd.nb = 1;
-
-                        // Apply the operation
-                        Op(opd);
-                     }
-                  }
-
-                  buf += nldofs;
-               }
-            }
-         }
-         break;
-      }
-   }
-
-   comm_lock = 0; // 0 - no lock
-   num_requests = 0;
-}
-
 template <class T>
 void GroupCommunicator::Sum(OpData<T> opd)
 {
@@ -1291,8 +1171,6 @@ void GroupCommunicator::Max(OpData<T> opd)
 template <class T>
 void GroupCommunicator::BitOR(OpData<T> opd)
 {
-   static_assert(std::is_integral<T>::value,
-                 "BitOR reduction requires an integral type.");
    for (int i = 0; i < opd.nldofs; i++)
    {
       T data = opd.ldata[opd.ldofs[i]];
@@ -1304,33 +1182,6 @@ void GroupCommunicator::BitOR(OpData<T> opd)
    }
 }
 
-template <class T>
-void GroupCommunicator::MaxAbs(OpData<T> opd)
-{
-   for (int i = 0; i < opd.nldofs; i++)
-   {
-      T data = opd.ldata[opd.ldofs[i]];
-      T abs_data = std::abs(data);
-
-      for (int j = 0; j < opd.nb; j++)
-      {
-         T b = opd.buf[j*opd.nldofs+i];
-         T abs_b = std::abs(b);
-
-         // On an equal-magnitude tie keep the more positive value, so
-         // opposite-sign ties resolve deterministically to the positive one.
-         if (abs_data < abs_b || (abs_data == abs_b && data < b))
-         {
-            data = b;
-            abs_data = abs_b;
-         }
-      }
-
-      opd.ldata[opd.ldofs[i]] = data;
-   }
-}
-
-
 void GroupCommunicator::PrintInfo(std::ostream &os) const
 {
    char c = '\0';
@@ -1467,24 +1318,18 @@ template void GroupCommunicator::BcastEnd<int>(int *, int) const;
 template void GroupCommunicator::ReduceBegin<int>(const int *) const;
 template void GroupCommunicator::ReduceEnd<int>(
    int *, int, void (*)(OpData<int>)) const;
-template void GroupCommunicator::ReduceMarked<int>(
-   int*, const Array<int>&, int, void (*)(OpData<int>)) const;
 
 template void GroupCommunicator::BcastBegin<double>(double *, int) const;
 template void GroupCommunicator::BcastEnd<double>(double *, int) const;
 template void GroupCommunicator::ReduceBegin<double>(const double *) const;
 template void GroupCommunicator::ReduceEnd<double>(
    double *, int, void (*)(OpData<double>)) const;
-template void GroupCommunicator::ReduceMarked<double>(
-   double*, const Array<int>&, int, void (*)(OpData<double>)) const;
 
 template void GroupCommunicator::BcastBegin<float>(float *, int) const;
 template void GroupCommunicator::BcastEnd<float>(float *, int) const;
 template void GroupCommunicator::ReduceBegin<float>(const float *) const;
 template void GroupCommunicator::ReduceEnd<float>(
    float *, int, void (*)(OpData<float>)) const;
-template void GroupCommunicator::ReduceMarked<float>(
-   float*, const Array<int>&, int, void (*)(OpData<float>)) const;
 
 // @endcond
 
@@ -1493,17 +1338,14 @@ template void GroupCommunicator::Sum<int>(OpData<int>);
 template void GroupCommunicator::Min<int>(OpData<int>);
 template void GroupCommunicator::Max<int>(OpData<int>);
 template void GroupCommunicator::BitOR<int>(OpData<int>);
-template void GroupCommunicator::MaxAbs<int>(OpData<int>);
 
 template void GroupCommunicator::Sum<double>(OpData<double>);
 template void GroupCommunicator::Min<double>(OpData<double>);
 template void GroupCommunicator::Max<double>(OpData<double>);
-template void GroupCommunicator::MaxAbs<double>(OpData<double>);
 
 template void GroupCommunicator::Sum<float>(OpData<float>);
 template void GroupCommunicator::Min<float>(OpData<float>);
 template void GroupCommunicator::Max<float>(OpData<float>);
-template void GroupCommunicator::MaxAbs<float>(OpData<float>);
 
 
 #ifdef __bgq__

general/communication.hpp

@@ -22,7 +22,6 @@
 #include "globals.hpp"
 #include <mpi.h>
 #include <cstdint>
-#include <type_traits>
 
 // can't directly use MPI_CXX_BOOL because Microsoft's MPI implementation
 // doesn't include MPI_CXX_BOOL. Fallback to MPI_C_BOOL if unavailable.
@@ -409,38 +408,14 @@ public:
    template <class T> void Reduce(Array<T> &ldata, void (*Op)(OpData<T>)) const
    { Reduce<T>((T *)ldata, Op); }
 
-   /// Reduce operation Sum, instantiated for int, double and float
+   /// Reduce operation Sum, instantiated for int and double
    template <class T> static void Sum(OpData<T>);
-   /// Reduce operation Min, instantiated for int, double and float
+   /// Reduce operation Min, instantiated for int and double
    template <class T> static void Min(OpData<T>);
-   /// Reduce operation Max, instantiated for int, double and float
+   /// Reduce operation Max, instantiated for int and double
    template <class T> static void Max(OpData<T>);
    /// Reduce operation bitwise OR, instantiated for int only
    template <class T> static void BitOR(OpData<T>);
-   /// Reduce operation selecting the signed value with the largest absolute
-   /// value, instantiated for int, double and float. The result keeps its sign;
-   /// it is not the non-negative absolute value. Equal-magnitude ties are
-   /// broken deterministically toward the more positive value, so opposite-sign
-   /// ties resolve to the positive one regardless of accumulation order.
-   template <class T> static void MaxAbs(OpData<T>);
-
-   /** @brief Finalize reduction operation started with ReduceBegin(), but only apply
-       the reduction to DOFs marked in the marker array.
-
-       @note The reduction is carried out in the signed type @a T, so the result
-       is signed even for bitwise operations.
-   */
-   template <class T>
-   void ReduceMarked(T *ldata, const Array<int> &marker, int layout,
-                     void (*Op)(OpData<T>)) const;
-
-   /** @brief Reduce within each group where the master is the root, but only for marked DOFs. */
-   template <class T>
-   void Reduce(T *ldata, const Array<int> &marker, void (*Op)(OpData<T>)) const
-   {
-      ReduceBegin(ldata);
-      ReduceMarked(ldata, marker, 0, Op);
-   }
 
    /// Print information about the GroupCommunicator from all MPI ranks.
    void PrintInfo(std::ostream &out = mfem::out) const;

general/cuda.hpp

@@ -18,8 +18,14 @@
 // CUDA block size used by MFEM.
 #define MFEM_CUDA_BLOCKS 256
 
-#if defined(MFEM_USE_CUDA)
+#if defined(MFEM_USE_CUDA) && defined(__CUDACC__)
 #define MFEM_USE_CUDA_OR_HIP
+constexpr bool mfem_use_gpu = true;
+#define MFEM_DEVICE __device__
+#define MFEM_HOST __host__
+#define MFEM_LAMBDA __host__
+#define MFEM_LAUNCH_BOUNDS __launch_bounds__
+// #define MFEM_HOST_DEVICE __host__ __device__ // defined in config/config.hpp
 #define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(cudaDeviceSynchronize())
 #define MFEM_STREAM_SYNC MFEM_GPU_CHECK(cudaStreamSynchronize(0))
 // Define a CUDA error check macro, MFEM_GPU_CHECK(x), where x returns/is of
@@ -34,15 +40,6 @@
     }                                                                          \
   } while (0)
 
-// Macros defined only when compiling with CUDA language
-#if defined(__CUDACC__)
-#define MFEM_USE_CUDA_OR_HIP_LANG
-#define MFEM_DEVICE __device__
-#define MFEM_HOST __host__
-#define MFEM_LAMBDA __host__
-#define MFEM_LAUNCH_BOUNDS __launch_bounds__
-// #define MFEM_HOST_DEVICE __host__ __device__ // defined in config/config.hpp
-
 // Define the MFEM inner threading macros
 #if defined(__CUDA_ARCH__)
 #define MFEM_SHARED __shared__
@@ -70,13 +67,12 @@
    if (int ix = threadIdx.k % (OX), iy = threadIdx.k / (OX), iz = iy / (OY);   \
        (ix < (SX)) && ((iy %= (OY)) < (SY)) && (iz < (SZ)))
 #endif // defined(__CUDA_ARCH__)
-#endif // defined(__CUDACC__)
-#endif // defined(MFEM_USE_CUDA)
+#endif // defined(MFEM_USE_CUDA) && defined(__CUDACC__)
 
 namespace mfem
 {
 
-#if defined(MFEM_USE_CUDA)
+#if defined(MFEM_USE_CUDA) && defined(__CUDACC__)
 // Function used by the macro MFEM_GPU_CHECK.
 void mfem_cuda_error(cudaError_t err, const char *expr, const char *func,
                      const char *file, int line);