Added support for MultiVector and cleaned up.

ComplexGridFunction Lp error implementation

.github/workflows/README.md

@@ -29,16 +29,12 @@ Runs a number of static repository-level sanity checks.
 
 - `branch-history` guards against accidental commits of large files using the `--history` option of the `config/githooks/pre-push` script.
 
-## `mfem-analysis.yml` (`build-analysis`)
-
-Checks if the code builds and satisfies minimal requirements.
-
-- `gitignore` builds hypre, METIS, and MFEM using `mfem/github-actions/build-hypre`, `mfem/github-actions/build-metis`, and `mfem/github-actions/build-mfem` and checks for correct `.gitignore` settings by running the `tests/scripts/gitignore` script.
-
 ## `builds-and-tests.yml`
 
 Runs a matrix of builds and tests runs with different compilers, OS, mfem/hypre settings, etc. Also processes and upload Codecov reports.
 
+One matrix job runs `tests/scripts/gitignore` after `make test-noclean` to check generated artifacts against `.gitignore`.
+
 Uses the following GitHub Actions from <https://github.com/mfem/github-actions>:
 
 - `mfem/github-actions/build-hypre`

.github/workflows/builds-and-tests.yml

@@ -111,6 +111,7 @@ jobs:
             build-system: make
             hypre-target: int64
             precision: fp64
+            gitignore-check: YES
           - os: ubuntu-latest
             target: opt
             codecov: NO
@@ -317,7 +318,13 @@ jobs:
       - name: tests
         if: matrix.build-system == 'make' && (matrix.target == 'opt' || matrix.os == 'ubuntu-latest')
         run: |
-          cd ${{ env.MFEM_TOP_DIR }} && make test
+          cd ${{ env.MFEM_TOP_DIR }}
+          if [[ "${{ matrix.gitignore-check }}" == "YES" ]]; then
+            make test-noclean
+          else
+            make test
+          fi
+        shell: bash
 
       - name: cmake checks
         if: matrix.build-system == 'cmake' && matrix.target == 'dbg'
@@ -369,3 +376,9 @@ jobs:
           directories: "fem general linalg mesh"
         env:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
+
+      - name: gitignore
+        if: matrix.gitignore-check == 'YES'
+        run: |
+          cd ${{ env.MFEM_TOP_DIR }}/tests/scripts
+          ./runtest gitignore

.github/workflows/codeql-analysis.yml

@@ -14,9 +14,19 @@ name: "Static Analysis"
 on:
   push:
     branches: ["master", "next"]
+    paths-ignore: &docs-only-paths
+      - "**/*.md"
+      - "doc/**"
+      - ".binder/**"
+      - "CITATION.cff"
+      - "LICENSE"
+      - "NOTICE"
+      - "CHANGELOG"
+      - "INSTALL"
   pull_request:
     # The branches below must be a subset of the branches above
     branches: ["master"]
+    paths-ignore: *docs-only-paths
 
 concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}

.github/workflows/mfem-analysis.yml

@@ -1,102 +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.
-
-name: "Build Analysis"
-
-permissions:
-  actions: write
-
-on:
-  push:
-    branches:
-      - master
-      - next
-  pull_request:
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref }}
-  cancel-in-progress: true
-
-env:
-  HYPRE_ARCHIVE: v2.19.0.tar.gz
-  HYPRE_TOP_DIR: hypre-2.19.0
-  METIS_ARCHIVE: metis-4.0.3.tar.gz
-  METIS_TOP_DIR: metis-4.0.3
-  COVERAGE_ENV: mfem-coverage
-  MFEM_ACTIONS_VERSION: v2.7
-
-jobs:
-  gitignore:
-    runs-on: ubuntu-latest
-
-    steps:
-      - name: checkout MFEM
-        uses: actions/checkout@v6
-        with:
-          path: mfem
-
-      - name: Get MPI (Linux)
-        run: |
-          sudo apt-get install openmpi-bin libopenmpi-dev
-          export OMPI_MCA_rmaps_base_oversubscribe=1
-
-      - name: Cache Hypre Install
-        id: hypre-cache
-        uses: actions/cache@v5
-        with:
-          path: ${{ env.HYPRE_TOP_DIR }}
-          key: ${{ runner.os }}-ompi-build-${{ env.HYPRE_TOP_DIR }}-int32-fp64-${{ env.MFEM_ACTIONS_VERSION }}
-
-      - name: Get Hypre
-        if: steps.hypre-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.7
-        with:
-          archive: ${{ env.HYPRE_ARCHIVE }}
-          dir: ${{ env.HYPRE_TOP_DIR }}
-          target: int32
-          precision: fp64
-
-      - name: Cache Metis Install
-        id: metis-cache
-        uses: actions/cache@v5
-        with:
-          path: ${{ env.METIS_TOP_DIR }}
-          key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-${{ env.MFEM_ACTIONS_VERSION }}
-
-      - name: Install Metis
-        if: steps.metis-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.7
-        with:
-          archive: ${{ env.METIS_ARCHIVE }}
-          dir: ${{ env.METIS_TOP_DIR }}
-
-      # MFEM build and test
-      - name: build-mfem
-        uses: mfem/github-actions/build-mfem@v2.7
-        with:
-          os: ${{ runner.os }}
-          target: opt
-          codecov: NO
-          mpi: par
-          build-system: make
-          hypre-dir: ${{ env.HYPRE_TOP_DIR }}
-          metis-dir: ${{ env.METIS_TOP_DIR }}
-          mfem-dir: mfem
-
-      - name: test (no clean)
-        run: |
-          cd mfem && make test-noclean
-
-      - name: gitignore
-        run: |
-          cd mfem/tests/scripts
-          ./runtest gitignore

.github/workflows/sanitizers.yml

@@ -17,7 +17,17 @@ permissions:
 on:
   push:
     branches: ["master", "next"]
+    paths-ignore: &docs-only-paths
+      - "**/*.md"
+      - "doc/**"
+      - ".binder/**"
+      - "CITATION.cff"
+      - "LICENSE"
+      - "NOTICE"
+      - "CHANGELOG"
+      - "INSTALL"
   pull_request:
+    paths-ignore: *docs-only-paths
   workflow_dispatch:
 
 concurrency:

CHANGELOG

@@ -15,6 +15,10 @@ Version 4.9.1 (development)
 
 Discretization improvements
 ---------------------------
+- Improved FindPointsGSLIB surface mesh capability with support for simplices
+  and an option to specify axis-aligned bounding box padding for near-surface
+  point queries.
+
 - Added GPU-enabled partial assembly for simplicial Bernstein H1 basis based on
   ragged tensor algorithms (see DOI: 10.1137/11082539X) for mass and diffusion
   integrators.
@@ -66,6 +70,8 @@ Linear and nonlinear solvers
 
 GPU computing
 -------------
+- Added device assembly support for 3D H(curl) VectorFEDomainLFIntegrator.
+
 - 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.

CONTRIBUTING.md

@@ -6,7 +6,6 @@
 <a href="https://github.com/mfem/mfem/blob/master/LICENSE"><img alt="License" src="https://img.shields.io/badge/License-BSD-blue.svg"></a>
 <a href="https://github.com/mfem/mfem/releases/latest"><img alt="GitHub release" src="https://img.shields.io/github/v/release/mfem/mfem"></a>
 <a href="https://github.com/mfem/mfem/actions/workflows/repo-check.yml?query=branch%3Amaster"><img alt="Repo check" src="https://github.com/mfem/mfem/actions/workflows/repo-check.yml/badge.svg?branch=master"></a>
-<a href="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml?query=branch%3Amaster"><img alt="Build Analysis" src="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml/badge.svg?branch=master"></a>
 <a href="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml?query=branch%3Amaster"><img alt="Builds and Tests" src="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml/badge.svg?branch=master"></a>
 <a href="https://ci.appveyor.com/project/mfem/mfem"><img alt="Build Status" src="https://ci.appveyor.com/api/projects/status/19non9sqm6msi2wy?svg=true"></a>
 <a href="https://docs.mfem.org/html/index.html"><img alt="Documentation" src="https://img.shields.io/badge/code-documented-brightgreen.svg"></a>

config/cmake/modules/FindGSLIB.cmake

@@ -18,19 +18,17 @@
 
 if (MFEM_FETCH_GSLIB OR MFEM_FETCH_TPLS)
   enable_language(C)
-  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
   set(GSLIB_FETCH_VERSION 1.0.9)
-  set(GSLIB_C_FLAGS ${CMAKE_C_FLAGS_${BUILD_TYPE}})
-  if (CMAKE_C_FLAGS)
-    set(GSLIB_C_FLAGS "${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
-  endif()
-  if (BUILD_SHARED_LIBS)
-    set(GSLIB_C_FLAGS "${GSLIB_C_FLAGS} -fPIC")
-  endif()
   add_library(GSLIB STATIC IMPORTED)
+  # set options (technically flags because GSLIB does not use cmake)
+  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
+  set(GSLIB_FLAGS "${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
+  if (BUILD_SHARED_LIBS)
+    set(GSLIB_FLAGS "${GSLIB_FLAGS} -fPIC")
+  endif()
   # define external project and create future include directory so it is present
   # to pass CMake checks at end of MFEM configuration step
-  message(STATUS "Will fetch GSLIB ${GSLIB_FETCH_VERSION} to be built with ${GSLIB_C_FLAGS}")
+  message(STATUS "Will fetch GSLIB ${GSLIB_FETCH_VERSION} to be built with ${GSLIB_FLAGS}")
   set(PREFIX ${CMAKE_BINARY_DIR}/fetch/gslib)
   include(ExternalProject)
   ExternalProject_Add(gslib
@@ -40,7 +38,7 @@ if (MFEM_FETCH_GSLIB OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     PREFIX ${PREFIX}
     CONFIGURE_COMMAND ""
-    BUILD_COMMAND cd ${PREFIX}/src/gslib && $(MAKE) clean && $(MAKE) DESTDIR=${PREFIX} MPI=$<BOOL:${MFEM_USE_MPI}> "CFLAGS= ${GSLIB_C_FLAGS}"
+    BUILD_COMMAND cd ${PREFIX}/src/gslib && $(MAKE) clean && $(MAKE) DESTDIR=${PREFIX} MPI=$<BOOL:${MFEM_USE_MPI}> "CFLAGS=${GSLIB_FLAGS}"
     INSTALL_COMMAND "")
   file(MAKE_DIRECTORY ${PREFIX}/include)
   # set imported library target properties

config/cmake/modules/FindHYPRE.cmake

@@ -44,6 +44,9 @@ if (MFEM_FETCH_HYPRE OR MFEM_FETCH_TPLS)
   # set options and associated dependencies
   set(HYPRE_CMAKE_OPTIONS "")
   list(APPEND HYPRE_CMAKE_OPTIONS -DCMAKE_BUILD_TYPE:STRING=${CMAKE_BUILD_TYPE})
+  if (BUILD_SHARED_LIBS)
+    list(APPEND HYPRE_CMAKE_OPTIONS -DCMAKE_POSITION_INDEPENDENT_CODE:BOOL=ON)
+  endif()
   # collect all HYPRE_ENABLE variables and pass them to hypre, assuming they are BOOL.
   get_cmake_property(all_vars VARIABLES)
   foreach(var ${all_vars})
@@ -95,7 +98,6 @@ if (MFEM_FETCH_HYPRE OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     SOURCE_SUBDIR src
     PREFIX ${HYPRE_INSTALL}
-    BUILD_COMMAND ${CMAKE_COMMAND} --build . -- -j${CMAKE_BUILD_PARALLEL_LEVEL}
     CMAKE_CACHE_ARGS -DCMAKE_INSTALL_PREFIX:PATH=${HYPRE_INSTALL} -DCMAKE_INSTALL_LIBDIR:PATH=lib ${HYPRE_CMAKE_OPTIONS})
   file(MAKE_DIRECTORY ${HYPRE_INSTALL}/include)
   # set imported library target properties

config/cmake/modules/FindMETIS.cmake

@@ -19,10 +19,18 @@
 #   - METIS_VERSION_5 (cache variable)
 
 if (MFEM_FETCH_METIS OR MFEM_FETCH_TPLS)
+  enable_language(C)
   set(METIS_FETCH_VERSION 4.0.3)
   add_library(METIS STATIC IMPORTED)
+  # set options (technically flags because METIS does not use cmake)
+  set(METIS_FLAGS "-Wno-implicit-int -Wno-incompatible-pointer-types")
+  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
+  set(METIS_FLAGS "${METIS_FLAGS} ${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
+  if (BUILD_SHARED_LIBS)
+    set(METIS_FLAGS "${METIS_FLAGS} -fPIC")
+  endif()
   # define external project
-  message(STATUS "Will fetch METIS ${METIS_FETCH_VERSION} to be built with default options")
+  message(STATUS "Will fetch METIS ${METIS_FETCH_VERSION} to be built with ${METIS_FLAGS}")
   set(PREFIX ${CMAKE_BINARY_DIR}/fetch/metis)
   include(ExternalProject)
   ExternalProject_Add(metis
@@ -32,7 +40,7 @@ if (MFEM_FETCH_METIS OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     PREFIX ${PREFIX}
     CONFIGURE_COMMAND tar -xzf ../metis/metis-${METIS_FETCH_VERSION}-mac.tgz --strip=1
-    BUILD_COMMAND $(MAKE) COPTIONS=-Wno-incompatible-pointer-types
+    BUILD_COMMAND $(MAKE) clean && $(MAKE) "OPTFLAGS=${METIS_FLAGS}"
     INSTALL_COMMAND mkdir -p ${PREFIX}/lib && cp libmetis.a ${PREFIX}/lib/)
   # set imported library target properties
   add_dependencies(METIS metis)

config/cmake/modules/FindSuiteSparse.cmake

@@ -22,15 +22,15 @@ include(MfemCmakeUtilities)
 mfem_find_package(SuiteSparse SuiteSparse SuiteSparse_DIR "" "" "" ""
   "Paths to headers required by SuiteSparse."
   "Libraries required by SuiteSparse."
-  ADD_COMPONENT "UMFPACK" "include;suitesparse" umfpack.h "lib" umfpack
-  ADD_COMPONENT "KLU" "include;suitesparse" klu.h "lib" klu
-  ADD_COMPONENT "AMD" "include;suitesparse" amd.h "lib" amd
-  ADD_COMPONENT "BTF" "include;suitesparse" btf.h "lib" btf
-  ADD_COMPONENT "CHOLMOD" "include;suitesparse" cholmod.h "lib" cholmod
-  ADD_COMPONENT "COLAMD" "include;suitesparse" colamd.h "lib" colamd
-  ADD_COMPONENT "CAMD" "include;suitesparse" camd.h "lib" camd
-  ADD_COMPONENT "CCOLAMD" "include;suitesparse" ccolamd.h "lib" ccolamd
-  ADD_COMPONENT "config" "include;suitesparse" SuiteSparse_config.h "lib"
+  ADD_COMPONENT "UMFPACK" "include;include/suitesparse;suitesparse" umfpack.h "lib" umfpack
+  ADD_COMPONENT "KLU" "include;include/suitesparse;suitesparse" klu.h "lib" klu
+  ADD_COMPONENT "AMD" "include;include/suitesparse;suitesparse" amd.h "lib" amd
+  ADD_COMPONENT "BTF" "include;include/suitesparse;suitesparse" btf.h "lib" btf
+  ADD_COMPONENT "CHOLMOD" "include;include/suitesparse;suitesparse" cholmod.h "lib" cholmod
+  ADD_COMPONENT "COLAMD" "include;include/suitesparse;suitesparse" colamd.h "lib" colamd
+  ADD_COMPONENT "CAMD" "include;include/suitesparse;suitesparse" camd.h "lib" camd
+  ADD_COMPONENT "CCOLAMD" "include;include/suitesparse;suitesparse" ccolamd.h "lib" ccolamd
+  ADD_COMPONENT "config" "include;include/suitesparse;suitesparse" SuiteSparse_config.h "lib"
     suitesparseconfig)
 
 if (SuiteSparse_FOUND AND METIS_VERSION_5)

fem/CMakeLists.txt

@@ -133,7 +133,7 @@ set(SRCS
   tmop/assemble/diag2.cpp
   tmop/assemble/grad2_limit.cpp
   tmop/assemble/grad2.cpp
-  tmop/assemble/diag3_limit.cpp  
+  tmop/assemble/diag3_limit.cpp
   tmop/assemble/diag3.cpp
   tmop/assemble/grad3_limit.cpp
   tmop/assemble/grad3.cpp
@@ -311,6 +311,7 @@ set(HDRS
   tmop_tools.hpp
   tmop_amr.hpp
   gslib.hpp
+  gslib/gslib_kernel_helpers.hpp
   transfer.hpp
   hyperbolic.hpp
   integrator.hpp

fem/coefficient.cpp

@@ -54,6 +54,8 @@ void Coefficient::Project(QuadratureFunction &qf)
    QuadratureSpaceBase &qspace = *qf.GetSpace();
    const int ne = qspace.GetNE();
    Vector values;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);
@@ -327,6 +329,8 @@ void VectorCoefficient::Project(QuadratureFunction &qf)
    const int ne = qspace.GetNE();
    DenseMatrix values;
    Vector col;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);
@@ -695,6 +699,8 @@ void MatrixCoefficient::Project(QuadratureFunction &qf, bool transpose)
    QuadratureSpaceBase &qspace = *qf.GetSpace();
    const int ne = qspace.GetNE();
    DenseMatrix values, matrix;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);

fem/complex_fem.cpp

@@ -237,6 +237,81 @@ ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
    gfi->SyncAliasMemory(*this);
 }
 
+real_t
+ComplexGridFunction::ComputeLpError(const real_t p,
+                                    Coefficient &exsolr,
+                                    Coefficient &exsoli,
+                                    Coefficient *weight,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   real_t error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Vector valsr;
+   Vector valsi;
+
+   const GridFunction& gf_r = real();
+   const GridFunction& gf_i = imag();
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      if (elems != NULL && (*elems)[i] == 0) { continue; }
+      fe = fes->GetFE(i);
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         int intorder = 2*fe->GetOrder() + 3;
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      real_t elem_error = 0.0;
+      gf_r.GetValues(i, *ir, valsr);
+      gf_i.GetValues(i, *ir, valsi);
+      T = fes->GetElementTransformation(i);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         T->SetIntPoint(&ip);
+         real_t diffr = valsr(j) - exsolr.Eval(*T, ip);
+         real_t diffi = valsi(j) - exsoli.Eval(*T, ip);
+         real_t diff = hypot(diffr, diffi);
+         if (p < infinity())
+         {
+            diff = pow(diff, p);
+            if (weight)
+            {
+               diff *= weight->Eval(*T, ip);
+            }
+            elem_error += ip.weight * T->Weight() * diff;
+         }
+         else
+         {
+            if (weight)
+            {
+               diff *= weight->Eval(*T, ip);
+            }
+            error = std::max(error, diff);
+         }
+      }
+      if (p < infinity())
+      {
+         // negative quadrature weights may cause the error to be negative
+         error += fabs(elem_error);
+      }
+   }
+
+   if (p < infinity())
+   {
+      error = pow(error, 1./p);
+   }
+
+   return error;
+}
+
 void ComplexGridFunction::Save(std::ostream &os) const
 {
    os << "ComplexGridFunction\n";

fem/complex_fem.hpp

@@ -166,6 +166,75 @@ public:
       return sqrt(err_r * err_r + err_i * err_i);
    }
 
+   /// @brief Returns Max|u_ex - u_h| error for complex-valued H1 or L2 elements
+   ///
+   /// Compute the $L_\infty$ error across the entire domain.
+   ///
+   /// @param[in] exsolr  Coefficient object reproducing the real part of the
+   ///                    anticipated values of the scalar field, Re(u_ex).
+   /// @param[in] exsoli  Coefficient object reproducing the imaginary part of
+   ///                    the anticipated values of the scalar field, Im(u_ex).
+   /// @param[in] irs        Optional pointer to an array of custom integration
+   ///                       rules e.g. higher order than the default rules. If
+   ///                       present the array will be indexed by
+   ///                       Geometry::Type.
+   ///
+   /// @note Uses ComputeLpError internally. See the ComputeLpError
+   ///       documentation for generalizations of this error computation.
+   ///
+   /// @note If an array of integration rules is provided through @a irs, be
+   ///       sure to include valid rules for each element type that may occur
+   ///       in the list of elements.
+   ///
+   virtual real_t ComputeMaxError(Coefficient &exsolr,
+                                  Coefficient &exsoli,
+                                  const IntegrationRule *irs[] = NULL) const
+   {
+      return ComputeLpError(infinity(), exsolr, exsoli, NULL, irs);
+   }
+
+   /// @brief Returns ||u_ex - u_h||_Lp for complex-valued H1 or L2 elements
+   ///
+   /// Computes:
+   ///    $$(\sum_{elems} \int_{elem} w \, |u_{ex} - u_h|^p)^{1/p}$$
+   /// Where:
+   ///    $$|u_{ex} - u_h| = \sqrt{Re(u_{ex} - u_h)^2 + Im(u_{ex} - u_h)^2}$$
+   ///
+   /// @param[in] p       Real value indicating the exponent of the $L^p$ norm.
+   ///                    To avoid domain errors p should have a positive value,
+   ///                    either finite or infinite.
+   /// @param[in] exsolr  Coefficient object reproducing the real part of the
+   ///                    anticipated values of the scalar field, Re(u_ex).
+   /// @param[in] exsoli  Coefficient object reproducing the imaginary part of
+   ///                    the anticipated values of the scalar field, Im(u_ex).
+   /// @param[in] weight  Optional pointer to a Coefficient object reproducing
+   ///                    a weighting function, w.
+   /// @param[in] irs     Optional pointer to an array of custom integration
+   ///                    rules e.g. higher order than the default rules. If
+   ///                    present the array will be indexed by Geometry::Type.
+   /// @param[in] elems   Optional pointer to a marker array, with a length
+   ///                    equal to the number of local elements, indicating
+   ///                    which elements to integrate over. Only those elements
+   ///                    corresponding to non-zero entries in @a elems will
+   ///                    contribute to the computed L2 error.
+   ///
+   /// @note If an array of integration rules is provided through @a irs, be
+   ///       sure to include valid rules for each element type that may occur
+   ///       in the list of elements.
+   ///
+   /// @note Quadratures with negative weights (as in some simplex integration
+   ///       rules in MFEM) can produce negative integrals even with
+   ///       non-negative integrands. To avoid returning negative errors this
+   ///       function uses the absolute values of the element-wise integrals.
+   ///       This may lead to results which are not entirely consistent with
+   ///       such integration rules.
+   virtual real_t ComputeLpError(const real_t p,
+                                 Coefficient &exsolr,
+                                 Coefficient &exsoli,
+                                 Coefficient *weight = NULL,
+                                 const IntegrationRule *irs[] = NULL,
+                                 const Array<int> *elems = NULL) const;
+
    /// Save the ComplexGridFunction to an output stream.
    virtual void Save(std::ostream &out) const;
 

fem/datacollection.cpp

@@ -1181,12 +1181,14 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,
    DenseMatrix vval, pmat;
    std::vector<char> buf;
    int vec_dim = it->second->VectorDim();
+   int map_type = it->second->FESpace()->GetTypicalFE()->GetMapType();
    os << "<DataArray type=\"" << GetDataTypeString()
       << "\" Name=\"" << it->first
       << "\" NumberOfComponents=\"" << vec_dim << "\" "
       << VTKComponentLabels(vec_dim) << " "
       << "format=\"" << GetDataFormatString() << "\" >" << '\n';
-   if (vec_dim == 1)
+   if (vec_dim == 1 && (map_type == FiniteElement::VALUE ||
+                        map_type == FiniteElement::INTEGRAL))
    {
       for (int i = 0; i < mesh->GetNE(); i++)
       {

fem/datacollection.hpp

@@ -25,21 +25,35 @@
 namespace mfem
 {
 
-/// Lightweight adaptor over an std::map from strings to pointer to T
-template<typename T>
-class NamedFieldsMap
+/// Lightweight adaptor over an std::map from type K to type to V
+template<typename K, typename V,
+         typename = typename std::enable_if<std::is_default_constructible<V>::value>::type>
+class GenericFieldMap
 {
+private:
+   static constexpr bool ValueIsPointer = std::is_pointer<V>::value;
+
 public:
-   typedef std::map<std::string, T*> MapType;
+   typedef std::map<K, V> MapType;
    typedef typename MapType::iterator iterator;
    typedef typename MapType::const_iterator const_iterator;
 
-   /// Register field @a field with name @a fname
-   /** Replace existing field associated with @a fname (and optionally
-       delete associated pointer if @a own_data is true) */
-   void Register(const std::string& fname, T* field, bool own_data)
+   /// Register field @a field with name @a key
+   /// Only enabled if the template parameter V is not a pointer
+   template<typename = std::enable_if<!ValueIsPointer, bool>>
+   void Register(const K& key, V field)
    {
-      T*& ref = field_map[fname];
+      field_map[key] = field;
+   }
+
+   /// Register field @a field with name @a key
+   /** Replace existing field associated with @a key (and optionally
+       delete associated pointer if @a own_data is true).
+       Only enabled if the template parameter V is a pointer*/
+   template<typename = std::enable_if<ValueIsPointer, bool>>
+   void Register(const K& key, V field, bool own_data)
+   {
+      V& ref = field_map[key];
       if (own_data)
       {
          delete ref; // if newly allocated -> ref is null -> OK
@@ -47,23 +61,40 @@ public:
       ref = field;
    }
 
-   /// Unregister association between field @a field and name @a fname
-   /** Optionally delete associated pointer if @a own_data is true */
-   void Deregister(const std::string& fname, bool own_data)
+   /// Unregister association between field @a field and name @a key
+   /// Only enabled if the template parameter V is not a pointer
+   template<typename = std::enable_if<!ValueIsPointer, bool>>
+   void Deregister(const K& key)
    {
-      iterator it = field_map.find(fname);
+      iterator it = field_map.find(key);
+      if ( it != field_map.end() )
+      {
+         field_map.erase(it);
+      }
+   }
+
+   /// Unregister association between field @a field and name @a key
+   /** Optionally delete associated pointer if @a own_data is true.
+       Only enabled if the template parameter V is a pointer */
+   template<typename = std::enable_if<ValueIsPointer, bool>>
+   void Deregister(const K& key, bool own_data)
+   {
+      iterator it = field_map.find(key);
       if ( it != field_map.end() )
       {
          if (own_data)
          {
             delete it->second;
+            it->second = nullptr;
          }
          field_map.erase(it);
       }
    }
 
    /// Clear all associations between names and fields
-   /** Delete associated pointers when @a own_data is true */
+   /** Delete associated pointers when @a own_data is true.
+       Only enabled if the template parameter V is a pointer */
+   template<typename = std::enable_if<ValueIsPointer, bool>>
    void DeleteData(bool own_data)
    {
       for (iterator it = field_map.begin(); it != field_map.end(); ++it)
@@ -76,22 +107,37 @@ public:
       }
    }
 
-   /// Predicate to check if a field is associated with name @a fname
-   bool Has(const std::string& fname) const
+   /// Predicate to check if a field is associated with name @a key
+   bool Has(const K& key) const
    {
-      return field_map.find(fname) != field_map.end();
+      return field_map.find(key) != field_map.end();
    }
 
-   /// Get a pointer to the field associated with name @a fname
-   /** @return Pointer to field associated with @a fname or NULL */
-   T* Get(const std::string& fname) const
+   /// Get a pointer to the field associated with name @a key
+   /** @return Field associated with @a key or NULL,
+       if value is pointer and key not found */
+   V Get(const K& key) const
    {
-      const_iterator it = field_map.find(fname);
-      return it != field_map.end() ? it->second : NULL;
+      const_iterator it = field_map.find(key);
+      if (it != field_map.end())
+      {
+         return it->second;
+      }
+      else
+      {
+         if constexpr (ValueIsPointer)
+         {
+            return nullptr;
+         }
+         else
+         {
+            return V(); // Return default-constructed value for non-pointer types
+         }
+      }
    }
 
    /// Returns a const reference to the underlying map
-   const MapType& GetMap() const { return field_map; }
+   const MapType &GetMap() const { return field_map; }
 
    /// Returns the number of registered fields
    int NumFields() const { return field_map.size(); }
@@ -106,21 +152,24 @@ public:
    /// Returns an end const iterator to the registered fields
    const_iterator end() const { return field_map.end(); }
 
-   /// Returns an iterator to the field @a fname
-   iterator find(const std::string& fname)
-   { return field_map.find(fname); }
+   /// Returns an iterator to the field @a key
+   iterator find(const K& key)
+   { return field_map.find(key); }
 
-   /// Returns a const iterator to the field @a fname
-   const_iterator find(const std::string& fname) const
-   { return field_map.find(fname); }
+   /// Returns a const iterator to the field @a key
+   const_iterator find(const K& key) const
+   { return field_map.find(key); }
 
-   /// Clears the map of registered fields without reclaiming memory
+   /// Clears the map of registered fields
    void clear() { field_map.clear(); }
 
 protected:
    MapType field_map;
 };
 
+/// Lightweight adaptor over an std::map from strings to pointer to T
+template<typename T>
+using NamedFieldsMap = GenericFieldMap<std::string, T*>;
 
 /** A class for collecting finite element data that is part of the same
     simulation. Currently, this class groups together grid functions (fields),

fem/dfem/util.hpp

@@ -671,6 +671,20 @@ public:
                     MPI_COMM_WORLD);
    }
 
+   Operator& GetGradient(const Vector &x0) const override
+   {
+      x = x0;
+      f.UseDevice(x.UseDevice());
+      xpev.UseDevice(x.UseDevice());
+
+      op.Mult(x, f);
+      const real_t xnorm_local = x.Norml2();
+      MPI_Allreduce(&xnorm_local, &xnorm, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
+                    MPI_COMM_WORLD);
+
+      return const_cast<FDJacobian&>(*this);
+   }
+
    void Mult(const Vector &v, Vector &y) const override
    {
       // See [1] for choice of eps.
@@ -725,11 +739,11 @@ public:
 
 private:
    const Operator &op;
-   Vector x, f;
+   mutable Vector x, f;
    mutable Vector xpev;
    real_t lambda = 1.0e-6;
    real_t fixed_eps;
-   real_t xnorm;
+   mutable real_t xnorm;
 };
 
 /// @brief Find the index of a field descriptor in a vector of field descriptors.

fem/gslib.hpp

@@ -12,6 +12,9 @@
 #ifndef MFEM_GSLIB
 #define MFEM_GSLIB
 
+#include <map>
+#include <vector>
+
 #include "../config/config.hpp"
 #ifdef MFEM_USE_MPI
 #include "pgridfunc.hpp"
@@ -119,6 +122,11 @@ protected:
    // IntegrationRules for simplex->Quad/Hex and to project to p_max in-case of
    // p-refinement.
    Array<IntegrationRule *> ir_split;
+   /// Integration rules built at the field polynomial order (only for surface
+   /// meshes when mesh order is not the same as gridfunction order).
+   Array<IntegrationRule *> ir_split_sol;
+   /// Order at which #ir_split_sol was built; -1 means not built.
+   int ir_split_sol_order = -1;
    Array<FiniteElementSpace *> fes_rst_map; //FESpaces to map Quad/Hex->Simplex
    Array<GridFunction *> gf_rst_map; // GridFunctions to map Quad/Hex->Simplex
    FiniteElementCollection *fec_map_lin;
@@ -134,6 +142,8 @@ protected:
    AvgType avgtype;             // average type used for L2 functions
    Array<int> split_element_map;
    Array<int> split_element_index;
+   // Geometry::Type (as int) of the original element for each split quad.
+   Array<int> split_element_geom;
    int        NE_split_total;   // total number of elements after mesh splitting
    int        mesh_points_cnt;  // number of mesh nodes
    // Tolerance to ignore points found beyond the mesh boundary.
@@ -141,6 +151,12 @@ protected:
    double     bdr_tol;
    // Use CPU functions for Mesh/GridFunction on device for gslib1.0.7
    bool       gpu_to_cpu_fallback = false;
+   // Check if a point is inside the oriented bounding box of an
+   // element before the Newton iteration.
+   // Note: only used in MFEM implementation (not in gslib) which currently
+   // supports GPU kernels for area meshes in 2D, volume meshes in 3D,
+   // and surface meshes in 1D/2D/3D.
+   bool       obb_check = true;
 
    // Device specific data used for FindPoints
    struct DEV_STRUCT
@@ -162,6 +178,10 @@ protected:
       mutable double surf_dist_tol;
    } DEV;
 
+   // Helper function to setup and free gslib's crystal router.
+   void SetupCrystal(); // Called inside Setup and SetupSurf_base
+   void FreeCrystal();  // Called inside FreeData
+
    /// Use GSLIB for communication and interpolation. Updates field_out on
    /// host.
    virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out,
@@ -182,12 +202,26 @@ protected:
                                                  IntegrationRule *irule,
                                                  int order);
 
+   /** @brief Build integration rules at the given @a order for each split mesh
+    *  and store them in @a ir_out. Requires that \ref SetupSplitMeshes has
+    *  already been called. */
+   virtual void SetupIntegrationRules(const int order,
+                                      Array<IntegrationRule *> &ir_out);
+
    /** @brief Helper function that calls \ref SetupSplitMeshes and
-    * \ref SetupIntegrationRuleForSplitMesh. */
+    * \ref SetupIntegrationRules. */
    virtual void SetupSplitMeshesAndIntegrationRules(const int order);
 
-   /// Get GridFunction value at the points expected by GSLIB.
-   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals) const;
+   /** @brief Get GridFunction value at the points expected by GSLIB.
+    *  @param[in]  gf_in       Grid function to evaluate.
+    *  @param[out] node_vals   Output values.
+    *  @param[in]  ir_in       If non-null, use these rules instead of #ir_split.
+    *  @param[in]  by_element  If true, output has element-major layout
+    *                          [nel][vdim][ndofs]; otherwise component-major
+    *                          layout [vdim][total_pts]. */
+   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals,
+                               const Array<IntegrationRule *> *ir_in = nullptr,
+                               bool by_element = false) const;
 
    /** @brief Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For
     *  simplices, find the original element number (that was split into
@@ -292,29 +326,60 @@ protected:
    void findptsedge_setup_2(DEV_STRUCT &devs,
                             const double *const elx[2],
                             const unsigned n,
-                            const uint nel,
+                            const unsigned int nel,
                             const unsigned m,
-                            const double bbox_tol,
-                            const uint local_hash_size,
-                            const uint global_hash_size);
+                            const double bbox_rel_size_inc,
+                            const unsigned int local_hash_size,
+                            const unsigned int global_hash_size,
+                            const Vector *aabb_sz_inc);
 
    /// Preprocess 3D surface mesh needed for FindPoints.
    void findptssurf_setup_3(DEV_STRUCT &devs,
                             const double *const elx[3],
                             const unsigned n,
-                            const uint nel,
+                            const unsigned int nel,
                             const unsigned m,
-                            const double bbox_tol,
-                            const uint local_hash_size,
-                            const uint global_hash_size,
-                            const int rD);
+                            const double bbox_rel_size_inc,
+                            const unsigned int local_hash_size,
+                            const unsigned int global_hash_size,
+                            const int rD,
+                            const Vector *aabb_sz_inc);
 
+   /** @brief Shared implementation for the public surface-setup methods.
+    *
+    *  @details Initializes the surface-search data structures, builds the
+    *  split-element representation expected by gslib, and constructs the
+    *  element bounding boxes used by the MFEM surface kernels.
+    *
+    *  If @a aabb_sz_inc is null, the setup stores the default oriented
+    *  bounding boxes and uses @a bbox_rel_size_inc as their relative size
+    *  increase factor.
+    *
+    *  If @a aabb_sz_inc is non-null, the setup stores axis-aligned bounding
+    *  boxes only, applies the requested absolute AABB expansion in each
+    *  physical direction, and adjusts the tolerance @a bdr_tol so points
+    *  found in the expanded region are classified as border points.
+    *
+    *  @param[in] m                  Input surface mesh.
+    *  @param[in] bbox_rel_size_inc  Relative size increase applied when
+    *                                expanding each element bounding box during
+    *                                setup.
+    *  @param[in] aabb_sz_inc        Optional total absolute AABB expansion
+    *                                applied to the stored axis-aligned
+    *                                bounding boxes after construction.
+    *  @param[in] newt_tol           Newton tolerance for the point-search
+    *                                kernels.
+    */
+   void SetupSurf_Base(Mesh &m,
+                       const double bbox_rel_size_inc,
+                       const Vector *aabb_sz_inc,
+                       const double newt_tol);
 public:
    /// Serial constructor
    FindPointsGSLIB();
 
    /// Serial constructor + setup with given Mesh (see \ref Setup)
-   FindPointsGSLIB(Mesh &mesh_in, const double bb_t = 0.1,
+   FindPointsGSLIB(Mesh &mesh_in, const double bbox_rel_size_inc = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
@@ -323,7 +388,7 @@ public:
    FindPointsGSLIB(MPI_Comm comm_);
 
    /// Constructor + setup with given ParMesh (see \ref Setup)
-   FindPointsGSLIB(ParMesh &mesh_in, const double bb_t = 0.1,
+   FindPointsGSLIB(ParMesh &mesh_in, const double bbox_rel_size_inc = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 #endif
@@ -339,23 +404,59 @@ public:
        Note: not tested with periodic (L2).
        Note: the input mesh \p m must have Nodes set.
 
-       @param[in] m         Input mesh.
-       @param[in] bb_t      (Optional) Relative size of bounding box around
-                            each element.
-       @param[in] newt_tol  (Optional) Newton tolerance for the gslib
-                            search methods.
-       @param[in] npt_max   (Optional) Number of points for simultaneous
-                            iteration. This alters performance and
-                            memory footprint.
+       @param[in] m                  Input mesh.
+       @param[in] bbox_rel_size_inc  (Optional) Relative size increase applied
+                                     when expanding each element bounding box.
+       @param[in] newt_tol           (Optional) Newton tolerance for the gslib
+                                     search methods.
+       @param[in] npt_max            (Optional) Number of points for
+                                     simultaneous iteration. This alters
+                                     performance and memory footprint.
    */
-   void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+   void Setup(Mesh &m, const double bbox_rel_size_inc = 0.1,
+              const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
    /// Preprocess the surface mesh to compute data for FindPoints.
    void SetupSurf(Mesh &m,
-                  const double bb_t = 0.1,
-                  const double newt_tol = 1.0e-12,
-                  const int npt_max = 256);
+                  const double bbox_rel_size_inc = 0.1,
+                  const double newt_tol = 1.0e-12);
+
+   /** @brief Preprocess the surface mesh to compute data for FindPoints using
+    *  absolute AABB expansion.
+    *
+    *  @details This method computes only axis-aligned bounding boxes and
+    *  increases their total length by a user-specified amount in each
+    *  physical direction. The absolute AABB expansion is applied
+    *  symmetrically to the lower and upper bounds.
+    *
+    *  The size of @a aabb_sz_inc determines how the expansion values are
+    *  interpreted:
+    *  - `1`: one expansion value used in every direction for every element
+    *  - `NElements`: one expansion value per element, reused in x/y/z
+    *    directions
+    *  - `SpaceDim`: one expansion value per physical direction, reused for
+    *    every element
+    *  - `NElements*SpaceDim`: one expansion value per element and direction,
+    *    ordered as `(dx1,dy1,dz1, ... dxN,dyN,dzN)`
+    *
+    *  This method disables the oriented bounding-box precheck because the
+    *  stored boxes are modified only in their axis-aligned representation.
+    *
+    *  @param[in] m                  Input surface mesh.
+    *  @param[in] aabb_sz_inc        Total absolute AABB expansion applied in
+    *                                each physical direction to the stored
+    *                                axis-aligned bounding boxes.
+    *  @param[in] newt_tol           Newton tolerance for the point-search
+    *                                kernels.
+    *
+    *  @note We disable the oriented bounding box check with this setup.
+    *        @a bdr_tol is also adjusted so that all points in the AABBs can
+    *        be found.
+    */
+   void SetupSurfWithAABBExpansion(Mesh &m, const Vector &aabb_sz_inc,
+                                   const double newt_tol = 1.0e-12);
+
 
    /** @brief Searches positions given in physical space by \p point_pos.
 
@@ -402,7 +503,8 @@ public:
    /// Setup FindPoints and search positions
    void FindPoints(Mesh &m, const Vector &point_pos,
                    const int point_pos_ordering = Ordering::byNODES,
-                   const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+                   const double bbox_rel_size_inc = 0.1,
+                   const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
    /** @brief Interpolation of field values at prescribed reference space
@@ -473,7 +575,12 @@ public:
     *  @details When using FindPoints, gslib may return points as found on the
     *  boundary even when they are slightly outside the domain. This tolerance
     *  is used to filter such points based on the distance^2 value and mark them
-    *  as not found.*/
+    *  as not found.
+    *
+    *  @note When the SetupSurfWithAABBExpansion method is used for surface
+    *  meshes, this tolerance is automatically computed based on the size of
+    *  expanded AABBs. Using this method will override that computed tolerance.
+    *  */
    virtual void SetDistanceToleranceForPointsFoundOnBoundary(double bdr_tol_)
    {
       bdr_tol = bdr_tol_;
@@ -608,25 +715,28 @@ public:
        Note: not tested with periodic meshes (L2).
        Note: the input mesh \p m must have Nodes set.
 
-       @param[in] m         Input mesh.
-       @param[in] meshid    A unique # for each overlapping mesh. This id is
-                            used to make sure that points being searched are not
-                            looked for in the mesh that they belong to.
-       @param[in] gfmax     (Optional) GridFunction in H1 that is used as a
-                            discriminator when one point is located in multiple
-                            meshes. The mesh that maximizes gfmax is chosen.
-                            For example, using the distance field based on the
-                            overlapping boundaries is helpful for convergence
-                            during Schwarz iterations.
-       @param[in] bb_t      (Optional) Relative size of bounding box around
-                            each element.
-       @param[in] newt_tol  (Optional) Newton tolerance for the gslib
-                            search methods.
-       @param[in] npt_max   (Optional) Number of points for simultaneous
-                            iteration. This alters performance and
-                            memory footprint.*/
-   void Setup(Mesh &m, const int meshid, GridFunction *gfmax = NULL,
-              const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+       @param[in] m                  Input mesh.
+       @param[in] meshid             A unique # for each overlapping mesh.
+                                     This id is used to make sure that points
+                                     being searched are not looked for in the
+                                     mesh that they belong to.
+       @param[in] gfmax              (Optional) GridFunction in H1 that is used
+                                     as a discriminator when one point is
+                                     located in multiple meshes. The mesh that
+                                     maximizes gfmax is chosen. For example,
+                                     using the distance field based on the
+                                     overlapping boundaries is helpful for
+                                     convergence during Schwarz iterations.
+       @param[in] bbox_rel_size_inc  (Optional) Relative size increase applied
+                                     when expanding each element bounding box.
+       @param[in] newt_tol           (Optional) Newton tolerance for the gslib
+                                     search methods.
+       @param[in] npt_max            (Optional) Number of points for
+                                     simultaneous iteration. This alters
+                                     performance and memory footprint.*/
+   void Setup(Mesh &m, const int meshid, GridFunction *gfmax = nullptr,
+              const double bbox_rel_size_inc = 0.1,
+              const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
    /** Searches positions given in physical space by \p point_pos. All output
@@ -682,7 +792,7 @@ class GSOPGSLIB
 protected:
    struct gslib::crystal *cr;               // gslib's internal data
    struct gslib::comm *gsl_comm;            // gslib's internal data
-   struct gslib::gs_data *gsl_data = NULL;
+   struct gslib::gs_data *gsl_data = nullptr;
    int num_ids;
 
 public:

fem/gslib/findpts_local_2.cpp

@@ -11,7 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -27,8 +27,6 @@
 #pragma GCC diagnostic pop
 #endif
 
-#include <climits>
-
 namespace mfem
 {
 #if GSLIB_RELEASE_VERSION >= 10009
@@ -54,127 +52,14 @@ struct findptsElementGPT_t
    double x[DIM], jac[DIM * DIM], hes[4];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-struct obbox_t
-{
-   double c0[DIM], A[DIM * DIM];
-   dbl_range_t x[DIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[DIM];
-   double fac[DIM];
-   unsigned int *offset;
-   int max;
-};
-
-// Eval the ith Lagrange interpolant and its first derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
-                                                       int i, const double *z,
-                                                       const double *lCoeff,
-                                                       int pN)
-{
-   double u0 = 1, u1 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2 * (x - z[j]);
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-}
-
-// Eval the ith Lagrange interpolant and its first and second derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
-                                                        int i, const double *z,
-                                                        const double *lCoeff,
-                                                        int pN)
-{
-   double u0 = 1, u1 = 0, u2 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2 * (x - z[j]);
-         u2 = d_j * u2 + u1;
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-   p0[2*pN+i] = 8.0 * lCoeff[i] * u2;
-}
-
-// Axis-aligned bounding box test.
-static MFEM_HOST_DEVICE inline double AABB_test(const obbox_t *const b,
-                                                const double x[2])
-{
-   double test = 1;
-   for (int d = 0; d < 2; ++d)
-   {
-      double b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
-      test = test < 0 ? test : b_d;
-   }
-   return test;
-}
-
-// Axis-aligned bounding box test followed by oriented bounding-box test.
-static MFEM_HOST_DEVICE inline double bbox_test(const obbox_t *const b,
-                                                const double x[2])
-{
-   const double bxyz = AABB_test(b, x);
-   if (bxyz < 0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[2];
-      for (int d = 0; d < 2; ++d)
-      {
-         dxyz[d] = x[d] - b->c0[d];
-      }
-      double test = 1;
-      for (int d = 0; d < 2; ++d)
-      {
-         double rst = 0;
-         for (int e = 0; e < 2; ++e)
-         {
-            rst += b->A[d * 2 + e] * dxyz[e];
-         }
-         double brst = (rst + 1) * (1 - rst);
-         test = test < 0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-// Element index corresponding to hash mesh that the point is located in.
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[2])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d = 2 - 1; d >= 0; --d)
-   {
-      sum *= n;
-      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
-      sum += i < 0 ? 0 : (n - 1 < i ? n - 1 : i);
-   }
-   return sum;
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<DIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<DIM>;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_first_der;
+using gslib::lag_eval_second_der;
 
 /*Solve Ax=y. A is row-major */
 static MFEM_HOST_DEVICE inline void lin_solve_2(double x[2], const double A[4],
@@ -185,12 +70,6 @@ static MFEM_HOST_DEVICE inline void lin_solve_2(double x[2], const double A[4],
    x[1] = idet*(A[0]*y[1] - A[2]*y[0]);
 }
 
-/* L2 norm squared. */
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[2])
-{
-   return x[0] * x[0] + x[1] * x[1];
-}
-
 /* the bit structure of flags is CSSRR
    the C bit --- 1<<4 --- is set when the point is converged
    RR is 0 = 00b if r is unconstrained,
@@ -352,7 +231,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *res,
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<2>(resid);
    const double decr = p->dist2 - dist2;
    const double pred = p->dist2p;
    for (int d = 0; d < 2; ++d)
@@ -695,25 +574,25 @@ static MFEM_HOST_DEVICE double tensor_ig2_j(double *g_partials,
 }
 
 template<int T_D1D = 0>
-static void FindPointsLocal2D_Kernel(const int npt,
-                                     const double tol,
-                                     const double *x,
-                                     const int point_pos_ordering,
-                                     const double *xElemCoord,
-                                     const int nel,
-                                     const double *wtend,
-                                     const double *boxinfo,
-                                     const int hash_n,
-                                     const double *hashMin,
-                                     const double *hashFac,
-                                     unsigned int *hashOffset,
-                                     unsigned int *const code_base,
-                                     unsigned int *const el_base,
-                                     double *const r_base,
-                                     double *const dist2_base,
-                                     const double *gll1D,
-                                     const double *lagcoeff,
-                                     const int pN = 0)
+static void FindPointsLocal2DKernel(const int npt,
+                                    const double tol,
+                                    const double *x,
+                                    const int point_pos_ordering,
+                                    const double *xElemCoord,
+                                    const int nel,
+                                    const double *wtend,
+                                    const double *boxinfo,
+                                    const int hash_n,
+                                    const double *hashMin,
+                                    const double *hashFac,
+                                    unsigned int *hashOffset,
+                                    unsigned int *const code_base,
+                                    unsigned int *const el_base,
+                                    double *const r_base,
+                                    double *const dist2_base,
+                                    const double *gll1D,
+                                    const double *lagcoeff,
+                                    const int pN = 0)
 {
    const int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D = T_D1D ? T_D1D : pN;
@@ -1175,30 +1054,45 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsLocal2D_Kernel<2>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<2>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 3:
-         return FindPointsLocal2D_Kernel<3>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<3>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 4:
-         return FindPointsLocal2D_Kernel<4>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<4>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 5:
-         return FindPointsLocal2D_Kernel<5>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<5>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       default:
-         return FindPointsLocal2D_Kernel(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                         pgslm, NE_split_total, pwt, pbb, DEV.lh_nx,
-                                         plhm, plhf, plho, pcode, pelem,
-                                         pref, pdist, pgll1d, plc, DEV.dof1d);
+         FindPointsLocal2DKernel(npt, DEV.newt_tol, pp,
+                                 point_pos_ordering, pgslm,
+                                 NE_split_total, pwt, pbb,
+                                 DEV.lh_nx, plhm, plhf, plho,
+                                 pcode, pelem, pref, pdist,
+                                 pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef DIM2

fem/gslib/findpts_local_3.cpp

@@ -11,9 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
-
-#include <climits>
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -59,128 +57,15 @@ struct findptsElemPt
    double x[DIM], jac[DIM * DIM], hes[18];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-
-struct obbox_t
-{
-   double c0[DIM], A[DIM * DIM];
-   dbl_range_t x[DIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[DIM];
-   double fac[DIM];
-   unsigned int *offset;
-   // int max;
-};
-
-// Eval the ith Lagrange interpolant and its first derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
-                                                       int i, const double *z,
-                                                       const double *lCoeff,
-                                                       int pN)
-{
-   double u0 = 1, u1 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2*(x-z[j]);
-         u1 = d_j*u1+u0;
-         u0 = d_j*u0;
-      }
-   }
-   p0[i] = lCoeff[i]*u0;
-   p0[pN+i] = 2.0*lCoeff[i]*u1;
-}
-
-// Eval the ith Lagrange interpolant and its first and second derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
-                                                        int i, const double *z,
-                                                        const double *lCoeff,
-                                                        int pN)
-{
-   double u0 = 1, u1 = 0, u2 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2*(x-z[j]);
-         u2 = d_j*u2+u1;
-         u1 = d_j*u1+u0;
-         u0 = d_j*u0;
-      }
-   }
-   p0[i] = lCoeff[i]*u0;
-   p0[pN+i] = 2.0*lCoeff[i]*u1;
-   p0[2*pN+i] = 8.0*lCoeff[i]*u2;
-}
-
-// Axis-aligned bounding box test.
-static MFEM_HOST_DEVICE inline double AABB_test(const obbox_t *const b,
-                                                const double x[3])
-{
-   double b_d;
-   for (int d = 0; d < 3; ++d)
-   {
-      b_d = (x[d]-b->x[d].min)*(b->x[d].max-x[d]);
-      if (b_d < 0) { return b_d; }
-   }
-   return b_d;
-}
-
-// Axis-aligned bounding box test followed by oriented bounding-box test.
-static MFEM_HOST_DEVICE inline double bbox_test(const obbox_t *const b,
-                                                const double x[3])
-{
-   const double bxyz = AABB_test(b, x);
-   if (bxyz < 0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[3];
-      for (int d = 0; d < 3; ++d)
-      {
-         dxyz[d] = x[d]-b->c0[d];
-      }
-      double test = 1;
-      for (int d = 0; d < 3; ++d)
-      {
-         double rst = 0;
-         for (int e = 0; e < 3; ++e)
-         {
-            rst += b->A[d*3+e]*dxyz[e];
-         }
-         double brst = (rst+1)*(1-rst);
-         test = test < 0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-// Element index corresponding to hash mesh that the point is located in.
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[3])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d = 3-1; d >= 0; --d)
-   {
-      sum *= n;
-      int i = (int)floor((x[d]-p->bnd[d].min)*p->fac[d]);
-      sum += i < 0 ? 0 : (n-1 < i ? n-1 : i);
-   }
-   return sum;
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<DIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<DIM>;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_first_der;
+using gslib::lag_eval_second_der;
+using gslib::lin_solve_sym_2;
 
 // Solve Ax=y. A is row-major.
 static MFEM_HOST_DEVICE inline void lin_solve_3(double x[3], const double A[9],
@@ -199,22 +84,6 @@ static MFEM_HOST_DEVICE inline void lin_solve_3(double x[3], const double A[9],
    x[2] = idet*(inv6*y[0]+inv7*y[1]+inv8*y[2]);
 }
 
-// Solve Ax=y. A is a symmetric 2x2 matrix.
-static MFEM_HOST_DEVICE inline void lin_solve_sym_2(double x[2],
-                                                    const double A[3],
-                                                    const double y[2])
-{
-   const double idet = 1 / (A[0]*A[2]-A[1]*A[1]);
-   x[0] = idet*(A[2]*y[0]-A[1]*y[1]);
-   x[1] = idet*(A[0]*y[1]-A[1]*y[0]);
-}
-
-// L2 norm.
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[3])
-{
-   return x[0]*x[0]+x[1]*x[1]+x[2]*x[2];
-}
-
 /* the bit structure of flags is CTTSSRR
    the C bit --- 1<<6 --- is set when the point is converged
    RR is 0 = 00b if r is unconstrained,
@@ -459,7 +328,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsPt *res,
                                                  const findptsPt *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<3>(resid);
    const double decr = p->dist2-dist2;
    const double pred = p->dist2p;
    for (int d = 0; d < 3; ++d)
@@ -1809,33 +1678,36 @@ void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
    {
       case 2:
          FindPointsLocal3DKernel<2>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    pgslm, NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist, pgll1d, plc);
          break;
       case 3:
          FindPointsLocal3DKernel<3>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    pgslm, NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist, pgll1d, plc);
          break;
       case 4:
          FindPointsLocal3DKernel<4>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    pgslm, NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist, pgll1d, plc);
          break;
       case 5:
          FindPointsLocal3DKernel<5>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    pgslm, NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist, pgll1d, plc);
          break;
       default:
-         FindPointsLocal3DKernel(npt, DEV.newt_tol, pp, point_pos_ordering, pgslm,
-                                 NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                                 plho, pcode, pelem, pref, pdist, pgll1d, plc,
+         FindPointsLocal3DKernel(npt, DEV.newt_tol, pp,
+                                 point_pos_ordering, pgslm,
+                                 NE_split_total, pwt, pbb,
+                                 DEV.lh_nx, plhm, plhf, plho,
+                                 pcode, pelem, pref, pdist, pgll1d, plc,
                                  DEV.dof1d);
+         break;
    }
 }
 #undef pMax

fem/gslib/findptsedge_local_2.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -52,113 +53,14 @@ struct findptsElementGPT_t
    double x[sDIM], jac[sDIM*rDIM], hes[sDIM*rDIM];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-
-struct obbox_t
-{
-   double c0[sDIM], A[sDIM*sDIM];
-   dbl_range_t x[sDIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[sDIM];
-   double fac[sDIM];
-   unsigned int *offset;
-};
-
-static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
-                                                        int i, const double *z,
-                                                        const double *lCoeff,
-                                                        int pN)
-{
-   double u0 = 1, u1 = 0, u2 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2 * (x-z[j]);
-         u2 = d_j * u2 + u1;
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
-   p0[i] = lCoeff[i] * u0;
-   p1[i] = 2.0 * lCoeff[i] * u1;
-   p2[i] = 8.0 * lCoeff[i] * u2;
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
-                                                      const double x[sDIM])
-{
-   double b_d;
-   for (int d=0; d<sDIM; ++d)
-   {
-      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
-      if (b_d < 0)   // if outside in any dimension
-      {
-         return b_d;
-      }
-   }
-   return b_d;       // only positive if inside
-}
-
-/* positive when given point is possibly inside given obbox b */
-static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
-                                                 const double x[sDIM])
-{
-   const double bxyz = obbox_axis_test(b,x);
-   if (bxyz<0)   // test if point is in AABB
-   {
-      return bxyz;
-   }
-   else   // test OBB only if inside AABB
-   {
-      double dxyz[sDIM];
-      for (int d=0; d<sDIM; ++d)
-      {
-         dxyz[d] = x[d] - b->c0[d];
-      }
-      double test = 1;
-      for (int d=0; d<sDIM; ++d)
-      {
-         double rst = 0;
-         for (int e=0; e<sDIM; ++e)
-         {
-            rst += b->A[d*2 + e] * dxyz[e];
-         }
-         double brst = (rst+1)*(1-rst);
-         test = test<0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-/* Hash index in the hash table to the elements that possibly contain the point x */
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[2])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d=sDIM-1; d>=0; --d)
-   {
-      sum *= n;
-      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
-      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
-   }
-   return sum;
-}
-
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[2])
-{
-   return x[0] * x[0] + x[1] * x[1];
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
 
 /* the bit structure of flags is CRR
    the C bit --- 1<<2 --- is set when the point is converged
@@ -187,29 +89,29 @@ static MFEM_HOST_DEVICE inline int point_index(const int x)
 /* check reduction in objective against prediction, and adjust
    trust region radius (p->tr) accordingly;
    may reject the prior step, returning 1; otherwise returns 0
-   sets out->dist2, out->index, out->x, out->oldr in any event,
-   leaving out->r, out->dr, out->flags to be set when returning 0 */
-static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[2],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<2>(resid);
    const double decr = p->dist2 - dist2;
    const double pred = p->dist2p;
-   out->x[0] = p->x[0];
-   out->x[1] = p->x[1];
-   out->oldr = p->r;
-   out->dist2 = dist2;
+   out_pt->x[0] = p->x[0];
+   out_pt->x[1] = p->x[1];
+   out_pt->oldr = p->r;
+   out_pt->dist2 = dist2;
    if (decr >= 0.01*pred)
    {
       if (decr >= 0.9*pred)   // very good iteration
       {
-         out->tr = p->tr*2;
+         out_pt->tr = p->tr*2;
       }
       else                    // somewhat good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -220,21 +122,21 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          "very good iteration" --- this doubles the trust radius,
          which is why we divide by 4 below */
       double v0 = fabs(p->r - p->oldr);
-      out->tr = v0/4.0;
-      out->dist2 = p->dist2;
-      out->r = p->oldr;
-      out->flags = p->flags>>3;
-      out->dist2p = -HUGE_VAL;
+      out_pt->tr = v0/4.0;
+      out_pt->dist2 = p->dist2;
+      out_pt->r = p->oldr;
+      out_pt->flags = p->flags>>3;
+      out_pt->dist2p = -HUGE_VAL;
       if (pred < dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge( findptsElementPoint_t *const
-                                                 out,
+                                                 out_pt,
                                                  const double jac[2],
                                                  const double rhess,
                                                  const double resid[2],
@@ -304,9 +206,9 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r = newr;
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+   out_pt->r = newr;
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
 }
 
 static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
@@ -332,26 +234,27 @@ static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
 }
 
 template<int T_D1D = 0>
-static void FindPointsEdgeLocal2D_Kernel( const int     npt,
-                                          const double  tol,
-                                          const double  dist2tol,
-                                          const double  *x,
-                                          const int     point_pos_ordering,
-                                          const double  *xElemCoord,
-                                          const int     nel,
-                                          const double  *wtend,
-                                          const double  *boxinfo,
-                                          const int     hash_n,
-                                          const double  *hashMin,
-                                          const double  *hashFac,
-                                          unsigned int  *hashOffset,
-                                          unsigned int *const code_base,
-                                          unsigned int *const el_base,
-                                          double *const r_base,
-                                          double *const dist2_base,
-                                          const double  *gll1D,
-                                          const double  *lagcoeff,
-                                          const int     pN = 0 )
+static void FindPointsEdgeLocal2DKernel( const int     npt,
+                                         const double  tol,
+                                         const double  dist2tol,
+                                         const double  *x,
+                                         const int     point_pos_ordering,
+                                         const double  *xElemCoord,
+                                         const int     nel,
+                                         const double  *wtend,
+                                         const double  *boxinfo,
+                                         const bool    obb_check,
+                                         const int     hash_n,
+                                         const double  *hashMin,
+                                         const double  *hashFac,
+                                         unsigned int  *hashOffset,
+                                         unsigned int *const code_base,
+                                         unsigned int *const el_base,
+                                         double *const r_base,
+                                         double *const dist2_base,
+                                         const double  *gll1D,
+                                         const double  *lagcoeff,
+                                         const int     pN = 0 )
 {
    const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D   = T_D1D ? T_D1D : pN;
@@ -412,22 +315,34 @@ static void FindPointsEdgeLocal2D_Kernel( const int     npt,
       {
          const unsigned int el = *elp;
 
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            box.c0[idx] = boxinfo[n_box_ents*el + idx];
-            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
-            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            for (int idx = 0; idx < sDIM; ++idx)
+            {
+               box.c0[idx] = boxinfo[n_box_ents*el + idx];
+               box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+               box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            }
+            for (int idx = 0; idx < sDIM2; ++idx)
+            {
+               box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
+         }
+         else
+         {
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         for (int idx = 0; idx < sDIM2; ++idx)
-         {
-            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
-         }
-
-         if (obbox_test(&box,x_i)>=0)
+         if (pass_bb)
          {
             //------------ findpts_local ------------------
             {
@@ -684,28 +599,41 @@ void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsEdgeLocal2D_Kernel<2>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal2DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 3:
-         return FindPointsEdgeLocal2D_Kernel<3>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal2DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 4:
-         return FindPointsEdgeLocal2D_Kernel<4>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal2DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       default:
-         return FindPointsEdgeLocal2D_Kernel(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+         FindPointsEdgeLocal2DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef sDIM

fem/gslib/findptsedge_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -54,117 +55,14 @@ struct findptsElementGPT_t
    double x[sDIM], jac[sDIM], hes[sDIM*(1+1)];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-
-struct obbox_t
-{
-   double c0[sDIM], A[sDIM*sDIM];
-   dbl_range_t x[sDIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[sDIM];
-   double fac[sDIM];
-   unsigned int *offset;
-};
-
-static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
-                                                        int i, const double *z,
-                                                        const double *lCoeff,
-                                                        int pN)
-{
-   double u0 = 1, u1 = 0, u2 = 0;
-   for (int j=0; j<pN; ++j)
-   {
-      if (i!=j)
-      {
-         double d_j = 2 * (x-z[j]);
-         u2 = d_j * u2 + u1;
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
-   p0[i] = lCoeff[i] * u0;
-   p1[i] = 2.0 * lCoeff[i] * u1;
-   p2[i] = 8.0 * lCoeff[i] * u2;
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
-                                                      const double x[sDIM])
-{
-   double b_d;
-   for (int d=0; d<sDIM; ++d)
-   {
-      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
-      if (b_d < 0)   // if outside in any dimension
-      {
-         return b_d;
-      }
-   }
-   return b_d;       // only positive if inside in all dimensions
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
-                                                 const double x[sDIM])
-{
-   const double bxyz = obbox_axis_test(b, x);
-   if (bxyz<0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[3];
-      // dxyz: distance of the point from the center of the OBB
-      for (int d=0; d<sDIM; ++d)
-      {
-         dxyz[d] = x[d] - b->c0[d];
-      }
-      // transform dxyz to the local coordinate system of the OBB,
-      // and check if the point is inside the OBB [-1,1]^sDIM
-      double test = 1;
-      for (int d=0; d<sDIM; ++d)
-      {
-         double rst = 0;
-         for (int e=0; e<sDIM; ++e)
-         {
-            rst += b->A[d*sDIM + e] * dxyz[e];
-         }
-         double brst = (rst+1)*(1-rst);
-         test = test<0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-/* Hash index in the hash table to the elements that possibly contain the point x */
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[sDIM])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d=sDIM-1; d>=0; --d)
-   {
-      sum *= n;
-      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
-      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
-   }
-   return sum;
-}
-
-
-static MFEM_HOST_DEVICE inline double norm2(const double x[sDIM])
-{
-   return ( x[0]*x[0] + x[1]*x[1] + x[2]*x[2] );
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
 
 /* the bit structure of flags is CRR
    the C bit --- 1<<2 --- is set when the point is converged
@@ -190,31 +88,31 @@ static MFEM_HOST_DEVICE inline int point_index(const int x)
 /* check reduction in objective against prediction, and adjust
    trust region radius (p->tr) accordingly;
    may reject the prior step, returning 1; otherwise returns 0
-   sets out->dist2, out->index, out->x, out->oldr in any event,
-   leaving out->r, out->dr, out->flags to be set when returning 0 */
-static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[3],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = norm2(resid);
+   const double dist2 = l2norm2<sDIM>(resid);
    const double decr  = p->dist2 - dist2;
    const double pred  = p->dist2p;
    for (int d=0; d<sDIM; ++d)
    {
-      out->x[d] = p->x[d];
+      out_pt->x[d] = p->x[d];
    }
-   out->oldr = p->r;
-   out->dist2 = dist2;
+   out_pt->oldr = p->r;
+   out_pt->dist2 = dist2;
    if (decr>=0.01*pred)
    {
       if (decr>=0.9*pred)   // very good iteration
       {
-         out->tr = 2*p->tr;
+         out_pt->tr = 2*p->tr;
       }
       else   // good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -225,21 +123,21 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          "very good iteration" --- this doubles the trust radius,
          which is why we divide by 4 below */
       double v0 = fabs(p->r - p->oldr);
-      out->tr = v0/4.0;
-      out->dist2 = p->dist2;
-      out->r = p->oldr;
-      out->flags = p->flags>>3;
-      out->dist2p = -HUGE_VAL;
+      out_pt->tr = v0/4.0;
+      out_pt->dist2 = p->dist2;
+      out_pt->r = p->oldr;
+      out_pt->flags = p->flags>>3;
+      out_pt->dist2p = -HUGE_VAL;
       if (pred<dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
-                                                out,
+                                                out_pt,
                                                 const double jac[sDIM*rDIM],
                                                 const double rhes,
                                                 const double resid[sDIM],
@@ -313,9 +211,9 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r = nr;
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+   out_pt->r = nr;
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
 #undef EVAL
 }
 
@@ -337,31 +235,32 @@ static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
    {
       dx[d] = x[d] - elx[d][ir];
    }
-   dist2[ir] = norm2(dx);;
+   dist2[ir] = l2norm2(dx);
    r[ir] = z[ir];
 }
 
 template<int T_D1D = 0>
-static void FindPointsEdgeLocal3D_Kernel(const int npt,
-                                         const double tol,
-                                         const double dist2tol,
-                                         const double *x,
-                                         const int point_pos_ordering,
-                                         const double *xElemCoord,
-                                         const int nel,
-                                         const double *wtend,
-                                         const double *boxinfo,
-                                         const int hash_n,
-                                         const double *hashMin,
-                                         const double *hashFac,
-                                         unsigned int *hashOffset,
-                                         unsigned int *const code_base,
-                                         unsigned int *const el_base,
-                                         double *const r_base,
-                                         double *const dist2_base,
-                                         const double *gll1D,
-                                         const double *lagcoeff,
-                                         const int pN = 0)
+static void FindPointsEdgeLocal3DKernel(const int npt,
+                                        const double tol,
+                                        const double dist2tol,
+                                        const double *x,
+                                        const int point_pos_ordering,
+                                        const double *xElemCoord,
+                                        const int nel,
+                                        const double *wtend,
+                                        const double *boxinfo,
+                                        const bool obb_check,
+                                        const int hash_n,
+                                        const double *hashMin,
+                                        const double *hashFac,
+                                        unsigned int *hashOffset,
+                                        unsigned int *const code_base,
+                                        unsigned int *const el_base,
+                                        double *const r_base,
+                                        double *const dist2_base,
+                                        const double *gll1D,
+                                        const double *lagcoeff,
+                                        const int pN = 0)
 {
    const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D   = T_D1D ? T_D1D : pN;
@@ -418,21 +317,35 @@ static void FindPointsEdgeLocal3D_Kernel(const int npt,
       for (; elp!=ele; ++elp)
       {
          const unsigned int el = *elp;
+
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            box.c0[idx] = boxinfo[n_box_ents*el + idx];
-            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
-            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            for (int idx = 0; idx < sDIM; ++idx)
+            {
+               box.c0[idx] = boxinfo[n_box_ents*el + idx];
+               box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+               box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            }
+            for (int idx = 0; idx < sDIM2; ++idx)
+            {
+               box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
          }
-         for (int idx = 0; idx < sDIM2; ++idx)
+         else
          {
-            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         if (obbox_test(&box, x_i)>=0)
+         if (pass_bb)
          {
             //// findpts_local ////
             {
@@ -690,28 +603,41 @@ void FindPointsGSLIB::FindPointsEdgeLocal3(const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsEdgeLocal3D_Kernel<2>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal3DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 3:
-         return FindPointsEdgeLocal3D_Kernel<3>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal3DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 4:
-         return FindPointsEdgeLocal3D_Kernel<4>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsEdgeLocal3DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       default:
-         return FindPointsEdgeLocal3D_Kernel(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+         FindPointsEdgeLocal3DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef rDIM2

fem/gslib/findptssurf_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 #ifdef MFEM_USE_GSLIB
 
 #ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
@@ -51,124 +52,15 @@ struct findptsElementGPT_t
    double x[sDIM], jac[sDIM*rDIM], hes[sDIM*(rDIM+1)];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-
-struct obbox_t
-{
-   double c0[sDIM], A[sDIM*sDIM];
-   dbl_range_t x[sDIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[sDIM];
-   double fac[sDIM];
-   unsigned int *offset;
-};
-
-static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
-                                                        int i, const double *z,
-                                                        const double *lCoeff,
-                                                        int pN)
-{
-   double u0 = 1, u1 = 0, u2 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2 * (x - z[j]);
-         u2 = d_j * u2 + u1;
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-   p0[2*pN+i] = 8.0 * lCoeff[i] * u2;
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double AABB_test(const obbox_t *const b,
-                                                const double x[sDIM])
-{
-   double b_d;
-   for (int d=0; d<sDIM; ++d)
-   {
-      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
-      if (b_d < 0)   // if outside in any dimension
-      {
-         return b_d;
-      }
-   }
-   return b_d;       // only positive if inside in all dimensions
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double bbox_test(const obbox_t *const b,
-                                                const double x[sDIM])
-{
-   const double bxyz = AABB_test(b, x);
-   if (bxyz<0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[3];
-      // dxyz: distance of the point from the center of the OBB
-      for (int d=0; d<sDIM; ++d)
-      {
-         dxyz[d] = x[d] - b->c0[d];
-      }
-      // tranform dxyz to the local coordinate system of the OBB,
-      // and check if the point is inside the OBB [-1,1]^sDIM
-      double test = 1;
-      for (int d=0; d<sDIM; ++d)
-      {
-         double rst = 0;
-         for (int e=0; e<sDIM; ++e)
-         {
-            rst += b->A[d*sDIM + e] * dxyz[e];
-         }
-         double brst = (rst+1)*(1-rst);
-         test = test<0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-/* Hash index in the hash table to the elements that possibly contain the point x */
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[sDIM])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d=sDIM-1; d>=0; --d)
-   {
-      sum *= n;
-      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
-      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
-   }
-   return sum;
-}
-
-static MFEM_HOST_DEVICE inline void lin_solve_sym_2(double x[2],
-                                                    const double A[3],
-                                                    const double y[2])
-{
-   const double idet = 1 / (A[0] * A[2] - A[1] * A[1]);
-   x[0] = idet * (A[2] * y[0] - A[1] * y[1]);
-   x[1] = idet * (A[0] * y[1] - A[1] * y[0]);
-}
-
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[sDIM])
-{
-   return ( x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
+using gslib::lin_solve_sym_2;
 
 /* the bit structure of flags is CSSRR
    the C bit --- 1<<4 --- is set when the point is converged
@@ -303,34 +195,34 @@ static MFEM_HOST_DEVICE inline findptsElementGPT_t get_pt(const double *elx[3],
 /* check reduction in objective against prediction, and adjust
    trust region radius (p->tr) accordingly;
    may reject the prior step, returning 1; otherwise returns 0
-   sets out->dist2, out->index, out->x, out->oldr in any event,
-   leaving out->r, out->dr, out->flags to be set when returning 0 */
-static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[3],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<sDIM>(resid);
    const double decr  = p->dist2 - dist2;
    const double pred  = p->dist2p;
    for (int d=0; d<sDIM; ++d)
    {
-      out->x[d] = p->x[d];
+      out_pt->x[d] = p->x[d];
    }
    for (int d=0; d<rDIM; ++d)
    {
-      out->oldr[d] = p->r[d];
+      out_pt->oldr[d] = p->r[d];
    }
-   out->dist2 = dist2;
+   out_pt->dist2 = dist2;
    if (decr>=0.01*pred)
    {
       if (decr>=0.9*pred)   // very good iteration
       {
-         out->tr = 2*p->tr;
+         out_pt->tr = 2*p->tr;
       }
       else   // good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -342,17 +234,17 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          which is why we divide by 4 below */
       double v0 = fabs(p->r[0] - p->oldr[0]),
              v1 = fabs(p->r[1] - p->oldr[1]);
-      out->tr     = ( v0>v1 ? v0 : v1 )/4;
-      out->dist2  = p->dist2;
-      out->flags   = p->flags >> 5;
-      out->dist2p = -HUGE_VAL;
+      out_pt->tr     = ( v0>v1 ? v0 : v1 )/4;
+      out_pt->dist2  = p->dist2;
+      out_pt->flags   = p->flags >> 5;
+      out_pt->dist2p = -HUGE_VAL;
       for (int d=0; d<rDIM; ++d)
       {
-         out->r[d] = p->oldr[d];
+         out_pt->r[d] = p->oldr[d];
       }
       if (pred<dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
@@ -360,7 +252,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
 
 /* minimize ||resid - jac * dr||_2, with |dr| <= tr, |r0+dr|<=1
    (exact solution of trust region problem) */
-static MFEM_HOST_DEVICE void newton_face( findptsElementPoint_t *const out,
+static MFEM_HOST_DEVICE void newton_face( findptsElementPoint_t *const out_pt,
                                           const double jac[sDIM*rDIM],
                                           const double rhes[3],
                                           const double resid[sDIM],
@@ -531,19 +423,19 @@ newton_face_constrained:
    }
 
 newton_face_fin:
-   out->dist2p = -2*v;
+   out_pt->dist2p = -2*v;
    dr[0] = r[0] - p->r[0];
    dr[1] = r[1] - p->r[1];
    if ( fabs(dr[0])+fabs(dr[1]) < tol)
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r[0] = r[0], out->r[1] = r[1];
-   out->flags = new_flags | ((p->flags & FLAG_MASK)<<5);
+   out_pt->r[0] = r[0], out_pt->r[1] = r[1];
+   out_pt->flags = new_flags | ((p->flags & FLAG_MASK)<<5);
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
-                                                out,
+                                                out_pt,
                                                 const double jac[sDIM*rDIM],
                                                 const double rhes,
                                                 const double resid[sDIM],
@@ -628,10 +520,10 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r[de] = nr;
-   out->r[dn] = p->r[dn];
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<5);
+   out_pt->r[de] = nr;
+   out_pt->r[dn] = p->r[dn];
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<5);
 #undef EVAL
 }
 
@@ -667,26 +559,27 @@ static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
 // global memory access of element coordinates.
 // Are the structs being stored in "local memory" or registers?
 template<int T_D1D = 0>
-static void FindPointsSurfLocal3D_Kernel(const int npt,
-                                         const double tol,
-                                         const double dist2tol,
-                                         const double *x,
-                                         const int point_pos_ordering,
-                                         const double *xElemCoord,
-                                         const int nel,
-                                         const double *wtend,
-                                         const double *boxinfo,
-                                         const int hash_n,
-                                         const double *hashMin,
-                                         const double *hashFac,
-                                         unsigned int *hashOffset,
-                                         unsigned int *const code_base,
-                                         unsigned int *const el_base,
-                                         double *const r_base,
-                                         double *const dist2_base,
-                                         const double *gll1D,
-                                         const double *lagcoeff,
-                                         const int pN = 0)
+static void FindPointsSurfLocal3DKernel(const int npt,
+                                        const double tol,
+                                        const double dist2tol,
+                                        const double *x,
+                                        const int point_pos_ordering,
+                                        const double *xElemCoord,
+                                        const int nel,
+                                        const double *wtend,
+                                        const double *boxinfo,
+                                        const bool obb_check,
+                                        const int hash_n,
+                                        const double *hashMin,
+                                        const double *hashFac,
+                                        unsigned int *hashOffset,
+                                        unsigned int *const code_base,
+                                        unsigned int *const el_base,
+                                        double *const r_base,
+                                        double *const dist2_base,
+                                        const double *gll1D,
+                                        const double *lagcoeff,
+                                        const int pN = 0)
 {
    const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D   = T_D1D ? T_D1D : pN;
@@ -744,22 +637,36 @@ static void FindPointsSurfLocal3D_Kernel(const int npt,
       {
          const unsigned int el = *elp;
 
-         // construct obbox on the fly
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            box.c0[idx] = boxinfo[n_box_ents*el + idx];
-            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
-            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            // construct obbox on the fly
+            for (int idx = 0; idx < sDIM; ++idx)
+            {
+               box.c0[idx] = boxinfo[n_box_ents*el + idx];
+               box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+               box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+            }
+
+            for (int idx = 0; idx < sDIM2; ++idx)
+            {
+               box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
+         }
+         else
+         {
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         for (int idx = 0; idx < sDIM2; ++idx)
-         {
-            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
-         }
-
-         if (bbox_test(&box, x_i) < 0) { continue; }
+         if (!pass_bb) { continue; }
 
          //// findpts_local ////
          {
@@ -961,9 +868,11 @@ static void FindPointsSurfLocal3D_Kernel(const int npt,
                         findptsElementGEdge_t edge;
                         for (int d=0; d<sDIM; ++d)
                         {
-                           edge.x[d]     = constraint_workspace             + d*D1D;
-                           edge.dxdn[d]  = constraint_workspace +   sDIM*D1D + d*D1D;
-                           edge.d2xdn[d] = constraint_workspace + 2*sDIM*D1D + d*D1D;
+                           edge.x[d]     = constraint_workspace + d*D1D;
+                           edge.dxdn[d]  = constraint_workspace + d*D1D
+                                           + sDIM*D1D;
+                           edge.d2xdn[d] = constraint_workspace + d*D1D
+                                           + 2*sDIM*D1D;
                         }
 
                         MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
@@ -1214,29 +1123,42 @@ void FindPointsGSLIB::FindPointsSurfLocal3(const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
 
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsSurfLocal3D_Kernel<2>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsSurfLocal3DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 3:
-         return FindPointsSurfLocal3D_Kernel<3>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsSurfLocal3DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 4:
-         return FindPointsSurfLocal3D_Kernel<4>(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+         FindPointsSurfLocal3DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       default:
-         return FindPointsSurfLocal3D_Kernel(
-                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
-                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
-                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+         FindPointsSurfLocal3DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 

fem/gslib/gslib_kernel_helpers.hpp

@@ -0,0 +1,190 @@
+#ifndef MFEM_GSLIB_KERNEL_HELPERS_HPP
+#define MFEM_GSLIB_KERNEL_HELPERS_HPP
+
+#include "../../config/config.hpp"
+
+#include <cmath>
+
+namespace mfem
+{
+
+namespace gslib
+{
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+template <int SDIM>
+struct obbox_t
+{
+   double c0[SDIM], A[SDIM * SDIM];
+   dbl_range_t x[SDIM];
+};
+
+template <int SDIM>
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[SDIM];
+   double fac[SDIM];
+   unsigned int *offset;
+};
+
+// Eval the ith Lagrange interpolant at x.
+MFEM_HOST_DEVICE inline void lagrange_eval(double *p0, double x,
+                                           int i, int p_Nq,
+                                           double *z, double *lagrangeCoeff)
+{
+   double p_i = (1 << (p_Nq - 1));
+   for (int j = 0; j < p_Nq; ++j)
+   {
+      const double d_j = x - z[j];
+      p_i *= j == i ? 1 : d_j;
+   }
+   p0[i] = lagrangeCoeff[i] * p_i;
+}
+
+// Eval the ith Lagrange interpolant and its first derivative at x.
+MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
+                                                int i, const double *z,
+                                                const double *lCoeff,
+                                                int pN)
+{
+   double u0 = 1, u1 = 0;
+   for (int j = 0; j < pN; ++j)
+   {
+      if (i != j)
+      {
+         const double d_j = 2 * (x - z[j]);
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   p0[i] = lCoeff[i] * u0;
+   p0[pN + i] = 2.0 * lCoeff[i] * u1;
+}
+
+// Eval the ith Lagrange interpolant and its first and second derivative at x.
+MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
+                                                 int i, const double *z,
+                                                 const double *lCoeff,
+                                                 int pN)
+{
+   double u0 = 1, u1 = 0, u2 = 0;
+   for (int j = 0; j < pN; ++j)
+   {
+      if (i != j)
+      {
+         const double d_j = 2 * (x - z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   p0[i] = lCoeff[i] * u0;
+   p0[pN + i] = 2.0 * lCoeff[i] * u1;
+   p0[2 * pN + i] = 8.0 * lCoeff[i] * u2;
+}
+
+// Solve Ax=y where A is a symmetric 2x2 matrix packed as {a00, a01, a11}.
+MFEM_HOST_DEVICE inline void lin_solve_sym_2(double x[2],
+                                             const double A[3],
+                                             const double y[2])
+{
+   const double idet = 1 / (A[0] * A[2] - A[1] * A[1]);
+   x[0] = idet * (A[2] * y[0] - A[1] * y[1]);
+   x[1] = idet * (A[0] * y[1] - A[1] * y[0]);
+}
+
+// Positive when the point is inside the axis-aligned bounding box.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double AABB_test(const obbox_t<SDIM> *const b,
+                                         const double (&x)[SDIM])
+{
+   double test = 1.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      const double b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      test = test < 0.0 ? test : b_d;
+   }
+   return test;
+}
+
+// Positive when the point is inside the oriented bounding box.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double bbox_test(const obbox_t<SDIM> *const b,
+                                         const double (&x)[SDIM])
+{
+   const double bxyz = AABB_test(b, x);
+   if (bxyz < 0.0)
+   {
+      return bxyz;
+   }
+
+   double dxyz[SDIM];
+   for (int d = 0; d < SDIM; ++d)
+   {
+      dxyz[d] = x[d] - b->c0[d];
+   }
+
+   double test = 1.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      double rst = 0.0;
+      for (int e = 0; e < SDIM; ++e)
+      {
+         rst += b->A[d * SDIM + e] * dxyz[e];
+      }
+      const double brst = (rst + 1.0) * (1.0 - rst);
+      test = test < 0.0 ? test : brst;
+   }
+   return test;
+}
+
+// Hash index in the hash table for the point x.
+template <int SDIM>
+MFEM_HOST_DEVICE inline int hash_index(
+   const findptsLocalHashData_t<SDIM> *const p,
+   const double (&x)[SDIM])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d = SDIM - 1; d >= 0; --d)
+   {
+      sum *= n;
+      const int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
+      sum += i < 0 ? 0 : (n - 1 < i ? n - 1 : i);
+   }
+   return sum;
+}
+
+// Squared Euclidean norm.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double l2norm2(const double (&x)[SDIM])
+{
+   double sum = 0.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      sum += x[d] * x[d];
+   }
+   return sum;
+}
+
+template <int SDIM>
+MFEM_HOST_DEVICE inline double l2norm2(const double *x)
+{
+   double sum = 0.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      sum += x[d] * x[d];
+   }
+   return sum;
+}
+
+} // namespace gslib
+
+} // namespace mfem
+
+#endif

fem/gslib/interpolate_local_1.cpp

@@ -11,7 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -33,17 +33,7 @@ namespace mfem
 #define CODE_BORDER 1
 #define CODE_NOT_FOUND 2
 
-static MFEM_HOST_DEVICE void lagrange_eval(double *p0, double x,
-                                           int i, int p_Nq,
-                                           double *z, double *lagrangeCoeff)
-{
-   double p_i = (1 << (p_Nq - 1));
-   for (int j=0; j<p_Nq; ++j)
-   {
-      p_i *= j==i ? 1 : x-z[j];
-   }
-   p0[i] = lagrangeCoeff[i] * p_i;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal1DKernel(const double *const gf_in,
@@ -123,21 +113,26 @@ void FindPointsGSLIB::InterpolateLocal1( const Vector &field_in,
    auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
-      case 2: return InterpolateLocal1DKernel<2>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 3: return InterpolateLocal1DKernel<3>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 4: return InterpolateLocal1DKernel<4>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 5: return InterpolateLocal1DKernel<5>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      default: return InterpolateLocal1DKernel(pfin, pgsl, pgslr, pfout,
-                                                  npt, ncomp,
-                                                  pgll, plcf, dof1Dsol);
+      case 2:
+         InterpolateLocal1DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal1DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal1DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal1DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal1DKernel(pfin, pgsl, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 #undef CODE_INTERNAL

fem/gslib/interpolate_local_2.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -32,18 +33,7 @@ namespace mfem
 #define CODE_BORDER 1
 #define CODE_NOT_FOUND 2
 
-static MFEM_HOST_DEVICE void lagrange_eval(double *p0, double x,
-                                           int i, int p_Nq,
-                                           double *z, double *lagrangeCoeff)
-{
-   double p_i = (1 << (p_Nq - 1));
-   for (int j = 0; j < p_Nq; ++j)
-   {
-      double d_j = x - z[j];
-      p_i *= j == i ? 1 : d_j;
-   }
-   p0[i] = lagrangeCoeff[i] * p_i;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal2DKernel(const double *const gf_in,
@@ -132,21 +122,26 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
    auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
-      case 2: return InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 3: return InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 4: return InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 5: return InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      default: return InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
-                                                  npt, ncomp,
-                                                  pgll, plcf, dof1Dsol);
+      case 2:
+         InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 

fem/gslib/interpolate_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -32,18 +33,7 @@ namespace mfem
 #define CODE_BORDER 1
 #define CODE_NOT_FOUND 2
 
-static MFEM_HOST_DEVICE void lagrange_eval(double *p0, double x,
-                                           int i, int p_Nq,
-                                           double *z, double *lagrangeCoeff)
-{
-   double p_i = (1 << (p_Nq - 1));
-   for (int j = 0; j < p_Nq; ++j)
-   {
-      double d_j = x - z[j];
-      p_i *= j == i ? 1 : d_j;
-   }
-   p0[i] = lagrangeCoeff[i] * p_i;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal3DKernel(const double *const gf_in,
@@ -135,21 +125,26 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
    auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
-      case 2: return InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 3: return InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 4: return InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 5: return InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      default: return InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
-                                                  npt, ncomp,
-                                                  pgll, plcf, dof1Dsol);
+      case 2:
+         InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 

fem/integ/bilininteg_diffusion_kernels.hpp

@@ -19,6 +19,8 @@
 #include "../../linalg/vector.hpp"
 #include "../bilininteg.hpp"
 
+#include "bilininteg_diffusion_pa_simplices.hpp"
+
 namespace mfem
 {
 

fem/integ/bilininteg_mass_kernels.hpp

@@ -19,6 +19,8 @@
 #include "../../linalg/vector.hpp"
 #include "../bilininteg.hpp"
 
+#include "bilininteg_mass_pa_simplices.hpp"
+
 namespace mfem
 {
 

fem/integ/lininteg_domain_kernels.hpp

@@ -307,6 +307,506 @@ DomainLFIntegrator::AssembleKernels::Kernel()
    MFEM_ABORT("");
 }
 
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HdivDLFAssemble2D(const int ne, const Array<int> &markers,
+                              const Vector &jac, const Array<real_t> &weights,
+                              const Array<real_t> &testBO,
+                              const Array<real_t> &testBC, const Vector &coeff,
+                              Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 2 * (d - 1) * d * ne, "");
+
+   constexpr int vdim = 2;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1) : Reshape(F,vdim,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int vdim = 2;
+      if (M[e] == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q*D];
+      MFEM_SHARED real_t sBct[Q*D];
+      MFEM_SHARED real_t sQQ[vdim*Q*Q];
+      MFEM_SHARED real_t sQD[vdim*Q*D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d-1, q);
+      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
+
+      const DeviceCube QQ(sQQ, q, q, vdim);
+      const DeviceCube QD(sQD, q, d, vdim);
+
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const real_t cst_val_0 = C(0,0,0,0);
+         const real_t cst_val_1 = C(1,0,0,0);
+         MFEM_FOREACH_THREAD(y,y,q)
+         {
+            MFEM_FOREACH_THREAD(x,x,q)
+            {
+               const real_t J0 = J(x,y,0,vd,e);
+               const real_t J1 = J(x,y,1,vd,e);
+               const real_t C0 = cst ? cst_val_0 : C(0,x,y,e);
+               const real_t C1 = cst ? cst_val_1 : C(1,x,y,e);
+               QQ(x,y,vd) = W(x,y)*(J0*C0 + J1*C1);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(qy,y,q)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t qd = 0.0;
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  qd += QQ(qx,qy,vd) * Btx(dx,qx);
+               }
+               QD(dx,qy,vd) = qd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
+         DeviceTensor<4> Yxy(Y, nx, ny, vdim, ne);
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t dd = 0.0;
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  dd += QD(dx,qy,vd) * Bty(dy,qy);
+               }
+               Yxy(dx,dy,vd,e) += dd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HdivDLFAssemble3D(const int ne, const Array<int> &markers,
+                              const Vector &jac, const Array<real_t> &weights,
+                              const Array<real_t> &testBO,
+                              const Array<real_t> &testBC, const Vector &coeff,
+                              Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 3 * (d - 1) * (d - 1) * d * ne, "y wrong length");
+
+   constexpr int vdim = 3;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int vdim = 3;
+      if (M[e] == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q*D];
+      MFEM_SHARED real_t sBct[Q*D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d-1, q);
+      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
+
+      MFEM_SHARED real_t sm0[vdim*Q*Q*Q];
+      MFEM_SHARED real_t sm1[vdim*Q*Q*Q];
+      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
+      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
+      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
+
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const real_t cst_val_0 = C(0,0,0,0,0);
+         const real_t cst_val_1 = C(1,0,0,0,0);
+         const real_t cst_val_2 = C(2,0,0,0,0);
+         MFEM_FOREACH_THREAD(y,y,q)
+         {
+            MFEM_FOREACH_THREAD(x,x,q)
+            {
+               for (int z = 0; z < q; ++z)
+               {
+                  const real_t J0 = J(x,y,z,0,vd,e);
+                  const real_t J1 = J(x,y,z,1,vd,e);
+                  const real_t J2 = J(x,y,z,2,vd,e);
+                  const real_t C0 = cst ? cst_val_0 : C(0,x,y,z,e);
+                  const real_t C1 = cst ? cst_val_1 : C(1,x,y,z,e);
+                  const real_t C2 = cst ? cst_val_2 : C(2,x,y,z,e);
+                  QQQ(x,y,z,vd) = W(x,y,z)*(J0*C0 + J1*C1 + J2*C2);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(qy,y,q)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += QQQ(qx,qy,qz,vd) * Btx(dx,qx);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { DQQ(dx,qy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += DQQ(dx,qy,qz,vd) * Bty(dy,qy);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { DDQ(dx,dy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         const int nz = (vd == 2) ? d : d-1;
+         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
+         DeviceMatrix Btz = (vd == 2) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[D];
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  MFEM_UNROLL(D)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += DDQ(dx,dy,qz,vd) * Btz(dz,qz);
+                  }
+               }
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz) { Yxyz(dx,dy,dz,vd,e) += u[dz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+/// @param ne number of elements
+/// @param markers array where entry markers[e] == 0 to skip assembly over
+/// element e element
+/// @param jac Spatial Jacobians evaluated at all quadrature points
+/// @param weights 1D quadrature weights
+/// @param testBO 1D open basis test functions
+/// @param testBC 1D closed basis test functions
+/// @param coeff coefficient values evaluated at quadrature points, possibly
+/// compressed.
+/// @param d number of 1D closed dofs
+/// @param q number of 1D quadrature points
+/// @tparam T_D1D maximum number of dofs along any direction, or 0
+/// @tparam T_Q1D maximum number of quadrature points along any direction, or 0
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HcurlDLFAssemble3D(const int ne, const Array<int> &markers,
+                               const Vector &jac, const Array<real_t> &weights,
+                               const Array<real_t> &testBO,
+                               const Array<real_t> &testBC, const Vector &coeff,
+                               Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 3 * (d - 1) * d * d * ne, "y wrong length");
+
+   constexpr int vdim = 3;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE(int e)
+   {
+      if (M[e] == 0)
+      {
+         // ignore
+         return;
+      }
+
+      constexpr int vdim = 3;
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HCURL_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HCURL_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q * D];
+      MFEM_SHARED real_t sBct[Q * D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d - 1, q);
+      kernels::internal::LoadB<D, Q>(d - 1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D, Q>(d, q, BC, sBct);
+
+      MFEM_SHARED real_t sm0[vdim * Q * Q * Q];
+      MFEM_SHARED real_t sm1[vdim * Q * Q * Q];
+      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
+      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
+      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
+
+      const real_t cst_val_0 = C(0, 0, 0, 0, 0);
+      const real_t cst_val_1 = C(1, 0, 0, 0, 0);
+      const real_t cst_val_2 = C(2, 0, 0, 0, 0);
+
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         MFEM_FOREACH_THREAD(y, y, q)
+         {
+            MFEM_FOREACH_THREAD(x, x, q)
+            {
+               for (int z = 0; z < q; ++z)
+               {
+                  real_t curr[3];
+                  curr[0] = cst ? cst_val_0 : C(0, x, y, z, e);
+                  curr[1] = cst ? cst_val_1 : C(1, x, y, z, e);
+                  curr[2] = cst ? cst_val_2 : C(2, x, y, z, e);
+
+                  const real_t J11 = J(x, y, z, 0, 0, e);
+                  const real_t J21 = J(x, y, z, 1, 0, e);
+                  const real_t J31 = J(x, y, z, 2, 0, e);
+                  const real_t J12 = J(x, y, z, 0, 1, e);
+                  const real_t J22 = J(x, y, z, 1, 1, e);
+                  const real_t J32 = J(x, y, z, 2, 1, e);
+                  const real_t J13 = J(x, y, z, 0, 2, e);
+                  const real_t J23 = J(x, y, z, 1, 2, e);
+                  const real_t J33 = J(x, y, z, 2, 2, e);
+                  // adj(J)
+                  const real_t A11 = (J22 * J33) - (J23 * J32);
+                  const real_t A12 = (J32 * J13) - (J12 * J33);
+                  const real_t A13 = (J12 * J23) - (J22 * J13);
+                  const real_t A21 = (J31 * J23) - (J21 * J33);
+                  const real_t A22 = (J11 * J33) - (J13 * J31);
+                  const real_t A23 = (J21 * J13) - (J11 * J23);
+                  const real_t A31 = (J21 * J32) - (J31 * J22);
+                  const real_t A32 = (J31 * J12) - (J11 * J32);
+                  const real_t A33 = (J11 * J22) - (J12 * J21);
+                  const real_t A[9] = {A11, A12, A13, A21, A22,
+                                       A23, A31, A32, A33
+                                      };
+                  QQQ(x, y, z, vd) = W(x, y, z) * (A[vd * vdim] * curr[0] +
+                                                   A[vd * vdim + 1] * curr[1] +
+                                                   A[vd * vdim + 2] * curr[2]);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         DeviceMatrix Btx = (vd == 0) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(qy, y, q)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  u[qz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += QQQ(qx, qy, qz, vd) * Btx(dx, qx);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  DQQ(dx, qy, qz, vd) = u[qz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         const int ny = (vd == 1) ? d - 1 : d;
+         DeviceMatrix Bty = (vd == 1) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(dy, y, ny)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  u[qz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += DQQ(dx, qy, qz, vd) * Bty(dy, qy);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  DDQ(dx, dy, qz, vd) = u[qz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         const int ny = (vd == 1) ? d - 1 : d;
+         const int nz = (vd == 2) ? d - 1 : d;
+         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
+         DeviceMatrix Btz = (vd == 2) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(dy, y, ny)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[D];
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz)
+               {
+                  u[dz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  MFEM_UNROLL(D)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += DDQ(dx, dy, qz, vd) * Btz(dz, qz);
+                  }
+               }
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz)
+               {
+                  Yxyz(dx, dy, dz, vd, e) += u[dz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+template <FiniteElement::DerivType TestType, int DIM, int TEST_D1D, int Q1D>
+VectorFEDomainLFIntegrator::AssembleKernelType
+VectorFEDomainLFIntegrator::AssembleKernels::Kernel()
+{
+   if constexpr (TestType == FiniteElement::DIV)
+   {
+      if constexpr (DIM == 2)
+      {
+         return HdivDLFAssemble2D<TEST_D1D, Q1D>;
+      }
+      if constexpr (DIM == 3)
+      {
+         return HdivDLFAssemble3D<TEST_D1D, Q1D>;
+      }
+   }
+   if constexpr (TestType == FiniteElement::CURL)
+   {
+      if constexpr (DIM == 3)
+      {
+         return HcurlDLFAssemble3D<TEST_D1D, Q1D>;
+      }
+   }
+   MFEM_ABORT("");
+}
+
 /// \endcond DO_NOT_DOCUMENT
 
 } // namespace mfem

fem/integ/lininteg_domain_vectorfe.cpp

@@ -13,317 +13,76 @@
 #include "../../fem/kernels.hpp"
 #include "../fem.hpp"
 
+#include "lininteg_domain_kernels.hpp"
+
 namespace mfem
 {
 
-template<int T_D1D = 0, int T_Q1D = 0>
-static void HdivDLFAssemble2D(
-   const int ne, const int d, const int q, const int *markers, const real_t *bo,
-   const real_t *bc, const real_t *j, const real_t *weights,
-   const Vector &coeff, real_t *y)
+VectorFEDomainLFIntegrator::Kernels::Kernels()
 {
-   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
-               "Problem size too large.");
-   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
-               "Problem size too large.");
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 8, 8>();
 
-   static constexpr int vdim = 2;
-   const auto F = coeff.Read();
-   const auto M = Reshape(markers, ne);
-   const auto BO = Reshape(bo, q, d-1);
-   const auto BC = Reshape(bc, q, d);
-   const auto J = Reshape(j, q, q, vdim, vdim, ne);
-   const auto W = Reshape(weights, q, q);
-   const bool cst = coeff.Size() == vdim;
-   const auto C = cst ? Reshape(F,vdim,1,1,1) : Reshape(F,vdim,q,q,ne);
-   auto Y = Reshape(y, 2*(d-1)*d, ne);
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 8, 8>();
 
-   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
-   {
-      if (M(e) == 0) { return; } // ignore
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 8, 8>();
 
-      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
-      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
-
-      MFEM_SHARED real_t sBot[Q*D];
-      MFEM_SHARED real_t sBct[Q*D];
-      MFEM_SHARED real_t sQQ[vdim*Q*Q];
-      MFEM_SHARED real_t sQD[vdim*Q*D];
-
-      // Bo and Bc into shared memory
-      const DeviceMatrix Bot(sBot, d-1, q);
-      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
-      const DeviceMatrix Bct(sBct, d, q);
-      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
-
-      const DeviceCube QQ(sQQ, q, q, vdim);
-      const DeviceCube QD(sQD, q, d, vdim);
-
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const real_t cst_val_0 = C(0,0,0,0);
-         const real_t cst_val_1 = C(1,0,0,0);
-         MFEM_FOREACH_THREAD(y,y,q)
-         {
-            MFEM_FOREACH_THREAD(x,x,q)
-            {
-               const real_t J0 = J(x,y,0,vd,e);
-               const real_t J1 = J(x,y,1,vd,e);
-               const real_t C0 = cst ? cst_val_0 : C(0,x,y,e);
-               const real_t C1 = cst ? cst_val_1 : C(1,x,y,e);
-               QQ(x,y,vd) = W(x,y)*(J0*C0 + J1*C1);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(qy,y,q)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t qd = 0.0;
-               for (int qx = 0; qx < q; ++qx)
-               {
-                  qd += QQ(qx,qy,vd) * Btx(dx,qx);
-               }
-               QD(dx,qy,vd) = qd;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
-         DeviceTensor<4> Yxy(Y, nx, ny, vdim, ne);
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t dd = 0.0;
-               for (int qy = 0; qy < q; ++qy)
-               {
-                  dd += QD(dx,qy,vd) * Bty(dy,qy);
-               }
-               Yxy(dx,dy,vd,e) += dd;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-   });
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 1, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 2, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 3, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 4, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 5, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 6, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 7, 8>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 8, 9>();
 }
 
-template<int T_D1D = 0, int T_Q1D = 0>
-static void HdivDLFAssemble3D(
-   const int ne, const int d, const int q, const int *markers, const real_t *bo,
-   const real_t *bc, const real_t *j, const real_t *weights,
-   const Vector &coeff, real_t *y)
+/// \cond DO_NOT_DOCUMENT
+VectorFEDomainLFIntegrator::AssembleKernelType
+VectorFEDomainLFIntegrator::AssembleKernels::Fallback(
+   FiniteElement::DerivType TestType, int DIM, int, int)
 {
-   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
-               "Problem size too large.");
-   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
-               "Problem size too large.");
-
-   static constexpr int vdim = 3;
-   const auto F = coeff.Read();
-   const auto M = Reshape(markers, ne);
-   const auto BO = Reshape(bo, q, d-1);
-   const auto BC = Reshape(bc, q, d);
-   const auto J = Reshape(j, q, q, q, vdim, vdim, ne);
-   const auto W = Reshape(weights, q, q, q);
-   const bool cst = coeff.Size() == vdim;
-   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
-   auto Y = Reshape(y, 2*(d-1)*(d-1)*d, ne);
-
-   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   if (TestType == FiniteElement::DIV)
    {
-      if (M(e) == 0) { return; } // ignore
-
-      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
-      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
-
-      MFEM_SHARED real_t sBot[Q*D];
-      MFEM_SHARED real_t sBct[Q*D];
-
-      // Bo and Bc into shared memory
-      const DeviceMatrix Bot(sBot, d-1, q);
-      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
-      const DeviceMatrix Bct(sBct, d, q);
-      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
-
-      MFEM_SHARED real_t sm0[vdim*Q*Q*Q];
-      MFEM_SHARED real_t sm1[vdim*Q*Q*Q];
-      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
-      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
-      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
-
-      MFEM_FOREACH_THREAD(vd,z,vdim)
+      if (DIM == 2)
       {
-         const real_t cst_val_0 = C(0,0,0,0,0);
-         const real_t cst_val_1 = C(1,0,0,0,0);
-         const real_t cst_val_2 = C(2,0,0,0,0);
-         MFEM_FOREACH_THREAD(y,y,q)
-         {
-            MFEM_FOREACH_THREAD(x,x,q)
-            {
-               for (int z = 0; z < q; ++z)
-               {
-                  const real_t J0 = J(x,y,z,0,vd,e);
-                  const real_t J1 = J(x,y,z,1,vd,e);
-                  const real_t J2 = J(x,y,z,2,vd,e);
-                  const real_t C0 = cst ? cst_val_0 : C(0,x,y,z,e);
-                  const real_t C1 = cst ? cst_val_1 : C(1,x,y,z,e);
-                  const real_t C2 = cst ? cst_val_2 : C(2,x,y,z,e);
-                  QQQ(x,y,z,vd) = W(x,y,z)*(J0*C0 + J1*C1 + J2*C2);
-               }
-            }
-         }
+         return HdivDLFAssemble2D<0, 0>;
       }
-      MFEM_SYNC_THREAD;
-      // Apply Bt operator
-      MFEM_FOREACH_THREAD(vd,z,vdim)
+      if (DIM == 3)
       {
-         const int nx = (vd == 0) ? d : d-1;
-         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(qy,y,q)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[Q];
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qx = 0; qx < q; ++qx)
-               {
-                  MFEM_UNROLL(Q)
-                  for (int qz = 0; qz < q; ++qz)
-                  {
-                     u[qz] += QQQ(qx,qy,qz,vd) * Btx(dx,qx);
-                  }
-               }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { DQQ(dx,qy,qz,vd) = u[qz]; }
-            }
-         }
+         return HdivDLFAssemble3D<0, 0>;
       }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[Q];
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qy = 0; qy < q; ++qy)
-               {
-                  MFEM_UNROLL(Q)
-                  for (int qz = 0; qz < q; ++qz)
-                  {
-                     u[qz] += DQQ(dx,qy,qz,vd) * Bty(dy,qy);
-                  }
-               }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { DDQ(dx,dy,qz,vd) = u[qz]; }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         const int nz = (vd == 2) ? d : d-1;
-         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
-         DeviceMatrix Btz = (vd == 2) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[D];
-               MFEM_UNROLL(D)
-               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz)
-               {
-                  MFEM_UNROLL(D)
-                  for (int dz = 0; dz < nz; ++dz)
-                  {
-                     u[dz] += DDQ(dx,dy,qz,vd) * Btz(dz,qz);
-                  }
-               }
-               MFEM_UNROLL(D)
-               for (int dz = 0; dz < nz; ++dz) { Yxyz(dx,dy,dz,vd,e) += u[dz]; }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-   });
-}
-
-static void HdivDLFAssemble(const FiniteElementSpace &fes,
-                            const IntegrationRule *ir,
-                            const Array<int> &markers,
-                            const Vector &coeff,
-                            Vector &y)
-{
-   Mesh &mesh = *fes.GetMesh();
-   const int dim = mesh.Dimension();
-   const FiniteElement *el = fes.GetTypicalFE();
-   const auto *vel = dynamic_cast<const VectorTensorFiniteElement *>(el);
-   MFEM_VERIFY(vel != nullptr, "Must be VectorTensorFiniteElement");
-   const MemoryType mt = Device::GetDeviceMemoryType();
-   const DofToQuad &maps_o = vel->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   const DofToQuad &maps_c = vel->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int d = maps_c.ndof, q = maps_c.nqpt;
-   constexpr int flags = GeometricFactors::JACOBIANS;
-   const GeometricFactors *geom = mesh.GetGeometricFactors(*ir, flags, mt);
-   decltype(&HdivDLFAssemble2D<>) ker =
-      dim == 2 ? HdivDLFAssemble2D<> : HdivDLFAssemble3D<>;
-
-   if (dim==2)
-   {
-      if (d==1 && q==1) { ker=HdivDLFAssemble2D<1,1>; }
-      if (d==2 && q==2) { ker=HdivDLFAssemble2D<2,2>; }
-      if (d==3 && q==3) { ker=HdivDLFAssemble2D<3,3>; }
-      if (d==4 && q==4) { ker=HdivDLFAssemble2D<4,4>; }
-      if (d==5 && q==5) { ker=HdivDLFAssemble2D<5,5>; }
-      if (d==6 && q==6) { ker=HdivDLFAssemble2D<6,6>; }
-      if (d==7 && q==7) { ker=HdivDLFAssemble2D<7,7>; }
-      if (d==8 && q==8) { ker=HdivDLFAssemble2D<8,8>; }
    }
-
-   if (dim==3)
+   else if (TestType == FiniteElement::CURL)
    {
-      if (d==2 && q==2) { ker=HdivDLFAssemble3D<2,2>; }
-      if (d==3 && q==3) { ker=HdivDLFAssemble3D<3,3>; }
-      if (d==4 && q==4) { ker=HdivDLFAssemble3D<4,4>; }
-      if (d==5 && q==5) { ker=HdivDLFAssemble3D<5,5>; }
-      if (d==6 && q==6) { ker=HdivDLFAssemble3D<6,6>; }
-      if (d==7 && q==7) { ker=HdivDLFAssemble3D<7,7>; }
-      if (d==8 && q==8) { ker=HdivDLFAssemble3D<8,8>; }
+      if (DIM == 3)
+      {
+         return HcurlDLFAssemble3D<0, 0>;
+      }
    }
-
-   MFEM_VERIFY(ker, "No kernel ndof " << d << " nqpt " << q);
-
-   const int ne = mesh.GetNE();
-   const int *M = markers.Read();
-   const real_t *Bo = maps_o.B.Read();
-   const real_t *Bc = maps_c.B.Read();
-   const real_t *J = geom->J.Read();
-   const real_t *W = ir->GetWeights().Read();
-   real_t *Y = y.ReadWrite();
-   ker(ne, d, q, M, Bo, Bc, J, W, coeff, Y);
+   MFEM_ABORT("");
 }
+/// \endcond DO_NOT_DOCUMENT
 
 void VectorFEDomainLFIntegrator::AssembleDevice(const FiniteElementSpace &fes,
                                                 const Array<int> &markers,
@@ -337,15 +96,23 @@ void VectorFEDomainLFIntegrator::AssembleDevice(const FiniteElementSpace &fes,
    QuadratureSpace qs(*fes.GetMesh(), *ir);
    CoefficientVector coeff(QF, qs, CoefficientStorage::COMPRESSED);
 
-   const int fe_type = fe.GetDerivType();
-   if (fe_type == FiniteElement::DIV)
-   {
-      HdivDLFAssemble(fes, ir, markers, coeff, b);
-   }
-   else
-   {
-      MFEM_ABORT("Not implemented.");
-   }
+   const FiniteElement::DerivType fe_type =
+      static_cast<FiniteElement::DerivType>(fe.GetDerivType());
+
+   Mesh &mesh = *fes.GetMesh();
+   const int dim = mesh.Dimension();
+   const FiniteElement *el = fes.GetTypicalFE();
+   const auto *vel = dynamic_cast<const VectorTensorFiniteElement *>(el);
+   MFEM_VERIFY(vel != nullptr, "Must be VectorTensorFiniteElement");
+   const MemoryType mt = Device::GetDeviceMemoryType();
+   const DofToQuad &maps_o = vel->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   const DofToQuad &maps_c = vel->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   const int d = maps_c.ndof, q = maps_c.nqpt;
+   constexpr int flags = GeometricFactors::JACOBIANS;
+   const GeometricFactors *geom = mesh.GetGeometricFactors(*ir, flags, mt);
+
+   AssembleKernels::Run(fe_type, dim, d, q, mesh.GetNE(), markers, geom->J,
+                        ir->GetWeights(), maps_o.B, maps_c.B, coeff, b, d, q);
 }
 
 } // namespace mfem

fem/lininteg.cpp

@@ -471,6 +471,13 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    }
 }
 
+VectorFEDomainLFIntegrator::VectorFEDomainLFIntegrator(
+   VectorCoefficient &F, const IntegrationRule *ir)
+   : DeltaLFIntegrator(F, ir), QF(F)
+{
+   static Kernels kernels{};
+}
+
 void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {

fem/lininteg.hpp

@@ -369,8 +369,8 @@ private:
    Vector vec;
 
 public:
-   VectorFEDomainLFIntegrator(VectorCoefficient &F)
-      : DeltaLFIntegrator(F), QF(F) { }
+   VectorFEDomainLFIntegrator(VectorCoefficient &F,
+                              const IntegrationRule *ir = nullptr);
 
    void AssembleRHSElementVect(const FiniteElement &el,
                                ElementTransformation &Tr,
@@ -387,6 +387,40 @@ public:
                        Vector &b) override;
 
    using LinearFormIntegrator::AssembleRHSElementVect;
+
+   /// @param ne number of elements
+   /// @param markers array where entry markers[e] == 0 to skip assembly over
+   /// element e element
+   /// @param jac Spatial Jacobians evaluated at all quadrature points
+   /// @param weights 1D quadrature weights
+   /// @param testBO 1D open basis test functions
+   /// @param testBC 1D closed basis test functions
+   /// @param coeff coefficient values evaluated at quadrature points, possibly
+   /// compressed.
+   /// @param d number of 1D closed dofs
+   /// @param q number of 1D quadrature points
+   using AssembleKernelType = void (*)(const int NE, const Array<int> &markers,
+                                       const Vector &jac,
+                                       const Array<real_t> &weights,
+                                       const Array<real_t> &testBO,
+                                       const Array<real_t> &testBC,
+                                       const Vector &coeff, Vector &y,
+                                       const int testd1d, const int q1d);
+
+   /// parameters: test_fetype, ndims, test_d1d, q1d
+   MFEM_REGISTER_KERNELS(AssembleKernels, AssembleKernelType,
+                         (FiniteElement::DerivType, int, int, int));
+
+   struct Kernels
+   {
+      Kernels();
+   };
+
+   template <FiniteElement::DerivType TestType, int DIM, int TEST_D1D, int Q1D>
+   static void AddSpecialization()
+   {
+      AssembleKernels::Specialization<TestType, DIM, TEST_D1D, Q1D>::Add();
+   }
 };
 
 /// $ (Q, \mathrm{curl}(v))_{\Omega} $ for Nedelec Elements

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. */

general/backends.hpp

@@ -38,15 +38,6 @@
 #define CUB_IGNORE_DEPRECATED_CPP_DIALECT
 #define THRUST_IGNORE_DEPRECATED_CPP_DIALECT
 
-// MFEM only supports using RAJA/CAMP backends in default stream mode because
-// memory calls are performed outside of the RAJA ecosystem
-#ifndef CAMP_USE_PLATFORM_DEFAULT_STREAM
-#define CAMP_USE_PLATFORM_DEFAULT_STREAM 1
-#else
-#if !CAMP_USE_PLATFORM_DEFAULT_STREAM
-#error "MFEM only supports RAJA/CAMP with the default platform stream."
-#endif
-#endif
 #include "RAJA/RAJA.hpp"
 #if defined(RAJA_ENABLE_CUDA) && !defined(MFEM_USE_CUDA)
 #error When RAJA is built with CUDA, MFEM_USE_CUDA=YES is required

general/device.cpp

@@ -581,7 +581,9 @@ void Device::Setup(const std::string &device_option, const int device_id)
    if (Allows(Backend::CUDA)) { CudaDeviceSetup(dev, ngpu); }
    if (Allows(Backend::HIP)) { HipDeviceSetup(dev, ngpu); }
    if (Allows(Backend::RAJA_CUDA) || Allows(Backend::RAJA_HIP))
-   { RajaDeviceSetup(dev, ngpu); }
+   {
+      RajaDeviceSetup(dev, ngpu);
+   }
    // The check for MFEM_USE_OCCA is in the function OccaDeviceSetup().
    if (Allows(Backend::OCCA_MASK)) { OccaDeviceSetup(dev); }
    if (Allows(Backend::CEED_MASK))

general/device.hpp

@@ -16,6 +16,11 @@
 #include "globals.hpp"
 #include "mem_manager.hpp"
 
+#ifdef MFEM_USE_RAJA
+#include "RAJA/RAJA.hpp"
+#endif
+
+#include <memory>
 #include <string>
 
 namespace mfem
@@ -266,6 +271,18 @@ public:
    static inline bool Allows(unsigned long b_mask)
    { return Get().backends & b_mask; }
 
+#if defined(MFEM_USE_RAJA) &&                                                  \
+   (defined(RAJA_ENABLE_CUDA) || defined(RAJA_ENABLE_HIP))
+   static inline auto GetRajaResource()
+   {
+#if defined(RAJA_ENABLE_CUDA)
+      return RAJA::resources::Cuda::CudaFromStream(0, Get().GetId());
+#elif defined(RAJA_ENABLE_HIP)
+      return RAJA::resources::Hip::HipFromStream(0, Get().GetId());
+#endif
+   }
+#endif
+
    /** @brief Get the current Host MemoryType. This is the MemoryType used by
        most MFEM classes when allocating memory used on the host.
    */

general/forall.hpp

@@ -317,8 +317,8 @@ template <typename DBODY>
 void RajaCuWrap1D(const int N, DBODY &&d_body)
 {
    //true denotes asynchronous kernel
-   RAJA::forall<RAJA::cuda_exec<MFEM_CUDA_BLOCKS,true>>(RAJA::RangeSegment(0,N),
-                                                        d_body);
+   RAJA::forall<RAJA::cuda_exec<MFEM_CUDA_BLOCKS, true> >(
+      Device::GetRajaResource(), RAJA::RangeSegment(0, N), d_body);
 }
 
 template <typename DBODY>
@@ -331,9 +331,9 @@ void RajaCuWrap2D(const int N, DBODY &&d_body,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<cuda_launch_policy>
-   (LaunchParams(Teams(G), Threads(X, Y, BZ)),
-    [=] RAJA_DEVICE (LaunchContext ctx)
+   launch<cuda_launch_policy>(Device::GetRajaResource(),
+                              LaunchParams(Teams(G), Threads(X, Y, BZ)),
+                              [=] RAJA_DEVICE(LaunchContext ctx)
    {
 
       loop<cuda_teams_x>(ctx, RangeSegment(0, G), [&] (const int n)
@@ -349,7 +349,6 @@ void RajaCuWrap2D(const int N, DBODY &&d_body,
          });
 
       });
-
    });
 
    MFEM_GPU_CHECK(cudaGetLastError());
@@ -365,9 +364,9 @@ void RajaCuWrap2DLaunchBounds(const int N, DBODY &&d_body, const int X,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<cuda_launch_bounds_policy<LB> >
-   (LaunchParams(Teams(G), Threads(X, Y, BZ)),
-    [=] RAJA_DEVICE(LaunchContext ctx)
+   launch<cuda_launch_bounds_policy<LB> >(
+      Device::GetRajaResource(), LaunchParams(Teams(G), Threads(X, Y, BZ)),
+      [=] RAJA_DEVICE(LaunchContext ctx)
    {
       loop<cuda_teams_x>(ctx, RangeSegment(0, G), [&] (const int n)
       {
@@ -390,13 +389,12 @@ void RajaCuWrap3D(const int N, DBODY &&d_body,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<cuda_launch_policy>
-   (LaunchParams(Teams(GRID), Threads(X, Y, Z)),
-    [=] RAJA_DEVICE (LaunchContext ctx)
+   launch<cuda_launch_policy>(Device::GetRajaResource(),
+                              LaunchParams(Teams(GRID), Threads(X, Y, Z)),
+                              [=] RAJA_DEVICE(LaunchContext ctx)
    {
 
       loop<cuda_teams_x>(ctx, RangeSegment(0, N), d_body);
-
    });
 
    MFEM_GPU_CHECK(cudaGetLastError());
@@ -410,12 +408,10 @@ void RajaCuWrap3DLaunchBounds(const int N, DBODY &&d_body,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<cuda_launch_bounds_policy<LB> >
-   (LaunchParams(Teams(GRID), Threads(X, Y, Z)),
-    [=] RAJA_DEVICE(LaunchContext ctx)
-   {
-      loop<cuda_teams_x>(ctx, RangeSegment(0, N), d_body);
-   });
+   launch<cuda_launch_bounds_policy<LB> >(
+      Device::GetRajaResource(), LaunchParams(Teams(GRID), Threads(X, Y, Z)),
+      [=] RAJA_DEVICE(LaunchContext ctx)
+   { loop<cuda_teams_x>(ctx, RangeSegment(0, N), d_body); });
    MFEM_GPU_CHECK(cudaGetLastError());
 }
 
@@ -484,8 +480,8 @@ template <typename DBODY>
 void RajaHipWrap1D(const int N, DBODY &&d_body)
 {
    //true denotes asynchronous kernel
-   RAJA::forall<RAJA::hip_exec<MFEM_HIP_BLOCKS,true>>(RAJA::RangeSegment(0,N),
-                                                      d_body);
+   RAJA::forall<RAJA::hip_exec<MFEM_HIP_BLOCKS,true> >(RAJA::RangeSegment(0,N),
+                                                       d_body);
 }
 
 template <typename DBODY>
@@ -498,9 +494,9 @@ void RajaHipWrap2D(const int N, DBODY &&d_body,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<hip_launch_policy>
-   (LaunchParams(Teams(G), Threads(X, Y, BZ)),
-    [=] RAJA_DEVICE (LaunchContext ctx)
+   launch<hip_launch_policy>(Device::GetRajaResource(),
+                             LaunchParams(Teams(G), Threads(X, Y, BZ)),
+                             [=] RAJA_DEVICE(LaunchContext ctx)
    {
 
       loop<hip_teams_x>(ctx, RangeSegment(0, G), [&] (const int n)
@@ -516,7 +512,6 @@ void RajaHipWrap2D(const int N, DBODY &&d_body,
          });
 
       });
-
    });
 
    MFEM_GPU_CHECK(hipGetLastError());
@@ -532,9 +527,9 @@ void RajaHipWrap2DLaunchBounds(const int N, DBODY &&d_body, const int X,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<hip_launch_bounds_policy<LB> >
-   (LaunchParams(Teams(G), Threads(X, Y, BZ)),
-    [=] RAJA_DEVICE(LaunchContext ctx)
+   launch<hip_launch_bounds_policy<LB> >(
+      Device::GetRajaResource(), LaunchParams(Teams(G), Threads(X, Y, BZ)),
+      [=] RAJA_DEVICE(LaunchContext ctx)
    {
       loop<hip_teams_x>(ctx, RangeSegment(0, G), [&] (const int n)
       {
@@ -557,13 +552,12 @@ void RajaHipWrap3D(const int N, DBODY &&d_body,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<hip_launch_policy>
-   (LaunchParams(Teams(GRID), Threads(X, Y, Z)),
-    [=] RAJA_DEVICE (LaunchContext ctx)
+   launch<hip_launch_policy>(Device::GetRajaResource(),
+                             LaunchParams(Teams(GRID), Threads(X, Y, Z)),
+                             [=] RAJA_DEVICE(LaunchContext ctx)
    {
 
       loop<hip_teams_x>(ctx, RangeSegment(0, N), d_body);
-
    });
 
    MFEM_GPU_CHECK(hipGetLastError());
@@ -577,12 +571,10 @@ void RajaHipWrap3DLaunchBounds(const int N, DBODY &&d_body, const int X,
    using namespace RAJA;
    using RAJA::RangeSegment;
 
-   launch<hip_launch_bounds_policy<LB> >
-   (LaunchParams(Teams(GRID), Threads(X, Y, Z)),
-    [=] RAJA_DEVICE(LaunchContext ctx)
-   {
-      loop<hip_teams_x>(ctx, RangeSegment(0, N), d_body);
-   });
+   launch<hip_launch_bounds_policy<LB> >(
+      Device::GetRajaResource(), LaunchParams(Teams(GRID), Threads(X, Y, Z)),
+      [=] RAJA_DEVICE(LaunchContext ctx)
+   { loop<hip_teams_x>(ctx, RangeSegment(0, N), d_body); });
    MFEM_GPU_CHECK(hipGetLastError());
 }
 

linalg/CMakeLists.txt

@@ -27,6 +27,7 @@ list(APPEND SRCS
   handle.cpp
   matrix.cpp
   mma.cpp
+  multivector.cpp
   ode.cpp
   operator.cpp
   ordering.cpp
@@ -63,6 +64,7 @@ list(APPEND HDRS
   linalg.hpp
   matrix.hpp
   mma.hpp
+  multivector.hpp
   ode.hpp
   operator.hpp
   ordering.hpp

linalg/cudss.cpp

@@ -15,10 +15,20 @@
 
 #ifdef MFEM_USE_CUDSS
 
+#if CUDSS_VERSION >= 800
 #ifdef MFEM_USE_SINGLE
-#define CUDA_REAL_T CUDA_R_32F
+#define CUDSS_REAL_T CUDSS_R_32F
 #else
-#define CUDA_REAL_T CUDA_R_64F
+#define CUDSS_REAL_T CUDSS_R_64F
+#endif
+#define CUDSS_INT_T CUDSS_R_32I
+#else
+#ifdef MFEM_USE_SINGLE
+#define CUDSS_REAL_T CUDA_R_32F
+#else
+#define CUDSS_REAL_T CUDA_R_64F
+#endif
+#define CUDSS_INT_T CUDA_R_32I
 #endif
 
 // Define a cuDSS error check macro, MFEM_CUDSS_CHECK(x), where x returns/is of
@@ -65,8 +75,13 @@ CuDSSSolver::CuDSSSolver(MPI_Comm comm_) : mpi_comm(comm_)
 #endif
    MFEM_CUDSS_CHECK(cudssSetCommLayer(handle, comm_lib));
 
+#if CUDSS_VERSION >= 800
+   MFEM_CUDSS_CHECK(cudssDataSet(handle, solverData, CUDSS_DATA_COMM_HOST,
+                                 &mpi_comm, sizeof(MPI_Comm *)));
+#else
    MFEM_CUDSS_CHECK(cudssDataSet(handle, solverData, CUDSS_DATA_COMM,
                                  &mpi_comm, sizeof(MPI_Comm *)));
+#endif
 }
 #endif // MFEM_USE_MPI
 
@@ -257,11 +272,19 @@ void CuDSSSolver::SetMatrixCuDSS(int *csr_offsets, int *csr_columns,
          CuMemcpyDtoD(csr_offsets_d, csr_offsets, (n_loc + 1) * sizeof(int));
          CuMemcpyDtoD(csr_columns_d, csr_columns, nnz * sizeof(int));
 
+#if CUDSS_VERSION >= 800
          MFEM_CUDSS_CHECK(
             cudssMatrixCreateCsr(
                Ac.get(), n_global, n_global, nnz, csr_offsets_d, NULL,
-               csr_columns_d, csr_values_d, CUDA_R_32I, CUDA_REAL_T, mat_type, mview,
-               CUDSS_BASE_ZERO));
+               csr_columns_d, csr_values_d, CUDSS_INT_T, CUDSS_INT_T, CUDSS_REAL_T,
+               mat_type, mview, CUDSS_BASE_ZERO));
+#else
+         MFEM_CUDSS_CHECK(
+            cudssMatrixCreateCsr(
+               Ac.get(), n_global, n_global, nnz, csr_offsets_d, NULL,
+               csr_columns_d, csr_values_d, CUDSS_INT_T, CUDSS_REAL_T,
+               mat_type, mview, CUDSS_BASE_ZERO));
+#endif
       }
       else    // !reorder_reuse
       {
@@ -269,11 +292,19 @@ void CuDSSSolver::SetMatrixCuDSS(int *csr_offsets, int *csr_columns,
          {
             MFEM_CUDSS_CHECK(cudssMatrixDestroy(*Ac));
          }
+#if CUDSS_VERSION >= 800
          MFEM_CUDSS_CHECK(
             cudssMatrixCreateCsr(
-               Ac.get(), n_global, n_global, nnz, csr_offsets, NULL, csr_columns,
-               csr_values_d, CUDA_R_32I, CUDA_REAL_T, mat_type, mview,
-               CUDSS_BASE_ZERO));
+               Ac.get(), n_global, n_global, nnz, csr_offsets, NULL,
+               csr_columns, csr_values_d, CUDSS_INT_T, CUDSS_INT_T, CUDSS_REAL_T,
+               mat_type, mview, CUDSS_BASE_ZERO));
+#else
+         MFEM_CUDSS_CHECK(
+            cudssMatrixCreateCsr(
+               Ac.get(), n_global, n_global, nnz, csr_offsets, NULL,
+               csr_columns, csr_values_d, CUDSS_INT_T, CUDSS_REAL_T,
+               mat_type, mview, CUDSS_BASE_ZERO));
+#endif
       }
 #ifdef MFEM_USE_MPI
       if (Mpi::IsInitialized())
@@ -334,10 +365,10 @@ void CuDSSSolver::SetNumRHS(int nrhs_) const
       }
       // Create empty RHS and solution vectors
       MFEM_CUDSS_CHECK(cudssMatrixCreateDn(&xc, n_global, nrhs_, n_global, NULL,
-                                           CUDA_REAL_T, CUDSS_LAYOUT_COL_MAJOR));
+                                           CUDSS_REAL_T, CUDSS_LAYOUT_COL_MAJOR));
 
       MFEM_CUDSS_CHECK(cudssMatrixCreateDn(&yc, n_global, nrhs_, n_global, NULL,
-                                           CUDA_REAL_T, CUDSS_LAYOUT_COL_MAJOR));
+                                           CUDSS_REAL_T, CUDSS_LAYOUT_COL_MAJOR));
 
 #ifdef MFEM_USE_MPI
       MFEM_CUDSS_CHECK(cudssMatrixSetDistributionRow1d(xc, row_start, row_end));

linalg/ginkgo.hpp

@@ -39,6 +39,7 @@ namespace Ginkgo
 {
 
 template <typename T> using gko_array = gko::array<T>;
+#if defined(MFEM_USE_MPI) && GINKGO_BUILD_MPI
 // for inter-operability with hypre integer types
 using gko_hypre_int =
    std::conditional_t<sizeof(HYPRE_Int) == sizeof(std::int32_t), std::int32_t,
@@ -50,6 +51,7 @@ static_assert(!std::is_void_v<gko_hypre_int>,
               "HYPRE_Int type is incompatible with Ginkgo");
 static_assert(!std::is_void_v<gko_hypre_bigint>,
               "HYPRE_BigInt type is incompatible with Ginkgo");
+#endif
 
 /**
 * Helper class for a case where a wrapped MFEM Vector

linalg/hypre.cpp

@@ -2872,8 +2872,8 @@ void HypreParMatrix::Destroy()
    if (HypreUsingGPU() && ParCSROwner && (diagOwner < 0 || offdOwner < 0))
    {
       // Put the "host" or "hypre" pointers in {i,j,data} of A->{diag,offd}, so
-      // that they can be destroyed by hypre when hypre_ParCSRMatrixDestroy(A)
-      // is called below.
+      // that they can be destroyed by mfem_hypre_TFree_host() or hypre when
+      // hypre_ParCSRMatrixDestroy(A) is called below, respectively.
 
       // Check that if both diagOwner and offdOwner are negative then they have
       // the same value.
@@ -2882,7 +2882,33 @@ void HypreParMatrix::Destroy()
 
       MemoryClass mc = (diagOwner == -1 || offdOwner == -1) ?
                        Device::GetHostMemoryClass() : GetHypreMemoryClass();
-      Write(mc, diagOwner < 0, offdOwner <0);
+      Write(mc, diagOwner < 0, offdOwner < 0);
+      if (diagOwner == -1)
+      {
+         // Note: mfem_hypre_TFree_host() sets the pointer to NULL.
+         mfem_hypre_TFree_host(hypre_CSRMatrixI(A->diag));
+         if (hypre_CSRMatrixOwnsData(A->diag))
+         {
+            mfem_hypre_TFree_host(hypre_CSRMatrixJ(A->diag));
+            mfem_hypre_TFree_host(hypre_CSRMatrixData(A->diag));
+         }
+#if MFEM_HYPRE_VERSION >= 21800
+         hypre_CSRMatrixMemoryLocation(A->diag) = GetHypreMemoryLocation();
+#endif
+      }
+      if (offdOwner == -1)
+      {
+         // Note: mfem_hypre_TFree_host() sets the pointer to NULL.
+         mfem_hypre_TFree_host(hypre_CSRMatrixI(A->offd));
+         if (hypre_CSRMatrixOwnsData(A->offd))
+         {
+            mfem_hypre_TFree_host(hypre_CSRMatrixJ(A->offd));
+            mfem_hypre_TFree_host(hypre_CSRMatrixData(A->offd));
+         }
+#if MFEM_HYPRE_VERSION >= 21800
+         hypre_CSRMatrixMemoryLocation(A->offd) = GetHypreMemoryLocation();
+#endif
+      }
    }
 #endif
 

linalg/hypre.hpp

@@ -432,10 +432,11 @@ private:
    // and A->col_map_offd.
    // The possible values for diagOwner are:
    //  -1: no special treatment of A->diag (default)
-   //      when hypre is built with CUDA support, A->diag owns the "host"
-   //      pointers (according to A->diag->owns_data)
-   //  -2: used when hypre is built with CUDA support, A->diag owns the "hypre"
-   //      pointers (according to A->diag->owns_data)
+   //      when hypre is using GPU, A->diag owns the "host" pointers (according
+   //      to A->diag->owns_data); these host pointers are freed by MFEM using
+   //      hypre's host deallocation macros
+   //  -2: used when hypre is using GPU, A->diag owns the "hypre" pointers
+   //      (according to A->diag->owns_data)
    //   0: prevent hypre from destroying A->diag->{i,j,data}
    //   1: same as 0, plus own the "host" A->diag->{i,j}
    //   2: same as 0, plus own the "host" A->diag->data

linalg/linalg.hpp

@@ -15,6 +15,7 @@
 // Linear algebra header file
 
 #include "vector.hpp"
+#include "multivector.hpp"
 #include "operator.hpp"
 #include "matrix.hpp"
 #include "sparsemat.hpp"

linalg/multivector.cpp

@@ -0,0 +1,60 @@
+// 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 "multivector.hpp"
+
+namespace mfem
+{
+
+MultiVector::MultiVector(const Array<int> &vector_sizes)
+{
+   SetSizes(vector_sizes);
+}
+
+MultiVector::MultiVector(const Array<int> &vector_sizes, MemoryType mt)
+{
+   SetSizes(vector_sizes, mt);
+}
+
+MultiVector::MultiVector(Vector &base, const Array<int> &vector_sizes)
+{
+   MakeRef(base, vector_sizes);
+}
+
+void MultiVector::SetSizes(const Array<int> &vector_sizes)
+{
+   blocks.resize(vector_sizes.Size());
+   for (int i = 0; i < vector_sizes.Size(); i++)
+   {
+      operator[](i).SetSize(vector_sizes[i]);
+   }
+}
+
+void MultiVector::SetSizes(const Array<int> &vector_sizes, MemoryType mt)
+{
+   blocks.resize(vector_sizes.Size());
+   for (int i = 0; i < vector_sizes.Size(); i++)
+   {
+      operator[](i).SetSize(vector_sizes[i], mt);
+   }
+}
+
+void MultiVector::MakeRef(Vector &base, const Array<int> &vector_sizes)
+{
+   blocks.resize(vector_sizes.Size());
+   for (int offset = 0, i = 0; i < vector_sizes.Size(); i++)
+   {
+      blocks[i].emplace<0>(base, offset, vector_sizes[i]);
+      offset += vector_sizes[i];
+   }
+}
+
+} // namespace mfem

linalg/multivector.hpp

@@ -0,0 +1,198 @@
+// 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.
+
+#ifndef MFEM_MULTIVECTOR_HPP
+#define MFEM_MULTIVECTOR_HPP
+
+#include "../general/array.hpp"
+#include "vector.hpp"
+#include <vector>
+#include <array>
+#include <variant>
+
+namespace mfem
+{
+
+/// Class representing an array of Vectors with generally different sizes.
+/** This class is similar to BlockVector with the following two main
+    differences:
+    - the data for the individual Vector blocks does not need to be part of one
+      big contiguous memory allocation;
+    - this class does not inherit from class Vector (as a consequence of the
+      first bullet).
+
+    Internally, each Vector block is represented as either:
+    - (default) a Vector object constructed and owned by this class; this
+      object, in turn, as any Vector object, can own its Memory allocation or
+      refer to a sub-Memory of another Memory object; or
+    - a pointer to an externally allocated Vector or classes derived from
+      Vector. */
+class MultiVector
+{
+private:
+   std::vector<std::variant<Vector,Vector*>> blocks;
+
+public:
+   /// Create an empty MultiVector with zero blocks.
+   MultiVector() = default;
+
+   /** @brief Create a MultiVector with @a num_blocks blocks. The individual
+       Vector blocks are default initialized, i.e. they all have size zero. */
+   MultiVector(int num_blocks)
+      : blocks(num_blocks) { }
+
+   /** @brief Construct a MultiVector with number of blocks and individual block
+       Vector sizes given by @a vector_sizes.
+
+       @note The memory of the individual Vector blocks is NOT initialized. */
+   MultiVector(const Array<int> &vector_sizes);
+
+   /** @brief Construct a MultiVector with number of blocks and individual block
+       Vector sizes given by @a vector_sizes. All Vector blocks use the
+       MemoryType @a mt.
+
+       @note The memory of the individual Vector blocks is NOT initialized. */
+   MultiVector(const Array<int> &vector_sizes, MemoryType mt);
+
+   /** @brief Construct a MultiVector referencing data within a given monolithic
+       Vector @a base.
+
+       With this constructor, the Memory flags of @a base and of the individual
+       Vector blocks may need to be explicitly synchronized when data is moved
+       between host and device. */
+   MultiVector(Vector &base, const Array<int> &vector_sizes);
+
+   /** @brief Construct a MultiVector referencing multiple Vectors given as
+       arguments.
+
+       The VectorTypes reference arguments are expected to be static_cast-able
+       to (Vector &) which is the case if the types are derived from Vector,
+       e.g. HypreParVector, GridFunction, etc.
+
+       With this constructor, operations on individual Vector blocks are
+       performed directly on the objects @a vs. In particular, there is no need
+       to synchronize the Memory flags of @a vs and the ones of the individual
+       Vector blocks when data is moved between host and device. */
+   template <typename... VectorTypes,
+             std::enable_if_t<
+                std::conjunction_v<
+                   std::is_convertible<VectorTypes&,Vector&>...>, bool> = true>
+   MultiVector(VectorTypes &...vs) { MakeRef(vs...); }
+
+   /// Return the number of Vectors in the MultiVector.
+   int NumBlocks() const { return blocks.size(); }
+
+   /** @brief Set the number of Vectors in the MultiVector. Existing Vector
+       blocks will remain unmodified. New Vector blocks will be default
+       initialized, i.e. they all have size zero. */
+   void SetNumBlocks(int num_blocks) { blocks.resize(num_blocks); }
+
+   /// Read-write access to the i-th Vector.
+   inline Vector &operator[](int i);
+
+   /// Read-only access to the i-th Vector.
+   inline const Vector &operator[](int i) const;
+
+   /** @brief Update the MultiVector according to the given @a vector_sizes.
+
+       This method can be used to add or remove blocks. The individual Vector
+       sizes are updated using the method Vector::SetSize(int). */
+   void SetSizes(const Array<int> &vector_sizes);
+
+   /** @brief Update the MultiVector according to the given @a vector_sizes and
+       MemoryType @a mt.
+
+       This method can be used to add or remove blocks. The individual Vector
+       sizes and MemoryType are updated using the method
+       Vector::SetSize(int, MemoryType). */
+   void SetSizes(const Array<int> &vector_sizes, MemoryType mt);
+
+   /** @brief Update the MultiVector to reference data within a given monolithic
+       Vector @a base.
+
+       After calling this method, the Memory flags of @a base and of the
+       individual Vector blocks may need to be explicitly synchronized when data
+       is moved between host and device.*/
+   void MakeRef(Vector &base, const Array<int> &vector_sizes);
+
+   /** @brief Update the @a i-th MultiVector block to reference data within the
+       given monolithic Vector @a base at the given @a offset and with the given
+       @a size.
+
+       After calling this method, the Memory flags of @a base and of the @a i-th
+       Vector block may need to be explicitly synchronized when data is moved
+       between host and device.*/
+   inline void MakeRef(int i, Vector &base, int offset, int size)
+   {
+      blocks[i].emplace<0>(base, offset, size);
+   }
+
+   /** @brief Update the MultiVector to reference multiple Vectors given as
+       arguments.
+
+       The VectorTypes reference arguments are expected to be static_cast-able
+       to (Vector &) which is the case if the types are derived from Vector,
+       e.g. HypreParVector, GridFunction, etc.
+
+       After calling this method, operations on individual Vector blocks are
+       performed directly on the objects @a vs. In particular, there is no need
+       to synchronize the Memory flags of @a vs and the ones of the individual
+       Vector blocks when data is moved between host and device. */
+   template <typename... VectorTypes,
+             std::enable_if_t<
+                std::conjunction_v<
+                   std::is_convertible<VectorTypes&,Vector&>...>, bool> = true>
+   inline void MakeRef(VectorTypes &...vs);
+
+   /** @brief Update the @a i-th MultiVector block to reference the given
+       Vector @a v.
+
+       After calling this method, operations on the @a i-th Vector block are
+       performed directly on the Vector @a v. In particular, there is no need
+       to synchronize the Memory flags of @a v and the ones of the @a i-th
+       Vector blocks when data is moved between host and device. */
+   inline void MakeRef(int i, Vector &v) { blocks[i] = &v; }
+};
+
+// Inline and template methods
+
+inline Vector &MultiVector::operator[](int i)
+{
+   auto &bi = blocks[i];
+   return (bi.index() == 0) ? std::get<0>(bi) : *std::get<1>(bi);
+}
+
+inline const Vector &MultiVector::operator[](int i) const
+{
+   auto &bi = blocks[i];
+   return (bi.index() == 0) ? std::get<0>(bi) : *std::get<1>(bi);
+}
+
+template <typename... VectorTypes,
+          std::enable_if_t<
+             std::conjunction_v<
+                std::is_convertible<VectorTypes&,Vector&>...>, bool>>
+inline void MultiVector::MakeRef(VectorTypes &...vs)
+{
+   blocks.resize(sizeof...(vs));
+   if constexpr (sizeof...(vs) > 0)
+   {
+      const std::array vs_p{&static_cast<Vector&>(vs)...};
+      for (std::size_t i = 0; i < sizeof...(vs); i++)
+      {
+         blocks[i] = vs_p[i];
+      }
+   }
+}
+
+} // namespace mfem
+
+#endif // MFEM_MULTIVECTOR_HPP

linalg/operator.cpp

@@ -111,6 +111,16 @@ void Operator::ArrayAddMultTranspose(const Array<const Vector *> &X,
    }
 }
 
+void Operator::Mult(const MultiVector &, MultiVector &)
+{
+   MFEM_ABORT("this method is not overriden for this class!");
+}
+
+Operator &Operator::GetGradient(const MultiVector &) const
+{
+   MFEM_ABORT("this method is not overriden for this class!");
+}
+
 void Operator::FormLinearSystem(const Array<int> &ess_tdof_list,
                                 Vector &x, Vector &b,
                                 Operator* &Aout, Vector &X, Vector &B,

linalg/operator.hpp

@@ -13,6 +13,7 @@
 #define MFEM_OPERATOR
 
 #include "vector.hpp"
+#include "multivector.hpp"
 
 namespace mfem
 {
@@ -129,6 +130,16 @@ public:
    virtual void ArrayAddMultTranspose(const Array<const Vector *> &X,
                                       Array<Vector *> &Y, const real_t a = 1.0) const;
 
+   /** @brief Operator application, y = A(x), where the input @a x and the
+       output @a y are MultiVector objects, i.e. they generally use
+       non-contiguous memory representation.
+
+       The typical use case for this method are block operators like
+       DifferentiableOperator.
+
+       The base class implementation for the method is to generate an error. */
+   virtual void Mult(const MultiVector &x, MultiVector &y);
+
    /** @brief Evaluate the gradient operator at the point @a x. The default
        behavior in class Operator is to generate an error. */
    virtual Operator &GetGradient(const Vector &x) const
@@ -137,6 +148,16 @@ public:
       return const_cast<Operator &>(*this);
    }
 
+   /** @brief Evaluate the gradient operator at the point @a x. The input @a x
+       is provided as a MultiVector, i.e. it generally uses non-contiguous
+       memory representation.
+
+       The typical use case for this method are block operators like
+       DifferentiableOperator.
+
+       The base class implementation for the method is to generate an error. */
+   virtual Operator &GetGradient(const MultiVector &x) const;
+
    /** @brief Computes the diagonal entries into @a diag. Typically, this
        operation only makes sense for linear Operator%s. In some cases, only an
        approximation of the diagonal is computed. */

miniapps/CMakeLists.txt

@@ -22,6 +22,7 @@ add_subdirectory(common)
 add_subdirectory(contact)
 add_subdirectory(dfem)
 add_subdirectory(diag-smoothers)
+add_subdirectory(multiapp)
 add_subdirectory(dpg)
 add_subdirectory(electromagnetics)
 add_subdirectory(fluids/navier)

miniapps/gslib/findpts.cpp

@@ -49,6 +49,9 @@
 //    findpts -m ../../data/ref-square.mesh -o 2 -mo 1 -random 1 -surf
 //    findpts -m ../../data/ref-cube.mesh -o 2 -mo 1 -random 1 -surf
 //    findpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -random 1 -surf
+// Surface meshes + bounding box size increase:
+//    findpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -random 1 -surf -sabs 0.1
+//    findpts -m ../../data/tinyzoo-3d.mesh -o 4 -mo 2 -random 1 -surf -sabs 0.1
 
 #include "mfem.hpp"
 #include "../common/mfem-common.hpp"
@@ -109,6 +112,7 @@ int main (int argc, char *argv[])
    int randomization     = 0;
    int npt               = 100;
    bool surface          = false;
+   double surf_aabb_sz_inc = 0.0;
 
    // Parse command-line options.
    OptionsParser args(argc, argv);
@@ -150,6 +154,9 @@ int main (int argc, char *argv[])
    args.AddOption(&surface, "-surf", "--surface", "-no-surf",
                   "--no-surface",
                   "Extract surface mesh from volume mesh.");
+   args.AddOption(&surf_aabb_sz_inc, "-sabs", "--surface-aabb-size-inc",
+                  "Absolute AABB expansion applied to surface-search "
+                  "axis-aligned bounding boxes in FindPointsGSLIB surface meshes.");
 
    args.Parse();
    if (!args.Good())
@@ -384,8 +391,17 @@ int main (int argc, char *argv[])
 
    // Find and Interpolate FE function values on the desired points.
    Vector interp_vals(pts_cnt*vec_dim);
-   FindPointsGSLIB finder(*mesh);
-   finder.SetDistanceToleranceForPointsFoundOnBoundary(10);
+   FindPointsGSLIB finder;
+   if (surface && surf_aabb_sz_inc > 0.0)
+   {
+      Vector bb_size({surf_aabb_sz_inc});
+      finder.SetupSurfWithAABBExpansion(*mesh, bb_size);
+   }
+   else
+   {
+      finder.Setup(*mesh);
+      // finder.SetDistanceToleranceForPointsFoundOnBoundary(10);
+   }
    finder.SetL2AvgType(FindPointsGSLIB::NONE);
    finder.Interpolate(vxyz, field_vals, interp_vals, point_ordering);
    Array<unsigned int> code_out    = finder.GetCode();

miniapps/gslib/pfindpts.cpp

@@ -53,6 +53,9 @@
 //    mpirun -np 4 pfindpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -vis -random 1 -surf
 //    mpirun -np 4 pfindpts -m ../../data/star-q3.mesh -o 6 -mo 3 -vis -random 1 -surf
 //    mpirun -np 4 pfindpts -m ../../data/fichera-q2.mesh -o 6 -mo 3 -vis -random 1 -surf
+// Surface meshes + bounding box size increase:
+//    mpirun -np 4 pfindpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -vis -random 1 -surf -sabs 0.1
+//    mpirun -np 4 pfindpts -m ../../data/tinyzoo-3d.mesh -o 4 -mo 2 -vis -random 1 -surf -sabs 0.1
 
 #include "mfem.hpp"
 #include "../common/mfem-common.hpp"
@@ -102,6 +105,7 @@ int main (int argc, char *argv[])
    int randomization     = 0;
    int npt               = 100; //points per proc
    bool surface          = false;
+   double surf_aabb_sz_inc = 0.0;
 
    // Parse command-line options.
    OptionsParser args(argc, argv);
@@ -145,7 +149,9 @@ int main (int argc, char *argv[])
    args.AddOption(&surface, "-surf", "--surface", "-no-surf",
                   "--no-surface",
                   "Extract surface mesh from volume mesh.");
-
+   args.AddOption(&surf_aabb_sz_inc, "-sabs", "--surface-aabb-size-inc",
+                  "Absolute AABB expansion applied to surface-search "
+                  "axis-aligned bounding boxes in FindPointsGSLIB surface meshes.");
    args.Parse();
    if (!args.Good())
    {
@@ -343,7 +349,7 @@ int main (int argc, char *argv[])
             Geometry::GetRandomPoint(geom, ip);
             if (j < npt_face_per_elem)
             {
-               ip.x = 0.0; // force point to be on the face
+               ip.x = 0.0; // force point to be on a face
                npt_total_face++;
             }
             Vector pos_i(sdim);
@@ -373,8 +379,17 @@ int main (int argc, char *argv[])
 
    // Find and Interpolate FE function values on the desired points.
    Vector interp_vals(pts_cnt*vec_dim);
-   FindPointsGSLIB finder(pmesh);
-   finder.SetDistanceToleranceForPointsFoundOnBoundary(10);
+   FindPointsGSLIB finder;
+   if (surface && surf_aabb_sz_inc > 0.0)
+   {
+      Vector bb_size({surf_aabb_sz_inc});
+      finder.SetupSurfWithAABBExpansion(pmesh, bb_size);
+   }
+   else
+   {
+      finder.Setup(pmesh);
+   }
+   // finder.SetDistanceToleranceForPointsFoundOnBoundary(1e-10);
    // Enable GPU to CPU fallback for GPUData only if you are using an older
    // version of GSLIB.
    // finder.SetGPUtoCPUFallback(true);
@@ -460,6 +475,7 @@ int main (int argc, char *argv[])
            << endl;
    }
 
+
    delete fec;
 
    if (randomization != 0)

miniapps/hdiv-linear-solver/change_basis.hpp

@@ -80,6 +80,8 @@ public:
    // limitations
    void MultRT_2D(const Vector &x, Vector &y, Mode mode) const;
    void MultRT_3D(const Vector &x, Vector &y, Mode mode) const;
+   // suppress warning about hiding overloaded virtual function:
+   using Operator::Mult;
 };
 
 } // namespace mfem

miniapps/multiapp/CMakeLists.txt

@@ -0,0 +1,52 @@
+# 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.
+
+set(MESH_FILES
+  backward-facing-step.msh
+  channel-cylinder.msh
+)
+
+# Add a target to copy the mesh files from the source directory; used by sample
+# runs.
+set(SRC_MESH_FILES)
+foreach(MESH_FILE ${MESH_FILES})
+  list(APPEND SRC_MESH_FILES ${CMAKE_CURRENT_SOURCE_DIR}/${MESH_FILE})
+endforeach()
+add_custom_command(OUTPUT data_is_copied
+  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} .
+  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
+  COMMENT "Copying multiapp miniapps data files ...")
+add_custom_target(copy_miniapps_multiapp_data DEPENDS data_is_copied)
+
+
+list(APPEND MULTIAPP_COMMON_SOURCES
+	multiapp.cpp)
+
+list(APPEND MULTIAPP_COMMON_HEADERS
+	multiapp.hpp)
+
+set(MULTIAPP_COMMON_FILES
+	EXTRA_SOURCES ${MULTIAPP_COMMON_SOURCES}
+	EXTRA_HEADERS ${MULTIAPP_COMMON_HEADERS})
+
+
+# Parallel apps.
+if (MFEM_USE_MPI)
+  add_mfem_miniapp(coupled-diffusion
+    MAIN coupled-diffusion.cpp
+    ${MFEM_MINIAPPS_COMMON_HEADERS} ${MULTIAPP_COMMON_FILES}
+    LIBRARIES mfem-common)
+  add_dependencies(coupled-diffusion copy_miniapps_multiapp_data)
+
+# Add parallel tests.
+  # if (MFEM_ENABLE_TESTING)
+  # endif()
+endif()

miniapps/multiapp/coupled-diffusion.cpp

@@ -0,0 +1,895 @@
+#include "mfem.hpp"
+#include "multiapp.hpp"
+#include <fstream>
+using namespace mfem;
+using namespace std;
+
+struct CaseContext
+{
+   int ser_ref = 1;         // Serial mesh refinement
+   int order = 3;           // Finite element order
+   bool visualization = true;// Visualization on/off
+   int grad_mode = 1;       // Gradient mode for the coupled operator - 0: finite difference,
+                            //                                          1: back/forward propagation
+   bool coupled = true;     // Coupled (true) vs. uncoupled (false) solves
+   int nl_iter = 50;        // Maximum number of nonlinear iterations
+   int lin_iter = 2000;     // Maximum number of linear iterations
+
+#if defined(MFEM_USE_DOUBLE)
+   real_t tol_nsolve = 1e-4;
+   real_t tol_lsolve = 1e-6;
+#elif defined(MFEM_USE_SINGLE)
+   real_t tol_nsolve = 1e-3;
+   real_t tol_lsolve = 1e-3;
+#else
+#error "Only single and double precision are supported!"
+   real_t tol_nsolve = 0;
+   real_t tol_lsolve = 0;
+#endif
+} ctx;
+
+void SetSolverParameters(IterativeSolver *solver, real_t rtol, real_t atol , int max_it,
+                         int print_level, bool iterative_mode);
+
+
+/// A functional diffusion coefficient (i.e., k(T))
+class FunctionalCoefficient : public Coefficient
+{
+public:
+   enum Mode { FUNC = 0, GRAD = 1};
+
+protected:
+   ParGridFunction *T_gf = nullptr;
+   real_t kref = 1.0;
+   real_t a0 = 0.0, a1 = 0.0, a2 = 0.0;
+   int findex = 0;
+   Mode mode = Mode::FUNC; // otherwise, grad
+
+public:
+   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref): 
+                         T_gf(T_gf), kref(kref) { }
+
+   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref, real_t a0):
+                         T_gf(T_gf), kref(kref), a0(a0) { findex = 1; }
+
+   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref,
+                         real_t a0, real_t a1, real_t a2): T_gf(T_gf),
+                         kref(kref), a0(a0), a1(a1), a2(a2) { findex = 2; }
+
+    real_t Exponential(real_t x, bool eval_f) const
+    { 
+      real_t f = kref*exp(a0*x);
+      return (eval_f ? f : a0*f);
+    }
+    real_t Polynomial(real_t x, bool eval_f) const
+    { 
+      return (eval_f ? kref*(a0 + a1*x + a2*x*x) : kref*(a1 + 2*a2*x));
+    }
+
+    void SetMode(Mode mode) { this->mode = mode; }
+    Mode GetMode() const { return mode; }
+    
+    void UpdateGridFunction(ParGridFunction *gf) { T_gf = gf; }
+
+    real_t Eval(real_t x, bool eval_f) const
+    {
+        switch (findex)
+        {
+        case 1:
+         return Exponential(x, eval_f);
+        case 2:
+         return Polynomial(x, eval_f);
+        default:
+         return kref;
+        }
+    }
+
+    real_t Eval(ElementTransformation &Tr,
+              const IntegrationPoint &ip) override
+    {
+        real_t T = T_gf ? T_gf->GetValue(Tr, ip) : 0.0;
+        bool eval_f = (mode == Mode::FUNC);
+        return Eval(T, eval_f);
+    }
+};
+
+
+/// A coefficient defined by the product of grid functions, e.g. k(T) = prod_i x_i
+class GridFunctionProductCoefficient : public Coefficient
+{
+protected:
+   std::vector<ParGridFunction*> &x;
+
+public:
+   GridFunctionProductCoefficient(std::vector<ParGridFunction*> &x) : x(x) { }
+
+   real_t Eval(ElementTransformation &Tr, const IntegrationPoint &ip) override
+   {
+      real_t prod = 1.0;
+      for(size_t i = 0; i < x.size(); i++)
+      {
+         real_t val = x[i]->GetValue(Tr, ip);
+         prod *= val;
+      }
+      return prod;
+   }
+};
+
+class CoefficientIntegrator : public NonlinearFormIntegrator
+{
+protected:
+   FunctionalCoefficient *func = nullptr;
+   Vector shape;
+
+public:
+   CoefficientIntegrator(FunctionalCoefficient *func) : func(func) { }
+
+
+   void SetCoefficient(FunctionalCoefficient *f) { func = f; }
+
+   void AssembleElementVector(const FiniteElement &el,
+                              ElementTransformation &Tr,
+                              const Vector &elfun, Vector &elvect)
+   {
+      int dof = el.GetDof();
+      shape.SetSize(dof);
+      elvect.SetSize(dof);
+      elvect = 0.0;
+
+      const IntegrationRule *ir = &el.GetNodes();
+
+      for (int i = 0; i < ir->GetNPoints(); i++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(i);
+         el.CalcShape(ip, shape);
+         Tr.SetIntPoint(&ip);
+         real_t x = elfun * shape; // Evaluate the function at the integration point
+         real_t fval = func->Eval(x, true);
+         for (int j = 0; j < dof; j++)
+         {
+            elvect(j) += fval * shape(j);
+         }
+      }
+   }
+
+   void AssembleElementGrad(const FiniteElement &el, ElementTransformation &Tr,
+                            const Vector &elfun, DenseMatrix &elmat)
+   {
+      int dof = el.GetDof();
+      shape.SetSize(dof);
+      elmat.SetSize(dof);
+      elmat = 0.0;
+
+      const IntegrationRule *ir = &el.GetNodes();
+
+      for (int i = 0; i < ir->GetNPoints(); i++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(i);
+         el.CalcShape(ip, shape);
+         Tr.SetIntPoint(&ip);
+         real_t x = elfun * shape; // Evaluate the function at the integration point
+         real_t dfdx = func->Eval(x, false); // Evaluate the derivative of the function at the integration point
+         for (int j = 0; j < dof; j++)
+         {
+            elmat(j,j) += dfdx * shape(j); // Diagonal contribution to the Jacobian
+         }
+      }
+   }
+};
+
+
+class NonlinearDiffusionIntegrator : public NonlinearFormIntegrator
+{
+protected:
+   Coefficient *k;
+   Coefficient *dk;
+
+   Vector u, vec, shape;
+   DenseMatrix dshape, dshapedxt, adjJ;
+public:
+   NonlinearDiffusionIntegrator(Coefficient *kappa, Coefficient *dkappa) :
+                                k(kappa), dk(dkappa) { }
+
+   virtual void AssembleElementVector(const FiniteElement &el,
+                                      ElementTransformation &Tr,
+                                      const Vector &elfun, Vector &elvec)
+   {
+      int dim = el.GetDim();
+      int dof = el.GetDof();
+      real_t w;
+
+      elvec.SetSize(dof);
+      elvec = 0.0;
+
+      const IntegrationRule *ir = IntRule ? IntRule : &IntRules.Get(el.GetGeomType(), 2*el.GetOrder());
+      u.SetSize(dim);
+      vec.SetSize(dim);
+      dshape.SetSize(dof, dim);
+      adjJ.SetSize(dim, dim);
+
+      for (int i = 0; i < ir->GetNPoints(); i++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(i);
+         el.CalcDShape(ip, dshape);
+
+         Tr.SetIntPoint(&ip);
+         CalcAdjugate(Tr.Jacobian(), adjJ);
+         w = ip.weight / Tr.Weight();
+
+         dshape.MultTranspose(elfun, u);
+         adjJ.MultTranspose(u, vec);
+         if(k)
+         {
+            w *= k->Eval(Tr, ip);
+         }
+
+         vec *= w;
+         adjJ.Mult(vec, u);
+         dshape.AddMult(u, elvec);
+      }
+   }
+
+   void AssembleElementGrad(const FiniteElement &el, ElementTransformation &Tr,
+                            const Vector &elfun, DenseMatrix &elmat)
+   {
+      int dim = el.GetDim();
+      int dof = el.GetDof();
+      real_t w, k0 = 0.0, dk0 = 0.0;
+
+      elmat.SetSize(dof);
+      elmat = 0.0;
+
+      const IntegrationRule *ir = IntRule ? IntRule : &IntRules.Get(el.GetGeomType(), 2*el.GetOrder());
+      u.SetSize(dim);
+      shape.SetSize(dof);
+      vec.SetSize(dof);
+      dshape.SetSize(dof, dim);
+      dshapedxt.SetSize(dof, dim);
+
+      // f = grad(psi) * k(u) * grad(T)
+      // df/dT = grad(psi) ( k(u0) * grad(T) + k'(u0) * grad(u0) * T )
+      for (int i = 0; i < ir->GetNPoints(); i++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(i);
+         el.CalcShape(ip, shape);
+         el.CalcDShape(ip, dshape);
+
+         Tr.SetIntPoint(&ip);
+         w = ip.weight / Tr.Weight();
+
+         Mult(dshape, Tr.AdjugateJacobian(), dshapedxt);
+
+         k0  = k ? k->Eval(Tr, ip) : 0.0;
+         dk0 = dk ? dk->Eval(Tr, ip) : 0.0;
+
+         if(k0 != 0.0) // grad(psi) * k(u0) * grad(T)
+         {
+            real_t kdT = w*k0;
+            AddMult_a_AAt(kdT, dshapedxt, elmat);
+         }
+
+         if(dk0 != 0.0) // grad(psi) * (k'(T0) * grad(T0)) * T
+         {
+            dk0 = w*dk->Eval(Tr, ip);
+            dshapedxt.MultTranspose(elfun, u); // grad(T0) in physical space
+            u *= dk0; // k'(T0) * grad(T0)
+            dshapedxt.Mult(u, vec); // grad(psi) * k'(T0) * grad(T0)
+            AddMultVWt(vec, shape, elmat); // grad(psi) * k'(T0) * grad(T0) * T
+         }
+      }
+   }
+};
+
+/// An application that takes an input field T, and computes an output field k(T)
+// represented by the FunctionalCoefficient class.
+class DiffusionCoefficient : public GraphNode
+{
+public:
+   using Mode = FunctionalCoefficient::Mode;
+
+protected:
+   ParFiniteElementSpace &fes;
+   mutable ParGridFunction T, k;
+   mutable FunctionalCoefficient *kc;
+   // mutable Vector tdof, kdof, dk_dof, dT_dof;
+   mutable Mode mode = Mode::FUNC;
+
+   mutable ParNonlinearForm Nform;
+   mutable Operator *J = nullptr; // Jacobian for the nonlinear form
+
+   CoefficientIntegrator *coeff_integrator = nullptr;
+
+public:
+   DiffusionCoefficient(ParFiniteElementSpace &fes) :
+                        GraphNode(fes.GetTrueVSize()), fes(fes), T(&fes), k(&fes),
+                        kc(new FunctionalCoefficient(&T, 1.0, 5.0e-2)),
+                        Nform(&fes),
+                        coeff_integrator(new CoefficientIntegrator(kc))
+   {
+      k = 0.0;
+      T = 0.0;
+      k.ProjectCoefficient(*kc);
+
+      // Testing with the nonlinear form framework to compute k(T) and dk/dT
+      Nform.AddDomainIntegrator(coeff_integrator); // Transfer ownership
+      Nform.SetGradientType(Operator::Type::Hypre_ParCSR);
+      Nform.Setup();
+
+      SetInputOffsets(Array<int>({0, fes.GetTrueVSize()}));
+      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
+   }
+
+   void SetMode(Mode mode) { this->mode = mode; }
+
+   FunctionalCoefficient* GetCoefficient() { return kc; }
+
+   void SetCoefficient(FunctionalCoefficient *fc)
+   {
+      if(kc) delete kc;
+      kc = fc;
+      kc->SetMode(mode);
+      kc->UpdateGridFunction(&T);
+      coeff_integrator->SetCoefficient(kc);
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector yb(y.GetData(), OutputOffsets());
+
+      MultiVector xmv(1), ymv(1);
+      xmv.MakeRef(0, xb.GetBlock(0));
+      ymv.MakeRef(0, yb.GetBlock(0));
+
+      const_cast<DiffusionCoefficient*>(this)->Mult(xmv, ymv);
+   }
+
+   void Mult(const MultiVector &x, MultiVector &y) override
+   {
+      const Vector &tdof = x[0];
+      Vector &kdof = y[0];
+
+      Nform.Mult(tdof, kdof);
+      if(exec_mode == GraphNode::GRADIENT_MODE)
+      {
+         J = &Nform.GetGradient(tdof); // Store jacobian for JVP
+      }
+      else
+      {
+         J = nullptr; // Clear the Jacobian if not in gradient mode
+      }
+   }
+
+   // TODO: Possibly delete and only support MultiVector version of GradientMult
+   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector dxb(dx.GetData(), InputOffsets());
+      BlockVector dyb(dy.GetData(), OutputOffsets());
+
+      MultiVector xmv(1), dxmv(1), dymv(1);
+      xmv.MakeRef(0, xb.GetBlock(0));
+      dxmv.MakeRef(0, dxb.GetBlock(0));
+      dymv.MakeRef(0, dyb.GetBlock(0));
+      const_cast<DiffusionCoefficient*>(this)->GradientMult(xmv, dxmv, dymv);
+   }
+
+   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
+   {
+      const Vector &tdof = x[0];
+      const Vector &xadj = dx[0];
+      Vector &yadj = dy[0];
+
+      if(J)
+      {
+         J->Mult(xadj, yadj);
+      }
+      else
+      {
+         J = &Nform.GetGradient(tdof); // Store jacobian for JVP
+         J->Mult(xadj, yadj);
+      }
+   }
+
+   ~DiffusionCoefficient() override
+   {
+      if(kc) delete kc;
+   }
+};
+
+/// An application that takes n input fields x_i, and computes an output 
+/// field prod(x) := y = prod_i x_i.
+/// Also provides the derivative dy/dx_i = prod_{j!=i} x_j * dx_i/dx for i = 0,...,n-1.
+class ProductGridFunctions : public GraphNode
+{
+protected:
+
+   ParFiniteElementSpace &fes;
+   mutable std::vector<ParGridFunction*> x_gf;
+   mutable Vector dfdx;
+   mutable ParGridFunction y_gf;
+   mutable GridFunctionProductCoefficient prod_coeff;
+
+public:
+   ProductGridFunctions(ParFiniteElementSpace &fes, int n) :
+                     //   GraphNode(fes.GetTrueVSize()),
+                       GraphNode(fes.GetTrueVSize(), fes.GetTrueVSize() * n),
+                       fes(fes), x_gf(n),
+                       y_gf(&fes), prod_coeff(x_gf)
+   {
+      Array<int> offsets(n+1);
+      offsets[0] = 0;
+      for (int i = 0; i < n; i++)
+      {
+         x_gf[i]  = new ParGridFunction(&fes);
+         *x_gf[i] = 0.0;
+         offsets[i+1] = offsets[i] + fes.GetTrueVSize();
+      }
+      y_gf = 0.0;
+      y_gf.ProjectCoefficient(prod_coeff);
+
+      SetInputOffsets(offsets);
+      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector yb(y.GetData(), OutputOffsets());
+
+      MultiVector xmv(x_gf.size()), ymv(1);
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         xmv.MakeRef(i, xb.GetBlock(i));
+      }
+      ymv.MakeRef(0, yb.GetBlock(0));
+      const_cast<ProductGridFunctions*>(this)->Mult(xmv, ymv);
+   }
+
+   void Mult(const MultiVector &x, MultiVector &y) override
+   {
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         const Vector &x_dof = x[i];
+         x_gf[i]->SetFromTrueDofs(x_dof);
+      }
+
+      Field *out_field = OutputField(0);
+      Vector &y_dof = y[0];
+      y_gf.ProjectCoefficient(prod_coeff);
+      y_gf.GetTrueDofs(y_dof);
+   }
+
+   // TODO: Possibly delete and only support MultiVector version of GradientMult
+   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector dxb(dx.GetData(), InputOffsets());
+      BlockVector dyb(dy.GetData(), OutputOffsets());
+
+      MultiVector xmv(x_gf.size()), dxmv(x_gf.size()), dymv(1);
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         xmv.MakeRef(i, xb.GetBlock(i));
+         dxmv.MakeRef(i, dxb.GetBlock(i));
+      }
+      dymv.MakeRef(0, dyb.GetBlock(0));
+      const_cast<ProductGridFunctions*>(this)->GradientMult(xmv, dxmv, dymv);
+   }
+
+   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
+   {
+      // Jacobian vector product for y = prod_i x_i is:
+      // dy/dx = sum_i (prod_{j!=i} x_j * dx_i/dx)
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         const Vector &x_dof = x[i];
+         x_gf[i]->SetFromTrueDofs(x_dof); // Set all x_i
+      }
+
+      Vector &jvp = dy[0];
+      jvp = 0.0;
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         const Vector &x_dof = x[i];
+         const Vector &dx_dof = dx[i]; // Get dx_i/dx
+
+         x_gf[i]->SetFromTrueDofs(dx_dof); // Set x_i = dx_i/dx for i-th term in the product
+         y_gf.ProjectCoefficient(prod_coeff); // Recompute product with x_i replaced by dx_i/dx
+         y_gf.GetTrueDofs(dfdx); // Get prod_{j!=i} x_j * dx_i/dx for i-th term
+         jvp += dfdx; // Accumulate contribution from i-th term
+         x_gf[i]->SetFromTrueDofs(x_dof); // reset to original value for next iteration
+      }
+   }
+
+   ~ProductGridFunctions() override
+   {
+      for (size_t i = 0; i < x_gf.size(); i++)
+      {
+         if(x_gf[i]) delete x_gf[i];
+      }
+   }
+};
+
+
+/// An application that represents the nonlinear diffusion operator: f(T) = -Div(k(u) grad(T)) 
+/// with input field T and k, and output field f(T).
+class DiffusionOperator : public GraphNode
+{
+public:
+
+   // Mesh and finite element space
+   ParMesh &mesh;
+   ParFiniteElementSpace &fes;
+
+   /// Essential dof array.
+   Array<int> ess_tdofs;
+
+   /// Grid functions for the temperature and heat flux
+   mutable ParGridFunction T, k, dk;
+   mutable GridFunctionCoefficient k_gfc, dk_gfc;
+   mutable ParNonlinearForm Nform;
+   mutable ParLinearForm bform;
+   mutable Vector b;
+
+   ConstantCoefficient zero_coeff, one_coeff;
+
+   mutable FunctionalCoefficient *kc = nullptr;
+   mutable HypreParMatrix *dfdk_mat = nullptr, *dfdT_mat = nullptr;
+
+public:
+
+   DiffusionOperator(ParFiniteElementSpace &fes_) :
+                     // GraphNode(fes_.GetTrueVSize()),
+                     GraphNode(fes_.GetTrueVSize(),2*fes_.GetTrueVSize()),
+                     mesh(*fes_.GetParMesh()), fes(fes_),
+                     T(&fes), k(&fes), dk(&fes),
+                     k_gfc(&k), dk_gfc(&dk),
+                     Nform(&fes), bform(&fes),
+                     zero_coeff(0.0), one_coeff(1.0)
+   {
+      fes.GetBoundaryTrueDofs(ess_tdofs);
+      T = 0.0;
+      k = 0.0;
+      dk = 0.0;
+
+      bform.AddDomainIntegrator(new DomainLFIntegrator(one_coeff));
+      Nform.AddDomainIntegrator(new NonlinearDiffusionIntegrator(&k_gfc, &dk_gfc));
+      Nform.SetGradientType(Operator::Type::Hypre_ParCSR);
+
+      b.SetSize(fes.GetTrueVSize()); b = 0.0;
+      Assemble();
+
+      SetInputOffsets(Array<int>({0, fes.GetTrueVSize(), 2*fes.GetTrueVSize()}));
+      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
+   }
+
+   void SetCoefficient(FunctionalCoefficient *fc) { kc = fc; }
+
+   void Assemble()
+   {
+      AssembleLinearForms();
+      AssembleBilinearForms();
+      AssembleNonlinearForms();
+   }
+
+   void AssembleBilinearForms()
+   {}
+
+   void AssembleNonlinearForms()
+   {
+      Nform.SetEssentialTrueDofs(ess_tdofs);
+      Nform.Setup();
+   }
+
+   void AssembleLinearForms()
+   {
+      bform.Assemble();
+      bform.ParallelAssemble(b);
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector yb(y.GetData(), OutputOffsets());
+
+      MultiVector xmv(2), ymv(1);
+      xmv.MakeRef(0, xb.GetBlock(0));
+      xmv.MakeRef(1, xb.GetBlock(1));
+      ymv.MakeRef(0, yb.GetBlock(0));
+
+      const_cast<DiffusionOperator*>(this)->Mult(xmv, ymv);
+   }
+
+   void Mult(const MultiVector &x, MultiVector &y) override
+   {
+      const Vector &tdofs = x[0];
+      const Vector &kdofs = x[1];
+      Vector &fdofs = y[0];
+
+      k.SetFromTrueDofs(kdofs); // update for use in k_gfc
+
+      if(exec_mode == GraphNode::GRADIENT_MODE)
+      {
+         if(dfdT_mat) delete dfdT_mat;
+         if(dfdk_mat) delete dfdk_mat;
+
+         dk = 0.0;
+         k.SetFromTrueDofs(kdofs);
+         Operator* grad = &Nform.GetGradient(tdofs);
+         dfdT_mat = new HypreParMatrix(dynamic_cast<const HypreParMatrix&>(*grad)); // deep copy
+
+         dk = 1.0;
+         k  = 0.0;
+         grad = &Nform.GetGradient(tdofs);
+         dfdk_mat = new HypreParMatrix(dynamic_cast<const HypreParMatrix&>(*grad)); // deep copy
+      }
+      else
+      {
+         if(dfdT_mat) { delete dfdT_mat; dfdT_mat = nullptr; }
+         if(dfdk_mat) { delete dfdk_mat; dfdk_mat = nullptr; }
+      }
+
+      Nform.Mult(tdofs, fdofs);
+      fdofs.SetSubVector(ess_tdofs, 0.0);
+   }
+
+   // Exact block jacobian [df/dT, df/dk]
+   Operator& GetGradient(const Vector &x) const override
+   {
+      MFEM_ABORT("GetGradient not implemented for DiffusionOperator");
+   }
+
+   // TODO: Possibly delete and only support MultiVector version of GradientMult
+   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
+   {
+      BlockVector xb(x.GetData(), InputOffsets());
+      BlockVector dxb(dx.GetData(), InputOffsets());
+      BlockVector dyb(dy.GetData(), OutputOffsets());
+
+      Vector &Tadj = dxb.GetBlock(0);
+      Vector &kadj = dxb.GetBlock(1);
+      Vector &yadj = dyb.GetBlock(0);
+
+      Vector &tdofs = xb.GetBlock(0);
+      Vector &kdofs = xb.GetBlock(1);
+
+      dfdT_mat->Mult(Tadj, yadj);
+      dfdk_mat->AddMult(kadj, yadj);
+   }
+
+   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
+   {
+      const Vector &Tadj = dx[0];
+      const Vector &kadj = dx[1];
+      Vector &yadj = dy[0];
+
+      const Vector &tdofs = x[0];
+      const Vector &kdofs = x[1];
+
+      dfdT_mat->Mult(Tadj, yadj);
+      dfdk_mat->AddMult(kadj, yadj);
+   }
+
+   /// @brief Destroy the DiffusionOperator object
+   ~DiffusionOperator() override
+   {
+      if(dfdT_mat) delete dfdT_mat;
+      if(dfdk_mat) delete dfdk_mat;
+   }
+};
+
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+   Hypre::Init();
+
+   using GradMode = DAGraph::GradMode;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&ctx.order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&ctx.visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&ctx.ser_ref, "-rs", "--serial-refine",
+                  "Number of times to refine the mesh in serial.");
+
+   args.AddOption(&ctx.grad_mode, "-gm", "--grad-mode",
+                  "Gradient mode for the coupled operator (0: exact, 1: finite difference, 2: algorithmic differentiation)");
+   args.AddOption(&ctx.coupled, "-cp", "--coupled", "-ucp", "--uncoupled",
+                  "Coupled (true) vs. uncoupled (false) solves.");
+   args.ParseCheck();
+
+
+   int order = ctx.order;
+   std::string mesh_file = "../../data/star.mesh";
+   Mesh *serial_mesh = new Mesh(mesh_file);
+   int dim = serial_mesh->Dimension();
+
+   for (int i = 0; i < ctx.ser_ref; ++i) { serial_mesh->UniformRefinement(); }
+   serial_mesh->SetCurvature(order, false, dim, Ordering::byNODES);
+
+   ParMesh pmesh(MPI_COMM_WORLD, *serial_mesh);
+   delete serial_mesh;
+   pmesh.UniformRefinement();
+
+   // Finite element spaces
+   H1_FECollection fec(order, dim);
+   ParFiniteElementSpace fes(&pmesh, &fec);
+
+   // Build all operator nodes
+   DiffusionCoefficient diff_coeff_1(fes);
+   diff_coeff_1.SetName("k(T1)");
+   diff_coeff_1.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 3.5e-2));
+   // diff_coeff_1.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 1.0, 0.1, 0.0));
+
+   DiffusionCoefficient diff_coeff_2(fes);
+   diff_coeff_2.SetName("k(T2)");
+   diff_coeff_2.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 1.0, 2.0, 0.0));
+   // diff_coeff_2.SetCoefficient(new FunctionalCoefficient(nullptr, 1.5, 2.5e-2));
+
+   ProductGridFunctions prod_coeff(fes, 2);
+   prod_coeff.SetName("k(T1,T2)");
+
+   DiffusionOperator diff_op1(fes);
+   diff_op1.SetName("Div(k(T1,T2) grad(T1))");
+   diff_op1.SetCoefficient(diff_coeff_1.GetCoefficient());
+
+   DiffusionOperator diff_op2(fes);
+   diff_op2.SetName("Div(k(T1,T2) grad(T2))");
+   diff_op2.SetCoefficient(diff_coeff_2.GetCoefficient());
+
+
+   // Build the DAG in any order, and then sort it to ensure the correct execution order
+   DAGraph dag(5);
+   dag.AddOperator(&diff_coeff_1);
+   dag.AddOperator(&diff_op1, fes.GetTrueVSize());
+   dag.AddOperator(&diff_op2, fes.GetTrueVSize());
+   dag.AddOperator(&diff_coeff_2);
+   dag.AddOperator(&prod_coeff);
+
+   Vector k1vec(fes.GetTrueVSize()); k1vec = 0.0;
+   Vector k2vec(fes.GetTrueVSize()); k2vec = 0.0;
+   Vector kpvec(fes.GetTrueVSize()); kpvec = 0.0;
+
+   Vector k1adj(fes.GetTrueVSize()); k1adj = 0.0;
+   Vector k2adj(fes.GetTrueVSize()); k2adj = 0.0;
+   // Vector kpadj(fes.GetTrueVSize()); kpadj = 0.0;
+
+   // Input fields get data from 'x' in DAGraph::Mult(x, y)
+   Field T1_field(nullptr, nullptr);
+   Field T2_field(nullptr, nullptr);
+
+   // Write space for data and adjoint only needed
+   // for the intermediate fields k1, k2, and k_prod
+   Field k1_field(&k1vec, &k1adj);
+   Field k2_field(&k2vec, &k2adj);
+   Field kp_field(&kpvec, &kpvec); // can use same space for data & adjoint
+
+   // Output fields get data from 'y' in DAGraph::Mult(x, y)
+   Field f1_field(nullptr, nullptr);
+   Field f2_field(nullptr, nullptr);
+
+
+   // Add input and output to the DAG
+   int sz = fes.GetTrueVSize();
+   dag.AddInput(&T1_field, sz);
+   dag.AddInput(&T2_field, sz);
+   dag.AddOutput(&f1_field, sz);
+   dag.AddOutput(&f2_field, sz);
+
+   // Form connections between the nodes in the DAG
+   diff_coeff_1.AddInput(&T1_field);
+   diff_coeff_1.AddOutput(&k1_field);
+
+   diff_coeff_2.AddInput(&T2_field);
+   diff_coeff_2.AddOutput(&k2_field);
+
+   prod_coeff.AddInputs(&k1_field, &k2_field);
+   prod_coeff.AddOutput(&kp_field);
+
+   diff_op1.AddInput(&T1_field);
+   diff_op1.AddOutput(&f1_field);
+
+   diff_op2.AddInput(&T2_field);
+   diff_op2.AddOutput(&f2_field);
+
+   if(ctx.coupled)
+   {
+      diff_op1.AddInput(&kp_field); // kp_field
+      diff_op2.AddInput(prod_coeff.OutputField(0)); // Can also use kp_field directly
+   }
+   else
+   {
+      diff_op1.AddInput(&k1_field); // Can also use diff_coeff_1.OutputField(0)
+      diff_op2.AddInput(&k2_field); // Can also use diff_coeff_2.OutputField(0)
+   }
+
+   // Assemble DAG: topological sort, validate nodes, etc.
+   dag.Assemble();
+
+   std::string output_prefix = ctx.coupled ? "Coupled_Diffusion" : "Uncoupled_Diffusion";
+
+   if(Mpi::Root())
+   {
+      std::ofstream fout(output_prefix+"-dag.txt");
+      fout << "{\n";
+      dag.Save(fout);
+      fout << "}\n";
+      fout << std::flush;
+      fout.close();
+   }
+
+   // Set initial guess and boundary conditions for T1 and T2
+   Array<int> ess_tdofs;
+   fes.GetBoundaryTrueDofs(ess_tdofs);
+
+   int T1_idx = 0;
+   int T2_idx = 1;
+
+   BlockVector xb(dag.InputOffsets());
+   BlockVector yb(dag.OutputOffsets());
+
+   xb.GetBlock(T1_idx).Randomize();
+   xb.GetBlock(T2_idx).Randomize();
+   xb.GetBlock(T1_idx).SetSubVector(ess_tdofs, 0.0);
+   xb.GetBlock(T2_idx).SetSubVector(ess_tdofs, 0.0);
+
+   // Build the nonlinear solver and linear solver for the DAG
+   NewtonSolver newton_solver(pmesh.GetComm());
+   GMRESSolver linear_solver(pmesh.GetComm());
+   linear_solver.SetKDim(500);
+   SetSolverParameters(&newton_solver, ctx.tol_nsolve, 0.0, ctx.nl_iter, 1, true);
+   SetSolverParameters(&linear_solver, ctx.tol_lsolve, 0.0, ctx.lin_iter, 1, false);
+
+   newton_solver.SetPreconditioner(linear_solver);
+   linear_solver.SetPrintLevel(1);
+
+   // Set the gradient mode for the DAG and solve the coupled system
+   GradMode gm = static_cast<GradMode>(ctx.grad_mode);
+   dag.SetGradientMode(gm);
+   newton_solver.SetOperator(dag);
+   newton_solver.Mult(xb, yb);
+
+   ParaViewDataCollection *pv = nullptr;
+   if (ctx.visualization)
+   {
+      std::string pv_prefix;
+      switch (ctx.grad_mode)
+      {
+         case 0: pv_prefix = "FD"; break;
+         case 1: pv_prefix = "MF"; break;
+         default: pv_prefix = "Unknown"; break;
+      }
+
+      pv = new ParaViewDataCollection(output_prefix+"-"+pv_prefix, &pmesh);
+      pv->SetLevelsOfDetail(order);
+      pv->SetDataFormat(VTKFormat::BINARY);
+      pv->SetHighOrderOutput(true);
+
+      ParGridFunction T1_gf(&fes);
+      ParGridFunction T2_gf(&fes);
+      T1_gf.SetFromTrueDofs(yb.GetBlock(T1_idx));
+      T2_gf.SetFromTrueDofs(yb.GetBlock(T2_idx));
+
+      pv->RegisterField("T1", &T1_gf);
+      pv->RegisterField("T2", &T2_gf);
+      pv->Save();
+      delete pv;
+   }
+
+   std::cout << "Finished solving the coupled diffusion problem." << std::endl;
+   return 0;
+}
+
+void SetSolverParameters(IterativeSolver *solver, real_t rtol, real_t atol,
+                         int max_it, int print_level, bool iterative_mode)
+{
+    solver->SetRelTol(rtol);
+    solver->SetAbsTol(atol);
+    solver->SetMaxIter(max_it);
+    solver->SetPrintLevel(print_level);
+    solver->iterative_mode = iterative_mode;
+}

miniapps/multiapp/multiapp.cpp

@@ -0,0 +1,873 @@
+// 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 "multiapp.hpp"
+
+namespace mfem
+{
+
+DAGraph::~DAGraph()
+{
+    for(int i=0; i < nnodes; i++)
+    {
+        if(node_owned[i] && nodes[i]) delete nodes[i];
+    }
+    if(grad) delete grad;
+}
+
+void DAGraph::Assemble()
+{
+    // Sort graph nodes topologically to ensure correct execution order
+    // Ordering is not unique, hence, id->index maps are needed
+    TopologicalSort();
+
+    // Collect all fields from the nodes into the field map
+    CollectFieldMaps();
+
+    // Compute depth of the graph nodes
+    ComputeDepth();
+
+    // Validate each node
+    for (auto &node : nodes)
+    {
+        ValidateNode(*node);
+    }
+
+    // Update width and height of the DAG from offsets
+    // Check that the input and output offsets are consistent
+    ValidateOffsets();
+    width  = input_offsets.Last();
+    height = output_offsets.Last();
+
+    // Delete any existing gradient operator as node ordering may have changed
+    if (grad) delete grad;
+
+    assembled = true;
+}
+
+void DAGraph::ValidateOffsets()
+{
+    // Check that the input and output offsets are consistent
+    // with the number of inputs and outputs
+    if(InputFields().Size() > 1)
+    {
+        MFEM_ASSERT(input_offsets.Size() == InputFields().Size() + 1,
+                    "Input offsets size inconsistent with number of input fields");
+    }
+    else
+    {
+        input_offsets = Array<int>({0, nodes[0]->Width()});
+    }
+
+    if(OutputFields().Size() > 1)
+    {
+        MFEM_ASSERT(output_offsets.Size() == OutputFields().Size() + 1,
+                    "Output offsets size inconsistent with number of output fields");
+    }
+    else
+    {
+        output_offsets = Array<int>({0, nodes.Last()->Height()});
+    }
+}
+
+void DAGraph::ValidateNode(GraphNode &node)
+{
+    // Validate that the node's input and output fields are consistent with the graph's field map
+    auto inputs = node.InputFields();
+    auto outputs = node.OutputFields();
+
+    // Check offsets match width and height of the node
+    MFEM_ASSERT(node.InputOffsets().Last() == node.Width(),
+                "Node ID: " << node.ID() << " input offsets do not match node width.");
+    MFEM_ASSERT(node.OutputOffsets().Last() == node.Height(),
+                "Node ID: " << node.ID() << " output offsets do not match node height.");
+
+    // Check number of input and output fields match the offsets
+    MFEM_ASSERT(node.InputOffsets().Size() == inputs.Size() + 1,
+                "Node input offsets size inconsistent with number of input fields");
+    MFEM_ASSERT(node.OutputOffsets().Size() == outputs.Size() + 1,
+                "Node output offsets size inconsistent with number of output fields");
+
+    // Check that all input and output fields are registered in the graph's field map
+    for(auto input_field : inputs)
+    {
+        MFEM_ASSERT(fid_to_index.Has(input_field->ID()),
+                    "Input field ID " << input_field->ID() << " not found in graph's field map");
+    }
+    for(auto output_field : outputs)
+    {
+        MFEM_ASSERT(fid_to_index.Has(output_field->ID()),
+                    "Output field ID " << output_field->ID() << " not found in graph's field map");
+    }
+}
+
+void DAGraph::TopologicalSort()
+{
+    Array<int> sorted_indices;
+    sorted_indices.Reserve(nnodes);
+
+    Array<bool> visited(nnodes);
+    visited = false; // Initialize all nodes as unvisited
+
+    // Perform a depth-first search to sort the nodes topologically
+    std::function<void(int)> DepthFirstSearch = [&](int node_index)
+    {
+        if(visited[node_index]) return;
+        visited[node_index] = true;
+        auto node = nodes[node_index];
+        // Visit all nodes that this node depends on
+        for(auto input_field : node->InputFields())
+        {
+            for(int j=0; j < nnodes; j++)
+            {
+                auto other_node = nodes[j];
+                if(other_node == node) continue;
+                for(auto output_field : other_node->OutputFields())
+                {
+                    if(input_field->ID() == output_field->ID()) // Compare by unique ID
+                    {
+                        DepthFirstSearch(j);
+                    }
+                }
+            }
+        }
+        sorted_indices.push_back(node_index);
+    };
+
+    for(int i=0; i < nnodes; i++)
+    {
+        DepthFirstSearch(i);
+    }
+
+    nodes.Permute(sorted_indices);
+    node_owned.Permute(sorted_indices);
+
+    // Update the node indices after sorting
+    for(int i=0; i < nnodes; i++)
+    {
+        nodes[i]->SetNodeIndex(i);
+    }
+
+    sorted = true;
+}
+
+void DAGraph::ComputeDepth()
+{
+    // Compute depth of ordered nodes
+    node_depth.SetSize(nnodes);
+    node_depth = 0;
+    for(int i=0; i < nnodes; i++)
+    {
+        int max_depth = 0;
+        auto node = nodes[i];
+        for(auto input_field : node->InputFields())
+        {
+            for(int j=0; j < i; j++)
+            {
+                auto other_node = nodes[j];
+                if(other_node == node) continue;
+                for(auto output_field : other_node->OutputFields())
+                {
+                    if(input_field->ID() == output_field->ID()) // Compare by unique ID
+                    {
+                        max_depth = std::max(max_depth, node_depth[j] + 1);
+                    }
+                }
+            }
+        }
+        node_depth[i] = max_depth;
+    }
+}
+
+void DAGraph::CollectFieldMaps()
+{
+    MFEM_ASSERT(sorted, "DAGraph must be topologically sorted before collecting fields");
+
+    fid_to_index.clear();
+    fid_to_field.clear();
+
+    int nfields = 0;
+    for (auto f : InputFields())
+    {
+        fid_to_index.Register(f->ID(), nfields++);
+        fid_to_field.Register(f->ID(), f);
+    }
+
+    for (auto &node : nodes)
+    {
+        for (auto f : node->OutputFields())
+        {
+            if (!fid_to_index.Has(f->ID()))
+            {
+                fid_to_index.Register(f->ID(), nfields++);
+            }
+            if (!fid_to_field.Has(f->ID()))
+            {
+                fid_to_field.Register(f->ID(), f);
+            }
+        }
+    }
+    // TODO: Possibly add all intermediate fields from nodes to the graph's FieldCollection
+}
+
+void DAGraph::Mult(const Vector &x, Vector &y) const
+{
+    MFEM_ASSERT(width == x.Size(), "Input vector size (" << x.Size()
+                << ") must match matrix width (" << width << ")");
+
+    MFEM_ASSERT(height == y.Size(), "Output vector size (" << y.Size()
+                << ") must match matrix height (" << height << ")");
+
+    auto inputs  = InputFields();
+    auto outputs = OutputFields();
+
+    BlockVector xb(x.GetData(), input_offsets);
+    BlockVector yb(y.GetData(), output_offsets);
+    MultiVector xmv(inputs.Size()), ymv(outputs.Size());
+
+    // Set the data pointers of the input and output fields
+    // of the graph to point to the corresponding blocks of
+    // the input and output vectors
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        xmv.MakeRef(i, xb.GetBlock(i));
+    }
+
+    for(int i=0; i < outputs.Size(); i++)
+    {
+        ymv.MakeRef(i, yb.GetBlock(i));
+    }
+
+    const_cast<DAGraph*>(this)->Mult(xmv, ymv);
+}
+
+void DAGraph::Mult(const MultiVector &x, MultiVector &y)
+{
+    auto inputs  = InputFields();
+    auto outputs = OutputFields();
+
+    MFEM_ASSERT(inputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of input fields (" << inputs.Size() << ")");
+
+    MFEM_ASSERT(outputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of output fields (" << outputs.Size() << ")");
+
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        inputs[i]->SetData(const_cast<Vector*>(&x[i]));
+    }
+    for (int i=0; i < outputs.Size(); i++)
+    {
+        outputs[i]->SetData(&y[i]);
+    }
+
+    auto index_map = GetFieldIdToIndexMap();
+    auto fld_map = GetFieldIdToFieldMap();
+    int nfields = index_map.NumFields();
+    MultiVector ymv(nfields); // TODO: Should this be a member function?
+
+    // Assemble the multivector from the individual fields based on their IDs
+    // This multivector contains all input, output, and intermediate fields in the graph
+    for (auto const& [id, idx] : index_map)
+    {
+        if (fld_map.Has(id))
+        {
+            auto field = fld_map.Get(id);
+            ymv.MakeRef(idx, *field->Data());
+        }
+        else
+        {
+            MFEM_ABORT("Field ID " << id << " not found in field map");
+        }
+    }
+    
+    Execute(x, ymv);
+
+    for(auto &f : inputs)
+    {
+        f->SetData(nullptr);
+    }
+    for(auto &f : outputs)
+    {
+        f->SetData(nullptr);
+    }
+}
+
+void DAGraph::Execute(const MultiVector &x, MultiVector &y) const
+{
+    MFEM_ASSERT(assembled, "DAGraph must be assembled before calling Execute()");
+
+    MFEM_ASSERT(x.NumBlocks() == InputFields().Size(),
+                "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of input fields (" << InputFields().Size() << ")");
+    
+    auto index_map = GetFieldIdToIndexMap();
+    
+    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
+                "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of fields (" << index_map.NumFields() << ")");
+
+    auto inputs  = InputFields();
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        int idx = index_map.Get(inputs[i]->ID());
+        if(&y[idx] != &x[i]) // copy data, if address is different
+        {
+            y[idx] = x[i];
+        }
+    }
+
+    if(input_type == InputType::VECTOR)
+    {
+        x_node.SetSize(MaxWidth());
+        y_node.SetSize(MaxHeight());
+
+        for (auto node : nodes)
+        {
+            x_node.SetSize(node->Width());
+            y_node.SetSize(node->Height());
+
+            // Assemble input fields into a single vector for the node
+            auto node_inputs = node->InputFields();
+            auto ioffsets = node->InputOffsets();
+            for (int i=0; i < node_inputs.Size(); i++)
+            {
+                auto in_field = node_inputs[i];
+                int idx = index_map.Get(in_field->ID());
+                x_node.SetVector(y[idx],ioffsets[i]);
+            }
+
+            node->Mult(x_node, y_node);
+
+            // Disassemble output vector back
+            auto node_outputs = node->OutputFields();
+            BlockVector ynb(y_node.GetData(), node->OutputOffsets());
+            for (int i=0; i < node_outputs.Size(); i++)
+            {
+                auto out_field = node_outputs[i];
+                int idx = index_map.Get(out_field->ID());
+                y[idx] = ynb.GetBlock(i);
+            }
+        }
+    }
+    else if(input_type == InputType::MULTIVECTOR)
+    {
+        for (auto node : nodes)
+        {
+            auto node_inputs = node->InputFields();
+            auto node_outputs = node->OutputFields();
+            xmv_node.SetNumBlocks(node_inputs.Size());
+            ymv_node.SetNumBlocks(node_outputs.Size());
+
+            for (int i=0; i < node_inputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_inputs[i]->ID());
+                xmv_node.MakeRef(i, y[idx]);
+            }
+            for (int i=0; i < node_outputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_outputs[i]->ID());
+                ymv_node.MakeRef(i, y[idx]);
+            }
+            node->Mult(xmv_node, ymv_node);
+        }
+    }
+    else if(input_type == InputType::NONE)
+    {
+        Vector x_unused, y_unused;
+        for (auto node : nodes)
+        {
+            node->Mult(x_unused, y_unused);
+        }
+    }
+    else
+    {
+        MFEM_ABORT("DAGraph::Execute() not implemented for input type: "
+                    << static_cast<int>(input_type));
+    }
+}
+
+Operator& DAGraph::GetGradient(const Vector &x) const
+{
+    // TODO: Should/could be removed
+    if(grad_mode == GradMode::FINITE_DIFF)
+    {
+        if(!grad)
+        {
+            grad = new future::FDJacobian(*this, x, 1e-6);
+        }
+        else
+        {
+            grad->GetGradient(x); // Update the FDJacobian with new point x
+        }
+        return *grad;
+    }
+
+    MFEM_ASSERT(static_cast<int>(grad_mode) < static_cast<int>(GradMode::NONE),
+                "DAGraph::GetGradient() called with invalid grad_mode: "
+                << static_cast<int>(grad_mode));
+
+    if(!grad)
+    {
+        grad = new GraphGradient(const_cast<DAGraph&>(*this));
+    }
+
+    if(grad_mode == GradMode::ASSEMBLED)
+    {
+        return grad->GetGradient(x); // Assemble the Jacobian matrix
+    }
+    else // GradMode::MATRIX_FREE
+    {
+        dynamic_cast<GraphGradient*>(grad)->Update(x); // Update the GraphGradient with new point x
+    }
+
+    return *grad;
+}
+
+GraphGradient::GraphGradient(DAGraph &dag) : Operator(dag.Height(), dag.Width()),
+                                             graph(&dag)
+{
+    MFEM_ASSERT(graph->IsAssembled(), "GraphGradient requires an assembled DAGraph.");
+    MFEM_ASSERT(graph->IsSorted(), "GraphGradient requires a topologically sorted DAGraph.");
+
+    auto index_map = graph->GetFieldIdToIndexMap();
+    auto field_map = graph->GetFieldIdToFieldMap();
+
+    MFEM_ASSERT(index_map.NumFields() == field_map.NumFields(),
+                "Mismatch in number of fields between index_map and field_map");
+
+    x_work.DeleteAll(); // Clear any existing pointers
+    x_work.SetSize(index_map.NumFields());
+    x_work = nullptr; // Initialize all pointers to nullptr
+    xlin.SetNumBlocks(index_map.NumFields());
+
+    for (auto const& [id, idx] : index_map)
+    {
+        MFEM_ASSERT(idx >= 0 && idx < x_work.Size(), "Index out of bounds for field ID: " << id);
+        MFEM_ASSERT(field_map.Has(id), "Field ID not found in field_map: " << id);
+
+        if(x_work[idx] == nullptr)
+        {
+            x_work[idx] = new Vector(); // Allocate a new Vector for this field
+        }
+        xlin.MakeRef(idx, *x_work[idx]); // Make xlin refer to the allocated Vector
+    }
+
+}
+
+void GraphGradient::Update(const Vector &x)
+{
+    MFEM_ASSERT(graph != nullptr, "GraphGradient operator requires a non-null DAGraph pointer.");
+
+    auto set_exec_mode = [&](DAGraph::ExecutionMode mode)
+    {
+        for (auto &node : graph->Nodes())
+        {
+            node->SetExecutionMode(mode);
+        }
+    };
+
+    auto inputs = graph->InputFields();
+    BlockVector xb(x.GetData(), graph->InputOffsets());
+    MultiVector xmv(inputs.Size());
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        xmv.MakeRef(i, xb.GetBlock(i));
+    }
+
+    set_exec_mode(DAGraph::ExecutionMode::GRADIENT_MODE);
+    graph->Execute(xmv, xlin); // Forward pass to populate fields for gradient computations
+    set_exec_mode(DAGraph::ExecutionMode::DEFAULT_MODE); // Reset execution mode for forward pass
+}
+
+void GraphGradient::Mult(const Vector &x, Vector &y) const
+{
+    MFEM_ASSERT(x.Size() == graph->Width(), "Input vector size (" << x.Size()
+                << ") must match graph width (" << graph->Width() << ")");
+
+    MFEM_ASSERT(y.Size() == graph->Height(), "Output vector size (" << y.Size()
+                << ") must match graph height (" << graph->Height() << ")");
+
+    auto in_offsets  = graph->InputOffsets();
+    auto out_offsets = graph->OutputOffsets();
+
+    auto inputs  = graph->InputFields();
+    auto outputs = graph->OutputFields();
+
+    BlockVector xb(x.GetData(), in_offsets);
+    BlockVector yb(y.GetData(), out_offsets);
+    MultiVector xmv(inputs.Size()), ymv(outputs.Size());
+
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        xmv.MakeRef(i, xb.GetBlock(i));
+    }
+
+    for(int i=0; i < outputs.Size(); i++)
+    {
+        ymv.MakeRef(i, yb.GetBlock(i));
+    }
+
+    const_cast<GraphGradient*>(this)->Mult(xmv, ymv); // Forward mode: compute JVP, y = J(z) * x
+}
+
+void GraphGradient::Mult(const MultiVector &x, MultiVector &y)
+{
+    auto inputs  = graph->InputFields();
+    auto outputs = graph->OutputFields();
+
+    MFEM_ASSERT(inputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of input fields (" << inputs.Size() << ")");
+
+    MFEM_ASSERT(outputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of output fields (" << outputs.Size() << ")");
+
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        inputs[i]->SetAdjoint(const_cast<Vector*>(&x[i]));
+    }
+    for (int i=0; i < outputs.Size(); i++)
+    {
+        outputs[i]->SetAdjoint(&y[i]);
+    }
+
+    auto index_map = graph->GetFieldIdToIndexMap();
+    auto fld_map = graph->GetFieldIdToFieldMap();
+    int nfields = index_map.NumFields();
+    MultiVector ymv(nfields); // TODO: Should this be a member function?
+
+    // Assemble the multivector from the individual fields based on their IDs
+    // This multivector contains all input, output, and intermediate fields in the graph
+    for (auto const& [id, idx] : index_map)
+    {
+        if (fld_map.Has(id))
+        {
+            auto field = fld_map.Get(id);
+            ymv.MakeRef(idx, *field->Adjoint());
+        }
+        else
+        {
+            MFEM_ABORT("Field ID " << id << " not found in field map");
+        }
+    }
+
+    Forward(x, ymv); // Forward mode: compute JVP, y = J(z) * x
+
+    for (auto &f : inputs)
+    {
+        f->SetAdjoint(nullptr);
+    }
+    for (auto &f : outputs)
+    {
+        f->SetAdjoint(nullptr);
+    }
+}
+
+void GraphGradient::MultTranspose(const Vector &x, Vector &y) const
+{
+    MFEM_ASSERT(x.Size() == graph->Height(), "Input vector size (" << x.Size()
+                << ") must match graph height (" << graph->Height() << ")");
+    MFEM_ASSERT(y.Size() == graph->Width(), "Output vector size (" << y.Size()
+                << ") must match graph width (" << graph->Width() << ")");
+
+    auto in_offsets  = graph->InputOffsets();
+    auto out_offsets = graph->OutputOffsets();
+
+    auto inputs  = graph->InputFields();
+    auto outputs = graph->OutputFields();
+
+    BlockVector xb(x.GetData(), out_offsets);
+    BlockVector yb(y.GetData(), in_offsets);
+    MultiVector xmv(outputs.Size()), ymv(inputs.Size());
+
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        xmv.MakeRef(i, xb.GetBlock(i));
+    }
+
+    for(int i=0; i < outputs.Size(); i++)
+    {
+        ymv.MakeRef(i, yb.GetBlock(i));
+    }
+    const_cast<GraphGradient*>(this)->MultTranspose(xmv, ymv); // Reverse mode: compute VJP, y = J(z)^T * x
+}
+
+void GraphGradient::MultTranspose(const MultiVector &x, MultiVector &y)
+{
+    auto inputs  = graph->InputFields();
+    auto outputs = graph->OutputFields();
+
+    MFEM_ASSERT(outputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of output fields (" << outputs.Size() << ")");
+
+    MFEM_ASSERT(inputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of input fields (" << inputs.Size() << ")");
+
+    for(int i=0; i < outputs.Size(); i++)
+    {
+        outputs[i]->SetAdjoint(const_cast<Vector*>(&x[i]));
+    }
+    for (int i=0; i < inputs.Size(); i++)
+    {
+        inputs[i]->SetAdjoint(&y[i]);
+    }
+
+    auto index_map = graph->GetFieldIdToIndexMap();
+    auto fld_map = graph->GetFieldIdToFieldMap();
+    int nfields = index_map.NumFields();
+    MultiVector ymv(nfields); // TODO: Should this be a member function?
+
+    for(auto const& [id, idx] : index_map)
+    {
+        if (fld_map.Has(id))
+        {
+            auto field = fld_map.Get(id);
+            ymv.MakeRef(idx, *field->Adjoint());
+        }
+        else
+        {
+            MFEM_ABORT("Field ID " << id << " not found in field map");
+        }
+    }
+
+    Reverse(x, ymv); // Reverse mode: compute VJP, y = J(z)^T * x
+
+    for (auto &f : outputs)
+    {
+        f->SetAdjoint(nullptr);
+    }
+    for (auto &f : inputs)
+    {
+        f->SetAdjoint(nullptr);
+    }
+}
+
+void GraphGradient::Forward(const MultiVector &x, MultiVector &y) const
+{
+    MFEM_ASSERT(x.NumBlocks() == graph->InputFields().Size(),
+                "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of input fields (" << graph->InputFields().Size() << ")");
+    
+    auto in_type = graph->GetInputType();
+    auto index_map  = graph->GetFieldIdToIndexMap();
+    auto field_map = graph->GetFieldIdToFieldMap();
+
+    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
+                "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of fields (" << index_map.NumFields() << ")");
+
+    auto inputs  = graph->InputFields();
+    for(int i=0; i < inputs.Size(); i++)
+    {
+        int idx = index_map.Get(inputs[i]->ID());
+        if(&y[idx] != &x[i]) // copy data, if address is different
+        {
+            y[idx] = x[i];
+        }
+    }
+
+    if(in_type == InputType::VECTOR)
+    {
+        x0.SetSize(graph->MaxWidth());
+        dx.SetSize(graph->MaxWidth());
+        dy.SetSize(graph->MaxHeight());
+
+        auto nodes = graph->Nodes();
+        for (auto node : nodes)
+        {
+            x0.SetSize(node->Width());
+            dx.SetSize(node->Width());
+            dy.SetSize(node->Height());
+
+            // Assemble input fields into a single vector for the node
+            auto node_inputs = node->InputFields();
+            auto ioffsets = node->InputOffsets();
+            for(int i=0; i < node_inputs.Size(); i++)
+            {
+                auto in_field = node_inputs[i];
+                MFEM_ASSERT(index_map.Has(in_field->ID()), "Input field ID not found in index_map");
+                int idx = index_map.Get(in_field->ID());
+                x0.SetVector(xlin[idx], ioffsets[i]);
+                dx.SetVector(y[idx], ioffsets[i]);
+            }
+
+            node->GradientMult(x0, dx, dy); // Compute JVP for the node
+
+            // Disassemble output vector back
+            auto node_outputs = node->OutputFields();
+            BlockVector ynb(dy.GetData(), node->OutputOffsets());
+            for(int i=0; i < node_outputs.Size(); i++)
+            {
+                auto out_field = node_outputs[i];
+                MFEM_ASSERT(index_map.Has(out_field->ID()), "Output field ID not found in index_map");
+                int idx = index_map.Get(out_field->ID());
+                y[idx] = ynb.GetBlock(i);
+            }
+        }
+    }
+    else if(in_type == InputType::MULTIVECTOR)
+    {
+        auto nodes = graph->Nodes();
+        for (auto node : nodes)
+        {
+            auto node_inputs = node->InputFields();
+            auto node_outputs = node->OutputFields();
+            x0_mv.SetNumBlocks(node_inputs.Size());
+            dx_mv.SetNumBlocks(node_inputs.Size());
+            dy_mv.SetNumBlocks(node_outputs.Size());
+
+            for(int i=0; i < node_inputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_inputs[i]->ID());
+                x0_mv.MakeRef(i, xlin[idx]);
+                dx_mv.MakeRef(i, y[idx]);
+            }
+            for(int i=0; i < node_outputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_outputs[i]->ID());
+                dy_mv.MakeRef(i, y[idx]);
+            }
+            node->GradientMult(x0_mv, dx_mv, dy_mv); // Compute JVP for the node
+        }
+    }
+    else if(in_type == InputType::NONE)
+    {
+        Vector x_unused, dx_unused, dy_unused;
+        auto nodes = graph->Nodes();
+        for (auto node : nodes)
+        {
+            node->GradientMult(x_unused, dx_unused, dy_unused);
+        }
+    }
+    else
+    {
+        MFEM_ABORT("GraphGradient::Forward() not implemented for input type: "
+                    << static_cast<int>(in_type));
+    }
+}
+
+void GraphGradient::Reverse(const MultiVector &x, MultiVector &y) const
+{
+    MFEM_ASSERT(x.NumBlocks() == graph->OutputFields().Size(),
+                "Number of input blocks (" << x.NumBlocks()
+                << ") must match number of output fields (" << graph->OutputFields().Size() << ")");
+
+    auto in_type = graph->GetInputType();
+    auto index_map  = graph->GetFieldIdToIndexMap();
+    auto field_map = graph->GetFieldIdToFieldMap();
+    int nnodes  = graph->Size();
+
+    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
+                "Number of output blocks (" << y.NumBlocks()
+                << ") must match number of fields (" << index_map.NumFields() << ")");
+
+    auto outputs  = graph->OutputFields();
+    for(int i=0; i < outputs.Size(); i++)
+    {
+        int idx = index_map.Get(outputs[i]->ID());
+        if(&y[idx] != &x[i]) // copy data, if address is different
+        {
+            y[idx] = x[i];
+        }
+    }
+
+    if(in_type == InputType::VECTOR)
+    {
+        x0.SetSize(graph->MaxWidth());
+        dx.SetSize(graph->MaxHeight());
+        dy.SetSize(graph->MaxWidth());
+
+        for (int i=nnodes-1; i >= 0; i--)
+        {
+            auto node = graph->GetNode(i);
+            x0.SetSize(node->Width());
+            dx.SetSize(node->Height());
+            dy.SetSize(node->Width());
+
+            auto node_inputs = node->InputFields();
+            auto ioffsets = node->InputOffsets();
+            for(int i=0; i < node_inputs.Size(); i++)
+            {
+                auto in_field = node_inputs[i];
+                MFEM_ASSERT(index_map.Has(in_field->ID()), "Input field ID not found in index_map");
+                int idx = index_map.Get(in_field->ID());
+                x0.SetVector(xlin[idx], ioffsets[i]);
+            }
+
+            auto node_outputs = node->OutputFields();
+            auto ooffsets = node->OutputOffsets();
+            for(int i=0; i < node_outputs.Size(); i++)
+            {
+                auto out_field = node_outputs[i];
+                MFEM_ASSERT(index_map.Has(out_field->ID()), "Output field ID not found in index_map");
+                int idx = index_map.Get(out_field->ID());
+                dx.SetVector(y[idx], ooffsets[i]);
+            }
+
+            node->GradientMultTranspose(x0, dx, dy); // Compute JVP for the node
+
+            BlockVector dynb(dy.GetData(), node->InputOffsets());
+            for(int i=0; i < node_inputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_inputs[i]->ID());
+                y[idx] = dynb.GetBlock(i);
+            }
+        }
+    }
+    else if(in_type == InputType::MULTIVECTOR)
+    {
+        for (int i=nnodes-1; i >= 0; i--)
+        {
+            auto node = graph->GetNode(i);
+            auto node_inputs = node->InputFields();
+            auto node_outputs = node->OutputFields();
+            x0_mv.SetNumBlocks(node_inputs.Size());
+            dx_mv.SetNumBlocks(node_outputs.Size());
+            dy_mv.SetNumBlocks(node_inputs.Size());
+
+            for(int i=0; i < node_inputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_inputs[i]->ID());
+                x0_mv.MakeRef(i, xlin[idx]);
+                dy_mv.MakeRef(i, y[idx]);
+            }
+            for(int i=0; i < node_outputs.Size(); i++)
+            {
+                int idx = index_map.Get(node_outputs[i]->ID());
+                dx_mv.MakeRef(i, y[idx]);
+            }
+            node->GradientMultTranspose(x0_mv, dx_mv, dy_mv); // Compute JVP for the node
+        }
+    }
+    else if(in_type == InputType::NONE)
+    {
+        Vector x_unused, dx_unused, dy_unused;
+        for (int i=nnodes-1; i >= 0; i--)
+        {
+            auto node = graph->GetNode(i);
+            node->GradientMultTranspose(x_unused, dx_unused, dy_unused); // Compute VJP for the node
+        }
+    }
+    else
+    {
+        MFEM_ABORT("GraphGradient::Reverse() not implemented for input type: "
+                    << static_cast<int>(in_type));
+    }
+}
+
+Operator& GraphGradient::GetGradient(const Vector &x) const
+{
+    // Used to build Jacobian matrix
+    MFEM_ABORT("GraphGradient::GetGradient() not implemented");
+}
+
+
+} // namespace mfem

miniapps/multiapp/multiapp.hpp

@@ -0,0 +1,838 @@
+// 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.
+
+
+#ifndef MFEM_MULTIAPP_HPP
+#define MFEM_MULTIAPP_HPP
+
+#include "mfem.hpp"
+
+namespace mfem
+{
+
+/// Forward declarations needed below
+class Field;
+class FieldCollection;
+class GraphNode;
+class DAGraph;
+class GraphGradient;
+
+
+/// @brief Base class for storing data (Vector) and distinguishing
+/// fields variables
+class Field
+{
+public:
+    enum Type ///< Not used for now, but could be used to distinguish between input/output fields
+    {
+        INPUT , ///< Input field
+        OUTPUT, ///< Output field
+        DEFAULT ///< Any field
+    };
+
+    friend class GraphNode;
+
+private:
+    Type type = Type::DEFAULT;
+    inline static int next_id = 0;
+
+protected:
+    Vector *data = nullptr;
+    Vector *adjoint = nullptr; // For storing derivative info
+    int id = -1; // initialized to invalid id
+
+    std::string name; // Optional name for the field
+    Operator *oper  = nullptr; // Operator that outputs this field
+
+    int GetValidID(int id_, int lb=0, int ub = std::numeric_limits<int>::max())
+    {
+        return (id_ >= lb && id_ <= ub) ? id_ : next_id++;
+    }
+
+public:
+
+    ///@brief Constructor for a Field of type Type with optional ID
+    Field(Vector *field, Vector *adjoint, Type type, int id_ = -1) :
+          type(type), data(field), adjoint(adjoint), id(GetValidID(id_)),
+          name("Field_" + std::to_string(id)) { }
+
+    ///@brief Constructor for a Field of Default type with optional ID
+    Field(Vector *field, Vector *adjoint, int id_ = -1) : 
+          Field(field, adjoint, Type::DEFAULT, id_) { }
+
+    ///@brief Constructor for an input field
+    Field(Vector *field, int id_ = -1) :
+          Field(field, nullptr, Type::DEFAULT, id_) { }
+
+    ///@brief Constructor for a Field of type Type
+    Field(Vector *field, Type type, int id_ = -1) :
+          Field(field, nullptr, type, id_) { }
+
+    ///@brief Get the stored internally stored data pointer
+    Vector* Data() const { return data; }
+    Vector* Adjoint() const { return adjoint; }
+    Operator* GetOperator() const { return oper; }
+
+    ///@brief Set the internally stored data pointer
+    virtual void SetData(Vector *field) { data = field; }
+    virtual void SetAdjoint(Vector *adj) { adjoint = adj; }
+    virtual void SetOperator(Operator *op) { oper = op; }
+
+    virtual void GetData(Vector &field) const { field = *data; }
+    virtual void GetAdjoint(Vector &adj) const { adj = *adjoint; }
+
+    std::string Name() const { return name; }
+    void SetName(const std::string &n) { name = n; }
+    int ID() const { return id; }
+
+    void SetID(int i)
+    {
+        MFEM_ASSERT(i >= 0, "ID must be non-negative.");
+        id = i;
+    }
+
+    bool IsInput() const {return (type == Type::INPUT);}
+    bool IsOutput() const {return (type == Type::OUTPUT);}
+    bool IsDefault() const {return (type == Type::DEFAULT);}
+
+    virtual ~Field() = default;
+
+protected:
+
+    ///@brief Set the type of the field (prevents changing type of input/output fields)
+    void SetType(Type t)
+    {
+        type = t;
+    }
+};
+
+/// @brief A collection of Fields, each identified by a name
+class FieldCollection
+{
+public:
+    using FieldMap = GenericFieldMap<std::string, Field*>;
+    using IndexMap = GenericFieldMap<std::string, int>;
+
+private:
+    std::string name; /// Name of the collection
+    Operator *oper = nullptr; /// Operator associated with this collection (not owned)
+    FieldMap fields; /// Map from field name to Field pointer
+    IndexMap index_map; /// Map from field name to index in input/output vectors
+
+    Array<Field*> input_fields;  // Input fields for this node
+    Array<Field*> output_fields; // Output fields for this node
+
+public:
+
+    FieldCollection() = default;
+
+    /// @brief Constructor with collection name and optional associated operator
+    FieldCollection(std::string collection_name, Operator *op = nullptr):
+                    name(collection_name), oper(op) {}
+
+    /// @brief Constructor with associated operator and default collection name
+    FieldCollection(Operator *op) : name("FieldCollection"), oper(op) {}
+
+    /// @brief Get the number of fields in the collection
+    int Size() const { return fields.NumFields(); }
+
+    /// @brief Set the name of the collection
+    void SetName(const std::string &collection_name) { name = collection_name;}
+
+    /// @brief Get the name of the collection
+    std::string Name() const { return name; }
+
+    /// @brief Set the operator associated with this collection
+    void SetOperator(Operator *op){ oper = op; }
+
+    /// @brief Get the operator associated with this collection
+    const Operator* GetOperator() const { return oper; }
+
+    /// @brief Get the field associated with the given name, or nullptr if not found
+    Field* GetField(const std::string &field_name) const
+    {
+        return fields.Get(field_name);
+    }
+
+    /// @brief Add a field to the collection with a given name and ownership flag
+    void AddField(const std::string &field_name, Field *field, bool own = false)
+    {
+        if(fields.Has(field_name))
+        {
+            MFEM_WARNING("FieldCollection::AddField: Field with name "
+                         << field_name << " already exists. Replacing existing field.");
+        }
+        fields.Register(field_name, field, own);
+    }
+
+    void AddInput(const std::string &field_name,
+                  Field *field, bool own = false)
+    {
+        bool has_field = fields.Has(field_name);
+        bool has_index = index_map.Has(field_name);
+        if(has_field && has_index)
+        {
+            int i = index_map.Get(field_name);
+            input_fields[i] = field;
+        }
+        else
+        {
+            input_fields.push_back(field);
+            index_map.Register(field_name, input_fields.Size() - 1);
+        }
+        AddField(field_name, field, own);
+    }
+
+    void AddOutput(const std::string &field_name,
+                   Field *field, bool own = false)
+    {
+        bool has_field = fields.Has(field_name);
+        bool has_index = index_map.Has(field_name);
+        if(has_field && has_index)
+        {
+            int i = index_map.Get(field_name);
+            output_fields[i] = field;
+        }
+        else
+        {
+            output_fields.push_back(field);
+            index_map.Register(field_name, output_fields.Size() - 1);
+        }
+
+        AddField(field_name, field, own);
+        if(field->GetOperator() == nullptr)
+        {
+            field->SetOperator(oper);
+        }
+    }
+
+    Array<Field*>& InputFields() { return input_fields; }
+    Array<Field*>& OutputFields() { return output_fields; }
+
+    Field* InputField(int i) const { return input_fields[i]; }
+    Field *InputField(const std::string &field_name) const
+    {
+        bool has_index = index_map.Has(field_name);
+        if(!has_index)
+        {
+            MFEM_WARNING("FieldCollection::InputField: Field with name "
+                         << field_name << " does not exist in the collection.");
+            return nullptr;
+        }
+
+        int index = index_map.Get(field_name);
+        MFEM_VERIFY(index >= 0 && index < input_fields.Size(),
+                    "FieldCollection::InputField: Invalid index for field name: "
+                    << field_name << ".");
+        return input_fields[index];
+    }
+
+    Field* OutputField(int i) const { return output_fields[i]; }
+    Field *OutputField(const std::string &field_name) const
+    {
+        bool has_index = index_map.Has(field_name);
+        if(!has_index)
+        {
+            MFEM_WARNING("FieldCollection::OutputField: Field with name "
+                         << field_name << " does not exist in the collection.");
+            return nullptr;
+        }
+
+        int index = index_map.Get(field_name);
+        MFEM_VERIFY(index >= 0 && index < output_fields.Size(),
+                    "FieldCollection::OutputField: Invalid index for field name: "
+                    << field_name << ".");
+        return output_fields[index];
+    }
+
+    FieldMap &Fields() { return fields; }
+    FieldMap Fields() const { return fields; }
+
+    virtual void Save (std::ostream &out) const
+    {
+        out << "\"Fields\":\n";
+        out << "{\n";
+        for (auto f = fields.begin(); f != fields.end(); ++f)
+        {
+            std::string f_name = f->first;
+            Field *f_obj = f->second;
+            // out << "  " << f_name << ": ID " << f_obj->ID() << ",\n";
+            // out << f_obj->ID() << ": " << f_name << ",\n";
+            out << '\"' << f_obj->ID() << "\": \"" << f_name << "\"";
+            if(f != std::prev(fields.end())) out << ",";
+            out << "\n";
+        }
+        out << "},\n";
+
+        out << "\"Inputs\":\n";
+        out << "{\n";
+        for (int i = 0; i < input_fields.Size(); ++i)
+        {
+            Field *f_obj = input_fields[i];
+            out << '\"' << f_obj->ID() << "\": \"" << f_obj->Name() << "\"";
+            if(i != input_fields.Size() - 1) out << ",";
+            out << "\n";
+        }
+        out << "},\n";
+
+        out << "\"Outputs\":\n";
+        out << "{\n";
+        for (int i = 0; i < output_fields.Size(); ++i)
+        {
+            Field *f_obj = output_fields[i];
+            out << '\"' << f_obj->ID() << "\": \"" << f_obj->Name() << "\"";
+            if(i != output_fields.Size() - 1) out << ",";
+            out << "\n";
+        }
+        out << "}\n";
+    }
+
+    Field* HasField(const Field &field) const
+    {
+        for (auto f = fields.begin(); f != fields.end(); ++f)
+        {
+            if(f->second == &field)
+            {
+                return f->second;
+            }
+        }
+        return nullptr;
+    }
+
+    Field* HasField(const std::string &field_name) const
+    {
+        return fields.Get(field_name);
+    }
+
+    Field* HasField(const int id) const
+    {
+        for (auto f = fields.begin(); f != fields.end(); ++f)
+        {
+            if(f->second->ID() == id)
+            {
+                return f->second;
+            }
+        }
+        return nullptr;
+    }
+
+    ~FieldCollection(){}
+
+};
+
+
+class GraphNode : public Operator
+{
+public:
+    enum ExecutionMode
+    {
+        GRADIENT_MODE, ///< Node is being executed as part of a gradient evaluation
+        DEFAULT_MODE   ///< Node is being executed as default, operator evaluation
+    };
+
+private:
+    inline static int next_id = 0;
+
+protected:
+    int id = -1;
+    int node_index = -1;
+    mutable ExecutionMode exec_mode = DEFAULT_MODE;
+
+    std::string name;
+    mutable FieldCollection field_collection; ///< Collection of fields associated with this node
+
+    // Offsets to be used for operation on BlockVector
+    Array<int> input_offsets;  ///< Offsets for input fields
+    Array<int> output_offsets; ///< Offsets for output fields
+
+    int GetValidID(int id_, int lb=0, int ub = std::numeric_limits<int>::max())
+    {
+        return (id_ >= lb && id_ <= ub) ? id_ : next_id++;
+    }
+
+public:
+
+    GraphNode(int h, int w) : Operator(h,w), id(GetValidID(-1)),
+                              name("Node_" + std::to_string(id)),
+                              field_collection(this) { }
+
+    GraphNode(int s = 0) : GraphNode(s, s) { }
+
+    void SetNodeIndex(int index){ node_index = index; }
+    int GetNodeIndex() const { return node_index; }
+
+    void SetExecutionMode(ExecutionMode mode) { exec_mode = mode; }
+    ExecutionMode GetExecutionMode() const { return exec_mode; }
+
+    void SetName(const std::string &name_) { name = name_; }
+    std::string Name() const { return name; }
+
+    void SetID(int id_) { id = id_; }
+    int ID() const { return id; }
+
+    FieldCollection::FieldMap& Fields() { return field_collection.Fields(); }
+    Field* Fields(const std::string &f) { return field_collection.GetField(f); }
+
+    FieldCollection::FieldMap Fields() const { return field_collection.Fields(); }
+    Field* Fields(const std::string &f) const { return field_collection.GetField(f); }
+
+    Array<Field*>& InputFields() const { return field_collection.InputFields(); }
+    Array<Field*>& OutputFields() const { return field_collection.OutputFields(); }
+    Field* InputField(int i) const { return field_collection.InputField(i); }
+    Field* OutputField(int i) const { return field_collection.OutputField(i); }
+
+
+    virtual void AddInput(const std::string &field_name,
+                          Field *field, bool own = false)
+    { field_collection.AddInput(field_name, field, own); }
+
+    virtual void AddInput(Field *field, bool own = false)
+    { AddInput(field->Name(), field, own); }
+
+    template<bool OwnInputs = false,
+             typename... Args,
+             bool AreFields = std::conjunction<std::is_base_of<Field, std::remove_pointer_t<Args>> ...>::value,
+             typename std::enable_if<AreFields, bool>::type = true >
+    void AddInputs(Args... args)
+    {
+        ((AddInput(std::forward<Args>(args), OwnInputs)), ...);
+    }
+
+    virtual void AddOutput(const std::string &field_name,
+                           Field *field, bool own = false)
+    { field_collection.AddOutput(field_name, field, own); }
+
+    virtual void AddOutput(Field *field, bool own = false)
+    { AddOutput(field->Name(), field, own); }
+
+    template<bool OwnOutputs = false,
+             typename... Args,
+             bool AreFields = std::conjunction<std::is_base_of<Field, std::remove_pointer_t<Args>> ...>::value,
+             typename std::enable_if<AreFields, bool>::type = true >
+    void AddOutputs(Args... args)
+    {
+        ((AddOutput(std::forward<Args>(args), OwnOutputs)), ...);
+    }
+
+    virtual void Save (std::ostream &out) const
+    {
+        out << "\"Node-" << id << "\" : " << std::endl;
+        out << "{\n";
+        out << "\"Name\": \"" << name << "\",\n";
+        field_collection.Save(out);
+        out << "}";
+    }
+
+    virtual void Mult(const Vector &x, Vector &y) const override
+    {
+        MFEM_ABORT("GraphNode::Mult() not implemented");
+    }
+
+    virtual void Mult(const MultiVector &x, MultiVector &y) override
+    {
+        MFEM_ABORT("GraphNode::Mult(MultiVector) not implemented");
+    }
+
+    using Operator::GetGradient;
+
+    // TODO: Possibly remove this and only support MultiVector version of GradientMult
+    virtual void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const
+    {
+        MFEM_ABORT("GraphNode::GradientMult() not implemented");
+        GetGradient(x).Mult(dx, dy);
+    }
+
+    virtual void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const
+    {
+        MFEM_ABORT("GraphNode::GradientMult() not implemented");
+        GetGradient(x).Mult(dx, dy);
+    }
+
+    // TODO: Possibly remove this and only support MultiVector version of GradientMultTranspose
+    virtual void GradientMultTranspose(const Vector &x, const Vector &dx, Vector &dy) const
+    {
+        MFEM_ABORT("GraphNode::GradientMultTranspose() not implemented");
+        GetGradient(x).MultTranspose(dx, dy);
+    }
+
+    virtual void GradientMultTranspose(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const
+    {
+        MFEM_ABORT("GraphNode::GradientMultTranspose() not implemented");
+        // GetGradient(x).MultTranspose(dx, dy); // Not yet implemented
+    }
+
+    /// @brief Return the input offsets for block starts.
+    Array<int>& InputOffsets() { return input_offsets; }
+
+    /// @brief Read only access to the input offsets for block starts.
+    const Array<int>& InputOffsets() const { return input_offsets; }
+
+    void SetInputOffsets(const Array<int> &offsets) { input_offsets = offsets; }
+
+    /// @brief Return the output offsets for block starts.
+    Array<int>& OutputOffsets() { return output_offsets; }
+
+    /// @brief Read only access to the output offsets for block starts.
+    const Array<int>& OutputOffsets() const { return output_offsets; }
+
+    void SetOutputOffsets(const Array<int> &offsets) { output_offsets = offsets; }
+
+    virtual ~GraphNode() = default;
+};
+
+
+/**
+   @brief An abstract, type-erased class to define the interface for 
+   operators, not inherited from @a GraphNode. It performs SFINAE 
+   checks for stored operator's member functions and override the Mult
+   to call the stored object's functions.
+ */
+template <typename OpType>
+class AbstractOperator : public GraphNode
+{
+protected:
+    /// Define a template class 'check' to test for the existence of member functions
+    template <typename C>
+    class CheckMember{
+        private:
+
+        /// @brief A type trait to check if the erased class has the function Mult
+        /// with the needed signatures.
+        template<class T>
+        using Mult = decltype(std::declval<T&>().Mult(std::declval<const Vector&>(),
+                                                      std::declval<Vector&>()));
+
+        template<class T>
+        using MultPtr = decltype(std::declval<T&>().Mult(std::declval<const int>(),
+                                                         std::declval<const real_t*>(),
+                                                         std::declval<const int>(),
+                                                         std::declval<real_t*>()));
+        // ---------------------------------------------------------------------
+        
+        template <typename T, template<typename> typename Func, typename R>
+        static constexpr auto Check(T*) -> typename std::is_same< Func<T>, R>::type;
+
+        template <typename, template<typename> typename, typename >
+        static constexpr std::false_type Check(...);
+
+        // --- Check for the existence of the member functions
+        typedef decltype(Check<C,Mult,void>(0)) Has_Mult;
+        typedef decltype(Check<C,MultPtr,void>(0)) Has_MultPtr;
+    public:
+        static constexpr bool HasMult  = Has_Mult::value;
+        static constexpr bool HasMultPtr  = Has_MultPtr::value;
+    };
+
+    OpType *op;  ///< Pointer to the operator
+
+public:
+
+    constexpr bool HasExecute(){return CheckMember<OpType>::HasStep;}
+    constexpr bool HasMult(){return CheckMember<OpType>::HasMult;}
+
+
+    /// @brief Constructor for the type-erased AbstractOperator class
+    AbstractOperator(OpType *op_, int h, int w) : GraphNode(h,w), op(op_)
+    { }
+
+    /// @brief Constructor for the type-erased AbstractOperator class.
+    AbstractOperator(OpType *op_, int s = 0) : AbstractOperator(op_,s,s) {}
+
+    /**
+       @brief Perform Mult operation with the stored operator, if it exists.
+     */
+    void Mult(const Vector &x, Vector &y) const override
+    {
+        if constexpr (CheckMember<OpType>::HasMult)
+        {
+            op->Mult(x,y);
+        }
+        else if constexpr (CheckMember<OpType>::HasMultPtr)
+        {
+            op->Mult(x.Size(), x.GetData(), y.Size(), y.GetData());
+        }
+        else
+        {
+            MFEM_ABORT("The AbstractOperator does not have the function, "
+                       "Mult(const Vector&, Vector&) or "
+                       "Mult(int, double*, int, double*).");
+        }
+    }
+};
+
+
+/**
+   @brief A class to store and coupled multiple operators together.
+ */
+class DAGraph : public GraphNode
+{
+public:
+
+    using IntToIntMap = GenericFieldMap<int, int>;
+    using IntToFieldMap = GenericFieldMap<int, Field*>;
+
+    enum class GradMode
+    {
+        FINITE_DIFF = 0,  ///< Finite difference Jacobian
+        MATRIX_FREE = 1,  ///< Matrix-free Jacobian
+        ASSEMBLED = 2,    ///< Assembled Jacobian
+        NONE = 3          ///< Not implemented
+    };
+
+    enum InputType
+    {
+        VECTOR,      ///< Asemble the input blockvector from individual fields
+        MULTIVECTOR, ///< Asemble the multivector from individual fields
+        NONE         ///< No input
+    };
+
+protected:
+    Array<GraphNode*> nodes; ///< Vector of individual operators
+    Array<bool> node_owned; ///< Whether the operators are owned
+    Array<int> node_depth; ///< Depth of each operator in the graph
+
+    int max_width  = 0;     ///< Largest operator width
+    int max_height = 0;     ///< Largest operator height
+    int nnodes     = 0;     ///< The number of nodes
+    bool sorted    = false; ///< True if the nodes are topologically sorted
+    bool assembled = false; ///< True if the graph is assembled
+
+    GradMode grad_mode = GradMode::MATRIX_FREE; ///< Gradient mode for the graph
+    mutable Operator *grad = nullptr; ///< Gradient operator
+
+    InputType input_type = InputType::MULTIVECTOR; ///< Input type for the graph
+    mutable Vector x_node, y_node; ///< Temporary vectors for evaluating nodes
+    mutable MultiVector xmv_node, ymv_node; ///< Temporary multivectors for evaluating nodes
+
+    IntToFieldMap fid_to_field; ///< Map from Field ID to Field pointer
+    IntToIntMap fid_to_index; ///< Map from ID to index in an array; needed since ordering is not unique
+
+    friend class GraphGradient;
+
+public:
+    /**
+       @brief Construct a new CoupledOperator object.
+       @param nop Total number of operators to couple
+     */
+    DAGraph(const int nop) : GraphNode()
+    {
+        nodes.Reserve(nop);
+        node_owned.Reserve(nop);
+    }
+
+    /**
+       @brief Construct a new CoupledOperator object for an 
+       abstract non/mfem operator.
+     */
+    template <class OpType>
+    DAGraph(const OpType &op) : DAGraph(1)
+    {
+        AddOperator(op);
+    }
+
+    /**
+       @brief Add an operator to the list of coupled operator and
+       return pointer to it. Not owned unless it's not derived from GraphNode.
+     */
+    template <class OpType>
+    GraphNode* AddOperator(OpType *op_, int h, int w)
+    {
+        // Add operator to list of operators
+        if constexpr(std::is_base_of<GraphNode, OpType>::value)
+        {
+            nodes.push_back(op_);
+            node_owned.Append(false);
+        } 
+        else
+        {
+            nodes.push_back(new AbstractOperator<OpType>(op_,h,w));
+            node_owned.Append(true);
+        }
+        nnodes++;
+
+        // Update size of the coupled operator and the block offsets
+        GraphNode* op = nodes.Last();
+        op->SetNodeIndex(nnodes-1); // Set the index of the operator
+
+        int ht = op->Height();
+        int wt = op->Width();
+
+        max_width = std::max(max_width, wt);
+        max_height = std::max(max_height, ht);
+        sorted = false;
+
+        return op;
+    }
+
+    /// @brief Add an operator to the list of coupled operator and return pointer to it.
+    template <class OpType>
+    GraphNode* AddOperator(OpType *op_, int s = 0) { return AddOperator(op_,s,s);}
+
+    /// @brief Get the number of coupled operators
+    int Size(){return nnodes;}
+
+    /// @brief Get the size of the largest operator
+    int MaxWidth() const {return max_width;}
+    int MaxHeight() const {return max_height;}
+
+    IntToIntMap &GetFieldIdToIndexMap() { return fid_to_index; }
+    IntToIntMap GetFieldIdToIndexMap() const { return fid_to_index; }
+
+    IntToFieldMap &GetFieldIdToFieldMap() { return fid_to_field; }
+    IntToFieldMap GetFieldIdToFieldMap() const { return fid_to_field; }
+
+    /// @brief Get the operator at index @a i
+    GraphNode* GetNode(const int i)
+    {
+        MFEM_ASSERT(i >= 0 && i < nnodes,
+               "index [" << i << "] is out of range [0," << nnodes << ")");
+        return nodes[i];
+    }
+
+    Array<GraphNode*>& Nodes() { return nodes; }
+
+    /// @brief Specify whether the operator at index @a i is owned.
+    void OwnNode(const int i, bool own = true)
+    {
+        MFEM_ASSERT(i >= 0 && i < nnodes,
+               "index [" << i << "] is out of range [0," << nnodes << ")");
+        node_owned[i] = own;
+    }
+
+    void Assemble();
+    bool IsAssembled() const { return assembled; }
+
+    void TopologicalSort();
+    bool IsSorted() const { return sorted; }
+
+    void ComputeDepth();
+
+    void ValidateOffsets();
+
+    void ValidateNode(GraphNode &node);
+
+    void CollectFieldMaps();
+
+    using GraphNode::AddInput;
+    void AddInput(Field *field, int sz, bool own = false)
+    {
+        if(input_offsets.Size() == 0)
+        {   // First entry
+            input_offsets.Append(0);
+        }
+        input_offsets.Append(input_offsets.Last() + sz);
+        AddInput(field, own);
+    }
+
+    using GraphNode::AddOutput;
+    void AddOutput(Field *field, int sz, bool own = false)
+    {
+        if(output_offsets.Size() == 0)
+        {   // First entry
+            output_offsets.Append(0);
+        }
+        output_offsets.Append(output_offsets.Last() + sz);
+        AddOutput(field, own);
+    }
+
+    /// @brief Set the gradient mode for the coupled operator
+    void SetGradientMode(GradMode mode)
+    {
+        if(mode != grad_mode)
+        {
+            if(grad) { delete grad; grad = nullptr; }
+            grad_mode = mode;
+        }
+    }
+
+    void SetInputType(InputType type) { input_type = type; }
+    InputType GetInputType() const { return input_type; }
+
+    /**
+       @brief Apply the operator to the vector @a x 
+       and return the result in @a y.
+     */
+    virtual void Mult(const Vector &x, Vector &y) const override;
+
+    virtual void Mult(const MultiVector &x, MultiVector &y) override;
+
+    virtual void Execute(const MultiVector &x, MultiVector &y) const;
+
+    virtual void Save (std::ostream &out) const
+    {
+        out << "\"DAGraph\":\n";
+        out << "{\n";
+        // out << "\"nodes\" : " << nnodes << ",\n";
+        out << "\"Nodes\":\n";
+        out << "{\n";
+        for (int i = 0; i < nodes.Size(); i++)
+        {
+            nodes[i]->Save(out);
+            if(i != nodes.Size()-1) out << ",";
+            out << "\n";
+        }
+        out << "},\n"; // End of Nodes
+        field_collection.Save(out);
+        out << "}\n";
+    }
+
+    Operator& GetGradient(const Vector &x) const override;
+
+    /// @brief Destroy the Coupled Application object
+    ~DAGraph();
+};
+
+
+
+class GraphGradient : public Operator
+{
+public:
+    using InputType = DAGraph::InputType;
+
+protected:
+    mutable DAGraph *graph = nullptr; ///< Pointer to the DAGraph for which this is the gradient operator
+    Array<Vector*> x_work; ///< Array to store linearization point (intermediate fields)
+    mutable MultiVector xlin;
+    mutable Vector x0, dx, dy;
+    mutable MultiVector x0_mv, dx_mv, dy_mv;
+
+public:
+    GraphGradient(DAGraph &dag);
+
+    void Update(const Vector &x);
+
+    void Mult(const Vector &x, Vector &y) const override;
+
+    void Mult(const MultiVector &x, MultiVector &y) override;
+
+    void MultTranspose(const Vector &x, Vector &y) const override;
+
+    void MultTranspose(const MultiVector &x, MultiVector &y);
+
+    Operator &GetGradient(const Vector &x) const override;
+
+    void Forward(const MultiVector &x, MultiVector &y) const;
+
+    void Reverse(const MultiVector &x, MultiVector &y) const;
+
+    ~GraphGradient()
+    {
+        for (auto &v : x_work)
+        {
+            if(v) { delete v; v = nullptr; }
+        }
+        x_work.DeleteAll();
+    }
+};
+
+} //mfem namespace
+
+#endif

miniapps/spde/spde_solver.hpp

@@ -83,7 +83,7 @@ real_t IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
 /// where A is
 /// A = div ( Theta(x) grad + Id ) u(x)
 /// and alpha is given as
-/// alpha = (2 nu + dim) / 2.
+/// alpha = (2 nu + dim) / 4.
 /// Theta (anisotropy tensor) and nu (smoothness) can be specified in the
 /// constructor. Traditionally, the SPDE method requires the specification of
 /// a white noise right hands side. SPDESolver accepts arbitrary right hand

tests/unit/fem/test_gslib.cpp

@@ -12,6 +12,8 @@
 #include "unit_tests.hpp"
 #include "mfem.hpp"
 
+#include <random>
+
 using namespace mfem;
 #ifdef MFEM_USE_GSLIB
 namespace gslib_test
@@ -36,6 +38,165 @@ void F_exact(const Vector &p, Vector &F)
 
 enum class Space { H1, L2 };
 
+enum class SurfaceMeshType { Segment2D, Segment3D, Quad3D, Tri3D };
+
+const char *SurfaceMeshName(const SurfaceMeshType type)
+{
+   switch (type)
+   {
+      case SurfaceMeshType::Segment2D: return "segment-2d";
+      case SurfaceMeshType::Segment3D: return "segment-3d";
+      case SurfaceMeshType::Quad3D:    return "quad-3d";
+      case SurfaceMeshType::Tri3D:     return "tri-3d";
+   }
+   return "unknown";
+}
+
+int SurfaceSpaceDim(const SurfaceMeshType type)
+{
+   switch (type)
+   {
+      case SurfaceMeshType::Segment2D: return 2;
+      case SurfaceMeshType::Segment3D: return 3;
+      case SurfaceMeshType::Quad3D:    return 3;
+      case SurfaceMeshType::Tri3D:     return 3;
+   }
+   return -1;
+}
+
+Mesh MakeSurfaceMesh(const SurfaceMeshType type, const int ne)
+{
+   switch (type)
+   {
+      case SurfaceMeshType::Segment2D:
+         return Mesh::MakeCartesian1D(ne);
+      case SurfaceMeshType::Segment3D:
+         return Mesh::MakeCartesian1D(ne);
+      case SurfaceMeshType::Quad3D:
+         return Mesh::MakeCartesian2D(ne, ne, Element::QUADRILATERAL);
+      case SurfaceMeshType::Tri3D:
+         return Mesh::MakeCartesian2D(ne, ne, Element::TRIANGLE);
+   }
+   MFEM_ABORT("Unknown surface mesh type.");
+   return Mesh();
+}
+
+void GetSurfaceInteriorPoints(Mesh &mesh, const int npt_per_el,
+                              const int ordering, Vector &xyz,
+                              const int p0 = 0)
+{
+   MFEM_VERIFY(mesh.GetNodes() != nullptr, "Mesh nodes are required.");
+
+   const int sdim = mesh.SpaceDimension();
+   const int npt = xyz.Size()/sdim;
+   MFEM_VERIFY((p0 + mesh.GetNE()*npt_per_el)*sdim <= xyz.Size(),
+               "Output vector is too small.");
+   Vector point(sdim);
+   std::mt19937 gen(123);
+   std::uniform_real_distribution<double> uni(0.01, 0.99);
+   int p = p0;
+
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      const Geometry::Type geom = mesh.GetElementBaseGeometry(e);
+      for (int j = 0; j < npt_per_el; j++)
+      {
+         IntegrationPoint ip;
+         real_t xv = uni(gen);
+         if (geom == Geometry::SEGMENT)
+         {
+            ip.x = xv;
+         }
+         else if (geom == Geometry::SQUARE)
+         {
+            ip.Set2(xv, uni(gen));
+         }
+         else
+         {
+            MFEM_VERIFY(geom == Geometry::TRIANGLE,
+                        "Unsupported surface element geometry.");
+            ip.Set2(xv, uni(gen)*(1.0 - xv));
+         }
+         T->Transform(ip, point);
+         for (int d = 0; d < sdim; d++)
+         {
+            const int idx = (ordering == Ordering::byNODES) ?
+                            d*npt + p :
+                            p*sdim + d;
+            xyz(idx) = point(d);
+         }
+         p++;
+      }
+   }
+}
+
+void GetSurfaceBoundaryPoints(Mesh &mesh, const int npt_per_el,
+                              const int ordering, Vector &xyz,
+                              const int p0 = 0)
+{
+   MFEM_VERIFY(mesh.GetNodes() != nullptr, "Mesh nodes are required.");
+
+   const int sdim = mesh.SpaceDimension();
+   const int npt = xyz.Size()/sdim;
+   MFEM_VERIFY((p0 + mesh.GetNE()*npt_per_el)*sdim <= xyz.Size(),
+               "Output vector is too small.");
+   Vector point(sdim);
+   std::mt19937 gen(246);
+   std::uniform_real_distribution<double> uni(0.01, 0.99);
+   int p = p0;
+
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      const Geometry::Type geom = mesh.GetElementBaseGeometry(e);
+      for (int j = 0; j < npt_per_el; j++)
+      {
+         IntegrationPoint ip;
+         if (geom == Geometry::SEGMENT)
+         {
+            MFEM_VERIFY(npt_per_el == 2,
+                        "Segment boundary sampling requires npt_per_el = 2.");
+            ip.x = (j == 0) ? 0.0 : 1.0;
+         }
+         else
+         {
+            const double t = uni(gen);
+            if (geom == Geometry::SQUARE)
+            {
+               switch (j % 4)
+               {
+                  case 0: ip.Set2(t, 0.0);     break;
+                  case 1: ip.Set2(1.0, t);     break;
+                  case 2: ip.Set2(t, 1.0);     break;
+                  case 3: ip.Set2(0.0, t);     break;
+               }
+            }
+            else
+            {
+               MFEM_VERIFY(geom == Geometry::TRIANGLE,
+                           "Unsupported surface element geometry.");
+               switch (j % 3)
+               {
+                  case 0: ip.Set2(t, 0.0);     break;
+                  case 1: ip.Set2(t, 1.0 - t); break;
+                  case 2: ip.Set2(0.0, t);     break;
+               }
+            }
+         }
+         T->Transform(ip, point);
+         for (int d = 0; d < sdim; d++)
+         {
+            const int idx = (ordering == Ordering::byNODES) ?
+                            d*npt + p :
+                            p*sdim + d;
+            xyz(idx) = point(d);
+         }
+         p++;
+      }
+   }
+}
+
 TEST_CASE("GSLIBInterpolate", "[GSLIBInterpolate][GSLIB]")
 {
    auto space               = GENERATE(Space::H1, Space::L2);
@@ -190,6 +351,92 @@ TEST_CASE("GSLIBInterpolate", "[GSLIBInterpolate][GSLIB]")
    delete c_fec;
 }
 
+TEST_CASE("GSLIBSurfInterpolate", "[GSLIBSurfInterpolate][GSLIB]")
+{
+   auto surface_mesh_type   = GENERATE(SurfaceMeshType::Segment2D,
+                                       SurfaceMeshType::Segment3D,
+                                       SurfaceMeshType::Quad3D,
+                                       SurfaceMeshType::Tri3D);
+   func_order               = GENERATE(1, 2);
+   int mesh_order           = GENERATE(1, 2);
+   int mesh_node_ordering   = GENERATE(0, 1);
+   int point_ordering       = GENERATE(0, 1);
+   int ncomp                = GENERATE(1, 2);
+   int gf_ordering          = GENERATE(0, 1);
+   int func_out_ordering    = GENERATE(0, 1);
+
+   const char *mesh_name = SurfaceMeshName(surface_mesh_type);
+   CAPTURE(mesh_name, func_order, mesh_order, mesh_node_ordering,
+           point_ordering, ncomp, gf_ordering, func_out_ordering);
+
+   if (ncomp == 1 && gf_ordering == 1)
+   {
+      return;
+   }
+
+   Mesh mesh = MakeSurfaceMesh(surface_mesh_type, 4);
+   const int sdim = SurfaceSpaceDim(surface_mesh_type);
+   mesh.SetCurvature(mesh_order, false, sdim, mesh_node_ordering);
+
+   H1_FECollection c_fec(func_order, mesh.Dimension());
+   FiniteElementSpace c_fespace(&mesh, &c_fec, ncomp, gf_ordering);
+   GridFunction field_vals(&c_fespace);
+
+   VectorFunctionCoefficient F(ncomp, F_exact);
+   field_vals.ProjectCoefficient(F);
+
+   const int npt_per_el = 8;
+   const int pts_cnt = mesh.GetNE()*npt_per_el;
+   Vector vxyz(pts_cnt*sdim);
+   GetSurfaceInteriorPoints(mesh, npt_per_el, point_ordering, vxyz);
+
+   Vector interp_vals(pts_cnt*ncomp);
+   FindPointsGSLIB finder;
+   finder.SetupSurf(mesh);
+   finder.SetL2AvgType(FindPointsGSLIB::NONE);
+   finder.Interpolate(vxyz, field_vals, interp_vals, point_ordering,
+                      func_out_ordering);
+
+   Array<unsigned int> code_out = finder.GetCode();
+   Vector dist_p_out = finder.GetDist();
+
+   int not_found = 0;
+   double err = 0.0, max_err = 0.0, max_dist = 0.0;
+   Vector pos(sdim);
+   Vector exact_val(ncomp);
+
+   for (int i = 0; i < pts_cnt; i++)
+   {
+      max_dist = std::max(max_dist, dist_p_out(i));
+      for (int d = 0; d < sdim; d++)
+      {
+         const int idx = (point_ordering == Ordering::byNODES) ?
+                         d*pts_cnt + i :
+                         i*sdim + d;
+         pos(d) = vxyz(idx);
+      }
+      F_exact(pos, exact_val);
+      for (int j = 0; j < ncomp; j++)
+      {
+         if (code_out[i] < 2)
+         {
+            err = func_out_ordering == Ordering::byNODES ?
+                  fabs(exact_val(j) - interp_vals[i + j*pts_cnt]) :
+                  fabs(exact_val(j) - interp_vals[i*ncomp + j]);
+            max_err = std::max(max_err, err);
+         }
+         else if (j == 0)
+         {
+            not_found++;
+         }
+      }
+   }
+
+   REQUIRE(max_err < 1e-12);
+   REQUIRE(max_dist < 1e-10);
+   REQUIRE(not_found == 0);
+}
+
 // Generates meshes with different element types, followed by points at
 // element faces and interior, and finally checks to see if these points are
 // correctly detected at element boundary or not.
@@ -257,9 +504,8 @@ TEST_CASE("GSLIBFindAtElementBoundary",
       int nptface = xyz.Size()/dim;
 
       // Generate points inside each element
-      FiniteElementCollection *l2_fec = new L2_FECollection(l2_order, dim);
-      FiniteElementSpace l2_fespace =
-         FiniteElementSpace(&mesh, l2_fec, 1);
+      L2_FECollection l2_fec(l2_order, dim);
+      FiniteElementSpace l2_fespace(&mesh, &l2_fec, 1);
       DenseMatrix vals;
       DenseMatrix tr;
       for (int e = 0; e < mesh.GetNE(); e++)
@@ -295,7 +541,92 @@ TEST_CASE("GSLIBFindAtElementBoundary",
          cmax = std::max(code_out[i], cmax);
       }
       REQUIRE((cmin == 0 && cmax == 0)); // should be found inside element
-      delete l2_fec;
+   }
+}
+
+TEST_CASE("GSLIBSurfFindAtElementBoundary",
+          "[GSLIBSurfFindAtElementBoundary][GSLIB]")
+{
+   auto surface_mesh_type = GENERATE(SurfaceMeshType::Segment2D,
+                                     SurfaceMeshType::Segment3D,
+                                     SurfaceMeshType::Quad3D,
+                                     SurfaceMeshType::Tri3D);
+   const char *mesh_name = SurfaceMeshName(surface_mesh_type);
+   CAPTURE(mesh_name);
+
+   Mesh mesh = MakeSurfaceMesh(surface_mesh_type, 4);
+   const int sdim = SurfaceSpaceDim(surface_mesh_type);
+   mesh.SetCurvature(2, false, sdim);
+
+   const int nptface_per_el = (mesh.Dimension() == 1) ? 2 : 8;
+   const int nptint_per_el = 8;
+   const int nptface = mesh.GetNE()*nptface_per_el;
+   const int nptint = mesh.GetNE()*nptint_per_el;
+   Vector xyz((nptface + nptint)*sdim);
+   GetSurfaceBoundaryPoints(mesh, nptface_per_el, Ordering::byVDIM, xyz, 0);
+   GetSurfaceInteriorPoints(mesh, nptint_per_el, Ordering::byVDIM, xyz,
+                            nptface);
+
+   FindPointsGSLIB finder;
+   finder.SetupSurf(mesh);
+   finder.FindPoints(xyz, Ordering::byVDIM);
+   Array<unsigned int> code_out = finder.GetCode();
+
+   for (int i = 0; i < nptface; i++)
+   {
+      REQUIRE(code_out[i] == 1);
+   }
+   for (int i = nptface; i < nptface + nptint; i++)
+   {
+      REQUIRE(code_out[i] == 0);
+   }
+}
+
+TEST_CASE("GSLIBSurfAABBExpansion", "[GSLIBSurfAABBExpansion][GSLIB]")
+{
+   auto surface_mesh_type = GENERATE(SurfaceMeshType::Segment2D,
+                                     SurfaceMeshType::Segment3D,
+                                     SurfaceMeshType::Quad3D,
+                                     SurfaceMeshType::Tri3D);
+   const char *mesh_name = SurfaceMeshName(surface_mesh_type);
+   CAPTURE(mesh_name);
+
+   constexpr double offset = 1.0e-3;
+   const int npt_per_el = 8;
+
+   Mesh mesh = MakeSurfaceMesh(surface_mesh_type, 4);
+   const int sdim = SurfaceSpaceDim(surface_mesh_type);
+   mesh.SetCurvature(2, false, sdim);
+
+   const int npt = mesh.GetNE()*npt_per_el;
+   Vector xyz(npt*sdim);
+   GetSurfaceInteriorPoints(mesh, npt_per_el, Ordering::byVDIM, xyz);
+   // offset them to move away from the surface
+   const int off_d = (surface_mesh_type == SurfaceMeshType::Segment2D) ? 1 : 2;
+   for (int i = 0; i < npt; i++)
+   {
+      xyz(i*sdim + off_d) += offset;
+   }
+
+   FindPointsGSLIB finder;
+   finder.SetupSurf(mesh, 0.0);
+   finder.FindPoints(xyz, Ordering::byVDIM);
+   Array<unsigned int> code_no_pad = finder.GetCode();
+
+   for (int i = 0; i < code_no_pad.Size(); i++)
+   {
+      REQUIRE(code_no_pad[i] == 2);
+   }
+
+   // make aabb at least big enough to include the offset points
+   Vector aabb_sz_inc({2.1*offset});
+   finder.SetupSurfWithAABBExpansion(mesh, aabb_sz_inc);
+   finder.FindPoints(xyz, Ordering::byVDIM);
+   Array<unsigned int> code_with_pad = finder.GetCode();
+
+   for (int i = 0; i < npt; i++)
+   {
+      REQUIRE(code_with_pad[i] == 1);
    }
 }
 
@@ -322,9 +653,8 @@ TEST_CASE("GSLIBInterpolateL2ElementBoundary",
    mesh.SetCurvature(mesh_order);
 
    // Set GridFunction to be interpolated
-   FiniteElementCollection *c_fec = new L2_FECollection(3, dim);
-   FiniteElementSpace c_fespace =
-      FiniteElementSpace(&mesh, c_fec, 1);
+   L2_FECollection c_fec(3, dim);
+   FiniteElementSpace c_fespace(&mesh, &c_fec, 1);
    GridFunction field_vals(&c_fespace);
    Array<int> dofs;
    double leftval = 1.0;
@@ -366,7 +696,6 @@ TEST_CASE("GSLIBInterpolateL2ElementBoundary",
    REQUIRE(interp_vals(0) == MFEM_Approx(0.5*(leftval+rightval)));
 
    finder.FreeData();
-   delete c_fec;
 }
 
 #ifdef MFEM_USE_MPI

tests/unit/fem/test_linearform_ext.cpp

@@ -328,7 +328,7 @@ TEST_CASE("Linear Form Extension", "[LinearFormExtension], [GPU]")
    }
 }
 
-TEST_CASE("H(div) Linear Form Extension", "[LinearFormExtension], [GPU]")
+TEST_CASE("Vector FE Linear Form Extension", "[LinearFormExtension], [GPU]")
 {
    const bool all = launch_all_non_regression_tests;
 
@@ -341,26 +341,44 @@ TEST_CASE("H(div) Linear Form Extension", "[LinearFormExtension], [GPU]")
    Mesh mesh(mesh_file);
    const int dim = mesh.Dimension();
 
-   CAPTURE(mesh_file, dim, p);
+   {
+      const auto space_type =
+         dim == 3 ? GENERATE(FiniteElement::DIV, FiniteElement::CURL)
+         : FiniteElement::DIV;
 
-   RT_FECollection fec(p, dim);
-   FiniteElementSpace fes(&mesh, &fec);
+      CAPTURE(mesh_file, dim, p, space_type);
 
-   VectorFunctionCoefficient coeff(dim, fvec_dim);
+      std::unique_ptr<FiniteElementCollection> fec;
 
-   LinearForm d1(&fes);
-   d1.AddDomainIntegrator(new VectorFEDomainLFIntegrator(coeff));
-   d1.UseFastAssembly(true);
-   d1.Assemble();
+      switch (space_type)
+      {
+         case FiniteElement::DIV:
+            fec.reset(new RT_FECollection(p, dim));
+            break;
+         case FiniteElement::CURL:
+            fec.reset(new ND_FECollection(p, dim));
+            break;
+         default:
+            MFEM_ABORT("unsupported space type");
+      }
+      FiniteElementSpace fes(&mesh, fec.get());
 
-   LinearForm d2(&fes);
-   d2.AddDomainIntegrator(new VectorFEDomainLFIntegrator(coeff));
-   d2.UseFastAssembly(false);
-   d2.Assemble();
+      VectorFunctionCoefficient coeff(dim, fvec_dim);
 
-   CAPTURE(d1.Norml2(), d2.Norml2());
-   d1 -= d2;
-   REQUIRE(d1.Norml2() == MFEM_Approx(0.0));
+      LinearForm d1(&fes);
+      d1.AddDomainIntegrator(new VectorFEDomainLFIntegrator(coeff));
+      d1.UseFastAssembly(true);
+      d1.Assemble();
+
+      LinearForm d2(&fes);
+      d2.AddDomainIntegrator(new VectorFEDomainLFIntegrator(coeff));
+      d2.UseFastAssembly(false);
+      d2.Assemble();
+
+      CAPTURE(d1.Norml2(), d2.Norml2());
+      d1 -= d2;
+      REQUIRE(d1.Norml2() == MFEM_Approx(0.0));
+   }
 }
 
 #ifdef MFEM_USE_MPI

tests/unit/fem/test_project_bdr.cpp

@@ -124,8 +124,8 @@ TEST_CASE("3D ProjectBdrCoefficientNormal Scalar",
 
    const double tol = 1e-6;
 
-   const char bdrs_axis[] = {2, 1, 0, 1, 0, 2};
-   const char bdrs_sign[] = {-1, -1, +1, +1, -1, +1};
+   const int bdrs_axis[] = {2, 1, 0, 1, 0, 2};
+   const int bdrs_sign[] = {-1, -1, +1, +1, -1, +1};
 
    for (int type = (int)Element::TETRAHEDRON;
         type <= (int)Element::HEXAHEDRON; type++)

tests/unit/linalg/test_complex_operator.cpp

@@ -113,3 +113,65 @@ TEST_CASE("ComplexOperator Quaternion Tests", "[ComplexOperator]")
       REQUIRE(qikx.Normlinf() < tol);
    }
 }
+
+#ifdef MFEM_USE_MPI
+
+TEST_CASE("ComplexHypreParMatrix GetSystemMatrix",
+          "[ComplexOperator][Parallel][GPU]")
+{
+   // This test reproduces the issue described in PR #5200 on GitHub. See also
+   // the follow up PR #5346.
+
+   // 1. Construct ComplexHypreParMatrix similar to ex25p.
+   const char mesh_file[] = "../../data/inline-quad.mesh";
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+   int ref_levels = 1;
+   for (int l = 0; l < ref_levels; l++)
+   {
+      mesh->UniformRefinement();
+   }
+   ParMesh pmesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   int par_ref_levels = 1;
+   for (int l = 0; l < par_ref_levels; l++)
+   {
+      pmesh.UniformRefinement();
+   }
+   int order = 1;
+   ND_FECollection fec(order, dim);
+   ParFiniteElementSpace fespace(&pmesh, &fec);
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr;
+   if (pmesh.bdr_attributes.Size())
+   {
+      ess_bdr.SetSize(pmesh.bdr_attributes.Max());
+      ess_bdr = 1;
+   }
+   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   ComplexOperator::Convention conv = ComplexOperator::HERMITIAN;
+   VectorConstantCoefficient f(Vector{1_r, 2_r});
+   ParComplexLinearForm b(&fespace, conv);
+   b.AddDomainIntegrator(NULL, new VectorFEDomainLFIntegrator(f));
+   b = 0.0;
+   b.Assemble();
+   ParComplexGridFunction x(&fespace);
+   x = 0.0;
+   ConstantCoefficient one(1_r);
+   ParSesquilinearForm a(&fespace, conv);
+   a.AddDomainIntegrator(new CurlCurlIntegrator(one),
+                         new CurlCurlIntegrator(one));
+   a.AddDomainIntegrator(new VectorFEMassIntegrator(one),
+                         new VectorFEMassIntegrator(one));
+   a.Assemble();
+   OperatorPtr Ah;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);
+
+   // 2. Test the call to ComplexHypreParMatrix::GetSystemMatrix and destroying
+   //    the returned matrix.
+   HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
+   delete A;
+}
+
+#endif // MFEM_USE_MPI