trying some things

2025-12-03 12:56:24 -08:00
316 changed files with 38200 additions and 36840 deletions
@@ -92,10 +92,6 @@ examples/ex9.mesh
 examples/ex9-mesh.*
 examples/ex9-init.*
 examples/ex9-final.*
-examples/ex41.mesh
-examples/ex41-mesh.*
-examples/ex41-init.*
-examples/ex41-final.*
 examples/deformed.*
 examples/velocity.*
 examples/elastic_energy.*
@@ -227,9 +223,6 @@ miniapps/electromagnetics/Joule_[0-9]*
 miniapps/electromagnetics/Lorentz_[0-9]*
 miniapps/electromagnetics/Lorentz.dat

-miniapps/fluids/schrodinger-flow/schrodinger_flow
-miniapps/fluids/schrodinger-flow/pschrodinger_flow
-
 miniapps/gslib/field-diff
 miniapps/gslib/field-interp
 miniapps/gslib/findpts
@@ -237,7 +230,6 @@ miniapps/gslib/pfindpts
 miniapps/gslib/schwarz_ex1
 miniapps/gslib/schwarz_ex1p
 miniapps/gslib/interpolated.gf
-miniapps/gslib/particles_redist

 miniapps/meshing/mobius-strip
 miniapps/meshing/klein-bottle
@@ -284,8 +276,10 @@ miniapps/meshing/refined.mesh
 miniapps/meshing/bounding-box*
 miniapps/meshing/jacobian-determinant*

-miniapps/mtop/ParaView/
-miniapps/mtop/mtop_test_iso_elasticity
+miniapps/mtop/parheat
+miniapps/mtop/ParHeat/*
+miniapps/mtop/seqheat
+miniapps/mtop/SeqHeat/*

 miniapps/autodiff/paradiff
 miniapps/autodiff/seqadiff
@@ -295,26 +289,21 @@ miniapps/autodiff/seq_example
 miniapps/autodiff/seq_test
 miniapps/autodiff/Example/*

-miniapps/fluids/navier/navier_mms
-miniapps/fluids/navier/navier_kovasznay
-miniapps/fluids/navier/navier_kovasznay_vs
-miniapps/fluids/navier/navier_tgv
-miniapps/fluids/navier/navier_shear
-miniapps/fluids/navier/navier_3dfoc
-miniapps/fluids/navier/navier_turbchan
-miniapps/fluids/navier/navier_cht
-miniapps/fluids/navier/navier_bifurcation
-miniapps/fluids/navier/Navier_Bifurcation_[0-9]*
-miniapps/fluids/navier/ParaView
-miniapps/fluids/navier/tgv_out*.txt
-miniapps/fluids/navier/*_output
+miniapps/navier/navier_mms
+miniapps/navier/navier_kovasznay
+miniapps/navier/navier_kovasznay_vs
+miniapps/navier/navier_tgv
+miniapps/navier/navier_shear
+miniapps/navier/navier_3dfoc
+miniapps/navier/navier_turbchan
+miniapps/navier/navier_cht
+miniapps/navier/tgv_out*.txt
+miniapps/navier/*_output

 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
 miniapps/nurbs/nurbs_ex3
 miniapps/nurbs/nurbs_ex5
-miniapps/nurbs/nurbs_ex10
-miniapps/nurbs/nurbs_ex10p
 miniapps/nurbs/nurbs_ex11p
 miniapps/nurbs/nurbs_ex24
 miniapps/nurbs/nurbs_solenoidal
@@ -340,14 +329,7 @@ miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
 miniapps/nurbs/glvis_naca-cmesh.mesh
 miniapps/nurbs/Naca_cmesh
-miniapps/nurbs/nurbs_mesh_info
-miniapps/nurbs/k*_*.dat
 miniapps/nurbs/*-Surface.mesh
-miniapps/nurbs/*.mesh
-miniapps/nurbs/*.sol
-miniapps/nurbs/deformed.*
-miniapps/nurbs/elastic_energy.*
-miniapps/nurbs/velocity.*

 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -369,7 +351,6 @@ miniapps/shifted/lsf_integral
 miniapps/tools/display-basis
 miniapps/tools/load-dc
 miniapps/tools/convert-dc
-miniapps/tools/compare-dc
 miniapps/tools/gridfunction-bounds
 miniapps/tools/lor-transfer
 miniapps/tools/plor-transfer
@@ -440,9 +421,6 @@ miniapps/tribol/contact-patch-test
 miniapps/diag-smoothers/abs-l1-jacobi
 miniapps/diag-smoothers/mg-abs-l1-jacobi

-miniapps/contact/contact
-miniapps/contact/ParaView
-
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests
@@ -8,6 +8,8 @@
                               https://mfem.org


+FIXME: this file needs to be updated
+
 This directory contains most of the GitLab CI configuration. MFEM runs both PR
 and nightly testing on GitLab.

@@ -32,7 +32,7 @@ mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}

 # run
 if [[ "${MACHINE_NAME}" == "dane" ]]; then
-  salloc --nodes=1 -t 60 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+  salloc --nodes=1 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 elif [[ ${MACHINE_NAME} == "corona" ]]; then
  salloc --nodes=1 -t 60 -p pbatch ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 else
@@ -8,29 +8,9 @@
                               https://mfem.org


-Version 4.9.1 (development)
+Version 4.8.1 (development)
 ===========================

-Discretization improvements
---------------------------
- Improved the gridfunction projection routines. Projections work for Scalar,
-  Vector and VectorFE, also NURBS versions. Optionally different types of
-  projections can be selected, default behaviour has not changed.
-
-Meshing improvements
--------------------
- Improved support for 1D NURBS meshes with variable order, including using
-  the patches construct for 1D NURBS meshes.
-
-New and updated examples and miniapps
-------------------------------------
- Electromagnetics/lorentz miniapp has been updated to leverage the ParticleSet
-  capability.
-
-
-Version 4.9, released on Dec 11, 2025
-=====================================
-
 Starting with this version, MFEM requires a C++17 compiler.

 Discretization improvements
@@ -39,149 +19,86 @@ Discretization improvements
  nonlinear finite element operators, based on Enzyme or dual numbers AD at
  quadrature points. These features are part of the new mfem::future namespace
  and some of the API can change in the future. See the new dFEM minimal surface
-  miniapp in the miniapps/dfem/ directory for illustration of dFEM's use. Using
-  Enzyme for AD in MFEM is tested with clang v19 and requires clang/LLVM built
-  with plugin support. See INSTALL for more details.
+  miniapp in the miniapps/dfem/ directory for illustration of dFEM's use.

- Introduced initial support for particle methods in MFEM with new classes
-  Particle, ParticleSet and ParticleVector.
-  * Particle is a convenient interface for individual particle data.
-  * ParticleSet manages and stores particle data in a struct-of-arrays form,
-    carrying particle coordinates and IDs along with an arbitrary number of
-    Vector and integer data for each particle.
-  * ParticleVector is a Vector-derived container that stores vector data for an
-    arbitrary number of particles contiguously based on specified vdim/ordering.
-  See the new particle miniapps in miniapps/gslib/ and miniapps/fluids/navier/.
-
- Added a new miniapp and specialized AMG solver (AMGF) for optimization-based
-  contact mechanics. The miniapp solves large-scale frictionless contact using a
-  self-contained Interior Point (IP) solver, mortar-based contact constraints
-  provided by Tribol. The resulting linear systems are solved with the new AMGF
-  solver (see below). Benchmark examples include the two-block, ironing, and
-  beam-sphere problems. See the miniapps/contact/ directory.
-
- Added support for boundary integration to the hyperbolic framework. Two new
-  classes BdrHyperbolicDirichletIntegrator and BoundaryHyperbolicFlowIntegrator
-  have been introduced for implementation of weak Dirichlet boundary conditions
-  with a general flux or for the linear case respectively.
-
- Added a method to compute piecewise linear bounds on high-order functions on
-  tensor-product elements.
-
- Added support for interior face integration enabling DG methods in
-  ParMixedBilinearForm, ParNonlinearForm and ParBlockNonlinearForm.
+- Using Enzyme for AD in MFEM is tested with clang v19 and requires clang/LLVM
+  built with plugin support. See INSTALL for more details.

 - In the ParMoonolith integration, added support for variational resampling of
  H1 vector fields.

- Introduced IMEX ODE solvers based on a split-operator framework. Added
-  examples ex41 and ex41p demonstrating IMEX DG/CG discretizations of the
-  convection–diffusion equation, with ex41p using DG LOR preconditioning.
+- Added support for boundary integration to the hyperbolic framework. In this
+  regard, new classes `BdrHyperbolicDirichletIntegrator` and
+  `BoundaryHyperbolicFlowIntegrator` have been introduced for implementation
+  of weak Dirichlet boundary conditions with a general flux or for the linear
+  case respectively.
+
+- Added method to compute piecewise linear bounds on high-order functions on
+  tensor-product elements.
+
+- Parallel anisotropic refinement of hexahedral meshes is now supported,
+  provided that neighboring hexahedra are not refined in conflicting directions.
+  A new ParMesh method is added to check for such conflicts, before refinement.

 Meshing improvements
 --------------------
+
 - The TMOP kernel hierarchy has been restructured to reduce compilation time.
-  Most large kernels have been split into smaller specific kernels for each
-  metric. The directory structure has been updated with assemble, metrics, mult
-  and tools subdirectories. New kernel dispatch and specialization system has
-  also been integrated. Unit tests have been revised to ensure --all tests pass.
+  Most large kernels have been split into smaller, specific ones, with kernels
+  for each metric. The directory structure has been updated with assemble,
+  metrics, mult and tools subdirectories. The new kernel dispatch and
+  specialization system has also been integrated.
+  Unit tests have been revised to ensure --all tests pass.

 - Introduced NC-patch NURBS meshes, which are conforming element-wise but allow
  for nonconforming patch topology. This new mesh format supports element
  spacing formulas for refinement, as well as local refinement factors for a
  subset of knot vectors.

+- Added support for higher order meshes in Mesh::MakeSimplicial and
+  ParMesh::MakeSimplicial.
+
 - Added a new miniapp for interpolating a surface grid of points in 3D using a
  smooth NURBS surface, that can then be sampled at arbitrary resolution while
  staying close to the original geometry. See miniapps/nurbs/nurbs_surface.

- Parallel anisotropic refinement of hexahedral meshes is now supported,
-  provided that neighboring hexahedra are not refined in conflicting directions.
-  A new ParMesh method is added to check for such conflicts, before refinement.
-
- Added support for higher order meshes in (Par)Mesh::MakeSimplicial.
-
-Linear and nonlinear solvers
----------------------------
- Added FilteredSolver: a base class for solvers with filtering. It handles
-  cases where a solver performs well except in small subspaces, by adding a
-  filtering step formulated as a subspace correction.
-
- Added AMGFSolver: a derived class of FilteredSolver, specialized for AMG with
-  Filtering (AMGF), providing robust preconditioning for linear systems arising
-  in constrained optimization problems such as frictionless contact.
-
-  Added 'GetResiduals' and 'GetFinalAbsResidualNorm' to 'HyprePCG',
-  'HypreGMRES', and 'HypreFGMRES' to get 'r' and '|r|_p'. Note that the latter
-  computes '|r|_p' from 'r' instead of returning a cached value like the
-  relative 'GetFinalResidualNorm'. These require Hypre >= 2.15.0.
-
-  Changed the default solver parameters for 'HyprePCG' to 'tol=1e-6' and
-  'max_iter=1000'. This matches the default parameters in Hypre 3.0.
-
-  Added various helper functions for querying/modifying Hypre solvers:
-  'HypreSmoother::GetType', 'HypreSmoother::GetSOROptions',
-  'HypreSmoother::GetPolyOptions', 'HypreSmoother::GetWindowParameters',
-  'HypreSmoother::IsOperatorSymmetric', 'HyprePCG::GetTol',
-  'HyprePCG::GetAbsTol', 'HyprePCG::GetMaxIter', 'HyprePCG::SetUseTwoNorm',
-  'HypreGMRES::GetTol', 'HypreGMRES::GetAbsTol', 'HypreGMRES::GetMaxIter',
-  'HypreGMRES::GetKDim', 'HypreFGMRES::GetTol', 'HypreFGMRES::GetMaxIter',
-  'HypreFGMRES::GetKDim', and 'HypreBoomerAMG::GetMaxIter'.
-
 GPU computing
 -------------
- Added the 'gpu', 'raja-gpu', and 'ceed-gpu' backend aliases/shortcuts which
-  automatically select between CUDA or HIP.
-
- Added the option to enable GPU-aware MPI in MFEM using the environment
-  variable 'MFEM_GPU_AWARE_MPI' set to any value. Setting this environment
-  variable is an alternative to calling 'Device::SetGPUAwareMPI(true)'.
-
- Implemented a GPU-accelerated matrix-free AMR derefinement GridFunction update
-  operator. This supports mixed geometry meshes and variable order spaces, and
-  is the default derefinement operator constructed by FiniteElementSpace::Update
-  and ParFiniteElementSpace::Update. The operator requires the finite element
-  space to be nonconforming.
+- The function Vector::SetSubVector(const Array<int> &, const real_t) now
+  executes on device if either the vector or the array have the device flag
+  set. This is most often used for setting constant essential boundary
+  conditions. A new function Vector::SetSubVectorHost has been added in cases
+  where host execution is always needed (e.g. when the DOFs array is small).

 - Introduced MFEM_FOREACH_THREAD_DIRECT, which directly maps loop tasks to GPU
  threads, assigning one task per thread.

- The function Vector::SetSubVector(const Array<int> &, const real_t) now
-  executes on device if either the vector or the array have the device flag
-  set. This is most often used for setting constant essential BCs. A new method,
-  SetSubVectorHost, has been added for cases where host execution is always
-  needed (e.g. when the DOFs array is small).
-
- Added GPU support in GradientGridFunction and InnerProduct Coefficient classes
-  by implementing their Project methods.
-
+- Implemented a GPU-accelerated matrix-free AMR derefinement `GridFunction`
+  update operator. This supports mixed geometry meshes and variable order
+  spaces, and is the default derefinement operator constructed by
+  `FiniteElementSpace::Update` and `ParFiniteElementSpace::Update`.
+  The operator requires `FiniteElementSpace::Nonconforming() == true`.
 - Added new method: GridFunction::GetGradients, with GPU support, for computing
  the gradients of a GridFunction on all elements.
+- Added GPU support in GradientGridFunctionCoefficient and
+  InnerProductCoefficient by implementing their Project methods.

- The CUDA-specific names used by some of the unit tests like 'cunit_tests' and
-  'pcunit_tests' were replaced by names using 'gpu' instead of 'c' (short for
-  CUDA) or 'cuda'. These tests automatically run the CUDA/HIP tests based on the
-  MFEM build configuration.
+Linear and nonlinear solvers
+----------------------------
+- Added `FilteredSolver`: a base class for solvers with filtering. It handles cases 
+  where a solver performs well except in small subspaces, by adding a filtering step 
+  formulated as a subspace correction.
+- Added `AMGFSolver`: a derived class of `FilteredSolver`, specialized for 
+  AMG with Filtering (AMGF), providing robust preconditioning for linear systems 
+  arising in constrained optimization problems such as frictionless contact.

 New and updated examples and miniapps
 -------------------------------------
- Added the miniapps/fluids directory and moved the previous Navier and the new
-  incompressible Schrödinger flow miniapps into it.
-
- Introduced the new Incompressible Schrödinger Flow (ISF) miniapp, which models
-  inviscid fluid dynamics by solving the linear Schrödinger equation, leveraging
-  the hydrodynamical analogy to quantum mechanics.
-
- New particle-related miniapps:
-  * New transient Navier-Stokes fluid-particles solver NavierParticles in
-    miniapps/fluids/navier/navier_particles, for modeling tracer particles in
-    fluid flow, demonstrating use of the new ParticleSet class.
-  * New Navier miniapp, miniapps/fluids/navier/navier_bifurcation, showing the
-    use of NavierParticles in a 2D bifurcating channel flow.
-  * New FindPointsGSLIB miniapp, miniapps/gslib/particles_redist, showing
-    parallel-redistribution of particle data between MPI ranks.
-  * Particle visualization features in common/particles_extras for viewing
-    particle locations and trajectories (ParticleTrajectories) using GLVis.
+- Added miniapps to demonstrate an implementation of the absolute-value
+  L(1)-Jacobi preconditioners in partially assembled operators. This includes
+  Multigrid wrapper to demonstrate the effectiveness of these Jacobi-type
+  operators as smoothers.
+  These miniapps can be found in `miniapps/diag-smoothers`.

 - Added a new miniapp (meshing/mesh-bounding-boxes) that computes the bounding
  boxes for each element of a given mesh, and the bounds on the determinant of
@@ -194,44 +111,36 @@ New and updated examples and miniapps
  of a charged particle, subject to Lorentz forces, in electrostatic and/or
  magnetostatic fields as computed by the volta or tesla miniapps.

- Added miniapps to demonstrate an implementation of the absolute-value
-  l1-Jacobi preconditioners in partially assembled operators. This includes
-  Multigrid wrapper to demonstrate the effectiveness of these Jacobi-type
-  operators as smoothers. See the miniapps/diag-smoothers/ directory.
-
- Updated the mtop miniapp with a GPU enabled forward and adjoint solver for
-  isotropic linear elasticity.
-
-Miscellaneous
-------------
- Introduced MFEM_FETCH_TPLS CMake option to enable downloading, configuring,
-  and building of TPLs alongside MFEM (currently supported TPLs are hypre,
-  METIS, and GSLIB).
-
- Added quadrature function support to the VisIt and Conduit data collections.
-
- Added access to the internal parallel matrix in Par(Mixed)BilinearForm and
-  related utility methods for elimination of BCs.
-
- FindPointsGSLIB has a new constructor that accepts the mesh object and
-  internally calls the Setup() method so users do not have to. The FreeData()
-  method has also been moved to the destructor so users do not need to manually
-  free-up the memory if the destructor is called before MPI_Finalize().
-
- Added parallel Address Sanitizer, serial and parallel Undefined Behavior
-  Sanitizer and serial Memory Sanitizer GitHub actions tests on Ubuntu.
-
-API changes
+API changes:
 -----------
 - mfem::internal::tensor and mfem::internal::dual have been moved to
  mfem::future::tensor and mfem::future::dual.

- API addition: in class Operator, added virtual functions: AbsMult, and
-  AbsMultTranspose; in class Vector, added Abs and Pow.
+- API addition: in class `Operator`, added virtual functions: `AbsMult`, and
+  `AbsMultTranspose`; in class `Vector`, added `Abs` and `Pow`.

- ParBilinearForm::EliminateEssentialVDofsInRhs() has been deprecated in favor
-  of ParallelEliminateEssentialTDofsInRhs().
+Miscellaneous
+-------------
+- Added the "gpu", "raja-gpu", and "ceed-gpu" backend aliases/shortcuts which
+  automatically select between CUDA or HIP.

+- The CUDA-specific names used by some of the unit tests like 'cunit_tests' and
+  'pcunit_tests' were replaced by names using 'gpu' instead of 'c' (short for
+  CUDA) or 'cuda'. These tests automatically run the CUDA/HIP tests based on the
+  MFEM build configuration.
+
+- Added the option to enable GPU-aware MPI in MFEM using the environment
+  variable 'MFEM_GPU_AWARE_MPI' set to any value. Setting this environment
+  variable is an alternative to calling 'Device::SetGPUAwareMPI(true)'.
+
+- Added parallel Address Sanitizer, serial and parallel Undefined Behavior
+  Sanitizer and serial Memory Sanitizer GitHub actions tests on Ubuntu.
+
+- FindPointsGSLIB has a new constructor that accepts the mesh object and
+  internally calls the Setup() method so that the user does not have to.
+  The FreeData() method has also been moved to the destructor so the user does
+  not need to manually free-up the memory if the destructor is called before
+  MPI_Finalize().

 Version 4.8, released on Apr 9, 2025
 ====================================
@@ -59,7 +59,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 4.9.1)
+set(${PROJECT_NAME}_VERSION 4.8.1)

 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -723,7 +723,6 @@ set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX})

 # Declaring the library
 mfem_add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
-target_compile_features(mfem PUBLIC cxx_std_${CMAKE_CXX_STANDARD})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
 target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES} ${TPL_TARGETS})
 if (TPL_TARGETS)
@@ -870,12 +869,11 @@ add_dependencies(exec
 #  - https://cmake.org/Bug/view.php?id=8438

 # Add a target to copy the mfem data directory to the build directory
-# Implementable as a single copy_directory_if_different command w/ CMake >= 3.26
-file(GLOB DATA_FILES CONFIGURE_DEPENDS ${PROJECT_SOURCE_DIR}/data/*)
-add_custom_target(copy_data
-  COMMAND ${CMAKE_COMMAND} -E make_directory data
-  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${DATA_FILES} data
-  COMMENT "Syncing the data directory ...")
+add_custom_command(OUTPUT data_is_copied
+  COMMAND ${CMAKE_COMMAND} -E copy_directory ${PROJECT_SOURCE_DIR}/data data
+  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
+  COMMENT "Copying the data directory ...")
+add_custom_target(copy_data DEPENDS data_is_copied)
 # Add 'copy_data' as a prerequisite for all executables, if the source and the
 # build directories are not the same.
 if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
@@ -1007,10 +1005,6 @@ install(FILES
 install(EXPORT ${PROJECT_NAME_UC}Targets
    DESTINATION ${INSTALL_CMAKE_DIR})

-# Install the data directory if present, i.e. if the copy_data target is built
-install(DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/data
-  DESTINATION ${MFEM_INSTALL_DIR} OPTIONAL)
-
 #-------------------------------------------------------------------------------
 # Create 'config.mk' from 'config.mk.in' for the build and install locations and
 # define install rules for 'config.mk' and 'test.mk'
@@ -129,10 +129,6 @@ The MFEM source code has the following structure:
  │   ├── moonolith
  │   ├── qinterp
  │   └── tmop
-  │   |   ├── assemble
-  │   |   ├── metrics
-  │   |   ├── mult
-  │   |   └── tools
  ├── general
  ├── linalg
  │   ├── batched
@@ -143,19 +139,16 @@ The MFEM source code has the following structure:
  │   ├── adjoint
  │   ├── autodiff
  │   ├── common
-  │   ├── contact
  │   ├── dfem
  │   ├── dpg
  │   ├── electromagnetics
-  │   ├── fluids
-  │   │   ├── navier
-  │   │   └── schrodinger-flow
  │   ├── gslib
  │   ├── hdiv-linear-solver
  │   ├── hooke
  │   ├── meshing
  │   ├── mtop
  │   ├── multidomain
+  │   ├── navier
  │   ├── nurbs
  │   ├── parelag
  │   ├── performance
@@ -725,9 +725,7 @@ The specific libraries and their options are:
  URL: https://ginkgo-project.github.io
  Options: GINKGO_OPT, GINKGO_LIB, GINKGO_DIR, GINKGO_BUILD_TYPE (Release or
           Debug).
-  Versions: Ginkgo >= 1.9.0. When building Ginkgo with distributed support, a
-            recent version of the "develop" branch is required (1.11 as defined
-            in include/ginkgo/config.hpp).
+  Versions: Ginkgo >= 1.9.0.

 - AmgX (optional), used when MFEM_USE_AMGX = YES.
  URL: https://github.com/NVIDIA/AMGX
@@ -18,7 +18,6 @@
 # Some choices below are based on the OS type:
 NOTMAC := $(subst Darwin,,$(shell uname -s))

-ASTYLE_BIN = astyle
 ETAGS_BIN = $(shell command -v etags 2> /dev/null)
 EGREP_BIN = $(shell command -v egrep 2> /dev/null)

@@ -408,7 +407,7 @@ AMGX_LIB = -L$(AMGX_DIR)/lib -lamgx -lcusparse -lcusolver -lcublas -lnvToolsExt
 # MAGMA library configuration
 MAGMA_DIR = @MFEM_DIR@/../magma
 MAGMA_OPT = -I$(MAGMA_DIR)/include
-MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a $(LAPACK_LIB)
+MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a -lcublas -lcusparse $(LAPACK_LIB)

 # GnuTLS library configuration
 GNUTLS_OPT =
@@ -101,7 +101,7 @@ $ cd ../miniapps
 $ ls
 CMakeLists.txt  common            meshing  nurbs        shifted  toys
 adjoint         electromagnetics  mtop     parelag      solvers
-autodiff        gslib             fluids   performance  tools
+autodiff        gslib             navier   performance  tools
 ```

 And an example in "toys"
@@ -85,10 +85,6 @@ groups_serial=(
   "DPG miniapps:"
   "miniapps/dpg"
   "{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
-'"isf"
-   "Schrodinger flow miniapps:"
-   "miniapps/fluids/schrodinger-flow"
-   "schrodinger_flow.cpp"'
 '"gslib"
   "GSLIB miniapps:"
   "miniapps/gslib"
@@ -170,10 +166,6 @@ groups_parallel=(
   "miniapps/electromagnetics"
   "joule.cpp"'
 #   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
-'"isf"
-   "Schrodinger flow miniapps:"
-   "miniapps/fluids/schrodinger-flow"
-   "pschrodinger_flow.cpp"'
 '"adjoint"
   "Adjoint miniapps:"
   "miniapps/adjoint"
@@ -199,7 +191,7 @@ groups_parallel=(
 # todo: miniapps/multidomain
 '"navier"
   "Navier miniapps:"
-   "miniapps/fluids/navier"
+   "miniapps/navier"
   "navier_cht.cpp"'
 # todo: add other navier miniapps
 '"nurbs"
@@ -289,10 +281,6 @@ groups_all=(
   "miniapps/electromagnetics"
   "joule.cpp"'
 #   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
-'"isf"
-   "Schrodinger flow miniapps:"
-   "miniapps/fluids/schrodinger-flow"
-   "{,p}schrodinger_flow.cpp"'
 '"adjoint"
   "Adjoint miniapps:"
   "miniapps/adjoint"
@@ -320,7 +308,7 @@ groups_all=(
 # todo: miniapps/multidomain
 '"navier"
   "Navier miniapps:"
-   "miniapps/fluids/navier"
+   "miniapps/navier"
   "navier_cht.cpp"'
 # todo: add other navier miniapps
 '"nurbs"
@@ -1,156 +0,0 @@
-MFEM mesh v1.0
-
-#
-# MFEM Geometry Types (see fem/geom.hpp):
-#
-# POINT       = 0
-# SEGMENT     = 1
-# TRIANGLE    = 2
-# SQUARE      = 3
-# TETRAHEDRON = 4
-# CUBE        = 5
-# PRISM       = 6
-# PYRAMID     = 7
-#
-
-dimension
-2
-
-elements
-25
-3 3 0 1 2 3
-3 3 1 4 5 2
-3 3 4 6 7 5
-3 3 6 8 9 7
-3 3 8 10 11 9
-3 3 10 12 13 11
-3 3 12 14 15 13
-3 3 14 16 17 15
-3 3 16 18 19 17
-3 3 18 20 21 19
-3 3 20 22 23 21
-3 3 22 24 25 23
-3 3 24 26 27 25
-3 3 26 28 29 27
-3 3 28 30 31 29
-3 3 30 32 33 31
-3 3 32 34 35 33
-3 3 17 19 36 37
-3 3 37 36 38 39
-3 3 39 38 40 41
-3 3 41 40 42 43
-3 3 43 42 44 45
-3 3 45 44 46 47
-3 3 47 46 48 49
-3 3 49 48 50 51
-
-boundary
-52
-2 1 0 1
-2 1 2 3
-1 1 3 0
-2 1 1 4
-2 1 5 2
-2 1 4 6
-2 1 7 5
-2 1 6 8
-2 1 9 7
-2 1 8 10
-2 1 11 9
-2 1 10 12
-2 1 13 11
-2 1 12 14
-2 1 15 13
-2 1 14 16
-2 1 17 15
-2 1 16 18
-2 1 18 20
-2 1 21 19
-2 1 20 22
-2 1 23 21
-2 1 22 24
-2 1 25 23
-2 1 24 26
-2 1 27 25
-2 1 26 28
-2 1 29 27
-2 1 28 30
-2 1 31 29
-2 1 30 32
-2 1 33 31
-2 1 32 34
-3 1 34 35
-2 1 35 33
-2 1 19 36
-2 1 37 17
-2 1 36 38
-2 1 39 37
-2 1 38 40
-2 1 41 39
-2 1 40 42
-2 1 43 41
-2 1 42 44
-2 1 45 43
-2 1 44 46
-2 1 47 45
-2 1 46 48
-2 1 49 47
-2 1 48 50
-4 1 50 51
-2 1 51 49
-
-vertices
-52
-2
-0 0
-1 0
-1 1
-0 1
-2 0
-2 1
-3 0
-3 1
-4 0
-4 1
-5 0
-5 1
-6 0
-6 1
-7 0
-7 1
-8 0
-8 1
-9 0
-9 1
-10 0
-10 1
-11 0
-11 1
-12 0
-12 1
-13 0
-13 1
-14 0
-14 1
-15 0
-15 1
-16 0
-16 1
-17 0
-17 1
-9 2
-8 2
-9 3
-8 3
-9 4
-8 4
-9 5
-8 5
-9 6
-8 6
-9 7
-8 7
-9 8
-8 8
-9 9
-8 9
@@ -1,86 +0,0 @@
-MFEM NURBS mesh v1.0
-
-dimension
-1
-
-# Four segments with different NURBS orders, described via patches.
-elements
-4
-1 1 0 1
-2 1 2 3
-3 1 4 5
-4 1 6 7
-
-boundary
-0
-
-edges
-4
-0 0 1
-1 2 3
-2 4 5
-3 6 7
-
-vertices
-8
-
-patches
-
-# Patch 0: linear (order 1, 3 spans)
-knotvectors
-1
-1 4  0 0  .4 .6 1 1
-
-dimension
-2
-
-controlpoints
-0.0  0.0  1.0
-0.6  0.4  1.0
-0.4  0.6  1.0
-1.0  1.0  1.0
-
-# Patch 1: quadratic (order 2, 2 spans)
-knotvectors
-1
-2 4  0 0 0  .5 1 1 1
-
-dimension
-2
-
-controlpoints
-1.0  0.0  1.0
-1.9  0.0  1.21
-2.0  0.9  1.22
-2.0  1.0  1.0
-
-# Patch 2: cubic (order 3, 3 spans)
-knotvectors
-1
-3 6  0 0 0 0 .33 .66 1 1 1 1
-
-dimension
-2
-
-controlpoints
-2.0   0.0  1.0
-2.1   0.2  1.31
-3.5   0.4  1.32
-2.5   0.6  1.33
-2.9   1.0  1.34
-3.0   1.0  1.0
-
-# Patch 3: quartic (order 4, 1 span)
-knotvectors
-1
-4 5  0 0 0 0 0 1 1 1 1 1
-
-dimension
-2
-
-controlpoints
-3.0    0.0  1.0
-3.45   0.5  1.41
-3.50   1.0  1.42
-3.75   0.8  1.43
-4.0    0.0  1.0
@@ -1,79 +0,0 @@
-MFEM NURBS mesh v1.0
-
-#
-# MFEM Geometry Types (see fem/geom.hpp):
-#
-# SEGMENT     = 1
-# SQUARE      = 3
-# CUBE        = 5
-#
-
-dimension
-1
-
-# Three segments with different NURBS orders, described via patches.
-elements
-3
-1 1 0 1
-2 1 2 3
-3 1 4 5
-
-boundary
-6
-1 0 0
-1 0 1
-1 0 2
-1 0 3
-1 0 4
-1 0 5
-
-edges
-3
-0 0 1
-1 2 3
-2 4 5
-
-vertices
-6
-
-patches
-
-# Patch 0: linear (order 1, 2 control points)
-knotvectors
-1
-1 2  0 0  1 1
-
-dimension
-2
-
-controlpoints
-0.0  0.0  1.0
-1.0  1.0  1.0
-
-# Patch 1: quadratic (order 2, 3 control points)
-knotvectors
-1
-2 3  0 0 0  1 1 1
-
-dimension
-2
-
-controlpoints
-1.0  0.0   1.0
-1.02 1.02  1.2
-2.0  1.0   1.0
-
-# Patch 2: cubic (order 3, 4 control points)
-knotvectors
-1
-3 4  0 0 0 0  1 1 1 1
-
-dimension
-2
-
-controlpoints
-2.0   0.0   1.0
-2.03  0.83  1.31
-2.33  1.03  1.32
-3.0   1.0   1.0
-
@@ -1,72 +0,0 @@
-MFEM NURBS mesh v1.0
-
-#
-# MFEM Geometry Types (see fem/geom.hpp):
-#
-# SEGMENT     = 1
-# SQUARE      = 3
-# CUBE        = 5
-#
-
-dimension
-1
-
-elements
-3
-1 1 0 1
-2 1 2 3
-3 1 4 5
-
-boundary
-6
-1 0 0
-1 0 1
-1 0 2
-1 0 3
-1 0 4
-1 0 5
-
-edges
-3
-0 0 1
-1 2 3
-2 4 5
-
-vertices
-6
-
-# Edge 0: linear (order 1, 2 control points)
-# Edge 1: quadratic (order 2, 3 control points)
-# Edge 2: cubic (order 3, 4 control points)
-knotvectors
-3
-1 2  0 0  1 1
-2 3  0 0 0  1 1 1
-3 4  0 0 0 0  1 1 1 1
-
-# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
-weights
-1
-1
-1
-1
-1
-1
-1.2
-1.31
-1.32
-
-FiniteElementSpace
-FiniteElementCollection: NURBS
-VDim: 2
-Ordering: 1
-
-0.0  0.0
-1.0  1.0
-1.0  0.0
-2.0  1.0
-2.0  0.0
-3.0  1.0
-1.02 1.02
-2.03 0.83
-2.33 1.03
@@ -1,79 +0,0 @@
-MFEM NURBS mesh v1.0
-
-#
-# MFEM Geometry Types (see fem/geom.hpp):
-#
-# SEGMENT     = 1
-# SQUARE      = 3
-# CUBE        = 5
-#
-
-dimension
-1
-
-# Three segments with different NURBS orders, described via patches.
-elements
-3
-1 1 0 1
-2 1 2 3
-3 1 4 5
-
-boundary
-6
-1 0 0
-1 0 1
-1 0 2
-1 0 3
-1 0 4
-1 0 5
-
-edges
-3
-0 0 1
-1 2 3
-2 4 5
-
-vertices
-6
-
-patches
-
-# Patch 0: linear (order 1, 2 control points)
-knotvectors
-1
-1 2  0 0  1 1
-
-dimension
-3
-
-controlpoints
-0.0  0.0  0.01 1.0
-1.0  1.0  1.01 1.0
-
-# Patch 1: quadratic (order 2, 3 control points)
-knotvectors
-1
-2 3  0 0 0  1 1 1
-
-dimension
-3
-
-controlpoints
-1.0  0.0   0.02 1.0
-1.02 1.02  0.52 1.2
-2.0  1.0   1.02 1.0
-
-# Patch 2: cubic (order 3, 4 control points)
-knotvectors
-1
-3 4  0 0 0 0  1 1 1 1
-
-dimension
-3
-
-controlpoints
-2.0   0.0   0.03 1.0
-2.03  0.83  0.33 1.31
-2.33  1.03  0.63 1.32
-3.0   1.0   1.03 1.0
-
@@ -1,72 +0,0 @@
-MFEM NURBS mesh v1.0
-
-#
-# MFEM Geometry Types (see fem/geom.hpp):
-#
-# SEGMENT     = 1
-# SQUARE      = 3
-# CUBE        = 5
-#
-
-dimension
-1
-
-elements
-3
-1 1 0 1
-2 1 2 3
-3 1 4 5
-
-boundary
-6
-1 0 0
-1 0 1
-1 0 2
-1 0 3
-1 0 4
-1 0 5
-
-edges
-3
-0 0 1
-1 2 3
-2 4 5
-
-vertices
-6
-
-# Edge 0: linear (order 1, 2 control points)
-# Edge 1: quadratic (order 2, 3 control points)
-# Edge 2: cubic (order 3, 4 control points)
-knotvectors
-3
-1 2  0 0  1 1
-2 3  0 0 0  1 1 1
-3 4  0 0 0 0  1 1 1 1
-
-# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
-weights
-1
-1
-1
-1
-1
-1
-1.2
-1.31
-1.32
-
-FiniteElementSpace
-FiniteElementCollection: NURBS
-VDim: 3
-Ordering: 1
-
-0.0  0.0   0.01
-1.0  1.0   1.01
-1.0  0.0   0.02
-2.0  1.0   1.02
-2.0  0.0   0.03
-3.0  1.0   1.03
-1.02 1.02  0.52
-2.03 0.83  0.33
-2.33 1.03  0.63
@@ -48,7 +48,7 @@ PROJECT_NAME           = MFEM
 # could be handy for archiving the generated documentation or if some version
 # control system is used.

-PROJECT_NUMBER         = v4.9.1
+PROJECT_NUMBER         = v4.8.1

 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a
@@ -973,13 +973,10 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/miniapps/adjoint \
                         @MFEM_SOURCE_DIR@/miniapps/autodiff \
                         @MFEM_SOURCE_DIR@/miniapps/common \
-                         @MFEM_SOURCE_DIR@/miniapps/contact \
                         @MFEM_SOURCE_DIR@/miniapps/dfem \
                         @MFEM_SOURCE_DIR@/miniapps/dpg \
                         @MFEM_SOURCE_DIR@/miniapps/dpg/util \
                         @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
-                         @MFEM_SOURCE_DIR@/miniapps/fluids/navier \
-                         @MFEM_SOURCE_DIR@/miniapps/fluids/schrodinger-flow \
                         @MFEM_SOURCE_DIR@/miniapps/gslib \
                         @MFEM_SOURCE_DIR@/miniapps/hdiv-linear-solver \
                         @MFEM_SOURCE_DIR@/miniapps/hooke \
@@ -990,6 +987,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/miniapps/meshing \
                         @MFEM_SOURCE_DIR@/miniapps/mtop \
                         @MFEM_SOURCE_DIR@/miniapps/multidomain \
+                         @MFEM_SOURCE_DIR@/miniapps/navier \
                         @MFEM_SOURCE_DIR@/miniapps/nurbs \
                         @MFEM_SOURCE_DIR@/miniapps/parelag \
                         @MFEM_SOURCE_DIR@/miniapps/performance \
@@ -117,8 +117,6 @@ namespace mfem {
 * - <a class="el" href="ex39p_8cpp_source.html">Example 39p</a>: parallel named mesh attributes
 * - <a class="el" href="ex40_8cpp_source.html">Example 40</a>: eikonal equation
 * - <a class="el" href="ex40p_8cpp_source.html">Example 40p</a>: parallel eikonal equation
- * - <a class="el" href="ex41_8cpp_source.html">Example 41</a>: DG/CG IMEX time-dependent advection-diffusion
- * - <a class="el" href="ex41p_8cpp_source.html">Example 41p</a>: parallel DG/CG IMEX time-dependent advection-diffusion
 *
 * <H4>AmgX Examples</H4>
 * - Variants of Examples
@@ -190,8 +188,6 @@ namespace mfem {
 *  <a class="el" href="nurbs__ex1p_8cpp_source.html">1p</a>,
 *  <a class="el" href="nurbs__ex3_8cpp_source.html">3</a>,
 *  <a class="el" href="nurbs__ex5_8cpp_source.html">5</a>,
- *  <a class="el" href="nurbs__ex10_8cpp_source.html">10</a>,
- *  <a class="el" href="nurbs__ex10p_8cpp_source.html">10p</a>,
 *  <a class="el" href="nurbs__ex11p_8cpp_source.html">11p</a>, and
 *  <a class="el" href="nurbs__ex24_8cpp_source.html">24</a>,
 *   demonstrating howto perform NURBS-based Isogeometric Analysis.
@@ -200,7 +196,6 @@ namespace mfem {
 * - <a class="el" href="nurbs__curveint_8cpp_source.html">NURBS Interpolation</a>: NURBS interpolation of given geometry
 * - <a class="el" href="nurbs__naca__cmesh_8cpp_source.html">NURBS NACA Mesher</a>: generate NURBS based mesh around a NACA foil
 * - <a class="el" href="nurbs__printfunc_8cpp_source.html">NURBS Printer</a>: print the NURBS-basis
- * - <a class="el" href="nurbs__mesh_info_8cpp_source.html">NURBS Mesh info</a>: print the info of a NURBS mesh
 *
 * <H3>Miniapps</H3>
 * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
@@ -239,8 +234,7 @@ namespace mfem {
 * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Poisson problem
 * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Poisson problem
 * - <a class="el" href="generate__random__field_8cpp_source.html">SPDE Solvers</a>: SPDE solver random field generation
- * - <a class="el" href="contact-patch-test_8cpp_source.html">Tribol</a>: mortar contact patch test for elasticity
- * - <a class="el" href="contact_8cpp_source.html">Contact</a>: Frictionless contact examples using <a class="el" href="classmfem_1_1IPSolver.html#details">IP optimization</a> and the <a class="el" href="classmfem_1_1AMGFSolver.html#details">AMGF solver</a>
+ * - <a class="el" href="contact-patch-test_8cpp_source.html">Contact</a>: mortar contact patch test for elasticity
 * - <a class="el" href="multidomain_8cpp_source.html">Multidomain miniapp</a>: Multidomain and Submesh demonstration miniapp
 * - <a class="el" href="pdiffusion_8cpp_source.html">DPG Diffusion example</a>: DPG formulation for the diffusion problem
 * - <a class="el" href="pmaxwell_8cpp_source.html">DPG Maxwell example</a>: DPG formulation for the indefinite Maxwell problem
@@ -46,7 +46,6 @@ list(APPEND ALL_EXE_SRCS
  ex38.cpp
  ex39.cpp
  ex40.cpp
-  ex41.cpp
  )

 if (MFEM_USE_MPI)
@@ -90,7 +89,7 @@ if (MFEM_USE_MPI)
    ex37p.cpp
    ex39p.cpp
    ex40p.cpp
-    ex41p.cpp
+    ex999p.cpp
  )
 endif()

@@ -133,8 +132,6 @@ if (MFEM_ENABLE_TESTING)
      list(APPEND THIS_TEST_OPTIONS "-dg")
    elseif(${TEST_NAME} MATCHES "ex37p*")
      list(APPEND THIS_TEST_OPTIONS "-mi" "3")
-    elseif(${TEST_NAME} MATCHES "ex41p*")
-      list(APPEND THIS_TEST_OPTIONS "-tf" "1.0")
    endif()

    if (NOT (${TEST_NAME} MATCHES ".*p$"))
@@ -105,7 +105,6 @@ int main(int argc, char *argv[])
   bool visualization = true;
   bool visit = false;
   int vis_steps = 5;
-   bool solve_implicit_state = false;

   int precision = 8;
   cout.precision(precision);
@@ -127,9 +126,6 @@ int main(int argc, char *argv[])
                  "Alpha coefficient.");
   args.AddOption(&kappa, "-k", "--kappa",
                  "Kappa coefficient offset.");
-   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
-                  "-imp-slope", "--implicit-slope",
-                  "Implicitly solve for stage state or slope.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -183,11 +179,6 @@ int main(int argc, char *argv[])

   // 7. Initialize the conduction operator and the visualization.
   ConductionOperator oper(fespace, alpha, kappa, u);
-   using ImplicitVariableType = ConductionOperator::ImplicitVariableType;
-   ImplicitVariableType imp_var = solve_implicit_state ?
-                                  ImplicitVariableType::STATE
-                                  : ImplicitVariableType::SLOPE;
-   oper.SetImplicitVariableType(imp_var);

   u_gf.SetFromTrueDofs(u);
   {
@@ -325,14 +316,11 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 }

 void ConductionOperator::ImplicitSolve(const real_t dt,
-                                       const Vector &u, Vector &k)
+                                       const Vector &u, Vector &du_dt)
 {
   // Solve the equation:
-   //    M*k = -K(u + dt*k) for k = du/dt, if solving for stage-slope
-   // or
-   //    M*k = -dt*K(k) + M*u for k = u_s, if solving for stage-state
-   // where K is linearized by using u from the previous timestep, and
-   // the stage-state and slope relation: du/dt = (u_s - u)/dt.
+   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
+   // for du_dt, where K is linearized by using u from the previous timestep
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -340,20 +328,9 @@ void ConductionOperator::ImplicitSolve(const real_t dt,
      T_solver.SetOperator(*T);
   }
   MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
-
-   // Construct current right-hand side for stage state vs. slope solve
-   if (ImplicitVarTypeIsState())
-   {
-      // k, on return, is the stage value u_s
-      Mmat.Mult(u, z);
-   }
-   else
-   {
-      // k, on return, is the stage slope du/dt
-      Kmat.Mult(u, z);
-      z.Neg();
-   }
-   T_solver.Mult(z, k);
+   Kmat.Mult(u, z);
+   z.Neg();
+   T_solver.Mult(z, du_dt);
 }

 void ConductionOperator::SetParameters(const Vector &u)
@@ -115,7 +115,6 @@ int main(int argc, char *argv[])
   bool visit = false;
   int vis_steps = 5;
   bool adios2 = false;
-   bool solve_implicit_state = false;

   int precision = 8;
   cout.precision(precision);
@@ -139,9 +138,6 @@ int main(int argc, char *argv[])
                  "Alpha coefficient.");
   args.AddOption(&kappa, "-k", "--kappa",
                  "Kappa coefficient offset.");
-   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
-                  "-imp-slope", "--implicit-slope",
-                  "Implicitly solve for stage state or slope.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -216,11 +212,6 @@ int main(int argc, char *argv[])

   // 9. Initialize the conduction operator and the VisIt visualization.
   ConductionOperator oper(fespace, alpha, kappa, u);
-   using ImplicitVariableType = ConductionOperator::ImplicitVariableType;
-   ImplicitVariableType imp_var = solve_implicit_state ?
-                                  ImplicitVariableType::STATE
-                                  : ImplicitVariableType::SLOPE;
-   oper.SetImplicitVariableType(imp_var);

   u_gf.SetFromTrueDofs(u);
   {
@@ -416,14 +407,11 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 }

 void ConductionOperator::ImplicitSolve(const real_t dt,
-                                       const Vector &u, Vector &k)
+                                       const Vector &u, Vector &du_dt)
 {
   // Solve the equation:
-   //    M*k = -K(u + dt*k) for k = du/dt, if solving for stage-slope
-   // or
-   //    M*k = -dt*K(k) + M*u for k = u_s, if solving for stage-state
-   // where K is linearized by using u from the previous timestep, and
-   // the stage-state and slope relation: du/dt = (u_s - u)/dt.
+   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
+   // for du_dt, where K is linearized by using u from the previous timestep
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -431,20 +419,9 @@ void ConductionOperator::ImplicitSolve(const real_t dt,
      T_solver.SetOperator(*T);
   }
   MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
-
-   // Construct current right-hand side for stage state vs. slope solve
-   if (ImplicitVarTypeIsState())
-   {
-      // k, on return, is the stage value u
-      Mmat.Mult(u, z);
-   }
-   else
-   {
-      // k, on return, is the stage slope du/dt
-      Kmat.Mult(u, z);
-      z.Neg();
-   }
-   T_solver.Mult(z, k);
+   Kmat.Mult(u, z);
+   z.Neg();
+   T_solver.Mult(z, du_dt);
 }

 void ConductionOperator::SetParameters(const Vector &u)
@@ -119,7 +119,7 @@ int main(int argc, char *argv[])
   }

   LinearForm b(&fespace);
-   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));

   // 6. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the linear elasticity integrator with piece-wise
@@ -140,7 +140,7 @@ int main(int argc, char *argv[])
   }

   ParLinearForm b(&fespace);
-   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));

   // 6. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the linear elasticity integrator with piece-wise
@@ -9,7 +9,6 @@
 //               ex4 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex4 -m ../data/escher.mesh
 //               ex4 -m ../data/fichera.mesh -o 2 -hb
-//               ex4 -m ../data/fichera.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-q2.vtk
 //               ex4 -m ../data/fichera-q3.mesh -o 2 -sc
 //               ex4 -m ../data/square-disc-nurbs.mesh
@@ -19,7 +18,6 @@
 //               ex4 -m ../data/amr-quad.mesh
 //               ex4 -m ../data/amr-hex.mesh
 //               ex4 -m ../data/amr-hex.mesh -o 2 -hb
-//               ex4 -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
 //               ex4 -m ../data/ref-prism.mesh -o 1
 //               ex4 -m ../data/octahedron.mesh -o 1
@@ -27,8 +25,6 @@
 //
 // Device sample runs:
 //               ex4 -m ../data/star.mesh -pa -d cuda
-//               ex4 -m ../data/star.mesh -hb -ea -d cuda
-//               ex4 -m ../data/amr-quad.mesh -hb -ea -d cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-omp
 //               ex4 -m ../data/beam-hex.mesh -pa -d cuda
@@ -197,7 +193,7 @@ int main(int argc, char *argv[])
   cout << "Size of linear system: " << A->Height() << endl;

   // 11. Solve the linear system A X = B.
-   if (!pa && (!ea || hybridization))
+   if (!pa)
   {
 #ifndef MFEM_USE_SUITESPARSE
      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
@@ -1,589 +0,0 @@
-//                                MFEM Example 41
-//
-// Compile with: make ex41
-//
-// Sample runs:
-//  ex41
-//  ex41 -cg
-//  ex41 -m ../data/periodic-hexagon.mesh -p 0 -r 2 -dt 0.005 -tf 10
-//  ex41 -m ../data/periodic-square.mesh -p 1 -r 2 -dt 0.005 -tf 9
-//  ex41 -m ../data/periodic-hexagon.mesh -p 1 -r 2 -dt 0.005 -tf 9
-//  ex41 -m ../data/amr-quad.mesh -p 1 -r 2 -dt 0.002 -tf 9
-//  ex41 -m ../data/star-q3.mesh -p 1 -r 2 -dt 0.001 -tf 9
-//  ex41 -m ../data/star-mixed.mesh -p 1 -r 2 -dt 0.005 -tf 9
-//  ex41 -m ../data/disc-nurbs.mesh -p 1 -r 3 -dt 0.005 -tf 9
-//  ex41 -m ../data/disc-nurbs.mesh -p 2 -r 3 -dt 0.005 -tf 9
-//  ex41 -m ../data/periodic-square.mesh -p 3 -r 4 -dt 0.0025 -tf 9 -vs 20
-//  ex41 -m ../data/periodic-cube.mesh -p 0 -r 2 -o 2 -dt 0.01 -tf 8
-//
-// Device sample runs:
-//
-// Description:  This example code solves the time-dependent advection-diffusion
-//               equation du/dt + v.grad(u) - a div(grad(u)) = 0, where v is a
-//               given fluid velocity, a is the diffusion coefficient, and
-//               u0(x)=u(0,x) is a given initial condition.
-//
-//               The example demonstrates the use of Discontinuous Galerkin (DG)
-//               bilinear forms in MFEM (face integrators), and the use of IMEX
-//               ODE time integrators.
-//
-//               The option to use continuous finite elements is available too.
-
-#include "mfem.hpp"
-
-using namespace std;
-using namespace mfem;
-
-// Mesh bounding box
-Vector bb_min, bb_max;
-
-// Velocity coefficient
-template<int problem=0>
-void velocity_function(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-
-   // map to the reference [-1,1] domain
-   Vector X(dim);
-   for (int i = 0; i < dim; i++)
-   {
-      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
-      X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
-   }
-   switch (problem)
-   {
-      case 0:
-      {
-         // Translations in 1D, 2D, and 3D
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = sqrt(2./3.); v(1) = sqrt(1./3.); break;
-            case 3: v(0) = sqrt(3./6.); v(1) = sqrt(2./6.); v(2) = sqrt(1./6.);
-               break;
-         }
-         break;
-      }
-      case 1:
-      case 2:
-      {
-         // Clockwise rotation in 2D around the origin
-         const real_t w = M_PI/2;
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = w*X(1); v(1) = -w*X(0); break;
-            case 3: v(0) = w*X(1); v(1) = -w*X(0); v(2) = 0.0; break;
-         }
-         break;
-      }
-      case 3:
-      {
-         // Clockwise twisting rotation in 2D around the origin
-         const real_t w = M_PI/2;
-         real_t d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
-         d = d*d;
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = d*w*X(1); v(1) = -d*w*X(0); break;
-            case 3: v(0) = d*w*X(1); v(1) = -d*w*X(0); v(2) = 0.0; break;
-         }
-         break;
-      }
-   }
-}
-
-// Initial condition
-template<int problem=0>
-real_t u0_function(const Vector &x)
-{
-   int dim = x.Size();
-
-   // map to the reference [-1,1] domain
-   Vector X(dim);
-   for (int i = 0; i < dim; i++)
-   {
-      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
-      X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
-   }
-
-   switch (problem)
-   {
-      case 0:
-      case 1:
-      {
-         switch (dim)
-         {
-            case 1:
-               return exp(-40.*pow(X(0)-0.5,2));
-            case 2:
-            case 3:
-            {
-               real_t rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
-               if (dim == 3)
-               {
-                  const real_t s = (1. + 0.25*cos(2*M_PI*X(2)));
-                  rx *= s;
-                  ry *= s;
-               }
-               return ( std::erfc(w*(X(0)-cx-rx))*std::erfc(-w*(X(0)-cx+rx)) *
-                        std::erfc(w*(X(1)-cy-ry))*std::erfc(-w*(X(1)-cy+ry)) )/16;
-            }
-         }
-      }
-      case 2:
-      {
-         real_t x_ = X(0), y_ = X(1), rho, phi;
-         rho = std::hypot(x_, y_);
-         phi = atan2(y_, x_);
-         return pow(sin(M_PI*rho),2)*sin(3*phi);
-      }
-      case 3:
-      {
-         const real_t f = M_PI;
-         return sin(f*X(0))*sin(f*X(1));
-      }
-   }
-   return 0.0;
-}
-
-/// Solver for the implicit part of the ODE (the diffusion term).
-/// Solves systems of the form: (M + dt*S) k = rhs.
-class Implicit_Solver : public Solver
-{
-private:
-   SparseMatrix &M, &S, A;
-   CGSolver linear_solver;
-   BlockILU prec;
-   real_t dt;
-public:
-   Implicit_Solver(SparseMatrix &M_, SparseMatrix &S_,
-                   const FiniteElementSpace &fes)
-      : M(M_),
-        S(S_),
-        prec(fes.GetTypicalFE()->GetDof(),
-             BlockILU::Reordering::MINIMUM_DISCARDED_FILL),
-        dt(1.0)
-   {
-      linear_solver.iterative_mode = false;
-      linear_solver.SetRelTol(1e-9);
-      linear_solver.SetAbsTol(0.0);
-      linear_solver.SetMaxIter(100);
-      linear_solver.SetPrintLevel(0);
-      linear_solver.SetPreconditioner(prec);
-   }
-
-   void SetTimeStep(real_t dt_)
-   {
-      real_t ddt = dt-dt_;
-
-      real_t epsilon;
-      epsilon = std::numeric_limits<real_t>::epsilon();
-      epsilon*=10;
-
-      if (std::abs(ddt) > epsilon)
-      {
-         dt = dt_;
-         // Form operator A = M + dt*S
-         A = S;
-         A *= dt;
-         A += M;
-
-         // this will also call SetOperator on the preconditioner
-         linear_solver.SetOperator(A);
-      }
-   }
-
-   void SetOperator(const Operator &op) override
-   {
-      linear_solver.SetOperator(op);
-   }
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      linear_solver.Mult(x, y);
-   }
-};
-
-/** A time-dependent operator for the right-hand side of the ODE. The weak
-    form of the advection-diffusion equation is M du/dt = K u - S u + b,
-    where M is the mass matrix, K and S are the advection and diffusion
-    matrices, and b describes the flow on the boundary. In the case of IMEX
-    evolution, the diffusion term is treated implicitly, and the advection
-    term is treated explicitly.  */
-class IMEX_Evolution : public TimeDependentOperator
-{
-private:
-   BilinearForm &M, &K, &S;
-   const Vector &b;
-   unique_ptr<Solver> M_prec;
-   CGSolver M_solver;
-   unique_ptr<Implicit_Solver> implicit_solver;
-
-   mutable Vector z;
-
-public:
-   IMEX_Evolution(BilinearForm &M_, BilinearForm &K_, BilinearForm &S_,
-                  const Vector &b_);
-
-   /// Evaluate k1=M^{-1}*G1(u,t); -> k1 = M^{-1}*(K*u + b)
-   void Mult1(const Vector &x, Vector &y) const;
-
-   /// Evaluate k2: M*k2 = G2(u+k2*dt,t); -> (M+S*dt)*k2=-S*u
-   void ImplicitSolve2(const real_t dt, const Vector &x, Vector &k);
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_1 == GetEvalMode())
-      {
-         Mult1(x,y);
-      }
-      else
-      {
-         mfem_error("TimeDependentOperator::Mult() is not overridden!");
-      }
-   }
-
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override
-   {
-      if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_2 == GetEvalMode())
-      {
-         ImplicitSolve2(dt,x,k);
-      }
-      else
-      {
-         mfem_error("TimeDependentOperator::ImplicitSolve() is not overridden!");
-      }
-   }
-
-};
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   int problem = 0;
-   const char *mesh_file = "../data/periodic-square.mesh";
-   int ref_levels = 2;
-   int order = 3;
-   int ode_solver_type = 64; //IMEXRK3(3,4,3)
-   real_t t_final = 10.0;
-   real_t dt = 0.01;
-   bool paraview = false;
-   bool cg = false;
-   int vis_steps = 50;
-   real_t diffusion_term = 0.01;
-   real_t kappa = -1.0;
-   real_t sigma = -1.0;
-   bool visualization = true;
-   bool visit = false;
-   bool binary = false;
-   int precision = 8;
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
-   args.AddOption(&problem, "-p", "--problem",
-                  "Problem setup to use. See options in velocity_function().");
-   args.AddOption(&ref_levels, "-r", "--refine",
-                  "Number of times to refine the mesh uniformly.");
-   args.AddOption(&order, "-o", "--order", "Order of the finite elements.");
-   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  ODESolver::IMEXTypes.c_str());
-   args.AddOption(&t_final, "-tf", "--t-final", "Final time; start time is 0.");
-   args.AddOption(&dt, "-dt", "--time-step", "Time step.");
-   args.AddOption(&diffusion_term, "-dc", "--diffusion-coeff",
-                  "Diffusion coefficient in the PDE.");
-   args.AddOption(&paraview, "-paraview", "--paraview-datafiles", "-no-paraview",
-                  "--no-paraview-datafiles",
-                  "Save data files for ParaView (paraview.org) visualization.");
-   args.AddOption(&vis_steps, "-vs", "--visualization-steps",
-                  "Visualize every n-th timestep.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&binary, "-binary", "--binary-datafiles", "-ascii",
-                  "--ascii-datafiles",
-                  "Use binary (Sidre) or ascii format for VisIt data files.");
-   args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
-                  "--no-visit-datafiles",
-                  "Save data files for VisIt (visit.llnl.gov) visualization.");
-   args.AddOption(&cg, "-cg", "--continuous-galerkin", "-dg",
-                  "--discontinuous-galerkin",
-                  "Use Continuous-Galerkin Finite elements (Default is DG)");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   if (kappa < 0)
-   {
-      kappa = (order+1)*(order+1);
-   }
-   args.PrintOptions(cout);
-
-   // 2. Read the mesh from the given mesh file. We can handle geometrically
-   //    periodic meshes in this code.
-   Mesh mesh(mesh_file);
-   const int dim = mesh.Dimension();
-
-   // 3. Define the IMEX (Split) ODE solver used for time integration. The IMEX
-   // solvers currently available are: 61 - Forward Backward Euler,
-   // 62 - IMEXRK2(2,2,2), 63 - IMEXRK2(2,3,2), and  64 - IMEX_DIRK_RK3.
-   unique_ptr<ODESolver> ode_solver = ODESolver::SelectIMEX(ode_solver_type);
-
-   // 4. Refine the mesh to increase the resolution. In this example we do
-   //    'ref_levels' of uniform refinement, where 'ref_levels' is a
-   //    command-line parameter.
-   for (int lev = 0; lev < ref_levels; lev++) {mesh.UniformRefinement();}
-   if (mesh.NURBSext) {mesh.SetCurvature(max(order, 1));}
-   mesh.GetBoundingBox(bb_min, bb_max, max(order, 1));
-
-   // 5. Define the discontinuous DG finite element space of the given
-   //    polynomial order on the refined mesh.
-   FiniteElementCollection *fec = NULL;
-   if (cg)
-   {
-      fec = new H1_FECollection(order, dim);
-   }
-   else
-   {
-      fec = new DG_FECollection(order, dim, BasisType::GaussLobatto);
-   }
-   FiniteElementSpace fes(&mesh, fec);
-
-   cout << "Number of unknowns: " << fes.GetVSize() << endl;
-
-   // 6. Set up and assemble the bilinear and linear forms corresponding to the
-   //    DG discretization. The DGTraceIntegrator involves integrals over mesh
-   //    interior faces.
-   std::unique_ptr<VectorFunctionCoefficient> velocity;
-   if (0==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<0>));
-   }
-   else if (1==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<1>));
-   }
-   else if (2==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<2>));
-   }
-   else if (3==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<3>));
-   }
-
-   ConstantCoefficient diff_coeff(diffusion_term);
-
-   BilinearForm m(&fes);
-   BilinearForm k(&fes);
-   BilinearForm s(&fes);
-
-   Vector b(fes.GetTrueVSize());
-   b = 0.0; //The inflow on the boundaries is set to zero.
-
-   m.AddDomainIntegrator(new MassIntegrator);
-
-   constexpr real_t alpha = -1.0;
-   k.AddDomainIntegrator(new ConvectionIntegrator(*velocity, alpha));
-
-   s.AddDomainIntegrator(new DiffusionIntegrator(diff_coeff));
-   if (!cg)
-   {
-      k.AddInteriorFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity,
-                                                                       alpha));
-      k.AddBdrFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity, alpha));
-      s.AddInteriorFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma,
-                                                            kappa));
-      s.AddBdrFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma, kappa));
-   }
-
-
-   int skip_zeros = 0;
-   m.Assemble(skip_zeros);
-   k.Assemble(skip_zeros);
-   s.Assemble(skip_zeros);
-
-   m.Finalize(skip_zeros);
-   k.Finalize(skip_zeros);
-   s.Finalize(skip_zeros);
-
-   // 7. Define the initial conditions.
-   std::unique_ptr<FunctionCoefficient> u0;
-   if (0==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<0>));
-   }
-   else if (1==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<1>));
-   }
-   else if (2==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<2>));
-   }
-   else if (3==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<3>));
-   }
-
-   GridFunction u(&fes);
-   u.ProjectCoefficient(*u0);
-
-   // Create data collection for solution output: either VisItDataCollection for
-   // ascii data files, or SidreDataCollection for binary data files.
-   DataCollection *dc = NULL;
-   if (visit)
-   {
-      if (binary)
-      {
-#ifdef MFEM_USE_SIDRE
-         dc = new SidreDataCollection("Example41", &mesh);
-#else
-         MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
-#endif
-      }
-      else
-      {
-         dc = new VisItDataCollection("Example41", &mesh);
-         dc->SetPrecision(precision);
-      }
-      dc->RegisterField("solution", &u);
-      dc->SetCycle(0);
-      dc->SetTime(0.0);
-      dc->Save();
-   }
-
-   // 8. Set up paraview visualization, if desired.
-   unique_ptr<ParaViewDataCollection> pv;
-   if (paraview)
-   {
-      pv = make_unique<ParaViewDataCollection>("Example41", &mesh);
-      pv->SetPrefixPath("ParaView");
-      pv->RegisterField("solution", &u);
-      pv->SetLevelsOfDetail(order);
-      pv->SetDataFormat(VTKFormat::BINARY);
-      pv->SetHighOrderOutput(true);
-      pv->SetCycle(0);
-      pv->SetTime(0.0);
-      pv->Save();
-   }
-
-   socketstream sout;
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      sout.open(vishost, visport);
-      if (!sout)
-      {
-         cout << "Unable to connect to GLVis server at "
-              << vishost << ':' << visport << endl;
-         visualization = false;
-         cout << "GLVis visualization disabled.\n";
-      }
-      else
-      {
-         sout.precision(precision);
-         sout << "solution\n" << mesh << u;
-         sout << "pause\n";
-         sout << flush;
-         cout << "GLVis visualization paused."
-              << " Press space (in the GLVis window) to resume it.\n";
-      }
-   }
-
-   // 9. Define the time-dependent evolution operator describing the ODE
-   //    right-hand side, and perform time-integration (looping over the time
-   //    iterations, ti, with a time-step dt).
-   IMEX_Evolution adv(m, k, s, b);
-
-   real_t t = 0.0;
-   adv.SetTime(t);
-   ode_solver->Init(adv);
-
-   bool done = false;
-   for (int ti = 0; !done; )
-   {
-      real_t dt_real = min(dt, t_final - t);
-      ode_solver->Step(u, t, dt_real);
-      ti++;
-
-      done = (t >= t_final - 1e-8*dt);
-
-      if (done || ti % vis_steps == 0)
-      {
-         cout << "time step: " << ti << ", time: " << t << endl;
-         if (paraview)
-         {
-            pv->SetCycle(ti);
-            pv->SetTime(t);
-            pv->Save();
-         }
-         if (visualization)
-         {
-            sout << "solution\n" << mesh << u << flush;
-         }
-         if (visit)
-         {
-            dc->SetCycle(ti);
-            dc->SetTime(t);
-            dc->Save();
-         }
-
-      }
-   }
-
-   delete fec;
-   return 0;
-}
-
-
-// Implementation of class IMEX_Evolution
-IMEX_Evolution::IMEX_Evolution(BilinearForm &M_, BilinearForm &K_,
-                               BilinearForm &S_, const Vector &b_)
-   : TimeDependentOperator(M_.FESpace()->GetTrueVSize()),
-     M(M_), K(K_), S(S_), b(b_), z(height)
-{
-   Array<int> ess_tdof_list;
-   if (M.GetAssemblyLevel() == AssemblyLevel::LEGACY)
-   {
-      M_prec = make_unique<DSmoother>(M.SpMat());
-      M_solver.SetOperator(M.SpMat());
-      implicit_solver = make_unique<Implicit_Solver>(M.SpMat(), S.SpMat(),
-                                                     *M.FESpace());
-   }
-   else
-   {
-      MFEM_ABORT("Implicit time integration is not supported with partial assembly");
-   }
-   M_solver.SetPreconditioner(*M_prec);
-   M_solver.iterative_mode = false;
-   M_solver.SetRelTol(1e-9);
-   M_solver.SetAbsTol(0.0);
-   M_solver.SetMaxIter(100);
-   M_solver.SetPrintLevel(0);
-}
-
-void IMEX_Evolution::Mult1(const Vector &x, Vector &y) const
-{
-   // Perform the explicit step
-   // y = M^{-1} (K x + b)
-   K.Mult(x, z);
-   z += b;
-   M_solver.Mult(z, y);
-}
-
-void IMEX_Evolution::ImplicitSolve2(const real_t dt, const Vector &x, Vector &k)
-{
-   // Perform the implicit step
-   // solve for k, k = -(M+dt S)^{-1} S x
-   MFEM_VERIFY(implicit_solver != NULL,
-               "Implicit time integration is not supported with partial assembly");
-   S.Mult(x, z);
-   z.Neg();
-   implicit_solver->SetTimeStep(dt);
-   implicit_solver->Mult(z, k);
-}
@@ -1,737 +0,0 @@
-//                                MFEM Example 41 - Parallel Version
-//
-// Compile with: make ex41p
-//
-// Sample runs:
-//  mpirun -np 4 ex41p
-//  mpirun -np 4 ex41p -cg
-//  mpirun -np 4 ex41p -m ../data/periodic-hexagon.mesh -p 0 -dt 0.005 -tf 10
-//  mpirun -np 4 ex41p -m ../data/periodic-square.mesh -p 1 -dt 0.005 -tf 9
-//  mpirun -np 4 ex41p -m ../data/periodic-hexagon.mesh -p 1  -dt 0.005 -tf 9
-//  mpirun -np 4 ex41p -m ../data/star-q3.mesh -p 1 -rp 1 -dt 0.001 -tf 9
-//  mpirun -np 4 ex41p -m ../data/disc-nurbs.mesh -p 1 -rp 1 -dt 0.005 -tf 9
-//  mpirun -np 4 ex41p -m ../data/disc-nurbs.mesh -p 2 -rp 1 -dt 0.005 -tf 9
-//  mpirun -np 4 ex41p -m ../data/periodic-square.mesh -rp 2 -dt 0.0025 -tf 9 -vs 20
-//  mpirun -np 4 ex41p -m ../data/periodic-cube.mesh -p 0 -rs 2 -o 2 -dt 0.01 -tf 8
-//
-// Device sample runs:
-//
-// Description:  This example code solves the time-dependent advection-diffusion
-//               equation du/dt + v.grad(u) - a div(grad(u)) = 0, where v is a
-//               given fluid velocity, a is the diffusion coefficient, and
-//               u0(x)=u(0,x) is a given initial condition.
-//
-//               The example demonstrates the use of Discontinuous Galerkin (DG)
-//               bilinear forms in MFEM (face integrators), DG-LOR Preconditioning
-//               and the use of IMEX ODE time integrators.
-//
-//               The Option to use Continuous Finite Elements is available too.
-
-#include "mfem.hpp"
-
-using namespace std;
-using namespace mfem;
-
-// Mesh bounding box
-Vector bb_min, bb_max;
-
-// Velocity coefficient
-template<int problem=0>
-void velocity_function(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-
-   // map to the reference [-1,1] domain
-   Vector X(dim);
-   for (int i = 0; i < dim; i++)
-   {
-      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
-      X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
-   }
-   switch (problem)
-   {
-      case 0:
-      {
-         // Translations in 1D, 2D, and 3D
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = sqrt(2./3.); v(1) = sqrt(1./3.); break;
-            case 3: v(0) = sqrt(3./6.); v(1) = sqrt(2./6.); v(2) = sqrt(1./6.);
-               break;
-         }
-         break;
-      }
-      case 1:
-      case 2:
-      {
-         // Clockwise rotation in 2D around the origin
-         const real_t w = M_PI/2;
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = w*X(1); v(1) = -w*X(0); break;
-            case 3: v(0) = w*X(1); v(1) = -w*X(0); v(2) = 0.0; break;
-         }
-         break;
-      }
-      case 3:
-      {
-         // Clockwise twisting rotation in 2D around the origin
-         const real_t w = M_PI/2;
-         real_t d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
-         d = d*d;
-         switch (dim)
-         {
-            case 1: v(0) = 1.0; break;
-            case 2: v(0) = d*w*X(1); v(1) = -d*w*X(0); break;
-            case 3: v(0) = d*w*X(1); v(1) = -d*w*X(0); v(2) = 0.0; break;
-         }
-         break;
-      }
-   }
-}
-
-
-// Initial condition
-template<int problem=0>
-real_t u0_function(const Vector &x)
-{
-   int dim = x.Size();
-
-   // map to the reference [-1,1] domain
-   Vector X(dim);
-   for (int i = 0; i < dim; i++)
-   {
-      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
-      X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
-   }
-
-   switch (problem)
-   {
-      case 0:
-      case 1:
-      {
-         switch (dim)
-         {
-            case 1:
-               return exp(-40.*pow(X(0)-0.5,2));
-            case 2:
-            case 3:
-            {
-               real_t rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
-               if (dim == 3)
-               {
-                  const real_t s = (1. + 0.25*cos(2*M_PI*X(2)));
-                  rx *= s;
-                  ry *= s;
-               }
-               return ( std::erfc(w*(X(0)-cx-rx))*std::erfc(-w*(X(0)-cx+rx)) *
-                        std::erfc(w*(X(1)-cy-ry))*std::erfc(-w*(X(1)-cy+ry)) )/16;
-            }
-         }
-      }
-      case 2:
-      {
-         real_t x_ = X(0), y_ = X(1), rho, phi;
-         rho = std::hypot(x_, y_);
-         phi = atan2(y_, x_);
-         return pow(sin(M_PI*rho),2)*sin(3*phi);
-      }
-      case 3:
-      {
-         const real_t f = M_PI;
-         return sin(f*X(0))*sin(f*X(1));
-      }
-   }
-   return 0.0;
-}
-
-
-class Implicit_Solver : public Solver
-{
-private:
-   HypreParMatrix &M, &S;
-   HypreParMatrix *A;
-   CGSolver linear_solver;
-   real_t dt;
-   SparseMatrix M_diag;
-public:
-   Implicit_Solver(HypreParMatrix &M_, HypreParMatrix &S_,
-                   const FiniteElementSpace &fes)
-      : M(M_),
-        S(S_),
-        A(nullptr),
-        linear_solver(M.GetComm()),
-        dt(1.0)
-   {
-      linear_solver.iterative_mode = false;
-      linear_solver.SetRelTol(1e-9);
-      linear_solver.SetAbsTol(0.0);
-      linear_solver.SetMaxIter(100);
-      linear_solver.SetPrintLevel(0);
-
-      M.GetDiag(M_diag);
-   }
-
-   void SetTimeStep(real_t dt_)
-   {
-      real_t ddt = dt-dt_;
-
-      // syncronize ddt across all processes
-      MPI_Comm comm = M.GetComm();
-      int myrank;
-      MPI_Comm_rank(comm, &myrank);
-      MPI_Bcast(&ddt, 1, MPI_DOUBLE, 0, comm);
-
-      real_t epsilon;
-      epsilon = std::numeric_limits<real_t>::epsilon();
-      // allow for some tolerance in the time stepping process
-      epsilon*=10;
-
-      if (fabs(ddt) > epsilon)
-      {
-         if (0==myrank)
-         {
-            cout << "Updating Implicit_Solver time step from " << dt
-                 << " to " << dt_ << endl;
-         }
-
-         delete A;
-         dt = dt_;
-         // Form operator A = M + dt*S
-         A = Add(dt, S, 1.0, M);
-         linear_solver.SetOperator(*A);
-      }
-   }
-
-   void SetOperator(const Operator &op) override
-   {
-      linear_solver.SetOperator(op);
-   }
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      linear_solver.Mult(x, y);
-   }
-
-   void SetPreconditioner(Solver &precond)
-   {
-      linear_solver.SetPreconditioner(precond);
-   }
-
-   ~Implicit_Solver() override
-   {
-      delete A;
-   }
-};
-
-/** A time-dependent operator for the right-hand side of the ODE. The DG weak
-    form of the advection-diffusion equation is (M + dt S) du/dt = Su - K u + b
-    , where M and K are the mass and advection matrices, and b describes the
-    flow on the boundary. In the case of IMEX evolution, the diffusion term is
-    treated implicitly, and the advection term is treated explicitly.  */
-class IMEX_Evolution : public TimeDependentOperator
-{
-private:
-   OperatorHandle M, K, S, A;
-   const Vector &b;
-   Solver *M_prec;
-   CGSolver M_solver;
-   Implicit_Solver *implicit_solver;
-   LORSolver<HypreBoomerAMG>* lor_solver;
-
-   mutable Vector z;
-   mutable Vector w;
-
-public:
-   IMEX_Evolution(ParBilinearForm &M_, ParBilinearForm &K_, ParBilinearForm &S_,
-                  const Vector &b_, ParBilinearForm &A_);
-
-   virtual
-   ~IMEX_Evolution()
-   {
-      delete implicit_solver;
-      delete lor_solver;
-      delete M_prec;
-   }
-
-   void Mult1(const Vector &x, Vector &y) const;
-
-   void ImplicitSolve2(const real_t dt, const Vector &x, Vector &k);
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_1 == GetEvalMode())
-      {
-         Mult1(x,y);
-      }
-      else
-      {
-         mfem_error("TimeDependentOperator::Mult() is not overridden!");
-      }
-   }
-
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override
-   {
-      if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_2 == GetEvalMode())
-      {
-         ImplicitSolve2(dt,x,k);
-      }
-      else
-      {
-         mfem_error("TimeDependentOperator::ImplicitSolve() is not overridden!");
-      }
-   }
-};
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI and HYPRE.
-   Mpi::Init();
-   int num_procs = Mpi::WorldSize();
-   int myid = Mpi::WorldRank();
-   Hypre::Init();
-
-   // 2. Parse command-line options.
-   int problem = 0;
-   const char *mesh_file = "../data/periodic-square.mesh";
-   int ser_ref_levels = 2;
-   int par_ref_levels = 0;
-   int order = 3;
-   int ode_solver_type = 64; // 61 - Forward Backward Euler
-   // 62 - IMEXRK2(2,2,2)
-   // 63 - IMEXRK2(2,3,2)
-   // 64 - IMEXRK3(3,4,3)
-   real_t t_final = 10.0;
-   real_t dt = 0.01;
-   bool paraview = false;
-   bool cg = false;
-   int vis_steps = 50;
-   bool adios2 = false;
-   bool binary = false;
-   real_t diffusion_term = 0.01;
-   real_t kappa = -1.0;
-   real_t sigma = -1.0;
-   bool visualization = true;
-   bool visit = false;
-   int precision = 16;
-   cout.precision(precision);
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&problem, "-p", "--problem",
-                  "Problem setup to use. See options in velocity_function().");
-   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
-                  "Number of times to refine the mesh uniformly in serial.");
-   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
-                  "Number of times to refine the mesh uniformly in parallel.");
-   args.AddOption(&order, "-o", "--order",
-                  "Order (degree) of the finite elements.");
-   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  ODESolver::IMEXTypes.c_str());
-   args.AddOption(&t_final, "-tf", "--t-final",
-                  "Final time; start time is 0.");
-   args.AddOption(&dt, "-dt", "--time-step",
-                  "Time step.");
-   args.AddOption(&diffusion_term, "-dc", "--diffusion-coeff",
-                  "Diffusion coefficient in the PDE.");
-   args.AddOption(&paraview, "-paraview", "--paraview-datafiles", "-no-paraview",
-                  "--no-paraview-datafiles",
-                  "Save data files for ParaView (paraview.org) visualization.");
-   args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
-                  "--no-visit-datafiles",
-                  "Save data files for VisIt (visit.llnl.gov) visualization.");
-   args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
-                  "--no-adios2-streams",
-                  "Save data using adios2 streams.");
-   args.AddOption(&binary, "-binary", "--binary-datafiles", "-ascii",
-                  "--ascii-datafiles",
-                  "Use binary (Sidre) or ascii format for VisIt data files.");
-   args.AddOption(&vis_steps, "-vs", "--visualization-steps",
-                  "Visualize every n-th timestep.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&cg, "-cg", "--continuous-galerkin", "-dg",
-                  "--discontinuous-galerkin",
-                  "Use Continuous-Galerkin Finite elements (Default is DG)");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (Mpi::Root())
-      {
-         args.PrintUsage(cout);
-      }
-      return 1;
-   }
-   if (Mpi::Root())
-   {
-      args.PrintOptions(cout);
-   }
-   if (kappa < 0)
-   {
-      kappa = (order+1)*(order+1);
-   }
-
-   // 3. Read the mesh from the given mesh file. We can handle geometrically
-   //    periodic meshes in this code.
-   Mesh *mesh = new Mesh(mesh_file);
-   const int dim = mesh->Dimension();
-
-   // 4. Define the IMEX (Split) ODE solver used for time integration. The IMEX
-   // solvers currently available are: 55 - Forward Backward Euler,
-   // 56 - IMEXRK2(2,2,2), 57 - IMEXRK2(2,3,2), and
-   unique_ptr<ODESolver> ode_solver = ODESolver::SelectIMEX(ode_solver_type);
-
-   // 5. Refine the mesh to increase the resolution. In this example we do
-   //    'ref_levels' of uniform refinement, where 'ref_levels' is a
-   //    command-line parameter.
-   for (int lev = 0; lev < ser_ref_levels; lev++) { mesh->UniformRefinement(); }
-   if (mesh->NURBSext)
-   {
-      mesh->SetCurvature(max(order, 1));
-   }
-   mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
-
-
-   // 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
-   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted.
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-   for (int lev = 0; lev < par_ref_levels; lev++)
-   {
-      pmesh->UniformRefinement();
-   }
-
-   // 7. Define the discontinuous DG finite element space of the given
-   //    polynomial order on the refined mesh.
-   FiniteElementCollection *fec = NULL;
-   if (cg)
-   {
-      fec = new H1_FECollection(order, dim);
-   }
-   else
-   {
-      fec = new DG_FECollection(order, dim, BasisType::GaussLobatto);
-   }
-   ParFiniteElementSpace *fes = new ParFiniteElementSpace(pmesh, fec);
-
-   HYPRE_BigInt global_vSize = fes->GlobalTrueVSize();
-   if (Mpi::Root())
-   {
-      cout << "Number of unknowns: " << global_vSize << endl;
-   }
-
-   // 8. Set up and assemble the bilinear and linear forms corresponding to the
-   //    DG discretization. The DGTraceIntegrator involves integrals over mesh
-   //    interior faces.
-   std::unique_ptr<VectorFunctionCoefficient> velocity;
-   if (0==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<0>));
-   }
-   else if (1==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<1>));
-   }
-   else if (2==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<2>));
-   }
-   else if (3==problem)
-   {
-      velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<3>));
-   }
-   ConstantCoefficient diff_coeff(diffusion_term);
-   ConstantCoefficient dt_diff_coeff(dt*diffusion_term);
-
-   ParBilinearForm *m = new ParBilinearForm(fes);
-   ParBilinearForm *k = new ParBilinearForm(fes);
-   ParBilinearForm *s = new ParBilinearForm(fes);
-
-   m->AddDomainIntegrator(new MassIntegrator());
-
-   constexpr real_t alpha = -1.0;
-   k->AddDomainIntegrator(new ConvectionIntegrator(*velocity, alpha));
-
-   s->AddDomainIntegrator(new DiffusionIntegrator(diff_coeff));
-
-   // For the preconditioner - create billinear form corresponding to
-   // operator (M + dt S)
-   ParBilinearForm *a = new ParBilinearForm(fes);
-   a->AddDomainIntegrator(new MassIntegrator);
-   a->AddDomainIntegrator(new DiffusionIntegrator(dt_diff_coeff));
-   if (!cg)
-   {
-      k->AddInteriorFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity,
-                                                                        alpha));
-      k->AddBdrFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity, alpha));
-      s->AddInteriorFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma,
-                                                             kappa));
-      s->AddBdrFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma, kappa));
-      a->AddInteriorFaceIntegrator(new DGDiffusionIntegrator(dt_diff_coeff, sigma,
-                                                             kappa));
-      a->AddBdrFaceIntegrator(new DGDiffusionIntegrator(dt_diff_coeff, sigma, kappa));
-   }
-
-   int skip_zeros = 0;
-   m->Assemble(skip_zeros);
-   k->Assemble(skip_zeros);
-   s->Assemble(skip_zeros);
-   a->Assemble();
-
-   m->Finalize(skip_zeros);
-   k->Finalize(skip_zeros);
-   s->Finalize(skip_zeros);
-   a->Finalize(skip_zeros);
-   HypreParVector b(fes);
-   b = 0.0;
-
-   // 9. Define the initial conditions. Set up visualization (if desired).
-   std::unique_ptr<FunctionCoefficient> u0;
-   if (0==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<0>));
-   }
-   else if (1==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<1>));
-   }
-   else if (2==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<2>));
-   }
-   else if (3==problem)
-   {
-      u0.reset(new FunctionCoefficient(u0_function<3>));
-   }
-   ParGridFunction *u = new ParGridFunction(fes);
-   u->ProjectCoefficient(*u0);
-   HypreParVector *U = u->GetTrueDofs();
-
-   DataCollection *dc = NULL;
-   if (visit)
-   {
-      if (binary)
-      {
-#ifdef MFEM_USE_SIDRE
-         dc = new SidreDataCollection("Example41-Parallel", pmesh);
-#else
-         MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
-#endif
-      }
-      else
-      {
-         dc = new VisItDataCollection("Example41-Parallel", pmesh);
-         dc->SetPrecision(precision);
-         // To save the mesh using MFEM's parallel mesh format:
-         // dc->SetFormat(DataCollection::PARALLEL_FORMAT);
-      }
-      dc->RegisterField("solution", u);
-      dc->SetCycle(0);
-      dc->SetTime(0.0);
-      dc->Save();
-   }
-   ParaViewDataCollection *pd = NULL;
-   if (paraview)
-   {
-      pd = new ParaViewDataCollection("Example41P", pmesh);
-      pd->SetPrefixPath("ParaView");
-      pd->RegisterField("solution", u);
-      pd->SetLevelsOfDetail(order);
-      pd->SetDataFormat(VTKFormat::BINARY);
-      pd->SetHighOrderOutput(true);
-      pd->SetCycle(0);
-      pd->SetTime(0.0);
-      pd->Save();
-   }
-   socketstream sout;
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      sout.open(vishost, visport);
-      if (!sout)
-      {
-         if (Mpi::Root())
-         {
-            cout << "Unable to connect to GLVis server at "
-                 << vishost << ':' << visport << endl;
-         }
-         visualization = false;
-         if (Mpi::Root())
-         {
-            cout << "GLVis visualization disabled.\n";
-         }
-      }
-      else
-      {
-         sout << "parallel " << num_procs << " " << myid << "\n";
-         sout.precision(precision);
-         sout << "solution\n" << *pmesh << *u;
-         sout << "pause\n";
-         sout << flush;
-         if (Mpi::Root())
-         {
-            cout << "GLVis visualization paused."
-                 << " Press space (in the GLVis window) to resume it.\n";
-         }
-      }
-   }
-#ifdef MFEM_USE_ADIOS2
-   ADIOS2DataCollection *adios2_dc = NULL;
-   if (adios2)
-   {
-      std::string postfix(mesh_file);
-      postfix.erase(0, std::string("../data/").size() );
-      postfix += "_o" + std::to_string(order);
-      const std::string collection_name = "ex41-p-" + postfix + ".bp";
-
-      adios2_dc = new ADIOS2DataCollection(MPI_COMM_WORLD, collection_name, pmesh);
-      // output data substreams are half the number of mpi processes
-      adios2_dc->SetParameter("SubStreams", std::to_string(num_procs/2) );
-      // adios2_dc->SetLevelsOfDetail(2);
-      adios2_dc->RegisterField("solution", u);
-      adios2_dc->SetCycle(0);
-      adios2_dc->SetTime(0.0);
-      adios2_dc->Save();
-   }
-#endif
-
-
-   // 10. Define the time-dependent evolution operator describing the
-   //     ODE right-hand side, and perform time-integration (looping
-   //     over the time iterations, ti, with a time-step dt).
-   IMEX_Evolution adv(*m, *k, *s, b, *a);
-
-   real_t t = 0.0;
-   adv.SetTime(t);
-   ode_solver->Init(adv);
-
-
-   bool done = false;
-   for (int ti = 0; !done; )
-   {
-      real_t dt_real = min(dt, t_final - t);
-      ode_solver->Step(*U, t, dt_real);
-      ti++;
-
-      done = (t >= t_final - 1e-8*dt);
-
-      if (done || ti % vis_steps == 0)
-      {
-         if (Mpi::Root())
-         {
-            cout << "time step: " << ti << ", time: " << t << endl;
-         }
-         *u = *U;
-         if (visualization)
-         {
-            sout << "parallel " << num_procs << " " << myid << "\n";
-            sout << "solution\n" << *pmesh << *u << flush;
-         }
-         if (paraview)
-         {
-            pd->SetCycle(ti);
-            pd->SetTime(t);
-            pd->Save();
-         }
-#ifdef MFEM_USE_ADIOS2
-         // transient solutions can be visualized with ParaView
-         if (adios2)
-         {
-            adios2_dc->SetCycle(ti);
-            adios2_dc->SetTime(t);
-            adios2_dc->Save();
-         }
-#endif
-      }
-   }
-
-   // 11. Free the used memory.
-   delete pd;
-   delete U;
-   delete u;
-   delete a;
-   delete s;
-   delete k;
-   delete m;
-   delete fes;
-   delete pmesh;
-   delete dc;
-   delete fec;
-
-   return 0;
-}
-
-// Implementation of class IMEX_Evolution
-IMEX_Evolution::IMEX_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
-                               ParBilinearForm &S_, const Vector &b_, ParBilinearForm &A_)
-   : TimeDependentOperator(M_.ParFESpace()->GetTrueVSize()), b(b_),
-     M_solver(M_.ParFESpace()->GetComm()), z(height), w(height)
-{
-   if (M_.GetAssemblyLevel()==AssemblyLevel::LEGACY)
-   {
-      M.Reset(M_.ParallelAssemble(), true);
-      K.Reset(K_.ParallelAssemble(), true);
-      S.Reset(S_.ParallelAssemble(), true);
-   }
-   else
-   {
-      M.Reset(&M_, false);
-      K.Reset(&K_, false);
-      S.Reset(&S_, false);
-   }
-
-   M_solver.SetOperator(*M);
-
-   Array<int> ess_tdof_list;
-   if (M_.GetAssemblyLevel() == AssemblyLevel::LEGACY)
-   {
-      A.Reset(A_.ParallelAssemble(), true);
-      HypreParMatrix &M_mat = *M.As<HypreParMatrix>();
-      HypreParMatrix &S_mat = *S.As<HypreParMatrix>();
-      HypreSmoother *hypre_prec = new HypreSmoother(M_mat, HypreSmoother::Jacobi);
-      M_prec = hypre_prec;
-
-      implicit_solver = new Implicit_Solver(M_mat, S_mat, *M_.FESpace());
-      lor_solver = new LORSolver<HypreBoomerAMG>(A_, ess_tdof_list);
-      lor_solver->GetSolver().SetSystemsOptions(A_.ParFESpace()->GetVDim(), true);
-      implicit_solver -> SetPreconditioner(*lor_solver);
-   }
-   else
-   {
-      MFEM_ABORT("Implicit time integration is not supported with partial assembly");
-   }
-   M_solver.SetPreconditioner(*M_prec);
-   M_solver.iterative_mode = false;
-   M_solver.SetRelTol(1e-9);
-   M_solver.SetAbsTol(0.0);
-   M_solver.SetMaxIter(100);
-   M_solver.SetPrintLevel(0);
-}
-
-void IMEX_Evolution::Mult1(const Vector &x, Vector &y) const
-{
-   // Perform the explicit step
-   // y = M^{-1} (K x + b)
-   K->Mult(x, z);
-   z += b;
-   M_solver.Mult(z, y);
-}
-
-void IMEX_Evolution::ImplicitSolve2(const real_t dt, const Vector &x, Vector &k)
-{
-   // Perform the implicit step
-   // solve for k, k = -(M+dt S)^{-1} S x
-   MFEM_VERIFY(implicit_solver != NULL,
-               "Implicit time integration is not supported with partial assembly");
-   S->Mult(x, z);
-   z*= -1.0;
-   implicit_solver->SetTimeStep(dt);
-   implicit_solver->Mult(z, k);
-}
@@ -9,7 +9,6 @@
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex4p -m ../data/escher.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb
-//               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/fichera-q2.vtk
 //               mpirun -np 4 ex4p -m ../data/fichera-q3.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/square-disc-nurbs.mesh -o 3
@@ -18,18 +17,14 @@
 //               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
 //               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
-//               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
-//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/ref-prism.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
 // Device sample runs:
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d cuda
-//               mpirun -np 4 ex4p -m ../data/star.mesh -ea -hb -d cuda
-//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -ea -hb -d cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-omp
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -pa -d cuda
@@ -235,7 +230,7 @@ int main(int argc, char *argv[])
   pcg->SetMaxIter(2000);
   pcg->SetPrintLevel(1);
   if (hybridization) { prec = new HypreBoomerAMG(*A.As<HypreParMatrix>()); }
-   else if (pa || ea) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
+   else if (pa) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
   else
   {
      ParFiniteElementSpace *prec_fespace =
@@ -160,7 +160,6 @@ int main(int argc, char *argv[])
   bool paraview = false;
   bool binary = false;
   int vis_steps = 5;
-   bool solve_implicit_state = false;

   int precision = 8;
   cout.precision(precision);
@@ -188,9 +187,6 @@ int main(int argc, char *argv[])
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
                  "Time step.");
-   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
-                  "-imp-slope", "--implicit-slope",
-                  "Implicitly solve for stage state or slope.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -370,11 +366,6 @@ int main(int argc, char *argv[])
   //    right-hand side, and perform time-integration (looping over the time
   //    iterations, ti, with a time-step dt).
   FE_Evolution adv(m, k, b);
-   using ImplicitVariableType = FE_Evolution::ImplicitVariableType;
-   ImplicitVariableType imp_var = solve_implicit_state ?
-                                  ImplicitVariableType::STATE
-                                  : ImplicitVariableType::SLOPE;
-   adv.SetImplicitVariableType(imp_var);

   real_t t = 0.0;
   adv.SetTime(t);
@@ -468,17 +459,7 @@ void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
   MFEM_VERIFY(dg_solver != NULL,
               "Implicit time integration is not supported with partial assembly");
-   // Construct current right-hand side for stage state vs. slope solve
-   if (ImplicitVarTypeIsState())
-   {
-      // k, on return, is the stage value u
-      M.Mult(x, z);
-   }
-   else
-   {
-      // k, on return, is the stage slope du/dt
-      K.Mult(x, z);
-   }
+   K.Mult(x, z);
   z += b;
   dg_solver->SetTimeStep(dt);
   dg_solver->Mult(z, k);
@@ -0,0 +1,159 @@
+#include <mfem.hpp>
+#include "nlohmann/json.hpp"
+#include "minja.hpp"
+#include "myqfunction.hpp"
+
+using namespace mfem;
+using namespace mfem::future;
+
+template<class T>
+struct remove_cvref
+{
+   using type = std::remove_cv_t<std::remove_reference_t<T>>;
+};
+
+template <typename qf_t>
+auto process(qf_t qf)
+{
+   using qfsig = typename create_function_signature<qf_t>::type;
+   using qfpar_t = typename qfsig::parameter_ts;
+   using qfout_t = typename qfsig::return_t;
+
+   auto qfparams = decay_tuple<qfpar_t> {};
+
+   auto in_str = apply([](auto&&... arg)
+   {
+      return std::vector<std::string>
+      {
+         std::string(get_type_name<typename remove_cvref<decltype(arg)>::type>())...
+      };
+   }, qfparams);
+
+   std::vector<std::string> out_str
+   {
+      std::string(get_type_name<typename remove_cvref<qfout_t>::type>())
+   };
+
+   return std::tuple{in_str, out_str};
+}
+
+int main()
+{
+   // load the kernel template
+   std::ifstream
+   kernel_istream("/Users/andrej1/repos/mfem/examples/kernel_skeleton.jinja");
+   if (!kernel_istream.is_open())
+   {
+      std::cerr << "error opening jinja template file" << std::endl;
+      return 1;
+   }
+   std::stringstream buffer;
+   buffer << kernel_istream.rdbuf();
+
+   std::string fileContent = buffer.str();
+   auto kernel_tmpl = minja::Parser::parse(buffer.str(), /* options= */ {});
+
+   auto [in_str, out_str] = process(myqfunction0);
+
+   for (auto &v : in_str)
+   {
+      std::cout << v << " ";
+   }
+   std::cout << std::endl;
+
+   const size_t DUMMY_STRIDE = 64*32*32;
+   const size_t basis_p_1d = 2;
+
+   json context_json{};
+   context_json["kernel_name"] = "demo";
+
+   context_json["spaces"].push_back(
+   {
+      {"P_1D", basis_p_1d},
+      {"dim", 3},
+      {"needs_value", true},
+      {"needs_grad", true},
+   });
+
+   context_json["spaces"].push_back(
+   {
+      {"P_1D", basis_p_1d},
+   });
+
+   context_json["inputs"].push_back(
+   {
+      {"name", "potential"},
+      {"space_idx", 0},
+      {"num_comp", 1},
+      {"comp_stride", DUMMY_STRIDE},
+      {"eval_grad", true},
+   });
+
+   context_json["inputs"].push_back(
+   {
+      {"name", "weights"},
+      {"space_idx", 0},
+      {"num_comp", 1},
+      {"comp_stride", DUMMY_STRIDE},
+      {"is_qdata", true},
+   });
+
+   context_json["outputs"].push_back(
+   {
+      {"name", "solution"},
+      {"space_idx", 0},
+      {"num_comp", 1},
+      {"comp_stride", DUMMY_STRIDE},
+      {"eval_grad", true},
+   });
+
+   const size_t nqf = 1;
+   const std::vector<std::string> qfunc_names = {"myqfunction0"};
+   const std::vector<std::vector<size_t>> qfunc_inputs = {{0, 1, 2}};
+
+   for (size_t i = 0; i < nqf; i++)
+   {
+      json inarr = json::array();
+      for (size_t j = 0; j < qfunc_inputs[i].size(); j++)
+      {
+         inarr.push_back(
+         {
+            {"index", j},
+            {"datatype", in_str[j]}
+         });
+      }
+
+      context_json["qfuncs"].push_back(
+      {
+         {"name", qfunc_names[i]},
+         {"inputs", inarr}
+      });
+   }
+
+   std::cout << context_json.dump(2) << std::endl;
+
+   auto context = minja::Context::make(context_json);
+   auto kernel_source = kernel_tmpl->render(context);
+
+   std::cout << ">>> generated kernel source\n"
+             << kernel_source
+             << "\n<<< generated kernel source\n"
+             << std::endl;
+
+   {
+      // test casting
+      std::vector<real_t> d(4);
+      int i = 0;
+      for (auto &v : d)
+      {
+         v = ++i;
+      }
+
+      mfem::future::tensor<real_t, 2, 2> *dudxi =
+         reinterpret_cast<mfem::future::tensor<real_t, 2, 2> *>(d.data());
+
+      std::cout << *dudxi << std::endl;
+   }
+
+   return 0;
+}
@@ -257,7 +257,6 @@ int main(int argc, char *argv[])
   bool adios2 = false;
   bool binary = false;
   int vis_steps = 5;
-   bool solve_implicit_state = false;
 #if MFEM_HYPRE_VERSION >= 21800
   PrecType prec_type = PrecType::AIR;
 #else
@@ -291,9 +290,6 @@ int main(int argc, char *argv[])
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
                  "Time step.");
-   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
-                  "-imp-slope", "--implicit-slope",
-                  "Implicitly solve for stage state or slope.");
   args.AddOption((int *)&prec_type, "-pt", "--prec-type", "Preconditioner for "
                  "implicit solves. 0 for ILU, 1 for pAIR-AMG.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -540,11 +536,6 @@ int main(int argc, char *argv[])
   //     right-hand side, and perform time-integration (looping over the time
   //     iterations, ti, with a time-step dt).
   FE_Evolution adv(*m, *k, *B, prec_type);
-   using ImplicitVariableType = FE_Evolution::ImplicitVariableType;
-   ImplicitVariableType imp_var = solve_implicit_state ?
-                                  ImplicitVariableType::STATE
-                                  : ImplicitVariableType::SLOPE;
-   adv.SetImplicitVariableType(imp_var);

   real_t t = 0.0;
   adv.SetTime(t);
@@ -685,17 +676,7 @@ FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
 //    (M - dt*K) d = K*u + b
 void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
-   // Construct current right-hand side for stage state vs. slope solve
-   if (ImplicitVarTypeIsState())
-   {
-      // k, on return, is the stage value u
-      M->Mult(x, z);
-   }
-   else
-   {
-      // k, on return, is the stage slope du/dt
-      K->Mult(x, z);
-   }
+   K->Mult(x, z);
   z += b;
   dg_solver->SetTimeStep(dt);
   dg_solver->Mult(z, k);
@@ -14,12 +14,6 @@ list(APPEND GINKGO_EXAMPLES_SRCS
  ex1.cpp
 )

-if (MFEM_USE_MPI AND GINKGO_BUILD_MPI)
-    list(APPEND GINKGO_EXAMPLES_SRCS
-    ex1p.cpp
-)
-endif()
-
 # Include the source directory where mfem.hpp and mfem-performance.hpp are.
 include_directories(BEFORE ${PROJECT_BINARY_DIR})

@@ -207,7 +207,7 @@ int main(int argc, char *argv[])
            Ginkgo::IcPreconditioner ginkgo_precond(exec, "paric", 30);
            Ginkgo::CGSolver ginkgo_solver(exec, ginkgo_precond);
            ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(sqrt(1e-12));
+            ginkgo_solver.SetRelTol(1e-12);
            ginkgo_solver.SetAbsTol(0.0);
            ginkgo_solver.SetMaxIter(400);
            ginkgo_solver.SetOperator(*(A.Ptr()));
@@ -225,7 +225,7 @@ int main(int argc, char *argv[])
            Ginkgo::MFEMPreconditioner gko_M(exec, M);
            Ginkgo::CGSolver ginkgo_solver(exec, gko_M);
            ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(sqrt(1e-12));
+            ginkgo_solver.SetRelTol(1e-12);
            ginkgo_solver.SetAbsTol(0.0);
            ginkgo_solver.SetMaxIter(400);
            ginkgo_solver.SetOperator(*(A.Ptr()));
@@ -283,7 +283,7 @@ int main(int argc, char *argv[])
               Ginkgo::MFEMPreconditioner gko_M(exec, M);
               Ginkgo::CGSolver ginkgo_solver(exec, gko_M);
               ginkgo_solver.SetPrintLevel(print_lvl);
-               ginkgo_solver.SetRelTol(sqrt(1e-12));
+               ginkgo_solver.SetRelTol(1e-12);
               ginkgo_solver.SetAbsTol(0.0);
               ginkgo_solver.SetMaxIter(400);
               ginkgo_solver.SetOperator(*(A.Ptr()));
@@ -1,436 +0,0 @@
-//                       MFEM Example 1 - Parallel Version
-//                             GINKGO Modification
-//
-// Compile with: make ex1p
-//
-// Sample runs:  mpirun -np 4 ex1p -m ../data/square-disc.mesh
-//               mpirun -np 4 ex1p -m ../data/star.mesh
-//               mpirun -np 4 ex1p -m ../data/star-mixed.mesh
-//               mpirun -np 4 ex1p -m ../data/escher.mesh
-//               mpirun -np 4 ex1p -m ../data/fichera.mesh
-//               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
-//               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
-//               mpirun -np 4 ex1p -m ../data/octahedron.mesh -o 1
-//               mpirun -np 4 ex1p -m ../data/periodic-annulus-sector.msh
-//               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
-//               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
-//               mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
-//               mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1
-//               mpirun -np 4 ex1p -m ../data/star-mixed-p2.mesh -o 2
-//               mpirun -np 4 ex1p -m ../data/disc-nurbs.mesh -o -1
-//               mpirun -np 4 ex1p -m ../data/pipe-nurbs.mesh -o -1
-//               mpirun -np 4 ex1p -m ../data/ball-nurbs.mesh -o 2
-//               mpirun -np 4 ex1p -m ../data/fichera-mixed-p2.mesh -o 2
-//               mpirun -np 4 ex1p -m ../data/star-surf.mesh
-//               mpirun -np 4 ex1p -m ../data/square-disc-surf.mesh
-//               mpirun -np 4 ex1p -m ../data/inline-segment.mesh
-//               mpirun -np 4 ex1p -m ../data/amr-quad.mesh
-//               mpirun -np 4 ex1p -m ../data/amr-hex.mesh
-//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh
-//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh -o -1 -sc
-//
-// Device sample runs:
-//               mpirun -np 4 ex1p -pa -d cuda
-//               mpirun -np 4 ex1p -fa -d cuda
-//               mpirun -np 4 ex1p -pa -d occa-cuda
-//               mpirun -np 4 ex1p -pa -d raja-omp
-//               mpirun -np 4 ex1p -pa -d ceed-cpu
-//               mpirun -np 4 ex1p -pa -d ceed-cpu -o 4 -a
-//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/square-mixed.mesh
-//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/fichera-mixed.mesh
-//             * mpirun -np 4 ex1p -pa -d ceed-cuda
-//             * mpirun -np 4 ex1p -pa -d ceed-hip
-//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
-//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
-//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
-//               mpirun -np 4 ex1p -m ../data/beam-tet.mesh -pa -d ceed-cpu
-//
-// Description:  This example code demonstrates the use of MFEM to define a
-//               simple finite element discretization of the Laplace problem
-//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
-//               Specifically, we discretize using a FE space of the specified
-//               order, or if order < 1 using an isoparametric/isogeometric
-//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
-//               NURBS mesh, etc.)
-//
-//               The example highlights the use of mesh refinement, finite
-//               element grid functions, as well as linear and bilinear forms
-//               corresponding to the left-hand side and right-hand side of the
-//               discrete linear system. We also cover the explicit elimination
-//               of essential boundary conditions, static condensation, and the
-//               optional connection to the GLVis tool for visualization.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-#ifndef MFEM_USE_GINKGO
-#error This example requires that MFEM is built with MFEM_USE_GINKGO=YES
-#endif
-
-using namespace std;
-using namespace mfem;
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI and HYPRE.
-   Mpi::Init();
-   int num_procs = Mpi::WorldSize();
-   int myid = Mpi::WorldRank();
-   Hypre::Init();
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../../data/star.mesh";
-   int order = 1;
-   bool static_cond = false;
-   bool pa = false;
-   bool fa = false;
-   const char *device_config = "cpu";
-   bool visualization = true;
-   int solver_config = 0;
-   int print_lvl = 1;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree) or -1 for"
-                  " isoparametric space.");
-   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
-                  "--no-static-condensation", "Enable static condensation.");
-   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
-                  "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
-                  "--no-full-assembly", "Enable Full Assembly.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&solver_config, "-s", "--solver-config",
-                  "Solver and preconditioner combination: \n\t"
-                  "   0 - Ginkgo solver and Ginkgo preconditioner, \n\t"
-                  "   1 - Ginkgo solver and MFEM preconditioner, \n\t"
-                  "   2 - MFEM solver and Ginkgo preconditioner, \n\t"
-                  "   3 - MFEM solver and MFEM preconditioner.");
-   args.AddOption(&print_lvl, "-pl", "--print-level",
-                  "Print level for iterative solver (1 prints every iteration).");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0)
-      {
-         args.PrintUsage(cout);
-      }
-      return 1;
-   }
-   if (myid == 0)
-   {
-      args.PrintOptions(cout);
-   }
-
-   // 3. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   device.SetGPUAwareMPI(true);
-   if (myid == 0) { device.Print(); }
-
-   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
-   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
-   //    and volume meshes with the same code.
-   Mesh mesh(mesh_file, 1, 1);
-   int dim = mesh.Dimension();
-
-   // 5. Refine the serial mesh on all processors to increase the resolution. In
-   //    this example we do 'ref_levels' of uniform refinement. We choose
-   //    'ref_levels' to be the largest number that gives a final mesh with no
-   //    more than 10,000 elements.
-   {
-      int ref_levels =
-         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
-      for (int l = 0; l < ref_levels; l++)
-      {
-         mesh.UniformRefinement();
-      }
-   }
-
-   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
-   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted.
-   ParMesh pmesh(MPI_COMM_WORLD, mesh);
-   mesh.Clear();
-   {
-      int par_ref_levels = 2;
-      for (int l = 0; l < par_ref_levels; l++)
-      {
-         pmesh.UniformRefinement();
-      }
-   }
-
-   // 7. Define a parallel finite element space on the parallel mesh. Here we
-   //    use continuous Lagrange finite elements of the specified order. If
-   //    order < 1, we instead use an isoparametric/isogeometric space.
-   FiniteElementCollection *fec;
-   bool delete_fec;
-   if (order > 0)
-   {
-      fec = new H1_FECollection(order, dim);
-      delete_fec = true;
-   }
-   else if (pmesh.GetNodes())
-   {
-      fec = pmesh.GetNodes()->OwnFEC();
-      delete_fec = false;
-      if (myid == 0)
-      {
-         cout << "Using isoparametric FEs: " << fec->Name() << endl;
-      }
-   }
-   else
-   {
-      fec = new H1_FECollection(order = 1, dim);
-      delete_fec = true;
-   }
-   ParFiniteElementSpace fespace(&pmesh, fec);
-   HYPRE_BigInt size = fespace.GlobalTrueVSize();
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-   }
-
-   // 8. Determine the list of true (i.e. parallel conforming) essential
-   //    boundary dofs. In this example, the boundary conditions are defined
-   //    by marking all the boundary attributes from the mesh as essential
-   //    (Dirichlet) and converting them to a list of true dofs.
-   Array<int> ess_tdof_list;
-   if (pmesh.bdr_attributes.Size())
-   {
-      Array<int> ess_bdr(pmesh.bdr_attributes.Max());
-      ess_bdr = 1;
-      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-   // 9. Set up the parallel linear form b(.) which corresponds to the
-   //    right-hand side of the FEM linear system, which in this case is
-   //    (1,phi_i) where phi_i are the basis functions in fespace.
-   ParLinearForm b(&fespace);
-   ConstantCoefficient one(1.0);
-   b.AddDomainIntegrator(new DomainLFIntegrator(one));
-   b.Assemble();
-
-   // 10. Define the solution vector x as a parallel finite element grid
-   //     function corresponding to fespace. Initialize x with initial guess of
-   //     zero, which satisfies the boundary conditions.
-   ParGridFunction x(&fespace);
-   x = 0.0;
-
-   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
-   //     corresponding to the Laplacian operator -Delta, by adding the
-   //     Diffusion domain integrator.
-   ParBilinearForm a(&fespace);
-   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   if (fa)
-   {
-      a.SetAssemblyLevel(AssemblyLevel::FULL);
-      // Sort the matrix column indices when running on GPU or with OpenMP (i.e.
-      // when Device::IsEnabled() returns true). This makes the results
-      // bit-for-bit deterministic at the cost of somewhat longer run time.
-      a.EnableSparseMatrixSorting(Device::IsEnabled());
-   }
-   a.AddDomainIntegrator(new DiffusionIntegrator(one));
-
-   // 12. Assemble the parallel bilinear form and the corresponding linear
-   //     system, applying any necessary transformations such as: parallel
-   //     assembly, eliminating boundary conditions, applying conforming
-   //     constraints for non-conforming AMR, static condensation, etc.
-   if (static_cond) { a.EnableStaticCondensation(); }
-   a.Assemble();
-
-   OperatorPtr A;
-   Vector B, X;
-   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
-
-   // 13. Solve the linear system A X = B.
-   if (!pa)
-   {
-      switch (solver_config)
-      {
-         // Solve the linear system with CG + Schwarz (with IC) from Ginkgo
-         case 0:
-         {
-            if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
-            Ginkgo::GinkgoExecutor exec(device);
-            Ginkgo::IcPreconditioner local_solver(exec, "exact");
-            Ginkgo::SchwarzPreconditioner gko_M(exec, MPI_COMM_WORLD, local_solver);
-            Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
-            ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(sqrt(1e-12));
-            ginkgo_solver.SetAbsTol(0.0);
-            ginkgo_solver.SetMaxIter(400);
-            ginkgo_solver.SetOperator(*(A.Ptr()));
-            ginkgo_solver.Mult(B, X);
-            break;
-         }
-
-         // Solve the linear system with CG from Ginkgo + MFEM preconditioner
-         case 1:
-         {
-            if (myid == 0) { cout << "Using Ginkgo solver + MFEM preconditioner...\n"; }
-            Ginkgo::GinkgoExecutor exec(device);
-            //Create MFEM preconditioner and wrap it for Ginkgo's use.
-            HypreBoomerAMG M((HypreParMatrix&)(*A));
-            Ginkgo::MFEMPreconditioner gko_M(exec, M, MPI_COMM_WORLD);
-            Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
-            ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(sqrt(1e-12));
-            ginkgo_solver.SetAbsTol(0.0);
-            ginkgo_solver.SetMaxIter(400);
-            ginkgo_solver.SetOperator(*(A.Ptr()));
-            ginkgo_solver.Mult(B, X);
-            break;
-         }
-
-         // Ginkgo Schwarz preconditioner (local ParIC) +  MFEM CG solver
-         case 2:
-         {
-            if (myid == 0) { cout << "Using MFEM solver + Ginkgo preconditioner...\n"; }
-            Ginkgo::GinkgoExecutor exec(device);
-            Ginkgo::IcPreconditioner local_M(exec, "exact");
-            Ginkgo::SchwarzPreconditioner M(exec, MPI_COMM_WORLD, local_M);
-            M.SetOperator(*(A.Ptr()));  // Generate the preconditioner for the matrix A.
-            CGSolver cg(MPI_COMM_WORLD);
-            cg.SetRelTol(sqrt(1e-12));
-            cg.SetMaxIter(400);
-            cg.SetPrintLevel(1);
-            cg.SetPreconditioner(M);
-            cg.SetOperator(*A);
-            cg.Mult(B, X);
-            break;
-         }
-
-         // MFEM solver + MFEM preconditioner
-         case 3:
-         {
-            if (myid == 0) { cout << "Using MFEM solver + MFEM preconditioner...\n"; }
-            HypreBoomerAMG M((HypreParMatrix&)(*A));
-            CGSolver cg(MPI_COMM_WORLD);
-            cg.SetRelTol(sqrt(1e-12));
-            cg.SetMaxIter(400);
-            cg.SetPrintLevel(1);
-            cg.SetPreconditioner(M);
-            cg.SetOperator(*A);
-            cg.Mult(B, X);
-            break;
-         }
-      } // End switch on solver_config
-   }
-   // Partial assembly mode.  Cannot use Ginkgo preconditioners, but can use Ginkgo
-   // solvers.
-   else
-   {
-      if (UsesTensorBasis(fespace))
-      {
-         // Use Jacobi preconditioning in partial assembly mode.
-         OperatorJacobiSmoother M(a, ess_tdof_list);
-         switch (solver_config)
-         {
-            case 0:
-            {
-               if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
-               MFEM_ABORT("Cannot use Ginkgo preconditioner in partial assembly mode.\n"
-                          "            Try -s 1 to test Ginkgo solver with an MFEM preconditioner.");
-               break;
-            }
-
-            // Use Ginkgo solver with MFEM preconditioner
-            case 1:
-            {
-               if (myid == 0) { cout << "Using Ginkgo solver + MFEM preconditioner...\n"; }
-               Ginkgo::GinkgoExecutor exec(device);
-               // Wrap MFEM preconditioner for Ginkgo's use.
-               Ginkgo::MFEMPreconditioner gko_M(exec, M, MPI_COMM_WORLD);
-               Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
-               ginkgo_solver.SetPrintLevel(print_lvl);
-               ginkgo_solver.SetRelTol(sqrt(1e-12));
-               ginkgo_solver.SetAbsTol(0.0);
-               ginkgo_solver.SetMaxIter(400);
-               ginkgo_solver.SetOperator(*(A.Ptr()));
-               ginkgo_solver.Mult(B, X);
-               break;
-            }
-
-            // No Ginkgo preconditioners work with matrix-free; error
-            case 2:
-            {
-               if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
-               MFEM_ABORT("Cannot use Ginkgo preconditioner in partial assembly mode.\n"
-                          "            Try -s 1 to test Ginkgo solver with an MFEM preconditioner.");
-               break;
-            }
-
-            // Use MFEM solver and preconditioner
-            case 3:
-            {
-               if (myid == 0) { cout << "Using MFEM solver + MFEM preconditioner...\n"; }
-               CGSolver cg(MPI_COMM_WORLD);
-               cg.SetRelTol(sqrt(1e-12));
-               cg.SetMaxIter(400);
-               cg.SetPrintLevel(1);
-               cg.SetPreconditioner(M);
-               cg.SetOperator(*A);
-               cg.Mult(B, X);
-               break;
-            }
-         } // End switch on solver_config
-      }
-      else // CG with no preconditioning
-      {
-         if (myid == 0) { cout << "Using MFEM solver + no preconditioner...\n"; }
-         CGSolver cg(MPI_COMM_WORLD);
-         cg.SetRelTol(sqrt(1e-12));
-         cg.SetMaxIter(400);
-         cg.SetPrintLevel(1);
-         cg.SetOperator(*A);
-         cg.Mult(B, X);
-      }
-   }
-
-   // 14. Recover the parallel grid function corresponding to X. This is the
-   //     local finite element solution on each processor.
-   a.RecoverFEMSolution(X, b, x);
-
-   // 15. Save the refined mesh and the solution in parallel. This output can
-   //     be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
-   {
-      ostringstream mesh_name, sol_name;
-      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
-      sol_name << "sol." << setfill('0') << setw(6) << myid;
-
-      ofstream mesh_ofs(mesh_name.str().c_str());
-      mesh_ofs.precision(8);
-      pmesh.Print(mesh_ofs);
-
-      ofstream sol_ofs(sol_name.str().c_str());
-      sol_ofs.precision(8);
-      x.Save(sol_ofs);
-   }
-
-   // 16. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << pmesh << x << flush;
-   }
-
-   // 17. Free the used memory.
-   if (delete_fec)
-   {
-      delete fec;
-   }
-
-   return 0;
-}
@@ -20,8 +20,9 @@ CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

+# Currently there are only serial Ginkgo examples
 SEQ_EXAMPLES = ex1
-PAR_EXAMPLES = ex1p
+PAR_EXAMPLES =
 ifeq ($(MFEM_USE_MPI),NO)
   EXAMPLES = $(SEQ_EXAMPLES)
 else
@@ -0,0 +1,21 @@
+#include "util.hpp"
+
+#define NUM_SPACES {{ spaces | count }}
+#define NUM_INPUTS {{ inputs | count }}
+#define NUM_OUTPUTS {{ outputs | count }}
+
+extern "C" __global__ void dfem_jit_{{kernel_name}}(int num_entities, const real_t *fields[NUM_INPUTS], real_t *outputs[NUM_OUTPUTS], const real_t *B[NUM_SPACES]) {
+  // transform fields
+  const real_t *inputs = ...;
+
+  // call qfunctions
+  {% for qf in qfuncs -%}
+  {
+    {%- for qfinput in qf.inputs %}
+    {{ qfinput.datatype }}* in{{ loop.index0 }} =
+      reinterpret_cast<{{ qfinput.datatype }}>(inputs[{{ qfinput.index }}]);
+    {% endfor %}
+    {{ qf.name }}({% for qfinput in qf.inputs %}*in{{ loop.index0 }}{{ "," if not loop.last else "" }}{% endfor %});
+  }
+  {% endfor %}
+}
@@ -22,11 +22,11 @@ MFEM_LIB_FILE = mfem_is_not_built

 SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
   ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
-   ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40 ex41
+   ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40
 PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
   ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
   ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
-   ex37p ex39p ex40p ex41p
+   ex37p ex39p ex40p
 SEQ_DEVICE_EXAMPLES = ex1 ex3 ex4 ex5 ex6 ex9 ex14 ex22 ex24 ex25 ex26 ex34
 PAR_DEVICE_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex14p \
   ex22p ex24p ex25p ex26p ex34p ex35p
@@ -157,10 +157,6 @@ ex37-test-seq: ex37
 	@$(call mfem-test,$<,, Serial example,-mi 3)
 ex37p-test-par: ex37p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-mi 3)
-ex41-test-seq: ex41
-	@$(call mfem-test,$<,, Serial example,-tf 1.0)
-ex41p-test-par: ex41p
-	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-tf 1.0)
 # Testing: optional tests
 ifeq ($(MFEM_USE_STRUMPACK),YES)
 ex11p-test-strumpack: ex11p
@@ -0,0 +1,17 @@
+#include <mfem.hpp>
+
+using namespace mfem;
+using mfem::future::tensor;
+
+constexpr int dim = 2;
+
+tensor<real_t, dim, dim> myqfunction0(
+   const tensor<real_t, dim, dim> &dvdxi,
+   const tensor<real_t, dim, dim> &J,
+   const real_t &w)
+{
+   const auto invJ = inv(J);
+   const auto dvdx = dvdxi * invJ;
+   const auto test_function_terms = inv(J);
+   return dot(dvdx, J) * det(J) * w * test_function_terms;
+}
@@ -0,0 +1,183 @@
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+#ifndef INCLUDE_NLOHMANN_JSON_FWD_HPP_
+#define INCLUDE_NLOHMANN_JSON_FWD_HPP_
+
+#include <cstdint> // int64_t, uint64_t
+#include <map>     // map
+#include <memory>  // allocator
+#include <string>  // string
+#include <vector>  // vector
+
+// #include <nlohmann/detail/abi_macros.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+// This file contains all macro definitions affecting or depending on the ABI
+
+#ifndef JSON_SKIP_LIBRARY_VERSION_CHECK
+#if defined(NLOHMANN_JSON_VERSION_MAJOR) &&                                    \
+    defined(NLOHMANN_JSON_VERSION_MINOR) &&                                    \
+    defined(NLOHMANN_JSON_VERSION_PATCH)
+#if NLOHMANN_JSON_VERSION_MAJOR != 3 || NLOHMANN_JSON_VERSION_MINOR != 12 ||   \
+    NLOHMANN_JSON_VERSION_PATCH != 0
+#warning "Already included a different version of the library!"
+#endif
+#endif
+#endif
+
+#define NLOHMANN_JSON_VERSION_MAJOR 3  // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_MINOR 12 // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_PATCH 0  // NOLINT(modernize-macro-to-enum)
+
+#ifndef JSON_DIAGNOSTICS
+#define JSON_DIAGNOSTICS 0
+#endif
+
+#ifndef JSON_DIAGNOSTIC_POSITIONS
+#define JSON_DIAGNOSTIC_POSITIONS 0
+#endif
+
+#ifndef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+#define JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON 0
+#endif
+
+#if JSON_DIAGNOSTICS
+#define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS _diag
+#else
+#define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS
+#endif
+
+#if JSON_DIAGNOSTIC_POSITIONS
+#define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS _dp
+#else
+#define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS
+#endif
+
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+#define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON _ldvcmp
+#else
+#define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_NO_VERSION
+#define NLOHMANN_JSON_NAMESPACE_NO_VERSION 0
+#endif
+
+// Construct the namespace ABI tags component
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c) json_abi##a##b##c
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT(a, b, c)                                 \
+  NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c)
+
+#define NLOHMANN_JSON_ABI_TAGS                                                 \
+  NLOHMANN_JSON_ABI_TAGS_CONCAT(                                               \
+      NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS,                                       \
+      NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON,                 \
+      NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS)
+
+// Construct the namespace version component
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch)         \
+  _v##major##_##minor##_##patch
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(major, minor, patch)            \
+  NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch)
+
+#if NLOHMANN_JSON_NAMESPACE_NO_VERSION
+#define NLOHMANN_JSON_NAMESPACE_VERSION
+#else
+#define NLOHMANN_JSON_NAMESPACE_VERSION                                        \
+  NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(NLOHMANN_JSON_VERSION_MAJOR,          \
+                                         NLOHMANN_JSON_VERSION_MINOR,          \
+                                         NLOHMANN_JSON_VERSION_PATCH)
+#endif
+
+// Combine namespace components
+#define NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b) a##b
+#define NLOHMANN_JSON_NAMESPACE_CONCAT(a, b)                                   \
+  NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b)
+
+#ifndef NLOHMANN_JSON_NAMESPACE
+#define NLOHMANN_JSON_NAMESPACE                                                \
+  nlohmann::NLOHMANN_JSON_NAMESPACE_CONCAT(NLOHMANN_JSON_ABI_TAGS,             \
+                                           NLOHMANN_JSON_NAMESPACE_VERSION)
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_BEGIN
+#define NLOHMANN_JSON_NAMESPACE_BEGIN                                          \
+  namespace nlohmann {                                                         \
+  inline namespace NLOHMANN_JSON_NAMESPACE_CONCAT(                             \
+      NLOHMANN_JSON_ABI_TAGS, NLOHMANN_JSON_NAMESPACE_VERSION) {
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_END
+#define NLOHMANN_JSON_NAMESPACE_END                                            \
+  } /* namespace (inline namespace) NOLINT(readability/namespace) */           \
+  } // namespace nlohmann
+#endif
+
+/*!
+@brief namespace for Niels Lohmann
+@see https://github.com/nlohmann
+@since version 1.0.0
+*/
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/*!
+@brief default JSONSerializer template argument
+
+This serializer ignores the template arguments and uses ADL
+([argument-dependent lookup](https://en.cppreference.com/w/cpp/language/adl))
+for serialization.
+*/
+template <typename T = void, typename SFINAE = void> struct adl_serializer;
+
+/// a class to store JSON values
+/// @sa https://json.nlohmann.me/api/basic_json/
+template <template <typename U, typename V, typename... Args> class ObjectType =
+          std::map,
+          template <typename U, typename... Args> class ArrayType = std::vector,
+          class StringType = std::string, class BooleanType = bool,
+          class NumberIntegerType = std::int64_t,
+          class NumberUnsignedType = std::uint64_t,
+          class NumberFloatType = double,
+          template <typename U> class AllocatorType = std::allocator,
+          template <typename T, typename SFINAE = void> class JSONSerializer =
+          adl_serializer,
+          class BinaryType =
+          std::vector<std::uint8_t>, // cppcheck-suppress syntaxError
+          class CustomBaseClass = void>
+class basic_json;
+
+/// @brief JSON Pointer defines a string syntax for identifying a specific value
+/// within a JSON document
+/// @sa https://json.nlohmann.me/api/json_pointer/
+template <typename RefStringType> class json_pointer;
+
+/*!
+@brief default specialization
+@sa https://json.nlohmann.me/api/json/
+*/
+using json = basic_json<>;
+
+/// @brief a minimal map-like container that preserves insertion order
+/// @sa https://json.nlohmann.me/api/ordered_map/
+template <class Key, class T, class IgnoredLess, class Allocator>
+struct ordered_map;
+
+/// @brief specialization that maintains the insertion order of object keys
+/// @sa https://json.nlohmann.me/api/ordered_json/
+using ordered_json = basic_json<nlohmann::ordered_map>;
+
+NLOHMANN_JSON_NAMESPACE_END
+
+#endif // INCLUDE_NLOHMANN_JSON_FWD_HPP_
@@ -179,7 +179,6 @@ set(SRCS
  hyperbolic.cpp
  integrator.cpp
  bounds.cpp
-  particleset.cpp
  )

 set(HDRS
@@ -309,7 +308,6 @@ set(HDRS
  hyperbolic.hpp
  integrator.hpp
  bounds.hpp
-  particleset.hpp
  )

 if (MFEM_USE_SIDRE)
@@ -825,46 +825,14 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
                                    Vector &b, OperatorHandle &A, Vector &X,
                                    Vector &B, int copy_interior)
 {
-   const SparseMatrix *P = fes->GetConformingProlongation();
-   const SparseMatrix *R = fes->GetConformingRestriction();
   if (ext)
   {
      if (hybridization)
      {
         FormSystemMatrix(ess_tdof_list, A);
-
-         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
-         {
-            Operator *op;
-            Operator::FormSystemOperator(ess_tdof_list, op);
-            return dynamic_cast<ConstrainedOperator*>(op);
-         }());
-         MFEM_ASSERT(A_constrained != nullptr, "");
-
-         Vector conf_b, conf_x;
-         if (P)
-         {
-            // Nonconforming
-            conf_b.SetSize(P->Width());
-            conf_x.SetSize(P->Width());
-            P->MultTranspose(b, conf_b);
-            R->Mult(x, conf_x);
-         }
-         else
-         {
-            // Conforming
-            conf_b.MakeRef(b, 0, b.Size());
-            conf_x.MakeRef(x, 0, x.Size());
-         }
-
-         A_constrained->EliminateRHS(conf_x, conf_b);
-
-         if (P)
-         {
-            R->MultTranspose(conf_b, b); // store eliminated rhs in b
-         }
-
-         hybridization->ReduceRHS(conf_b, B);
+         ConstrainedOperator A_constrained(this, ess_tdof_list);
+         A_constrained.EliminateRHS(x, b);
+         hybridization->ReduceRHS(b, B);
         X.SetSize(B.Size());
         X = 0.0;
      }
@@ -874,6 +842,7 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      }
      return;
   }
+   const SparseMatrix *P = fes->GetConformingProlongation();
   FormSystemMatrix(ess_tdof_list, A);

   // Transform the system and perform the elimination in B, based on the
@@ -909,6 +878,7 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      if (hybridization)
      {
         // Reduction to the Lagrange multipliers system
+         const SparseMatrix *R = fes->GetConformingRestriction();
         Vector conf_b(P->Width()), conf_x(P->Width());
         P->MultTranspose(b, conf_b);
         R->Mult(x, conf_x);
@@ -921,6 +891,7 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      else
      {
         // Variational restriction with P
+         const SparseMatrix *R = fes->GetConformingRestriction();
         B.SetSize(P->Width());
         P->MultTranspose(b, B);
         X.SetSize(R->Height());
@@ -207,8 +207,7 @@ void PLBound::Setup(const int nb_i, const int ncp_i,
   }
 }

-PLBound::PLBound(const FiniteElementSpace *fes, const int ncp_i,
-                 const int cp_type_i)
+PLBound::PLBound(FiniteElementSpace *fes, int ncp_i, int cp_type_i)
 {
   MFEM_VERIFY(!fes->IsVariableOrder(),
               "Variable order meshes not yet supported.");
@@ -265,8 +264,7 @@ PLBound::PLBound(const FiniteElementSpace *fes, const int ncp_i,
   Setup(nb, ncp, b_type, cp_type, tol);
 }

-void PLBound::Get1DBounds(const Vector &coeff, Vector &intmin,
-                          Vector &intmax) const
+void PLBound::Get1DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const
 {
   real_t x,w;
   intmin.SetSize(ncp);
@@ -348,8 +346,7 @@ void PLBound::Get1DBounds(const Vector &coeff, Vector &intmin,
   }
 }

-void PLBound::Get2DBounds(const Vector &coeff, Vector &intmin,
-                          Vector &intmax) const
+void PLBound::Get2DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const
 {
   intmin.SetSize(ncp*ncp);
   intmax.SetSize(ncp*ncp);
@@ -485,8 +482,7 @@ void PLBound::Get2DBounds(const Vector &coeff, Vector &intmin,
   }
 }

-void PLBound::Get3DBounds(const Vector &coeff, Vector &intmin,
-                          Vector &intmax) const
+void PLBound::Get3DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const
 {
   int nb2 = nb*nb,
       ncp2 = ncp*ncp,
@@ -628,7 +624,7 @@ void PLBound::Get3DBounds(const Vector &coeff, Vector &intmin,
   }
 }

-void PLBound::GetNDBounds(const int rdim, const Vector &coeff,
+void PLBound::GetNDBounds(int rdim, Vector &coeff,
                          Vector &intmin, Vector &intmax) const
 {
   if (rdim == 1)
@@ -9,8 +9,8 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.

-#ifndef MFEM_BOUNDS
-#define MFEM_BOUNDS
+#ifndef MFEM_BOUND
+#define MFEM_BOUND

 #include "../config/config.hpp"
 #include "fespace.hpp"
@@ -89,8 +89,7 @@ public:
   }

   // Constructor
-   PLBound(const FiniteElementSpace *fes,
-           const int ncp_i = -1, const int cp_type_i = 0);
+   PLBound(FiniteElementSpace *fes, int ncp_i = -1, int cp_type_i = 0);

   // Get minimum number of control points needed to bound the given bases
   int GetMinimumPointsForGivenBases(int nb_i, int b_type_i,
@@ -106,7 +105,7 @@ public:

   /// Compute piecewise linear bounds for the lexicographically-ordered
   /// coefficients in @a coeff in 1D/2D/3D.
-   void GetNDBounds(const int rdim, const Vector &coeff,
+   void GetNDBounds(int rdim, Vector &coeff,
                    Vector &intmin, Vector &intmax) const;

   /// Get number of control points used to compute the bounds.
@@ -114,15 +113,15 @@ public:
 private:
   /// Compute piecewise linear bounds for the lexicographically-ordered
   /// coefficients in @a coeff in 1D.
-   void Get1DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
+   void Get1DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const;

   /// Compute piecewise linear bounds for the lexicographically-ordered
   /// coefficients in @a coeff in 2D.
-   void Get2DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
+   void Get2DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const;

   /// Compute piecewise linear bounds for the lexicographically-ordered
   /// coefficients in @a coeff in 3D.
-   void Get3DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
+   void Get3DBounds(Vector &coeff, Vector &intmin, Vector &intmax) const;

   /// Setup matrix used to compute values at given 1D locations in [0,1]
   /// for Bernstein bases.
@@ -134,4 +133,4 @@ private:

 } // namespace mfem

-#endif // MFEM_BOUNDS
+#endif // MFEM_BOUND
@@ -1302,73 +1302,6 @@ real_t TraceCoefficient::Eval(ElementTransformation &T,
   return ma.Trace();
 }

-VectorComponentCoefficient::VectorComponentCoefficient(VectorCoefficient &A,
-                                                       int c)
-   : a(&A), va(A.GetVDim())
-{
-   SetComponent(c);
-}
-
-void VectorComponentCoefficient::SetComponent(int c)
-{
-   MFEM_ASSERT(c < a->GetVDim() && c >= 0,
-               "VectorComponentCoefficient:  "
-               "Index not in range.");
-
-   component = c;
-}
-
-void VectorComponentCoefficient::SetTime(real_t t)
-{
-   if (a) { a->SetTime(t); }
-   this->Coefficient::SetTime(t);
-}
-
-real_t VectorComponentCoefficient::Eval(ElementTransformation &T,
-                                        const IntegrationPoint &ip)
-{
-   a->Eval(va, T, ip);
-   return va[component];
-}
-
-MatrixComponentCoefficient::MatrixComponentCoefficient(MatrixCoefficient &A,
-                                                       int ri, int ci)
-   : a(&A), ma(A.GetHeight(), A.GetWidth())
-{
-   SetRowIndex(ri);
-   SetColumnIndex(ci);
-}
-
-void MatrixComponentCoefficient::SetRowIndex(int ri)
-{
-   MFEM_ASSERT(ri < a->GetHeight() && ri >= 0,
-               "MatrixComponentCoefficient:  "
-               "Row index not in range.");
-
-   row_idx = ri;
-}
-
-void MatrixComponentCoefficient::SetColumnIndex(int ci)
-{
-   MFEM_ASSERT(ci < a->GetWidth() && ci >= 0,
-               "MatrixComponentCoefficient:  "
-               "Column index not in range.");
-   col_idx = ci;
-}
-
-void MatrixComponentCoefficient::SetTime(real_t t)
-{
-   if (a) { a->SetTime(t); }
-   this->Coefficient::SetTime(t);
-}
-
-real_t MatrixComponentCoefficient::Eval(ElementTransformation &T,
-                                        const IntegrationPoint &ip)
-{
-   a->Eval(ma, T, ip);
-   return ma(row_idx,col_idx);
-}
-
 VectorSumCoefficient::VectorSumCoefficient(int dim)
   : VectorCoefficient(dim),
     ACoef(NULL), BCoef(NULL),
@@ -2094,7 +2027,7 @@ void CoefficientVector::Project(MatrixCoefficient &coeff, bool transpose)
 {
   if (auto *const_coeff = dynamic_cast<MatrixConstantCoefficient*>(&coeff))
   {
-      SetConstant(const_coeff->GetMatrix(), transpose);
+      SetConstant(const_coeff->GetMatrix());
   }
   else if (auto *const_sym_coeff =
               dynamic_cast<SymmetricMatrixConstantCoefficient*>(&coeff))
@@ -2155,7 +2088,7 @@ void CoefficientVector::SetConstant(const Vector &constant)
   }
 }

-void CoefficientVector::SetConstant(const DenseMatrix &constant, bool transpose)
+void CoefficientVector::SetConstant(const DenseMatrix &constant)
 {
   const int nq = (storage & CoefficientStorage::CONSTANTS) ? 1 : qs.GetSize();
   const int width = constant.Width();
@@ -2168,8 +2101,7 @@ void CoefficientVector::SetConstant(const DenseMatrix &constant, bool transpose)
      {
         for (int i = 0; i < height; ++i)
         {
-            const real_t val = transpose ? constant(j,i) : constant(i,j);
-            (*this)[i + j*height + iq*vdim] = val;
+            (*this)[i + j*height + iq*vdim] = constant(i, j);
         }
      }
   }
@@ -114,10 +114,11 @@ public:
   /// Construct the constant coefficient using a vector of constants.
   /** @a c should be a vector defined by attributes, so for region with
       attribute @a i @a c[i-1] is the coefficient in that region */
-   PWConstCoefficient(const Vector &c) { UpdateConstants(c); }
+   PWConstCoefficient(Vector &c)
+   { constants.SetSize(c.Size()); constants=c; }

   /// Update the constants with vector @a c.
-   void UpdateConstants(const Vector &c) { constants = c; }
+   void UpdateConstants(Vector &c) { constants.SetSize(c.Size()); constants=c; }

   /// Return a reference to the i-th constant
   real_t &operator()(int i) { return constants(i-1); }
@@ -1331,8 +1332,8 @@ public:
   /// Get the coefficient located at (i,j) in the matrix.
   Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }

-   /** @brief Set the coefficient located at (i,j) in the matrix.  By default
-       this will take ownership of the Coefficient passed in, but this
+   /** @brief Set the coefficient located at (i,j) in the matrix.  By default by
+       default this will take ownership of the Coefficient passed in, but this
       can be overridden with the @a own parameter. */
   void Set(int i, int j, Coefficient * c, bool own=true);

@@ -1872,85 +1873,6 @@ public:
               const IntegrationPoint &ip) override;
 };

-/// Scalar coefficient defined as component of a vector coefficient
-class VectorComponentCoefficient : public Coefficient
-{
-private:
-   VectorCoefficient *a = nullptr;
-
-   mutable Vector va;
-   int component;
-
-public:
-   /// Construct with a vector coefficient.
-   VectorComponentCoefficient(VectorCoefficient &A)
-      : a(&A), va(A.GetVDim()), component(0) {};
-
-   VectorComponentCoefficient(VectorCoefficient &A, int c);
-
-   /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
-
-   /// Reset the vector coefficient
-   void SetACoef(VectorCoefficient &A) { a = &A; }
-
-   /// Return the vector coefficient
-   VectorCoefficient * GetACoef() const { return a; }
-
-   /// Set the component
-   void SetComponent(int c);
-
-   /// Return the component
-   int GetComponent() const { return component; }
-
-   /// Evaluate the trace coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
-};
-
-/// Scalar coefficient defined as component of a matrix coefficient
-class MatrixComponentCoefficient : public Coefficient
-{
-private:
-   MatrixCoefficient *a = nullptr;
-
-   mutable DenseMatrix ma;
-   int row_idx,col_idx;
-
-public:
-   MatrixComponentCoefficient(MatrixCoefficient &A)
-      : a(&A), ma(A.GetHeight(), A.GetWidth()), row_idx(0), col_idx(0) {};
-
-   /// Construct with the matrix coefficient.
-   MatrixComponentCoefficient(MatrixCoefficient &A, int ri, int ci);
-
-   /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
-
-   /// Reset the matrix coefficient
-   void SetACoef(MatrixCoefficient &A) { a = &A; }
-
-   /// Return the matrix coefficient
-   MatrixCoefficient * GetACoef() const { return a; }
-
-   /// Reset the index
-   void SetRowIndex(int ri);
-
-   /// Return the index
-   int GetRowIndex() const { return row_idx; }
-
-   /// Reset the index
-   void SetColumnIndex(int ci);
-
-   /// Return the index
-   int GetColumnIndex() const { return col_idx; }
-
-
-   /// Evaluate the trace coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
-};
-
 /// Vector coefficient defined as the linear combination of two vectors
 class VectorSumCoefficient : public VectorCoefficient
 {
@@ -2598,7 +2520,7 @@ public:
   void SetConstant(const Vector &constant);

   /// Set this vector to the given constant matrix.
-   void SetConstant(const DenseMatrix &constant, bool transpose=false);
+   void SetConstant(const DenseMatrix &constant);

   /// Set this vector to the given constant symmetric matrix.
   void SetConstant(const DenseSymmetricMatrix &constant);
@@ -70,8 +70,8 @@ ConduitDataCollection::~ConduitDataCollection()
 void ConduitDataCollection::Save()
 {
   std::string dir_name = MeshDirectoryName();
-   int err_ = create_directory(dir_name, mesh, myid);
-   if (err_)
+   int err = create_directory(dir_name, mesh, myid);
+   if (err)
   {
      MFEM_ABORT("Error creating directory: " << dir_name);
   }
@@ -88,7 +88,6 @@ void ConduitDataCollection::Save()
                 << verify_info.to_json());
   }

-   // wrap all grid functions
   FieldMapConstIterator itr;
   for ( itr = field_map.begin(); itr != field_map.end(); itr++)
   {
@@ -104,16 +103,6 @@ void ConduitDataCollection::Save()
      }
   }

-   // wrap all quadrature functions
-   QFieldMapConstIterator qf_itr;
-   for ( qf_itr = q_field_map.begin(); qf_itr != q_field_map.end(); qf_itr++)
-   {
-      std::string name = qf_itr->first;
-      QuadratureFunction *qf = qf_itr->second;
-      QuadratureFunctionToBlueprintField(qf,
-                                         n_mesh["fields"][name]);
-   }
-
   // save mesh data
   SaveMeshAndFields(myid,
                     n_mesh,
@@ -168,16 +157,6 @@ ConduitDataCollection::SetProtocol(const std::string &protocol)
   relay_protocol = protocol;
 }

-// Conduit data type id for the MFEM precision
-constexpr conduit::index_t mfem_precision_conduit_id =
-#if defined(MFEM_USE_DOUBLE)
-   CONDUIT_NATIVE_DOUBLE_ID;
-#elif defined(MFEM_USE_SINGLE)
-   CONDUIT_NATIVE_FLOAT_ID;
-#else
-#error Unknown MFEM precision
-#endif
-
 //------------------------------
 // begin static public methods
 //------------------------------
@@ -227,41 +206,42 @@ ConduitDataCollection::BlueprintMeshToMesh(const Node &n_mesh,
   // get the number of points
   int num_verts = n_coordset_vals[0].dtype().number_of_elements();
   // get vals for points
-   const real_t *verts_ptr = NULL;
+   const double *verts_ptr = NULL;

   // the mfem mesh constructor needs coords with interleaved (aos) type
-   // ordering, even for 1d + 2d we always need 3 real_t (double/float) b/c it
-   // uses Array<Vertex> and Vertex is a pod of 3 real_t. we check for this
+   // ordering, even for 1d + 2d we always need 3 doubles b/c it uses
+   // Array<Vertex> and Vertex is a pod of 3 doubles. we check for this
   // case, if we don't have it we convert the data

   if (ndims == 3 &&
-       n_coordset_vals[0].dtype().id() == mfem_precision_conduit_id &&
+       n_coordset_vals[0].dtype().is_double() &&
       blueprint::mcarray::is_interleaved(n_coordset_vals) )
   {
-      // already interleaved mcarray of 3 real_t (double/float),
+      // already interleaved mcarray of 3 doubles,
      // return ptr to beginning
      verts_ptr = n_coordset_vals[0].value();
   }
   else
   {
      Node n_tmp;
-      // check all vals, if we don't have real_t (double/float) convert
-      // to real_t
+      // check all vals, if we don't have doubles convert
+      // to doubles
      NodeConstIterator itr = n_coordset_vals.children();
      while (itr.has_next())
      {
         const Node &c_vals = itr.next();
         std::string c_name = itr.name();

-         if ( c_vals.dtype().id() == mfem_precision_conduit_id )
+         if ( c_vals.dtype().is_double() )
         {
            // zero copy current coords
            n_tmp[c_name].set_external(c_vals);
+
         }
         else
         {
            // convert
-            c_vals.to_data_type(mfem_precision_conduit_id, n_tmp[c_name]);
+            c_vals.to_double_array(n_tmp[c_name]);
         }
      }

@@ -270,13 +250,13 @@ ConduitDataCollection::BlueprintMeshToMesh(const Node &n_mesh,
      if (ndims < 3)
      {
         // add dummy z
-         n_tmp["z"].set(DataType(mfem_precision_conduit_id, num_verts));
+         n_tmp["z"].set(DataType::c_double(num_verts));
      }

      if (ndims < 2)
      {
         // add dummy y
-         n_tmp["y"].set(DataType(mfem_precision_conduit_id, num_verts));
+         n_tmp["y"].set(DataType::c_double(num_verts));
      }

      Node &n_conv_coords_vals = n_conv["coordsets"][coords_name]["values"];
@@ -472,7 +452,7 @@ ConduitDataCollection::BlueprintMeshToMesh(const Node &n_mesh,
   //       if nodes gf is attached later, it resets the space dim based
   //       on the gf's fes.
   Mesh *mesh = new Mesh(// from coordset
-      const_cast<real_t*>(verts_ptr),
+      const_cast<double*>(verts_ptr),
      num_verts,
      // from topology
      const_cast<int*>(elem_indices),
@@ -539,7 +519,7 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,
   // can't return a gf that zero copies the conduit data
   Node n_conv;

-   const real_t *vals_ptr = NULL;
+   const double *vals_ptr = NULL;

   int vdim = 1;

@@ -549,10 +529,10 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,
   {
      vdim = n_field["values"].number_of_children();

-      // need to check that we have real_t (double/float) and
+      // need to check that we have doubles and
      // cover supported layouts

-      if ( n_field["values"][0].dtype().id() == mfem_precision_conduit_id )
+      if ( n_field["values"][0].dtype().is_double() )
      {
         // check for contig
         if (n_field["values"].is_contiguous())
@@ -576,26 +556,27 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,
            vals_ptr = n_conv["values"].child(0).value();
         }
      }
-      else // convert to real_t (double/float) and use contig
+      else // convert to doubles and use contig
      {
         Node n_tmp;
-         // check all vals, if we don't have real_t (double/float) convert
-         // to real_t
+         // check all vals, if we don't have doubles convert
+         // to doubles
         NodeConstIterator itr = n_field["values"].children();
         while (itr.has_next())
         {
            const Node &c_vals = itr.next();
            std::string c_name = itr.name();

-            if ( c_vals.dtype().id() == mfem_precision_conduit_id )
+            if ( c_vals.dtype().is_double() )
            {
               // zero copy current coords
               n_tmp[c_name].set_external(c_vals);
+
            }
            else
            {
               // convert
-               c_vals.to_data_type(mfem_precision_conduit_id, n_tmp[c_name]);
+               c_vals.to_double_array(n_tmp[c_name]);
            }
         }

@@ -608,15 +589,14 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,
   }
   else
   {
-      if (n_field["values"].dtype().id() == mfem_precision_conduit_id &&
+      if (n_field["values"].dtype().is_double() &&
          n_field["values"].is_compact())
      {
         vals_ptr = n_field["values"].value();
      }
      else
      {
-         n_field["values"].to_data_type(mfem_precision_conduit_id,
-                                        n_conv["values"]);
+         n_field["values"].to_double_array(n_conv["values"]);
         vals_ptr = n_conv["values"].value();
      }
   }
@@ -640,14 +620,14 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,

   if (zero_copy)
   {
-      res = new GridFunction(fes,const_cast<real_t*>(vals_ptr));
+      res = new GridFunction(fes,const_cast<double*>(vals_ptr));
   }
   else
   {
      // copy case, this constructor will alloc the space for the GF data
      res = new GridFunction(fes);
      // create an mfem vector that wraps the conduit data
-      Vector vals_vec(const_cast<real_t*>(vals_ptr),fes->GetVSize());
+      Vector vals_vec(const_cast<double*>(vals_ptr),fes->GetVSize());
      // copy values into the result
      (*res) = vals_vec;
   }
@@ -659,155 +639,6 @@ ConduitDataCollection::BlueprintFieldToGridFunction(Mesh *mesh,
   return res;
 }

-//---------------------------------------------------------------------------//
-mfem::QuadratureFunction *
-ConduitDataCollection::BlueprintFieldToQuadratureFunction(Mesh *mesh,
-                                                          const Node &n_field,
-                                                          bool zero_copy)
-{
-   // n_conv holds converted data (when necessary for mfem api)
-   // if n_conv is used ( !n_conv.dtype().empty() ) we
-   // know that some data allocation was necessary, so we
-   // can't return a qf that zero copies the conduit data
-   Node n_conv;
-
-   const real_t *vals_ptr = NULL;
-   int vdim = 1;
-
-   if (n_field["values"].dtype().is_object())
-   {
-      vdim = n_field["values"].number_of_children();
-
-      // need to check that we have real_t (double/float) and
-      // cover supported layouts
-      if ( n_field["values"][0].dtype().id() == mfem_precision_conduit_id )
-      {
-         // quad funcs use what mfem calls byVDIM
-         // and what conduit calls interleaved
-         // check for interleaved
-         if (blueprint::mcarray::is_interleaved(n_field["values"]))
-         {
-            // conduit mcarray interleaved == mfem byVDIM
-            vals_ptr = n_field["values"].child(0).value();
-         }
-         else
-         {
-            // for mcarray generic case --  default to byVDIM
-            // aka interleaved
-            blueprint::mcarray::to_interleaved(n_field["values"],
-                                               n_conv["values"]);
-            vals_ptr = n_conv["values"].child(0).value();
-         }
-      }
-      else // convert to real_t (double/float) and use interleaved
-      {
-         Node n_tmp;
-         // check all vals, if we don't have real_t (double/float) convert
-         // to real_t
-         NodeConstIterator itr = n_field["values"].children();
-         while (itr.has_next())
-         {
-            const Node &c_vals = itr.next();
-            std::string c_name = itr.name();
-
-            if ( c_vals.dtype().id() == mfem_precision_conduit_id )
-            {
-               // zero copy current coords
-               n_tmp[c_name].set_external(c_vals);
-            }
-            else
-            {
-               // convert
-               c_vals.to_data_type(mfem_precision_conduit_id, n_tmp[c_name]);
-            }
-         }
-
-         // for mcarray generic case --  default to byVDIM
-         // aka interleaved
-         blueprint::mcarray::to_interleaved(n_tmp,
-                                            n_conv["values"]);
-         vals_ptr = n_conv["values"].child(0).value();
-      }
-   }
-   else // scalar case
-   {
-      if (n_field["values"].dtype().id() == mfem_precision_conduit_id &&
-          n_field["values"].is_compact())
-      {
-         vals_ptr = n_field["values"].value();
-      }
-      else
-      {
-         n_field["values"].to_data_type(mfem_precision_conduit_id,
-                                        n_conv["values"]);
-         vals_ptr = n_conv["values"].value();
-      }
-   }
-
-   if (zero_copy && !n_conv.dtype().is_empty())
-   {
-      //Info: "Cannot zero-copy since data conversions were necessary"
-      zero_copy = false;
-   }
-
-   // we need basis name to create the proper mfem quad space and quad func
-   // the pattern used to encode the quad space params is:
-   // QF_{ORDER}_{VDIM}
-   // ORDER is the degree of the polynomials for the quad rule
-   // VDIM  is the number of components at each quad point (scalar, vector, etc)
-
-   int qf_order = 0;
-   int qf_vdim  = 0;
-   std::string qf_name = n_field["basis"].as_string();
-   const char *qf_name_cstr = qf_name.c_str();
-   if (!strncmp(qf_name_cstr, "QF_", 3))
-   {
-      // parse {ORDER}
-      qf_order = atoi(qf_name_cstr + 3);
-      // find second `_`
-      const char *qf_vdim_cstr = strstr(qf_name_cstr+3,"_");
-      if (qf_vdim_cstr == NULL)
-      {
-         MFEM_ABORT("Error parsing quadrature function description string: "
-                    << qf_name << std::endl
-                    << "Expected: QF_{ORDER}_{VDIM}");
-      }
-      // parse {VDIM}
-      qf_vdim  = atoi(qf_vdim_cstr+1);
-   }
-   else
-   {
-      MFEM_ABORT("Error parsing quadrature function description string: "
-                 << qf_name << std::endl
-                 << "Expected: QF_{ORDER}_{VDIM}");
-   }
-   MFEM_VERIFY(qf_vdim == vdim, "vector dimension mismatch: vdim = " << vdim
-               << ", qf_vdim = " << qf_vdim);
-
-   mfem::QuadratureSpace *quad_space = new mfem::QuadratureSpace(mesh, qf_order);
-   mfem::QuadratureFunction *res = new mfem::QuadratureFunction();
-
-   if (zero_copy)
-   {
-      res->SetSpace(quad_space, const_cast<real_t*>(vals_ptr), vdim);
-      res->SetOwnsSpace(true);
-   }
-   else
-   {
-      res->SetSpace(quad_space, vdim);
-      res->SetOwnsSpace(true);
-      // copy case, this constructor will alloc the space for the quad data
-      // create an mfem vector that wraps the conduit data
-      Vector vals_vec(const_cast<real_t*>(vals_ptr),res->Size());
-      // copy values into the result
-      (*res) = vals_vec;
-   }
-
-   return res;
-}
-
-
-
 //---------------------------------------------------------------------------//
 void
 ConduitDataCollection::MeshToBlueprintMesh(Mesh *mesh,
@@ -825,20 +656,20 @@ ConduitDataCollection::MeshToBlueprintMesh(Mesh *mesh,
   // Setup main coordset
   ////////////////////////////////////////////

-   // Assumes  mfem::Vertex has the layout of a real_t (double/float) array.
+   // Assumes  mfem::Vertex has the layout of a double array.

-   // this logic assumes an mfem vertex is always 3 real_t (double/float) wide
+   // this logic assumes an mfem vertex is always 3 doubles wide
   int stride = sizeof(mfem::Vertex);
   int num_vertices = mesh->GetNV();

-   MFEM_ASSERT( ( stride == 3 * sizeof(real_t) ),
+   MFEM_ASSERT( ( stride == 3 * sizeof(double) ),
                "Unexpected stride for Vertex");

   Node &n_mesh_coords = n_mesh["coordsets"][coordset_name];
   n_mesh_coords["type"] =  "explicit";


-   real_t *coords_ptr = mesh->GetVertex(0);
+   double *coords_ptr = mesh->GetVertex(0);

   n_mesh_coords["values/x"].set_external(coords_ptr,
                                          num_vertices,
@@ -849,14 +680,14 @@ ConduitDataCollection::MeshToBlueprintMesh(Mesh *mesh,
   {
      n_mesh_coords["values/y"].set_external(coords_ptr,
                                             num_vertices,
-                                             sizeof(real_t),
+                                             sizeof(double),
                                             stride);
   }
   if (dim >= 3)
   {
      n_mesh_coords["values/z"].set_external(coords_ptr,
                                             num_vertices,
-                                             sizeof(real_t) * 2,
+                                             sizeof(double) * 2,
                                             stride);
   }

@@ -1111,59 +942,6 @@ ConduitDataCollection::GridFunctionToBlueprintField(mfem::GridFunction *gf,

 }

-//---------------------------------------------------------------------------//
-void
-ConduitDataCollection::QuadratureFunctionToBlueprintField(
-   mfem::QuadratureFunction *qf,
-   Node &n_field,
-   const std::string &main_topology_name)
-{
-   // For quadrature functions, use basis pattern:
-   //   QF_{ORDER}_{VDIM}
-
-   int qf_vdim  = qf->GetVDim();
-   int qf_order = qf->GetSpace()->GetOrder();
-   int qf_size  = qf->GetSpace()->GetSize();
-
-   {
-      std::ostringstream oss;
-      oss << "QF_" << qf_order << "_" << qf_vdim;
-
-      n_field["basis"] = oss.str();
-      n_field["topology"] = main_topology_name;
-   }
-
-   if (qf_vdim == 1) // scalar case
-   {
-      n_field["values"].set_external(const_cast<real_t *>(qf->HostRead()),
-                                     qf_size);
-   }
-   else // vector case
-   {
-      // deal with striding of all components
-      // quadrature functions are always byVDIM
-      // or what conduit calls interleaved
-
-      index_t offset = 0;
-      index_t stride = sizeof(real_t) * qf_vdim;
-
-      for (int d = 0;  d < qf_vdim; d++)
-      {
-         std::ostringstream oss;
-         oss << "v" << d;
-         std::string comp_name = oss.str();
-         n_field["values"][comp_name].set_external(const_cast<real_t *>(qf->HostRead()),
-                                                   qf_size,
-                                                   offset,
-                                                   stride);
-         offset += sizeof(real_t);
-      }
-   }
-
-}
-
-
-
 //------------------------------
 // end static public methods
 //------------------------------
@@ -1189,7 +967,7 @@ ConduitDataCollection::RootFileName()
 //---------------------------------------------------------------------------//
 std::string
 ConduitDataCollection::MeshFileName(int domain_id,
-                                    const std::string &relay_protocol_)
+                                    const std::string &relay_protocol)
 {
   std::string res = prefix_path +
                     name  +
@@ -1198,7 +976,7 @@ ConduitDataCollection::MeshFileName(int domain_id,
                     "/domain_" +
                     to_padded_string(domain_id, pad_digits_rank) +
                     "." +
-                     relay_protocol_;
+                     relay_protocol;

   return res;
 }
@@ -1216,7 +994,7 @@ ConduitDataCollection::MeshDirectoryName()

 //---------------------------------------------------------------------------//
 std::string
-ConduitDataCollection::MeshFilePattern(const std::string &relay_protocol_)
+ConduitDataCollection::MeshFilePattern(const std::string &relay_protocol)
 {
   std::ostringstream oss;
   oss << name
@@ -1225,7 +1003,7 @@ ConduitDataCollection::MeshFilePattern(const std::string &relay_protocol_)
       << "/domain_%0"
       << pad_digits_rank
       << "d."
-       << relay_protocol_;
+       << relay_protocol;

   return oss.str();
 }
@@ -1235,14 +1013,14 @@ ConduitDataCollection::MeshFilePattern(const std::string &relay_protocol_)
 void
 ConduitDataCollection::SaveRootFile(int num_domains,
                                    const Node &n_mesh,
-                                    const std::string &relay_protocol_)
+                                    const std::string &relay_protocol)
 {
   // default to json root file, except for hdf5 case
   std::string root_proto = "json";

-   if (relay_protocol_ == "hdf5")
+   if (relay_protocol == "hdf5")
   {
-      root_proto = relay_protocol_;
+      root_proto = relay_protocol;
   }

   Node n_root;
@@ -1273,14 +1051,14 @@ ConduitDataCollection::SaveRootFile(int num_domains,
      }
   }
   // add extra header info
-   n_root["protocol/name"]    =  relay_protocol_;
+   n_root["protocol/name"]    =  relay_protocol;
   n_root["protocol/version"] = "0.3.1";


   // we will save one file per domain, so trees == files
   n_root["number_of_files"]  = num_domains;
   n_root["number_of_trees"]  = num_domains;
-   n_root["file_pattern"]     = MeshFilePattern(relay_protocol_);
+   n_root["file_pattern"]     = MeshFilePattern(relay_protocol);
   n_root["tree_pattern"]     = "";

   // Add the time, time step, and cycle
@@ -1295,9 +1073,9 @@ ConduitDataCollection::SaveRootFile(int num_domains,
 void
 ConduitDataCollection::SaveMeshAndFields(int domain_id,
                                         const Node &n_mesh,
-                                         const std::string &relay_protocol_)
+                                         const std::string &relay_protocol)
 {
-   relay::io::save(n_mesh, MeshFileName(domain_id, relay_protocol_));
+   relay::io::save(n_mesh, MeshFileName(domain_id, relay_protocol));
 }

 //---------------------------------------------------------------------------//
@@ -1394,13 +1172,13 @@ ConduitDataCollection::LoadRootFile(Node &root_out)
 //---------------------------------------------------------------------------//
 void
 ConduitDataCollection::LoadMeshAndFields(int domain_id,
-                                         const std::string &relay_protocol_)
+                                         const std::string &relay_protocol)
 {
   // Note: This path doesn't use any info from the root file
   // it uses the implicit mfem ConduitDataCollection layout

   Node n_mesh;
-   relay::io::load( MeshFileName(domain_id, relay_protocol_), n_mesh);
+   relay::io::load( MeshFileName(domain_id, relay_protocol), n_mesh);


   Node verify_info;
@@ -50,11 +50,11 @@ namespace mfem
    Those that construct MFEM objects from Conduit Nodes (Conduit Blueprint to
    MFEM) provide a zero-copy option. Zero-copy is only possible if the
    blueprint data matches the data types provided by the MFEM API, for example:
-    ints for connectivity arrays, real_t (double/float) for field value arrays,
-    allocations that match MFEM's striding options, etc. If these constraints
-    are not met, MFEM objects that own the data are created and returned. In
-    either case pointers to new MFEM object instances are returned, the
-    zero-copy only applies to data backing the MFEM object instances.
+    ints for connectivity arrays, doubles for field value arrays, allocations
+    that match MFEM's striding options, etc. If these constraints are not met,
+    MFEM objects that own the data are created and returned. In either case
+    pointers to new MFEM object instances are returned, the zero-copy only
+    applies to data backing the MFEM object instances.

    @note QuadratureFunction%s (q-fields) are not supported.

@@ -183,21 +183,6 @@ public:
                                            conduit::Node &out,
                                            const std::string &main_topology_name = "main");

-   /// Describes a MFEM quadrature function using the mesh blueprint
-   /** Sets up passed conduit::Node out to describe the given quadrature function
-       using the mesh field blueprint.
-
-       Zero-copies as much data as possible.
-
-       @a main_toplogy_name is used to set the associated topology name.
-       With the default setting, the resulting field is associated with the
-       topology `main`.
-   */
-   static void QuadratureFunctionToBlueprintField(QuadratureFunction *qf,
-                                                  conduit::Node &out,
-                                                  const std::string &main_topology_name = "main");
-
-
   /// Constructs and MFEM mesh from a Conduit Blueprint Description
   /** @a main_topology_name is used to select which topology to use, when
       empty ("") the first topology entry will be used.
@@ -205,7 +190,7 @@ public:
       If zero_copy == true, tries to construct a mesh that points to the data
       described by the conduit node. This is only possible if the data in the
       node matches the data types needed for the MFEM API (ints for
-       connectivity, real_t for field values, etc). If these constraints are
+       connectivity, doubles for field values, etc). If these constraints are
       not met, a mesh that owns the data is created and returned.
   */
   static Mesh *BlueprintMeshToMesh(const conduit::Node &n_mesh,
@@ -215,7 +200,7 @@ public:
   /// Constructs and MFEM Grid Function from a Conduit Blueprint Description
   /** If zero_copy == true, tries to construct a grid function that points to
       the data described by the conduit node. This is only possible if the data
-       in the node matches the data types needed for the MFEM API (real_t for
+       in the node matches the data types needed for the MFEM API (doubles for
       field values, allocated in soa or aos ordering, etc).  If these
       constraints are not met, a grid function that owns the data is created
       and returned.
@@ -223,17 +208,6 @@ public:
   static GridFunction *BlueprintFieldToGridFunction(Mesh *mesh,
                                                     const conduit::Node &n_field,
                                                     bool zero_copy = false);
-   /// Constructs and MFEM Quadrature Function from a Conduit Blueprint Description
-   /** If zero_copy == true, tries to construct a quadrature function that points to
-       the data described by the conduit node. This is only possible if the data
-       in the node matches the data types needed for the MFEM API (real_t for
-       field values, allocated in an interleavred/byVDIM order, etc). If these
-       constraints are not met, a grid function that owns the data is created
-       and returned.
-   */
-   static QuadratureFunction *BlueprintFieldToQuadratureFunction(Mesh *mesh,
-                                                                 const conduit::Node &n_field,
-                                                                 bool zero_copy = false);

 private:
   /// Converts from MFEM element type enum to mesh bp shape name
@@ -430,9 +430,7 @@ void VisItDataCollection::RegisterField(const std::string& name,
   }

   DataCollection::RegisterField(name, gf);
-   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim(), LOD,
-                                         gf->FESpace()->FEColl()->Name(),
-                                         gf->FESpace()->FEColl()->GetOrder());
+   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim(), LOD);
   visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
 }

@@ -451,14 +449,7 @@ void VisItDataCollection::RegisterQField(const std::string& name,
   }

   DataCollection::RegisterQField(name, qf);
-   // For quadrature functions, use basis pattern:
-   //   QF_{ORDER}_{VDIM}
-   int qf_vdim  = qf->GetVDim();
-   int qf_order = qf->GetSpace()->GetOrder();
-   std::ostringstream oss;
-   oss << "QF_" << qf_order << "_" << qf_vdim;
-   field_info_map[name] = VisItFieldInfo("quadrature", qf->GetVDim(), LOD,
-                                         oss.str(), qf_order);
+   field_info_map[name] = VisItFieldInfo("elements", 1, LOD);
   visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
 }

@@ -632,8 +623,7 @@ void VisItDataCollection::LoadFields()
         {
            field_map.Register(it->first, new GridFunction(mesh, file), own_data);
         }
-         else if ((it->second).association == "elements" || // old style
-                  (it->second).association == "quadrature") // new style
+         else if ((it->second).association == "elements")
         {
            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
         }
@@ -647,8 +637,7 @@ void VisItDataCollection::LoadFields()
               it->first,
               new ParGridFunction(dynamic_cast<ParMesh*>(mesh), file), own_data);
         }
-         else if ((it->second).association == "elements" || // old style
-                  (it->second).association == "quadrature") // new style
+         else if ((it->second).association == "elements")
         {
            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
         }
@@ -687,8 +676,6 @@ std::string VisItDataCollection::GetVisItRootString()
      ftags["assoc"] = picojson::value((it->second).association);
      ftags["comps"] = picojson::value(to_string((it->second).num_components));
      ftags["lod"] = picojson::value(to_string((it->second).lod));
-      ftags["basis"] = picojson::value((it->second).basis);
-      ftags["order"] = picojson::value(to_string((it->second).order));
      field["path"] = picojson::value(path_str + it->first + file_ext_format);
      field["tags"] = picojson::value(ftags);
      fields[it->first] = picojson::value(field);
@@ -765,31 +752,9 @@ void VisItDataCollection::ParseVisItRootString(const std::string& json)
           it != fields_obj.end(); ++it)
      {
         picojson::value tags = it->second.get("tags");
-
-         // defaults that allow us to parse older mfem_root files
-         int lod = 1;
-         std::string basis = "";
-         int order = -1;
-
-         if (tags.contains("lod"))
-         {
-            lod = to_int(tags.get("lod").get<std::string>());
-         }
-
-         if (tags.contains("basis"))
-         {
-            basis = tags.get("comps").get<std::string>();
-         }
-
-         if (tags.contains("order"))
-         {
-            order = to_int(tags.get("comps").get<std::string>());
-         }
-
         field_info_map[it->first] =
            VisItFieldInfo(tags.get("assoc").get<std::string>(),
-                           to_int(tags.get("comps").get<std::string>()),
-                           lod, basis, order);
+                           to_int(tags.get("comps").get<std::string>()));
      }
   }
 }
@@ -408,18 +408,12 @@ public:
 class VisItFieldInfo
 {
 public:
-   std::string association = "";
-   int num_components = 0;
-   int lod = 1;
-   std::string basis = "";
-   int order = -1;
-   VisItFieldInfo() = default;
-   VisItFieldInfo(std::string association_, int num_components_, int lod_ = 1,
-                  std::string basis_ = "", int order_ = -1)
-   {
-      association = association_; num_components = num_components_; lod =lod_;
-      basis = basis_; order = order_;
-   }
+   std::string association;
+   int num_components;
+   int lod;
+   VisItFieldInfo() { association = ""; num_components = 0; lod = 1;}
+   VisItFieldInfo(std::string association_, int num_components_, int lod_ = 1)
+   { association = association_; num_components = num_components_; lod =lod_;}
 };

 /// Data collection with VisIt I/O routines
@@ -1,403 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-#pragma once
-
-#include "util.hpp"
-
-namespace mfem::future
-{
-
-/// @brief Assemble element matrix for three dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_t3d(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& q1d,
-   const int& td1d)
-{
-   constexpr int dimension = 3;
-
-   // [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, num_qp]
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-
-   // [num_test_dof, ...]
-   const auto num_test_dof = A.GetShape()[0];
-
-   for (int Jx = 0; Jx < td1d; Jx++)
-   {
-      for (int Jy = 0; Jy < td1d; Jy++)
-      {
-         for (int Jz = 0; Jz < td1d; Jz++)
-         {
-            const int J = Jx + td1d * (Jy + td1d * Jz);
-
-            for (int j = 0; j < trial_vdim; j++)
-            {
-               for (int tv = 0; tv < test_vdim; tv++)
-               {
-                  for (int tod = 0; tod < test_op_dim; tod++)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-                              fhat(tv, tod, q) = 0.0;
-                           }
-                        }
-                     }
-                  }
-               }
-
-               // MSVC lambda capture workaround
-               [[maybe_unused]] const auto& inputs_ref = inputs;
-
-               int m_offset = 0;
-               for_constexpr<num_inputs>([&](auto s)
-               {
-                  using fop_t = std::decay_t<decltype(get<s>(inputs_ref))>;
-
-                  const int trial_op_dim = static_cast<int>(itod(static_cast<int>(s)));
-                  if (trial_op_dim == 0)
-                  {
-                     // This is inside a lambda so we have to return
-                     // instead of idiomatic 'continue'.
-                     return;
-                  }
-
-                  auto& B = input_dtqmaps[s].B;
-                  auto& G = input_dtqmaps[s].G;
-
-                  if constexpr (is_value_fop<fop_t>::value)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-
-                              for (int m = 0; m < trial_op_dim; m++)
-                              {
-                                 for (int i = 0; i < test_vdim; i++)
-                                 {
-                                    for (int k = 0; k < test_op_dim; k++)
-                                    {
-                                       const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                       fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy) * B(qz, 0, Jz);
-                                    }
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-                  else if constexpr (is_gradient_fop<fop_t>::value)
-                  {
-                     MFEM_FOREACH_THREAD(qx, x, q1d)
-                     {
-                        MFEM_FOREACH_THREAD(qy, y, q1d)
-                        {
-                           MFEM_FOREACH_THREAD(qz, z, q1d)
-                           {
-                              const int q = qx + q1d * (qy + q1d * qz);
-                              for (int m = 0; m < trial_op_dim; m++)
-                              {
-                                 for (int i = 0; i < test_vdim; i++)
-                                 {
-                                    for (int k = 0; k < test_op_dim; k++)
-                                    {
-                                       const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                       if (m == 0)
-                                       {
-                                          fhat(i, k, q) += f * G(qx, 0, Jx) * B(qy, 0, Jy) * B(qz, 0, Jz);
-                                       }
-                                       else if (m == 1)
-                                       {
-                                          fhat(i, k, q) += f * B(qx, 0, Jx) * G(qy, 0, Jy) * B(qz, 0, Jz);
-                                       }
-                                       else if (m == 2)
-                                       {
-                                          fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy) * G(qz, 0, Jz);
-                                       }
-                                    }
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-                  else
-                  {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-                     MFEM_ABORT("sum factorized sparse matrix assemble routine "
-                                "not implemented for field operator");
-#endif
-                  }
-                  MFEM_SYNC_THREAD;
-                  m_offset += trial_op_dim;
-               });
-
-               auto bvtfhat = Reshape(&A(0, 0, J, j), num_test_dof, test_vdim);
-               map_quadrature_data_to_fields(bvtfhat, fhat, output, output_dtqmap,
-                                             scratch_shmem, dimension, true);
-            }
-         }
-      }
-   }
-}
-
-/// @brief Assemble element matrix for two dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_t2d(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& q1d,
-   const int& td1d)
-{
-   constexpr int dimension = 2;
-
-   // [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, num_qp]
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-
-   // [num_test_dof, ...]
-   const auto num_test_dof = A.GetShape()[0];
-
-   for (int Jx = 0; Jx < td1d; Jx++)
-   {
-      for (int Jy = 0; Jy < td1d; Jy++)
-      {
-         const int J = Jy + Jx * td1d;
-
-         for (int j = 0; j < trial_vdim; j++)
-         {
-            for (int tv = 0; tv < test_vdim; tv++)
-            {
-               for (int tod = 0; tod < test_op_dim; tod++)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        fhat(tv, tod, q) = 0.0;
-                     }
-                  }
-               }
-            }
-
-            // MSVC lambda capture workaround
-            [[maybe_unused]] const auto& inputs_ref = inputs;
-
-            int m_offset = 0;
-            for_constexpr<num_inputs>([&](auto s)
-            {
-               using fop_t = std::decay_t<decltype(get<s>(inputs_ref))>;
-
-               const int trial_op_dim = static_cast<int>(itod(static_cast<int>(s)));
-               if (trial_op_dim == 0)
-               {
-                  // This is inside a lambda so we have to return
-                  // instead of idiomatic 'continue'.
-                  return;
-               }
-
-               auto& B = input_dtqmaps[s].B;
-               auto& G = input_dtqmaps[s].G;
-
-               if constexpr (is_value_fop<fop_t>::value)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        for (int m = 0; m < trial_op_dim; m++)
-                        {
-                           for (int i = 0; i < test_vdim; i++)
-                           {
-                              for (int k = 0; k < test_op_dim; k++)
-                              {
-                                 const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                 fhat(i, k, q) += f * B(qx, 0, Jx) * B(qy, 0, Jy);
-                              }
-                           }
-                        }
-                     }
-                  }
-               }
-               else if constexpr (is_gradient_fop<fop_t>::value)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, q1d)
-                  {
-                     MFEM_FOREACH_THREAD(qy, y, q1d)
-                     {
-                        const int q = qy + qx * q1d;
-                        for (int m = 0; m < trial_op_dim; m++)
-                        {
-                           for (int i = 0; i < test_vdim; i++)
-                           {
-                              for (int k = 0; k < test_op_dim; k++)
-                              {
-                                 const real_t f = qpdc(i, k, j, m + m_offset, q);
-                                 if (m == 0)
-                                 {
-                                    fhat(i, k, q) += f * B(qx, 0, Jx) * G(qy, 0, Jy);
-                                 }
-                                 else
-                                 {
-                                    fhat(i, k, q) += f * G(qx, 0, Jx) * B(qy, 0, Jy);
-                                 }
-                              }
-                           }
-                        }
-                     }
-                  }
-               }
-               else
-               {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-                  MFEM_ABORT("sum factorized sparse matrix assemble routine "
-                             "not implemented for field operator");
-#endif
-               }
-               MFEM_SYNC_THREAD;
-               m_offset += trial_op_dim;
-            });
-
-            auto bvtfhat = Reshape(&A(0, 0, J, j), num_test_dof, test_vdim);
-            map_quadrature_data_to_fields(bvtfhat, fhat, output, output_dtqmap,
-                                          scratch_shmem, dimension, true);
-         }
-      }
-   }
-}
-
-/// @brief Assemble element matrix for two or three dimensional data.
-///
-/// Note: In the below layouts, total_trial_op_dim is > 1 if
-/// there are more than one inputs dependent on the derivative variable.
-///
-/// @param A Memory for one element matrix with layout
-/// [test_ndof, test_vdim, trial_ndof, trial_vdim].
-/// @param fhat Memory to hold the residual computation with layout
-/// [test_vdim, test_op_dim, nqp].
-/// @param qpdc The quadrature point data cache with data layout
-/// [test_vdim, test_op_dim, trial_vdim, total_trial_op_dim, nqp].
-/// @param itod Input Trial Operator Dimension array. If the trial
-/// operator is not dependent, the dimension is 0 to indicate that.
-/// @param inputs The input field operator types.
-/// @param output The output field operator types.
-/// @param input_dtqmaps The input DofToQuad maps.
-/// @param output_dtqmap The output DofToQuad maps.
-/// @param scratch_shmem Scratch shared memory for computations.
-/// @param dimension The spatial dimension.
-/// @param q1d The number of quadrature points in one dimension.
-/// @param td1d The number of trial dofs in one dimension.
-/// @param use_sum_factorization Indicator if sum factorization is used.
-template <typename input_fop_ts, size_t num_inputs, typename output_fop_t>
-MFEM_HOST_DEVICE void assemble_element_mat_naive(
-   const DeviceTensor<4, real_t>& A,
-   const DeviceTensor<3, real_t>& fhat,
-   const DeviceTensor<5, const real_t>& qpdc,
-   const DeviceTensor<1, const real_t>& itod,
-   const input_fop_ts& inputs,
-   const output_fop_t& output,
-   const std::array<DofToQuadMap, num_inputs>& input_dtqmaps,
-   const DofToQuadMap& output_dtqmap,
-   std::array<DeviceTensor<1>, 6>& scratch_shmem,
-   const int& dimension,
-   const int& q1d,
-   const int& td1d,
-   const bool& use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 2)
-      {
-         assemble_element_mat_t2d(A, fhat, qpdc, itod, inputs, output,
-                                  input_dtqmaps, output_dtqmap, scratch_shmem, q1d, td1d);
-      }
-      else if (dimension == 3)
-      {
-         assemble_element_mat_t3d(A, fhat, qpdc, itod, inputs, output,
-                                  input_dtqmaps, output_dtqmap, scratch_shmem, q1d, td1d);
-      }
-   }
-   else
-   {
-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-      MFEM_ABORT("element matrix assemble not implemented for non tensor "
-                 "product basis");
-#endif
-   }
-}
-
-} // namespace mfem::future
@@ -22,7 +22,6 @@
 #include "interpolate.hpp"
 #include "integrate.hpp"
 #include "qfunction_apply.hpp"
-#include "assemble.hpp"

 namespace mfem::future
 {
@@ -31,23 +30,14 @@ namespace mfem::future
 using action_t =
   std::function<void(std::vector<Vector> &, const std::vector<Vector> &, Vector &)>;

-/// @brief Type alias for a function that computes the cache for the action of a derivative
-using derivative_setup_t =
-   std::function<void(std::vector<Vector> &, const Vector &)>;
-
 /// @brief Type alias for a function that computes the action of a derivative
 using derivative_action_t =
   std::function<void(std::vector<Vector> &, const Vector &, Vector &)>;

-/// @brief Type alias for a function that assembles the SparseMatrix of a
-/// derivative operator
-using assemble_derivative_sparsematrix_callback_t =
-   std::function<void(std::vector<Vector> &, SparseMatrix *&)>;
-
-/// @brief Type alias for a function that assembles the HypreParMatrix of a
+/// @brief Type alias for a function that assembles the sparse matrix of a
 /// derivative operator
 using assemble_derivative_hypreparmatrix_callback_t =
-   std::function<void(std::vector<Vector> &, HypreParMatrix *&)>;
+   std::function<void(std::vector<Vector> &, HypreParMatrix &)>;

 /// @brief Type alias for a function that applies the appropriate restriction to
 /// the solution and parameters
@@ -91,8 +81,6 @@ public:
      const std::vector<Vector *> &parameters_l,
      const restriction_callback_t &restriction_callback,
      const std::function<void(Vector &, Vector &)> &prolongation_transpose,
-      const std::vector<assemble_derivative_sparsematrix_callback_t>
-      &assemble_derivative_sparsematrix_callbacks,
      const std::vector<assemble_derivative_hypreparmatrix_callback_t>
      &assemble_derivative_hypreparmatrix_callbacks) :
      Operator(height, width),
@@ -103,8 +91,6 @@ public:
      derivative_actions_transpose(derivative_actions_transpose),
      transpose_direction(transpose_direction),
      prolongation_transpose(prolongation_transpose),
-      assemble_derivative_sparsematrix_callbacks(
-         assemble_derivative_sparsematrix_callbacks),
      assemble_derivative_hypreparmatrix_callbacks(
         assemble_derivative_hypreparmatrix_callbacks)
   {
@@ -170,29 +156,14 @@ public:
      prolongation_transpose(daction_l, result_t);
   };

-   /// @brief Assemble the derivative operator into a SparseMatrix.
-   ///
-   /// @param A The SparseMatrix to assemble the derivative operator into. Can
-   /// be an uninitialized object.
-   void Assemble(SparseMatrix *&A)
-   {
-      MFEM_ASSERT(!assemble_derivative_sparsematrix_callbacks.empty(),
-                  "derivative can't be assembled into a SparseMatrix");
-
-      for (const auto &f : assemble_derivative_sparsematrix_callbacks)
-      {
-         f(fields_e, A);
-      }
-   }
-
   /// @brief Assemble the derivative operator into a HypreParMatrix.
   ///
   /// @param A The HypreParMatrix to assemble the derivative operator into. Can
   /// be an uninitialized object.
-   void Assemble(HypreParMatrix *&A)
+   void Assemble(HypreParMatrix &A)
   {
      MFEM_ASSERT(!assemble_derivative_hypreparmatrix_callbacks.empty(),
-                  "derivative can't be assembled into a HypreParMatrix");
+                  "derivative can't be assembled into a matrix");

      for (const auto &f : assemble_derivative_hypreparmatrix_callbacks)
      {
@@ -225,10 +196,6 @@ private:

   std::function<void(Vector &, Vector &)> prolongation_transpose;

-   /// Callbacks that assemble derivatives into a SparseMatrix.
-   std::vector<assemble_derivative_sparsematrix_callback_t>
-   assemble_derivative_sparsematrix_callbacks;
-
   /// Callbacks that assemble derivatives into a HypreParMatrix.
   std::vector<assemble_derivative_hypreparmatrix_callback_t>
   assemble_derivative_hypreparmatrix_callbacks;
@@ -431,34 +398,6 @@ public:

      const size_t derivative_idx = FindIdx(derivative_id, fields);

-      std::vector<Vector> s_l(solutions_l.size());
-      for (size_t i = 0; i < s_l.size(); i++)
-      {
-         s_l[i] = *sol_l[i];
-      }
-
-      std::vector<Vector> p_l(parameters_l.size());
-      for (size_t i = 0; i < p_l.size(); i++)
-      {
-         p_l[i] = *par_l[i];
-      }
-
-      fields_e.resize(solutions_l.size() + parameters_l.size());
-      restriction_callback(s_l, p_l, fields_e);
-
-      // Dummy
-      Vector dir_l;
-      if (derivative_idx > s_l.size())
-      {
-         dir_l = p_l[derivative_idx - s_l.size()];
-      }
-      else
-      {
-         dir_l = s_l[derivative_idx];
-      }
-
-      derivative_setup_callbacks[derivative_id][0](fields_e, dir_l);
-
      return std::make_shared<DerivativeOperator>(
                height,
                GetTrueVSize(fields[derivative_idx]),
@@ -472,7 +411,6 @@ public:
                par_l,
                restriction_callback,
                prolongation_transpose,
-                assemble_derivative_sparsematrix_callbacks[derivative_id],
                assemble_derivative_hypreparmatrix_callbacks[derivative_id]);
   }

@@ -482,14 +420,10 @@ private:
   MultLevel mult_level = TVECTOR;

   std::vector<action_t> action_callbacks;
-   std::map<size_t, std::vector<derivative_setup_t>> derivative_setup_callbacks;
   std::map<size_t,
       std::vector<derivative_action_t>> derivative_action_callbacks;
   std::map<size_t,
       std::vector<derivative_action_t>> daction_transpose_callbacks;
-   std::map<size_t,
-       std::vector<assemble_derivative_sparsematrix_callback_t>>
-       assemble_derivative_sparsematrix_callbacks;
   std::map<size_t,
       std::vector<assemble_derivative_hypreparmatrix_callback_t>>
       assemble_derivative_hypreparmatrix_callbacks;
@@ -510,8 +444,6 @@ private:
   std::function<void(Vector &, Vector &)> output_restriction_transpose;
   restriction_callback_t restriction_callback;

-   std::map<size_t, Vector> derivative_qp_caches;
-
   std::map<size_t, size_t> assembled_vector_sizes;

   bool use_tensor_product_structure = true;
@@ -631,13 +563,6 @@ void DifferentiableOperator::AddIntegrator(
   auto output_to_field =
      create_descriptors_to_fields_map<entity_t>(fields, outputs);

-   // TODO: factor out
-   std::vector<int> inputs_vdim(num_inputs);
-   for_constexpr<num_inputs>([&](auto i)
-   {
-      inputs_vdim[i] = get<i>(inputs).vdim;
-   });
-
   const Array<int> *elem_attributes = nullptr;
   if constexpr (std::is_same_v<entity_t, Entity::Element>)
   {
@@ -904,8 +829,7 @@ void DifferentiableOperator::AddIntegrator(

         // print_shared_memory_info(shmem_info);

-         Vector direction_e(get_restriction<entity_t>(fields[d_field_idx],
-                                                      element_dof_ordering)->Height());
+         Vector direction_e;
         Vector derivative_action_e(output_e_size);
         derivative_action_e = 0.0;

@@ -917,152 +841,6 @@ void DifferentiableOperator::AddIntegrator(
         }
         const auto input_is_dependent = it->second;

-         // Trial operator dimension for each input.
-         // The trial operator dimension is set for each input that is
-         // dependent and if it is independent the dimension is 0.
-         Vector inputs_trial_op_dim(num_inputs);
-         int total_trial_op_dim = 0;
-         {
-            auto itod = Reshape(inputs_trial_op_dim.HostReadWrite(), num_inputs);
-            int idx = 0;
-            for_constexpr<num_inputs>([&](auto s)
-            {
-               if (!input_is_dependent[s])
-               {
-                  itod(idx) = 0;
-               }
-               else
-               {
-                  // TODO: BUG! Make this a general function that works for all kinds of inputs.
-                  itod(idx) = input_size_on_qp[s] / get<s>(inputs).vdim;
-               }
-               total_trial_op_dim += static_cast<int>(itod(idx));
-               idx++;
-            });
-         }
-
-         // First Input index of the derivative
-         const size_t d_input_idx = [d_field_idx, &input_to_field]
-         {
-            for (size_t i = 0; i < input_to_field.size(); i++)
-            {
-               if (input_to_field[i] == d_field_idx)
-               {
-                  return i;
-               }
-            }
-            return size_t(SIZE_MAX);
-         }();
-
-         const int trial_vdim = GetVDim(fields[d_field_idx]);
-         const int num_trial_dof =
-            get_restriction<entity_t>(fields[d_field_idx], element_dof_ordering)->Height() /
-            inputs_vdim[d_input_idx] / num_entities;
-         const int num_trial_dof_1d =
-            input_dtq_maps[d_input_idx].B.GetShape()[DofToQuadMap::Index::DOF];
-
-         Vector Ae_mem(num_test_dof * test_vdim * num_trial_dof * trial_vdim *
-                       num_entities);
-         Ae_mem = 0.0;
-
-         // Quadrature point local derivative cache for each element, with data
-         // layout:
-         // [test_vdim, test_op_dim, trial_vdim, trial_op_dim, qp, num_entities].
-         derivative_qp_caches[derivative_id] = Vector(test_vdim * test_op_dim *
-                                                      trial_vdim *
-                                                      total_trial_op_dim * num_qp * num_entities);
-         // Create local references for MSVC lambda capture compatibility
-         auto& fields_ref = this->fields;
-         auto& derivative_qp_caches_ref = this->derivative_qp_caches[derivative_id];
-
-         // In each of the callbacks we're saving the derivatives in the quadrature point
-         // caches. This trades memory with computational effort but also minimizes
-         // data movement on each multiplication of the gradient with a directional
-         // vector.
-         derivative_setup_callbacks[derivative_id].push_back(
-            [
-               // capture by copy:
-               dimension,             // int
-               num_entities,          // int
-               num_qp,                // int
-               q1d,                   // int
-               test_vdim,             // int (= output_fop.vdim)
-               test_op_dim,           // int (derived from output_fop)
-               inputs,                // mfem::future::tuple
-               attributes,     // Array<int>
-               ir_weights,            // DeviceTensor
-               use_sum_factorization, // bool
-               input_dtq_maps,        // std::array<DofToQuadMap, num_fields>
-               output_dtq_maps,       // std::array<DofToQuadMap, num_fields>
-               input_to_field,        // std::array<int, s>
-               qfunc,                 // qfunc_t
-               thread_blocks,         // ThreadBlocks
-               shmem_cache,           // Vector (local)
-               shmem_info,            // SharedMemoryInfo
-               // TODO: make this Array<int> a member of the DifferentiableOperator
-               //       and capture it by ref.
-               elem_attributes,       // Array<int>
-               element_dof_ordering,  // ElementDofOrdering
-
-               direction,             // FieldDescriptor
-               direction_e,           // Vector
-               da_size_on_qp,         // int
-
-               total_trial_op_dim,
-               trial_vdim,
-               inputs_trial_op_dim,
-
-               // capture by ref:
-               &qpdc_mem = derivative_qp_caches_ref
-            ](std::vector<Vector> &f_e, const Vector &dir_l) mutable
-         {
-            restriction<entity_t>(direction, dir_l, direction_e,
-                                  element_dof_ordering);
-            auto wrapped_fields_e = wrap_fields(f_e, shmem_info.field_sizes,
-                                                num_entities);
-            auto wrapped_direction_e = Reshape(direction_e.ReadWrite(),
-                                               shmem_info.direction_size,
-                                               num_entities);
-
-            auto qpdc = Reshape(qpdc_mem.ReadWrite(), test_vdim, test_op_dim,
-                                trial_vdim, total_trial_op_dim, num_qp, num_entities);
-
-            auto itod = Reshape(inputs_trial_op_dim.Read(), num_inputs);
-
-            const auto d_elem_attr = elem_attributes->Read();
-            const bool has_attr = attributes.Size() > 0;
-            const auto d_domain_attr = attributes.Read();
-
-            forall([=] MFEM_HOST_DEVICE (int e, real_t *shmem)
-            {
-               if (has_attr && !d_domain_attr[d_elem_attr[e] - 1]) { return; }
-
-               auto [input_dtq_shmem, output_dtq_shmem, fields_shmem,
-                                      direction_shmem, input_shmem,
-                                      shadow_shmem_, residual_shmem,
-                                      scratch_shmem] =
-                        unpack_shmem(shmem, shmem_info, input_dtq_maps, output_dtq_maps,
-                                     wrapped_fields_e, wrapped_direction_e, num_qp, e);
-               auto &shadow_shmem = shadow_shmem_;
-
-               map_fields_to_quadrature_data(
-                  input_shmem, fields_shmem, input_dtq_shmem, input_to_field,
-                  inputs, ir_weights, scratch_shmem, dimension,
-                  use_sum_factorization);
-
-               set_zero(shadow_shmem);
-
-               auto qpdc_e = Reshape(&qpdc(0, 0, 0, 0, 0, e), test_vdim, test_op_dim,
-                                     trial_vdim, total_trial_op_dim, num_qp);
-               call_qfunction_derivative<qf_param_ts>(
-                  qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc_e, itod, da_size_on_qp,
-                  q1d, dimension, use_sum_factorization);
-            }, num_entities, thread_blocks, shmem_info.total_size,
-            shmem_cache.ReadWrite());
-         });
-
-         // The derivative action only uses the quadrature point caches and applies
-         // them to an input vector before integrating with the desired trial operator.
         derivative_action_callbacks[derivative_id].push_back(
            [
               // capture by copy:
@@ -1079,7 +857,9 @@ void DifferentiableOperator::AddIntegrator(
               use_sum_factorization, // bool
               input_dtq_maps,        // std::array<DofToQuadMap, num_fields>
               output_dtq_maps,       // std::array<DofToQuadMap, num_fields>
+               input_to_field,        // std::array<int, s>
               output_fop,            // class derived from FieldOperator
+               qfunc,                 // qfunc_t
               thread_blocks,         // ThreadBlocks
               shmem_cache,           // Vector (local)
               shmem_info,            // SharedMemoryInfo
@@ -1092,11 +872,9 @@ void DifferentiableOperator::AddIntegrator(
               direction_e,           // Vector
               derivative_action_e,   // Vector
               element_dof_ordering,  // ElementDofOrdering
-               inputs_trial_op_dim,
-               total_trial_op_dim,
-               trial_vdim,
+               da_size_on_qp,         // int
+
               // capture by ref:
-               &qpdc_mem = derivative_qp_caches_ref,
               &or_transpose
            ](
               std::vector<Vector> &f_e, const Vector &dir_l,
@@ -1112,11 +890,6 @@ void DifferentiableOperator::AddIntegrator(
                                               shmem_info.direction_size,
                                               num_entities);

-            auto qpdc = Reshape(qpdc_mem.Read(), test_vdim, test_op_dim,
-                                trial_vdim, total_trial_op_dim, num_qp, num_entities);
-
-            auto itod = Reshape(inputs_trial_op_dim.Read(), num_inputs);
-
            const bool has_attr = attributes.Size() > 0;
            const auto d_attr = attributes.Read();
            const auto d_elem_attr = elem_attributes->Read();
@@ -1134,20 +907,25 @@ void DifferentiableOperator::AddIntegrator(
                                     wrapped_fields_e, wrapped_direction_e, num_qp, e);
               auto &shadow_shmem = shadow_shmem_;

+               map_fields_to_quadrature_data(
+                  input_shmem, fields_shmem, input_dtq_shmem, input_to_field,
+                  inputs, ir_weights, scratch_shmem, dimension,
+                  use_sum_factorization);
+
+               // TODO: Probably redundant
+               set_zero(shadow_shmem);
+
               map_direction_to_quadrature_data_conditional(
                  shadow_shmem, direction_shmem, input_dtq_shmem, inputs,
                  ir_weights, scratch_shmem, input_is_dependent, dimension,
                  use_sum_factorization);

+               call_qfunction_derivative_action<qf_param_ts>(
+                  qfunc, input_shmem, shadow_shmem, residual_shmem,
+                  da_size_on_qp, num_qp, q1d, dimension, use_sum_factorization);
+
               auto fhat = Reshape(&residual_shmem(0, 0), test_vdim,
                                   test_op_dim, num_qp);
-
-               auto qpdce = Reshape(&qpdc(0, 0, 0, 0, 0, e), test_vdim, test_op_dim,
-                                    trial_vdim, total_trial_op_dim, num_qp);
-
-               apply_qpdc(fhat, shadow_shmem, qpdce, itod, q1d, dimension,
-                          use_sum_factorization);
-
               auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
               map_quadrature_data_to_fields(
                  y, fhat, output_fop, output_dtq_shmem[0],
@@ -1156,246 +934,6 @@ void DifferentiableOperator::AddIntegrator(
            shmem_cache.ReadWrite());
            or_transpose(derivative_action_e, der_action_l);
         });
-
-         assemble_derivative_sparsematrix_callbacks[derivative_id].push_back(
-            [
-               // capture by copy:
-               dimension,             // int
-               num_entities,          // int
-               num_test_dof,          // int
-               num_qp,                // int
-               q1d,                   // int
-               test_vdim,             // int (= output_fop.vdim)
-               test_op_dim,           // int (derived from output_fop)
-               inputs,                // mfem::future::tuple
-               attributes,     // Array<int>
-               use_sum_factorization, // bool
-               input_dtq_maps,        // std::array<DofToQuadMap, num_fields>
-               output_dtq_maps,       // std::array<DofToQuadMap, num_fields>
-               input_to_field,        // std::array<int, s>
-               output_fop,            // class derived from FieldOperator
-               thread_blocks,         // ThreadBlocks
-               shmem_cache,           // Vector (local)
-               shmem_info,            // SharedMemoryInfo
-               // TODO: make this Array<int> a member of the DifferentiableOperator
-               //       and capture it by ref.
-               elem_attributes,       // Array<int>
-
-               input_is_dependent,    // std::array<bool, num_inputs>
-               direction_e,           // Vector
-               total_trial_op_dim,
-               trial_vdim,
-               num_trial_dof,
-               num_trial_dof_1d,
-               inputs_trial_op_dim,
-               Ae_mem,
-               output_to_field,
-
-               // capture by ref:
-               &qpdc_mem = derivative_qp_caches_ref,
-               &fields = fields_ref
-            ](std::vector<Vector> &f_e, SparseMatrix *&A) mutable
-         {
-            auto wrapped_fields_e = wrap_fields(f_e, shmem_info.field_sizes,
-                                                num_entities);
-            auto wrapped_direction_e = Reshape(direction_e.ReadWrite(),
-                                               shmem_info.direction_size,
-                                               num_entities);
-
-            auto qpdc = Reshape(qpdc_mem.Read(), test_vdim, test_op_dim,
-                                trial_vdim, total_trial_op_dim, num_qp, num_entities);
-
-            auto itod = Reshape(inputs_trial_op_dim.Read(), num_inputs);
-
-            auto Ae = Reshape(Ae_mem.ReadWrite(), num_test_dof, test_vdim, num_trial_dof,
-                              trial_vdim, num_entities);
-
-            const auto d_elem_attr = elem_attributes->Read();
-            const bool has_attr = attributes.Size() > 0;
-            const auto d_domain_attr = attributes.Read();
-
-            forall([=] MFEM_HOST_DEVICE (int e, real_t *shmem)
-            {
-               if (has_attr && !d_domain_attr[d_elem_attr[e] - 1]) { return; }
-
-               auto [input_dtq_shmem, output_dtq_shmem, fields_shmem,
-                                      direction_shmem, input_shmem,
-                                      shadow_shmem_, residual_shmem,
-                                      scratch_shmem] =
-                        unpack_shmem(shmem, shmem_info, input_dtq_maps, output_dtq_maps,
-                                     wrapped_fields_e, wrapped_direction_e, num_qp, e);
-
-               auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
-               auto Aee = Reshape(&Ae(0, 0, 0, 0, e), num_test_dof, test_vdim, num_trial_dof,
-                                  trial_vdim);
-               auto qpdce = Reshape(&qpdc(0, 0, 0, 0, 0, e), test_vdim, test_op_dim,
-                                    trial_vdim, total_trial_op_dim, num_qp);
-               assemble_element_mat_naive(Aee, fhat, qpdce, itod, inputs, output_fop,
-                                          input_dtq_shmem, output_dtq_shmem[0], scratch_shmem, dimension, q1d,
-                                          num_trial_dof_1d, use_sum_factorization);
-            }, num_entities, thread_blocks, shmem_info.total_size,
-            shmem_cache.ReadWrite());
-
-            FieldDescriptor *trial_field = nullptr;
-            for (size_t s = 0; s < num_inputs; s++)
-            {
-               if (input_is_dependent[s])
-               {
-                  trial_field = &fields[input_to_field[s]];
-               }
-            }
-
-            auto trial_fes = *std::get_if<const ParFiniteElementSpace *>
-                             (&trial_field->data);
-            auto test_fes = *std::get_if<const ParFiniteElementSpace *>
-                            (&fields[output_to_field[0]].data);
-
-            A = new SparseMatrix(test_fes->GetVSize(), trial_fes->GetVSize());
-
-            auto tmp = Reshape(Ae_mem.HostReadWrite(), num_test_dof * test_vdim,
-                               num_trial_dof * trial_vdim, num_entities);
-            for (int e = 0; e < num_entities; e++)
-            {
-               DenseMatrix Aee(&tmp(0, 0, e), num_test_dof * test_vdim,
-                               num_trial_dof * trial_vdim);
-
-               Array<int> test_vdofs, trial_vdofs;
-               test_fes->GetElementVDofs(e, test_vdofs);
-               trial_fes->GetElementVDofs(e, trial_vdofs);
-
-               if (use_sum_factorization)
-               {
-                  Array<int> test_vdofs_mapped(test_vdofs.Size());
-
-                  const Array<int> &test_dofmap =
-                     dynamic_cast<const TensorBasisElement&>(*test_fes->GetFE(0)).GetDofMap();
-
-                  if (test_dofmap.Size() == 0)
-                  {
-                     test_vdofs_mapped = test_vdofs;
-                  }
-                  else
-                  {
-                     MFEM_ASSERT(test_dofmap.Size() == num_test_dof,
-                                 "internal error: dof map of the test space does not "
-                                 "match previously determined number of test space dofs");
-
-                     for (int vd = 0; vd < test_vdim; vd++)
-                     {
-                        for (int i = 0; i < num_test_dof; i++)
-                        {
-                           test_vdofs_mapped[i + vd * num_test_dof] =
-                              test_vdofs[test_dofmap[i] + vd * num_test_dof];
-                        }
-                     }
-                  }
-
-                  Array<int> trial_vdofs_mapped(trial_vdofs.Size());
-                  const Array<int> &trial_dofmap =
-                     dynamic_cast<const TensorBasisElement&>(*trial_fes->GetFE(0)).GetDofMap();
-
-                  if (trial_dofmap.Size() == 0)
-                  {
-                     trial_vdofs_mapped = trial_vdofs;
-                  }
-                  else
-                  {
-                     MFEM_ASSERT(trial_dofmap.Size() == num_trial_dof,
-                                 "internal error: dof map of the test space does not "
-                                 "match previously determined number of test space dofs");
-
-                     for (int vd = 0; vd < trial_vdim; vd++)
-                     {
-                        for (int i = 0; i < num_trial_dof; i++)
-                        {
-                           trial_vdofs_mapped[i + vd * num_trial_dof] =
-                              trial_vdofs[trial_dofmap[i] + vd * num_trial_dof];
-                        }
-                     }
-                  }
-
-                  A->AddSubMatrix(test_vdofs_mapped, trial_vdofs_mapped, Aee, 1);
-               }
-               else
-               {
-                  A->AddSubMatrix(test_vdofs, trial_vdofs, Aee, 1);
-               }
-            }
-            A->Finalize();
-         });
-
-         // Create local references for MSVC lambda capture compatibility
-         auto& assemble_derivative_sparsematrix_callbacks_ref =
-            this->assemble_derivative_sparsematrix_callbacks[derivative_id];
-
-         assemble_derivative_hypreparmatrix_callbacks[derivative_id].push_back(
-            [
-               input_is_dependent,
-               input_to_field,
-               output_to_field,
-               &spmatcb = assemble_derivative_sparsematrix_callbacks_ref,
-               &fields = fields_ref
-            ](std::vector<Vector> &f_e, HypreParMatrix *&A) mutable
-         {
-            SparseMatrix *spmat = nullptr;
-            for (const auto &f : spmatcb)
-            {
-               f(f_e, spmat);
-            }
-
-            if (spmat == nullptr)
-            {
-               MFEM_ABORT("internal error");
-            }
-
-            bool same_test_and_trial = false;
-            for (size_t s = 0; s < num_inputs; s++)
-            {
-               if (input_is_dependent[s])
-               {
-                  if (output_to_field[0] == input_to_field[s])
-                  {
-                     same_test_and_trial = true;
-                     break;
-                  }
-               }
-            }
-
-            FieldDescriptor *trial_field = nullptr;
-            for (size_t s = 0; s < num_inputs; s++)
-            {
-               if (input_is_dependent[s])
-               {
-                  trial_field = &fields[input_to_field[s]];
-               }
-            }
-
-            auto trial_fes = *std::get_if<const ParFiniteElementSpace *>
-                             (&trial_field->data);
-            auto test_fes = *std::get_if<const ParFiniteElementSpace *>
-                            (&fields[output_to_field[0]].data);
-
-            if (same_test_and_trial)
-            {
-               HypreParMatrix tmp(test_fes->GetComm(),
-                                  test_fes->GlobalVSize(),
-                                  test_fes->GetDofOffsets(),
-                                  spmat);
-               A = RAP(&tmp, test_fes->Dof_TrueDof_Matrix());
-            }
-            else
-            {
-               HypreParMatrix tmp(test_fes->GetComm(),
-                                  test_fes->GlobalVSize(),
-                                  trial_fes->GlobalVSize(),
-                                  test_fes->GetDofOffsets(),
-                                  trial_fes->GetDofOffsets(),
-                                  spmat);
-               A = RAP(test_fes->Dof_TrueDof_Matrix(), &tmp,
-                       trial_fes->Dof_TrueDof_Matrix());
-            }
-            delete spmat;
-         });
      }, derivative_ids);
   }
 }
@@ -511,7 +511,7 @@ void map_fields_to_quadrature_data(
   std::array<DeviceTensor<2>, num_inputs> &fields_qp,
   const std::array<DeviceTensor<1>, num_fields> &fields_e,
   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
-   const std::array<size_t, num_inputs> &input_to_field,
+   const std::array<int, num_inputs> &input_to_field,
   const field_operator_ts &fops,
   const DeviceTensor<1, const real_t> &integration_weights,
   const std::array<DeviceTensor<1>, 6> &scratch_mem,
@@ -526,8 +526,7 @@ void map_fields_to_quadrature_data(
   for_constexpr<num_inputs>([&](auto i)
   {
      const DeviceTensor<1> &field_e =
-         (input_to_field[i] == SIZE_MAX) ? dummy_field_weight :
-         fields_e[input_to_field[i]];
+         (input_to_field[i] == -1) ? dummy_field_weight : fields_e[input_to_field[i]];

      if (use_sum_factorization)
      {
@@ -638,7 +637,7 @@ void map_direction_to_quadrature_data_conditional(
   const std::array<DeviceTensor<1>, 6> &scratch_mem,
   const std::array<bool, num_inputs> &conditions,
   const int &dimension,
-   const bool &use_sum_factorization)
+   const bool &use_sum_factorization = false)
 {
   for_constexpr<num_inputs>([&](auto i)
   {
@@ -46,7 +46,7 @@ void call_qfunction(
   {
      if (dimension == 1)
      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
+         MFEM_FOREACH_THREAD(q, x, q1d)
         {
            auto qf_args = decay_tuple<qf_param_ts> {};
            auto r = Reshape(&residual_shmem(0, q), rs_qp);
@@ -55,9 +55,9 @@ void call_qfunction(
      }
      else if (dimension == 2)
      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+         MFEM_FOREACH_THREAD(qx, x, q1d)
         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qy, y, q1d)
            {
               const int q = qx + q1d * qy;
               auto qf_args = decay_tuple<qf_param_ts> {};
@@ -68,11 +68,11 @@ void call_qfunction(
      }
      else if (dimension == 3)
      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+         MFEM_FOREACH_THREAD(qx, x, q1d)
         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qy, y, q1d)
            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
+               MFEM_FOREACH_THREAD(qz, z, q1d)
               {
                  const int q = qx + q1d * (qy + q1d * qz);
                  auto qf_args = decay_tuple<qf_param_ts> {};
@@ -92,7 +92,7 @@ void call_qfunction(
   }
   else
   {
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
+      MFEM_FOREACH_THREAD(q, x, num_qp)
      {
         auto qf_args = decay_tuple<qf_param_ts> {};
         auto r = Reshape(&residual_shmem(0, q), rs_qp);
@@ -134,7 +134,7 @@ void call_qfunction_derivative_action(
   {
      if (dimension == 1)
      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
+         MFEM_FOREACH_THREAD(q, x, q1d)
         {
            auto r = Reshape(&residual_shmem(0, q), das_qp);
            auto qf_args = decay_tuple<qf_param_ts> {};
@@ -149,9 +149,9 @@ void call_qfunction_derivative_action(
      }
      else if (dimension == 2)
      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+         MFEM_FOREACH_THREAD(qx, x, q1d)
         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qy, y, q1d)
            {
               const int q = qx + q1d * qy;
               auto r = Reshape(&residual_shmem(0, q), das_qp);
@@ -168,11 +168,11 @@ void call_qfunction_derivative_action(
      }
      else if (dimension == 3)
      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
+         MFEM_FOREACH_THREAD(qx, x, q1d)
         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
+            MFEM_FOREACH_THREAD(qy, y, q1d)
            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
+               MFEM_FOREACH_THREAD(qz, z, q1d)
               {
                  const int q = qx + q1d * (qy + q1d * qz);
                  auto r = Reshape(&residual_shmem(0, q), das_qp);
@@ -195,7 +195,7 @@ void call_qfunction_derivative_action(
   }
   else
   {
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
+      MFEM_FOREACH_THREAD(q, x, num_qp)
      {
         auto r = Reshape(&residual_shmem(0, q), das_qp);
         auto qf_args = decay_tuple<qf_param_ts> {};
@@ -211,300 +211,6 @@ void call_qfunction_derivative_action(
   MFEM_SYNC_THREAD;
 }

-namespace detail
-{
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction_derivative(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   DeviceTensor<2> &residual_shmem,
-   DeviceTensor<5> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &das_qp,
-   const int &q)
-{
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-   const int num_qp = qpdc.GetShape()[4];
-   const size_t num_inputs = itod.GetShape()[0];
-
-   for (int j = 0; j < trial_vdim; j++)
-   {
-      int m_offset = 0;
-      for (size_t s = 0; s < num_inputs; s++)
-      {
-         const int trial_op_dim = static_cast<int>(itod(s));
-         if (trial_op_dim == 0)
-         {
-            continue;
-         }
-
-         auto d_qp = Reshape(&(shadow_shmem[s])[0], trial_vdim, trial_op_dim, num_qp);
-         for (int m = 0; m < trial_op_dim; m++)
-         {
-            d_qp(j, m, q) = 1.0;
-
-            auto r = Reshape(&residual_shmem(0, q), das_qp);
-            auto qf_args = decay_tuple<qf_param_ts> {};
-#ifdef MFEM_USE_ENZYME
-            auto qf_shadow_args = decay_tuple<qf_param_ts> {};
-            apply_kernel_fwddiff_enzyme(r, qfunc, qf_args, qf_shadow_args, input_shmem,
-                                        shadow_shmem, q);
-#else
-            apply_kernel_native_dual(r, qfunc, qf_args, input_shmem, shadow_shmem, q);
-#endif
-            d_qp(j, m, q) = 0.0;
-
-            auto f = Reshape(&r(0), test_vdim, test_op_dim);
-            for (int i = 0; i < test_vdim; i++)
-            {
-               for (int k = 0; k < test_op_dim; k++)
-               {
-                  qpdc(i, k, j, m + m_offset, q) = f(i, k);
-               }
-            }
-         }
-         m_offset += trial_op_dim;
-      }
-   }
-}
-}
-
-/// @brief Call a qfunction with the given parameters and
-/// compute it's derivative represented by the Jacobian on
-/// each quadrature point.
-///
-/// @param qfunc the qfunction to call.
-/// @param input_shmem the input shared memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param residual_shmem the residual shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param das_qp the size of the derivative action.
-/// @param q1d the number of quadrature points in 1D.
-/// @param dimension the spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-/// @tparam qf_param_ts the tuple type of the qfunction parameters.
-template <
-   typename qf_param_ts,
-   typename qfunc_t,
-   std::size_t num_fields>
-MFEM_HOST_DEVICE inline
-void call_qfunction_derivative(
-   qfunc_t &qfunc,
-   const std::array<DeviceTensor<2>, num_fields> &input_shmem,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   DeviceTensor<2> &residual_shmem,
-   DeviceTensor<5> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &das_qp,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            detail::call_qfunction_derivative<qf_param_ts>(
-               qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               detail::call_qfunction_derivative<qf_param_ts>(
-                  qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  detail::call_qfunction_derivative<qf_param_ts>(
-                     qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-               }
-            }
-         }
-      }
-      else
-      {
-         MFEM_ABORT_KERNEL("unsupported dimension");
-      }
-   }
-   else
-   {
-      const int num_qp = qpdc.GetShape()[4];
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         detail::call_qfunction_derivative<qf_param_ts>(
-            qfunc, input_shmem, shadow_shmem, residual_shmem, qpdc, itod, das_qp, q);
-      }
-   }
-   MFEM_SYNC_THREAD;
-}
-
-namespace detail
-{
-
-/// @brief Apply the quadrature point data cache (qpdc) to a vector
-/// (usually a direction) on quadrature point q.
-///
-/// The qpdc consists of compatible data to be used for integration with a test
-/// operator, e.g. Jacobians of a linearization from a FE operation with a trial
-/// function including integration weights and necessesary transformations.
-///
-/// @param fhat the qpdc applied to a vector in shadow_memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param q the current quadrature point index.
-template <size_t num_fields>
-MFEM_HOST_DEVICE inline
-void apply_qpdc(
-   DeviceTensor<3> &fhat,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   const DeviceTensor<5, const real_t> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &q)
-{
-   const int test_vdim = qpdc.GetShape()[0];
-   const int test_op_dim = qpdc.GetShape()[1];
-   const int trial_vdim = qpdc.GetShape()[2];
-   const int num_qp = qpdc.GetShape()[4];
-   const size_t num_inputs = itod.GetShape()[0];
-
-   for (int i = 0; i < test_vdim; i++)
-   {
-      for (int k = 0; k < test_op_dim; k++)
-      {
-         real_t sum = 0.0;
-         int m_offset = 0;
-         for (size_t s = 0; s < num_inputs; s++)
-         {
-            const int trial_op_dim = static_cast<int>(itod(s));
-            if (trial_op_dim == 0)
-            {
-               continue;
-            }
-            const auto d_qp =
-               Reshape(&(shadow_shmem[s])[0], trial_vdim, trial_op_dim, num_qp);
-            for (int j = 0; j < trial_vdim; j++)
-            {
-               for (int m = 0; m < trial_op_dim; m++)
-               {
-                  sum += qpdc(i, k, j, m + m_offset, q) * d_qp(j, m, q);
-               }
-            }
-            m_offset += trial_op_dim;
-         }
-         fhat(i, k, q) = sum;
-      }
-   }
-}
-}
-
-/// @brief Apply the quadrature point data cache (qpdc) to a vector
-/// (usually a direction).
-///
-/// The qpdc consists of compatible data to be used for integration with a test
-/// operator, e.g. Jacobians of a linearization from a FE operation with a trial
-/// function including integration weights and necessesary transformations.
-///
-/// @param fhat the qpdc applied to a vector in shadow_memory.
-/// @param shadow_shmem the shadow shared memory.
-/// @param qpdc the quadrature point data cache holding the resulting
-/// Jacobians on each quadrature point.
-/// @param itod inputs trial operator dimension.
-/// If input is dependent the value corresponds to the spatial dimension, otherwise
-/// a zero indicates non-dependence on the variable.
-/// @param q1d number of quadrature points in 1D.
-/// @param dimension spatial dimension.
-/// @param use_sum_factorization whether to use sum factorization.
-template <size_t num_fields>
-MFEM_HOST_DEVICE inline
-void apply_qpdc(
-   DeviceTensor<3> &fhat,
-   const std::array<DeviceTensor<2>, num_fields> &shadow_shmem,
-   const DeviceTensor<5, const real_t> &qpdc,
-   const DeviceTensor<1, const real_t> &itod,
-   const int &q1d,
-   const int &dimension,
-   const bool &use_sum_factorization)
-{
-   if (use_sum_factorization)
-   {
-      if (dimension == 1)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(q, x, q1d)
-         {
-            detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-         }
-      }
-      else if (dimension == 2)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               const int q = qx + q1d * qy;
-               detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-            }
-         }
-      }
-      else if (dimension == 3)
-      {
-         MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
-         {
-            MFEM_FOREACH_THREAD_DIRECT(qy, y, q1d)
-            {
-               MFEM_FOREACH_THREAD_DIRECT(qz, z, q1d)
-               {
-                  const int q = qx + q1d * (qy + q1d * qz);
-                  detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-               }
-            }
-         }
-      }
-      else
-      {
-         MFEM_ABORT_KERNEL("unsupported dimension");
-      }
-   }
-   else
-   {
-      const int num_qp = qpdc.GetShape()[4];
-      MFEM_FOREACH_THREAD_DIRECT(q, x, num_qp)
-      {
-         detail::apply_qpdc(fhat, shadow_shmem, qpdc, itod, q);
-      }
-   }
-}
-
 template <typename qfunc_t, typename args_ts, size_t num_args>
 MFEM_HOST_DEVICE inline
 void apply_kernel(
@@ -10,7 +10,7 @@
 // CONTRIBUTING.md for details.
 #pragma once

-// This is smith's tuple implementation
+// This is serac's tuple implementation

 #include <ostream>
 #include "../../config/config.hpp"
@@ -20,7 +20,6 @@
 #include <vector>
 #include <type_traits>
 #include <numeric>
-#include <iomanip>

 #include "../../general/communication.hpp"
 #include "../../general/forall.hpp"
@@ -108,33 +107,26 @@ constexpr void for_constexpr_with_arg(lambda&& f, arg_t&& arg)
                          indices{});
 }

-template <std::size_t I, typename Tuple, std::size_t... Is>
-std::array<bool, sizeof...(Is)>
-make_dependency_array(const Tuple& inputs, std::index_sequence<Is...>)
-{
-   return { (get<I>(inputs).GetFieldId() == get<Is>(inputs).GetFieldId())... };
-}
-
 template <typename... input_ts, std::size_t... Is>
-auto make_dependency_map_impl(tuple<input_ts...> inputs,
-                              std::index_sequence<Is...>)
+auto make_dependency_map_impl(
+   tuple<input_ts...> inputs,
+   std::index_sequence<Is...>)
 {
-   constexpr std::size_t N = sizeof...(input_ts);
-
-   if constexpr (N == 0)
-      return std::unordered_map<int, std::array<bool, 0>> {};
-
-   std::unordered_map<int, std::array<bool, N>> map;
-
-   (void)std::initializer_list<int>
+   auto make_dependency_array = [&](auto i)
   {
-      (
-         map[get<Is>(inputs).GetFieldId()] =
-      make_dependency_array<Is>(inputs, std::make_index_sequence<N>{}),
-      0
-      )...
+      return std::array<bool, sizeof...(input_ts)>
+      {
+         (get<i>(inputs).GetFieldId() == get<Is>(inputs).GetFieldId())...
+      };
   };

+   std::unordered_map<int, std::array<bool, sizeof...(input_ts)>> map;
+   for_constexpr<sizeof...(input_ts)>([&](auto i)
+   {
+      map[get<i>(inputs).GetFieldId()] =
+         make_dependency_array(std::integral_constant<std::size_t, i> {});
+   });
+
   return map;
 }

@@ -208,45 +200,24 @@ void print_tuple(const std::tuple<Args...>& t)
 ///             ..., vmn]]
 /// which is compatible with numpy syntax.
 ///
-/// @param out ostream to print to
-/// @param A mfem::DenseMatrix to print
+/// @param m mfem::DenseMatrix to print
 inline
-void pretty_print(std::ostream &out, const mfem::DenseMatrix &A)
+void pretty_print(const mfem::DenseMatrix& m)
 {
-   // Determine the max width of any entry in scientific notation
-   int max_width = 0;
-   for (int i = 0; i < A.NumRows(); ++i)
+   out << "[";
+   for (int i = 0; i < m.NumRows(); i++)
   {
-      for (int j = 0; j < A.NumCols(); ++j)
+      for (int j = 0; j < m.NumCols(); j++)
      {
-         std::ostringstream oss;
-         oss << std::scientific << std::setprecision(2) << A(i, j);
-         max_width = std::max(max_width, static_cast<int>(oss.str().length()));
-      }
-   }
-
-   out << "[\n";
-   for (int i = 0; i < A.NumRows(); ++i)
-   {
-      out << "  [";
-      for (int j = 0; j < A.NumCols(); ++j)
-      {
-         out << std::setw(max_width) << std::scientific << std::setprecision(2) <<
-             A(i, j);
-
-         if (j < A.NumCols() - 1)
+         out << m(i, j);
+         if (j < m.NumCols() - 1)
         {
            out << ", ";
         }
      }
-      out << "]";
-      if (i < A.NumRows() - 1)
+      if (i < m.NumRows() - 1)
      {
-         out << ",\n";
-      }
-      else
-      {
-         out << "\n";
+         out << ", ";
      }
   }
   out << "]\n";
@@ -385,7 +356,7 @@ void print_mpi_sync(const std::string& msg)
   else
   {
      // Other ranks: Send message to rank 0
-      MPI_Send(const_cast<char*>(msg.c_str()), static_cast<int>(msg_len), MPI_CHAR,
+      MPI_Send(msg.c_str(), static_cast<int>(msg_len), MPI_CHAR,
               0, 0, MPI_COMM_WORLD);
   }

@@ -1433,12 +1404,12 @@ int GetSizeOnQP(const field_operator_t &, const FieldDescriptor &f)
 /// @tparam entity_t the entity type (see Entity).
 /// @returns an array mapping field operator types to field descriptor indices.
 template <typename entity_t, typename field_operator_ts>
-std::array<size_t, tuple_size<field_operator_ts>::value>
+std::array<int, tuple_size<field_operator_ts>::value>
 create_descriptors_to_fields_map(
   const std::vector<FieldDescriptor> &fields,
   field_operator_ts &fops)
 {
-   std::array<size_t, tuple_size<field_operator_ts>::value> map;
+   std::array<int, tuple_size<field_operator_ts>::value> map;

   auto find_id = [](const std::vector<FieldDescriptor> &fields, std::size_t i)
   {
@@ -1450,9 +1421,9 @@ create_descriptors_to_fields_map(

      if (it == fields.end())
      {
-         return SIZE_MAX;
+         return -1;
      }
-      return static_cast<size_t>(it - fields.begin());
+      return static_cast<int>(it - fields.begin());
   };

   auto f = [&](auto &fop, auto &map)
@@ -1463,7 +1434,7 @@ create_descriptors_to_fields_map(
         fop.dim = GetDimension<entity_t>(fields[0]);
         fop.vdim = 1;
         fop.size_on_qp = 1;
-         map = SIZE_MAX;
+         map = -1;
      }
      else
      {
@@ -2249,7 +2220,7 @@ template <
 std::array<DofToQuadMap, N> create_dtq_maps_impl(
   field_operator_ts &fops,
   std::vector<const DofToQuad*> &dtqs,
-   const std::array<size_t, N> &field_map,
+   const std::array<int, N> &field_map,
   std::index_sequence<Is...>)
 {
   auto f = [&](auto fop, std::size_t idx)
@@ -2334,7 +2305,7 @@ template <
 std::array<DofToQuadMap, num_fields> create_dtq_maps(
   field_operator_ts &fops,
   std::vector<const DofToQuad*> &dtqmaps,
-   const std::array<size_t, num_fields> &to_field_map)
+   const std::array<int, num_fields> &to_field_map)
 {
   return create_dtq_maps_impl<entity_t>(
             fops, dtqmaps,
@@ -12,6 +12,7 @@
 #include "dgmassinv.hpp"
 #include "bilinearform.hpp"
 #include "dgmassinv_kernels.hpp"
+#include "../general/forall.hpp"

 namespace mfem
 {
@@ -118,6 +119,151 @@ void DGMassInverse::Update()

 DGMassInverse::~DGMassInverse() = default;

+template<int DIM, int D1D, int Q1D>
+void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
+{
+   using namespace internal; // host/device kernel functions
+
+   const int NE = fes.GetNE();
+   const int d1d = m->dofs1D;
+   const int q1d = m->quad1D;
+
+   const int ND = static_cast<int>(pow(d1d, DIM));
+
+   const auto B = m->maps->B.Read();
+   const auto Bt = m->maps->Bt.Read();
+   const auto pa_data = m->pa_data.Read();
+   const auto dinv = diag_inv.Read();
+   auto r = r_.Write();
+   auto d = d_.Write();
+   auto z = z_.Write();
+   auto u = u_.ReadWrite();
+
+   const real_t RELTOL = rel_tol;
+   const real_t ABSTOL = abs_tol;
+   const int MAXIT = max_iter;
+   const bool IT_MODE = iterative_mode;
+   const bool CHANGE_BASIS = (d2q != nullptr);
+
+   // b is the right-hand side (if no change of basis, this just points to the
+   // incoming RHS vector, if we have to change basis, this points to the
+   // internal b2 vector where we put the transformed RHS)
+   const real_t *b;
+   // the following are non-null if we have to change basis
+   real_t *b2 = nullptr; // non-const access to b2
+   const real_t *b_orig = nullptr; // RHS vector in "original" basis
+   const real_t *d2q_B = nullptr; // matrix to transform initial guess
+   const real_t *q2d_B = nullptr; // matrix to transform solution
+   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
+   if (CHANGE_BASIS)
+   {
+      d2q_B = d2q->B.Read();
+      q2d_B = B_.Read();
+      q2d_Bt = Bt_.Read();
+
+      b2 = b2_.Write();
+      b_orig = b_.Read();
+      b = b2;
+   }
+   else
+   {
+      b = b_.Read();
+   }
+
+   static constexpr int NB = Q1D ? Q1D : 1; // block size
+
+   mfem::forall_2D(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
+   {
+      // Perform change of basis if needed
+      if (CHANGE_BASIS)
+      {
+         // Transform RHS
+         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
+         if (IT_MODE)
+         {
+            // Transform initial guess
+            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
+         }
+      }
+
+      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
+
+      // Compute first residual
+      if (IT_MODE)
+      {
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
+         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
+      }
+      else
+      {
+         // if not in iterative mode, use zero initial guess
+         const int BX = MFEM_THREAD_SIZE(x);
+         const int BY = MFEM_THREAD_SIZE(y);
+         const int bxy = BX*BY;
+         const auto B = ConstDeviceMatrix(b, ND, NE);
+         auto U = DeviceMatrix(u, ND, NE);
+         auto R = DeviceMatrix(r, ND, NE);
+         for (int i = tid; i < ND; i += bxy)
+         {
+            U(i, e) = 0.0;
+            R(i, e) = B(i, e);
+         }
+         MFEM_SYNC_THREAD;
+      }
+
+      DGMassPreconditioner(e, NE, ND, dinv, r, z);
+      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
+
+      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
+      if (nom < 0.0) { return; /* Not positive definite */ }
+      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
+      if (nom <= r0) { return; /* Converged */ }
+
+      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
+      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
+      if (den <= 0.0)
+      {
+         DGMassDot<NB>(e, NE, ND, d, d);
+         // d2 > 0 => not positive definite
+         if (den == 0.0) { return; }
+      }
+
+      // start iteration
+      int i = 1;
+      while (true)
+      {
+         const real_t alpha = nom/den;
+         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
+         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
+
+         DGMassPreconditioner(e, NE, ND, dinv, r, z);
+
+         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
+         if (betanom < 0.0) { return; /* Not positive definite */ }
+         if (betanom <= r0) { break; /* Converged */ }
+
+         if (++i > MAXIT) { break; }
+
+         const real_t beta = betanom/nom;
+         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
+         den = DGMassDot<NB>(e, NE, ND, d, z);
+         if (den <= 0.0)
+         {
+            DGMassDot<NB>(e, NE, ND, d, d);
+            // d2 > 0 => not positive definite
+            if (den == 0.0) { break; }
+         }
+         nom = betanom;
+      }
+
+      if (CHANGE_BASIS)
+      {
+         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
+      }
+   });
+}
+
 void DGMassInverse::Mult(const Vector &Mu, Vector &u) const
 {
   // Dispatch to templated version based on dim, d1d, and q1d.
@@ -160,4 +306,23 @@ DGMassInvKernels::DGMassInvKernels()
   k::Specialization<3,6,7>::Add();
 }

+/// @cond Suppress_Doxygen_warnings
+
+template <int DIM, int D1D, int Q1D>
+DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
+{
+   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
+}
+
+DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
+   int dim, int, int)
+{
+   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
+   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
+   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
+   else { MFEM_ABORT("Unsupported dimension."); }
+}
+
+/// @endcond
+
 } // namespace mfem
@@ -15,7 +15,6 @@
 #include "../linalg/kernels.hpp"
 #include "kernels.hpp"
 #include "integ/bilininteg_mass_kernels.hpp"
-#include "dgmassinv.hpp"

 namespace mfem
 {
@@ -334,170 +333,6 @@ void DGMassBasis(const int e,

 } // namespace internal

-template<int DIM, int D1D, int Q1D>
-void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
-{
-   using namespace internal; // host/device kernel functions
-
-   const int NE = fes.GetNE();
-   const int d1d = m->dofs1D;
-   const int q1d = m->quad1D;
-
-   const int ND = static_cast<int>(pow(d1d, DIM));
-
-   const auto B = m->maps->B.Read();
-   const auto Bt = m->maps->Bt.Read();
-   const auto pa_data = m->pa_data.Read();
-   const auto dinv = diag_inv.Read();
-   auto r = r_.Write();
-   auto d = d_.Write();
-   auto z = z_.Write();
-   auto u = u_.ReadWrite();
-
-   const real_t RELTOL = rel_tol;
-   const real_t ABSTOL = abs_tol;
-   const int MAXIT = max_iter;
-   const bool IT_MODE = iterative_mode;
-   const bool CHANGE_BASIS = (d2q != nullptr);
-
-   // b is the right-hand side (if no change of basis, this just points to the
-   // incoming RHS vector, if we have to change basis, this points to the
-   // internal b2 vector where we put the transformed RHS)
-   const real_t *b;
-   // the following are non-null if we have to change basis
-   real_t *b2 = nullptr; // non-const access to b2
-   const real_t *b_orig = nullptr; // RHS vector in "original" basis
-   const real_t *d2q_B = nullptr; // matrix to transform initial guess
-   const real_t *q2d_B = nullptr; // matrix to transform solution
-   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
-   if (CHANGE_BASIS)
-   {
-      d2q_B = d2q->B.Read();
-      q2d_B = B_.Read();
-      q2d_Bt = Bt_.Read();
-
-      b2 = b2_.Write();
-      b_orig = b_.Read();
-      b = b2;
-   }
-   else
-   {
-      b = b_.Read();
-   }
-
-   static constexpr int NB = Q1D ? Q1D : 1; // block size
-
-   mfem::forall_2D<NB*NB>(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
-   {
-      // Perform change of basis if needed
-      if (CHANGE_BASIS)
-      {
-         // Transform RHS
-         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
-         if (IT_MODE)
-         {
-            // Transform initial guess
-            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
-         }
-      }
-
-      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
-
-      // Compute first residual
-      if (IT_MODE)
-      {
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
-         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
-      }
-      else
-      {
-         // if not in iterative mode, use zero initial guess
-         const int BX = MFEM_THREAD_SIZE(x);
-         const int BY = MFEM_THREAD_SIZE(y);
-         const int bxy = BX*BY;
-         const auto B = ConstDeviceMatrix(b, ND, NE);
-         auto U = DeviceMatrix(u, ND, NE);
-         auto R = DeviceMatrix(r, ND, NE);
-         for (int i = tid; i < ND; i += bxy)
-         {
-            U(i, e) = 0.0;
-            R(i, e) = B(i, e);
-         }
-         MFEM_SYNC_THREAD;
-      }
-
-      DGMassPreconditioner(e, NE, ND, dinv, r, z);
-      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
-
-      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
-      if (nom < 0.0) { return; /* Not positive definite */ }
-      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
-      if (nom <= r0) { return; /* Converged */ }
-
-      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
-      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
-      if (den <= 0.0)
-      {
-         DGMassDot<NB>(e, NE, ND, d, d);
-         // d2 > 0 => not positive definite
-         if (den == 0.0) { return; }
-      }
-
-      // start iteration
-      int i = 1;
-      while (true)
-      {
-         const real_t alpha = nom/den;
-         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
-         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
-
-         DGMassPreconditioner(e, NE, ND, dinv, r, z);
-
-         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
-         if (betanom < 0.0) { return; /* Not positive definite */ }
-         if (betanom <= r0) { break; /* Converged */ }
-
-         if (++i > MAXIT) { break; }
-
-         const real_t beta = betanom/nom;
-         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
-         den = DGMassDot<NB>(e, NE, ND, d, z);
-         if (den <= 0.0)
-         {
-            DGMassDot<NB>(e, NE, ND, d, d);
-            // d2 > 0 => not positive definite
-            if (den == 0.0) { break; }
-         }
-         nom = betanom;
-      }
-
-      if (CHANGE_BASIS)
-      {
-         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
-      }
-   });
-}
-
-/// @cond Suppress_Doxygen_warnings
-
-template <int DIM, int D1D, int Q1D>
-inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
-{
-   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
-}
-
-inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
-   int dim, int, int)
-{
-   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
-   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
-   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
-   else { MFEM_ABORT("Unsupported dimension."); }
-}
-
-/// @endcond
-
 } // namespace mfem

 #endif
@@ -69,9 +69,9 @@ inline int ToLexOrdering2D(const int face_id, const int size1d, const int i)
 }

 /// @brief Given a face DOF index on a shared face, ordered lexicographically
-/// relative to the element (where the local face is face_id), return the
-/// corresponding face DOF index ordered lexicographically relative to the face
-/// itself.
+/// relative to element the element (where the local face is face_id), and
+/// return the corresponding face DOF index ordered lexicographically relative
+/// to the face itself.
 MFEM_HOST_DEVICE
 inline int PermuteFace2D(const int face_id, const int orientation,
                         const int size1d, const int index)
@@ -231,7 +231,7 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
   {
      for (int nd = 0; nd < dof; nd++)
      {
-         Laplacian[nd] = hess(nd,0) + hess(nd,3) + hess(nd,5);
+         Laplacian[nd] = hess(nd,0) + hess(nd,4) + hess(nd,5);
      }
   }
   else if (dim == 2)
@@ -268,9 +268,11 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
      scale[0] =   Gij(0,0);
      scale[1] = 2*Gij(0,1);
      scale[2] = 2*Gij(0,2);
-      scale[3] =   Gij(1,1);
-      scale[4] = 2*Gij(1,2);
-      scale[5] =   Gij(2,2);
+
+      scale[3] = 2*Gij(1,2);
+      scale[4] =   Gij(2,2);
+
+      scale[5] =   Gij(1,1);
   }
   else if (dim == 2)
   {
@@ -307,12 +309,12 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
      map[2] = 2;

      map[3] = 1;
-      map[4] = 3;
-      map[5] = 4;
+      map[4] = 5;
+      map[5] = 3;

      map[6] = 2;
-      map[7] = 4;
-      map[8] = 5;
+      map[7] = 3;
+      map[8] = 4;
   }
   else if (dim == 2)
   {
@@ -380,7 +382,11 @@ const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &ir,
   #pragma omp critical (DofToQuad)
 #endif
   {
-      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
+      for (int i = 0; i < dof2quad_array.Size(); i++)
+      {
+         d2q = dof2quad_array[i];
+         if (d2q->IntRule != &ir || d2q->mode != mode) { d2q = nullptr; }
+      }
      if (!d2q)
      {
 #ifdef MFEM_THREAD_SAFE
@@ -655,22 +661,14 @@ void ScalarFiniteElement::ScalarLocalL2Restriction(
 void NodalFiniteElement::CreateLexicographicFullMap(const IntegrationRule &ir)
 const
 {
-   // Get the FULL version of the map. This call contains omp critical region,
-   // so it is done before the critical region below.
-   auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);

 #if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
   #pragma omp critical (DofToQuad)
 #endif
   {
-      // If the new Dof2Quad is already present, e.g. added in a previous call
-      // or added by another omp thread, return.
-      if (DofToQuad::SearchArray(dof2quad_array, ir,
-                                 DofToQuad::LEXICOGRAPHIC_FULL))
-      { return; }
-
-      // Undo the native ordering which is what FiniteElement::GetDofToQuad
-      // returns.
+      // Get the FULL version of the map.
+      auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);
+      //Undo the native ordering which is what FiniteElement::GetDofToQuad returns.
      auto *d2q_new = new DofToQuad(d2q);
      d2q_new->mode = DofToQuad::LEXICOGRAPHIC_FULL;
      const int nqpt = ir.GetNPoints();
@@ -726,7 +724,13 @@ const DofToQuad &NodalFiniteElement::GetDofToQuad(const IntegrationRule &ir,
   #pragma omp critical (DofToQuad)
 #endif
   {
-      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
+      //Should make this loop a function of FiniteElement
+      for (int i = 0; i < dof2quad_array.Size(); i++)
+      {
+         d2q = dof2quad_array[i];
+         if (d2q->IntRule == &ir && d2q->mode == mode) { break; }
+         d2q = nullptr;
+      }
   }
   if (d2q) { return *d2q; }
   if (mode != DofToQuad::LEXICOGRAPHIC_FULL)
@@ -2627,7 +2631,15 @@ const DofToQuad &TensorBasisElement::GetTensorDofToQuad(
   #pragma omp critical (DofToQuad)
 #endif
   {
-      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
+      for (int i = 0; i < dof2quad_array.Size(); i++)
+      {
+         auto* d2q_ = dof2quad_array[i];
+         if (d2q_->IntRule == &ir && d2q_->mode == mode)
+         {
+            d2q = d2q_;
+            break;
+         }
+      }
      if (!d2q)
      {
         d2q = new DofToQuad;
@@ -44,7 +44,7 @@ public:
      NumBasisTypes   = 9   /**< Keep track of maximum types to prevent
                                 hard-coding */
   };
-   /** @brief If the input does not represent a valid BasisType, abort with an
+   /** @brief If the input does not represents a valid BasisType, abort with an
       error; otherwise return the input. */
   static int Check(int b_type)
   {
@@ -52,7 +52,7 @@ public:
                  "unknown BasisType: " << b_type);
      return b_type;
   }
-   /** @brief If the input does not represent a valid nodal BasisType, abort
+   /** @brief If the input does not represents a valid nodal BasisType, abort
       with an error; otherwise return the input. */
   static int CheckNodal(int b_type)
   {
@@ -222,12 +222,6 @@ public:

   /// Returns absolute value of the maps
   DofToQuad Abs() const;
-
-   /// Auxiliary function for searching DofToQuad arrays.
-   static inline DofToQuad *SearchArray(
-      const Array<DofToQuad*> &dof2quad_array,
-      const IntegrationRule &ir,
-      DofToQuad::Mode mode);
 };

 /// Describes the function space on each element
@@ -413,7 +407,6 @@ public:
   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
       part of the Hessian of one shape function.
       The order in 2D is {u_xx, u_xy, u_yy}.
-       The order in 3D is {u_xx, u_xy, u_xz, u_yy, u_yz, u_zz}.
       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &Hessian) const;
@@ -1127,7 +1120,7 @@ public:
      return GetPoints(p, btype, on_device);
   }

-   /// Get coordinates of a closed (GaussLobatto) set of points if degree @a p
+   /// Get coordinates of a closed (GaussLegendre) set of points if degree @a p
   const real_t *ClosedPoints(const int p,
                              const int btype = BasisType::GaussLobatto,
                              bool on_device = false)
@@ -1383,21 +1376,6 @@ public:
 void InvertLinearTrans(ElementTransformation &trans,
                       const IntegrationPoint &pt, Vector &x);

-
-// static inline method
-inline DofToQuad *DofToQuad::SearchArray(
-   const Array<DofToQuad*> &dof2quad_array,
-   const IntegrationRule &ir,
-   DofToQuad::Mode mode)
-{
-   for (int i = 0; i < dof2quad_array.Size(); i++)
-   {
-      DofToQuad *d2q = dof2quad_array[i];
-      if (d2q->IntRule == &ir && d2q->mode == mode) { return d2q; }
-   }
-   return nullptr;
-}
-
 } // namespace mfem

 #endif
@@ -60,12 +60,6 @@ void Linear1DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(1,0) =  1.;
 }

-void Linear1DFiniteElement::CalcHessian(const IntegrationPoint &ip,
-                                        DenseMatrix &h) const
-{
-   h = 0.0;
-}
-
 Linear2DFiniteElement::Linear2DFiniteElement()
   : NodalFiniteElement(2, Geometry::TRIANGLE, 3, 1)
 {
@@ -93,11 +87,6 @@ void Linear2DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(2,0) =  0.; dshape(2,1) =  1.;
 }

-void Linear2DFiniteElement::CalcHessian(const IntegrationPoint &ip,
-                                        DenseMatrix &h) const
-{
-   h = 0.0;
-}

 BiLinear2DFiniteElement::BiLinear2DFiniteElement()
   : NodalFiniteElement(2, Geometry::SQUARE, 4, 1, FunctionSpace::Qk)
@@ -1267,12 +1256,6 @@ void Linear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   }
 }

-void Linear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
-                                        DenseMatrix &h) const
-{
-   h = 0.0;
-}
-
 void Linear3DFiniteElement::GetFaceDofs (int face, int **dofs, int *ndofs)
 const
 {
@@ -1649,37 +1632,6 @@ void TriLinear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(7,2) =   ox *  y;
 }

-void TriLinear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
-                                           DenseMatrix &h) const
-{
-   real_t x = ip.x, y = ip.y, z = ip.z;
-   real_t ox = 1.-x, oy = 1.-y, oz = 1.-z;
-
-   h(0,0) = 0.;   h(0,1) =  oz;   h(0,2) = oy;
-   h(0,3) = 0.;   h(0,4) =  ox;   h(0,5) = 0.;
-
-   h(1,0) = 0.;   h(1,1) = -oz;   h(1,2) = -oy;
-   h(1,3) = 0.;   h(1,4) =  x;    h(1,5) = 0.;
-
-   h(2,0) = 0.;   h(2,1) =  oz;   h(2,2) = -y;
-   h(2,3) = 0.;   h(2,4) =  -x;   h(2,5) = 0.;
-
-   h(3,0) = 0.;   h(3,1) = -oz;   h(3,2) = y;
-   h(3,3) = 0.;   h(3,4) = -ox;   h(3,5) = 0.;
-
-   h(4,0) = 0.;   h(4,1) =  z;    h(4,2) = -oy;
-   h(4,3) = 0.;   h(4,4) = -ox;   h(4,5) = 0.;
-
-   h(5,0) = 0.;   h(5,1) = -z;    h(5,2) = oy;
-   h(5,3) = 0.;   h(5,4) = -x;    h(5,5) = 0.;
-
-   h(6,0) = 0.;   h(6,1) =  z;    h(6,2) = y;
-   h(6,3) = 0.;   h(6,4) =  x;    h(6,5) = 0.;
-
-   h(7,0) = 0.;   h(7,1) = -z;    h(7,2) = -y;
-   h(7,3) = 0.;   h(7,4) = ox;    h(7,5) = 0.;
-}
-

 P0SegmentFiniteElement::P0SegmentFiniteElement(int Ord)
   : NodalFiniteElement(1, Geometry::SEGMENT, 1, Ord)   // default Ord = 0
@@ -50,8 +50,6 @@ public:
       contains the derivative of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
-   void CalcHessian(const IntegrationPoint &ip,
-                    DenseMatrix &h) const override;
 };

 /// A 2D linear element on triangle with nodes at the vertices of the triangle
@@ -72,8 +70,6 @@ public:
       so that each row contains the derivatives of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
-   void CalcHessian(const IntegrationPoint &ip,
-                    DenseMatrix &h) const override;
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }
 };
@@ -408,9 +404,6 @@ public:
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;

-   void CalcHessian(const IntegrationPoint &ip,
-                    DenseMatrix &h) const override;
-
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }

@@ -452,8 +445,7 @@ public:
       so that each row contains the derivatives of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
-   void CalcHessian(const IntegrationPoint &ip,
-                    DenseMatrix &h) const override;
+
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }
 };
@@ -84,46 +84,6 @@ void NURBS1DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   add(1.0, hess, (-d2sum + 2*dsum*dsum*sum)*sum*sum, shape_x, hess);
 }

-void NURBS1DFiniteElement::Project(Coefficient &coeff,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   IntegrationPoint ip;
-
-   for (int i = 0; i <= order; i++)
-   {
-      real_t kx = kv[0]->GetBotella(ijk[0] + i);
-      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
-      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
-
-      Trans.SetIntPoint(&ip);
-      dofs(i) = coeff.Eval(Trans, ip);
-   }
-}
-
-void NURBS1DFiniteElement::Project(VectorCoefficient &vc,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
-   Vector x(vc.GetVDim());
-   IntegrationPoint ip;
-
-   for (int i = 0; i <= order; i++)
-   {
-      real_t kx = kv[0]->GetBotella(ijk[0] + i);
-      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
-      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
-
-      Trans.SetIntPoint(&ip);
-      vc.Eval(x, Trans, ip);
-      for (int j = 0; j < x.Size(); j++)
-      {
-         dofs(dof*j+i) = x(j);
-      }
-   }
-}
-

 void NURBS2DFiniteElement::SetOrder() const
 {
@@ -255,63 +215,6 @@ void NURBS2DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   }
 }

-void NURBS2DFiniteElement::Project(Coefficient &coeff,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   IntegrationPoint ip;
-   for (int o = 0, j = 0; j <= orders[1]; j++)
-   {
-      real_t ky = kv[1]->GetBotella(ijk[1] + j);
-      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-      {
-         o += orders[0] + 1;
-         continue;
-      }
-      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-      for (int i = 0; i <= orders[0]; i++, o++)
-      {
-         real_t kx = kv[0]->GetBotella(ijk[0] + i);
-         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-         Trans.SetIntPoint(&ip);
-         dofs(o) = coeff.Eval(Trans, ip);
-      }
-   }
-}
-
-void NURBS2DFiniteElement::Project(VectorCoefficient &vc,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
-   Vector x(vc.GetVDim());
-   IntegrationPoint ip;
-   for (int o = 0, j = 0; j <= orders[1]; j++)
-   {
-      real_t ky = kv[1]->GetBotella(ijk[1] + j);
-      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-      {
-         o += orders[0] + 1;
-         continue;
-      }
-      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-      for (int i = 0; i <= orders[0]; i++, o++)
-      {
-         real_t kx = kv[0]->GetBotella(ijk[0] + i);
-         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-         Trans.SetIntPoint(&ip);
-         vc.Eval(x, Trans, ip);
-         for (int v = 0; v < x.Size(); v++)
-         {
-            dofs(dof*v+o) = x(v);
-         }
-      }
-   }
-}

 void NURBS3DFiniteElement::SetOrder() const
 {
@@ -445,10 +348,11 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
            d2sum[0] += ( hessian(o,0) = d2sx*sy*sz*weights(o) );
            d2sum[1] += ( hessian(o,1) = dsx*dsy*sz*weights(o) );
            d2sum[2] += ( hessian(o,2) = dsx*sy*dsz*weights(o) );
-            d2sum[3] += ( hessian(o,3) = sx*d2sy*sz*weights(o) );
-            d2sum[4] += ( hessian(o,4) = sx*dsy*dsz*weights(o) );
-            d2sum[5] += ( hessian(o,5) = sx*sy*d2sz*weights(o) );

+            d2sum[3] += ( hessian(o,3) = sx*dsy*dsz*weights(o) );
+
+            d2sum[4] += ( hessian(o,4) = sx*sy*d2sz*weights(o) );
+            d2sum[5] += ( hessian(o,5) = sx*d2sy*sz*weights(o) );
         }
      }
   }
@@ -497,85 +401,6 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   }
 }

-void NURBS3DFiniteElement::Project(Coefficient &coeff,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   IntegrationPoint ip;
-
-   for (int o = 0, k = 0; k <= orders[2]; k++)
-   {
-      real_t kz = kv[2]->GetBotella(ijk[2] + k);
-      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
-      {
-         o += (orders[0] + 1)*(orders[1] + 1);
-         continue;
-      }
-      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
-      for (int j = 0; j <= orders[1]; j++)
-      {
-         real_t ky = kv[1]->GetBotella(ijk[1] + j);
-         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-         {
-            o += orders[0] + 1;
-            continue;
-         }
-         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-         for (int i = 0; i <= orders[0]; i++, o++)
-         {
-            real_t kx = kv[0]->GetBotella(ijk[0] + i);
-            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-            Trans.SetIntPoint(&ip);
-            dofs(o) = coeff.Eval(Trans, ip);
-         }
-      }
-   }
-}
-
-void NURBS3DFiniteElement::Project(VectorCoefficient &vc,
-                                   ElementTransformation &Trans,
-                                   Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
-   Vector x(vc.GetVDim());
-   IntegrationPoint ip;
-
-   for (int o = 0, k = 0; k <= orders[2]; k++)
-   {
-      real_t kz = kv[2]->GetBotella(ijk[2] + k);
-      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
-      {
-         o += (orders[0] + 1)*(orders[1] + 1);
-         continue;
-      }
-      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
-      for (int j = 0; j <= orders[1]; j++)
-      {
-         real_t ky = kv[1]->GetBotella(ijk[1] + j);
-         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-         {
-            o += orders[0] + 1;
-            continue;
-         }
-         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-         for (int i = 0; i <= orders[0]; i++, o++)
-         {
-            real_t kx = kv[0]->GetBotella(ijk[0] + i);
-            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-            for (int v = 0; v < x.Size(); v++)
-            {
-               dofs(dof*v+o) = x(v);
-            }
-         }
-      }
-   }
-}

 void NURBS_HDiv2DFiniteElement::SetOrder() const
 {
@@ -692,63 +517,6 @@ void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
   }
 }

-void NURBS_HDiv2DFiniteElement::Project(VectorCoefficient &vc,
-                                        ElementTransformation &Trans,
-                                        Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == dof, "");
-   MFEM_ASSERT(vc.GetVDim() == 2, "");
-   Vector x(2), mx(2);
-   IntegrationPoint ip;
-   int o = 0;
-
-   for (int j = 0; j <= orders[1]; j++)
-   {
-      real_t ky = kv[1]->GetBotella(ijk[1] + j);
-      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-      {
-         o += orders[0] + 2;
-         continue;
-      }
-      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-      for (int i = 0; i <= orders[0]+1; i++, o++)
-      {
-         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
-         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
-         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
-
-         Trans.SetIntPoint(&ip);
-         vc.Eval(x, Trans, ip);
-
-         Trans.AdjugateJacobian().Mult(x,mx);
-         dofs(o) = mx(0);
-      }
-   }
-
-   for (int j = 0; j <= orders[1]+1; j++)
-   {
-      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
-      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
-      {
-         o += orders[0] + 1;
-         continue;
-      }
-      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
-      for (int i = 0; i <= orders[0]; i++, o++)
-      {
-         real_t kx = kv[0]->GetBotella(ijk[0] + i);
-         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-         Trans.SetIntPoint(&ip);
-         vc.Eval(x, Trans, ip);
-
-         Trans.AdjugateJacobian().Mult(x,mx);
-         dofs(o) = mx(1);
-      }
-   }
-}
-
 NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -928,120 +696,6 @@ void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
   }
 }

-
-void NURBS_HDiv3DFiniteElement::Project(VectorCoefficient &vc,
-                                        ElementTransformation &Trans,
-                                        Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == dof, "");
-   MFEM_ASSERT(vc.GetVDim() == 3, "");
-   Vector x(2), mx(3);
-   IntegrationPoint ip;
-
-   int o = 0;
-
-   for (int k = 0; k <= orders[2]; k++)
-   {
-      real_t kz = kv[2]->GetBotella(ijk[2] + k);
-      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
-      {
-         o += (orders[0] + 2)*(orders[1] + 1);
-         continue;
-      }
-      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
-      for (int j = 0; j <= orders[1]; j++)
-      {
-         real_t ky = kv[1]->GetBotella(ijk[1] + j);
-         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-         {
-            o += orders[0] + 2;
-            continue;
-         }
-         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-         for (int i = 0; i <= orders[0]+1; i++, o++)
-         {
-            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
-            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
-            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.AdjugateJacobian().Mult(x,mx);
-            dofs(o) = mx(0);
-         }
-      }
-   }
-
-   for (int k = 0; k <= orders[2]; k++)
-   {
-      real_t kz = kv[2]->GetBotella(ijk[2] + k);
-      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
-      {
-         o += (orders[0] + 1)*(orders[1] + 2);
-         continue;
-      }
-      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
-      for (int j = 0; j <= orders[1]+1; j++)
-      {
-         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
-         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
-         {
-            o += orders[0] + 1;
-            continue;
-         }
-         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
-         for (int i = 0; i <= orders[0]; i++, o++)
-         {
-            real_t kx = kv[0]->GetBotella(ijk[0] + i);
-            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.AdjugateJacobian().Mult(x,mx);
-            dofs(o) = mx(1);
-         }
-      }
-   }
-
-   for (int k = 0; k <= orders[2]+1; k++)
-   {
-      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
-      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
-      {
-         o += (orders[0] + 1)*(orders[1] + 1);
-         continue;
-      }
-      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
-      for (int j = 0; j <= orders[1]; j++)
-      {
-         real_t ky = kv[1]->GetBotella(ijk[1] + j);
-         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-         {
-            o += orders[0] + 1;
-            continue;
-         }
-         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-         for (int i = 0; i <= orders[0]; i++, o++)
-         {
-            real_t kx = kv[0]->GetBotella(ijk[0] + i);
-            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.AdjugateJacobian().Mult(x,mx);
-            dofs(o) = mx(2);
-         }
-      }
-   }
-
-}
-
-
 NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -1163,68 +817,13 @@ void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
   }
 }

-void NURBS_HCurl2DFiniteElement::Project(VectorCoefficient &vc,
-                                         ElementTransformation &Trans,
-                                         Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == dof, "");
-   MFEM_ASSERT(vc.GetVDim() == 2, "");
-   Vector x(2), xm(2);
-   IntegrationPoint ip;
-   int i, j, o;
-   for (o = 0, j = 0; j <= orders[1]+1; j++)
-   {
-      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
-      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
-      {
-         o += orders[0] + 1;
-         continue;
-      }
-      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
-      for (i = 0; i <= orders[0]; i++, o++)
-      {
-         real_t kx = kv[0]->GetBotella(ijk[0] + i);
-         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-         Trans.SetIntPoint(&ip);
-         vc.Eval(x, Trans, ip);
-
-         Trans.Jacobian().MultTranspose(x,xm);
-         dofs(o) = xm(0);
-      }
-   }
-
-   for (j = 0; j <= orders[1]; j++)
-   {
-      real_t ky = kv[1]->GetBotella(ijk[1] + j);
-      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-      {
-         o += orders[0] + 2;
-         continue;
-      }
-      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-      for (i = 0; i <= orders[0]+1; i++, o++)
-      {
-         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
-         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
-         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
-
-         Trans.SetIntPoint(&ip);
-         vc.Eval(x, Trans, ip);
-
-         Trans.Jacobian().MultTranspose(x,xm);
-         dofs(o) = xm(1);
-      }
-   }
-}
-
 NURBS_HCurl2DFiniteElement::~NURBS_HCurl2DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
   if (kv1[1]) { delete kv1[1]; }
 }

+
 void NURBS_HCurl3DFiniteElement::SetOrder() const
 {
   orders[0] = kv[0]->GetOrder();
@@ -1404,124 +1003,11 @@ void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
            curl_shape(o,0) = shape1_x(i)*dsy1_sz;
            curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
            curl_shape(o,2) = 0.0;
-
         }
      }
   }
 }

-void NURBS_HCurl3DFiniteElement::Project(VectorCoefficient &vc,
-                                         ElementTransformation &Trans,
-                                         Vector &dofs) const
-{
-   MFEM_ASSERT(dofs.Size() == dof, "");
-   MFEM_ASSERT(vc.GetVDim() == 3, "");
-   Vector x(3), xm(3);
-   IntegrationPoint ip;
-
-   int o = 0;
-   for (int k = 0; k <= orders[2]+1; k++)
-   {
-      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
-      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
-      {
-         o += (orders[0] + 1)*(orders[1] + 2);
-         continue;
-      }
-      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
-      for (int j = 0; j <= orders[1]+1; j++)
-      {
-         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
-         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
-         {
-            o += orders[0] + 1;
-            continue;
-         }
-         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
-         for (int i = 0; i <= orders[0]; i++, o++)
-         {
-            real_t kx = kv[0]->GetBotella(ijk[0] + i);
-            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
-            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.Jacobian().MultTranspose(x,xm);
-            dofs(o) = xm(0);
-         }
-      }
-   }
-
-   for (int k = 0; k <= orders[2]+1; k++)
-   {
-      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
-      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
-      {
-         o += (orders[0] + 2)*(orders[1] + 1);
-         continue;
-      }
-      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
-      for (int j = 0; j <= orders[1]; j++)
-      {
-         real_t ky = kv[1]->GetBotella(ijk[1] + j);
-         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
-         {
-            o += orders[0] + 2;
-            continue;
-         }
-         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
-         for (int i = 0; i <= orders[0]+1; i++, o++)
-         {
-            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
-            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
-            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.Jacobian().MultTranspose(x,xm);
-            dofs(o) = xm(1);
-         }
-      }
-   }
-
-   for (int k = 0; k <= orders[2]; k++)
-   {
-      real_t kz = kv[2]->GetBotella(ijk[2] + k);
-      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
-      {
-         o += (orders[0] + 2)*(orders[1] + 2);
-         continue;
-      }
-      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
-      for (int j = 0; j <= orders[1]+1; j++)
-      {
-         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
-         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
-         {
-            o += orders[0] + 2;
-            continue;
-         }
-         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
-         for (int i = 0; i <= orders[0]+1; i++, o++)
-         {
-            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
-            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
-            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
-
-            Trans.SetIntPoint(&ip);
-            vc.Eval(x, Trans, ip);
-
-            Trans.Jacobian().MultTranspose(x,xm);
-            dofs(o) = xm(2);
-         }
-      }
-   }
-
-}
-
-
 NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -86,18 +86,6 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
-
-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(Coefficient &coeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
 };

 /// An arbitrary order 2D NURBS element on a square
@@ -133,18 +121,6 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
-
-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(Coefficient &coeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
 };

 /// An arbitrary order 3D NURBS element on a cube
@@ -185,18 +161,6 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
-
-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(Coefficient &coeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
 };


@@ -278,13 +242,6 @@ public:
   void CalcDivShape(const IntegrationPoint &ip,
                     Vector &divshape) const override;

-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
   ~NURBS_HDiv2DFiniteElement();
 };

@@ -379,13 +336,6 @@ public:
   void CalcDivShape(const IntegrationPoint &ip,
                     Vector &divshape) const override;

-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
   ~NURBS_HDiv3DFiniteElement();
 };

@@ -465,13 +415,6 @@ public:
   void CalcCurlShape(const IntegrationPoint &ip,
                      DenseMatrix &curl_shape) const override;

-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
   ~NURBS_HCurl2DFiniteElement();
 };

@@ -563,13 +506,6 @@ public:
   void CalcCurlShape(const IntegrationPoint &ip,
                      DenseMatrix &curl_shape) const override;

-   using FiniteElement::Project;
-
-   /** Evaluate the dofs that are defined on this element.
-       Dofs that can not be evaluated will remain unmodified. */
-   void Project(VectorCoefficient &vcoeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
-
   ~NURBS_HCurl3DFiniteElement();
 };

@@ -509,7 +509,7 @@ GetFace(int &nv, v_t &v, int &ne, e_t &e, eo_t &eo,
      int v0 = v[f_consts::Edges[i][0]];
      int v1 = v[f_consts::Edges[i][1]];
      int eor = 0;
-      if (v0 > v1) { std::swap(v0, v1); eor = 1; }
+      if (v0 > v1) { swap(v0, v1); eor = 1; }
      for (int j = g_consts::VertToVert::I[v0]; true; j++)
      {
         MFEM_ASSERT(j < g_consts::VertToVert::I[v0+1],
@@ -111,36 +111,36 @@ public:
   | :------: | :---: | :---: | :-------: | :-----: | :---: |
   | H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
   | H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
-   | H1Pos_[DIM]_[ORDER] | H1 | * | 2 | VALUE | H1 nodal elements |
+   | H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
   | H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
   | H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
   | ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
   | ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
-   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
-   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * / * | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
+   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
+   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
   | ND_R1D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
   | ND_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
   | ND_R2D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
   | ND_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
   | RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
   | RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
-   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
   | RT_R1D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
   | RT_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
   | RT_R2D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
   | RT_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
-   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | VALUE | Discontinuous L2 elements |
+   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
-   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | INTEGRAL | Discontinuous L2 elements |
+   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
   | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | * | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
   | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | * | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
   | NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
   | LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
   | CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
@@ -172,7 +172,7 @@ public:
   | :------: | :--------: |
   | [DIM]    | Dimension of the elements (1D, 2D, 3D) |
   | [ORDER]  | Approximation order of the elements (P0, P1, P2, ...) |
-   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1-GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform 6-Serendipity 7-ClosedGL 8-IntegratedGLL) |
+   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
   | [OBTYPE] | Open BasisType of the element for elements which have both types |
   | [CBTYPE] | Closed BasisType of the element for elements which have both types |

@@ -50,7 +50,6 @@
 #include "dgmassinv.hpp"
 #include "hyperbolic.hpp"
 #include "bounds.hpp"
-#include "particleset.hpp"

 #include "dfem/doperator.hpp"

@@ -27,6 +27,37 @@ using namespace std;

 namespace mfem
 {
+template <>
+void Ordering::DofsToVDofs<Ordering::byNODES>(int ndofs, int vdim,
+                                              Array<int> &dofs)
+{
+   // static method
+   int size = dofs.Size();
+   dofs.SetSize(size*vdim);
+   for (int vd = 1; vd < vdim; vd++)
+   {
+      for (int i = 0; i < size; i++)
+      {
+         dofs[i+size*vd] = Map<byNODES>(ndofs, vdim, dofs[i], vd);
+      }
+   }
+}
+
+template <>
+void Ordering::DofsToVDofs<Ordering::byVDIM>(int ndofs, int vdim,
+                                             Array<int> &dofs)
+{
+   // static method
+   int size = dofs.Size();
+   dofs.SetSize(size*vdim);
+   for (int vd = vdim-1; vd >= 0; vd--)
+   {
+      for (int i = 0; i < size; i++)
+      {
+         dofs[i+size*vd] = Map<byVDIM>(ndofs, vdim, dofs[i], vd);
+      }
+   }
+}

 FiniteElementSpace::FiniteElementSpace()
   : mesh(NULL), fec(NULL), vdim(0), ordering(Ordering::byNODES),
@@ -1516,87 +1547,42 @@ const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
   const bool is_dg_space = IsDGSpace();
   const L2FaceValues m = (is_dg_space && mul==L2FaceValues::DoubleValued) ?
                          L2FaceValues::DoubleValued : L2FaceValues::SingleValued;
-   auto key = std::make_tuple(is_dg_space, f_ordering, type, m);
+   key_face key = std::make_tuple(is_dg_space, f_ordering, type, m);
   auto itr = L2F.find(key);
   if (itr != L2F.end())
   {
-      return itr->second.get();
+      return itr->second;
   }
   else
   {
-      std::unique_ptr<FaceRestriction> res;
+      FaceRestriction *res;
      if (is_dg_space)
      {
         if (Conforming())
         {
-            res.reset(new L2FaceRestriction(*this, f_ordering, type, m));
+            res = new L2FaceRestriction(*this, f_ordering, type, m);
         }
         else
         {
-            res.reset(new NCL2FaceRestriction(*this, f_ordering, type, m));
+            res = new NCL2FaceRestriction(*this, f_ordering, type, m);
         }
      }
      else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
      {
-         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
+         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
      }
      else
      {
-         res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
+         res = new ConformingFaceRestriction(*this, f_ordering, type);
      }
-      return L2F.emplace(key, std::move(res)).first->second.get();
-   }
-}
-
-const InterpolationManager &FiniteElementSpace::GetInterpolationManager(
-   ElementDofOrdering f_ordering, FaceType type) const
-{
-   const auto key = make_tuple(f_ordering, type);
-
-   auto it = interpolations.find(key);
-   if (it != interpolations.end())
-   {
-      return *it->second;
-   }
-   else
-   {
-      auto interp = make_unique<InterpolationManager>(*this, f_ordering, type);
-
-      int face_idx = 0;
-      for (int f = 0; f < mesh->GetNumFacesWithGhost(); ++f)
-      {
-         Mesh::FaceInformation face = mesh->GetFaceInformation(f);
-         if (!face.IsOfFaceType(type) || face.IsNonconformingCoarse())
-         {
-            continue;
-         }
-         if (face.IsConforming() || face.IsBoundary())
-         {
-            interp->RegisterFaceConformingInterpolation(face, face_idx);
-         }
-         else
-         {
-            interp->RegisterFaceCoarseToFineInterpolation(face, face_idx);
-         }
-         ++face_idx;
-      }
-
-      // Transform the interpolation matrix map into contiguous memory.
-      interp->LinearizeInterpolatorMapIntoVector();
-      interp->InitializeNCInterpConfig();
-
-      return *interpolations.emplace(key, std::move(interp)).first->second;
+      L2F[key] = res;
+      return res;
   }
 }

 const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
   const IntegrationRule &ir) const
 {
-   if (!QuadratureInterpolator::SupportsFESpace(*this))
-   {
-      return nullptr;
-   }
-
   for (int i = 0; i < E2Q_array.Size(); i++)
   {
      const QuadratureInterpolator *qi = E2Q_array[i];
@@ -1611,11 +1597,6 @@ const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
 const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
   const QuadratureSpace &qs) const
 {
-   if (!QuadratureInterpolator::SupportsFESpace(*this))
-   {
-      return nullptr;
-   }
-
   for (int i = 0; i < E2Q_array.Size(); i++)
   {
      const QuadratureInterpolator *qi = E2Q_array[i];
@@ -1631,11 +1612,6 @@ const FaceQuadratureInterpolator
 *FiniteElementSpace::GetFaceQuadratureInterpolator(
   const IntegrationRule &ir, FaceType type) const
 {
-   if (!FaceQuadratureInterpolator::SupportsFESpace(*this))
-   {
-      return nullptr;
-   }
-
   if (type==FaceType::Interior)
   {
      for (int i = 0; i < E2IFQ_array.Size(); i++)
@@ -4009,8 +3985,11 @@ void FiniteElementSpace::Destroy()
      delete E2Q_array[i];
   }
   E2Q_array.SetSize(0);
+   for (auto &x : L2F)
+   {
+      delete x.second;
+   }
   L2F.clear();
-   interpolations.clear();
   for (int i = 0; i < E2IFQ_array.Size(); i++)
   {
      delete E2IFQ_array[i];
@@ -13,8 +13,6 @@
 #define MFEM_FESPACE

 #include "../config/config.hpp"
-#include "../general/hash_util.hpp"
-#include "../linalg/ordering.hpp"
 #include "../linalg/sparsemat.hpp"
 #include "../mesh/mesh.hpp"
 #include "fe_coll.hpp"
@@ -26,6 +24,29 @@
 namespace mfem
 {

+/** @brief The ordering method used when the number of unknowns per mesh node
+    (vector dimension) is bigger than 1. */
+class Ordering
+{
+public:
+   /// %Ordering methods:
+   enum Type
+   {
+      byNODES, /**< loop first over the nodes (inner loop) then over the vector
+                    dimension (outer loop); symbolically it can be represented
+                    as: XXX...,YYY...,ZZZ... */
+      byVDIM   /**< loop first over the vector dimension (inner loop) then over
+                    the nodes (outer loop); symbolically it can be represented
+                    as: XYZ,XYZ,XYZ,... */
+   };
+
+   template <Type Ord>
+   static inline int Map(int ndofs, int vdim, int dof, int vd);
+
+   template <Type Ord>
+   static void DofsToVDofs(int ndofs, int vdim, Array<int> &dofs);
+};
+
 /// @brief Type describing possible layouts for Q-vectors.
 /// @sa QuadratureInterpolator and FaceQuadratureInterpolator.
 enum class QVectorLayout
@@ -43,6 +64,20 @@ enum class QVectorLayout
   byVDIM
 };

+template <> inline int
+Ordering::Map<Ordering::byNODES>(int ndofs, int vdim, int dof, int vd)
+{
+   MFEM_ASSERT(dof < ndofs && -1-dof < ndofs && 0 <= vd && vd < vdim, "");
+   return (dof >= 0) ? dof+ndofs*vd : dof-ndofs*vd;
+}
+
+template <> inline int
+Ordering::Map<Ordering::byVDIM>(int ndofs, int vdim, int dof, int vd)
+{
+   MFEM_ASSERT(dof < ndofs && -1-dof < ndofs && 0 <= vd && vd < vdim, "");
+   return (dof >= 0) ? vd+vdim*dof : -1-(vd+vdim*(-1-dof));
+}
+
 /// Constants describing the possible orderings of the DOFs in one element.
 enum class ElementDofOrdering
 {
@@ -321,11 +356,18 @@ protected:
   mutable OperatorHandle L2E_nat, L2E_lex;
   /// The face restriction operators, see GetFaceRestriction().
   using key_face = std::tuple<bool, ElementDofOrdering, FaceType, L2FaceValues>;
-   mutable std::unordered_map<key_face,std::unique_ptr<FaceRestriction>,
-           TupleHasher> L2F;
-
-   mutable std::unordered_map<std::tuple<ElementDofOrdering,FaceType>,
-           std::unique_ptr<InterpolationManager>, TupleHasher> interpolations;
+   struct key_hash
+   {
+      std::size_t operator()(const key_face& k) const
+      {
+         return std::get<0>(k)
+                + 2 * (int)std::get<1>(k)
+                + 4 * (int)std::get<2>(k)
+                + 8 * (int)std::get<3>(k);
+      }
+   };
+   using map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>;
+   mutable map_L2F L2F;

   mutable Array<QuadratureInterpolator*> E2Q_array;
   mutable Array<FaceQuadratureInterpolator*> E2IFQ_array;
@@ -745,9 +787,6 @@ public:
      ElementDofOrdering f_ordering, FaceType,
      L2FaceValues mul = L2FaceValues::DoubleValued) const;

-   const InterpolationManager &GetInterpolationManager(
-      ElementDofOrdering f_ordering, FaceType type) const;
-
   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
       quadrature point values and/or derivatives (Q-vectors). */
   /** An E-vector represents the element-wise discontinuous version of the FE
@@ -760,10 +799,7 @@ public:
       @note The returned pointer is shared. A good practice, before using it,
       is to set all its properties to their expected values, as other parts of
       the code may also change them. That is, it's good to call
-       SetOutputLayout() and DisableTensorProducts() before interpolating.
-
-       @note If the space is not supported by QuadratureInterpolator, nullptr is
-       returned. */
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const QuadratureInterpolator *GetQuadratureInterpolator(
      const IntegrationRule &ir) const;

@@ -779,10 +815,7 @@ public:
       @note The returned pointer is shared. A good practice, before using it,
       is to set all its properties to their expected values, as other parts of
       the code may also change them. That is, it's good to call
-       SetOutputLayout() and DisableTensorProducts() before interpolating.
-
-       @note If the space is not supported by QuadratureInterpolator, nullptr is
-       returned. */
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const QuadratureInterpolator *GetQuadratureInterpolator(
      const QuadratureSpace &qs) const;

@@ -792,10 +825,7 @@ public:
       @note The returned pointer is shared. A good practice, before using it,
       is to set all its properties to their expected values, as other parts of
       the code may also change them. That is, it's good to call
-       SetOutputLayout() and DisableTensorProducts() before interpolating.
-
-       @note If the space is not supported by FaceQuadratureInterpolator,
-       nullptr is returned. */
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const FaceQuadratureInterpolator *GetFaceQuadratureInterpolator(
      const IntegrationRule &ir, FaceType type) const;

@@ -2352,83 +2352,52 @@ void GridFunction::ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
   }
 }

-void GridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
+void GridFunction::ProjectCoefficient(Coefficient &coeff)
 {
   DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
   DofTransformation doftrans;
-   Array<int> vdofs;
-   Vector vals;

   if (delta_c == NULL)
   {
      if (fes->GetNURBSext() == NULL)
      {
-         switch (type)
+         Array<int> vdofs;
+         Vector vals;
+
+         for (int i = 0; i < fes->GetNE(); i++)
         {
-            case ProjectType::ELEMENT_L2:
-               ProjectCoefficientElementL2(coeff);
-               return;
-            case ProjectType::GLOBAL_L2:
-               ProjectCoefficientGlobalL2(coeff);
-               return;
-            default:
-               for (int i = 0; i < fes->GetNE(); i++)
-               {
-                  fes->GetElementVDofs(i, vdofs, doftrans);
-                  vals.SetSize(vdofs.Size());
-                  fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
-                  doftrans.TransformPrimal(vals);
-                  SetSubVector(vdofs, vals);
-               }
+            fes->GetElementVDofs(i, vdofs, doftrans);
+            vals.SetSize(vdofs.Size());
+            fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+            doftrans.TransformPrimal(vals);
+            SetSubVector(vdofs, vals);
         }
      }
      else
      {
-         switch (type)
-         {
-            case ProjectType::DEFAULT:
-            case ProjectType::ELEMENT_L2:
-               ProjectCoefficientElementL2(coeff);
-               return;
-            case ProjectType::GLOBAL_L2:
-               ProjectCoefficientGlobalL2(coeff);
-               return;
-            case ProjectType::ELEMENT:
-               constexpr real_t signal = std::numeric_limits<real_t>::min();
+         // Define and assemble linear form
+         LinearForm b(fes);
+         b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+         b.Assemble();

-               for (int i = 0; i < fes->GetNE(); i++)
-               {
-                  fes->GetElementVDofs(i, vdofs, doftrans);
-                  vals.SetSize(vdofs.Size());
-                  vals = signal;
+         // Define and assemble bilinear form
+         BilinearForm a(fes);
+         a.AddDomainIntegrator(new MassIntegrator());
+         a.Assemble();

-                  fes->GetFE(i)->Project(coeff,
-                                         *fes->GetElementTransformation(i),
-                                         vals);
-                  doftrans.TransformPrimal(vals);
+         // Set solver and preconditioner
+         SparseMatrix A(a.SpMat());
+         GSSmoother  prec(A);
+         CGSolver cg;
+         cg.SetOperator(A);
+         cg.SetPreconditioner(prec);
+         cg.SetRelTol(1e-12);
+         cg.SetMaxIter(1000);
+         cg.SetPrintLevel(0);

-                  // Remove undefined dofs
-                  // The knot location (either Botella, Demko or Greville point)
-                  // where the NURBS dof are evaluated might fall outside of the
-                  // domain of the element. In that case the value is not set, and
-                  // the value remains the signal value.
-                  int s = 0;
-                  for (int ii = 0; ii < vals.Size(); ii++)
-                  {
-                     if (vals[ii] != signal)
-                     {
-                        vdofs[s] = vdofs[ii];
-                        vals(s) = vals(ii);
-                        s++;
-                     }
-                  }
-                  vdofs.SetSize(s);
-                  vals.SetSize(s);
-
-                  // Add reduced dofs to global vector
-                  SetSubVector(vdofs, vals);
-               }
-         }
+         // Solve and get solution
+         *this = 0.0;
+         cg.Mult(b,*this);
      }
   }
   else
@@ -2441,167 +2410,6 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
   }
 }

-void GridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff, real_t rtol,
-                                              int iter)
-{
-   // Define and assemble linear form
-   LinearForm b(fes);
-   b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
-   b.Assemble();
-
-   // Define and assemble bilinear form
-   BilinearForm a(fes);
-   a.AddDomainIntegrator(new MassIntegrator());
-   a.Assemble();
-
-   // Set solver and preconditioner
-   SparseMatrix A(a.SpMat());
-   GSSmoother  prec(A);
-   CGSolver cg;
-   cg.SetOperator(A);
-   cg.SetPreconditioner(prec);
-   cg.SetRelTol(rtol);
-   cg.SetMaxIter(iter);
-   cg.SetPrintLevel(0);
-
-   // Solve and get solution
-   *this = 0.0;
-   cg.Mult(b,*this);
-}
-
-void GridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
-{
-   Vector Va;
-   ProjectCoefficientElementL2_(coeff, *this, Va);
-   (*this) /= Va;
-}
-
-void GridFunction::ProjectCoefficientElementL2_(Coefficient &coeff,
-                                                Vector &x, Vector &Va)
-{
-   DofTransformation doftrans;
-   Array<int> vdofs;
-   Vector shape,shape2, elvect, elwght;
-   DenseMatrix elmat;
-   Va.SetSize(fes->GetNDofs() );
-   x.SetSize(fes->GetNDofs() );
-   Va = 0.0;
-   x = 0.0;
-
-   if (fes->GetNURBSext() == NULL)
-   {
-      for (int e = 0; e < fes->GetNE(); e++)
-      {
-         fes->GetElementDofs (e, vdofs, doftrans);
-         ElementTransformation &tr = *fes -> GetElementTransformation (e);
-         const FiniteElement &el = *fes->GetFE(e);
-         int dof = el.GetDof();
-         shape.SetSize(dof);
-         elvect.SetSize(dof);
-         elwght.SetSize(dof);
-         elmat.SetSize(dof,dof);
-         elvect = 0.0;
-         elwght = 0.0;
-         elmat = 0.0;
-
-         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
-                                                  2 * el.GetOrder() + 1);
-
-         // Element vector & weight
-         for (int i = 0; i < ir.GetNPoints(); i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-
-            tr.SetIntPoint (&ip);
-            real_t wght = ip.weight*tr.Weight();
-            real_t val = coeff.Eval(tr, ip);
-
-            el.CalcPhysShape(tr, shape);
-
-            elvect.Add(wght * val, shape);
-            elwght.Add(wght, shape);
-            AddMult_a_VVt(wght, shape, elmat);
-         }
-
-         // Solve
-         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
-         {
-            MFEM_WARNING("Error in inverting element local matrix");
-         }
-
-         // Scale
-         elvect *= elwght;
-
-         // Add reduced dofs to global vector
-         x.AddElementVector(vdofs, elvect);
-         Va.AddElementVector(vdofs, elwght);
-      }
-   }
-   else
-   {
-      for (int e = 0; e < fes->GetNE(); e++)
-      {
-         fes->GetElementDofs (e, vdofs, doftrans);
-         ElementTransformation &tr = *fes -> GetElementTransformation (e);
-         const FiniteElement &el = *fes->GetFE(e);
-         int dof = el.GetDof();
-         int dim = el.GetDim();
-         int p = el.GetOrder();
-         L2_FECollection fe_coll(p,  dim);
-         //H1_FECollection fe_coll(p,  dim, BasisType::Positive);
-         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
-         MFEM_ASSERT(el2.GetDof() == dof, "Element dofs do not match.");
-
-         shape.SetSize(dof);
-         shape2.SetSize(dof);
-         elvect.SetSize(dof);
-         elwght.SetSize(dof);
-         elmat.SetSize(dof,dof);
-         elvect = 0.0;
-         elwght = 0.0;
-         elmat = 0.0;
-
-         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
-                                                  2 * el.GetOrder() + 1);
-
-         // Element vector & weight
-         for (int i = 0; i < ir.GetNPoints(); i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-
-            tr.SetIntPoint (&ip);
-            real_t wght = ip.weight*tr.Weight();
-            real_t val = coeff.Eval(tr, ip);
-            el.CalcPhysShape(tr, shape);
-            el2.CalcPhysShape(tr, shape2);
-
-            elvect.Add(wght * val, shape2);
-            elwght.Add(wght, shape);
-            AddMult_a_VVt(wght, shape2, elmat);
-         }
-         // Solve
-         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
-         {
-            MFEM_WARNING("Error in inverting element local matrix 2");
-         }
-         // Map to NURBS
-         DenseMatrix I;
-         el2.Project(el,tr,I);
-         if (!LinearSolve(I, elvect.GetData(),1e-32))
-         {
-            MFEM_WARNING("Error in inverting element local matrix 3");
-         }
-
-         // Scale
-         elvect *= elwght;
-
-         // Add reduced dofs to global vector
-         x.AddElementVector(vdofs, elvect);
-         Va.AddElementVector(vdofs, elwght);
-      }
-   }
-}
-
 void GridFunction::ProjectCoefficient(
   Coefficient &coeff, Array<int> &dofs, int vd)
 {
@@ -2626,318 +2434,49 @@ void GridFunction::ProjectCoefficient(
   }
 }

-void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
-                                      ProjectType type)
+void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
 {
-   Array<int> vdofs;
-   Vector vals;
   DofTransformation doftrans;
-
   if (fes->GetNURBSext() == NULL)
   {
-      switch (type)
+      int i;
+      Array<int> vdofs;
+      Vector vals;
+
+      for (i = 0; i < fes->GetNE(); i++)
      {
-         case ProjectType::ELEMENT_L2:
-            ProjectCoefficientElementL2(vcoeff);
-            return;
-         case ProjectType::GLOBAL_L2:
-            ProjectCoefficientGlobalL2(vcoeff);
-            return;
-         default:
-            for (int i = 0; i < fes->GetNE(); i++)
-            {
-               fes->GetElementVDofs(i, vdofs, doftrans);
-               vals.SetSize(vdofs.Size());
-               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-               doftrans.TransformPrimal(vals);
-               SetSubVector(vdofs, vals);
-            }
+         fes->GetElementVDofs(i, vdofs, doftrans);
+         vals.SetSize(vdofs.Size());
+         fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+         doftrans.TransformPrimal(vals);
+         SetSubVector(vdofs, vals);
      }
   }
   else
   {
-      switch (type)
-      {
-         case ProjectType::DEFAULT:
-         case ProjectType::ELEMENT_L2:
-            ProjectCoefficientElementL2(vcoeff);
-            return;
-         case ProjectType::GLOBAL_L2:
-            ProjectCoefficientGlobalL2(vcoeff);
-            return;
-         case ProjectType::ELEMENT:
-            constexpr real_t signal = std::numeric_limits<real_t>::min();
-            for (int i = 0; i < fes->GetNE(); i++)
-            {
-               fes->GetElementVDofs(i, vdofs, doftrans);
-               vals.SetSize(vdofs.Size());
-               vals = signal;
-               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-               doftrans.TransformPrimal(vals);
-               // Remove undefined dofs
-               // The knot location (either Botella, Demko or Greville point)
-               // where the NURBS dof are evaluated might fall outside of the
-               // domain of the element. In that case the value is not set, and
-               // the value remains the signal value.
-               int s = 0;
-               for (int ii = 0; ii < vals.Size(); ii++)
-               {
-                  if (vals[ii] != signal)
-                  {
-                     vdofs[s] = vdofs[ii];
-                     vals(s) = vals(ii);
-                     s++;
-                  }
-               }
-               vdofs.SetSize(s);
-               vals.SetSize(s);
-
-               // Add reduced dofs to global vector
-               SetSubVector(vdofs, vals);
-            }
-      }
-   }
-}
-
-void GridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
-                                              real_t rtol, int iter)
-{
-   // Define and assemble linear form
-   LinearForm b(fes);
-   BilinearForm a(fes);
-
-   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
-   {
+      // Define and assemble linear form
+      LinearForm b(fes);
      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
+      b.Assemble();
+
+      // Define and assemble bilinear form
+      BilinearForm a(fes);
      a.AddDomainIntegrator(new VectorFEMassIntegrator());
-   }
-   else
-   {
-      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
-      a.AddDomainIntegrator(new VectorMassIntegrator());
-   }
-   a.Assemble();
-   b.Assemble();
+      a.Assemble();

-   // Set solver and preconditioner
-   SparseMatrix A(a.SpMat());
-   GSSmoother  prec(A);
-   CGSolver cg;
-   cg.SetOperator(A);
-   cg.SetPreconditioner(prec);
-   cg.SetRelTol(rtol);
-   cg.SetMaxIter(iter);
-   cg.SetPrintLevel(0);
+      // Set solver and preconditioner
+      SparseMatrix A(a.SpMat());
+      GSSmoother  prec(A);
+      CGSolver cg;
+      cg.SetOperator(A);
+      cg.SetPreconditioner(prec);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(1000);
+      cg.SetPrintLevel(0);

-   // Solve and get solution
-   *this = 0.0;
-   cg.Mult(b,*this);
-}
-
-void GridFunction::ProjectCoefficientElementL2_(VectorCoefficient &vcoeff,
-                                                Vector &x, Vector &Va)
-{
-   DofTransformation doftrans;
-   Array<int> vdofs;
-   Vector shapel2, elvect, elwght, val;
-   DenseMatrix  shape, elmat;
-   Va.SetSize(Size());
-   x.SetSize(Size());
-   Va = 0.0;
-   x = 0.0;
-
-   if (fes->GetNURBSext() == NULL)
-   {
-      for (int e = 0; e < fes->GetNE(); e++)
-      {
-         fes->GetElementVDofs (e, vdofs, doftrans);
-         ElementTransformation &tr = *fes -> GetElementTransformation (e);
-         const FiniteElement &el = *fes->GetFE(e);
-         int dof = el.GetDof();
-         int dim = el.GetRangeDim();
-         shape.SetSize(dof,dim);
-         shapel2.SetSize(dof);
-         elvect.SetSize(dof);
-         elwght.SetSize(dof);
-         elmat.SetSize(dof,dof);
-         elvect = 0.0;
-         elwght = 0.0;
-         elmat = 0.0;
-
-         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
-                                                  2 * el.GetOrder() + 1);
-
-         // Element vector & weight
-         for (int i = 0; i < ir.GetNPoints(); i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-
-            tr.SetIntPoint (&ip);
-            real_t wght = ip.weight*tr.Weight();
-            vcoeff.Eval(val, tr, ip);
-            val *= wght;
-
-            el.CalcPhysVShape(tr, shape);
-
-            shape.AddMult (val, elvect);
-            AddMult_a_AAt(wght, shape, elmat);
-
-            shape.GetRowl2(shapel2);
-            elwght.Add(wght, shapel2);
-         }
-
-         // Solve
-         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
-         {
-            MFEM_WARNING("Error in inverting element local matrix");
-         }
-
-         // Scale
-         elvect *= elwght;
-
-         // Add to global vector
-         x.AddElementVector(vdofs, elvect);
-
-         // Add to weight vector -- no need for an orientation
-         for (int i = 0; i < vdofs.Size(); i++)
-         {
-            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
-         }
-         Va.AddElementVector(vdofs, elwght);
-      }
-   }
-   else
-   {
-      DenseMatrix partelmat;
-      Vector shape2;
-
-      if (fes->GetTypicalFE()->GetOrder() >= 6 )
-      {
-         MFEM_WARNING("This project is not stable for"
-                      "NURBS VectorFE with order >= 5");
-      }
-      for (int e = 0; e < fes->GetNE(); e++)
-      {
-         fes->GetElementVDofs (e, vdofs, doftrans);
-         ElementTransformation &tr = *fes -> GetElementTransformation (e);
-         const FiniteElement &el = *fes->GetFE(e);
-         int dof = el.GetDof();
-         int dim = el.GetRangeDim();
-         int p = el.GetOrder();
-         L2_FECollection fe_coll(p,  dim);
-         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
-         int dof2 = el2.GetDof();
-         MFEM_ASSERT(dof2*dim >= dof, "Element dofs do not match.");
-         shape2.SetSize(dof2);
-         shape.SetSize(dof,dim);
-         shapel2.SetSize(dof);
-         elvect.SetSize(dof2*dim);
-         elwght.SetSize(dof);
-         elmat.SetSize(dof2*dim,dof2*dim);
-         partelmat.SetSize(dof2,dof2);
-         elvect = 0.0;
-         elwght = 0.0;
-         elmat = 0.0;
-
-         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
-                                                  2 * el.GetOrder() + 1);
-
-         // Element vector & weight
-         for (int i = 0; i < ir.GetNPoints(); i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-
-            tr.SetIntPoint (&ip);
-            real_t wght = ip.weight*tr.Weight();
-            vcoeff.Eval(val, tr, ip);
-            val *= wght;
-
-            el2.CalcPhysShape(tr, shape2);
-            el.CalcPhysVShape(tr, shape);
-
-            for (int k = 0; k < dim; k++)
-            {
-               for (int s = 0; s < dof2; s++)
-               {
-                  elvect(dof2*k+s) += val(k) * shape2(s);
-               }
-            }
-
-            MultVVt(shape2, partelmat);
-            partelmat *= wght;
-            for (int k = 0; k < dim; k++)
-            {
-               elmat.AddMatrix(partelmat, dof2*k, dof2*k);
-            }
-
-            shape.GetRowl2(shapel2);
-            elwght.Add(wght, shapel2);
-         }
-
-         // Solve
-         if (!LinearSolve(elmat, elvect.GetData()))
-         {
-            MFEM_WARNING("Error in inverting element local matrix");
-         }
-
-         // Map to NURBS
-         DenseMatrix I;
-         el2.Project(el,tr,I);
-
-         // LSQ solve
-         // For higher order NURBS solving this non-square matrix causes issues.
-         // For Order <=4 the routine seems to work fine.
-         Vector vec(dof);
-         DenseMatrix mat(dof, dof);
-         I.Transpose();
-         I.Mult(elvect, vec);
-         MultAAt(I, mat);
-         if (!LinearSolve(mat, vec.GetData(), 1e-24))
-         {
-            mat.TestInversion();
-            MFEM_WARNING("Error in inverting element local matrix");
-         }
-         elvect = vec;
-
-         // Scale
-         elvect *= elwght;
-
-         // Add to global vector
-         x.AddElementVector(vdofs, elvect);
-
-         // Add to weight vector -- no need for an orientation
-         for (int i = 0; i < vdofs.Size(); i++)
-         {
-            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
-         }
-         Va.AddElementVector(vdofs, elwght);
-      }
-   }
-}
-
-void GridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
-{
-   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
-   {
-      Vector Va;
-      ProjectCoefficientElementL2_(vcoeff, *this, Va);
-      (*this) /= Va;
-   }
-   else
-   {
-      Array<int> vdofs(fes->GetNDofs());
-      Vector x, Va;
-      VectorComponentCoefficient coeff(vcoeff,
-                                       0);  // 0  to ensure we have a valid object
-
-      for (int v = 0; v < VectorDim(); v++)
-      {
-         coeff.SetComponent(v);
-         ProjectCoefficientElementL2_(coeff, x, Va);
-         x /= Va;
-         fes->GetVDofs(v, vdofs);
-         SetSubVector(vdofs, x);
-      }
+      // Solve and get solution
+      *this = 0.0;
+      cg.Mult(b,*this);
   }
 }

@@ -5071,7 +4610,7 @@ GridFunction *Extrude1DGridFunction(Mesh *mesh, Mesh *mesh2d,
 void GridFunction::GetElementBoundsAtControlPoints(const int elem,
                                                   const PLBound &plb,
                                                   Vector &lower, Vector &upper,
-                                                   const int vdim) const
+                                                   const int vdim)
 {
   const FiniteElement *fe = fes->GetFE(elem);
   int fes_dim  = fes->GetVDim();
@@ -5087,7 +4626,7 @@ void GridFunction::GetElementBoundsAtControlPoints(const int elem,
   fes->GetElementDofs(elem, dof_idx);
   int ndofs = dof_idx.Size();

-   int n_c_pts = static_cast<int>(std::pow(plb.GetNControlPoints(), rdim));
+   int n_c_pts = std::pow(plb.GetNControlPoints(), rdim);
   lower.SetSize(n_c_pts*(vdim > 0 ? 1 : fes_dim));
   upper.SetSize(n_c_pts*(vdim > 0 ? 1 : fes_dim));

@@ -5119,13 +4658,13 @@ void GridFunction::GetElementBoundsAtControlPoints(const int elem,

 void GridFunction::GetElementBounds(const int elem, const PLBound &plb,
                                    Vector &lower, Vector &upper,
-                                    const int vdim) const
+                                    const int vdim)
 {
   Vector lowerC, upperC;
   GetElementBoundsAtControlPoints(elem, plb, lowerC, upperC, vdim);
   const FiniteElement *fe = fes->GetFE(elem);
   int rdim  = fe->GetDim();
-   int n_c_pts = static_cast<int>(std::pow(plb.GetNControlPoints(), rdim));
+   int n_c_pts = std::pow(plb.GetNControlPoints(), rdim);
   int fes_dim  = fes->GetVDim();
   lower.SetSize((vdim > 0 ? 1 :fes_dim));
   upper.SetSize((vdim > 0 ? 1 :fes_dim));
@@ -5142,7 +4681,7 @@ void GridFunction::GetElementBounds(const int elem, const PLBound &plb,

 void GridFunction::GetElementBounds(const PLBound &plb,
                                    Vector &lower, Vector &upper,
-                                    const int vdim) const
+                                    const int vdim)
 {
   int nel  = fes->GetNE();
   int fes_dim  = fes->GetVDim();
@@ -5165,7 +4704,7 @@ void GridFunction::GetElementBounds(const PLBound &plb,
 PLBound GridFunction::GetElementBounds(Vector &lower,
                                       Vector &upper,
                                       const int ref_factor,
-                                       const int vdim) const
+                                       const int vdim)
 {
   int max_order = fes->GetMaxElementOrder();
   PLBound plb(fes, ref_factor*(max_order+1));
@@ -5174,7 +4713,7 @@ PLBound GridFunction::GetElementBounds(Vector &lower,
 }

 PLBound GridFunction::GetBounds(Vector &lower, Vector &upper,
-                                const int ref_factor, const int vdim) const
+                                const int ref_factor, const int vdim)
 {
   int max_order = fes->GetMaxElementOrder();
   PLBound plb(fes, ref_factor*(max_order+1));
@@ -27,24 +27,6 @@
 namespace mfem
 {

-/** This enumerated type describes the three main projection types:
-    - ELEMENT, assigns the degree of freedom per element, as specified in the
-      specific element
-    - GLOBAL_L2, solves a global L2 projection
-    - ELEMENT_L2, solves a element level L2 projection. Inter element
-      connectivity is dealt with similar as in:
-      Bezier-Projection : A unified approach for local projection and
-      quadrature-free refinement and coarsening of NURBS and T-splines with
-      particular application to isogeometric design and analysis
-      [CMAME (284) 2015 pg 55-105]
-    - DEFAULT, for NURBS spaces this is ELEMENT_L2, while for all other spaces
-      this ELEMENT.
-   Note 1: ELEMENT_L2 also works for non NURBS elements
-   Note 2: For NURBS elements the ELEMENT projection gives results without
-   over and undershoots. However, the gradient near the boundary does not
-   converge.*/
-enum class ProjectType { DEFAULT, ELEMENT, GLOBAL_L2, ELEMENT_L2 };
-
 /// Class for grid function - Vector with associated FE space.
 class GridFunction : public Vector
 {
@@ -84,17 +66,13 @@ protected:
       degree of freedom. */
   void ProjectDiscCoefficient(VectorCoefficient &coeff, Array<int> &dof_attr);

-   /** Helper function for ProjectCoefficientElementL2 */
-   void ProjectCoefficientElementL2_(Coefficient &coeff, Vector &sol, Vector &Va);
-   void ProjectCoefficientElementL2_(VectorCoefficient &vcoeff, Vector &sol,
-                                     Vector &Va);
-
   /// Loading helper.
   void LegacyNCReorder();

   void Destroy();

 public:
+
   GridFunction() { fes = NULL; fec_owned = NULL; fes_sequence = 0; UseDevice(true); }

   /// Copy constructor. The internal true-dof vector #t_vec is not copied.
@@ -106,10 +84,6 @@ public:
   GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }

-   /// Same as above but specify the memory type
-   GridFunction(FiniteElementSpace *f, MemoryType mt) : Vector(f->GetVSize(), mt)
-   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
-
   /// Construct a GridFunction using previously allocated array @a data.
   /** The GridFunction does not assume ownership of @a data which is assumed to
       be of size at least `f->GetVSize()`. Similar to the Vector constructor
@@ -446,30 +420,9 @@ public:
   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
       projection computation depends on the choice of the FiniteElementSpace
       #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). For elements without a projection
-       member function one could use ProjectCoefficientGlobalL2 instead.
-       NOTE: For parallel simulations with NURBS elements some dofs might
-       not be defined, if the evaluation point does not reside on this rank.
-       If that is the case it is defined on another rank, and the issue is
-       rectified with the appropriate communication, see in ParGridFunction.
-       */
-   virtual void ProjectCoefficient(Coefficient &coeff,
-                                   ProjectType type = ProjectType::DEFAULT);
-
-   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
-       projection is a global L2 projection. This routine can be used a
-       fallback for elements without a projection member function.*/
-   virtual void ProjectCoefficientGlobalL2(Coefficient &coeff,
-                                           real_t rtol = 1e-12,
-                                           int iter = 1000);
-
-   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
-       projection is an element local L2 projection, with an appropriate
-       weighting for Dofs that are shared between elements. Inspired on
-       Bezier-Projection [CMAME (284) 2015 pg 55-105]
-       This routine can be used a fallback for elements without a projection
-       member function.*/
-   virtual void ProjectCoefficientElementL2(Coefficient &coeff);
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
+   virtual void ProjectCoefficient(Coefficient &coeff);

   /** @brief Project @a coeff Coefficient to @a this GridFunction, using one
       element for each degree of freedom in @a dofs and nodal interpolation on
@@ -479,26 +432,9 @@ public:
   /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction. The
       projection computation depends on the choice of the FiniteElementSpace
       #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). For elements without a projection
-       member function one could use ProjectCoefficientGlobalL2 instead.
-       NOTE: For parallel simulations with NURBS elements some dofs might
-       not be defined, if the evaluation point does not reside on this rank.
-       If that is the case it is defined on another rank, and the issue is
-       rectified with the appropriate communication, see in ParGridFunction.*/
-   virtual void ProjectCoefficient(VectorCoefficient &vcoeff,
-                                   ProjectType type = ProjectType::DEFAULT);
-
-   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
-       projection is a global L2 projection. This routine can be used a
-       fallback for elements without a projection member function.*/
-   virtual void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
-                                           real_t rtol = 1e-12,
-                                           int iter = 1000);
-
-   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
-       projection is a global L2 projection. This routine can be used a
-       fallback for elements without a projection member function.*/
-   virtual void ProjectCoefficientElementL2(VectorCoefficient &vcoeff);
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
+   void ProjectCoefficient(VectorCoefficient &vcoeff);

   /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction, using
       one element for each degree of freedom in @a dofs and nodal interpolation
@@ -1668,7 +1604,7 @@ public:
   /// We compute the bounds for each vdim if @a vdim < 1.
   /// Note: For most cases, this method/interface will be sufficient.
   virtual PLBound GetBounds(Vector &lower, Vector &upper,
-                             const int ref_factor=1, const int vdim=-1) const;
+                             const int ref_factor=1, const int vdim=-1);

   /// Computes the \ref PLBound for the gridfunction with number of control
   /// points based on @a ref_factor, and returns the bounds for each element
@@ -1678,27 +1614,27 @@ public:
   /// PLBound object used to compute the bounds.
   /// We compute the bounds for each vdim if @a vdim < 1.
   PLBound GetElementBounds(Vector &lower, Vector &upper,
-                            const int ref_factor=1, const int vdim=-1) const;
+                            const int ref_factor=1, const int vdim=-1);

   /// Compute piecewise linear bounds on the given element at the grid of
   /// [plb.ncp x plb.ncp x plb.ncp] control points for each of the vdim
   /// components of the gridfunction.
   void GetElementBoundsAtControlPoints(const int elem, const PLBound &plb,
                                        Vector &lower, Vector &upper,
-                                        const int vdim = -1) const;
+                                        const int vdim = -1);

   /// Compute bounds on the grid function for the given element.
   /// The bounds are stored in @b lower and @b upper.
   void GetElementBounds(const int elem, const PLBound &plb,
                         Vector &lower, Vector &upper,
-                         const int vdim = -1) const;
+                         const int vdim = -1);

   /// Compute bounds on the grid function for all the elements. The bounds
   /// are returned in @b lower and @b upper, ordered byVDim:
   /// lower_{0,0}, lower_{1,0}, ..., lower_{ne-1,0},
   /// lower_{0,1}, ..., lower_{ne-1,vdim-1}
   void GetElementBounds(const PLBound &plb, Vector &lower, Vector &upper,
-                         const int vdim=-1) const;
+                         const int vdim=-1);
   ///@}

   /// Destroys grid function.
@@ -234,7 +234,7 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
 }

 void FindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                 const int point_pos_ordering)
+                                 int point_pos_ordering)
 {
   MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
   bool dev_mode = (point_pos.UseDevice() && Device::IsEnabled());
@@ -324,7 +324,6 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
         gsl_elem[i] = 0;
         for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
         gsl_code[i] = 2;
-         gsl_proc[i] = gsl_comm->id;
      }
   }

@@ -482,7 +481,7 @@ void FindPointsGSLIB::SetupDevice()
 }

 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         const int point_pos_ordering)
+                                         int point_pos_ordering)
 {
   if (!DEV.setup_device)
   {
@@ -505,13 +504,13 @@ void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,

   if (dim == 2)
   {
-      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem,
-                       gsl_ref, gsl_dist, points_cnt);
+      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
+                       gsl_dist, points_cnt);
   }
   else
   {
-      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem,
-                       gsl_ref, gsl_dist, points_cnt);
+      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
+                       gsl_dist, points_cnt);
   }

   // Sync from device to host
@@ -1085,7 +1084,7 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #else
 void FindPointsGSLIB::SetupDevice() {};
 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         const int point_pos_ordering) {};
+                                         int point_pos_ordering) {};
 void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
                                          Vector &field_out,
                                          const int nel, const int ncomp,
@@ -1094,8 +1093,7 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #endif

 void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
-                                 const int point_pos_ordering,
-                                 const double bb_t,
+                                 int point_pos_ordering, const double bb_t,
                                 const double newt_tol, const int npt_max)
 {
   if (!setupflag || (mesh != &m) )
@@ -1106,28 +1104,16 @@ void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
 }

 void FindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                  const GridFunction &field_in,
-                                  Vector &field_out,
-                                  const int point_pos_ordering)
+                                  const GridFunction &field_in, Vector &field_out,
+                                  int point_pos_ordering)
 {
   FindPoints(point_pos, point_pos_ordering);
   Interpolate(field_in, field_out);
 }

-void FindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                  const GridFunction &field_in,
-                                  Vector &field_out,
-                                  const int point_pos_ordering,
-                                  const int field_out_ordering)
-{
-   FindPoints(point_pos, point_pos_ordering);
-   Interpolate(field_in, field_out, field_out_ordering);
-}
-
 void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
-                                  const GridFunction &field_in,
-                                  Vector &field_out,
-                                  const int point_pos_ordering)
+                                  const GridFunction &field_in, Vector &field_out,
+                                  int point_pos_ordering)
 {
   FindPoints(m, point_pos, point_pos_ordering);
   Interpolate(field_in, field_out);
@@ -1483,7 +1469,7 @@ void FindPointsGSLIB::SetupSplitMeshesAndIntegrationRules(const int order)
 }

 void FindPointsGSLIB::GetNodalValues(const GridFunction *gf_in,
-                                     Vector &node_vals) const
+                                     Vector &node_vals)
 {
   const GridFunction *nodes     = gf_in;
   const FiniteElementSpace *fes = nodes->FESpace();
@@ -1771,13 +1757,6 @@ void FindPointsGSLIB::MapRefPosAndElemIndices()

 void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
                                  Vector &field_out)
-{
-   Interpolate(field_in, field_out, field_in.FESpace()->GetOrdering());
-}
-
-void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
-                                  Vector &field_out,
-                                  const int field_out_ordering)
 {
   const int  gf_order   = field_in.FESpace()->GetMaxElementOrder(),
              mesh_order = mesh->GetNodalFESpace()->GetMaxElementOrder();
@@ -1820,7 +1799,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
      const int maxOrder = field_in.FESpace()->GetMaxElementOrder();

      InterpolateOnDevice(node_vals, field_out, NE_split_total, ncomp,
-                          maxOrder+1, field_out_ordering);
+                          maxOrder+1, field_in.FESpace()->GetOrdering());
      return;
 #endif
   }
@@ -1832,13 +1811,12 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
       field_in.FESpace()->IsVariableOrder() ==
       mesh->GetNodalFESpace()->IsVariableOrder())
   {
-      InterpolateH1(field_in, field_out, field_out_ordering);
+      InterpolateH1(field_in, field_out);
      return;
   }
   else
   {
-      InterpolateGeneral(field_in, field_out,
-                         field_out_ordering);
+      InterpolateGeneral(field_in, field_out);
      if (!fec_l2 || avgtype == AvgType::NONE) { return; }
   }

@@ -1882,11 +1860,11 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,

      if (gf_order_h1 == mesh_order) // basis is GaussLobatto by default
      {
-         InterpolateH1(field_in_h1, field_out_l2, field_out_ordering);
+         InterpolateH1(field_in_h1, field_out_l2);
      }
      else
      {
-         InterpolateGeneral(field_in_h1, field_out_l2, field_out_ordering);
+         InterpolateGeneral(field_in_h1, field_out_l2);
      }

      // Copy interpolated values for the points on element border
@@ -1894,7 +1872,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
      {
         for (int i = 0; i < indl2.Size(); i++)
         {
-            int idx = field_out_ordering == Ordering::byNODES?
+            int idx = field_in_h1.FESpace()->GetOrdering() == Ordering::byNODES?
                      indl2[i] + j*points_cnt:
                      indl2[i]*ncomp + j;
            field_out(idx) = field_out_l2(idx);
@@ -1904,8 +1882,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
 }

 void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
-                                    Vector &field_out,
-                                    const int field_out_ordering)
+                                    Vector &field_out)
 {
   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
   if (field_in.FESpace()->IsVariableOrder())
@@ -1935,8 +1912,7 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                dataptrout = i*points_cnt;
      if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
      {
-         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin,
-                                        points_fld);
+         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
      }
      else
      {
@@ -1968,7 +1944,7 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                        (gslib::findpts_data_3 *)this->fdataD);
      }
   }
-   if (field_out_ordering == Ordering::byVDIM)
+   if (field_in.FESpace()->GetOrdering() == Ordering::byVDIM)
   {
      Vector field_out_temp = field_out;
      for (int i = 0; i < ncomp; i++)
@@ -1982,8 +1958,7 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
 }

 void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
-                                         Vector &field_out,
-                                         const int field_out_ordering)
+                                         Vector &field_out)
 {
   int ncomp   = field_in.VectorDim(),
       nptorig = points_cnt,
@@ -2003,7 +1978,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
         if (dim == 3) { ip.z = gsl_mfem_ref(index*dim + 2); }
         Vector localval(ncomp);
         field_in.GetVectorValue(gsl_mfem_elem[index], ip, localval);
-         if (field_out_ordering == Ordering::byNODES)
+         if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
         {
            for (int i = 0; i < ncomp; i++)
            {
@@ -2038,10 +2013,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
      for (int index = 0; index < npt; index++)
      {
         if (gsl_code[index] == 2) { continue; }
-         for (int d = 0; d < dim; ++d)
-         {
-            pt->r[d]= gsl_mfem_ref(index*dim + d);
-         }
+         for (int d = 0; d < dim; ++d) { pt->r[d]= gsl_mfem_ref(index*dim + d); }
         pt->index = index;
         pt->proc  = gsl_proc[index];
         pt->el    = gsl_mfem_elem[index];
@@ -2131,7 +2103,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
            sdpt = (struct send_pt *)sendpt->ptr;
            for (int index = 0; index < static_cast<int>(sendpt->n); index++)
            {
-               int idx = field_out_ordering == Ordering::byNODES ?
+               int idx = field_in.FESpace()->GetOrdering() == Ordering::byNODES ?
                         sdpt->index + j*nptorig :
                         sdpt->index*ncomp + j;
               field_out(idx) = sdpt->ival;
@@ -2273,7 +2245,7 @@ void FindPointsGSLIB::DistributeInterpolatedValues(const Vector &int_vals,
   }
 }

-void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb) const
+void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb)
 {
   MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
   auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2344,7 +2316,7 @@ void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb) const
 }

 void FindPointsGSLIB::GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
-                                               Vector &obbV) const
+                                               Vector &obbV)
 {
   MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
   auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2529,8 +2501,8 @@ void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
 }

 void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                        const Array<unsigned int> &point_id,
-                                        const int point_pos_ordering)
+                                        Array<unsigned int> &point_id,
+                                        int point_pos_ordering)
 {
   MFEM_VERIFY(setupflag, "Use OversetFindPointsGSLIB::Setup before "
               "finding points.");
@@ -2609,10 +2581,10 @@ void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
 }

 void OversetFindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                         const Array<unsigned int> &point_id,
+                                         Array<unsigned int> &point_id,
                                         const GridFunction &field_in,
                                         Vector &field_out,
-                                         const int point_pos_ordering)
+                                         int point_pos_ordering)
 {
   FindPoints(point_pos, point_id, point_pos_ordering);
   Interpolate(field_in, field_out);
@@ -119,13 +119,11 @@ protected:
   } DEV;

   /// Use GSLIB for communication and interpolation
-   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out,
-                              const int field_out_ordering);
+   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out);
   /// Uses GSLIB Crystal Router for communication followed by MFEM's
   /// interpolation functions
   virtual void InterpolateGeneral(const GridFunction &field_in,
-                                   Vector &field_out,
-                                   const int field_out_ordering);
+                                   Vector &field_out);

   /// Since GSLIB is designed to work with quads/hexes, we split every
   /// triangle/tet/prism/pyramid element into quads/hexes.
@@ -142,7 +140,7 @@ protected:
   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;
+   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals);

   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices,
   /// find the original element number (that was split into micro quads/hexes)
@@ -184,7 +182,7 @@ protected:
       These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
       byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering. */
   void FindPointsOnDevice(const Vector &point_pos,
-                           const int point_pos_ordering = Ordering::byNODES);
+                           int point_pos_ordering = Ordering::byNODES);

   /** Interpolation of field values at prescribed reference space positions.
       @param[in] field_in_evec E-vector of grid function to be interpolated.
@@ -255,15 +253,10 @@ public:
       #gsl_dist        Distance between the sought and the found point
                        in physical space. */
   void FindPoints(const Vector &point_pos,
-                   const int point_pos_ordering = Ordering::byNODES);
-   /// Convenience function when point positions are in a ParticleVector
-   void FindPoints(const ParticleVector &point_pos)
-   {
-      FindPoints(point_pos, point_pos.GetOrdering());
-   }
+                   int point_pos_ordering = Ordering::byNODES);
   /// Setup FindPoints and search positions
   void FindPoints(Mesh &m, const Vector &point_pos,
-                   const int point_pos_ordering = Ordering::byNODES,
+                   int point_pos_ordering = Ordering::byNODES,
                   const double bb_t = 0.1, const double newt_tol = 1.0e-12,
                   const int npt_max = 256);

@@ -273,28 +266,20 @@ public:
                              \p field_in is in H1 and in the same space as the
                              mesh that was given to Setup().
       @param[out] field_out  Interpolated values. For points that are not found
-                              the value is set to #default_interp_value.
-                              The output ordering is determined from field_in.*/
+                              the value is set to #default_interp_value. */
   virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
-   /// Interpolation of field values, with output ordering specification.
-   virtual void Interpolate(const GridFunction &field_in, Vector &field_out,
-                            const int field_out_ordering);
   /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
       the output values in \p field_out corresponds to the ordering used
       in the input GridFunction \p field_in. */
   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                    Vector &field_out,
-                    const int point_pos_ordering = Ordering::byNODES);
-   /// Search positions and interpolate with given point and output ordering.
-   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
-                    Vector &field_out, const int point_pos_ordering,
-                    const int field_out_ordering);
+                    int point_pos_ordering = Ordering::byNODES);
   /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
       or byVDIM) of the output values in \p field_out corresponds to the
       ordering used in the input GridFunction \p field_in. */
   void Interpolate(Mesh &m, const Vector &point_pos,
                    const GridFunction &field_in, Vector &field_out,
-                    const int point_pos_ordering = Ordering::byNODES);
+                    int point_pos_ordering = Ordering::byNODES);

   /// Average type to be used for L2 functions in-case a point is located at
   /// an element boundary where the function might be multi-valued.
@@ -391,7 +376,7 @@ public:
   /// The size of the returned vector is (nel x nverts x dim), where nel is the
   /// number of elements (after splitting for simplcies), nverts is number of
   /// vertices (4 in 2D, 8 in 3D), and dim is the spatial dimension.
-   void GetAxisAlignedBoundingBoxes(Vector &aabb) const;
+   void GetAxisAlignedBoundingBoxes(Vector &aabb);

   /// Return the oriented bounding boxes (OBB) computed during \ref Setup.
   /// Each OBB is represented using the inverse transformation (A^{-1}) and
@@ -401,8 +386,7 @@ public:
   /// size (dim x dim x nel), and the OBB centers are returned in \p obbC,
   /// a vector of size (nel x dim). The vertices of the OBBs are returned in
   /// \p obbV, a vector of size (nel x nverts x dim) .
-   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
-                                 Vector &obbV) const;
+   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC, Vector &obbV);
 };

 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -462,14 +446,13 @@ public:
                                       byNodes: (XXX...,YYY...,ZZZ) or
                                       byVDim: (XYZ,XYZ,....XYZ) */
   void FindPoints(const Vector &point_pos,
-                   const Array<unsigned int> &point_id,
-                   const int point_pos_ordering = Ordering::byNODES);
+                   Array<unsigned int> &point_id,
+                   int point_pos_ordering = Ordering::byNODES);

   /** Search positions and interpolate */
-   void Interpolate(const Vector &point_pos,
-                    const Array<unsigned int> &point_id,
+   void Interpolate(const Vector &point_pos, Array<unsigned int> &point_id,
                    const GridFunction &field_in, Vector &field_out,
-                    const int point_pos_ordering = Ordering::byNODES);
+                    int point_pos_ordering = Ordering::byNODES);
   using FindPointsGSLIB::Interpolate;
 };

@@ -789,6 +789,7 @@ void Hybridization::ComputeH()
   }
   else
   {
+      // TODO: add ones on the diagonal of zero rows
      V->Finalize();
      Array<HYPRE_BigInt> V_J(V->NumNonZeroElems());
      MFEM_ASSERT(c_pfes, "");
@@ -822,13 +823,6 @@ void Hybridization::ComputeH()
      MFEM_VERIFY(pH.Type() != Operator::PETSC_MATIS, "To be implemented");
      pH.MakePtAP(plpH, pP);
      delete lpH;
-
-      HypreParMatrix *hH = pH.As<HypreParMatrix>();
-      MFEM_ASSERT(hH, "");
-
-      SparseMatrix H_diag;
-      hH->GetDiag(H_diag);
-      H_diag.SetDiagIdentity();
   }
 #endif
 }
@@ -14,11 +14,8 @@

 #include "../config/config.hpp"
 #include "../general/array.hpp"
-#include "../linalg/operator.hpp"
 #include "../linalg/vector.hpp"

-#include <memory>
-
 namespace mfem
 {

@@ -48,30 +45,15 @@ protected:
   Array<int> hat_dof_gather_map;
   Array<DofType> hat_dof_marker;

-   Array<int> el_to_face; ///< Element to face connectivity.
-   Array<int> el_face_offsets; ///< Per-element offsets into @a el_to_face.
-   Array<int> face_to_el; ///< Face-to-element connectivity.
-   Array<int> face_face_offsets; ///< Face-to-face offsets.
-
-   int n_el_face; ///< Total number of element-to-face connections.
-   int n_face_face; ///< Total number of face-to-face connections.
-
+   Array<int> el_to_face;
+   Array<int> face_to_el;
   Vector Ct_mat; ///< Constraint matrix (transposed) stored element-wise.

-   /// @name For parallel non-conforming meshes
-   ///@{
-   std::unique_ptr<Operator> P_pc; ///< Partially conforming prolongation.
-   std::unique_ptr<Operator> P_nbr; ///< Face-neighbor prolongation.
-   ///@}
-
   Array<int> idofs, bdofs;

   Vector Ahat, Ahat_ii, Ahat_ib, Ahat_bi, Ahat_bb;
   Array<int> Ahat_ii_piv, Ahat_bb_piv;

-   /// Return the (partially) conforming prolongation on the constraint space.
-   const Operator &GetProlongation() const;
-
 public:
   /// Construct the constraint matrix.
   void ConstructC();
@@ -25,9 +25,9 @@ static void PADGDiffusionSetup2D(const int Q1D, const int NE, const int NF,
                                 const GeometricFactors &el_geom,
                                 const FaceGeometricFactors &face_geom,
                                 const FaceNeighborGeometricFactors *nbr_geom,
-                                 const Vector &q, const int coeff_dim,
-                                 const real_t sigma, const real_t kappa,
-                                 Vector &pa_data, const Array<int> &face_info_)
+                                 const Vector &q, const real_t sigma,
+                                 const real_t kappa, Vector &pa_data,
+                                 const Array<int> &face_info_)
 {
   const auto J_loc = Reshape(el_geom.J.Read(), Q1D, Q1D, 2, 2, NE);
   const auto detJe_loc = Reshape(el_geom.detJ.Read(), Q1D, Q1D, NE);
@@ -41,9 +41,9 @@ static void PADGDiffusionSetup2D(const int Q1D, const int NE, const int NF,
   const auto detJf = Reshape(face_geom.detJ.Read(), Q1D, NF);
   const auto n = Reshape(face_geom.normal.Read(), Q1D, 2, NF);

-   const bool const_q = (q.Size() == coeff_dim);
-   const auto Q = const_q ? Reshape(q.Read(), coeff_dim, 1, 1)
-                  : Reshape(q.Read(), coeff_dim, Q1D, NF);
+   const bool const_q = (q.Size() == 1);
+   const auto Q =
+      const_q ? Reshape(q.Read(), 1, 1) : Reshape(q.Read(), Q1D, NF);

   const auto W = w.Read();

@@ -53,12 +53,6 @@ static void PADGDiffusionSetup2D(const int Q1D, const int NE, const int NF,
   // (q, 1/h, J0_0, J0_1, J1_0, J1_1)
   auto pa = Reshape(pa_data.Write(), 6, Q1D, NF);

-   auto get_coeff = [const_q] MFEM_HOST_DEVICE (const decltype(Q) &Q, int i,
-                                                int qx, int e)
-   {
-      return const_q ? Q(i,0,0) : Q(i,qx,e);
-   };
-
   mfem::forall(NF, [=] MFEM_HOST_DEVICE(int f) -> void
   {
      const int normal_dir[] = {face_info(0, f), face_info(1, f)};
@@ -77,26 +71,10 @@ static void PADGDiffusionSetup2D(const int Q1D, const int NE, const int NF,

      for (int p = 0; p < Q1D; ++p)
      {
-         real_t qh = 0.0;
+         const real_t Qp = const_q ? Q(0, 0) : Q(p, f);
+         pa(0, p, f) = kappa * Qp * W[p] * detJf(p, f);
+
         real_t hi = 0.0;
-
-         real_t Qtn[2];
-         if (coeff_dim > 1)
-         {
-            // matrix coefficient
-            Qtn[0] = get_coeff(Q,0,p,f)*n(p,0,f) + get_coeff(Q,1,p,f)*n(p,1,f);
-            Qtn[1] = get_coeff(Q,2,p,f)*n(p,0,f) + get_coeff(Q,3,p,f)*n(p,1,f);
-            qh = Qtn[0]*n(p,0,f) + Qtn[1]*n(p,1,f);
-         }
-         else
-         {
-            qh = get_coeff(Q, 0, p, f);
-            Qtn[0] = qh*n(p,0,f);
-            Qtn[1] = qh*n(p,1,f);
-         }
-
-         pa(0, p, f) = kappa * qh * W[p] * detJf(p, f);
-
         for (int side = 0; side < nsides; ++side)
         {
            int i, j;
@@ -111,13 +89,15 @@ static void PADGDiffusionSetup2D(const int Q1D, const int NE, const int NF,
            const auto &detJ = (side == 1 && shared) ? detJ_shared : detJe_loc;

            real_t nJi[2];
-            nJi[0] = Qtn[0]*J(i, j, 1, 1, e) - Qtn[1]*J(i, j, 0, 1, e);
-            nJi[1] = -Qtn[0]*J(i, j, 1, 0, e) + Qtn[1]*J(i, j, 0, 0, e);
+            nJi[0] =
+               n(p, 0, f) * J(i, j, 1, 1, e) - n(p, 1, f) * J(i, j, 0, 1, e);
+            nJi[1] =
+               -n(p, 0, f) * J(i, j, 1, 0, e) + n(p, 1, f) * J(i, j, 0, 0, e);

            const real_t dJe = detJ(i, j, e);
            const real_t dJf = detJf(p, f);

-            const real_t w = factor * W[p] * dJf / dJe;
+            const real_t w = factor * Qp * W[p] * dJf / dJe;

            const int ni = normal_dir[side];
            const int ti = 1 - ni;
@@ -146,9 +126,9 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
                                 const GeometricFactors &el_geom,
                                 const FaceGeometricFactors &face_geom,
                                 const FaceNeighborGeometricFactors *nbr_geom,
-                                 const Vector &q, const int coeff_dim,
-                                 const real_t sigma, const real_t kappa,
-                                 Vector &pa_data, const Array<int> &face_info_)
+                                 const Vector &q, const real_t sigma,
+                                 const real_t kappa, Vector &pa_data,
+                                 const Array<int> &face_info_)
 {
   const auto J_loc = Reshape(el_geom.J.Read(), Q1D, Q1D, Q1D, 3, 3, NE);
   const auto detJe_loc = Reshape(el_geom.detJ.Read(), Q1D, Q1D, Q1D, NE);
@@ -162,9 +142,9 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
   const auto detJf = Reshape(face_geom.detJ.Read(), Q1D, Q1D, NF);
   const auto n = Reshape(face_geom.normal.Read(), Q1D, Q1D, 3, NF);

-   const bool const_q = (q.Size() == coeff_dim);
-   const auto Q = const_q ? Reshape(q.Read(), coeff_dim, 1, 1, 1)
-                  : Reshape(q.Read(), coeff_dim, Q1D, Q1D, NF);
+   const bool const_q = (q.Size() == 1);
+   const auto Q =
+      const_q ? Reshape(q.Read(), 1, 1, 1) : Reshape(q.Read(), Q1D, Q1D, NF);

   const auto W = Reshape(w.Read(), Q1D, Q1D);

@@ -177,12 +157,6 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
   // (J00, J01, J02, J10, J11, J12, q/h)
   const auto pa = Reshape(pa_data.Write(), 7, Q1D, Q1D, NF);

-   auto get_coeff = [const_q] MFEM_HOST_DEVICE (const decltype(Q) &Q, int i,
-                                                int qx, int qy, int e)
-   {
-      return const_q ? Q(i,0,0,0) : Q(i,qx,qy,e);
-   };
-
   mfem::forall_2D(NF, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int f) -> void
   {
      MFEM_SHARED int perm[2][3];
@@ -218,32 +192,11 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
      {
         MFEM_FOREACH_THREAD(p2, y, Q1D)
         {
+            const real_t Qp = const_q ? Q(0, 0, 0) : Q(p1, p2, f);
            const real_t dJf = detJf(p1, p2, f);

            real_t hi = 0.0;

-            real_t Qtn[3];
-            real_t qh = 0.0;
-
-            if (coeff_dim > 1)
-            {
-               // matrix coefficient
-               for (int d = 0; d < 3; ++d)
-               {
-                  Qtn[d] = get_coeff(Q,0+3*d,p1,p2,f)*n(p1,p2,0,f)
-                           + get_coeff(Q,1+3*d,p1,p2,f)*n(p1,p2,1,f)
-                           + get_coeff(Q,2+3*d,p1,p2,f)*n(p1,p2,2,f);
-                  qh += Qtn[d] * n(p1,p2,d,f);
-               }
-            }
-            else
-            {
-               qh = get_coeff(Q,0,p1,p2,f);
-               Qtn[0] = qh * n(p1,p2,0,f);
-               Qtn[1] = qh * n(p1,p2,1,f);
-               Qtn[2] = qh * n(p1,p2,2,f);
-            }
-
            for (int side = 0; side < nsides; ++side)
            {
               int i, j, k;
@@ -257,29 +210,38 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
               // *INDENT-OFF*
               real_t nJi[3];
               nJi[0] = (-J(i, j, k, 1, 2, e) * J(i, j, k, 2, 1, e) +
-                         J(i, j, k, 1, 1, e) * J(i, j, k, 2, 2, e)) * Qtn[0] +
-                         (J(i, j, k, 0, 2, e) * J(i, j, k, 2, 1, e) -
-                         J(i, j, k, 0, 1, e) * J(i, j, k, 2, 2, e)) * Qtn[1] +
-                         (-J(i, j, k, 0, 2, e) * J(i, j, k, 1, 1, e) +
-                         J(i, j, k, 0, 1, e) * J(i, j, k, 1, 2, e)) * Qtn[2];
+                         J(i, j, k, 1, 1, e) * J(i, j, k, 2, 2, e)) *
+                           n(p1, p2, 0, f) +
+                        (J(i, j, k, 0, 2, e) * J(i, j, k, 2, 1, e) -
+                         J(i, j, k, 0, 1, e) * J(i, j, k, 2, 2, e)) *
+                           n(p1, p2, 1, f) +
+                        (-J(i, j, k, 0, 2, e) * J(i, j, k, 1, 1, e) +
+                         J(i, j, k, 0, 1, e) * J(i, j, k, 1, 2, e)) *
+                           n(p1, p2, 2, f);

               nJi[1] = (J(i, j, k, 1, 2, e) * J(i, j, k, 2, 0, e) -
-                         J(i, j, k, 1, 0, e) * J(i, j, k, 2, 2, e)) * Qtn[0] +
-                         (-J(i, j, k, 0, 2, e) * J(i, j, k, 2, 0, e) +
-                         J(i, j, k, 0, 0, e) * J(i, j, k, 2, 2, e)) * Qtn[1] +
-                         (J(i, j, k, 0, 2, e) * J(i, j, k, 1, 0, e) -
-                         J(i, j, k, 0, 0, e) * J(i, j, k, 1, 2, e)) * Qtn[2];
+                         J(i, j, k, 1, 0, e) * J(i, j, k, 2, 2, e)) *
+                           n(p1, p2, 0, f) +
+                        (-J(i, j, k, 0, 2, e) * J(i, j, k, 2, 0, e) +
+                         J(i, j, k, 0, 0, e) * J(i, j, k, 2, 2, e)) *
+                           n(p1, p2, 1, f) +
+                        (J(i, j, k, 0, 2, e) * J(i, j, k, 1, 0, e) -
+                         J(i, j, k, 0, 0, e) * J(i, j, k, 1, 2, e)) *
+                           n(p1, p2, 2, f);

               nJi[2] = (-J(i, j, k, 1, 1, e) * J(i, j, k, 2, 0, e) +
-                         J(i, j, k, 1, 0, e) * J(i, j, k, 2, 1, e)) * Qtn[0] +
-                         (J(i, j, k, 0, 1, e) * J(i, j, k, 2, 0, e) -
-                         J(i, j, k, 0, 0, e) * J(i, j, k, 2, 1, e)) * Qtn[1] +
-                         (-J(i, j, k, 0, 1, e) * J(i, j, k, 1, 0, e) +
-                         J(i, j, k, 0, 0, e) * J(i, j, k, 1, 1, e)) * Qtn[2];
+                         J(i, j, k, 1, 0, e) * J(i, j, k, 2, 1, e)) *
+                           n(p1, p2, 0, f) +
+                        (J(i, j, k, 0, 1, e) * J(i, j, k, 2, 0, e) -
+                         J(i, j, k, 0, 0, e) * J(i, j, k, 2, 1, e)) *
+                           n(p1, p2, 1, f) +
+                        (-J(i, j, k, 0, 1, e) * J(i, j, k, 1, 0, e) +
+                         J(i, j, k, 0, 0, e) * J(i, j, k, 1, 1, e)) *
+                           n(p1, p2, 2, f);
               // *INDENT-ON*

               const real_t dJe = detJe(i, j, k, e);
-               const real_t val = factor * W(p1, p2) * dJf / dJe;
+               const real_t val = factor * Qp * W(p1, p2) * dJf / dJe;

               for (int d = 0; d < 3; ++d)
               {
@@ -298,7 +260,7 @@ static void PADGDiffusionSetup3D(const int Q1D, const int NE, const int NF,
               pa(5, p1, p2, f) = 0.0;
            }

-            pa(6, p1, p2, f) = kappa * hi * qh * W(p1, p2) * dJf;
+            pa(6, p1, p2, f) = kappa * hi * Qp * W(p1, p2) * dJf;
         }
      }
   });
@@ -540,12 +502,19 @@ void DGDiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,

   // Evaluate the coefficient at the face quadrature points.
   FaceQuadratureSpace fqs(mesh, ir, type);
-   CoefficientVector q(fqs, CoefficientStorage::CONSTANTS);
-   if (Q) { q.Project(*Q); }
-   else if (MQ) { q.Project(*MQ); }
-   else { q.SetConstant(1.0); }
-
-   const int coeff_dim = q.GetVDim();
+   CoefficientVector q(fqs, CoefficientStorage::COMPRESSED);
+   if (Q)
+   {
+      q.Project(*Q);
+   }
+   else if (MQ)
+   {
+      MFEM_ABORT("Not yet implemented"); /* q.Project(*MQ); */
+   }
+   else
+   {
+      q.SetConstant(1.0);
+   }

   Array<int> face_info;
   if (dim == 1)
@@ -556,15 +525,15 @@ void DGDiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
   {
      PADGDiffusionSetupFaceInfo2D(nf, mesh, type, face_info);
      PADGDiffusionSetup2D(quad1D, ne, nf, ir.GetWeights(), *el_geom,
-                           *face_geom, nbr_geom.get(), q, coeff_dim, sigma,
-                           kappa, pa_data, face_info);
+                           *face_geom, nbr_geom.get(), q, sigma, kappa, pa_data,
+                           face_info);
   }
   else if (dim == 3)
   {
      PADGDiffusionSetupFaceInfo3D(nf, mesh, type, face_info);
      PADGDiffusionSetup3D(quad1D, ne, nf, ir.GetWeights(), *el_geom,
-                           *face_geom, nbr_geom.get(), q, coeff_dim, sigma,
-                           kappa, pa_data, face_info);
+                           *face_geom, nbr_geom.get(), q, sigma, kappa, pa_data,
+                           face_info);
   }
 }

@@ -134,19 +134,14 @@ void PADiffusionSetup2D<2>(const int Q1D,
                           Vector &d)
 {
   const bool symmetric = (coeffDim != 4);
-   const bool const_c = c.Size() == coeffDim;
+   const bool const_c = c.Size() == 1;
+   MFEM_VERIFY(coeffDim < 3 ||
+               !const_c, "Constant matrix coefficient not supported");
   const auto W = Reshape(w.Read(), Q1D,Q1D);
   const auto J = Reshape(j.Read(), Q1D,Q1D,2,2,NE);
-   const auto C = const_c ? Reshape(c.Read(), coeffDim,1,1,1) :
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1,1) :
                  Reshape(c.Read(), coeffDim,Q1D,Q1D,NE);
   auto D = Reshape(d.Write(), Q1D,Q1D, symmetric ? 3 : 4, NE);
-
-   auto get_coeff = [const_c] MFEM_HOST_DEVICE
-                    (const decltype(C) &C, int i, int qx, int qy, int e)
-   {
-      return const_c ? C(i,0,0,0) : C(i,qx,qy,e);
-   };
-
   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
   {
      MFEM_FOREACH_THREAD(qx,x,Q1D)
@@ -161,11 +156,10 @@ void PADiffusionSetup2D<2>(const int Q1D,
            if (coeffDim == 3 || coeffDim == 4) // Matrix coefficient
            {
               // First compute entries of R = MJ^{-T}, without det J factor.
-               const real_t M11 = get_coeff(C,0,qx,qy,e);
-               const real_t M12 = get_coeff(C,1,qx,qy,e);
-               const real_t M21 = symmetric ? M12 : get_coeff(C,2,qx,qy,e);
-               const real_t M22 = symmetric ? get_coeff(C,2,qx,qy,e)
-                                  : get_coeff(C,3,qx,qy,e);
+               const real_t M11 = C(0,qx,qy,e);
+               const real_t M12 = C(1,qx,qy,e);
+               const real_t M21 = symmetric ? M12 : C(2,qx,qy,e);
+               const real_t M22 = symmetric ? C(2,qx,qy,e) : C(3,qx,qy,e);
               const real_t R11 = M11*J22 - M12*J12;
               const real_t R21 = M21*J22 - M22*J12;
               const real_t R12 = -M11*J21 + M12*J11;
@@ -183,8 +177,9 @@ void PADiffusionSetup2D<2>(const int Q1D,
            }
            else // Vector or scalar coefficient
            {
-               const real_t C1 = get_coeff(C,0,qx,qy,e);
-               const real_t C2 = get_coeff(C,coeffDim==2?1:0,qx,qy,e);
+               const real_t C1 = const_c ? C(0,0,0,0) : C(0,qx,qy,e);
+               const real_t C2 = const_c ? C(0,0,0,0) :
+                                 (coeffDim == 2 ? C(1,qx,qy,e) : C(0,qx,qy,e));

               D(qx,qy,0,e) =  w_detJ * (C2*J12*J12 + C1*J22*J22); // 1,1
               D(qx,qy,1,e) = -w_detJ * (C2*J12*J11 + C1*J22*J21); // 1,2
@@ -249,19 +244,14 @@ void PADiffusionSetup3D(const int Q1D,
                        Vector &d)
 {
   const bool symmetric = (coeffDim != 9);
-   const bool const_c = c.Size() == coeffDim;
+   const bool const_c = c.Size() == 1;
+   MFEM_VERIFY(coeffDim < 6 ||
+               !const_c, "Constant matrix coefficient not supported");
   const auto W = Reshape(w.Read(), Q1D,Q1D,Q1D);
   const auto J = Reshape(j.Read(), Q1D,Q1D,Q1D,3,3,NE);
-   const auto C = const_c ? Reshape(c.Read(), coeffDim,1,1,1,1) :
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1,1,1) :
                  Reshape(c.Read(), coeffDim,Q1D,Q1D,Q1D,NE);
   auto D = Reshape(d.Write(), Q1D,Q1D,Q1D, symmetric ? 6 : 9, NE);
-
-   auto get_coeff = [const_c] MFEM_HOST_DEVICE
-                    (const decltype(C) &C, int i, int qx, int qy, int qz, int e)
-   {
-      return const_c ? C(i,0,0,0,0) : C(i,qx,qy,qz,e);
-   };
-
   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
   {
      MFEM_FOREACH_THREAD(qx,x,Q1D)
@@ -297,18 +287,15 @@ void PADiffusionSetup3D(const int Q1D,
               if (coeffDim == 6 || coeffDim == 9) // Matrix coefficient version
               {
                  // Compute entries of R = MJ^{-T} = M adj(J)^T, without det J.
-                  const real_t M11 = get_coeff(C, 0, qx,qy,qz, e);
-                  const real_t M12 = get_coeff(C, 1, qx,qy,qz, e);
-                  const real_t M13 = get_coeff(C, 2, qx,qy,qz, e);
-                  const real_t M21 = (!symmetric) ? get_coeff(C, 3, qx,qy,qz, e) : M12;
-                  const real_t M22 = (!symmetric) ? get_coeff(C, 4, qx,qy,qz, e)
-                                     : get_coeff(C, 3, qx,qy,qz, e);
-                  const real_t M23 = (!symmetric) ? get_coeff(C, 5, qx,qy,qz, e)
-                                     : get_coeff(C, 4, qx,qy,qz, e);
-                  const real_t M31 = (!symmetric) ? get_coeff(C, 6, qx,qy,qz, e) : M13;
-                  const real_t M32 = (!symmetric) ? get_coeff(C, 7, qx,qy,qz, e) : M23;
-                  const real_t M33 = (!symmetric) ? get_coeff(C, 8, qx,qy,qz, e)
-                                     : get_coeff(C, 5, qx,qy,qz, e);
+                  const real_t M11 = C(0, qx,qy,qz, e);
+                  const real_t M12 = C(1, qx,qy,qz, e);
+                  const real_t M13 = C(2, qx,qy,qz, e);
+                  const real_t M21 = (!symmetric) ? C(3, qx,qy,qz, e) : M12;
+                  const real_t M22 = (!symmetric) ? C(4, qx,qy,qz, e) : C(3, qx,qy,qz, e);
+                  const real_t M23 = (!symmetric) ? C(5, qx,qy,qz, e) : C(4, qx,qy,qz, e);
+                  const real_t M31 = (!symmetric) ? C(6, qx,qy,qz, e) : M13;
+                  const real_t M32 = (!symmetric) ? C(7, qx,qy,qz, e) : M23;
+                  const real_t M33 = (!symmetric) ? C(8, qx,qy,qz, e) : C(5, qx,qy,qz, e);

                  const real_t R11 = M11*A11 + M12*A12 + M13*A13;
                  const real_t R12 = M11*A21 + M12*A22 + M13*A23;
@@ -348,9 +335,11 @@ void PADiffusionSetup3D(const int Q1D,
               }
               else  // Vector or scalar coefficient version
               {
-                  const real_t C1 = get_coeff(C,0,qx,qy,qz,e);
-                  const real_t C2 = get_coeff(C,coeffDim==3?1:0,qx,qy,qz,e);
-                  const real_t C3 = get_coeff(C,coeffDim==3?2:0,qx,qy,qz,e);
+                  const real_t C1 = const_c ? C(0,0,0,0,0) : C(0,qx,qy,qz,e);
+                  const real_t C2 = const_c ? C(0,0,0,0,0) :
+                                    (coeffDim == 3 ? C(1,qx,qy,qz,e) : C(0,qx,qy,qz,e));
+                  const real_t C3 = const_c ? C(0,0,0,0,0) :
+                                    (coeffDim == 3 ? C(2,qx,qy,qz,e) : C(0,qx,qy,qz,e));

                  // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
                  D(qx,qy,qz,0,e) = w_detJ * (C1*A11*A11 + C2*A12*A12 + C3*A13*A13); // 1,1
@@ -201,7 +201,7 @@ inline void SmemPADiffusionDiagonal2D(const int NE,
      MFEM_SHARED real_t BG[2][MQ1*MD1];
      real_t (*B)[MD1] = (real_t (*)[MD1]) (BG+0);
      real_t (*G)[MD1] = (real_t (*)[MD1]) (BG+1);
-      MFEM_SHARED real_t QD[3][NBZ][MQ1][MD1];
+      MFEM_SHARED real_t QD[3][NBZ][MD1][MQ1];
      real_t (*QD0)[MD1] = (real_t (*)[MD1])(QD[0] + tidz);
      real_t (*QD1)[MD1] = (real_t (*)[MD1])(QD[1] + tidz);
      real_t (*QD2)[MD1] = (real_t (*)[MD1])(QD[2] + tidz);
@@ -1004,16 +1004,13 @@ inline void SmemPADiffusionApply3D(const int NE,
   const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
   MFEM_VERIFY(D1D <= max_d1d, "");
   MFEM_VERIFY(Q1D <= max_q1d, "");
-   const auto b = Reshape(b_.Read(), Q1D, D1D);
-   const auto g = Reshape(g_.Read(), Q1D, D1D);
-   const auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
-   const auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
+   auto b = Reshape(b_.Read(), Q1D, D1D);
+   auto g = Reshape(g_.Read(), Q1D, D1D);
+   auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
+   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
   MFEM_VERIFY(D1D <= Q1D, "THREAD_DIRECT requires D1D <= Q1D");
-
-   mfem::forall_3D<T_Q1D*T_Q1D*T_Q1D>(NE,
-                                      Q1D, Q1D, Q1D,
-                                      [=] MFEM_HOST_DEVICE (int e)
+   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
   {
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1133,11 +1133,11 @@ inline void SmemPAMassApply3D(const int NE,
   const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
   MFEM_VERIFY(D1D <= max_d1d, "");
   MFEM_VERIFY(Q1D <= max_q1d, "");
-   const auto b = b_.Read();
-   const auto d = d_.Read();
-   const auto x = x_.Read();
+   auto b = b_.Read();
+   auto d = d_.Read();
+   auto x = x_.Read();
   auto y = y_.ReadWrite();
-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
   {
      internal::SmemPAMassApply3D_Element<T_D1D,T_Q1D>(e, NE, b, d, x, y, d1d, q1d);
   });
@@ -1156,8 +1156,8 @@ inline void EAMassAssemble1D(const int NE,
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
-   const auto B = Reshape(basis.Read(), Q1D, D1D);
-   const auto D = Reshape(padata.Read(), Q1D, NE);
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, NE);
   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(), D1D, D1D, NE);
   mfem::forall_2D(NE, D1D, D1D, [=] MFEM_HOST_DEVICE (int e)
   {
@@ -28,7 +28,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   const FaceType ftype = FaceType::Interior;
   const int nf = mesh.GetNFbyType(ftype);

-   const Geometry::Type geom = mesh.GetTypicalFaceGeometry();
+   const Geometry::Type geom = mesh.GetFaceGeometry(0);
   const int trial_order = trial_fes.GetMaxElementOrder();
   const int test_order = test_fes.GetMaxElementOrder();
   const int qorder = test_order + trial_order - 1;
@@ -47,7 +47,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      });
   }

-   const FiniteElement &trial_face_el = *trial_fes.GetTypicalTraceElement();
+   const FiniteElement &trial_face_el = *trial_fes.GetFaceElement(0);
   const auto maps = &trial_face_el.GetDofToQuad(ir, DofToQuad::TENSOR);
   const int ndof_face = trial_face_el.GetDof();

@@ -72,7 +72,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      MFEM_ABORT("Unknown kernel.");
   }

-   const FiniteElement &test_el = *test_fes.GetTypicalFE();
+   const FiniteElement &test_el = *test_fes.GetFE(0);
   const int n_faces_per_el = 2*dim; // assuming tensor product
   // Get all the local face maps (mapping from lexicographic face index to
   // lexicographic volume index, depending on the local face index).
@@ -90,10 +90,10 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   Array<int> face_info(nf * 4);
   {
      int fidx = 0;
-      for (int f = 0; f < mesh.GetNumFacesWithGhost(); ++f)
+      for (int f = 0; f < mesh.GetNumFaces(); ++f)
      {
         Mesh::FaceInformation finfo = mesh.GetFaceInformation(f);
-         if (!finfo.IsInterior() || finfo.IsNonconformingCoarse()) { continue; }
+         if (!finfo.IsInterior()) { continue; }
         face_info[0 + fidx*4] = finfo.element[0].local_face_id;
         face_info[1 + fidx*4] = finfo.element[0].orientation;
         face_info[2 + fidx*4] = finfo.element[1].local_face_id;
@@ -114,7 +114,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   else
   {
      d_emat = emat.Write();
-      emat = 0.0; // Will execute on device, since Write() sets the device flag
+      mfem::forall(emat.Size(), [=] MFEM_HOST_DEVICE (int i) { d_emat[i] = 0.0; });
   }

   const auto face_mats = Reshape(mass_emat.Read(), ndof_face, ndof_face, nf);
@@ -133,104 +133,26 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      }
   };

-   auto permute_face_2 = [=] MFEM_HOST_DEVICE(int local_face_1, int local_face_2,
-                                              int orient, int size1d, int index)
+   mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
   {
-      if (dim == 2)
+      MFEM_FOREACH_THREAD(el_i, z, 2)
      {
-         return internal::PermuteFace2D(local_face_1, local_face_2, orient,
-                                        size1d, index);
-      }
-      else // dim == 3
-      {
-         return internal::PermuteFace3D(local_face_1, local_face_2, orient,
-                                        size1d, index);
-      }
-   };
-
-   if (mesh.Conforming())
-   {
-      mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
-      {
-         MFEM_FOREACH_THREAD(el_i, z, 2)
+         const int lf_i = d_face_info(0, el_i, f);
+         const int orient = d_face_info(1, el_i, f);
+         // Loop over face indices in "native ordering"
+         MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
         {
-            const int lf_i = d_face_info(0, el_i, f);
-            const int orient = d_face_info(1, el_i, f);
-            // Loop over face indices in "native ordering"
-            MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
+            // Convert to lexicographic relative to the face itself
+            const int i_face = permute_face(lf_i, orient, d1d, i_lex);
+            // Convert from lexicographic face DOF to volume DOF
+            const int i = d_face_maps(i_lex, lf_i);
+            MFEM_FOREACH_THREAD(j, y, ndof_face)
            {
-               // Convert to lexicographic relative to the face itself
-               const int i_face = permute_face(lf_i, orient, d1d, i_lex);
-               // Convert from lexicographic face DOF to volume DOF
-               const int i = d_face_maps(i_lex, lf_i);
-               MFEM_FOREACH_THREAD(j, y, ndof_face)
-               {
-                  el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
-               }
+               el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
            }
         }
-      });
-   }
-   else
-   {
-      const InterpolationManager &interp =
-         test_fes.GetInterpolationManager(ElementDofOrdering::LEXICOGRAPHIC, ftype);
-
-      auto interp_configs = interp.GetFaceInterpConfig().Read();
-      const int nc_size = interp.GetNumInterpolators();
-      auto d_interp = Reshape(interp.GetInterpolators().Read(),
-                              ndof_face, ndof_face, nc_size);
-
-      mfem::forall(nf, [=] MFEM_HOST_DEVICE (int f)
-      {
-         const InterpConfig conf = interp_configs[f];
-         const int master_side = conf.master_side;
-         const int interp_index = conf.index;
-
-         const int lf_0 = d_face_info(0, 0, f);
-
-         for (int el_i = 0; el_i < 2; ++el_i)
-         {
-            const int lf_i = d_face_info(0, el_i, f);
-            const int orient = d_face_info(1, el_i, f);
-
-            for (int j = 0; j < ndof_face; j++)
-            {
-               for (int i_lex = 0; i_lex < ndof_face; i_lex++)
-               {
-                  real_t val = 0.0;
-                  if (conf.is_non_conforming && el_i == master_side)
-                  {
-                     // Interpolate from el_i (coarse element) to the fine face.
-                     // The mapping is given by d_interp, which uses indices
-                     // relative to element 0.
-
-                     // i0 is lexicographic relative to element 0
-                     const int i0 = permute_face_2(lf_i, lf_0, orient, d1d, i_lex);
-
-                     // k0 is lexicographic relative to element 0
-                     for (int k0 = 0; k0 < ndof_face; k0++)
-                     {
-                        // k is relative to the face itself
-                        const int k = permute_face(lf_0, orient, d1d, k0);
-                        val += d_interp(k0, i0, interp_index)
-                               * face_mats(k, j, f);
-                     }
-                  }
-                  else
-                  {
-                     // Convert to lexicographic relative to the face itself
-                     const int i_face = permute_face(lf_i, orient, d1d, i_lex);
-                     val = face_mats(i_face, j, f);
-                  }
-                  // Convert from lexicographic face DOF to volume DOF
-                  const int i = d_face_maps(i_lex, lf_i);
-                  el_mats(i, j, el_i, f) += val;
-               }
-            }
-         }
-      });
-   }
+      }
+   });
 }

 }
@@ -54,7 +54,7 @@ void SmemPAVectorDiffusionApply2D(const int NE,
   const auto XE = Reshape(x.Read(), D1D, D1D, SDIM, NE);
   auto YE = Reshape(y.ReadWrite(), D1D, D1D, SDIM, NE);

-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -120,7 +120,7 @@ void SmemPAVectorDiffusionApply3D(const int NE,
   const auto XE = Reshape(x.Read(), D1D, D1D, D1D, SDIM, NE);
   auto YE = Reshape(y.ReadWrite(), D1D, D1D, D1D, SDIM, NE);

-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -51,7 +51,7 @@ void SmemPAVectorMassApply2D(const int NE,
   const auto X = Reshape(x.Read(), D1D, D1D, VDIM, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, VDIM, NE);

-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -119,7 +119,7 @@ void SmemPAVectorMassApply3D(const int NE,
   const auto X = Reshape(x.Read(), D1D, D1D, D1D, VDIM, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, D1D, VDIM, NE);

-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -14,7 +14,6 @@

 #include "../config/config.hpp"
 #include "kernel_reporter.hpp"
-#include "../general/hash_util.hpp"
 #include <unordered_map>
 #include <tuple>
 #include <type_traits>
@@ -87,6 +86,35 @@ namespace mfem
    }                                                                          \
  }

+/// @brief Hashes variadic packs for which each type contained in the variadic
+/// pack has a specialization of `std::hash` available.
+///
+/// For example, packs containing int, bool, enum values, etc.
+template<typename ...KernelParameters>
+struct KernelDispatchKeyHash
+{
+private:
+   template<int N>
+   size_t operator()(std::tuple<KernelParameters...> value) const { return 0; }
+
+   // The hashing formula here is taken directly from the Boost library, with
+   // the magic number 0x9e3779b9 chosen to minimize hashing collisions.
+   template<std::size_t N, typename THead, typename... TTail>
+   size_t operator()(std::tuple<KernelParameters...> value) const
+   {
+      constexpr int Index = N - sizeof...(TTail) - 1;
+      auto lhs_hash = std::hash<THead>()(std::get<Index>(value));
+      auto rhs_hash = operator()<N, TTail...>(value);
+      return lhs_hash^(rhs_hash + 0x9e3779b9 + (lhs_hash<<6) + (lhs_hash>>2));
+   }
+public:
+   /// Returns the hash of the given @a value.
+   size_t operator()(std::tuple<KernelParameters...> value) const
+   {
+      return operator()<sizeof...(KernelParameters),KernelParameters...>(value);
+   }
+};
+
 namespace internal { template<typename... Types> struct KernelTypeList { }; }

 template<typename... T> class KernelDispatchTable { };
@@ -100,8 +128,8 @@ class KernelDispatchTable<Kernels,
         internal::KernelTypeList<Params...>,
         internal::KernelTypeList<OptParams...>>
 {
-   using TableType =
-      std::unordered_map<std::tuple<Params...>, Signature, TupleHasher>;
+   using TableType = std::unordered_map<std::tuple<Params...>,
+         Signature, KernelDispatchKeyHash<Params...>>;
   TableType table;

   /// @brief Call function @a f with arguments @a args (perfect forwaring).
@@ -23,8 +23,6 @@ class BatchedLOR_DG : BatchedLORKernel
 {
   IntegrationRule ir_face; ///< Collocated Gauss-Lobatto face quadrature rule.
   real_t kappa; ///< DG penalty parameter.
-   bool has_bdr_integ; ///< Is there a boundary integrator?
-   const Array<int> *bdr_markers; ///< Boundary integrator markers.
 public:
   template <int ORDER, int SDIM> void Assemble2D();
   template <int ORDER> void Assemble3D();
@@ -40,7 +38,8 @@ public:
      ProjectLORCoefficient<MassIntegrator>(a, c1);
      ProjectLORCoefficient<DiffusionIntegrator>(a, c2);

-      if (auto *integ = GetInteriorFaceIntegrator<DGDiffusionIntegrator>(a))
+      auto *integ = GetInteriorFaceIntegrator<DGDiffusionIntegrator>(a);
+      if (integ)
      {
         kappa = integ->GetPenaltyParameter();
      }
@@ -48,19 +47,6 @@ public:
      {
         kappa = 0.0;
      }
-
-      has_bdr_integ = false;
-      auto *bdr_face_integs = a.GetBFBFI();
-      for (int i = 0; i < bdr_face_integs->Size(); ++i)
-      {
-         if (auto *integ = dynamic_cast<DGDiffusionIntegrator*>((*bdr_face_integs)[i]))
-         {
-            kappa = integ->GetPenaltyParameter();
-            bdr_markers = (*a.GetBFBFI_Marker())[i];
-            has_bdr_integ = true;
-            break;
-         }
-      }
   }

   /// @brief Compute and return the face info array.
@@ -22,13 +22,9 @@ namespace mfem
 Array<int> BatchedLOR_DG::GetFaceInfo() const
 {
   Mesh &mesh = *fes_ho.GetMesh();
-   const Array<int> &bdr_face_attrs = mesh.GetBdrFaceAttributes();
   const int nf = mesh.GetNumFaces();
   Array<int> face_info(nf * 6); // (e0, f0, o0, e1, f1, o1)
   auto h_face_info = Reshape(face_info.HostWrite(), 6, nf);
-
-   int bdr_face_counter = 0;
-
   for (int f = 0; f < nf; ++f)
   {
      auto finfo = mesh.GetFaceInformation(f);
@@ -47,19 +43,6 @@ Array<int> BatchedLOR_DG::GetFaceInfo() const
         h_face_info(4, f) = -1;
         h_face_info(5, f) = -1;
      }
-
-      if (finfo.IsBoundary())
-      {
-         // Check if Neumann boundary; skip these when adding boundary penalties
-         const int bdr_attr = bdr_face_attrs[bdr_face_counter];
-         if (!has_bdr_integ || (bdr_markers && !(*bdr_markers)[bdr_attr - 1]))
-         {
-            h_face_info(0, f) = -1;
-            h_face_info(1, f) = -1;
-            h_face_info(2, f) = -1;
-         }
-         bdr_face_counter += 1;
-      }
   }
   return face_info;
 }
@@ -161,7 +144,6 @@ void BatchedLOR_DG::AssembleFaceTerms()
   {
      const int f_0 = d_face_info(1, f);
      const int f_1 = d_face_info(4, f);
-      if (f_0 < 0) { return; } // Skip Neumann boundary faces
      const int nsides = (f_1 >= 0) ? 2 : 1;
      for (int el_i = 0; el_i < nsides; ++el_i)
      {
@@ -78,7 +78,10 @@ template <int Dim>
 void BuildBoxes(const Mesh &mesh,
                std::vector<::moonolith::AABB<Dim, double>> &element_boxes)
 {
-   MFEM_ASSERT(mesh.Dimension() == Dim, "Mesh and box dimensions mismatched");
+#ifndef NDEBUG
+   const int dim = mesh.Dimension();
+   assert(dim == Dim);
+#endif
   element_boxes.resize(mesh.GetNE());

   DenseMatrix pts;
@@ -1,950 +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.
-
-#include "particleset.hpp"
-
-#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
-
-// Ignore warnings from the gslib header (GCC version)
-#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wunused-function"
-#endif
-
-namespace gslib
-{
-extern "C"
-{
-#include <gslib.h>
-} // extern C
-} // namespace gslib
-
-#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
-#pragma GCC diagnostic pop
-#endif
-
-#endif // MFEM_USE_MPI && MFEM_USE_GSLIB
-
-
-namespace mfem
-{
-
-Particle::Particle(int dim, const Array<int> &field_vdims, int num_tags)
-   : coords(dim), fields(), tags()
-{
-   coords = 0.0;
-
-   fields.reserve(field_vdims.Size());
-   for (int f = 0; f < field_vdims.Size(); f++)
-   {
-      fields.emplace_back(field_vdims[f]);
-      fields.back() = 0.0;
-   }
-
-   tags.reserve(num_tags);
-   for (int t = 0; t < num_tags; t++)
-   {
-      tags.emplace_back(1);
-      tags.back()[0] = 0;
-   }
-}
-
-void Particle::SetTagRef(int t, int *tag_data)
-{
-   MFEM_ASSERT(t >= 0 &&
-               static_cast<size_t>(t) < tags.size(), "Invalid tag index");
-   tags[t].MakeRef(tag_data, 1);
-}
-
-void Particle::SetFieldRef(int f, real_t *field_data)
-{
-   MFEM_ASSERT(f >= 0 &&
-               static_cast<size_t>(f) < fields.size(), "Invalid field "
-               "index");
-   Vector temp(field_data, fields[f].Size());
-   fields[f].MakeRef(temp, 0, fields[f].Size());
-}
-
-bool Particle::operator==(const Particle &rhs) const
-{
-   // Compare coordinate size and values
-   if (coords.Size() != rhs.coords.Size())
-   {
-      return false;
-   }
-   for (int d = 0; d < coords.Size(); d++)
-   {
-      if (coords[d] != rhs.coords[d])
-      {
-         return false;
-      }
-   }
-   // Compare fields vdim and values
-   if (fields.size() != rhs.fields.size())
-   {
-      return false;
-   }
-   for (size_t f = 0; f < fields.size(); f++)
-   {
-      if (fields[f].Size() != rhs.fields[f].Size())
-      {
-         return false;
-      }
-      for (int c = 0; c < fields[f].Size(); c++)
-      {
-         if (fields[f][c] != rhs.fields[f][c])
-         {
-            return false;
-         }
-      }
-   }
-   // Compare tags size and values
-   if (tags.size() != rhs.tags.size())
-   {
-      return false;
-   }
-   for (size_t t = 0; t < tags.size(); t++)
-   {
-      if (tags[t][0] != rhs.tags[t][0])
-      {
-         return false;
-      }
-   }
-
-   return true;
-}
-
-void Particle::Print(std::ostream &os) const
-{
-   os << "Coords: (";
-   for (int d = 0; d < coords.Size(); d++)
-   {
-      os << coords[d] << ( (d+1 < coords.Size()) ? "," : ")\n");
-   }
-   for (size_t f = 0; f < fields.size(); f++)
-   {
-      os << "Field " << f << ": (";
-      for (int c = 0; c < fields[f].Size(); c++)
-      {
-         os << fields[f][c] << ( (c+1 < fields[f].Size()) ? "," : ")\n");
-      }
-   }
-   for (size_t t = 0; t < tags.size(); t++)
-   {
-      os << "Tag " << t << ": " << tags[t][0] << "\n";
-   }
-}
-
-Array<Ordering::Type> ParticleSet::GetOrderingArray(Ordering::Type o, int N)
-{
-   Array<Ordering::Type> ordering_arr(N);
-   ordering_arr = o;
-   return ordering_arr;
-}
-std::string ParticleSet::GetDefaultFieldName(int i)
-{
-   return "Field_" + std::to_string(i);
-}
-
-std::string ParticleSet::GetDefaultTagName(int i)
-{
-   return "Tag_" + std::to_string(i);
-}
-
-Array<const char*> ParticleSet::GetEmptyNameArray(int N)
-{
-   Array<const char*> names(N);
-   names = nullptr;
-   return names;
-}
-
-#ifdef MFEM_USE_MPI
-int ParticleSet::GetRank(MPI_Comm comm_)
-{
-   int r; MPI_Comm_rank(comm_, &r);
-   return r;
-}
-int ParticleSet::GetSize(MPI_Comm comm_)
-{
-   int s; MPI_Comm_size(comm_, &s);
-   return s;
-}
-#endif // MFEM_USE_MPI
-
-void ParticleSet::Reserve(int res)
-{
-   ids.Reserve(res);
-
-   // Reserve fields
-   for (int f = -1; f < GetNFields(); f++)
-   {
-      ParticleVector &pv = (f == -1 ? coords : *fields[f]);
-      pv.Reserve(res*pv.GetVDim());
-   }
-
-   // Reserve tags
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      tags[t]->Reserve(res);
-   }
-
-}
-
-const Array<int> ParticleSet::GetFieldVDims() const
-{
-   Array<int> field_vdims(GetNFields());
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      field_vdims[f] = Field(f).GetVDim();
-   }
-   return field_vdims;
-}
-
-void ParticleSet::AddParticles(const Array<IDType> &new_ids,
-                               Array<int> *new_indices)
-{
-   int num_add = new_ids.Size();
-   int old_np = GetNParticles();
-   int new_np = old_np + num_add;
-
-   // Set indices of new particles
-   if (new_indices)
-   {
-      new_indices->SetSize(num_add);
-      for (int i = 0; i < num_add; i++)
-      {
-         (*new_indices)[i] = ids.Size() + i;
-      }
-   }
-   // Add new ids
-   ids.Append(new_ids);
-
-   // Update data
-   for (int f = -1; f < GetNFields(); f++)
-   {
-      ParticleVector &pv = (f == -1 ? coords : *fields[f]);
-      pv.SetNumParticles(new_np); // does not delete existing data
-   }
-
-   // Update tags
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      tags[t]->SetSize(new_np);
-   }
-}
-
-#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
-
-/// \cond DO_NOT_DOCUMENT
-template<size_t NBytes>
-void ParticleSet::TransferParticlesImpl(ParticleSet &pset,
-                                        const Array<int> &send_idxs,
-                                        const Array<unsigned int> &send_ranks)
-{
-   struct pdata_t
-   {
-      alignas(real_t) std::array<std::byte, NBytes> data;
-      IDType id;
-   };
-
-   int nreals = pset.GetFieldVDims().Sum() + pset.Coords().GetVDim();
-   int ntags = pset.GetNTags();
-   size_t nbytes = nreals*sizeof(real_t) + ntags*sizeof(int);
-   MFEM_VERIFY(nbytes <= NBytes, "More data than can be packed.");
-
-   using parr_t = pdata_t;
-   gslib::array gsl_arr;
-   parr_t *pdata_arr;
-   array_init(parr_t, &gsl_arr, send_idxs.Size());
-   pdata_arr = (parr_t*) gsl_arr.ptr;
-
-   gsl_arr.n = send_idxs.Size();
-   for (int i = 0; i < send_idxs.Size(); i++)
-   {
-      parr_t &pdata = pdata_arr[i];
-      pdata.id = pset.GetIDs()[send_idxs[i]];
-
-      // Copy particle data directly into pdata
-      size_t counter = 0;
-      for (int f = -1; f < pset.GetNFields(); f++)
-      {
-         ParticleVector &pv = (f == -1 ? pset.Coords() : pset.Field(f));
-         for (int c = 0; c < pv.GetVDim(); c++)
-         {
-            std::memcpy(pdata.data.data() + counter, &pv(send_idxs[i], c),
-                        sizeof(real_t));
-            counter += sizeof(real_t);
-         }
-      }
-
-      // Copy tags
-      for (int t = 0; t < pset.GetNTags(); t++)
-      {
-         Array<int> &tag_arr = pset.Tag(t);
-         std::memcpy(pdata.data.data() + counter, &tag_arr[send_idxs[i]],
-                     sizeof(int));
-         counter += sizeof(int);
-      }
-   }
-
-   int nparticles = pset.GetNParticles();
-   int nsend      = send_idxs.Size();
-
-   // Transfer particles
-   sarray_transfer_ext(parr_t, &gsl_arr, send_ranks.GetData(),
-                       sizeof(unsigned int), pset.cr);
-
-   // Make sure we have enough space for received particles
-   int nrecv = (int) gsl_arr.n;
-   int ndelete = nsend - nrecv;
-   if (ndelete > 0)
-   {
-      // Remove unneeded particles
-      auto datap = const_cast<int*>(send_idxs.GetData());
-      Array<int> delete_idxs(datap + nrecv, ndelete);
-      pset.RemoveParticles(delete_idxs);
-   }
-   else
-   {
-      pset.Reserve(nparticles-ndelete);
-   }
-
-   pdata_arr = (parr_t*) gsl_arr.ptr;
-
-   // Add newly-recvd data directly to active state
-   for (int i = 0; i < nrecv; i++)
-   {
-      parr_t &pdata = pdata_arr[i];
-      IDType id = pdata.id;
-
-      int new_loc_idx;
-      if (i < nsend) // update existing particle
-      {
-         new_loc_idx = send_idxs[i];
-         pset.UpdateID(new_loc_idx, id);
-      }
-      else
-      {
-         // add new particle
-         Array<int> idx_temp;
-         pset.AddParticles(Array<IDType>({id}), &idx_temp);
-         new_loc_idx = idx_temp[0]; // Get index of newly-added particle
-      }
-
-      size_t counter = 0;
-      for (int f = -1; f < pset.GetNFields(); f++)
-      {
-         ParticleVector &pv = (f == -1 ? pset.Coords() : pset.Field(f));
-         for (int c = 0; c < pv.GetVDim(); c++)
-         {
-            real_t& val = pv(new_loc_idx, c);
-            std::memcpy(&val, pdata.data.data() + counter, sizeof(real_t));
-            counter += sizeof(real_t);
-         }
-      }
-
-      for (int t = 0; t < pset.GetNTags(); t++)
-      {
-         Array<int> &tag_arr = pset.Tag(t);
-         std::memcpy(&tag_arr[new_loc_idx],
-                     pdata.data.data() + counter, sizeof(int));
-         counter += sizeof(int);
-      }
-   }
-   array_free(&gsl_arr);
-}
-
-template<size_t NBytes>
-ParticleSet::TransferParticlesType ParticleSet::TransferParticles::Kernel()
-{
-   return &ParticleSet::TransferParticlesImpl<NBytes>;
-}
-
-ParticleSet::Kernels::Kernels()
-{
-   constexpr size_t sizd = sizeof(real_t);
-   TransferParticles::Specialization<2*sizd>::Add();
-   TransferParticles::Specialization<3*sizd>::Add();
-   TransferParticles::Specialization<4*sizd>::Add();
-   TransferParticles::Specialization<8*sizd>::Add();
-   TransferParticles::Specialization<12*sizd>::Add();
-   TransferParticles::Specialization<16*sizd>::Add();
-   TransferParticles::Specialization<20*sizd>::Add();
-   TransferParticles::Specialization<24*sizd>::Add();
-   TransferParticles::Specialization<28*sizd>::Add();
-   TransferParticles::Specialization<32*sizd>::Add();
-   TransferParticles::Specialization<36*sizd>::Add();
-   TransferParticles::Specialization<40*sizd>::Add();
-}
-
-auto ParticleSet::TransferParticles::Fallback(size_t bufsize)
-> ParticleSet::TransferParticlesType
-{
-   constexpr size_t sizd = sizeof(real_t);
-   if (bufsize < 4*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<4*sizd>;
-   }
-   else if (bufsize < 8*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<8*sizd>;
-   }
-   else if (bufsize < 12*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<12*sizd>;
-   }
-   else if (bufsize < 16*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<16*sizd>;
-   }
-   else if (bufsize < 20*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<20*sizd>;
-   }
-   else if (bufsize < 24*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<24*sizd>;
-   }
-   else if (bufsize < 28*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<28*sizd>;
-   }
-   else if (bufsize < 32*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<32*sizd>;
-   }
-   else if (bufsize < 36*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<36*sizd>;
-   }
-   else if (bufsize < 40*sizd)
-   {
-      return &ParticleSet::TransferParticlesImpl<40*sizd>;
-   }
-   return &ParticleSet::TransferParticlesImpl<60*sizd>;
-}
-/// \endcond DO_NOT_DOCUMENT
-
-void ParticleSet::Redistribute(const Array<unsigned int> &rank_list)
-{
-   MFEM_ASSERT(rank_list.Size() == GetNParticles(),
-               "rank_list must be of size GetNParticles().");
-
-   int rank = GetRank(comm);
-
-   // Get particles to be transferred
-   // (Avoid unnecessary copies of particle data into and out of buffers)
-   Array<int> send_idxs;
-   Array<unsigned int> send_ranks;
-   send_idxs.Reserve(rank_list.Size());
-   send_ranks.Reserve(rank_list.Size());
-   for (int i = 0; i < rank_list.Size(); i++)
-   {
-      if (rank != static_cast<int>(rank_list[i]))
-      {
-         send_idxs.Append(i);
-         send_ranks.Append(rank_list[i]);
-      }
-   }
-
-   // Compute number of bytes of a single particle
-   int nreals = GetFieldVDims().Sum() + coords.GetVDim();
-   int ntags = GetNTags();
-   size_t nbytes = nreals*sizeof(real_t) + ntags*sizeof(int);
-
-   // Dispatch to appropriate redistribution function for this size
-   TransferParticles::Run(nbytes, *this, send_idxs, send_ranks);
-}
-
-#endif // MFEM_USE_MPI && MFEM_USE_GSLIB
-
-Particle ParticleSet::CreateParticle() const
-{
-   return Particle(GetDim(), GetFieldVDims(), GetNTags());
-}
-
-void ParticleSet::WriteToFile(const char *fname,
-                              const std::stringstream &ss_header, const std::stringstream &ss_data)
-{
-
-#ifdef MFEM_USE_MPI
-   // Parallel:
-   int rank = GetRank(comm);
-
-   MPI_File_delete(fname, MPI_INFO_NULL); // delete old file if it exists
-   MPI_File file;
-   int mpi_err = MPI_File_open(comm, fname, MPI_MODE_CREATE | MPI_MODE_WRONLY,
-                               MPI_INFO_NULL, &file);
-   MFEM_VERIFY(mpi_err == MPI_SUCCESS, "MPI_File_open failed.");
-
-   // Print header
-   if (rank == 0)
-   {
-      MPI_File_write_at(file, 0, ss_header.str().data(), ss_header.str().size(),
-                        MPI_CHAR, MPI_STATUS_IGNORE);
-   }
-
-   // Compute the data size in bytes
-   MPI_Offset data_size = ss_data.str().size();
-   MPI_Offset offset;
-
-   // Compute the offsets using an exclusive scan
-   MPI_Exscan(&data_size, &offset, 1, MPI_OFFSET, MPI_SUM, comm);
-   if (rank == 0)
-   {
-      offset = 0;
-   }
-
-   // Add offset from the header
-   offset += ss_header.str().size();
-
-   // Write data collectively
-   MPI_File_write_at_all(file, offset, ss_data.str().data(),
-                         data_size, MPI_BYTE, MPI_STATUS_IGNORE);
-
-   // Close file
-   MPI_File_close(&file);
-#else
-   // Serial:
-   std::ofstream ofs(fname);
-   MFEM_VERIFY(ofs.is_open() && !ofs.fail(),
-               "Error: Could not open file " << fname << " for writing.");
-   ofs << ss_header.str() << ss_data.str();
-   ofs.close();
-#endif // MFEM_USE_MPI
-}
-
-ParticleSet::ParticleSet(int id_stride_, IDType id_counter_, int num_particles,
-                         int dim, Ordering::Type coords_ordering, const Array<int> &field_vdims,
-                         const Array<Ordering::Type> &field_orderings,
-                         const Array<const char*> &field_names_, int num_tags,
-                         const Array<const char*> &tag_names_)
-   : id_stride(id_stride_),
-     id_counter(id_counter_),
-     coords(dim, coords_ordering)
-{
-   // Initialize fields
-   for (int f = 0; f < field_vdims.Size(); f++)
-   {
-      AddField(field_vdims[f], field_orderings[f], field_names_[f]);
-   }
-
-   // Initialize tags
-   for (int t = 0; t < num_tags; t++)
-   {
-      AddTag(tag_names_[t]);
-   }
-
-   // Add num_particles
-   Array<IDType> init_ids(num_particles);
-   for (int i = 0; i < num_particles; i++)
-   {
-      init_ids[i] = id_counter;
-      id_counter += id_stride;
-   }
-   AddParticles(init_ids);
-}
-
-bool ParticleSet::IsValidParticle(const Particle &p) const
-{
-   if (p.GetDim() != GetDim())
-   {
-      return false;
-   }
-   if (p.GetNFields() != GetNFields())
-   {
-      return false;
-   }
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      if (p.GetFieldVDim(f) != Field(f).GetVDim())
-      {
-         return false;
-      }
-   }
-   if (p.GetNTags() != GetNTags())
-   {
-      return false;
-   }
-
-   return true;
-
-}
-
-ParticleSet::ParticleSet(int num_particles, int dim,
-                         Ordering::Type coords_ordering)
-   : ParticleSet(1, 0, num_particles, dim, coords_ordering, Array<int>(),
-                 Array<Ordering::Type>(), Array<const char*>(), 0,
-                 Array<const char*>())
-{
-
-}
-
-ParticleSet::ParticleSet(int num_particles, int dim,
-                         const Array<int> &field_vdims, int num_tags,
-                         Ordering::Type all_ordering)
-   : ParticleSet(1, 0, num_particles, dim, all_ordering, field_vdims,
-                 GetOrderingArray(all_ordering, field_vdims.Size()),
-                 GetEmptyNameArray(field_vdims.Size()), num_tags,
-                 GetEmptyNameArray(num_tags))
-{
-}
-
-ParticleSet::ParticleSet(int num_particles, int dim,
-                         const Array<int> &field_vdims, const Array<const
-                         char*> &field_names_, int num_tags,
-                         const Array<const char*> &tag_names_,
-                         Ordering::Type all_ordering)
-   : ParticleSet(1, 0, num_particles, dim, all_ordering, field_vdims,
-                 GetOrderingArray(all_ordering, field_vdims.Size()),
-                 field_names_, num_tags,
-                 tag_names_)
-{
-
-}
-
-ParticleSet::ParticleSet(int num_particles, int dim,
-                         Ordering::Type coords_ordering,
-                         const Array<int> &field_vdims,
-                         const Array<Ordering::Type> &field_orderings,
-                         const Array<const char*> &field_names_, int num_tags,
-                         const Array<const char*> &tag_names_)
-   : ParticleSet(1, 0, num_particles, dim, coords_ordering, field_vdims,
-                 field_orderings, field_names_, num_tags, tag_names_)
-{
-
-}
-
-
-
-#ifdef MFEM_USE_MPI
-ParticleSet::ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-                         Ordering::Type coords_ordering)
-   : ParticleSet(comm_, rank_num_particles, dim, coords_ordering, Array<int>(),
-                 Array<Ordering::Type>(), Array<const char*>(), 0,
-                 Array<const char*>())
-{
-
-};
-
-ParticleSet::ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-                         const Array<int> &field_vdims, int num_tags,
-                         Ordering::Type all_ordering)
-   : ParticleSet(comm_, rank_num_particles, dim, all_ordering, field_vdims,
-                 GetOrderingArray(all_ordering, field_vdims.Size()),
-                 GetEmptyNameArray(field_vdims.Size()), num_tags,
-                 GetEmptyNameArray(num_tags))
-{
-
-}
-
-ParticleSet::ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-                         const Array<int> &field_vdims, const Array<const
-                         char*> &field_names_,
-                         int num_tags, const Array<const char*> &tag_names_,
-                         Ordering::Type all_ordering)
-   : ParticleSet(comm_, rank_num_particles, dim, all_ordering, field_vdims,
-                 GetOrderingArray(all_ordering, field_vdims.Size()),
-                 field_names_, num_tags,
-                 tag_names_)
-{
-
-}
-
-ParticleSet::ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-                         Ordering::Type coords_ordering,
-                         const Array<int> &field_vdims,
-                         const Array<Ordering::Type> &field_orderings,
-                         const Array<const char*> &field_names_, int num_tags,
-                         const Array<const char*> &tag_names_)
-   : ParticleSet(GetSize(comm_), (IDType)GetRank(comm_),
-                 rank_num_particles,
-                 dim,
-                 coords_ordering,
-                 field_vdims,
-                 field_orderings,
-                 field_names_,
-                 num_tags,
-                 tag_names_)
-{
-   comm = comm_;
-#ifdef MFEM_USE_GSLIB
-   gsl_comm = new gslib::comm;
-   cr       = new gslib::crystal;
-   comm_init(gsl_comm, comm);
-   crystal_init(cr, gsl_comm);
-#endif // MFEM_USE_GSLIB
-}
-#endif // MFEM_USE_MPI
-
-ParticleSet::IDType ParticleSet::GetGlobalNParticles() const
-{
-   IDType total = (IDType)GetNParticles();
-#ifdef MFEM_USE_MPI
-   MPI_Allreduce(MPI_IN_PLACE, &total, 1, MPI_UNSIGNED_LONG_LONG,
-                 MPI_SUM, comm);
-#endif // MFEM_USE_MPI
-   return total;
-}
-
-int ParticleSet::AddField(int vdim, Ordering::Type field_ordering,
-                          const char* field_name)
-{
-   std::string field_name_str(field_name ? field_name : "");
-   if (!field_name)
-   {
-      field_name_str = GetDefaultFieldName(field_names.size());
-   }
-   fields.emplace_back(std::make_unique<ParticleVector>(vdim, field_ordering,
-                                                        GetNParticles()));
-   field_names.emplace_back(field_name_str);
-
-   return GetNFields() - 1;
-}
-
-int ParticleSet::AddTag(const char* tag_name)
-{
-   std::string tag_name_str(tag_name ? tag_name : "");
-   if (!tag_name)
-   {
-      tag_name_str = GetDefaultTagName(tag_names.size());
-   }
-   tags.emplace_back(std::make_unique<Array<int>>(GetNParticles()));
-   tag_names.emplace_back(tag_name_str);
-
-   return GetNTags() - 1;
-}
-
-void ParticleSet::AddParticle(const Particle &p)
-{
-   MFEM_ASSERT(IsValidParticle(p),
-               "Particle is incompatible with ParticleSet.");
-
-   // Add the particle
-   Array<int> idxs;
-   AddParticles(Array<IDType>({id_counter}), &idxs);
-   id_counter += id_stride;
-
-   // Set the new particle data
-   int idx = idxs[0];
-   SetParticle(idx, p);
-}
-
-void ParticleSet::AddParticles(int num_particles, Array<int> *new_indices)
-{
-   Array<IDType> add_ids(num_particles);
-   for (int i = 0; i < num_particles; i++)
-   {
-      add_ids[i] = id_counter;
-      id_counter += id_stride;
-   }
-
-   AddParticles(add_ids, new_indices);
-}
-
-void ParticleSet::RemoveParticles(const Array<int> &list)
-{
-   // Delete IDs
-   ids.DeleteAt(list);
-
-   // Delete data
-   for (int f = -1; f < GetNFields(); f++)
-   {
-      ParticleVector &pv = (f == -1 ? coords : *fields[f]);
-      pv.DeleteParticles(list);
-   }
-
-   // Delete tags
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      tags[t]->DeleteAt(list);
-   }
-}
-
-Particle ParticleSet::GetParticle(int i) const
-{
-   Particle p = CreateParticle();
-
-   Coords().GetValues(i, p.Coords());
-
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      Field(f).GetValues(i, p.Field(f));
-   }
-
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      p.Tag(t) = Tag(t)[i];
-   }
-
-   return p;
-}
-
-bool ParticleSet::IsParticleRefValid() const
-{
-   if (coords.GetOrdering() == Ordering::byNODES)
-   {
-      return false;
-   }
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      if (fields[f]->GetOrdering() == Ordering::byNODES)
-      {
-         return false;
-      }
-   }
-   return true;
-}
-
-Particle ParticleSet::GetParticleRef(int i)
-{
-   Particle p = CreateParticle();
-
-   Coords().GetValuesRef(i, p.Coords());
-
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      MFEM_ASSERT(Field(f).GetOrdering() == Ordering::byVDIM,
-                  "GetParticleRef only valid when all fields ordered byVDIM.");
-      p.SetFieldRef(f, Field(f).GetData() + i*Field(f).GetVDim());
-   }
-
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      p.SetTagRef(t, &(*tags[t])[i]);
-   }
-
-   return p;
-}
-
-void ParticleSet::SetParticle(int i, const Particle &p)
-{
-   MFEM_ASSERT(IsValidParticle(p),
-               "Particle is incompatible with ParticleSet.");
-
-   Coords().SetValues(i, p.Coords());
-
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      Field(f).SetValues(i, p.Field(f));
-   }
-
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      Tag(t)[i] = p.Tag(t);
-   }
-}
-
-void ParticleSet::PrintCSV(const char *fname, int precision)
-{
-   Array<int> all_field_idxs(GetNFields()), all_tag_idxs(GetNTags());
-
-   for (int f = 0; f < GetNFields(); f++)
-   {
-      all_field_idxs[f] = f;
-   }
-
-   for (int t = 0; t < GetNTags(); t++)
-   {
-      all_tag_idxs[t] = t;
-   }
-
-   PrintCSV(fname, all_field_idxs, all_tag_idxs, precision);
-}
-
-void ParticleSet::PrintCSV(const char *fname, const Array<int> &field_idxs,
-                           const Array<int> &tag_idxs, int precision)
-{
-   std::stringstream ss_header;
-
-   // Configure header:
-   ss_header << "id";
-
-#ifdef MFEM_USE_MPI
-   ss_header << ",rank";
-#endif // MFEM_USE_MPI
-
-   std::array<char, 3> ax = {'X', 'Y', 'Z'};
-   for (int c = 0; c < coords.GetVDim(); c++)
-   {
-      ss_header << "," << ax[c];
-   }
-
-   for (int f = 0; f < field_idxs.Size(); f++)
-   {
-      ParticleVector &pv = *fields[field_idxs[f]];
-      for (int c = 0; c < pv.GetVDim(); c++)
-      {
-         ss_header << "," << field_names[field_idxs[f]] <<
-                   (pv.GetVDim() > 1 ? "_" + std::to_string(c) : "");
-      }
-   }
-
-   for (int t = 0; t < tag_idxs.Size(); t++)
-   {
-      ss_header << "," << tag_names[tag_idxs[t]];
-   }
-   ss_header << "\n";
-
-   // Configure data
-   std::stringstream ss_data;
-   ss_data.precision(precision);
-#ifdef MFEM_USE_MPI
-   int rank = GetRank(comm);
-#endif // MFEM_USE_MPI
-   for (int i = 0; i < GetNParticles(); i++)
-   {
-      ss_data << ids[i];
-#ifdef MFEM_USE_MPI
-      ss_data << "," << rank;
-#endif // MFEM_USE_MPI
-
-      for (int c = 0; c < coords.GetVDim(); c++)
-      {
-         ss_data << "," << coords(i, c);
-      }
-      for (int f = 0; f < field_idxs.Size(); f++)
-      {
-         ParticleVector &pv = *fields[field_idxs[f]];
-         for (int c = 0; c < pv.GetVDim(); c++)
-         {
-            ss_data << "," << pv(i, c);
-         }
-      }
-      for (int t = 0; t < tag_idxs.Size(); t++)
-      {
-         ss_data << "," << (*tags[tag_idxs[t]])[i];
-      }
-      ss_data << "\n";
-   }
-
-   // Write
-   WriteToFile(fname, ss_header, ss_data);
-}
-
-ParticleSet::~ParticleSet()
-{
-#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
-   if (gsl_comm)
-   {
-      if (!Mpi::IsFinalized())  // currently segfaults inside gslib otherwise
-      {
-         crystal_free(cr);
-         comm_free(gsl_comm);
-         delete gsl_comm;
-         delete cr;
-      }
-   }
-#endif // MFEM_USE_MPI && MFEM_USE_GSLIB
-}
-
-
-} // namespace mfem
@@ -1,685 +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.
-
-#ifndef MFEM_PARTICLESET
-#define MFEM_PARTICLESET
-
-#include "../config/config.hpp"
-#include "../linalg/linalg.hpp"
-#include "gslib.hpp"
-#include "kernel_dispatch.hpp"
-
-namespace mfem
-{
-
-/** @brief  Container for data associated with a single particle.
- *
- *  @note This class mainly serves as a convenience interface to individual
- *  particle data from ParticleSet. We recommend seeing ParticleSet first.
- *
- *  @details As described in ParticleSet documentation, each particle has a
- *  position (\ref coords), arbitrary number of scalar or vector \ref real_t
- *  data (\ref fields), and arbitrary number of integers (\ref tags)
- *  associated with it.
- *
- *  \ref fields can thus hold data such as mass, momentum, and velocity, while
- *  \ref tags can hold integer data such as particle type, color, etc.
- *
- *  Each particle also has a unique global ID, but that is managed by the
- *  ParticleSet class and not stored in this Particle class. Simiarly, the names
- *  of the fields and tags, typically useful for output purposes, are managed by
- *  the ParticleSet class.
- *
- *
- * For clarity, we will use the particles below to illustrate the data layout
- * for \ref coords, \ref fields, and \ref tags
- *
- * @anchor sample_particle_data
- * @code
- * Particle_0: coords = (x0, y0),
- *             fields = {'mass'=m0, 'vel' = (vx0, vy0)},
- *               tags = {'type'=t0, 'color'=color0}
- * Particle_1: coords = (x1, y1),
- *             fields = {'mass'=m1, 'vel' = (vx1, vy1)},
- *               tags = {'type'=t1, 'color'=color1}
- * Particle_2: coords = (x2, y2),
- *             fields = {'mass'=m2, 'vel' = (vx2, vy2)},
- *               tags = {'type'=t2, 'color'=color2}
- * @endcode
- *
- */
-class Particle
-{
-protected:
-   /** @brief Spatial coordinates
-    *
-    *  @details For the \ref sample_particle_data, \ref coords would hold
-    *  (x_i, y_i) for each particle i.
-    */
-   Vector coords;
-
-   /** @brief A std::vector of Vector where each Vector holds data for a given
-    *  field (e.g., mass, momentum or velocity) associated with the particle.
-    *
-    *  @details For the \ref sample_particle_data, \ref fields would be
-    *  fields[0]=(m_i), fields[1]=(vx_i,vy_i) for each particle i.
-    */
-   std::vector<Vector> fields;
-
-   /** @brief A std::vector of Array<int> where each Array<int> holds data
-    *  for a given tag.
-    *
-    *  @details For the \ref sample_particle_data, \ref tags would be
-    *  tags[0]=(type_i), tags[1]=(color_i) for each particle i. \n
-    *
-    *  @note An Array of length 1 is used for EACH tag, strictly for
-    *  its owning/non-owning semantics (see Array<T>::MakeRef).
-    */
-   std::vector<Array<int>> tags;
-public:
-   /** @brief Construct a Particle instance.
-    *  @param[in] dim          Spatial dimension (size of #coords).
-    *  @param[in] field_vdims  Vector dimensions of particle fields.
-    *  @param[in] num_tags     Number of integer tags.
-    */
-   Particle(int dim, const Array<int> &field_vdims, int num_tags);
-
-   // Force default constructors and destructor
-   Particle(const Particle&) = default;
-   Particle& operator=(const Particle&) = default;
-   Particle(Particle&&) = default;
-   Particle& operator=(Particle&&) = default;
-   ~Particle() = default;
-
-   /// Get the spatial dimension of this particle.
-   int GetDim() const { return coords.Size(); }
-
-   /// Get the number of fields associated with this particle.
-   int GetNFields() const { return fields.size(); }
-
-   /// Get the vector dimension of field \p f .
-   int GetFieldVDim(int f) const { return fields[f].Size(); }
-
-   /// Get the number of tags associated with this particle.
-   int GetNTags() const { return tags.size(); }
-
-   /// Get reference to particle coordinates Vector.
-   Vector& Coords() { return coords; }
-
-   /// Get const reference to particle coordinates Vector.
-   const Vector& Coords() const { return coords; }
-
-   /// Get reference to field \p f , component \p c value.
-   real_t& FieldValue(int f, int c=0)
-   {
-      MFEM_ASSERT(f >= 0 && static_cast<std::size_t>(f) < fields.size(),
-                  "Invalid field index");
-      MFEM_ASSERT(c >= 0 && c < fields[f].Size(),
-                  "Invalid component index");
-      return fields[f][c];
-   }
-
-   /// Get const reference to field \p f , component \p c value.
-   const real_t& FieldValue(int f, int c=0) const
-   {
-      MFEM_ASSERT(f >= 0 && static_cast<std::size_t>(f) <  fields.size(),
-                  "invalid field index");
-      MFEM_ASSERT(c >= 0 && c < fields[f].Size(),
-                  "invalid component index");
-      return fields[f][c];
-   }
-
-   /// Get reference to field \p f Vector.
-   Vector& Field(int f)
-   {
-      MFEM_ASSERT(f >= 0 && static_cast<std::size_t>(f) <  fields.size(),
-                  "invalid field index");
-      return fields[f];
-   }
-
-   /// Get const reference to field \p f Vector.
-   const Vector& Field(int f) const
-   {
-      MFEM_ASSERT(f >= 0 && static_cast<std::size_t>(f) <  fields.size(),
-                  "invalid field index");
-      return fields[f];
-   }
-
-   /// Get reference to tag \p t .
-   int& Tag(int t)
-   {
-      MFEM_ASSERT(t >= 0 && static_cast<std::size_t>(t) <  tags.size(),
-                  "invalid tag index");
-      return tags[t][0];
-   }
-
-   /// Get const reference to tag \p t .
-   const int& Tag(int t) const
-   {
-      MFEM_ASSERT(t >= 0 && static_cast<std::size_t>(t) <  tags.size(),
-                  "invalid tag index");
-      return tags[t][0];
-   }
-
-   /// Set tag \p t to reference external data.
-   void SetTagRef(int t, int *tag_data);
-
-   /// Set field \p f to reference external data.
-   void SetFieldRef(int f, real_t *field_data);
-
-   /// Particle equality operator.
-   bool operator==(const Particle &rhs) const;
-
-   /// Particle inequality operator.
-   bool operator!=(const Particle &rhs) const { return !operator==(rhs); }
-
-   /// Print all particle data to \p os.
-   void Print(std::ostream &os=mfem::out) const;
-};
-
-/** @brief ParticleSet initializes and manages data associated with particles.
- *
- *  @details Particles are inherently initialized to have a position and an ID,
- *  and optionally can have any number of Vector (of arbitrary vdim) and scalar
- *  integer data in the form of @b fields and @b tags respectively. All particle
- *  data are internally stored in a Struct-of-Arrays fashion, as elaborated on
- *  below.
- *
- *  @par Coordinates:
- *  All particle coordinates are stored in a ParticleVector with vector
- *  dimension equal to the spatial dimension, ordered either byNODES or byVDIM.
- *  The ParticleVector \ref coords contains the coordinates of all particles.
- *
- *  @par IDs:
- *  Each particle is assigned a unique global ID of type IDType. In parallel,
- *  IDs are initialized starting with @b rank and striding by @b size. The IDs
- *  of all particles owned by this rank are stored in \ref ids.
- *
- *  @par Fields:
- *  Fields represent scalar or vector \ref real_t data to be associated with
- *  each particles, such as mass, momentum, or moment. For a given field, all
- *  particle data is stored in a single ParticleVector with a given
- *  vector dimension (1 for scalar data) and Ordering::Type (byNODES or
- *  byVDIM). The unique_ptrs to all the ParticleVectors are stored in the
- *  std::vector \ref fields.
- *
- *  @par Tags:
- *  Tags represent integers associated with each particle. For a given tag,
- *  all particle data are stored in a single Array<int>. The unique_ptrs to all
- *  the Array<int> is stored in the std::vector \ref tags.
- *
- *  @par Names:
- *  Each field and tag can optionally be given a name (string) to be used when
- *  printing particle data in CSV format using PrintCSV(). The names of all
- *  fields and tags are stored in the std::vectors \ref field_names and
- *  \ref tag_names, respectively.
- *
- *  @note We assume that all particles in a ParticleSet have the same number
- *  of fields and tags.
- *
- *  Following the example in the Particle class, we will use the
- *  particles below to illustrate the data layout for \ref coords, \ref ids,
- *  \ref fields, \ref tags, \ref field_names, and \ref tag_names.
- *  In each case, the name of the field and tag is enclosed in '...' for
- *  clarity. Additionally, we assume for this example that the particle
- *  coordinates and the 'vel' field are ordered byVDIM in their respective
- *  ParticleVector.
- *  @anchor sample_particleset_data
- *  @code
- *  Particle_0: id = id0, coords = (x0, y0),
- *              fields = {'mass'=m0, 'vel' = (vx0, vy0)},
- *              tags = {'type'=t0, 'color'=c0}
- *  Particle_1: id = id1, coords = (x1, y1),
- *              fields = {'mass'=m1, 'vel' = (vx1, vy1)},
- *              tags = {'type'=t1, 'color'=c1}
- *  Particle_2: id = id2, coords = (x2, y2),
- *              fields = {'mass'=m2, 'vel' = (vx2, vy2)},
- *              tags = {'type'=t2, 'color'=c2}
- *  @endcode
- */
-class ParticleSet
-{
-public:
-   using IDType = unsigned long long;
-private:
-   /// Constructs an Array of size N filled with Ordering::Type o.
-   static Array<Ordering::Type> GetOrderingArray(Ordering::Type o, int N);
-
-   /// Returns default field name for field index i. "Field_{i}"
-   static std::string GetDefaultFieldName(int i);
-
-   /// Returns default tag name for tag index i. "Tag_{i}"
-   static std::string GetDefaultTagName(int i);
-
-   /// Constructs an Array of size N filled with nullptr.
-   static Array<const char*> GetEmptyNameArray(int N);
-
-#ifdef MFEM_USE_MPI
-   static int GetRank(MPI_Comm comm_);
-   static int GetSize(MPI_Comm comm_);
-#endif // MFEM_USE_MPI
-
-protected:
-   /// Stride for IDs (used internally when new particles are added).
-   /** In parallel, this defaults to the number of MPI ranks. */
-   const int id_stride;
-
-   /// Current globally unique ID to be assigned to the next particle added.
-   /** In parallel, this starts locally as the rank and increments with
-    * id_stride, ensuring a global unique identifier whenever a particle is
-    * added.
-    */
-   IDType id_counter;
-
-   /** @brief Global unique IDs of particles owned by this rank.
-    *
-    *  @details For the \ref sample_particleset_data, \ref ids would be
-    *  ids[0]=id0, ids[1]=id1, ids[2]=id2.
-    */
-   Array<IDType> ids;
-
-   /** @brief Spatial coordinates of particles owned by this rank.
-    *
-    *  @details For the \ref sample_particleset_data, \ref coords would be
-    *  coords=(x0,y0,x1,y1,x2,y2) assuming coords ordering is byVDIM.
-    */
-   ParticleVector coords;
-
-   /** @brief All particle fields for particles owned by this rank.
-    *
-    *  @details For the \ref sample_particleset_data, \ref fields would be
-    *  *fields[0]=(m0,m1,m2), *fields[1]=(vx0,vy0,vx1,vy1,vx2,vy2)
-    *  assuming fields[1] ordering is byVDIM.
-    */
-   std::vector<std::unique_ptr<ParticleVector>> fields;
-
-   /** @brief All particle tags for particles owned by this rank.
-    *
-    *  @details For the \ref sample_particleset_data, \ref tags would be
-    *  *tags[0]=(t0,t1,t2), *tags[1]=(c0,c1,c2).
-    */
-   std::vector<std::unique_ptr<Array<int>>> tags;
-
-   /** @brief Field names, to be written when PrintCSV() is called.
-    *
-    *  @details For the \ref sample_particleset_data, \ref field_names would be
-    *  field_names[0]='mass', field_names[1]='vel'.
-    */
-   std::vector<std::string> field_names;
-
-   /** @brief Tag names, to be written when PrintCSV() is called.
-    *
-    *  @details For the \ref sample_particleset_data, \ref tag_names would be
-    *  tag_names[0]='type', tag_names[1]='color'.
-    */
-   std::vector<std::string> tag_names;
-
-   /** @brief Add particles with global identifiers \p new_ids and
-    *  optionally get the local indices of new particles in \p new_indices .
-    *
-    *  @details Note the data of new particles is uninitialized and must be
-    *  set.
-    */
-   void AddParticles(const Array<IDType> &new_ids,
-                     Array<int> *new_indices=nullptr);
-
-#ifdef MFEM_USE_MPI
-   MPI_Comm comm;
-#endif // MFEM_USE_MPI
-
-#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
-   struct gslib::crystal *cr = nullptr;               // gslib's internal data
-   struct gslib::comm *gsl_comm = nullptr;            // gslib's internal data
-
-   /// \cond DO_NOT_DOCUMENT
-   template<std::size_t NBytes>
-   static void TransferParticlesImpl(ParticleSet &pset,
-                                     const Array<int> &send_idxs,
-                                     const Array<unsigned int> &send_ranks);
-
-   using TransferParticlesType = void (*)(ParticleSet &pset,
-                                          const Array<int> &send_idxs,
-                                          const Array<unsigned int> &send_ranks);
-
-   // Specialization parameter: NBytes
-   MFEM_REGISTER_KERNELS(TransferParticles, TransferParticlesType, (size_t));
-   friend TransferParticles;
-   struct Kernels
-   {
-      Kernels();
-   };
-   /// \endcond
-
-#endif // MFEM_USE_MPI && MFEM_USE_GSLIB
-
-   /** @brief  Update global ID of a particle.
-    *
-    *  @details This method updates the global ID of the particle at given
-    *  local index after Redistribute().
-    *
-    *  @note This method must be used very carefully as it updates global
-    *  ID of a particle.
-    */
-   void UpdateID(int local_idx, IDType new_global_id)
-   { ids[local_idx] = new_global_id; }
-
-   /** @brief Create a Particle object with the same spatial dimension,
-    *  number of fields and field vdims, and number of tags as this ParticleSet.
-    */
-   Particle CreateParticle() const;
-
-   /** @brief Write string in \p ss_header , followed by \p ss_data , to a
-    *  single file; compatible in parallel.
-    */
-   void WriteToFile(const char *fname, const std::stringstream &ss_header,
-                    const std::stringstream &ss_data);
-
-   /** @brief Check if a particle could belong in this ParticleSet by
-    *  comparing field and tag dimension.
-    */
-   bool IsValidParticle(const Particle &p) const;
-
-   /** @brief Hidden main constructor of ParticleSet
-    *
-    *  @param[in] id_stride_          ID stride.
-    *  @param[in] id_counter_         Starting ID counter.
-    *  @param[in] num_particles       Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] coords_ordering     Ordering of coordinates
-    *  @param[in] field_vdims         Array of field vector dimensions
-    *  @param[in] field_orderings     Array of field ordering types.
-    *  @param[in] field_names_        Array of field names.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] tag_names_          Array of tag names.
-    */
-   ParticleSet(int id_stride_, IDType id_counter_, int num_particles, int dim,
-               Ordering::Type coords_ordering, const Array<int> &field_vdims,
-               const Array<Ordering::Type> &field_orderings,
-               const Array<const char*> &field_names_, int num_tags,
-               const Array<const char*> &tag_names_);
-
-public:
-
-   /** @brief Construct a serial ParticleSet.
-    *
-    *  @param[in] num_particles       Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] coords_ordering     Ordering of coordinates.
-    */
-   ParticleSet(int num_particles, int dim,
-               Ordering::Type coords_ordering=Ordering::byVDIM);
-
-   /** @brief Construct a serial ParticleSet with specified fields and tags at
-    *  construction.
-    *
-    *  @param[in] num_particles       Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] field_vdims         Array of field vector dimensions.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] all_ordering        (Optional) Ordering of coordinates and
-    *                                 field ParticleVector.
-    */
-   ParticleSet(int num_particles, int dim, const Array<int> &field_vdims,
-               int num_tags, Ordering::Type all_ordering=Ordering::byVDIM);
-
-   /** @brief Construct a serial ParticleSet with specified fields and tags at
-    *  construction, with names.
-    *
-    *  @param[in] num_particles       Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] field_vdims         Array of field vector dimensions.
-    *  @param[in] field_names_        Array of field names.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] tag_names_          Array of tag names.
-    *  @param[in] all_ordering        (Optional) Ordering of coordinates and
-    *                                 field ParticleVector.
-    */
-   ParticleSet(int num_particles, int dim, const Array<int> &field_vdims,
-               const Array<const char*> &field_names_, int num_tags,
-               const Array<const char*> &tag_names_,
-               Ordering::Type all_ordering=Ordering::byVDIM);
-
-   /** @brief Comprehensive serial constructor of ParticleSet.
-    *
-    *  @param[in] num_particles       Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] coords_ordering     Ordering of coordinates.
-    *  @param[in] field_vdims         Array of field vector dimensions.
-    *  @param[in] field_orderings     Array of field ordering types.
-    *  @param[in] field_names_        Array of field names.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] tag_names_          Array of tag names.
-    */
-   ParticleSet(int num_particles, int dim, Ordering::Type coords_ordering,
-               const Array<int> &field_vdims,
-               const Array<Ordering::Type> &field_orderings,
-               const Array<const char*> &field_names_, int num_tags,
-               const Array<const char*> &tag_names_);
-
-#ifdef MFEM_USE_MPI
-   /** @brief Construct a parallel ParticleSet.
-    *
-    *  @param[in] comm_               MPI communicator.
-    *  @param[in] rank_num_particles  Number of particles to initialize.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] coords_ordering     (Optional) Ordering of coordinates.
-    */
-   ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-               Ordering::Type coords_ordering=Ordering::byVDIM);
-
-   /** @brief Construct a parallel ParticleSet with specified fields and tags
-    *  at construction.
-    *
-    *  @param[in] comm_               MPI communicator.
-    *  @param[in] rank_num_particles  # of particles to initialize on this rank.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] field_vdims         Array of field vector dimensions.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] all_ordering        (Optional) Ordering of coordinates and
-    *                                 field ParticleVector.
-    */
-   ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-               const Array<int> &field_vdims, int num_tags,
-               Ordering::Type all_ordering=Ordering::byVDIM);
-
-   /** @brief Construct a parallel ParticleSet with specified fields and tags
-    *  at construction, with names (for PrintCSV()).
-    *
-    *  @param[in] comm_               MPI communicator.
-    *  @param[in] rank_num_particles  # of particles to initialize on this rank.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] field_vdims         Array of field vector dimension.
-    *  @param[in] field_names_        Array of field names.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] tag_names_          Array of tag names.
-    *  @param[in] all_ordering        (Optional) Ordering of coordinates and
-    *                                 field ParticleVector.
-    */
-   ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-               const Array<int> &field_vdims,
-               const Array<const char*> &field_names_,
-               int num_tags, const Array<const char*> &tag_names_,
-               Ordering::Type all_ordering=Ordering::byVDIM);
-
-   /** @brief Comprehensive parallel constructor of ParticleSet.
-    *
-    *  @param[in] comm_               MPI communicator.
-    *  @param[in] rank_num_particles  # of particles to initialize on this rank.
-    *  @param[in] dim                 Particle spatial dimension.
-    *  @param[in] coords_ordering     Ordering of coordinates.
-    *  @param[in] field_vdims         Array of field vector dimensions.
-    *  @param[in] field_orderings     Array of field ordering types.
-    *  @param[in] field_names_        Array of field names.
-    *  @param[in] num_tags            Number of tags to register.
-    *  @param[in] tag_names_          Array of tag names.
-    */
-   ParticleSet(MPI_Comm comm_, int rank_num_particles, int dim,
-               Ordering::Type coords_ordering, const Array<int> &field_vdims,
-               const Array<Ordering::Type> &field_orderings,
-               const Array<const char*> &field_names_, int num_tags,
-               const Array<const char*> &tag_names_);
-
-   /// Get the MPI communicator for this ParticleSet.
-   MPI_Comm GetComm() const { return comm; };
-#endif // MFEM_USE_MPI
-   /// Get the global number of active particles across all ranks.
-   IDType GetGlobalNParticles() const;
-
-   /// Get the spatial dimension.
-   int GetDim() const { return coords.GetVDim(); }
-
-   /// Get the global IDs of the active particles owned by this ParticleSet.
-   const Array<IDType>& GetIDs() const { return ids; }
-
-   /** @brief Add a field to the ParticleSet.
-    *
-    *  @param[in] vdim             Vector dimension of the field.
-    *  @param[in] field_ordering   (Optional) Ordering::Type of the field.
-    *  @param[in] field_name       (Optional) Name of the field.
-    *
-    *  @return Index of the newly-added field.
-    */
-   int AddField(int vdim, Ordering::Type field_ordering=Ordering::byVDIM,
-                const char* field_name=nullptr);
-
-   /** @brief Add a field to the ParticleSet.
-    *
-    *  @details Same as AddField() but with different parameter order
-    *  for convenience
-    */
-   int AddNamedField(int vdim, const char* field_name,
-                     Ordering::Type field_ordering=Ordering::byVDIM)
-   {
-      return AddField(vdim, field_ordering, field_name);
-   }
-
-   /** @brief Add a tag to the ParticleSet.
-    *
-    *  @param[in] tag_name      (Optional) Name of the tag.
-    *
-    *  @return Index of the newly-added tag.
-    */
-   int AddTag(const char* tag_name=nullptr);
-
-   /// Reserve memory for \p res particles.
-   /** Can help to avoid re-allocation for adding + removing particles. */
-   void Reserve(int res);
-
-   /// Get the number of active particles currently held by this ParticleSet.
-   int GetNParticles() const { return ids.Size(); }
-
-   /// Get the number of fields registered to particles.
-   int GetNFields() const { return fields.size(); }
-
-   /// Get an Array<int> of the field vector-dimensions registered to particles.
-   const Array<int> GetFieldVDims() const;
-
-   /// Get Field vector-dimension
-   int FieldVDim(int f) const { return fields[f]->GetVDim(); }
-
-   /// Get the number of tags registered to particles.
-   int GetNTags() const { return tags.size(); }
-
-   /// Add a particle using Particle .
-   void AddParticle(const Particle &p);
-
-   /** @brief Add \p num_particles particles, and optionally get the local
-    *  indices of new particles in \p new_indices .
-    *
-    *  @details The data of new particles is uninitialized and must be
-    *  set.
-    */
-   void AddParticles(int num_particles, Array<int> *new_indices=nullptr);
-
-   /// Remove particle data specified by \p list of particle indices.
-   void RemoveParticles(const Array<int> &list);
-
-   /// Get a reference to the coordinates ParticleVector.
-   ParticleVector& Coords() { return coords; }
-
-   /// Get a const reference to the coordinates ParticleVector.
-   const ParticleVector& Coords() const { return coords; }
-
-   /// Get a reference to field \p f 's ParticleVector.
-   ParticleVector& Field(int f) { return *fields[f]; }
-
-   /// Get a const reference to field \p f 's ParticleVector.
-   const ParticleVector& Field(int f) const { return *fields[f]; }
-
-   /// Get a reference to tag \p t 's Array<int>.
-   Array<int>& Tag(int t) { return *tags[t]; }
-
-   /// Get a const reference to tag \p t 's Array<int>.
-   const Array<int>& Tag(int t) const { return *tags[t]; }
-
-   /** @brief Get new Particle object with copy of data associated with
-       particle \p i . */
-   Particle GetParticle(int i) const;
-
-   /** @brief Get Particle object whose members reference the actual data
-    *  associated with particle \p i in this ParticleSet.
-    *
-    *  @see IsParticleRefValid for when this method can be used.
-    *
-    *  @warning If particles are added, removed, or redistributed after
-    *  invoking this, the returned Particle member references may be
-    *  invalidated.
-    */
-   Particle GetParticleRef(int i);
-
-   /** @brief Determine if GetParticleRef is valid.
-    *
-    * If coordinates and all fields are ordered byVDIM, then returns true.
-    * Otherwise, false.
-    */
-   bool IsParticleRefValid() const;
-
-   /// Set data for particle at index \p i with data from provided particle \p p
-   void SetParticle(int i, const Particle &p);
-
-   /** @brief Print all particle data to a comma-delimited CSV file.
-    *
-    *  The first row contains the header. We include the particle ID,
-    *  owning rank (in parallel), coordinates, followed by all fields and
-    *  tags.
-    *
-    *  The output can be visualized in Paraview by loading the csv files, and
-    *  applying the "Table To Points" filter.
-    */
-   void PrintCSV(const char *fname, int precision=16);
-
-   /** @brief Print only particle field and tags given by \p field_idxs and
-       \p tag_idxs respectively to a CSV file. */
-   void PrintCSV(const char *fname, const Array<int> &field_idxs,
-                 const Array<int> &tag_idxs, int precision=16);
-
-#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
-
-   /** @brief Redistribute particle data to \p rank_list
-
-       @param[in] rank_list    Array of size GetNParticles() denoting ultimate
-                               destination of particle data. Index = this rank
-                               means no data is moved.
-     */
-   void Redistribute(const Array<unsigned int> &rank_list);
-
-#endif // MFEM_USE_MPI && MFEM_USE_GSLIB
-
-   /// Destructor
-   ~ParticleSet();
-   ParticleSet(const ParticleSet&) = delete;
-   ParticleSet& operator=(const ParticleSet&) = delete;
-};
-
-} // namespace mfem
-
-
-#endif // MFEM_PARTICLESET
@@ -488,16 +488,10 @@ void ParBilinearForm::FormLinearSystem(
         R.Mult(x, true_X);

         FormSystemMatrix(ess_tdof_list, A);
-
-         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
-         {
-            Operator *op;
-            Operator::FormSystemOperator(ess_tdof_list, op);
-            return dynamic_cast<ConstrainedOperator*>(op);
-         }());
-         MFEM_ASSERT(A_constrained != nullptr, "");
-
+         ConstrainedOperator *A_constrained;
+         Operator::FormConstrainedSystemOperator(ess_tdof_list, A_constrained);
         A_constrained->EliminateRHS(true_X, true_B);
+         delete A_constrained;
         R.MultTranspose(true_B, b);
         hybridization->ReduceRHS(true_B, B);
         X.SetSize(B.Size());
@@ -646,38 +646,39 @@ const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
   auto itr = L2F.find(key);
   if (itr != L2F.end())
   {
-      return itr->second.get();
+      return itr->second;
   }
   else
   {
-      std::unique_ptr<FaceRestriction> res;
+      FaceRestriction *res;
      if (is_dg_space)
      {
         if (Conforming())
         {
-            res.reset(new ParL2FaceRestriction(*this, f_ordering, type, m));
+            res = new ParL2FaceRestriction(*this, f_ordering, type, m);
         }
         else
         {
-            res.reset(new ParNCL2FaceRestriction(*this, f_ordering, type, m));
+            res = new ParNCL2FaceRestriction(*this, f_ordering, type, m);
         }
      }
      else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
      {
-         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
+         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
      }
      else
      {
         if (Conforming())
         {
-            res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
+            res = new ConformingFaceRestriction(*this, f_ordering, type);
         }
         else
         {
-            res.reset(new ParNCH1FaceRestriction(*this, f_ordering, type));
+            res = new ParNCH1FaceRestriction(*this, f_ordering, type);
         }
      }
-      return L2F.emplace(key, std::move(res)).first->second.get();
+      L2F[key] = res;
+      return res;
   }
 }

@@ -5270,8 +5271,7 @@ DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(
   MFEM_ASSERT(R->Finalized(), "");
   const int tdofs = R->Height();
   MFEM_ASSERT(tdofs == R->HostReadI()[tdofs], "");
-   ltdof_ldof.SetSize(tdofs);
-   ltdof_ldof.CopyFrom(R->HostReadJ());
+   ltdof_ldof = Array<int>(const_cast<int*>(R->HostReadJ()), tdofs);
   {
      Table nbr_ltdof;
      gc.GetNeighborLTDofTable(nbr_ltdof);
@@ -5294,13 +5294,9 @@ DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(
         }
         Table unique_shr;
         Transpose(shared_ltdof, unique_shr, unique_ltdof.Size());
-         unq_ltdof = unique_ltdof;
-         // Steal I and J arrays from the unique_shr table.
-         unq_shr_i.GetMemory() = unique_shr.GetIMemory();
-         unq_shr_i.SetSize(unique_shr.Size()+1);
-         unq_shr_j.GetMemory() = unique_shr.GetJMemory();
-         unq_shr_j.SetSize(unique_shr.Size_of_connections());
-         unique_shr.LoseData();
+         unq_ltdof = Array<int>(unique_ltdof, unique_ltdof.Size());
+         unq_shr_i = Array<int>(unique_shr.GetI(), unique_shr.Size()+1);
+         unq_shr_j = Array<int>(unique_shr.GetJ(), unique_shr.Size_of_connections());
      }
      nbr_ltdof.GetJMemory().Delete();
      nbr_ltdof.LoseData();
@@ -483,8 +483,6 @@ public:
   const FiniteElement *GetFaceNbrFaceFE(int i) const;
   const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() { return face_nbr_glob_dof_map; }
   const HYPRE_BigInt *GetFaceNbrGlobalDofMap() { return face_nbr_glob_dof_map; }
-   const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() const
-   { return face_nbr_glob_dof_map; }
   ElementTransformation *GetFaceNbrElementTransformation(int i) const
   { return pmesh->GetFaceNbrElementTransformation(i); }

@@ -543,22 +543,13 @@ void ParGridFunction::GetElementDofValues(int el, Vector &dof_vals) const
   }
 }

-void ParGridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
+void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
 {
   DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);

   if (delta_c == NULL)
   {
-      (*this) = std::numeric_limits<real_t>::min();
-      GridFunction::ProjectCoefficient(coeff,type);
-
-      // Accumulate for all vdofs.
-      if (pfes->GetNURBSext())
-      {
-         GroupCommunicator &gcomm = pfes->GroupComm();
-         gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
-         gcomm.Bcast<real_t>(data);
-      }
+      GridFunction::ProjectCoefficient(coeff);
   }
   else
   {
@@ -574,147 +565,6 @@ void ParGridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
   }
 }

-void ParGridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
-                                         ProjectType type)
-{
-   GridFunction::ProjectCoefficient(vcoeff, type);
-
-   // Accumulate for all vdofs.
-   if (pfes->GetNURBSext())
-   {
-      GroupCommunicator &gcomm = pfes->GroupComm();
-      gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
-      gcomm.Bcast<real_t>(data);
-   }
-}
-
-void ParGridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff,
-                                                 real_t rtol,
-                                                 int iter)
-{
-   // Define and assemble linear form
-   ParLinearForm b(pfes);
-   b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
-   b.Assemble();
-
-   // Define and assemble bilinear form
-   ParBilinearForm a(pfes);
-   a.AddDomainIntegrator(new MassIntegrator());
-   a.Assemble();
-
-   // Configure solver
-   OperatorPtr A;
-   Vector B, X, x(*this);
-   Array<int> ess_tdof_list;
-   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
-   Solver *prec = new HypreBoomerAMG;
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(rtol);
-   cg.SetMaxIter(iter);
-   cg.SetPrintLevel(0);
-   cg.SetPreconditioner(*prec);
-   cg.SetOperator(*A);
-   cg.Mult(B, X);
-   a.RecoverFEMSolution(X, b, x);
-   delete prec;
-}
-
-void ParGridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
-{
-   Vector Va;
-   ProjectCoefficientElementL2_(coeff, *this, Va);
-
-   GroupCommunicator &gcomm = pfes->GroupComm();
-   gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
-   gcomm.Bcast<real_t>(GetData());
-
-   gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
-   gcomm.Bcast<real_t>(Va.GetData());
-   (*this)/=Va;
-}
-
-void ParGridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
-                                                 real_t rtol, int iter)
-{
-   // Define and assemble linear form
-   ParLinearForm b(pfes);
-   ParBilinearForm a(pfes);
-
-   // Dimension argument to GetRangeType is arbitrary to be 3, could also be 2.
-   if (fes->FEColl()->GetRangeType(3)  == mfem::FiniteElement::VECTOR)
-   {
-      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
-      a.AddDomainIntegrator(new VectorFEMassIntegrator());
-   }
-   else
-   {
-      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
-      a.AddDomainIntegrator(new VectorMassIntegrator());
-   }
-   b.Assemble();
-   a.Assemble();
-
-   // Configure solver
-   OperatorPtr A;
-   Vector B, X, x(*this);
-   x = 0.0;
-   Array<int> ess_tdof_list;
-   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
-   Solver *prec = new HypreBoomerAMG;
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(rtol);
-   cg.SetMaxIter(iter);
-   cg.SetPrintLevel(0);
-   cg.SetPreconditioner(*prec);
-   cg.SetOperator(*A);
-   cg.Mult(B, X);
-   a.RecoverFEMSolution(X, b, x);
-   x.Print();
-   delete prec;
-}
-
-void ParGridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
-{
-   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
-   {
-      Vector Va;
-      ProjectCoefficientElementL2_(vcoeff, *this, Va);
-
-      GroupCommunicator &gcomm = pfes->GroupComm();
-      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
-      gcomm.Bcast<real_t>(GetData());
-
-      gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
-      gcomm.Bcast<real_t>(Va.GetData());
-      (*this)/=Va;
-   }
-   else
-   {
-      Array<int> vdofs(fes->GetNDofs());
-      Vector x, Va, gVa(Size());
-      VectorComponentCoefficient coeff(vcoeff,0);
-      *this = 0.0;
-      gVa = 0.0;
-      for (int v = 0; v < VectorDim(); v++)
-      {
-         coeff.SetComponent(v);
-         ProjectCoefficientElementL2_(coeff, x, Va);
-         fes->GetVDofs(v, vdofs);
-         SetSubVector(vdofs, x);
-         gVa.SetSubVector(vdofs, Va);
-      }
-
-      GroupCommunicator &gcomm = pfes->GroupComm();
-      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
-      gcomm.Bcast<real_t>(GetData());
-
-      gcomm.Reduce<real_t>(gVa.GetData(), GroupCommunicator::Sum);
-      gcomm.Bcast<real_t>(gVa.GetData());
-      *this /= gVa;
-   }
-}
-
-
 void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
 {
   // local maximal element attribute for each dof
@@ -1557,7 +1407,7 @@ real_t L2ZZErrorEstimator(BilinearFormIntegrator &flux_integrator,
 }

 PLBound ParGridFunction::GetBounds(Vector &lower, Vector &upper,
-                                   const int ref_factor, const int vdim) const
+                                   const int ref_factor, const int vdim)
 {
   PLBound plb = GridFunction::GetBounds(lower, upper, ref_factor, vdim);
   int siz = vdim > 0 ? 1 : fes->GetVDim();
@@ -72,10 +72,6 @@ public:

   ParGridFunction(ParFiniteElementSpace *pf) : GridFunction(pf), pfes(pf) { }

-   /// Same as above but specify the device memory type
-   ParGridFunction(ParFiniteElementSpace *pf, MemoryType mt) :
-      GridFunction(pf, mt), pfes(pf) { }
-
   /// Construct a ParGridFunction using previously allocated array @a data.
   /** The ParGridFunction does not assume ownership of @a data which is assumed
       to be of size at least `pf->GetVSize()`. Similar to the GridFunction and
@@ -261,11 +257,7 @@ public:
   void GetElementDofValues(int el, Vector &dof_vals) const override;

   using GridFunction::ProjectCoefficient;
-   void ProjectCoefficient(Coefficient &coeff,
-                           ProjectType type = ProjectType::DEFAULT) override;
-
-   void ProjectCoefficient(VectorCoefficient &vcoeff,
-                           ProjectType type = ProjectType::DEFAULT) override;
+   void ProjectCoefficient(Coefficient &coeff) override;

   using GridFunction::ProjectDiscCoefficient;
   /** @brief Project a discontinuous vector coefficient as a grid function on
@@ -290,18 +282,6 @@ public:
   void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                     const Array<int> &bdr_attr) override;

-   void ProjectCoefficientGlobalL2(Coefficient &coeff,
-                                   real_t rtol = 1e-12,
-                                   int iter = 1000) override;
-
-   void ProjectCoefficientElementL2(Coefficient &coeff) override;
-
-   void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
-                                   real_t rtol = 1e-12,
-                                   int iter = 1000) override;
-
-   void ProjectCoefficientElementL2(VectorCoefficient &vcoeff) override;
-
   /// @brief Returns ||u_ex - u_h||_L1 in parallel for H1 or L2 elements
   ///
   /// @see GridFunction::ComputeL1Error(Coefficient *exsol[],
@@ -607,7 +587,7 @@ public:
   /// PLBound object used to compute the bounds. Note: if vdim < 1, we compute
   /// the bounds for each vector dimension.
   PLBound GetBounds(Vector &lower, Vector &upper,
-                     const int ref_factor=1, const int vdim=-1) const override;
+                     const int ref_factor=1, const int vdim=-1) override;

   /** Save the local portion of the ParGridFunction. This differs from the
       serial GridFunction::Save in that it takes into account the signs of
@@ -994,6 +994,7 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
      {
         if ( face.IsConforming() )
         {
+            interpolations.RegisterFaceConformingInterpolation(face,f_ind);
            SetFaceDofsScatterIndices1(face,f_ind);
            if ( m==L2FaceValues::DoubleValued )
            {
@@ -1009,6 +1010,7 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
         }
         else // Non-conforming face
         {
+            interpolations.RegisterFaceCoarseToFineInterpolation(face,f_ind);
            SetFaceDofsScatterIndices1(face,f_ind);
            if ( m==L2FaceValues::DoubleValued )
            {
@@ -1026,6 +1028,7 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
      }
      else if (type==FaceType::Boundary && face.IsBoundary())
      {
+         interpolations.RegisterFaceConformingInterpolation(face,f_ind);
         SetFaceDofsScatterIndices1(face,f_ind);
         if ( m==L2FaceValues::DoubleValued )
         {
@@ -1043,6 +1046,10 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
   {
      gather_offsets[i] += gather_offsets[i - 1];
   }
+
+   // Transform the interpolation matrix map into a contiguous memory structure.
+   interpolations.LinearizeInterpolatorMapIntoVector();
+   interpolations.InitializeNCInterpConfig();
 }

 void ParNCL2FaceRestriction::ComputeGatherIndices()
@@ -326,7 +326,9 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows. */
+                                 default behavior is to disregard those rows.
+
+       @warning This method is not implemented yet. */
   void FillI(SparseMatrix &mat,
              const bool keep_nbr_block = false) const override;

@@ -362,7 +364,9 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows. */
+                                 default behavior is to disregard those rows.
+
+       @warning This method is not implemented yet. */
   void FillJAndData(const Vector &fea_data,
                     SparseMatrix &mat,
                     const bool keep_nbr_block = false) const override;
@@ -56,20 +56,6 @@ void QuadratureFunction::Save(std::ostream &os) const
   os.flush();
 }

-void QuadratureFunction::ProjectGridFunctionFallback(const GridFunction &gf)
-{
-   if (gf.VectorDim() == 1)
-   {
-      GridFunctionCoefficient coeff(&gf);
-      coeff.Coefficient::Project(*this);
-   }
-   else
-   {
-      VectorGridFunctionCoefficient coeff(&gf);
-      coeff.VectorCoefficient::Project(*this);
-   }
-}
-
 void QuadratureFunction::ProjectGridFunction(const GridFunction &gf)
 {
   SetVDim(gf.VectorDim());
@@ -82,23 +68,14 @@ void QuadratureFunction::ProjectGridFunction(const GridFunction &gf)
                                          ElementDofOrdering::LEXICOGRAPHIC :
                                          ElementDofOrdering::NATIVE;

-      // Use quadrature interpolator to go from E-vector to Q-vector
-      const QuadratureInterpolator *qi =
-         gf_fes.GetQuadratureInterpolator(*qs_elem);
-
-      // If quadrature interpolator doesn't support this space, then fallback
-      // on slower (non-device) version, and return early.
-      if (!qi)
-      {
-         ProjectGridFunctionFallback(gf);
-         return;
-      }
-
      // Use element restriction to go from L-vector to E-vector
      const Operator *R = gf_fes.GetElementRestriction(ordering);
      Vector e_vec(R->Height());
      R->Mult(gf, e_vec);

+      // Use quadrature interpolator to go from E-vector to Q-vector
+      const QuadratureInterpolator *qi =
+         gf_fes.GetQuadratureInterpolator(*qs_elem);
      qi->SetOutputLayout(QVectorLayout::byVDIM);
      qi->DisableTensorProducts(!use_tensor_products);
      qi->PhysValues(e_vec, *this);
@@ -106,25 +83,12 @@ void QuadratureFunction::ProjectGridFunction(const GridFunction &gf)
   else if (auto *qs_face = dynamic_cast<FaceQuadratureSpace*>(qspace))
   {
      const FiniteElementSpace &gf_fes = *gf.FESpace();
-      const FaceType face_type = qs_face->GetFaceType();
      const bool use_tensor_products = UsesTensorBasis(gf_fes);
      const ElementDofOrdering ordering = use_tensor_products ?
                                          ElementDofOrdering::LEXICOGRAPHIC :
                                          ElementDofOrdering::NATIVE;

-      // Use quadrature interpolator to go from E-vector to Q-vector
-      const FaceQuadratureInterpolator *qi =
-         gf_fes.GetFaceQuadratureInterpolator(qspace->GetIntRule(0), face_type);
-
-      // If quadrature interpolator doesn't support this space, then fallback
-      // on slower (non-device) version, and return early. Also, currently,
-      // ElementDofOrdering::NATIVE in FaceRestriction, so fall back in that
-      // case too.
-      if (qi == nullptr || ordering == ElementDofOrdering::NATIVE)
-      {
-         ProjectGridFunctionFallback(gf);
-         return;
-      }
+      const FaceType face_type = qs_face->GetFaceType();

      // Use element restriction to go from L-vector to E-vector
      const Operator *R = gf_fes.GetFaceRestriction(
@@ -132,6 +96,9 @@ void QuadratureFunction::ProjectGridFunction(const GridFunction &gf)
      Vector e_vec(R->Height());
      R->Mult(gf, e_vec);

+      // Use quadrature interpolator to go from E-vector to Q-vector
+      const FaceQuadratureInterpolator *qi =
+         gf_fes.GetFaceQuadratureInterpolator(qspace->GetIntRule(0), face_type);
      qi->SetOutputLayout(QVectorLayout::byVDIM);
      qi->DisableTensorProducts(!use_tensor_products);
      qi->Values(e_vec, *this);
@@ -27,8 +27,6 @@ protected:
   bool own_qspace; ///< Does this own the associated QuadratureSpaceBase?
   int vdim; ///< Vector dimension.

-   void ProjectGridFunctionFallback(const GridFunction &gf);
-
 public:
   /// Default constructor, results in an empty vector.
   QuadratureFunction() : qspace(nullptr), own_qspace(false), vdim(0)
@@ -50,13 +50,7 @@ QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Fallback(
   int DIM, int SDIM, int D1D, int Q1D)
 {
-   if (DIM == 1)
-   {
-      if (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
-      else if (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<0,0,2>; }
-      else if (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<0,0,3>; }
-      else { MFEM_ABORT(""); }
-   }
+   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D; }
   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface; }
   else if (DIM == 3)
--- a/Show More
+++ b/Show More