fix missing std::array and std::ignore

# Conflicts:
#	CMakeLists.txt

.gitignore

@@ -272,16 +272,27 @@ miniapps/navier/*_output
 
 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
+miniapps/nurbs/nurbs_ex3
+miniapps/nurbs/nurbs_ex5
 miniapps/nurbs/nurbs_ex11p
+miniapps/nurbs/nurbs_ex24
+miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
+miniapps/nurbs/sol_?.gf
 miniapps/nurbs/sol.*
 miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
+miniapps/nurbs/Example3*
+miniapps/nurbs/Example5*
+miniapps/nurbs/Solenoidal*
+miniapps/nurbs/ParaView
 miniapps/nurbs/sin-fit.mesh
+miniapps/nurbs/ex5.mesh
+miniapps/nurbs/exsol.mesh
 miniapps/nurbs/CurveInt
 miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh

.gitlab-ci.yml

@@ -22,7 +22,7 @@ include:
 # the "needs" keyword and express the DAG of jobs for more efficiency.
 # - We use setup and setup_baseline phases to download content outside of mfem
 #   directory.
-# - Allocate/Release is where quartz resource are allocated/released once for all.
+# - Allocate/Release is where ruby resource are allocated/released once for all.
 # - Build and Test is where we build and MFEM for multiple toolchains.
 # - Baseline_checks gathers baseline-type test suites execution
 # - Baseline_publish, only available on master, allows to update baseline
@@ -53,7 +53,7 @@ variables:
   AUTOTEST_COMMIT: "YES"
 
 # Trigger subpipelines:
-quartz-build-and-test:
+ruby-build-and-test:
   stage: sub-pipelines
   variables:
     # Explicitly pass down values that we want to be able to set when triggering
@@ -61,10 +61,10 @@ quartz-build-and-test:
     AUTOTEST: "${AUTOTEST}"
     AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
   trigger:
-    include: .gitlab/quartz-build-and-test.yml
+    include: .gitlab/ruby-build-and-test.yml
     strategy: depend
 
-quartz-baseline:
+ruby-baseline:
   stage: sub-pipelines
   variables:
     # Explicitly pass down values that we want to be able to set when triggering
@@ -73,7 +73,7 @@ quartz-baseline:
     AUTOTEST: "${AUTOTEST}"
     AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
   trigger:
-    include: .gitlab/quartz-baseline.yml
+    include: .gitlab/ruby-baseline.yml
     strategy: depend
 
 lassen-build-and-test:

.gitlab/README.md

@@ -24,7 +24,7 @@ and `test type`.
 
 Machines typically include:
 
-* Quartz: Intel bi-socket x86
+* Ruby: 2nd Gen Intel Xeon (Cascade Lake)
 * Lassen: Power9 + Nvidia GPU
 * Corona: AMD GPU
 
@@ -76,13 +76,13 @@ with a spack spec of MFEM, within the limits permitted by the MFEM spack
 package.
 
 In any build-and-test sub-pipeline a job basically consists in defining the
-spack spec to use. Adding a job on quartz for example resumes to:
+spack spec to use. Adding a job on ruby for example resumes to:
 
 ```yaml
 <job_name>:
   variables:
     SPEC: "<spack_spec>"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 ```
 
 The remaining and non trivial work is to make sure this spec is working. To

.gitlab/configs/common.yml

@@ -24,7 +24,7 @@ variables:
 # TODO: add a clean-up mechanism
   BUILD_ROOT: ${USER_CI_TOP_DIR}/${CI_PROJECT_NAME}-${MACHINE_NAME}-pipeline-${CI_PIPELINE_ID}
 
-# On LLNL's quartz, there is only one allocation shared among jobs in order to
+# On LLNL's ruby, there is only one allocation shared among jobs in order to
 # save time and resource. This allocation has to be uniquely named so that we
 # are sure to retrieve it.
   ALLOC_NAME: ${CI_PROJECT_NAME}_ci_${CI_PIPELINE_ID}

.gitlab/configs/ruby-config.yml

@@ -9,17 +9,17 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-# GitLab pipelines configurations for the Quartz machine at LLNL
+# GitLab pipelines configurations for the Ruby machine at LLNL
 variables:
-  MACHINE_NAME: quartz
+  MACHINE_NAME: ruby
 
-.on_quartz:
+.on_ruby:
   tags:
     - shell
-    - quartz
+    - ruby
   rules:
-    # Don't run quartz jobs if...
-    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"'
+    # Don't run ruby jobs if...
+    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_RUBY == "OFF"'
       when: never
     # Don't run autotest update if...
     - if: '$CI_JOB_NAME =~ /report/ && $AUTOTEST != "YES"'
@@ -40,13 +40,13 @@ variables:
     - when: on_success
 
 # Spack helped builds
-# Generic quartz build job, extending build script
-.build_and_test_on_quartz:
-  extends: [.on_quartz]
+# Generic ruby build job, extending build script
+.build_and_test_on_ruby:
+  extends: [.on_ruby]
   stage: build_and_test
   script:
     # THREADS is used by 'tests/gitlab/build_and_test', run below
-    - export THREADS=12
+    - export THREADS=16
     - echo ${ALLOC_NAME}
     - export JOBID=$(squeue -h --name=${ALLOC_NAME} --format=%A)
     - echo ${JOBID}

.gitlab/configs/setup-baseline.yml

@@ -18,7 +18,7 @@
 setup_baseline:
   tags:
     - shell
-    - quartz
+    - ruby
   stage: setup
   variables:
     GIT_STRATEGY: none

.gitlab/configs/setup-build-and-test.yml

@@ -16,7 +16,7 @@
 setup:
   tags:
     - shell
-    - quartz
+    - ruby
   stage: setup
   variables:
     GIT_STRATEGY: none

.gitlab/ruby-baseline.yml

@@ -19,8 +19,8 @@ stages:
   - cleanup
   - baseline_publish
 
-baselinecheck_mfem_intel_quartz:
-  extends: [.on_quartz]
+baselinecheck_mfem_intel_ruby:
+  extends: [.on_ruby]
   stage: baseline_check
   variables:
     # TPLS_DIR is used in .gitlab/scripts/baseline to provide the tpls location
@@ -32,7 +32,7 @@ baselinecheck_mfem_intel_quartz:
     - echo ${BUILD_ROOT}
     - echo ${TPLS_DIR}
     # Used by the tests in MFEM/tests:
-    - export MFEM_TEST_NP=32
+    - export MFEM_TEST_NP=48
     # The next script uses the following environment variables:
     # * BASELINE_TEST, SYS_TYPE, CI_PROJECT_DIR, ARTIFACTS_DIR,
     # * BUILD_ROOT, TPLS_DIR, MACHINE_NAME
@@ -44,18 +44,16 @@ baselinecheck_mfem_intel_quartz:
   allow_failure: true
 
 cleanup:
-  extends: .on_quartz
+  extends: .on_ruby
   stage: cleanup
   variables:
     GIT_STRATEGY: none
   script:
     - echo "BUILD_ROOT=${BUILD_ROOT}"
     - rm -rf "${BUILD_ROOT}" || true
-    - echo "CI_PROJECT_DIR=${CI_PROJECT_DIR}"
-    - make -C "${CI_PROJECT_DIR}" distclean
 
 report_baseline:
-  extends: [.on_quartz]
+  extends: [.on_ruby]
   stage: baseline_report
   script:
     - echo ${MACHINE_NAME}
@@ -115,8 +113,8 @@ report_baseline:
         exit $err
       ) 9> autotest.lock
 
-baselinepublish_mfem_quartz:
-  extends: [.on_quartz]
+baselinepublish_mfem_ruby:
+  extends: [.on_ruby]
   stage: baseline_publish
   rules:
     # - if: '$CI_COMMIT_BRANCH == "master" || $REBASELINE == "YES"'
@@ -131,5 +129,5 @@ baselinepublish_mfem_quartz:
 
 include:
   - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-config.yml
+  - local: .gitlab/configs/ruby-config.yml
   - local: .gitlab/configs/setup-baseline.yml

.gitlab/ruby-build-and-test.yml

@@ -19,54 +19,54 @@ stages:
 allocate_resource:
   variables:
     GIT_STRATEGY: none
-  extends: .on_quartz
+  extends: .on_ruby
   stage: allocate_resource
   script:
     - echo ${ALLOC_NAME}
     - salloc --exclusive --nodes=1 --reservation=ci --time=60 --no-shell --job-name=${ALLOC_NAME}
   timeout: 6h
 
-# GitLab jobs for the Quartz machine at LLNL
+# GitLab jobs for the Ruby machine at LLNL
 debug_ser_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 +debug~mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 debug_par_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 +debug+mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_ser_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 ~mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_sundials:
   variables:
     SPEC: "%gcc@10.3.1 +sundials"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_petsc:
   variables:
     SPEC: "%gcc@10.3.1 +petsc ^petsc+mumps~superlu-dist"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_pumi:
   variables:
     SPEC: "%gcc@10.3.1 +pumi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 # Release
 release_resource:
   variables:
     GIT_STRATEGY: none
-  extends: .on_quartz
+  extends: .on_ruby
   stage: release_resource_and_report
   script:
     - echo ${ALLOC_NAME}
@@ -78,17 +78,17 @@ release_resource:
 report_job_success:
   stage: release_resource_and_report
   extends:
-    - .on_quartz
+    - .on_ruby
     - .report_job_success
 
 report_job_failure:
   stage: release_resource_and_report
   extends:
-    - .on_quartz
+    - .on_ruby
     - .report_job_failure
 
 include:
   - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-config.yml
+  - local: .gitlab/configs/ruby-config.yml
   - local: .gitlab/configs/setup-build-and-test.yml
   - local: .gitlab/configs/report-build-and-test.yml

.gitlab/scripts/baseline

@@ -14,7 +14,7 @@
 # locals
 glob_err=${BASELINE_TEST}.err
 base=${BASELINE_TEST}-${SYS_TYPE}
-if [[ "${MACHINE_NAME}" == "quartz" ]]; then
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
   base="${BASELINE_TEST}-${MACHINE_NAME}"
 fi
 base_diff=${base}.diff
@@ -31,8 +31,8 @@ cd tests
 mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}
 
 # run
-if [[ "${MACHINE_NAME}" == "quartz" || "${MACHINE_NAME}" == "ruby" ]]; then
-  salloc --nodes=1 --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
+  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}"
 elif [[ ${MACHINE_NAME} == "lassen" ]]; then
@@ -41,11 +41,11 @@ else
   echo "Unknown machine: MACHINE_NAME=$MACHINE_NAME"
   exit 1
 fi
+status="$?"
 
 # post
 mkdir ${artifacts_path}
 
-status=0
 if [[ -f ${BASELINE_TEST}.out ]]; then
   cp ${BASELINE_TEST}.out ${artifacts_path}
 fi

.gitlab/scripts/rebaseline

@@ -11,7 +11,7 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-# There will be collision between corona and quartz baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 ARTIFACT_PATH=${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/baseline-${SYS_TYPE}
@@ -21,7 +21,7 @@ PATCH_FILE=${ARTIFACT_PATH}.patch
 FULL_FILE=${ARTIFACT_PATH}.out
 DIFF_FILE=${ARTIFACT_PATH}.diff
 
-# There will be collision between corona and quartz baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 SAVED_NAME=baseline-${SYS_TYPE}.saved

CHANGELOG

@@ -11,9 +11,46 @@
 Version 4.7.1 (development)
 ===========================
 
+Discretization improvements
+---------------------------
+- Added NURBS-based H(div) and H(curl) elements in 2D and 3D. Only on single
+  patch meshes. Only implemented for serial computations.
+
+- Added support for boundary constraints to the hybridization class.
+
+Meshing improvements
+--------------------
+- The ExodusII reader now handles pyramid and wedge element types. Mixed meshes
+  are also supported.
+
+New and updated examples and miniapps
+-------------------------------------
+- Added miniapps to demonstrate the H(div) and H(curl) NURBS elements.
+
 - Added an MFEM example for the eikonal equation. This new solver is based on
   the proximal Galerkin method introduced by Keith and Surowiec.
 
+GPU computing
+-------------
+- Added support for GPU-accelerated batched linear algebra (using cuBLAS,
+  hipBLAS, MAGMA, or native MFEM functionality) through the BatchedLinAlg class.
+
+Miscellaneous
+-------------
+- Refactored the `ARKStepSolver` class (ARKODE interface) to use
+  `TimeDependentOperator::Mult` only when the associated ODE operator is
+  expressed in explicit form (i.e., `TimeDependentOperator::isExplicit()`),
+  otherwise `TimeDependentOperator::ExplicitMult` is used. A check has been
+  added to `ARKStepSolver` to verify that the associated ODE operator is not in
+  explicit form when a mass matrix solver is enabled via a call to either the
+  `UseMFEMMassLinearSolver` or `UseSundialsMassLinearSolver` methods. This is
+  because enabling a mass matrix solver assumes that F(u,k,t) = M k in the
+  associated ODE operator.
+
+- Added support for custom interpolation procedure in FindPointsGSLIB.
+
+API changes
+-----------
 - API change: in class GridFunction, 'fec' was renamed to 'fec_owned'.
 
 
@@ -40,6 +77,9 @@ Meshing improvements
 
 - Added support for internal boundary elements in nonconforming meshes.
 
+- Added ExodusII output capability. The writer can handle first-order (Pyramid5,
+  Wedge6, Hex8, Tet4) and second-order FE types (Pyramid14, Wedge18, Hex27, Tet10).
+
 - The ReadCubit Genesis mesh importer has been rewritten to improve readability.
 
 Discretization improvements

CMakeLists.txt

@@ -146,7 +146,9 @@ if (MFEM_USE_CUDA)
    set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS}")
    find_package(CUDAToolkit REQUIRED)
    set(CUSPARSE_FOUND TRUE)
+   set(CUBLAS_FOUND TRUE)
    get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
+   get_target_property(CUBLAS_LIBRARIES CUDA::cublas LOCATION)
 endif()
 
 if (XSDK_ENABLE_C)
@@ -231,6 +233,7 @@ if (MFEM_USE_HIP)
     list(INSERT CMAKE_PREFIX_PATH 0 ${ROCM_PATH})
   endif()
   find_package(HIP REQUIRED)
+  find_package(HIPBLAS REQUIRED)
   find_package(HIPSPARSE REQUIRED)
 endif()
 
@@ -396,6 +399,10 @@ if (MFEM_USE_AMGX)
   find_package(AMGX REQUIRED)
 endif()
 
+if (MFEM_USE_MAGMA)
+  find_package(MAGMA REQUIRED)
+endif()
+
 if (MFEM_USE_CONDUIT)
     find_package(Conduit REQUIRED conduit relay blueprint)
 endif()
@@ -515,7 +522,10 @@ endif()
 
 # Enzyme
 if (MFEM_USE_ENZYME)
-   find_package(ENZYME REQUIRED)
+    find_package(Enzyme REQUIRED HINTS ${ENZYME_DIR})
+    message(STATUS "Enzyme found in ${ENZYME_DIR}.")
+    set(ENZYME_INCLUDE_DIRS ${ENZYME_DIR}/include)
+    set(ENZYME_FOUND 1)
 endif()
 
 # MFEM_TIMER_TYPE
@@ -557,8 +567,9 @@ find_package(Threads REQUIRED)
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
     SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
     NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
-    ADIOS2 CUSPARSE MKL_CPARDISO MKL_PARDISO AMGX CALIPER CODIPACK
-    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)
+    ADIOS2 MKL_CPARDISO MKL_PARDISO AMGX MAGMA CUSPARSE CUBLAS CALIPER CODIPACK
+    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPBLAS HIPSPARSE MOONOLITH BLITZ
+    ALGOIM ENZYME)
 
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
@@ -621,6 +632,11 @@ set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX} CACHE PATH
 mfem_add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
 target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES})
+
+if (MFEM_USE_ENZYME)
+  target_link_libraries(mfem PUBLIC ClangEnzymeFlags)
+endif()
+
 if (MINGW)
   target_link_libraries(mfem PRIVATE ws2_32)
 endif()
@@ -673,7 +689,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
 #include \"${PROJECT_SOURCE_DIR}/${Header}\"
 ")
 
-    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different
       "${PROJECT_BINARY_DIR}/${Header}.tmp"
       "${PROJECT_BINARY_DIR}/${Header}"
     )
@@ -687,7 +703,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
 #include \"mfem/${Header}\"
 ")
 
-    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different
       "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}.tmp"
       "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}"
     )

INSTALL

@@ -273,7 +273,13 @@ Installation options:
    PREFIX  - Specify the installation directory. The library (libmfem.a) will be
              installed in $(PREFIX)/lib, the headers in $(PREFIX)/include, and
              the configuration makefile (config.mk) in $(PREFIX)/share/mfem.
-   INSTALL - Specify the install program, e.g /usr/bin/install
+   INSTALL - Specify the install program, default = /usr/bin/install
+   INSTALL_DEF_PERM - Specify the default install permissions. This affects
+                      headers and configuration makefiles, default = 644
+   INSTALL_BIN_PERM - Specify the install permissions for binaries. This only
+                      affects the shared version of the library, default = 755
+   INSTALL_DIR_PERM - Specify the install permissions for directories and,
+                      on macOS/BSD, for symlinks as well, default = 755
 
 MFEM library features/options (GNU make)
 ----------------------------------------
@@ -388,6 +394,11 @@ MFEM_USE_AMGX = YES/NO
    Allows the user to use SparseMatrices and HypreParMatrices to solve linear
    systems with the routines from the AmgX library.
 
+MFEM_USE_MAGMA = YES/NO
+   Enable MFEM functionality based on the MAGMA high-performance linear algebra
+   library. The MAGMA library provides a BLAS/LAPACK interface, with
+   implementations that have been optimized for Nvidia and AMD GPUs.
+
 MFEM_USE_GNUTLS = YES/NO
    Enable secure socket support in class socketstream, using the auxiliary
    GnuTLS_* classes, based on the GnuTLS library. This option may be useful in
@@ -699,6 +710,11 @@ The specific libraries and their options are:
   Options: AMGX_OPT, AMGX_LIB.
   Versions: AmgX >= 2.1, older versions may work too.
 
+- MAGMA (optional), used with MFEM_USE_MAGMA = YES.
+  URL: https://icl.utk.edu/magma/
+  Options: MAGMA_OPT, MAGMA_LIB
+  Versions: MAGMA >= 2.8.0
+
 - GnuTLS (optional), used when MFEM_USE_GNUTLS = YES. On most Linux systems,
   GnuTLS is available as a development package, e.g. gnutls-devel. On Mac OS X,
   one can get the library through the Homebrew package manager (http://brew.sh).

config/cmake/MFEMConfig.cmake.in

@@ -37,6 +37,7 @@ set(MFEM_USE_MUMPS @MFEM_USE_MUMPS@)
 set(MFEM_USE_STRUMPACK @MFEM_USE_STRUMPACK@)
 set(MFEM_USE_GINKGO @MFEM_USE_GINKGO@)
 set(MFEM_USE_AMGX @MFEM_USE_AMGX@)
+set(MFEM_USE_MAGMA @MFEM_USE_MAGMA@)
 set(MFEM_USE_HIOP @MFEM_USE_HIOP@)
 set(MFEM_USE_GNUTLS @MFEM_USE_GNUTLS@)
 set(MFEM_USE_GSLIB @MFEM_USE_GSLIB@)

config/cmake/config.hpp.in

@@ -114,6 +114,9 @@
 // Enable MFEM functionality based on the AmgX library.
 #cmakedefine MFEM_USE_AMGX
 
+// Enable MFEM functionality based on the MAGMA library.
+#cmakedefine MFEM_USE_MAGMA
+
 // Enable secure socket streams based on the GNUTLS library.
 #cmakedefine MFEM_USE_GNUTLS
 

config/cmake/modules/FindENZYME.cmake

@@ -1,27 +0,0 @@
-# Copyright (c) 2010-2024, 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.
-
-message(STATUS "Looking for ENZYME ...")
-message(STATUS "   in ENZYME_DIR = ${ENZYME_DIR}")
-
-# Make sure the directory and version combination works. Do nothing otherwise.
-if(EXISTS "${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
-  message(STATUS "Found ENZYME: ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
-
-  # Set ENZYME_FOUND
-  set(ENZYME_FOUND TRUE CACHE BOOL "ENZYME was found." FORCE)
-
-  # Set CXX flags to accommodate the Enzyme Clang plugin
-  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Xclang -load -Xclang ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so -mllvm -enzyme-loose-types=1")
-  set(MFEM_USE_ENZYME YES)
-else()
-
-endif()

config/cmake/modules/FindMAGMA.cmake

@@ -0,0 +1,37 @@
+# Copyright (c) 2010-2024, 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.
+
+# Defines the following variables:
+#   - MAGMA_FOUND
+#   - MAGMA_LIBRARIES
+#   - MAGMA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(MAGMA MAGMA MAGMA_DIR "include" "magma.h" "lib" "magma"
+  "Paths to headers required by MAGMA." "Libraries required by MAGMA.")
+
+if (MAGMA_FOUND AND MFEM_USE_CUDA)
+  get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
+  get_target_property(CUBLAS_LIBRARIES CUDA::cublas LOCATION)
+  list(APPEND MAGMA_LIBRARIES ${CUSPARSE_LIBRARIES} ${CUBLAS_LIBRARIES})
+  set(MAGMA_LIBRARIES ${MAGMA_LIBRARIES} CACHE STRING
+      "MAGMA libraries + dependencies." FORCE)
+  message(STATUS "Updated MAGMA_LIBRARIES: ${MAGMA_LIBRARIES}")
+endif()
+
+if (MAGMA_FOUND AND MFEM_USE_HIP)
+  find_package(HIPBLAS REQUIRED)
+  find_package(HIPSPARSE REQUIRED)
+  list(APPEND MAGMA_LIBRARIES ${HIPBLAS_LIBRARIES} ${HIPSPARSE_LIBRARIES})
+  set(MAGMA_LIBRARIES ${MAGMA_LIBRARIES} CACHE STRING
+      "MAGMA libraries + dependencies." FORCE)
+  message(STATUS "Updated MAGMA_LIBRARIES: ${MAGMA_LIBRARIES}")
+endif()

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -846,14 +846,14 @@ function(mfem_export_mk_files)
       MFEM_USE_ZLIB MFEM_USE_LIBUNWIND MFEM_USE_LAPACK MFEM_THREAD_SAFE
       MFEM_USE_LEGACY_OPENMP MFEM_USE_OPENMP MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS
       MFEM_USE_SUITESPARSE MFEM_USE_SUPERLU MFEM_USE_SUPERLU5 MFEM_USE_MUMPS
-      MFEM_USE_STRUMPACK MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_GNUTLS
-      MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_SLEPC MFEM_USE_MPFR MFEM_USE_SIDRE
-      MFEM_USE_FMS MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_GSLIB
-      MFEM_USE_CUDA MFEM_USE_HIP MFEM_USE_RAJA MFEM_USE_OCCA MFEM_USE_CEED
-      MFEM_USE_CALIPER MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2
-      MFEM_USE_MKL_CPARDISO MFEM_USE_MKL_PARDISO MFEM_USE_ADFORWARD
-      MFEM_USE_CODIPACK MFEM_USE_BENCHMARK MFEM_USE_PARELAG MFEM_USE_TRIBOL
-      MFEM_USE_MOONOLITH MFEM_USE_ALGOIM MFEM_USE_ENZYME)
+      MFEM_USE_STRUMPACK MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_MAGMA
+      MFEM_USE_GNUTLS MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_SLEPC
+      MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_FMS MFEM_USE_CONDUIT MFEM_USE_PUMI
+      MFEM_USE_HIOP MFEM_USE_GSLIB MFEM_USE_CUDA MFEM_USE_HIP MFEM_USE_RAJA
+      MFEM_USE_OCCA MFEM_USE_CEED MFEM_USE_CALIPER MFEM_USE_UMPIRE MFEM_USE_SIMD
+      MFEM_USE_ADIOS2 MFEM_USE_MKL_CPARDISO MFEM_USE_MKL_PARDISO
+      MFEM_USE_ADFORWARD MFEM_USE_CODIPACK MFEM_USE_BENCHMARK MFEM_USE_PARELAG
+      MFEM_USE_TRIBOL MFEM_USE_MOONOLITH MFEM_USE_ALGOIM MFEM_USE_ENZYME)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)

config/config.hpp.in

@@ -114,6 +114,9 @@
 // Enable MFEM functionality based on the AmgX library.
 // #define MFEM_USE_AMGX
 
+// Enable MFEM functionality based on the MAGMA library.
+// #define MFEM_USE_MAGMA
+
 // Enable secure socket streams based on the GNUTLS library.
 // #define MFEM_USE_GNUTLS
 

config/config.mk.in

@@ -38,6 +38,7 @@ MFEM_USE_MUMPS         = @MFEM_USE_MUMPS@
 MFEM_USE_STRUMPACK     = @MFEM_USE_STRUMPACK@
 MFEM_USE_GINKGO        = @MFEM_USE_GINKGO@
 MFEM_USE_AMGX          = @MFEM_USE_AMGX@
+MFEM_USE_MAGMA         = @MFEM_USE_MAGMA@
 MFEM_USE_GNUTLS        = @MFEM_USE_GNUTLS@
 MFEM_USE_NETCDF        = @MFEM_USE_NETCDF@
 MFEM_USE_PETSC         = @MFEM_USE_PETSC@

config/defaults.cmake

@@ -40,6 +40,7 @@ option(MFEM_USE_MUMPS "Enable MUMPS usage" OFF)
 option(MFEM_USE_STRUMPACK "Enable STRUMPACK usage" OFF)
 option(MFEM_USE_GINKGO "Enable Ginkgo usage" OFF)
 option(MFEM_USE_AMGX "Enable AmgX usage" OFF)
+option(MFEM_USE_MAGMA "Enable MAGMA usage" OFF)
 option(MFEM_USE_GNUTLS "Enable GNUTLS usage" OFF)
 option(MFEM_USE_GSLIB "Enable GSLIB usage" OFF)
 option(MFEM_USE_NETCDF "Enable NETCDF usage" OFF)
@@ -183,6 +184,10 @@ set(Ginkgo_DIR "${MFEM_DIR}/../ginkgo" CACHE PATH "Path to the Ginkgo library.")
 
 set(AMGX_DIR "${MFEM_DIR}/../amgx" CACHE PATH "Path to AmgX")
 
+set(MAGMA_DIR "${MFEM_DIR}/../magma" CACHE PATH "Path to MAGMA")
+set(MAGMA_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
+    "Additional packages required by MAGMA.")
+
 set(GNUTLS_DIR "" CACHE PATH "Path to the GnuTLS library.")
 
 set(GSLIB_DIR "" CACHE PATH "Path to the GSLIB library.")
@@ -259,7 +264,7 @@ set(PARELAG_LIBRARIES "${PARELAG_DIR}/build/src/libParELAG.a" CACHE STRING
     "The ParELAG library.")
 
 set(TRIBOL_DIR "${MFEM_DIR}/../tribol" CACHE PATH "Path to Tribol")
-set(Tribol_REQUIRED_PACKAGES "Axom/core/mint/slam/slic" CACHE STRING 
+set(Tribol_REQUIRED_PACKAGES "Axom/core/mint/slam/slic" CACHE STRING
     "Additional packages required by Tribol")
 
 set(BLAS_INCLUDE_DIRS "" CACHE STRING "Path to BLAS headers.")

config/defaults.mk

@@ -95,6 +95,10 @@ else
    # Silence unused command line argument warnings when generating dependencies
    # with mpicxx and clang
    DEP_FLAGS := -Wno-unused-command-line-argument $(DEP_FLAGS)
+   # Silence "ignoring duplicate libraries" warnings on new (Xcode 15) linker
+   ifneq (,$(findstring PROJECT:dyld,$(shell ld -v 2>&1)))
+      LDFLAGS_INTERNAL = -Xlinker -no_warn_duplicate_libraries
+   endif
 endif
 
 # Set CXXFLAGS to overwrite the default selection of DEBUG_FLAGS/OPTIM_FLAGS
@@ -139,6 +143,7 @@ MFEM_USE_MUMPS         = NO
 MFEM_USE_STRUMPACK     = NO
 MFEM_USE_GINKGO        = NO
 MFEM_USE_AMGX          = NO
+MFEM_USE_MAGMA         = NO
 MFEM_USE_GNUTLS        = NO
 MFEM_USE_NETCDF        = NO
 MFEM_USE_PETSC         = NO
@@ -390,6 +395,11 @@ AMGX_DIR = @MFEM_DIR@/../amgx
 AMGX_OPT = -I$(AMGX_DIR)/include
 AMGX_LIB = -L$(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 -lcublas -lcusparse $(LAPACK_LIB)
+
 # GnuTLS library configuration
 GNUTLS_OPT =
 GNUTLS_LIB = -lgnutls
@@ -497,11 +507,11 @@ GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs
 
 # CUDA library configuration
 CUDA_OPT =
-CUDA_LIB = -lcusparse
+CUDA_LIB = -lcusparse -lcublas
 
 # HIP library configuration
 HIP_OPT =
-HIP_LIB = -L$(HIP_DIR)/lib $(XLINKER)-rpath,$(HIP_DIR)/lib -lhipsparse
+HIP_LIB = -L$(HIP_DIR)/lib $(XLINKER)-rpath,$(HIP_DIR)/lib -lhipsparse -lhipblas
 
 # OCCA library configuration
 OCCA_DIR = @MFEM_DIR@/../occa

config/sample-runs.sh

@@ -32,7 +32,7 @@ groups_serial=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1,2,3}[0-9].cpp"'
+   "ex{,[1-9]}[0-9].cpp"'
 #   "ex1.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -58,6 +58,10 @@ groups_serial=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
@@ -66,25 +70,38 @@ groups_serial=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
     mesh-optimizer.cpp minimal-surface.cpp"'
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
    "cvsRoberts_ASAi_dns.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp"' # 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp "'
+# todo: miniapps/mtop
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
    "nurbs_ex1.cpp"'
+# todo: add other nurbs miniapps
+# todo: miniapps/solvers (serial)
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
    "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
     lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
    "Toys miniapps:"
    "miniapps/toys"
@@ -100,7 +117,7 @@ groups_parallel=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1,2,3}[0-9]p.cpp"'
+   "ex{,[1-9]}[0-9]p.cpp"'
 #   "ex1p.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -126,6 +143,10 @@ groups_parallel=(
    "HiOp examples:"
    "examples/hiop"
    "ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex{1,2}p.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
@@ -138,24 +159,41 @@ groups_parallel=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp"'
+   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
    "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
    "adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "par_example.cpp"'
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "p{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "pfindpts.cpp schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
    "Navier miniapps:"
    "miniapps/navier"
    "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
@@ -164,14 +202,18 @@ groups_parallel=(
    "Shifted miniapps:"
    "miniapps/shifted"
    "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
    "Solvers miniapps:"
    "miniapps/solvers"
    "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
-   "convert-cd.cpp get-values.cpp load-dc.cpp"'
+   "convert-dc.cpp get-values.cpp load-dc.cpp"'
+# todo: add other tools miniapps
 '"convergence"
    "Convergence tests:"
    "tests/convergence"
@@ -186,7 +228,7 @@ groups_all=(
 '"examples"
    "Examples:"
    "examples"
-   "ex\"{,1,2,3}[0-9]\"{,p}.cpp"'
+   "ex\"{,[1-9]}[0-9]\"{,p}.cpp"'
 '"sundials"
    "SUNDIALS examples:"
    "examples/sundials"
@@ -215,10 +257,14 @@ groups_all=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp ex{1,2}p.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
-   "ex1.cpp ex1p.cpp ex2.cpp ex6p.cpp"'
+   "ex1.cpp ex2.cpp ex1p.cpp ex6p.cpp"'
 '"superlu"
    "Superlu examples:"
    "examples/superlu"
@@ -226,43 +272,67 @@ groups_all=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp"'
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
+    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
    "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
-   "adjoint_advection_diffusion.cpp cvsRoberts_ASAi_dns.cpp"'
+   "cvsRoberts_ASAi_dns.cpp adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp par_example.cpp"'
+# 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{,p}{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp pfindpts.cpp
     schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
    "Navier miniapps:"
    "miniapps/navier"
    "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
    "nurbs_ex1.cpp nurbs_ex1p.cpp nurbs_ex11p.cpp"'
+# todo: add other nurbs miniapps
 '"shifted"
    "Shifted miniapps:"
    "miniapps/shifted"
    "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
    "Solvers miniapps:"
    "miniapps/solvers"
    "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
    "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
     lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
    "Toys miniapps:"
    "miniapps/toys"
@@ -386,7 +456,7 @@ function help_message()
       mfem_config [${mfem_config}]
          Set MFEM configuration options
       make [${make}], mpiexec [${mpiexec}], mpiexec_np [${mpiexec_np}]
-         Their values can also set using the respective uppercase environment
+         Their values can also be set using the respective uppercase environment
          variable
       mfem_build_dir [${mfem_build_dir}]
          Same as '-d': set this variable to something different from <mfem_dir>

data/cube-space-time.mesh

@@ -1,102 +0,0 @@
-MFEM mesh v1.0
-
-dimension
-4
-
-elements
-24
-1 7 4 5 8 11 13
-1 7 1 4 5 7 8
-1 7 1 4 5 8 11
-1 7 1 5 8 11 13
-1 7 1 5 7 8 13
-1 7 4 5 7 8 13
-1 7 1 3 4 8 11
-1 7 1 3 4 5 11
-1 7 1 5 10 11 13
-1 7 1 8 10 11 13
-1 7 1 3 5 10 11
-1 7 1 2 3 5 10
-1 7 0 1 3 4 8
-1 7 0 1 4 7 8
-1 7 1 5 6 7 13
-1 7 1 6 7 8 13
-1 7 6 7 8 13 15
-1 7 4 7 8 13 15
-1 7 4 8 12 13 15
-1 7 4 8 11 12 13
-1 7 6 8 13 14 15
-1 7 1 6 8 13 14
-1 7 1 8 9 10 13
-1 7 1 8 9 13 14
-
-boundary
-48
-1 4 0 1 3 4
-1 4 0 1 3 8
-1 4 0 3 4 8
-1 4 0 1 4 7
-1 4 0 1 7 8
-1 4 0 4 7 8
-1 4 1 4 5 7
-1 4 1 3 8 11
-1 4 1 3 4 5
-1 4 1 5 10 13
-1 4 1 8 10 11
-1 4 1 3 10 11
-1 4 1 2 3 5
-1 4 1 2 3 10
-1 4 1 2 5 10
-1 4 1 5 6 7
-1 4 1 5 6 13
-1 4 1 6 7 8
-1 4 1 6 8 14
-1 4 1 6 13 14
-1 4 1 8 9 10
-1 4 1 9 10 13
-1 4 1 8 9 14
-1 4 1 9 13 14
-1 4 2 3 5 10
-1 4 3 4 8 11
-1 4 3 4 5 11
-1 4 3 5 10 11
-1 4 4 5 11 13
-1 4 4 5 7 13
-1 4 4 7 8 15
-1 4 4 7 13 15
-1 4 4 8 12 15
-1 4 4 12 13 15
-1 4 4 8 11 12
-1 4 4 11 12 13
-1 4 5 10 11 13
-1 4 5 6 7 13
-1 4 6 7 8 15
-1 4 6 7 13 15
-1 4 6 8 14 15
-1 4 6 13 14 15
-2 4 8 10 11 13
-2 4 8 12 13 15
-2 4 8 11 12 13
-2 4 8 13 14 15
-2 4 8 9 10 13
-2 4 8 9 13 14
-
-vertices
-16
-4
-0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000

data/cube4d_24.MFEM

@@ -1,102 +0,0 @@
-MFEM mesh v1.0
-
-dimension
-4
-
-elements
-24
-17 8 4 5 8 11 13
-11 8 1 4 5 7 8
-15 8 1 4 5 8 11
-16 8 1 5 8 11 13
-12 8 1 5 7 8 13
-13 8 4 5 7 8 13
-7  8 1 3 4 8 11
-2  8 1 3 4 5 11
-4  8 1 5 10 11 13
-10 8 1 8 10 11 13
-3  8 1 3 5 10 11
-1  8 1 2 3 5 10
-6  8 0 1 3 4 8
-8  8 0 1 4 7 8
-5  8 1 5 6 7 13
-20 8 1 6 7 8 13
-19 8 6 7 8 13 15
-14 8 4 7 8 13 15
-21 8 4 8 12 13 15
-22 8 4 8 11 12 13
-23 8 6 8 13 14 15
-24 8 1 6 8 13 14
-9  8 1 8 9 10 13
-18 8 1 8 9 13 14
-
-boundary
-48
-1 4 0 1 3 4
-3 4 0 1 3 8
-3 4 0 3 4 8
-1 4 0 1 4 7
-3 4 0 1 7 8
-3 4 0 4 7 8
-1 4 1 4 5 7
-3 4 1 3 8 11
-1 4 1 3 4 5
-3 4 1 5 10 13
-3 4 1 8 10 11
-3 4 1 3 10 11
-1 4 1 2 3 5
-3 4 1 2 3 10
-3 4 1 2 5 10
-1 4 1 5 6 7
-3 4 1 5 6 13
-3 4 1 6 7 8
-3 4 1 6 8 14
-3 4 1 6 13 14
-3 4 1 8 9 10
-3 4 1 9 10 13
-3 4 1 8 9 14
-3 4 1 9 13 14
-3 4 2 3 5 10
-3 4 3 4 8 11
-3 4 3 4 5 11
-3 4 3 5 10 11
-3 4 4 5 11 13
-3 4 4 5 7 13
-3 4 4 7 8 15
-3 4 4 7 13 15
-3 4 4 8 12 15
-3 4 4 12 13 15
-3 4 4 8 11 12
-3 4 4 11 12 13
-3 4 5 10 11 13
-3 4 5 6 7 13
-3 4 6 7 8 15
-3 4 6 7 13 15
-3 4 6 8 14 15
-3 4 6 13 14 15
-5 4 8 10 11 13
-5 4 8 12 13 15
-5 4 8 11 12 13
-5 4 8 13 14 15
-5 4 8 9 10 13
-5 4 8 9 13 14
-
-vertices
-16
-4
-0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000

data/cube4d_96.MFEM

@@ -1,231 +0,0 @@
-MFEM mesh v1.0
-
-dimension
-4
-
-elements
-96
-1 8 0 1 7 8 9
-1 8 1 6 7 8 9
-1 8 4 5 6 8 9
-1 8 4 6 7 8 9
-1 8 0 1 3 8 9
-1 8 1 2 3 8 9
-1 8 0 4 7 8 9
-1 8 0 3 4 8 9
-1 8 1 2 6 8 9
-1 8 2 5 6 8 9
-1 8 3 4 5 8 9
-1 8 2 3 5 8 9
-1 8 9 10 11 17 18
-1 8 9 11 16 17 18
-1 8 9 14 15 16 18
-1 8 9 14 16 17 18
-1 8 9 10 11 13 18
-1 8 9 11 12 13 18
-1 8 9 10 14 17 18
-1 8 9 10 13 14 18
-1 8 9 11 12 16 18
-1 8 9 12 15 16 18
-1 8 9 13 14 15 18
-1 8 9 12 13 15 18
-1 8 9 12 15 16 19
-1 8 9 11 12 16 19
-1 8 1 6 9 11 19
-1 8 6 9 11 16 19
-1 8 1 2 6 9 19
-1 8 2 5 6 9 19
-1 8 2 5 9 15 19
-1 8 2 9 12 15 19
-1 8 5 6 9 16 19
-1 8 5 9 15 16 19
-1 8 1 9 11 12 19
-1 8 1 2 9 12 19
-1 8 9 10 13 14 20
-1 8 9 10 14 17 20
-1 8 0 9 10 17 20
-1 8 0 7 9 17 20
-1 8 0 3 4 9 20
-1 8 0 4 7 9 20
-1 8 3 4 9 13 20
-1 8 4 9 13 14 20
-1 8 4 7 9 14 20
-1 8 7 9 14 17 20
-1 8 0 3 9 10 20
-1 8 3 9 10 13 20
-1 8 2 5 9 15 21
-1 8 2 9 12 15 21
-1 8 2 3 5 9 21
-1 8 3 4 5 9 21
-1 8 9 13 14 15 21
-1 8 9 12 13 15 21
-1 8 4 5 9 14 21
-1 8 5 9 14 15 21
-1 8 2 3 9 12 21
-1 8 3 9 12 13 21
-1 8 3 4 9 13 21
-1 8 4 9 13 14 21
-1 8 1 6 9 11 22
-1 8 6 9 11 16 22
-1 8 6 7 9 16 22
-1 8 7 9 16 17 22
-1 8 0 7 9 17 22
-1 8 0 9 10 17 22
-1 8 0 1 9 10 22
-1 8 1 9 10 11 22
-1 8 0 1 7 9 22
-1 8 1 6 7 9 22
-1 8 9 10 11 17 22
-1 8 9 11 16 17 22
-1 8 5 9 15 16 23
-1 8 5 6 9 16 23
-1 8 6 7 9 16 23
-1 8 7 9 16 17 23
-1 8 7 9 14 17 23
-1 8 4 7 9 14 23
-1 8 4 5 9 14 23
-1 8 5 9 14 15 23
-1 8 4 6 7 9 23
-1 8 4 5 6 9 23
-1 8 9 14 15 16 23
-1 8 9 14 16 17 23
-1 8 1 2 9 12 24
-1 8 1 9 11 12 24
-1 8 0 1 9 10 24
-1 8 1 9 10 11 24
-1 8 0 3 9 10 24
-1 8 3 9 10 13 24
-1 8 2 3 9 12 24
-1 8 3 9 12 13 24
-1 8 1 2 3 9 24
-1 8 0 1 3 9 24
-1 8 9 10 11 13 24
-1 8 9 11 12 13 24
-
-boundary
-96
-1 4 0 1 7 8
-1 4 0 1 3 8
-1 4 0 4 7 8
-1 4 0 3 4 8
-2 4 0 10 17 20
-2 4 0 7 17 20
-2 4 0 3 4 20
-2 4 0 4 7 20
-2 4 0 3 10 20
-2 4 0 7 17 22
-2 4 0 10 17 22
-2 4 0 1 10 22
-2 4 0 1 7 22
-2 4 0 1 10 24
-2 4 0 3 10 24
-2 4 0 1 3 24
-1 4 1 6 7 8
-1 4 1 2 3 8
-1 4 1 2 6 8
-2 4 1 6 11 19
-2 4 1 2 6 19
-2 4 1 11 12 19
-2 4 1 2 12 19
-2 4 1 6 11 22
-2 4 1 10 11 22
-2 4 1 6 7 22
-2 4 1 2 12 24
-2 4 1 11 12 24
-2 4 1 10 11 24
-2 4 1 2 3 24
-1 4 2 5 6 8
-1 4 2 3 5 8
-2 4 2 5 6 19
-2 4 2 5 15 19
-2 4 2 12 15 19
-2 4 2 5 15 21
-2 4 2 12 15 21
-2 4 2 3 5 21
-2 4 2 3 12 21
-2 4 2 3 12 24
-1 4 3 4 5 8
-2 4 3 4 13 20
-2 4 3 10 13 20
-2 4 3 4 5 21
-2 4 3 12 13 21
-2 4 3 4 13 21
-2 4 3 10 13 24
-2 4 3 12 13 24
-1 4 4 5 6 8
-1 4 4 6 7 8
-2 4 4 13 14 20
-2 4 4 7 14 20
-2 4 4 5 14 21
-2 4 4 13 14 21
-2 4 4 7 14 23
-2 4 4 5 14 23
-2 4 4 6 7 23
-2 4 4 5 6 23
-2 4 5 6 16 19
-2 4 5 15 16 19
-2 4 5 14 15 21
-2 4 5 15 16 23
-2 4 5 6 16 23
-2 4 5 14 15 23
-2 4 6 11 16 19
-2 4 6 11 16 22
-2 4 6 7 16 22
-2 4 6 7 16 23
-2 4 7 14 17 20
-2 4 7 16 17 22
-2 4 7 16 17 23
-2 4 7 14 17 23
-3 4 10 11 17 18
-3 4 10 11 13 18
-3 4 10 14 17 18
-3 4 10 13 14 18
-2 4 10 13 14 20
-2 4 10 14 17 20
-2 4 10 11 17 22
-2 4 10 11 13 24
-3 4 11 16 17 18
-3 4 11 12 13 18
-3 4 11 12 16 18
-2 4 11 12 16 19
-2 4 11 16 17 22
-2 4 11 12 13 24
-3 4 12 15 16 18
-3 4 12 13 15 18
-2 4 12 15 16 19
-2 4 12 13 15 21
-3 4 13 14 15 18
-2 4 13 14 15 21
-3 4 14 15 16 18
-3 4 14 16 17 18
-2 4 14 15 16 23
-2 4 14 16 17 23
-
-vertices
-25
-4
-0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 0.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000
-0.5000000000000000 0.5000000000000000 0.5000000000000000 0.0000000000000000
-0.5000000000000000 0.5000000000000000 0.5000000000000000 0.5000000000000000
-0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 0.0000000000000000 1.0000000000000000
-0.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000
-1.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000
-0.0000000000000000 0.0000000000000000 1.0000000000000000 1.0000000000000000
-0.5000000000000000 0.5000000000000000 0.5000000000000000 1.0000000000000000
-1.0000000000000000 0.5000000000000000 0.5000000000000000 0.5000000000000000
-0.0000000000000000 0.5000000000000000 0.5000000000000000 0.5000000000000000
-0.5000000000000000 1.0000000000000000 0.5000000000000000 0.5000000000000000
-0.5000000000000000 0.0000000000000000 0.5000000000000000 0.5000000000000000
-0.5000000000000000 0.5000000000000000 1.0000000000000000 0.5000000000000000
-0.5000000000000000 0.5000000000000000 0.0000000000000000 0.5000000000000000

data/pipe-nurbs-2d.mesh

@@ -18,9 +18,9 @@ elements
 boundary
 4
 1 1 0 1
-1 1 2 3
-1 1 3 0
-1 1 1 2
+2 1 2 3
+3 1 3 0
+4 1 1 2
 
 edges
 4

data/skewed-square.mesh

@@ -16,21 +16,20 @@ dimension
 2
 
 elements
-2
-1 2 2 0 1
-1 2 0 2 3
+1
+1 3 0 1 2 3
 
 boundary
 4
 1 1 0 1
-1 1 1 2
-2 1 2 3
-1 1 3 0
+2 1 1 2
+3 1 2 3
+4 1 3 0
 
 vertices
 4
 2
 0 0
-1 0
-1 1
-0 1
+1 0.3
+1.4 1.2
+0.25 1.34

data/square-space-time.mesh

@@ -1,52 +0,0 @@
-MFEM mesh v1.0
-
-#
-# MFEM Geometry Types (see mesh/geom.hpp):
-#
-# POINT       = 0
-# SEGMENT     = 1
-# TRIANGLE    = 2
-# SQUARE      = 3
-# TETRAHEDRON = 4
-# CUBE        = 5
-# PRISM       = 6
-#
-
-dimension
-3
-
-elements
-6
-1 4 3 1 7 5
-1 4 1 6 7 4
-1 4 6 1 0 2
-1 4 1 6 4 2
-1 4 6 1 3 0
-1 4 1 6 3 7
-
-boundary
-12
-1 2 6 0 3
-1 2 0 6 2
-1 2 1 3 0
-1 2 3 1 5
-1 2 3 7 6
-1 2 7 3 5
-1 2 4 6 7
-1 2 6 4 2
-2 2 1 7 5
-2 2 7 1 4
-1 2 1 2 4
-1 2 2 1 0
-
-vertices
-8
-3
-0 0 0
-0 0 1
-1 0 0
-0 1 0
-1 0 1
-0 1 1
-1 1 0
-1 1 1

doc/CodeDocumentation.conf.in

@@ -938,6 +938,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                          @MFEM_SOURCE_DIR@/config \
                          @MFEM_SOURCE_DIR@/general \
                          @MFEM_SOURCE_DIR@/linalg \
+                         @MFEM_SOURCE_DIR@/linalg/batched \
                          @MFEM_SOURCE_DIR@/linalg/simd \
                          @MFEM_SOURCE_DIR@/mesh \
                          @MFEM_SOURCE_DIR@/mesh/submesh \
@@ -1049,7 +1050,8 @@ RECURSIVE              = NO
 EXCLUDE                = @MFEM_SOURCE_DIR@/config/_config.hpp \
                          @MFEM_SOURCE_DIR@/config/get_hypre_version.cpp \
                          @MFEM_SOURCE_DIR@/general/tinyxml2.h \
-                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp
+                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp \
+                         @MFEM_SOURCE_DIR@/linalg/lapack.hpp
 
 # The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
 # directories that are symbolic links (a Unix file system feature) are excluded
@@ -1208,13 +1210,13 @@ STRIP_CODE_COMMENTS    = NO
 # entity all documented functions referencing it will be listed.
 # The default value is: NO.
 
-REFERENCED_BY_RELATION = YES
+REFERENCED_BY_RELATION = NO
 
 # If the REFERENCES_RELATION tag is set to YES then for each documented function
 # all documented entities called/used by that function will be listed.
 # The default value is: NO.
 
-REFERENCES_RELATION    = YES
+REFERENCES_RELATION    = NO
 
 # If the REFERENCES_LINK_SOURCE tag is set to YES and SOURCE_BROWSER tag is set
 # to YES then the hyperlinks from functions in REFERENCES_RELATION and

doc/CodeDocumentation.dox

@@ -182,6 +182,21 @@ namespace mfem {
  *   <a class="el" href="examples_2superlu_2ex1p_8cpp_source.html">1p</a>,
  *   demonstrating the use of MFEM's \link superlu.hpp SuperLU integration\endlink.
  *
+ * <H4>NURBS Examples</H4>
+ * - Variants of Examples
+ *  <a class="el" href="nurbs__ex1_8cpp_source.html">1</a>,
+ *  <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__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.
+ * - Variant of Example <a class="el" href="nurbs__patch__ex1_8cpp_source.html">1</a>: demonstrates the use of patch integration
+ * - <a class="el" href="nurbs__solenoidal_8cpp_source.html">NURBS Divergence-free</a>: solve a solenoidal vector projection with NURBS-based H(div) elements
+ * - <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
+ *
  * <H3>Miniapps</H3>
  * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
  * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code

examples/CMakeLists.txt

@@ -50,6 +50,28 @@ list(APPEND ALL_EXE_SRCS
 
 if (MFEM_USE_MPI)
   list(APPEND ALL_EXE_SRCS
+    dfem_poisson.cpp
+    dfem_stokes.cpp
+    enzyme_interface_smoketest.cpp
+    test_dfem_dual.cpp
+    test_dfem.cpp
+    dfem_laghos.cpp
+    dfem_minimal_example.cpp
+    dfem_test_diffusion_2d.cpp
+    dfem_test_diffusion_3d.cpp
+    dfem_test_diffusion_3d_refactor.cpp
+    dfem_test_ordering.cpp
+    dfem_test_vector_diffusion.cpp
+    dfem_test_elasticity.cpp
+    dfem_test_nonlinear_elasticity_3d.cpp
+    dfem_test_nonlinear_diffusion_3d.cpp
+    dfem_test_interpolate_linear_scalar.cpp
+    dfem_test_interpolate_linear_scalar_3d.cpp
+    dfem_test_interpolate_gradient_linear_scalar_3d.cpp
+    dfem_test_mass_scalar_3d.cpp
+    dfem_test_mass_scalar_2d.cpp
+    dfem_test_interpolate_linear_vector.cpp
+    dfem_test_interpolate_linear_vector_3d.cpp
     ex0p.cpp
     ex1p.cpp
     ex2p.cpp
@@ -73,9 +95,6 @@ if (MFEM_USE_MPI)
     ex20p.cpp
     ex21p.cpp
     ex22p.cpp
-    ex1p_4d.cpp
-    ex3p_4d.cpp
-    ex4D_DivSkew.cpp
     ex24p.cpp
     ex25p.cpp
     ex26p.cpp
@@ -113,6 +132,17 @@ include_directories(BEFORE ${PROJECT_BINARY_DIR})
 # Add one executable per cpp file
 add_mfem_examples(ALL_EXE_SRCS)
 
+target_link_libraries(dfem_poisson ClangEnzymeFlags)
+target_link_libraries(dfem_stokes ClangEnzymeFlags)
+target_link_libraries(enzyme_interface_smoketest ClangEnzymeFlags)
+target_link_libraries(test_dfem ClangEnzymeFlags)
+target_link_libraries(dfem_laghos ClangEnzymeFlags)
+target_link_libraries(dfem_minimal_example ClangEnzymeFlags)
+target_link_libraries(dfem_test_diffusion_3d ClangEnzymeFlags)
+target_link_libraries(dfem_test_diffusion_3d_refactor ClangEnzymeFlags)
+target_link_libraries(dfem_test_nonlinear_diffusion_3d ClangEnzymeFlags)
+target_link_libraries(dfem_test_nonlinear_elasticity_3d ClangEnzymeFlags)
+
 # Add a test for each example
 if (MFEM_ENABLE_TESTING)
   foreach(SRC_FILE ${ALL_EXE_SRCS})

examples/amgx/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/amgx/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/caliper/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/caliper,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/dfem/cxxtimer.hpp

@@ -0,0 +1,184 @@
+/*
+
+MIT License
+
+Copyright (c) 2017 André L. Maravilha
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+
+*/
+
+#ifndef CXX_TIMER_HPP
+#define CXX_TIMER_HPP
+
+#include <chrono>
+
+
+namespace cxxtimer {
+
+/**
+ * This class works as a stopwatch.
+ */
+class Timer {
+
+public:
+
+    /**
+     * Constructor.
+     *
+     * @param   start
+     *          If true, the timer is started just after construction.
+     *          Otherwise, it will not be automatically started.
+     */
+    Timer(bool start = false);
+
+    /**
+     * Copy constructor.
+     *
+     * @param   other
+     *          The object to be copied.
+     */
+    Timer(const Timer& other) = default;
+
+    /**
+     * Transfer constructor.
+     *
+     * @param   other
+     *          The object to be transferred.
+     */
+    Timer(Timer&& other) = default;
+
+    /**
+     * Destructor.
+     */
+    virtual ~Timer() = default;
+
+    /**
+     * Assignment operator by copy.
+     *
+     * @param   other
+     *          The object to be copied.
+     *
+     * @return  A reference to this object.
+     */
+    Timer& operator=(const Timer& other) = default;
+
+    /**
+     * Assignment operator by transfer.
+     *
+     * @param   other
+     *          The object to be transferred.
+     *
+     * @return  A reference to this object.
+     */
+    Timer& operator=(Timer&& other) = default;
+
+    /**
+     * Start/resume the timer.
+     */
+    void start();
+
+    /**
+     * Stop/pause the timer.
+     */
+    void stop();
+
+    /**
+     * Reset the timer.
+     */
+    void reset();
+
+    /**
+     * Return the elapsed time.
+     *
+     * @param   duration_t
+     *          The duration type used to return the time elapsed. If not
+     *          specified, it returns the time as represented by
+     *          std::chrono::milliseconds.
+     *
+     * @return  The elapsed time.
+     */
+    template <class duration_t = std::chrono::milliseconds>
+    typename duration_t::rep count() const;
+
+private:
+
+    bool started_;
+    bool paused_;
+    std::chrono::steady_clock::time_point reference_;
+    std::chrono::duration<long double> accumulated_;
+};
+
+}
+
+
+inline cxxtimer::Timer::Timer(bool start) :
+        started_(false), paused_(false),
+        reference_(std::chrono::steady_clock::now()),
+        accumulated_(std::chrono::duration<long double>(0)) {
+    if (start) {
+        this->start();
+    }
+}
+
+inline void cxxtimer::Timer::start() {
+    if (!started_) {
+        started_ = true;
+        paused_ = false;
+        accumulated_ = std::chrono::duration<long double>(0);
+        reference_ = std::chrono::steady_clock::now();
+    } else if (paused_) {
+        reference_ = std::chrono::steady_clock::now();
+        paused_ = false;
+    }
+}
+
+inline void cxxtimer::Timer::stop() {
+    if (started_ && !paused_) {
+        std::chrono::steady_clock::time_point now = std::chrono::steady_clock::now();
+        accumulated_ = accumulated_ + std::chrono::duration_cast< std::chrono::duration<long double> >(now - reference_);
+        paused_ = true;
+    }
+}
+
+inline void cxxtimer::Timer::reset() {
+    if (started_) {
+        started_ = false;
+        paused_ = false;
+        reference_ = std::chrono::steady_clock::now();
+        accumulated_ = std::chrono::duration<long double>(0);
+    }
+}
+
+template <class duration_t>
+typename duration_t::rep cxxtimer::Timer::count() const {
+    if (started_) {
+        if (paused_) {
+            return std::chrono::duration_cast<duration_t>(accumulated_).count();
+        } else {
+            return std::chrono::duration_cast<duration_t>(
+                    accumulated_ + (std::chrono::steady_clock::now() - reference_)).count();
+        }
+    } else {
+        return duration_t(0).count();
+    }
+}
+
+
+#endif

examples/dfem/dfem.hpp

@@ -0,0 +1,4 @@
+#pragma once
+
+#include "dfem_differentiable_operator.hpp"
+#include "dfem_element_operator.hpp"

examples/dfem/dfem_action_callback.icc

@@ -0,0 +1,232 @@
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels>::Action::create_action_callback(
+        kernel_t kernel,
+        mult_func_t &func)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs, std::make_index_sequence<kernel.num_koutputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(op.fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(kernel.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(op.mesh);
+   const int num_entities = GetNumEntities<entity_t>(op.mesh);
+   const int num_qp = op.integration_rule.GetNPoints();
+
+   // All solutions T-vector sizes make up the width of the operator, since
+   // they are explicitly provided in Mult() for example.
+
+   op.width = GetTrueVSize(op.fields[test_space_field_idx]);
+   op.residual_lsize = GetVSize(op.fields[test_space_field_idx]);
+
+   if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      op.height = 1;
+   }
+   else
+   {
+      op.height = op.residual_lsize;
+   }
+
+   residual_l.SetSize(op.residual_lsize);
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : op.fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(field, op.integration_rule,
+                                              doftoquad_mode));
+   }
+   const int q1d = (int)floor(pow(num_qp, 1.0/op.mesh.Dimension()) + 0.5);
+
+   residual_e.SetSize(R->Height());
+
+   const int residual_size_on_qp = GetSizeOnQP<entity_t>(
+                                      mfem::get<hardcoded_output_idx>(kernel.outputs),
+                                      op.fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(kernel.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(kernel.outputs, dtq,
+                                                    koutput_to_field);
+
+   auto input_fops = create_bare_fops(kernel.inputs);
+   auto output_fops = create_bare_fops(kernel.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(output_fops).size_on_qp /
+      mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(output_fops).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(this->op.integration_rule.GetWeights().Read(),
+                             num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(kernel.inputs,
+                                                std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto shmem_info = get_shmem_info<entity_t>(input_dtq_maps,
+                                              output_dtq_maps,
+                                              op.fields,
+                                              num_entities,
+                                              kernel.inputs,
+                                              num_qp,
+                                              input_size_on_qp,
+                                              residual_size_on_qp);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   print_shared_memory_info(shmem_info);
+
+   func = [=](Vector &ye_mem) mutable
+   {
+      restriction<entity_t>(op.solutions, solutions_l, this->fields_e,
+                            op.element_dof_ordering);
+      restriction<entity_t>(op.parameters, parameters_l, this->fields_e,
+                            op.element_dof_ordering,
+                            op.solutions.size());
+
+      auto ye = Reshape(ye_mem.ReadWrite(), test_vdim, num_test_dof, num_entities);
+      auto wrapped_fields_e = wrap_fields(this->fields_e, shmem_info.field_sizes, num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, void *shmem)
+      {
+         // printf("\ne: %d\n", e);
+         // tic();
+         auto input_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT_DTQ],
+            shmem_info.input_dtq_sizes,
+            input_dtq_maps);
+
+         auto output_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT_DTQ],
+            shmem_info.output_dtq_sizes,
+            output_dtq_maps);
+
+         auto fields_shmem = load_field_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::FIELD],
+            shmem_info.field_sizes,
+            kinput_to_field,
+            wrapped_fields_e,
+            e);
+
+         // These methods don't copy, they simply create a `DeviceTensor` object
+         // that points to correct chunks of the shared memory pool.
+         auto input_shmem = load_input_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT],
+            shmem_info.input_sizes,
+            num_qp);
+
+         auto residual_shmem = load_residual_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT],
+            shmem_info.residual_size,
+            num_qp);
+
+         auto scratch_mem = load_scratch_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::TEMP],
+            shmem_info.temp_sizes);
+
+         MFEM_SYNC_THREAD;
+         // printf("shmem load elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, input_fops, ir_weights, scratch_mem,
+         std::make_index_sequence<kernel.num_kinputs> {});
+         // printf("interpolate elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         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);
+                  auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+                  auto r = Reshape(&residual_shmem(0, q), residual_size_on_qp);
+                  apply_kernel(r, kernel.func, kernel_args, input_shmem, q);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+         // printf("qf elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(output_fops),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_mem);
+         // printf("integrate elapsed: %.1fus\n", toc() * 1e6);
+
+      }, num_entities, q1d, q1d, q1d, shmem_info.total_size, shmem_cache.ReadWrite());
+
+      if constexpr (std::is_same_v<decltype(output_fop), None>)
+      {
+         residual_l = ye_mem;
+      }
+      else
+      {
+         R->MultTranspose(ye_mem, residual_l);
+      }
+   };
+
+   if constexpr (std::is_same_v<decltype(output_fop), None>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         y = r_local;
+      };
+   }
+   else if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         double local_sum = r_local.Sum();
+         MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+                       op.mesh.GetComm());
+         MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      };
+   }
+   else
+   {
+      auto P = get_prolongation(op.fields[test_space_field_idx]);
+      prolongation_transpose = [P](const Vector &r_local, Vector &y)
+      {
+         P->MultTranspose(r_local, y);
+      };
+   }
+}

examples/dfem/dfem_assemble_hypreparmatrix.icc

@@ -0,0 +1,308 @@
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels
+   >
+template <
+   size_t derivative_idx
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels>::Derivative<derivative_idx>::assemble_hypreparmatrix_impl(
+        kernel_t kernel, HypreParMatrix &A)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs,
+                                                                     std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs,
+                                                                      std::make_index_sequence<kernel.num_koutputs> {});
+
+   auto output_fop = std::get<0>(kernel.outputs);
+
+   constexpr int hardcoded_output_idx = 0;
+
+   int num_qp = op.integration_rule.GetNPoints();;
+   int num_el = 0;
+   int dimension = 0;
+   if constexpr (std::is_same_v<entity_t, Entity::Element>)
+   {
+      num_el = op.mesh.GetNE();
+      dimension = op.dim;
+   }
+   else if (std::is_same_v<entity_t, Entity::Face>)
+   {
+      num_el = op.mesh.GetNumFacesWithGhost();
+      dimension = op.dim - 1;
+   }
+   else
+   {
+      static_assert(always_false<entity_t>, "not implemented");
+   }
+
+   std::vector<const DofToQuad*> dtqmaps;
+   for (const auto &field : op.fields)
+   {
+      dtqmaps.emplace_back(GetDofToQuad<entity_t>(field, op.integration_rule,
+                                                  doftoquad_mode));
+   }
+
+   // Allocate memory for fields on quadrature points
+   auto input_qp_mem = create_input_qp_memory(num_qp, kernel.inputs,
+                                              std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto directions_qp_mem = create_input_qp_memory(num_qp, kernel.inputs,
+                                                   std::make_index_sequence<kernel.num_kinputs> {});
+
+   for (auto &d_qp_mem : directions_qp_mem)
+   {
+      d_qp_mem = 0.0;
+   }
+
+   std::array<bool, kernel.num_kinputs> kinput_is_dependent;
+   bool no_kinput_is_dependent = true;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_to_field[i] == derivative_idx)
+      {
+         no_kinput_is_dependent = false;
+         kinput_is_dependent[i] = true;
+         // out << "function input " << i << " is dependent on "
+         //     << op.fields[kinput_to_field[i]].field_label << "\n";
+      }
+      else
+      {
+         kinput_is_dependent[i] = false;
+      }
+   }
+
+   if (no_kinput_is_dependent)
+   {
+      return;
+   }
+
+   auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+   auto kernel_shadow_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+
+   DeviceTensor<1, const double> integration_weights(
+      this->op.integration_rule.GetWeights().Read(), num_qp);
+
+   Vector zero;
+   GeometricFactorMaps geometric_factors
+   {
+      DeviceTensor<3, const double>(zero.Read(), 0, 0, 0)
+   };
+
+   // fields interpolated to the quadrature points in the order of
+   // kernel function arguments
+   auto input_qp = map_inputs_to_memory(input_qp_mem, num_qp,
+                                        kernel.inputs,
+                                        std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto directions_qp = map_inputs_to_memory(directions_qp_mem, num_qp,
+                                             kernel.inputs,
+                                             std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto input_dtq_ops = create_dtq_operators<entity_t>(kernel.inputs, dtqmaps,
+                                                       kinput_to_field);
+   auto dependent_input_dtq_ops = create_dtq_operators_conditional<entity_t>(
+                                     kernel.inputs,
+                                     dtqmaps,
+                                     kinput_to_field,
+                                     kinput_is_dependent, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto output_dtq_ops = create_dtq_operators<entity_t>(kernel.outputs, dtqmaps,
+                                                        koutput_to_field);
+
+   constexpr int fixed_output_idx = 0;
+   auto Bv = output_dtq_ops[fixed_output_idx];
+   auto [num_test_qp, test_op_dim, num_test_dof] = Bv.GetShape();
+   const int test_vdim = std::get<0>(kernel.outputs).vdim;
+
+   const int num_trial_dof = dependent_input_dtq_ops[0].GetShape()[2];
+   int trial_vdim = 0;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_is_dependent[i])
+      {
+         trial_vdim = GetVDim(op.fields[kinput_to_field[i]]);
+         break;
+      }
+   }
+
+   // All trial operators dimensions accumulated
+   int total_trial_op_dim = 0;
+   for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+   {
+      total_trial_op_dim += dependent_input_dtq_ops[s].GetShape()[1];
+   }
+
+   Vector a_qp_mem(test_vdim * test_op_dim * trial_vdim * total_trial_op_dim *
+                   num_qp *
+                   num_el);
+   const auto a_qp = Reshape(a_qp_mem.ReadWrite(), test_vdim, test_op_dim,
+                             trial_vdim, total_trial_op_dim, num_qp,
+                             num_el);
+
+   Vector Ae_mem(num_test_dof * test_vdim * num_trial_dof * trial_vdim * num_el);
+   Ae_mem = 0.0;
+
+   auto A_e = Reshape(Ae_mem.ReadWrite(), num_test_dof, test_vdim, num_trial_dof,
+                      trial_vdim, num_el);
+
+   for (int e = 0; e < num_el; e++)
+   {
+      map_fields_to_quadrature_data(
+         input_qp, e, this->fields_e,
+         kinput_to_field, input_dtq_ops,
+         integration_weights, geometric_factors, kernel.inputs,
+         std::make_index_sequence<kernel.num_kinputs> {});
+
+      for (int q = 0; q < num_qp; q++)
+      {
+         for (int j = 0; j < trial_vdim; j++)
+         {
+            size_t m_offset = 0;
+            for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+            {
+               auto Bu = dependent_input_dtq_ops[s];
+               auto [unused1, trial_op_dim, unused2] = Bu.GetShape();
+               auto d_qp = Reshape(&(directions_qp[Bu.which_input])[0], trial_vdim,
+                                   trial_op_dim, num_qp);
+               for (int m = 0; m < trial_op_dim; m++)
+               {
+                  d_qp(j, m, q) = 1.0;
+                  Vector f_qp = apply_kernel_fwddiff_enzyme(
+                                   kernel.func,
+                                   kernel_args,
+                                   input_qp,
+                                   kernel_shadow_args,
+                                   directions_qp,
+                                   q);
+                  // Vector f_qp = apply_kernel_fwddiff_dual(
+                  //                  kernel.func,
+                  //                  kernel_args,
+                  //                  input_qp,
+                  //                  directions_qp,
+                  //                  q);
+                  d_qp(j, m, q) = 0.0;
+
+                  auto f = Reshape(f_qp.Read(), test_vdim, test_op_dim);
+
+                  for (int i = 0; i < test_vdim; i++)
+                  {
+                     for (int k = 0; k < test_op_dim; k++)
+                     {
+                        a_qp(i, k, j, m + m_offset, q, e) = f(i, k);
+                     }
+                  }
+               }
+               m_offset += trial_op_dim;
+            }
+         }
+      }
+
+      Vector fhat_mem(test_op_dim * num_qp * dimension);
+      auto fhat = Reshape(fhat_mem.ReadWrite(), test_vdim, test_op_dim, num_qp);
+      for (int J = 0; J < num_trial_dof; J++)
+      {
+         for (int j = 0; j < trial_vdim; j++)
+         {
+            fhat_mem = 0.0;
+            size_t m_offset = 0;
+            for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+            {
+               auto Bu = dependent_input_dtq_ops[s];
+               int trial_op_dim = dependent_input_dtq_ops[s].GetShape()[1];
+               for (int q = 0; q < num_qp; q++)
+               {
+                  for (int i = 0; i < test_vdim; i++)
+                  {
+                     for (int k = 0; k < test_op_dim; k++)
+                     {
+                        for (int m = 0; m < trial_op_dim; m++)
+                        {
+                           fhat(i, k, q) += a_qp(i, k, j, m + m_offset, q, e) * Bu(q, m, J);
+                        }
+                     }
+                  }
+               }
+               m_offset += trial_op_dim;
+            }
+
+            auto bvtfhat = Reshape(&A_e(0, 0, J, j, e), num_test_dof, test_vdim);
+            map_quadrature_data_to_fields(bvtfhat, fhat, output_fop,
+                                          output_dtq_ops[hardcoded_output_idx]);
+         }
+      }
+   }
+
+   bool same_test_and_trial = false;
+   if (koutput_to_field[0] ==
+       kinput_to_field[dependent_input_dtq_ops[0].which_input])
+   {
+      same_test_and_trial = true;
+   }
+
+   auto trial_fes = *std::get_if<const ParFiniteElementSpace *>
+                    (&op.fields[kinput_to_field[dependent_input_dtq_ops[0].which_input]].data);
+
+   auto test_fes = *std::get_if<const ParFiniteElementSpace *>
+                   (&op.fields[koutput_to_field[0]].data);
+
+   SparseMatrix mat(test_fes->GlobalVSize(), trial_fes->GlobalVSize());
+
+   if (test_fes == nullptr)
+   {
+      MFEM_ABORT("error");
+   }
+
+   for (int e = 0; e < num_el; e++)
+   {
+      auto tmp = Reshape(Ae_mem.ReadWrite(), num_test_dof * test_vdim,
+                         num_trial_dof * trial_vdim,
+                         num_el);
+      DenseMatrix A_e(&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);
+      GetElementVDofs(
+         op.fields[kinput_to_field[dependent_input_dtq_ops[0].which_input]], e,
+         trial_vdofs);
+      mat.AddSubMatrix(test_vdofs, trial_vdofs, A_e, 1);
+   }
+   mat.Finalize();
+
+   if (same_test_and_trial)
+   {
+      HypreParMatrix tmp(test_fes->GetComm(),
+                         test_fes->GlobalVSize(),
+                         test_fes->GetDofOffsets(),
+                         &mat);
+
+      A = *RAP(&tmp, test_fes->Dof_TrueDof_Matrix());
+      A.EliminateBC(op.ess_tdof_list, DiagonalPolicy::DIAG_ONE);
+   }
+   else
+   {
+      HypreParMatrix tmp(test_fes->GetComm(),
+                         test_fes->GlobalVSize(),
+                         trial_fes->GlobalVSize(),
+                         test_fes->GetDofOffsets(),
+                         trial_fes->GetDofOffsets(),
+                         &mat);
+
+      A = *RAP(test_fes->Dof_TrueDof_Matrix(), &tmp, trial_fes->Dof_TrueDof_Matrix());
+      // A.EliminateBC(op.ess_tdof_list, DiagonalPolicy::DIAG_ONE);
+   }
+}

examples/dfem/dfem_assemble_vector.icc

@@ -0,0 +1,233 @@
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels
+   >
+template <
+   size_t derivative_idx
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels>::Derivative<derivative_idx>::assemble_vector_impl(
+        kernel_t kernel, Vector &v)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs,
+                                                                     std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs,
+                                                                      std::make_index_sequence<kernel.num_koutputs> {});
+
+   auto output_fop = std::get<0>(kernel.outputs);
+
+   constexpr int hardcoded_output_idx = 0;
+
+   int num_qp = op.integration_rule.GetNPoints();;
+   int num_el = 0;
+   int dimension = 0;
+   if constexpr (std::is_same_v<entity_t, Entity::Element>)
+   {
+      num_el = op.mesh.GetNE();
+      dimension = op.dim;
+   }
+   else if (std::is_same_v<entity_t, Entity::Face>)
+   {
+      num_el = op.mesh.GetNumFacesWithGhost();
+      dimension = op.dim - 1;
+   }
+   else
+   {
+      static_assert(always_false<entity_t>, "not implemented");
+   }
+
+   std::vector<const DofToQuad*> dtqmaps;
+   for (const auto &field : op.fields)
+   {
+      dtqmaps.emplace_back(GetDofToQuad<entity_t>(field, op.integration_rule,
+                                                  doftoquad_mode));
+   }
+
+   // Allocate memory for fields on quadrature points
+   auto input_qp_mem = create_input_qp_memory(num_qp, kernel.inputs,
+                                              std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto directions_qp_mem = create_input_qp_memory(num_qp, kernel.inputs,
+                                                   std::make_index_sequence<kernel.num_kinputs> {});
+
+   for (auto &d_qp_mem : directions_qp_mem)
+   {
+      d_qp_mem = 0.0;
+   }
+
+   std::array<bool, kernel.num_kinputs> kinput_is_dependent;
+   bool no_kinput_is_dependent = true;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_to_field[i] == derivative_idx)
+      {
+         no_kinput_is_dependent = false;
+         kinput_is_dependent[i] = true;
+         // out << "function input " << i << " is dependent on "
+         //     << op.fields[kinput_to_field[i]].field_label << "\n";
+      }
+      else
+      {
+         kinput_is_dependent[i] = false;
+      }
+   }
+
+   if (no_kinput_is_dependent)
+   {
+      return;
+   }
+
+   auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+   auto kernel_shadow_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+
+   DeviceTensor<1, const double> integration_weights(
+      this->op.integration_rule.GetWeights().Read(), num_qp);
+
+   Vector zero;
+   GeometricFactorMaps geometric_factors
+   {
+      DeviceTensor<3, const double>(zero.Read(), 0, 0, 0)
+   };
+
+   // fields interpolated to the quadrature points in the order of
+   // kernel function arguments
+   auto input_qp = map_inputs_to_memory(input_qp_mem, num_qp,
+                                        kernel.inputs,
+                                        std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto directions_qp = map_inputs_to_memory(directions_qp_mem, num_qp,
+                                             kernel.inputs,
+                                             std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto input_dtq_ops = create_dtq_operators<entity_t>(kernel.inputs, dtqmaps,
+                                                       kinput_to_field);
+   auto dependent_input_dtq_ops = create_dtq_operators_conditional<entity_t>(
+                                     kernel.inputs,
+                                     dtqmaps,
+                                     kinput_to_field,
+                                     kinput_is_dependent, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto output_dtq_ops = create_dtq_operators<entity_t>(kernel.outputs, dtqmaps,
+                                                        koutput_to_field);
+
+   constexpr int fixed_output_idx = 0;
+   auto Bv = output_dtq_ops[fixed_output_idx];
+   auto [num_test_qp, test_op_dim, num_test_dof] = Bv.GetShape();
+   const int test_vdim = std::get<0>(kernel.outputs).vdim;
+
+   const int num_trial_dof = dependent_input_dtq_ops[0].GetShape()[2];
+   int trial_vdim = 0;
+   int dependent_field_idx = -1;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_is_dependent[i])
+      {
+         dependent_field_idx = kinput_to_field[i];
+         break;
+      }
+   }
+
+   trial_vdim = GetVDim(op.fields[dependent_field_idx]);
+
+   // All trial operators dimensions accumulated
+   int total_trial_op_dim = 0;
+   for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+   {
+      total_trial_op_dim += dependent_input_dtq_ops[s].GetShape()[1];
+   }
+
+   Vector a_qp_mem(trial_vdim * total_trial_op_dim * num_qp * num_el);
+   const auto a_qp = Reshape(a_qp_mem.ReadWrite(), trial_vdim,
+                             total_trial_op_dim, num_qp, num_el);
+   Vector ve_mem(num_trial_dof * trial_vdim * num_el);
+   ve_mem = 0.0;
+
+   for (int e = 0; e < num_el; e++)
+   {
+      map_fields_to_quadrature_data(
+         input_qp, e, this->fields_e,
+         kinput_to_field, input_dtq_ops,
+         integration_weights, geometric_factors, kernel.inputs,
+         std::make_index_sequence<kernel.num_kinputs> {});
+
+      for (int q = 0; q < num_qp; q++)
+      {
+         for (int j = 0; j < trial_vdim; j++)
+         {
+            size_t m_offset = 0;
+            for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+            {
+               auto Bu = dependent_input_dtq_ops[s];
+               auto [unused1, trial_op_dim, unused2] = Bu.GetShape();
+               auto d_qp = Reshape(&(directions_qp[Bu.which_input])[0], trial_vdim,
+                                   trial_op_dim, num_qp);
+               for (int m = 0; m < trial_op_dim; m++)
+               {
+                  d_qp(j, m, q) = 1.0;
+                  // Vector f_qp = apply_kernel_fwddiff_dual(
+                  //                  kernel.func,
+                  //                  kernel_args,
+                  //                  input_qp,
+                  //                  directions_qp,
+                  //                  q);
+                  Vector f_qp = apply_kernel_fwddiff_enzyme(
+                                   kernel.func,
+                                   kernel_args,
+                                   input_qp,
+                                   kernel_shadow_args,
+                                   directions_qp,
+                                   q);
+                  d_qp(j, m, q) = 0.0;
+
+                  auto f = Reshape(f_qp.Read(), test_vdim);
+                  a_qp(j, m + m_offset, q, e) = f(0);
+               }
+               m_offset += trial_op_dim;
+            }
+         }
+      }
+
+      auto shat = Reshape(ve_mem.ReadWrite(), num_trial_dof, trial_vdim, num_el);
+      for (int J = 0; J < num_trial_dof; J++)
+      {
+         for (int j = 0; j < trial_vdim; j++)
+         {
+            size_t m_offset = 0;
+            for (int s = 0; s < dependent_input_dtq_ops.size(); s++)
+            {
+               auto Bu = dependent_input_dtq_ops[s];
+               int trial_op_dim = dependent_input_dtq_ops[s].GetShape()[1];
+               for (int q = 0; q < num_qp; q++)
+               {
+                  for (int m = 0; m < trial_op_dim; m++)
+                  {
+                     shat(J, j, e) += a_qp(j, m + m_offset, q, e) * Bu(q, m, J);
+                  }
+               }
+               m_offset += trial_op_dim;
+            }
+         }
+      }
+   }
+
+   auto R = get_element_restriction(op.fields[dependent_field_idx],
+                                    element_dof_ordering);
+   Vector ve(R->Width());
+   R->MultTranspose(ve_mem, ve);
+
+   get_prolongation(op.fields[dependent_field_idx])->MultTranspose(ve, v);
+}

examples/dfem/dfem_derivative_callback.icc

@@ -0,0 +1,244 @@
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels
+   >
+template <
+   size_t derivative_idx
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels>::Derivative<derivative_idx>::create_callback(kernel_t kernel,
+                                                               mult_func_t &func)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs, std::make_index_sequence<kernel.num_koutputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(op.fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(kernel.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(op.mesh);
+   const int num_entities = GetNumEntities<entity_t>(op.mesh);
+   const int num_qp = op.integration_rule.GetNPoints();
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : op.fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(field, op.integration_rule,
+                                              doftoquad_mode));
+   }
+   const int q1d = dtq[0]->nqpt;
+
+   derivative_action_e.SetSize(R->Height());
+
+   const int da_size_on_qp = GetSizeOnQP<entity_t>(
+                                mfem::get<hardcoded_output_idx>(kernel.outputs),
+                                op.fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(kernel.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(kernel.outputs, dtq,
+                                                    koutput_to_field);
+
+   auto input_fops = create_bare_fops(kernel.inputs);
+   auto output_fops = create_bare_fops(kernel.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(output_fops).size_on_qp /
+      mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(output_fops).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(this->op.integration_rule.GetWeights().Read(),
+                             num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(kernel.inputs,
+                                                std::make_index_sequence<kernel.num_kinputs> {});
+
+   // Check which qf inputs are dependent on the dependent variable
+   std::array<bool, kernel.num_kinputs> kinput_is_dependent;
+   bool no_kinput_is_dependent = true;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_to_field[i] == derivative_idx)
+      {
+         no_kinput_is_dependent = false;
+         kinput_is_dependent[i] = true;
+         // out << "function input " << i << " is dependent on "
+         //     << op.fields[kinput_to_field[i]].field_label << "\n";
+      }
+      else
+      {
+         kinput_is_dependent[i] = false;
+      }
+   }
+
+   bool with_derivatives = true;
+   auto shmem_info = get_shmem_info<entity_t>(input_dtq_maps,
+                                              output_dtq_maps,
+                                              op.fields,
+                                              num_entities,
+                                              kernel.inputs,
+                                              num_qp,
+                                              input_size_on_qp,
+                                              da_size_on_qp,
+                                              derivative_idx);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   print_shared_memory_info(shmem_info);
+
+   func = [=](Vector &ye_mem) mutable
+   {
+      if (no_kinput_is_dependent)
+      {
+         return;
+      }
+
+      restriction<entity_t>(direction, direction_l, direction_e,
+                            op.element_dof_ordering);
+
+      auto ye = Reshape(ye_mem.ReadWrite(), num_test_dof, test_vdim, num_entities);
+      auto wrapped_fields_e = wrap_fields(this->fields_e, shmem_info.field_sizes, num_entities);
+      auto wrapped_direction_e = Reshape(direction_e.Read(), shmem_info.direction_size, num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, double *shmem)
+      {
+         auto input_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT_DTQ],
+            shmem_info.input_dtq_sizes,
+            input_dtq_maps);
+
+         auto output_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT_DTQ],
+            shmem_info.output_dtq_sizes,
+            output_dtq_maps);
+
+         auto fields_shmem = load_field_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::FIELD],
+            shmem_info.field_sizes,
+            kinput_to_field,
+            wrapped_fields_e,
+            e);
+
+         auto direction_shmem = load_direction_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::DIRECTION],
+            shmem_info.direction_size,
+            wrapped_direction_e,
+            e);
+
+         // These methods don't copy, they simply create a `DeviceTensor` object
+         // that points to correct chunks of the shared memory pool.
+         auto input_shmem = load_input_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT],
+            shmem_info.input_sizes,
+            num_qp);
+
+         auto shadow_shmem = load_input_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::SHADOW],
+            shmem_info.input_sizes,
+            num_qp);
+
+         auto residual_shmem = load_residual_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT],
+            shmem_info.residual_size,
+            num_qp);
+
+         auto scratch_mem = load_scratch_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::TEMP],
+            shmem_info.temp_sizes);
+
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, input_fops, ir_weights, scratch_mem,
+         std::make_index_sequence<kernel.num_kinputs> {});
+
+         zero_all(shadow_shmem);
+         map_direction_to_quadrature_data_conditional<TensorProduct>(
+            shadow_shmem, direction_shmem, input_dtq_shmem, input_fops, ir_weights,
+            scratch_mem, kinput_is_dependent,
+            std::make_index_sequence<kernel.num_kinputs> {});
+
+         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);
+
+                  auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+                  auto kernel_shadow_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+
+                  auto r = Reshape(&residual_shmem(0, q), da_size_on_qp);
+                  apply_kernel_fwddiff_enzyme(
+                     r,
+                     kernel.func,
+                     kernel_args,
+                     input_shmem,
+                     kernel_shadow_args,
+                     shadow_shmem,
+                     q);
+                  // printf(">>>>> WARNING: AD DISABLED\n");
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(output_fops),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_mem);
+      }, num_entities, q1d, q1d, 1, shmem_info.total_size, shmem_cache.ReadWrite());
+
+      R->MultTranspose(ye_mem, derivative_action_l);
+   };
+
+   if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         double local_sum = r_local.Sum();
+         MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+                       op.mesh.GetComm());
+         MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      };
+   }
+   else
+   {
+      auto P = get_prolongation(op.fields[test_space_field_idx]);
+      prolongation_transpose = [P](const Vector &r_local, Vector &y)
+      {
+         P->MultTranspose(r_local, y);
+      };
+   }
+}

examples/dfem/dfem_differentiable_operator.hpp

@@ -0,0 +1,820 @@
+#pragma once
+
+#include <algorithm>
+#include <cstdlib>
+#include <functional>
+#include <iostream>
+#include <utility>
+#include <variant>
+#include <vector>
+#include <type_traits>
+#include <mfem.hpp>
+#include <type_traits>
+#include "dfem_fieldoperator.hpp"
+#include "dfem_parametricspace.hpp"
+#include "general/tic_toc.hpp"
+#include "tuple.hpp"
+#include <linalg/tensor.hpp>
+#include <enzyme/utils>
+#include <enzyme/enzyme>
+#include "dfem_util.hpp"
+#include "dfem_interpolate.hpp"
+#include "dfem_qfunction.hpp"
+#include "dfem_qfunction_dual.hpp"
+#include "dfem_integrate.hpp"
+
+namespace mfem
+{
+
+using mult_func_t = std::function<void(Vector &)>;
+
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields = num_solutions + num_parameters,
+   size_t num_kernels = mfem::tuple_size<kernels_tuple>::value,
+   typename autodiff_t = AutoDiff::NativeDualNumber
+   >
+class DifferentiableOperator : public Operator
+{
+public:
+   DifferentiableOperator(DifferentiableOperator&) = delete;
+   DifferentiableOperator(DifferentiableOperator&&) = delete;
+
+   class Action : public Operator
+   {
+   public:
+      template <typename kernel_t>
+      void create_action_callback(kernel_t kernel, mult_func_t &func);
+
+      template<std::size_t... idx>
+      void materialize_callbacks(kernels_tuple &ks,
+                                 std::array<mult_func_t, num_kernels>,
+                                 std::index_sequence<idx...> const&)
+      {
+         (create_action_callback(mfem::get<idx>(ks), funcs[idx]), ...);
+      }
+
+      Action(DifferentiableOperator &op, kernels_tuple &ks) : op(op)
+      {
+         materialize_callbacks(ks, funcs,
+                               std::make_index_sequence<mfem::tuple_size<kernels_tuple>::value>());
+      }
+
+      void Mult(const Vector &x, Vector &y) const
+      {
+         prolongation(op.solutions, x, solutions_l);
+
+         residual_e = 0.0;
+         for (const auto &f : funcs)
+         {
+            f(residual_e);
+         }
+
+         prolongation_transpose(residual_l, y);
+
+         y.SetSubVector(op.ess_tdof_list, 0.0);
+      }
+
+      void SetParameters(std::vector<Vector *> p) const
+      {
+         MFEM_ASSERT(num_parameters == p.size(),
+                     "number of parameters doesn't match descriptors");
+         for (int i = 0; i < num_parameters; i++)
+         {
+            p[i]->Read();
+            parameters_l[i] = *p[i];
+            // parameters_l[i].MakeRef(p[i], 0, p[i]->Size());
+         }
+      }
+
+   protected:
+      DifferentiableOperator &op;
+      std::array<mult_func_t, num_kernels> funcs;
+
+      std::function<void(Vector &, Vector &)> prolongation_transpose;
+
+      mutable std::array<Vector, num_solutions> solutions_l;
+      mutable std::array<Vector, num_parameters> parameters_l;
+      mutable Vector residual_l;
+
+      mutable std::array<Vector, num_fields> fields_e;
+      mutable Vector residual_e;
+   };
+
+   template <size_t derivative_idx>
+   class Derivative : public Operator
+   {
+   public:
+      template <typename kernel_t>
+      void create_callback(kernel_t kernel, mult_func_t &func);
+
+      template<std::size_t... idx>
+      void materialize_callbacks(kernels_tuple &ks,
+                                 std::array<mult_func_t, num_kernels>,
+                                 std::index_sequence<idx...> const&)
+      {
+         (create_callback(mfem::get<idx>(ks), funcs[idx]), ...);
+      }
+
+      Derivative(
+         DifferentiableOperator &op,
+         std::array<Vector *, num_solutions> &solutions,
+         std::array<Vector *, num_parameters> &parameters,
+         kernels_tuple &ks) : op(op), ks(ks)
+      {
+         for (int i = 0; i < num_solutions; i++)
+         {
+            solutions_l[i] = *solutions[i];
+         }
+
+         for (int i = 0; i < num_parameters; i++)
+         {
+            parameters_l[i] = *parameters[i];
+         }
+
+         // G
+         // if constexpr (std::is_same_v<OperatesOn, OperatesOnElement>)
+         // {
+         element_restriction(op.solutions, solutions_l, fields_e,
+                             op.element_dof_ordering);
+         element_restriction(op.parameters, parameters_l, fields_e,
+                             op.element_dof_ordering,
+                             op.solutions.size());
+         // }
+         // else
+         // {
+         //    MFEM_ABORT("restriction not implemented for OperatesOn");
+         // }
+         direction = op.fields[derivative_idx];
+
+         size_t derivative_action_l_size = 0;
+         for (auto &s : op.solutions)
+         {
+            derivative_action_l_size += GetVSize(s);
+            this->width += GetTrueVSize(s);
+         }
+         this->height = derivative_action_l_size;
+         derivative_action_l.SetSize(derivative_action_l_size);
+
+         materialize_callbacks(ks, funcs,
+                               std::make_index_sequence<num_kernels>());
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         current_direction_t = x;
+         current_direction_t.SetSubVector(op.ess_tdof_list, 0.0);
+
+         prolongation(direction, current_direction_t, direction_l);
+
+         derivative_action_e = 0.0;
+         for (const auto &f : funcs)
+         {
+            f(derivative_action_e);
+         }
+
+         prolongation_transpose(derivative_action_l, y);
+
+         y.SetSubVector(op.ess_tdof_list, 0.0);
+      }
+
+      template <typename kernel_t>
+      void assemble_vector_impl(kernel_t kernel, Vector &v);
+
+      template<std::size_t... idx>
+      void assemble_vector(
+         kernels_tuple &ks,
+         Vector &v,
+         std::index_sequence<idx...> const&)
+      {
+         (assemble_vector_impl(mfem::get<idx>(ks), v), ...);
+      }
+
+      void Assemble(Vector &v)
+      {
+         assemble_vector(ks, v, std::make_index_sequence<num_kernels>());
+      }
+
+      template <typename kernel_t>
+      void assemble_hypreparmatrix_impl(kernel_t kernel, HypreParMatrix &A);
+
+      template<std::size_t... idx>
+      void assemble_hypreparmatrix(
+         kernels_tuple &ks,
+         HypreParMatrix &A,
+         std::index_sequence<idx...> const&)
+      {
+         (assemble_hypreparmatrix_impl(mfem::get<idx>(ks), A), ...);
+      }
+
+      void Assemble(HypreParMatrix &A)
+      {
+         assemble_hypreparmatrix(ks, A, std::make_index_sequence<num_kernels>());
+      }
+
+      void AssembleDiagonal(Vector &d) const override {}
+
+   protected:
+      DifferentiableOperator &op;
+      kernels_tuple &ks;
+      std::array<mult_func_t, num_kernels> funcs;
+
+      std::function<void(Vector &, Vector &)> prolongation_transpose;
+
+      FieldDescriptor direction;
+
+      std::array<Vector, num_solutions> solutions_l;
+      std::array<Vector, num_parameters> parameters_l;
+      mutable Vector direction_l;
+      mutable Vector derivative_action_l;
+
+      mutable std::array<Vector, num_fields> fields_e;
+      mutable Vector direction_e;
+      mutable Vector derivative_action_e;
+
+      mutable Vector current_direction_t;
+   };
+
+   DifferentiableOperator(std::array<FieldDescriptor, num_solutions> s,
+                          std::array<FieldDescriptor, num_parameters> p,
+                          kernels_tuple ks,
+                          ParMesh &m,
+                          autodiff_t ad = AutoDiff::NativeDualNumber{}) :
+      kernels(ks),
+      mesh(m),
+      dim(mesh.Dimension()),
+      solutions(s),
+      parameters(p)
+   {
+      for (int i = 0; i < num_solutions; i++)
+      {
+         fields[i] = solutions[i];
+      }
+
+      for (int i = 0; i < num_parameters; i++)
+      {
+         fields[i + num_solutions] = parameters[i];
+      }
+
+      residual.reset(new Action(*this, kernels));
+   }
+
+   void SetParameters(std::vector<Vector *> p) const
+   {
+      residual->SetParameters(p);
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      residual->Mult(x, y);
+   }
+
+   template <int derivative_idx>
+   std::shared_ptr<Derivative<derivative_idx>>
+                                            GetDerivativeWrt(std::array<Vector *, num_solutions> solutions,
+                                                             std::array<Vector *, num_parameters> parameters)
+   {
+      return std::shared_ptr<Derivative<derivative_idx>>(
+                new Derivative<derivative_idx>(*this, solutions, parameters, kernels));
+   }
+
+   void SetEssentialTrueDofs(const Array<int> &l)
+   {
+      l.Copy(ess_tdof_list);
+   }
+
+   kernels_tuple kernels;
+   ParMesh &mesh;
+   const int dim;
+
+   std::array<FieldDescriptor, num_solutions> solutions;
+   std::array<FieldDescriptor, num_parameters> parameters;
+   // solutions and parameters
+   std::array<FieldDescriptor, num_fields> fields;
+
+   int residual_lsize = 0;
+
+   mutable std::array<Vector, num_solutions> current_state_l;
+   mutable Vector direction_l;
+
+   mutable Vector current_direction_t;
+
+   Array<int> ess_tdof_list;
+
+   static constexpr ElementDofOrdering element_dof_ordering =
+      ElementDofOrdering::LEXICOGRAPHIC;
+
+   static constexpr DofToQuad::Mode doftoquad_mode =
+      DofToQuad::Mode::TENSOR;
+
+   // static constexpr ElementDofOrdering element_dof_ordering =
+   //    ElementDofOrdering::NATIVE;
+
+   // static constexpr DofToQuad::Mode doftoquad_mode =
+   //    DofToQuad::Mode::FULL;
+
+   std::shared_ptr<Action> residual;
+};
+
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels,
+   typename autodiff_t
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels,
+     autodiff_t>::Action::create_action_callback(
+        kernel_t kernel,
+        mult_func_t &func)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs, std::make_index_sequence<kernel.num_koutputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(op.fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(kernel.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(op.mesh);
+   const int num_entities = GetNumEntities<entity_t>(op.mesh);
+   const int num_qp = kernel.integration_rule.GetNPoints();
+
+   // All solutions T-vector sizes make up the width of the operator, since
+   // they are explicitly provided in Mult() for example.
+
+   op.width = GetTrueVSize(op.fields[test_space_field_idx]);
+   op.residual_lsize = GetVSize(op.fields[test_space_field_idx]);
+
+   if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      op.height = 1;
+   }
+   else
+   {
+      op.height = op.residual_lsize;
+   }
+
+   residual_l.SetSize(op.residual_lsize);
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : op.fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(field, kernel.integration_rule,
+                                              doftoquad_mode));
+   }
+   const int q1d = (int)floor(pow(num_qp, 1.0/op.mesh.Dimension()) + 0.5);
+
+   residual_e.SetSize(R->Height());
+
+   const int residual_size_on_qp = GetSizeOnQP<entity_t>(
+                                      mfem::get<hardcoded_output_idx>(kernel.outputs),
+                                      op.fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(kernel.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(kernel.outputs, dtq,
+                                                    koutput_to_field);
+
+   auto input_fops = create_bare_fops(kernel.inputs);
+   auto output_fops = create_bare_fops(kernel.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(output_fops).size_on_qp /
+      mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(output_fops).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(kernel.integration_rule.GetWeights().Read(), num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(kernel.inputs,
+                                                std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto shmem_info = get_shmem_info<entity_t>(input_dtq_maps,
+                                              output_dtq_maps,
+                                              op.fields,
+                                              num_entities,
+                                              kernel.inputs,
+                                              num_qp,
+                                              input_size_on_qp,
+                                              residual_size_on_qp);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   // print_shared_memory_info(shmem_info);
+
+   func = [=](Vector &ye_mem) mutable
+   {
+      restriction<entity_t>(op.solutions, solutions_l, this->fields_e,
+                            op.element_dof_ordering);
+      restriction<entity_t>(op.parameters, parameters_l, this->fields_e,
+                            op.element_dof_ordering,
+                            op.solutions.size());
+
+      auto ye = Reshape(ye_mem.ReadWrite(), test_vdim, num_test_dof, num_entities);
+      auto wrapped_fields_e = wrap_fields(this->fields_e, shmem_info.field_sizes, num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, void *shmem)
+      {
+         // printf("\ne: %d\n", e);
+         // tic();
+         auto input_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT_DTQ],
+            shmem_info.input_dtq_sizes,
+            input_dtq_maps);
+
+         auto output_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT_DTQ],
+            shmem_info.output_dtq_sizes,
+            output_dtq_maps);
+
+         auto fields_shmem = load_field_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::FIELD],
+            shmem_info.field_sizes,
+            kinput_to_field,
+            input_fops,
+            wrapped_fields_e,
+            e,
+         std::make_index_sequence<kernel.num_kinputs> {});
+
+         // These functions don't copy, they simply create a `DeviceTensor` object
+         // that points to correct chunks of the shared memory pool.
+         auto input_shmem = load_input_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::INPUT],
+                               shmem_info.input_sizes,
+                               num_qp);
+
+         auto residual_shmem = load_residual_mem(
+                                  shmem,
+                                  shmem_info.offsets[SharedMemory::Index::OUTPUT],
+                                  shmem_info.residual_size,
+                                  num_qp);
+
+         auto scratch_mem = load_scratch_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::TEMP],
+                               shmem_info.temp_sizes);
+
+         MFEM_SYNC_THREAD;
+         // printf("shmem load elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, input_fops, ir_weights, scratch_mem,
+            std::make_index_sequence<kernel.num_kinputs> {});
+         // printf("interpolate elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         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);
+                  auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+                  auto r = Reshape(&residual_shmem(0, q), residual_size_on_qp);
+                  apply_kernel(r, kernel.func, kernel_args, input_shmem, q);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+         // printf("qf elapsed: %.1fus\n", toc() * 1e6);
+
+         // tic();
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(output_fops),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_mem);
+         // printf("integrate elapsed: %.1fus\n", toc() * 1e6);
+
+      }, num_entities, q1d, q1d, q1d, shmem_info.total_size, shmem_cache.ReadWrite());
+
+      if constexpr (std::is_same_v<decltype(output_fop), None>)
+      {
+         residual_l = ye_mem;
+      }
+      else
+      {
+         R->MultTranspose(ye_mem, residual_l);
+      }
+   };
+
+   if constexpr (std::is_same_v<decltype(output_fop), None>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         y = r_local;
+      };
+   }
+   else if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         double local_sum = r_local.Sum();
+         MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+                       op.mesh.GetComm());
+         MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      };
+   }
+   else
+   {
+      auto P = get_prolongation(op.fields[test_space_field_idx]);
+      prolongation_transpose = [P](const Vector &r_local, Vector &y)
+      {
+         P->MultTranspose(r_local, y);
+      };
+   }
+}
+
+template <
+   typename kernels_tuple,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t num_fields,
+   size_t num_kernels,
+   typename autodiff_t
+   >
+template <
+   size_t derivative_idx
+   >
+template <
+   typename kernel_t
+   >
+void DifferentiableOperator<kernels_tuple,
+     num_solutions,
+     num_parameters,
+     num_fields,
+     num_kernels,
+     autodiff_t>::Derivative<derivative_idx>::create_callback(kernel_t kernel,
+                                                              mult_func_t &func)
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                     kernel.inputs, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+                                                                      kernel.outputs, std::make_index_sequence<kernel.num_koutputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(op.fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(kernel.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(op.mesh);
+   const int num_entities = GetNumEntities<entity_t>(op.mesh);
+   const int num_qp = kernel.integration_rule.GetNPoints();
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : op.fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(field, kernel.integration_rule,
+                                              doftoquad_mode));
+   }
+   const int q1d = dtq[0]->nqpt;
+
+   derivative_action_e.SetSize(R->Height());
+
+   const int da_size_on_qp = GetSizeOnQP<entity_t>(
+                                mfem::get<hardcoded_output_idx>(kernel.outputs),
+                                op.fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(kernel.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(kernel.outputs, dtq,
+                                                    koutput_to_field);
+
+   auto input_fops = create_bare_fops(kernel.inputs);
+   auto output_fops = create_bare_fops(kernel.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(output_fops).size_on_qp /
+      mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(output_fops).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(kernel.integration_rule.GetWeights().Read(), num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(kernel.inputs,
+                                                std::make_index_sequence<kernel.num_kinputs> {});
+
+   // Check which qf inputs are dependent on the dependent variable
+   std::array<bool, kernel.num_kinputs> kinput_is_dependent;
+   bool no_kinput_is_dependent = true;
+   for (int i = 0; i < kinput_is_dependent.size(); i++)
+   {
+      if (kinput_to_field[i] == derivative_idx)
+      {
+         no_kinput_is_dependent = false;
+         kinput_is_dependent[i] = true;
+         // out << "function input " << i << " is dependent on "
+         //     << op.fields[kinput_to_field[i]].field_label << "\n";
+      }
+      else
+      {
+         kinput_is_dependent[i] = false;
+      }
+   }
+
+   bool with_derivatives = true;
+   auto shmem_info = get_shmem_info<entity_t>(input_dtq_maps,
+                                              output_dtq_maps,
+                                              op.fields,
+                                              num_entities,
+                                              kernel.inputs,
+                                              num_qp,
+                                              input_size_on_qp,
+                                              da_size_on_qp,
+                                              derivative_idx);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   // print_shared_memory_info(shmem_info);
+
+   func = [=](Vector &ye_mem) mutable
+   {
+      if (no_kinput_is_dependent)
+      {
+         return;
+      }
+
+      restriction<entity_t>(direction, direction_l, direction_e,
+                            op.element_dof_ordering);
+
+      auto ye = Reshape(ye_mem.ReadWrite(), num_test_dof, test_vdim, num_entities);
+      auto wrapped_fields_e = wrap_fields(this->fields_e, shmem_info.field_sizes, num_entities);
+      auto wrapped_direction_e = Reshape(direction_e.ReadWrite(), shmem_info.direction_size, num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, double *shmem)
+      {
+         auto input_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT_DTQ],
+            shmem_info.input_dtq_sizes,
+            input_dtq_maps);
+
+         auto output_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT_DTQ],
+            shmem_info.output_dtq_sizes,
+            output_dtq_maps);
+
+         auto fields_shmem = load_field_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::FIELD],
+            shmem_info.field_sizes,
+            kinput_to_field,
+            input_fops,
+            wrapped_fields_e,
+            e,
+         std::make_index_sequence<kernel.num_kinputs> {});
+
+         auto direction_shmem = load_direction_mem(
+                                   shmem,
+                                   shmem_info.offsets[SharedMemory::Index::DIRECTION],
+                                   shmem_info.direction_size,
+                                   wrapped_direction_e,
+                                   e);
+
+         // These methods don't copy, they simply create a `DeviceTensor` object
+         // that points to correct chunks of the shared memory pool.
+         auto input_shmem = load_input_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::INPUT],
+                               shmem_info.input_sizes,
+                               num_qp);
+
+         auto shadow_shmem = load_input_mem(
+                                shmem,
+                                shmem_info.offsets[SharedMemory::Index::SHADOW],
+                                shmem_info.input_sizes,
+                                num_qp);
+
+         auto residual_shmem = load_residual_mem(
+                                  shmem,
+                                  shmem_info.offsets[SharedMemory::Index::OUTPUT],
+                                  shmem_info.residual_size,
+                                  num_qp);
+
+         auto scratch_mem = load_scratch_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::TEMP],
+                               shmem_info.temp_sizes);
+
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, input_fops, ir_weights, scratch_mem,
+            std::make_index_sequence<kernel.num_kinputs> {});
+
+         zero_all(shadow_shmem);
+         map_direction_to_quadrature_data_conditional<TensorProduct>(
+            shadow_shmem, direction_shmem, input_dtq_shmem, input_fops, ir_weights,
+            scratch_mem, kinput_is_dependent,
+            std::make_index_sequence<kernel.num_kinputs> {});
+
+         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);
+                  auto r = Reshape(&residual_shmem(0, q), da_size_on_qp);
+                  auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+
+                  if constexpr (std::is_same_v<autodiff_t, AutoDiff::EnzymeForward>)
+                  {
+                     auto kernel_shadow_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+                     apply_kernel_fwddiff_enzyme(
+                        r,
+                        kernel.func,
+                        kernel_args,
+                        kernel_shadow_args,
+                        input_shmem,
+                        shadow_shmem,
+                        q);
+                  }
+                  else if constexpr (std::is_same_v<autodiff_t, AutoDiff::NativeDualNumber>)
+                  {
+                     apply_kernel_native_dual(
+                        r,
+                        kernel.func,
+                        kernel_args,
+                        input_shmem,
+                        shadow_shmem,
+                        q);
+                  }
+                  else
+                  {
+                     static_assert(always_false<autodiff_t>, "unknown autodiff type");
+                  }
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(output_fops),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_mem);
+      }, num_entities, q1d, q1d, 1, shmem_info.total_size, shmem_cache.ReadWrite());
+
+      R->MultTranspose(ye_mem, derivative_action_l);
+   };
+
+   if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         double local_sum = r_local.Sum();
+         MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+                       op.mesh.GetComm());
+         MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      };
+   }
+   else
+   {
+      auto P = get_prolongation(op.fields[test_space_field_idx]);
+      prolongation_transpose = [P](const Vector &r_local, Vector &y)
+      {
+         P->MultTranspose(r_local, y);
+      };
+   }
+}
+
+} // namespace mfem

examples/dfem/dfem_element_operator.hpp

@@ -0,0 +1,79 @@
+#include "dfem_util.hpp"
+
+namespace mfem
+{
+
+template <typename func_t, typename input_t, typename output_t, typename dependency_map_t>
+struct ElementOperator;
+
+template <typename func_t, typename... input_ts, typename... output_ts, typename dependency_map_t>
+struct ElementOperator<func_t, mfem::tuple<input_ts...>, mfem::tuple<output_ts...>, dependency_map_t>
+{
+   using entity_t = Entity::Element;
+
+   func_t qfunc;
+
+   mfem::tuple<input_ts...> inputs;
+   mfem::tuple<output_ts...> outputs;
+
+   dependency_map_t dependency_map;
+
+   using qf_param_ts = typename create_function_signature<
+                       decltype(&func_t::operator())>::type::parameter_ts;
+   using qf_output_t = typename create_function_signature<
+                       decltype(&func_t::operator())>::type::return_t;
+
+   static constexpr size_t num_inputs =
+      mfem::tuple_size<decltype(inputs)>::value;
+   static constexpr size_t num_outputs =
+      mfem::tuple_size<decltype(outputs)>::value;
+
+   ElementOperator(func_t qfunc,
+                   mfem::tuple<input_ts...> inputs,
+                   mfem::tuple<output_ts...> outputs)
+      : qfunc(qfunc), inputs(inputs), outputs(outputs),
+        dependency_map(make_dependency_map(inputs))
+   {
+      // Consistency checks
+      if constexpr (num_outputs > 1)
+      {
+         static_assert(always_false<func_t>,
+                       "more than one output per kernel is not supported right now");
+      }
+
+      constexpr size_t num_qfinputs = mfem::tuple_size<qf_param_ts>::value;
+      static_assert(num_qfinputs == num_inputs,
+                    "kernel function inputs and descriptor inputs have to match");
+
+      constexpr size_t num_qf_outputs = mfem::tuple_size<qf_output_t>::value;
+      static_assert(num_qf_outputs == num_qf_outputs,
+                    "kernel function outputs and descriptor outputs have to match");
+   }
+};
+
+template <typename func_t, typename... input_ts, typename... output_ts>
+ElementOperator(func_t, mfem::tuple<input_ts...>, mfem::tuple<output_ts...>)
+-> ElementOperator<func_t, mfem::tuple<input_ts...>, mfem::tuple<output_ts...>,
+decltype(make_dependency_map(std::declval<mfem::tuple<input_ts...>>()))>;
+
+// template <typename func_t, typename input_t, typename output_t>
+// struct BoundaryElementOperator : public
+//    ElementOperator<func_t, input_t, output_t>
+// {
+// public:
+//    using entity_t = Entity::BoundaryElement;
+//    BoundaryElementOperator(func_t func, input_t inputs, output_t outputs)
+//       : ElementOperator<func_t, input_t, output_t>(func, inputs, outputs) {}
+// };
+
+// template <typename func_t, typename input_t, typename output_t>
+// struct FaceOperator : public
+//    ElementOperator<func_t, input_t, output_t>
+// {
+// public:
+//    using entity_t = Entity::Face;
+//    FaceOperator(func_t func, input_t inputs, output_t outputs)
+//       : ElementOperator<func_t, input_t, output_t>(func, inputs, outputs) {}
+// };
+
+} // namespace mfem

examples/dfem/dfem_fieldoperator.hpp

@@ -0,0 +1,227 @@
+#pragma once
+
+#include <string>
+
+namespace mfem
+{
+
+template <int FIELD_ID = -1>
+class FieldOperator
+{
+public:
+   constexpr FieldOperator(int size_on_qp = 0) :
+      size_on_qp(size_on_qp) {};
+
+   static constexpr int GetFieldId() { return FIELD_ID; }
+
+   int size_on_qp = -1;
+
+   int dim = -1;
+
+   int vdim = -1;
+};
+
+template <int FIELD_ID = -1>
+class None : public FieldOperator<FIELD_ID>
+{
+public:
+   constexpr None() : FieldOperator<FIELD_ID>() {}
+};
+
+template< typename T >
+struct is_none_fop
+{
+   static const bool value = false;
+};
+
+template <int FIELD_ID>
+struct is_none_fop<None<FIELD_ID>>
+{
+   static const bool value = true;
+};
+
+template <typename T>
+struct DisableAD
+{
+   T& operator()() const { return fop; }
+   T fop;
+};
+
+class Weight : public FieldOperator<-1>
+{
+public:
+   constexpr Weight() : FieldOperator<-1>() {};
+};
+
+template< typename T >
+struct is_weight_fop
+{
+   static const bool value = false;
+};
+
+template <>
+struct is_weight_fop<Weight>
+{
+   static const bool value = true;
+};
+
+template <int FIELD_ID = -1>
+class Value : public FieldOperator<FIELD_ID>
+{
+public:
+   constexpr Value() : FieldOperator<FIELD_ID>() {};
+};
+
+template< typename T >
+struct is_value_fop
+{
+   static const bool value = false;
+};
+
+template <int FIELD_ID>
+struct is_value_fop<Value<FIELD_ID>>
+{
+   static const bool value = true;
+};
+
+template <typename T>
+struct is_value_fop<DisableAD<T>>
+{
+   static const bool value = is_value_fop<T>::value;
+};
+
+template <int FIELD_ID = -1>
+class Gradient : public FieldOperator<FIELD_ID>
+{
+public:
+   constexpr Gradient() : FieldOperator<FIELD_ID>() {};
+};
+
+template< typename T >
+struct is_gradient_fop
+{
+   static const bool value = false;
+};
+
+template <int FIELD_ID>
+struct is_gradient_fop<Gradient<FIELD_ID>>
+{
+   static const bool value = true;
+};
+
+// class FieldOperator
+// {
+// public:
+//    FieldOperator(std::string field_label = "", int size_on_qp = 0) :
+//       field_label(field_label),
+//       size_on_qp(size_on_qp) {};
+
+//    std::string field_label;
+
+//    int size_on_qp = -1;
+
+//    int dim = -1;
+
+//    int vdim = -1;
+// };
+
+// class None : public FieldOperator
+// {
+// public:
+//    None(std::string field_label) :
+//       FieldOperator(field_label) {}
+// };
+
+// class Weight : public FieldOperator
+// {
+// public:
+//    Weight() : FieldOperator("quadrature_weights") {};
+// };
+
+// class Value : public FieldOperator
+// {
+// public:
+//    Value(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class Gradient : public FieldOperator
+// {
+// public:
+//    Gradient(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class Curl : public FieldOperator
+// {
+// public:
+//    Curl(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class Div : public FieldOperator
+// {
+// public:
+//    Div(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class FaceValueLeft : public FieldOperator
+// {
+// public:
+//    FaceValueLeft(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class FaceValueRight : public FieldOperator
+// {
+// public:
+//    FaceValueRight(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class FaceNormal : public FieldOperator
+// {
+// public:
+//    FaceNormal(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// class One : public FieldOperator
+// {
+// public:
+//    One(std::string field_label) : FieldOperator(field_label) {};
+// };
+
+// namespace BareFieldOperator
+// {
+
+// struct Base
+// {
+//    Base(FieldOperator &o)
+//    {
+//       size_on_qp = o.size_on_qp;
+//       dim = o.dim;
+//       vdim = o.vdim;
+//    };
+//    int size_on_qp = -1;
+//    int dim = -1;
+//    int vdim = -1;
+// };
+
+// struct None : Base
+// {
+//    None(FieldOperator &o) : Base(o) {}
+// };
+
+// struct Weight : Base
+// {
+//    Weight(FieldOperator &o) : Base(o) {}
+// };
+
+// struct Value : Base
+// {
+//    Value(FieldOperator &o) : Base(o) {}
+// };
+
+// struct Gradient : Base
+// {
+//    Gradient(FieldOperator &o) : Base(o) {}
+// };
+
+// }
+
+} // namespace mfem

examples/dfem/dfem_integrate.hpp

@@ -0,0 +1,290 @@
+#pragma once
+
+#include "dfem_util.hpp"
+#include <type_traits>
+
+namespace mfem
+{
+
+template <typename output_t>
+MFEM_HOST_DEVICE
+void map_quadrature_data_to_fields_impl(DeviceTensor<2, double> &y,
+                                        const DeviceTensor<3, double> &f,
+                                        const output_t &output,
+                                        const DofToQuadMap &dtq)
+{
+   auto B = dtq.B;
+   auto G = dtq.G;
+   // assuming the quadrature point residual has to "play nice with
+   // the test function"
+   if constexpr (std::is_same_v<std::decay_t<output_t>, Value<>>)
+   {
+      const auto [num_qp, cdim, num_dof] = B.GetShape();
+      const int vdim = output.vdim > 0 ? output.vdim : cdim ;
+      for (int dof = 0; dof < num_dof; dof++)
+      {
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            double acc = 0.0;
+            for (int qp = 0; qp < num_qp; qp++)
+            {
+               acc += B(qp, 0, dof) * f(vd, 0, qp);
+            }
+            y(dof, vd) += acc;
+         }
+      }
+   }
+   else if constexpr (
+      std::is_same_v<std::decay_t<output_t>, Gradient<>>)
+   {
+      const auto [num_qp, dim, num_dof] = G.GetShape();
+      const int vdim = output.vdim;
+      for (int dof = 0; dof < num_dof; dof++)
+      {
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            double acc = 0.0;
+            for (int d = 0; d < dim; d++)
+            {
+               for (int qp = 0; qp < num_qp; qp++)
+               {
+                  acc += G(qp, d, dof) * f(vd, d, qp);
+               }
+            }
+            y(dof, vd) += acc;
+         }
+      }
+   }
+   // else if constexpr (std::is_same_v<std::decay_t<output_t>, One>)
+   // {
+   //    // This is the "integral over all quadrature points type" applying
+   //    // B = 1 s.t. B^T * C \in R^1.
+   //    const auto [a, b, num_qp] = B.GetShape();
+   //    auto cc = Reshape(&c(0, 0, 0), num_qp);
+   //    for (int i = 0; i < num_qp; i++)
+   //    {
+   //       y(0, 0) += cc(i);
+   //    }
+   // }
+   else if constexpr (
+      std::is_same_v<std::decay_t<output_t>, None<>>)
+   {
+      const auto [vdim, dim, num_qp] = G.GetShape();
+      auto cc = Reshape(&f(0, 0, 0), num_qp * vdim);
+      auto yy = Reshape(&y(0, 0), num_qp * vdim);
+      for (int i = 0; i < num_qp * vdim; i++)
+      {
+         yy(i) = cc(i);
+      }
+   }
+   else
+   {
+      MFEM_ABORT("quadrature data mapping to field is not implemented for"
+                 " this field descriptor");
+   }
+}
+
+template <typename output_t>
+MFEM_HOST_DEVICE
+void map_quadrature_data_to_fields_tensor_impl(DeviceTensor<2, double> &y,
+                                               const DeviceTensor<3, double> &f,
+                                               const output_t &output,
+                                               const DofToQuadMap &dtq,
+                                               std::array<DeviceTensor<1>, 6> &scratch_mem)
+{
+   auto B = dtq.B;
+   auto G = dtq.G;
+
+   if constexpr (is_value_fop<std::decay_t<output_t>>::value)
+   {
+      const auto [q1d, unused, d1d] = B.GetShape();
+      const int vdim = output.vdim;
+      const int test_dim = output.size_on_qp / vdim;
+
+      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d, q1d);
+      auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
+
+      auto s0 = Reshape(&scratch_mem[0](0), q1d, q1d, d1d);
+      auto s1 = Reshape(&scratch_mem[1](0), q1d, d1d, d1d);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         MFEM_FOREACH_THREAD(qy, y, q1d)
+         {
+            MFEM_FOREACH_THREAD(dx, x, d1d)
+            {
+               MFEM_FOREACH_THREAD(qz, z, q1d)
+               {
+                  double acc = 0.0;
+                  for (int qx = 0; qx < q1d; qx++)
+                  {
+                     acc += fqp(vd, 0, qx, qy, qz) * B(qx, 0, dx);
+                  }
+                  s0(qz, qy, dx) = acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(dy, y, d1d)
+         {
+            MFEM_FOREACH_THREAD(dx, x, d1d)
+            {
+               MFEM_FOREACH_THREAD(qz, z, q1d)
+               {
+                  double acc = 0.0;
+                  for (int qy = 0; qy < q1d; qy++)
+                  {
+                     acc += s0(qz, qy, dx) * B(qy, 0, dy);
+                  }
+                  s1(qz, dy, dx) = acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+
+         MFEM_FOREACH_THREAD(dy, y, d1d)
+         {
+            MFEM_FOREACH_THREAD(dx, x, d1d)
+            {
+               MFEM_FOREACH_THREAD(dz, z, d1d)
+               {
+                  double acc = 0.0;
+                  for (int qz = 0; qz < q1d; qz++)
+                  {
+                     acc += s1(qz, dy, dx) * B(qz, 0, dz);
+                  }
+                  yd(dx, dy, dz, vd) += acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+   else if constexpr (is_gradient_fop<std::decay_t<output_t>>::value)
+   {
+      const auto [q1d, unused, d1d] = G.GetShape();
+      const int vdim = output.vdim;
+      const int test_dim = output.size_on_qp / vdim;
+      auto fqp = Reshape(&f(0, 0, 0), vdim, test_dim, q1d, q1d, q1d);
+      auto yd = Reshape(&y(0, 0), d1d, d1d, d1d, vdim);
+
+      auto s0 = Reshape(&scratch_mem[0](0), q1d, q1d, d1d);
+      auto s1 = Reshape(&scratch_mem[1](0), q1d, q1d, d1d);
+      auto s2 = Reshape(&scratch_mem[2](0), q1d, q1d, d1d);
+      auto s3 = Reshape(&scratch_mem[3](0), q1d, d1d, d1d);
+      auto s4 = Reshape(&scratch_mem[4](0), q1d, d1d, d1d);
+      auto s5 = Reshape(&scratch_mem[5](0), q1d, d1d, d1d);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         MFEM_FOREACH_THREAD(qz, z, q1d)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD(dx, x, d1d)
+               {
+                  real_t uvw[3] = {0.0, 0.0, 0.0};
+                  for (int qx = 0; qx < q1d; qx++)
+                  {
+                     uvw[0] += fqp(vd, 0, qx, qy, qz) * G(qx, 0, dx);
+                     uvw[1] += fqp(vd, 1, qx, qy, qz) * B(qx, 0, dx);
+                     uvw[2] += fqp(vd, 2, qx, qy, qz) * B(qx, 0, dx);
+                  }
+                  s0(qz, qy, dx) = uvw[0];
+                  s1(qz, qy, dx) = uvw[1];
+                  s2(qz, qy, dx) = uvw[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(qz, z, q1d)
+         {
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            {
+               MFEM_FOREACH_THREAD(dx, x, d1d)
+               {
+                  real_t uvw[3] = {0.0, 0.0, 0.0};
+                  for (int qy = 0; qy < q1d; qy++)
+                  {
+                     uvw[0] += s0(qz, qy, dx) * B(qy, 0, dy);
+                     uvw[1] += s1(qz, qy, dx) * G(qy, 0, dy);
+                     uvw[2] += s2(qz, qy, dx) * B(qy, 0, dy);
+                  }
+                  s3(qz, dy, dx) = uvw[0];
+                  s4(qz, dy, dx) = uvw[1];
+                  s5(qz, dy, dx) = uvw[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(dz, z, d1d)
+         {
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            {
+               MFEM_FOREACH_THREAD(dx, x, d1d)
+               {
+                  real_t uvw[3] = {0.0, 0.0, 0.0};
+                  for (int qz = 0; qz < q1d; qz++)
+                  {
+                     uvw[0] += s3(qz, dy, dx) * B(qz, 0, dz);
+                     uvw[1] += s4(qz, dy, dx) * B(qz, 0, dz);
+                     uvw[2] += s5(qz, dy, dx) * G(qz, 0, dz);
+                  }
+                  yd(dx, dy, dz, vd) += uvw[0] + uvw[1] + uvw[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+   else if constexpr (is_none_fop<std::decay_t<output_t>>::value)
+   {
+      const auto [q1d, unused, d1d] = B.GetShape();
+      auto fqp = Reshape(&f(0, 0, 0), output.size_on_qp, q1d, q1d, q1d);
+      auto yqp = Reshape(&y(0, 0), output.size_on_qp, q1d, q1d, q1d);
+
+      for (int sq = 0; sq < output.size_on_qp; sq++)
+      {
+         MFEM_FOREACH_THREAD(qx, x, q1d)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD(qz, z, q1d)
+               {
+                  yqp(sq, qx, qy, qz) = fqp(sq, qx, qy, qz);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+   else
+   {
+      MFEM_ABORT("quadrature data mapping to field is not implemented for"
+                 " this field descriptor with sum factorization on tensor product elements");
+   }
+}
+
+template <typename T = NonTensorProduct, typename output_t>
+MFEM_HOST_DEVICE
+void map_quadrature_data_to_fields(DeviceTensor<2, double> &y,
+                                   const DeviceTensor<3, double> &f,
+                                   const output_t &output,
+                                   const DofToQuadMap &dtq,
+                                   std::array<DeviceTensor<1>, 6> &scratch_mem)
+{
+   if constexpr (std::is_same_v<T, NonTensorProduct>)
+   {
+      map_quadrature_data_to_fields_impl(y, f, output, dtq);
+   }
+   else if constexpr (std::is_same_v<T, TensorProduct>)
+   {
+      map_quadrature_data_to_fields_tensor_impl(y, f, output, dtq, scratch_mem);
+   }
+}
+
+}

examples/dfem/dfem_interpolate.hpp

@@ -0,0 +1,403 @@
+#pragma once
+
+#include "dfem_util.hpp"
+
+namespace mfem
+{
+
+template <typename field_operator_t>
+MFEM_HOST_DEVICE inline
+void map_field_to_quadrature_data_tensor_product(
+   DeviceTensor<2> &field_qp,
+   const DofToQuadMap &dtq,
+   const DeviceTensor<1> &field_e,
+   const field_operator_t &input,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem)
+{
+   auto B = dtq.B;
+   auto G = dtq.G;
+
+   if constexpr (is_value_fop<std::decay_t<field_operator_t>>::value)
+   {
+      auto [q1d, unused, d1d] = B.GetShape();
+      const int vdim = input.vdim;
+      const auto field = Reshape(&field_e[0], d1d, d1d, d1d, vdim);
+      auto fqp = Reshape(&field_qp[0], vdim, q1d, q1d, q1d);
+      auto s0 = Reshape(&scratch_mem[0](0), d1d, d1d, q1d);
+      auto s1 = Reshape(&scratch_mem[1](0), d1d, q1d, q1d);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         MFEM_FOREACH_THREAD(dz, z, d1d)
+         {
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            {
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               {
+                  double acc = 0.0;
+                  for (int dx = 0; dx < d1d; dx++)
+                  {
+                     acc += B(qx, 0, dx) * field(dx, dy, dz, vd);
+                  }
+                  s0(dz, dy, qx) = acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(dz, z, d1d)
+         {
+            MFEM_FOREACH_THREAD(qx, x, q1d)
+            {
+               MFEM_FOREACH_THREAD(qy, y, q1d)
+               {
+                  double acc = 0.0;
+                  for (int dy = 0; dy < d1d; dy++)
+                  {
+                     acc += s0(dz, dy, qx) * B(qy, 0, dy);
+                  }
+                  s1(dz, qy, qx) = acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(qz, z, q1d)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               {
+                  double acc = 0.0;
+                  for (int dz = 0; dz < d1d; dz++)
+                  {
+                     acc += s1(dz, qy, qx) * B(qz, 0, dz);
+                  }
+                  fqp(vd, qx, qy, qz) = acc;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+   else if constexpr (
+      is_gradient_fop<std::decay_t<field_operator_t>>::value)
+   {
+      const auto [q1d, unused, d1d] = B.GetShape();
+      const int vdim = input.vdim;
+      const int dim = input.dim;
+      const auto field = Reshape(&field_e[0], d1d, d1d, d1d, vdim);
+      auto fqp = Reshape(&field_qp[0], vdim, dim, q1d, q1d, q1d);
+
+      auto s0 = Reshape(&scratch_mem[0](0), d1d, d1d, q1d);
+      auto s1 = Reshape(&scratch_mem[1](0), d1d, d1d, q1d);
+      auto s2 = Reshape(&scratch_mem[2](0), d1d, q1d, q1d);
+      auto s3 = Reshape(&scratch_mem[3](0), d1d, q1d, q1d);
+      auto s4 = Reshape(&scratch_mem[4](0), d1d, q1d, q1d);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         MFEM_FOREACH_THREAD(dz, z, d1d)
+         {
+            MFEM_FOREACH_THREAD(dy, y, d1d)
+            {
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               {
+                  real_t uv[2] = {0.0, 0.0};
+                  for (int dx = 0; dx < d1d; dx++)
+                  {
+                     const real_t f = field(dx, dy, dz, vd);
+                     uv[0] += f * B(qx, 0, dx);
+                     uv[1] += f * G(qx, 0, dx);
+                  }
+                  s0(dz, dy, qx) = uv[0];
+                  s1(dz, dy, qx) = uv[1];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(dz, z, d1d)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               {
+                  real_t uvw[3] = {0.0, 0.0, 0.0};
+                  for (int dy = 0; dy < d1d; dy++)
+                  {
+                     const real_t s0i = s0(dz, dy, qx);
+                     uvw[0] += s1(dz, dy, qx) * B(qy, 0, dy);
+                     uvw[1] += s0i * G(qy, 0, dy);
+                     uvw[2] += s0i * B(qy, 0, dy);
+                  }
+                  s2(dz, qy, qx) = uvw[0];
+                  s3(dz, qy, qx) = uvw[1];
+                  s4(dz, qy, qx) = uvw[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(qz, z, q1d)
+         {
+            MFEM_FOREACH_THREAD(qy, y, q1d)
+            {
+               MFEM_FOREACH_THREAD(qx, x, q1d)
+               {
+                  real_t uvw[3] = {0.0, 0.0, 0.0};
+                  for (int dz = 0; dz < d1d; dz++)
+                  {
+                     uvw[0] += s2(dz, qy, qx) * B(qz, 0, dz);
+                     uvw[1] += s3(dz, qy, qx) * B(qz, 0, dz);
+                     uvw[2] += s4(dz, qy, qx) * G(qz, 0, dz);
+                  }
+                  fqp(vd, 0, qx, qy, qz) = uvw[0];
+                  fqp(vd, 1, qx, qy, qz) = uvw[1];
+                  fqp(vd, 2, qx, qy, qz) = uvw[2];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   }
+   // TODO: Create separate function for clarity
+   else if constexpr (
+      std::is_same_v<std::decay_t<field_operator_t>, Weight>)
+   {
+      const int num_qp = integration_weights.GetShape()[0];
+      // TODO: eeek
+      const int q1d = (int)floor(pow(num_qp, 1.0/input.dim) + 0.5);
+      auto w = Reshape(&integration_weights[0], q1d, q1d, q1d);
+      auto f = Reshape(&field_qp[0], q1d, q1d, q1d);
+      MFEM_FOREACH_THREAD(qx, x, q1d)
+      {
+         MFEM_FOREACH_THREAD(qy, y, q1d)
+         {
+            MFEM_FOREACH_THREAD(qz, z, q1d)
+            {
+               f(qx, qy, qz) = w(qx, qy, qz);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   }
+   else if constexpr (is_none_fop<std::decay_t<field_operator_t>>::value)
+   {
+      const int q1d = B.GetShape()[0];
+      auto field = Reshape(&field_e[0], input.size_on_qp, q1d * q1d * q1d);
+      field_qp = field;
+   }
+   else
+   {
+      static_assert(always_false<std::decay_t<field_operator_t>>,
+                    "can't map field to quadrature data");
+   }
+}
+
+
+template <typename field_operator_t>
+MFEM_HOST_DEVICE
+void map_field_to_quadrature_data(
+   DeviceTensor<2> field_qp,
+   const DofToQuadMap &dtq,
+   const DeviceTensor<1, const double> &field_e,
+   field_operator_t &input,
+   DeviceTensor<1, const double> integration_weights)
+{
+   auto B = dtq.B;
+   auto G = dtq.G;
+   if constexpr (is_value_fop<field_operator_t>::value)
+   {
+      auto [num_qp, dim, num_dof] = B.GetShape();
+      const int vdim = input.vdim;
+      const auto field = Reshape(&field_e(0), num_dof, vdim);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         for (int qp = 0; qp < num_qp; qp++)
+         {
+            double acc = 0.0;
+            for (int dof = 0; dof < num_dof; dof++)
+            {
+               acc += B(qp, 0, dof) * field(dof, vd);
+            }
+            field_qp(vd, qp) = acc;
+         }
+      }
+   }
+   else if constexpr (is_gradient_fop<field_operator_t>::value)
+   {
+      const auto [num_qp, dim, num_dof] = G.GetShape();
+      const int vdim = input.vdim;
+      const auto field = Reshape(&field_e(0), num_dof, vdim);
+
+      auto f = Reshape(&field_qp[0], vdim, dim, num_qp);
+      for (int qp = 0; qp < num_qp; qp++)
+      {
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            for (int d = 0; d < dim; d++)
+            {
+               double acc = 0.0;
+               for (int dof = 0; dof < num_dof; dof++)
+               {
+                  acc += G(qp, d, dof) * field(dof, vd);
+               }
+               f(vd, d, qp) = acc;
+            }
+         }
+      }
+   }
+   // else if constexpr (std::is_same_v<field_operator_t, FaceNormal>)
+   // {
+   //    auto normal = geometric_factors.normal;
+   //    auto [num_qp, dim, num_entities] = normal.GetShape();
+   //    auto f = Reshape(&field_qp[0], dim, num_qp);
+   //    for (int qp = 0; qp < num_qp; qp++)
+   //    {
+   //       for (int d = 0; d < dim; d++)
+   //       {
+   //          f(d, qp) = normal(qp, d, entity_idx);
+   //       }
+   //    }
+   // }
+   // TODO: Create separate function for clarity
+   else if constexpr (std::is_same_v<field_operator_t, Weight>)
+   {
+      const int num_qp = integration_weights.GetShape()[0];
+      auto f = Reshape(&field_qp[0], num_qp);
+      for (int qp = 0; qp < num_qp; qp++)
+      {
+         f(qp) = integration_weights(qp);
+      }
+   }
+   else if constexpr (is_none_fop<field_operator_t>::value)
+   {
+      auto [num_qp, unused, num_dof] = B.GetShape();
+      const int size_on_qp = input.size_on_qp;
+      const auto field = Reshape(&field_e[0], size_on_qp * num_qp);
+      auto f = Reshape(&field_qp[0], size_on_qp * num_qp);
+      for (int i = 0; i < size_on_qp * num_qp; i++)
+      {
+         f(i) = field(i);
+      }
+   }
+   else
+   {
+      static_assert(always_false<field_operator_t>,
+                    "can't map field to quadrature data");
+
+   }
+}
+
+template <typename T = NonTensorProduct, typename field_operator_ts, size_t num_inputs, size_t num_fields>
+MFEM_HOST_DEVICE inline
+void map_fields_to_quadrature_data(
+   std::array<DeviceTensor<2>, num_inputs> &fields_qp,
+   const std::array<DeviceTensor<1>, num_fields> &fields_e,
+   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
+   const std::array<int, num_inputs> &input_to_field,
+   const field_operator_ts &fops,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem)
+{
+   for_constexpr<num_inputs>([&](auto i)
+   {
+      if constexpr (std::is_same_v<T, TensorProduct>)
+      {
+         map_field_to_quadrature_data_tensor_product(
+            fields_qp[i],
+            dtqmaps[i],
+            fields_e[input_to_field[i]],
+            mfem::get<i>(fops),
+            integration_weights,
+            scratch_mem);
+      }
+      else
+      {
+         map_field_to_quadrature_data(
+            fields_qp[i],
+            dtqmaps[i],
+            fields_e[i],
+            mfem::get<i>(fops),
+            integration_weights);
+      }
+   });
+}
+
+template <typename T, typename field_operator_t>
+MFEM_HOST_DEVICE
+void map_field_to_quadrature_data_conditional(
+   DeviceTensor<2> &field_qp,
+   const DeviceTensor<1> &field_e,
+   const DofToQuadMap &dtqmap,
+   field_operator_t &fop,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem,
+   const bool &condition)
+{
+   if (condition)
+   {
+      if constexpr (std::is_same_v<T, TensorProduct>)
+      {
+         map_field_to_quadrature_data_tensor_product(field_qp, dtqmap,
+                                                     field_e, fop,
+                                                     integration_weights,
+                                                     scratch_mem);
+      }
+      else
+      {
+         map_field_to_quadrature_data(field_qp, dtqmap, field_e, fop,
+                                      integration_weights);
+      }
+   }
+}
+
+template <typename T = NonTensorProduct, size_t num_fields, size_t num_kinputs, typename field_operator_ts, std::size_t... i>
+MFEM_HOST_DEVICE
+void map_fields_to_quadrature_data_conditional(
+   std::array<DeviceTensor<2>, num_kinputs> &fields_qp,
+   const std::array<DeviceTensor<1, const double>, num_fields> &fields_e,
+   const std::array<DofToQuadMap, num_kinputs> &dtqmaps,
+   field_operator_ts fops,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem,
+   const std::array<bool, num_kinputs> &conditions,
+   std::index_sequence<i...>)
+{
+   (map_field_to_quadrature_data_conditional<T>(fields_qp[i],
+                                                fields_e[i],
+                                                dtqmaps[i],
+                                                mfem::get<i>(fops),
+                                                integration_weights,
+                                                scratch_mem,
+                                                conditions[i]),
+    ...);
+}
+
+template <typename T = NonTensorProduct, size_t num_inputs, typename field_operator_ts>
+MFEM_HOST_DEVICE
+void map_direction_to_quadrature_data_conditional(
+   std::array<DeviceTensor<2>, num_inputs> &directions_qp,
+   const DeviceTensor<1> &direction_e,
+   const std::array<DofToQuadMap, num_inputs> &dtqmaps,
+   field_operator_ts fops,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem,
+   const std::array<bool, num_inputs> &conditions)
+{
+   for_constexpr<num_inputs>([&](auto i)
+   {
+      map_field_to_quadrature_data_conditional<T>(directions_qp[i],
+                                                  direction_e,
+                                                  dtqmaps[i],
+                                                  mfem::get<i>(fops),
+                                                  integration_weights,
+                                                  scratch_mem,
+                                                  conditions[i]);
+   });
+}
+
+}

examples/dfem/dfem_parametricspace.hpp

@@ -0,0 +1,99 @@
+#pragma once
+
+#include <mfem.hpp>
+
+namespace mfem
+{
+
+class ParametricSpace
+{
+
+public:
+   ParametricSpace(int spatial_dim, int local_size, int element_size,
+                   int total_size) :
+      spatial_dim(spatial_dim),
+      local_size(local_size),
+      element_size(element_size),
+      total_size(total_size),
+      identity(total_size)
+   {
+      dtq.ndof = (int)floor(pow(element_size, 1.0/spatial_dim) + 0.5);
+      dtq.nqpt = dtq.ndof;
+   }
+
+   ParametricSpace(int local_size) :
+      local_size(local_size),
+      element_size(local_size),
+      total_size(local_size),
+      identity(local_size)
+   {
+      dtq.ndof = (int)floor(pow(element_size, 1.0/spatial_dim) + 0.5);
+      dtq.nqpt = dtq.ndof;
+   }
+
+   int Dimension() const
+   {
+      return spatial_dim;
+   }
+
+   int GetLocalSize() const
+   {
+      return local_size;
+   }
+
+   int GetElementSize() const
+   {
+      return element_size;
+   }
+
+   int GetTotalSize() const
+   {
+      return total_size;
+   }
+
+   const DofToQuad &GetDofToQuad() const
+   {
+      return dtq;
+   }
+
+   const Operator *GetProlongation() const
+   {
+      return &identity;
+   }
+
+   const Operator *GetRestriction() const
+   {
+      return &identity;
+   }
+
+private:
+   int spatial_dim;
+
+   // Hint for the local dimension. E.g. the size on the quadrature point or vdim.
+   int local_size;
+
+   // Size of the data on an element
+   int element_size;
+
+   int total_size;
+
+   IdentityOperator identity;
+
+   DofToQuad dtq;
+};
+
+class ParametricFunction : public Vector
+{
+public:
+   ParametricFunction(ParametricSpace &space) :
+      Vector(space.GetTotalSize()),
+      space(space)
+   {}
+
+   ParametricSpace &space;
+
+   using Vector::operator=;
+
+};
+
+}

examples/dfem/dfem_qfunction.hpp

@@ -0,0 +1,253 @@
+#pragma once
+#include "dfem_util.hpp"
+
+#ifdef MFEM_USE_ENZYME
+#include <enzyme/utils>
+#include <enzyme/enzyme>
+#endif
+
+namespace mfem
+{
+
+template <typename T0, typename T1>
+MFEM_HOST_DEVICE
+void process_kf_arg(const T0 &, T1 &)
+{
+   static_assert(always_false<T0, T1>,
+                 "process_kf_arg not implemented for arg type");
+}
+
+template <typename T>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1, T> &u,
+   T &arg)
+{
+   arg = u(0);
+}
+
+template <typename T>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1, T> &u,
+   internal::tensor<T> &arg)
+{
+   arg(0) = u(0);
+}
+
+template <typename T, int n>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   internal::tensor<T, n> &arg)
+{
+   for (int i = 0; i < n; i++)
+   {
+      arg(i) = u(i);
+   }
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   internal::tensor<T, n, m> &arg)
+{
+   for (int i = 0; i < m; i++)
+   {
+      for (int j = 0; j < n; j++)
+      {
+         arg(j, i) = u((i * m) + j);
+      }
+   }
+}
+
+template <typename arg_type>
+MFEM_HOST_DEVICE
+void process_kf_arg(const DeviceTensor<2> &u, arg_type &arg, int qp)
+{
+   const auto u_qp = Reshape(&u(0, qp), u.GetShape()[0]);
+   process_kf_arg(u_qp, arg);
+}
+
+template <size_t num_fields, typename kf_args, std::size_t... i>
+MFEM_HOST_DEVICE
+void process_kf_args(
+   const std::array<DeviceTensor<2>, num_fields> &u,
+   kf_args &args,
+   const int &qp,
+   std::index_sequence<i...>)
+{
+   (process_kf_arg(u[i], mfem::get<i>(args), qp), ...);
+}
+
+template <typename T0, typename T1> inline
+Vector process_kf_result(T0, T1)
+{
+   static_assert(always_false<T0, T1>,
+                 "process_kf_result not implemented for result type");
+}
+
+template <typename T>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const double &x)
+{
+   r(0) = x;
+}
+
+template <typename T>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<T> &x)
+{
+   r(0) = x(0);
+}
+
+template <typename T, int n>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<T, n> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      r(i) = x(i);
+   }
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<T, n, m> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      for (size_t j = 0; j < m; j++)
+      {
+         r(i + n * j) = x(i, j);
+      }
+   }
+}
+
+template <typename T>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   const DeviceTensor<1> &v,
+   double &arg)
+{
+   arg = u(0);
+}
+
+template <int n, int m>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   const DeviceTensor<1> &v,
+   internal::tensor<double, n, m> &arg)
+{
+   for (int i = 0; i < m; i++)
+   {
+      for (int j = 0; j < n; j++)
+      {
+         arg(j, i) = u((i * m) + j);
+      }
+   }
+}
+
+template <typename kernel_func_t, typename kernel_args_ts, size_t num_args>
+MFEM_HOST_DEVICE inline
+void apply_kernel(
+   DeviceTensor<1, double> &f_qp,
+   const kernel_func_t &kf,
+   kernel_args_ts &args,
+   const std::array<DeviceTensor<2>, num_args> &u,
+   int qp)
+{
+   process_kf_args(u, args, qp,
+                   std::make_index_sequence<mfem::tuple_size<kernel_args_ts>::value> {});
+
+   process_kf_result(f_qp, mfem::get<0>(mfem::apply(kf, args)));
+}
+
+#ifdef MFEM_USE_ENZYME
+// Version for active function arguments only
+//
+// This is an Enzyme regression and can be removed in later versions.
+template <typename kernel_t, typename arg_ts, std::size_t... Is,
+          typename inactive_arg_ts>
+MFEM_HOST_DEVICE inline
+auto fwddiff_apply_enzyme_indexed(kernel_t kernel, arg_ts &&args,
+                                  arg_ts &&shadow_args,
+                                  std::index_sequence<Is...>,
+                                  inactive_arg_ts &&inactive_args,
+                                  std::index_sequence<>)
+{
+   using kf_return_t = typename create_function_signature<
+                       decltype(&kernel_t::operator())>::type::return_t;
+   return __enzyme_fwddiff<kf_return_t>(
+             +kernel, enzyme_dup, &mfem::get<Is>(args)..., enzyme_interleave,
+             &mfem::get<Is>(shadow_args)...);
+}
+
+// Interleave function arguments for enzyme
+template <typename kernel_t, typename arg_ts, std::size_t... Is,
+          typename inactive_arg_ts, std::size_t... Js>
+MFEM_HOST_DEVICE inline
+auto fwddiff_apply_enzyme_indexed(kernel_t kernel, arg_ts &&args,
+                                  arg_ts &&shadow_args,
+                                  std::index_sequence<Is...>,
+                                  inactive_arg_ts &&inactive_args,
+                                  std::index_sequence<Js...>)
+{
+   using kf_return_t = typename create_function_signature<
+                       decltype(&kernel_t::operator())>::type::return_t;
+   return __enzyme_fwddiff<kf_return_t>(
+             +kernel, enzyme_dup, &std::get<Is>(args)..., enzyme_const,
+             &mfem::get<Js>(inactive_args)..., enzyme_interleave,
+             &mfem::get<Is>(shadow_args)...);
+}
+
+template <typename kernel_t, typename arg_ts, typename inactive_arg_ts>
+MFEM_HOST_DEVICE inline
+auto fwddiff_apply_enzyme(kernel_t kernel, arg_ts &&args,
+                          arg_ts &&shadow_args,
+                          inactive_arg_ts &&inactive_args)
+{
+   auto arg_indices = std::make_index_sequence<
+                      mfem::tuple_size<std::remove_reference_t<arg_ts>>::value> {};
+
+   auto inactive_arg_indices = std::make_index_sequence<
+                               mfem::tuple_size<std::remove_reference_t<inactive_arg_ts>>::value> {};
+
+   return fwddiff_apply_enzyme_indexed(kernel, args, shadow_args, arg_indices,
+                                       inactive_args, inactive_arg_indices);
+}
+
+template <typename kf_t, typename kernel_arg_ts, size_t num_args>
+MFEM_HOST_DEVICE inline
+void apply_kernel_fwddiff_enzyme(
+   DeviceTensor<1, double> &f_qp,
+   const kf_t &kf,
+   kernel_arg_ts &args,
+   kernel_arg_ts &shadow_args,
+   const std::array<DeviceTensor<2>, num_args> &u,
+   const std::array<DeviceTensor<2>, num_args> &v,
+   int qp_idx)
+{
+   process_kf_args(u, args, qp_idx,
+                   std::make_index_sequence<mfem::tuple_size<kernel_arg_ts>::value> {});
+
+   process_kf_args(v, shadow_args, qp_idx,
+                   std::make_index_sequence<mfem::tuple_size<kernel_arg_ts>::value> {});
+
+   process_kf_result(f_qp,
+                     mfem::get<0>(fwddiff_apply_enzyme(kf, args, shadow_args, mfem::tuple<> {})));
+}
+#endif // MFEM_USE_ENZYME
+
+} // namespace mfem

examples/dfem/dfem_qfunction_dual.hpp

@@ -0,0 +1,187 @@
+#pragma once
+#include "dfem_util.hpp"
+#include "dfem_qfunction.hpp"
+
+namespace mfem
+{
+
+MFEM_HOST_DEVICE
+template <typename T0, typename T1, typename T2>
+void process_kf_arg(const T0 &, const T1 &, T2 &)
+{
+   static_assert(always_false<T0, T1, T2>,
+                 "process_kf_arg not implemented for arg type");
+}
+
+template <typename T>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1, T> &u,
+   const DeviceTensor<1, T> &v,
+   T &arg)
+{
+   arg = u(0);
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   internal::tensor<internal::dual<T, T>, n, m> &arg)
+{
+   for (int i = 0; i < m; i++)
+   {
+      for (int j = 0; j < n; j++)
+      {
+         arg(j, i).value = u((i * m) + j);
+      }
+   }
+}
+
+template <typename T>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   internal::dual<T, T> &arg)
+{
+   arg.value = u(0);
+}
+
+template <typename T>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   const DeviceTensor<1> &v,
+   internal::dual<T, T> &arg)
+{
+   arg.value = u(0);
+   arg.gradient = v(0);
+}
+
+template <typename T, int n>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   const DeviceTensor<1> &v,
+   internal::tensor<internal::dual<T, T>, n> &arg)
+{
+   for (int i = 0; i < n; i++)
+   {
+      arg(i).value = u(i);
+      arg(i).gradient = v(i);
+   }
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   const DeviceTensor<1> &v,
+   internal::tensor<internal::dual<T, T>, n, m> &arg)
+{
+   for (int i = 0; i < m; i++)
+   {
+      for (int j = 0; j < n; j++)
+      {
+         arg(j, i).value = u((i * m) + j);
+         arg(j, i).gradient = v((i * m) + j);
+      }
+   }
+}
+
+template <typename T, int n>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<internal::dual<T, T>, n> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      r(i) = x(i).value;
+   }
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE inline
+void process_kf_result(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<internal::dual<T, T>, n, m> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      for (size_t j = 0; j < m; j++)
+      {
+         r(i + n * j) = x(i, j).value;
+      }
+   }
+}
+
+template <typename arg_type>
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<2> &u,
+   const DeviceTensor<2> &v,
+   arg_type &arg,
+   const int &qp)
+{
+   const auto u_qp = Reshape(&u(0, qp), u.GetShape()[0]);
+   const auto v_qp = Reshape(&v(0, qp), v.GetShape()[0]);
+   process_kf_arg(u_qp, v_qp, arg);
+}
+
+template <size_t num_args, typename kf_args, std::size_t... Is>
+MFEM_HOST_DEVICE inline
+void process_kf_args(
+   const std::array<DeviceTensor<2>, num_args> &u,
+   const std::array<DeviceTensor<2>, num_args> &v,
+   kf_args &args,
+   const int &qp,
+   std::index_sequence<Is...>)
+{
+   (process_kf_arg(u[Is], v[Is], mfem::get<Is>(args), qp), ...);
+}
+
+template <typename T, int n, int m>
+MFEM_HOST_DEVICE inline
+void process_derivative_from_native_dual(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<internal::dual<T, T>, n, m> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      for (size_t j = 0; j < m; j++)
+      {
+         r(i + n * j) = x(i, j).gradient;
+      }
+   }
+}
+
+template <typename T, int n>
+MFEM_HOST_DEVICE inline
+void process_derivative_from_native_dual(
+   DeviceTensor<1, T> &r,
+   const internal::tensor<internal::dual<T, T>, n> &x)
+{
+   for (size_t i = 0; i < n; i++)
+   {
+      r(i) = x(i).gradient;
+   }
+}
+
+template <typename kf_t, typename kernel_arg_ts, size_t num_args>
+MFEM_HOST_DEVICE inline
+void apply_kernel_native_dual(
+   DeviceTensor<1, double> &f_qp,
+   const kf_t &kf,
+   kernel_arg_ts &args,
+   const std::array<DeviceTensor<2>, num_args> &u,
+   const std::array<DeviceTensor<2>, num_args> &v,
+   const int &qp_idx)
+{
+   process_kf_args(u, v, args, qp_idx,
+                   std::make_index_sequence<mfem::tuple_size<kernel_arg_ts>::value> {});
+   auto r = mfem::get<0>(mfem::apply(kf, args));
+   process_derivative_from_native_dual(f_qp, r);
+}
+
+} // namespace mfem

examples/dfem/dfem_refactor.hpp

@@ -0,0 +1,530 @@
+#pragma once
+
+#include <mfem.hpp>
+#include <utility>
+#include "dfem_interpolate.hpp"
+#include "dfem_integrate.hpp"
+#include "dfem_qfunction.hpp"
+#include "dfem_qfunction_dual.hpp"
+#include "examples/dfem/dfem_util.hpp"
+
+namespace mfem
+{
+
+class DerivativeOperator : public Operator
+{
+   using derivative_action_t =
+      std::function<void(std::vector<Vector> &, const Vector &, Vector &)>;
+
+   using restriction_callback_t =
+      std::function<void(std::vector<Vector> &,
+                         const std::vector<Vector> &,
+                         std::vector<Vector> &)>;
+
+public:
+   DerivativeOperator(
+      const std::vector<derivative_action_t> &derivative_actions,
+      const FieldDescriptor &direction,
+      const std::vector<Vector *> &solutions_l,
+      const std::vector<Vector *> &parameters_l,
+      const std::vector<restriction_callback_t> &restriction_callbacks,
+      const std::function<void(Vector &, Vector &)> prolongation_transpose) :
+      derivative_actions(derivative_actions),
+      direction(direction),
+      restriction_callbacks(restriction_callbacks),
+      derivative_action_l(GetVSize(direction)),
+      prolongation_transpose(prolongation_transpose)
+   {
+      MFEM_ASSERT(derivative_actions.size() == restriction_callbacks.size(),
+                  "internal error");
+
+      derivative_action_l = 0.0;
+      this->solutions_l.resize(solutions_l.size());
+      this->parameters_l.resize(parameters_l.size());
+
+      for (int i = 0; i < solutions_l.size(); i++)
+      {
+         this->solutions_l[i] = *solutions_l[i];
+      }
+
+      for (int i = 0; i < parameters_l.size(); i++)
+      {
+         this->parameters_l[i] = *parameters_l[i];
+      }
+
+      fields_e.resize(solutions_l.size() + parameters_l.size());
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      direction_t = x;
+      direction_t.SetSubVector(ess_tdof_list, 0.0);
+
+      prolongation(direction, direction_t, direction_l);
+      for (int i = 0; i < derivative_actions.size(); i++)
+      {
+         restriction_callbacks[i](solutions_l, parameters_l, fields_e);
+         derivative_actions[i](fields_e, direction_l, derivative_action_l);
+      }
+      prolongation_transpose(derivative_action_l, y);
+
+      y.SetSubVector(ess_tdof_list, 0.0);
+   };
+
+private:
+   std::vector<derivative_action_t> derivative_actions;
+
+   mutable std::vector<Vector> solutions_l;
+   std::vector<Vector> parameters_l;
+
+   FieldDescriptor direction;
+   mutable Vector direction_t;
+   mutable Vector direction_e;
+   mutable Vector direction_l;
+
+   mutable Vector derivative_action_e;
+   mutable Vector derivative_action_l;
+
+   mutable std::vector<Vector> fields_e;
+
+   Array<int> ess_tdof_list;
+   std::vector<restriction_callback_t> restriction_callbacks;
+   std::function<void(Vector &, Vector &)> prolongation_transpose;
+};
+
+class DifferentiableOperator : public Operator
+{
+   using action_t =
+      std::function<void(std::vector<Vector> &, const std::vector<Vector> &, Vector &)>;
+
+   using derivative_action_t =
+      std::function<void(std::vector<Vector> &, const Vector &, Vector &)>;
+
+   using restriction_callback_t =
+      std::function<void(std::vector<Vector> &,
+                         const std::vector<Vector> &,
+                         std::vector<Vector> &)>;
+
+public:
+   DifferentiableOperator(
+      const std::vector<FieldDescriptor> &solutions,
+      const std::vector<FieldDescriptor> &parameters,
+      const ParMesh &mesh);
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      MFEM_ASSERT(!action_callbacks.empty(), "no integrators have been set");
+      prolongation(solutions, x, solutions_l);
+      for (auto &action : action_callbacks)
+      {
+         action(solutions_l, parameters_l, residual_l);
+      }
+      prolongation_transpose(residual_l, y);
+
+      y.SetSubVector(ess_tdof_list, 0.0);
+   }
+
+   template <
+      typename func_t,
+      typename... input_ts,
+      typename... output_ts,
+      typename derivative_indices_t>
+   void AddDomainIntegrator(
+      func_t qfunc,
+      mfem::tuple<input_ts...> inputs,
+      mfem::tuple<output_ts...> outputs,
+      const IntegrationRule &integration_rule,
+      const derivative_indices_t derivative_indices = {});
+
+   void SetParameters(std::vector<Vector *> p) const;
+
+   std::shared_ptr<DerivativeOperator> GetDerivative(
+      size_t derivative_idx,
+      std::vector<Vector *> solutions_l,
+      std::vector<Vector *> parameters_l)
+   {
+      MFEM_ASSERT(derivative_action_callbacks.find(derivative_idx) !=
+                  derivative_action_callbacks.end(),
+                  "no derivative action has been found for index " << derivative_idx);
+
+      return std::make_shared<DerivativeOperator>(
+                derivative_action_callbacks[derivative_idx],
+                fields[derivative_idx],
+                solutions_l,
+                parameters_l,
+                restriction_callbacks,
+                prolongation_transpose);
+   }
+
+private:
+   const ParMesh &mesh;
+
+   std::vector<action_t> action_callbacks;
+   std::map<size_t, std::vector<derivative_action_t>> derivative_action_callbacks;
+
+   std::vector<FieldDescriptor> solutions;
+   std::vector<FieldDescriptor> parameters;
+   // solutions and parameters
+   std::vector<FieldDescriptor> fields;
+
+   Array<int> ess_tdof_list;
+
+   mutable std::vector<Vector> solutions_l;
+   mutable std::vector<Vector> parameters_l;
+   mutable Vector residual_l;
+
+   mutable std::vector<Vector> fields_e;
+   mutable Vector residual_e;
+
+   std::function<void(Vector &, Vector &)> prolongation_transpose;
+   std::vector<restriction_callback_t> restriction_callbacks;
+};
+
+void DifferentiableOperator::SetParameters(std::vector<Vector *> p) const
+{
+   MFEM_ASSERT(parameters.size() == p.size(),
+               "number of parameters doesn't match descriptors");
+   for (int i = 0; i < parameters.size(); i++)
+   {
+      p[i]->Read();
+      parameters_l[i] = *p[i];
+   }
+}
+
+DifferentiableOperator::DifferentiableOperator(
+   const std::vector<FieldDescriptor> &solutions,
+   const std::vector<FieldDescriptor> &parameters,
+   const ParMesh &mesh) :
+   mesh(mesh),
+   solutions(solutions),
+   parameters(parameters)
+{
+   fields.resize(solutions.size() + parameters.size());
+   fields_e.resize(fields.size());
+   solutions_l.resize(solutions.size());
+   parameters_l.resize(parameters.size());
+
+   for (int i = 0; i < solutions.size(); i++)
+   {
+      fields[i] = solutions[i];
+   }
+
+   for (int i = 0; i < parameters.size(); i++)
+   {
+      fields[i + solutions.size()] = parameters[i];
+   }
+}
+
+template <
+   typename func_t,
+   typename... input_ts,
+   typename... output_ts,
+   typename derivative_indices_t = std::make_index_sequence<0>>
+void DifferentiableOperator::AddDomainIntegrator(
+   func_t qfunc,
+   mfem::tuple<input_ts...> inputs,
+   mfem::tuple<output_ts...> outputs,
+   const IntegrationRule &integration_rule,
+   const derivative_indices_t derivative_indices)
+{
+   using entity_t = Entity::Element;
+
+   static constexpr size_t num_inputs =
+      mfem::tuple_size<decltype(inputs)>::value;
+
+   static constexpr size_t num_outputs =
+      mfem::tuple_size<decltype(outputs)>::value;
+
+   using qf_param_ts = typename create_function_signature<
+                       decltype(&func_t::operator())>::type::parameter_ts;
+
+   using qf_output_t = typename create_function_signature<
+                       decltype(&func_t::operator())>::type::return_t;
+
+   // Consistency checks
+   if constexpr (num_outputs > 1)
+   {
+      static_assert(always_false<func_t>,
+                    "more than one output per kernel is not supported right now");
+   }
+
+   constexpr size_t num_qfinputs = mfem::tuple_size<qf_param_ts>::value;
+   static_assert(num_qfinputs == num_inputs,
+                 "kernel function inputs and descriptor inputs have to match");
+
+   constexpr size_t num_qf_outputs = mfem::tuple_size<qf_output_t>::value;
+   static_assert(num_qf_outputs == num_qf_outputs,
+                 "kernel function outputs and descriptor outputs have to match");
+
+   constexpr auto field_tuple = std::tuple_cat(std::tuple<input_ts...> {},
+                                               std::tuple<output_ts...> {});
+   constexpr auto filtered_field_tuple = filter_fields(field_tuple);
+   constexpr size_t num_fields = count_unique_field_ids(filtered_field_tuple);
+
+   constexpr auto dependency_map = make_dependency_map(mfem::tuple<input_ts...> {});
+
+   // Create the action callback
+   auto input_to_field = create_descriptors_to_fields_map<entity_t>(
+                            fields,
+                            inputs,
+                            std::make_index_sequence<num_inputs> {});
+
+   auto output_to_field = create_descriptors_to_fields_map<entity_t>(
+                             fields,
+                             outputs,
+                             std::make_index_sequence<num_outputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = output_to_field[hardcoded_output_idx];
+
+   ElementDofOrdering element_dof_ordering = ElementDofOrdering::LEXICOGRAPHIC;
+   DofToQuad::Mode doftoquad_mode = DofToQuad::Mode::TENSOR;
+
+   const Operator *R = get_restriction<entity_t>(fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   // The explicit captures are necessary to avoid dependency on
+   // the specific instance of this class (this pointer).
+   auto restriction_callback =
+      [=, solutions = this->solutions, parameters = this->parameters]
+      (std::vector<Vector> &solutions_l,
+       const std::vector<Vector> &parameters_l,
+       std::vector<Vector> &fields_e)
+   {
+      restriction<entity_t>(solutions, solutions_l, fields_e,
+                            element_dof_ordering);
+      restriction<entity_t>(parameters, parameters_l, fields_e,
+                            element_dof_ordering,
+                            solutions.size());
+   };
+   restriction_callbacks.push_back(restriction_callback);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(outputs);
+
+   if constexpr (is_none_fop<decltype(output_fop)>::value)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         y = r_local;
+      };
+   }
+   // else if constexpr (std::is_same_v<decltype(output_fop), One>)
+   // {
+   //    prolongation_transpose = [&](Vector &r_local, Vector &y)
+   //    {
+   //       double local_sum = r_local.Sum();
+   //       MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+   //                     op.mesh.GetComm());
+   //       MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+   //    };
+   // }
+   else
+   {
+      auto P = get_prolongation(fields[test_space_field_idx]);
+      prolongation_transpose = [P](const Vector &r_local, Vector &y)
+      {
+         P->MultTranspose(r_local, y);
+      };
+   }
+
+   const int num_elements = GetNumEntities<Entity::Element>(mesh);
+   const int num_entities = GetNumEntities<entity_t>(mesh);
+   const int num_qp = integration_rule.GetNPoints();
+
+   size_t residual_lsize = GetVSize(fields[test_space_field_idx]);
+
+   // if constexpr (std::is_same_v<decltype(output_fop), One>)
+   // {
+   //    this->width = 1;
+   // }
+   // else
+   {
+      width = residual_lsize;
+   }
+
+   residual_l.SetSize(residual_lsize);
+
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(
+                          field,
+                          integration_rule,
+                          doftoquad_mode));
+   }
+   const int q1d = (int)floor(pow(num_qp, 1.0/mesh.Dimension()) + 0.5);
+
+   residual_e.SetSize(R->Height());
+
+   const int residual_size_on_qp =
+      GetSizeOnQP<entity_t>(mfem::get<hardcoded_output_idx>(outputs),
+                            fields[test_space_field_idx]);
+
+   auto input_dtq_maps =
+      create_dtq_maps<entity_t>(inputs, dtq, input_to_field);
+   auto output_dtq_maps =
+      create_dtq_maps<entity_t>(outputs, dtq, output_to_field);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(outputs).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(inputs).size_on_qp /
+      mfem::get<hardcoded_output_idx>(outputs).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(outputs).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(integration_rule.GetWeights().Read(), num_qp);
+
+   auto input_size_on_qp =
+      get_input_size_on_qp(inputs, std::make_index_sequence<num_inputs> {});
+
+   auto action_shmem_info =
+      get_shmem_info<entity_t, num_fields, num_inputs, num_outputs>
+      (input_dtq_maps, output_dtq_maps, fields, num_entities, inputs, num_qp,
+       input_size_on_qp, residual_size_on_qp);
+
+   Vector shmem_cache(action_shmem_info.total_size);
+
+   // print_shared_memory_info(action_shmem_info);
+
+   action_callbacks.push_back(
+      [=](std::vector<Vector> &solutions_l,
+          const std::vector<Vector> &parameters_l,
+          Vector &residual_l) mutable
+   {
+      restriction_callback(solutions_l, parameters_l, fields_e);
+
+      residual_e = 0.0;
+      auto ye = Reshape(residual_e.ReadWrite(), test_vdim, num_test_dof, num_entities);
+
+      auto wrapped_fields_e = wrap_fields(fields_e,
+                                          action_shmem_info.field_sizes,
+                                          num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, void *shmem)
+      {
+         auto [input_dtq_shmem, output_dtq_shmem, fields_shmem, input_shmem,
+                                residual_shmem, scratch_shmem] =
+         unpack_shmem(shmem, action_shmem_info, input_dtq_maps, output_dtq_maps,
+                      wrapped_fields_e, num_qp, e);
+
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, input_to_field, inputs, ir_weights,
+            scratch_shmem);
+
+         call_qfunction<TensorProduct, qf_param_ts>(
+            qfunc, input_shmem, residual_shmem,
+            residual_size_on_qp, num_qp, q1d);
+
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(outputs),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_shmem);
+      }, num_entities, q1d, q1d, q1d, action_shmem_info.total_size, shmem_cache.ReadWrite());
+
+      if constexpr (is_none_fop<decltype(output_fop)>::value)
+      {
+         residual_l = residual_e;
+      }
+      else
+      {
+         R->MultTranspose(residual_e, residual_l);
+      }
+   });
+
+   for_constexpr([&](auto derivative_idx)
+   {
+      // bool is_dependent = false;
+      // for_constexpr<num_inputs>([&](auto input_idx)
+      // {
+      //    constexpr auto input_is_dependent_on_field_idx =
+      //       std::get<derivative_idx>(std::get<input_idx>(dependency_map));
+
+      //    if constexpr (input_is_dependent_on_field_idx == 1)
+      //    {
+      //       is_dependent = true;
+      //    }
+      // });
+
+      // if (!is_dependent)
+      // {
+      //    derivative_action_callbacks[derivative_idx].push_back(
+      //       [=](const Vector &direction_l, Vector &y) mutable
+      //    {
+      //       y += 0.0;
+      //    });
+
+      //    return;
+      // }
+
+      auto direction = fields[derivative_idx];
+      size_t derivative_action_l_size = GetVSize(direction);
+
+      const int da_size_on_qp = GetSizeOnQP<entity_t>(
+                                   mfem::get<hardcoded_output_idx>(outputs),
+                                   fields[test_space_field_idx]);
+
+      auto shmem_info =
+         get_shmem_info<entity_t, num_fields, num_inputs, num_outputs>
+         (input_dtq_maps, output_dtq_maps, fields, num_entities, inputs, num_qp,
+          input_size_on_qp, residual_size_on_qp, derivative_idx);
+
+      Vector shmem_cache(shmem_info.total_size);
+
+      // print_shared_memory_info(shmem_info);
+
+      Vector direction_e;
+      Vector derivative_action_e(R->Height());
+      derivative_action_e = 0.0;
+
+      auto input_is_dependent = get_array_from_tuple(std::get<derivative_idx>
+                                                     (dependency_map));
+
+      derivative_action_callbacks[derivative_idx].push_back(
+         [=](std::vector<Vector> &fields_e, const Vector &direction_l,
+             Vector &derivative_action_l) mutable
+      {
+         restriction<entity_t>(direction, direction_l, direction_e, element_dof_ordering);
+         auto ye = Reshape(derivative_action_e.ReadWrite(), num_test_dof, test_vdim, num_entities);
+         auto wrapped_fields_e = wrap_fields(fields_e, shmem_info.field_sizes, num_entities);
+         auto wrapped_direction_e = Reshape(direction_e.ReadWrite(), shmem_info.direction_size, num_entities);
+         forall([=] MFEM_HOST_DEVICE (int e, double *shmem)
+         {
+            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);
+
+            map_fields_to_quadrature_data<TensorProduct>(
+               input_shmem, fields_shmem, input_dtq_shmem, input_to_field, inputs, ir_weights,
+               scratch_shmem);
+
+            zero_all(shadow_shmem);
+            map_direction_to_quadrature_data_conditional<TensorProduct>(
+               shadow_shmem, direction_shmem, input_dtq_shmem, inputs, ir_weights,
+               scratch_shmem, input_is_dependent);
+
+            call_qfunction_derivative_action<TensorProduct, qf_param_ts>(
+               qfunc, input_shmem, shadow_shmem, residual_shmem,
+               da_size_on_qp, num_qp, q1d);
+
+            auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+            auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+            map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                         mfem::get<0>(outputs),
+                                                         output_dtq_shmem[hardcoded_output_idx],
+                                                         scratch_shmem);
+         }, num_entities, q1d, q1d, q1d, shmem_info.total_size, shmem_cache.ReadWrite());
+
+         R->MultTranspose(derivative_action_e, derivative_action_l);
+      });
+   }, derivative_indices);
+}
+
+
+} // namespace mfem
+
+// #include "dfem_refactor_action.hpp"
+// #include "dfem_refactor_derivatives.hpp"

examples/dfem/dfem_refactor_action.hpp

@@ -0,0 +1,232 @@
+#pragma once
+
+#include "dfem_refactor.hpp"
+
+namespace mfem
+{
+
+template <typename element_operator_t, size_t num_fields>
+void DifferentiableOperator::instantiate_action(
+   element_operator_t element_operator, action_t &action)
+{
+   using entity_t = typename element_operator_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(
+                             fields,
+                             element_operator.inputs,
+                             std::make_index_sequence<element_operator.num_inputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(
+                              fields,
+                              element_operator.outputs,
+                              std::make_index_sequence<element_operator.num_outputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(element_operator.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(mesh);
+   const int num_entities = GetNumEntities<entity_t>(mesh);
+   const int num_qp = integration_rule.GetNPoints();
+
+   this->width = GetTrueVSize(fields[test_space_field_idx]);
+   size_t residual_lsize = GetVSize(fields[test_space_field_idx]);
+
+   // if constexpr (std::is_same_v<decltype(output_fop), One>)
+   // {
+   //    this->width = 1;
+   // }
+   // else
+   {
+      this->width = residual_lsize;
+   }
+
+   residual_l.SetSize(residual_lsize);
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(
+                          field,
+                          integration_rule,
+                          doftoquad_mode));
+   }
+   const int q1d = (int)floor(pow(num_qp, 1.0/mesh.Dimension()) + 0.5);
+
+   residual_e.SetSize(R->Height());
+
+   const int residual_size_on_qp = GetSizeOnQP<entity_t>(
+                                      mfem::get<hardcoded_output_idx>(element_operator.outputs),
+                                      fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(element_operator.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(element_operator.outputs, dtq,
+                                                    koutput_to_field);
+
+   // auto input_fops = create_bare_fops(element_operator.inputs);
+   // auto output_fops = create_bare_fops(element_operator.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>
+                         (element_operator.outputs).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(element_operator.inputs).size_on_qp /
+      mfem::get<hardcoded_output_idx>(element_operator.outputs).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(element_operator.outputs).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(integration_rule.GetWeights().Read(), num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(
+                              element_operator.inputs,
+                              std::make_index_sequence<element_operator.num_inputs> {});
+
+   auto shmem_info =
+      get_shmem_info<entity_t, num_fields, element_operator.num_inputs, element_operator.num_outputs>
+      (input_dtq_maps,
+       output_dtq_maps,
+       fields,
+       num_entities,
+       element_operator.inputs,
+       num_qp,
+       input_size_on_qp,
+       residual_size_on_qp);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   print_shared_memory_info(shmem_info);
+
+   action = [=](const Vector &x, Vector &y) mutable
+   {
+      prolongation(solutions, x, solutions_l);
+
+      restriction<entity_t>(solutions, solutions_l, this->fields_e,
+                            element_dof_ordering);
+      restriction<entity_t>(parameters, parameters_l, this->fields_e,
+                            element_dof_ordering,
+                            solutions.size());
+
+      residual_e = 0.0;
+      auto ye = Reshape(residual_e.ReadWrite(), test_vdim, num_test_dof,
+                        num_entities);
+
+      auto wrapped_fields_e = wrap_fields(this->fields_e,
+                                          shmem_info.field_sizes,
+                                          num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, void *shmem)
+      {
+         // printf("\ne: %d\n", e);
+         // tic();
+         auto input_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::INPUT_DTQ],
+            shmem_info.input_dtq_sizes,
+            input_dtq_maps);
+
+         auto output_dtq_shmem = load_dtq_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::OUTPUT_DTQ],
+            shmem_info.output_dtq_sizes,
+            output_dtq_maps);
+
+         auto fields_shmem = load_field_mem(
+            shmem,
+            shmem_info.offsets[SharedMemory::Index::FIELD],
+            shmem_info.field_sizes,
+            kinput_to_field,
+            element_operator.inputs,
+            wrapped_fields_e,
+            e,
+         std::make_index_sequence<element_operator.num_inputs> {});
+
+         // These functions don't copy, they simply create a `DeviceTensor` object
+         // that points to correct chunks of the shared memory pool.
+         auto input_shmem = load_input_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::INPUT],
+                               shmem_info.input_sizes,
+                               num_qp);
+
+         auto residual_shmem = load_residual_mem(
+                                  shmem,
+                                  shmem_info.offsets[SharedMemory::Index::OUTPUT],
+                                  shmem_info.residual_size,
+                                  num_qp);
+
+         auto scratch_mem = load_scratch_mem(
+                               shmem,
+                               shmem_info.offsets[SharedMemory::Index::TEMP],
+                               shmem_info.temp_sizes);
+
+         MFEM_SYNC_THREAD;
+         // // printf("shmem load elapsed: %.1fus\n", toc() * 1e6);
+
+         // // tic();
+         map_fields_to_quadrature_data<TensorProduct>(
+            input_shmem, fields_shmem, input_dtq_shmem, element_operator.inputs, ir_weights,
+            scratch_mem,
+            std::make_index_sequence<element_operator.num_inputs> {});
+         // printf("interpolate elapsed: %.1fus\n", toc() * 1e6);
+
+         // // tic();
+         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);
+                  auto qf_args = decay_tuple<typename element_operator_t::qf_param_ts> {};
+                  auto r = Reshape(&residual_shmem(0, q), residual_size_on_qp);
+                  apply_kernel(r, element_operator.qfunc, qf_args, input_shmem, q);
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+         // // printf("qf elapsed: %.1fus\n", toc() * 1e6);
+
+         // // tic();
+         auto fhat = Reshape(&residual_shmem(0, 0), test_vdim, test_op_dim, num_qp);
+         auto y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         map_quadrature_data_to_fields<TensorProduct>(y, fhat,
+                                                      mfem::get<0>(element_operator.outputs),
+                                                      output_dtq_shmem[hardcoded_output_idx],
+                                                      scratch_mem);
+         // printf("integrate elapsed: %.1fus\n", toc() * 1e6);
+
+      }, num_entities, q1d, q1d, q1d, shmem_info.total_size, shmem_cache.ReadWrite());
+
+      if constexpr (std::is_same_v<decltype(output_fop), None<>>)
+      {
+         residual_l = y;
+      }
+      else
+      {
+         R->MultTranspose(residual_e, residual_l);
+      }
+
+      if constexpr (std::is_same_v<decltype(output_fop), None<>>)
+      {
+         y = residual_l;
+      }
+      // else if constexpr (std::is_same_v<decltype(output_fop), One>)
+      // {
+      //    double local_sum = residual_l.Sum();
+      //    MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM, mesh.GetComm());
+      //    MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      // }
+      else
+      {
+         get_prolongation(fields[test_space_field_idx])->MultTranspose(residual_l, y);
+      }
+   };
+}
+
+}

examples/dfem/dfem_refactor_derivatives.hpp

@@ -0,0 +1,132 @@
+#pragma once
+
+#include "dfem_refactor.hpp"
+
+template<typename T, T... Ints>
+void print_sequence(std::integer_sequence<T, Ints...>)
+{
+   ((std::cout << Ints << " "), ...);
+   std::cout << std::endl;
+}
+
+namespace mfem
+{
+
+template <
+   typename element_operator_t,
+   size_t num_solutions,
+   size_t num_parameters,
+   size_t derivative_idx>
+DerivativeOperator::DerivativeOperator(
+   element_operator_t element_operator,
+   const std::array<FieldDescriptor, num_solutions> &solutions,
+   const std::array<FieldDescriptor, num_parameters> &parameters,
+   const std::vector<FieldDescriptor> &fields,
+   ParMesh &mesh,
+   const IntegrationRule &integration_rule,
+   const ElementDofOrdering &element_dof_ordering,
+   const DofToQuad::Mode &doftoquad_mode,
+   std::integral_constant<size_t, derivative_idx>)
+{
+   direction = fields[derivative_idx];
+
+   size_t derivative_action_l_size = 0;
+   for (auto &s : solutions)
+   {
+      derivative_action_l_size += GetVSize(s);
+      this->width += GetTrueVSize(s);
+   }
+   this->height = derivative_action_l_size;
+   derivative_action_l.SetSize(derivative_action_l_size);
+
+   constexpr size_t num_fields = num_solutions + num_parameters;
+   using entity_t = typename element_operator_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(
+                             fields,
+                             element_operator.inputs,
+                             std::make_index_sequence<element_operator.num_inputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(
+                              fields,
+                              element_operator.outputs,
+                              std::make_index_sequence<element_operator.num_outputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(element_operator.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(mesh);
+   const int num_entities = GetNumEntities<entity_t>(mesh);
+   const int num_qp = integration_rule.GetNPoints();
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(
+                          field,
+                          integration_rule,
+                          doftoquad_mode));
+   }
+   const int q1d = (int)floor(pow(num_qp, 1.0/mesh.Dimension()) + 0.5);
+
+   derivative_action_e.SetSize(R->Height());
+
+   const int da_size_on_qp = GetSizeOnQP<entity_t>(
+                                mfem::get<hardcoded_output_idx>(element_operator.outputs),
+                                fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(element_operator.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(element_operator.outputs, dtq,
+                                                    koutput_to_field);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>
+                         (element_operator.outputs).vdim;
+   const int test_op_dim =
+      mfem::get<hardcoded_output_idx>(element_operator.inputs).size_on_qp /
+      mfem::get<hardcoded_output_idx>(element_operator.outputs).vdim;
+   const int num_test_dof = R->Height() /
+                            mfem::get<hardcoded_output_idx>(element_operator.outputs).vdim /
+                            num_entities;
+
+   auto ir_weights = Reshape(integration_rule.GetWeights().Read(), num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(
+                              element_operator.inputs,
+                              std::make_index_sequence<element_operator.num_inputs> {});
+
+   auto input_is_dependent = std::get<derivative_idx>
+                             (element_operator.dependency_map);
+
+   constexpr bool with_derivatives = true;
+   auto shmem_info =
+      get_shmem_info<entity_t, num_fields, element_operator.num_inputs, element_operator.num_outputs>
+      (input_dtq_maps,
+       output_dtq_maps,
+       fields,
+       num_entities,
+       element_operator.inputs,
+       num_qp,
+       input_size_on_qp,
+       da_size_on_qp,
+       derivative_idx);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   print_shared_memory_info(shmem_info);
+
+   action_callback = [=](const Vector &x, Vector &y) mutable
+   {
+      restriction<entity_t>(direction, direction_l, direction_e,
+                            element_dof_ordering);
+
+   };
+}
+
+} // namespace mfem

examples/dfem/dfem_smm.hpp

@@ -0,0 +1,116 @@
+#pragma once
+
+#include <mfem.hpp>
+
+class SharedMemoryManager
+{
+private:
+   struct MemoryBlock
+   {
+      char* ptr;
+      int size;
+      bool used;
+   };
+
+   MFEM_HOST_DEVICE static const int MAX_BLOCKS = 16;
+   MFEM_HOST_DEVICE static MemoryBlock blocks[MAX_BLOCKS];
+   MFEM_HOST_DEVICE static int num_blocks;
+   MFEM_HOST_DEVICE static char* base_ptr;
+
+public:
+   MFEM_HOST_DEVICE static void init(void* shmem, int total_size)
+   {
+      base_ptr = static_cast<char*>(shmem);
+      num_blocks = 1;
+      blocks[0] = {base_ptr, total_size, false};
+   }
+
+   template<typename T>
+   MFEM_HOST_DEVICE static T* reserve(int n)
+   {
+      int size_bytes = n * sizeof(T);
+      for (int i = 0; i < num_blocks; ++i)
+      {
+         if (!blocks[i].used && blocks[i].size >= size_bytes)
+         {
+            blocks[i].used = true;
+            if (blocks[i].size > size_bytes)
+            {
+               // Split block
+               if (num_blocks < MAX_BLOCKS)
+               {
+                  blocks[num_blocks] = {blocks[i].ptr + size_bytes, blocks[i].size - size_bytes, false};
+                  ++num_blocks;
+                  blocks[i].size = size_bytes;
+               }
+            }
+            return reinterpret_cast<T*>(blocks[i].ptr);
+         }
+      }
+      return nullptr; // Allocation failed
+   }
+
+   MFEM_HOST_DEVICE static void release(void* ptr)
+   {
+      for (int i = 0; i < num_blocks; ++i)
+      {
+         if (blocks[i].ptr == ptr)
+         {
+            blocks[i].used = false;
+            return;
+         }
+      }
+   }
+
+   MFEM_HOST_DEVICE static void release_and_try_merge(void* ptr)
+   {
+      for (int i = 0; i < num_blocks; ++i)
+      {
+         if (blocks[i].ptr == ptr)
+         {
+            blocks[i].used = false;
+            merge_adjacent_free_blocks();
+            return;
+         }
+      }
+   }
+
+private:
+   MFEM_HOST_DEVICE static void merge_adjacent_free_blocks()
+   {
+      // Simple bubble sort for simplicity (can be optimized)
+      for (int i = 0; i < num_blocks - 1; ++i)
+      {
+         for (int j = 0; j < num_blocks - i - 1; ++j)
+         {
+            if (blocks[j].ptr > blocks[j + 1].ptr)
+            {
+               MemoryBlock temp = blocks[j];
+               blocks[j] = blocks[j + 1];
+               blocks[j + 1] = temp;
+            }
+         }
+      }
+
+      for (int i = 0; i < num_blocks - 1; ++i)
+      {
+         if (!blocks[i].used && !blocks[i + 1].used)
+         {
+            blocks[i].size += blocks[i + 1].size;
+            for (int j = i + 1; j < num_blocks - 1; ++j)
+            {
+               blocks[j] = blocks[j + 1];
+            }
+            --num_blocks;
+            --i;
+         }
+      }
+   }
+};
+
+MFEM_HOST_DEVICE SharedMemoryManager::MemoryBlock
+SharedMemoryManager::blocks[SharedMemoryManager::MAX_BLOCKS];
+
+MFEM_HOST_DEVICE int SharedMemoryManager::num_blocks;
+
+MFEM_HOST_DEVICE char* SharedMemoryManager::base_ptr;

examples/dfem/dfem_test_macro.hpp

@@ -0,0 +1,39 @@
+#pragma once
+#include "dfem_refactor.hpp"
+
+#define DFEM_TEST_MAIN(function)                                               \
+   int main(int argc, char* argv[])                                            \
+   {                                                                           \
+      Mpi::Init();                                                             \
+                                                                               \
+      const char* device_config = "cpu";                                       \
+      const char* mesh_file = "../data/ref-square.mesh";                       \
+      int polynomial_order = 1;                                                \
+      int ir_order = 2;                                                        \
+      int refinements = 0;                                                     \
+                                                                               \
+      OptionsParser args(argc, argv);                                          \
+      args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");         \
+      args.AddOption(&polynomial_order, "-o", "--order", "");                  \
+      args.AddOption(&refinements, "-r", "--r", "");                           \
+      args.AddOption(&ir_order, "-iro", "--iro", "");                          \
+      args.AddOption(&device_config, "-d", "--device",                         \
+         "Device configuration string, see Device::Configure().");             \
+      args.ParseCheck();                                                       \
+                                                                               \
+      Device device(device_config);                                            \
+      if (Mpi::Root() == 0)                                                    \
+      {                                                                        \
+         device.Print();                                                       \
+      }                                                                        \
+                                                                               \
+      out << std::setprecision(12);                                            \
+                                                                               \
+      int ret;                                                                 \
+                                                                               \
+      ret = function(mesh_file, refinements, polynomial_order);                \
+      out << #function;                                                        \
+      ret ? out << " FAILURE\n" : out << " OK\n";                              \
+                                                                               \
+      return ret;                                                              \
+   }\

examples/dfem/noisy.hpp

@@ -0,0 +1,130 @@
+// SPDX-ArtifactOfProjectName:     noisy
+// SPDX-ArtifactOfProjectHomePage: https://github.com/VincentZalzal/noisy
+// SPDX-FileCopyrightText:         Copyright 2024 Vincent Zalzal
+// SPDX-License-Identifier:        MIT
+
+#pragma once
+
+#include <iomanip>
+#include <iostream>
+
+namespace vz {
+
+struct Counters {
+    unsigned m_def_ctor    = 0;
+    unsigned m_copy_ctor   = 0;
+    unsigned m_move_ctor   = 0;
+    unsigned m_copy_assign = 0;
+    unsigned m_move_assign = 0;
+    unsigned m_dtor        = 0;
+
+    void reset() {
+        *this = {};
+    }
+
+    bool leaks() const {
+        return m_def_ctor + m_copy_ctor + m_move_ctor != m_dtor;
+    }
+
+    friend std::ostream& operator<<(std::ostream& os, const Counters& c) {
+        stream_counter(os, "Default constructor count: ", c.m_def_ctor   );
+        stream_counter(os, "Copy constructor count:    ", c.m_copy_ctor  );
+        stream_counter(os, "Move constructor count:    ", c.m_move_ctor  );
+        stream_counter(os, "Copy assignment count:     ", c.m_copy_assign);
+        stream_counter(os, "Move assignment count:     ", c.m_move_assign);
+        stream_counter(os, "Destructor count:          ", c.m_dtor       );
+        return os;
+    }
+
+    friend bool operator==(const Counters& lhs, const Counters& rhs) {
+        return
+            lhs.m_def_ctor    == rhs.m_def_ctor    &&
+            lhs.m_copy_ctor   == rhs.m_copy_ctor   &&
+            lhs.m_move_ctor   == rhs.m_move_ctor   &&
+            lhs.m_copy_assign == rhs.m_copy_assign &&
+            lhs.m_move_assign == rhs.m_move_assign &&
+            lhs.m_dtor        == rhs.m_dtor        ;
+    }
+
+    friend bool operator!=(const Counters& lhs, const Counters& rhs) { return !(lhs == rhs); }
+
+private:
+    static void stream_counter(std::ostream& os, const char* msg, unsigned value) {
+        if (value != 0)
+            os << msg << std::setw(2) << value << '\n';
+    }
+};
+
+namespace detail {
+
+struct Globals {
+    ~Globals() {
+        if (m_verbose)
+            std::cout << "\n===== Noisy counters =====\n" << m_counters;
+    }
+
+    Counters m_counters;
+    unsigned m_next_id = 0;
+    bool     m_verbose = true;
+};
+
+}
+
+class Noisy {
+private:
+    static detail::Globals& globals() {
+        static detail::Globals s_globals;
+        return s_globals;
+    }
+
+public:
+    static Counters& counters() { return globals().m_counters; }
+    static void set_verbose(bool verbose) { globals().m_verbose = verbose; }
+
+    Noisy() {
+        if (globals().m_verbose)
+            std::cout << *this << ": default constructor\n";
+        globals().m_counters.m_def_ctor++;
+    }
+
+    Noisy(const Noisy& other) {
+        if (globals().m_verbose)
+            std::cout << *this << ": copy constructor from " << other << '\n';
+        globals().m_counters.m_copy_ctor++;
+    }
+
+    Noisy(Noisy&& other) noexcept {
+        if (globals().m_verbose)
+            std::cout << *this << ": move constructor from " << other << '\n';
+        globals().m_counters.m_move_ctor++;
+    }
+
+    ~Noisy() {
+        if (globals().m_verbose)
+            std::cout << *this << ": destructor\n";
+        globals().m_counters.m_dtor++;
+    }
+
+    Noisy& operator=(const Noisy& other) {
+        if (globals().m_verbose)
+            std::cout << *this << ": copy assignment from " << other << '\n';
+        globals().m_counters.m_copy_assign++;
+        return *this;
+    }
+
+    Noisy& operator=(Noisy&& other) noexcept {
+        if (globals().m_verbose)
+            std::cout << *this << ": move assignment from " << other << '\n';
+        globals().m_counters.m_move_assign++;
+        return *this;
+    }
+
+    unsigned id() const { return m_id; }
+
+    friend std::ostream& operator<<(std::ostream& os, const Noisy& noisy) { return os << "Noisy(" << std::setw(2) << noisy.m_id << ')'; }
+
+private:
+    unsigned m_id = globals().m_next_id++;
+};
+
+}

examples/dfem/old_derivative_action_callback.icc

@@ -0,0 +1,188 @@
+{
+   using entity_t = typename kernel_t::entity_t;
+
+   auto kinput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+   kernel.inputs, std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto koutput_to_field = create_descriptors_to_fields_map<entity_t>(op.fields,
+   kernel.outputs, std::make_index_sequence<kernel.num_koutputs> {});
+
+   constexpr int hardcoded_output_idx = 0;
+   const int test_space_field_idx = koutput_to_field[hardcoded_output_idx];
+
+   const Operator *R = get_restriction<entity_t>(op.fields[test_space_field_idx],
+                                                 element_dof_ordering);
+
+   auto output_fop = mfem::get<hardcoded_output_idx>(kernel.outputs);
+
+   const int num_elements = GetNumEntities<Entity::Element>(op.mesh);
+   const int num_entities = GetNumEntities<entity_t>(op.mesh);
+   const int num_qp = op.integration_rule.GetNPoints();
+
+   // assume only a single element type for now
+   std::vector<const DofToQuad*> dtq;
+   for (const auto &field : op.fields)
+   {
+      dtq.emplace_back(GetDofToQuad<entity_t>(field, op.integration_rule,
+                                              doftoquad_mode));
+   }
+   const int q1d = dtq[0]->nqpt;
+
+   derivative_action_e.SetSize(R->Height());
+
+   const int da_size_on_qp = GetSizeOnQP<entity_t>(
+      mfem::get<hardcoded_output_idx>(kernel.outputs),
+      op.fields[test_space_field_idx]);
+
+   auto input_dtq_maps = create_dtq_maps<entity_t>(kernel.inputs, dtq,
+                                                   kinput_to_field);
+   auto output_dtq_maps = create_dtq_maps<entity_t>(kernel.outputs, dtq,
+                                                    koutput_to_field);
+
+   auto input_fops = create_bare_fops(kernel.inputs);
+   auto output_fops = create_bare_fops(kernel.outputs);
+
+   const int test_vdim = mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int test_op_dim =
+   mfem::get<hardcoded_output_idx>(output_fops).size_on_qp /
+   mfem::get<hardcoded_output_idx>(output_fops).vdim;
+   const int num_test_dof = R->Height() /
+   mfem::get<hardcoded_output_idx>(output_fops).vdim /
+   num_entities;
+
+   auto ir_weights = Reshape(this->op.integration_rule.GetWeights().Read(),
+                             num_qp);
+
+   auto input_size_on_qp = get_input_size_on_qp(kernel.inputs,
+   std::make_index_sequence<kernel.num_kinputs> {});
+
+   auto shmem_info = get_shmem_info<entity_t>(input_dtq_maps,
+                                              output_dtq_maps,
+                                              op.fields,
+                                              num_entities,
+                                              kernel.inputs,
+                                              num_qp,
+                                              input_size_on_qp,
+                                              da_size_on_qp);
+
+   Vector shmem_cache(shmem_info.total_size);
+
+   func = [=](Vector &ye_mem) mutable
+   {
+      restriction<entity_t>(direction, direction_l, direction_e,
+                            op.element_dof_ordering, derivative_idx);
+
+      // Check which qf inputs are dependent on the dependent variable
+      std::array<bool, kernel.num_kinputs> kinput_is_dependent;
+      bool no_qfinput_is_dependent = true;
+      for (int i = 0; i < kinput_is_dependent.size(); i++)
+      {
+         if (kinput_to_field[i] == derivative_idx)
+         {
+            no_qfinput_is_dependent = false;
+            kinput_is_dependent[i] = true;
+            // out << "function input " << i << " is dependent on "
+            //     << op.fields[kinput_to_field[i]].field_label << "\n";
+         }
+         else
+         {
+            kinput_is_dependent[i] = false;
+         }
+      }
+
+      if (no_qfinput_is_dependent)
+      {
+         return;
+      }
+
+      // auto kernel_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+      // auto kernel_shadow_args = decay_tuple<typename kernel_t::kf_param_ts> {};
+
+      // DeviceTensor<1, const double> integration_weights(
+      //    this->op.integration_rule.GetWeights().Read(), num_qp);
+
+      // Vector zero;
+      // GeometricFactorMaps geometric_factors
+      // {
+      //    DeviceTensor<3, const double>(zero.Read(), 0, 0, 0)
+      // };
+
+      // // Fields interpolated to the quadrature points in the order of
+      // // kernel function arguments
+      // auto input_qp = map_inputs_to_memory(input_qp_mem, num_qp,
+      //                                      kernel.inputs,
+      //                                      std::make_index_sequence<kernel.num_kinputs> {});
+
+      // auto directions_qp = map_inputs_to_memory(directions_qp_mem, num_qp,
+      //                                           kernel.inputs,
+      //                                           std::make_index_sequence<kernel.num_kinputs> {});
+
+      // constexpr int fixed_output_idx = 0;
+      // auto Bv = output_dtq_maps[fixed_output_idx];
+      // auto [num_test_qp, test_op_dim, num_test_dof] = Bv.GetShape();
+      // const int test_vdim = mfem::get<0>(kernel.outputs).vdim;
+      // DeviceTensor<3> ye = Reshape(ye_mem.ReadWrite(), num_test_dof, test_vdim, num_entities);
+
+      forall([=] MFEM_HOST_DEVICE (int e, double *shmem)
+      {
+         // map_fields_to_quadrature_data(
+         //    input_qp, e, this->fields_e,
+         //    kinput_to_field, input_dtq_maps,
+         //    integration_weights, geometric_factors, kernel.inputs,
+         //    std::make_index_sequence<kernel.num_kinputs> {});
+
+         // map_fields_to_quadrature_data_conditional(
+         //    directions_qp, e,
+         //    directions_e, kinput_to_field,
+         //    input_dtq_maps,
+         //    integration_weights,
+         //    geometric_factors,
+         //    kinput_is_dependent,
+         //    kernel.inputs,
+         //    std::make_index_sequence<kernel.num_kinputs> {});
+
+         // for (int qp = 0; qp < num_qp; qp++)
+         // {
+         //    auto f_qp = apply_kernel_fwddiff_enzyme(
+         //                   kernel.func,
+         //                   kernel_args,
+         //                   input_qp,
+         //                   kernel_shadow_args,
+         //                   directions_qp,
+         //                   qp);
+
+         //    auto r_qp = Reshape(&da_qp(0, qp, e), da_size_on_qp);
+         //    for (int i = 0; i < da_size_on_qp; i++)
+         //    {
+         //       r_qp(i) = f_qp(i);
+         //    }
+         // }
+
+         // DeviceTensor<3> fhat = Reshape(&da_qp(0, 0, e), test_vdim, test_op_dim, num_qp);
+         // DeviceTensor<2> y = Reshape(&ye(0, 0, e), num_test_dof, test_vdim);
+         // map_quadrature_data_to_fields(y, fhat,
+         //                               output_fop,
+         //                               output_dtq_maps[hardcoded_output_idx]);
+      }, num_entities, q1d, q1d, 1, shmem_info.total_size, shmem_cache.GetData());
+
+      R->MultTranspose(ye_mem, derivative_action_l);
+   };
+
+   if constexpr (std::is_same_v<decltype(output_fop), One>)
+   {
+      prolongation_transpose = [&](Vector &r_local, Vector &y)
+      {
+         double local_sum = r_local.Sum();
+         MPI_Allreduce(&local_sum, y.GetData(), 1, MPI_DOUBLE, MPI_SUM,
+                       op.mesh.GetComm());
+         MFEM_ASSERT(y.Size() == 1, "output size doesn't match kernel description");
+      };
+   }
+   else
+   {
+      auto P = get_prolongation(op.fields[test_space_field_idx]);
+      prolongation_transpose = [P](Vector &r_l, Vector &y)
+      {
+         P->MultTranspose(r_l, y);
+      };
+   }

examples/dfem/shared_mem_calc.md

@@ -0,0 +1,49 @@
+* Calculate shared memory requirements
+* Interpolation and integration
+---
+* If grad involved, need B and G
+* Fit largest field, depends on polynomial order (#dofs)
+  -> vdim is irrelevant
+* Temporaries for each sum
+  - DDQ (d1d x d1d x q1d) x 2 -> DDQ0, DDQ1
+  - DQQ (d1d x q1d x q1d) x 3 -> DQQ0, DQQ1, DQQ2
+  - QQQ (q1d x q1d x q1d) x 3 -> QQQ0, QQQ1, QQQ2
+
+We need the following combinations at the same time
+(1) DDQ0 + DDQ1 + DQQ0 + DQQ1 + DQQ2
+(2) DQQ0 + DQQ1 + DQQ2 + QQQ0 + QQQ1 + QQQ2
+(3) QQQ0 + QQQ1 + QQQ2 + QQD0 + QQD1 + QQD2
+(4) QQD0 + QQD1 + QQD2 + QDD0 + QDD1 + QDD2
+
+Allocate largest memory footprint from 2, 3 or 4 and
+add memory footprint of fields and B/G.
+
+Annotations with NR and R mean "not reusable" and
+"reusable", respectively. This means the memory location is
+reused for _all_ e.g. interpolation of a value etc.
+
+----
+For the action of nonlinear diffusion in 2D we have
+(rho * |u|^2 \nabla u, \nabla v)
+
+* Load
+RHO (D x D) | R (after interpolation)
+U (D x D x VDIM) | R (after interpolation)
+B (Q x D) | NR
+G (Q x D) | NR
+
+* Interpolate Value
+Temporary (Q x D) | R
+R (Q x Q) | NR
+U (Q x Q x VDIM) | NR
+
+* Interpolate Grad
+Temporaries (Q x D) + (Q x D) | R
+U (Q x Q x DIM x VDIM) | NR
+
+Quadrature point function
+-> purely thread local
+
+* Integrate Grad
+R | temp from Interpolation
+R | U from Load

examples/dfem/tuple.hpp

@@ -0,0 +1,845 @@
+// This is serac's tuple implementation
+
+#pragma once
+
+#include "general/backends.hpp"
+#include <utility>
+#include <mfem.hpp>
+#include <tuple>
+
+namespace mfem
+{
+
+/**
+ * @tparam T the types stored in the tuple
+ * @brief This is a class that mimics most of std::tuple's interface,
+ * except that it is usable in CUDA kernels and admits some arithmetic operator overloads.
+ *
+ * see https://en.cppreference.com/w/cpp/utility/tuple for more information about std::tuple
+ */
+template <typename... T>
+struct tuple
+{
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ */
+template <typename T0>
+struct tuple<T0>
+{
+   T0 v0;  ///< The first member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ */
+template <typename T0, typename T1>
+struct tuple<T0, T1>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2>
+struct tuple<T0, T1, T2>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ * @tparam T3 The fourth type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2, typename T3>
+struct tuple<T0, T1, T2, T3>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ * @tparam T3 The fourth type stored in the tuple
+ * @tparam T4 The fifth type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2, typename T3, typename T4>
+struct tuple<T0, T1, T2, T3, T4>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+   T4 v4;  ///< The fifth member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ * @tparam T3 The fourth type stored in the tuple
+ * @tparam T4 The fifth type stored in the tuple
+ * @tparam T5 The sixth type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5>
+struct tuple<T0, T1, T2, T3, T4, T5>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+   T4 v4;  ///< The fifth member of the tuple
+   T5 v5;  ///< The sixth member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ * @tparam T3 The fourth type stored in the tuple
+ * @tparam T4 The fifth type stored in the tuple
+ * @tparam T5 The sixth type stored in the tuple
+ * @tparam T6 The seventh type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
+struct tuple<T0, T1, T2, T3, T4, T5, T6>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+   T4 v4;  ///< The fifth member of the tuple
+   T5 v5;  ///< The sixth member of the tuple
+   T6 v6;  ///< The seventh member of the tuple
+};
+
+/**
+ * @brief Type that mimics std::tuple
+ *
+ * @tparam T0 The first type stored in the tuple
+ * @tparam T1 The second type stored in the tuple
+ * @tparam T2 The third type stored in the tuple
+ * @tparam T3 The fourth type stored in the tuple
+ * @tparam T4 The fifth type stored in the tuple
+ * @tparam T5 The sixth type stored in the tuple
+ * @tparam T6 The seventh type stored in the tuple
+ * @tparam T7 The eighth type stored in the tuple
+ */
+template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6, typename T7>
+struct tuple<T0, T1, T2, T3, T4, T5, T6, T7>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+   T4 v4;  ///< The fifth member of the tuple
+   T5 v5;  ///< The sixth member of the tuple
+   T6 v6;  ///< The seventh member of the tuple
+   T7 v7;  ///< The eighth member of the tuple
+};
+
+template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6, typename T7, typename T8>
+struct tuple<T0, T1, T2, T3, T4, T5, T6, T7, T8>
+{
+   T0 v0;  ///< The first member of the tuple
+   T1 v1;  ///< The second member of the tuple
+   T2 v2;  ///< The third member of the tuple
+   T3 v3;  ///< The fourth member of the tuple
+   T4 v4;  ///< The fifth member of the tuple
+   T5 v5;  ///< The sixth member of the tuple
+   T6 v6;  ///< The seventh member of the tuple
+   T7 v7;  ///< The eighth member of the tuple
+   T8 v8;
+};
+
+/**
+ * @brief Class template argument deduction rule for tuples
+ * @tparam T The variadic template parameter for tuple types
+ */
+template <typename... T>
+MFEM_HOST_DEVICE
+tuple(T...) -> tuple<T...>;
+
+/**
+ * @brief helper function for combining a list of values into a tuple
+ * @tparam T types of the values to be tuple-d
+ * @param args the actual values to be put into a tuple
+ */
+template <typename... T>
+MFEM_HOST_DEVICE tuple<T...> make_tuple(const T&... args)
+{
+   return tuple<T...> {args...};
+}
+
+template <class... Types>
+struct tuple_size
+{
+};
+
+template <class... Types>
+struct tuple_size<mfem::tuple<Types...>> :
+                                      std::integral_constant<std::size_t, sizeof...(Types)>
+{
+};
+
+/**
+ * @tparam i the tuple index to access
+ * @tparam T the types stored in the tuple
+ * @brief return a reference to the ith tuple entry
+ */
+template <int i, typename... T>
+MFEM_HOST_DEVICE constexpr auto& get(tuple<T...>& values)
+{
+   static_assert(i < sizeof...(T), "");
+   if constexpr (i == 0)
+   {
+      return values.v0;
+   }
+   if constexpr (i == 1)
+   {
+      return values.v1;
+   }
+   if constexpr (i == 2)
+   {
+      return values.v2;
+   }
+   if constexpr (i == 3)
+   {
+      return values.v3;
+   }
+   if constexpr (i == 4)
+   {
+      return values.v4;
+   }
+   if constexpr (i == 5)
+   {
+      return values.v5;
+   }
+   if constexpr (i == 6)
+   {
+      return values.v6;
+   }
+   if constexpr (i == 7)
+   {
+      return values.v7;
+   }
+   if constexpr (i == 8)
+   {
+      return values.v8;
+   }
+}
+
+/**
+ * @tparam i the tuple index to access
+ * @tparam T the types stored in the tuple
+ * @brief return a copy of the ith tuple entry
+ */
+template <int i, typename... T>
+MFEM_HOST_DEVICE constexpr const auto& get(const tuple<T...>& values)
+{
+   static_assert(i < sizeof...(T), "");
+   if constexpr (i == 0)
+   {
+      return values.v0;
+   }
+   if constexpr (i == 1)
+   {
+      return values.v1;
+   }
+   if constexpr (i == 2)
+   {
+      return values.v2;
+   }
+   if constexpr (i == 3)
+   {
+      return values.v3;
+   }
+   if constexpr (i == 4)
+   {
+      return values.v4;
+   }
+   if constexpr (i == 5)
+   {
+      return values.v5;
+   }
+   if constexpr (i == 6)
+   {
+      return values.v6;
+   }
+   if constexpr (i == 7)
+   {
+      return values.v7;
+   }
+   if constexpr (i == 8)
+   {
+      return values.v8;
+   }
+}
+
+/**
+ * @brief a function intended to be used for extracting the ith type from a tuple.
+ *
+ * @note type<i>(my_tuple) returns a value, whereas get<i>(my_tuple) returns a reference
+ *
+ * @tparam i the index of the tuple to query
+ * @tparam T the types stored in the tuple
+ * @param values the tuple of values
+ * @return a copy of the ith entry of the input
+ */
+template <int i, typename... T>
+MFEM_HOST_DEVICE constexpr auto type(const tuple<T...>& values)
+{
+   static_assert(i < sizeof...(T), "");
+   if constexpr (i == 0)
+   {
+      return values.v0;
+   }
+   if constexpr (i == 1)
+   {
+      return values.v1;
+   }
+   if constexpr (i == 2)
+   {
+      return values.v2;
+   }
+   if constexpr (i == 3)
+   {
+      return values.v3;
+   }
+   if constexpr (i == 4)
+   {
+      return values.v4;
+   }
+   if constexpr (i == 5)
+   {
+      return values.v5;
+   }
+   if constexpr (i == 6)
+   {
+      return values.v6;
+   }
+   if constexpr (i == 7)
+   {
+      return values.v7;
+   }
+   if constexpr (i == 8)
+   {
+      return values.v8;
+   }
+}
+
+/**
+ * @brief A helper function for the + operator of tuples
+ *
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param y tuple of values
+ * @return the returned tuple sum
+ */
+template <typename... S, typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto plus_helper(const tuple<S...>& x,
+                                            const tuple<T...>& y,
+                                            std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) + get<i>(y)...};
+}
+
+/**
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief return a tuple of values defined by elementwise sum of x and y
+ */
+template <typename... S, typename... T>
+MFEM_HOST_DEVICE constexpr auto operator+(const tuple<S...>& x,
+                                          const tuple<T...>& y)
+{
+   static_assert(sizeof...(S) == sizeof...(T));
+   return plus_helper(x, y,
+                      std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
+}
+
+/**
+ * @brief A helper function for the += operator of tuples
+ *
+ * @tparam T the types stored in the tuples x and y
+ * @tparam i integer sequence used to index the tuples
+ * @param x tuple of values to be incremented
+ * @param y tuple of increment values
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr void plus_equals_helper(tuple<T...>& x,
+                                                   const tuple<T...>& y,
+                                                   std::integer_sequence<int, i...>)
+{
+   ((get<i>(x) += get<i>(y)), ...);
+}
+
+/**
+ * @tparam T the types stored in the tuples x and y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief add values contained in y, to the tuple x
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator+=(tuple<T...>& x,
+                                           const tuple<T...>& y)
+{
+   return plus_equals_helper(x, y,
+                             std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @brief A helper function for the -= operator of tuples
+ *
+ * @tparam T the types stored in the tuples x and y
+ * @tparam i integer sequence used to index the tuples
+ * @param x tuple of values to be subracted from
+ * @param y tuple of values to subtract from x
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr void minus_equals_helper(tuple<T...>& x,
+                                                    const tuple<T...>& y,
+                                                    std::integer_sequence<int, i...>)
+{
+   ((get<i>(x) -= get<i>(y)), ...);
+}
+
+/**
+ * @tparam T the types stored in the tuples x and y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief add values contained in y, to the tuple x
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator-=(tuple<T...>& x,
+                                           const tuple<T...>& y)
+{
+   return minus_equals_helper(x, y,
+                              std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @brief A helper function for the - operator of tuples
+ *
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param y tuple of values
+ * @return the returned tuple difference
+ */
+template <typename... S, typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto minus_helper(const tuple<S...>& x,
+                                             const tuple<T...>& y,
+                                             std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) - get<i>(y)...};
+}
+
+/**
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief return a tuple of values defined by elementwise difference of x and y
+ */
+template <typename... S, typename... T>
+MFEM_HOST_DEVICE constexpr auto operator-(const tuple<S...>& x,
+                                          const tuple<T...>& y)
+{
+   static_assert(sizeof...(S) == sizeof...(T));
+   return minus_helper(x, y,
+                       std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
+}
+
+/**
+ * @brief A helper function for the - operator of tuples
+ *
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @return the returned tuple difference
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto unary_minus_helper(const tuple<T...>& x,
+                                                   std::integer_sequence<int, i...>)
+{
+   return tuple{-get<i>(x)...};
+}
+
+/**
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of values
+ * @brief return a tuple of values defined by applying the unary minus operator to each element of x
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator-(const tuple<T...>& x)
+{
+   return unary_minus_helper(x,
+                             std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @brief A helper function for the / operator of tuples
+ *
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param y tuple of values
+ * @return the returned tuple ratio
+ */
+template <typename... S, typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto div_helper(const tuple<S...>& x,
+                                           const tuple<T...>& y,
+                                           std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) / get<i>(y)...};
+}
+
+/**
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief return a tuple of values defined by elementwise division of x by y
+ */
+template <typename... S, typename... T>
+MFEM_HOST_DEVICE constexpr auto operator/(const tuple<S...>& x,
+                                          const tuple<T...>& y)
+{
+   static_assert(sizeof...(S) == sizeof...(T));
+   return div_helper(x, y,
+                     std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
+}
+
+/**
+ * @brief A helper function for the / operator of tuples
+ *
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param a the constant numerator
+ * @return the returned tuple ratio
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto div_helper(const double a,
+                                           const tuple<T...>& x, std::integer_sequence<int, i...>)
+{
+   return tuple{a / get<i>(x)...};
+}
+
+/**
+ * @brief A helper function for the / operator of tuples
+ *
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param a the constant denomenator
+ * @return the returned tuple ratio
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto div_helper(const tuple<T...>& x,
+                                           const double a, std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) / a...};
+}
+
+/**
+ * @tparam T the types stored in the tuple x
+ * @param a the numerator
+ * @param x a tuple of denominator values
+ * @brief return a tuple of values defined by division of a by the elements of x
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator/(const double a, const tuple<T...>& x)
+{
+   return div_helper(a, x,
+                     std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of numerator values
+ * @param a a denominator
+ * @brief return a tuple of values defined by elementwise division of x by a
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator/(const tuple<T...>& x, const double a)
+{
+   return div_helper(x, a,
+                     std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @brief A helper function for the * operator of tuples
+ *
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param y tuple of values
+ * @return the returned tuple product
+ */
+template <typename... S, typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto mult_helper(const tuple<S...>& x,
+                                            const tuple<T...>& y,
+                                            std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) * get<i>(y)...};
+}
+
+/**
+ * @tparam S the types stored in the tuple x
+ * @tparam T the types stored in the tuple y
+ * @param x a tuple of values
+ * @param y a tuple of values
+ * @brief return a tuple of values defined by elementwise multiplication of x and y
+ */
+template <typename... S, typename... T>
+MFEM_HOST_DEVICE constexpr auto operator*(const tuple<S...>& x,
+                                          const tuple<T...>& y)
+{
+   static_assert(sizeof...(S) == sizeof...(T));
+   return mult_helper(x, y,
+                      std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
+}
+
+/**
+ * @brief A helper function for the * operator of tuples
+ *
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param a a constant multiplier
+ * @return the returned tuple product
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto mult_helper(const double a,
+                                            const tuple<T...>& x, std::integer_sequence<int, i...>)
+{
+   return tuple{a * get<i>(x)...};
+}
+
+/**
+ * @brief A helper function for the * operator of tuples
+ *
+ * @tparam T the types stored in the tuple y
+ * @tparam i The integer sequence to i
+ * @param x tuple of values
+ * @param a a constant multiplier
+ * @return the returned tuple product
+ */
+template <typename... T, int... i>
+MFEM_HOST_DEVICE constexpr auto mult_helper(const tuple<T...>& x,
+                                            const double a, std::integer_sequence<int, i...>)
+{
+   return tuple{get<i>(x) * a...};
+}
+
+/**
+ * @tparam T the types stored in the tuple
+ * @param a a scaling factor
+ * @param x the tuple object
+ * @brief multiply each component of x by the value a on the left
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator*(const double a, const tuple<T...>& x)
+{
+   return mult_helper(a, x,
+                      std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @tparam T the types stored in the tuple
+ * @param x the tuple object
+ * @param a a scaling factor
+ * @brief multiply each component of x by the value a on the right
+ */
+template <typename... T>
+MFEM_HOST_DEVICE constexpr auto operator*(const tuple<T...>& x, const double a)
+{
+   return mult_helper(x, a,
+                      std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @tparam T the types stored in the tuple
+ * @tparam i a list of indices used to acces each element of the tuple
+ * @param out the ostream to write the output to
+ * @param A the tuple of values
+ * @brief helper used to implement printing a tuple of values
+ */
+template <typename... T, std::size_t... i>
+auto& print_helper(std::ostream& out, const mfem::tuple<T...>& A,
+                   std::integer_sequence<size_t, i...>)
+{
+   out << "tuple{";
+   (..., (out << (i == 0 ? "" : ", ") << mfem::get<i>(A)));
+   out << "}";
+   return out;
+}
+
+/**
+ * @tparam T the types stored in the tuple
+ * @param out the ostream to write the output to
+ * @param A the tuple of values
+ * @brief print a tuple of values
+ */
+template <typename... T>
+auto& operator<<(std::ostream& out, const mfem::tuple<T...>& A)
+{
+   return print_helper(out, A, std::make_integer_sequence<size_t, sizeof...(T)>());
+}
+
+/**
+ * @brief A helper to apply a lambda to a tuple
+ *
+ * @tparam lambda The functor type
+ * @tparam T The tuple types
+ * @tparam i The integer sequence to i
+ * @param f The functor to apply to the tuple
+ * @param args The input tuple
+ * @return The functor output
+ */
+template <typename lambda, typename... T, int... i>
+MFEM_HOST_DEVICE auto apply_helper(lambda f, tuple<T...>& args,
+                                   std::integer_sequence<int, i...>)
+{
+   return f(get<i>(args)...);
+}
+
+/**
+ * @tparam lambda a callable type
+ * @tparam T the types of arguments to be passed in to f
+ * @param f the callable object
+ * @param args a tuple of arguments
+ * @brief a way of passing an n-tuple to a function that expects n separate arguments
+ *
+ *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
+ */
+template <typename lambda, typename... T>
+MFEM_HOST_DEVICE auto apply(lambda f, tuple<T...>& args)
+{
+   return apply_helper(f, std::move(args),
+                       std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @overload
+ */
+template <typename lambda, typename... T, int... i>
+MFEM_HOST_DEVICE auto apply_helper(lambda f, const tuple<T...>& args,
+                                   std::integer_sequence<int, i...>)
+{
+   return f(get<i>(args)...);
+}
+
+/**
+ * @tparam lambda a callable type
+ * @tparam T the types of arguments to be passed in to f
+ * @param f the callable object
+ * @param args a tuple of arguments
+ * @brief a way of passing an n-tuple to a function that expects n separate arguments
+ *
+ *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
+ */
+template <typename lambda, typename... T>
+MFEM_HOST_DEVICE auto apply(lambda f, const tuple<T...>& args)
+{
+   return apply_helper(f, std::move(args),
+                       std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
+}
+
+/**
+ * @brief a struct used to determine the type at index I of a tuple
+ *
+ * @note see: https://en.cppreference.com/w/cpp/utility/tuple/tuple_element
+ *
+ * @tparam I the index of the desired type
+ * @tparam T a tuple of different types
+ */
+template <size_t I, class T>
+struct tuple_element;
+
+// recursive case
+/// @overload
+template <size_t I, class Head, class... Tail>
+struct tuple_element<I, tuple<Head, Tail...>> : tuple_element<I - 1,
+                                              tuple<Tail...>>
+{
+};
+
+// base case
+/// @overload
+template <class Head, class... Tail>
+struct tuple_element<0, tuple<Head, Tail...>>
+{
+   using type = Head;  ///< the type at the specified index
+};
+
+/**
+ * @brief Trait for checking if a type is a @p mfem::tuple
+ */
+template <typename T>
+struct is_tuple : std::false_type
+{
+};
+
+/// @overload
+template <typename... T>
+struct is_tuple<mfem::tuple<T...>> : std::true_type
+{
+};
+
+/**
+ * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
+ */
+template <typename T>
+struct is_tuple_of_tuples : std::false_type
+{
+};
+
+/**
+ * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
+ */
+template <typename... T>
+struct is_tuple_of_tuples<mfem::tuple<T...>>
+{
+   static constexpr bool value = (is_tuple<T>::value &&
+                                  ...);  ///< true/false result of type check
+};
+
+}  // namespace mfem

examples/dfem_dg.cpp

@@ -0,0 +1,123 @@
+#include "dfem/dfem_refactor.hpp"
+#include "fem/bilininteg.hpp"
+#include "fem/coefficient.hpp"
+#include "linalg/auxiliary.hpp"
+#include "linalg/hypre.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-square.mesh";
+   int polynomial_order = 1;
+   int ir_order = 2;
+   int refinements = 1;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   L2_FECollection fec(polynomial_order, dim, BasisType::GaussLobatto);
+   ParFiniteElementSpace fes(&mesh, &fec);
+
+   const IntegrationRule &ir = IntRules.Get(fes.GetFE(0)->GetGeomType(),
+                                            ir_order * fec.GetOrder());
+   const IntegrationRule &ir_face = IntRules.Get(
+                                       fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0))->GetGeomType(),
+                                       ir_order * fec.GetOrder());
+   ParGridFunction u(&fes);
+
+   // // -\nabla \cdot (\nabla u + p * I) -> (\nabla u + p * I, \nabla v)
+   // auto advection_kernel = [](const tensor<double, 2> &dudxi,
+   //                            const tensor<double, 2, 2> &J,
+   //                            const double &w)
+   // {
+   //    constexpr tensor<double, 2> b{1.0, 1.0};
+   //    return std::tuple{dot(b, dudxi * inv(J)) * det(J) * w};
+   // };
+
+   // std::tuple argument_operators_0{Gradient{"quantity"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   // std::tuple output_operator_0{Value{"quantity"}};
+   // ElementOperator op_0{advection_kernel, argument_operators_0, output_operator_0};
+
+   // std::array solutions{FieldDescriptor{&fes, "quantity"}};
+   // std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   // DifferentiableOperator advection_op{solutions, parameters, std::tuple{op_0}, mesh, ir};
+
+   // auto adv_du = advection_op.template GetDerivativeWrt<0>({&u}, {mesh_nodes});
+   // HypreParMatrix A;
+   // adv_du->Assemble(A);
+
+   // std::ofstream mmatofs("dfem_mat.dat");
+   // A.PrintMatlab(mmatofs);
+   // mmatofs.close();
+
+   auto trace_kernel = [](const double &uL, const double &uR, const double &J,
+                          const double &w)
+   {
+      return std::tuple{1.0 / J * w};
+   };
+
+   std::tuple argument_operators_0
+   {
+      FaceValueLeft{"quantity"},
+      FaceValueRight{"quantity"},
+      Gradient{"coordinates"},
+      Weight{"integration_weights"}
+   };
+   std::tuple output_operator_0{Value{"quantity"}};
+   FaceElementOperator op_0{trace_kernel, argument_operators_0, output_operator_0};
+
+   std::array solutions{FieldDescriptor{&fes, "quantity"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator trace_op{solutions, parameters, std::tuple{op_0}, mesh, ir_face};
+
+   auto vector_func = [](const Vector &, Vector &u)
+   {
+      u = 1.0;
+   };
+
+   VectorFunctionCoefficient vel_coeff(dim, vector_func);
+
+   ParBilinearForm adv_form(&fes);
+   constexpr double alpha = 1.0;
+   auto integ = new ConvectionIntegrator(vel_coeff, alpha);
+   integ->SetIntRule(&ir);
+   adv_form.AddInteriorFaceIntegrator(
+      new NonconservativeDGTraceIntegrator(vel_coeff, alpha));
+   // adv_form.AddDomainIntegrator(integ);
+   adv_form.Assemble();
+   adv_form.Finalize();
+
+   auto K = adv_form.ParallelAssemble();
+   std::ofstream kmatofs("mfem_mat.dat");
+   K->PrintMatlab(kmatofs);
+   kmatofs.close();
+
+   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" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_elasticity.cpp

@@ -0,0 +1,150 @@
+#include "dfem.hpp"
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+
+   std::cout << std::setprecision(9);
+
+   const char *mesh_file = "../data/star.mesh";
+   int polynomial_order = 1;
+   int refinements = 0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&polynomial_order, "-o", "--order", "");
+   args.AddOption(&refinements, "-r", "--r", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial(mesh_file, 1, 1);
+   mesh_serial.SetCurvature(1);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   const int dim = mesh_serial.Dimension();
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh_serial.Clear();
+
+   constexpr int vdim = 2;
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   std::cout << "nqpts = " << ir.GetNPoints() << std::endl;
+   std::cout << "ndofs = " << h1fes.GlobalTrueVSize() << std::endl;
+
+   ParGridFunction u(&h1fes);
+
+   auto exact_solution = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = x*x + y;
+      u(1) = x + 0.5*y*y;
+   };
+
+   VectorFunctionCoefficient exact_solution_coeff(dim, exact_solution);
+
+   auto elasticity_kernel = [](tensor<double, 2, 2> &dudxi,
+                               tensor<double, 2, 2> &J,
+                               double &w)
+   {
+      using mfem::internal::tensor;
+      using mfem::internal::IsotropicIdentity;
+
+      double lambda, mu;
+      {
+         lambda = 1.0;
+         mu = 1.0;
+      }
+      static constexpr auto I = IsotropicIdentity<2>();
+      auto eps = sym(dudxi * inv(J));
+      auto JxW = transpose(inv(J)) * det(J) * w;
+      auto r = (lambda * tr(eps) * I + 2.0 * mu * eps) * JxW;
+      return r;
+   };
+
+   tensor<double, 2, 2> dudxi, s_dudxi, J;
+   double w = 1.0;
+
+   enzyme::get<0>
+   (enzyme::autodiff<enzyme::Forward,
+    enzyme::DuplicatedNoNeed<tensor<double, 2, 2>>>
+    (+elasticity_kernel,
+     enzyme::Duplicated<tensor<double, 2, 2> *>(&dudxi, &s_dudxi),
+     enzyme::Const<tensor<double, 2, 2>*>(&J),
+     enzyme::Const<double*>(&w)));
+
+   // std::tuple input_descriptors = {Gradient{"displacement"}, Gradient{"coordinates"}, Weight{"integration_weight"}};
+   // std::tuple output_descriptors = {Gradient{"displacement"}};
+   // ElementOperator qf {elasticity_kernel, input_descriptors, output_descriptors};
+
+   // ElementOperator forcing_qf
+   // {
+   //    [](tensor<double, 2> x, tensor<double, 2, 2> J, double w)
+   //    {
+   //       double lambda, mu;
+   //       {
+   //          lambda = 1.0;
+   //          mu = 1.0;
+   //       }
+   //       auto f = x;
+   //       f(0) = 4.0*mu + 2.0*lambda;
+   //       f(1) = 2.0*mu + lambda;
+   //       return f * det(J) * w;
+   //    },
+   //    // inputs
+   //    std::tuple{
+   //       Value{"coordinates"},
+   //       Gradient{"coordinates"},
+   //       Weight{"integration_weight"}},
+   //    // outputs
+   //    std::tuple{
+   //       Value{"displacement"}}
+   // };
+
+   // std::vector<Field> solutions{{&u, "displacement"}};
+   // std::vector<Field> parameters{{mesh.GetNodes(), "coordinates"}};
+   // std::vector<Field> dependent_fields{{&u, "displacement"}};
+   // DifferentiableForm dop(solutions, parameters, dependent_fields, mesh);
+
+   // dop.AddElementOperator<AD::Enzyme>(qf, ir);
+   // dop.AddElementOperator<AD::None>(forcing_qf, ir);
+   // dop.SetEssentialTrueDofs(ess_tdof_list);
+
+   // GMRESSolver gmres(MPI_COMM_WORLD);
+   // gmres.SetRelTol(1e-12);
+   // gmres.SetMaxIter(5000);
+   // gmres.SetPrintLevel(IterativeSolver::PrintLevel().Summary());
+
+   // NewtonSolver newton(MPI_COMM_WORLD);
+   // newton.SetSolver(gmres);
+   // newton.SetOperator(dop);
+   // newton.SetRelTol(1e-12);
+   // newton.SetMaxIter(100);
+   // newton.SetPrintLevel(1);
+
+   // u = 1e-6;
+   // u.ProjectBdrCoefficient(exact_solution_coeff, ess_bdr);
+   // Vector x;
+   // u.GetTrueDofs(x);
+
+   // Vector zero;
+   // newton.Mult(zero, x);
+
+   // u.Distribute(x);
+
+   // std::cout << "|u-u_ex|_L2 = " << u.ComputeL2Error(exact_solution_coeff) << "\n";
+
+   return 0;
+}

examples/dfem_minimal_example.cpp

@@ -0,0 +1,115 @@
+#include <tuple>
+#include <type_traits>
+#include <iostream>
+#include <enzyme/enzyme>
+
+template <typename T>
+constexpr auto get_type_name() -> std::string_view
+{
+#if defined(__clang__)
+   constexpr auto prefix = std::string_view {"[T = "};
+   constexpr auto suffix = "]";
+   constexpr auto function = std::string_view{__PRETTY_FUNCTION__};
+#elif defined(__GNUC__)
+   constexpr auto prefix = std::string_view {"with T = "};
+   constexpr auto suffix = "; ";
+   constexpr auto function = std::string_view{__PRETTY_FUNCTION__};
+#elif defined(_MSC_VER)
+   constexpr auto prefix = std::string_view {"get_type_name<"};
+   constexpr auto suffix = ">(void)";
+   constexpr auto function = std::string_view{__FUNCSIG__};
+#else
+#error Unsupported compiler
+#endif
+
+   const auto start = function.find(prefix) + prefix.size();
+   const auto end = function.find(suffix);
+   const auto size = end - start;
+
+   return function.substr(start, size);
+}
+
+template <typename ... Ts>
+constexpr auto decay_types(std::tuple<Ts...> const &)
+-> std::tuple<std::remove_cv_t<std::remove_reference_t<Ts>>...>;
+
+template <typename T>
+using decay_tuple = decltype(decay_types(std::declval<T>()));
+
+template <class F> struct FunctionSignature;
+
+template <typename output_t, typename... input_ts>
+struct FunctionSignature<output_t(input_ts...)>
+{
+   using return_t = output_t;
+   using parameter_ts = std::tuple<input_ts...>;
+};
+
+template <class T> struct create_function_signature;
+
+template <typename output_t, typename T, typename... input_ts>
+struct create_function_signature<output_t (T::*)(input_ts...) const>
+{
+   using type = FunctionSignature<output_t(input_ts...)>;
+};
+
+template <typename arg_ts, std::size_t... Is>
+auto create_enzyme_args(arg_ts &args,
+                        arg_ts &shadow_args,
+                        std::index_sequence<Is...>)
+{
+   ((std::cout << std::get<Is>(shadow_args) << "\n"), ...);
+   return std::tuple<enzyme::Duplicated<decltype(std::get<Is>(args))>...>
+   {
+      { std::get<Is>(args), std::get<Is>(shadow_args) }...
+   };
+}
+
+template <typename kernel_t, typename arg_ts>
+auto fwddiff_apply_enzyme(kernel_t kernel, arg_ts &&args, arg_ts &&shadow_args)
+{
+   auto arg_indices =
+      std::make_index_sequence<std::tuple_size_v<std::remove_reference_t<arg_ts>>> {};
+
+   auto enzyme_args = create_enzyme_args(args, shadow_args, arg_indices);
+
+   using kf_return_t = typename create_function_signature<
+                       decltype(&kernel_t::operator())>::type::return_t;
+
+   std::cout << "args is " << get_type_name<decltype(args)>() << "\n\n";
+   std::cout << "enzyme_args type is " << get_type_name<decltype(enzyme_args)>() <<
+             "\n\n";
+   std::cout << "return type is " << get_type_name<decltype(kf_return_t{})>() <<
+             "\n\n";
+
+   return std::apply([&](auto &&...args)
+   {
+      return enzyme::get<0>(
+                enzyme::autodiff<enzyme::Forward>
+                (+kernel, args...));
+   },
+   enzyme_args);
+}
+
+int main()
+{
+
+   auto func = [](const double &x)
+   {
+      return x*x;
+   };
+
+   using kf_param_ts = typename create_function_signature<
+                       decltype(&decltype(func)::operator())>::type::parameter_ts;
+   using kf_output_t = typename create_function_signature<
+                       decltype(&decltype(func)::operator())>::type::return_t;
+   auto kernel_args = decay_tuple<kf_param_ts> {};
+   auto kernel_shadow_args = decay_tuple<kf_param_ts> {};
+
+   std::get<0>(kernel_args) = 3;
+   std::get<0>(kernel_shadow_args) = 1;
+   const auto res = fwddiff_apply_enzyme(func, kernel_args, kernel_shadow_args);
+   std::cout << res << " == 6\n";
+
+   return 0;
+}

examples/dfem_objective.cpp

@@ -0,0 +1,114 @@
+#include "dfem.hpp"
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+
+   std::cout << std::setprecision(9);
+
+   const char *mesh_file = "../data/star.mesh";
+   int polynomial_order = 1;
+   int refinements = 0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&polynomial_order, "-o", "--order", "");
+   args.AddOption(&refinements, "-r", "--r", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial(mesh_file, 1, 1);
+   mesh_serial.SetCurvature(1);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   const int dim = mesh_serial.Dimension();
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh_serial.Clear();
+
+   constexpr int vdim = 2;
+
+   // test_partial_assembly_setup_qf(mesh, 1, polynomial_order);
+   // exit(0);
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   std::cout << "nqpts = " << ir.GetNPoints() << std::endl;
+   std::cout << "ndofs = " << h1fes.GlobalTrueVSize() << std::endl;
+
+   ParGridFunction u(&h1fes);
+   ParGridFunction g(&h1fes);
+   ParGridFunction rho(&h1fes);
+
+   auto exact_solution = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = x*x + y;
+      u(1) = x + 0.5*y*y;
+   };
+
+   VectorFunctionCoefficient exact_solution_coeff(dim, exact_solution);
+
+   auto objective = [](tensor<double, 2> u, double rho,
+                       tensor<double, 2, 2> J,
+                       double w)
+   {
+      return sqnorm(u) * det(J) * w;
+   };
+
+   std::tuple inputs{Value{"displacement"}, Value{"density"}, Gradient{"coordinates"}, Weight{"integration_weight"}};
+   std::tuple outputs{ One{"integral"} };
+   ElementOperator objective_eop { objective, inputs, outputs };
+
+   std::vector<Field> solution_fields{{&u, "displacement"}};
+   std::vector<Field> parameter_fields{{mesh.GetNodes(), "coordinates"}, {&rho, "density"}};
+   std::vector<Field> dependent_variables{{&u, "displacement"}};
+   DifferentiableForm dop(solution_fields, parameter_fields, dependent_variables,
+                          mesh);
+
+   dop.AddElementOperator(objective_eop, ir);
+
+   u.ProjectCoefficient(exact_solution_coeff);
+   Vector zero;
+
+   Vector y(1);
+   Vector utdof;
+   u.GetTrueDofs(utdof);
+   dop.Mult(utdof, y);
+
+   // finite difference test
+   Vector dgdu(u.Size());
+   Vector fx(y);
+   out << "g: ";
+   print_vector(fx);
+   out << "\n";
+
+   for (int i = 0; i < u.Size(); i++)
+   {
+      double h = 1e-6;
+      u(i) += h;
+      dop.Mult(u, y);
+      u(i) -= h;
+      y -= fx;
+      y /= h;
+      dgdu(i) = y(0);
+   }
+
+   out << "dgdu: ";
+   print_vector(dgdu);
+
+   // Vector dgdu = dop.GetGradientWrt({&u, "displacement"});
+
+   return 0;
+}

examples/dfem_plaplacian.cpp

@@ -0,0 +1,138 @@
+#include "dfem.hpp"
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+
+   std::cout << std::setprecision(9);
+
+   const char *mesh_file = "../data/star.mesh";
+   int polynomial_order = 1;
+   int refinements = 0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&polynomial_order, "-o", "--order", "");
+   args.AddOption(&refinements, "-r", "--r", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial(mesh_file, 1, 1);
+   mesh_serial.SetCurvature(1);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   const int dim = mesh_serial.Dimension();
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh_serial.Clear();
+
+   constexpr int vdim = 1;
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   std::cout << "nqpts = " << ir.GetNPoints() << std::endl;
+   std::cout << "ndofs = " << h1fes.GlobalTrueVSize() << std::endl;
+
+   ParGridFunction u(&h1fes);
+
+   auto exact_solution = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      // PRESENT
+      return pow(x,2) + 0.5*x*pow(y,2);
+   };
+
+   FunctionCoefficient exact_solution_coeff(exact_solution);
+
+   auto plaplacian = [](double u,
+                        tensor<double, 2> dudxi,
+                        tensor<double, 2, 2> J,
+                        double w)
+   {
+      using mfem::internal::tensor;
+      auto dudx = dudxi * inv(J);
+      auto JxW = transpose(inv(J)) * det(J) * w;
+      // PRESENT: Implement (1+u^2) * ∇u
+      return (1.0 + u*u) * dudx * JxW;
+   };
+
+   // PRESENT: Implement descriptors
+   std::tuple input_descriptors = {Value{"potential"}, Gradient{"potential"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   // PRESENT: Implement descriptors
+   std::tuple output_descriptors = {Gradient{"potential"}};
+
+   ElementOperator qf {plaplacian, input_descriptors, output_descriptors};
+
+   ElementOperator forcing_qf
+   {
+      [](tensor<double, 2> coords, tensor<double, 2, 2> J, double w)
+      {
+         int p = 2;
+         double x = coords(0);
+         double y = coords(1);
+         // *INDENT-OFF*
+         double mathematica_please_help_me = 2.*pow(x,2)*pow(y,2)*(pow(x,2) + 0.5*x*pow(y,2)) + 2*pow(2*x + 0.5*pow(y,2),2)*(pow(x,2) + 0.5*x*pow(y,2)) + 2*(1 + pow(pow(x,2) + 0.5*x*pow(y,2),2)) + 1.*x*(1 + pow(pow(x,2) + 0.5*x*pow(y,2),2));
+         return mathematica_please_help_me * det(J) * w;
+        // *INDENT-ON*
+      },
+      // inputs
+      std::tuple{
+         Value{"coordinates"},
+         Gradient{"coordinates"},
+         Weight{"integration_weight"}},
+      // outputs
+      std::tuple{
+         Value{"potential"}}
+   };
+
+   std::tuple list_of_qfs{qf_1, qf_2, qf_n};
+
+   std::vector<Field> solutions{{&u, "potential"}};
+   std::vector<Field> parameters{{mesh.GetNodes(), "coordinates"}};
+   DifferentiableForm dop(solutions, parameters, mesh);
+   dop.SetEssentialTrueDofs(ess_tdof_list);
+
+   auto R = dop.GetResidual(list_of_qfs, ir);
+   auto Jacobian_aka_dRdu = dop.GetDerivative<0>(list_of_qfs, ir);
+
+   // R(u) = (\grad u, \grad v) + (f, v)
+   // dop.AddElementOperator<AD::Enzyme>(qf, ir);
+   // dop.AddElementOperator<AD::None>(forcing_qf, ir);
+
+   GMRESSolver gmres(MPI_COMM_WORLD);
+   gmres.SetRelTol(1e-12);
+   gmres.SetMaxIter(5000);
+   gmres.SetPrintLevel(IterativeSolver::PrintLevel().Summary());
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetSolver(gmres);
+   newton.SetOperator(dop);
+   newton.SetRelTol(1e-12);
+   newton.SetMaxIter(100);
+   newton.SetPrintLevel(1);
+
+   u = 1e-6;
+   u.ProjectBdrCoefficient(exact_solution_coeff, ess_bdr);
+   Vector x;
+   u.GetTrueDofs(x);
+
+   Vector zero;
+   newton.Mult(zero, x);
+
+   u.Distribute(x);
+
+   std::cout << "|u-u_ex|_L2 = " << u.ComputeL2Error(exact_solution_coeff) << "\n";
+
+   return 0;
+}

examples/dfem_poisson.cpp

@@ -0,0 +1,192 @@
+#include "dfem/dfem_refactor.hpp"
+#include "linalg/hypre.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+template <typename diffusion_t, typename force_t>
+class DiffusionOperator : public Operator
+{
+   template <typename diffusion_du_t>
+   class DiffusionJacobianOperator : public Operator
+   {
+   public:
+      DiffusionJacobianOperator(const DiffusionOperator *diffusion,
+                                std::shared_ptr<diffusion_du_t> diff_du) :
+         Operator(diffusion->Height()), s(diffusion)
+      {
+         diff_du->Assemble(A);
+         A.EliminateBC(s->ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         A.Mult(x, y);
+      }
+
+      const DiffusionOperator *s;
+      HypreParMatrix A;
+   };
+
+public:
+   DiffusionOperator(diffusion_t &diffusion, force_t &force,
+                     Array<int> &ess_tdofs) :
+      Operator(diffusion.Height()), diffusion(diffusion),
+      force(force), ess_tdofs(ess_tdofs), f(force.Height()) {}
+
+   void SetParameters(ParGridFunction &mesh_nodes)
+   {
+      diffusion.SetParameters({&mesh_nodes});
+      force.SetParameters({&mesh_nodes});
+
+      Vector zero;
+
+      this->mesh_nodes.SetSpace(mesh_nodes.ParFESpace());
+      this->mesh_nodes = mesh_nodes;
+   }
+
+   void Mult(const Vector &x, Vector &r) const override
+   {
+      diffusion.Mult(x, r);
+      force.Mult(x, f);
+      r -= f;
+      r.SetSubVector(ess_tdofs, 0.0);
+   }
+
+   Operator &GetGradient(const Vector &x) const override
+   {
+      ParGridFunction u(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&diffusion.solutions[0].data)));
+      u.SetFromTrueDofs(x);
+
+      auto dfdu = diffusion.template GetDerivativeWrt<0>({&u}, {&mesh_nodes});
+      dfdu->Assemble(A);
+      A.EliminateBC(ess_tdofs, DiagonalPolicy::DIAG_ONE);
+      return A;
+      // delete jacobian_operator;
+      // jacobian_operator = new
+      // DiffusionJacobianOperator<typename std::remove_pointer<decltype(dfdu.get())>::type>
+      // (this, dfdu);
+      // return *jacobian_operator;
+   }
+
+   diffusion_t &diffusion;
+   force_t &force;
+
+   const Array<int> ess_tdofs;
+   mutable Vector f;
+
+   mutable ParGridFunction mesh_nodes;
+
+   mutable Operator *jacobian_operator = nullptr;
+   mutable HypreParMatrix A;
+};
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-square.mesh";
+   int polynomial_order = 2;
+   int ir_order = 2;
+   int refinements = 4;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection potential_fec(polynomial_order, dim);
+   ParFiniteElementSpace potential_fes(&mesh, &potential_fec);
+
+   const IntegrationRule &potential_ir =
+      IntRules.Get(potential_fes.GetFE(0)->GetGeomType(),
+                   ir_order * potential_fec.GetOrder());
+
+   Array<int> bdr_attr_is_ess(mesh.bdr_attributes.Max());
+   bdr_attr_is_ess = 1;
+   Array<int> ess_tdofs;
+   potential_fes.GetEssentialTrueDofs(bdr_attr_is_ess, ess_tdofs);
+
+   ParGridFunction u(&potential_fes);
+   u = 0.0;
+
+   auto diffusion_kernel = [](const internal::dual<double, double> &u,
+                              const tensor<internal::dual<double, double>, 2> &dudxi,
+                              const tensor<double, 2, 2> &J,
+                              const double &w)
+   {
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      return std::tuple{(1.0 + u * u) * dudx * det(J) * w * transpose(invJ)};
+   };
+
+   std::tuple argument_operators_0{Value{"potential"}, Gradient{"potential"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator_0{Gradient{"potential"}};
+   ElementOperator op_0{diffusion_kernel, argument_operators_0, output_operator_0};
+
+   auto force_kernel = [](const tensor<double, 2, 2> &J,
+                          const double &w)
+   {
+      return std::tuple{1.0 * det(J) * w};
+   };
+   std::tuple argument_operators_1{Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator_1{Value{"potential"}};
+   ElementOperator op_1{force_kernel, argument_operators_1, output_operator_1};
+
+   std::array solutions{FieldDescriptor{&potential_fes, "potential"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator diffusion_op{solutions, parameters, std::tuple{op_0}, mesh, potential_ir};
+   DifferentiableOperator force_op{solutions, parameters, std::tuple{op_1}, mesh, potential_ir};
+
+   DiffusionOperator diffusion(diffusion_op, force_op, ess_tdofs);
+
+   diffusion.SetParameters({*mesh_nodes});
+
+   HypreBoomerAMG amg;
+   amg.SetPrintLevel(0);
+
+   CGSolver solver(MPI_COMM_WORLD);
+   solver.SetAbsTol(1e-12);
+   solver.SetRelTol(1e-12);
+   solver.SetMaxIter(500);
+   solver.SetPrintLevel(2);
+   solver.SetPreconditioner(amg);
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetOperator(diffusion);
+   newton.SetSolver(solver);
+   newton.SetRelTol(1e-8);
+   newton.SetMaxIter(10);
+   newton.SetPrintLevel(1);
+
+   Vector zero;
+   Vector x(potential_fes.GetTrueVSize());
+   u.ParallelProject(x);
+   newton.Mult(zero, x);
+
+   u.SetFromTrueDofs(x);
+
+   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" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_refactor.cpp

@@ -0,0 +1,102 @@
+#include "mfem.hpp"
+#include "dfem/dfem_refactor.hpp"
+
+using namespace mfem;
+
+auto main(int argc, char *argv[]) -> int
+{
+   Mpi::Init();
+
+   std::cout << std::setprecision(9);
+
+   const char *mesh_file = "../data/star.mesh";
+   int polynomial_order = 1;
+   int refinements = 0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&polynomial_order, "-o", "--order", "");
+   args.AddOption(&refinements, "-r", "--r", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial(mesh_file, 1, 1);
+   mesh_serial.SetCurvature(1);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   const int dim = mesh_serial.Dimension();
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   constexpr int vdim = 1;
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   std::cout << "nqpts = " << ir.GetNPoints() << std::endl;
+   std::cout << "ndofs = " << h1fes.GlobalTrueVSize() << std::endl;
+
+   ParGridFunction u(&h1fes);
+
+   auto exact_solution = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      return 2.345 + x + y;
+   };
+
+   FunctionCoefficient exact_solution_coeff(exact_solution);
+
+   u.ProjectCoefficient(exact_solution_coeff);
+
+   auto domain_qf = [](const double &u,
+                       const tensor<double, 2, 2> &J,
+                       const double &w)
+   {
+      out << u << "\n" << J << "\n" << w << "\n\n";
+      return std::tuple{u * det(J) * w};
+   };
+
+   std::tuple input_descriptors = {Value{"potential"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_descriptors = {Value{"potential"}};
+   ElementOperator eop{domain_qf, input_descriptors, output_descriptors};
+
+   auto ops = std::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+   DifferentiableOperator dop{solutions, parameters, ops, mesh, ir};
+
+   Vector x(h1fes.GetTrueVSize()), y(h1fes.GetTrueVSize());
+
+   u.GetTrueDofs(x);
+
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   // Derivative wrt "potential", indicated by the index 0 of the set {solutions} \cup {parameters}
+   auto dFd0 = dop.GetDerivativeWrt<0>({&u}, {mesh_nodes});
+   dFd0->Mult(x, y);
+
+   Vector dFd0_vec;
+   dFd0->Assemble(dFd0_vec);
+
+   // Derivative wrt "coordinates", indicated by the index 1 of the set {solutions} \cup {parameters}
+   auto dFd1 = dop.GetDerivativeWrt<1>({&u}, {mesh_nodes});
+   dFd1->Mult(x, y);
+
+   return 0;
+}

examples/dfem_stokes.cpp

@@ -0,0 +1,302 @@
+#include "dfem/dfem.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+template <typename momentum_t, typename mass_conservation_t>
+class NavierStokesOperator : public Operator
+{
+   template <typename momentum_du_t, typename momentum_dp_t>
+   class NavierStokesJacobianOperator : public Operator
+   {
+   public:
+      NavierStokesJacobianOperator(const NavierStokesOperator *ns,
+                                   std::shared_ptr<momentum_du_t> mom_du,
+                                   std::shared_ptr<momentum_dp_t> mom_dp) :
+         Operator(ns->Height()), ns(ns), block_op(ns->block_offsets)
+      {
+         mom_du->Assemble(A);
+         A.EliminateBC(ns->vel_ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+
+         mom_dp->Assemble(D);
+         D.EliminateRows(ns->vel_ess_tdofs);
+
+         Dt = new TransposeOperator(D);
+
+         block_op.SetBlock(0, 0, &A);
+         block_op.SetBlock(0, 1, &D);
+         block_op.SetBlock(1, 0, Dt);
+         // std::ofstream amatofs("dfem_mat.dat");
+         // block_op.PrintMatlab(amatofs);
+         // amatofs.close();
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         block_op.Mult(x, y);
+      }
+
+      ~NavierStokesJacobianOperator()
+      {
+         delete Dt;
+      }
+
+      const NavierStokesOperator *ns = nullptr;
+      HypreParMatrix A, D;
+      TransposeOperator *Dt = nullptr;
+      BlockOperator block_op;
+   };
+
+public:
+   NavierStokesOperator(momentum_t &momentum,
+                        mass_conservation_t &mass_conservation,
+                        Array<int> &offsets, Array<int> &vel_ess_tdofs) :
+      Operator(offsets.Last()), momentum(momentum),
+      mass_conservation(mass_conservation),
+      block_offsets(offsets), vel_ess_tdofs(vel_ess_tdofs) {}
+
+   void SetParameters(ParGridFunction &mesh_nodes)
+   {
+      momentum.SetParameters({&mesh_nodes});
+      mass_conservation.SetParameters({&mesh_nodes});
+      this->mesh_nodes.SetSpace(mesh_nodes.ParFESpace());
+      this->mesh_nodes = mesh_nodes;
+   }
+
+   void Mult(const Vector &x, Vector &r) const override
+   {
+      Vector ru(r.ReadWrite() + block_offsets[0],
+                block_offsets[1] - block_offsets[0]);
+      Vector rp(r.ReadWrite() + block_offsets[1],
+                block_offsets[2] - block_offsets[1]);
+
+      momentum.Mult(x, ru);
+
+      mass_conservation.Mult(x, rp);
+
+      ru.SetSubVector(vel_ess_tdofs, 0.0);
+   }
+
+   Operator &GetGradient(const Vector &x) const override
+   {
+      xtmp = x;
+      BlockVector xb(xtmp.ReadWrite(), block_offsets);
+
+      ParGridFunction u(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&momentum.solutions[0].data)));
+      ParGridFunction p(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&momentum.solutions[1].data)));
+      u.SetFromTrueDofs(xb.GetBlock(0));
+      p.SetFromTrueDofs(xb.GetBlock(1));
+      auto mom_du = momentum.template GetDerivativeWrt<0>({&u, &p}, {&mesh_nodes});
+      auto mom_dp = momentum.template GetDerivativeWrt<1>({&u, &p}, {&mesh_nodes});
+      delete jacobian_operator;
+      jacobian_operator = new NavierStokesJacobianOperator<
+      typename std::remove_pointer<decltype(mom_du.get())>::type,
+      typename std::remove_pointer<decltype(mom_dp.get())>::type>(this, mom_du,
+                                                                  mom_dp);
+      return *jacobian_operator;
+   }
+
+   momentum_t &momentum;
+   mass_conservation_t &mass_conservation;
+
+   const Array<int> block_offsets;
+   const Array<int> vel_ess_tdofs;
+   mutable Vector xtmp;
+
+   mutable ParGridFunction mesh_nodes;
+
+   mutable Operator *jacobian_operator = nullptr;
+};
+
+double reynolds = 10.0;
+
+int main(int argc, char *argv[])
+{
+   constexpr int dim = 3;
+   constexpr int vdim = dim;
+
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-cube.mesh";
+   int polynomial_order = 2;
+   int ir_order = 2;
+   int refinements = 2;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&refinements, "-r", "--refinements", "");
+   args.AddOption(&reynolds, "-rey", "--reynolds", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection velocity_fec(polynomial_order, dim);
+   ParFiniteElementSpace velocity_fes(&mesh, &velocity_fec, dim);
+
+   H1_FECollection pressure_fec(polynomial_order - 1, dim);
+   ParFiniteElementSpace pressure_fes(&mesh, &pressure_fec);
+
+   const IntegrationRule &velocity_ir =
+      IntRules.Get(velocity_fes.GetFE(0)->GetGeomType(),
+                   ir_order * velocity_fec.GetOrder());
+
+   const IntegrationRule &pressure_ir =
+      IntRules.Get(pressure_fes.GetFE(0)->GetGeomType(),
+                   ir_order * pressure_fec.GetOrder());
+
+   Array<int> bdr_attr_is_ess(mesh.bdr_attributes.Max());
+   bdr_attr_is_ess = 1;
+   Array<int> vel_ess_tdofs;
+   velocity_fes.GetEssentialTrueDofs(bdr_attr_is_ess, vel_ess_tdofs);
+
+   ParGridFunction u(&velocity_fes);
+   ParGridFunction p(&pressure_fes);
+
+   auto u_f = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double z = coords(2);
+      if (z >= 1.0)
+      {
+         u(0) = 1.0;
+      }
+      else
+      {
+         u(0) = 0.0;
+      }
+      u(1) = 0.0;
+      u(2) = 0.0;
+   };
+   auto u_coef = VectorFunctionCoefficient(dim, u_f);
+
+   u.ProjectCoefficient(u_coef);
+   p = 0.0;
+
+   // -\nabla \cdot (\nabla u + p * I) -> (\nabla u + p * I, \nabla v)
+   auto momentum_kernel = [](const tensor<double, dim> &u,
+                             const tensor<double, dim, dim> &dudxi,
+                             const double &p,
+                             const tensor<double, dim, dim> &J,
+                             const double &w)
+   {
+      static constexpr auto I = mfem::internal::IsotropicIdentity<dim>();
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      double Re = reynolds;
+      return mfem::tuple{(outer(u, u) - 1.0 / Re * dudx + p * I) * det(J) * w * transpose(invJ)};
+   };
+
+   mfem::tuple argument_operators_0{Value{"velocity"}, Gradient{"velocity"}, Value{"pressure"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator_0{Gradient{"velocity"}};
+   ElementOperator op_0{momentum_kernel, argument_operators_0, output_operator_0};
+
+   // (\nabla \cdot u, q)
+   auto mass_conservation_kernel = [](const tensor<double, dim, dim> &dudxi,
+                                      const tensor<double, dim, dim> &J,
+                                      const double &w)
+   {
+      return mfem::tuple{tr(dudxi * inv(J)) * det(J) * w};
+   };
+
+   mfem::tuple argument_operators_1{Gradient{"velocity"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator_1{Value{"pressure"}};
+   ElementOperator op_1{mass_conservation_kernel, argument_operators_1, output_operator_1};
+
+   std::array solutions{FieldDescriptor{&velocity_fes, "velocity"}, FieldDescriptor{&pressure_fes, "pressure"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator momentum_op{solutions, parameters, mfem::tuple{op_0}, mesh, velocity_ir};
+   DifferentiableOperator mass_conservation_op{solutions, parameters, mfem::tuple{op_1}, mesh, pressure_ir};
+
+   // Preconditioner form
+   auto pressure_mass_kernel = [](const double &p,
+                                  const tensor<double, dim, dim> &J,
+                                  const double &w)
+   {
+      return mfem::tuple{p * det(J) * w};
+   };
+
+   mfem::tuple pms_args{Value{"pressure"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple pms_outs{Value{"pressure"}};
+   ElementOperator pressure_mass{pressure_mass_kernel, pms_args, pms_outs};
+   std::array pms_sols{FieldDescriptor{&pressure_fes, "pressure"}};
+   std::array pms_params{FieldDescriptor{&mesh_fes, "coordinates"}};
+   DifferentiableOperator pressure_mass_op{pms_sols, pms_params, mfem::tuple{pressure_mass}, mesh, pressure_ir};
+
+   Array<int> block_offsets(3);
+   block_offsets[0] = 0;
+   block_offsets[1] = velocity_fes.GetTrueVSize();
+   block_offsets[2] = pressure_fes.GetTrueVSize();
+   block_offsets.PartialSum();
+
+   NavierStokesOperator navierstokes(momentum_op, mass_conservation_op,
+                                     block_offsets,
+                                     vel_ess_tdofs);
+
+   BlockVector x(block_offsets), y(block_offsets);
+   u.ParallelProject(x.GetBlock(0));
+   // p.ParallelProject(x.GetBlock(1));
+   navierstokes.SetParameters(*mesh_nodes);
+
+   HypreParMatrix A;
+   momentum_op.template GetDerivativeWrt<0>({&u, &p}, {mesh_nodes})->Assemble(A);
+   A.EliminateBC(vel_ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+   HypreBoomerAMG amg(A);
+   amg.SetMaxLevels(50);
+   amg.SetPrintLevel(0);
+
+   HypreParMatrix Mp;
+   pressure_mass_op.template GetDerivativeWrt<0>({&p}, {mesh_nodes})->Assemble(Mp);
+
+   HypreDiagScale Mp_inv(Mp);
+
+   BlockDiagonalPreconditioner prec(block_offsets);
+   prec.SetDiagonalBlock(0, &amg);
+   prec.SetDiagonalBlock(1, &Mp_inv);
+
+   GMRESSolver solver(MPI_COMM_WORLD);
+   solver.SetAbsTol(0.0);
+   solver.SetRelTol(1e-8);
+   solver.SetKDim(100);
+   solver.SetMaxIter(500);
+   solver.SetPrintLevel(2);
+   solver.SetPreconditioner(prec);
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetOperator(navierstokes);
+   newton.SetSolver(solver);
+   newton.SetRelTol(1e-8);
+   newton.SetMaxIter(50);
+   newton.SetPrintLevel(1);
+
+   Vector zero;
+   newton.Mult(zero, x);
+
+   u.SetFromTrueDofs(x.GetBlock(0));
+
+   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" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_test_diffusion_2d.cpp

@@ -0,0 +1,174 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_diffusion(
+   std::string mesh_file, int refinements, int polynomial_order)
+{
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == 2, "incorrect mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   out << "#el: " << mesh.GetNE() << "\n";
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction*>(mesh.GetNodes());
+   ParFiniteElementSpace& mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   out << "#dofs " << h1fes.GetTrueVSize() << "\n";
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder());
+
+   out << "#qp: " << ir.GetNPoints() << "\n";
+
+   ParGridFunction f1_g(&h1fes);
+   ParGridFunction rho_g(&h1fes);
+
+   auto kernel = [] MFEM_HOST_DEVICE(const tensor<double, 2, 2>& J,
+                                     const double& w, const tensor<double, 2>& dudxi)
+   {
+      auto invJ = inv(J);
+      return mfem::tuple{dudxi * invJ * transpose(invJ) * det(J) * w};
+   };
+
+   mfem::tuple argument_operators =
+   {
+      Gradient{"coordinates"}, Weight{}, Gradient{"potential"}
+   };
+   mfem::tuple output_operator = {Gradient{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector& coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      return 2.345 + 0.25 * x * x * y + y * y * x;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+   y.HostRead();
+
+   ParBilinearForm a(&h1fes);
+   a.AddDomainIntegrator(new DiffusionIntegrator);
+   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   a.Assemble();
+   a.Finalize();
+
+   Vector y2(h1fes.TrueVSize());
+   a.Mult(x, y2);
+   y2.HostRead();
+   Vector diff(y2);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(y2);
+      print_vector(y);
+      return 1;
+   }
+
+   // // Test linearization here as well
+   // auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {mesh_nodes});
+
+   // if (dFdu->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdu unexpected height of " << dFdu->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdu->Mult(x, y);
+   // y.HostRead();
+   // a.Mult(x, y2);
+   // y2.HostRead();
+
+   // diff = y2;
+   // diff -= y;
+   // if (diff.Norml2() > 1e-10)
+   // {
+   //    print_vector(diff);
+   //    print_vector(y2);
+   //    print_vector(y);
+   //    return 1;
+   // }
+
+   // // fd jacobian test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(x), xpv(x), xmv(x), fxpv(x.Size()), fxmv(x.Size());
+   //    v *= eps;
+   //    xpv += v;
+   //    xmv -= v;
+   //    dop.Mult(xpv, fxpv);
+   //    dop.Mult(xmv, fxmv);
+   //    fxpv -= fxmv;
+   //    fxpv /= (2.0*eps);
+
+   //    fxpv -= y;
+   //    if (fxpv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << fxpv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   // f1_g.ProjectCoefficient(f1_c);
+   // rho_g.ProjectCoefficient(rho_c);
+   // auto dFdrho = dop.GetDerivativeWrt<1>({&f1_g}, {&rho_g, mesh_nodes});
+   // if (dFdrho->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdrho unexpected height of " << dFdrho->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdrho->Mult(rho_g, y);
+
+   // // fd test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(rho_g), rhopv(rho_g), rhomv(rho_g), frhopv(x.Size()),
+   //    frhomv(x.Size()); v *= eps; rhopv += v; rhomv -= v;
+   //    dop.SetParameters({&rhopv, mesh_nodes});
+   //    dop.Mult(x, frhopv);
+   //    dop.SetParameters({&rhomv, mesh_nodes});
+   //    dop.Mult(x, frhomv);
+   //    frhopv -= frhomv;
+   //    frhopv /= (2.0*eps);
+
+   //    frhopv -= y;
+   //    if (frhopv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << frhopv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_diffusion);

examples/dfem_test_diffusion_3d.cpp

@@ -0,0 +1,296 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "examples/dfem/dfem_parametricspace.hpp"
+#include "fem/bilininteg.hpp"
+#include "general/tic_toc.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+using mfem::internal::dual;
+
+int test_diffusion_3d(
+   std::string mesh_file, int refinements, int polynomial_order)
+{
+   constexpr int num_samples = 10;
+   constexpr int dim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "incorrect mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(polynomial_order);
+   mesh_serial.Clear();
+
+   out << "#el: " << mesh.GetNE() << "\n";
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction*>(mesh.GetNodes());
+   ParFiniteElementSpace& mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+
+   out << "#dofs " << h1fes.GetTrueVSize() << "\n";
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(),
+                   h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(
+                      0)->GetDim() - 1);
+
+   printf("#ndof per el = %d\n", h1fes.GetFE(0)->GetDof());
+   printf("#nqp = %d\n", ir.GetNPoints());
+   printf("#q1d = %d\n", (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5));
+
+   ParametricSpace qdata_space(dim, dim * dim, ir.GetNPoints(),
+                               dim * dim * ir.GetNPoints() * mesh.GetNE());
+   ParametricFunction qdata(qdata_space);
+
+   ParGridFunction f1_g(&h1fes);
+   ParGridFunction rho_g(&h1fes);
+
+   auto f1 = [](const Vector& coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + x + x*y + 1.25 * z*x;
+   };
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(h1fes.GetTrueVSize());
+   {
+      auto diffusion_mf_kernel =
+         [] MFEM_HOST_DEVICE (
+            const tensor<dual<real_t, real_t>, dim>& dudxi,
+            const tensor<double, dim, dim>& J,
+            const double& w)
+      {
+         auto invJ = inv(J);
+         return mfem::tuple{dudxi * invJ * transpose(invJ) * det(J) * w};
+      };
+
+      mfem::tuple argument_operators = {Gradient{"potential"}, Gradient{"coordinates"}, Weight{}};
+      mfem::tuple output_operator = {Gradient{"potential"}};
+
+      ElementOperator eop = {diffusion_mf_kernel, argument_operators, output_operator};
+      auto ops = mfem::tuple{eop};
+
+      auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+      auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+      DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+      dop.SetParameters({mesh_nodes});
+      StopWatch sw;
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         dop.Mult(x, y);
+      }
+      sw.Stop();
+      printf("dfem mf:       %fs\n", sw.RealTime() / num_samples);
+      y.HostRead();
+   }
+
+   {
+      auto diffusion_setup_kernel =
+         [] MFEM_HOST_DEVICE (
+            const tensor<double, dim, dim>& J,
+            const double& w)
+      {
+         auto invJ = inv(J);
+         return mfem::tuple{invJ * transpose(invJ) * det(J) * w};
+      };
+
+      mfem::tuple argument_operators = {Gradient{"coordinates"}, Weight{}};
+      mfem::tuple output_operator = {None{"qdata"}};
+
+      ElementOperator eop = {diffusion_setup_kernel, argument_operators, output_operator};
+      auto ops = mfem::tuple{eop};
+
+      auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+      auto parameters = std::array
+      {
+         FieldDescriptor{&mesh_fes, "coordinates"},
+         FieldDescriptor{&qdata_space, "qdata"}};
+
+      DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+      dop.SetParameters({mesh_nodes, &qdata});
+      StopWatch sw;
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         dop.Mult(x, qdata);
+      }
+      sw.Stop();
+      printf("dfem pa setup: %fs\n", sw.RealTime() / num_samples);
+      qdata.HostRead();
+   }
+
+   // printf("qdata: ");
+   // print_vector(qdata);
+
+   {
+      auto diffusion_apply_kernel =
+         [] MFEM_HOST_DEVICE (
+            const tensor<dual<real_t, real_t>, dim>& dudxi,
+            const tensor<double, dim, dim>& qdata)
+      {
+         return mfem::tuple{dudxi * qdata};
+      };
+
+      mfem::tuple argument_operators = {Gradient{"potential"}, None{"qdata"}};
+      mfem::tuple output_operator = {Gradient{"potential"}};
+
+      ElementOperator eop = {diffusion_apply_kernel, argument_operators, output_operator};
+      auto ops = mfem::tuple{eop};
+
+      auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+      auto parameters = std::array{FieldDescriptor{&qdata_space, "qdata"}};
+
+      DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+      dop.SetParameters({&qdata});
+      StopWatch sw;
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         dop.Mult(x, y);
+      }
+      sw.Stop();
+      printf("dfem pa apply: %fs\n", sw.RealTime() / num_samples);
+      y.HostRead();
+   }
+
+   // printf("y: ");
+   // print_vector(y);
+
+   Vector y2(h1fes.TrueVSize());
+   {
+      ParBilinearForm a(&h1fes);
+      auto diff_integ = new DiffusionIntegrator;
+      diff_integ->SetIntRule(&ir);
+      a.AddDomainIntegrator(diff_integ);
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+
+      OperatorPtr A;
+      StopWatch sw;
+      sw.Start();
+      a.Assemble();
+      a.Finalize();
+      Array<int> empty;
+      a.FormSystemMatrix(empty, A);
+      sw.Stop();
+      printf("mfem pa setup: %fs\n", sw.RealTime());
+
+      sw.Clear();
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         A->Mult(x, y2);
+      }
+      sw.Stop();
+      printf("mfem pa apply: %fs\n", sw.RealTime() / num_samples);
+      y2.HostRead();
+   }
+   // printf("y2: ");
+   // print_vector(y2);
+
+   Vector diff(y2);
+   diff -= y;
+   if (diff.Norml2() > 1e-15)
+   {
+      // printf("y ");
+      // print_vector(y);
+      // printf("y2: ");
+      // print_vector(y2);
+      // printf("diff: ");
+      // print_vector(diff);
+      return 1;
+   }
+
+   // Test linearization here as well
+   // auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {mesh_nodes});
+
+   // if (dFdu->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdu unexpected height of " << dFdu->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdu->Mult(x, y);
+   // y.HostRead();
+   // a.Mult(x, y2);
+   // y2.HostRead();
+
+   // diff = y2;
+   // diff -= y;
+   // if (diff.Norml2() > 1e-10)
+   // {
+   //    print_vector(diff);
+   //    print_vector(y2);
+   //    print_vector(y);
+   //    return 1;
+   // }
+
+   // // fd jacobian test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(x), xpv(x), xmv(x), fxpv(x.Size()), fxmv(x.Size());
+   //    v *= eps;
+   //    xpv += v;
+   //    xmv -= v;
+   //    dop.Mult(xpv, fxpv);
+   //    dop.Mult(xmv, fxmv);
+   //    fxpv -= fxmv;
+   //    fxpv /= (2.0*eps);
+
+   //    fxpv -= y;
+   //    if (fxpv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << fxpv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   // f1_g.ProjectCoefficient(f1_c);
+   // rho_g.ProjectCoefficient(rho_c);
+   // auto dFdrho = dop.GetDerivativeWrt<1>({&f1_g}, {&rho_g, mesh_nodes});
+   // if (dFdrho->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdrho unexpected height of " << dFdrho->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdrho->Mult(rho_g, y);
+
+   // // fd test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(rho_g), rhopv(rho_g), rhomv(rho_g), frhopv(x.Size()),
+   //    frhomv(x.Size()); v *= eps; rhopv += v; rhomv -= v;
+   //    dop.SetParameters({&rhopv, mesh_nodes});
+   //    dop.Mult(x, frhopv);
+   //    dop.SetParameters({&rhomv, mesh_nodes});
+   //    dop.Mult(x, frhomv);
+   //    frhopv -= frhomv;
+   //    frhopv /= (2.0*eps);
+
+   //    frhopv -= y;
+   //    if (frhopv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << frhopv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_diffusion_3d);

examples/dfem_test_diffusion_3d_refactor.cpp

@@ -0,0 +1,309 @@
+#include "dfem/dfem_test_macro.hpp"
+#include "examples/dfem/dfem_fieldoperator.hpp"
+#include "examples/dfem/dfem_refactor.hpp"
+#include "fem/bilininteg.hpp"
+#include "general/tic_toc.hpp"
+#include <utility>
+
+using namespace mfem;
+using mfem::internal::tensor;
+using mfem::internal::dual;
+
+int test_diffusion_3d(
+   std::string mesh_file, int refinements, int polynomial_order)
+{
+   constexpr int num_samples = 100;
+   constexpr int dim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "incorrect mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(polynomial_order);
+   mesh_serial.Clear();
+
+   out << "#el: " << mesh.GetNE() << "\n";
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction*>(mesh.GetNodes());
+   ParFiniteElementSpace& mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   out << "#dofs " << h1fes.GetTrueVSize() << "\n";
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(),
+                   h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(
+                      0)->GetDim() - 1);
+
+   printf("#ndof per el = %d\n", h1fes.GetFE(0)->GetDof());
+   printf("#nqp = %d\n", ir.GetNPoints());
+   printf("#q1d = %d\n", (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5));
+
+   ParametricSpace qdata_space(dim, dim * dim, ir.GetNPoints(),
+                               dim * dim * ir.GetNPoints() * mesh.GetNE());
+   ParametricFunction qdata(qdata_space);
+
+   ParGridFunction f1_g(&h1fes);
+   ParGridFunction rho_g(&h1fes);
+
+   auto f1 = [](const Vector& coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + x + x*y + 1.25 * z*x;
+   };
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(h1fes.GetTrueVSize());
+   {
+      std::shared_ptr<DerivativeOperator> dpotential;
+      {
+         auto diffusion_mf_kernel =
+            [] MFEM_HOST_DEVICE (
+               const tensor<real_t, dim>& dudxi,
+               const tensor<real_t, dim, dim>& J,
+               const real_t& w)
+         {
+            auto invJ = inv(J);
+            return mfem::tuple{dudxi * invJ * transpose(invJ) * det(J) * w};
+         };
+
+         constexpr int Potential = 0;
+         constexpr int Coordinates = 1;
+
+         auto input_operators = mfem::tuple{Gradient<Potential>{}, Gradient<Coordinates>{}, Weight{}};
+         auto output_operator = mfem::tuple{Gradient<Potential>{}};
+
+         auto solutions = std::vector{FieldDescriptor{Potential, &h1fes}};
+         auto parameters = std::vector{FieldDescriptor{Coordinates, &mesh_fes}};
+
+         DifferentiableOperator dop(solutions, parameters, mesh);
+         auto derivatives = std::integer_sequence<size_t, Potential> {};
+         dop.AddDomainIntegrator(
+            diffusion_mf_kernel, input_operators, output_operator, ir, derivatives);
+
+         dop.SetParameters({mesh_nodes});
+         StopWatch sw;
+         sw.Start();
+         for (int i = 0; i < num_samples; i++)
+         {
+            dop.Mult(x, y);
+         }
+         sw.Stop();
+         printf("dfem mf:       %fs\n", sw.RealTime() / num_samples);
+         y.HostRead();
+
+         dpotential = dop.GetDerivative(Potential, {&f1_g}, {mesh_nodes});
+      }
+      dpotential->Mult(x, y);
+   }
+
+   {
+      auto diffusion_setup_kernel =
+         [] MFEM_HOST_DEVICE (
+            const tensor<double, dim, dim>& J,
+            const double& w)
+      {
+         auto invJ = inv(J);
+         return mfem::tuple{invJ * transpose(invJ) * det(J) * w};
+      };
+
+      constexpr int Potential = 0;
+      constexpr int Coordinates = 1;
+      constexpr int QData = 2;
+
+      auto input_operators = mfem::tuple{Gradient<Coordinates>{}, Weight{}};
+      auto output_operator = mfem::tuple{None<QData>{}};
+
+      auto solutions = std::vector{FieldDescriptor{Potential, &h1fes}};
+      auto parameters = std::vector{FieldDescriptor{Coordinates, &mesh_fes},
+                                    FieldDescriptor{QData, &qdata_space}};
+
+      DifferentiableOperator dop(solutions, parameters, mesh);
+      dop.AddDomainIntegrator(
+         diffusion_setup_kernel, input_operators, output_operator, ir);
+
+      dop.SetParameters({mesh_nodes, &qdata});
+      StopWatch sw;
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         dop.Mult(x, qdata);
+      }
+      sw.Stop();
+      printf("dfem pa setup: %fs\n", sw.RealTime() / num_samples);
+      qdata.HostRead();
+   }
+
+   // printf("qdata: ");
+   // print_vector(qdata);
+
+   {
+      auto diffusion_apply_kernel =
+         [] MFEM_HOST_DEVICE (
+            const tensor<real_t, dim>& dudxi,
+            const tensor<double, dim, dim>& qdata)
+      {
+         return mfem::tuple{dudxi * qdata};
+      };
+
+      constexpr int Potential = 0;
+      constexpr int QData = 1;
+
+      auto input_operators = mfem::tuple{Gradient<Potential>{}, None<QData>{}};
+      auto output_operator = mfem::tuple{Gradient<Potential>{}};
+
+      auto solutions = std::vector{FieldDescriptor{Potential, &h1fes}};
+      auto parameters = std::vector{FieldDescriptor{QData, &qdata_space}};
+
+      DifferentiableOperator dop(solutions, parameters, mesh);
+      dop.AddDomainIntegrator(
+         diffusion_apply_kernel, input_operators, output_operator, ir);
+
+      dop.SetParameters({&qdata});
+      StopWatch sw;
+      sw.Start();
+      for (int i = 0; i < num_samples; i++)
+      {
+         dop.Mult(x, y);
+      }
+      sw.Stop();
+      printf("dfem pa apply: %fs\n", sw.RealTime() / num_samples);
+      y.HostRead();
+   }
+
+   // printf("y: ");
+   // print_vector(y);
+
+   Vector y2(h1fes.TrueVSize());
+   {
+      ParBilinearForm a(&h1fes);
+      auto diff_integ = new DiffusionIntegrator;
+      diff_integ->SetIntRule(&ir);
+      a.AddDomainIntegrator(diff_integ);
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+
+      OperatorPtr A;
+      StopWatch sw;
+      sw.Start();
+      a.Assemble();
+      a.Finalize();
+      Array<int> empty;
+      a.FormSystemMatrix(empty, A);
+      sw.Stop();
+      printf("mfem pa setup: %fs\n", sw.RealTime());
+
+      sw.Clear();
+      sw.Start();
+      y2 = 0.0;
+      for (int i = 0; i < num_samples; i++)
+      {
+         A->Mult(x, y2);
+      }
+      sw.Stop();
+      printf("mfem pa apply: %fs\n", sw.RealTime() / num_samples);
+      y2.HostRead();
+   }
+   // printf("y2: ");
+   // print_vector(y2);
+
+   Vector diff(y2);
+   diff -= y;
+   if (diff.Norml2() > 1e-15)
+   {
+      printf("y: ");
+      print_vector(y);
+      printf("y2: ");
+      print_vector(y2);
+      printf("diff: ");
+      print_vector(diff);
+      return 1;
+   }
+
+   // Test linearization here as well
+   // auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {mesh_nodes});
+
+   // if (dFdu->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdu unexpected height of " << dFdu->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdu->Mult(x, y);
+   // y.HostRead();
+   // a.Mult(x, y2);
+   // y2.HostRead();
+
+   // diff = y2;
+   // diff -= y;
+   // if (diff.Norml2() > 1e-10)
+   // {
+   //    print_vector(diff);
+   //    print_vector(y2);
+   //    print_vector(y);
+   //    return 1;
+   // }
+
+   // // fd jacobian test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(x), xpv(x), xmv(x), fxpv(x.Size()), fxmv(x.Size());
+   //    v *= eps;
+   //    xpv += v;
+   //    xmv -= v;
+   //    dop.Mult(xpv, fxpv);
+   //    dop.Mult(xmv, fxmv);
+   //    fxpv -= fxmv;
+   //    fxpv /= (2.0*eps);
+
+   //    fxpv -= y;
+   //    if (fxpv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << fxpv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   // f1_g.ProjectCoefficient(f1_c);
+   // rho_g.ProjectCoefficient(rho_c);
+   // auto dFdrho = dop.GetDerivativeWrt<1>({&f1_g}, {&rho_g, mesh_nodes});
+   // if (dFdrho->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdrho unexpected height of " << dFdrho->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdrho->Mult(rho_g, y);
+
+   // // fd test
+   // {
+   //    double eps = 1.0e-6;
+   //    Vector v(rho_g), rhopv(rho_g), rhomv(rho_g), frhopv(x.Size()),
+   //    frhomv(x.Size()); v *= eps; rhopv += v; rhomv -= v;
+   //    dop.SetParameters({&rhopv, mesh_nodes});
+   //    dop.Mult(x, frhopv);
+   //    dop.SetParameters({&rhomv, mesh_nodes});
+   //    dop.Mult(x, frhomv);
+   //    frhopv -= frhomv;
+   //    frhopv /= (2.0*eps);
+
+   //    frhopv -= y;
+   //    if (frhopv.Norml2() > eps)
+   //    {
+   //       out << "||dFdu_FD u^* - ex||_l2 = " << frhopv.Norml2() << "\n";
+   //       return 1;
+   //    }
+   // }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_diffusion_3d);

examples/dfem_test_elasticity.cpp

@@ -0,0 +1,109 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_elasticity(std::string mesh_file,
+                    int refinements,
+                    int polynomial_order)
+{
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   const int vdim = dim;
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   Array<int> ess_tdof;
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 6 * h1fec.GetOrder());
+
+   out << "#qp: " << ir.GetNPoints() << "\n";
+   out << "#dof_el: " << h1fes.GetRestrictionMatrix()->Height() / mesh.GetNE() <<
+       "\n";
+
+   ParGridFunction u(&h1fes);
+
+   auto f1 = [](const Vector& coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = 2.345 + 0.25 * x * x * y + y * y * x;
+      u(1) = 2.345 - 0.25 * x * y * y + y * x * x;
+   };
+
+   VectorFunctionCoefficient u_c(dim, f1);
+   u.ProjectCoefficient(u_c);
+
+   ConstantCoefficient l_coeff(0.5), m_coeff(0.25);
+
+   ParBilinearForm A_form(&h1fes);
+   auto A_integ = new ElasticityIntegrator(l_coeff, m_coeff);
+   A_integ->SetIntegrationRule(ir);
+   A_form.AddDomainIntegrator(A_integ);
+   A_form.Assemble();
+   A_form.Finalize();
+
+   auto elasticity_kernel = [](const tensor<double, 2, 2> &dudxi,
+                               const tensor<double, 2, 2> &J,
+                               const double &w)
+   {
+      constexpr double lambda = 0.5;
+      constexpr double mu = 0.25;
+      static constexpr auto I = mfem::internal::IsotropicIdentity<2>();
+      auto invJ = inv(J);
+      auto eps = sym(dudxi * invJ);
+      return mfem::tuple{transpose(lambda * tr(eps) * I + 2.0 * mu * eps) * det(J) * w * transpose(invJ)};
+   };
+
+   mfem::tuple argument_operators{Gradient{"displacement"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator{Gradient{"displacement"}};
+
+   ElementOperator op{elasticity_kernel, argument_operators, output_operator};
+
+   std::array solutions{FieldDescriptor{&h1fes, "displacement"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop{solutions, parameters, mfem::tuple{op}, mesh, ir};
+
+   Vector x(u), y1(h1fes.GetTrueVSize()),
+          y2(h1fes.GetTrueVSize());
+
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y1);
+   y1.HostRead();
+
+   A_form.Mult(x, y2);
+   y2.HostRead();
+
+   Vector diff(y2);
+   diff -= y1;
+   if (diff.Norml2() > 1e-10)
+   {
+      out << "||F(u) - ex||_l2 = " << diff.Norml2() << "\n";
+      print_vector(diff);
+      print_vector(y1);
+      print_vector(y2);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_elasticity);

examples/dfem_test_interpolate_gradient_linear_scalar_3d.cpp

@@ -0,0 +1,115 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "examples/dfem/dfem_parametricspace.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_interpolate_gradient_linear_scalar_3d(std::string mesh_file,
+                                               int refinements,
+                                               int polynomial_order)
+{
+   constexpr int dim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "wrong mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction *mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   // const IntegrationRule &ir =
+   //    IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+   IntegrationRules gll_rules(0, Quadrature1D::GaussLobatto);
+   const IntegrationRule &ir = gll_rules.Get(h1fes.GetFE(0)->GetGeomType(),
+                                             2 * polynomial_order - 1);
+
+   ParGridFunction f1_g(&h1fes);
+
+   ParametricSpace pspace(dim, dim, ir.GetNPoints(),
+                          dim * ir.GetNPoints() * mesh.GetNE());
+   ParametricFunction qdata(pspace);
+
+   auto kernel = [](const tensor<double, dim> &dudxi,
+                    const tensor<double, dim, dim> &J)
+   {
+      return mfem::tuple{dudxi * inv(J)};
+   };
+
+   mfem::tuple argument_operators = {Gradient{"potential"}, Gradient{"coordinates"}};
+   mfem::tuple output_operator = {None{"qdata"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array
+   {
+      FieldDescriptor{&mesh_fes, "coordinates"},
+      FieldDescriptor{&pspace, "qdata"}
+   };
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + x * y * z + y * z;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(*f1_g.GetTrueDofs()), y(h1fes.TrueVSize() * dim);
+   dop.SetParameters({mesh_nodes, &qdata});
+   dop.Mult(x, y);
+
+   Vector f_test(h1fes.GetElementRestriction(
+                    ElementDofOrdering::LEXICOGRAPHIC)->Height() * dim);
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+
+      for (int qp = 0; qp < ir.GetNPoints(); qp++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(qp);
+         T->SetIntPoint(&ip);
+
+         Vector g(dim);
+         f1_g.GetGradient(*T, g);
+         // printf("(%f, %f, %f): (%f, %f, %f)\n", ip.x, ip.y, ip.z,  g(0), g(1), g(2));
+         for (int d = 0; d < dim; d++)
+         {
+            int qpo = qp * dim;
+            int eo = e * (ir.GetNPoints() * dim);
+            f_test(d + qpo + eo) = g(d);
+         }
+      }
+   }
+
+   Vector diff(f_test);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(f_test);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_interpolate_gradient_linear_scalar_3d);

examples/dfem_test_interpolate_linear_scalar.cpp

@@ -0,0 +1,91 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_interpolate_linear_scalar(std::string mesh_file,
+                                   int refinements,
+                                   int polynomial_order)
+{
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const double &u, const tensor<double, 2, 2> &J,
+                    const double &w)
+   {
+      return mfem::tuple{u};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator = {None{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      return 2.345 + x + y;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(*f1_g.GetTrueDofs()), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   Vector f_test(h1fes.GetElementRestriction(
+                    ElementDofOrdering::LEXICOGRAPHIC)->Height());
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      for (int qp = 0; qp < ir.GetNPoints(); qp++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(qp);
+         T->SetIntPoint(&ip);
+
+         f_test((e * ir.GetNPoints()) + qp) = f1_c.Eval(*T, ip);
+      }
+   }
+
+   Vector diff(f_test);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(f_test);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_interpolate_linear_scalar);

examples/dfem_test_interpolate_linear_scalar_3d.cpp

@@ -0,0 +1,93 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_interpolate_linear_scalar_3d(std::string mesh_file,
+                                      int refinements,
+                                      int polynomial_order)
+{
+   constexpr int dim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "wrong mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction *mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const double &u)
+   {
+      return mfem::tuple{u};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}};
+   mfem::tuple output_operator = {None{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + x + y + 1.25 * z;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(*f1_g.GetTrueDofs()), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   Vector f_test(h1fes.GetElementRestriction(
+                    ElementDofOrdering::LEXICOGRAPHIC)->Height());
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      for (int qp = 0; qp < ir.GetNPoints(); qp++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(qp);
+         T->SetIntPoint(&ip);
+
+         f_test((e * ir.GetNPoints()) + qp) = f1_c.Eval(*T, ip);
+      }
+   }
+
+   Vector diff(f_test);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(f_test);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_interpolate_linear_scalar_3d);

examples/dfem_test_interpolate_linear_vector.cpp

@@ -0,0 +1,100 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_interpolate_linear_vector(std::string mesh_file, int refinements,
+                                   int polynomial_order)
+{
+   constexpr int vdim = 2;
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   QuadratureSpace qspace(mesh, ir);
+   QuadratureFunction qf(&qspace, vdim);
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const tensor<double, 2> &u)
+   {
+      return mfem::tuple{u};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}};
+   mfem::tuple output_operator = {None{"potential"}};
+
+   ElementOperator eop{kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = 2.345 + x + y;
+      u(1) = 12.345 + x + y;
+   };
+
+   VectorFunctionCoefficient f1_c(vdim, f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(f1_g.Size());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   Vector f_test(qf.Size());
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      for (int qp = 0; qp < ir.GetNPoints(); qp++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(qp);
+         T->SetIntPoint(&ip);
+
+         Vector f(vdim);
+         f1_g.GetVectorValue(*T, ip, f);
+         for (int d = 0; d < vdim; d++)
+         {
+            int qpo = qp * vdim;
+            int eo = e * (ir.GetNPoints() * vdim);
+            f_test(d + qpo + eo) = f(d);
+         }
+      }
+   }
+
+   Vector diff(f_test);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(f_test);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_interpolate_linear_vector);

examples/dfem_test_interpolate_linear_vector_3d.cpp

@@ -0,0 +1,105 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_interpolate_linear_vector_3d(std::string mesh_file, int refinements,
+                                      int polynomial_order)
+{
+
+   constexpr int dim = 3;
+   constexpr int vdim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "wrong mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   QuadratureSpace qspace(mesh, ir);
+   QuadratureFunction qf(&qspace, vdim);
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const tensor<double, vdim> &u)
+   {
+      return mfem::tuple{u};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}};
+   mfem::tuple output_operator = {None{"potential"}};
+
+   ElementOperator eop{kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      u(0) = 2.345 + x + y + 3.0 * z;
+      u(1) = 12.345 + x + y + 2.0 * z;
+      u(2) = 5.345 + x + y + 1.0 * z;
+   };
+
+   VectorFunctionCoefficient f1_c(vdim, f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(f1_g.Size());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   Vector f_test(qf.Size());
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      ElementTransformation *T = mesh.GetElementTransformation(e);
+      for (int qp = 0; qp < ir.GetNPoints(); qp++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(qp);
+         T->SetIntPoint(&ip);
+
+         Vector f(vdim);
+         f1_g.GetVectorValue(*T, ip, f);
+         for (int d = 0; d < vdim; d++)
+         {
+            int qpo = qp * vdim;
+            int eo = e * (ir.GetNPoints() * vdim);
+            f_test(d + qpo + eo) = f(d);
+         }
+      }
+   }
+
+   Vector diff(f_test);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(f_test);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_interpolate_linear_vector_3d);

examples/dfem_test_mass_scalar_2d.cpp

@@ -0,0 +1,113 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "fem/bilininteg.hpp"
+#include "fem/normal_deriv_restriction.hpp"
+#include <fstream>
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int dfem_test_mass_scalar_2d(std::string mesh_file,
+                             int refinements,
+                             int polynomial_order)
+{
+   constexpr int dim = 2;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "wrong mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction *mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() + 1);
+
+   // IntegrationRules gll_rules(0, Quadrature1D::GaussLobatto);
+   // const IntegrationRule &ir = gll_rules.Get(h1fes.GetFE(0)->GetGeomType(),
+   //                                           2 * polynomial_order - 1);
+
+   printf("#nqp = %d\n", ir.GetNPoints());
+   printf("#q1d = %d\n", (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5));
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const double& u,
+                    const tensor<double, dim> x,
+                    const tensor<double, dim, dim> J,
+                    const double& w)
+   {
+      out << x << ": " << u << "\n";
+      return mfem::tuple{u * w * det(J)};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}, Value{"coordinates"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator = {Value{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      return 2.345 + x + x*y + 1.25 * x;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector f1_g_e(f1_g.Size());
+   auto R = h1fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC);
+   // R->Mult(f1_g, f1_g_e);
+   auto r_out = std::ofstream("r_mat.mtx");
+   R->PrintMatlab(r_out);
+   r_out.close();
+   print_vector(f1_g);
+   // print_vector(f1_g_e);
+
+   Vector x(*f1_g.GetTrueDofs()), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   ParBilinearForm a(&h1fes);
+   auto mass_integ = new MassIntegrator;
+   mass_integ->SetIntRule(&ir);
+   a.AddDomainIntegrator(mass_integ);
+   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   a.Assemble();
+   a.Finalize();
+
+   Vector y2(h1fes.TrueVSize());
+   a.Mult(x, y2);
+   y2.HostRead();
+
+   Vector diff(y2);
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      print_vector(diff);
+      print_vector(y2);
+      print_vector(y);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(dfem_test_mass_scalar_2d);

examples/dfem_test_mass_scalar_3d.cpp

@@ -0,0 +1,147 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "fem/bilininteg.hpp"
+#include "fem/fe/fe_base.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int dfem_test_mass_scalar_3d(std::string mesh_file,
+                             int refinements,
+                             int polynomial_order)
+{
+   constexpr int dim = 3;
+   Mesh mesh_serial = Mesh(mesh_file);
+   MFEM_ASSERT(mesh_serial.Dimension() == dim, "wrong mesh dimension");
+
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(polynomial_order);
+   mesh_serial.Clear();
+
+   ParGridFunction *mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(),
+                   h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(
+                      0)->GetDim() - 1);
+
+   // IntegrationRules gll_rules(0, Quadrature1D::GaussLobatto);
+   // const IntegrationRule &ir = gll_rules.Get(h1fes.GetFE(0)->GetGeomType(),
+   //                                           2 * polynomial_order - 1);
+
+   auto dtq = h1fes.GetFE(0)->GetDofToQuad(ir, DofToQuad::TENSOR);
+   // printf("\n B: ");
+   // dtq.B.Print(out, dtq.B.Size());
+   // printf("\n G: ");
+   // dtq.G.Print(out, dtq.G.Size());
+   // printf("\n w: ");
+   // ir.GetWeights().Print(out, ir.GetWeights().Size());
+
+   // printf("#ndof per el = %d\n", h1fes.GetFE(0)->GetDof());
+   // printf("#nqp = %d\n", ir.GetNPoints());
+   // printf("#q1d = %d\n", (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5));
+
+   // printf("nodes: ");
+   // print_vector(*mesh_nodes);
+
+   ParGridFunction f1_g(&h1fes);
+
+   auto kernel = [](const double &u,
+                    const tensor<double, dim, dim> &J,
+                    const double &w)
+   {
+      return mfem::tuple{u * det(J) * w};
+   };
+
+   mfem::tuple argument_operators = {Value{"potential"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator = {Value{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + x + x*y + 1.25 * z*x;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+   // printf("\nf1_g: ");
+   // print_vector(f1_g);
+
+   auto R = h1fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC);
+   // Vector f1_g_e(R->Height());
+   // R->Mult(f1_g, f1_g_e);
+   // printf("\nf1_g_e: ");
+   // print_vector(f1_g_e);
+   // auto r_out = std::ofstream("r_mat.mtx");
+   // R->PrintMatlab(r_out);
+   // r_out.close();
+
+   Vector x(*f1_g.GetTrueDofs()), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   ParBilinearForm a(&h1fes);
+   auto mass_integ = new MassIntegrator;
+   mass_integ->SetIntRule(&ir);
+   a.AddDomainIntegrator(mass_integ);
+   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   a.Assemble();
+   a.Finalize();
+
+   Vector y2(h1fes.TrueVSize());
+   a.Mult(x, y2);
+   y2.HostRead();
+
+   Vector diff(y2);
+   diff -= y;
+   if (diff.Norml2() > 1e-15)
+   {
+      printf("y ");
+      print_vector(y);
+      printf("y2: ");
+      print_vector(y2);
+      printf("diff: ");
+      print_vector(diff);
+      return 1;
+   }
+
+   Vector y3(h1fes.TrueVSize());
+   auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {mesh_nodes});
+
+   dFdu->Mult(x, y3);
+   diff = y2;
+   diff -= y;
+   if (diff.Norml2() > 1e-15)
+   {
+      printf("y2 ");
+      print_vector(y2);
+      printf("y3: ");
+      print_vector(y3);
+      printf("diff: ");
+      print_vector(diff);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(dfem_test_mass_scalar_3d);

examples/dfem_test_neo_hookean_elasticity_2d.cpp

@@ -0,0 +1,114 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_neo_hookean_elasticity_2d(
+   std::string mesh_file, int refinements, int polynomial_order)
+{
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   MFEM_ASSERT(dim == 2, "This test is for 2D meshes only");
+   mesh_serial.Clear();
+
+   out << "#el: " << mesh.GetNE() << "\n";
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction*>(mesh.GetNodes());
+   ParFiniteElementSpace& mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, dim);
+
+   out << "#dofs " << h1fes.GetTrueVSize() << "\n";
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder());
+
+   out << "#qp: " << ir.GetNPoints() << "\n";
+
+   ParGridFunction u_g(&h1fes);
+
+   auto kernel = [] MFEM_HOST_DEVICE(const tensor<double, 2, 2>& J,
+                                     const double& w,
+                                     const tensor<double, 2, 2>& dudxi)
+   {
+      // Neo-Hookean parameters
+      const double lambda = 1.0;
+      const double mu = 0.5;
+
+      static constexpr auto I = mfem::internal::IsotropicIdentity<2>();
+      auto F = I + (dudxi * inv(J));
+      auto E = 0.5 * (transpose(F) * F - I);
+      auto invF = inv(F);
+
+      // 2D plane strain formulation
+      auto P = mu * (F - transpose(invF)) + lambda * log(det(F)) * transpose(invF);
+
+      return mfem::tuple{P * det(J) * w};
+   };
+
+   mfem::tuple argument_operators = {Gradient{"coordinates"}, Weight{},
+                                     Gradient{"displacement"}
+                                    };
+   mfem::tuple output_operator = {Gradient{"displacement"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "displacement"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto displacement = [](const Vector& coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = 0.1 * x * y;
+      u(1) = 0.1 * y * x;
+   };
+
+   VectorFunctionCoefficient disp_coeff(2, displacement);
+   u_g.ProjectCoefficient(disp_coeff);
+
+   Vector x(u_g), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+   y.HostRead();
+
+   // Test linearization
+   auto dFdu = dop.GetDerivativeWrt<0>({&u_g}, {mesh_nodes});
+   dFdu->Mult(x, y);
+
+   // Finite difference Jacobian test
+   {
+      double eps = 1.0e-6;
+      Vector v(x), xpv(x), xmv(x), fxpv(x.Size()), fxmv(x.Size());
+      v *= eps;
+      xpv += v;
+      xmv -= v;
+      dop.Mult(xpv, fxpv);
+      dop.Mult(xmv, fxmv);
+      fxpv -= fxmv;
+      fxpv /= (2.0*eps);
+
+      fxpv -= y;
+      if (fxpv.Norml2() > eps)
+      {
+         out << "||dFdu_FD u^* - ex||_l2 = " << fxpv.Norml2() << "\n";
+         return 1;
+      }
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_neo_hookean_elasticity_2d);

examples/dfem_test_nonlinear_diffusion_3d.cpp

@@ -0,0 +1,169 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_nonlinear_diffusion(
+   std::string mesh_file, int refinements, int polynomial_order)
+{
+   constexpr int dim = 3;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   out << "#el: " << mesh.GetNE() << "\n";
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction*>(mesh.GetNodes());
+   ParFiniteElementSpace& mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec);
+
+   out << "#dofs " << h1fes.GetTrueVSize() << "\n";
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(),
+                   h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(
+                      0)->GetDim() - 1);
+
+   out << "#qp: " << ir.GetNPoints() << "\n";
+
+   ParGridFunction f1_g(&h1fes);
+
+   bool inactive_derivative = false;
+
+   auto kernel = [] MFEM_HOST_DEVICE(
+                    const tensor<double, dim, dim>& J,
+                    const double& w,
+                    const tensor<double, dim>& dudxi,
+                    const double& u)
+   {
+      auto invJ = inv(J);
+      return mfem::tuple{(u * u) * dudxi * invJ * transpose(invJ) * det(J) * w};
+   };
+
+   mfem::tuple argument_operators =
+   {
+      Gradient{"coordinates"},
+      Weight{},
+      Gradient{"potential"},
+      Value{"potential"}
+   };
+
+   mfem::tuple output_operator =
+   {
+      Gradient{"potential"}
+   };
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = mfem::tuple{eop};
+
+   auto solutions = std::array
+   {
+      FieldDescriptor{&h1fes, "potential"}
+   };
+   auto parameters = std::array
+   {
+      FieldDescriptor{&mesh_fes, "coordinates"}
+   };
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   auto f1 = [](const Vector& coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      const double z = coords(2);
+      return 2.345 + 0.25 * x * x * y + y * y * x + z;
+   };
+
+   FunctionCoefficient f1_c(f1);
+   f1_g.ProjectCoefficient(f1_c);
+
+   Vector x(f1_g), y(h1fes.TrueVSize());
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+   y.HostRead();
+
+   ParBilinearForm a(&h1fes);
+   GridFunctionCoefficient f1gc(&f1_g);
+   TransformedCoefficient tf_c(&f1gc, [](double f) { return f * f; });
+   a.AddDomainIntegrator(new DiffusionIntegrator(tf_c));
+   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   a.Assemble();
+   a.Finalize();
+
+   Vector y2(h1fes.TrueVSize()), diff(h1fes.TrueVSize());
+   a.Mult(x, y2);
+   y2.HostRead();
+   diff = y2;
+   diff -= y;
+   if (diff.Norml2() > 1e-10)
+   {
+      out << "||F(u) - ex||_l2 = " << diff.Norml2() << "\n";
+      print_vector(diff);
+      print_vector(y);
+      print_vector(y2);
+      return 1;
+   }
+
+   // Test linearization here as well
+   auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {mesh_nodes});
+   dFdu->Mult(x, y);
+
+   // fd jacobian test
+   {
+      double eps = 1.0e-6;
+      Vector v(x), xpv(x), xmv(x), fxpv(x.Size()), fxmv(x.Size());
+      v *= eps;
+      xpv += v;
+      xmv -= v;
+      dop.Mult(xpv, fxpv);
+      dop.Mult(xmv, fxmv);
+      fxpv -= fxmv;
+      fxpv /= (2.0*eps);
+
+      fxpv -= y;
+      if (fxpv.Norml2() > eps)
+      {
+         out << "||dFdu_FD u^* - ex||_l2 = " << fxpv.Norml2() << "\n";
+         return 1;
+      }
+   }
+
+   // ParBilinearForm da(&h1fes);
+   // TransformedCoefficient dtf_c(&f1gc, [](double f) { return 2.0 * f; });
+   // da.AddDomainIntegrator(new DiffusionIntegrator(dtf_c));
+   // da.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   // da.Assemble();
+   // da.Finalize();
+
+   // if (dFdu->Height() != h1fes.GetTrueVSize())
+   // {
+   //    out << "dFdu unexpected height of " << dFdu->Height() << "\n";
+   //    return 1;
+   // }
+
+   // dFdu->Mult(x, y);
+   // print_vector(y);
+   // da.Mult(x, y2);
+   // print_vector(y2);
+   // y2 -= y;
+   // out << "||dFdu x - A x||_l2 = " << y2.Norml2() << "\n";
+   // if (y2.Norml2() > 1e-10)
+   // {
+   //    out << "||dFdu u^* - ex||_l2 = " << y2.Norml2() << "\n";
+   // }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_nonlinear_diffusion);

examples/dfem_test_nonlinear_elasticity_3d.cpp

@@ -0,0 +1,267 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include <fstream>
+
+using namespace mfem;
+using mfem::internal::tensor;
+using mfem::internal::dual;
+
+class FDJacobian : public Operator
+{
+public:
+   FDJacobian(const Operator &op, const Vector &x) :
+      Operator(op.Height()),
+      op(op),
+      x(x)
+   {
+      f.SetSize(Height());
+      xpev.SetSize(Height());
+      op.Mult(x, f);
+      xnorm = x.Norml2();
+   }
+
+   void Mult(const Vector &v, Vector &y) const override
+   {
+      x.HostRead();
+
+      // See [1] for choice of eps.
+      //
+      // [1] Woodward, C.S., Gardner, D.J. and Evans, K.J., 2015. On the use of
+      // finite difference matrix-vector products in Newton-Krylov solvers for
+      // implicit climate dynamics with spectral elements. Procedia Computer
+      // Science, 51, pp.2036-2045.
+      real_t eps = lambda * (lambda + xnorm / v.Norml2());
+
+      for (int i = 0; i < x.Size(); i++)
+      {
+         xpev(i) = x(i) + eps * v(i);
+      }
+
+      // y = f(x + eps * v)
+      op.Mult(xpev, y);
+
+      // y = (f(x + eps * v) - f(x)) / eps
+      for (int i = 0; i < x.Size(); i++)
+      {
+         y(i) = (y(i) - f(i)) / eps;
+      }
+   }
+
+   virtual MemoryClass GetMemoryClass() const override
+   {
+      return Device::GetDeviceMemoryClass();
+   }
+
+private:
+   const Operator &op;
+   Vector x, f;
+   mutable Vector xpev;
+   real_t lambda = 1.0e-6;
+   real_t xnorm;
+};
+
+template <typename elasticity_t>
+class ElasticityOperator : public Operator
+{
+   template <typename elasticity_du_t>
+   class ElasticityJacobianOperator : public Operator
+   {
+   public:
+      ElasticityJacobianOperator(const ElasticityOperator *elasticity,
+                                 std::shared_ptr<elasticity_du_t> dRdu) :
+         Operator(elasticity->Height()),
+         elasticity(elasticity),
+         dRdu(dRdu),
+         x_ess(dRdu->Height())
+      {
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         x_ess = x;
+         x_ess.SetSubVector(elasticity->ess_tdofs, 0.0);
+
+         dRdu->Mult(x_ess, y);
+
+         for (int i = 0; i < elasticity->ess_tdofs.Size(); i++)
+         {
+            y[elasticity->ess_tdofs[i]] = x[elasticity->ess_tdofs[i]];
+         }
+      }
+
+      const ElasticityOperator *elasticity = nullptr;
+      std::shared_ptr<elasticity_du_t> dRdu;
+      mutable Vector x_ess;
+   };
+
+public:
+   ElasticityOperator(ParFiniteElementSpace &fes, elasticity_t &elasticity,
+                      Array<int> &ess_tdofs) :
+      Operator(fes.GetTrueVSize()),
+      fes(fes),
+      elasticity(elasticity),
+      ess_tdofs(ess_tdofs) {}
+
+   void Mult(const Vector &x, Vector &r) const override
+   {
+      elasticity.Mult(x, r);
+      r.SetSubVector(ess_tdofs, 0.0);
+   }
+
+   Operator &GetGradient(const Vector &x) const override
+   {
+      ParGridFunction u(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&elasticity.solutions[0].data)));
+
+      u.SetFromTrueDofs(x);
+      auto dRdu = elasticity.template GetDerivativeWrt<0>({&u}, {mesh_nodes});
+
+      jacobian.reset(
+         new ElasticityJacobianOperator<
+         typename std::remove_pointer<decltype(dRdu.get())>::type> (this, dRdu));
+
+      // jacobian.reset(new FDJacobian(*this, x));
+
+      return *jacobian;
+   }
+
+   void SetParameters(ParGridFunction &mesh_nodes)
+   {
+      elasticity.SetParameters({&mesh_nodes});
+      this->mesh_nodes = &mesh_nodes;
+   }
+
+   ParFiniteElementSpace &fes;
+   elasticity_t &elasticity;
+   Array<int> ess_tdofs;
+   mutable ParGridFunction *mesh_nodes = nullptr;
+   mutable std::shared_ptr<Operator> jacobian;
+};
+
+int test_nonlinear_elasticity_3d(std::string mesh_file,
+                                 int refinements,
+                                 int polynomial_order)
+{
+   constexpr int dim = 3;
+   constexpr int vdim = dim;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(polynomial_order);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_tdof_list, ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 0;
+   ess_bdr[0] = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   const IntegrationRule& ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(),
+                   h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(0)->GetOrder() + h1fes.GetFE(
+                      0)->GetDim() - 1);
+
+   out << "#qp: " << ir.GetNPoints() << "\n";
+   out << "#dof: " << h1fes.GetNDofs() << "\n";
+
+   ParGridFunction u(&h1fes);
+
+   auto elasticity_kernel = [] MFEM_HOST_DEVICE
+                            (const tensor<dual<real_t, real_t>, dim, dim> &dudxi,
+                             const tensor<real_t, dim, dim> &J,
+                             const real_t &w)
+   {
+      // shear modulus
+      real_t D1{0.1e6};
+      // bulk modulus
+      real_t C1{1.0e6};
+      constexpr auto I = mfem::internal::IsotropicIdentity<dim>();
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      auto F = det(I + dudx);
+      auto p = -2.0 * D1 * F * (F - 1);
+      auto devB = dev(dudx + transpose(dudx) + dot(dudx, transpose(dudx)));
+      auto sigma = -(p / F) * I + 2.0 * (C1 / pow(F, 5.0 / 3.0)) * devB;
+
+      return mfem::tuple{sigma * det(J) * w * transpose(invJ)};
+   };
+
+   mfem::tuple argument_operators{Gradient{"displacement"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator{Gradient{"displacement"}};
+
+   // B^T D(B0*dudxi, B1*J, B2*w)
+   ElementOperator op(elasticity_kernel, argument_operators, output_operator, ir);
+
+   std::array solutions{FieldDescriptor{&h1fes, "displacement"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, mfem::tuple{op}, mesh,
+                              AutoDiff::NativeDualNumber{});
+
+   ElasticityOperator elasticity(h1fes, dop, ess_tdof_list);
+
+   VectorArrayCoefficient f(dim);
+   for (int i = 0; i < dim-1; i++)
+   {
+      f.Set(i, new ConstantCoefficient(0.0));
+   }
+   {
+      Vector pull_force(mesh.bdr_attributes.Max());
+      pull_force = 0.0;
+      pull_force(1) = -1.0e-2;
+      f.Set(dim-1, new PWConstCoefficient(pull_force));
+   }
+
+   ParLinearForm b(&h1fes);
+   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.UseFastAssembly(true);
+   b.Assemble();
+   auto B = b.ParallelAssemble();
+
+   Vector X = u.GetTrueVector();
+
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(1e-8);
+   cg.SetMaxIter(1000);
+   cg.SetPrintLevel(IterativeSolver::PrintLevel().Summary());
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetSolver(cg);
+   newton.SetOperator(elasticity);
+   newton.SetRelTol(1e-6);
+   newton.SetMaxIter(100);
+   // newton.SetAdaptiveLinRtol();
+   newton.SetPrintLevel(IterativeSolver::PrintLevel().Iterations());
+
+   elasticity.SetParameters(*mesh_nodes);
+
+   // Vector zero;
+   newton.Mult(*B, X);
+
+   u.SetFromTrueDofs(X);
+
+   ParaViewDataCollection paraview_dc("dfem", &mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(polynomial_order);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetTime(0.0);
+   paraview_dc.RegisterField("displacement", &u);
+   paraview_dc.Save();
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_nonlinear_elasticity_3d);

examples/dfem_test_ordering.cpp

@@ -0,0 +1,82 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "fem/coefficient.hpp"
+#include "fem/pgridfunc.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_ordering(std::string mesh_file,
+                  int refinements,
+                  int polynomial_order)
+{
+   constexpr int dim = 2;
+   constexpr int vdim = dim;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(polynomial_order);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   const IntegrationRule &ir =
+      IntRules.Get(mesh_fes.GetFE(0)->GetGeomType(),
+                   2 * mesh_fes.FEColl()->GetOrder() - 1);
+
+   for (int q = 0; q < ir.GetNPoints(); q++)
+   {
+      out << "(" << ir.IntPoint(q).x << ", " << ir.IntPoint(q).y << ")\n";
+   }
+
+   ParGridFunction u(&mesh_fes);
+   auto f = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = x*x*y + 1.0;
+      u(1) = y*y*x*x + 2.0;
+   };
+
+   VectorFunctionCoefficient uc(dim, f);
+   u.ProjectCoefficient(uc);
+
+   auto kernel = [](const tensor<double, dim> &xi,
+                    const tensor<double, vdim, dim> &J,
+                    const tensor<double, dim> &u,
+                    const tensor<double, vdim, dim> &dudxi)
+   {
+      out << "xi: " << xi << "\n";
+      out << "J: " << J << "\n";
+      out << "u: " << u << "\n";
+      out << "dudxi: " << dudxi << "\n\n";
+      return mfem::tuple{J};
+   };
+
+   mfem::tuple argument_operators{Value{"coordinates"}, Gradient{"coordinates"}, Value{"potential"}, Gradient{"potential"}};
+   mfem::tuple output_operator{Gradient{"potential"}};
+
+   ElementOperator op{kernel, argument_operators, output_operator};
+
+   std::array solutions{FieldDescriptor{&mesh_fes, "potential"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop{solutions, parameters, mfem::tuple{op}, mesh, ir};
+
+   Vector y(u);
+
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(u, y);
+
+   print_vector(y);
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_ordering);

examples/dfem_test_vector_diffusion.cpp

@@ -0,0 +1,102 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int test_vector_diffusion(std::string mesh_file,
+                          int refinements,
+                          int polynomial_order)
+{
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   const int vdim = dim;
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection h1fec(polynomial_order, dim);
+   ParFiniteElementSpace h1fes(&mesh, &h1fec, vdim);
+
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   Array<int> ess_tdof;
+   ess_bdr = 1;
+   h1fes.GetEssentialTrueDofs(ess_bdr, ess_tdof);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder() - 1);
+
+   ParGridFunction u(&h1fes);
+
+   auto f1 = [](const Vector& coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = 2.345 + 0.25 * x * x * y + y * y * x;
+      u(1) = 2.345 - 0.25 * x * y * y + y * x * x;
+   };
+
+   VectorFunctionCoefficient u_c(dim, f1);
+   u.ProjectCoefficient(u_c);
+
+   auto vector_diffusion_kernel = [](const tensor<double, 2> &xi,
+                                     const tensor<double, 2, 2> &dudxi,
+                                     const tensor<double, 2, 2> &J,
+                                     const double &w)
+   {
+      out << "xi: " << xi << "\n";
+      out << "dudxi: " << dudxi << "\n";
+      return mfem::tuple{dudxi * inv(J) * det(J) * w * transpose(inv(J))};
+      // return mfem::tuple{dudxi};
+   };
+
+   mfem::tuple argument_operators{Value{"coordinates"}, Gradient{"potential"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator{Gradient{"potential"}};
+
+   ElementOperator op{vector_diffusion_kernel, argument_operators, output_operator};
+
+   std::array solutions{FieldDescriptor{&h1fes, "potential"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop{solutions, parameters, mfem::tuple{op}, mesh, ir};
+
+   Vector x(u), y1(h1fes.GetTrueVSize()),
+          y2(h1fes.GetTrueVSize());
+
+   ParBilinearForm A_form(&h1fes);
+   auto A_integ = new VectorDiffusionIntegrator(vdim);
+   A_integ->SetIntegrationRule(ir);
+   A_form.AddDomainIntegrator(A_integ);
+   A_form.Assemble();
+   A_form.Finalize();
+
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y1);
+   y1.HostRead();
+
+   A_form.Mult(x, y2);
+   y2.HostRead();
+
+   Vector diff(y2);
+   diff -= y1;
+   if (diff.Norml2() > 1e-10)
+   {
+      out << "||F(u) - ex||_l2 = " << diff.Norml2() << "\n";
+      print_vector(diff);
+      print_vector(y1);
+      print_vector(y2);
+      return 1;
+   }
+
+   return 0;
+}
+
+DFEM_TEST_MAIN(test_vector_diffusion);

examples/enzyme_interface_smoketest.cpp

@@ -0,0 +1,122 @@
+#include <tuple>
+#include <type_traits>
+#include <iostream>
+#include <enzyme/enzyme>
+
+template <typename T>
+constexpr auto get_type_name() -> std::string_view
+{
+#if defined(__clang__)
+   constexpr auto prefix = std::string_view {"[T = "};
+   constexpr auto suffix = "]";
+   constexpr auto function = std::string_view{__PRETTY_FUNCTION__};
+#elif defined(__GNUC__)
+   constexpr auto prefix = std::string_view {"with T = "};
+   constexpr auto suffix = "; ";
+   constexpr auto function = std::string_view{__PRETTY_FUNCTION__};
+#elif defined(_MSC_VER)
+   constexpr auto prefix = std::string_view {"get_type_name<"};
+   constexpr auto suffix = ">(void)";
+   constexpr auto function = std::string_view{__FUNCSIG__};
+#else
+#error Unsupported compiler
+#endif
+
+   const auto start = function.find(prefix) + prefix.size();
+   const auto end = function.find(suffix);
+   const auto size = end - start;
+
+   return function.substr(start, size);
+}
+
+template <typename ... Ts>
+constexpr auto decay_types(std::tuple<Ts...> const &)
+-> std::tuple<std::remove_cv_t<std::remove_reference_t<Ts>>...>;
+
+template <typename T>
+using decay_tuple = decltype(decay_types(std::declval<T>()));
+
+template <class F> struct FunctionSignature;
+
+template <typename output_t, typename... input_ts>
+struct FunctionSignature<output_t(input_ts...)>
+{
+   using return_t = output_t;
+   using parameter_ts = std::tuple<input_ts...>;
+};
+
+template <class T> struct create_function_signature;
+
+template <typename output_t, typename T, typename... input_ts>
+struct create_function_signature<output_t (T::*)(input_ts...) const>
+{
+   using type = FunctionSignature<output_t(input_ts...)>;
+};
+
+template <typename arg_ts, std::size_t... Is>
+auto create_enzyme_args(arg_ts &args,
+                        arg_ts &shadow_args,
+                        std::index_sequence<Is...>)
+{
+   // (std::cout << ... << std::get<Is>(shadow_args));
+   return std::tuple<enzyme::Duplicated<decltype(std::get<Is>(args))>...>
+   {
+      { std::get<Is>(args), std::get<Is>(shadow_args) }...
+   };
+}
+
+template <typename kernel_t, typename arg_ts>
+auto fwddiff_apply_enzyme(kernel_t kernel, arg_ts &&args, arg_ts &&shadow_args)
+{
+   auto arg_indices =
+      std::make_index_sequence<std::tuple_size_v<std::remove_reference_t<arg_ts>>> {};
+
+   auto enzyme_args = create_enzyme_args(args, shadow_args, arg_indices);
+
+   // using kf_return_t = typename create_function_signature<
+   //                     decltype(&kernel_t::operator())>::type::return_t;
+
+   std::cout << "\n";
+   std::cout << "args is " << get_type_name<decltype(args)>() << "\n\n";
+   std::cout << "enzyme_args type is " << get_type_name<decltype(enzyme_args)>() <<
+             "\n\n";
+   // std::cout << "return type is " << get_type_name<decltype(kf_return_t{})>() <<
+   //           "\n\n";
+
+   std::cout << "args " << std::get<0>(args) << "\n";
+   std::cout << "shadow args " << std::get<0>(shadow_args) << "\n";
+
+   return std::apply([&](auto &&...args)
+   {
+      // std::cout << enzyme::autodiff<enzyme::Forward>(+kernel, args...) << "\n";
+      return enzyme::get<0>
+             (enzyme::autodiff<enzyme::Forward>(+kernel, args...));
+   },
+   enzyme_args);
+}
+
+int main()
+{
+
+   auto func = [](const double &x, double &y)
+   {
+      std::cout << "func( x = " << x << " )\n";
+      return x*x;
+   };
+
+   using kf_param_ts = typename create_function_signature<
+                       decltype(&decltype(func)::operator())>::type::parameter_ts;
+   using kf_output_t = typename create_function_signature<
+                       decltype(&decltype(func)::operator())>::type::return_t;
+   auto kernel_args = decay_tuple<kf_param_ts> {};
+   auto kernel_shadow_args = decay_tuple<kf_param_ts> {};
+
+   std::get<0>(kernel_args) = 3;
+   std::get<0>(kernel_shadow_args) = 1;
+
+   auto dx = fwddiff_apply_enzyme(func, kernel_args, kernel_shadow_args);
+
+   std::cout << "dfdx = " << dx << "\n";
+
+   return 0;
+}

examples/ex14.cpp

@@ -20,7 +20,6 @@
 //               ex14 -m ../data/fichera-amr.mesh
 //               ex14 -pa -r 1 -o 3
 //               ex14 -pa -r 1 -o 3 -m ../data/fichera.mesh
-//               ex14 -m ../data/inline-tet.mesh -o 0 -nt 4 -s 1
 //
 // Device sample runs:
 //               ex14 -pa -r 2 -d cuda -o 3
@@ -56,16 +55,10 @@ int main(int argc, char *argv[])
    bool pa = false;
    bool visualization = 1;
    const char *device_config = "cpu";
-   int nt = 0;
-   double st = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
-   args.AddOption(&nt, "-nt", "--number-of-timeslices",
-                  "Number of slices through the hyper-prism in the 4th coordinate.");
-   args.AddOption(&st, "-st", "--size-time",
-                  "Length of hyper-prims in 4th coordinate (e.g. time).");
    args.AddOption(&ref_levels, "-r", "--refine",
                   "Number of times to refine the mesh uniformly, -1 for auto.");
    args.AddOption(&order, "-o", "--order",
@@ -104,17 +97,8 @@ int main(int argc, char *argv[])
    // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
    //    NURBS meshes are projected to second order meshes.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-   if (dim == 3 && nt > 0)
-   {
-      Mesh* spat_mesh = mesh;
-      mesh = new Mesh(spat_mesh, nt, Element::PENTATOPE, true, st);
-      delete spat_mesh;
-
-      ref_levels = 0;
-      dim = 4;
-   }
+   Mesh mesh(mesh_file);
+   const int dim = mesh.Dimension();
 
    // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. By default, or if ref_levels < 0,
@@ -123,23 +107,23 @@ int main(int argc, char *argv[])
    {
       if (ref_levels < 0)
       {
-         ref_levels = (int)floor(log(50000./mesh->GetNE())/log(2.)/(dim < 4 ? dim : 1.));
+         ref_levels = (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
       }
       for (int l = 0; l < ref_levels; l++)
       {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
       }
    }
-   if (mesh->NURBSext)
+   if (mesh.NURBSext)
    {
-      mesh->SetCurvature(max(order, 1));
+      mesh.SetCurvature(max(order, 1));
    }
 
    // 5. Define a finite element space on the mesh. Here we use discontinuous
    //    finite elements of the specified order >= 0.
    const auto bt = pa ? BasisType::GaussLobatto : BasisType::GaussLegendre;
    DG_FECollection fec(order, dim, bt);
-   FiniteElementSpace fespace(mesh, &fec);
+   FiniteElementSpace fespace(&mesh, &fec);
    cout << "Number of unknowns: " << fespace.GetVSize() << endl;
 
    // 6. Set up the linear form b(.) which corresponds to the right-hand side of
@@ -214,7 +198,7 @@ int main(int argc, char *argv[])
    //     later using GLVis: "glvis -m refined.mesh -g sol.gf".
    ofstream mesh_ofs("refined.mesh");
    mesh_ofs.precision(8);
-   mesh->Print(mesh_ofs);
+   mesh.Print(mesh_ofs);
    ofstream sol_ofs("sol.gf");
    sol_ofs.precision(8);
    x.Save(sol_ofs);
@@ -226,10 +210,8 @@ int main(int argc, char *argv[])
       int  visport   = 19916;
       socketstream sol_sock(vishost, visport);
       sol_sock.precision(8);
-      sol_sock << "solution\n" << *mesh << x << flush;
+      sol_sock << "solution\n" << mesh << x << flush;
    }
 
-   delete mesh;
-
    return 0;
 }

examples/ex14p.cpp

@@ -19,7 +19,6 @@
 //               mpirun -np 4 ex14p -m ../data/amr-hex.mesh
 //               mpirun -np 4 ex14p -pa -rs 1 -rp 0 -o 3
 //               mpirun -np 4 ex14p -pa -rs 1 -rp 0 -m ../data/fichera.mesh -o 3
-//               mpirun -np 4 ex14p -m ../data/inline-tet.mesh -o 0 -nt 4 -s 1
 //
 // Device sample runs:
 //               mpirun -np 4 ex14p -pa -rs 2 -rp 0 -d cuda -o 3
@@ -91,16 +90,10 @@ int main(int argc, char *argv[])
    bool pa = false;
    bool visualization = 1;
    const char *device_config = "cpu";
-   int nt = 0;
-   double st = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
-   args.AddOption(&nt, "-nt", "--number-of-timeslices",
-                  "Number of slices through the hyper-prism in the 4th coordinate.");
-   args.AddOption(&st, "-st", "--size-time",
-                  "Length of hyper-prims in 4th coordinate (e.g. time).");
    args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
                   "Number of times to refine the mesh uniformly in serial,"
                   " -1 for auto.");
@@ -146,17 +139,8 @@ int main(int argc, char *argv[])
    // 3. Read the (serial) mesh from the given mesh file on all processors. We
    //    can handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code. NURBS meshes are projected to second order meshes.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-   if (dim == 3 && nt > 0)
-   {
-      Mesh* spat_mesh = mesh;
-      mesh = new Mesh(spat_mesh, nt, Element::PENTATOPE, true, st);
-      delete spat_mesh;
-      dim = 4;
-   }
-   if (dim == 4)
-      ser_ref_levels = 0;
+   Mesh mesh(mesh_file);
+   int dim = mesh.Dimension();
 
    // 4. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ser_ref_levels' of uniform refinement. By default,
@@ -165,23 +149,23 @@ int main(int argc, char *argv[])
    {
       if (ser_ref_levels < 0)
       {
-         ser_ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+         ser_ref_levels = (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
       }
       for (int l = 0; l < ser_ref_levels; l++)
       {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
       }
    }
-   if (mesh->NURBSext)
+   if (mesh.NURBSext)
    {
-      mesh->SetCurvature(max(order, 1));
+      mesh.SetCurvature(max(order, 1));
    }
 
    // 5. 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);
-   delete mesh;
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
    {
       for (int l = 0; l < par_ref_levels; l++)
       {

examples/ex1p_4d.cpp

@@ -1,412 +0,0 @@
-//                       MFEM Example 1 - Parallel Version
-//
-// 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/escher.mesh
-//               mpirun -np 4 ex1p -m ../data/fichera.mesh
-//               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/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/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
-//
-// 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>
-
-#include "./spe10_coeff.cpp"
-
-
-int* LoadIterations(int NRows, int NCol)
-{
-   ifstream in("iter_grad.txt");
-
-   //initialize
-   int *iters = new int[NCol*NRows];
-   for (int col = 0; col < NCol; col++)
-   {
-      for (int row = 0; row < NRows; row++)
-      {
-         iters[row*NCol+col] = -1;
-      }
-   }
-
-   if (!in)
-   {
-      cout << "Cannot open file.\n";
-      return iters;
-   }
-
-   for (int row = 0; row < NRows; row++)
-      for (int col = 0; col < NCol; col++)
-      {
-         if (in.eof())
-         {
-            in.close();
-            return iters;
-         }
-         in >> iters[row*NCol+col];
-      }
-
-
-   in.close();
-
-   return iters;
-}
-
-void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
-{
-   iters[row*NCol+col] = iter;
-}
-
-void WriteIterations(int *iters, int NRows, int NCol)
-{
-   ofstream out;
-   out.open("iter_grad.txt",fstream::out);
-
-   if (!out)
-   {
-      cout << "Cannot open file.\n";
-      delete[] iters;
-
-      return;
-   }
-
-   for (int row = 0; row < NRows; row++)
-   {
-      for (int col = 0; col < NCol; col++)
-      {
-         out << iters[row*NCol+col] << "\t";
-      }
-      out << endl;
-   }
-   out.close();
-
-   delete[] iters;
-}
-
-
-using namespace std;
-using namespace mfem;
-
-double kappa = 1.0;
-
-double u_exact(const Vector &x)
-{
-   int dim = x.Size();
-
-   if (dim==4)
-   {
-      return cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
-   }
-   else { return 0.0; }
-}
-
-double f_exact(const Vector &x)
-{
-   int dim = x.Size();
-
-   if (dim==4)
-   {
-      return (kappa + 4.0 * M_PI*M_PI) * cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(
-                                                                              2))*cos(M_PI*x(3));
-   }
-   else { return 0.0; }
-}
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   int num_procs, myid;
-   MPI_Init(&argc, &argv);
-   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
-   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
-
-   bool verbose = (myid==0);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/cube4d_96.MFEM";
-   int order = 1;
-   bool static_cond = false;
-   bool visualization = 1;
-   int sequ_ref_levels = 0;
-   int par_ref_levels = 0;
-   double tol = 1e-6;
-   bool set_bc = true;
-   bool standardCG = true;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
-                  "Number of sequential refinement steps.");
-   args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
-                  "Number of parallel refinement steps.");
-   args.AddOption(&order, "-o", "--order",
-                  "Polynomial order of the finite element space.");
-   args.AddOption(&tol, "-tol", "--tol",
-                  "A parameter.");
-   args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
-                  "Impose or not essential boundary conditions.");
-   args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
-                  "Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   if (verbose) { args.PrintOptions(cout); }
-
-   Mesh *mesh;
-   ifstream imesh(mesh_file);
-   if (!imesh)
-   {
-      cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
-      return 2;
-   }
-
-   mesh = new Mesh(imesh, 1, 1);
-   imesh.close();
-
-   int dim = mesh->Dimension();
-   int sdim = mesh->SpaceDimension();
-
-   //   if(dim !=4 || sdim != 4)
-   //   {
-   //    MPI_Finalize();
-   //    return 0;
-   //   }
-
-   for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
-   if (verbose) { mesh->PrintCharacteristics(); }
-
-   if (verbose) { cout << "now we partition the mesh..." << endl << endl; }
-
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-
-   for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }
-
-   pmesh->PrintInfo(std::cout);
-   if (verbose) { cout << endl; }
-
-   // 6. 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;
-   if (order > 0)
-   {
-      if (dim==4)
-      {
-         if (order==1) { fec = new LinearFECollection; }
-         else { fec = new QuadraticFECollection; }
-      }
-      else { fec = new H1_FECollection(order, dim); }
-   }
-   else if (pmesh->GetNodes())
-   {
-      fec = pmesh->GetNodes()->OwnFEC();
-      if (myid == 0)
-      {
-         cout << "Using isoparametric FEs: " << fec->Name() << endl;
-      }
-   }
-   else
-   {
-      fec = new H1_FECollection(order = 1, dim);
-   }
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-   }
-
-   // 7. 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 = set_bc ? 1 : 0;
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-
-   FunctionCoefficient uExact(u_exact);
-   ParGridFunction x(fespace);
-
-   int NExpo =8;
-   for (int expo=-NExpo; expo<=NExpo; expo++)
-   {
-      double weight = pow(10.0,expo);
-      kappa = weight;
-
-      x.ProjectCoefficient(uExact);
-
-      ParLinearForm *b = new ParLinearForm(fespace);
-      FunctionCoefficient ffunc(f_exact);
-      b->AddDomainIntegrator(new DomainLFIntegrator(ffunc));
-      b->Assemble();
-
-      x = 0.0;
-
-      // 10. Set up the parallel bilinear form a(.,.) on the finite element space
-      //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
-      //     domain integrator.
-
-      //    std::string permFile = "spe_perm.dat";
-      //    InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
-      //    FunctionCoefficient *cspe10 = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
-      Coefficient *beta = new ConstantCoefficient(weight);
-
-      ParBilinearForm *a = new ParBilinearForm(fespace);
-      a->AddDomainIntegrator(new DiffusionIntegrator);
-      a->AddDomainIntegrator(new MassIntegrator(*beta));
-
-      // 11. 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();
-
-      HypreParMatrix A;
-      Vector B, X;
-      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
-
-      if (myid == 0)
-      {
-         cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
-      }
-
-      // 12. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
-      //     preconditioner from hypre.
-      HypreSolver *amg = new HypreBoomerAMG(A);
-
-      int iter = -1;
-      if (standardCG)
-      {
-         IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-         pcg->SetOperator(A);
-         pcg->SetRelTol(tol);
-         pcg->SetMaxIter(5000);
-         pcg->SetPrintLevel(1);
-         pcg->SetPreconditioner(*amg);
-         pcg->Mult(B, X);
-
-         iter = pcg->GetNumIterations();
-
-         delete pcg;
-      }
-      else
-      {
-         HyprePCG *pcg = new HyprePCG(A);
-         pcg->SetTol(tol);
-         pcg->SetMaxIter(5000);
-         pcg->SetResidualConvergenceOptions(1,tol);
-         pcg->SetPrintLevel(2);
-         pcg->SetPreconditioner(*amg);
-         pcg->Mult(B, X);
-
-         pcg->GetNumIterations(iter);
-
-         delete pcg;
-      }
-
-
-      if (myid==0)
-      {
-         cout << "Weigth: " << weight << " " << iter << endl;
-
-         int *iters = LoadIterations(10, 2*NExpo+1);
-         putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
-                              2*NExpo+1, iters);
-         WriteIterations(iters, 10, 2*NExpo+1);
-      }
-
-
-      // 13. Recover the parallel grid function corresponding to X. This is the
-      //     local finite element solution on each processor.
-      a->RecoverFEMSolution(X, *b, x);
-
-      {
-         double err = x.ComputeL2Error(uExact);
-         if (myid == 0)
-         {
-            cout << "\n|| u - u_h ||_{L^2} = " << err << '\n' << endl;
-         }
-      }
-
-      // 14. 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);
-      //   }
-
-      // 15. 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;
-      //   }
-
-      delete amg;
-      delete a;
-      delete beta;
-      delete b;
-   }
-
-   // 16. Free the used memory.
-
-   delete fespace;
-   if (order > 0) { delete fec; }
-   delete pmesh;
-
-   MPI_Finalize();
-
-   return 0;
-}

examples/ex23.cpp

@@ -44,7 +44,7 @@ protected:
    BilinearForm *M;
    BilinearForm *K;
 
-   SparseMatrix Mmat, Kmat, Kmat0;
+   SparseMatrix Mmat, Kmat;
    SparseMatrix *T; // T = M + dt K
    real_t current_dt;
 
@@ -83,25 +83,24 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
    : SecondOrderTimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0),
      fespace(f), M(NULL), K(NULL), T(NULL), current_dt(0.0), z(height)
 {
-   const real_t rel_tol = 1e-8;
-
-   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-
+   // Assemble Laplace matrix
    c2 = new ConstantCoefficient(speed*speed);
-
    K = new BilinearForm(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(*c2));
    K->Assemble();
 
-   Array<int> dummy;
-   K->FormSystemMatrix(dummy, Kmat0);
-   K->FormSystemMatrix(ess_tdof_list, Kmat);
-
+   // Assemble Mass matrix
    M = new BilinearForm(&fespace);
    M->AddDomainIntegrator(new MassIntegrator());
    M->Assemble();
+
+   // Apply Bcs
+   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   K->FormSystemMatrix(ess_tdof_list, Kmat);
    M->FormSystemMatrix(ess_tdof_list, Mmat);
 
+   // Configure preconditioner
+   const real_t rel_tol = 1e-8;
    M_solver.iterative_mode = false;
    M_solver.SetRelTol(rel_tol);
    M_solver.SetAbsTol(0.0);
@@ -110,14 +109,13 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
+   // Configure solver
    T_solver.iterative_mode = false;
    T_solver.SetRelTol(rel_tol);
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
-
-   T = NULL;
 }
 
 void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
@@ -126,9 +124,11 @@ void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
    // Compute:
    //    d2udt2 = M^{-1}*-K(u)
    // for d2udt2
-   Kmat.Mult(u, z);
+   K->FullMult(u, z);
    z.Neg(); // z = -z
+   z.SetSubVector(ess_tdof_list, 0.0);
    M_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }
 
 void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
@@ -142,14 +142,11 @@ void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
       T = Add(1.0, Mmat, fac0, Kmat);
       T_solver.SetOperator(*T);
    }
-   Kmat0.Mult(u, z);
+   K->FullMult(u, z);
    z.Neg();
-
-   for (int i = 0; i < ess_tdof_list.Size(); i++)
-   {
-      z[ess_tdof_list[i]] = 0.0;
-   }
+   z.SetSubVector(ess_tdof_list, 0.0);
    T_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }
 
 void WaveOperator::SetParameters(const Vector &u)
@@ -314,7 +311,6 @@ int main(int argc, char *argv[])
          ess_bdr = 0;
       }
    }
-
    WaveOperator oper(fespace, ess_bdr, speed);
 
    u_gf.SetFromTrueDofs(u);

examples/ex3p.cpp

@@ -58,180 +58,6 @@ void f_exact(const Vector &, Vector &);
 real_t freq = 1.0, kappa;
 int dim;
 
-class Curl4dPrec : public Solver
-{
-
-private:
-   HypreParMatrix *A;
-   ParFiniteElementSpace *fespace;
-
-   HypreParMatrix *idMat;
-   HypreParMatrix *H1VecLaplaceMat;
-   HypreBoomerAMG *amgVecH1;
-
-
-   HypreParMatrix *gradMat;
-   HypreParMatrix *H1LaplaceMat;
-   HypreBoomerAMG *amgH1;
-
-   HypreSmoother * smoother;
-   CGSolver *pcgGrad;
-   CGSolver *pcgH1Vec;
-
-   Vector *f;
-   Vector *fGrad, *uGrad;
-   Vector *fH1Vec, *uH1Vec;
-
-   bool exactSolves;
-
-public:
-   Curl4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
-              const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
-   {
-      A = AUser;
-      fespace = fespaceUser;
-      ParMesh *pmesh = fespace->GetParMesh();
-      int dim = pmesh->Dimension();
-
-      exactSolves = exactSolvesUser;
-
-      int orderIm=1;  //vecH1  --> H(curl)
-      int orderKer=orderKernel; //grad V --> H(curl)
-
-      smoother = new HypreSmoother(*A, 16, 3);
-
-      //    //for the pure dirichlet case
-      //    Array<int> essBnd(pmesh->bdr_attributes.Max()); essBnd = 1;
-
-      Array<int> HCurl_essDof(fespace->GetVSize()); HCurl_essDof = 0;
-      fespace->GetEssentialVDofs(essBnd, HCurl_essDof);
-
-      //setup the H1 FESpace
-      FiniteElementCollection* fecH1;
-      if (orderKer==1) { fecH1 = new LinearFECollection; }
-      else { fecH1 = new QuadraticFECollection; }
-
-      ParFiniteElementSpace *H1FESpace = new ParFiniteElementSpace(pmesh, fecH1);
-      Array<int> H1_essDof(H1FESpace->GetVSize()); H1_essDof = 0;
-      H1FESpace->GetEssentialVDofs(essBnd, H1_essDof);
-
-      //setup the discrete gradient
-      ParDiscreteLinearOperator *disGrad = new ParDiscreteLinearOperator(H1FESpace,
-                                                                         fespace);
-      disGrad->AddDomainInterpolator(new GradientInterpolator);
-      disGrad->Assemble();
-      disGrad->Finalize();
-      SparseMatrix* smat = &(disGrad->SpMat());
-      smat->EliminateCols(H1_essDof);
-      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smat->EliminateRow(dof); }
-      gradMat = disGrad->ParallelAssemble();
-      delete disGrad;
-
-      //setup the H1 preconditioner
-      ParBilinearForm* H1Varf = new ParBilinearForm(H1FESpace);
-      H1Varf->AddDomainIntegrator(new DiffusionIntegrator);
-      H1Varf->AddDomainIntegrator(new MassIntegrator);
-      H1Varf->Assemble();
-      H1Varf->Finalize();
-
-      SparseMatrix &matH1(H1Varf->SpMat());
-      for (int dof=0; dof<H1_essDof.Size(); dof++) if (H1_essDof[dof]<0) { matH1.EliminateRowCol(dof); }
-      H1LaplaceMat = H1Varf->ParallelAssemble();
-      delete H1Varf;
-      amgH1 = new HypreBoomerAMG(*H1LaplaceMat);
-
-
-      //setup the H1 injection
-      FiniteElementCollection* fecH1Vec;
-      if (orderIm==1) { fecH1Vec = new LinearFECollection; }
-      else { fecH1Vec = new QuadraticFECollection; }
-      ParFiniteElementSpace *H1VecFESpace = new ParFiniteElementSpace(pmesh, fecH1Vec,
-                                                                      dim, Ordering::byVDIM);
-      Array<int> H1Vec_essDof(H1VecFESpace->GetVSize()); H1Vec_essDof = 0;
-      H1VecFESpace->GetEssentialVDofs(essBnd, H1Vec_essDof);
-
-      //setup the discrete gradient
-      ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
-         H1VecFESpace, fespace);
-      disInterpol->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpol->Assemble();
-      disInterpol->Finalize();
-      SparseMatrix* smatID = &(disInterpol->SpMat());
-      smatID->EliminateCols(H1Vec_essDof);
-      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smatID->EliminateRow(dof); }
-      idMat = disInterpol->ParallelAssemble();
-      delete disInterpol;
-
-      //setup the H1-vec preconditioner
-      ParBilinearForm* H1VecVarf = new ParBilinearForm(H1VecFESpace);
-      H1VecVarf->AddDomainIntegrator(new VectorDiffusionIntegrator);
-      H1VecVarf->AddDomainIntegrator(new VectorMassIntegrator);
-      H1VecVarf->Assemble();
-      H1VecVarf->Finalize();
-
-      SparseMatrix &matH1Vec(H1VecVarf->SpMat());
-      for (int dof=0; dof<H1Vec_essDof.Size(); dof++) if (H1Vec_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
-      H1VecLaplaceMat = H1VecVarf->ParallelAssemble();
-      delete H1VecVarf;
-      amgVecH1 = new HypreBoomerAMG(*H1VecLaplaceMat);
-      amgVecH1->SetSystemsOptions(dim);
-
-
-      f = new Vector(fespace->GetTrueVSize());
-
-      fGrad = new Vector(H1FESpace->GetTrueVSize());
-      uGrad = new Vector(H1FESpace->GetTrueVSize());
-
-      fH1Vec = new Vector(H1VecFESpace->GetTrueVSize());
-      uH1Vec = new Vector(H1VecFESpace->GetTrueVSize());;
-
-
-      amgH1->Mult(*fGrad, *uGrad);
-      amgVecH1->Mult(*fH1Vec, *uH1Vec);
-
-      pcgGrad = new CGSolver(MPI_COMM_WORLD);
-      pcgGrad->SetOperator(*H1LaplaceMat);
-      pcgGrad->SetPreconditioner(*amgH1);
-      pcgGrad->SetRelTol(1e-16);
-      pcgGrad->SetMaxIter(100000000);
-      pcgGrad->SetPrintLevel(-2);
-
-      pcgH1Vec = new CGSolver(MPI_COMM_WORLD);
-      pcgH1Vec->SetOperator(*H1VecLaplaceMat);
-      pcgH1Vec->SetPreconditioner(*amgVecH1);
-      pcgH1Vec->SetRelTol(1e-16);
-      pcgH1Vec->SetMaxIter(100000000);
-      pcgH1Vec->SetPrintLevel(-2);
-
-   }
-
-   void setExactSolve(bool exSol)
-   {
-      exactSolves = exSol;
-   }
-
-   virtual void Mult(const Vector &x, Vector &y) const
-   {
-      smoother->Mult(x,y);
-
-      idMat->MultTranspose(x,*fH1Vec);
-      *uH1Vec = 0.0;
-      if (exactSolves) { pcgH1Vec->Mult(*fH1Vec, *uH1Vec); }
-      else { amgVecH1->Mult(*fH1Vec, *uH1Vec); }
-      idMat->Mult(1.0, *uH1Vec, 1.0, y);
-
-      gradMat->MultTranspose(x,*fGrad);
-      *uGrad = 0.0;
-      if (exactSolves) { pcgGrad->Mult(*fGrad, *uGrad); }
-      else { amgH1->Mult(*fGrad, *uGrad); }
-      gradMat->Mult(1.0, *uGrad, 1.0, y);
-
-   }
-
-   virtual void SetOperator(const Operator &op) {};
-
-};
-
 int main(int argc, char *argv[])
 {
    // 1. Initialize MPI and HYPRE.
@@ -336,13 +162,7 @@ int main(int argc, char *argv[])
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Nedelec finite elements of the specified order.
-   FiniteElementCollection *fec;
-   if (dim==4)
-   {
-      if (order==1) { fec = new ND1_4DFECollection; }
-      else { fec = new ND2_4DFECollection; }
-   }
-   else { fec = new ND_FECollection(order, dim); }
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
    ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
    HYPRE_BigInt size = fespace->GlobalTrueVSize();
    if (myid == 0)
@@ -428,29 +248,15 @@ int main(int argc, char *argv[])
 
       ParFiniteElementSpace *prec_fespace =
          (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
-      Solver *prec;
       HypreAMS ams(*A.As<HypreParMatrix>(), prec_fespace);
-      if (dim <= 3)
-      {
-         prec = new HypreAMS(*A.As<HypreParMatrix>(), prec_fespace);
-      }
-      else if (dim == 4)
-      {
-         prec = new Curl4dPrec(A.As<HypreParMatrix>(), fespace, ess_bdr, order, false);
-      }
-      IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-      pcg->SetOperator(*A.As<HypreParMatrix>());
-      pcg->SetTol(1e-12);
-      pcg->SetMaxIter(500);
-      pcg->SetPrintLevel(2);
-      pcg->SetPreconditioner(*prec);
-      pcg->Mult(B, X);
-
-      delete pcg;
-      delete prec;
+      HyprePCG pcg(*A.As<HypreParMatrix>());
+      pcg.SetTol(1e-12);
+      pcg.SetMaxIter(500);
+      pcg.SetPrintLevel(2);
+      pcg.SetPreconditioner(ams);
+      pcg.Mult(B, X);
    }
 
-   // 13. Recover the parallel grid function corresponding to X. This is the
    // 14. Recover the parallel grid function corresponding to X. This is the
    //     local finite element solution on each processor.
    a->RecoverFEMSolution(X, *b, x);
@@ -506,14 +312,7 @@ int main(int argc, char *argv[])
 
 void E_exact(const Vector &x, Vector &E)
 {
-   if (dim==4)
-   {
-      E(0) =  sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
-      E(1) = -cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
-      E(2) =  cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(M_PI*x(3));
-      E(3) = -cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(M_PI*x(3));
-   }
-   else if (dim == 3)
+   if (dim == 3)
    {
       E(0) = sin(kappa * x(1));
       E(1) = sin(kappa * x(2));
@@ -529,19 +328,7 @@ void E_exact(const Vector &x, Vector &E)
 
 void f_exact(const Vector &x, Vector &f)
 {
-   //f_exact = E +  DivSkew P( curl E ), where P is the 4d permutation operator
-   if (dim==4)
-   {
-      f(0) =  (1.0+4.0*M_PI*M_PI)*sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(
-                 M_PI*x(3));
-      f(1) = -(1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(
-                M_PI*x(3));
-      f(2) =  (1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(
-                 M_PI*x(3));
-      f(3) = -(1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(
-                M_PI*x(3));
-   }
-   else if (dim == 3)
+   if (dim == 3)
    {
       f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
       f(1) = (1. + kappa * kappa) * sin(kappa * x(2));

examples/ex3p_4d.cpp

@@ -1,650 +0,0 @@
-//                       MFEM Example 3 - Parallel Version
-//
-// Compile with: make ex3p
-//
-// Sample runs:  mpirun -np 4 ex3p -m ../data/star.mesh
-//               mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
-//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
-//               mpirun -np 4 ex3p -m ../data/escher.mesh
-//               mpirun -np 4 ex3p -m ../data/fichera.mesh
-//               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
-//               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
-//               mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
-//               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
-//               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
-//               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
-//               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
-//
-// Description:  This example code solves a simple electromagnetic diffusion
-//               problem corresponding to the second order definite Maxwell
-//               equation curl curl E + E = f with boundary condition
-//               E x n = <given tangential field>. Here, we use a given exact
-//               solution E and compute the corresponding r.h.s. f.
-//               We discretize with Nedelec finite elements in 2D or 3D.
-//
-//               The example demonstrates the use of H(curl) finite element
-//               spaces with the curl-curl and the (vector finite element) mass
-//               bilinear form, as well as the computation of discretization
-//               error when the exact solution is known. Static condensation is
-//               also illustrated.
-//
-//               We recommend viewing examples 1-2 before viewing this example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-#include "./spe10_coeff.cpp"
-
-using namespace std;
-using namespace mfem;
-
-
-int* LoadIterations(int NRows, int NCol)
-{
-   ifstream in("iter_curl.txt");
-
-   //initialize
-   int *iters = new int[NCol*NRows];
-   for (int col = 0; col < NCol; col++)
-   {
-      for (int row = 0; row < NRows; row++)
-      {
-         iters[row*NCol+col] = -1;
-      }
-   }
-
-   if (!in)
-   {
-      cout << "Cannot open file.\n";
-      return iters;
-   }
-
-   for (int row = 0; row < NRows; row++)
-      for (int col = 0; col < NCol; col++)
-      {
-         if (in.eof())
-         {
-            in.close();
-            return iters;
-         }
-         in >> iters[row*NCol+col];
-      }
-
-
-   in.close();
-
-   return iters;
-}
-
-void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
-{
-   iters[row*NCol+col] = iter;
-}
-
-void WriteIterations(int *iters, int NRows, int NCol)
-{
-   ofstream out;
-   out.open("iter_curl.txt",fstream::out);
-
-   if (!out)
-   {
-      cout << "Cannot open file.\n";
-      delete[] iters;
-
-      return;
-   }
-
-   for (int row = 0; row < NRows; row++)
-   {
-      for (int col = 0; col < NCol; col++)
-      {
-         out << iters[row*NCol+col] << "\t";
-      }
-      out << endl;
-   }
-   out.close();
-
-   delete[] iters;
-}
-
-
-// Exact solution, E, and r.h.s., f. See below for implementation.
-void E_exact(const Vector &, Vector &);
-void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa = 1.0;
-int dim;
-
-double osziCoeff(const Vector &x)
-{
-   return 1.0001 + sin(100*x(0))*sin(200*x(1))*sin(300*x(2))*sin(400*x(3));
-}
-
-class Curl4dPrec : public Solver
-{
-
-private:
-   HypreParMatrix *A;
-   ParFiniteElementSpace *fespace;
-   Coefficient *alpha_, *beta_, *neg_beta_;
-
-   HypreParMatrix *idMat;
-   HypreParMatrix *H1VecLaplaceMat;
-   HypreBoomerAMG *amgVecH1;
-
-
-   HypreParMatrix *gradMat;
-   HypreParMatrix *H1LaplaceMat;
-   HypreBoomerAMG *amgH1;
-
-   HypreSmoother * smoother;
-   CGSolver *pcgGrad;
-   CGSolver *pcgH1Vec;
-
-   Vector *f;
-   Vector *fGrad, *uGrad;
-   Vector *fH1Vec, *uH1Vec;
-
-   bool exactSolves;
-
-public:
-   ~Curl4dPrec()
-   {
-      delete pcgH1Vec;
-      delete pcgGrad;
-
-      delete   f, fGrad, uGrad, fH1Vec, uH1Vec;
-
-      delete smoother;
-
-      delete amgVecH1, H1VecLaplaceMat;
-      delete idMat;
-      delete amgH1, H1LaplaceMat;
-      delete gradMat;
-   }
-
-   Curl4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
-              Coefficient *alpha, Coefficient *beta, Coefficient *neg_beta,
-              const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
-   {
-      A = AUser;
-      fespace = fespaceUser;
-      alpha_ = alpha;
-      beta_ = beta;
-      neg_beta_=neg_beta;
-
-      ParMesh *pmesh = fespace->GetParMesh();
-      int dim = pmesh->Dimension();
-
-      exactSolves = exactSolvesUser;
-
-      int orderIm=1;  //vecH1  --> H(curl)
-      int orderKer=orderKernel; //grad V --> H(curl)
-
-      smoother = new HypreSmoother(*A, 16, 3);
-
-      //    //for the pure dirichlet case
-      //    Array<int> essBnd(pmesh->bdr_attributes.Max()); essBnd = 1;
-
-      Array<int> HCurl_essDof(fespace->GetVSize()); HCurl_essDof = 0;
-      fespace->GetEssentialVDofs(essBnd, HCurl_essDof);
-
-      //setup the H1 FESpace
-      FiniteElementCollection* fecH1;
-      if (orderKer==1) { fecH1 = new LinearFECollection; }
-      else { fecH1 = new QuadraticFECollection; }
-
-      ParFiniteElementSpace *H1FESpace = new ParFiniteElementSpace(pmesh, fecH1);
-      Array<int> H1_essDof(H1FESpace->GetVSize()); H1_essDof = 0;
-      H1FESpace->GetEssentialVDofs(essBnd, H1_essDof);
-
-      //setup the discrete gradient
-      ParDiscreteLinearOperator *disGrad = new ParDiscreteLinearOperator(H1FESpace,
-                                                                         fespace);
-      disGrad->AddDomainInterpolator(new GradientInterpolator);
-      disGrad->Assemble();
-      disGrad->Finalize();
-      SparseMatrix* smat = &(disGrad->SpMat());
-      smat->EliminateCols(H1_essDof);
-      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smat->EliminateRow(dof); }
-      gradMat = disGrad->ParallelAssemble();
-      delete disGrad;
-
-      //setup the H1 preconditioner
-      ParBilinearForm* H1Varf = new ParBilinearForm(H1FESpace);
-      H1Varf->AddDomainIntegrator(new DiffusionIntegrator(*beta_));
-      //    H1Varf->AddDomainIntegrator(new MassIntegrator);
-      H1Varf->Assemble();
-      H1Varf->Finalize();
-
-      SparseMatrix &matH1(H1Varf->SpMat());
-      for (int dof=0; dof<H1_essDof.Size(); dof++) if (H1_essDof[dof]<0) { matH1.EliminateRowCol(dof); }
-      H1LaplaceMat = H1Varf->ParallelAssemble();
-      delete H1Varf;
-      amgH1 = new HypreBoomerAMG(*H1LaplaceMat);
-
-
-      //setup the H1 injection
-      FiniteElementCollection* fecH1Vec;
-      if (orderIm==1) { fecH1Vec = new LinearFECollection; }
-      else { fecH1Vec = new QuadraticFECollection; }
-      ParFiniteElementSpace *H1VecFESpace = new ParFiniteElementSpace(pmesh, fecH1Vec,
-                                                                      dim, Ordering::byVDIM);
-      Array<int> H1Vec_essDof(H1VecFESpace->GetVSize()); H1Vec_essDof = 0;
-      H1VecFESpace->GetEssentialVDofs(essBnd, H1Vec_essDof);
-
-      //setup the discrete gradient
-      ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
-         H1VecFESpace, fespace);
-      disInterpol->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpol->Assemble();
-      disInterpol->Finalize();
-      SparseMatrix* smatID = &(disInterpol->SpMat());
-      smatID->EliminateCols(H1Vec_essDof);
-      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smatID->EliminateRow(dof); }
-      idMat = disInterpol->ParallelAssemble();
-      delete disInterpol;
-
-      //setup the H1-vec preconditioner
-      ParBilinearForm* H1VecVarf = new ParBilinearForm(H1VecFESpace);
-      H1VecVarf->AddDomainIntegrator(new VectorDiffusionIntegrator(*alpha_));
-      H1VecVarf->AddDomainIntegrator(new VectorMassIntegrator(*neg_beta_));
-      H1VecVarf->Assemble();
-      H1VecVarf->Finalize();
-
-      SparseMatrix &matH1Vec(H1VecVarf->SpMat());
-      for (int dof=0; dof<H1Vec_essDof.Size(); dof++) if (H1Vec_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
-      H1VecLaplaceMat = H1VecVarf->ParallelAssemble();
-      delete H1VecVarf;
-      amgVecH1 = new HypreBoomerAMG(*H1VecLaplaceMat);
-      amgVecH1->SetSystemsOptions(dim);
-
-
-      f = new Vector(fespace->GetTrueVSize());
-
-      fGrad = new Vector(H1FESpace->GetTrueVSize());
-      uGrad = new Vector(H1FESpace->GetTrueVSize());
-
-      fH1Vec = new Vector(H1VecFESpace->GetTrueVSize());
-      uH1Vec = new Vector(H1VecFESpace->GetTrueVSize());
-
-
-      amgH1->Mult(*fGrad, *uGrad);
-      amgVecH1->Mult(*fH1Vec, *uH1Vec);
-
-      pcgGrad = new CGSolver(MPI_COMM_WORLD);
-      pcgGrad->SetOperator(*H1LaplaceMat);
-      pcgGrad->SetPreconditioner(*amgH1);
-      pcgGrad->SetRelTol(1e-16);
-      pcgGrad->SetMaxIter(100000000);
-      pcgGrad->SetPrintLevel(-2);
-
-      pcgH1Vec = new CGSolver(MPI_COMM_WORLD);
-      pcgH1Vec->SetOperator(*H1VecLaplaceMat);
-      pcgH1Vec->SetPreconditioner(*amgVecH1);
-      pcgH1Vec->SetRelTol(1e-16);
-      pcgH1Vec->SetMaxIter(100000000);
-      pcgH1Vec->SetPrintLevel(-2);
-
-      delete H1FESpace; delete fecH1;
-      delete H1VecFESpace; delete fecH1Vec;
-
-   }
-
-   void setExactSolve(bool exSol)
-   {
-      exactSolves = exSol;
-   }
-
-   virtual void Mult(const Vector &x, Vector &y) const
-   {
-      smoother->Mult(x,y);
-
-      idMat->MultTranspose(x,*fH1Vec);
-      *uH1Vec = 0.0;
-      if (exactSolves) { pcgH1Vec->Mult(*fH1Vec, *uH1Vec); }
-      else { amgVecH1->Mult(*fH1Vec, *uH1Vec); }
-      idMat->Mult(1.0, *uH1Vec, 1.0, y);
-
-      gradMat->MultTranspose(x,*fGrad);
-      *uGrad = 0.0;
-      if (exactSolves) { pcgGrad->Mult(*fGrad, *uGrad); }
-      else { amgH1->Mult(*fGrad, *uGrad); }
-      gradMat->Mult(1.0, *uGrad, 1.0, y);
-
-   }
-
-   virtual void SetOperator(const Operator &op) {};
-
-};
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   int num_procs, myid;
-   MPI_Init(&argc, &argv);
-   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
-   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
-
-   bool verbose = (myid==0);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/cube4d_96.MFEM";
-   int order = 1;
-   bool set_bc = true;
-   bool static_cond = false;
-   bool visualization = 1;
-   int sequ_ref_levels = 0;
-   int par_ref_levels = 0;
-   double tol = 1e-6;
-   double coeffWeight = 1.0;
-   bool exactH1Solver = false;
-   bool spe10Coeff = false;
-   bool standardCG = true;
-
-   int NExpo = 8;
-   int weightStart = -NExpo;
-   int weightEnd = NExpo;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
-                  "Number of sequential refinement steps.");
-   args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
-                  "Number of parallel refinement steps.");
-   args.AddOption(&order, "-o", "--order",
-                  "Polynomial order of the finite element space.");
-   args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
-                  "Impose or not essential boundary conditions.");
-   args.AddOption(&tol, "-tol", "--tol",
-                  "A parameter.");
-   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
-                  " solution.");
-   args.AddOption(&coeffWeight, "-c", "--coeffMass",
-                  "the weight for the mass term.");
-   args.AddOption(&exactH1Solver, "-exH1Sol", "--exactH1Solver", "-H1prec",
-                  "--H1preconditioner",
-                  "Use exact H1 solvers for the preconditioner.");
-   args.AddOption(&spe10Coeff, "-spe10", "--useSPE10Coeff", "-constCoeff",
-                  "--constCoeff",
-                  "Switch between the coefficients for the mass bilinear form.");
-   args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
-                  "Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
-   args.AddOption(&weightStart, "-ws", "--weightStart",
-                  "the exponent for the starting weight (for the mass term).");
-   args.AddOption(&weightEnd, "-we", "--weightEnd",
-                  "the exponent for the weight at the end (for the mass term).");
-
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   if (verbose) { args.PrintOptions(cout); }
-
-   kappa = freq * M_PI;
-
-   Mesh *mesh;
-   ifstream imesh(mesh_file);
-   if (!imesh)
-   {
-      cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
-      return 2;
-   }
-
-   mesh = new Mesh(imesh, 1, 1);
-   imesh.close();
-
-   dim = mesh->Dimension();
-   int sdim = mesh->SpaceDimension();
-
-
-   if (dim !=4 || sdim != 4)
-   {
-      MPI_Finalize();
-      return 0;
-   }
-
-   for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
-   if (verbose) { mesh->PrintCharacteristics(); }
-
-   if (verbose) { cout << "now we partition the mesh..." << endl << endl; }
-
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-
-   for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }
-
-   pmesh->ReorientTetMesh();
-
-   pmesh->PrintInfo(std::cout);
-   if (verbose) { cout << endl; }
-
-   // 6. Define a parallel finite element space on the parallel mesh. Here we
-   //    use the Nedelec finite elements of the specified order.
-   FiniteElementCollection *fec;
-   if (dim==4)
-   {
-      if (order==1) { fec = new ND1_4DFECollection; }
-      else { fec = new ND2_4DFECollection; }
-   }
-   else { fec = new ND_FECollection(order, dim); }
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-   }
-
-   // 7. 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;
-   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
-   ess_bdr = set_bc ? 1 : 0;
-   if (pmesh->bdr_attributes.Size())
-   {
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-   // 8. Set up the parallel linear form b(.) which corresponds to the
-   //    right-hand side of the FEM linear system, which in this case is
-   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
-   //    basis functions in the finite element fespace.
-
-
-   // 9. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x by projecting the exact
-   //    solution. Note that only values from the boundary edges will be used
-   //    when eliminating the non-homogeneous boundary condition to modify the
-   //    r.h.s. vector b.
-   ParGridFunction x(fespace);
-   VectorFunctionCoefficient E(sdim, E_exact);
-
-   for (int expo=weightStart; expo<=weightEnd; expo++)
-   {
-      double weight = pow(10.0,expo);
-      kappa = weight;
-
-      VectorFunctionCoefficient f(sdim, f_exact);
-      ParLinearForm *b = new ParLinearForm(fespace);
-      b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
-      b->Assemble();
-
-      x.ProjectCoefficient(E);
-
-      // 10. Set up the parallel bilinear form corresponding to the EM diffusion
-      //     operator curl muinv curl + sigma I, by adding the curl-curl and the
-      //     mass domain integrators.
-      //    std::string permFile = "spe_perm.dat";
-      //    InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
-
-      Coefficient *alpha = new ConstantCoefficient(1.0);
-      Coefficient *beta;
-      //    if(spe10Coeff) beta = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
-      //    else
-      beta = new ConstantCoefficient(weight);
-      Coefficient *neg_beta = new ConstantCoefficient(-weight);
-
-      ParBilinearForm *a = new ParBilinearForm(fespace);
-      a->AddDomainIntegrator(new CurlCurlIntegrator(*alpha));
-      a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));
-
-      // 11. 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();
-
-      HypreParMatrix A;
-      Vector B, X;
-      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
-
-      if (myid == 0)
-      {
-         cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
-      }
-
-      // 12. Define and apply a parallel PCG solver for AX=B with the AMS
-      //     preconditioner from hypre.
-      ParFiniteElementSpace *prec_fespace =
-         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
-      Solver *prec;
-      if (dim<=3) { prec = new HypreAMS(A, prec_fespace); }
-      else if (dim==4) { prec = new Curl4dPrec(&A, fespace, alpha, beta, neg_beta, ess_bdr, order, false); }
-      IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-      pcg->SetOperator(A);
-      pcg->SetRelTol(tol);
-      pcg->SetMaxIter(5000);
-      pcg->SetPrintLevel(1);
-      pcg->SetPreconditioner(*prec);
-      pcg->Mult(B, X);
-
-      int iter = pcg->GetNumIterations();
-      if (myid==0)
-      {
-         cout << "Weigth: " << weight << " " << iter << endl;
-
-         int *iters = LoadIterations(10, 2*NExpo+1);
-         putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
-                              2*NExpo+1, iters);
-         WriteIterations(iters, 10, 2*NExpo+1);
-      }
-
-      // 13. Recover the parallel grid function corresponding to X. This is the
-      //     local finite element solution on each processor.
-      a->RecoverFEMSolution(X, *b, x);
-
-      // 14. Compute and print the L^2 norm of the error.
-      {
-         double err = x.ComputeL2Error(E);
-         if (myid == 0)
-         {
-            cout << "\n|| E_h - E ||_{L^2} = " << err << '\n' << endl;
-         }
-      }
-
-      // 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;
-      //   }
-
-      delete pcg;
-      delete prec;
-      delete a;
-      delete alpha;
-      delete beta;
-      delete b;
-
-   }
-
-   // 17. Free the used memory.
-
-   delete fespace;
-   delete fec;
-   delete pmesh;
-
-   MPI_Finalize();
-
-   return 0;
-}
-
-
-void E_exact(const Vector &x, Vector &E)
-{
-   if (dim==4)
-   {
-      E(0) =  sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
-      E(1) = -cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
-      E(2) =  cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(M_PI*x(3));
-      E(3) = -cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(M_PI*x(3));
-   }
-   else if (dim == 3)
-   {
-      E(0) = sin(kappa * x(1));
-      E(1) = sin(kappa * x(2));
-      E(2) = sin(kappa * x(0));
-   }
-   else
-   {
-      E(0) = sin(kappa * x(1));
-      E(1) = sin(kappa * x(0));
-      if (x.Size() == 3) { E(2) = 0.0; }
-   }
-}
-
-void f_exact(const Vector &x, Vector &f)
-{
-   //f_exact = E +  DivSkew P( curl E ), where P is the 4d permutation operator
-   if (dim==4)
-   {
-      f(0) =  (kappa+4.0*M_PI*M_PI)*sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(
-                 M_PI*x(3));
-      f(1) = -(kappa+4.0*M_PI*M_PI)*cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(
-                M_PI*x(3));
-      f(2) =  (kappa+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(
-                 M_PI*x(3));
-      f(3) = -(kappa+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(
-                M_PI*x(3));
-   }
-   else if (dim == 3)
-   {
-      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
-      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
-      f(2) = (1. + kappa * kappa) * sin(kappa * x(0));
-   }
-   else
-   {
-      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
-      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
-      if (x.Size() == 3) { f(2) = 0.0; }
-   }
-}

examples/ex40.cpp

@@ -67,6 +67,8 @@ public:
    ZCoefficient(int vdim, GridFunction &psi_, real_t alpha_ = 1.0)
       : VectorCoefficient(vdim), psi(&psi_), alpha(alpha_) { }
 
+   using VectorCoefficient::Eval;
+
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }

examples/ex40p.cpp

@@ -67,6 +67,8 @@ public:
    ZCoefficient(int vdim, ParGridFunction &psi_, real_t alpha_ = 1.0)
       : VectorCoefficient(vdim), psi(&psi_), alpha(alpha_) { }
 
+   using VectorCoefficient::Eval;
+
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }

examples/ex4D_DivSkew.cpp

@@ -1,782 +0,0 @@
-//                       MFEM Example 3 - Parallel Version
-//
-// Compile with: make ex3p
-//
-// Sample runs:  mpirun -np 4 ex3p -m ../data/star.mesh
-//               mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
-//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
-//               mpirun -np 4 ex3p -m ../data/escher.mesh
-//               mpirun -np 4 ex3p -m ../data/fichera.mesh
-//               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
-//               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
-//               mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
-//               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
-//               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
-//               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
-//               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
-//               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
-//
-// Description:  This example code solves a simple electromagnetic diffusion
-//               problem corresponding to the second order definite Maxwell
-//               equation curl curl E + E = f with boundary condition
-//               E x n = <given tangential field>. Here, we use a given exact
-//               solution E and compute the corresponding r.h.s. f.
-//               We discretize with Nedelec finite elements in 2D or 3D.
-//
-//               The example demonstrates the use of H(curl) finite element
-//               spaces with the curl-curl and the (vector finite element) mass
-//               bilinear form, as well as the computation of discretization
-//               error when the exact solution is known. Static condensation is
-//               also illustrated.
-//
-//               We recommend viewing examples 1-2 before viewing this example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-#include "./spe10_coeff.cpp"
-
-using namespace std;
-using namespace mfem;
-
-
-int* LoadIterations(int NRows, int NCol)
-{
-   ifstream in("iter_DivSkew.txt");
-
-   //initialize
-   int *iters = new int[NCol*NRows];
-   for (int col = 0; col < NCol; col++)
-   {
-      for (int row = 0; row < NRows; row++)
-      {
-         iters[row*NCol+col] = -1;
-      }
-   }
-
-   if (!in)
-   {
-      cout << "Cannot open file.\n";
-      return iters;
-   }
-
-   for (int row = 0; row < NRows; row++)
-      for (int col = 0; col < NCol; col++)
-      {
-         if (in.eof())
-         {
-            in.close();
-            return iters;
-         }
-         in >> iters[row*NCol+col];
-      }
-
-   in.close();
-
-   return iters;
-}
-
-void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
-{
-   iters[row*NCol+col] = iter;
-}
-
-void WriteIterations(int *iters, int NRows, int NCol)
-{
-   ofstream out;
-   out.open("iter_DivSkew.txt",fstream::out);
-
-   if (!out)
-   {
-      cout << "Cannot open file.\n";
-      delete[] iters;
-
-      return;
-   }
-
-   for (int row = 0; row < NRows; row++)
-   {
-      for (int col = 0; col < NCol; col++)
-      {
-         out << iters[row*NCol+col] << "\t";
-      }
-      out << endl;
-   }
-   out.close();
-
-   delete[] iters;
-}
-
-
-// Exact solution, E, and r.h.s., f. See below for implementation.
-void E_exact_vec(const Vector &x, Vector &E);
-void E_exact(const Vector &, DenseMatrix &);
-void f_exact(const Vector &, DenseMatrix &);
-
-
-class DivSkew4dPrec : public Solver
-{
-
-private:
-   HypreParMatrix *A;
-   ParFiniteElementSpace *fespace;
-   Coefficient *alpha_, *beta_;
-
-   //kernel operators
-   HypreParMatrix *P_d_HCurl_HDivSkew;
-
-
-   HypreParMatrix *P_H1_HCurl;
-   HypreParMatrix *H1_KernelMat;
-   HypreBoomerAMG *amgH1_Kernel;
-
-   //"image" operators
-   HypreParMatrix *P_H1_HDivSkew;
-   HypreParMatrix *H1_ImageMat;
-   HypreBoomerAMG *amgH1_Image;
-
-
-   HypreParMatrix *HCurlMat;
-   HypreSmoother * smootherDivSkew;
-   HypreSmoother * smootherCurl;
-
-   CGSolver *pcgKernel;
-   CGSolver *pcgImage;
-
-   Vector *f;
-   Vector *fKernel, *uKernel;
-   Vector *fImage, *uImage;
-   Vector *fCurl, *uCurl;
-
-   bool exactSolves;
-
-   FiniteElementCollection* fecHCurlKernel;
-   ParFiniteElementSpace *HCurlKernelFESpace;
-
-
-public:
-   ~DivSkew4dPrec()
-   {
-      delete pcgImage, pcgKernel;
-
-      delete f, fKernel, uKernel, fImage, uImage, fCurl, uCurl;
-
-      delete smootherCurl, HCurlMat;
-
-      delete P_d_HCurl_HDivSkew, P_H1_HDivSkew, P_H1_HCurl;
-
-      delete amgH1_Image, H1_ImageMat;
-      delete amgH1_Kernel, H1_KernelMat;
-
-      delete smootherDivSkew;
-
-      delete HCurlKernelFESpace, fecHCurlKernel;
-   }
-   DivSkew4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
-                 Coefficient *alpha, Coefficient *beta,
-                 const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
-   {
-      A = AUser;
-      fespace = fespaceUser;
-      alpha_ = alpha;
-      beta_ = beta;
-
-      ParMesh *pmesh = fespace->GetParMesh();
-      int dim = pmesh->Dimension();
-
-      exactSolves = exactSolvesUser;
-
-      int orderIm=1;  //H1  --> H(divSkew)
-      int orderKer=orderKernel; //curl V --> H(divSkew)
-
-      smootherDivSkew = new HypreSmoother(*A, 16, 3);
-
-      Array<int> HDivSkew_essDof(fespace->GetVSize()); HDivSkew_essDof = 0;
-      fespace->GetEssentialVDofs(essBnd, HDivSkew_essDof);
-
-      //setup the H1 FESpace for the kernel
-      FiniteElementCollection* fecH1Kernel = new H1_FECollection(orderKer, 4);
-
-      ParFiniteElementSpace *H1KernelFESpace = new ParFiniteElementSpace(pmesh,
-                                                                         fecH1Kernel, dim, Ordering::byVDIM);
-      Array<int> H1Kernel_essDof(H1KernelFESpace->GetVSize()); H1Kernel_essDof = 0;
-      H1KernelFESpace->GetEssentialVDofs(essBnd, H1Kernel_essDof);
-
-
-      //setup the H(curl) FESpace for the kernel
-      if (orderKer==1) { fecHCurlKernel = new ND1_4DFECollection; }
-      else { fecHCurlKernel = new ND2_4DFECollection; }
-
-      HCurlKernelFESpace = new ParFiniteElementSpace(pmesh,
-                                                     fecHCurlKernel);
-      Array<int> HCurlKernel_essDof(HCurlKernelFESpace->GetVSize());
-      HCurlKernel_essDof = 0;
-      HCurlKernelFESpace->GetEssentialVDofs(essBnd, HCurlKernel_essDof);
-
-
-      //setup the FESpace for the H1 injection
-      FiniteElementCollection* fecH1Vec;
-      if (orderIm==1) { fecH1Vec = new LinearFECollection; }
-      else { fecH1Vec = new QuadraticFECollection; }
-      ParFiniteElementSpace *H1_ImageFESpace = new ParFiniteElementSpace(pmesh,
-                                                                         fecH1Vec, 6, Ordering::byVDIM);
-      Array<int> H1Image_essDof(H1_ImageFESpace->GetVSize()); H1Image_essDof = 0;
-      H1_ImageFESpace->GetEssentialVDofs(essBnd, H1Image_essDof);
-
-
-
-      //setup the H1 preconditioner for the kernel
-      ParBilinearForm* H1Varf = new ParBilinearForm(H1KernelFESpace);
-      H1Varf->AddDomainIntegrator(new VectorDiffusionIntegrator(*beta_));
-      //      H1Varf->AddDomainIntegrator(new VectorMassIntegrator);
-      H1Varf->Assemble();
-      H1Varf->Finalize();
-      SparseMatrix &matH1(H1Varf->SpMat());
-      for (int dof = 0; dof < H1Kernel_essDof.Size(); dof++)
-         if (H1Kernel_essDof[dof] < 0)
-         {
-            matH1.EliminateRowCol(dof);
-         }
-      H1_KernelMat = H1Varf->ParallelAssemble();
-      delete H1Varf;
-      amgH1_Kernel = new HypreBoomerAMG(*H1_KernelMat);
-      amgH1_Kernel->SetSystemsOptions(dim);
-      amgH1_Kernel->SetPrintLevel(0);
-
-      //setup the H1 preconditioner for the image
-      ParBilinearForm* H1VecVarf = new ParBilinearForm(H1_ImageFESpace);
-      VectorDiffusionIntegrator *alpha_integ = new VectorDiffusionIntegrator(*alpha_);
-      alpha_integ->SetVDim(6);
-      H1VecVarf->AddDomainIntegrator(alpha_integ);
-      VectorMassIntegrator *beta_integ = new VectorMassIntegrator(*beta);
-      beta_integ->SetVDim(6);
-      H1VecVarf->AddDomainIntegrator(beta_integ);
-      H1VecVarf->Assemble();
-      H1VecVarf->Finalize();
-      SparseMatrix &matH1Vec(H1VecVarf->SpMat());
-      for (int dof=0; dof<H1Image_essDof.Size(); dof++) if (H1Image_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
-      H1_ImageMat = H1VecVarf->ParallelAssemble();
-      delete H1VecVarf;
-      amgH1_Image = new HypreBoomerAMG(*H1_ImageMat);
-      amgH1_Image->SetSystemsOptions(6);
-      amgH1_Image->SetPrintLevel(0);
-
-
-      //setup the injection of H1 into H(curl)
-      ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
-         H1KernelFESpace, HCurlKernelFESpace);
-      disInterpol->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpol->Assemble();
-      disInterpol->Finalize();
-      SparseMatrix* smatID = &(disInterpol->SpMat());
-      smatID->EliminateCols(H1Kernel_essDof);
-      for (int dof=0; dof<HCurlKernel_essDof.Size();
-           dof++) if (HCurlKernel_essDof[dof]<0) { smatID->EliminateRow(dof); }
-      P_H1_HCurl = disInterpol->ParallelAssemble();
-      delete disInterpol;
-
-      //setup the injection of H1 into H(DivSkew)
-      ParDiscreteLinearOperator *disInterpolIm = new ParDiscreteLinearOperator(
-         H1_ImageFESpace, fespace);
-      disInterpolIm->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpolIm->Assemble();
-      disInterpolIm->Finalize();
-      SparseMatrix* smatIDIm = &(disInterpolIm->SpMat());
-      smatIDIm->EliminateCols(H1Image_essDof);
-      for (int dof=0; dof<HDivSkew_essDof.Size(); dof++) if (HDivSkew_essDof[dof]<0) { smatIDIm->EliminateRow(dof); }
-      P_H1_HDivSkew = disInterpolIm->ParallelAssemble();
-      delete disInterpolIm;
-
-
-      //setup the injection of the curl(H(curl)) into H(DivSkew)
-      ParDiscreteLinearOperator *disCurl = new ParDiscreteLinearOperator(
-         HCurlKernelFESpace, fespace);
-      disCurl->AddDomainInterpolator(new CurlInterpolator);
-      disCurl->Assemble();
-      disCurl->Finalize();
-      SparseMatrix* smatCurl = &(disCurl->SpMat());
-      smatCurl->EliminateCols(HCurlKernel_essDof);
-      for (int dof=0; dof<HDivSkew_essDof.Size(); dof++) if (HDivSkew_essDof[dof]<0) { smatCurl->EliminateRow(dof); }
-      P_d_HCurl_HDivSkew = disCurl->ParallelAssemble();
-      delete disCurl;
-
-      //setup the smoother for H(curl)
-      //      Coefficient *massC = new ConstantCoefficient(1.0);
-      //      Coefficient *CurlCurlC = new ConstantCoefficient(1.0);
-      ParBilinearForm *a_HCurl = new ParBilinearForm(HCurlKernelFESpace);
-      a_HCurl->AddDomainIntegrator(new CurlCurlIntegrator(*beta_));
-      //      a_HCurl->AddDomainIntegrator(new CurlCurlIntegrator(*CurlCurlC));
-      //      a_HCurl->AddDomainIntegrator(new VectorFEMassIntegrator(*massC));
-      a_HCurl->Assemble();
-      a_HCurl->Finalize();
-      SparseMatrix &matHCurl(a_HCurl->SpMat());
-      for (int dof=0; dof<HCurlKernel_essDof.Size();
-           dof++) if (HCurlKernel_essDof[dof]<0) { matHCurl.EliminateRowCol(dof); }
-      HCurlMat = a_HCurl->ParallelAssemble();
-      delete a_HCurl;
-      smootherCurl = new HypreSmoother(*HCurlMat, 16, 3);
-
-      f = new Vector(fespace->GetTrueVSize());
-
-      fKernel = new Vector(H1KernelFESpace->GetTrueVSize());
-      uKernel = new Vector(H1KernelFESpace->GetTrueVSize());
-
-      fImage = new Vector(H1_ImageFESpace->GetTrueVSize());
-      uImage = new Vector(H1_ImageFESpace->GetTrueVSize());
-
-      fCurl = new Vector(HCurlKernelFESpace->GetTrueVSize());
-      uCurl = new Vector(HCurlKernelFESpace->GetTrueVSize());
-
-
-      amgH1_Kernel->Mult(*fKernel, *uKernel);
-      amgH1_Image->Mult(*fImage, *uImage);
-
-      pcgKernel = new CGSolver(MPI_COMM_WORLD);
-      pcgKernel->SetOperator(*H1_KernelMat);
-      pcgKernel->SetPreconditioner(*amgH1_Kernel);
-      pcgKernel->SetRelTol(1e-16);
-      pcgKernel->SetMaxIter(100000000);
-      pcgKernel->SetPrintLevel(-2);
-
-      pcgImage = new CGSolver(MPI_COMM_WORLD);
-      pcgImage->SetOperator(*H1_ImageMat);
-      pcgImage->SetPreconditioner(*amgH1_Image);
-      pcgImage->SetRelTol(1e-16);
-      pcgImage->SetMaxIter(100000000);
-      pcgImage->SetPrintLevel(-2);
-
-      delete H1KernelFESpace, fecH1Kernel;
-      delete H1_ImageFESpace, fecH1Vec;
-   }
-
-   void setExactSolve(bool exSol)
-   {
-      exactSolves = exSol;
-   }
-
-   virtual void Mult(const Vector &x, Vector &y) const
-   {
-      smootherDivSkew->Mult(x,y);
-
-      P_H1_HDivSkew->MultTranspose(x,*fImage);
-      *uImage = 0.0;
-      if (exactSolves) { pcgImage->Mult(*fImage, *uImage); }
-      else { amgH1_Image->Mult(*fImage, *uImage); }
-      P_H1_HDivSkew->Mult(1.0, *uImage, 1.0, y);
-
-      *uCurl = 0.0;
-      P_d_HCurl_HDivSkew->MultTranspose(x,*fCurl);
-
-      smootherCurl->Mult(*fCurl, *uCurl);
-
-      P_H1_HCurl->MultTranspose(*fCurl,*fKernel);
-      *uKernel = 0.0;
-      if (exactSolves) { pcgKernel->Mult(*fKernel, *uKernel); }
-      else { amgH1_Kernel->Mult(*fKernel, *uKernel); }
-      P_H1_HCurl->Mult(1.0, *uKernel, 1.0, *uCurl);
-
-      P_d_HCurl_HDivSkew->Mult(1.0, *uCurl, 1.0, y);
-   }
-
-   virtual void SetOperator(const Operator &op) {};
-
-};
-
-
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   int num_procs, myid;
-   MPI_Init(&argc, &argv);
-   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
-   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
-
-   bool verbose = (myid==0);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/cube4d_96.MFEM";
-   int order = 1;
-   bool set_bc = true;
-   bool static_cond = false;
-   bool visualization = 1;
-   int sequ_ref_levels = 0;
-   int par_ref_levels = 0;
-   double tol = 1e-6;
-   double coeffWeight = 1.0;
-   bool exactH1Solver = false;
-   bool spe10Coeff = false;
-   bool standardCG = true;
-
-   int NExpo = 8;
-   int weightStart = -NExpo;
-   int weightEnd = NExpo;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
-                  "Number of sequential refinement steps.");
-   args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
-                  "Number of parallel refinement steps.");
-   args.AddOption(&order, "-o", "--order",
-                  "Polynomial order of the finite element space.");
-   args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
-                  "Impose or not essential boundary conditions.");
-   args.AddOption(&tol, "-tol", "--tol",
-                  "A parameter.");
-   args.AddOption(&coeffWeight, "-c", "--coeffMass",
-                  "the weight for the mass term.");
-   args.AddOption(&exactH1Solver, "-exH1Sol", "--exactH1Solver", "-H1prec",
-                  "--H1preconditioner",
-                  "Use exact H1 solvers for the preconditioner.");
-   args.AddOption(&spe10Coeff, "-spe10", "--useSPE10Coeff", "-constCoeff",
-                  "--constCoeff",
-                  "Switch between the coefficients for the mass bilinear form.");
-   args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
-                  "Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
-   args.AddOption(&weightStart, "-ws", "--weightStart",
-                  "the exponent for the starting weight (for the mass term).");
-   args.AddOption(&weightEnd, "-we", "--weightEnd",
-                  "the exponent for the weight at the end (for the mass term).");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   if (verbose) { args.PrintOptions(cout); }
-
-   Mesh *mesh;
-   ifstream imesh(mesh_file);
-   if (!imesh)
-   {
-      cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
-      return 2;
-   }
-
-   mesh = new Mesh(imesh, 1, 1);
-   imesh.close();
-
-   int dim = mesh->Dimension();
-   int sdim = mesh->SpaceDimension();
-
-   if (dim !=4 || sdim != 4)
-   {
-      MPI_Finalize();
-      return 0;
-   }
-
-   for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
-   if (verbose) { mesh->PrintCharacteristics(); }
-
-   if (verbose) { cout << "now we partition the mesh..." << endl << endl; }
-
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-
-   for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }
-
-   pmesh->PrintInfo(std::cout);
-   if (verbose) { cout << endl; }
-
-   // 6. Define a parallel finite element space on the parallel mesh. Here we
-   //    use the Nedelec finite elements of the specified order.
-   FiniteElementCollection *fec;
-   if (order==1) { fec = new DivSkew1_4DFECollection; }
-   //    else fec = new F2K1_4DFECollection;
-
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   fespace->SetUpdateOperatorType(Operator::Hypre_ParCSR);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
-
-   // 7. 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;
-   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
-   ess_bdr = set_bc ? 1 : 0;
-   if (pmesh->bdr_attributes.Size())
-   {
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-
-   }
-
-   // 8. Set up the parallel linear form b(.) which corresponds to the
-   //    right-hand side of the FEM linear system, which in this case is
-   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
-   //    basis functions in the finite element fespace.
-   MatrixFunctionCoefficient f(sdim, f_exact);
-   MatrixFunctionCoefficient solMat(sdim, E_exact);
-   VectorFunctionCoefficient solVec(6, E_exact_vec);
-
-
-
-
-   // 9. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x by projecting the exact
-   //    solution. Note that only values from the boundary edges will be used
-   //    when eliminating the non-homogeneous boundary condition to modify the
-   //    r.h.s. vector b.
-   ParGridFunction x(fespace);
-
-   for (int expo=weightStart; expo<=weightEnd; expo++)
-   {
-      double weight = pow(10.0,expo);
-
-      x.ProjectCoefficient(solVec);
-
-      ParLinearForm *b = new ParLinearForm(fespace);
-      b->AddDomainIntegrator(new MatFEDomainLFIntegrator(f));
-      b->Assemble();
-
-      //   cout << x << endl;
-      //   x = 0.0;
-
-      // 10. Set up the parallel bilinear form corresponding to the EM diffusion
-      //     operator curl muinv curl + sigma I, by adding the curl-curl and the
-      //     mass domain integrators.
-      //    std::string permFile = "spe_perm.dat";
-      //    InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
-
-      Coefficient *alpha = new ConstantCoefficient(1.0);
-      Coefficient *beta;
-      //    if(spe10Coeff) beta = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
-      //    else
-      beta = new ConstantCoefficient(weight);
-
-      ParBilinearForm *a = new ParBilinearForm(fespace);
-      a->AddDomainIntegrator(new DivSkewDivSkewIntegrator(*alpha));
-      a->AddDomainIntegrator(new VectorFE_DivSkewMassIntegrator(*beta));
-
-      // 11. 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();
-
-      HypreParMatrix A;
-      Vector B, X;
-      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
-
-      if (myid == 0)
-      {
-         cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
-      }
-
-      //Define the preconditioner
-
-      if (myid == 0) { cout << "Set up the preconditioner" << endl; }
-      Solver *prec;
-      if (dim==4) { prec = new DivSkew4dPrec(&A, fespace, alpha, beta, ess_bdr, order, exactH1Solver); }
-
-      IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-      pcg->SetOperator(A);
-      pcg->SetRelTol(tol);
-      pcg->SetMaxIter(500);
-      pcg->SetPrintLevel(1);
-      pcg->SetPreconditioner(*prec);
-      pcg->Mult(B, X);
-
-      delete prec;
-
-      int iter = pcg->GetNumIterations();
-      if (myid==0)
-      {
-         cout << "Weigth: " << weight << " " << iter << endl;
-
-         int *iters = LoadIterations(10, 2*NExpo+1);
-         putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
-                              2*NExpo+1, iters);
-         WriteIterations(iters, 10, 2*NExpo+1);
-      }
-
-      // 13. Recover the parallel grid function corresponding to X. This is the
-      //     local finite element solution on each processor.
-      a->RecoverFEMSolution(X, *b, x);
-
-      // 14. Compute and print the L^2 norm of the error.
-      {
-         double error = 0.0;
-         for (int i = 0; i < fespace->GetNE(); i++)
-         {
-            const FiniteElement* fe = fespace->GetFE(i);
-            int fdof = fe->GetDof();
-            ElementTransformation* transf = fespace->GetElementTransformation(i);
-            DenseMatrix shape(fdof,dim*dim);
-
-            int intorder = 2*fe->GetOrder() + 1; // <----------
-            const IntegrationRule *ir;
-            ir = &(IntRules.Get(fe->GetGeomType(), intorder));
-
-            Vector elSol(dim*dim);
-            DenseMatrix elSolMat(dim,dim);
-            DenseMatrix exactSol(dim,dim);
-            Vector exactSolVec(dim*dim);
-
-
-
-            Array<int> vdofs;
-            fespace->GetElementVDofs(i, vdofs);
-            for (int j = 0; j < ir->GetNPoints(); j++)
-            {
-               const IntegrationPoint &ip = ir->IntPoint(j);
-               transf->SetIntPoint(&ip);
-
-               fe->CalcVShape(*transf, shape);
-
-               elSol = 0.0;
-               for (int k = 0; k < fdof; k++)
-               {
-                  if (vdofs[k] >= 0)
-                  {
-                     for (int l=0; l<dim*dim; l++) { elSol(l) += shape(k,l)*x(vdofs[k]); }
-                  }
-                  else
-                  {
-                     for (int l=0; l<dim*dim; l++) { elSol(l) -= shape(k,l)*x(-1-vdofs[k]); }
-                  }
-               }
-               for (int k=0; k<dim; k++)
-                  for (int l=0; l<dim; l++)
-                  {
-                     elSolMat(k,l) = elSol(dim*k+l);
-                  }
-
-
-               solMat.Eval(exactSol,*transf, ip);
-               for (int k=0; k<dim; k++)
-                  for (int l=0; l<dim; l++)
-                  {
-                     exactSolVec(dim*k+l) = exactSol(k,l);
-                  }
-               elSol.Add(-1.0, exactSolVec);
-
-               error += ip.weight * fabs(transf->Weight()) * (elSol * elSol);
-            }
-         }
-         double globalError = 0.0;
-         MPI_Allreduce(&error, &globalError, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-         if (myid==0) { std::cout << "L2 error: " << sqrt(globalError) << std::endl; }
-
-
-      }
-
-      delete pcg;
-      delete a;
-      delete alpha;
-      delete beta;
-
-      delete b;
-   }
-
-   // 17. Free the used memory.
-
-
-
-   delete fespace;
-   delete fec;
-   delete pmesh;
-
-
-   MPI_Finalize();
-
-   return 0;
-}
-
-void E_exact_vec(const Vector &x, Vector &E)
-{
-   int dim = x.Size();
-
-   if (dim==4)
-   {
-      E.SetSize(6);
-
-      double s0 = sin(M_PI*x(0)), s1 = sin(M_PI*x(1)), s2 = sin(M_PI*x(2)),
-             s3 = sin(M_PI*x(3));
-      double c0 = cos(M_PI*x(0)), c1 = cos(M_PI*x(1)), c2 = cos(M_PI*x(2)),
-             c3 = cos(M_PI*x(3));
-
-      E(0) =  c0*c1*s2*s3;
-      E(1) = -c0*s1*c2*s3;
-      E(2) =  c0*s1*s2*c3;
-      E(3) =  s0*c1*c2*s3;
-      E(4) = -s0*c1*s2*c3;
-      E(5) =  s0*s1*c2*c3;
-   }
-}
-
-void E_exact(const Vector &x, DenseMatrix &E)
-{
-   int dim = x.Size();
-
-   E.SetSize(dim*dim);
-
-   if (dim==4)
-   {
-      Vector vecE; E_exact_vec(x, vecE);
-
-      E = 0.0;
-
-      E(0,1) = vecE(0);
-      E(0,2) = vecE(1);
-      E(0,3) = vecE(2);
-      E(1,2) = vecE(3);
-      E(1,3) = vecE(4);
-      E(2,3) = vecE(5);
-
-      E(1,0) =  -E(0,1);
-      E(2,0) =  -E(0,2);
-      E(3,0) =  -E(0,3);
-      E(2,1) =  -E(1,2);
-      E(3,1) =  -E(1,3);
-      E(3,2) =  -E(2,3);
-   }
-}
-
-
-
-//f_exact = E + 0.5 * P( curl DivSkew E ), where P is the 4d permutation operator
-void f_exact(const Vector &x, DenseMatrix &f)
-{
-   int dim = x.Size();
-
-   f.SetSize(dim,dim);
-
-   if (dim==4)
-   {
-      f = 0.0;
-
-      double s0 = sin(M_PI*x(0)), s1 = sin(M_PI*x(1)), s2 = sin(M_PI*x(2)),
-             s3 = sin(M_PI*x(3));
-      double c0 = cos(M_PI*x(0)), c1 = cos(M_PI*x(1)), c2 = cos(M_PI*x(2)),
-             c3 = cos(M_PI*x(3));
-
-      f(0,1) =  (1.0 + 1.0  * M_PI*M_PI)*c0*c1*s2*s3;
-      f(0,2) = -(1.0 + 0.0  * M_PI*M_PI)*c0*s1*c2*s3;
-      f(0,3) =  (1.0 + 1.0  * M_PI*M_PI)*c0*s1*s2*c3;
-      f(1,2) =  (1.0 - 1.0  * M_PI*M_PI)*s0*c1*c2*s3;
-      f(1,3) = -(1.0 + 0.0  * M_PI*M_PI)*s0*c1*s2*c3;
-      f(2,3) =  (1.0 + 1.0  * M_PI*M_PI)*s0*s1*c2*c3;
-
-      f(1,0) =  -f(0,1);
-      f(2,0) =  -f(0,2);
-      f(3,0) =  -f(0,3);
-      f(2,1) =  -f(1,2);
-      f(3,1) =  -f(1,3);
-      f(3,2) =  -f(2,3);
-   }
-}

examples/ex4p_4d.cpp

@@ -1,800 +0,0 @@
-//                       MFEM Example 4 - Parallel Version
-//
-// Compile with: make ex4p
-//
-// Sample runs:  mpirun -np 4 ex4p -m ../data/square-disc.mesh
-//               mpirun -np 4 ex4p -m ../data/star.mesh
-//               mpirun -np 4 ex4p -m ../data/beam-tet.mesh
-//               mpirun -np 4 ex4p -m ../data/beam-hex.mesh
-//               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-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
-//               mpirun -np 4 ex4p -m ../data/beam-hex-nurbs.mesh -o 3
-//               mpirun -np 4 ex4p -m ../data/periodic-square.mesh -no-bc
-//               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
-//               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
-//               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/star-surf.mesh -o 3 -hb
-//
-// Description:  This example code solves a simple 2D/3D H(div) diffusion
-//               problem corresponding to the second order definite equation
-//               -grad(alpha div F) + beta F = f with boundary condition F dot n
-//               = <given normal field>. Here, we use a given exact solution F
-//               and compute the corresponding r.h.s. f.  We discretize with
-//               Raviart-Thomas finite elements.
-//
-//               The example demonstrates the use of H(div) finite element
-//               spaces with the grad-div and H(div) vector finite element mass
-//               bilinear form, as well as the computation of discretization
-//               error when the exact solution is known. Bilinear form
-//               hybridization and static condensation are also illustrated.
-//
-//               We recommend viewing examples 1-3 before viewing this example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-#include "./spe10_coeff.cpp"
-
-using namespace std;
-using namespace mfem;
-
-
-int* LoadIterations(int NRows, int NCol)
-{
-   ifstream in("iter_div.txt");
-
-   //initialize
-   int *iters = new int[NCol*NRows];
-   for (int col = 0; col < NCol; col++)
-   {
-      for (int row = 0; row < NRows; row++)
-      {
-         iters[row*NCol+col] = -1;
-      }
-   }
-
-   if (!in)
-   {
-      cout << "Cannot open file.\n";
-      return iters;
-   }
-
-   for (int row = 0; row < NRows; row++)
-      for (int col = 0; col < NCol; col++)
-      {
-         if (in.eof())
-         {
-            in.close();
-            return iters;
-         }
-         in >> iters[row*NCol+col];
-      }
-
-
-   in.close();
-
-   return iters;
-}
-
-void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
-{
-   iters[row*NCol+col] = iter;
-}
-
-void WriteIterations(int *iters, int NRows, int NCol)
-{
-   ofstream out;
-   out.open("iter_div.txt",fstream::out);
-
-   if (!out)
-   {
-      cout << "Cannot open file.\n";
-      delete[] iters;
-
-      return;
-   }
-
-   for (int row = 0; row < NRows; row++)
-   {
-      for (int col = 0; col < NCol; col++)
-      {
-         out << iters[row*NCol+col] << "\t";
-      }
-      out << endl;
-   }
-   out.close();
-
-   delete[] iters;
-}
-
-
-// Exact solution, F, and r.h.s., f. See below for implementation.
-void F_exact(const Vector &, Vector &);
-void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa;
-
-
-
-class div4dPrec : public Solver
-{
-
-private:
-   HypreParMatrix *A;
-   ParFiniteElementSpace *fespace;
-
-   Coefficient *alpha_, *beta_;
-
-   //kernel operators
-   HypreParMatrix *P_d_HSkewDiv_Hdiv;
-
-   HypreParMatrix *P_H1_HDivSkew;
-   HypreParMatrix *H1_KernelMat;
-   HypreBoomerAMG *amgH1_Kernel;
-
-   //"image" operators
-   HypreParMatrix *P_H1_Hdiv;
-   HypreParMatrix *H1_ImageMat;
-   HypreBoomerAMG *amgH1_Image;
-
-   HypreParMatrix *HDivSkewMat;
-   HypreSmoother * smootherdiv;
-   HypreSmoother * smootherDivSkew;
-
-   CGSolver *pcgKernel;
-   CGSolver *pcgImage;
-
-   Vector *f;
-   Vector *fKernel, *uKernel;
-   Vector *fImage, *uImage;
-   Vector *fDivSkew, *uDivSkew;
-
-   FiniteElementCollection* fecHDivSkewKernel;
-   ParFiniteElementSpace *HDivSkewKernelFESpace;
-
-   bool exactSolves;
-
-public:
-   ~div4dPrec()
-   {
-      delete pcgImage;
-      delete pcgKernel;
-
-      delete uDivSkew, fDivSkew, uImage, fImage, uKernel, fKernel, f;
-
-      delete smootherDivSkew;
-      delete HDivSkewMat;
-
-      delete P_d_HSkewDiv_Hdiv;
-      delete P_H1_Hdiv;
-      delete P_H1_HDivSkew;
-
-      delete amgH1_Image, H1_ImageMat;
-      delete amgH1_Kernel, H1_KernelMat;
-
-      delete smootherdiv;
-
-      delete HDivSkewKernelFESpace;
-      delete fecHDivSkewKernel;
-   }
-   div4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
-             Coefficient *alpha, Coefficient *beta, const Array<int> &essBnd,
-             int orderKernel=1, bool exactSolvesUser=false)
-   {
-      A = AUser;
-      fespace = fespaceUser;
-      alpha_ = alpha;
-      beta_ = beta;
-
-
-      ParMesh *pmesh = fespace->GetParMesh();
-      int dim = pmesh->Dimension();
-
-      exactSolves = exactSolvesUser;
-
-
-
-
-      int orderIm=1;  //H1  --> H(div)
-      int orderKer=orderKernel; //DivSkew V --> H(div)
-
-
-
-      smootherdiv = new HypreSmoother(*A, 16, 3);
-
-      Array<int> Hdiv_essDof(fespace->GetVSize()); Hdiv_essDof = 0;
-      fespace->GetEssentialVDofs(essBnd, Hdiv_essDof);
-
-
-
-
-      //setup the H1 FESpace for the kernel
-      FiniteElementCollection* fecH1Kernel;
-      if (orderKer==1) { fecH1Kernel = new LinearFECollection; }
-      else { fecH1Kernel = new QuadraticFECollection; }
-      ParFiniteElementSpace *H1KernelFESpace = new ParFiniteElementSpace(pmesh,
-                                                                         fecH1Kernel, 6, Ordering::byVDIM);
-      Array<int> H1Kernel_essDof(H1KernelFESpace->GetVSize()); H1Kernel_essDof = 0;
-      H1KernelFESpace->GetEssentialVDofs(essBnd, H1Kernel_essDof);
-
-
-      //setup the H(DivSkew) FESpace for the kernel
-      if (orderKer==1) { fecHDivSkewKernel = new DivSkew1_4DFECollection; }
-      //       else fecHDivSkewKernel = new DivSkewFull1_4DFECollection;
-      HDivSkewKernelFESpace = new ParFiniteElementSpace(pmesh, fecHDivSkewKernel);
-      Array<int> HDivSkewKernel_essDof(HDivSkewKernelFESpace->GetVSize());
-      HDivSkewKernel_essDof = 0;
-      HDivSkewKernelFESpace->GetEssentialVDofs(essBnd, HDivSkewKernel_essDof);
-
-
-      //setup the FESpace for the H1 injection
-      FiniteElementCollection* fecH1Vec;
-      if (orderIm==1) { fecH1Vec = new LinearFECollection; }
-      else { fecH1Vec = new QuadraticFECollection; }
-      ParFiniteElementSpace *H1_ImageFESpace = new ParFiniteElementSpace(pmesh,
-                                                                         fecH1Vec, dim, Ordering::byVDIM);
-      Array<int> H1Image_essDof(H1_ImageFESpace->GetVSize()); H1Image_essDof = 0;
-      H1_ImageFESpace->GetEssentialVDofs(essBnd, H1Image_essDof);
-
-
-
-      //setup the H1 preconditioner for the kernel
-      ParBilinearForm* H1Varf = new ParBilinearForm(H1KernelFESpace);
-      //    H1Varf->AddDomainIntegrator(new VectorDiffusionIntegrator(*alpha_, 6));
-      //    H1Varf->AddDomainIntegrator(new VectorMassIntegrator(6, beta_));
-
-      H1Varf->AddDomainIntegrator(new VectorDiffusionIntegrator(*beta_, 6));
-      H1Varf->Assemble();
-      H1Varf->Finalize();
-      SparseMatrix &matH1(H1Varf->SpMat());
-      for (int dof=0; dof<H1Kernel_essDof.Size(); dof++) if (H1Kernel_essDof[dof]<0) { matH1.EliminateRowCol(dof); }
-      H1_KernelMat = H1Varf->ParallelAssemble();
-      delete H1Varf;
-      amgH1_Kernel = new HypreBoomerAMG(*H1_KernelMat);
-      amgH1_Kernel->SetSystemsOptions(6);
-
-      //setup the H1 preconditioner for the image
-      ParBilinearForm* H1VecVarf = new ParBilinearForm(H1_ImageFESpace);
-      H1VecVarf->AddDomainIntegrator(new VectorDiffusionIntegrator(*alpha_));
-      H1VecVarf->AddDomainIntegrator(new VectorMassIntegrator(-1, beta_));
-      H1VecVarf->Assemble();
-      H1VecVarf->Finalize();
-      SparseMatrix &matH1Vec(H1VecVarf->SpMat());
-      for (int dof=0; dof<H1Image_essDof.Size(); dof++) if (H1Image_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
-      H1_ImageMat = H1VecVarf->ParallelAssemble();
-      delete H1VecVarf;
-      amgH1_Image = new HypreBoomerAMG(*H1_ImageMat);
-      amgH1_Image->SetSystemsOptions(dim);
-
-
-      //setup the injection of H1 into H(DivSkew)
-      ParDiscreteLinearOperator *disInterpolIm = new ParDiscreteLinearOperator(
-         H1KernelFESpace, HDivSkewKernelFESpace);
-      disInterpolIm->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpolIm->Assemble();
-      disInterpolIm->Finalize();
-      SparseMatrix* smatIDIm = &(disInterpolIm->SpMat());
-      smatIDIm->EliminateCols(H1Kernel_essDof);
-      for (int dof=0; dof<HDivSkewKernel_essDof.Size();
-           dof++) if (HDivSkewKernel_essDof[dof]<0) { smatIDIm->EliminateRow(dof); }
-      P_H1_HDivSkew = disInterpolIm->ParallelAssemble();
-      delete disInterpolIm;
-
-      //setup the injection of H1 into H(div)
-      ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
-         H1_ImageFESpace, fespace);
-      disInterpol->AddDomainInterpolator(new IdentityInterpolator);
-      disInterpol->Assemble();
-      disInterpol->Finalize();
-      SparseMatrix* smatID = &(disInterpol->SpMat());
-      smatID->EliminateCols(H1Image_essDof);
-      for (int dof=0; dof<Hdiv_essDof.Size(); dof++) if (Hdiv_essDof[dof]<0) { smatID->EliminateRow(dof); }
-      P_H1_Hdiv = disInterpol->ParallelAssemble();
-      delete disInterpol;
-
-
-
-
-      //setup the injection of the DivSkew(H(DivSkew)) into H(div)
-      ParDiscreteLinearOperator *disDivSkew = new ParDiscreteLinearOperator(
-         HDivSkewKernelFESpace, fespace);
-      disDivSkew->AddDomainInterpolator(new DivSkewInterpolator);
-      disDivSkew->Assemble();
-      disDivSkew->Finalize();
-      SparseMatrix* smatDivSkew= &(disDivSkew->SpMat());
-      smatDivSkew->EliminateCols(HDivSkewKernel_essDof);
-      for (int dof=0; dof<Hdiv_essDof.Size(); dof++) if (Hdiv_essDof[dof]<0) { smatDivSkew->EliminateRow(dof); }
-      P_d_HSkewDiv_Hdiv = disDivSkew->ParallelAssemble();
-      delete disDivSkew;
-
-
-      //setup the smoother for H(DivSkew)
-      ParBilinearForm *a_HDivSkew = new ParBilinearForm(HDivSkewKernelFESpace);
-      //    a_HDivSkew->AddDomainIntegrator(new DivSkewDivSkewIntegrator(*alpha_));
-      //    a_HDivSkew->AddDomainIntegrator(new VectorFE_DivSkewMassIntegrator(*beta_));
-
-      a_HDivSkew->AddDomainIntegrator(new DivSkewDivSkewIntegrator(*beta_));
-
-      a_HDivSkew->Assemble();
-      a_HDivSkew->Finalize();
-      SparseMatrix &matHDivSkew(a_HDivSkew->SpMat());
-      for (int dof=0; dof<HDivSkewKernel_essDof.Size();
-           dof++) if (HDivSkewKernel_essDof[dof]<0) { matHDivSkew.EliminateRowCol(dof); }
-      HDivSkewMat = a_HDivSkew->ParallelAssemble();
-      delete a_HDivSkew;
-      smootherDivSkew = new HypreSmoother(*HDivSkewMat, 16, 3);
-
-
-
-      f = new Vector(fespace->GetTrueVSize());
-
-      fKernel = new Vector(H1KernelFESpace->GetTrueVSize());
-      uKernel = new Vector(H1KernelFESpace->GetTrueVSize());
-
-      fImage = new Vector(H1_ImageFESpace->GetTrueVSize());
-      uImage = new Vector(H1_ImageFESpace->GetTrueVSize());
-
-      fDivSkew = new Vector(HDivSkewKernelFESpace->GetTrueVSize());
-      uDivSkew = new Vector(HDivSkewKernelFESpace->GetTrueVSize());
-
-      amgH1_Kernel->Mult(*fKernel, *uKernel);
-      amgH1_Image->Mult(*fImage, *uImage);
-
-      pcgKernel = new CGSolver(MPI_COMM_WORLD);
-      pcgKernel->SetOperator(*H1_KernelMat);
-      pcgKernel->SetPreconditioner(*amgH1_Kernel);
-      pcgKernel->SetRelTol(1e-16);
-      pcgKernel->SetMaxIter(100000000);
-      pcgKernel->SetPrintLevel(-2);
-
-      pcgImage = new CGSolver(MPI_COMM_WORLD);
-      pcgImage->SetOperator(*H1_ImageMat);
-      pcgImage->SetPreconditioner(*amgH1_Image);
-      pcgImage->SetRelTol(1e-16);
-      pcgImage->SetMaxIter(100000000);
-      pcgImage->SetPrintLevel(-2);
-
-      delete H1_ImageFESpace;
-      delete H1KernelFESpace;
-      delete fecH1Kernel;
-      delete fecH1Vec;
-   }
-
-   void setExactSolve(bool exSol)
-   {
-      exactSolves = exSol;
-   }
-
-   virtual void Mult(const Vector &x, Vector &y) const
-   {
-      smootherdiv->Mult(x,y);
-
-      P_H1_Hdiv->MultTranspose(x,*fImage);
-      *uImage = 0.0;
-      if (exactSolves) { pcgImage->Mult(*fImage, *uImage); }
-      else { amgH1_Image->Mult(*fImage, *uImage); }
-      P_H1_Hdiv->Mult(1.0, *uImage, 1.0, y);
-
-
-      *uDivSkew = 0.0;
-      P_d_HSkewDiv_Hdiv->MultTranspose(x,*fDivSkew);
-
-      smootherDivSkew->Mult(*fDivSkew, *uDivSkew);
-
-      P_H1_HDivSkew->MultTranspose(*fDivSkew,*fKernel);
-      *uKernel = 0.0;
-      if (exactSolves) { pcgKernel->Mult(*fKernel, *uKernel); }
-      else { amgH1_Kernel->Mult(*fKernel, *uKernel); }
-      P_H1_HDivSkew->Mult(1.0, *uKernel, 1.0, *uDivSkew);
-
-      P_d_HSkewDiv_Hdiv->Mult(1.0, *uDivSkew, 1.0, y);
-   }
-
-   virtual void SetOperator(const Operator &op) {};
-
-};
-
-
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   int num_procs, myid;
-   MPI_Init(&argc, &argv);
-   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
-   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
-
-   bool verbose = (myid==0);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/star.mesh";
-   int order = 1;
-   bool set_bc = true;
-   bool static_cond = false;
-   bool hybridization = false;
-   bool visualization = 1;
-   int sequ_ref_levels = 0;
-   int par_ref_levels = 0;
-   double tol = 1e-6;
-   double coeffWeight = 1.0;
-   bool spe10Coeff = false;
-   bool exactH1Solver = false;
-   bool standardCG = true;
-
-   int NExpo = 8;
-   int weightStart = -NExpo;
-   int weightEnd = NExpo;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree).");
-   args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
-                  "Number of sequential refinement steps.");
-   args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
-                  "Number of parallel refinement steps.");
-   args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
-                  "Impose or not essential boundary conditions.");
-   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
-                  " solution.");
-   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
-                  "--no-static-condensation", "Enable static condensation.");
-   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
-                  "--no-hybridization", "Enable hybridization.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&tol, "-tol", "--tol",
-                  "A parameter.");
-   args.AddOption(&coeffWeight, "-c", "--coeffMass",
-                  "the weight for the mass term.");
-   args.AddOption(&exactH1Solver, "-exH1Sol", "--exactH1Solver", "-H1prec",
-                  "--H1preconditioner",
-                  "Use exact H1 solvers for the preconditioner.");
-   args.AddOption(&spe10Coeff, "-spe10", "--useSPE10Coeff", "-constCoeff",
-                  "--constCoeff",
-                  "Switch between the coefficients for the mass bilinear form.");
-   args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
-                  "Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
-   args.AddOption(&weightStart, "-ws", "--weightStart",
-                  "the exponent for the starting weight (for the mass term).");
-   args.AddOption(&weightEnd, "-we", "--weightEnd",
-                  "the exponent for the weight at the end (for the mass term).");
-
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0)
-      {
-         args.PrintUsage(cout);
-      }
-      MPI_Finalize();
-      return 1;
-   }
-   if (myid == 0)
-   {
-      args.PrintOptions(cout);
-   }
-   kappa = freq * M_PI;
-
-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
-   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
-   //    and volume, as well as periodic meshes with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-   int sdim = mesh->SpaceDimension();
-
-   // 4. 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 1,000 elements.
-   {
-      for (int l = 0; l < sequ_ref_levels; l++)
-      {
-         mesh->UniformRefinement();
-      }
-   }
-
-   // 5. 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. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them (this is needed in the ADS solver below).
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-   {
-      for (int l = 0; l < par_ref_levels; l++)
-      {
-         pmesh->UniformRefinement();
-      }
-   }
-   pmesh->ReorientTetMesh();
-
-   // 6. Define a parallel finite element space on the parallel mesh. Here we
-   //    use the Raviart-Thomas finite elements of the specified order.
-   FiniteElementCollection *fec;
-   if (dim==4) { fec = new RT0_4DFECollection; }
-   else { fec = new RT_FECollection(order-1, dim); }
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-   }
-
-   // 7. 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;
-   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
-   ess_bdr = set_bc ? 1 : 0;
-   if (pmesh->bdr_attributes.Size())
-   {
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-
-   // 8. Set up the parallel linear form b(.) which corresponds to the
-   //    right-hand side of the FEM linear system, which in this case is
-   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
-   //    basis functions in the finite element fespace.
-
-
-   // 9. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x by projecting the exact
-   //    solution. Note that only values from the boundary faces will be used
-   //    when eliminating the non-homogeneous boundary condition to modify the
-   //    r.h.s. vector b.
-   ParGridFunction x(fespace);
-   VectorFunctionCoefficient F(sdim, F_exact);
-
-   for (int expo=weightStart; expo<=weightEnd; expo++)
-   {
-      double weight = pow(10.0,expo);
-      kappa = weight;
-
-      x.ProjectCoefficient(F);
-
-      VectorFunctionCoefficient f(sdim, f_exact);
-      ParLinearForm *b = new ParLinearForm(fespace);
-      b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
-      b->Assemble();
-
-      // 10. Set up the parallel bilinear form corresponding to the H(div)
-      //     diffusion operator grad alpha div + beta I, by adding the div-div and
-      //     the mass domain integrators.
-
-      //    std::string permFile = "spe_perm.dat";
-      //    InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
-
-      Coefficient *alpha = new ConstantCoefficient(1.0);
-      Coefficient *beta;
-      //    if(spe10Coeff) beta = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
-      //    else
-      beta = new ConstantCoefficient(weight);
-
-      ParBilinearForm *a = new ParBilinearForm(fespace);
-      a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
-      a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));
-
-      // 11. 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,
-      //     hybridization, etc.
-      FiniteElementCollection *hfec = NULL;
-      ParFiniteElementSpace *hfes = NULL;
-      if (static_cond)
-      {
-         a->EnableStaticCondensation();
-      }
-      else if (hybridization)
-      {
-         hfec = new DG_Interface_FECollection(order-1, dim);
-         hfes = new ParFiniteElementSpace(pmesh, hfec);
-         a->EnableHybridization(hfes, new NormalTraceJumpIntegrator(),
-                                ess_tdof_list);
-      }
-      a->Assemble();
-
-      HypreParMatrix A;
-      Vector B, X;
-      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
-
-      HYPRE_Int glob_size = A.GetGlobalNumRows();
-      if (myid == 0)
-      {
-         cout << "Size of linear system: " << glob_size << endl;
-      }
-
-      // 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
-      //     the 3D ADS preconditioners from hypre. If using hybridization, the
-      //     system is preconditioned with hypre's BoomerAMG.
-      Solver *prec = NULL;
-      if (hybridization) { prec = new HypreBoomerAMG(A); }
-      else
-      {
-         ParFiniteElementSpace *prec_fespace =
-            (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
-         if (dim == 2)   { prec = new HypreAMS(A, prec_fespace); }
-         else if (dim==3) { prec = new HypreADS(A, prec_fespace); }
-         else if (dim==4) { prec = new div4dPrec(&A, fespace, alpha, beta, ess_bdr, order, exactH1Solver); }
-         else { prec = NULL; }
-      }
-
-      int iter = -1;
-      if (standardCG)
-      {
-         IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-         pcg->SetOperator(A);
-         pcg->SetRelTol(tol);
-         pcg->SetMaxIter(500);
-         pcg->SetPrintLevel(1);
-         pcg->SetPreconditioner(*prec);
-         pcg->Mult(B, X);
-
-         iter = pcg->GetNumIterations();
-
-         delete pcg;
-      }
-      else
-      {
-         HyprePCG *pcg = new HyprePCG(A);
-         pcg->SetTol(tol);
-         pcg->SetMaxIter(5000);
-         pcg->SetResidualConvergenceOptions(1,tol);
-         pcg->SetPrintLevel(2);
-         //          pcg->SetPreconditioner(*prec);
-         pcg->Mult(B, X);
-
-         pcg->GetNumIterations(iter);
-
-         delete pcg;
-      }
-
-      if (myid==0)
-      {
-         cout << "Weigth: " << weight << " " << iter << endl;
-
-         int *iters = LoadIterations(10, 2*NExpo+1);
-         putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
-                              2*NExpo+1, iters);
-         WriteIterations(iters, 10, 2*NExpo+1);
-      }
-
-
-      // 13. Recover the parallel grid function corresponding to X. This is the
-      //     local finite element solution on each processor.
-      a->RecoverFEMSolution(X, *b, x);
-
-      // 14. Compute and print the L^2 norm of the error.
-      {
-         double err = x.ComputeL2Error(F);
-         if (myid == 0)
-         {
-            cout << "\n|| F_h - F ||_{L^2} = " << err << '\n' << endl;
-         }
-      }
-
-      // 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;
-      //    }
-
-      if (prec!=NULL) { delete prec; }
-      delete hfes;
-      delete hfec;
-      delete a;
-      delete alpha;
-      delete beta;
-
-      delete b;
-   }
-
-   // 17. Free the used memory.
-
-
-   delete fespace;
-   delete fec;
-   delete pmesh;
-
-   MPI_Finalize();
-
-   return 0;
-}
-
-
-// The exact solution (for non-surface meshes)
-void F_exact(const Vector &p, Vector &F)
-{
-   int dim = p.Size();
-
-   if (dim==4)
-   {
-      double s0 = sin(M_PI*p(0)), s1 = sin(M_PI*p(1)), s2 = sin(M_PI*p(2)),
-             s3 = sin(M_PI*p(3));
-      double c0 = cos(M_PI*p(0)), c1 = cos(M_PI*p(1)), c2 = cos(M_PI*p(2)),
-             c3 = cos(M_PI*p(3));
-
-      F(0) = c0 * s1 * s2 * s3;
-      F(1) = s0 * c1 * s2 * s3;
-      F(2) = s0 * s1 * c2 * s3;
-      F(3) = s0 * s1 * s2 * c3;
-   }
-   else
-   {
-      double x = p(0);
-      double y = p(1);
-      // double z = (dim == 3) ? p(2) : 0.0;
-
-      F(0) = cos(kappa*x)*sin(kappa*y);
-      F(1) = cos(kappa*y)*sin(kappa*x);
-      if (dim == 3)
-      {
-         F(2) = 0.0;
-      }
-   }
-}
-
-// The right hand side
-void f_exact(const Vector &p, Vector &f)
-{
-   int dim = p.Size();
-   if (dim==4)
-   {
-      double s0 = sin(M_PI*p(0)), s1 = sin(M_PI*p(1)), s2 = sin(M_PI*p(2)),
-             s3 = sin(M_PI*p(3));
-      double c0 = cos(M_PI*p(0)), c1 = cos(M_PI*p(1)), c2 = cos(M_PI*p(2)),
-             c3 = cos(M_PI*p(3));
-
-      f(0) = c0 * s1 * s2 * s3;
-      f(1) = s0 * c1 * s2 * s3;
-      f(2) = s0 * s1 * c2 * s3;
-      f(3) = s0 * s1 * s2 * c3;
-
-      f *= (kappa + 4.0 * M_PI*M_PI);
-   }
-   else
-   {
-      double x = p(0);
-      double y = p(1);
-      // double z = (dim == 3) ? p(2) : 0.0;
-
-      double temp = 1 + 2*kappa*kappa;
-
-      f(0) = temp*cos(kappa*x)*sin(kappa*y);
-      f(1) = temp*cos(kappa*y)*sin(kappa*x);
-      if (dim == 3)
-      {
-         f(2) = 0;
-      }
-   }
-}

examples/ginkgo/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ginkgo/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/hiop/ex9p.cpp

@@ -96,6 +96,7 @@ public:
    {
       Vector w_glob(width);
       pfes.Dof_TrueDof_Matrix()->MultTranspose(w, w_glob);
+      w_glob.HostReadWrite(); // read+write -> can use w_glob(i) (non-const)
       for (int i = 0; i < width; i++) { grad(0, i) = w_glob(i); }
    }
 

examples/hiop/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/hiop/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ..
 MFEM_BUILD_DIR ?= ..
+MFEM_INSTALL_DIR ?= ../mfem
 SRC = $(if $(MFEM_DIR:..=),$(MFEM_DIR)/examples/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -27,8 +26,7 @@ SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
 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 \
-   ex1p_4d ex3p_4d ex4D_DivSkew
+   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

examples/moonolith/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/moonolith/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)