directly pass through quadrature point data

# Conflicts:
#	CMakeLists.txt

.gitignore

@@ -57,6 +57,8 @@ examples/ex2[0-9]
 examples/ex2[0-9]p
 examples/ex3[0-9]
 examples/ex3[0-9]p
+examples/ex4[0-9]
+examples/ex4[0-9]p
 
 examples/refined.mesh
 examples/displaced.mesh
@@ -270,16 +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

@@ -13,13 +13,16 @@
 # at Lawrence Livermore National Laboratory (LLNL). This entire pipeline is
 # LLNL-specific!
 
+include:
+  - project: 'lc-templates/id_tokens'
+    file: 'id_tokens.yml'
 
 # The pipeline is divided into stages. Usually, jobs in a given stage wait for
 # the preceding stages to complete before to start. However, we sometimes use
 # 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
@@ -50,7 +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
@@ -58,10 +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
@@ -70,7 +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

@@ -9,6 +9,10 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
+include:
+  - project: 'lc-templates/id_tokens'
+    file: 'id_tokens.yml'
+
 # We define the following GitLab pipeline variables:
 variables:
 
@@ -20,7 +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/lassen-config.yml

@@ -35,9 +35,8 @@ variables:
     - when: on_success
 
 # Lassen uses a different job scheduler (spectrum lsf) that does not allow
-# pre-allocation the same way slurm does.  We use pdebug queue on lassen
-# to speed-up the allocation.  However this would not be scalable to
-# multiple builds.
+# pre-allocation the same way slurm does.  We use the pci queue on lassen
+# to speed-up the allocation.
 .build_and_test_on_lassen:
   extends: [.on_lassen]
   stage: build_and_test
@@ -45,5 +44,5 @@ variables:
     - echo ${MFEM_DATA_DIR}
     - echo ${SPEC}
     # Next script uses 'THREADS': leaving it empty --> it uses 'make all -j'
-    - lalloc 1 -W 45 -q pdebug --atsdisable tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data
+    - lalloc 1 -W 45 -q pci --atsdisable tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data
   needs: [setup]

.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"'
@@ -40,16 +40,16 @@ 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}
     - echo ${MFEM_DATA_DIR}
     - echo ${SPEC}
-    - srun $( [[ -n "${JOBID}" ]] && echo "--jobid=${JOBID}" ) -t 45 -N 1 tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data
+    - srun $( [[ -n "${JOBID}" ]] && echo "--jobid=${JOBID}" ) --reservation=ci -t 45 -N 1 tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data

.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/lassen-build-and-test.yml

@@ -14,14 +14,14 @@ stages:
   - build_and_test
   - report
 
-opt_mpi_cuda_xl_16_1_1_12:
+opt_mpi_cuda_gcc:
   variables:
-    SPEC: "%xl@16.1.1.12 +mpi +cuda cuda_arch=70"
+    SPEC: "%gcc@8.3.1 +mpi +cuda cuda_arch=70"
   extends: .build_and_test_on_lassen
 
-opt_mpi_cuda_hypre_cuda_xl:
+opt_mpi_cuda_hypre_cuda_gcc:
   variables:
-    SPEC: "%xl@16.1.1.12 +mpi +cuda cuda_arch=70 ^hypre+cuda~shared cuda_arch=70"
+    SPEC: "%gcc@8.3.1 +mpi +cuda cuda_arch=70 ^hypre+cuda~shared cuda_arch=70"
   extends: .build_and_test_on_lassen
 
 # Jobs report

.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
@@ -31,21 +31,21 @@ cd tests
 mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}
 
 # run
-if [[ "${MACHINE_NAME}" == "quartz" || "${MACHINE_NAME}" == "ruby" ]]; then
-  salloc --nodes=1 -p pdebug ../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 [[ ${MACHINE_NAME} == "lassen" ]]; then
-  lalloc 1 -q pdebug ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+  lalloc 1 -q pci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 else
   echo "Unknown machine: MACHINE_NAME=$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

@@ -11,6 +11,48 @@
 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'.
+
 
 Version 4.7, released on May 7, 2024
 ====================================
@@ -35,6 +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/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

@@ -0,0 +1,35 @@
+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
+2
+
+elements
+1
+1 3 0 1 2 3
+
+boundary
+4
+1 1 0 1
+2 1 1 2
+3 1 2 3
+4 1 3 0
+
+vertices
+4
+2
+0 0
+1 0.3
+1.4 1.2
+0.25 1.34

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

doc/CodeDocumentation.dox

@@ -114,7 +114,9 @@ namespace mfem {
  * - <a class="el" href="ex37p_8cpp_source.html">Example 37p</a>: parallel topology optimization
  * - <a class="el" href="ex38_8cpp_source.html">Example 38</a>: cut-surface and cut-volume integration
  * - <a class="el" href="ex39_8cpp_source.html">Example 39</a>: named mesh attributes
- * - <a class="el" href="ex39p_8cpp_source.html">Example 39</a>: parallel named mesh attributes
+ * - <a class="el" href="ex39p_8cpp_source.html">Example 39p</a>: parallel named mesh attributes
+ * - <a class="el" href="ex40_8cpp_source.html">Example 40</a>: eikonal equation
+ * - <a class="el" href="ex40p_8cpp_source.html">Example 40p</a>: parallel eikonal equation
  *
  * <H4>AmgX Examples</H4>
  * - Variants of Examples
@@ -180,6 +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

@@ -45,10 +45,32 @@ list(APPEND ALL_EXE_SRCS
   ex37.cpp
   ex38.cpp
   ex39.cpp
+  ex40.cpp
   )
 
 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_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
@@ -87,6 +109,7 @@ if (MFEM_USE_MPI)
     ex36p.cpp
     ex37p.cpp
     ex39p.cpp
+    ex40p.cpp
   )
 endif()
 
@@ -108,6 +131,16 @@ 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_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})
@@ -146,10 +179,10 @@ if (MFEM_ENABLE_TESTING)
   # Add CUDA/HIP tests.
   set(DEVICE_EXAMPLES
       # serial examples with device support:
-      ex1 ex3 ex4 ex5 ex6 ex9 ex22 ex24 ex25 ex26 ex34
+      ex1 ex3 ex4 ex5 ex6 ex9 ex14 ex22 ex24 ex25 ex26 ex34
       # parallel examples with device support:
-      ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex22p ex24p ex25p ex26p
-      ex34p ex35p)
+      ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex14p ex22p ex24p ex25p
+      ex26p ex34p ex35p)
   set(MFEM_TEST_DEVICE)
   if (MFEM_USE_CUDA)
     set(MFEM_TEST_DEVICE "cuda")
@@ -159,6 +192,11 @@ if (MFEM_ENABLE_TESTING)
   if (MFEM_TEST_DEVICE)
     foreach(TEST_NAME ${DEVICE_EXAMPLES})
       set(THIS_TEST_OPTIONS "-no-vis" "-d" "${MFEM_TEST_DEVICE}")
+      if (${TEST_NAME} MATCHES "ex14p")
+        list(APPEND THIS_TEST_OPTIONS "-rs" "2" "-rp" "0" "-pa")
+      elseif (${TEST_NAME} MATCHES "ex14")
+        list(APPEND THIS_TEST_OPTIONS "-r" "2" "-pa")
+      endif()
       if (NOT (${TEST_NAME} MATCHES ".*p$"))
         add_test(NAME ${TEST_NAME}_${MFEM_TEST_DEVICE}_ser
           COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})

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/dfem.hpp

@@ -0,0 +1,3 @@
+#pragma once
+
+#include "dfem_differentiable_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 +1,806 @@
+#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_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
+   >
+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,
+                          const IntegrationRule &integration_rule) :
+      kernels(ks),
+      mesh(m),
+      dim(mesh.Dimension()),
+      integration_rule(integration_rule),
+      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;
+   const IntegrationRule &integration_rule;
+
+   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
+   >
+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,
+            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
+   >
+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.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 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);
+      };
+   }
+}
+
+// #include "dfem_assemble_vector.icc"
+// #include "dfem_assemble_hypreparmatrix.icc"
+
+}

examples/dfem/dfem_fieldoperator.hpp

@@ -0,0 +1,118 @@
+#pragma once
+
+#include <string>
+
+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) {}
+};
+
+}

examples/dfem/dfem_integrate.hpp

@@ -0,0 +1,292 @@
+#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>, BareFieldOperator::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>, BareFieldOperator::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>, BareFieldOperator::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 (std::is_same_v<std::decay_t<output_t>, BareFieldOperator::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 (
+      std::is_same_v<std::decay_t<output_t>, BareFieldOperator::Gradient>)
+   {
+      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 (
+      std::is_same_v<std::decay_t<output_t>, BareFieldOperator::None>)
+   {
+      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 +1,400 @@
+#pragma once
+
+#include "dfem_util.hpp"
+#include <type_traits>
+
+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 (
+      std::is_same_v<std::decay_t<field_operator_t>, BareFieldOperator::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 (
+      std::is_same_v<std::decay_t<field_operator_t>, BareFieldOperator::Gradient>)
+   {
+      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>, BareFieldOperator::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 (
+      std::is_same_v<std::decay_t<field_operator_t>, BareFieldOperator::None>)
+   {
+      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 (std::is_same_v<field_operator_t, BareFieldOperator::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 (
+      std::is_same_v<field_operator_t, BareFieldOperator::Gradient>)
+   {
+      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, BareFieldOperator::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 (std::is_same_v<field_operator_t, BareFieldOperator::None>)
+   {
+      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, size_t num_kinputs, typename field_operator_ts, std::size_t... i>
+MFEM_HOST_DEVICE inline
+void map_fields_to_quadrature_data(
+   std::array<DeviceTensor<2>, num_kinputs> &fields_qp,
+   const std::array<DeviceTensor<1>, num_kinputs> &fields_e,
+   const std::array<DofToQuadMap, num_kinputs> &dtqmaps,
+   const field_operator_ts &fops,
+   const DeviceTensor<1, const double> &integration_weights,
+   const std::array<DeviceTensor<1>, 6> &scratch_mem,
+   std::index_sequence<i...>)
+{
+   if constexpr (std::is_same_v<T, TensorProduct>)
+   {
+
+      (map_field_to_quadrature_data_tensor_product(fields_qp[i],
+                                                   dtqmaps[i], fields_e[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_kinputs, typename field_operator_ts, std::size_t... i>
+MFEM_HOST_DEVICE
+void map_direction_to_quadrature_data_conditional(
+   std::array<DeviceTensor<2>, num_kinputs> &directions_qp,
+   const DeviceTensor<1> &direction_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>(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 +1,268 @@
+#pragma once
+#include "dfem_util.hpp"
+
+namespace mfem
+{
+
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   double &arg)
+{
+   arg = u(0);
+}
+
+MFEM_HOST_DEVICE inline
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   internal::tensor<double> &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 <int n, int m>
+MFEM_HOST_DEVICE
+void process_kf_arg(
+   const DeviceTensor<1> &u,
+   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);
+      }
+   }
+   // assuming col major layout. translating to row major.
+   // i + N_i*j
+   // arg(0, 0) = u(0);
+   // arg(0, 1) = u(0 + 2 * 1);
+   // arg(1, 0) = u(1 + 2 * 0);
+   // arg(1, 1) = u(1 + 2 * 1);
+}
+
+template <typename arg_type>
+MFEM_HOST_DEVICE
+void process_kf_arg(const DeviceTensor<2> &u, arg_type &arg, int qp)
+{
+   // out << "qp: " << qp << "\n";
+   // for (int i = 0; i < u.GetShape()[0] * u.GetShape()[1]; i++)
+   // {
+   //    out << (&u(0, 0))[i] << " ";
+   // }
+   // out << "\n";
+
+   const auto u_qp = Reshape(&u(0, qp), u.GetShape()[0]);
+   // for (int i = 0; i < u_qp.GetShape()[0]; i++)
+   // {
+   //    out << (&u_qp(0))[i] << " ";
+   // }
+   // out << "\n";
+
+   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, 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)
+{
+   // out << "x: " << x << "\n";
+   for (size_t i = 0; i < n; i++)
+   {
+      for (size_t j = 0; j < m; j++)
+      {
+         r(i + n * j) = x(i, j);
+      }
+   }
+
+   // out << "r: ";
+   // for (int i = 0; i < r.GetShape()[0]; i++)
+   // {
+   //    out << r(i) << " ";
+   // }
+   // out << "\n\n";
+}
+
+template <typename T> inline
+void process_kf_arg(const DeviceTensor<1> &u, const DeviceTensor<1> &v,
+                    double &arg)
+{
+   arg = u(0);
+}
+
+template <int n, int m> 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 arg_type> inline
+void process_kf_arg(const DeviceTensor<2> &u, const DeviceTensor<2> &v,
+                    arg_type &arg, 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_fields, typename kf_args, std::size_t... i> inline
+void process_kf_args(std::array<DeviceTensor<2>, num_fields> &u,
+                     std::array<DeviceTensor<2>, num_fields> &v,
+                     kf_args &args, int qp, std::index_sequence<i...>)
+{
+   (process_kf_arg(u[i], v[i], mfem::get<i>(args), qp), ...);
+}
+
+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)));
+}
+
+// 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>
+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>
+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>
+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,
+   const std::array<DeviceTensor<2>, num_args> &u,
+   kernel_arg_ts &shadow_args,
+   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<> {})));
+}
+
+}

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.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/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;
+
+
+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<double, 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<double, 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_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 +1,268 @@
+#include "dfem/dfem.hpp"
+#include "dfem/dfem_test_macro.hpp"
+#include "fem/pfespace.hpp"
+#include "linalg/hypre.hpp"
+#include "linalg/operator.hpp"
+#include "linalg/solvers.hpp"
+#include <fstream>
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+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<real_t, dim, dim> &dudxi,
+                             const tensor<real_t, dim, dim> &J,
+                             const double &w)
+   {
+      // shear modulus
+      mfem::real_t D1 = 0.1e6;
+      // bulk modulus
+      mfem::real_t C1 = 1.0e6;
+      constexpr auto I = mfem::internal::IsotropicIdentity<dim>();
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      real_t F = det(I + dudx);
+      real_t 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"}};
+
+   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};
+
+   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/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/ex40.cpp

@@ -0,0 +1,376 @@
+//                                MFEM Example 40
+//
+// Compile with: make ex40
+//
+// Sample runs: ex40 -step 10 -gr 2.0
+//              ex40 -step 10 -gr 2.0 -o 3 -r 1
+//              ex40 -step 10 -gr 2.0 -r 4 -m ../data/l-shape.mesh
+//              ex40 -step 10 -gr 2.0 -r 2 -m ../data/fichera.mesh
+//
+// Description: This example code demonstrates how to use MFEM to solve the
+//              eikonal equation,
+//
+//                      |∇𝑢| = 1 in Ω,  𝑢 = g on ∂Ω.
+//
+//              The solution of this problem coincides with the unique optimum of
+//              the nonlinear program
+//
+//                   maximize ∫_Ω 𝑢 d𝑥 subject to |∇𝑢| ≤ 1,   𝑢 = g on Ω,      (⋆)
+//
+//              which is the foundation for method implemented below.
+//
+//              Following the proximal Galerkin methodology [1] (see also Example
+//              36), we construct a Legendre function for the unit ball
+//              𝐵₁ := {𝑥 ∈ Rⁿ | |𝑥| < 1}. Our choice is the Hellinger entropy,
+//
+//                    h(𝑥) = −( 1 − |𝑥|² )^{1/2},
+//
+//              although other choices are possible, each leading to a slightly
+//              different algorithm. We then adaptively regularize the optimization
+//              problem (⋆) with the Bregman divergence of the Hellinger entropy,
+//
+//                 maximize  ∫_Ω 𝑢 d𝑥 - αₖ⁻¹ Dₕ(∇𝑢,∇𝑢ₖ₋₁)  subject to  𝑢 = g on Ω.
+//
+//              This results in a sequence of functions ( 𝜓ₖ , 𝑢ₖ ),
+//
+//                      𝑢ₖ → 𝑢,    𝜓ₖ/|𝜓ₖ| → ∇𝑢    as k → \infty,
+//
+//              defined by the nonlinear saddle-point problems
+//
+//               Find 𝜓ₖ ∈ H(div,Ω) and 𝑢ₖ ∈ L²(Ω) such that
+//               ( Zₖ(𝜓ₖ) , τ ) + ( 𝑢ₖ , ∇⋅τ ) = ⟨ g , τ⋅n ⟩         ∀ τ ∈ H(div,Ω)
+//               ( ∇⋅𝜓ₖ , v )                 = ( ∇⋅𝜓ₖ₋₁ - 1 , v )   ∀ v ∈ L²(Ω)
+//
+//              where Zₖ(𝜓) := ∇h⁻¹(αₖ 𝜓) = 𝜓 / ( αₖ⁻² + |𝜓|² )^{1/2} and step size
+//              αₖ > 0. These saddle-point problems are solved using a damped Newton's
+//              method. This example assumes that g = 0 and allows the step size to
+//              grow geometrically, αₖ = α₀rᵏ, where r ≥ 1 is the growth rate.
+//
+//              [1] Keith, B. and Surowiec, T. (2023) Proximal Galerkin: A structure-
+//                  preserving finite element method for pointwise bound constraints.
+//                  arXiv:2307.12444 [math.NA]
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+class ZCoefficient : public VectorCoefficient
+{
+protected:
+   GridFunction *psi;
+   real_t alpha;
+
+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_; }
+};
+
+class DZCoefficient : public MatrixCoefficient
+{
+protected:
+   GridFunction *psi;
+   real_t alpha;
+
+public:
+   DZCoefficient(int height, GridFunction &psi_, real_t alpha_ = 1.0)
+      : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }
+
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   void SetAlpha(real_t alpha_) { alpha = alpha_; }
+};
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../data/star.mesh";
+   int order = 1;
+   int max_it = 5;
+   int ref_levels = 3;
+   real_t alpha = 1.0;
+   real_t growth_rate = 1.0;
+   real_t newton_scaling = 0.9;
+   real_t tichonov = 1e-1;
+   real_t tol = 1e-4;
+   bool visualization = true;
+
+   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(&ref_levels, "-r", "--refs",
+                  "Number of h-refinements.");
+   args.AddOption(&max_it, "-mi", "--max-it",
+                  "Maximum number of iterations");
+   args.AddOption(&tol, "-tol", "--tol",
+                  "Stopping criteria based on the difference between"
+                  "successive solution updates");
+   args.AddOption(&alpha, "-step", "--step",
+                  "Initial size alpha");
+   args.AddOption(&growth_rate, "-gr", "--growth-rate",
+                  "Growth rate of the step size alpha");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Read the mesh from the mesh file.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+   int sdim = mesh.SpaceDimension();
+
+   MFEM_ASSERT(mesh.bdr_attributes.Size(),
+               "This example does not currently support meshes"
+               " without boundary attributes."
+              )
+
+   // 3. Postprocess the mesh.
+   // 3A. Refine the mesh to increase the resolution.
+   for (int l = 0; l < ref_levels; l++)
+   {
+      mesh.UniformRefinement();
+   }
+
+   // 3B. Interpolate the geometry after refinement to control geometry error.
+   // NOTE: Minimum second-order interpolation is used to improve the accuracy.
+   int curvature_order = max(order,2);
+   mesh.SetCurvature(curvature_order);
+
+   // 4. Define the necessary finite element spaces on the mesh.
+   RT_FECollection RTfec(order, dim);
+   FiniteElementSpace RTfes(&mesh, &RTfec);
+
+   L2_FECollection L2fec(order, dim);
+   FiniteElementSpace L2fes(&mesh, &L2fec);
+
+   cout << "Number of H(div) dofs: "
+        << RTfes.GetTrueVSize() << endl;
+   cout << "Number of L² dofs: "
+        << L2fes.GetTrueVSize() << endl;
+
+   // 5. Define the offsets for the block matrices
+   Array<int> offsets(3);
+   offsets[0] = 0;
+   offsets[1] = RTfes.GetVSize();
+   offsets[2] = L2fes.GetVSize();
+   offsets.PartialSum();
+
+   BlockVector x(offsets), rhs(offsets);
+   x = 0.0; rhs = 0.0;
+
+   // 6. Define the solution vectors as a finite element grid functions
+   //    corresponding to the fespaces.
+   GridFunction u_gf, delta_psi_gf;
+   delta_psi_gf.MakeRef(&RTfes,x,offsets[0]);
+   u_gf.MakeRef(&L2fes,x,offsets[1]);
+
+   GridFunction psi_old_gf(&RTfes);
+   GridFunction psi_gf(&RTfes);
+   GridFunction u_old_gf(&L2fes);
+
+   // 7. Define initial guesses for the solution variables.
+   delta_psi_gf = 0.0;
+   psi_gf = 0.0;
+   u_gf = 0.0;
+   psi_old_gf = psi_gf;
+   u_old_gf = u_gf;
+
+   // 8. Prepare for glvis output.
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock;
+   if (visualization)
+   {
+      sol_sock.open(vishost,visport);
+      sol_sock.precision(8);
+   }
+
+   // 9. Coefficients to be used later.
+   ConstantCoefficient neg_one(-1.0);
+   ConstantCoefficient zero(0.0);
+   ConstantCoefficient tichonov_cf(tichonov);
+   ConstantCoefficient neg_tichonov_cf(-1.0*tichonov);
+   ZCoefficient Z(sdim, psi_gf, alpha);
+   DZCoefficient DZ(sdim, psi_gf, alpha);
+   ScalarVectorProductCoefficient neg_Z(-1.0, Z);
+   DivergenceGridFunctionCoefficient div_psi_cf(&psi_gf);
+   DivergenceGridFunctionCoefficient div_psi_old_cf(&psi_old_gf);
+   SumCoefficient psi_old_minus_psi(div_psi_old_cf, div_psi_cf, 1.0, -1.0);
+
+   // 10. Assemble constant matrices/vectors to avoid reassembly in the loop.
+   LinearForm b0, b1;
+   b0.MakeRef(&RTfes,rhs.GetBlock(0),0);
+   b1.MakeRef(&L2fes,rhs.GetBlock(1),0);
+
+   b0.AddDomainIntegrator(new VectorFEDomainLFIntegrator(neg_Z));
+   b1.AddDomainIntegrator(new DomainLFIntegrator(neg_one));
+   b1.AddDomainIntegrator(new DomainLFIntegrator(psi_old_minus_psi));
+
+   BilinearForm a00(&RTfes);
+   a00.AddDomainIntegrator(new VectorFEMassIntegrator(DZ));
+   a00.AddDomainIntegrator(new VectorFEMassIntegrator(tichonov_cf));
+
+   MixedBilinearForm a10(&RTfes,&L2fes);
+   a10.AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+   a10.Assemble();
+   a10.Finalize();
+   SparseMatrix &A10 = a10.SpMat();
+   SparseMatrix *A01 = Transpose(A10);
+
+   BilinearForm a11(&L2fes);
+   a11.AddDomainIntegrator(new MassIntegrator(neg_tichonov_cf));
+   a11.Assemble();
+   a11.Finalize();
+   SparseMatrix &A11 = a11.SpMat();
+
+   // 11. Iterate.
+   int k;
+   int total_iterations = 0;
+   real_t increment_u = 0.1;
+   GridFunction u_tmp(&L2fes);
+   for (k = 0; k < max_it; k++)
+   {
+      u_tmp = u_old_gf;
+      Z.SetAlpha(alpha);
+      DZ.SetAlpha(alpha);
+
+      mfem::out << "\nOUTER ITERATION " << k+1 << endl;
+
+      int j;
+      for ( j = 0; j < 5; j++)
+      {
+         total_iterations++;
+
+         b0.Assemble();
+         b1.Assemble();
+
+         a00.Assemble(false);
+         a00.Finalize(false);
+         SparseMatrix &A00 = a00.SpMat();
+
+         // Construct Schur-complement preconditioner
+         Vector A00_diag(a00.Height());
+         A00.GetDiag(A00_diag);
+         A00_diag.Reciprocal();
+         SparseMatrix *S = Mult_AtDA(*A01, A00_diag);
+
+         BlockDiagonalPreconditioner prec(offsets);
+         prec.SetDiagonalBlock(0,new DSmoother(A00));
+#ifndef MFEM_USE_SUITESPARSE
+         prec.SetDiagonalBlock(1,new GSSmoother(*S));
+#else
+         prec.SetDiagonalBlock(1,new UMFPackSolver(*S));
+#endif
+         prec.owns_blocks = 1;
+
+         BlockOperator A(offsets);
+         A.SetBlock(0,0,&A00);
+         A.SetBlock(1,0,&A10);
+         A.SetBlock(0,1,A01);
+         A.SetBlock(1,1,&A11);
+
+         GMRES(A,prec,rhs,x,0,2000,500,1e-12,0.0);
+         delete S;
+
+         u_tmp -= u_gf;
+         real_t Newton_update_size = u_tmp.ComputeL2Error(zero);
+         u_tmp = u_gf;
+
+         // Damped Newton update
+         psi_gf.Add(newton_scaling, delta_psi_gf);
+         a00.Update();
+
+         if (visualization)
+         {
+            sol_sock << "solution\n" << mesh << u_gf << "window_title 'Discrete solution'"
+                     << flush;
+         }
+
+         mfem::out << "Newton_update_size = " << Newton_update_size << endl;
+
+         if (Newton_update_size < increment_u)
+         {
+            break;
+         }
+      }
+
+      u_tmp = u_gf;
+      u_tmp -= u_old_gf;
+      increment_u = u_tmp.ComputeL2Error(zero);
+
+      mfem::out << "Number of Newton iterations = " << j+1 << endl;
+      mfem::out << "Increment (|| uₕ - uₕ_prvs||) = " << increment_u << endl;
+
+      u_old_gf = u_gf;
+      psi_old_gf = psi_gf;
+
+      if (increment_u < tol || k == max_it-1)
+      {
+         break;
+      }
+
+      alpha *= max(growth_rate, 1_r);
+
+   }
+
+   mfem::out << "\n Outer iterations: " << k+1
+             << "\n Total iterations: " << total_iterations
+             << "\n Total dofs:       " << RTfes.GetTrueVSize() + L2fes.GetTrueVSize()
+             << endl;
+
+   delete A01;
+   return 0;
+}
+
+void ZCoefficient::Eval(Vector &V, ElementTransformation &T,
+                        const IntegrationPoint &ip)
+{
+   MFEM_ASSERT(psi != NULL, "grid function is not set");
+   MFEM_ASSERT(alpha > 0, "alpha is not positive");
+
+   Vector psi_vals(vdim);
+   psi->GetVectorValue(T, ip, psi_vals);
+   real_t norm = psi_vals.Norml2();
+   real_t phi = 1.0 / sqrt(1.0/(alpha*alpha) + norm*norm);
+
+   V = psi_vals;
+   V *= phi;
+}
+
+void DZCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
+                         const IntegrationPoint &ip)
+{
+   MFEM_ASSERT(psi != NULL, "grid function is not set");
+   MFEM_ASSERT(alpha > 0, "alpha is not positive");
+
+   Vector psi_vals(height);
+   psi->GetVectorValue(T, ip, psi_vals);
+   real_t norm = psi_vals.Norml2();
+   real_t phi = 1.0 / sqrt(1.0/(alpha*alpha) + norm*norm);
+
+   K = 0.0;
+   for (int i = 0; i < height; i++)
+   {
+      K(i,i) = phi;
+      for (int j = 0; j < height; j++)
+      {
+         K(i,j) -= psi_vals(i) * psi_vals(j) * pow(phi, 3);
+      }
+   }
+}

examples/ex40p.cpp

@@ -0,0 +1,438 @@
+//                       MFEM Example 40 - Parallel Version
+//
+// Compile with: make ex40p
+//
+// Sample runs: mpirun -np 4 ex40p -step 10 -gr 2.0
+//              mpirun -np 4 ex40p -step 10 -gr 2.0 -o 3 -r 1
+//              mpirun -np 4 ex40p -step 10 -gr 2.0 -r 4 -m ../data/l-shape.mesh
+//              mpirun -np 4 ex40p -step 10 -gr 2.0 -r 2 -m ../data/fichera.mesh
+//
+// Description: This example code demonstrates how to use MFEM to solve the
+//              eikonal equation,
+//
+//                      |∇𝑢| = 1 in Ω,  𝑢 = g on ∂Ω.
+//
+//              The solution of this problem coincides with the unique optimum of
+//              the nonlinear program
+//
+//                   maximize ∫_Ω 𝑢 d𝑥 subject to |∇𝑢| ≤ 1,   𝑢 = g on Ω,      (⋆)
+//
+//              which is the foundation for method implemented below.
+//
+//              Following the proximal Galerkin methodology [1] (see also Example
+//              36), we construct a Legendre function for the unit ball
+//              𝐵₁ := {𝑥 ∈ Rⁿ | |𝑥| < 1}. Our choice is the Hellinger entropy,
+//
+//                    h(𝑥) = −( 1 − |𝑥|² )^{1/2},
+//
+//              although other choices are possible, each leading to a slightly
+//              different algorithm. We then adaptively regularize the optimization
+//              problem (⋆) with the Bregman divergence of the Hellinger entropy,
+//
+//                 maximize  ∫_Ω 𝑢 d𝑥 - αₖ⁻¹ Dₕ(∇𝑢,∇𝑢ₖ₋₁)  subject to  𝑢 = g on Ω.
+//
+//              This results in a sequence of functions ( 𝜓ₖ , 𝑢ₖ ),
+//
+//                      𝑢ₖ → 𝑢,    𝜓ₖ/|𝜓ₖ| → ∇𝑢    as k → \infty,
+//
+//              defined by the nonlinear saddle-point problems
+//
+//               Find 𝜓ₖ ∈ H(div,Ω) and 𝑢ₖ ∈ L²(Ω) such that
+//               ( Zₖ(𝜓ₖ) , τ ) + ( 𝑢ₖ , ∇⋅τ ) = ⟨ g , τ⋅n ⟩         ∀ τ ∈ H(div,Ω)
+//               ( ∇⋅𝜓ₖ , v )                 = ( ∇⋅𝜓ₖ₋₁ - 1 , v )   ∀ v ∈ L²(Ω)
+//
+//              where Zₖ(𝜓) := ∇h⁻¹(αₖ 𝜓) = 𝜓 / ( αₖ⁻² + |𝜓|² )^{1/2} and step size
+//              αₖ > 0. These saddle-point problems are solved using a damped Newton's
+//              method. This example assumes that g = 0 and allows the step size to
+//              grow geometrically, αₖ = α₀rᵏ, where r ≥ 1 is the growth rate.
+//
+//              [1] Keith, B. and Surowiec, T. (2023) Proximal Galerkin: A structure-
+//                  preserving finite element method for pointwise bound constraints.
+//                  arXiv:2307.12444 [math.NA]
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+class ZCoefficient : public VectorCoefficient
+{
+protected:
+   ParGridFunction *psi;
+   real_t alpha;
+
+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_; }
+};
+
+class DZCoefficient : public MatrixCoefficient
+{
+protected:
+   ParGridFunction *psi;
+   real_t alpha;
+
+public:
+   DZCoefficient(int height, ParGridFunction &psi_, real_t alpha_ = 1.0)
+      : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }
+
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   void SetAlpha(real_t alpha_) { alpha = alpha_; }
+};
+
+int main(int argc, char *argv[])
+{
+   // 0. Initialize MPI and HYPRE.
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "../data/star.mesh";
+   int order = 1;
+   int max_it = 5;
+   int ref_levels = 3;
+   real_t alpha = 1.0;
+   real_t growth_rate = 1.0;
+   real_t newton_scaling = 0.9;
+   real_t tichonov = 1e-1;
+   real_t tol = 1e-4;
+   bool visualization = true;
+
+   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(&ref_levels, "-r", "--refs",
+                  "Number of h-refinements.");
+   args.AddOption(&max_it, "-mi", "--max-it",
+                  "Maximum number of iterations");
+   args.AddOption(&tol, "-tol", "--tol",
+                  "Stopping criteria based on the difference between"
+                  "successive solution updates");
+   args.AddOption(&alpha, "-step", "--step",
+                  "Initial size alpha");
+   args.AddOption(&growth_rate, "-gr", "--growth-rate",
+                  "Growth rate of the step size alpha");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 2. Read the mesh from the mesh file.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+   int sdim = mesh.SpaceDimension();
+
+   MFEM_ASSERT(mesh.bdr_attributes.Size(),
+               "This example does not currently support meshes"
+               " without boundary attributes."
+              )
+
+   // 3. Postprocess the mesh.
+   // 3A. Refine the mesh to increase the resolution.
+   for (int l = 0; l < ref_levels; l++)
+   {
+      mesh.UniformRefinement();
+   }
+
+   // 3B. Interpolate the geometry after refinement to control geometry error.
+   // NOTE: Minimum second-order interpolation is used to improve the accuracy.
+   int curvature_order = max(order,2);
+   mesh.SetCurvature(curvature_order);
+
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
+
+   // 4. Define the necessary finite element spaces on the mesh.
+   RT_FECollection RTfec(order, dim);
+   ParFiniteElementSpace RTfes(&pmesh, &RTfec);
+
+   L2_FECollection L2fec(order, dim);
+   ParFiniteElementSpace L2fes(&pmesh, &L2fec);
+
+   int num_dofs_RT = RTfes.GlobalTrueVSize();
+   int num_dofs_L2 = L2fes.GlobalTrueVSize();
+   if (myid == 0)
+   {
+      cout << "Number of H(div) dofs: "
+           << num_dofs_RT << endl;
+      cout << "Number of L² dofs: "
+           << num_dofs_L2 << endl;
+   }
+
+   // 5. Define the offsets for the block matrices
+   Array<int> offsets(3);
+   offsets[0] = 0;
+   offsets[1] = RTfes.GetVSize();
+   offsets[2] = L2fes.GetVSize();
+   offsets.PartialSum();
+
+   Array<int> toffsets(3);
+   toffsets[0] = 0;
+   toffsets[1] = RTfes.GetTrueVSize();
+   toffsets[2] = L2fes.GetTrueVSize();
+   toffsets.PartialSum();
+
+   BlockVector x(offsets), rhs(offsets);
+   x = 0.0; rhs = 0.0;
+
+   BlockVector tx(toffsets), trhs(toffsets);
+   tx = 0.0; trhs = 0.0;
+
+   // 6. Define the solution vectors as a finite element grid functions
+   //    corresponding to the fespaces.
+   ParGridFunction u_gf, delta_psi_gf;
+   delta_psi_gf.MakeRef(&RTfes,x,offsets[0]);
+   u_gf.MakeRef(&L2fes,x,offsets[1]);
+
+   ParGridFunction psi_old_gf(&RTfes);
+   ParGridFunction psi_gf(&RTfes);
+   ParGridFunction u_old_gf(&L2fes);
+
+   // 7. Define initial guesses for the solution variables.
+   delta_psi_gf = 0.0;
+   psi_gf = 0.0;
+   u_gf = 0.0;
+   psi_old_gf = psi_gf;
+   u_old_gf = u_gf;
+
+   // 8. Prepare for glvis output.
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock;
+   if (visualization)
+   {
+      sol_sock.open(vishost,visport);
+      sol_sock.precision(8);
+   }
+
+   // 9. Coefficients to be used later.
+   ConstantCoefficient neg_one(-1.0);
+   ConstantCoefficient zero(0.0);
+   ConstantCoefficient tichonov_cf(tichonov);
+   ConstantCoefficient neg_tichonov_cf(-1.0*tichonov);
+   ZCoefficient Z(sdim, psi_gf, alpha);
+   DZCoefficient DZ(sdim, psi_gf, alpha);
+   ScalarVectorProductCoefficient neg_Z(-1.0, Z);
+   DivergenceGridFunctionCoefficient div_psi_cf(&psi_gf);
+   DivergenceGridFunctionCoefficient div_psi_old_cf(&psi_old_gf);
+   SumCoefficient psi_old_minus_psi(div_psi_old_cf, div_psi_cf, 1.0, -1.0);
+
+   // 10. Assemble constant matrices/vectors to avoid reassembly in the loop.
+   ParLinearForm b0, b1;
+   b0.MakeRef(&RTfes,rhs.GetBlock(0),0);
+   b1.MakeRef(&L2fes,rhs.GetBlock(1),0);
+
+   b0.AddDomainIntegrator(new VectorFEDomainLFIntegrator(neg_Z));
+   b1.AddDomainIntegrator(new DomainLFIntegrator(neg_one));
+   b1.AddDomainIntegrator(new DomainLFIntegrator(psi_old_minus_psi));
+
+   ParBilinearForm a00(&RTfes);
+   a00.AddDomainIntegrator(new VectorFEMassIntegrator(DZ));
+   a00.AddDomainIntegrator(new VectorFEMassIntegrator(tichonov_cf));
+
+   ParMixedBilinearForm a10(&RTfes,&L2fes);
+   a10.AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+   a10.Assemble();
+   a10.Finalize();
+   HypreParMatrix *A10 = a10.ParallelAssemble();
+
+   HypreParMatrix *A01 = A10->Transpose();
+
+   ParBilinearForm a11(&L2fes);
+   a11.AddDomainIntegrator(new MassIntegrator(neg_tichonov_cf));
+   a11.Assemble();
+   a11.Finalize();
+   HypreParMatrix *A11 = a11.ParallelAssemble();
+
+   // 11. Iterate.
+   int k;
+   int total_iterations = 0;
+   real_t increment_u = 0.1;
+   ParGridFunction u_tmp(&L2fes);
+   for (k = 0; k < max_it; k++)
+   {
+      u_tmp = u_old_gf;
+      Z.SetAlpha(alpha);
+      DZ.SetAlpha(alpha);
+
+      if (myid == 0)
+      {
+         mfem::out << "\nOUTER ITERATION " << k+1 << endl;
+      }
+
+      int j;
+      for ( j = 0; j < 5; j++)
+      {
+         total_iterations++;
+
+         b0.Assemble();
+         b0.ParallelAssemble(trhs.GetBlock(0));
+
+         b1.Assemble();
+         b1.ParallelAssemble(trhs.GetBlock(1));
+
+         a00.Assemble(false);
+         a00.Finalize(false);
+         HypreParMatrix *A00 = a00.ParallelAssemble();
+
+         // Construct Schur-complement preconditioner
+         HypreParVector A00_diag(MPI_COMM_WORLD, A00->GetGlobalNumRows(),
+                                 A00->GetRowStarts());
+         A00->GetDiag(A00_diag);
+         HypreParMatrix S_tmp(*A01);
+         S_tmp.InvScaleRows(A00_diag);
+         HypreParMatrix *S = ParMult(A10, &S_tmp, true);
+
+         BlockDiagonalPreconditioner prec(toffsets);
+         HypreBoomerAMG P00(*A00);
+         P00.SetPrintLevel(0);
+         HypreBoomerAMG P11(*S);
+         P11.SetPrintLevel(0);
+         prec.SetDiagonalBlock(0,&P00);
+         prec.SetDiagonalBlock(1,&P11);
+
+         BlockOperator A(toffsets);
+         A.SetBlock(0,0,A00);
+         A.SetBlock(1,0,A10);
+         A.SetBlock(0,1,A01);
+         A.SetBlock(1,1,A11);
+
+         GMRESSolver gmres(MPI_COMM_WORLD);
+         gmres.SetPrintLevel(-1);
+         gmres.SetRelTol(1e-8);
+         gmres.SetMaxIter(2000);
+         gmres.SetKDim(500);
+         gmres.SetOperator(A);
+         gmres.SetPreconditioner(prec);
+         gmres.Mult(trhs,tx);
+         delete S;
+         delete A00;
+
+         delta_psi_gf.SetFromTrueDofs(tx.GetBlock(0));
+         u_gf.SetFromTrueDofs(tx.GetBlock(1));
+
+         u_tmp -= u_gf;
+         real_t Newton_update_size = u_tmp.ComputeL2Error(zero);
+         u_tmp = u_gf;
+
+         // Damped Newton update
+         psi_gf.Add(newton_scaling, delta_psi_gf);
+         a00.Update();
+
+         if (visualization)
+         {
+            sol_sock << "parallel " << num_procs << " " << myid << "\n";
+            sol_sock << "solution\n" << pmesh << u_gf << "window_title 'Discrete solution'"
+                     << flush;
+         }
+
+         if (myid == 0)
+         {
+            mfem::out << "Newton_update_size = " << Newton_update_size << endl;
+         }
+
+         if (Newton_update_size < increment_u)
+         {
+            break;
+         }
+      }
+
+      u_tmp = u_gf;
+      u_tmp -= u_old_gf;
+      increment_u = u_tmp.ComputeL2Error(zero);
+
+      if (myid == 0)
+      {
+         mfem::out << "Number of Newton iterations = " << j+1 << endl;
+         mfem::out << "Increment (|| uₕ - uₕ_prvs||) = " << increment_u << endl;
+      }
+
+      u_old_gf = u_gf;
+      psi_old_gf = psi_gf;
+
+      if (increment_u < tol || k == max_it-1)
+      {
+         break;
+      }
+
+      alpha *= max(growth_rate, 1_r);
+
+   }
+
+   // 12. Print stats.
+   if (myid == 0)
+   {
+      mfem::out << "\n Outer iterations: " << k+1
+                << "\n Total iterations: " << total_iterations
+                << "\n Total dofs:       " << RTfes.GetTrueVSize() + L2fes.GetTrueVSize()
+                << endl;
+   }
+
+   // 13. Free the used memory.
+   delete A01;
+   delete A10;
+   delete A11;
+   return 0;
+}
+
+void ZCoefficient::Eval(Vector &V, ElementTransformation &T,
+                        const IntegrationPoint &ip)
+{
+   MFEM_ASSERT(psi != NULL, "grid function is not set");
+   MFEM_ASSERT(alpha > 0, "alpha is not positive");
+
+   Vector psi_vals(vdim);
+   psi->GetVectorValue(T, ip, psi_vals);
+   real_t norm = psi_vals.Norml2();
+   real_t phi = 1.0 / sqrt(1.0/(alpha*alpha) + norm*norm);
+
+   V = psi_vals;
+   V *= phi;
+}
+
+void DZCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
+                         const IntegrationPoint &ip)
+{
+   MFEM_ASSERT(psi != NULL, "grid function is not set");
+   MFEM_ASSERT(alpha > 0, "alpha is not positive");
+
+   Vector psi_vals(height);
+   psi->GetVectorValue(T, ip, psi_vals);
+   real_t norm = psi_vals.Norml2();
+   real_t phi = 1.0 / sqrt(1.0/(alpha*alpha) + norm*norm);
+
+   K = 0.0;
+   for (int i = 0; i < height; i++)
+   {
+      K(i,i) = phi;
+      for (int j = 0; j < height; j++)
+      {
+         K(i,j) -= psi_vals(i) * psi_vals(j) * pow(phi, 3);
+      }
+   }
+}

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

@@ -12,25 +12,24 @@
 # 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)
 
 SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
    ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
-   ex31 ex33 ex34 ex36 ex37 ex38 ex39
+   ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40
 PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
    ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
    ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
-   ex37p ex39p
-SEQ_DEVICE_EXAMPLES = ex1 ex3 ex4 ex5 ex6 ex9 ex22 ex24 ex25 ex26 ex34
-PAR_DEVICE_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex22p \
-   ex24p ex25p ex26p ex34p ex35p
+   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
 
 ifeq ($(MFEM_USE_LAPACK),YES)
    SEQ_EXAMPLES += ex38
@@ -138,6 +137,14 @@ ex10-test-seq: ex10
 	@$(call mfem-test,$<,, Serial example,-tf 5)
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-tf 5)
+ex14-test-seq-cuda: ex14
+	@$(call mfem-test,$<,, Serial CUDA example,-r 2 -pa -d cuda)
+ex14p-test-par-cuda: ex14p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel CUDA example,-rs 2 -rp 0 -pa -d cuda)
+ex14-test-seq-hip: ex14
+	@$(call mfem-test,$<,, Serial HIP example,-r 2 -pa -d hip)
+ex14p-test-par-hip: ex14p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel HIP example,-rs 2 -rp 0 -pa -d hip)
 ex15-test-seq: ex15
 	@$(call mfem-test,$<,, Serial example,-e 1)
 ex15p-test-par: ex15p

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)

examples/petsc/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/petsc/,)
-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/pumi/ex1.cpp

@@ -66,7 +66,6 @@ int main(int argc, char *argv[])
 {
    // 1. Initialize MPI (required by PUMI) and HYPRE.
    Mpi::Init(argc, argv);
-   int num_procs = Mpi::WorldSize();
    int myid = Mpi::WorldRank();
    Hypre::Init();
 

examples/pumi/ex2.cpp

@@ -80,8 +80,6 @@ int main(int argc, char *argv[])
 {
    // 1. Initialize MPI (required by PUMI) and HYPRE.
    Mpi::Init(argc, argv);
-   int num_proc = Mpi::WorldSize();
-   int myId = Mpi::WorldRank();
    Hypre::Init();
 
    // 2. Parse command-line options.

examples/pumi/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/pumi/,)
-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/sundials/CMakeLists.txt

@@ -31,11 +31,21 @@ include_directories(BEFORE ${PROJECT_BINARY_DIR})
 add_custom_target(test_sundials
   ${CMAKE_CTEST_COMMAND} -R sundials USES_TERMINAL)
 
-# Add one executable per cpp file, adding "sundials_" as prefix. Sets
-# "test_sundials" as a target that depends on the given examples.
+# Add one executable per cpp file, adding "sundials_" as prefix so the CMake
+# target is unique from those in the non-SUNDIALS examples. Also sets
+# "test_sundials" as a target that depends on the given SUNDIALS examples.
 set(PFX sundials_)
 add_mfem_examples(SUNDIALS_EXAMPLES_SRCS ${PFX} "" test_sundials)
 
+# Remove "sundials_" prefix from exectuable name for consistency with GNU build
+# system.
+foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})
+  get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
+  string(REPLACE ".cpp" "" TARGET_NAME "${PFX}${SRC_FILENAME}")
+  string(REPLACE ${PFX} "" EXE_NAME ${TARGET_NAME})
+  set_target_properties(${TARGET_NAME} PROPERTIES OUTPUT_NAME ${EXE_NAME})
+endforeach()
+
 # Testing.
 # The SUNDIALS tests can be run separately using the target "test_sundials"
 # which builds the examples and runs:
@@ -51,7 +61,10 @@ if (MFEM_ENABLE_TESTING)
   set(EX10_COMMON_OPTS -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -tf 6 -vs 10)
   set(EX10_TEST_OPTS ${EX10_COMMON_OPTS}  -r  2)
   set(EX10P_TEST_OPTS ${EX10_COMMON_OPTS} -rp 1)
-  # Example 16: use the default options
+  # Example 16: test ARKODE with implicit time stepping using mass form
+  set(EX16_COMMON_OPTS -s 15)
+  set(EX16_TEST_OPTS ${EX16_COMMON_OPTS})
+  set(EX16P_TEST_OPTS ${EX16_COMMON_OPTS})
 
   # Add the tests: one test per source file.
   foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})

examples/sundials/ex10.cpp

@@ -1,7 +1,9 @@
 //                                MFEM Example 10
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10
+// Compile with:
+//    make ex10             (GNU make)
+//    make sundials_ex10    (CMake)
 //
 // Sample runs:
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10

examples/sundials/ex10p.cpp

@@ -1,7 +1,9 @@
 //                       MFEM Example 10 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10p
+// Compile with:
+//    make ex10p            (GNU make)
+//    make sundials_ex10p   (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10

examples/sundials/ex16.cpp

@@ -1,15 +1,21 @@
 //                                MFEM Example 16
 //                             SUNDIALS Modification
 //
-// Compile with: make ex16
+// Compile with:
+//    make ex16             (GNU make)
+//    make sundials_ex16    (CMake)
 //
 // Sample runs:  ex16
 //               ex16 -m ../../data/inline-tri.mesh
 //               ex16 -m ../../data/disc-nurbs.mesh -tf 2
 //               ex16 -s 12 -a 0.0 -k 1.0
+//               ex16 -s 15 -a 0.0 -k 1.0
 //               ex16 -s 8 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
+//               ex16 -s 11 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
 //               ex16 -s 9 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
+//               ex16 -s 12 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
 //               ex16 -s 10 -dt 1.0e-4 -tf 4.0e-2 -vs 40
+//               ex16 -s 13 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               ex16 -m ../../data/fichera-q2.mesh
 //               ex16 -m ../../data/escher.mesh
 //               ex16 -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -37,75 +43,102 @@
 using namespace std;
 using namespace mfem;
 
-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
  *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
  *
  *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
  *  (\kappa + \alpha u).
  *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
  */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
    FiniteElementSpace &fespace;
    Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.
 
-   BilinearForm *M;
-   BilinearForm *K;
+   BilinearForm M;
+   SparseMatrix Mmat;
 
-   SparseMatrix Mmat, Kmat;
-   SparseMatrix *T; // T = M + dt K
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
+   SparseMatrix Kmat;
+
+   std::unique_ptr<SparseMatrix> T; // T = M + gam K(u)
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
    DSmoother M_prec;  // Preconditioner for the mass matrix M
 
-   CGSolver T_solver; // Implicit solver for T = M + dt K
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
    DSmoother T_prec;  // Preconditioner for the implicit solver
 
-   double alpha, kappa;
-
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(FiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);
 
-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(FiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);
 
-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);
 
-   /// Custom Jacobian system solver for the SUNDIALS time integrators.
-   /** For the ODE system represented by ConductionOperator
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+    operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+      approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;
 
-           M du/dt = -K(u),
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;
 
-       this class facilitates the solution of linear systems of the form
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;
 
-           (M + γK) y = M b,
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;
 
-       for given b, u (not used), and γ = GetTimeStep(). */
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;
 
-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   int SUNMassSetup() override;
 
-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;
 
-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
-
-   virtual ~ConductionOperator();
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+
 
 int main(int argc, char *argv[])
 {
@@ -117,16 +150,16 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 2;
    int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;
 
    int precision = 8;
    cout.precision(precision);
@@ -151,7 +184,10 @@ int main(int argc, char *argv[])
                   "9  - CVODE (implicit BDF),\n\t"
                   "10 - ARKODE (default explicit),\n\t"
                   "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -174,16 +210,13 @@ int main(int argc, char *argv[])
       args.PrintUsage(cout);
       return 1;
    }
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      return 3;
-   }
    args.PrintOptions(cout);
 
+   bool use_mass_solver = ode_solver_type >= 13;
+
    // 2. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 1));
    int dim = mesh->Dimension();
 
    // 3. Refine the mesh to increase the resolution. In this example we do
@@ -197,7 +230,7 @@ int main(int argc, char *argv[])
    // 4. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
    H1_FECollection fe_coll(order, dim);
-   FiniteElementSpace fespace(mesh, &fe_coll);
+   FiniteElementSpace fespace(mesh.get(), &fe_coll);
 
    int fe_size = fespace.GetTrueVSize();
    cout << "Number of temperature unknowns: " << fe_size << endl;
@@ -211,8 +244,17 @@ int main(int argc, char *argv[])
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 6. Initialize the conduction operator and the visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 6. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -224,7 +266,7 @@ int main(int argc, char *argv[])
       u_gf.Save(osol);
    }
 
-   VisItDataCollection visit_dc("Example16", mesh);
+   VisItDataCollection visit_dc("Example16", mesh.get());
    visit_dc.RegisterField("temperature", &u_gf);
    if (visit)
    {
@@ -258,52 +300,75 @@ int main(int argc, char *argv[])
    }
 
    // 7. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
    switch (ode_solver_type)
    {
       // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
       // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
       // CVODE
       case 8:
-         cvode = new CVODESolver(CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
       case 9:
-         cvode = new CVODESolver(CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(new CVODESolver(cvode_solver_type));
          cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
       // ARKODE
       case 10:
       case 11:
-         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(arkode_solver_type));
          arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
          {
             arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
          }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -311,8 +376,14 @@ int main(int argc, char *argv[])
 
    // Since we want to update the diffusion coefficient after every time step,
    // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }
 
    // 8. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
@@ -323,7 +394,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       // Note that since we are using the "one-step" mode of the SUNDIALS
       // solvers, they will, generally, step over the final time and will not
@@ -337,8 +408,14 @@ int main(int argc, char *argv[])
       if (last_step || (ti % vis_steps) == 0)
       {
          cout << "step " << ti << ", t = " << t << endl;
-         if (cvode) { cvode->PrintInfo(); }
-         if (arkode) { arkode->PrintInfo(); }
+         if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+         {
+            cvode->PrintInfo();
+         }
+         else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+         {
+            arkode->PrintInfo();
+         }
 
          u_gf.SetFromTrueDofs(u);
          if (visualization)
@@ -353,137 +430,153 @@ int main(int argc, char *argv[])
             visit_dc.Save();
          }
       }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
    }
    tic_toc.Stop();
    cout << "Done, " << tic_toc.RealTime() << "s." << endl;
 
    // 9. Save the final solution. This output can be viewed later using GLVis:
    //    "glvis -m ex16.mesh -g ex16-final.gf".
-   {
-      ofstream osol("ex16-final.gf");
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 10. Free the used memory.
-   delete ode_solver;
-   delete mesh;
+   u_gf.Save("ex16-final.gf", precision);
 
    return 0;
 }
 
-ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), z(height)
+ConductionOperator::ConductionOperator(FiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;
 
-   M = new BilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble();
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble();
+   M.FormSystemMatrix(ess_tdof_list, Mmat);
 
    M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    M_solver.SetAbsTol(0.0);
    M_solver.SetMaxIter(50);
    M_solver.SetPrintLevel(0);
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
-   alpha = al;
-   kappa = kap;
-
    T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
 
-   SetParameters(u);
+   SetConductionTensor(u);
 }
 
-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
    GridFunction u_alpha_gf(&fespace);
    u_alpha_gf.SetFromTrueDofs(u);
    for (int i = 0; i < u_alpha_gf.Size(); i++)
    {
       u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
    }
-
-   delete K;
-   K = new BilinearForm(&fespace);
-
    GridFunctionCoefficient u_coeff(&u_alpha_gf);
 
+   K = std::make_unique<BilinearForm>(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
    K->Assemble();
    K->FormSystemMatrix(ess_tdof_list, Kmat);
 }
 
-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
+}
+
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
+{
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
    T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
+   T_solver.Mult(z, k);
 }
 
-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
 {
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
 }
 
-ConductionOperator::~ConductionOperator()
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
 {
-   delete T;
-   delete M;
-   delete K;
-}
-
-double InitialTemperature(const Vector &x)
-{
-   if (x.Norml2() < 0.5)
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
    {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
    }
    else
    {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
    }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}
+

examples/sundials/ex16p.cpp

@@ -1,16 +1,22 @@
 //                         MFEM Example 16 - Parallel Version
 //                              SUNDIALS Modification
 //
-// Compile with: make ex16p
+// Compile with:
+//    make ex16p            (GNU make)
+//    make sundials_ex16p   (CMake)
 //
 // Sample runs:
 //     mpirun -np 4 ex16p
 //     mpirun -np 4 ex16p -m ../../data/inline-tri.mesh
 //     mpirun -np 4 ex16p -m ../../data/disc-nurbs.mesh -tf 2
 //     mpirun -np 4 ex16p -s 12 -a 0.0 -k 1.0
+//     mpirun -np 4 ex16p -s 15 -a 0.0 -k 1.0
 //     mpirun -np 4 ex16p -s 8 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
+//     mpirun -np 4 ex16p -s 11 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
 //     mpirun -np 8 ex16p -s 9 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
+//     mpirun -np 8 ex16p -s 12 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
 //     mpirun -np 4 ex16p -s 10 -dt 2.0e-4 -tf 4.0e-2
+//     mpirun -np 4 ex16p -s 13 -dt 2.0e-4 -tf 4.0e-2
 //     mpirun -np 16 ex16p -m ../../data/fichera-q2.mesh
 //     mpirun -np 16 ex16p -m ../../data/escher-p2.mesh
 //     mpirun -np 8 ex16p -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -38,66 +44,102 @@
 using namespace std;
 using namespace mfem;
 
-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
  *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
  *
  *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
  *  (\kappa + \alpha u).
  *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where either
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
  */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
    ParFiniteElementSpace &fespace;
    Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.
 
-   ParBilinearForm *M;
-   ParBilinearForm *K;
-
+   ParBilinearForm M;
    HypreParMatrix Mmat;
+
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
    HypreParMatrix Kmat;
-   HypreParMatrix *T; // T = M + dt K
-   double current_dt;
 
-   CGSolver M_solver;    // Krylov solver for inverting the mass matrix M
-   HypreSmoother M_prec; // Preconditioner for the mass matrix M
+   std::unique_ptr<HypreParMatrix> T; // T = M + gam K(u)
 
-   CGSolver T_solver;    // Implicit solver for T = M + dt K
-   HypreSmoother T_prec; // Preconditioner for the implicit solver
+   CGSolver M_solver; // Krylov solver for inverting the mass matrix M
+   HypreSmoother M_prec;  // Preconditioner for the mass matrix M
 
-   double alpha, kappa;
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
+   HypreSmoother T_prec;  // Preconditioner for the implicit solver
 
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(ParFiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);
 
-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(ParFiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);
 
-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);
 
-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+       operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+       approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;
 
-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;
 
-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;
 
-   virtual ~ConductionOperator();
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;
+
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;
+
+   int SUNMassSetup() override;
+
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;
+
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+
 
 int main(int argc, char *argv[])
 {
@@ -114,16 +156,16 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 2;
    int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;
 
    int precision = 8;
    cout.precision(precision);
@@ -150,7 +192,10 @@ int main(int argc, char *argv[])
                   "9  - CVODE (implicit BDF),\n\t"
                   "10 - ARKODE (default explicit),\n\t"
                   "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -174,40 +219,33 @@ int main(int argc, char *argv[])
       return 1;
    }
 
-   if (myid == 0)
+   if (Mpi::Root())
    {
       args.PrintOptions(cout);
    }
 
-   // check for valid ODE solver option
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      if (myid == 0)
-      {
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      }
-      return 1;
-   }
+   bool use_mass_solver = ode_solver_type >= 13;
 
-   // 3. Read the serial mesh from the given mesh file on all processors. We can
+   // 3. Define a parallel mesh by a partitioning of a serial mesh. 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.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-
-   // 4. Refine the mesh in serial to increase the resolution. In this example
-   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
-   //    a command-line parameter.
-   for (int lev = 0; lev < ser_ref_levels; lev++)
+   std::unique_ptr<ParMesh> pmesh;
    {
-      mesh->UniformRefinement();
-   }
+      std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 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 = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
+      // 4. Refine the mesh in serial to increase the resolution. In this example
+      //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
+      //    a command-line parameter.
+      for (int lev = 0; lev < ser_ref_levels; lev++)
+      {
+         mesh->UniformRefinement();
+      }
+
+      // 5. Refine this mesh further in parallel to increase the resolution.
+      //    Once the parallel mesh is defined, the serial mesh can be deleted.
+      pmesh = std::make_unique<ParMesh>(MPI_COMM_WORLD, *mesh);
+   }
    for (int lev = 0; lev < par_ref_levels; lev++)
    {
       pmesh->UniformRefinement();
@@ -215,8 +253,9 @@ int main(int argc, char *argv[])
 
    // 6. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
+   int dim = pmesh->Dimension();
    H1_FECollection fe_coll(order, dim);
-   ParFiniteElementSpace fespace(pmesh, &fe_coll);
+   ParFiniteElementSpace fespace(pmesh.get(), &fe_coll);
 
    int fe_size = fespace.GlobalTrueVSize();
    if (myid == 0)
@@ -233,8 +272,17 @@ int main(int argc, char *argv[])
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 8. Initialize the conduction operator and the VisIt visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 8. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -249,7 +297,7 @@ int main(int argc, char *argv[])
       u_gf.Save(osol);
    }
 
-   VisItDataCollection visit_dc("Example16-Parallel", pmesh);
+   VisItDataCollection visit_dc("Example16-Parallel", pmesh.get());
    visit_dc.RegisterField("temperature", &u_gf);
    if (visit)
    {
@@ -293,52 +341,76 @@ int main(int argc, char *argv[])
    }
 
    // 9. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
    switch (ode_solver_type)
    {
       // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
       // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
       // CVODE
       case 8:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
       case 9:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(
+            new CVODESolver(MPI_COMM_WORLD, cvode_solver_type));
          cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
       // ARKODE
       case 10:
       case 11:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(MPI_COMM_WORLD, arkode_solver_type));
          arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
          {
             arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
          }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -346,12 +418,18 @@ int main(int argc, char *argv[])
 
    // Since we want to update the diffusion coefficient after every time step,
    // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }
 
    // 10. Perform time-integration (looping over the time iterations, ti, with a
    //     time-step dt).
-   if (myid == 0)
+   if (Mpi::Root())
    {
       cout << "Integrating the ODE ..." << endl;
    }
@@ -361,7 +439,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       // Note that since we are using the "one-step" mode of the SUNDIALS
       // solvers, they will, generally, step over the final time and will not
@@ -377,8 +455,14 @@ int main(int argc, char *argv[])
          if (myid == 0)
          {
             cout << "step " << ti << ", t = " << t << endl;
-            if (cvode) { cvode->PrintInfo(); }
-            if (arkode) { arkode->PrintInfo(); }
+            if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+            {
+               cvode->PrintInfo();
+            }
+            else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+            {
+               arkode->PrintInfo();
+            }
          }
 
          u_gf.SetFromTrueDofs(u);
@@ -395,46 +479,38 @@ int main(int argc, char *argv[])
             visit_dc.Save();
          }
       }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
    }
    tic_toc.Stop();
-   if (myid == 0)
+   if (Mpi::Root())
    {
       cout << "Done, " << tic_toc.RealTime() << "s." << endl;
    }
 
    // 11. Save the final solution in parallel. This output can be viewed later
    //     using GLVis: "glvis -np <np> -m ex16-mesh -g ex16-final".
-   {
-      ostringstream sol_name;
-      sol_name << "ex16-final." << setfill('0') << setw(6) << myid;
-      ofstream osol(sol_name.str().c_str());
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 12. Free the used memory.
-   delete ode_solver;
-   delete pmesh;
+   u_gf.Save("ex16-final", precision);
 
    return 0;
 }
 
-ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL),
-     M_solver(f.GetComm()), T_solver(f.GetComm()), z(height)
+ConductionOperator::ConductionOperator(ParFiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace),
+     M_solver(fes.GetComm()), T_solver(fes.GetComm()), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;
 
-   M = new ParBilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble(0); // keep sparsity pattern of M and K the same
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
+   M.FormSystemMatrix(ess_tdof_list, Mmat);
 
    M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    M_solver.SetAbsTol(0.0);
    M_solver.SetMaxIter(100);
    M_solver.SetPrintLevel(0);
@@ -442,97 +518,118 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
-   alpha = al;
-   kappa = kap;
-
    T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
 
-   SetParameters(u);
+   SetConductionTensor(u);
 }
 
-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
-{
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
-   T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
-}
-
-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
-{
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
    ParGridFunction u_alpha_gf(&fespace);
    u_alpha_gf.SetFromTrueDofs(u);
    for (int i = 0; i < u_alpha_gf.Size(); i++)
    {
       u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
    }
-
-   delete K;
-   K = new ParBilinearForm(&fespace);
-
    GridFunctionCoefficient u_coeff(&u_alpha_gf);
 
+   K = std::make_unique<ParBilinearForm>(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
-   K->Assemble(0); // keep sparsity pattern of M and K the same
+   K->Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
    K->FormSystemMatrix(ess_tdof_list, Kmat);
 }
 
-ConductionOperator::~ConductionOperator()
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   delete T;
-   delete M;
-   delete K;
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
 }
 
-double InitialTemperature(const Vector &x)
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
 {
-   if (x.Norml2() < 0.5)
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   T_solver.Mult(z, k);
+}
+
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
+{
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
+{
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
    {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
    }
    else
    {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
    }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}

examples/sundials/ex9.cpp

@@ -1,7 +1,9 @@
 //                                MFEM Example 9
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9
+// Compile with:
+//    make ex9              (GNU make)
+//    make sundials_ex9     (CMake)
 //
 // Sample runs:
 //    ex9 -m ../../data/periodic-segment.mesh -p 0 -r 2 -s 7 -dt 0.005

examples/sundials/ex9p.cpp

@@ -1,7 +1,9 @@
 //                       MFEM Example 9 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9p
+// Compile with:
+//    make ex9p             (GNU make)
+//    make sundials_ex9p    (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex9p -m ../../data/periodic-segment.mesh -p 1 -rp 1 -s 7 -dt 0.0025

examples/sundials/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/sundials/,)
-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 $(CONFIG_MK)
@@ -100,6 +99,12 @@ ex10-test-seq: ex10
 	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX10_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX10P_ARGS))
+# Example 16: test ARKODE with implicit time stepping using mass form
+EX16_COMMON_ARGS := -s 15
+ex16-test-seq: ex16
+	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX16_COMMON_ARGS))
+ex16p-test-par: ex16p
+	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX16_COMMON_ARGS))
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

examples/superlu/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/superlu/,)
-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/test_dfem_dual.cpp

@@ -0,0 +1,305 @@
+#include "dfem/dfem_refactor.hpp"
+#include "linalg/hypre.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+using mfem::internal::dual;
+
+int test_diffusion_integrator(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());
+
+   ParGridFunction f1_g(&h1fes);
+   ParGridFunction rho_g(&h1fes);
+
+   auto rho_f = [](const Vector &coords)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      return x + y;
+   };
+
+   FunctionCoefficient rho_c(rho_f);
+   rho_g.ProjectCoefficient(rho_c);
+
+   auto kernel = [](const tensor<dual<double, double>, 2> &grad_u,
+                    const dual<double, double> &rho,
+                    const tensor<double, 2, 2> &J,
+                    const double &w)
+   {
+      auto invJ = inv(J);
+      return std::tuple{rho*rho * grad_u * invJ * transpose(invJ) * det(J) * w};
+   };
+
+   std::tuple argument_operators = {Gradient{"potential"}, Value{"density"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator = {Gradient{"potential"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = std::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "potential"}};
+   auto parameters = std::array
+   {
+      FieldDescriptor{&h1fes, "density"},
+      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({&rho_g, mesh_nodes});
+   dop.Mult(x, y);
+
+   ParBilinearForm a(&h1fes);
+   TransformedCoefficient rho_c2(&rho_c, [](double c) {return c*c;});
+   a.AddDomainIntegrator(new DiffusionIntegrator(rho_c2));
+   a.Assemble();
+   a.Finalize();
+
+   Vector y2(h1fes.TrueVSize());
+   a.Mult(x, y2);
+   y2 -= y;
+   if (y2.Norml2() > 1e-10)
+   {
+      out << "||F(u) - ex||_l2 = " << y2.Norml2() << "\n";
+      return 1;
+   }
+
+   // Test linearization here as well
+   auto dFdu = dop.GetDerivativeWrt<0>({&f1_g}, {&rho_g, mesh_nodes});
+
+   // HypreParMatrix A;
+   // dFdu->Assemble(A);
+
+   if (dFdu->Height() != h1fes.GetTrueVSize())
+   {
+      out << "dFdu unexpected height of " << dFdu->Height() << "\n";
+      return 1;
+   }
+
+   dFdu->Mult(x, y);
+   a.Mult(x, y2);
+   y2 -= y;
+   if (y2.Norml2() > 1e-10)
+   {
+      out << "||dFdu u^* - ex||_l2 = " << y2.Norml2() << "\n";
+      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;
+}
+
+int test_qoi(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, dim);
+
+   const IntegrationRule &ir =
+      IntRules.Get(h1fes.GetFE(0)->GetGeomType(), 2 * h1fec.GetOrder());
+
+   ParGridFunction rho_g(&h1fes);
+
+   auto rho_f = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double y = coords(1);
+      u(0) = x + y;
+      u(1) = x + y;
+   };
+
+   VectorFunctionCoefficient rho_c(dim, rho_f);
+   rho_g.ProjectCoefficient(rho_c);
+
+   auto kernel = [](const tensor<dual<double, double>, 2> &rho,
+                    const tensor<dual<double, double>, 2, 2> &drhodxi,
+                    const tensor<double, 2, 2> &J,
+                    const double &w)
+   {
+      const double eps = 1.2345;
+      const auto drhodx = drhodxi * inv(J);
+      return std::tuple{(0.5 * eps * dot(rho, rho) + ddot(drhodx, drhodx)) * det(J) * w};
+   };
+
+   std::tuple argument_operators = {Value{"density"}, Gradient{"density"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator = {One{"density"}};
+
+   ElementOperator eop = {kernel, argument_operators, output_operator};
+   auto ops = std::tuple{eop};
+
+   auto solutions = std::array{FieldDescriptor{&h1fes, "density"}};
+   auto parameters = std::array{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator dop(solutions, parameters, ops, mesh, ir);
+
+   Vector x(rho_g), y(1);
+   dop.SetParameters({mesh_nodes});
+   dop.Mult(x, y);
+
+   // print_vector(y);
+
+   auto dFdrho = dop.GetDerivativeWrt<0>({&rho_g}, {mesh_nodes});
+   // Vector dFdrho_vec;
+   // dFdrho->Assemble(dFdrho_vec);
+
+   // print_vector(dFdrho_vec);
+
+   // fd jacobian test
+   {
+      double eps = 1.0e-8;
+      Vector v(x), fxpv(1), fxmv(1), dfdx(x.Size());
+      for (int i = 0; i < x.Size(); i++)
+      {
+         v(i) += eps;
+         dop.Mult(v, fxpv);
+         v(i) -= 2.0 * eps;
+         dop.Mult(v, fxmv);
+         fxpv -= fxmv;
+         fxpv /= (2.0*eps);
+         dfdx(i) = fxpv(0);
+      }
+
+      // print_vector(dfdx);
+      dfdx -= dFdrho_vec;
+      if (dfdx.Norml2() > 1e-6)
+      {
+         out << "||dFdu_FD u^* - ex||_l2 = " << dfdx.Norml2() << "\n";
+         return 1;
+      }
+   }
+
+   return 0;
+}
+
+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 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.ParseCheck();
+
+   out << std::setprecision(12);
+
+   int ret;
+
+   ret = test_diffusion_integrator(mesh_file,
+                                   refinements,
+                                   polynomial_order);
+   out << "test_diffusion_integrator";
+   ret ? out << " FAILURE\n" : out << " OK\n";
+
+   ret = test_qoi(mesh_file, refinements, polynomial_order);
+   out << "test_qoi";
+   ret ? out << " FAILURE\n" : out << " OK\n";
+
+   return 0;
+}

fem/bilinearform.cpp

@@ -280,7 +280,7 @@ void BilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
    boundary_face_integs_marker.Append(&bdr_marker);
 }
 
-void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
+void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
 {
    if (element_matrices)
    {
@@ -308,7 +308,7 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
    }
 }
 
-void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
    if (boundary_integs.Size())
    {
@@ -329,6 +329,79 @@ void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
    }
 }
 
+void BilinearForm::ComputeFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *tr;
+   Mesh *mesh = fes -> GetMesh();
+   tr = mesh -> GetFaceElementTransformations (i);
+
+   const FiniteElement *fe1, *fe2;
+   fe1 = fes->GetFE(tr->Elem1No);
+   if (tr->Elem2No >= 0)
+   {
+      fe2 = fes->GetFE(tr->Elem2No);
+   }
+   else
+   {
+      // The fe2 object is really a dummy and not used on the
+      // boundaries, but we can't dereference a NULL pointer, and we don't
+      // want to actually make a fake element.
+      fe2 = fe1;
+   }
+
+   if (interior_face_integs.Size())
+   {
+      interior_face_integs[0] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elmat);
+      for (int k = 1; k < interior_face_integs.Size(); k++)
+      {
+         interior_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      int ndof = fe1->GetDof() * fes->GetVDim();
+      if (tr->Elem2No >= 0)
+      {
+         ndof += fe2->GetDof() * fes->GetVDim();
+      }
+
+      elmat.SetSize(ndof);
+      elmat = 0.0;
+   }
+}
+
+void BilinearForm::ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *tr;
+   Mesh *mesh = fes -> GetMesh();
+   tr = mesh -> GetBdrFaceTransformations (i);
+
+   const FiniteElement *fe1, *fe2;
+
+   fe1 = fes -> GetFE (tr -> Elem1No);
+   // The fe2 object is really a dummy and not used on the boundaries,
+   // but we can't dereference a NULL pointer, and we don't want to
+   // actually make a fake element.
+   fe2 = fe1;
+
+   if (boundary_face_integs.Size())
+   {
+      boundary_face_integs[0] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elmat);
+      for (int k = 1; k < boundary_face_integs.Size(); k++)
+      {
+         boundary_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      int ndof = fe1->GetDof() * fes->GetVDim();
+      elmat.SetSize(ndof);
+      elmat = 0.0;
+   }
+}
+
 void BilinearForm::AssembleElementMatrix(
    int i, const DenseMatrix &elmat, int skip_zeros)
 {
@@ -1692,7 +1765,7 @@ void MixedBilinearForm::ConformingAssemble()
 }
 
 
-void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
+void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
 {
    if (domain_integs.Size())
    {
@@ -1717,7 +1790,7 @@ void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
    }
 }
 
-void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
    if (boundary_integs.Size())
    {
@@ -1742,6 +1815,94 @@ void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
    }
 }
 
+void MixedBilinearForm::ComputeTraceFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetFaceElementTransformations(i);
+   MFEM_ASSERT(ftr, "No associated face transformation.");
+
+   const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
+
+   trial_face_fe = trial_fes->GetFaceElement(i);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   if (ftr->Elem2No >= 0)
+   {
+      test_fe2 = test_fes->GetFE(ftr->Elem2No);
+   }
+   else
+   {
+      // The test_fe2 object is really a dummy and not used on the
+      // boundaries, but we can't dereference a NULL pointer, and we don't
+      // want to actually make a fake element.
+      test_fe2 = test_fe1;
+   }
+
+   if (trace_face_integs.Size())
+   {
+      trace_face_integs[0]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                               *ftr, elmat);
+      for (int k = 1; k < trace_face_integs.Size(); k++)
+      {
+         trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                                  *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      const int tr_face_dofs = trial_face_fe->GetDof() * trial_fes->GetVDim();
+      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+      if (ftr->Elem2No >= 0)
+      {
+         te_dofs += test_fe2->GetDof() * test_fes->GetVDim();
+      }
+
+      elmat.SetSize(te_dofs, tr_face_dofs);
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeBdrTraceFaceMatrix(int i,
+                                                  DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetBdrFaceTransformations(i);
+   MFEM_ASSERT(ftr, "No associated boundary face.");
+
+   const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
+   int iface = mesh->GetBdrElementFaceIndex(i);
+   trial_face_fe = trial_fes->GetFaceElement(iface);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   // The test_fe2 object is really a dummy and not used on the
+   // boundaries, but we can't dereference a NULL pointer, and we don't
+   // want to actually make a fake element.
+   test_fe2 = test_fe1;
+
+   if (boundary_trace_face_integs.Size())
+   {
+      boundary_trace_face_integs[0]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
+                                                        *test_fe2,
+                                                        *ftr, elmat);
+      for (int k = 1; k < boundary_trace_face_integs.Size(); k++)
+      {
+         boundary_trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
+                                                           *test_fe2,
+                                                           *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      const int tr_face_dofs = trial_face_fe->GetDof() * trial_fes->GetVDim();
+      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+
+      elmat.SetSize(te_dofs, tr_face_dofs);
+      elmat = 0.0;
+   }
+}
+
 void MixedBilinearForm::AssembleElementMatrix(
    int i, const DenseMatrix &elmat, int skip_zeros)
 {

fem/bilinearform.hpp

@@ -119,8 +119,8 @@ protected:
    Array<BilinearFormIntegrator*> boundary_face_integs;
    Array<Array<int>*> boundary_face_integs_marker; ///< Entries are not owned.
 
-   DenseMatrix elemmat;
-   Array<int>  vdofs;
+   mutable DenseMatrix elemmat;
+   mutable Array<int>  vdofs;
 
    DenseTensor *element_matrices; ///< Owned.
 
@@ -580,10 +580,18 @@ public:
        or the one stored internally by a prior call of ComputeElementMatrices()
        is returned when available.
    */
-   void ComputeElementMatrix(int i, DenseMatrix &elmat);
+   void ComputeElementMatrix(int i, DenseMatrix &elmat) const;
 
    /// Compute the boundary element matrix of the given boundary element
-   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the face matrix of the given face element
+   void ComputeFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the boundary face matrix of the given boundary element
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const;
 
    /// Assemble the given element matrix
    /** The element matrix @a elmat is assembled for the element @a i, i.e.
@@ -771,8 +779,8 @@ protected:
    /// Entries are not owned.
    Array<Array<int>*> boundary_trace_face_integs_marker;
 
-   DenseMatrix elemmat;
-   Array<int>  trial_vdofs, test_vdofs;
+   mutable DenseMatrix elemmat;
+   mutable Array<int>  trial_vdofs, test_vdofs;
 
 private:
    /// Copy construction is not supported; body is undefined.
@@ -944,10 +952,18 @@ public:
    void ConformingAssemble();
 
    /// Compute the element matrix of the given element
-   void ComputeElementMatrix(int i, DenseMatrix &elmat);
+   void ComputeElementMatrix(int i, DenseMatrix &elmat) const;
 
    /// Compute the boundary element matrix of the given boundary element
-   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the trace face matrix of the given face element
+   void ComputeTraceFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the boundary trace face matrix of the given boundary element
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrTraceFaceMatrix(int i, DenseMatrix &elmat) const;
 
    /// Assemble the given element matrix
    /** The element matrix @a elmat is assembled for the element @a i, i.e.