fix missing std::array and std::ignore

# Conflicts:
#	CMakeLists.txt

.github/workflows/trigger-pymfem-ci.yml

@@ -1,31 +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.
-
-name: "Trigger PyMFEM CI"
-
-on:
-  push:
-    branches:
-      - master
-
-jobs:
-  trigger-pymfem:
-    runs-on: ubuntu-latest
-    steps:
-    - name: Send POST request to trigger PyMFEM CI
-      run: |
-        curl -L \
-             -X POST \
-             -H "Accept: application/vnd.github+json" \
-             -H "Authorization: Bearer ${{ secrets.PYMFEM_CI_TOKEN }}" \
-             -H "X-GitHub-Api-Version: 2022-11-28" \
-             https://api.github.com/repos/mfem/pymfem/actions/workflows/build-and-test-dispatch.yml/dispatches \
-             -d '{"ref":"master", "inputs":{"test_options":"fast"}}'

.gitignore

@@ -15,9 +15,6 @@
 CMakeCache.txt
 CMakeFiles/
 
-# Clangd server cache
-*.cache*
-
 # Backup files
 *~
 

CHANGELOG

@@ -30,26 +30,11 @@ New and updated examples and miniapps
 - Added an MFEM example for the eikonal equation. This new solver is based on
   the proximal Galerkin method introduced by Keith and Surowiec.
 
-- Added a command line option to all miniapps (`-p` or `--send-port`) for
-  specifying the GLVis server socket port (19916 by default).
-
 GPU computing
 -------------
 - Added support for GPU-accelerated batched linear algebra (using cuBLAS,
   hipBLAS, MAGMA, or native MFEM functionality) through the BatchedLinAlg class.
 
-- A new GPU kernel dispatch mechanism was introduced. Users can instantiate
-  specialized kernels for specific combinations of (for example) polynomial
-  degree and number of quadrature points using
-  `DiffusionIntegrator::AddSpecialization` and
-  `MassIntegrator::AddSpecialization` (this functionality may be added to more
-  integrators in the future).
-
-- Calls to slower fallback kernels can be reported to `mfem::err` by setting
-  the environment variable `MFEM_REPORT_KERNELS` to any value other than `NO`
-  or by explicitly calling `KernelReporter::Enable`. Users can then add
-  specializations for these kernels to achieve higher performance.
-
 Miscellaneous
 -------------
 - Refactored the `ARKStepSolver` class (ARKODE interface) to use

CMakeLists.txt

@@ -522,7 +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
@@ -629,6 +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()

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()

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

examples/CMakeLists.txt

@@ -50,6 +50,28 @@ list(APPEND ALL_EXE_SRCS
 
 if (MFEM_USE_MPI)
   list(APPEND ALL_EXE_SRCS
+    dfem_poisson.cpp
+    dfem_stokes.cpp
+    enzyme_interface_smoketest.cpp
+    test_dfem_dual.cpp
+    test_dfem.cpp
+    dfem_laghos.cpp
+    dfem_minimal_example.cpp
+    dfem_test_diffusion_2d.cpp
+    dfem_test_diffusion_3d.cpp
+    dfem_test_diffusion_3d_refactor.cpp
+    dfem_test_ordering.cpp
+    dfem_test_vector_diffusion.cpp
+    dfem_test_elasticity.cpp
+    dfem_test_nonlinear_elasticity_3d.cpp
+    dfem_test_nonlinear_diffusion_3d.cpp
+    dfem_test_interpolate_linear_scalar.cpp
+    dfem_test_interpolate_linear_scalar_3d.cpp
+    dfem_test_interpolate_gradient_linear_scalar_3d.cpp
+    dfem_test_mass_scalar_3d.cpp
+    dfem_test_mass_scalar_2d.cpp
+    dfem_test_interpolate_linear_vector.cpp
+    dfem_test_interpolate_linear_vector_3d.cpp
     ex0p.cpp
     ex1p.cpp
     ex2p.cpp
@@ -110,6 +132,17 @@ include_directories(BEFORE ${PROJECT_BINARY_DIR})
 # Add one executable per cpp file
 add_mfem_examples(ALL_EXE_SRCS)
 
+target_link_libraries(dfem_poisson ClangEnzymeFlags)
+target_link_libraries(dfem_stokes ClangEnzymeFlags)
+target_link_libraries(enzyme_interface_smoketest ClangEnzymeFlags)
+target_link_libraries(test_dfem ClangEnzymeFlags)
+target_link_libraries(dfem_laghos ClangEnzymeFlags)
+target_link_libraries(dfem_minimal_example ClangEnzymeFlags)
+target_link_libraries(dfem_test_diffusion_3d ClangEnzymeFlags)
+target_link_libraries(dfem_test_diffusion_3d_refactor ClangEnzymeFlags)
+target_link_libraries(dfem_test_nonlinear_diffusion_3d ClangEnzymeFlags)
+target_link_libraries(dfem_test_nonlinear_elasticity_3d ClangEnzymeFlags)
+
 # Add a test for each example
 if (MFEM_ENABLE_TESTING)
   foreach(SRC_FILE ${ALL_EXE_SRCS})

examples/dfem/cxxtimer.hpp

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

examples/dfem/dfem.hpp

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

examples/dfem/dfem_action_callback.icc

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

examples/dfem/dfem_assemble_hypreparmatrix.icc

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

examples/dfem/dfem_assemble_vector.icc

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

examples/dfem/dfem_derivative_callback.icc

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

examples/dfem/dfem_differentiable_operator.hpp

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

examples/dfem/dfem_element_operator.hpp

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

examples/dfem/dfem_fieldoperator.hpp

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

examples/dfem/dfem_integrate.hpp

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

examples/dfem/dfem_interpolate.hpp

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

examples/dfem/dfem_parametricspace.hpp

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

examples/dfem/dfem_qfunction.hpp

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

examples/dfem/dfem_qfunction_dual.hpp

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

examples/dfem/dfem_refactor.hpp

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

examples/dfem/dfem_refactor_action.hpp

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

examples/dfem/dfem_refactor_derivatives.hpp

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

examples/dfem/dfem_smm.hpp

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

examples/dfem/dfem_test_macro.hpp

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

examples/dfem/noisy.hpp

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

examples/dfem/old_derivative_action_callback.icc

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

examples/dfem/shared_mem_calc.md

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

examples/dfem/tuple.hpp

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

examples/dfem_dg.cpp

@@ -0,0 +1,123 @@
+#include "dfem/dfem_refactor.hpp"
+#include "fem/bilininteg.hpp"
+#include "fem/coefficient.hpp"
+#include "linalg/auxiliary.hpp"
+#include "linalg/hypre.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-square.mesh";
+   int polynomial_order = 1;
+   int ir_order = 2;
+   int refinements = 1;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   L2_FECollection fec(polynomial_order, dim, BasisType::GaussLobatto);
+   ParFiniteElementSpace fes(&mesh, &fec);
+
+   const IntegrationRule &ir = IntRules.Get(fes.GetFE(0)->GetGeomType(),
+                                            ir_order * fec.GetOrder());
+   const IntegrationRule &ir_face = IntRules.Get(
+                                       fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0))->GetGeomType(),
+                                       ir_order * fec.GetOrder());
+   ParGridFunction u(&fes);
+
+   // // -\nabla \cdot (\nabla u + p * I) -> (\nabla u + p * I, \nabla v)
+   // auto advection_kernel = [](const tensor<double, 2> &dudxi,
+   //                            const tensor<double, 2, 2> &J,
+   //                            const double &w)
+   // {
+   //    constexpr tensor<double, 2> b{1.0, 1.0};
+   //    return std::tuple{dot(b, dudxi * inv(J)) * det(J) * w};
+   // };
+
+   // std::tuple argument_operators_0{Gradient{"quantity"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   // std::tuple output_operator_0{Value{"quantity"}};
+   // ElementOperator op_0{advection_kernel, argument_operators_0, output_operator_0};
+
+   // std::array solutions{FieldDescriptor{&fes, "quantity"}};
+   // std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   // DifferentiableOperator advection_op{solutions, parameters, std::tuple{op_0}, mesh, ir};
+
+   // auto adv_du = advection_op.template GetDerivativeWrt<0>({&u}, {mesh_nodes});
+   // HypreParMatrix A;
+   // adv_du->Assemble(A);
+
+   // std::ofstream mmatofs("dfem_mat.dat");
+   // A.PrintMatlab(mmatofs);
+   // mmatofs.close();
+
+   auto trace_kernel = [](const double &uL, const double &uR, const double &J,
+                          const double &w)
+   {
+      return std::tuple{1.0 / J * w};
+   };
+
+   std::tuple argument_operators_0
+   {
+      FaceValueLeft{"quantity"},
+      FaceValueRight{"quantity"},
+      Gradient{"coordinates"},
+      Weight{"integration_weights"}
+   };
+   std::tuple output_operator_0{Value{"quantity"}};
+   FaceElementOperator op_0{trace_kernel, argument_operators_0, output_operator_0};
+
+   std::array solutions{FieldDescriptor{&fes, "quantity"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator trace_op{solutions, parameters, std::tuple{op_0}, mesh, ir_face};
+
+   auto vector_func = [](const Vector &, Vector &u)
+   {
+      u = 1.0;
+   };
+
+   VectorFunctionCoefficient vel_coeff(dim, vector_func);
+
+   ParBilinearForm adv_form(&fes);
+   constexpr double alpha = 1.0;
+   auto integ = new ConvectionIntegrator(vel_coeff, alpha);
+   integ->SetIntRule(&ir);
+   adv_form.AddInteriorFaceIntegrator(
+      new NonconservativeDGTraceIntegrator(vel_coeff, alpha));
+   // adv_form.AddDomainIntegrator(integ);
+   adv_form.Assemble();
+   adv_form.Finalize();
+
+   auto K = adv_form.ParallelAssemble();
+   std::ofstream kmatofs("mfem_mat.dat");
+   K->PrintMatlab(kmatofs);
+   kmatofs.close();
+
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock(vishost, visport);
+   sol_sock << "parallel " << num_procs << " " << myid << "\n";
+   sol_sock.precision(8);
+   sol_sock << "solution\n" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_elasticity.cpp

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

examples/dfem_minimal_example.cpp

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

examples/dfem_objective.cpp

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

examples/dfem_plaplacian.cpp

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

examples/dfem_poisson.cpp

@@ -0,0 +1,192 @@
+#include "dfem/dfem_refactor.hpp"
+#include "linalg/hypre.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+template <typename diffusion_t, typename force_t>
+class DiffusionOperator : public Operator
+{
+   template <typename diffusion_du_t>
+   class DiffusionJacobianOperator : public Operator
+   {
+   public:
+      DiffusionJacobianOperator(const DiffusionOperator *diffusion,
+                                std::shared_ptr<diffusion_du_t> diff_du) :
+         Operator(diffusion->Height()), s(diffusion)
+      {
+         diff_du->Assemble(A);
+         A.EliminateBC(s->ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         A.Mult(x, y);
+      }
+
+      const DiffusionOperator *s;
+      HypreParMatrix A;
+   };
+
+public:
+   DiffusionOperator(diffusion_t &diffusion, force_t &force,
+                     Array<int> &ess_tdofs) :
+      Operator(diffusion.Height()), diffusion(diffusion),
+      force(force), ess_tdofs(ess_tdofs), f(force.Height()) {}
+
+   void SetParameters(ParGridFunction &mesh_nodes)
+   {
+      diffusion.SetParameters({&mesh_nodes});
+      force.SetParameters({&mesh_nodes});
+
+      Vector zero;
+
+      this->mesh_nodes.SetSpace(mesh_nodes.ParFESpace());
+      this->mesh_nodes = mesh_nodes;
+   }
+
+   void Mult(const Vector &x, Vector &r) const override
+   {
+      diffusion.Mult(x, r);
+      force.Mult(x, f);
+      r -= f;
+      r.SetSubVector(ess_tdofs, 0.0);
+   }
+
+   Operator &GetGradient(const Vector &x) const override
+   {
+      ParGridFunction u(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&diffusion.solutions[0].data)));
+      u.SetFromTrueDofs(x);
+
+      auto dfdu = diffusion.template GetDerivativeWrt<0>({&u}, {&mesh_nodes});
+      dfdu->Assemble(A);
+      A.EliminateBC(ess_tdofs, DiagonalPolicy::DIAG_ONE);
+      return A;
+      // delete jacobian_operator;
+      // jacobian_operator = new
+      // DiffusionJacobianOperator<typename std::remove_pointer<decltype(dfdu.get())>::type>
+      // (this, dfdu);
+      // return *jacobian_operator;
+   }
+
+   diffusion_t &diffusion;
+   force_t &force;
+
+   const Array<int> ess_tdofs;
+   mutable Vector f;
+
+   mutable ParGridFunction mesh_nodes;
+
+   mutable Operator *jacobian_operator = nullptr;
+   mutable HypreParMatrix A;
+};
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-square.mesh";
+   int polynomial_order = 2;
+   int ir_order = 2;
+   int refinements = 4;
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   const int dim = mesh.Dimension();
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection potential_fec(polynomial_order, dim);
+   ParFiniteElementSpace potential_fes(&mesh, &potential_fec);
+
+   const IntegrationRule &potential_ir =
+      IntRules.Get(potential_fes.GetFE(0)->GetGeomType(),
+                   ir_order * potential_fec.GetOrder());
+
+   Array<int> bdr_attr_is_ess(mesh.bdr_attributes.Max());
+   bdr_attr_is_ess = 1;
+   Array<int> ess_tdofs;
+   potential_fes.GetEssentialTrueDofs(bdr_attr_is_ess, ess_tdofs);
+
+   ParGridFunction u(&potential_fes);
+   u = 0.0;
+
+   auto diffusion_kernel = [](const internal::dual<double, double> &u,
+                              const tensor<internal::dual<double, double>, 2> &dudxi,
+                              const tensor<double, 2, 2> &J,
+                              const double &w)
+   {
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      return std::tuple{(1.0 + u * u) * dudx * det(J) * w * transpose(invJ)};
+   };
+
+   std::tuple argument_operators_0{Value{"potential"}, Gradient{"potential"}, Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator_0{Gradient{"potential"}};
+   ElementOperator op_0{diffusion_kernel, argument_operators_0, output_operator_0};
+
+   auto force_kernel = [](const tensor<double, 2, 2> &J,
+                          const double &w)
+   {
+      return std::tuple{1.0 * det(J) * w};
+   };
+   std::tuple argument_operators_1{Gradient{"coordinates"}, Weight{"integration_weights"}};
+   std::tuple output_operator_1{Value{"potential"}};
+   ElementOperator op_1{force_kernel, argument_operators_1, output_operator_1};
+
+   std::array solutions{FieldDescriptor{&potential_fes, "potential"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator diffusion_op{solutions, parameters, std::tuple{op_0}, mesh, potential_ir};
+   DifferentiableOperator force_op{solutions, parameters, std::tuple{op_1}, mesh, potential_ir};
+
+   DiffusionOperator diffusion(diffusion_op, force_op, ess_tdofs);
+
+   diffusion.SetParameters({*mesh_nodes});
+
+   HypreBoomerAMG amg;
+   amg.SetPrintLevel(0);
+
+   CGSolver solver(MPI_COMM_WORLD);
+   solver.SetAbsTol(1e-12);
+   solver.SetRelTol(1e-12);
+   solver.SetMaxIter(500);
+   solver.SetPrintLevel(2);
+   solver.SetPreconditioner(amg);
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetOperator(diffusion);
+   newton.SetSolver(solver);
+   newton.SetRelTol(1e-8);
+   newton.SetMaxIter(10);
+   newton.SetPrintLevel(1);
+
+   Vector zero;
+   Vector x(potential_fes.GetTrueVSize());
+   u.ParallelProject(x);
+   newton.Mult(zero, x);
+
+   u.SetFromTrueDofs(x);
+
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock(vishost, visport);
+   sol_sock << "parallel " << num_procs << " " << myid << "\n";
+   sol_sock.precision(8);
+   sol_sock << "solution\n" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_refactor.cpp

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

examples/dfem_stokes.cpp

@@ -0,0 +1,302 @@
+#include "dfem/dfem.hpp"
+
+using namespace mfem;
+using mfem::internal::tensor;
+
+template <typename momentum_t, typename mass_conservation_t>
+class NavierStokesOperator : public Operator
+{
+   template <typename momentum_du_t, typename momentum_dp_t>
+   class NavierStokesJacobianOperator : public Operator
+   {
+   public:
+      NavierStokesJacobianOperator(const NavierStokesOperator *ns,
+                                   std::shared_ptr<momentum_du_t> mom_du,
+                                   std::shared_ptr<momentum_dp_t> mom_dp) :
+         Operator(ns->Height()), ns(ns), block_op(ns->block_offsets)
+      {
+         mom_du->Assemble(A);
+         A.EliminateBC(ns->vel_ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+
+         mom_dp->Assemble(D);
+         D.EliminateRows(ns->vel_ess_tdofs);
+
+         Dt = new TransposeOperator(D);
+
+         block_op.SetBlock(0, 0, &A);
+         block_op.SetBlock(0, 1, &D);
+         block_op.SetBlock(1, 0, Dt);
+         // std::ofstream amatofs("dfem_mat.dat");
+         // block_op.PrintMatlab(amatofs);
+         // amatofs.close();
+      }
+
+      void Mult(const Vector &x, Vector &y) const override
+      {
+         block_op.Mult(x, y);
+      }
+
+      ~NavierStokesJacobianOperator()
+      {
+         delete Dt;
+      }
+
+      const NavierStokesOperator *ns = nullptr;
+      HypreParMatrix A, D;
+      TransposeOperator *Dt = nullptr;
+      BlockOperator block_op;
+   };
+
+public:
+   NavierStokesOperator(momentum_t &momentum,
+                        mass_conservation_t &mass_conservation,
+                        Array<int> &offsets, Array<int> &vel_ess_tdofs) :
+      Operator(offsets.Last()), momentum(momentum),
+      mass_conservation(mass_conservation),
+      block_offsets(offsets), vel_ess_tdofs(vel_ess_tdofs) {}
+
+   void SetParameters(ParGridFunction &mesh_nodes)
+   {
+      momentum.SetParameters({&mesh_nodes});
+      mass_conservation.SetParameters({&mesh_nodes});
+      this->mesh_nodes.SetSpace(mesh_nodes.ParFESpace());
+      this->mesh_nodes = mesh_nodes;
+   }
+
+   void Mult(const Vector &x, Vector &r) const override
+   {
+      Vector ru(r.ReadWrite() + block_offsets[0],
+                block_offsets[1] - block_offsets[0]);
+      Vector rp(r.ReadWrite() + block_offsets[1],
+                block_offsets[2] - block_offsets[1]);
+
+      momentum.Mult(x, ru);
+
+      mass_conservation.Mult(x, rp);
+
+      ru.SetSubVector(vel_ess_tdofs, 0.0);
+   }
+
+   Operator &GetGradient(const Vector &x) const override
+   {
+      xtmp = x;
+      BlockVector xb(xtmp.ReadWrite(), block_offsets);
+
+      ParGridFunction u(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&momentum.solutions[0].data)));
+      ParGridFunction p(const_cast<ParFiniteElementSpace *>
+                        (*std::get_if<const ParFiniteElementSpace *>
+                         (&momentum.solutions[1].data)));
+      u.SetFromTrueDofs(xb.GetBlock(0));
+      p.SetFromTrueDofs(xb.GetBlock(1));
+      auto mom_du = momentum.template GetDerivativeWrt<0>({&u, &p}, {&mesh_nodes});
+      auto mom_dp = momentum.template GetDerivativeWrt<1>({&u, &p}, {&mesh_nodes});
+      delete jacobian_operator;
+      jacobian_operator = new NavierStokesJacobianOperator<
+      typename std::remove_pointer<decltype(mom_du.get())>::type,
+      typename std::remove_pointer<decltype(mom_dp.get())>::type>(this, mom_du,
+                                                                  mom_dp);
+      return *jacobian_operator;
+   }
+
+   momentum_t &momentum;
+   mass_conservation_t &mass_conservation;
+
+   const Array<int> block_offsets;
+   const Array<int> vel_ess_tdofs;
+   mutable Vector xtmp;
+
+   mutable ParGridFunction mesh_nodes;
+
+   mutable Operator *jacobian_operator = nullptr;
+};
+
+double reynolds = 10.0;
+
+int main(int argc, char *argv[])
+{
+   constexpr int dim = 3;
+   constexpr int vdim = dim;
+
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   const char *mesh_file = "../data/ref-cube.mesh";
+   int polynomial_order = 2;
+   int ir_order = 2;
+   int refinements = 2;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&refinements, "-r", "--refinements", "");
+   args.AddOption(&reynolds, "-rey", "--reynolds", "");
+   args.ParseCheck();
+
+   Mesh mesh_serial = Mesh(mesh_file);
+   for (int i = 0; i < refinements; i++)
+   {
+      mesh_serial.UniformRefinement();
+   }
+   ParMesh mesh(MPI_COMM_WORLD, mesh_serial);
+
+   mesh.SetCurvature(1);
+   mesh_serial.Clear();
+
+   ParGridFunction* mesh_nodes = static_cast<ParGridFunction *>(mesh.GetNodes());
+   ParFiniteElementSpace &mesh_fes = *mesh_nodes->ParFESpace();
+
+   H1_FECollection velocity_fec(polynomial_order, dim);
+   ParFiniteElementSpace velocity_fes(&mesh, &velocity_fec, dim);
+
+   H1_FECollection pressure_fec(polynomial_order - 1, dim);
+   ParFiniteElementSpace pressure_fes(&mesh, &pressure_fec);
+
+   const IntegrationRule &velocity_ir =
+      IntRules.Get(velocity_fes.GetFE(0)->GetGeomType(),
+                   ir_order * velocity_fec.GetOrder());
+
+   const IntegrationRule &pressure_ir =
+      IntRules.Get(pressure_fes.GetFE(0)->GetGeomType(),
+                   ir_order * pressure_fec.GetOrder());
+
+   Array<int> bdr_attr_is_ess(mesh.bdr_attributes.Max());
+   bdr_attr_is_ess = 1;
+   Array<int> vel_ess_tdofs;
+   velocity_fes.GetEssentialTrueDofs(bdr_attr_is_ess, vel_ess_tdofs);
+
+   ParGridFunction u(&velocity_fes);
+   ParGridFunction p(&pressure_fes);
+
+   auto u_f = [](const Vector &coords, Vector &u)
+   {
+      const double x = coords(0);
+      const double z = coords(2);
+      if (z >= 1.0)
+      {
+         u(0) = 1.0;
+      }
+      else
+      {
+         u(0) = 0.0;
+      }
+      u(1) = 0.0;
+      u(2) = 0.0;
+   };
+   auto u_coef = VectorFunctionCoefficient(dim, u_f);
+
+   u.ProjectCoefficient(u_coef);
+   p = 0.0;
+
+   // -\nabla \cdot (\nabla u + p * I) -> (\nabla u + p * I, \nabla v)
+   auto momentum_kernel = [](const tensor<double, dim> &u,
+                             const tensor<double, dim, dim> &dudxi,
+                             const double &p,
+                             const tensor<double, dim, dim> &J,
+                             const double &w)
+   {
+      static constexpr auto I = mfem::internal::IsotropicIdentity<dim>();
+      auto invJ = inv(J);
+      auto dudx = dudxi * invJ;
+      double Re = reynolds;
+      return mfem::tuple{(outer(u, u) - 1.0 / Re * dudx + p * I) * det(J) * w * transpose(invJ)};
+   };
+
+   mfem::tuple argument_operators_0{Value{"velocity"}, Gradient{"velocity"}, Value{"pressure"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator_0{Gradient{"velocity"}};
+   ElementOperator op_0{momentum_kernel, argument_operators_0, output_operator_0};
+
+   // (\nabla \cdot u, q)
+   auto mass_conservation_kernel = [](const tensor<double, dim, dim> &dudxi,
+                                      const tensor<double, dim, dim> &J,
+                                      const double &w)
+   {
+      return mfem::tuple{tr(dudxi * inv(J)) * det(J) * w};
+   };
+
+   mfem::tuple argument_operators_1{Gradient{"velocity"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple output_operator_1{Value{"pressure"}};
+   ElementOperator op_1{mass_conservation_kernel, argument_operators_1, output_operator_1};
+
+   std::array solutions{FieldDescriptor{&velocity_fes, "velocity"}, FieldDescriptor{&pressure_fes, "pressure"}};
+   std::array parameters{FieldDescriptor{&mesh_fes, "coordinates"}};
+
+   DifferentiableOperator momentum_op{solutions, parameters, mfem::tuple{op_0}, mesh, velocity_ir};
+   DifferentiableOperator mass_conservation_op{solutions, parameters, mfem::tuple{op_1}, mesh, pressure_ir};
+
+   // Preconditioner form
+   auto pressure_mass_kernel = [](const double &p,
+                                  const tensor<double, dim, dim> &J,
+                                  const double &w)
+   {
+      return mfem::tuple{p * det(J) * w};
+   };
+
+   mfem::tuple pms_args{Value{"pressure"}, Gradient{"coordinates"}, Weight{}};
+   mfem::tuple pms_outs{Value{"pressure"}};
+   ElementOperator pressure_mass{pressure_mass_kernel, pms_args, pms_outs};
+   std::array pms_sols{FieldDescriptor{&pressure_fes, "pressure"}};
+   std::array pms_params{FieldDescriptor{&mesh_fes, "coordinates"}};
+   DifferentiableOperator pressure_mass_op{pms_sols, pms_params, mfem::tuple{pressure_mass}, mesh, pressure_ir};
+
+   Array<int> block_offsets(3);
+   block_offsets[0] = 0;
+   block_offsets[1] = velocity_fes.GetTrueVSize();
+   block_offsets[2] = pressure_fes.GetTrueVSize();
+   block_offsets.PartialSum();
+
+   NavierStokesOperator navierstokes(momentum_op, mass_conservation_op,
+                                     block_offsets,
+                                     vel_ess_tdofs);
+
+   BlockVector x(block_offsets), y(block_offsets);
+   u.ParallelProject(x.GetBlock(0));
+   // p.ParallelProject(x.GetBlock(1));
+   navierstokes.SetParameters(*mesh_nodes);
+
+   HypreParMatrix A;
+   momentum_op.template GetDerivativeWrt<0>({&u, &p}, {mesh_nodes})->Assemble(A);
+   A.EliminateBC(vel_ess_tdofs, Operator::DiagonalPolicy::DIAG_ONE);
+   HypreBoomerAMG amg(A);
+   amg.SetMaxLevels(50);
+   amg.SetPrintLevel(0);
+
+   HypreParMatrix Mp;
+   pressure_mass_op.template GetDerivativeWrt<0>({&p}, {mesh_nodes})->Assemble(Mp);
+
+   HypreDiagScale Mp_inv(Mp);
+
+   BlockDiagonalPreconditioner prec(block_offsets);
+   prec.SetDiagonalBlock(0, &amg);
+   prec.SetDiagonalBlock(1, &Mp_inv);
+
+   GMRESSolver solver(MPI_COMM_WORLD);
+   solver.SetAbsTol(0.0);
+   solver.SetRelTol(1e-8);
+   solver.SetKDim(100);
+   solver.SetMaxIter(500);
+   solver.SetPrintLevel(2);
+   solver.SetPreconditioner(prec);
+
+   NewtonSolver newton(MPI_COMM_WORLD);
+   newton.SetOperator(navierstokes);
+   newton.SetSolver(solver);
+   newton.SetRelTol(1e-8);
+   newton.SetMaxIter(50);
+   newton.SetPrintLevel(1);
+
+   Vector zero;
+   newton.Mult(zero, x);
+
+   u.SetFromTrueDofs(x.GetBlock(0));
+
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock(vishost, visport);
+   sol_sock << "parallel " << num_procs << " " << myid << "\n";
+   sol_sock.precision(8);
+   sol_sock << "solution\n" << mesh << u << std::flush;
+
+   return 0;
+}

examples/dfem_test_diffusion_2d.cpp

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

examples/dfem_test_diffusion_3d.cpp

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

examples/dfem_test_diffusion_3d_refactor.cpp

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

examples/dfem_test_elasticity.cpp

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

examples/dfem_test_interpolate_gradient_linear_scalar_3d.cpp

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

examples/dfem_test_interpolate_linear_scalar.cpp

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

examples/dfem_test_interpolate_linear_scalar_3d.cpp

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

examples/dfem_test_interpolate_linear_vector.cpp

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

examples/dfem_test_interpolate_linear_vector_3d.cpp

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

examples/dfem_test_mass_scalar_2d.cpp

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

examples/dfem_test_mass_scalar_3d.cpp

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

examples/dfem_test_neo_hookean_elasticity_2d.cpp

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

examples/dfem_test_nonlinear_diffusion_3d.cpp

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

examples/dfem_test_nonlinear_elasticity_3d.cpp

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

examples/dfem_test_ordering.cpp

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

examples/dfem_test_vector_diffusion.cpp

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

examples/enzyme_interface_smoketest.cpp

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

examples/ex10.cpp

@@ -87,16 +87,16 @@ public:
                         real_t visc, real_t mu, real_t K);
 
    /// Compute the right-hand side of the ODE system.
-   void Mult(const Vector &vx, Vector &dvx_dt) const override;
+   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
    real_t ElasticEnergy(const Vector &x) const;
    real_t KineticEnergy(const Vector &v) const;
    void GetElasticEnergyDensity(const GridFunction &x, GridFunction &w) const;
 
-   ~HyperelasticOperator() override;
+   virtual ~HyperelasticOperator();
 };
 
 /** Nonlinear operator of the form:
@@ -120,12 +120,12 @@ public:
    void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);
 
    /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
-   void Mult(const Vector &k, Vector &y) const override;
+   virtual void Mult(const Vector &k, Vector &y) const;
 
    /// Compute J = M + dt S + dt^2 grad_H(x + dt (v + dt k)).
-   Operator &GetGradient(const Vector &k) const override;
+   virtual Operator &GetGradient(const Vector &k) const;
 
-   ~ReducedSystemOperator() override;
+   virtual ~ReducedSystemOperator();
 };
 
 
@@ -141,8 +141,8 @@ private:
 public:
    ElasticEnergyCoefficient(HyperelasticModel &m, const GridFunction &x_)
       : model(m), x(x_) { }
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
-   ~ElasticEnergyCoefficient() override { }
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual ~ElasticEnergyCoefficient() { }
 };
 
 void InitialDeformation(const Vector &x, Vector &y);

examples/ex10p.cpp

@@ -89,17 +89,17 @@ public:
                         real_t visc, real_t mu, real_t K);
 
    /// Compute the right-hand side of the ODE system.
-   void Mult(const Vector &vx, Vector &dvx_dt) const override;
+   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
    real_t ElasticEnergy(const ParGridFunction &x) const;
    real_t KineticEnergy(const ParGridFunction &v) const;
    void GetElasticEnergyDensity(const ParGridFunction &x,
                                 ParGridFunction &w) const;
 
-   ~HyperelasticOperator() override;
+   virtual ~HyperelasticOperator();
 };
 
 /** Nonlinear operator of the form:
@@ -125,12 +125,12 @@ public:
    void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);
 
    /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
-   void Mult(const Vector &k, Vector &y) const override;
+   virtual void Mult(const Vector &k, Vector &y) const;
 
    /// Compute J = M + dt S + dt^2 grad_H(x + dt (v + dt k)).
-   Operator &GetGradient(const Vector &k) const override;
+   virtual Operator &GetGradient(const Vector &k) const;
 
-   ~ReducedSystemOperator() override;
+   virtual ~ReducedSystemOperator();
 };
 
 
@@ -146,8 +146,8 @@ private:
 public:
    ElasticEnergyCoefficient(HyperelasticModel &m, const ParGridFunction &x_)
       : model(m), x(x_) { }
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
-   ~ElasticEnergyCoefficient() override { }
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual ~ElasticEnergyCoefficient() { }
 };
 
 void InitialDeformation(const Vector &x, Vector &y);

examples/ex14p.cpp

@@ -53,7 +53,7 @@ public:
       pmesh(pmesh_),
       pgf(pgf_) {}
 
-   void MonitorSolution(int i, real_t norm, const Vector &x, bool final) override
+   void MonitorSolution(int i, real_t norm, const Vector &x, bool final)
    {
       char vishost[] = "localhost";
       int  visport   = 19916;

examples/ex16.cpp

@@ -76,15 +76,15 @@ public:
    ConductionOperator(FiniteElementSpace &f, real_t alpha, real_t kappa,
                       const Vector &u);
 
-   void Mult(const Vector &u, Vector &du_dt) const override;
+   virtual void Mult(const Vector &u, Vector &du_dt) const;
    /** 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.*/
-   void ImplicitSolve(const real_t dt, const Vector &u, Vector &k) override;
+   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
 
-   ~ConductionOperator() override;
+   virtual ~ConductionOperator();
 };
 
 real_t InitialTemperature(const Vector &x);

examples/ex16p.cpp

@@ -78,15 +78,15 @@ public:
    ConductionOperator(ParFiniteElementSpace &f, real_t alpha, real_t kappa,
                       const Vector &u);
 
-   void Mult(const Vector &u, Vector &du_dt) const override;
+   virtual void Mult(const Vector &u, Vector &du_dt) const;
    /** 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.*/
-   void ImplicitSolve(const real_t dt, const Vector &u, Vector &k) override;
+   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
 
-   ~ConductionOperator() override;
+   virtual ~ConductionOperator();
 };
 
 real_t InitialTemperature(const Vector &x);

examples/ex17.cpp

@@ -69,7 +69,7 @@ public:
    void SetDisplacement(GridFunction &u_) { u = &u_; }
    void SetComponent(int i, int j) { si = i; sj = j; }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 // Simple GLVis visualization manager.
@@ -89,7 +89,7 @@ public:
    void NewWindow();
    void CloseConnection();
    void PositionWindow();
-   ~VisMan() override;
+   virtual ~VisMan();
 };
 
 // Manipulators for the GLVis visualization manager.

examples/ex17p.cpp

@@ -69,7 +69,7 @@ public:
    void SetDisplacement(GridFunction &u_) { u = &u_; }
    void SetComponent(int i, int j) { si = i; sj = j; }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 // Simple GLVis visualization manager.
@@ -89,7 +89,7 @@ public:
    void NewWindow();
    void CloseConnection();
    void PositionWindow();
-   ~VisMan() override;
+   virtual ~VisMan();
 };
 
 // Manipulators for the GLVis visualization manager.

examples/ex19.cpp

@@ -48,7 +48,7 @@ public:
       print_level = print_lvl;
    }
 
-   void MonitorResidual(int it, real_t norm, const Vector &r, bool final) override;
+   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
 
 private:
    const std::string prefix;
@@ -116,10 +116,10 @@ public:
    JacobianPreconditioner(Array<FiniteElementSpace *> &fes,
                           SparseMatrix &mass, Array<int> &offsets);
 
-   void Mult(const Vector &k, Vector &y) const override;
-   void SetOperator(const Operator &op) override;
+   virtual void Mult(const Vector &k, Vector &y) const;
+   virtual void SetOperator(const Operator &op);
 
-   ~JacobianPreconditioner() override;
+   virtual ~JacobianPreconditioner();
 };
 
 // After spatial discretization, the rubber model can be written as:
@@ -161,13 +161,13 @@ public:
                   int iter, Coefficient &mu);
 
    // Required to use the native newton solver
-   Operator &GetGradient(const Vector &xp) const override;
-   void Mult(const Vector &k, Vector &y) const override;
+   virtual Operator &GetGradient(const Vector &xp) const;
+   virtual void Mult(const Vector &k, Vector &y) const;
 
    // Driver for the newton solver
    void Solve(Vector &xp) const;
 
-   ~RubberOperator() override;
+   virtual ~RubberOperator();
 };
 
 // Visualization driver

examples/ex19p.cpp

@@ -62,7 +62,7 @@ public:
 #endif
    }
 
-   void MonitorResidual(int it, real_t norm, const Vector &r, bool final) override;
+   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
 
 private:
    const std::string prefix;
@@ -130,10 +130,10 @@ public:
    JacobianPreconditioner(Array<ParFiniteElementSpace *> &fes,
                           Operator &mass, Array<int> &offsets);
 
-   void Mult(const Vector &k, Vector &y) const override;
-   void SetOperator(const Operator &op) override;
+   virtual void Mult(const Vector &k, Vector &y) const;
+   virtual void SetOperator(const Operator &op);
 
-   ~JacobianPreconditioner() override;
+   virtual ~JacobianPreconditioner();
 };
 
 // After spatial discretization, the rubber model can be written as:
@@ -175,13 +175,13 @@ public:
                   int iter, Coefficient &mu);
 
    // Required to use the native newton solver
-   Operator &GetGradient(const Vector &xp) const override;
-   void Mult(const Vector &k, Vector &y) const override;
+   virtual Operator &GetGradient(const Vector &xp) const;
+   virtual void Mult(const Vector &k, Vector &y) const;
 
    // Driver for the newton solver
    void Solve(Vector &xp) const;
 
-   ~RubberOperator() override;
+   virtual ~RubberOperator();
 };
 
 // Visualization driver

examples/ex20.cpp

@@ -79,14 +79,14 @@ class GradT : public Operator
 {
 public:
    GradT() : Operator(1) {}
-   void Mult(const Vector &x, Vector &y) const override { y.Set(1.0/m_, x); }
+   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
 };
 
 class NegGradV : public TimeDependentOperator
 {
 public:
    NegGradV() : TimeDependentOperator(1) {}
-   void Mult(const Vector &x, Vector &y) const override;
+   void Mult(const Vector &x, Vector &y) const;
 };
 
 int main(int argc, char *argv[])

examples/ex20p.cpp

@@ -84,14 +84,14 @@ class GradT : public Operator
 {
 public:
    GradT() : Operator(1) {}
-   void Mult(const Vector &x, Vector &y) const override { y.Set(1.0/m_, x); }
+   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
 };
 
 class NegGradV : public TimeDependentOperator
 {
 public:
    NegGradV() : TimeDependentOperator(1) {}
-   void Mult(const Vector &x, Vector &y) const override;
+   void Mult(const Vector &x, Vector &y) const;
 };
 
 int main(int argc, char *argv[])

examples/ex23.cpp

@@ -61,20 +61,20 @@ public:
    WaveOperator(FiniteElementSpace &f, Array<int> &ess_bdr, real_t speed);
 
    using SecondOrderTimeDependentOperator::Mult;
-   void Mult(const Vector &u, const Vector &du_dt,
-             Vector &d2udt2) const override;
+   virtual void Mult(const Vector &u, const Vector &du_dt,
+                     Vector &d2udt2) const;
 
    /** Solve the Backward-Euler equation:
        d2udt2 = f(u + fac0*d2udt2,dudt + fac1*d2udt2, t),
        for the unknown d2udt2. */
    using SecondOrderTimeDependentOperator::ImplicitSolve;
-   void ImplicitSolve(const real_t fac0, const real_t fac1,
-                      const Vector &u, const Vector &dudt, Vector &d2udt2) override;
+   virtual void ImplicitSolve(const real_t fac0, const real_t fac1,
+                              const Vector &u, const Vector &dudt, Vector &d2udt2);
 
    ///
    void SetParameters(const Vector &u);
 
-   ~WaveOperator() override;
+   virtual ~WaveOperator();
 };
 
 

examples/ex25.cpp

@@ -103,8 +103,8 @@ public:
 
    using VectorCoefficient::Eval;
 
-   void Eval(Vector &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &K, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    {
       real_t x[3];
       Vector transip(x, 3);

examples/ex25p.cpp

@@ -102,8 +102,8 @@ public:
 
    using VectorCoefficient::Eval;
 
-   void Eval(Vector &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &K, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    {
       real_t x[3];
       Vector transip(x, 3);

examples/ex26p.cpp

@@ -58,7 +58,7 @@ public:
       }
    }
 
-   ~DiffusionMultigrid() override
+   virtual ~DiffusionMultigrid()
    {
       delete amg;
    }

examples/ex36.cpp

@@ -53,7 +53,7 @@ public:
                                     real_t min_val_=-36)
       : u(&u_), obstacle(&obst_), min_val(min_val_) { }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -69,7 +69,7 @@ public:
                                       real_t min_val_=0.0, real_t max_val_=1e6)
       : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 int main(int argc, char *argv[])
@@ -258,7 +258,7 @@ int main(int argc, char *argv[])
          MixedBilinearForm a10(&H1fes,&L2fes);
          a10.AddDomainIntegrator(new MixedScalarMassIntegrator());
          a10.Assemble();
-         a10.EliminateTrialEssentialBC(ess_bdr, x.GetBlock(0), rhs.GetBlock(1));
+         a10.EliminateTrialDofs(ess_bdr, x.GetBlock(0), rhs.GetBlock(1));
          a10.Finalize();
          SparseMatrix &A10 = a10.SpMat();
 

examples/ex36p.cpp

@@ -53,7 +53,7 @@ public:
                                     real_t min_val_=-36)
       : u(&u_), obstacle(&obst_), min_val(min_val_) { }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -69,7 +69,7 @@ public:
                                       real_t min_val_=0.0, real_t max_val_=1e6)
       : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 int main(int argc, char *argv[])

examples/ex37.hpp

@@ -52,8 +52,8 @@ public:
        fun(fun_) {}
 
 
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    {
       return fun(GridFunctionCoefficient::Eval(T, ip));
    }
@@ -83,8 +83,8 @@ public:
        OtherGridF_cf(OtherGridF),
        fun(fun_) {}
 
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    {
       const real_t value1 = fun(GridFunctionCoefficient::Eval(T, ip));
       const real_t value2 = fun(OtherGridF_cf.Eval(T, ip));
@@ -108,7 +108,7 @@ public:
       : rho_filter(rho_filter_), min_val(min_val_), max_val(max_val_),
         exponent(exponent_) { }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    {
       real_t val = rho_filter->GetValue(T, ip);
       real_t coeff = min_val + pow(val,exponent)*(max_val-min_val);
@@ -142,7 +142,7 @@ public:
       MFEM_ASSERT(rho_filter, "density field is not set");
    }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    {
       real_t L = lambda->Eval(T, ip);
       real_t M = mu->Eval(T, ip);
@@ -176,8 +176,8 @@ public:
 
    using VectorCoefficient::Eval;
 
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    {
       Vector xx; xx.SetSize(T.GetDimension());
       T.Transform(ip,xx);

examples/ex38.cpp

@@ -408,9 +408,9 @@ public:
     @param [in] Tr transformation of finite element
     @param [out] elvect vector containing the
    */
-   void AssembleRHSElementVect(const FiniteElement &el,
-                               ElementTransformation &Tr,
-                               Vector &elvect) override
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect) override
    {
       int dof = el.GetDof();
       shape.SetSize(dof);
@@ -476,9 +476,9 @@ public:
     @param [in] Tr transformation of finite element
     @param [out] elvect vector containing the
    */
-   void AssembleRHSElementVect(const FiniteElement &el,
-                               ElementTransformation &Tr,
-                               Vector &elvect) override
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect) override
    {
       int dof = el.GetDof();
       shape.SetSize(dof);

examples/ex40.cpp

@@ -69,8 +69,8 @@ public:
 
    using VectorCoefficient::Eval;
 
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };
 
@@ -84,8 +84,8 @@ public:
    DZCoefficient(int height, GridFunction &psi_, real_t alpha_ = 1.0)
       : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }
 
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };
 

examples/ex40p.cpp

@@ -69,8 +69,8 @@ public:
 
    using VectorCoefficient::Eval;
 
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };
 
@@ -84,8 +84,8 @@ public:
    DZCoefficient(int height, ParGridFunction &psi_, real_t alpha_ = 1.0)
       : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }
 
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };
 

examples/ex8.cpp

@@ -157,7 +157,7 @@ int main(int argc, char *argv[])
    MixedBilinearForm *B0 = new MixedBilinearForm(x0_space,test_space);
    B0->AddDomainIntegrator(new DiffusionIntegrator(one));
    B0->Assemble();
-   B0->EliminateTrialEssentialBC(ess_bdr, x.GetBlock(x0_var), F);
+   B0->EliminateTrialDofs(ess_bdr, x.GetBlock(x0_var), F);
    B0->Finalize();
 
    MixedBilinearForm *Bhat = new MixedBilinearForm(xhat_space,test_space);

examples/ex9.cpp

@@ -104,12 +104,12 @@ public:
       }
    }
 
-   void SetOperator(const Operator &op) override
+   void SetOperator(const Operator &op)
    {
       linear_solver.SetOperator(op);
    }
 
-   void Mult(const Vector &x, Vector &y) const override
+   virtual void Mult(const Vector &x, Vector &y) const
    {
       linear_solver.Mult(x, y);
    }
@@ -134,10 +134,10 @@ private:
 public:
    FE_Evolution(BilinearForm &M_, BilinearForm &K_, const Vector &b_);
 
-   void Mult(const Vector &x, Vector &y) const override;
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+   virtual void Mult(const Vector &x, Vector &y) const;
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
-   ~FE_Evolution() override;
+   virtual ~FE_Evolution();
 };
 
 

examples/ex9p.cpp

@@ -92,7 +92,7 @@ private:
 public:
    AIR_prec(int blocksize_) : AIR_solver(NULL), blocksize(blocksize_) { }
 
-   void SetOperator(const Operator &op) override
+   void SetOperator(const Operator &op)
    {
       width = op.Width();
       height = op.Height();
@@ -110,7 +110,7 @@ public:
       AIR_solver->SetMaxLevels(50);
    }
 
-   void Mult(const Vector &x, Vector &y) const override
+   virtual void Mult(const Vector &x, Vector &y) const
    {
       // Scale the rhs by block inverse and solve system
       HypreParVector z_s;
@@ -119,7 +119,7 @@ public:
       AIR_solver->Mult(z_s, y);
    }
 
-   ~AIR_prec() override
+   ~AIR_prec()
    {
       delete AIR_solver;
    }
@@ -185,17 +185,17 @@ public:
       }
    }
 
-   void SetOperator(const Operator &op) override
+   void SetOperator(const Operator &op)
    {
       linear_solver.SetOperator(op);
    }
 
-   void Mult(const Vector &x, Vector &y) const override
+   virtual void Mult(const Vector &x, Vector &y) const
    {
       linear_solver.Mult(x, y);
    }
 
-   ~DG_Solver() override
+   ~DG_Solver()
    {
       delete prec;
       delete A;
@@ -223,10 +223,10 @@ public:
    FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_, const Vector &b_,
                 PrecType prec_type);
 
-   void Mult(const Vector &x, Vector &y) const override;
-   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+   virtual void Mult(const Vector &x, Vector &y) const;
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
-   ~FE_Evolution() override;
+   virtual ~FE_Evolution();
 };
 
 

examples/petsc/ex10p.cpp

@@ -206,7 +206,6 @@ int main(int argc, char *argv[])
    bool use_petsc = true;
    const char *petscrc_file = "";
    bool petsc_use_jfnk = false;
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -244,8 +243,6 @@ int main(int argc, char *argv[])
    args.AddOption(&petsc_use_jfnk, "-jfnk", "--jfnk", "-no-jfnk",
                   "--no-jfnk",
                   "Use JFNK with user-defined preconditioner factory.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.Parse();
    if (!args.Good())
    {
@@ -260,12 +257,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc)
    {
       MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL);

examples/petsc/ex2p.cpp

@@ -67,7 +67,6 @@ int main(int argc, char *argv[])
    bool use_petsc = true;
    const char *petscrc_file = "";
    bool use_nonoverlapping = false;
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -96,8 +95,6 @@ int main(int argc, char *argv[])
                   "-no-nonoverlapping", "--no-nonoverlapping",
                   "Use or not the block diagonal PETSc's matrix format "
                   "for non-overlapping domain decomposition.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.Parse();
    if (!args.Good())
    {
@@ -112,12 +109,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We

examples/petsc/ex3p.cpp

@@ -61,7 +61,6 @@ int main(int argc, char *argv[])
    bool use_petsc = true;
    const char *petscrc_file = "";
    bool use_nonoverlapping = false;
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -88,8 +87,6 @@ int main(int argc, char *argv[])
                   "-no-nonoverlapping", "--no-nonoverlapping",
                   "Use or not the block diagonal PETSc's matrix format "
                   "for non-overlapping domain decomposition.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.Parse();
    if (!args.Good())
    {
@@ -103,15 +100,9 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
-   kappa = freq * M_PI;
-
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
+   kappa = freq * M_PI;
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface

examples/petsc/ex4p.cpp

@@ -58,7 +58,6 @@ int main(int argc, char *argv[])
    bool use_petsc = true;
    const char *petscrc_file = "";
    bool use_nonoverlapping = false;
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -89,8 +88,6 @@ int main(int argc, char *argv[])
                   "-no-nonoverlapping", "--no-nonoverlapping",
                   "Use or not the block diagonal PETSc's matrix format "
                   "for non-overlapping domain decomposition.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.Parse();
    if (!args.Good())
    {
@@ -104,15 +101,9 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
-   kappa = freq * M_PI;
-
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
+   kappa = freq * M_PI;
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface

examples/petsc/ex5p.cpp

@@ -59,8 +59,6 @@ int main(int argc, char *argv[])
 
    // 2. Parse command-line options.
    const char *mesh_file = "../../data/star.mesh";
-   int ser_ref_levels = -1;
-   int par_ref_levels = 2;
    int order = 1;
    bool par_format = false;
    bool visualization = 1;
@@ -68,22 +66,15 @@ int main(int argc, char *argv[])
    bool use_nonoverlapping = false;
    bool local_bdr_spec = false;
    const char *petscrc_file = "";
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
-   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
-                  "Number of times to refine the mesh uniformly in serial.");
-   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
-                  "Number of times to refine the mesh uniformly in parallel.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
                   "--serial-format",
                   "Format to use when saving the results for VisIt.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -112,13 +103,7 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
-
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -132,11 +117,9 @@ int main(int argc, char *argv[])
    //    'ref_levels' to be the largest number that gives a final mesh with no
    //    more than 10,000 elements.
    {
-      if (ser_ref_levels < 0)
-      {
-         ser_ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
-      }
-      for (int l = 0; l < ser_ref_levels; l++)
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
       {
          mesh->UniformRefinement();
       }
@@ -148,6 +131,7 @@ int main(int argc, char *argv[])
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
    {
+      int par_ref_levels = 2;
       for (int l = 0; l < par_ref_levels; l++)
       {
          pmesh->UniformRefinement();
@@ -203,26 +187,21 @@ int main(int argc, char *argv[])
 
    // 9. Define the parallel grid function and parallel linear forms, solution
    //    vector and rhs.
-   MemoryType mt = device.GetMemoryType();
-   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
-   BlockVector trueX(block_trueOffsets, mt), trueRhs(block_trueOffsets, mt);
+   BlockVector x(block_offsets), rhs(block_offsets);
+   BlockVector trueX(block_trueOffsets), trueRhs(block_trueOffsets);
 
    ParLinearForm *fform(new ParLinearForm);
    fform->Update(R_space, rhs.GetBlock(0), 0);
    fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
    fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
    fform->Assemble();
-   fform->SyncAliasMemory(rhs);
    fform->ParallelAssemble(trueRhs.GetBlock(0));
-   trueRhs.GetBlock(0).SyncAliasMemory(trueRhs);
 
    ParLinearForm *gform(new ParLinearForm);
    gform->Update(W_space, rhs.GetBlock(1), 0);
    gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
    gform->Assemble();
-   gform->SyncAliasMemory(rhs);
    gform->ParallelAssemble(trueRhs.GetBlock(1));
-   trueRhs.GetBlock(1).SyncAliasMemory(trueRhs);
 
    // 10. Assemble the finite element matrices for the Darcy operator
    //

examples/petsc/ex6p.cpp

@@ -53,7 +53,6 @@ int main(int argc, char *argv[])
    bool use_petsc = true;
    const char *petscrc_file = "";
    bool use_nonoverlapping = false;
-   const char *device_config = "cpu";
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -74,8 +73,6 @@ int main(int argc, char *argv[])
                   "-no-nonoverlapping", "--no-nonoverlapping",
                   "Use or not the block diagonal PETSc's matrix format "
                   "for non-overlapping domain decomposition.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
    args.Parse();
    if (!args.Good())
    {
@@ -89,13 +86,7 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
-
-   // 2b. Enable hardware devices such as GPUs, and programming models such as
-   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
-   Device device(device_config);
-   if (myid == 0) { device.Print(); }
-
-   // 2c. We initialize PETSc
+   // 2b. We initialize PETSc
    if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We

examples/sundials/ex10.cpp

@@ -9,9 +9,9 @@
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10
 //    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 16 -dt 0.3  -vs 5
 //    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 12 -dt 0.2  -vs 5
-//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  2 -dt 3 -nls 1
-//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  2 -dt 3 -nls 2
-//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  2 -dt 3 -nls 4
+//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  2 -dt 3 -nls kinsol
+//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  2 -dt 3 -nls kinsol
+//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  2 -dt 3 -nls kinsol
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 14 -dt 0.15 -vs 10
 //    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 17 -dt 0.01 -vs 30
 //    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 14 -dt 0.15 -vs 10
@@ -99,11 +99,16 @@ protected:
    double saved_gamma; // saved gamma value from implicit setup
 
 public:
+   /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
+   enum NonlinearSolverType
+   {
+      NEWTON = 0, ///< Use MFEM's plain NewtonSolver
+      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
+   };
 
    HyperelasticOperator(FiniteElementSpace &f, Array<int> &ess_bdr,
                         double visc, double mu, double K,
-                        int kinsol_nls_type = -1, double kinsol_damping = 0.0,
-                        int kinsol_aa_n = 0);
+                        NonlinearSolverType nls_type);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -221,10 +226,8 @@ int main(int argc, char *argv[])
    double mu = 0.25;
    double K = 5.0;
    bool visualization = true;
-   int nonlinear_solver_type = 0;
+   const char *nls = "newton";
    int vis_steps = 1;
-   double kinsol_damping = 0.0;
-   int kinsol_aa_n = -1;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
    const double reltol = 1e-1, abstol = 1e-1;
@@ -261,18 +264,9 @@ int main(int argc, char *argv[])
                   "15 - ARKODE implicit, approximate Jacobian,\n\t"
                   "16 - ARKODE implicit, specified Jacobian,\n\t"
                   "17 - ARKODE explicit, 4th order.");
-   args.AddOption(&nonlinear_solver_type, "-nls", "--nonlinear-solver",
-                  "Nonlinear system solver:\n\t"
-                  "0  - MFEM Newton method,\n\t"
-                  "1  - KINSOL Newton method,\n\t"
-                  "2  - KINSOL Newton method with globalization,\n\t"
-                  "3  - KINSOL fixed-point method (with or without AA),\n\t"
-                  "4  - KINSOL Picard method (with or without AA).");
-   args.AddOption(&kinsol_damping, "-damp", "--kinsol-damping",
-                  "Picard or Fixed-Point damping parameter (only valid with KINSOL): "
-                  "0 < d <= 1.0");
-   args.AddOption(&kinsol_aa_n, "-aan", "--anderson-subspace",
-                  "Anderson Acceleration subspace size (only valid with KINSOL)");
+   args.AddOption(&nls, "-nls", "--nonlinear-solver",
+                  "Nonlinear systems solver: "
+                  "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -303,32 +297,22 @@ int main(int argc, char *argv[])
       return 1;
    }
 
-   // check for valid nonlinear solver options
-   if (nonlinear_solver_type < 0 || nonlinear_solver_type > 4)
-   {
-      cout << "Unknown nonlinear solver type: " << nonlinear_solver_type << "\n";
-      return 1;
-   }
-   if (kinsol_damping > 0.0 &&
-       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
-   {
-      cout << "Only KINSOL fixed-point and Picard methods can use damping\n";
-      return 1;
-   }
-   if (kinsol_aa_n > 0 &&
-       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
-   {
-      cout << "Only KINSOL fixed-point and Picard methods can use AA\n";
-      return 1;
-   }
-
-
    // 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);
    int dim = mesh->Dimension();
 
-   // 3. Refine the mesh to increase the resolution. In this example we do
+   // 3. Setup the nonlinear solver
+   map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
+   nls_map["newton"] = HyperelasticOperator::NEWTON;
+   nls_map["kinsol"] = HyperelasticOperator::KINSOL;
+   if (nls_map.find(nls) == nls_map.end())
+   {
+      cout << "Unknown type of nonlinear solver: " << nls << endl;
+      return 4;
+   }
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement, where 'ref_levels' is a
    //    command-line parameter.
    for (int lev = 0; lev < ref_levels; lev++)
@@ -336,7 +320,7 @@ int main(int argc, char *argv[])
       mesh->UniformRefinement();
    }
 
-   // 4. Define the vector finite element spaces representing the mesh
+   // 5. Define the vector finite element spaces representing the mesh
    //    deformation x, the velocity v, and the initial configuration, x_ref.
    //    Define also the elastic energy density, w, which is in a discontinuous
    //    higher-order space. Since x and v are integrated in time as a system,
@@ -364,7 +348,7 @@ int main(int argc, char *argv[])
    FiniteElementSpace w_fespace(mesh, &w_fec);
    GridFunction w(&w_fespace);
 
-   // 5. Set the initial conditions for v and x, and the boundary conditions on
+   // 6. Set the initial conditions for v and x, and the boundary conditions on
    //    a beam-like mesh (see description above).
    VectorFunctionCoefficient velo(dim, InitialVelocity);
    v.ProjectCoefficient(velo);
@@ -377,34 +361,9 @@ int main(int argc, char *argv[])
    ess_bdr = 0;
    ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
 
-   // 6. Initialize the hyperelastic operator, the GLVis visualization and print
+   // 7. Initialize the hyperelastic operator, the GLVis visualization and print
    //    the initial energies.
-   std::unique_ptr<HyperelasticOperator> oper;
-   if (nonlinear_solver_type == 0)
-      oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr, visc, mu,
-                                                    K);
-   else
-   {
-      switch (nonlinear_solver_type)
-      {
-         case 1:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_NONE);
-            break;
-         case 2:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_LINESEARCH);
-            break;
-         case 3:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_FP, kinsol_damping, kinsol_aa_n);
-            break;
-         case 4:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_PICARD, kinsol_damping, kinsol_aa_n);
-            break;
-      }
-   }
+   HyperelasticOperator oper(fespace, ess_bdr, visc, mu, K, nls_map[nls]);
 
    socketstream vis_v, vis_w;
    if (visualization)
@@ -418,23 +377,23 @@ int main(int argc, char *argv[])
       vis_w.open(vishost, visport);
       if (vis_w)
       {
-         oper->GetElasticEnergyDensity(x, w);
+         oper.GetElasticEnergyDensity(x, w);
          vis_w.precision(8);
          visualize(vis_w, mesh, &x, &w, "Elastic energy density", true);
       }
    }
 
-   double ee0 = oper->ElasticEnergy(x.GetTrueVector());
-   double ke0 = oper->KineticEnergy(v.GetTrueVector());
+   double ee0 = oper.ElasticEnergy(x.GetTrueVector());
+   double ke0 = oper.KineticEnergy(v.GetTrueVector());
    cout << "initial elastic energy (EE) = " << ee0 << endl;
    cout << "initial kinetic energy (KE) = " << ke0 << endl;
    cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
 
-   // 7. Define the ODE solver used for time integration. Several implicit
+   // 8. Define the ODE solver used for time integration. Several implicit
    //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
    //    explicit Runge-Kutta methods are available.
    double t = 0.0;
-   oper->SetTime(t);
+   oper.SetTime(t);
 
    ODESolver *ode_solver = NULL;
    CVODESolver *cvode = NULL;
@@ -458,7 +417,7 @@ int main(int argc, char *argv[])
       case 11:
       case 12:
          cvode = new CVODESolver(CV_BDF);
-         cvode->Init(*oper);
+         cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
          cvode->SetMaxStep(dt);
@@ -471,7 +430,7 @@ int main(int argc, char *argv[])
       case 13:
       case 14:
          cvode = new CVODESolver(CV_ADAMS);
-         cvode->Init(*oper);
+         cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
          cvode->SetMaxStep(dt);
@@ -484,7 +443,7 @@ int main(int argc, char *argv[])
       case 15:
       case 16:
          arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
-         arkode->Init(*oper);
+         arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
          arkode->SetMaxStep(dt);
@@ -496,16 +455,16 @@ int main(int argc, char *argv[])
       // ARKStep Explicit methods
       case 17:
          arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
-         arkode->Init(*oper);
+         arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
          ode_solver = arkode; break;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
-   if (ode_solver_type < 11) { ode_solver->Init(*oper); }
+   if (ode_solver_type < 11) { ode_solver->Init(oper); }
 
-   // 8. Perform time-integration (looping over the time iterations, ti, with a
+   // 9. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -518,8 +477,8 @@ int main(int argc, char *argv[])
 
       if (last_step || (ti % vis_steps) == 0)
       {
-         double ee = oper->ElasticEnergy(x.GetTrueVector());
-         double ke = oper->KineticEnergy(v.GetTrueVector());
+         double ee = oper.ElasticEnergy(x.GetTrueVector());
+         double ke = oper.KineticEnergy(v.GetTrueVector());
 
          cout << "step " << ti << ", t = " << t << ", EE = " << ee << ", KE = "
               << ke << ", ΔTE = " << (ee+ke)-(ee0+ke0) << endl;
@@ -533,14 +492,14 @@ int main(int argc, char *argv[])
             visualize(vis_v, mesh, &x, &v);
             if (vis_w)
             {
-               oper->GetElasticEnergyDensity(x, w);
+               oper.GetElasticEnergyDensity(x, w);
                visualize(vis_w, mesh, &x, &w);
             }
          }
       }
    }
 
-   // 9. Save the displaced mesh, the velocity and elastic energy.
+   // 10. Save the displaced mesh, the velocity and elastic energy.
    {
       v.SetFromTrueVector(); x.SetFromTrueVector();
       GridFunction *nodes = &x;
@@ -555,11 +514,11 @@ int main(int argc, char *argv[])
       v.Save(velo_ofs);
       ofstream ee_ofs("elastic_energy.sol");
       ee_ofs.precision(8);
-      oper->GetElasticEnergyDensity(x, w);
+      oper.GetElasticEnergyDensity(x, w);
       w.Save(ee_ofs);
    }
 
-   // 10. Free the used memory.
+   // 11. Free the used memory.
    delete ode_solver;
    delete mesh;
 
@@ -643,9 +602,7 @@ ReducedSystemOperator::~ReducedSystemOperator()
 HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
                                            double mu, double K,
-                                           int kinsol_nls_type,
-                                           double kinsol_damping,
-                                           int kinsol_aa_n)
+                                           NonlinearSolverType nls_type)
    : TimeDependentOperator(2*f.GetTrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), z(height/2),
@@ -696,28 +653,15 @@ HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
    J_prec = NULL;
 #endif
 
-   if (kinsol_nls_type > 0)
+   if (nls_type == KINSOL)
    {
-      KINSolver *kinsolver = new KINSolver(kinsol_nls_type, true);
-      if (kinsol_nls_type != KIN_PICARD)
-      {
-         kinsolver->SetJFNK(true);
-         kinsolver->SetLSMaxIter(100);
-      }
-      if (kinsol_aa_n > 0)
-      {
-         kinsolver->EnableAndersonAcc(kinsol_aa_n);
-      }
+      KINSolver *kinsolver = new KINSolver(KIN_NONE, true);
       newton_solver = kinsolver;
       newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(200);
       newton_solver->SetRelTol(rel_tol);
       newton_solver->SetPrintLevel(0);
       kinsolver->SetMaxSetupCalls(4);
-      if (kinsol_damping > 0.0)
-      {
-         kinsolver->SetDamping(kinsol_damping);
-      }
    }
    else
    {

examples/sundials/ex10p.cpp

@@ -9,9 +9,9 @@
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 16 -dt 0.25 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 12 -dt 0.15 -vs 10
-//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  2 -dt 3 -nls 1
-//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  2 -dt 3 -nls 2
-//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rs 1 -o 2 -s  2 -dt 3 -nls 4
+//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
+//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
+//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rs 1 -o 2 -s  2 -dt 3 -nls kinsol
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 14 -dt 0.15 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 17 -dt 5e-3 -vs 60
 //    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 14 -dt 0.15 -vs 10
@@ -101,11 +101,16 @@ protected:
    double saved_gamma; // saved gamma value from implicit setup
 
 public:
+   /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
+   enum NonlinearSolverType
+   {
+      NEWTON = 0, ///< Use MFEM's plain NewtonSolver
+      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
+   };
 
    HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
                         double visc, double mu, double K,
-                        int kinsol_nls_type = -1, double kinsol_damping = 0.0,
-                        int kinsol_aa_n = 0);
+                        NonlinearSolverType nls_type);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -230,10 +235,8 @@ int main(int argc, char *argv[])
    double mu = 0.25;
    double K = 5.0;
    bool visualization = true;
-   int nonlinear_solver_type = 0;
+   const char *nls = "newton";
    int vis_steps = 1;
-   double kinsol_damping = 0.0;
-   int kinsol_aa_n = -1;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
    const double reltol = 1e-1, abstol = 1e-1;
@@ -272,18 +275,9 @@ int main(int argc, char *argv[])
                   "15 - ARKODE implicit, approximate Jacobian,\n\t"
                   "16 - ARKODE implicit, specified Jacobian,\n\t"
                   "17 - ARKODE explicit, 4th order.");
-   args.AddOption(&nonlinear_solver_type, "-nls", "--nonlinear-solver",
-                  "Nonlinear system solver:\n\t"
-                  "0  - MFEM Newton method,\n\t"
-                  "1  - KINSOL Newton method,\n\t"
-                  "2  - KINSOL Newton method with globalization,\n\t"
-                  "3  - KINSOL fixed-point method (with or without AA),\n\t"
-                  "4  - KINSOL Picard method (with or without AA).");
-   args.AddOption(&kinsol_damping, "-damp", "--kinsol-damping",
-                  "Picard or Fixed-Point damping parameter (only valid with KINSOL): "
-                  "0 < d <= 1.0");
-   args.AddOption(&kinsol_aa_n, "-aan", "--anderson-subspace",
-                  "Anderson Acceleration subspace size (only valid with KINSOL)");
+   args.AddOption(&nls, "-nls", "--nonlinear-solver",
+                  "Nonlinear systems solver: "
+                  "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -323,42 +317,27 @@ int main(int argc, char *argv[])
       return 1;
    }
 
-   // check for valid nonlinear solver options
-   if (nonlinear_solver_type < 0 || nonlinear_solver_type > 4)
-   {
-      if (myid == 0)
-      {
-         cout << "Unknown nonlinear solver type: " << nonlinear_solver_type
-              << "\n";
-      }
-      return 1;
-   }
-   if (kinsol_damping > 0.0 &&
-       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
-   {
-      if (myid == 0)
-      {
-         cout << "Only KINSOL fixed-point and Picard methods can use damping\n";
-      }
-      return 1;
-   }
-   if (kinsol_aa_n > 0 &&
-       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
-   {
-      if (myid == 0)
-      {
-         cout << "Only KINSOL fixed-point and Picard methods can use AA\n";
-      }
-      return 1;
-   }
-
    // 3. Read the serial mesh from the given mesh file on all processors. We can
    //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code.
    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
+   // 4. Nonlinear solver
+   map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
+   nls_map["newton"] = HyperelasticOperator::NEWTON;
+   nls_map["kinsol"] = HyperelasticOperator::KINSOL;
+   if (nls_map.find(nls) == nls_map.end())
+   {
+      if (myid == 0)
+      {
+         cout << "Unknown type of nonlinear solver: " << nls << endl;
+      }
+      delete mesh;
+      return 4;
+   }
+
+   // 5. 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++)
@@ -366,7 +345,7 @@ int main(int argc, char *argv[])
       mesh->UniformRefinement();
    }
 
-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
    //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -376,7 +355,7 @@ int main(int argc, char *argv[])
       pmesh->UniformRefinement();
    }
 
-   // 6. Define the parallel vector finite element spaces representing the mesh
+   // 7. Define the parallel vector finite element spaces representing the mesh
    //    deformation x_gf, the velocity v_gf, and the initial configuration,
    //    x_ref. Define also the elastic energy density, w_gf, which is in a
    //    discontinuous higher-order space. Since x and v are integrated in time
@@ -408,7 +387,7 @@ int main(int argc, char *argv[])
    ParFiniteElementSpace w_fespace(pmesh, &w_fec);
    ParGridFunction w_gf(&w_fespace);
 
-   // 7. Set the initial conditions for v_gf, x_gf and vx, and define the
+   // 8. Set the initial conditions for v_gf, x_gf and vx, and define the
    //    boundary conditions on a beam-like mesh (see description above).
    VectorFunctionCoefficient velo(dim, InitialVelocity);
    v_gf.ProjectCoefficient(velo);
@@ -423,38 +402,9 @@ int main(int argc, char *argv[])
    ess_bdr = 0;
    ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
 
-   // 8. Initialize the hyperelastic operator, the GLVis visualization and print
+   // 9. Initialize the hyperelastic operator, the GLVis visualization and print
    //    the initial energies.
-   std::unique_ptr<HyperelasticOperator> oper;
-   if (nonlinear_solver_type == 0)
-      oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr, visc, mu,
-                                                    K);
-   else
-   {
-      switch (nonlinear_solver_type)
-      {
-         case 1:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_NONE);
-            break;
-         case 2:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_LINESEARCH);
-            break;
-         case 3:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_FP, kinsol_damping, kinsol_aa_n);
-            break;
-         case 4:
-            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
-                                                          visc, mu, K, KIN_PICARD, kinsol_damping, kinsol_aa_n);
-            break;
-         default:
-            cout << "Unknown type of nonlinear solver: "
-                 << nonlinear_solver_type << endl;
-            return 4;
-      }
-   }
+   HyperelasticOperator oper(fespace, ess_bdr, visc, mu, K, nls_map[nls]);
 
    socketstream vis_v, vis_w;
    if (visualization)
@@ -470,14 +420,14 @@ int main(int argc, char *argv[])
       vis_w.open(vishost, visport);
       if (vis_w)
       {
-         oper->GetElasticEnergyDensity(x_gf, w_gf);
+         oper.GetElasticEnergyDensity(x_gf, w_gf);
          vis_w.precision(8);
          visualize(vis_w, pmesh, &x_gf, &w_gf, "Elastic energy density", true);
       }
    }
 
-   double ee0 = oper->ElasticEnergy(x_gf);
-   double ke0 = oper->KineticEnergy(v_gf);
+   double ee0 = oper.ElasticEnergy(x_gf);
+   double ke0 = oper.KineticEnergy(v_gf);
    if (myid == 0)
    {
       cout << "initial elastic energy (EE) = " << ee0 << endl;
@@ -485,11 +435,11 @@ int main(int argc, char *argv[])
       cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
    }
 
-   // 9. Define the ODE solver used for time integration. Several implicit
-   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
-   //    explicit Runge-Kutta methods are available.
+   // 10. Define the ODE solver used for time integration. Several implicit
+   //     singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
+   //     explicit Runge-Kutta methods are available.
    double t = 0.0;
-   oper->SetTime(t);
+   oper.SetTime(t);
 
    ODESolver *ode_solver = NULL;
    CVODESolver *cvode = NULL;
@@ -513,7 +463,7 @@ int main(int argc, char *argv[])
       case 11:
       case 12:
          cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
-         cvode->Init(*oper);
+         cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
          cvode->SetMaxStep(dt);
@@ -526,7 +476,7 @@ int main(int argc, char *argv[])
       case 13:
       case 14:
          cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
-         cvode->Init(*oper);
+         cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
          cvode->SetMaxStep(dt);
@@ -539,7 +489,7 @@ int main(int argc, char *argv[])
       case 15:
       case 16:
          arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
-         arkode->Init(*oper);
+         arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
          arkode->SetMaxStep(dt);
@@ -551,16 +501,16 @@ int main(int argc, char *argv[])
       // ARKStep Explicit methods
       case 17:
          arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
-         arkode->Init(*oper);
+         arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
          ode_solver = arkode; break;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
-   if (ode_solver_type < 11) { ode_solver->Init(*oper); }
+   if (ode_solver_type < 11) { ode_solver->Init(oper); }
 
-   // 10. Perform time-integration
+   // 11. Perform time-integration
    //     (looping over the time iterations, ti, with a time-step dt).
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -575,8 +525,8 @@ int main(int argc, char *argv[])
       {
          v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();
 
-         double ee = oper->ElasticEnergy(x_gf);
-         double ke = oper->KineticEnergy(v_gf);
+         double ee = oper.ElasticEnergy(x_gf);
+         double ke = oper.KineticEnergy(v_gf);
 
          if (myid == 0)
          {
@@ -592,14 +542,14 @@ int main(int argc, char *argv[])
             visualize(vis_v, pmesh, &x_gf, &v_gf);
             if (vis_w)
             {
-               oper->GetElasticEnergyDensity(x_gf, w_gf);
+               oper.GetElasticEnergyDensity(x_gf, w_gf);
                visualize(vis_w, pmesh, &x_gf, &w_gf);
             }
          }
       }
    }
 
-   // 11. Save the displaced mesh, the velocity and elastic energy.
+   // 12. Save the displaced mesh, the velocity and elastic energy.
    {
       v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();
       GridFunction *nodes = &x_gf;
@@ -620,11 +570,11 @@ int main(int argc, char *argv[])
       v_gf.Save(velo_ofs);
       ofstream ee_ofs(ee_name.str().c_str());
       ee_ofs.precision(8);
-      oper->GetElasticEnergyDensity(x_gf, w_gf);
+      oper.GetElasticEnergyDensity(x_gf, w_gf);
       w_gf.Save(ee_ofs);
    }
 
-   // 12. Free the used memory.
+   // 13. Free the used memory.
    delete ode_solver;
    delete pmesh;
 
@@ -714,10 +664,7 @@ ReducedSystemOperator::~ReducedSystemOperator()
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
                                            double mu, double K,
-                                           int kinsol_nls_type,
-                                           double kinsol_damping,
-                                           int kinsol_aa_n)
-
+                                           NonlinearSolverType nls_type)
    : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), M_solver(f.GetComm()), z(height/2),
@@ -769,28 +716,17 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
    J_minres->SetPreconditioner(*J_prec);
    J_solver = J_minres;
 
-   if (kinsol_nls_type > 0)
+   if (nls_type == KINSOL)
    {
-      KINSolver *kinsolver = new KINSolver(f.GetComm(), kinsol_nls_type, true);
-      if (kinsol_nls_type != KIN_PICARD)
-      {
-         kinsolver->SetJFNK(true);
-         kinsolver->SetLSMaxIter(100);
-      }
-      if (kinsol_aa_n > 0)
-      {
-         kinsolver->EnableAndersonAcc(kinsol_aa_n);
-      }
+      KINSolver *kinsolver = new KINSolver(f.GetComm(), KIN_LINESEARCH, true);
+      kinsolver->SetJFNK(true);
+      kinsolver->SetLSMaxIter(100);
       newton_solver = kinsolver;
       newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(200);
       newton_solver->SetRelTol(rel_tol);
-      newton_solver->SetPrintLevel(0);
+      newton_solver->SetPrintLevel(1);
       kinsolver->SetMaxSetupCalls(4);
-      if (kinsol_damping > 0.0)
-      {
-         kinsolver->SetDamping(kinsol_damping);
-      }
    }
    else
    {

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/CMakeLists.txt

@@ -112,6 +112,8 @@ set(SRCS
   qinterp/eval_by_vdim.cpp
   qinterp/grad_by_nodes.cpp
   qinterp/grad_by_vdim.cpp
+  qinterp/grad_phys_by_nodes.cpp
+  qinterp/grad_phys_by_vdim.cpp
   qspace.cpp
   quadinterpolator.cpp
   quadinterpolator_face.cpp
@@ -190,9 +192,6 @@ set(HDRS
   hybridization.hpp
   intrules.hpp
   intrules_cut.hpp
-  kernel_dispatch.hpp
-  kernel_reporter.hpp
-  kernels.hpp
   ceed/interface/basis.hpp
   ceed/interface/integrator.hpp
   ceed/interface/interface.hpp
@@ -224,6 +223,7 @@ set(HDRS
   nonlinearform_ext.hpp
   nonlininteg.hpp
   qfunction.hpp
+  qinterp/dispatch.hpp
   qinterp/eval.hpp
   qinterp/grad.hpp
   qspace.hpp

fem/bilinearform.cpp

@@ -289,10 +289,9 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
       return;
    }
 
-   const FiniteElement &fe = *fes->GetFE(i);
-
    if (domain_integs.Size())
    {
+      const FiniteElement &fe = *fes->GetFE(i);
       ElementTransformation *eltrans = fes->GetElementTransformation(i);
       domain_integs[0]->AssembleElementMatrix(fe, *eltrans, elmat);
       for (int k = 1; k < domain_integs.Size(); k++)
@@ -303,18 +302,17 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
    }
    else
    {
-      const int ndof = fe.GetDof() * fes->GetVDim();
-      elmat.SetSize(ndof);
+      fes->GetElementVDofs(i, vdofs);
+      elmat.SetSize(vdofs.Size());
       elmat = 0.0;
    }
 }
 
 void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
-   const FiniteElement &be = *fes->GetBE(i);
-
    if (boundary_integs.Size())
    {
+      const FiniteElement &be = *fes->GetBE(i);
       ElementTransformation *eltrans = fes->GetBdrElementTransformation(i);
       boundary_integs[0]->AssembleElementMatrix(be, *eltrans, elmat);
       for (int k = 1; k < boundary_integs.Size(); k++)
@@ -325,8 +323,8 @@ void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
    }
    else
    {
-      const int ndof = be.GetDof() * fes->GetVDim();
-      elmat.SetSize(ndof);
+      fes->GetBdrElementVDofs(i, vdofs);
+      elmat.SetSize(vdofs.Size());
       elmat = 0.0;
    }
 }
@@ -1431,50 +1429,32 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const
    mat->GetBlocks(blocks);
 }
 
-void MixedBilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi)
+void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
 {
-   domain_integs.Append(bfi);
+   domain_integs.Append (bfi);
    domain_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }
 
-void MixedBilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi,
-                                            Array<int> &elem_marker)
+void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi,
+                                             Array<int> &elem_marker)
 {
-   domain_integs.Append(bfi);
+   domain_integs.Append (bfi);
    domain_integs_marker.Append(&elem_marker);
 }
 
-void MixedBilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi)
+void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
 {
-   boundary_integs.Append(bfi);
+   boundary_integs.Append (bfi);
    boundary_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }
 
-void MixedBilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi,
-                                              Array<int> &bdr_marker)
+void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
+                                               Array<int> &bdr_marker)
 {
-   boundary_integs.Append(bfi);
+   boundary_integs.Append (bfi);
    boundary_integs_marker.Append(&bdr_marker);
 }
 
-void MixedBilinearForm::AddInteriorFaceIntegrator(BilinearFormIntegrator *bfi)
-{
-   interior_face_integs.Append(bfi);
-}
-
-void MixedBilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi)
-{
-   boundary_face_integs.Append(bfi);
-   boundary_face_integs_marker.Append(NULL); // NULL marker means apply everywhere
-}
-
-void MixedBilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
-                                             Array<int> &bdr_marker)
-{
-   boundary_face_integs.Append(bfi);
-   boundary_face_integs_marker.Append(&bdr_marker);
-}
-
 void MixedBilinearForm::AddTraceFaceIntegrator (BilinearFormIntegrator * bfi)
 {
    trace_face_integs.Append (bfi);
@@ -1607,108 +1587,6 @@ void MixedBilinearForm::Assemble(int skip_zeros)
       }
    }
 
-   if (interior_face_integs.Size())
-   {
-      FaceElementTransformations *ftr;
-      Array<int> trial_vdofs2, test_vdofs2;
-      const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
-
-      int nfaces = mesh->GetNumFaces();
-      for (int i = 0; i < nfaces; i++)
-      {
-         ftr = mesh->GetInteriorFaceTransformations(i);
-         if (ftr != NULL)
-         {
-            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
-            trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
-            test_fe1 = test_fes->GetFE(ftr->Elem1No);
-            if (ftr->Elem2No >= 0)
-            {
-               trial_fes->GetElementVDofs(ftr->Elem2No, trial_vdofs2);
-               test_fes->GetElementVDofs(ftr->Elem2No, test_vdofs2);
-               trial_vdofs.Append(trial_vdofs2);
-               test_vdofs.Append(test_vdofs2);
-               trial_fe2 = trial_fes->GetFE(ftr->Elem2No);
-               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.
-               trial_fe2 = trial_fe1;
-               test_fe2 = test_fe1;
-            }
-            for (int k = 0; k < interior_face_integs.Size(); k++)
-            {
-               interior_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                           *test_fe2,
-                                                           *ftr, elemmat);
-               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
-            }
-         }
-      }
-   }
-
-   if (boundary_face_integs.Size())
-   {
-      FaceElementTransformations *ftr;
-      Array<int> tr_vdofs2, te_vdofs2;
-      const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
-
-      // Which boundary attributes need to be processed?
-      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
-                                 mesh->bdr_attributes.Max() : 0);
-      bdr_attr_marker = 0;
-      for (int k = 0; k < boundary_face_integs.Size(); k++)
-      {
-         if (boundary_face_integs_marker[k] == NULL)
-         {
-            bdr_attr_marker = 1;
-            break;
-         }
-         Array<int> &bdr_marker = *boundary_face_integs_marker[k];
-         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
-                     "invalid boundary marker for boundary face integrator #"
-                     << k << ", counting from zero");
-         for (int i = 0; i < bdr_attr_marker.Size(); i++)
-         {
-            bdr_attr_marker[i] |= bdr_marker[i];
-         }
-      }
-
-      for (int i = 0; i < trial_fes -> GetNBE(); i++)
-      {
-         const int bdr_attr = mesh->GetBdrAttribute(i);
-         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
-
-         ftr = mesh -> GetBdrFaceTransformations (i);
-         if (ftr != NULL)
-         {
-            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
-            trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
-            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.
-            trial_fe2 = trial_fe1;
-            test_fe2 = test_fe1;
-            for (int k = 0; k < boundary_face_integs.Size(); k++)
-            {
-               if (boundary_face_integs_marker[k] &&
-                   (*boundary_face_integs_marker[k])[bdr_attr-1] == 0) { continue; }
-
-               boundary_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                           *test_fe2,
-                                                           *ftr, elemmat);
-               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
-            }
-         }
-      }
-   }
-
    if (trace_face_integs.Size())
    {
       FaceElementTransformations *ftr;
@@ -1889,11 +1767,10 @@ void MixedBilinearForm::ConformingAssemble()
 
 void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
 {
-   const FiniteElement &trial_fe = *trial_fes->GetFE(i);
-   const FiniteElement &test_fe = *test_fes->GetFE(i);
-
    if (domain_integs.Size())
    {
+      const FiniteElement &trial_fe = *trial_fes->GetFE(i);
+      const FiniteElement &test_fe = *test_fes->GetFE(i);
       ElementTransformation *eltrans = test_fes->GetElementTransformation(i);
       domain_integs[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
                                                elmat);
@@ -1906,21 +1783,19 @@ void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
    }
    else
    {
-      const int tr_dofs = trial_fe.GetDof() * trial_fes->GetVDim();
-      const int te_dofs = test_fe.GetDof() * test_fes->GetVDim();
-
-      elmat.SetSize(te_dofs, tr_dofs);
+      trial_fes->GetElementVDofs(i, trial_vdofs);
+      test_fes->GetElementVDofs(i, test_vdofs);
+      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
       elmat = 0.0;
    }
 }
 
 void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
-   const FiniteElement &trial_be = *trial_fes->GetBE(i);
-   const FiniteElement &test_be = *test_fes->GetBE(i);
-
    if (boundary_integs.Size())
    {
+      const FiniteElement &trial_be = *trial_fes->GetBE(i);
+      const FiniteElement &test_be = *test_fes->GetBE(i);
       ElementTransformation *eltrans = test_fes->GetBdrElementTransformation(i);
       boundary_integs[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
                                                  elmat);
@@ -1933,103 +1808,9 @@ void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
    }
    else
    {
-      const int tr_dofs = trial_be.GetDof() * trial_fes->GetVDim();
-      const int te_dofs = test_be.GetDof() * test_fes->GetVDim();
-
-      elmat.SetSize(te_dofs, tr_dofs);
-      elmat = 0.0;
-   }
-}
-
-void MixedBilinearForm::ComputeFaceMatrix(int i, DenseMatrix &elmat) const
-{
-   FaceElementTransformations *ftr;
-   Mesh *mesh = test_fes -> GetMesh();
-   ftr = mesh->GetFaceElementTransformations(i);
-   MFEM_ASSERT(ftr, "No associated face transformations.");
-
-   const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
-
-   trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
-   test_fe1 = test_fes->GetFE(ftr->Elem1No);
-   if (ftr->Elem2No >= 0)
-   {
-      trial_fe2 = trial_fes->GetFE(ftr->Elem2No);
-      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.
-      trial_fe2 = trial_fe1;
-      test_fe2 = test_fe1;
-   }
-
-   if (interior_face_integs.Size())
-   {
-      interior_face_integs[0]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                  *test_fe2,
-                                                  *ftr, elmat);
-      for (int k = 1; k < interior_face_integs.Size(); k++)
-      {
-         interior_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                     *test_fe2,
-                                                     *ftr, elemmat);
-         elmat += elemmat;
-      }
-   }
-   else
-   {
-      int tr_dofs = trial_fe1->GetDof() * trial_fes->GetVDim();
-      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
-      if (ftr->Elem2No >= 0)
-      {
-         tr_dofs += trial_fe2->GetDof() * trial_fes->GetVDim();
-         te_dofs += test_fe2->GetDof() * test_fes->GetVDim();
-      }
-
-      elmat.SetSize(te_dofs, tr_dofs);
-      elmat = 0.0;
-   }
-}
-
-void MixedBilinearForm::ComputeBdrFaceMatrix(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_fe1, *trial_fe2, *test_fe1, *test_fe2;
-
-   trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
-   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.
-   trial_fe2 = trial_fe1;
-   test_fe2 = test_fe1;
-
-   if (boundary_face_integs.Size())
-   {
-      boundary_face_integs[0]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                  *test_fe2,
-                                                  *ftr, elmat);
-      for (int k = 1; k < boundary_face_integs.Size(); k++)
-      {
-         boundary_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
-                                                     *test_fe2,
-                                                     *ftr, elemmat);
-         elmat += elemmat;
-      }
-   }
-   else
-   {
-      const int tr_dofs = trial_fe1->GetDof() * trial_fes->GetVDim();
-      const int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
-
-      elmat.SetSize(te_dofs, tr_dofs);
+      trial_fes->GetBdrElementVDofs(i, trial_vdofs);
+      test_fes->GetBdrElementVDofs(i, test_vdofs);
+      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
       elmat = 0.0;
    }
 }
@@ -2160,59 +1941,36 @@ void MixedBilinearForm::AssembleBdrElementMatrix(
    mat->AddSubMatrix(test_vdofs_, trial_vdofs_, elmat, skip_zeros);
 }
 
-void MixedBilinearForm::EliminateTrialEssentialBC(
+void MixedBilinearForm::EliminateTrialDofs (
    const Array<int> &bdr_attr_is_ess, const Vector &sol, Vector &rhs )
 {
-   Array<int> trial_ess_dofs;
-   trial_fes->GetEssentialVDofs(bdr_attr_is_ess, trial_ess_dofs);
-   mat->EliminateCols(trial_ess_dofs, &sol, &rhs);
+   int i, j, k;
+   Array<int> tr_vdofs, cols_marker (trial_fes -> GetVSize());
+
+   cols_marker = 0;
+   for (i = 0; i < trial_fes -> GetNBE(); i++)
+      if (bdr_attr_is_ess[trial_fes -> GetBdrAttribute (i)-1])
+      {
+         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
+         for (j = 0; j < tr_vdofs.Size(); j++)
+         {
+            if ( (k = tr_vdofs[j]) < 0 )
+            {
+               k = -1-k;
+            }
+            cols_marker[k] = 1;
+         }
+      }
+   mat -> EliminateCols (cols_marker, &sol, &rhs);
 }
 
-void MixedBilinearForm::EliminateTrialEssentialBC(const Array<int>
-                                                  &bdr_attr_is_ess)
-{
-   Array<int> trial_ess_dofs;
-   trial_fes->GetEssentialVDofs(bdr_attr_is_ess, trial_ess_dofs);
-   mat->EliminateCols(trial_ess_dofs);
-}
-
-void MixedBilinearForm::EliminateTrialVDofs(const Array<int> &trial_vdofs_,
-                                            const Vector &sol, Vector &rhs)
-{
-   Array<int> trial_vdofs_marker;
-   FiniteElementSpace::ListToMarker(trial_vdofs_, mat->Width(),
-                                    trial_vdofs_marker);
-   mat->EliminateCols(trial_vdofs_marker, &sol, &rhs);
-}
-
-void MixedBilinearForm::EliminateTrialVDofs(const Array<int> &trial_vdofs_)
-{
-   if (mat_e == NULL)
-   {
-      mat_e = new SparseMatrix(mat->Height(), mat->Width());
-   }
-
-   Array<int> trial_vdofs_marker;
-   FiniteElementSpace::ListToMarker(trial_vdofs_, mat->Width(),
-                                    trial_vdofs_marker);
-   mat->EliminateCols(trial_vdofs_marker, *mat_e);
-   mat_e->Finalize();
-}
-
-void MixedBilinearForm::EliminateTrialVDofsInRHS(const Array<int> &trial_vdofs_,
-                                                 const Vector &x, Vector &b)
-{
-   mat_e->AddMult(x, b, -1.);
-}
-
-void MixedBilinearForm::EliminateEssentialBCFromTrialDofs(
+void MixedBilinearForm::EliminateEssentialBCFromTrialDofs (
    const Array<int> &marked_vdofs, const Vector &sol, Vector &rhs)
 {
-   mat->EliminateCols(marked_vdofs, &sol, &rhs);
+   mat -> EliminateCols (marked_vdofs, &sol, &rhs);
 }
 
-void MixedBilinearForm::EliminateTestEssentialBC(const Array<int>
-                                                 &bdr_attr_is_ess)
+void MixedBilinearForm::EliminateTestDofs (const Array<int> &bdr_attr_is_ess)
 {
    int i, j, k;
    Array<int> te_vdofs;
@@ -2232,14 +1990,6 @@ void MixedBilinearForm::EliminateTestEssentialBC(const Array<int>
       }
 }
 
-void MixedBilinearForm::EliminateTestVDofs(const Array<int> &test_vdofs_)
-{
-   for (int i=0; i<test_vdofs_.Size(); ++i)
-   {
-      mat->EliminateRow(test_vdofs_[i]);
-   }
-}
-
 void MixedBilinearForm::FormRectangularSystemMatrix(
    const Array<int> &trial_tdof_list,
    const Array<int> &test_tdof_list,
@@ -2276,9 +2026,20 @@ void MixedBilinearForm::FormRectangularSystemMatrix(
       mat = m;
    }
 
-   EliminateTrialVDofs(trial_tdof_list);
-   EliminateTestVDofs(test_tdof_list);
+   Array<int> ess_trial_tdof_marker, ess_test_tdof_marker;
+   FiniteElementSpace::ListToMarker(trial_tdof_list, trial_fes->GetTrueVSize(),
+                                    ess_trial_tdof_marker);
+   FiniteElementSpace::ListToMarker(test_tdof_list, test_fes->GetTrueVSize(),
+                                    ess_test_tdof_marker);
 
+   mat_e = new SparseMatrix(mat->Height(), mat->Width());
+   mat->EliminateCols(ess_trial_tdof_marker, *mat_e);
+
+   for (int i=0; i<test_tdof_list.Size(); ++i)
+   {
+      mat->EliminateRow(test_tdof_list[i]);
+   }
+   mat_e->Finalize();
    A.Reset(mat, false);
 }
 
@@ -2307,7 +2068,7 @@ void MixedBilinearForm::FormRectangularLinearSystem(
                                   A); // Set A = mat_e
    }
    // Eliminate essential BCs with B -= Ab xb
-   EliminateTrialVDofsInRHS(trial_tdof_list, X, B);
+   mat_e->AddMult(X, B, -1.0);
 
    B.SetSubVector(test_tdof_list, 0.0);
 }
@@ -2333,10 +2094,6 @@ MixedBilinearForm::~MixedBilinearForm()
       for (i = 0; i < domain_integs.Size(); i++) { delete domain_integs[i]; }
       for (i = 0; i < boundary_integs.Size(); i++)
       { delete boundary_integs[i]; }
-      for (i = 0; i < interior_face_integs.Size(); i++)
-      { delete interior_face_integs[i]; }
-      for (i = 0; i < boundary_face_integs.Size(); i++)
-      { delete boundary_face_integs[i]; }
       for (i = 0; i < trace_face_integs.Size(); i++)
       { delete trace_face_integs[i]; }
       for (i = 0; i < boundary_trace_face_integs.Size(); i++)

fem/bilinearform.hpp

@@ -294,13 +294,13 @@ public:
    const real_t &operator()(int i, int j) { return (*mat)(i,j); }
 
    /// Returns a reference to: $ M_{ij} $
-   real_t &Elem(int i, int j) override;
+   virtual real_t &Elem(int i, int j);
 
    /// Returns constant reference to: $ M_{ij} $
-   const real_t &Elem(int i, int j) const override;
+   virtual const real_t &Elem(int i, int j) const;
 
    /// Matrix vector multiplication:  $ y = M x $
-   void Mult(const Vector &x, Vector &y) const override;
+   virtual void Mult(const Vector &x, Vector &y) const;
 
    /** @brief Matrix vector multiplication with the original uneliminated
        matrix.  The original matrix is $ M + M_e $ so we have:
@@ -309,7 +309,7 @@ public:
    { mat->Mult(x, y); mat_e->AddMult(x, y); }
 
    /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const override
+   virtual void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const
    { mat -> AddMult (x, y, a); }
 
    /** @brief Add the original uneliminated matrix vector multiple to a vector.
@@ -319,8 +319,8 @@ public:
    { mat->AddMult(x, y); mat_e->AddMult(x, y); }
 
    /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
-   void AddMultTranspose(const Vector & x, Vector & y,
-                         const real_t a = 1.0) const override
+   virtual void AddMultTranspose(const Vector & x, Vector & y,
+                                 const real_t a = 1.0) const
    { mat->AddMultTranspose(x, y, a); }
 
    /** @brief Add the original uneliminated matrix transpose vector
@@ -330,7 +330,7 @@ public:
    { mat->AddMultTranspose(x, y); mat_e->AddMultTranspose(x, y); }
 
    /// Matrix transpose vector multiplication:  $ y = M^T x $
-   void MultTranspose(const Vector & x, Vector & y) const override;
+   virtual void MultTranspose(const Vector & x, Vector & y) const;
 
    /// Compute $ y^T M x $
    real_t InnerProduct(const Vector &x, const Vector &y) const
@@ -338,13 +338,13 @@ public:
 
    /** @brief Returns a pointer to (approximation) of the matrix inverse:
        $ M^{-1} $ (currently returns NULL) */
-   MatrixInverse *Inverse() const override;
+   virtual MatrixInverse *Inverse() const;
 
    /** @brief Finalizes the matrix initialization if the ::AssemblyLevel is
        AssemblyLevel::LEGACY.
        The matrix that gets finalized is different if you are using static
        condensation or hybridization.*/
-   void Finalize(int skip_zeros = 1) override;
+   virtual void Finalize(int skip_zeros = 1);
 
    /** @brief Returns a const reference to the sparse matrix:  $ M $
     *
@@ -458,18 +458,18 @@ public:
        conforming prolongation, and |.| denotes the entry-wise absolute value.
        In general, this is just an approximation of the exact diagonal for this
        case. */
-   void AssembleDiagonal(Vector &diag) const override;
+   virtual void AssembleDiagonal(Vector &diag) const;
 
    /// Get the finite element space prolongation operator.
-   const Operator *GetProlongation() const override
+   virtual const Operator *GetProlongation() const
    { return fes->GetConformingProlongation(); }
 
    /// Get the finite element space restriction operator
-   const Operator *GetRestriction() const override
+   virtual const Operator *GetRestriction() const
    { return fes->GetConformingRestriction(); }
 
    /// Get the output finite element space prolongation matrix
-   const Operator *GetOutputProlongation() const override
+   virtual const Operator *GetOutputProlongation() const
    { return GetProlongation(); }
 
    /** @brief Returns the output fe space restriction matrix, transposed
@@ -477,11 +477,11 @@ public:
        Logically, this is the transpose of GetOutputRestriction, but in
        practice it is convenient to have it in transposed form for
        construction of RAP operators in matrix-free methods. */
-   const Operator *GetOutputRestrictionTranspose() const override
+   virtual const Operator *GetOutputRestrictionTranspose() const
    { return fes->GetRestrictionTransposeOperator(); }
 
    /// Get the output finite element space restriction matrix
-   const Operator *GetOutputRestriction() const override
+   virtual const Operator *GetOutputRestriction() const
    { return GetRestriction(); }
 
    /// Compute serial RAP operator and store it in @a A as a SparseMatrix.
@@ -566,8 +566,7 @@ public:
        FormLinearSystem() method to recover the solution as a GridFunction-size
        vector in @a x. Use the same arguments as in the FormLinearSystem() call.
    */
-   void RecoverFEMSolution(const Vector &X, const Vector &b,
-                           Vector &x) override;
+   virtual void RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x);
 
    /// Compute and store internally all element matrices.
    void ComputeElementMatrices();
@@ -772,14 +771,6 @@ protected:
    /// Entries are not owned.
    Array<Array<int>*> boundary_integs_marker;
 
-   /// Interior face integrators.
-   Array<BilinearFormIntegrator*> interior_face_integs;
-
-   /// Boundary face integrators.
-   Array<BilinearFormIntegrator*> boundary_face_integs;
-   /// Entries are not owned.
-   Array<Array<int>*> boundary_face_integs_marker;
-
    /// Trace face (skeleton) integrators.
    Array<BilinearFormIntegrator*> trace_face_integs;
 
@@ -820,32 +811,32 @@ public:
                      MixedBilinearForm *mbf);
 
    /// Returns a reference to: $ M_{ij} $
-   real_t &Elem(int i, int j) override;
+   virtual real_t &Elem(int i, int j);
 
    /// Returns a reference to: $ M_{ij} $
-   const real_t &Elem(int i, int j) const override;
+   virtual const real_t &Elem(int i, int j) const;
 
    /// Matrix multiplication: $ y = M x $
-   void Mult(const Vector & x, Vector & y) const override;
+   virtual void Mult(const Vector & x, Vector & y) const;
 
    /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   void AddMult(const Vector & x, Vector & y,
-                const real_t a = 1.0) const override;
+   virtual void AddMult(const Vector & x, Vector & y,
+                        const real_t a = 1.0) const;
 
    /// Matrix transpose vector multiplication:  $ y = M^T x $
-   void MultTranspose(const Vector & x, Vector & y) const override;
+   virtual void MultTranspose(const Vector & x, Vector & y) const;
 
    /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
-   void AddMultTranspose(const Vector & x, Vector & y,
-                         const real_t a = 1.0) const override;
+   virtual void AddMultTranspose(const Vector & x, Vector & y,
+                                 const real_t a = 1.0) const;
 
    /** @brief Returns a pointer to (approximation) of the matrix inverse:
        $ M^{-1} $ (currently unimplemented and returns NULL)*/
-   MatrixInverse *Inverse() const override;
+   virtual MatrixInverse *Inverse() const;
 
    /** @brief Finalizes the matrix initialization if the ::AssemblyLevel is
        AssemblyLevel::LEGACY.*/
-   void Finalize(int skip_zeros = 1) override;
+   virtual void Finalize(int skip_zeros = 1);
 
    /** @brief Extract the associated matrix as SparseMatrix blocks. The number
        of block rows and columns is given by the vector dimensions (vdim) of the
@@ -856,37 +847,15 @@ public:
    /** This will segfault if the usual sparse mat is not defined
        like when static condensation is being used or AllocMat() has
        not yet been called. */
-   const SparseMatrix &SpMat() const
-   {
-      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
-      return *mat;
-   }
+   const SparseMatrix &SpMat() const { return *mat; }
 
    /// Returns a reference to the sparse matrix:  $ M $
-   SparseMatrix &SpMat()
-   {
-      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
-      return *mat;
-   }
+   SparseMatrix &SpMat() { return *mat; }
 
    /**  @brief Nullifies the internal matrix $ M $ and returns a pointer
         to it.  Used for transferring ownership. */
    SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }
 
-   /// Returns a const reference to the sparse matrix of eliminated b.c.:  $ M_e $
-   const SparseMatrix &SpMatElim() const
-   {
-      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
-      return *mat_e;
-   }
-
-   /// Returns a reference to the sparse matrix of eliminated b.c.:  $ M_e $
-   SparseMatrix &SpMatElim()
-   {
-      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
-      return *mat_e;
-   }
-
    /// Adds a domain integrator. Assumes ownership of @a bfi.
    void AddDomainIntegrator(BilinearFormIntegrator *bfi);
 
@@ -901,16 +870,6 @@ public:
    void AddBoundaryIntegrator(BilinearFormIntegrator * bfi,
                               Array<int> &bdr_marker);
 
-   /// Adds an interior face integrator. Assumes ownership of @a bfi.
-   void AddInteriorFaceIntegrator(BilinearFormIntegrator *bfi);
-
-   /// Adds a boundary face integrator. Assumes ownership of @a bfi.
-   void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi);
-
-   /// Adds a boundary face integrator. Assumes ownership of @a bfi.
-   void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
-                             Array<int> &bdr_marker);
-
    /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
 
        This type of integrator assembles terms over all faces of the mesh using
@@ -941,16 +900,6 @@ public:
        corresponding pointer (to Array<int>) will be NULL. */
    Array<Array<int>*> *GetBBFI_Marker() { return &boundary_integs_marker; }
 
-   /// Access all integrators added with AddInteriorFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetFBFI() { return &interior_face_integs; }
-
-   /// Access all integrators added with AddBdrFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetBFBFI() { return &boundary_face_integs; }
-   /** @brief Access all boundary markers added with AddBdrFaceIntegrator().
-       If no marker was specified when the integrator was added, the
-       corresponding pointer (to Array<int>) will be NULL. */
-   Array<Array<int>*> *GetBFBFI_Marker() { return &boundary_face_integs_marker; }
-
    /// Access all integrators added with AddTraceFaceIntegrator().
    Array<BilinearFormIntegrator*> *GetTFBFI() { return &trace_face_integs; }
 
@@ -979,19 +928,19 @@ public:
    void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
 
    /// Get the input finite element space prolongation matrix
-   const Operator *GetProlongation() const override
+   virtual const Operator *GetProlongation() const
    { return trial_fes->GetProlongationMatrix(); }
 
    /// Get the input finite element space restriction matrix
-   const Operator *GetRestriction() const override
+   virtual const Operator *GetRestriction() const
    { return trial_fes->GetRestrictionMatrix(); }
 
    /// Get the test finite element space prolongation matrix
-   const Operator *GetOutputProlongation() const override
+   virtual const Operator *GetOutputProlongation() const
    { return test_fes->GetProlongationMatrix(); }
 
    /// Get the test finite element space restriction matrix
-   const Operator *GetOutputRestriction() const override
+   virtual const Operator *GetOutputRestriction() const
    { return test_fes->GetRestrictionMatrix(); }
 
    /** @brief For partially conforming trial and/or test FE spaces, complete the
@@ -1016,13 +965,6 @@ public:
    /** @note The boundary attribute markers of the integrators are ignored. */
    void ComputeBdrTraceFaceMatrix(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.
        added to the system matrix. The flag @a skip_zeros skips the zero
@@ -1063,61 +1005,24 @@ public:
                                  Array<int> &test_vdofs,
                                  int skip_zeros = 1);
 
-   /// Eliminate essential boundary trial DOFs from the system.
+   /// Eliminate essential boundary DOFs from the columns of the system.
    /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
-       the essential part of the boundary. */
-   void EliminateTrialEssentialBC(const Array<int> &bdr_attr_is_ess,
-                                  const Vector &sol, Vector &rhs);
+       the essential part of the boundary.  All entries in the columns will be
+       set to 0.0 through elimination.*/
+   void EliminateTrialDofs(const Array<int> &bdr_attr_is_ess,
+                           const Vector &sol, Vector &rhs);
 
-   /// Eliminate essential boundary trial DOFs from the system matrix.
-   /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
-       the essential part of the boundary. */
-   void EliminateTrialEssentialBC(const Array<int> &bdr_attr_is_ess);
-
-   /// (DEPRECATED) Eliminate essential boundary trial DOFs from the system.
-   /** @see EliminateTrialEssentialBC() */
-   MFEM_DEPRECATED void EliminateTrialDofs(const Array<int> &bdr_attr_is_ess,
-                                           const Vector &sol, Vector &rhs)
-   { EliminateTrialEssentialBC(bdr_attr_is_ess, sol, rhs); }
-
-   /// Eliminate the given trial @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
-   /** In this case the eliminations are applied to the internal $ M $
-       and @a rhs without storing the elimination matrix $ M_e $. */
-   void EliminateTrialVDofs(const Array<int> &vdofs, const Vector &sol,
-                            Vector &rhs);
-
-   /// Eliminate the given trial @a vdofs, storing the eliminated part internally in $ M_e $.
-   /** This method works in conjunction with EliminateTrialVDofsInRHS() and allows
-       elimination of boundary conditions in multiple right-hand sides. In this
-       method, @a vdofs is a list of DOFs. */
-   void EliminateTrialVDofs(const Array<int> &vdofs);
-
-   /** @brief Use the stored eliminated part of the matrix (see
-       EliminateTrialVDofs(const Array<int> &)) to modify the r.h.s.
-       @a b; @a vdofs is a list of DOFs (non-directional, i.e. >= 0). */
-   void EliminateTrialVDofsInRHS(const Array<int> &vdofs, const Vector &x,
-                                 Vector &b);
-
-   /** @brief Similar to
-      EliminateTrialVDofs(const Array<int> &, const Vector &, Vector &)
-      but here @a ess_dofs is a marker (boolean) array on all vector-dofs
-      (@a ess_dofs[i] < 0 is true). */
+   /// Eliminate the list of DOFs from the columns of the system.
+   /** @a marked_vdofs is the of colunm numbers that will be eliminated.  All
+       entries in the columns will be set to 0.0 through elimination.*/
    void EliminateEssentialBCFromTrialDofs(const Array<int> &marked_vdofs,
                                           const Vector &sol, Vector &rhs);
 
-   /// Eliminate essential boundary test DOFs from the system matrix.
+   /// Eliminate essential boundary DOFs from the rows of the system.
    /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
-       the essential part of the boundary. */
-   void EliminateTestEssentialBC(const Array<int> &bdr_attr_is_ess);
-
-   /// (DEPRECATED) Eliminate essential boundary test DOFs from the system.
-   /** @see EliminateTestEssentialBC() */
-   MFEM_DEPRECATED virtual void EliminateTestDofs(const Array<int>
-                                                  &bdr_attr_is_ess)
-   { EliminateTestEssentialBC(bdr_attr_is_ess); }
-
-   /// Eliminate the given test @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
-   void EliminateTestVDofs(const Array<int> &vdofs);
+       the essential part of the boundary.  All entries in the rows will be
+       set to 0.0 through elimination.*/
+   virtual void EliminateTestDofs(const Array<int> &bdr_attr_is_ess);
 
    /** @brief Return in @a A that is column-constrained.
 
@@ -1273,7 +1178,7 @@ public:
 
    /** @brief Get the output finite element space restriction matrix in
        transposed form. */
-   const Operator *GetOutputRestrictionTranspose() const override
+   virtual const Operator *GetOutputRestrictionTranspose() const
    { return test_fes->GetRestrictionTransposeOperator(); }
 };
 

fem/bilinearform_ext.hpp

@@ -37,19 +37,19 @@ protected:
 public:
    BilinearFormExtension(BilinearForm *form);
 
-   MemoryClass GetMemoryClass() const override
+   virtual MemoryClass GetMemoryClass() const
    { return Device::GetDeviceMemoryClass(); }
 
    /// Get the finite element space prolongation matrix
-   const Operator *GetProlongation() const override;
+   virtual const Operator *GetProlongation() const;
 
    /// Get the finite element space restriction matrix
-   const Operator *GetRestriction() const override;
+   virtual const Operator *GetRestriction() const;
 
    /// Assemble at the level given for the BilinearFormExtension subclass
    virtual void Assemble() = 0;
 
-   void AssembleDiagonal(Vector &diag) const override
+   virtual void AssembleDiagonal(Vector &diag) const
    {
       MFEM_ABORT("AssembleDiagonal not implemented for this assembly level!");
    }
@@ -83,17 +83,16 @@ protected:
 public:
    PABilinearFormExtension(BilinearForm*);
 
-   void Assemble() override;
-   void AssembleDiagonal(Vector &diag) const override;
-   void FormSystemMatrix(const Array<int> &ess_tdof_list,
-                         OperatorHandle &A) override;
+   void Assemble();
+   void AssembleDiagonal(Vector &diag) const;
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
    void FormLinearSystem(const Array<int> &ess_tdof_list,
                          Vector &x, Vector &b,
                          OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0) override;
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
-   void Update() override;
+                         int copy_interior = 0);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+   void Update();
 
 protected:
    void SetupRestrictionOperators(const L2FaceValues m);
@@ -151,9 +150,9 @@ protected:
 public:
    EABilinearFormExtension(BilinearForm *form);
 
-   void Assemble() override;
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
+   void Assemble();
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
 };
 
 /// Data and methods for fully-assembled bilinear forms
@@ -166,19 +165,18 @@ private:
 public:
    FABilinearFormExtension(BilinearForm *form);
 
-   void Assemble() override;
+   void Assemble();
    void RAP(OperatorHandle &A);
    /** @note Always does `DIAG_ONE` policy to be consistent with
        `Operator::FormConstrainedSystemOperator`. */
    void EliminateBC(const Array<int> &ess_dofs, OperatorHandle &A);
-   void FormSystemMatrix(const Array<int> &ess_tdof_list,
-                         OperatorHandle &A) override;
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
    void FormLinearSystem(const Array<int> &ess_tdof_list,
                          Vector &x, Vector &b,
                          OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0) override;
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
+                         int copy_interior = 0);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
 
    /** DGMult and DGMultTranspose use the extended L-vector to perform the
        computation. */
@@ -201,17 +199,16 @@ protected:
 public:
    MFBilinearFormExtension(BilinearForm *form);
 
-   void Assemble() override;
-   void AssembleDiagonal(Vector &diag) const override;
-   void FormSystemMatrix(const Array<int> &ess_tdof_list,
-                         OperatorHandle &A) override;
+   void Assemble();
+   void AssembleDiagonal(Vector &diag) const;
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
    void FormLinearSystem(const Array<int> &ess_tdof_list,
                          Vector &x, Vector &b,
                          OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0) override;
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
-   void Update() override;
+                         int copy_interior = 0);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+   void Update();
 };
 
 /// Class extending the MixedBilinearForm class to support different AssemblyLevels.
@@ -228,20 +225,20 @@ protected:
 public:
    MixedBilinearFormExtension(MixedBilinearForm *form);
 
-   MemoryClass GetMemoryClass() const override
+   virtual MemoryClass GetMemoryClass() const
    { return Device::GetMemoryClass(); }
 
    /// Get the finite element space prolongation matrix
-   const Operator *GetProlongation() const override;
+   virtual const Operator *GetProlongation() const;
 
    /// Get the finite element space restriction matrix
-   const Operator *GetRestriction() const override;
+   virtual const Operator *GetRestriction() const;
 
    /// Get the output finite element space restriction matrix
-   const Operator *GetOutputProlongation() const override;
+   virtual const Operator *GetOutputProlongation() const;
 
    /// Get the output finite element space restriction matrix
-   const Operator *GetOutputRestriction() const override;
+   virtual const Operator *GetOutputRestriction() const;
 
    virtual void Assemble() = 0;
    virtual void FormRectangularSystemOperator(const Array<int> &trial_tdof_list,
@@ -276,7 +273,7 @@ public:
    PAMixedBilinearFormExtension(MixedBilinearForm *form);
 
    /// Partial assembly of all internal integrators
-   void Assemble() override;
+   void Assemble();
    /**
       @brief Setup OperatorHandle A to contain constrained linear operator
 
@@ -286,7 +283,7 @@ public:
    */
    void FormRectangularSystemOperator(const Array<int> &trial_tdof_list,
                                       const Array<int> &test_tdof_list,
-                                      OperatorHandle &A) override;
+                                      OperatorHandle &A);
    /**
       Setup OperatorHandle A to contain constrained linear operator and
       eliminate columns corresponding to essential dofs from system,
@@ -295,21 +292,20 @@ public:
    void FormRectangularLinearSystem(const Array<int> &trial_tdof_list,
                                     const Array<int> &test_tdof_list,
                                     Vector &x, Vector &b,
-                                    OperatorHandle &A, Vector &X, Vector &B) override;
+                                    OperatorHandle &A, Vector &X, Vector &B);
    /// y = A*x
-   void Mult(const Vector &x, Vector &y) const override;
+   void Mult(const Vector &x, Vector &y) const;
    /// y += c*A*x
-   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const override;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
    /// y = A^T*x
-   void MultTranspose(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const;
    /// y += c*A^T*x
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const real_t c=1.0) const override;
+   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
    /// Assemble the diagonal of ADA^T for a diagonal vector D.
-   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const override;
+   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
 
    /// Update internals for when a new MixedBilinearForm is given to this class
-   void Update() override;
+   void Update();
 };
 
 
@@ -326,17 +322,16 @@ public:
    PADiscreteLinearOperatorExtension(DiscreteLinearOperator *linop);
 
    /// Partial assembly of all internal integrators
-   void Assemble() override;
+   void Assemble();
 
-   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const override;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
 
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const real_t c=1.0) const override;
+   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
 
    void FormRectangularSystemOperator(const Array<int>&, const Array<int>&,
-                                      OperatorHandle& A) override;
+                                      OperatorHandle& A);
 
-   const Operator * GetOutputRestrictionTranspose() const override;
+   const Operator * GetOutputRestrictionTranspose() const;
 
 private:
    Vector test_multiplicity;

fem/bilininteg.cpp

@@ -170,16 +170,6 @@ void BilinearFormIntegrator::AssembleFaceMatrix(
               "   is not implemented for this class.");
 }
 
-void BilinearFormIntegrator::AssembleFaceMatrix(
-   const FiniteElement &trial_fe1, const FiniteElement &test_fe1,
-   const FiniteElement &trial_fe2, const FiniteElement &test_fe2,
-   FaceElementTransformations &Trans,
-   DenseMatrix &elmat)
-{
-   MFEM_ABORT("AssembleFaceMatrix (mixed form) is not implemented for this"
-              " Integrator class.");
-}
-
 void BilinearFormIntegrator::AssembleFaceMatrix(
    const FiniteElement &trial_face_fe, const FiniteElement &test_fe1,
    const FiniteElement &test_fe2, FaceElementTransformations &Trans,
@@ -233,38 +223,28 @@ void TransposeIntegrator::SetIntRule(const IntegrationRule *ir)
    bfi->SetIntRule(ir);
 }
 
-void TransposeIntegrator::AssembleElementMatrix(
+void TransposeIntegrator::AssembleElementMatrix (
    const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
-   bfi->AssembleElementMatrix(el, Trans, bfi_elmat);
+   bfi -> AssembleElementMatrix (el, Trans, bfi_elmat);
    // elmat = bfi_elmat^t
    elmat.Transpose (bfi_elmat);
 }
 
-void TransposeIntegrator::AssembleElementMatrix2(
+void TransposeIntegrator::AssembleElementMatrix2 (
    const FiniteElement &trial_fe, const FiniteElement &test_fe,
    ElementTransformation &Trans, DenseMatrix &elmat)
 {
-   bfi->AssembleElementMatrix2(test_fe, trial_fe, Trans, bfi_elmat);
+   bfi -> AssembleElementMatrix2 (test_fe, trial_fe, Trans, bfi_elmat);
    // elmat = bfi_elmat^t
    elmat.Transpose (bfi_elmat);
 }
 
-void TransposeIntegrator::AssembleFaceMatrix(
+void TransposeIntegrator::AssembleFaceMatrix (
    const FiniteElement &el1, const FiniteElement &el2,
    FaceElementTransformations &Trans, DenseMatrix &elmat)
 {
-   bfi->AssembleFaceMatrix(el1, el2, Trans, bfi_elmat);
-   // elmat = bfi_elmat^t
-   elmat.Transpose (bfi_elmat);
-}
-
-void TransposeIntegrator::AssembleFaceMatrix(
-   const FiniteElement &tr_el1, const FiniteElement &te_el1,
-   const FiniteElement &tr_el2, const FiniteElement &te_el2,
-   FaceElementTransformations &Trans, DenseMatrix &elmat)
-{
-   bfi->AssembleFaceMatrix(te_el1, tr_el1, te_el2, tr_el2, Trans, bfi_elmat);
+   bfi -> AssembleFaceMatrix (el1, el2, Trans, bfi_elmat);
    // elmat = bfi_elmat^t
    elmat.Transpose (bfi_elmat);
 }
@@ -3518,150 +3498,6 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
    }
 }
 
-void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &trial_fe1,
-                                           const FiniteElement &test_fe1,
-                                           const FiniteElement &trial_fe2,
-                                           const FiniteElement &test_fe2,
-                                           FaceElementTransformations &Trans,
-                                           DenseMatrix &elmat)
-{
-   int tr_ndof1, te_ndof1, tr_ndof2, te_ndof2;
-
-   real_t un, a, b, w;
-
-   dim = test_fe1.GetDim();
-   tr_ndof1 = trial_fe1.GetDof();
-   te_ndof1 = test_fe1.GetDof();
-   Vector vu(dim), nor(dim);
-
-   if (Trans.Elem2No >= 0)
-   {
-      tr_ndof2 = trial_fe2.GetDof();
-      te_ndof2 = test_fe2.GetDof();
-   }
-   else
-   {
-      tr_ndof2 = 0;
-      te_ndof2 = 0;
-   }
-
-   tr_shape1.SetSize(tr_ndof1);
-   te_shape1.SetSize(te_ndof1);
-   tr_shape2.SetSize(tr_ndof2);
-   te_shape2.SetSize(te_ndof2);
-   elmat.SetSize(te_ndof1 + te_ndof2, tr_ndof1 + tr_ndof2);
-   elmat = 0.0;
-
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      // Assuming order(u)==order(mesh)
-      if (Trans.Elem2No >= 0)
-         order = (min(Trans.Elem1->OrderW(), Trans.Elem2->OrderW()) +
-                  max(trial_fe1.GetOrder(), trial_fe2.GetOrder()) +
-                  max(test_fe1.GetOrder(), test_fe2.GetOrder()));
-      else
-      {
-         order = Trans.Elem1->OrderW() + trial_fe1.GetOrder() + test_fe1.GetOrder();
-      }
-      if (trial_fe1.Space() == FunctionSpace::Pk)
-      {
-         order++;
-      }
-      ir = &IntRules.Get(Trans.FaceGeom, order);
-   }
-
-   for (int p = 0; p < ir->GetNPoints(); p++)
-   {
-      const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip1, eip2;
-      Trans.Loc1.Transform(ip, eip1);
-      Trans.Elem1->SetIntPoint(&eip1);
-      if (tr_ndof2 && te_ndof2)
-      {
-         Trans.Loc2.Transform(ip, eip2);
-         Trans.Elem2->SetIntPoint(&eip2);
-      }
-      trial_fe1.CalcPhysShape(*Trans.Elem1, tr_shape1);
-      test_fe1.CalcPhysShape(*Trans.Elem1, te_shape1);
-
-      Trans.Face->SetIntPoint(&ip);
-
-      u->Eval(vu, *Trans.Elem1, eip1);
-
-      if (dim == 1)
-      {
-         nor(0) = 2*eip1.x - 1.0;
-      }
-      else
-      {
-         CalcOrtho(Trans.Face->Jacobian(), nor);
-      }
-
-      un = vu * nor;
-      a = 0.5 * alpha * un;
-      b = beta * fabs(un);
-      // note: if |alpha/2|==|beta| then |a|==|b|, i.e. (a==b) or (a==-b)
-      //       and therefore two blocks in the element matrix contribution
-      //       (from the current quadrature point) are 0
-
-      if (rho)
-      {
-         real_t rho_p;
-         if (un >= 0.0 && tr_ndof2 && te_ndof2)
-         {
-            Trans.Elem2->SetIntPoint(&eip2);
-            rho_p = rho->Eval(*Trans.Elem2, eip2);
-         }
-         else
-         {
-            rho_p = rho->Eval(*Trans.Elem1, eip1);
-         }
-         a *= rho_p;
-         b *= rho_p;
-      }
-
-      w = ip.weight * (a+b);
-      if (w != 0.0)
-      {
-         for (int i = 0; i < te_ndof1; i++)
-            for (int j = 0; j < tr_ndof1; j++)
-            {
-               elmat(i, j) += w * te_shape1(i) * tr_shape1(j);
-            }
-      }
-
-      if (tr_ndof2 && te_ndof2)
-      {
-         trial_fe2.CalcPhysShape(*Trans.Elem2, tr_shape2);
-         test_fe2.CalcPhysShape(*Trans.Elem2, te_shape2);
-
-         if (w != 0.0)
-            for (int i = 0; i < te_ndof2; i++)
-               for (int j = 0; j < tr_ndof1; j++)
-               {
-                  elmat(te_ndof1+i, j) -= w * te_shape2(i) * tr_shape1(j);
-               }
-
-         w = ip.weight * (b-a);
-         if (w != 0.0)
-         {
-            for (int i = 0; i < te_ndof2; i++)
-               for (int j = 0; j < tr_ndof2; j++)
-               {
-                  elmat(te_ndof1+i, tr_ndof1+j) += w * te_shape2(i) * tr_shape2(j);
-               }
-
-            for (int i = 0; i < te_ndof1; i++)
-               for (int j = 0; j < tr_ndof2; j++)
-               {
-                  elmat(i, tr_ndof1+j) -= w * te_shape1(i) * tr_shape2(j);
-               }
-         }
-      }
-   }
-}
 
 const IntegrationRule &DGTraceIntegrator::GetRule(
    Geometry::Type geom, int order, FaceElementTransformations &T)
@@ -4554,8 +4390,8 @@ struct ShapeCoefficient : public VectorCoefficient
       : VectorCoefficient(fe_.GetDof()), Q(q), fe(fe_) { }
 
    using VectorCoefficient::Eval;
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    {
       V.SetSize(vdim);
       fe.CalcPhysShape(T, V);
@@ -4597,8 +4433,8 @@ ScalarVectorProductInterpolator::AssembleElementMatrix2(
       VShapeCoefficient(Coefficient &q, const FiniteElement &fe_, int sdim)
          : MatrixCoefficient(fe_.GetDof(), sdim), Q(q), fe(fe_) { }
 
-      void Eval(DenseMatrix &M, ElementTransformation &T,
-                const IntegrationPoint &ip) override
+      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                        const IntegrationPoint &ip)
       {
          M.SetSize(height, width);
          fe.CalcPhysVShape(T, M);
@@ -4634,8 +4470,8 @@ VectorScalarProductInterpolator::AssembleElementMatrix2(
          : MatrixCoefficient(fe_.GetDof(), vq.GetVDim()), VQ(vq), fe(fe_),
            vc(width), shape(height) { }
 
-      void Eval(DenseMatrix &M, ElementTransformation &T,
-                const IntegrationPoint &ip) override
+      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                        const IntegrationPoint &ip)
       {
          M.SetSize(height, width);
          VQ.Eval(vc, T, ip);
@@ -4674,8 +4510,8 @@ ScalarCrossProductInterpolator::AssembleElementMatrix2(
            vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }
 
       using VectorCoefficient::Eval;
-      void Eval(Vector &V, ElementTransformation &T,
-                const IntegrationPoint &ip) override
+      virtual void Eval(Vector &V, ElementTransformation &T,
+                        const IntegrationPoint &ip)
       {
          V.SetSize(vdim);
          VQ.Eval(vc, T, ip);
@@ -4718,8 +4554,8 @@ VectorCrossProductInterpolator::AssembleElementMatrix2(
          MFEM_ASSERT(width == 3, "");
       }
 
-      void Eval(DenseMatrix &M, ElementTransformation &T,
-                const IntegrationPoint &ip) override
+      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                        const IntegrationPoint &ip)
       {
          M.SetSize(height, width);
          VQ.Eval(vc, T, ip);
@@ -4767,8 +4603,8 @@ struct VDotVShapeCoefficient : public VectorCoefficient
         vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }
 
    using VectorCoefficient::Eval;
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    {
       V.SetSize(vdim);
       VQ.Eval(vc, T, ip);

fem/coefficient.hpp

@@ -90,12 +90,12 @@ public:
    explicit ConstantCoefficient(real_t c = 1.0) { constant=c; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    { return (constant); }
 
    /// Fill the QuadratureFunction @a qf with the constant value.
-   void Project(QuadratureFunction &qf) override;
+   void Project(QuadratureFunction &qf);
 };
 
 /** @brief A piecewise constant coefficient with the constants keyed
@@ -130,8 +130,8 @@ public:
    int GetNConst() { return constants.Size(); }
 
    /// Evaluate the coefficient.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /** @brief A piecewise coefficient with the pieces keyed off the element
@@ -195,7 +195,7 @@ public:
    { InitMap(attr, coefs); }
 
    /// Set the time for time dependent coefficients
-   void SetTime(real_t t) override;
+   virtual void SetTime(real_t t);
 
    /// Replace a set of coefficients
    void UpdateCoefficients(const Array<int> & attr,
@@ -211,8 +211,8 @@ public:
    { pieces.erase(attr); }
 
    /// Evaluate the coefficient.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// A general function coefficient
@@ -254,8 +254,8 @@ public:
    }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// A common base class for returning individual components of the domain's
@@ -271,8 +271,8 @@ protected:
 
 public:
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient which returns the x-component of the evaluation point
@@ -307,8 +307,8 @@ public:
    CylindricalRadialCoefficient() : transip(3) {}
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient which returns the angular position or azimuth (often
@@ -323,8 +323,8 @@ public:
    CylindricalAzimuthalCoefficient() : transip(3) {}
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient which returns the height or altitude of
@@ -342,8 +342,8 @@ public:
    SphericalRadialCoefficient() : transip(3) {}
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient which returns the azimuthal angle (often denoted by phi)
@@ -357,8 +357,8 @@ public:
    SphericalAzimuthalCoefficient() : transip(3) {}
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient which returns the polar angle (often denoted by theta)
@@ -372,8 +372,8 @@ public:
    SphericalPolarCoefficient() : transip(3) {}
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 class GridFunction;
@@ -399,15 +399,15 @@ public:
    const GridFunction * GetGridFunction() const { return GridF; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 
    /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
    /// the quadrature points.
    ///
    /// This function uses the efficient QuadratureFunction::ProjectGridFunction
    /// to fill the QuadratureFunction.
-   void Project(QuadratureFunction &qf) override;
+   virtual void Project(QuadratureFunction &qf);
 };
 
 
@@ -433,10 +433,10 @@ public:
       : Q1(q1), Q2(q2), Transform2(std::move(F)) { Transform1 = 0; }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 /** @brief Delta function coefficient optionally multiplied by a weight
@@ -488,7 +488,7 @@ public:
    }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Set the center location of the delta function.
    void SetDeltaCenter(const Vector& center);
@@ -534,7 +534,7 @@ public:
    virtual real_t EvalDelta(ElementTransformation &T, const IntegrationPoint &ip);
    /** @brief A DeltaFunction cannot be evaluated. Calling this method will
        cause an MFEM error, terminating the application. */
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    { mfem_error("DeltaCoefficient::Eval"); return 0.; }
    virtual ~DeltaCoefficient() { delete weight; }
 };
@@ -555,10 +555,10 @@ public:
    { c = &c_; attr.Copy(active_attr); }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    { return active_attr[T.Attribute-1] ? c->Eval(T, ip, GetTime()) : 0.0; }
 };
 
@@ -628,8 +628,8 @@ public:
    using VectorCoefficient::Eval;
 
    ///  Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override { V = vec; }
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip) { V = vec; }
 
    /// Return a reference to the constant vector in this class.
    const Vector& GetVec() const { return vec; }
@@ -698,7 +698,7 @@ public:
       : VectorCoefficient(vd) { InitMap(attr, coefs); }
 
    /// Set the time for time dependent coefficients
-   void SetTime(real_t t) override;
+   virtual void SetTime(real_t t);
 
    /// Replace a set of coefficients
    void UpdateCoefficients(const Array<int> & attr,
@@ -713,8 +713,8 @@ public:
    { pieces.erase(attr); }
 
    /// Evaluate the coefficient.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -728,8 +728,8 @@ public:
 
    using VectorCoefficient::Eval;
    /// Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    virtual ~PositionVectorCoefficient() { }
 };
@@ -765,8 +765,8 @@ public:
 
    using VectorCoefficient::Eval;
    /// Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    virtual ~VectorFunctionCoefficient() { }
 };
@@ -787,7 +787,7 @@ public:
    explicit VectorArrayCoefficient(int dim);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Returns i'th coefficient.
    Coefficient* GetCoeff(int i) { return Coeff[i]; }
@@ -806,8 +806,8 @@ public:
    using VectorCoefficient::Eval;
    /** @brief Evaluate the coefficient. Each element of vector V comes from the
        associated array of scalar coefficients. */
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    /// Destroys vector coefficient.
    virtual ~VectorArrayCoefficient();
@@ -836,21 +836,21 @@ public:
    const GridFunction * GetGridFunction() const { return GridFunc; }
 
    /// Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    /** @brief Evaluate the vector coefficients at all of the locations in the
        integration rule and write the vectors into the columns of matrix @a
        M. */
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationRule &ir) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationRule &ir);
 
    /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
    /// the quadrature points.
    ///
    /// This function uses the efficient QuadratureFunction::ProjectGridFunction
    /// to fill the QuadratureFunction.
-   void Project(QuadratureFunction &qf) override;
+   virtual void Project(QuadratureFunction &qf);
 
    virtual ~VectorGridFunctionCoefficient() { }
 };
@@ -874,14 +874,14 @@ public:
    const GridFunction * GetGridFunction() const { return GridFunc; }
 
    /// Evaluate the gradient vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    /** @brief Evaluate the gradient vector coefficient at all of the locations
        in the integration rule and write the vectors into columns of matrix @a
        M. */
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationRule &ir) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationRule &ir);
 
    virtual ~GradientGridFunctionCoefficient() { }
 };
@@ -905,8 +905,8 @@ public:
 
    using VectorCoefficient::Eval;
    /// Evaluate the vector curl coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    virtual ~CurlGridFunctionCoefficient() { }
 };
@@ -929,8 +929,8 @@ public:
    const GridFunction * GetGridFunction() const { return GridFunc; }
 
    /// Evaluate the scalar divergence coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 
    virtual ~DivergenceGridFunctionCoefficient() { }
 };
@@ -973,7 +973,7 @@ public:
       : VectorCoefficient(dir_.Size()), dir(dir_), d(x,y,z,s) { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Replace the associated DeltaCoefficient with a new DeltaCoefficient.
    /** The new DeltaCoefficient cannot have a specified weight Coefficient, i.e.
@@ -998,8 +998,8 @@ public:
    using VectorCoefficient::Eval;
    /** @brief A VectorDeltaFunction cannot be evaluated. Calling this method
        will cause an MFEM error, terminating the application. */
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
    { mfem_error("VectorDeltaCoefficient::Eval"); }
    virtual ~VectorDeltaCoefficient() { }
 };
@@ -1021,17 +1021,17 @@ public:
    { c = &vc; attr.Copy(active_attr); }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    /** @brief Evaluate the vector coefficient at all of the locations in the
        integration rule and write the vectors into the columns of matrix @a
        M. */
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationRule &ir) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationRule &ir);
 };
 
 typedef VectorCoefficient DiagonalMatrixCoefficient;
@@ -1113,8 +1113,8 @@ public:
       : MatrixCoefficient(m.Height(), m.Width()), mat(m) { }
    using MatrixCoefficient::Eval;
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override { M = mat; }
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip) { M = mat; }
    /// Return a reference to the constant matrix.
    const DenseMatrix& GetMatrix() { return mat; }
 };
@@ -1207,7 +1207,7 @@ public:
       : MatrixCoefficient(h, w, symm) { InitMap(attr, coefs); }
 
    /// Set the time for time dependent coefficients
-   void SetTime(real_t t) override;
+   virtual void SetTime(real_t t);
 
    /// Replace a set of coefficients
    void UpdateCoefficients(const Array<int> & attr,
@@ -1222,8 +1222,8 @@ public:
    { pieces.erase(attr); }
 
    /// Evaluate the coefficient.
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /** @brief A matrix coefficient with an optional scalar coefficient multiplier
@@ -1280,16 +1280,16 @@ public:
    { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    /// (DEPRECATED) Evaluate the symmetric matrix coefficient at @a ip.
    /** @deprecated Use Eval() instead. */
-   void EvalSymmetric(Vector &K, ElementTransformation &T,
-                      const IntegrationPoint &ip) override;
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip);
 
    virtual ~MatrixFunctionCoefficient() { }
 };
@@ -1310,7 +1310,7 @@ public:
    explicit MatrixArrayCoefficient (int dim);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Get the coefficient located at (i,j) in the matrix.
    Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }
@@ -1328,8 +1328,8 @@ public:
    { return Coeff[i*width+j] ? Coeff[i*width+j] -> Eval(T, ip, GetTime()) : 0.0; }
 
    /// Evaluate the matrix coefficient @a ip.
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    virtual ~MatrixArrayCoefficient();
 };
@@ -1392,11 +1392,11 @@ public:
    { c = &mc; attr.Copy(active_attr); }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Coefficients based on sums, products, or other functions of coefficients.
@@ -1425,7 +1425,7 @@ public:
       : aConst(0.0), a(&A), b(&B), alpha(alpha_), beta(beta_) { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first term in the linear combination as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1453,8 +1453,8 @@ public:
    real_t GetBeta() const { return beta; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    {
       return alpha * ((a == NULL ) ? aConst : a->Eval(T, ip) )
              + beta * b->Eval(T, ip);
@@ -1502,8 +1502,8 @@ public:
        @note When this method is called, the caller must make sure that the
        IntegrationPoint associated with @a T is the same as @a ip. This can be
        achieved by calling T.SetIntPoint(&ip). */
-   void Eval(DenseMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
 
    /// @deprecated Return a reference to the internal matrix used when evaluating this coefficient as a DenseMatrix.
@@ -1525,8 +1525,8 @@ public:
       : SymmetricMatrixCoefficient(m.Height()), mat(m) { }
    using SymmetricMatrixCoefficient::Eval;
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override { M = mat; }
+   virtual void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip) { M = mat; }
 
    /// Return a reference to the constant matrix.
    const DenseSymmetricMatrix& GetMatrix() { return mat; }
@@ -1576,12 +1576,12 @@ public:
    { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    using SymmetricMatrixCoefficient::Eval;
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
    virtual ~SymmetricMatrixFunctionCoefficient() { }
 };
@@ -1606,7 +1606,7 @@ public:
       : aConst(0.0), a(&A), b(&B) { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first term in the product as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1624,8 +1624,8 @@ public:
    Coefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    { return ((a == NULL ) ? aConst : a->Eval(T, ip) ) * b->Eval(T, ip); }
 };
 
@@ -1654,7 +1654,7 @@ public:
       : aConst(0.0), bConst(B), a(&A), b(NULL) { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the numerator in the ratio as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1677,8 +1677,8 @@ public:
    Coefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    {
       real_t den = (b == NULL ) ? bConst : b->Eval(T, ip);
       MFEM_ASSERT(den != 0.0, "Division by zero in RatioCoefficient");
@@ -1700,7 +1700,7 @@ public:
       : a(&A), p(p_) { }
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the base coefficient
    void SetACoef(Coefficient &A) { a = &A; }
@@ -1713,8 +1713,8 @@ public:
    real_t GetExponent() const { return p; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
    { return pow(a->Eval(T, ip), p); }
 };
 
@@ -1733,7 +1733,7 @@ public:
    InnerProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first vector in the inner product
    void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1746,8 +1746,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient defined as a cross product of two vectors in the xy-plane.
@@ -1765,7 +1765,7 @@ public:
    VectorRotProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first vector in the product
    void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1778,8 +1778,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient defined as the determinant of a matrix coefficient
@@ -1795,7 +1795,7 @@ public:
    DeterminantCoefficient(MatrixCoefficient &A);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -1803,8 +1803,8 @@ public:
    MatrixCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the determinant coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Scalar coefficient defined as the trace of a matrix coefficient
@@ -1820,7 +1820,7 @@ public:
    TraceCoefficient(MatrixCoefficient &A);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -1828,8 +1828,8 @@ public:
    MatrixCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the trace coefficient at @a ip.
-   real_t Eval(ElementTransformation &T,
-               const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
 };
 
 /// Vector coefficient defined as the linear combination of two vectors
@@ -1866,7 +1866,7 @@ public:
                         Coefficient &alpha_, Coefficient &beta_);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first vector coefficient
    void SetACoef(VectorCoefficient &A_) { ACoef = &A_; }
@@ -1909,8 +1909,8 @@ public:
    real_t GetBeta() const { return beta; }
 
    /// Evaluate the coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -1930,7 +1930,7 @@ public:
    ScalarVectorProductCoefficient(Coefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the scalar factor as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1948,8 +1948,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -1971,7 +1971,7 @@ public:
    NormalizedVectorCoefficient(VectorCoefficient &A, real_t tol = 1e-6);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the vector coefficient
    void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1979,8 +1979,8 @@ public:
    VectorCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -1999,7 +1999,7 @@ public:
    VectorCrossProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first term in the product
    void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -2012,8 +2012,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -2033,7 +2033,7 @@ public:
    MatrixVectorProductCoefficient(MatrixCoefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2046,8 +2046,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the vector coefficient at @a ip.
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
 };
 
@@ -2066,8 +2066,8 @@ public:
       : MatrixCoefficient(d, d), dim(d) { }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the linear combination of two matrices
@@ -2088,7 +2088,7 @@ public:
                         real_t alpha_ = 1.0, real_t beta_ = 1.0);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2111,8 +2111,8 @@ public:
    real_t GetBeta() const { return beta; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the product of two matrices
@@ -2140,8 +2140,8 @@ public:
    MatrixCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /** @brief Matrix coefficient defined as a product of a scalar coefficient and a
@@ -2161,7 +2161,7 @@ public:
    ScalarMatrixProductCoefficient(Coefficient &A, MatrixCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the scalar factor as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -2179,8 +2179,8 @@ public:
    MatrixCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the transpose of a matrix coefficient
@@ -2194,7 +2194,7 @@ public:
    TransposeMatrixCoefficient(MatrixCoefficient &A);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2202,8 +2202,8 @@ public:
    MatrixCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the inverse of a matrix coefficient.
@@ -2217,7 +2217,7 @@ public:
    InverseMatrixCoefficient(MatrixCoefficient &A);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2225,8 +2225,8 @@ public:
    MatrixCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the exponential of a matrix coefficient.
@@ -2240,7 +2240,7 @@ public:
    ExponentialMatrixCoefficient(MatrixCoefficient &A);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the matrix coefficient
    void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2248,8 +2248,8 @@ public:
    MatrixCoefficient * GetACoef() const { return a; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /// Matrix coefficient defined as the outer product of two vector coefficients.
@@ -2267,7 +2267,7 @@ public:
    OuterProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the first vector in the outer product
    void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -2280,8 +2280,8 @@ public:
    VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 
 /** @brief Matrix coefficient defined as -a k x k x, for a vector k and scalar a
@@ -2305,7 +2305,7 @@ public:
    CrossCrossCoefficient(Coefficient &A, VectorCoefficient &K);
 
    /// Set the time for internally stored coefficients
-   void SetTime(real_t t) override;
+   void SetTime(real_t t);
 
    /// Reset the scalar factor as a constant
    void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -2323,8 +2323,8 @@ public:
    VectorCoefficient * GetKCoef() const { return k; }
 
    /// Evaluate the matrix coefficient at @a ip.
-   void Eval(DenseMatrix &M, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 };
 ///@}
 
@@ -2349,10 +2349,10 @@ public:
    const QuadratureFunction& GetQuadFunction() const { return QuadF; }
 
    using VectorCoefficient::Eval;
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
 
-   void Project(QuadratureFunction &qf) override;
+   virtual void Project(QuadratureFunction &qf);
 
    virtual ~VectorQuadratureFunctionCoefficient() { }
 };
@@ -2371,9 +2371,9 @@ public:
 
    const QuadratureFunction& GetQuadFunction() const { return QuadF; }
 
-   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 
-   void Project(QuadratureFunction &qf) override;
+   virtual void Project(QuadratureFunction &qf);
 
    virtual ~QuadratureFunctionCoefficient() { }
 };

fem/datacollection.hpp

@@ -454,28 +454,28 @@ public:
 #endif
 
    /// Set/change the mesh associated with the collection
-   void SetMesh(Mesh *new_mesh) override;
+   virtual void SetMesh(Mesh *new_mesh) override;
 
 #ifdef MFEM_USE_MPI
    /// Set/change the mesh associated with the collection.
-   void SetMesh(MPI_Comm comm, Mesh *new_mesh) override;
+   virtual void SetMesh(MPI_Comm comm, Mesh *new_mesh) override;
 #endif
 
    /// Add a grid function to the collection and update the root file
-   void RegisterField(const std::string& field_name,
-                      GridFunction *gf) override;
+   virtual void RegisterField(const std::string& field_name,
+                              GridFunction *gf) override;
 
    /// Add a quadrature function to the collection and update the root file.
    /** Visualization of quadrature function is not supported in VisIt(3.12).
        A patch has been sent to VisIt developers in June 2020. */
-   void RegisterQField(const std::string& q_field_name,
-                       QuadratureFunction *qf) override;
+   virtual void RegisterQField(const std::string& q_field_name,
+                               QuadratureFunction *qf) override;
 
    /// Set the number of digits used for both the cycle and the MPI rank
    /// @note VisIt seems to require 6 pad digits for the MPI rank. Therefore,
    /// this function uses this default value. This behavior can be overridden
    /// by calling SetPadDigitsCycle() and SetPadDigitsRank() instead.
-   void SetPadDigits(int digits) override
+   virtual void SetPadDigits(int digits) override
    { pad_digits_cycle=digits; pad_digits_rank=6; }
 
    /// Set VisIt parameter: default levels of detail for the MultiresControl
@@ -489,13 +489,13 @@ public:
    void DeleteAll();
 
    /// Save the collection and a VisIt root file
-   void Save() override;
+   virtual void Save() override;
 
    /// Save a VisIt root file for the collection
    void SaveRootFile();
 
    /// Load the collection based on its VisIt data (described in its root file)
-   void Load(int cycle_ = 0) override;
+   virtual void Load(int cycle_ = 0) override;
 
    /// We will delete the mesh and fields if we own them
    virtual ~VisItDataCollection() {}
@@ -546,7 +546,7 @@ public:
 
    /// Save the collection - the directory name is constructed based on the
    /// cycle value
-   void Save() override;
+   virtual void Save() override;
 
    /// Set the data format for the ParaView output files. Possible options are
    /// VTKFormat::ASCII, VTKFormat::BINARY, and VTKFormat::BINARY32.
@@ -590,7 +590,7 @@ public:
    void UseRestartMode(bool restart_mode_);
 
    /// Load the collection - not implemented in the ParaView writer
-   void Load(int cycle_ = 0) override;
+   virtual void Load(int cycle_ = 0) override;
 };
 
 }

fem/eltrans.hpp

@@ -385,10 +385,10 @@ private:
 
    /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
        store it in dFdx. */
-   const DenseMatrix &EvalJacobian() override;
+   virtual const DenseMatrix &EvalJacobian();
    // Evaluate the Hessian of the transformation at the IntPoint and store it
    // in d2Fdx2.
-   const DenseMatrix &EvalHessian() override;
+   virtual const DenseMatrix &EvalHessian();
 
 public:
    IsoparametricTransformation() : FElem(NULL) {}
@@ -430,32 +430,32 @@ public:
 
    /** @brief Transform integration point from reference coordinates to
        physical coordinates and store them in the vector. */
-   void Transform(const IntegrationPoint &, Vector &) override;
+   virtual void Transform(const IntegrationPoint &, Vector &);
 
    /** @brief Transform all the integration points from the integration rule
        from reference coordinates to physical
       coordinates and store them as column vectors in the matrix. */
-   void Transform(const IntegrationRule &, DenseMatrix &) override;
+   virtual void Transform(const IntegrationRule &, DenseMatrix &);
 
    /** @brief Transform all the integration points from the column vectors
        of @a matrix from reference coordinates to physical
        coordinates and store them as column vectors in @a result. */
-   void Transform(const DenseMatrix &matrix, DenseMatrix &result) override;
+   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
 
    /// Return the order of the current element we are using for the transformation.
-   int Order() const override { return FElem->GetOrder(); }
+   virtual int Order() const { return FElem->GetOrder(); }
 
    /// Return the order of the elements of the Jacobian of the transformation.
-   int OrderJ() const override;
+   virtual int OrderJ() const;
 
    /** @brief Return the order of the determinant of the Jacobian (weight)
        of the transformation. */
-   int OrderW() const override;
+   virtual int OrderW() const;
 
    /// Return the order of $ adj(J)^T \nabla fi $
-   int OrderGrad(const FiniteElement *fe) const override;
+   virtual int OrderGrad(const FiniteElement *fe) const;
 
-   int GetSpaceDim() const override { return PointMat.Height(); }
+   virtual int GetSpaceDim() const { return PointMat.Height(); }
 
    /** @brief Transform a point @a pt from physical space to a point @a ip in
        reference space and optionally can set a solver tolerance using @a phys_tol. */
@@ -463,8 +463,8 @@ public:
        point in physical space. If the inversion fails a non-zero value is
        returned. This method is not 100 percent reliable for non-linear
        transformations. */
-   int TransformBack (const Vector & v, IntegrationPoint & ip,
-                      const real_t phys_rel_tol = tol_0) override
+   virtual int TransformBack(const Vector & v, IntegrationPoint & ip,
+                             const real_t phys_rel_tol = tol_0)
    {
       InverseElementTransformation inv_tr(this);
       inv_tr.SetPhysicalRelTol(phys_rel_tol);
@@ -604,9 +604,9 @@ public:
        has been configured. */
    const IntegrationPoint &GetElement2IntPoint() { return eip2; }
 
-   void Transform(const IntegrationPoint &, Vector &) override;
-   void Transform(const IntegrationRule &, DenseMatrix &) override;
-   void Transform(const DenseMatrix &matrix, DenseMatrix &result) override;
+   virtual void Transform(const IntegrationPoint &, Vector &);
+   virtual void Transform(const IntegrationRule &, DenseMatrix &);
+   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
 
    ElementTransformation & GetElement1Transformation();
    ElementTransformation & GetElement2Transformation();