Demo of error and fix

FindPointsGSLIB for surface meshes

.github/actions/sanitize/mfem/action.yml

@@ -25,7 +25,7 @@ runs:
   steps:
     - uses: ./.github/actions/sanitize/config
 
-    - uses: actions/cache@v4
+    - uses: actions/cache@v5
       if: ${{env.DEBUG == 'true'}}
       id: debug
       with:
@@ -82,7 +82,7 @@ runs:
       run: find . -type f -name '*.o' -delete
       shell: bash
 
-    - uses: actions/upload-artifact@v4
+    - uses: actions/upload-artifact@v7
       with:
         name: build-${{inputs.par}}-${{inputs.sanitizer}}
         path: mfem/build

.github/actions/sanitize/restore/action.yml

@@ -36,7 +36,7 @@ runs:
   steps:
     - uses: ./.github/actions/sanitize/config
 
-    - uses: actions/cache@v4
+    - uses: actions/cache@v5
       if: ${{env.DEBUG == 'true' && inputs.cache-skip != 'true'}}
       id: debug
       with:
@@ -49,7 +49,7 @@ runs:
         par: ${{inputs.par}}
         sanitizer: ${{inputs.sanitizer}}
 
-    - uses: actions/download-artifact@v4
+    - uses: actions/download-artifact@v8
       with:
         name: build-${{inputs.par}}-${{inputs.sanitizer}}
         path: mfem/build

.github/actions/sanitize/setup/action.yml

@@ -23,7 +23,7 @@ inputs:
 runs:
   using: 'composite'
   steps:
-    - uses: actions/cache/restore@v4  # Cache for LLVM libcxx
+    - uses: actions/cache/restore@v5  # Cache for LLVM libcxx
       with:
         path: ${{env.LLVM_DIR}}
         fail-on-cache-miss: true
@@ -32,14 +32,14 @@ runs:
     - uses: ./.github/actions/sanitize/mpi
       if: ${{inputs.par == 'true'}}
 
-    - uses: actions/cache/restore@v4  # Cache for Hypre
+    - uses: actions/cache/restore@v5  # Cache for Hypre
       if: ${{inputs.par == 'true'}}
       with:
         path: ${{env.HYPRE_DIR}}
         fail-on-cache-miss: true
         key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
 
-    - uses: actions/cache/restore@v4  # Cache for Metis
+    - uses: actions/cache/restore@v5  # Cache for Metis
       if: ${{inputs.par == 'true'}}
       with:
         path: ${{env.METIS_DIR}}
@@ -51,13 +51,13 @@ runs:
       run: ln -s -f ${{env.HYPRE_DIR}} hypre && ln -s -f ${{env.METIS_DIR}} metis-4.0
       shell: bash
 
-    - uses: actions/cache/restore@v4  # Cache for LSAN suppression file
+    - uses: actions/cache/restore@v5  # Cache for LSAN suppression file
       with:
         path: ${{env.LSAN_DIR}}
         fail-on-cache-miss: true
         key: build-lsan-suppression-file
 
-    - uses: actions/checkout@v4  # Checkout the repository
+    - uses: actions/checkout@v6  # Checkout the repository
       with:
         path: mfem
         # ref: ${{env.BRANCH}}

.github/workflows/build-container.yml

@@ -43,7 +43,7 @@ jobs:
           remove-docker-images: 'true'
 
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
 
       # It's easier to reference named variables than indexes of the matrix
       - name: Set Environment

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

@@ -153,7 +153,7 @@ jobs:
       # /home/runner/work/mfem/mfem/mfem
       # Note: Done now to access "install-hypre" and "install-metis" actions.
       - name: checkout mfem
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
         with:
           path: ${{ env.MFEM_TOP_DIR }}
           # Fetch the complete history for codecov to access commits ID
@@ -225,7 +225,7 @@ jobs:
       - name: cache hypre
         id: hypre-cache
         if: matrix.mpi == 'par'
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{ env.HYPRE_TOP_DIR }}
           key: ${{ runner.os }}-ompi-build-${{ env.HYPRE_TOP_DIR }}-${{ matrix.hypre-target }}-${{ matrix.precision }}-v2.5
@@ -255,7 +255,7 @@ jobs:
       - name: cache metis
         id: metis-cache
         if: matrix.mpi == 'par' && matrix.os != 'windows-latest'
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{ env.METIS_TOP_DIR }}
           key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.5
@@ -270,7 +270,7 @@ jobs:
       - name: cache vcpkg (Windows)
         id: vcpkg-cache
         if: matrix.os == 'windows-latest'
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: vcpkg_cache
           key: ${{ runner.os }}-${{ matrix.mpi }}-vcpkg-v1
@@ -295,7 +295,8 @@ jobs:
           export HOMEBREW_NO_INSTALL_CLEANUP=1
           brew update
           brew install enzyme
-          ENZYME_LLVM=$(brew info enzyme | sed -n 's/^Required:.*\(llvm[^ ]*\).*/\1/p')
+          ENZYME_LLVM=$(brew info enzyme | sed -n 's/^Required.*:.*\(llvm[^ ]*\).*/\1/p')
+          echo "ENZYME_LLVM=$ENZYME_LLVM"
           LLVM_PREFIX=$(brew --prefix $ENZYME_LLVM)
           echo "LLVM_PREFIX=$LLVM_PREFIX" >> $GITHUB_ENV
           echo "OMPI_CC=$LLVM_PREFIX/bin/clang" >> $GITHUB_ENV

.github/workflows/codeql-analysis.yml

@@ -40,11 +40,11 @@ jobs:
 
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
 
       # Initializes the CodeQL tools for scanning.
       - name: Initialize CodeQL
-        uses: github/codeql-action/init@v2
+        uses: github/codeql-action/init@v4
         with:
           languages: ${{ matrix.language }}
           # If you wish to specify custom queries, you can do so here or in a config file.
@@ -57,7 +57,7 @@ jobs:
       # Autobuild attempts to build any compiled languages  (C/C++, C#, or Java).
       # If this step fails, then you should remove it and run the build manually (see below)
       - name: Autobuild
-        uses: github/codeql-action/autobuild@v2
+        uses: github/codeql-action/autobuild@v4
 
       # ℹ️ Command-line programs to run using the OS shell.
       # 📚 See https://docs.github.com/en/actions/using-workflows/workflow-syntax-for-github-actions#jobsjob_idstepsrun
@@ -70,4 +70,4 @@ jobs:
       #   ./location_of_script_within_repo/buildscript.sh
 
       - name: Perform CodeQL Analysis
-        uses: github/codeql-action/analyze@v2
+        uses: github/codeql-action/analyze@v4

.github/workflows/mfem-analysis.yml

@@ -39,7 +39,7 @@ jobs:
 
     steps:
       - name: checkout MFEM
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
         with:
           path: mfem
 
@@ -50,7 +50,7 @@ jobs:
 
       - name: Cache Hypre Install
         id: hypre-cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{ env.HYPRE_TOP_DIR }}
           key: ${{ runner.os }}-ompi-build-${{ env.HYPRE_TOP_DIR }}-v2.5
@@ -65,7 +65,7 @@ jobs:
 
       - name: Cache Metis Install
         id: metis-cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{ env.METIS_TOP_DIR }}
           key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.5

.github/workflows/repo-check.yml

@@ -38,7 +38,7 @@ jobs:
        github.event.pull_request.head.repo.full_name != github.repository)
     steps:
       - name: checkout mfem
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
 
       - name: copyright check
         id: copyright
@@ -93,7 +93,7 @@ jobs:
        github.event.pull_request.head.repo.full_name != github.repository)
     steps:
       - name: checkout mfem
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
 
       - name: get astyle
         run: |
@@ -110,7 +110,7 @@ jobs:
        github.event.pull_request.head.repo.full_name != github.repository)
     steps:
       - name: checkout mfem
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
 
       - name: get doxygen and graphviz
         run: |
@@ -135,7 +135,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: checkout mfem
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
         with:
           fetch-depth: 0
 

.github/workflows/sanitize-build-hypre.yml

@@ -17,11 +17,11 @@ jobs:
     runs-on: ubuntu-latest
     name: 2.19.0
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
       - name: Cache
         id: cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{env.HYPRE_DIR}}
           key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5

.github/workflows/sanitize-build-libcxx.yml

@@ -27,13 +27,13 @@ jobs:
             llvm_use_sanitizer: "Undefined"
     name: ${{matrix.sanitizer}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
         with:
           NO_FLAGS: true
       - name: Cache
         id: cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{env.LLVM_DIR}}
           key: build-libcxx-${{env.LLVM_VER}}-${{matrix.sanitizer}}

.github/workflows/sanitize-build-lsan.yml

@@ -17,11 +17,11 @@ jobs:
     runs-on: ubuntu-latest
     name: lsan.supp
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
       - name: Cache
         id: cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{env.LSAN_DIR}}
           key: build-lsan-suppression-file

.github/workflows/sanitize-build-metis.yml

@@ -17,11 +17,11 @@ jobs:
     runs-on: ubuntu-latest
     name: 4.0.3
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
       - name: Cache
         id: cache
-        uses: actions/cache@v4
+        uses: actions/cache@v5
         with:
           path: ${{env.METIS_DIR}}
           key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5

.github/workflows/sanitize-tests.yml

@@ -28,7 +28,7 @@ jobs:
   build:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/mfem
         with:
           par: ${{inputs.par}}
@@ -40,7 +40,7 @@ jobs:
     env:
       ex: ${{inputs.par && 'ex1p' || 'ex1'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -58,7 +58,7 @@ jobs:
     env:
       exclude: ${{inputs.par && '-E "_ser"' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -82,7 +82,7 @@ jobs:
     env:
       exclude: ${{inputs.par && '-E "_ser"' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -107,7 +107,7 @@ jobs:
       run: ${{inputs.par && '-R "_cpu_np"' || ''}}
       exclude: ${{inputs.par && '"unit_tests|debug"' || '"^unit_tests$|debug"'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -131,7 +131,7 @@ jobs:
     env:
       unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -146,7 +146,7 @@ jobs:
         if: ${{steps.restore.outputs.cache-hit != 'true'}}
         working-directory: mfem/build/tests/unit
         run: find . -type f -name '*.o' -delete
-      - uses: actions/upload-artifact@v4
+      - uses: actions/upload-artifact@v7
         with:
           name: tests-${{inputs.par}}-${{inputs.sanitizer}}
           path: mfem/build/tests/unit/${{env.unit_tests}}
@@ -165,14 +165,14 @@ jobs:
       unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
       np: ${{inputs.par && '_np=2' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
           par: ${{inputs.par}}
           sanitizer: ${{inputs.sanitizer}}
           cache-path: mfem/build/tests/unit/${{env.unit_tests}}
-      - uses: actions/download-artifact@v4
+      - uses: actions/download-artifact@v8
         if: ${{steps.restore.outputs.cache-hit != 'true'}}
         with:
           name: tests-${{inputs.par}}-${{inputs.sanitizer}}

.gitignore

@@ -443,6 +443,10 @@ miniapps/diag-smoothers/mg-abs-l1-jacobi
 miniapps/contact/contact
 miniapps/contact/ParaView
 
+miniapps/plasma/pic/electrostatic-*
+!miniapps/plasma/pic/electrostatic-*.cpp
+miniapps/plasma/pic/*.csv
+
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests

.gitlab/jobs/dane.yml

@@ -85,3 +85,8 @@ opt_par_gcc_10_pumi:
   extends: .mfem_job_on_dane
   variables:
     SPEC: "%gcc@10.3.1 +pumi"
+
+opt_par_gcc_10_gslib:
+  extends: .mfem_job_on_dane
+  variables:
+    SPEC: "%gcc@10.3.1 +gslib"

.gitlab/jobs/matrix.yml

@@ -63,3 +63,8 @@ opt_mpi_cuda_hypre_cuda_gcc:
   extends: .mfem_job_on_matrix
   variables:
     SPEC: "%gcc@10.3.1 +mpi +cuda cuda_arch=90 ^hypre+cuda"
+
+opt_mpi_cuda_gcc_gslib:
+  extends: .mfem_job_on_matrix
+  variables:
+    SPEC: "%gcc@10.3.1 +mpi +cuda +gslib cuda_arch=90 ^hypre+cuda"

.gitlab/scripts/baseline

@@ -32,9 +32,9 @@ mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}
 
 # run
 if [[ "${MACHINE_NAME}" == "dane" ]]; then
-  salloc --nodes=1 -t 60 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+  srun --nodes=1 -t 60 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 elif [[ ${MACHINE_NAME} == "corona" ]]; then
-  salloc --nodes=1 -t 60 -p pbatch ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+  srun --nodes=1 -t 60 -p pbatch ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 else
   echo "Unknown machine: MACHINE_NAME=$MACHINE_NAME"
   exit 1

CHANGELOG

@@ -11,12 +11,29 @@
 Version 4.9.1 (development)
 ===========================
 
+- Policy for AI-assisted contribution added to CONTRIBUTING.md
+
 Discretization improvements
 ---------------------------
+- Extend FindPointsGSLIB to support surface meshes.
+
+- Replaced legacy simplex quadrature rules with symmetric positive-weight
+  rules for triangles (orders 0-25) and tetrahedra (orders 0-20). These
+  rules guarantee all-positive weights and interior quadrature points,
+  improving numerical stability. Higher orders fall back to Grundmann-Moller.
+  Triangle rules: Witherden & Vincent, Comput. Math. Appl. 69(10):1232-1241,
+  2015.
+  Tet rules (d=1-13): Witherden & Vincent (ibid).
+  Tet rules (d=14-20): Chuluunbaatar et al., Comput. Math. Appl. 124:89-97,
+  2022.
+
 - Improved the gridfunction projection routines. Projections work for Scalar,
   Vector and VectorFE, also NURBS versions. Optionally different types of
   projections can be selected, default behaviour has not changed.
 
+- Added methods to estimate function extremum using piecewise linear bounds +
+  recursive subdivision.
+
 Meshing improvements
 --------------------
 - Improved support for 1D NURBS meshes with variable order, including using

CMakeLists.txt

@@ -652,6 +652,8 @@ foreach(TPL IN LISTS MFEM_TPLS)
   endif()
 endforeach(TPL)
 
+# reverse to remove the first instance of entries in TPL_LIBRARIES
+# so later duplicates are kept (for dependency ordering)
 list(REVERSE TPL_LIBRARIES)
 list(REMOVE_DUPLICATES TPL_LIBRARIES)
 list(REVERSE TPL_LIBRARIES)
@@ -1015,5 +1017,7 @@ install(DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/data
 # Create 'config.mk' from 'config.mk.in' for the build and install locations and
 # define install rules for 'config.mk' and 'test.mk'
 #-------------------------------------------------------------------------------
-
+if (MFEM_USE_CUDA OR MFEM_USE_HIP)
+  option(MFEM_EXPORT_GPU_CONFIG "Export config.mk for GPU-enabled downstream packages" ON)
+endif()
 mfem_export_mk_files()

CONTRIBUTING.md

@@ -24,6 +24,14 @@ must be made under this license.
 Note also that MFEM has a [Code of Conduct](CODE_OF_CONDUCT.md). By participating
 in the MFEM community, you agree to abide by its rules.
 
+## AI Policy
+- Use of AI code generation in MFEM is allowed but must be disclosed, e.g. by
+  selecting the `AI-assisted` label on the PR.
+- By submitting a PR, the author acknowledges that they have reviewed and
+  understand the changes they are proposing.
+- PR authors are still responsible for correctness, licensing, and attribution
+  of all changes.
+
 If you plan on contributing to MFEM, consider reviewing the
 [issue tracker](https://github.com/mfem/mfem/issues) first to check if a thread
 already exists for your desired feature or the bug you ran into. Use a pull

NOTICE

@@ -28,6 +28,7 @@ license files. These software products and their licenses are as follows:
 * AmgXWrapper (linalg/amgxsolver.{hpp,cpp}) -- MIT license
 * Catch++ (tests/unit/catch.hpp) -- Boost 1.0 license
 * Gecko (general/gecko.{cpp,hpp}) -- BSD 3-clause license
+* gslib (fem/gslib.{cpp,hpp}, mesh/bb_grid_map.{cpp,hpp}) -- BSD 3-clause license
 * Picojson (fem/picojson.h) -- Custom 2-clause license
 * TinyXML2 (general/tinyxml2.{cpp,h}) -- zlib license
 * Zstr (general/zstr.hpp) -- MIT license

config/cmake/MFEMConfig.cmake.in

@@ -109,6 +109,10 @@ if (MFEM_USE_RAJA)
    find_dependency(RAJA)
 endif()
 
+if (MFEM_USE_UMPIRE)
+   find_dependency(umpire)
+endif()
+
 if (NOT TARGET mfem)
   include(${CMAKE_CURRENT_LIST_DIR}/MFEMTargets.cmake)
 endif (NOT TARGET mfem)

config/cmake/modules/FindUMPIRE.cmake

@@ -14,12 +14,12 @@
 #   - UMPIRE_LIBRARIES
 #   - UMPIRE_INCLUDE_DIRS
 
-if (NOT umpire_DIR AND UMPIRE_DIR)
-  set(umpire_DIR ${UMPIRE_DIR}/lib/cmake/umpire)
+if (NOT umpire_ROOT AND UMPIRE_DIR)
+  set(umpire_ROOT ${UMPIRE_DIR})
 endif()
 message(STATUS "Looking for UMPIRE ...")
 message(STATUS "   in UMPIRE_DIR = ${UMPIRE_DIR}")
-message(STATUS "      umpire_DIR = ${umpire_DIR}")
+message(STATUS "      umpire_ROOT = ${umpire_ROOT}")
 find_package(umpire CONFIG)
 set(UMPIRE_FOUND ${umpire_FOUND})
 set(UMPIRE_LIBRARIES "umpire")

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -701,7 +701,6 @@ endfunction(mfem_find_library)
 # Extract compile and link options needed by the given target.
 #
 function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
-
   if (NOT TARGET ${Target})
     return()
   endif()
@@ -799,7 +798,12 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
           # message(STATUS "Lib = ${Lib}")
           # Filter-out generator expressions
           if (NOT ("${Lib}" MATCHES "^\\$"))
-            list(APPEND LinkOpts "${Lib}")
+            if(NOT ("${Lib}" STREQUAL "dl"))
+              list(APPEND LinkOpts "${Lib}")
+            else()
+              # for some reason libdl doesn't include the "-l"
+              list(APPEND LinkOpts "-ldl")
+            endif()
           endif()
         else()
           mfem_get_target_options(${Lib} COpts LOpts)
@@ -888,9 +892,18 @@ function(mfem_export_mk_files)
       set(${var} NO)
     endif()
   endforeach()
-  # TODO: Add support for MFEM_USE_CUDA=YES
-  set(MFEM_CXX ${CMAKE_CXX_COMPILER})
-  set(MFEM_HOST_CXX ${MFEM_CXX})
+  if (MFEM_USE_CUDA AND MFEM_EXPORT_GPU_CONFIG)
+    set(MFEM_CXX ${CMAKE_CUDA_COMPILER})
+    if(MFEM_CUDA_COMPILER_IS_NVCC)
+      set(MFEM_HOST_CXX ${CMAKE_CUDA_HOST_COMPILER})
+    else()
+      set(MFEM_HOST_CXX ${CMAKE_CXX_COMPILER})
+    endif()
+  else()
+    # mfem doesn't use enable_language(HIP)
+    set(MFEM_CXX ${CMAKE_CXX_COMPILER})
+    set(MFEM_HOST_CXX ${CMAKE_CXX_COMPILER})
+  endif()
   set(MFEM_CPPFLAGS "")
   get_target_property(cxx_std mfem CXX_STANDARD)
   # For now, we ignore the setting of the CXX_EXTENSIONS property. If this
@@ -900,6 +913,50 @@ function(mfem_export_mk_files)
   string(STRIP
          "${cxx_std_flag} ${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"
          MFEM_CXXFLAGS)
+  if(MFEM_EXPORT_GPU_CONFIG)
+    if (MFEM_USE_CUDA)
+      set(MFEM_CXXFLAGS "${MFEM_CXXFLAGS} ${CMAKE_CUDA_FLAGS}")
+      if (MFEM_CUDA_COMPILER_IS_NVCC)
+        set(MFEM_CXXFLAGS "-x=cu ${MFEM_CXXFLAGS} -ccbin ${CMAKE_CXX_COMPILER} --forward-unknown-to-host-compiler")
+        # The following intentionally hides CUDA deprecation warnings
+        foreach(ENTRY IN LISTS CUDAToolkit_INCLUDE_DIRS)
+          set(MFEM_CXXFLAGS "${MFEM_CXXFLAGS} -isystem ${ENTRY}")
+        endforeach()
+        if (CMAKE_VERSION VERSION_GREATER_EQUAL 3.18.0)
+          # architecture flags not part of CMAKE_CUDA_FLAGS
+          if ("all" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}"
+              OR "native" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}"
+              OR "all-major" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}")
+            set(MFEM_CXXFLAGS "${MFEM_CXXFLAGS} -arch=${CMAKE_CUDA_ARCHITECTURES}")
+          else()
+            foreach (ENTRY IN LISTS CMAKE_CUDA_ARCHITECTURES)
+              set(MFEM_CXXFLAGS
+                "${MFEM_CXXFLAGS} -gencode arch=compute_${ENTRY},code=sm_${ENTRY}")
+            endforeach()
+          endif()
+        endif()
+      else()
+        set(MFEM_CXXFLAGS "${MFEM_CXXFLAGS} -xcuda --cuda-path=${CUDAToolkit_LIBRARY_ROOT}")
+        if (CMAKE_VERSION VERSION_GREATER_EQUAL 3.18.0)
+          # architecture flags not part of CMAKE_CUDA_FLAGS
+          if ("all" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}"
+              OR "native" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}"
+              OR "all-major" STREQUAL "${CMAKE_CUDA_ARCHITECTURES}")
+            # TODO: not supported
+          else()
+            foreach(ENTRY IN LISTS CMAKE_CUDA_ARCHITECTURES)
+              set(MFEM_CXXFLAGS "-cuda-gpu-arch=sm_${ENTRY} ${MFEM_CXXFLAGS}")
+            endforeach()
+          endif()
+        endif()
+      endif()
+    elseif (MFEM_USE_HIP)
+      set(MFEM_CXXFLAGS "${MFEM_CXXFLAGS} -xhip")
+      foreach(ENTRY IN LISTS CMAKE_HIP_ARCHITECTURES)
+        set(MFEM_CXXFLAGS "--offload-arch=${ENTRY} ${MFEM_CXXFLAGS}")
+      endforeach()
+    endif()
+  endif()
   set(MFEM_TPLFLAGS "")
   foreach(dir ${TPL_INCLUDE_DIRS})
     set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} -I${dir}")
@@ -930,6 +987,9 @@ function(mfem_export_mk_files)
     set(MFEM_SHARED NO)
     set(MFEM_STATIC YES)
   endif()
+  if (MFEM_USE_CUDA)
+    set(MFEM_EXT_LIBS "${MFEM_EXT_LIBS} -lcudart")
+  endif()
   set(MFEM_BUILD_TAG "${CMAKE_SYSTEM}")
   set(MFEM_PREFIX "${CMAKE_INSTALL_PREFIX}")
   # For the next 4 variables, these are the values for the build-tree version of
@@ -938,8 +998,15 @@ function(mfem_export_mk_files)
   set(MFEM_LIB_DIR "${PROJECT_BINARY_DIR}")
   set(MFEM_TEST_MK "${PROJECT_SOURCE_DIR}/config/test.mk")
   set(MFEM_CONFIG_EXTRA "MFEM_BUILD_DIR ?= ${PROJECT_BINARY_DIR}")
-  # TODO: CUDA/HIP support:
-  set(MFEM_XLINKER "${CMAKE_CXX_LINKER_WRAPPER_FLAG}")
+  if (MFEM_USE_CUDA AND MFEM_EXPORT_GPU_CONFIG)
+    if (MFEM_CUDA_COMPILER_IS_NVCC)
+      set(MFEM_XLINKER "-Xlinker=")
+    else()
+      set(MFEM_XLINKER "${CMAKE_CUDA_LINKER_WRAPPER_FLAG}")
+    endif()
+  else()
+    set(MFEM_XLINKER "${CMAKE_CXX_LINKER_WRAPPER_FLAG}")
+  endif()
   set(MFEM_MPIEXEC ${MPIEXEC})
   if (NOT MFEM_MPIEXEC)
     set(MFEM_MPIEXEC "mpirun")
@@ -987,16 +1054,21 @@ function(mfem_export_mk_files)
     # handle interfaces (e.g., SCOREC::apf)
     if ("${lib}" MATCHES "SCOREC::.*" OR "${lib}" MATCHES "Ginkgo::.*" OR "${lib}" MATCHES "ParMoonolith::.*")
     elseif (TARGET "${lib}")
-      mfem_get_target_options(${lib} CompileOpts LinkOpts)
+      mfem_get_target_options(${lib} CompileOpts2 LinkOpts2)
+      # remove generator expressions
+      string(GENEX_STRIP "${CompileOpts2}" CompileOpts)
+      string(GENEX_STRIP "${LinkOpts2}" LinkOpts)
       # Removing duplicates may lead to issues:
       # list(REMOVE_DUPLICATES CompileOpts)
       # list(REMOVE_DUPLICATES LinkOpts)
-      string(REPLACE ";" " " COpts "${CompileOpts}")
-      string(REPLACE ";" " " LOpts "${LinkOpts}")
-      # message(STATUS "${lib}[COpts]: '${COpts}'")
-      # message(STATUS "${lib}[LOpts]: '${LOpts}'")
-      set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} ${COpts}")
-      set(MFEM_EXT_LIBS "${MFEM_EXT_LIBS} ${LOpts}")
+      # message(WARNING "${lib}[LinkOpts]: ${LinkOpts}")      
+      # message(WARNING "${lib}[CompileOpts]: ${CompileOpts}")
+      foreach(LOpt IN LISTS LinkOpts)
+        set(MFEM_EXT_LIBS "${MFEM_EXT_LIBS} ${LOpt}")
+      endforeach()
+      foreach(COpt IN LISTS CompileOpts)
+        set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} ${COpt}")
+      endforeach()
       # message(FATAL_ERROR "***** interface lib found ... exiting *****")
       # handle static and shared libs
     elseif ("${suffix}" STREQUAL "${CMAKE_SHARED_LIBRARY_SUFFIX}")
@@ -1004,7 +1076,7 @@ function(mfem_export_mk_files)
       get_filename_component(fullLibName ${lib} NAME_WE)
       string(REGEX REPLACE "^lib" "" libname ${fullLibName})
       set(MFEM_EXT_LIBS
-          "${MFEM_EXT_LIBS} ${shared_link_flag}${dir} -L${dir} -l${libname}")
+        "${MFEM_EXT_LIBS} ${shared_link_flag}${dir} -L${dir} -l${libname}")
     else()
       set(MFEM_EXT_LIBS "${MFEM_EXT_LIBS} ${lib}")
     endif()
@@ -1013,7 +1085,7 @@ function(mfem_export_mk_files)
   # Create the build-tree version of 'config.mk'
   configure_file(
     "${PROJECT_SOURCE_DIR}/config/config.mk.in"
-    "${PROJECT_BINARY_DIR}/config/config.mk")
+    "${PROJECT_BINARY_DIR}/config/config.mk" @ONLY)
   # Copy 'test.mk' from the source-tree to the build-tree
   configure_file(
     "${PROJECT_SOURCE_DIR}/config/test.mk"
@@ -1031,7 +1103,7 @@ function(mfem_export_mk_files)
   # Create the install-tree version of 'config.mk'
   configure_file(
     "${PROJECT_SOURCE_DIR}/config/config.mk.in"
-    "${PROJECT_BINARY_DIR}/config/config-install.mk")
+    "${PROJECT_BINARY_DIR}/config/config-install.mk" @ONLY)
 
   # Install rules for 'config.mk' and 'test.mk'
   install(FILES ${PROJECT_SOURCE_DIR}/config/test.mk

examples/CMakeLists.txt

@@ -215,7 +215,7 @@ if (MFEM_ENABLE_TESTING)
     add_test(NAME ex1p_ceed_np=${MFEM_MPI_NP}
       COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS}
-      $<TARGET_FILE:ex1p> "-no-vis" "-d ceed-cpu" "-pa" "-a"
+      $<TARGET_FILE:ex1p> "-no-vis" "-d" "ceed-cpu" "-pa" "-a"
       ${MPIEXEC_POSTFLAGS})
   endif()
 endif()

examples/amgx/makefile

@@ -64,7 +64,7 @@ PARALLEL_NAME := Parallel AMGX example
 $(MFEM_LIB_FILE):
 	$(error The MFEM library is not build)
 
-clean: clean-build
+clean: clean-build clean-exec
 
 clean-build:
 	rm -f *.o *~ $(SEQ_EXAMPLES) $(PAR_EXAMPLES)

examples/caliper/makefile

@@ -64,12 +64,12 @@ ex1p-test-par: ex1p
 $(MFEM_LIB_FILE):
 	$(error The MFEM library is not built)
 
-clean: clean-build clean-exec $(SUBDIRS_CLEAN)
+clean: clean-build clean-exec
 
 clean-build:
 	rm -f *.o *~ $(SEQ_EXAMPLES) $(PAR_EXAMPLES)
 	rm -rf *.dSYM *.TVD.*breakpoints
 
 clean-exec:
-	@rm -f refined.mesh displaced.mesh mesh.* ex5.mesh
-	@rm -f sphere_refined.* sol.* sol_u.* sol_p.* sol_r.* sol_i.*
+	@rm -f refined.mesh mesh.*
+	@rm -f sol.*

examples/ex1.cpp

@@ -137,6 +137,32 @@ int main(int argc, char *argv[])
       }
    }
 
+   mesh.EnsureNodes();
+   GridFunction *nodes = mesh.GetNodes();
+   GridFunction nodes2(nodes->FESpace());
+   nodes2 = *nodes; // 1-to-1 copy
+
+   VisItDataCollection vdc("check", &mesh);
+   vdc.RegisterField("d", nodes);
+   vdc.RegisterField("d2", &nodes2);
+   vdc.SetCycle(0);
+   vdc.Save();
+
+   // byNODES byVDIm shuffle
+   int nnode = nodes2.Size()/2;
+   for (int i = 0; i < nnode; i++)
+   {
+      for (int j = 0; j < dim; j++)
+      {
+         int xi = i + j*nnode;
+         int ni = j + i*dim;
+         nodes2[xi] = nodes->Elem(ni);
+      }
+   } 
+   vdc.SetCycle(1);
+   vdc.Save();
+
+
    // 5. Define a finite element space on the mesh. Here we use continuous
    //    Lagrange finite elements of the specified order. If order < 1, we
    //    instead use an isoparametric/isogeometric space.

examples/ex12p.cpp

@@ -5,9 +5,9 @@
 // Sample runs:
 //    mpirun -np 4 ex12p -m ../data/beam-tri.mesh
 //    mpirun -np 4 ex12p -m ../data/beam-quad.mesh
-//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -s 462 -n 10 -o 2 -elast
+//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -s 464 -n 10 -o 2 -elast
 //    mpirun -np 4 ex12p -m ../data/beam-hex.mesh -s 3878
-//    mpirun -np 4 ex12p -m ../data/beam-wedge.mesh -s 81
+//    mpirun -np 4 ex12p -m ../data/beam-wedge.mesh -s 82
 //    mpirun -np 4 ex12p -m ../data/beam-tri.mesh -s 3877 -o 2 -sys
 //    mpirun -np 4 ex12p -m ../data/beam-quad.mesh -s 4544 -n 6 -o 3 -elast
 //    mpirun -np 4 ex12p -m ../data/beam-quad-nurbs.mesh

examples/ex22p.cpp

@@ -302,15 +302,21 @@ int main(int argc, char *argv[])
       char vishost[] = "localhost";
       int  visport   = 19916;
       socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
       sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
       sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
       sol_sock_r << "solution\n" << *pmesh << u_exact->real()
                  << "window_title 'Exact: Real Part'" << flush;
+      // Make sure all ranks have sent their real solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
+      socketstream sol_sock_i(vishost, visport);
+      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock_i.precision(8);
       sol_sock_i << "solution\n" << *pmesh << u_exact->imag()
                  << "window_title 'Exact: Imaginary Part'" << flush;
+      // Make sure all ranks have sent their imaginary solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
    }
 
    // 11. Set up the parallel sesquilinear form a(.,.) on the finite element
@@ -534,15 +540,21 @@ int main(int argc, char *argv[])
       char vishost[] = "localhost";
       int  visport   = 19916;
       socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
       sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
       sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
       sol_sock_r << "solution\n" << *pmesh << u.real()
                  << "window_title 'Solution: Real Part'" << flush;
+      // Make sure all ranks have sent their real solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
+      socketstream sol_sock_i(vishost, visport);
+      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock_i.precision(8);
       sol_sock_i << "solution\n" << *pmesh << u.imag()
                  << "window_title 'Solution: Imaginary Part'" << flush;
+      // Make sure all ranks have sent their imaginary solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
    }
    if (visualization && exact_sol)
    {
@@ -551,15 +563,21 @@ int main(int argc, char *argv[])
       char vishost[] = "localhost";
       int  visport   = 19916;
       socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
       sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
       sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
       sol_sock_r << "solution\n" << *pmesh << u_exact->real()
                  << "window_title 'Error: Real Part'" << flush;
+      // Make sure all ranks have sent their real solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
+      socketstream sol_sock_i(vishost, visport);
+      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock_i.precision(8);
       sol_sock_i << "solution\n" << *pmesh << u_exact->imag()
                  << "window_title 'Error: Imaginary Part'" << flush;
+      // Make sure all ranks have sent their imaginary solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
    }
    if (visualization)
    {

examples/ex37.cpp

@@ -5,8 +5,8 @@
 // Sample runs:
 //     ex37 -alpha 10
 //     ex37 -alpha 10 -pv
-//     ex37 -lambda 0.1 -mu 0.1
-//     ex37 -o 2 -alpha 5.0 -mi 50 -vf 0.4 -ntol 1e-5
+//     ex37 -lambda 0.1 -mu 0.1 -growth 1
+//     ex37 -o 2 -alpha 10.0 -mi 50 -vf 0.4 -ntol 1e-5 -growth 1.5
 //     ex37 -r 6 -o 1 -alpha 25.0 -epsilon 0.02 -mi 50 -ntol 1e-5
 //
 // Description: This example code demonstrates the use of MFEM to solve a
@@ -55,53 +55,6 @@
 using namespace std;
 using namespace mfem;
 
-/**
- * @brief Bregman projection of ρ = sigmoid(ψ) onto the subspace
- *        ∫_Ω ρ dx = θ vol(Ω) as follows:
- *
- *        1. Compute the root of the R → R function
- *            f(c) = ∫_Ω sigmoid(ψ + c) dx - θ vol(Ω)
- *        2. Set ψ ← ψ + c.
- *
- * @param psi a GridFunction to be updated
- * @param target_volume θ vol(Ω)
- * @param tol Newton iteration tolerance
- * @param max_its Newton maximum iteration number
- * @return real_t Final volume, ∫_Ω sigmoid(ψ)
- */
-real_t proj(GridFunction &psi, real_t target_volume, real_t tol=1e-12,
-            int max_its=10)
-{
-   MappedGridFunctionCoefficient sigmoid_psi(&psi, sigmoid);
-   MappedGridFunctionCoefficient der_sigmoid_psi(&psi, der_sigmoid);
-
-   LinearForm int_sigmoid_psi(psi.FESpace());
-   int_sigmoid_psi.AddDomainIntegrator(new DomainLFIntegrator(sigmoid_psi));
-   LinearForm int_der_sigmoid_psi(psi.FESpace());
-   int_der_sigmoid_psi.AddDomainIntegrator(new DomainLFIntegrator(
-                                              der_sigmoid_psi));
-   bool done = false;
-   for (int k=0; k<max_its; k++) // Newton iteration
-   {
-      int_sigmoid_psi.Assemble(); // Recompute f(c) with updated ψ
-      const real_t f = int_sigmoid_psi.Sum() - target_volume;
-
-      int_der_sigmoid_psi.Assemble(); // Recompute df(c) with updated ψ
-      const real_t df = int_der_sigmoid_psi.Sum();
-
-      const real_t dc = -f/df;
-      psi += dc;
-      if (abs(dc) < tol) { done = true; break; }
-   }
-   if (!done)
-   {
-      mfem_warning("Projection reached maximum iteration without converging. "
-                   "Result may not be accurate.");
-   }
-   int_sigmoid_psi.Assemble();
-   return int_sigmoid_psi.Sum();
-}
-
 /*
  * ---------------------------------------------------------------
  *                      ALGORITHM PREAMBLE
@@ -180,10 +133,11 @@ int main(int argc, char *argv[])
    int ref_levels = 5;
    int order = 2;
    real_t alpha = 1.0;
+   real_t growth = 2;
    real_t epsilon = 0.01;
    real_t vol_fraction = 0.5;
    int max_it = 1e3;
-   real_t itol = 1e-1;
+   real_t itol = 1e-2;
    real_t ntol = 1e-4;
    real_t rho_min = 1e-6;
    real_t lambda = 1.0;
@@ -198,6 +152,8 @@ int main(int argc, char *argv[])
                   "Order (degree) of the finite elements.");
    args.AddOption(&alpha, "-alpha", "--alpha-step-length",
                   "Step length for gradient descent.");
+   args.AddOption(&growth, "-growth", "--alpha-growth-rate",
+                  "Growth rate of step length for gradient descent.");
    args.AddOption(&epsilon, "-epsilon", "--epsilon-thickness",
                   "Length scale for ρ.");
    args.AddOption(&max_it, "-mi", "--max-it",
@@ -332,6 +288,7 @@ int main(int argc, char *argv[])
    }
    FilterSolver->SetEssentialBoundary(ess_bdr_filter);
    FilterSolver->SetupFEM();
+   FilterSolver->AssembleDiffusionBilinear();
 
    BilinearForm mass(&control_fes);
    mass.AddDomainIntegrator(new InverseIntegrator(new MassIntegrator(one)));
@@ -385,7 +342,7 @@ int main(int argc, char *argv[])
    // 11. Iterate:
    for (int k = 1; k <= max_it; k++)
    {
-      if (k > 1) { alpha *= ((real_t) k) / ((real_t) k-1); }
+      if (k > 1) { alpha = std::pow((real_t) k,growth); }
 
       mfem::out << "\nStep = " << k << std::endl;
 
@@ -422,7 +379,9 @@ int main(int argc, char *argv[])
 
       // Step 5 - Update design variable ψ ← proj(ψ - αG)
       psi.Add(-alpha, grad);
-      const real_t material_volume = proj(psi, target_volume);
+      GridFunction alpha_grad(grad);
+      alpha_grad *= alpha;
+      const real_t material_volume = proj(psi, alpha_grad, target_volume);
 
       // Compute ||ρ - ρ_old|| in control fes.
       real_t norm_increment = zerogf.ComputeL1Error(succ_diff_rho);

examples/ex37.hpp

@@ -137,7 +137,7 @@ public:
         exponent(exponent_), rho_min(rho_min_)
    {
       MFEM_ASSERT(rho_min_ >= 0.0, "rho_min must be >= 0");
-      MFEM_ASSERT(rho_min_ < 1.0,  "rho_min must be > 1");
+      MFEM_ASSERT(rho_min_ < 1.0,  "rho_min must be < 1");
       MFEM_ASSERT(u, "displacement field is not set");
       MFEM_ASSERT(rho_filter, "density field is not set");
    }
@@ -231,9 +231,12 @@ private:
    FiniteElementCollection * fec = nullptr;
    FiniteElementSpace * fes = nullptr;
    Array<int> ess_bdr;
+   Array<int> ess_tdof_list;
    Array<int> neumann_bdr;
    GridFunction * u = nullptr;
    LinearForm * b = nullptr;
+   BilinearForm * a = nullptr;
+   OperatorPtr A;
    bool parallel;
 #ifdef MFEM_USE_MPI
    ParMesh * pmesh = nullptr;
@@ -267,6 +270,8 @@ public:
    void ResetFEM();
    void SetupFEM();
 
+   void UpdateEssentialTDofs();
+   void AssembleDiffusionBilinear(bool update_ess_tdofs=true);
    void Solve();
    GridFunction * GetFEMSolution();
    LinearForm * GetLinearForm() {return b;}
@@ -371,6 +376,130 @@ public:
 
 };
 
+/**
+ * @brief Bregman projection of ρ = sigmoid(ψ) onto the subspace
+ *        ∫_Ω ρ dx = θ vol(Ω) as follows:
+ *
+ *        1. Compute the root of the R → R function
+ *            f(c) = ∫_Ω sigmoid(ψ + c) dx - θ vol(Ω)
+ *           using the Illinois method
+ *        2. Set ψ ← ψ + c.
+ *
+ * @param psi a GridFunction to be updated
+ * @param alpha_grad alpha multiplied by gradient
+ * @param target_volume θ vol(Ω)
+ * @param tol Illinois iteration tolerance
+ * @param max_its Illinois maximum iteration number
+ * @return real_t Final volume (∫_Ω sigmoid(ψ) dx)
+ */
+real_t proj(GridFunction &psi, GridFunction &alpha_grad, real_t target_volume,
+            real_t tol = 1e-12, int max_its = 100)
+{
+#ifdef MFEM_USE_MPI
+   FiniteElementSpace *fes = psi.FESpace();
+   ParFiniteElementSpace *pfes = dynamic_cast<ParFiniteElementSpace*>(fes);
+#endif
+   ConstantCoefficient zero_cf(0.0);
+   real_t a = -alpha_grad.ComputeMaxError(zero_cf);
+   real_t b = -a;
+   real_t y = 0.0;
+
+   MappedGridFunctionCoefficient sigmoid_psi(
+   &psi, [&y](const real_t x) { return sigmoid(x + y); });
+   std::unique_ptr<LinearForm> int_sigmoid_psi;
+#ifdef MFEM_USE_MPI
+   ParGridFunction *par_psi = dynamic_cast<ParGridFunction *>(&psi);
+   if (par_psi)
+   {
+      int_sigmoid_psi.reset(new ParLinearForm(par_psi->ParFESpace()));
+   }
+   else
+   {
+      int_sigmoid_psi.reset(new LinearForm(psi.FESpace()));
+   }
+#else
+   int_sigmoid_psi.reset(new LinearForm(psi.FESpace()));
+#endif
+   int_sigmoid_psi->AddDomainIntegrator(new DomainLFIntegrator(sigmoid_psi));
+
+   y = a;
+   int_sigmoid_psi->Assemble();
+   real_t f_a = int_sigmoid_psi->Sum();  // f_a := f(a) + θ vol(Ω)
+
+   y = b;
+   int_sigmoid_psi->Assemble();
+   real_t f_b = int_sigmoid_psi->Sum();  // f_b := f(b) + θ vol(Ω)
+#ifdef MFEM_USE_MPI
+   if (pfes)
+   {
+      MPI_Allreduce(MPI_IN_PLACE, &f_a, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_SUM, MPI_COMM_WORLD);
+      MPI_Allreduce(MPI_IN_PLACE, &f_b, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_SUM, MPI_COMM_WORLD);
+   }
+#endif
+   f_a -= target_volume; // f_a := f(a)
+   f_b -= target_volume; // f_b := f(b)
+   real_t c = 0.0;
+   real_t f_c = 0.0;
+   int side = 0;
+
+   bool done = false;
+   for (int k=0; k < max_its; k++)
+   {
+      c = (f_a * b - f_b * a) / (f_a - f_b);
+
+      if (abs(b - a) < tol * abs(b + a)) { done = true; break; }
+
+      y = c;
+      int_sigmoid_psi->Assemble();
+      f_c = int_sigmoid_psi->Sum(); // f_c := f(c) + θ vol(Ω)
+#ifdef MFEM_USE_MPI
+      if (pfes)
+      {
+         MPI_Allreduce(MPI_IN_PLACE, &f_c, 1, MPITypeMap<real_t>::mpi_type,
+                       MPI_SUM, MPI_COMM_WORLD);
+      }
+#endif
+      f_c -= target_volume; // f_c := f(c)
+
+      if (f_c * f_b > 0)
+      {
+         b = c;
+         f_b = f_c;
+         if (side == -1) { f_a /= 2.0; }
+         side = -1;
+      }
+      else if (f_c * f_a > 0)
+      {
+         a = c;
+         f_a = f_c;
+         if (side == 1) { f_b /= 2.0; }
+         side = 1;
+      }
+      else
+      {
+         done = true; break;
+      }
+   }
+   if (!done)
+   {
+      mfem_warning("Projection reached maximum iteration without converging. "
+                   "Result may not be accurate.");
+   }
+   y = 0.0;
+   psi += c;
+   int_sigmoid_psi->Assemble();
+   real_t material_volume = int_sigmoid_psi->Sum();
+#ifdef MFEM_USE_MPI
+   if (pfes)
+   {
+      MPI_Allreduce(MPI_IN_PLACE, &material_volume, 1,
+                    MPITypeMap<real_t>::mpi_type, MPI_SUM, MPI_COMM_WORLD);
+   }
+#endif
+   return material_volume;
+}
 
 // Poisson solver
 
@@ -422,12 +551,8 @@ void DiffusionSolver::SetupFEM()
    }
 }
 
-void DiffusionSolver::Solve()
+void DiffusionSolver::UpdateEssentialTDofs()
 {
-   OperatorPtr A;
-   Vector B, X;
-   Array<int> ess_tdof_list;
-
 #ifdef MFEM_USE_MPI
    if (parallel)
    {
@@ -440,7 +565,39 @@ void DiffusionSolver::Solve()
 #else
    fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
 #endif
-   *u=0.0;
+}
+
+void DiffusionSolver::AssembleDiffusionBilinear(bool update_ess_tdofs)
+{
+   if (update_ess_tdofs)
+   {
+      UpdateEssentialTDofs();
+   }
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      a = new ParBilinearForm(pfes);
+   }
+   else
+   {
+      a = new BilinearForm(fes);
+   }
+#else
+   a = new BilinearForm(fes);
+#endif
+   a->AddDomainIntegrator(new DiffusionIntegrator(*diffcf));
+   if (masscf)
+   {
+      a->AddDomainIntegrator(new MassIntegrator(*masscf));
+   }
+   a->Assemble();
+   a->FormSystemMatrix(ess_tdof_list, A);
+}
+
+void DiffusionSolver::Solve()
+{
+   Vector B, X;
+
    if (b)
    {
       delete b;
@@ -475,31 +632,33 @@ void DiffusionSolver::Solve()
 
    b->Assemble();
 
-   BilinearForm * a = nullptr;
-
-#ifdef MFEM_USE_MPI
-   if (parallel)
-   {
-      a = new ParBilinearForm(pfes);
-   }
-   else
-   {
-      a = new BilinearForm(fes);
-   }
-#else
-   a = new BilinearForm(fes);
-#endif
-   a->AddDomainIntegrator(new DiffusionIntegrator(*diffcf));
-   if (masscf)
-   {
-      a->AddDomainIntegrator(new MassIntegrator(*masscf));
-   }
-   a->Assemble();
+   *u=0.0;
    if (essbdr_cf)
    {
       u->ProjectBdrCoefficient(*essbdr_cf,ess_bdr);
    }
-   a->FormLinearSystem(ess_tdof_list, *u, *b, A, X, B);
+
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      X.SetSize(pfes->TrueVSize());
+      B.SetSize(pfes->TrueVSize());
+      dynamic_cast<ParGridFunction*>(u)->ParallelAssemble(X);
+      dynamic_cast<ParLinearForm*>(b)->ParallelAssemble(B);
+      dynamic_cast<ParBilinearForm*>(a)->ParallelEliminateTDofsInRHS(
+         ess_tdof_list, X, B);
+   }
+   else
+   {
+      X.NewDataAndSize(u->GetData(), u->Size());
+      B.NewDataAndSize(b->GetData(), b->Size());
+      a->EliminateVDofsInRHS(ess_tdof_list, X, B);
+   }
+#else
+   X.NewDataAndSize(u->GetData(), u->Size());
+   B.NewDataAndSize(b->GetData(), b->Size());
+   a->EliminateVDofsInRHS(ess_tdof_list, X, B);
+#endif
 
    CGSolver * cg = nullptr;
    Solver * M = nullptr;
@@ -528,7 +687,6 @@ void DiffusionSolver::Solve()
    delete M;
    delete cg;
    a->RecoverFEMSolution(X, *b, *u);
-   delete a;
 }
 
 GridFunction * DiffusionSolver::GetFEMSolution()
@@ -560,6 +718,8 @@ DiffusionSolver::~DiffusionSolver()
 #endif
    delete fec; fec = nullptr;
    delete b;
+   A.Clear();
+   delete a;
 }
 
 

examples/ex37p.cpp

@@ -4,8 +4,8 @@
 //
 // Sample runs:
 //    mpirun -np 4 ex37p -alpha 10 -pv
-//    mpirun -np 4 ex37p -lambda 0.1 -mu 0.1
-//    mpirun -np 4 ex37p -o 2 -alpha 5.0 -mi 50 -vf 0.4 -ntol 1e-5
+//    mpirun -np 4 ex37p -lambda 0.1 -mu 0.1 -growth 1
+//    mpirun -np 4 ex37p -o 2 -alpha 10.0 -mi 50 -vf 0.4 -ntol 1e-5 -growth 1.5
 //    mpirun -np 4 ex37p -r 6 -o 2 -alpha 10.0 -epsilon 0.02 -mi 50 -ntol 1e-5
 //
 // Description: This example code demonstrates the use of MFEM to solve a
@@ -54,61 +54,6 @@
 using namespace std;
 using namespace mfem;
 
-/**
- * @brief Bregman projection of ρ = sigmoid(ψ) onto the subspace
- *        ∫_Ω ρ dx = θ vol(Ω) as follows:
- *
- *        1. Compute the root of the R → R function
- *            f(c) = ∫_Ω sigmoid(ψ + c) dx - θ vol(Ω)
- *        2. Set ψ ← ψ + c.
- *
- * @param psi a GridFunction to be updated
- * @param target_volume θ vol(Ω)
- * @param tol Newton iteration tolerance
- * @param max_its Newton maximum iteration number
- * @return real_t Final volume, ∫_Ω sigmoid(ψ)
- */
-real_t proj(ParGridFunction &psi, real_t target_volume, real_t tol=1e-12,
-            int max_its=10)
-{
-   MappedGridFunctionCoefficient sigmoid_psi(&psi, sigmoid);
-   MappedGridFunctionCoefficient der_sigmoid_psi(&psi, der_sigmoid);
-
-   ParLinearForm int_sigmoid_psi(psi.ParFESpace());
-   int_sigmoid_psi.AddDomainIntegrator(new DomainLFIntegrator(sigmoid_psi));
-   ParLinearForm int_der_sigmoid_psi(psi.ParFESpace());
-   int_der_sigmoid_psi.AddDomainIntegrator(new DomainLFIntegrator(
-                                              der_sigmoid_psi));
-   bool done = false;
-   for (int k=0; k<max_its; k++) // Newton iteration
-   {
-      int_sigmoid_psi.Assemble(); // Recompute f(c) with updated ψ
-      real_t f = int_sigmoid_psi.Sum();
-      MPI_Allreduce(MPI_IN_PLACE, &f, 1, MPITypeMap<real_t>::mpi_type,
-                    MPI_SUM, MPI_COMM_WORLD);
-      f -= target_volume;
-
-      int_der_sigmoid_psi.Assemble(); // Recompute df(c) with updated ψ
-      real_t df = int_der_sigmoid_psi.Sum();
-      MPI_Allreduce(MPI_IN_PLACE, &df, 1, MPITypeMap<real_t>::mpi_type,
-                    MPI_SUM, MPI_COMM_WORLD);
-
-      const real_t dc = -f/df;
-      psi += dc;
-      if (abs(dc) < tol) { done = true; break; }
-   }
-   if (!done)
-   {
-      mfem_warning("Projection reached maximum iteration without converging. "
-                   "Result may not be accurate.");
-   }
-   int_sigmoid_psi.Assemble();
-   real_t material_volume = int_sigmoid_psi.Sum();
-   MPI_Allreduce(MPI_IN_PLACE, &material_volume, 1,
-                 MPITypeMap<real_t>::mpi_type, MPI_SUM, MPI_COMM_WORLD);
-   return material_volume;
-}
-
 /*
  * ---------------------------------------------------------------
  *                      ALGORITHM PREAMBLE
@@ -193,10 +138,11 @@ int main(int argc, char *argv[])
    int ref_levels = 5;
    int order = 2;
    real_t alpha = 1.0;
+   real_t growth = 2;
    real_t epsilon = 0.01;
    real_t vol_fraction = 0.5;
    int max_it = 1e3;
-   real_t itol = 1e-1;
+   real_t itol = 1e-2;
    real_t ntol = 1e-4;
    real_t rho_min = 1e-6;
    real_t lambda = 1.0;
@@ -211,6 +157,8 @@ int main(int argc, char *argv[])
                   "Order (degree) of the finite elements.");
    args.AddOption(&alpha, "-alpha", "--alpha-step-length",
                   "Step length for gradient descent.");
+   args.AddOption(&growth, "-growth", "--alpha-growth-rate",
+                  "Growth rate of step length for gradient descent.");
    args.AddOption(&epsilon, "-epsilon", "--epsilon-thickness",
                   "Length scale for ρ.");
    args.AddOption(&max_it, "-mi", "--max-it",
@@ -359,6 +307,7 @@ int main(int argc, char *argv[])
    }
    FilterSolver->SetEssentialBoundary(ess_bdr_filter);
    FilterSolver->SetupFEM();
+   FilterSolver->AssembleDiffusionBilinear();
 
    ParBilinearForm mass(&control_fes);
    mass.AddDomainIntegrator(new InverseIntegrator(new MassIntegrator(one)));
@@ -412,7 +361,7 @@ int main(int argc, char *argv[])
    // 11. Iterate:
    for (int k = 1; k <= max_it; k++)
    {
-      if (k > 1) { alpha *= ((real_t) k) / ((real_t) k-1); }
+      if (k > 1) { alpha = std::pow((real_t) k,growth); }
 
       if (myid == 0)
       {
@@ -452,7 +401,9 @@ int main(int argc, char *argv[])
 
       // Step 5 - Update design variable ψ ← proj(ψ - αG)
       psi.Add(-alpha, grad);
-      const real_t material_volume = proj(psi, target_volume);
+      ParGridFunction alpha_grad(grad);
+      alpha_grad *= alpha;
+      const real_t material_volume = proj(psi, alpha_grad, target_volume);
 
       // Compute ||ρ - ρ_old|| in control fes.
       real_t norm_increment = zerogf.ComputeL1Error(succ_diff_rho);

examples/ginkgo/makefile

@@ -76,4 +76,4 @@ clean-build:
 	rm -rf *.dSYM *.TVD.*breakpoints
 
 clean-exec:
-	@rm -f refined.mesh sol.gf
+	@rm -f refined.mesh sol.gf mesh.* sol.*

examples/makefile

@@ -71,6 +71,7 @@ endif
 
 SUBDIRS_ALL = $(addsuffix /all,$(SUBDIRS))
 SUBDIRS_TEST = $(addsuffix /test,$(SUBDIRS))
+SUBDIRS_TEST_NOCLEAN = $(addsuffix /test-noclean,$(SUBDIRS))
 SUBDIRS_CLEAN = $(addsuffix /clean,$(SUBDIRS))
 SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))
 
@@ -87,8 +88,9 @@ SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))
 
 all: $(EXAMPLES) $(SUBDIRS_ALL)
 
-.PHONY: $(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_CLEAN) $(SUBDIRS_TPRINT)
-$(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_CLEAN):
+.PHONY: $(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_TEST_NOCLEAN) \
+   $(SUBDIRS_CLEAN) $(SUBDIRS_TPRINT)
+$(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_TEST_NOCLEAN) $(SUBDIRS_CLEAN):
 	$(MAKE) -C $(@D) $(@F)
 $(SUBDIRS_TPRINT):
 	@$(MAKE) -C $(@D) $(@F)
@@ -107,6 +109,7 @@ endif
 MFEM_TESTS = EXAMPLES
 include $(MFEM_TEST_MK)
 test: $(SUBDIRS_TEST)
+test-noclean: $(SUBDIRS_TEST_NOCLEAN)
 test-print: $(SUBDIRS_TPRINT)
 
 # Testing: Parallel vs. serial runs
@@ -157,6 +160,8 @@ ex37-test-seq: ex37
 	@$(call mfem-test,$<,, Serial example,-mi 3)
 ex37p-test-par: ex37p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-mi 3)
+ex39-test-seq: ex39
+	@$(call mfem-test,$<,, Serial example,-m ../data/compass.mesh)
 ex41-test-seq: ex41
 	@$(call mfem-test,$<,, Serial example,-tf 1.0)
 ex41p-test-par: ex41p

fem/CMakeLists.txt

@@ -171,8 +171,12 @@ set(SRCS
   tmop_tools.cpp
   tmop_amr.cpp
   gslib.cpp
+  gslib/findptsedge_local_2.cpp
+  gslib/findptsedge_local_3.cpp
+  gslib/findptssurf_local_3.cpp
   gslib/findpts_local_2.cpp
   gslib/findpts_local_3.cpp
+  gslib/interpolate_local_1.cpp
   gslib/interpolate_local_2.cpp
   gslib/interpolate_local_3.cpp
   transfer.cpp

fem/bilinearform.cpp

@@ -729,7 +729,8 @@ void BilinearForm::Assemble(int skip_zeros)
          tr = mesh -> GetBdrFaceTransformations (i);
          if (tr != NULL)
          {
-            fes -> GetElementVDofs (tr -> Elem1No, vdofs);
+            mfem::DofTransformation doftrans;
+            fes -> GetElementVDofs (tr -> Elem1No, vdofs, doftrans);
             fe1 = fes -> GetFE (tr -> Elem1No);
             // The fe2 object is really a dummy and not used on the boundaries,
             // but we can't dereference a NULL pointer, and we don't want to
@@ -743,6 +744,7 @@ void BilinearForm::Assemble(int skip_zeros)
 
                boundary_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr,
                                                               elemmat);
+               doftrans.TransformDual(elemmat);
                mat -> AddSubMatrix (vdofs, vdofs, elemmat, skip_zeros);
             }
          }
@@ -1723,6 +1725,7 @@ void MixedBilinearForm::Assemble(int skip_zeros)
          }
       }
 
+      DofTransformation dom_dof_trans, ran_dof_trans;
       for (int i = 0; i < trial_fes -> GetNBE(); i++)
       {
          const int bdr_attr = mesh->GetBdrAttribute(i);
@@ -1731,8 +1734,8 @@ void MixedBilinearForm::Assemble(int skip_zeros)
          ftr = mesh -> GetBdrFaceTransformations (i);
          if (ftr != NULL)
          {
-            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
+            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs, dom_dof_trans);
+            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs, ran_dof_trans);
             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
@@ -1748,6 +1751,7 @@ void MixedBilinearForm::Assemble(int skip_zeros)
                boundary_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
                                                            *test_fe2,
                                                            *ftr, elemmat);
+               TransformDual(ran_dof_trans, dom_dof_trans, elemmat);
                mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
             }
          }

fem/bilininteg.hpp

@@ -2710,7 +2710,7 @@ public:
 
 
 /** Integrator for $(-Q u, \nabla v)$ for Nedelec ($u$) and $H^1$ ($v$) elements.
-    This is equivalent to a weak divergence of the $H(curl$ basis functions. */
+    This is equivalent to a weak divergence of the $H(curl)$ basis functions. */
 class VectorFEWeakDivergenceIntegrator: public BilinearFormIntegrator
 {
 protected:

fem/bounds.cpp

@@ -39,8 +39,8 @@ void PLBound::Setup(const int nb_i, const int ncp_i,
    b_type = b_type_i;
    cp_type = cp_type_i;
    tol = tol_i;
-   lbound.SetSize(nb, ncp);
-   ubound.SetSize(nb, ncp);
+   lbound.SetSize(ncp, nb);
+   ubound.SetSize(ncp, nb);
    nodes.SetSize(nb);
    weights.SetSize(nb);
    control_points.SetSize(ncp);
@@ -125,21 +125,25 @@ void PLBound::Setup(const int nb_i, const int ncp_i,
       {
          if (j == 0)
          {
-            lbound(i, j) = bv(i);
-            ubound(i, j) = bv(i);
+            lbound(j,i) = bv(i);
+            ubound(j,i) = bv(i);
          }
          else if (j == ncp-1)
          {
-            lbound(i, j) = bv(i);
-            ubound(i, j) = bv(i);
+            lbound(j,i) = bv(i);
+            ubound(j,i) = bv(i);
          }
          else
          {
             vals(0)  = bv(i);
             vals(1) =  bmv(i) +  dm*bdmv(i);
             vals(2) =  bpv(i) +  dp*bdpv(i);
-            lbound(i, j) = vals.Min()-tol; // tolerance for good measure
-            ubound(i, j) = vals.Max()+tol; // tolerance for good measure
+            lbound(j,i) = vals.Min()-tol; // tolerance for good measure
+            ubound(j,i) = vals.Max()+tol; // tolerance for good measure
+            if (b_type == 2)
+            {
+               lbound(j,i) = std::max(lbound(j,i),0_r);
+            }
          }
       }
    }
@@ -273,8 +277,7 @@ void PLBound::Get1DBounds(const Vector &coeff, Vector &intmin,
    intmax.SetSize(ncp);
    intmin = 0.0;
    intmax = 0.0;
-   Vector coeffm(nb);
-   coeffm = 0.0;
+   Vector coeffm;
 
    real_t a0 = 0.0;
    real_t a1 = 0.0;
@@ -302,6 +305,8 @@ void PLBound::Get1DBounds(const Vector &coeff, Vector &intmin,
    // compute L2 projection for linear bases: a0 + a1*x
    if (proj)
    {
+      coeffm.SetSize(nb);
+      coeffm = 0.0;
       for (int i = 0; i < nb; i++)
       {
          x = 2.0*nodes_int(i)-1;
@@ -342,8 +347,8 @@ void PLBound::Get1DBounds(const Vector &coeff, Vector &intmin,
       real_t c = coeffm(i);
       for (int j = 0; j < ncp; j++)
       {
-         intmin(j) += min(lbound(i,j)*c, ubound(i,j)*c);
-         intmax(j) += max(lbound(i,j)*c, ubound(i,j)*c);
+         intmin(j) += min(lbound(j,i)*c, ubound(j,i)*c);
+         intmax(j) += max(lbound(j,i)*c, ubound(j,i)*c);
       }
    }
 }
@@ -474,10 +479,10 @@ void PLBound::Get2DBounds(const Vector &coeff, Vector &intmin,
          real_t w1 = intmaxT(id2++);
          for (int k = 0; k < ncp; k++) // kth row
          {
-            vals(0) = w0*lbound(j,k);
-            vals(1) = w0*ubound(j,k);
-            vals(2) = w1*lbound(j,k);
-            vals(3) = w1*ubound(j,k);
+            vals(0) = w0*lbound(k,j);
+            vals(1) = w0*ubound(k,j);
+            vals(2) = w1*lbound(k,j);
+            vals(3) = w1*ubound(k,j);
             intmin(k*ncp+i) += vals.Min();
             intmax(k*ncp+i) += vals.Max();
          }
@@ -553,17 +558,17 @@ void PLBound::Get3DBounds(const Vector &coeff, Vector &intmin,
             for (int i = 0; i < nb; i++)
             {
                x = 2.0*nodes(i)-1; // x-coordinate
-               minBounds(i) -= a0V(j) + a1V(j)*x;
-               maxBounds(i) -= a0V(j) + a1V(j)*x;
+               minNodalVals(i) -= a0V(j) + a1V(j)*x;
+               maxNodalVals(i) -= a0V(j) + a1V(j)*x;
             }
             // Compute Bernstein coefficients
             LUFactors lu(basisMatLU.GetData(), lu_ip.GetData());
-            lu.Solve(nb, 1, minBounds.GetData());
-            lu.Solve(nb, 1, maxBounds.GetData());
+            lu.Solve(nb, 1, minNodalVals.GetData());
+            lu.Solve(nb, 1, maxNodalVals.GetData());
             for (int i = 0; i < nb; i++)
             {
-               intminT(i*ncp2+j) = minBounds(i);
-               intmaxT(i*ncp2+j) = maxBounds(i);
+               intminT(i*ncp2+j) = minNodalVals(i);
+               intmaxT(i*ncp2+j) = maxNodalVals(i);
             }
          }
       }
@@ -617,10 +622,10 @@ void PLBound::Get3DBounds(const Vector &coeff, Vector &intmin,
          real_t w1 = intmaxT(id2++);
          for (int k = 0; k < ncp; k++) // kth slice
          {
-            vals(0) = w0*lbound(j,k);
-            vals(1) = w0*ubound(j,k);
-            vals(2) = w1*lbound(j,k);
-            vals(3) = w1*ubound(j,k);
+            vals(0) = w0*lbound(k,j);
+            vals(1) = w0*ubound(k,j);
+            vals(2) = w1*lbound(k,j);
+            vals(3) = w1*ubound(k,j);
             intmin(k*ncp2+i) += vals.Min();
             intmax(k*ncp2+i) += vals.Max();
          }
@@ -653,7 +658,8 @@ void PLBound::SetupBernsteinBasisMat(DenseMatrix &basisMat,
                                      Vector &nodesBern) const
 {
    const int nbern = nodesBern.Size();
-   L2_SegmentElement el(nbern-1, 2); // we use L2 to leverage lexicographic order
+   L2_SegmentElement el(nbern-1, 2);
+   // we use L2 to leverage lexicographic order
    Array<int> ordering = el.GetLexicographicOrdering();
    basisMat.SetSize(nbern, nbern);
    Vector shape(nbern);
@@ -666,6 +672,39 @@ void PLBound::SetupBernsteinBasisMat(DenseMatrix &basisMat,
    }
 }
 
+DenseMatrix PLBound::GetBoundingMatrix(int dim, bool is_lower) const
+{
+   if (dim > 1)
+   {
+      const int ncpd = static_cast<int>(std::pow(ncp, dim));
+      const int nbd = static_cast<int>(std::pow(nb, dim));
+      DenseMatrix boundND(ncpd, nbd);
+      Vector phimin, phimax, col;
+      Vector coeffs(nbd);
+      coeffs = 0.0;
+      for (int j = 0; j < nbd; j++)
+      {
+         coeffs(j) = 1.0;
+         boundND.GetColumnReference(j, col);
+         GetNDBounds(dim, coeffs, phimin, phimax);
+         col = is_lower ? phimin : phimax;
+         coeffs(j) = 0.0;
+      }
+      return boundND;
+   }
+   return is_lower ? lbound : ubound;
+}
+
+DenseMatrix PLBound::GetLowerBoundMatrix(int dim) const
+{
+   return GetBoundingMatrix(dim, true);
+}
+
+DenseMatrix PLBound::GetUpperBoundMatrix(int dim) const
+{
+   return GetBoundingMatrix(dim, false);
+}
+
 constexpr int PLBound::min_ncp_gl_x[2][11];
 constexpr int PLBound::min_ncp_gll_x[2][11];
 constexpr int PLBound::min_ncp_pos_x[2][11];
@@ -716,4 +755,4 @@ void PLBound::Print(std::ostream &outp) const
    ubound.Print(outp);
 }
 
-}
+}

fem/bounds.hpp

@@ -19,14 +19,18 @@ namespace mfem
 {
 
 /** @name Piecewise linear bounds of bases
-    \brief Piecewise linear bounds of bases can be used to compute bounds on the grid function in each element. The bounds for the bases are constructed based on the following parameters:
+    \brief Piecewise linear bounds of bases can be used to compute bounds on
+    the grid function in each element. The bounds for the bases are constructed
+    based on the following parameters:
 
     (i) @b nb: number of bases/nodes in 1D (i.e. polynomial order+1),
 
-    (ii) @b b_type: bases type, 0 - Lagrange interpolants on Gauss-Legendre nodes, 1 - Lagrange interpolants on Gauss-Lobatto-Legendre nodes, and
+    (ii) @b b_type: bases type, 0 - Lagrange interpolants on Gauss-Legendre
+    nodes, 1 - Lagrange interpolants on Gauss-Lobatto-Legendre nodes, and
     2 - Positive/Bernstein bases on uniformly distributed nodes,
 
-    (iii) @b ncp: number of control points used to construct the piecewise linear bounds
+    (iii) @b ncp: number of control points used to construct the piecewise
+    linear bounds
 
     (iv) @b cp_type: control point distribution. 0 - GL + end-points,
                     1 - Chebyshev.
@@ -35,7 +39,9 @@ namespace mfem
 
     If the user does not specify @b ncp and @b cp_type, the minimum value of
     @b ncp is used that would bound the bases for the @b cp_type. We default
-    to @b cp_type = 0 as it requires fewer number of points to bound the bases. Typically, @b ncp = 2 @b nb is sufficient to get fairly compact bounds, and increasing @b ncp results in tighter bounds.
+    to @b cp_type = 0 as it requires fewer number of points to bound the bases.
+    Typically, @b ncp = 2 @b nb is sufficient to get fairly compact bounds, and
+    increasing @b ncp results in tighter bounds.
 
     Finally, only tensor-product elements are currently supported.
 
@@ -54,7 +60,7 @@ private:
    bool proj = true; // Use linear projection to compute bounds.
    real_t tol = 0.0; // offset bounds to avoid round-off errors
    Vector nodes, weights, control_points;
-   DenseMatrix lbound, ubound; // nb x ncp matrices with bounds of all bases
+   DenseMatrix lbound, ubound; // ncp x nb matrices with bounds of all bases
    // Some auxillary storage for computing the bounds with Bernstein
    DenseMatrix basisMatNodes; // Bernstein bases at equispaced nodes
    DenseMatrix basisMatInt;   // Bernstein bases at GLL nodes
@@ -80,6 +86,9 @@ private:
       {3,5,8,9,11,12,13,13,14,15,16}
    };
 
+   /// Helper function to extract lower or upper bounding matrix
+   DenseMatrix GetBoundingMatrix(int dim, bool is_lower) const;
+
 public:
    // Constructor
    PLBound(const int nb_i, const int ncp_i, const int b_type_i,
@@ -92,40 +101,82 @@ public:
    PLBound(const FiniteElementSpace *fes,
            const int ncp_i = -1, const int cp_type_i = 0);
 
-   // Get minimum number of control points needed to bound the given bases
+   /// Get minimum number of control points needed to bound the given bases
    int GetMinimumPointsForGivenBases(int nb_i, int b_type_i,
                                      int cp_type_i) const;
 
-   // Print information about the bounds
+   /// Print information about the bounds
    void Print(std::ostream &outp = mfem::out) const;
 
-   // Enable (default) or disable linear projection before bounding.
-   // This projection increases the computational cost but results in tighter
-   // bounds.
+   /** @brief Enable (default) or disable linear projection before bounding.
+    *
+    *  @details This projection increases the computational cost but results in
+    *  tighter bounds.
+    */
    void SetProjectionFlagForBounding(bool proj_) { proj = proj_; }
 
-   /// Compute piecewise linear bounds for the lexicographically-ordered
-   /// coefficients in @a coeff in 1D/2D/3D.
+   /** @brief Compute piecewise linear bounds for the lexicographically-ordered
+    *  nodal coefficients in @a coeff in 1D/2D/3D.
+    *
+    *  @param[in] rdim    The spatial dimension of the element (1, 2, or 3).
+    *  @param[in] coeff   The vector of lexicographically-ordered coefficients.
+    *                     Should be of size nb^rdim, where nb is the number of
+    *                     bases/nodes in 1D. These coefficients must correspond
+    *                     to the bases type and number of bases, used in the
+    *                     constructor of PLBound.
+    *
+    *  @param[out] intmin The vector of minimum bound for all control points.
+    *  @param[out] intmax The vector of maximum bound for all control points.
+    *                     Both intmin and intmax are of size ncp^rdim, where
+    *                     ncp is the number of control points in 1D, and are
+    *                     ordered lexicographically.
+    */
    void GetNDBounds(const int rdim, const Vector &coeff,
                     Vector &intmin, Vector &intmax) const;
 
    /// Get number of control points used to compute the bounds.
    int GetNControlPoints() const { return ncp; }
+
+   /// Get 1D control point locations (lexicographic order) in [0,1].
+   const Vector &GetControlPoints() const { return control_points; }
+
+   /** @brief Get lower and upper bounding matrix (ncp^dim x nb^dim)
+    *
+    *  @details The matrices can be used to compute the bounds at control points
+    *           by a simple matrix-vector product with the
+    *           lexicographically-ordered nodal coefficients.
+    *           The resulting output is also lexicographically-ordered.
+    *
+    *  @note These matrices do not account for the linear projection step that
+    *        is optionally done in GetNDBounds before bounding the function.
+    */
+   ///@{
+   DenseMatrix GetLowerBoundMatrix(int dim = 1) const;
+   DenseMatrix GetUpperBoundMatrix(int dim = 1) const;
+   ///@}
+
 private:
-   /// Compute piecewise linear bounds for the lexicographically-ordered
-   /// coefficients in @a coeff in 1D.
+   /** @brief Compute piecewise linear bounds for the lexicographically-ordered
+    *  nodal coefficients in @a coeff in 1D.
+    *  See GetNDBounds for details of the input and output parameters.
+    */
    void Get1DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
 
-   /// Compute piecewise linear bounds for the lexicographically-ordered
-   /// coefficients in @a coeff in 2D.
+   /** @brief Compute piecewise linear bounds for the lexicographically-ordered
+    *  nodal coefficients in @a coeff in 2D.
+    *  See GetNDBounds for details of the input and output parameters.
+    */
    void Get2DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
 
-   /// Compute piecewise linear bounds for the lexicographically-ordered
-   /// coefficients in @a coeff in 3D.
+   /** @brief Compute piecewise linear bounds for the lexicographically-ordered
+    *  nodal coefficients in @a coeff in 3D.
+    *  See GetNDBounds for details of the input and output parameters.
+    */
    void Get3DBounds(const Vector &coeff, Vector &intmin, Vector &intmax) const;
 
-   /// Setup matrix used to compute values at given 1D locations in [0,1]
-   /// for Bernstein bases.
+   /** @brief Setup matrix used to compute values at given 1D locations in [0,1]
+    *  for Bernstein bases.
+    */
    void SetupBernsteinBasisMat(DenseMatrix &basisMat, Vector &nodesBern) const;
 
    void Setup(const int nb_i, const int ncp_i, const int b_type_i,

fem/coefficient.hpp

@@ -52,6 +52,9 @@ public:
    /// Get the time for time dependent coefficients
    real_t GetTime() { return time; }
 
+   /// Returns dimension of the vector.
+   int GetVDim() { return 1; }
+
    /** @brief Evaluate the coefficient in the element described by @a T at the
        point @a ip. */
    /** @note When this method is called, the caller must make sure that the

fem/complex_fem.hpp

@@ -82,6 +82,25 @@ public:
    /// underlying #fes
    int VectorDim() const;
 
+   /// Copy assignment. Only the data of the base class Vector is copied.
+   /** It is assumed that this object and @a rhs use FiniteElementSpace%s that
+       have the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignment operator. */
+   ComplexGridFunction &operator=(const ComplexGridFunction &rhs)
+   { return operator=((const Vector &)rhs); }
+
+   /// Copy the data from @a v.
+   /** The size of @a v must be equal to double of the size of the associated
+       FiniteElementSpace #fes. */
+   ComplexGridFunction &operator=(const Vector &v)
+   {
+      MFEM_ASSERT(fes && v.Size() == 2*fes->GetVSize(), "");
+      Vector::operator=(v);
+      return *this;
+   }
+
    /// Assign constant values to the ComplexGridFunction data.
    ComplexGridFunction &operator=(const std::complex<real_t> & value)
    { *gfr = value.real(); *gfi = value.imag(); return *this; }

fem/datacollection.cpp

@@ -492,6 +492,8 @@ void VisItDataCollection::SaveRootFile()
                            to_padded_string(cycle, pad_digits_cycle) +
                            ".mfem_root";
    std::ofstream root_file(root_name);
+   MFEM_VERIFY(root_file.is_open(),
+               "Failed to open ofstream " << root_name);
    root_file << GetVisItRootString();
    if (!root_file)
    {
@@ -977,7 +979,10 @@ void ParaViewDataCollection::Save()
    // Save the local part of the mesh and grid functions fields to the local
    // VTU file. Also save coefficient fields.
    {
-      std::ofstream os(vtu_prefix + GenerateVTUFileName("proc", myid));
+      std::string os_str = vtu_prefix + GenerateVTUFileName("proc", myid);
+      std::ofstream os(os_str);
+      MFEM_VERIFY(os.is_open(),
+                  "Failed to open ofstream " << os_str);
       os.precision(precision);
       SaveDataVTU(os, levels_of_detail);
    }
@@ -989,7 +994,10 @@ void ParaViewDataCollection::Save()
                   "QuadratureFunction output is not supported for "
                   "ParaViewDataCollection on domain boundary!");
       const std::string &field_name = qfield.first;
-      std::ofstream os(vtu_prefix + GenerateVTUFileName(field_name, myid));
+      std::string os_str = vtu_prefix + GenerateVTUFileName(field_name, myid);
+      std::ofstream os(os_str);
+      MFEM_VERIFY(os.is_open(),
+                  "Failed to open ofstream " << os_str);
       qfield.second->SaveVTU(os, pv_data_format, GetCompressionLevel(), field_name);
    }
 
@@ -1000,7 +1008,10 @@ void ParaViewDataCollection::Save()
    {
       // Create the main PVTU file
       {
-         std::ofstream pvtu_out(vtu_prefix + GeneratePVTUFileName("data"));
+         std::string os_str = vtu_prefix + GeneratePVTUFileName("data");
+         std::ofstream pvtu_out(os_str);
+         MFEM_VERIFY(pvtu_out.is_open(),
+                     "Failed to open ofstream " << os_str);
          WritePVTUHeader(pvtu_out);
 
          // Grid function fields and coefficient fields
@@ -1055,8 +1066,10 @@ void ParaViewDataCollection::Save()
          const std::string &q_field_name = q_field.first;
          std::string q_fname = GeneratePVTUPath() + "/"
                                + GeneratePVTUFileName(q_field_name);
-
-         std::ofstream pvtu_out(col_path + "/" + q_fname);
+         std::string os_str = col_path + "/" + q_fname;
+         std::ofstream pvtu_out(os_str);
+         MFEM_VERIFY(pvtu_out.is_open(),
+                     "Failed to open ofstream " << os_str);
          WritePVTUHeader(pvtu_out);
          int vec_dim = q_field.second->GetVDim();
          pvtu_out << "<PPointData>\n";

fem/dfem/integrate.hpp

@@ -90,8 +90,8 @@ void map_quadrature_data_to_fields_impl(
    }
    else
    {
-      MFEM_ABORT("quadrature data mapping to field is not implemented for"
-                 " this field descriptor");
+      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
+                        " for this field descriptor");
    }
 }
 
@@ -169,8 +169,9 @@ void map_quadrature_data_to_fields_tensor_impl_1d(
    }
    else
    {
-      MFEM_ABORT("quadrature data mapping to field is not implemented for"
-                 " this field descriptor with sum factorization on tensor product elements");
+      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
+                        "for this field descriptor with sum factorization on"
+                        " tensor product elements");
    }
 }
 
@@ -306,8 +307,9 @@ void map_quadrature_data_to_fields_tensor_impl_2d(
    }
    else
    {
-      MFEM_ABORT("quadrature data mapping to field is not implemented for"
-                 " this field descriptor with sum factorization on tensor product elements");
+      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
+                        " for this field descriptor with sum factorization on"
+                        " tensor product elements");
    }
 }
 
@@ -492,8 +494,9 @@ void map_quadrature_data_to_fields_tensor_impl_3d(
    }
    else
    {
-      MFEM_ABORT("quadrature data mapping to field is not implemented for"
-                 " this field descriptor with sum factorization on tensor product elements");
+      MFEM_ABORT_KERNEL("quadrature data mapping to field is not implemented"
+                        " for this field descriptor with sum factorization on"
+                        " tensor product elements");
    }
 }
 

fem/dgmassinv_kernels.hpp

@@ -57,7 +57,7 @@ void DGMassApply(const int e,
       }
       else if (DIM == 3)
       {
-         SmemPAMassApply3D_Element<TD1D,TQ1D,ACCUM>(e, NE, B, pa_data, x, y);
+         SmemPAMassApply3D_Element<TD1D,TQ1D,NBZ,ACCUM>(e, NE, B, pa_data, x, y);
       }
       else
       {

fem/estimators.hpp

@@ -320,8 +320,8 @@ public:
     error estimation procedure where the flux averaging is replaced by a global
     L2 projection (requiring a mass matrix solve).
 
-    The required BilinearFormIntegrator must implement the methods
-    ComputeElementFlux() and ComputeFluxEnergy().
+    The required BilinearFormIntegrator must implement the method
+    ComputeElementFlux().
 
     Implemented for the parallel case only.
  */
@@ -357,8 +357,8 @@ protected:
 
 public:
    /** @brief Construct a new L2ZienkiewiczZhuEstimator object.
-       @param integ    This BilinearFormIntegrator must implement the methods
-                       ComputeElementFlux() and ComputeFluxEnergy().
+       @param integ    This BilinearFormIntegrator must implement the method
+                       ComputeElementFlux().
        @param sol      The solution field whose error is to be estimated.
        @param flux_fes The L2ZienkiewiczZhuEstimator assumes ownership of this
                        FiniteElementSpace and will call its Update() method when
@@ -382,8 +382,8 @@ public:
    { }
 
    /** @brief Construct a new L2ZienkiewiczZhuEstimator object.
-       @param integ    This BilinearFormIntegrator must implement the methods
-                       ComputeElementFlux() and ComputeFluxEnergy().
+       @param integ    This BilinearFormIntegrator must implement the method
+                       ComputeElementFlux().
        @param sol      The solution field whose error is to be estimated.
        @param flux_fes The L2ZienkiewiczZhuEstimator does NOT assume ownership
                        of this FiniteElementSpace; will call its Update() method

fem/fe/fe_base.cpp

@@ -663,58 +663,59 @@ const
    #pragma omp critical (DofToQuad)
 #endif
    {
-      // If the new Dof2Quad is already present, e.g. added in a previous call
-      // or added by another omp thread, return.
+      // Do not run if the new Dof2Quad is already present, e.g. added in a
+      // previous call or added by another omp thread.
       if (DofToQuad::SearchArray(dof2quad_array, ir,
-                                 DofToQuad::LEXICOGRAPHIC_FULL))
-      { return; }
-
-      // Undo the native ordering which is what FiniteElement::GetDofToQuad
-      // returns.
-      auto *d2q_new = new DofToQuad(d2q);
-      d2q_new->mode = DofToQuad::LEXICOGRAPHIC_FULL;
-      const int nqpt = ir.GetNPoints();
-
-      const int b_dim = (range_type == VECTOR) ? dim : 1;
-
-      for (int i = 0; i < nqpt; i++)
+                                 DofToQuad::LEXICOGRAPHIC_FULL) == nullptr)
       {
-         for (int d = 0; d < b_dim; d++)
+         // Undo the native ordering which is what FiniteElement::GetDofToQuad
+         // returns.
+         auto *d2q_new = new DofToQuad(d2q);
+         d2q_new->mode = DofToQuad::LEXICOGRAPHIC_FULL;
+         const int nqpt = ir.GetNPoints();
+
+         const int b_dim = (range_type == VECTOR) ? dim : 1;
+
+         for (int i = 0; i < nqpt; i++)
          {
-            for (int j = 0; j < dof; j++)
+            for (int d = 0; d < b_dim; d++)
             {
-               const double val = d2q.B[i + nqpt*(d+b_dim*lex_ordering[j])];
-               d2q_new->B[i+nqpt*(d+b_dim*j)] = val;
-               d2q_new->Bt[j+dof*(i+nqpt*d)] = val;
+               for (int j = 0; j < dof; j++)
+               {
+                  const double val = d2q.B[i + nqpt*(d+b_dim*lex_ordering[j])];
+                  d2q_new->B[i+nqpt*(d+b_dim*j)] = val;
+                  d2q_new->Bt[j+dof*(i+nqpt*d)] = val;
+               }
             }
          }
-      }
 
-      const int g_dim = [this]()
-      {
-         switch (deriv_type)
+         const int g_dim = [this]()
          {
-            case GRAD: return dim;
-            case DIV: return 1;
-            case CURL: return cdim;
-            default: return 0;
-         }
-      }();
-
-      for (int i = 0; i < nqpt; i++)
-      {
-         for (int d = 0; d < g_dim; d++)
-         {
-            for (int j = 0; j < dof; j++)
+            switch (deriv_type)
             {
-               const double val = d2q.G[i + nqpt*(d+g_dim*lex_ordering[j])];
-               d2q_new->G[i+nqpt*(d+g_dim*j)] = val;
-               d2q_new->Gt[j+dof*(i+nqpt*d)] = val;
+               case GRAD: return dim;
+               case DIV: return 1;
+               case CURL: return cdim;
+               default: return 0;
+            }
+         }();
+
+         for (int i = 0; i < nqpt; i++)
+         {
+            for (int d = 0; d < g_dim; d++)
+            {
+               for (int j = 0; j < dof; j++)
+               {
+                  const double val = d2q.G[i + nqpt*(d+g_dim*lex_ordering[j])];
+                  d2q_new->G[i+nqpt*(d+g_dim*j)] = val;
+                  d2q_new->Gt[j+dof*(i+nqpt*d)] = val;
+               }
             }
          }
+
+         dof2quad_array.Append(d2q_new);
       }
 
-      dof2quad_array.Append(d2q_new);
    }
 }
 
@@ -1043,9 +1044,50 @@ void VectorFiniteElement::SetDerivMembers()
    switch (map_type)
    {
       case H_DIV:
-         deriv_type = DIV;
-         deriv_range_type = SCALAR;
-         deriv_map_type = INTEGRAL;
+         switch (dim)
+         {
+            case 3: // div: 3D H_DIV -> 3D INTEGRAL
+               deriv_type = DIV;
+               deriv_range_type = SCALAR;
+               deriv_map_type = INTEGRAL;
+               break;
+            case 2: // div: 2D H_DIV -> 2D INTEGRAL
+               deriv_type = DIV;
+               deriv_range_type = SCALAR;
+               deriv_map_type = INTEGRAL;
+               break;
+            default:
+               MFEM_ABORT("Invalid dimension, Dim = " << dim);
+         }
+         break;
+      case H_DIV_R2D:
+         switch (dim)
+         {
+            case 2: // div: 2D H_DIV_R2D -> 2D INTEGRAL
+               deriv_type = DIV;
+               deriv_range_type = SCALAR;
+               deriv_map_type = INTEGRAL;
+               break;
+            case 1: // div: 1D H_DIV_R2D -> 1D INTEGRAL
+               deriv_type = DIV;
+               deriv_range_type = SCALAR;
+               deriv_map_type = INTEGRAL;
+               break;
+            default:
+               MFEM_ABORT("Invalid dimension, Dim = " << dim);
+         }
+         break;
+      case H_DIV_R1D:
+         switch (dim)
+         {
+            case 1: // div: 1D H_DIV_R1D -> 1D INTEGRAL
+               deriv_type = DIV;
+               deriv_range_type = SCALAR;
+               deriv_map_type = INTEGRAL;
+               break;
+            default:
+               MFEM_ABORT("Invalid dimension, Dim = " << dim);
+         }
          break;
       case H_CURL:
          switch (dim)
@@ -1063,13 +1105,49 @@ void VectorFiniteElement::SetDerivMembers()
                break;
             case 1:
                deriv_type = NONE;
-               deriv_range_type = SCALAR;
-               deriv_map_type = INTEGRAL;
+               deriv_range_type = UNKNOWN_RANGE_TYPE;
+               deriv_map_type = UNKNOWN_MAP_TYPE;
                break;
             default:
                MFEM_ABORT("Invalid dimension, Dim = " << dim);
          }
          break;
+      case H_CURL_R2D:
+         switch (dim)
+         {
+            case 2:
+               // curl: 2D H_CURL_R2D -> H_DIV_R2D
+               deriv_type = CURL;
+               deriv_range_type = VECTOR;
+               deriv_map_type = H_DIV_R2D;
+               break;
+            case 1:
+               // curl: 1D H_CURL_R2D -> H_DIV_R2D
+               deriv_type = CURL;
+               deriv_range_type = VECTOR;
+               deriv_map_type = H_DIV_R2D;
+               break;
+            default:
+               MFEM_ABORT("Invalid dimension, Dim = " << dim);
+         }
+         break;
+      case H_CURL_R1D:
+         switch (dim)
+         {
+            case 1:
+               // curl: 1D H_CURL_R1D -> H_DIV_R1D
+               deriv_type = CURL;
+               deriv_range_type = VECTOR;
+               deriv_map_type = H_DIV_R1D;
+               break;
+            case 0:
+               deriv_type = NONE;
+               deriv_range_type = UNKNOWN_RANGE_TYPE;
+               deriv_map_type = UNKNOWN_MAP_TYPE;
+            default:
+               MFEM_ABORT("Invalid dimension, Dim = " << dim);
+         }
+         break;
       default:
          MFEM_ABORT("Invalid MapType = " << map_type);
    }

fem/fe/fe_base.hpp

@@ -295,10 +295,20 @@ public:
                           $ u(x) = (1/w) \hat u(\hat x) $ */
       H_DIV,     /**< For vector fields; preserves surface integrals of the
                           normal component $ u(x) = (J/w) \hat u(\hat x) $ */
-      H_CURL     /**< For vector fields; preserves line integrals of the
+      H_CURL,    /**< For vector fields; preserves line integrals of the
                           tangential component
                           $ u(x) = J^{-t} \hat u(\hat x) $ (square J),
                           $ u(x) = J(J^t J)^{-1} \hat u(\hat x) $ (general J) */
+      H_DIV_R2D, /**< For 3-component vector fields in 2D; equivalent to a
+                          direct sum of an H_DIV basis and an INTEGRAL basis */
+      H_CURL_R2D,/**< For 3-component vector fields in 2D; equivalent to a
+                          direct sum of an H_CURL basis and a VALUE basis */
+      H_DIV_R1D, /**< For 3-component vector fields in 1D; equivalent to a
+                          direct sum of a VALUE basis and a pair of INTEGRAL
+                          bases */
+      H_CURL_R1D /**< For 3-component vector fields in 1D; equivalent to a
+                          direct sum of an INTEGRAL basis and a pair of VALUE
+                          bases */
    };
 
    /** @brief Enumeration for DerivType: defines which derivative method
@@ -330,12 +340,28 @@ public:
    int GetDim() const { return dim; }
 
    /** @brief Returns the vector dimension for vector-valued finite elements,
-       which is also the dimension of the interpolation operation. */
+       which is also the dimension of the interpolation operation and the
+       width of the DenseMatrix argument in
+       CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape). */
    int GetRangeDim() const { return vdim; }
 
-   /// Returns the dimension of the curl for vector-valued finite elements.
+   /** @brief Returns the vector dimension, in physical space, for
+       vector-valued finite elements, which is also the width of the
+       DenseMatrix argument in
+       CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape). */
+   virtual int GetPhysRangeDim(int /* space_dim */) const { return vdim; }
+
+   /** Returns the dimension of the curl for vector-valued finite elements,
+       which is also the width of the DenseMatrix argument in
+       CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape). */
    int GetCurlDim() const { return cdim; }
 
+   /** Returns the dimension, in physical space, of the curl for vector-valued
+       finite elements, which is also the width of the DenseMatrix argument in
+       CalcPhysCurlShape(ElementTransformation &Trans, DenseMatrix &curl_shape).
+   */
+   virtual int GetPhysCurlDim(int /* space_dim */) const { return cdim; }
+
    /// Returns the Geometry::Type of the reference element.
    Geometry::Type GetGeomType() const { return geom_type; }
 
@@ -990,6 +1016,8 @@ protected:
 public:
    VectorFiniteElement(int D, Geometry::Type G, int Do, int O, int M,
                        int F = FunctionSpace::Pk);
+
+   int GetPhysRangeDim(int space_dim) const override { return space_dim; }
 };
 
 /// @brief Class for computing 1D special polynomials and their associated basis

fem/fe/fe_h1.cpp

@@ -589,7 +589,7 @@ void H1_TriangleElement::CalcHessian(const IntegrationPoint &ip,
    Vector   shape_x(p + 1),   shape_y(p + 1),   shape_l(p + 1);
    Vector  dshape_x(p + 1),  dshape_y(p + 1),  dshape_l(p + 1);
    Vector ddshape_x(p + 1), ddshape_y(p + 1), ddshape_l(p + 1);
-   DenseMatrix ddu(dof, dim);
+   DenseMatrix ddu(dof, (dim*(dim+1))/2);
 #endif
 
    poly1d.CalcBasis(p, ip.x, shape_x, dshape_x, ddshape_x);

fem/fe/fe_nd.cpp

@@ -2531,7 +2531,7 @@ void ND_FuentesPyramidElement::calcCurlBasis(const int p,
 
 ND_R1D_PointElement::ND_R1D_PointElement(int p)
    : VectorFiniteElement(1, Geometry::POINT, 2, p,
-                         H_CURL, FunctionSpace::Pk)
+                         H_CURL_R1D, FunctionSpace::Pk)
 {
    // VectorFiniteElement::SetDerivMembers doesn't support 0D H_CURL elements
    // so we mimic a 1D element and then correct the dimension here.
@@ -2562,7 +2562,7 @@ ND_R1D_SegmentElement::ND_R1D_SegmentElement(const int p,
                                              const int cb_type,
                                              const int ob_type)
    : VectorFiniteElement(1, Geometry::SEGMENT, 3 * p + 2, p,
-                         H_CURL, FunctionSpace::Pk),
+                         H_CURL_R1D, FunctionSpace::Pk),
      dof2tk(dof),
      cbasis1d(poly1d.GetBasis(p, VerifyClosed(cb_type))),
      obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(ob_type)))
@@ -2839,7 +2839,7 @@ ND_R2D_SegmentElement::ND_R2D_SegmentElement(const int p,
                                              const int cb_type,
                                              const int ob_type)
    : VectorFiniteElement(1, Geometry::SEGMENT, 2 * p + 1, p,
-                         H_CURL, FunctionSpace::Pk),
+                         H_CURL_R2D, FunctionSpace::Pk),
      dof2tk(dof),
      cbasis1d(poly1d.GetBasis(p, VerifyClosed(cb_type))),
      obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(ob_type)))
@@ -3023,7 +3023,7 @@ void ND_R2D_SegmentElement::Project(VectorCoefficient &vc,
 ND_R2D_FiniteElement::ND_R2D_FiniteElement(int p, Geometry::Type G, int Do,
                                            const real_t *tk_fe)
    : VectorFiniteElement(2, G, Do, p,
-                         H_CURL, FunctionSpace::Pk),
+                         H_CURL_R2D, FunctionSpace::Pk),
      tk(tk_fe),
      dof_map(dof),
      dof2tk(dof)

fem/fe/fe_nd.hpp

@@ -663,6 +663,9 @@ public:
                          const int cb_type = BasisType::GaussLobatto,
                          const int ob_type = BasisType::GaussLegendre);
 
+   int GetPhysRangeDim(int space_dim) const override { return 2; }
+   int GetPhysCurlDim(int space_dim) const override { return 1; }
+
    void CalcVShape(const IntegrationPoint &ip,
                    DenseMatrix &shape) const override;
 
@@ -705,6 +708,9 @@ private:
                            DenseMatrix &I) const;
 
 public:
+   int GetPhysRangeDim(int space_dim) const override { return 3; }
+   int GetPhysCurlDim(int space_dim) const override { return 3; }
+
    using FiniteElement::CalcVShape;
    using FiniteElement::CalcPhysCurlShape;
 

fem/fe/fe_rt.cpp

@@ -2006,7 +2006,7 @@ RT_R1D_SegmentElement::RT_R1D_SegmentElement(const int p,
                                              const int cb_type,
                                              const int ob_type)
    : VectorFiniteElement(1, Geometry::SEGMENT, 3 * p + 4, p + 1,
-                         H_DIV, FunctionSpace::Pk),
+                         H_DIV_R1D, FunctionSpace::Pk),
      dof2nk(dof),
      cbasis1d(poly1d.GetBasis(p + 1, VerifyClosed(cb_type))),
      obasis1d(poly1d.GetBasis(p, VerifyOpen(ob_type)))
@@ -2281,7 +2281,7 @@ const real_t RT_R2D_SegmentElement::nk[2] = { 0.,1.};
 RT_R2D_SegmentElement::RT_R2D_SegmentElement(const int p,
                                              const int ob_type)
    : VectorFiniteElement(1, Geometry::SEGMENT, p + 1, p + 1,
-                         H_DIV, FunctionSpace::Pk),
+                         H_DIV_R2D, FunctionSpace::Pk),
      dof2nk(dof),
      obasis1d(poly1d.GetBasis(p, VerifyOpen(ob_type)))
 {
@@ -2392,7 +2392,7 @@ void RT_R2D_SegmentElement::LocalInterpolation(const VectorFiniteElement &cfe,
 RT_R2D_FiniteElement::RT_R2D_FiniteElement(int p, Geometry::Type G, int Do,
                                            const real_t *nk_fe)
    : VectorFiniteElement(2, G, Do, p + 1,
-                         H_DIV, FunctionSpace::Pk),
+                         H_DIV_R2D, FunctionSpace::Pk),
      nk(nk_fe),
      dof_map(dof),
      dof2nk(dof)

fem/fe/fe_rt.hpp

@@ -510,6 +510,9 @@ public:
    RT_R2D_SegmentElement(const int p,
                          const int ob_type = BasisType::GaussLegendre);
 
+   int GetPhysRangeDim(int space_dim) const override { return 2; }
+   int GetPhysCurlDim(int space_dim) const override { return 0; }
+
    void CalcVShape(const IntegrationPoint &ip,
                    DenseMatrix &shape) const override;
 
@@ -547,6 +550,9 @@ private:
                            DenseMatrix &I) const;
 
 public:
+   int GetPhysRangeDim(int space_dim) const override { return 3; }
+   int GetPhysCurlDim(int space_dim) const override { return 0; }
+
    using FiniteElement::CalcVShape;
 
    void CalcVShape(ElementTransformation &Trans,

fem/fespace.cpp

@@ -282,14 +282,7 @@ int FiniteElementSpace::DofToVDof(int dof, int vd, int ndofs_) const
 void FiniteElementSpace::AdjustVDofs(Array<int> &vdofs)
 {
    int n = vdofs.Size(), *vdof = vdofs;
-   for (int i = 0; i < n; i++)
-   {
-      int j;
-      if ((j = vdof[i]) < 0)
-      {
-         vdof[i] = -1-j;
-      }
-   }
+   for (int i = 0; i < n; i++) { vdof[i] = UnsignIndex(vdof[i]); }
 }
 
 void FiniteElementSpace::GetElementVDofs(int i, Array<int> &vdofs,
@@ -483,13 +476,14 @@ void FiniteElementSpace::ReorderElementToDofTable()
    for (int k = 0, dof_counter = 0; k < nnz; k++)
    {
       const int sdof = J[k]; // signed dof
-      const int dof = (sdof < 0) ? -1-sdof : sdof;
+      const int dof = UnsignIndex(sdof);
       int new_dof = dof_marker[dof];
       if (new_dof < 0)
       {
          dof_marker[dof] = new_dof = dof_counter++;
       }
-      J[k] = (sdof < 0) ? -1-new_dof : new_dof; // preserve the sign of sdof
+      // Preserve the sign of sdof
+      J[k] = (sdof < 0) ? FlipIndexSign(new_dof) : new_dof;
    }
 }
 
@@ -547,7 +541,7 @@ void MarkDofs(const Array<int> &dofs, Array<int> &mark_array)
 {
    for (auto d : dofs)
    {
-      mark_array[d >= 0 ? d : -1 - d] = -1;
+      mark_array[UnsignIndex(d)] = -1;
    }
 }
 
@@ -931,7 +925,7 @@ void FiniteElementSpace::AddDependencies(
             if (std::abs(coef) > 1e-12)
             {
                const int mdof = master_dofs[j];
-               if (mdof != sdof && mdof != (-1-sdof))
+               if (mdof != sdof && mdof != FlipIndexSign(sdof))
                {
                   deps.Add(sdof, mdof, coef);
                }
@@ -1024,7 +1018,7 @@ int FiniteElementSpace::GetDegenerateFaceDofs(int index, Array<int> &dofs,
    // FiniteElementSpace::AddDependencies.
 
    Array<int> edof;
-   int order = GetEdgeDofs(-1 - index, edof, variant);
+   int order = GetEdgeDofs(FlipIndexSign(index), edof, variant);
 
    int nv = fec->DofForGeometry(Geometry::POINT);
    int ne = fec->DofForGeometry(Geometry::SEGMENT);
@@ -1710,8 +1704,8 @@ SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
 
          for (int i = 0; i < fine_ldof; i++)
          {
-            int r = DofToVDof(dofs[i], vd);
-            int m = (r >= 0) ? r : (-1 - r);
+            const int r = DofToVDof(dofs[i], vd);
+            const int m = UnsignIndex(r);
 
             if (!mark[m])
             {
@@ -1772,7 +1766,7 @@ SparseMatrix *FiniteElementSpace::VariableOrderRefinementMatrix(
          for (int i = 0; i < fine_ldof; i++)
          {
             const int r = DofToVDof(dofs[i], vd);
-            int m = (r >= 0) ? r : (-1 - r);
+            const int m = UnsignIndex(r);
 
             if (!mark[m])
             {
@@ -2482,8 +2476,8 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
          {
             if (!std::isfinite(lR(i, 0))) { continue; }
 
-            int r = DofToVDof(dofs[i], vd);
-            int m = (r >= 0) ? r : (-1 - r);
+            const int r = DofToVDof(dofs[i], vd);
+            const int m = UnsignIndex(r);
 
             if (is_dg || !mark[m])
             {
@@ -3201,7 +3195,7 @@ void FiniteElementSpace::CalcEdgeFaceVarOrders(
             else
             {
                // degenerate face (i.e., edge-face constraint)
-               slave_orders |= edge_orders[-1 - slave.index];
+               slave_orders |= edge_orders[FlipIndexSign(slave.index)];
             }
          }
 
@@ -3940,6 +3934,16 @@ const FiniteElement *FiniteElementSpace::GetBE(int i) const
    return BE;
 }
 
+const FiniteElement *FiniteElementSpace::GetTypicalBE() const
+{
+   if (mesh->GetNBE() > 0) { return GetBE(0); }
+
+   Geometry::Type geom = mesh->GetTypicalFaceGeometry();
+   const FiniteElement *be = fec->FiniteElementForGeometry(geom);
+   MFEM_VERIFY(be != nullptr, "Could not determine a typical BE!");
+   return be;
+}
+
 const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
 {
    MFEM_VERIFY(!IsVariableOrder(), "not implemented");
@@ -3970,6 +3974,11 @@ const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
    return fe;
 }
 
+const FiniteElement *FiniteElementSpace::GetTypicalFaceElement() const
+{
+   return fec->FiniteElementForGeometry(mesh->GetTypicalFaceGeometry());
+}
+
 const FiniteElement *FiniteElementSpace::GetEdgeElement(int i,
                                                         int variant) const
 {

fem/fespace.hpp

@@ -839,7 +839,7 @@ public:
        Note: For vector-valued elements, the results pads up the range dimension
        to the spatial dimension. E.g., consider a stack of 5 vector-valued
        elements each representing 2D vectors, living in a 3 dimensional space.
-       Then this fucntion would give 15, not 10.
+       Then this function would give 15, not 10.
        */
    int GetVectorDim() const;
 
@@ -1150,7 +1150,7 @@ public:
 
    /// Helper to return the DOF associated with a sign encoded DOF
    static inline int DecodeDof(int dof)
-   { return (dof >= 0) ? dof : (-1 - dof); }
+   { return UnsignIndex(dof); }
 
    /// Helper to determine the DOF and sign of a sign encoded DOF
    static inline int DecodeDof(int dof, real_t& sign)
@@ -1323,12 +1323,24 @@ public:
         associated with i'th boundary face in the mesh object. */
    const FiniteElement *GetBE(int i) const;
 
+   /// @brief Return a "typical" boundary element.
+   ///
+   /// This can be used in situations where the local mesh partition may be
+   /// empty.
+   const FiniteElement *GetTypicalBE() const;
+
    /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
         associated with i'th face in the mesh object.  Faces in this case refer
         to the MESHDIM-1 primitive so in 2D they are segments and in 1D they are
         points.*/
    const FiniteElement *GetFaceElement(int i) const;
 
+   /// @brief Return a "typical" face element.
+   ///
+   /// This can be used in situations where the local mesh partition may be
+   /// empty.
+   const FiniteElement *GetTypicalFaceElement() const;
+
    /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
         associated with i'th edge in the mesh object. */
    const FiniteElement *GetEdgeElement(int i, int variant = 0) const;

fem/gridfunc.cpp

@@ -30,6 +30,7 @@
 #include <cmath>
 #include <iostream>
 #include <algorithm>
+#include <queue>
 
 namespace mfem
 {
@@ -344,27 +345,6 @@ void GridFunction::ComputeFlux(BilinearFormIntegrator &blfi,
    }
 }
 
-int GridFunction::VectorDim() const
-{
-   const FiniteElement *fe = fes->GetTypicalFE();
-   if (!fe || fe->GetRangeType() == FiniteElement::SCALAR)
-   {
-      return fes->GetVDim();
-   }
-   return fes->GetVDim()*std::max(fes->GetMesh()->SpaceDimension(),
-                                  fe->GetRangeDim());
-}
-
-int GridFunction::CurlDim() const
-{
-   const FiniteElement *fe = fes->GetTypicalFE();
-   if (!fe || fe->GetRangeType() == FiniteElement::SCALAR)
-   {
-      return 2 * fes->GetMesh()->SpaceDimension() - 3;
-   }
-   return fes->GetVDim()*fe->GetCurlDim();
-}
-
 void GridFunction::GetTrueDofs(Vector &tv) const
 {
    const SparseMatrix *R = fes->GetRestrictionMatrix();
@@ -2049,6 +2029,18 @@ void GridFunction::AccumulateAndCountBdrValues(
    Coefficient *coeff[], VectorCoefficient *vcoeff, const Array<int> &attr,
    Array<int> &values_counter)
 {
+   if (vcoeff)
+   {
+      MFEM_VERIFY(fes->GetVDim() == vcoeff->GetVDim(),
+                  "vcoeff vdim != fes VDim");
+      MFEM_VERIFY(fes->GetTypicalBE()->GetMapType() == FiniteElement::VALUE &&
+                  fes->GetTypicalBE()->GetRangeType() ==
+                  FiniteElement::SCALAR,
+                  "Can only call ProjectBdrCoefficient on scalar value-type "
+                  "boundary elements. "
+                  "Did you intended to call ProjectBdrCoefficientNormal or "
+                  "ProjectBdrCoefficientTangent for vector finite elements?");
+   }
    Array<int> vdofs;
    Vector vc;
 
@@ -2201,6 +2193,9 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
    VectorCoefficient &vcoeff, const Array<int> &bdr_attr,
    Array<int> &values_counter)
 {
+   MFEM_VERIFY(fes->GetTypicalBE()->GetPhysRangeDim(
+                  fes->GetMesh()->SpaceDimension()) == vcoeff.GetVDim(),
+               "vcoeff vdim != PhysRangeDim");
    const FiniteElement *fe;
    ElementTransformation *T;
    Array<int> dofs;
@@ -2354,6 +2349,9 @@ void GridFunction::ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
 
 void GridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
+   MFEM_VERIFY(
+      VectorDim() == 1,
+      "Cannot project scalar Coefficient onto vector GridFunction");
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
    DofTransformation doftrans;
    Array<int> vdofs;
@@ -2629,6 +2627,7 @@ void GridFunction::ProjectCoefficient(
 void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
                                       ProjectType type)
 {
+   MFEM_VERIFY(VectorDim() == vcoeff.GetVDim(), "vcoeff vdim != VectorDim()");
    Array<int> vdofs;
    Vector vals;
    DofTransformation doftrans;
@@ -2944,6 +2943,7 @@ void GridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
 void GridFunction::ProjectCoefficient(
    VectorCoefficient &vcoeff, Array<int> &dofs)
 {
+   MFEM_VERIFY(VectorDim() == vcoeff.GetVDim(), "vcoeff vdim != VectorDim()");
    int el = -1;
    ElementTransformation *T = NULL;
    const FiniteElement *fe = NULL;
@@ -2973,6 +2973,7 @@ void GridFunction::ProjectCoefficient(
 
 void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff, int attribute)
 {
+   MFEM_VERIFY(VectorDim() == vcoeff.GetVDim(), "vcoeff vdim != VectorDim()");
    int i;
    Array<int> vdofs;
    Vector vals;
@@ -3029,9 +3030,14 @@ void GridFunction::ProjectCoefficient(Coefficient *coeff[])
    }
 }
 
-void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
-                                          Array<int> &dof_attr)
+void GridFunction::ProjectDiscCoefficient(
+   std::variant<Coefficient*, VectorCoefficient*> coeff, Array<int> &dof_attr)
 {
+   std::visit([&](auto* c)
+   {
+      MFEM_VERIFY(VectorDim() == c->GetVDim(), "coeff vdim != VectorDim()");
+   }, coeff);
+
    Array<int> vdofs;
    Vector vals;
 
@@ -3045,7 +3051,10 @@ void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
    {
       fes->GetElementVDofs(i, vdofs);
       vals.SetSize(vdofs.Size());
-      fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+      std::visit([&](auto* c)
+      {
+         fes->GetFE(i)->Project(*c, *fes->GetElementTransformation(i), vals);
+      }, coeff);
 
       // the values in shared dofs are determined from the element with maximal
       // attribute
@@ -3061,17 +3070,15 @@ void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
    }
 }
 
-void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
-{
-   Array<int> dof_attr;
-   ProjectDiscCoefficient(coeff, dof_attr);
-}
-
 void GridFunction::ProjectDiscCoefficient(Coefficient &coeff, AvgType type)
 {
    // Harmonic  (x1 ... xn) = [ (1/x1 + ... + 1/xn) / n ]^-1.
    // Arithmetic(x1 ... xn) = (x1 + ... + xn) / n.
 
+   MFEM_VERIFY(
+      VectorDim() == 1,
+      "Cannot project a scalar coefficient onto a vector GridFunction");
+
    Array<int> zones_per_vdof;
    AccumulateAndCountZones(coeff, type, zones_per_vdof);
 
@@ -3081,6 +3088,7 @@ void GridFunction::ProjectDiscCoefficient(Coefficient &coeff, AvgType type)
 void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
                                           AvgType type)
 {
+   MFEM_VERIFY(VectorDim() == coeff.GetVDim(), "coeff vdim != VectorDim()");
    Array<int> zones_per_vdof;
    AccumulateAndCountZones(coeff, type, zones_per_vdof);
 
@@ -3136,52 +3144,33 @@ void GridFunction::ProjectBdrCoefficient(Coefficient *coeff[],
 }
 
 void GridFunction::ProjectBdrCoefficientNormal(
-   VectorCoefficient &vcoeff, const Array<int> &bdr_attr)
+   Coefficient *coeff, VectorCoefficient *vcoeff, const Array<int> &bdr_attr)
 {
-#if 0
-   // implementation for the case when the face dofs are integrals of the
-   // normal component.
-   const FiniteElement *fe;
-   ElementTransformation *T;
-   Array<int> dofs;
-   int dim = vcoeff.GetVDim();
-   Vector vc(dim), nor(dim), lvec, shape;
-
-   for (int i = 0; i < fes->GetNBE(); i++)
+   MFEM_VERIFY(fes->GetVDim() == 1, "fespace VDim != 1");
+   MFEM_VERIFY(fes->GetTypicalBE()->GetRangeType() == FiniteElement::SCALAR &&
+               fes->GetTypicalBE()->GetMapType() == FiniteElement::INTEGRAL,
+               "Not an RT FE space!");
+   if (vcoeff)
    {
-      if (bdr_attr[fes->GetBdrAttribute(i)-1] == 0)
-      {
-         continue;
-      }
-      fe = fes->GetBE(i);
-      T = fes->GetBdrElementTransformation(i);
-      int intorder = 2*fe->GetOrder(); // !!!
-      const IntegrationRule &ir = IntRules.Get(fe->GetGeomType(), intorder);
-      int nd = fe->GetDof();
-      lvec.SetSize(nd);
-      shape.SetSize(nd);
-      lvec = 0.0;
-      for (int j = 0; j < ir.GetNPoints(); j++)
-      {
-         const IntegrationPoint &ip = ir.IntPoint(j);
-         T->SetIntPoint(&ip);
-         vcoeff.Eval(vc, *T, ip);
-         CalcOrtho(T->Jacobian(), nor);
-         fe->CalcShape(ip, shape);
-         lvec.Add(ip.weight * (vc * nor), shape);
-      }
-      fes->GetBdrElementDofs(i, dofs);
-      SetSubVector(dofs, lvec);
+      MFEM_VERIFY(vcoeff->GetVDim() == fes->GetMesh()->SpaceDimension(),
+                  "vcoeff vdim (" << vcoeff->GetVDim()
+                  << ") != SpaceDimension ("
+                  << fes->GetMesh()->SpaceDimension() << ")");
    }
-#else
+
    // implementation for the case when the face dofs are scaled point
    // values of the normal component.
    const FiniteElement *fe;
    ElementTransformation *T;
    Array<int> dofs;
-   int dim = vcoeff.GetVDim();
-   Vector vc(dim), nor(dim), lvec;
+   Vector vc, nor, lvec;
    DofTransformation doftrans;
+   if (vcoeff)
+   {
+      const int dim = vcoeff->GetVDim();
+      vc.SetSize(dim);
+      nor.SetSize(dim);
+   }
 
    for (int i = 0; i < fes->GetNBE(); i++)
    {
@@ -3197,15 +3186,22 @@ void GridFunction::ProjectBdrCoefficientNormal(
       {
          const IntegrationPoint &ip = ir.IntPoint(j);
          T->SetIntPoint(&ip);
-         vcoeff.Eval(vc, *T, ip);
-         CalcOrtho(T->Jacobian(), nor);
-         lvec(j) = (vc * nor);
+         if (coeff)
+         {
+            const real_t c = coeff->Eval(*T, ip);
+            lvec(j) = c * T->Weight();
+         }
+         else if (vcoeff)
+         {
+            vcoeff->Eval(vc, *T, ip);
+            CalcOrtho(T->Jacobian(), nor);
+            lvec(j) = (vc * nor);
+         }
       }
       fes->GetBdrElementDofs(i, dofs, doftrans);
       doftrans.TransformPrimal(lvec);
       SetSubVector(dofs, lvec);
    }
-#endif
 }
 
 void GridFunction::ProjectBdrCoefficientTangent(
@@ -5006,6 +5002,14 @@ real_t ExtrudeCoefficient::Eval(ElementTransformation &T,
    return sol_in.Eval(*T_in, ip);
 }
 
+void VectorExtrudeCoefficient::Eval(Vector &v, ElementTransformation &T,
+                                    const IntegrationPoint &ip)
+{
+   ElementTransformation *T_in =
+      mesh_in->GetElementTransformation(T.ElementNo / n);
+   T_in->SetIntPoint(&ip);
+   sol_in.Eval(v, *T_in, ip);
+}
 
 GridFunction *Extrude1DGridFunction(Mesh *mesh, Mesh *mesh2d,
                                     GridFunction *sol, const int ny)
@@ -5056,10 +5060,17 @@ GridFunction *Extrude1DGridFunction(Mesh *mesh, Mesh *mesh2d,
       return NULL;
    }
    FiniteElementSpace *solfes2d;
-   // assuming sol is scalar
-   solfes2d = new FiniteElementSpace(mesh2d, solfec2d);
+   const int vdim = sol->FESpace()->GetVDim();
+   solfes2d = new FiniteElementSpace(mesh2d, solfec2d, vdim);
    sol2d = new GridFunction(solfes2d);
    sol2d->MakeOwner(solfec2d);
+   if (vdim > 1)
+   {
+      VectorGridFunctionCoefficient vcsol(sol);
+      VectorExtrudeCoefficient vc2d(mesh, vcsol, ny);
+      sol2d->ProjectCoefficient(vc2d);
+   }
+   else
    {
       GridFunctionCoefficient csol(sol);
       ExtrudeCoefficient c2d(mesh, csol, ny);
@@ -5117,6 +5128,103 @@ void GridFunction::GetElementBoundsAtControlPoints(const int elem,
    }
 }
 
+void GridFunction::GetElementBoundsAtControlPoints(const int elem,
+                                                   const PLBound &plb,
+                                                   const Vector &ref_range,
+                                                   const int vdim,
+                                                   Vector &lower, Vector &upper,
+                                                   Vector &control_pos) const
+{
+   const FiniteElement *fe = fes->GetFE(elem);
+   const IntegrationRule ir_in = fe->GetNodes();
+   IntegrationRule ir_new(ir_in.GetNPoints());
+   const int dim = fes->GetMesh()->Dimension();
+   const L2_FECollection *l2fec = dynamic_cast<const L2_FECollection *>
+                                  (fes->FEColl());
+
+   const TensorBasisElement *tbe =
+      dynamic_cast<const TensorBasisElement *>(fe);
+   MFEM_VERIFY(tbe != NULL, "TensorBasis FiniteElement expected.");
+
+   const Array<int> &dof_map = tbe->GetDofMap();
+   bool lexico = (dof_map.Size() == 0);
+   bool bern = (tbe->GetBasisType() == BasisType::Positive);
+   bool h1   = (l2fec == nullptr);
+
+   Vector loc_data; // gridfunction values
+   // Construct an integration rule to evaluate the gridfunction in
+   // subinterval.
+   for (int i = 0; i < ir_in.GetNPoints(); i++)
+   {
+      IntegrationPoint &ip_new = ir_new.IntPoint(i);
+      const IntegrationPoint &ip_old =
+         ir_in.IntPoint((lexico || bern) ? i : dof_map[i]);
+      Vector ip_coord(dim);
+      ip_old.Get(ip_coord.GetData(), dim);
+      for (int d = 0; d < dim; d++)
+      {
+         ip_coord(d) = ref_range(d) +
+                       (ref_range(dim+d) - ref_range(d)) * ip_coord(d);
+      }
+      ip_new.Set(ip_coord.GetData(), dim);
+   }
+   GetValues(elem, ir_new, loc_data, vdim);
+   // At this point, the loc_data contains function values ordered
+   // lexicographically, unless we are using Bernstein bases.
+   // For Bernstein, we need to project and get coefficients first.
+
+   // For bernstein, we get coefficients corresponding to these function values
+   if (bern)
+   {
+      int bt = 4; // BasisType::ClosedUniform
+      int o = fe->GetOrder();
+      DenseMatrix projmat;
+      NodalTensorFiniteElement *ntfe = nullptr;
+      if (dim == 1)
+      {
+         if (h1) { ntfe = new H1_SegmentElement(o, bt); }
+         else    { ntfe = new L2_SegmentElement(o, bt); }
+      }
+      else if (dim == 2)
+      {
+         if (h1) { ntfe = new H1_QuadrilateralElement(o, bt); }
+         else    { ntfe = new L2_QuadrilateralElement(o, bt); }
+      }
+      else if (dim == 3)
+      {
+         if (h1) { ntfe = new H1_HexahedronElement(o, bt); }
+         else    { ntfe = new L2_HexahedronElement(o, bt); }
+      }
+      // projection matrix from H1 to Positive
+      ElementTransformation *eltran = fes->GetElementTransformation(elem);
+      fe->Project(*ntfe, *eltran, projmat);
+      Vector loc_data_temp(loc_data.Size());
+      projmat.Mult(loc_data, loc_data_temp);
+      for (int i = 0; i < dof_map.Size(); i++)
+      {
+         loc_data(i) = loc_data_temp(dof_map[i]);
+      }
+      if (dof_map.Size() == 0) { loc_data = loc_data_temp; }
+      delete ntfe;
+   }
+
+   // Get bounds at control points
+   plb.GetNDBounds(dim, loc_data, lower, upper);
+
+   // Save control point positions
+   int ncp = plb.GetNControlPoints();
+   control_pos.SetSize(dim * ncp);
+   const Vector control_pos_1D = plb.GetControlPoints();
+   for (int i = 0; i < ncp; i++)
+   {
+      for (int d = 0; d < dim; d++)
+      {
+         control_pos(i + d*ncp) =
+            ref_range(d) + (ref_range(dim+d)-ref_range(d))*control_pos_1D(i);
+      }
+   }
+}
+
 void GridFunction::GetElementBounds(const int elem, const PLBound &plb,
                                     Vector &lower, Vector &upper,
                                     const int vdim) const
@@ -5197,6 +5305,467 @@ PLBound GridFunction::GetBounds(Vector &lower, Vector &upper,
    return plb;
 }
 
+struct IntervalNode
+{
+   real_t val_min;
+   real_t val_max;
+   Array<IntervalNode *> child;
+   IntervalNode(real_t vmin, real_t vmax)
+      : val_min(vmin), val_max(vmax)
+   {
+      child.SetSize(0);
+   }
+   void AddChild(IntervalNode *ch) { child.Append(ch); }
+   real_t GetChildMinLower()
+   {
+      if (child.Size() == 0)
+      {
+         return val_min;
+      }
+      real_t valmin = numeric_limits<real_t>::max();
+      for (int i = 0; i < child.Size(); i++)
+      {
+         real_t candidate = child[i]->GetChildMinLower();
+         valmin = std::min(valmin, candidate);
+      }
+      return valmin;
+   }
+   real_t GetChildMinUpper()
+   {
+      if (child.Size() == 0)
+      {
+         return val_max;
+      }
+      real_t valmax = numeric_limits<real_t>::max();
+      for (int i = 0; i < child.Size(); i++)
+      {
+         real_t candidate = child[i]->GetChildMinUpper();
+         valmax = std::min(valmax, candidate);
+      }
+      return valmax;
+   }
+   real_t GetChildMaxLower()
+   {
+      if (child.Size() == 0)
+      {
+         return val_min;
+      }
+      real_t valmin = numeric_limits<real_t>::lowest();
+      for (int i = 0; i < child.Size(); i++)
+      {
+         real_t candidate = child[i]->GetChildMaxLower();
+         valmin = std::max(valmin, candidate);
+      }
+      return valmin;
+   }
+   real_t GetChildMaxUpper()
+   {
+      if (child.Size() == 0)
+      {
+         return val_max;
+      }
+      real_t valmax = numeric_limits<real_t>::lowest();
+      for (int i = 0; i < child.Size(); i++)
+      {
+         real_t candidate = child[i]->GetChildMaxUpper();
+         valmax = std::max(valmax, candidate);
+      }
+      return valmax;
+   }
+   void DeleteChildren()
+   {
+      for (int i = 0; i < child.Size(); i++)
+      {
+         child[i]->DeleteChildren();
+         delete child[i];
+      }
+      child.SetSize(0);
+   }
+};
+
+struct SearchInterval
+{
+   Vector ref_range;
+   int depth;
+   IntervalNode *node;
+   SearchInterval(const Vector &ref_range_in, int d, IntervalNode *n)
+      : ref_range(ref_range_in), depth(d), node(n)
+   { }
+};
+
+struct IntervalCompareMin
+{
+   bool operator()(const SearchInterval *a, const SearchInterval *b) const
+   {
+      return a->node->val_min > b->node->val_min;
+   }
+};
+
+struct IntervalCompareMax
+{
+   bool operator()(const SearchInterval *a, const SearchInterval *b) const
+   {
+      return a->node->val_max < b->node->val_max;
+   }
+};
+
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMinimum(
+   const int elem, const PLBound &plb, const int vdim,
+   const int max_depth, const real_t tol) const
+{
+   real_t min_threshold = std::numeric_limits<real_t>::max();
+   return EstimateFunctionMinimum(elem, plb, vdim, max_depth, tol,
+                                  min_threshold);
 }
 
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMinimum(
+   const int elem, const PLBound &plb, const int vdim,
+   const int max_depth, const real_t tol, real_t &min_threshold) const
+{
+   const int dim = this->FESpace()->GetMesh()->Dimension();
+   const int ncp = plb.GetNControlPoints();
+   Vector pos_range(2*dim); pos_range = 0.0;
+   for (int d = 0; d < dim; d++) { pos_range(d+dim) = 1.0; }
+   Vector lower, upper, cp_ref_loc;
 
+   GetElementBoundsAtControlPoints(elem, plb, lower, upper, vdim);
+   real_t val_min = lower.Min();
+   real_t val_max = upper.Min();
+
+   min_threshold = std::min(min_threshold, val_max);
+
+   // Pruning: if the element's lower bound is greater than the current global
+   // upper bound, this element cannot contain the global minimum.
+   if (val_min >= min_threshold)
+   {
+      return std::make_pair(val_min, val_max);
+   }
+
+   if (val_min == val_max || max_depth == 0)
+   {
+      min_threshold = std::min(min_threshold, val_min);
+      return std::make_pair(val_min, val_max);
+   }
+   real_t abs_tol = tol*(val_max-val_min);
+
+   IntervalNode *initial_node = new IntervalNode(val_min, val_max);
+   SearchInterval *initial_interval = new SearchInterval(pos_range, 0,
+                                                         initial_node);
+
+   std::priority_queue<SearchInterval*,
+       std::vector<SearchInterval*>, IntervalCompareMin> pq;
+   pq.push(initial_interval);
+
+   real_t min_upper_bound = upper.Min();
+   real_t min_lower_bound = lower.Min();
+
+   while (!pq.empty())
+   {
+      SearchInterval *current = pq.top();
+      pq.pop();
+      int curr_depth = current->depth;
+
+      // Reached max depth or this interval cannot contain the global minimum
+      if (current->node->val_min >= min_threshold || curr_depth >= max_depth)
+      {
+         delete current;
+         continue;
+      }
+
+      min_lower_bound = initial_node->GetChildMinLower();
+      if (min_upper_bound - min_lower_bound < abs_tol)
+      {
+         delete current;
+         break;
+      }
+
+      // Subdivide the interval and get bounds on it
+      GetElementBoundsAtControlPoints(elem, plb, current->ref_range,
+                                      vdim, lower, upper, cp_ref_loc);
+
+      // process the bounds and create sub-intervals
+      for (int k = 0; k < (dim == 3 ? ncp-1 : 1); k++)
+      {
+         for (int j = 0; j < (dim >= 2 ? ncp-1 : 1); j++)
+         {
+            for (int i = 0; i < ncp-1; i++)
+            {
+               real_t lv = 0.0, uv = 0.0;
+               if (dim == 1)
+               {
+                  lv = std::min(lower(i), lower(i+1));
+                  uv = std::min(upper(i), upper(i+1));
+               }
+               else if (dim == 2)
+               {
+                  lv = std::min({lower(i + j*ncp), lower((i+1) + j*ncp),
+                                 lower(i + (j+1)*ncp),
+                                 lower((i+1) + (j+1)*ncp)});
+                  uv = std::min({upper(i + j*ncp), upper((i+1) + j*ncp),
+                                 upper(i + (j+1)*ncp),
+                                 upper((i+1) + (j+1)*ncp)});
+               }
+               else if (dim == 3)
+               {
+                  lv = std::min({lower(i + j*ncp + k*ncp*ncp),
+                                 lower((i+1) + j*ncp + k*ncp*ncp),
+                                 lower(i + (j+1)*ncp + k*ncp*ncp),
+                                 lower((i+1) + (j+1)*ncp + k*ncp*ncp),
+                                 lower(i + j*ncp + (k+1)*ncp*ncp),
+                                 lower((i+1) + j*ncp + (k+1)*ncp*ncp),
+                                 lower(i + (j+1)*ncp + (k+1)*ncp*ncp),
+                                 lower((i+1) + (j+1)*ncp + (k+1)*ncp*ncp)});
+                  uv = std::min({upper(i + j*ncp + k*ncp*ncp),
+                                 upper((i+1) + j*ncp + k*ncp*ncp),
+                                 upper(i + (j+1)*ncp + k*ncp*ncp),
+                                 upper((i+1) + (j+1)*ncp + k*ncp*ncp),
+                                 upper(i + j*ncp + (k+1)*ncp*ncp),
+                                 upper((i+1) + j*ncp + (k+1)*ncp*ncp),
+                                 upper(i + (j+1)*ncp + (k+1)*ncp*ncp),
+                                 upper((i+1) + (j+1)*ncp + (k+1)*ncp*ncp)});
+               }
+               IntervalNode *child_node = new IntervalNode(lv, uv);
+               current->node->AddChild(child_node);
+
+               if (lv < min_threshold)
+               {
+                  min_upper_bound = std::min(min_upper_bound, uv);
+                  min_threshold = std::min(min_threshold, uv);
+                  if (curr_depth < max_depth)
+                  {
+                     pos_range(0) = cp_ref_loc(i);
+                     pos_range(0+dim) = cp_ref_loc(i+1);
+                     if (dim >= 2)
+                     {
+                        pos_range(1) = cp_ref_loc(ncp + j);
+                        pos_range(1+dim) = cp_ref_loc(ncp + j+1);
+                     }
+                     if (dim == 3)
+                     {
+                        pos_range(2) = cp_ref_loc(2*ncp + k);
+                        pos_range(2+dim) = cp_ref_loc(2*ncp + k+1);
+                     }
+                     SearchInterval *child_interval =
+                        new  SearchInterval(pos_range, curr_depth + 1,
+                                            child_node);
+                     pq.push(child_interval);
+                  }
+               }
+            }
+         }
+      }
+      delete current;
+   }
+
+   // clean up remaining intervals in queue
+   while (!pq.empty())
+   {
+      delete pq.top();
+      pq.pop();
+   }
+
+   min_lower_bound = initial_node->GetChildMinLower();
+   initial_node->DeleteChildren();
+   delete initial_node;
+
+   min_threshold = std::min(min_threshold, min_lower_bound);
+   return std::make_pair(min_lower_bound, min_upper_bound);
+}
+
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMaximum(
+   const int elem, const PLBound &plb, const int vdim,
+   const int max_depth, const real_t tol) const
+{
+   real_t max_threshold = std::numeric_limits<real_t>::lowest();
+   return EstimateFunctionMaximum(elem, plb, vdim, max_depth, tol,
+                                  max_threshold);
+}
+
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMaximum(
+   const int elem, const PLBound &plb, const int vdim,
+   const int max_depth, const real_t tol, real_t &max_threshold) const
+{
+   const int dim = this->FESpace()->GetMesh()->Dimension();
+   const int ncp = plb.GetNControlPoints();
+   Vector pos_range(2*dim); pos_range = 0.0;
+   for (int d = 0; d < dim; d++) { pos_range(d+dim) = 1.0; }
+   Vector lower, upper, cp_ref_loc;
+
+   GetElementBoundsAtControlPoints(elem, plb, lower, upper, vdim);
+   real_t val_min = lower.Max();
+   real_t val_max = upper.Max();
+
+   max_threshold = std::max(max_threshold, val_min);
+
+   // Pruning: if the element's upper bound is less than the current global
+   // lower bound, this element cannot contain the global maximum.
+   if (val_max <= max_threshold)
+   {
+      return std::make_pair(val_min, val_max);
+   }
+
+   if (val_min == val_max || max_depth == 0)
+   {
+      max_threshold = std::max(max_threshold, val_max);
+      return std::make_pair(val_min, val_max);
+   }
+   real_t abs_tol = tol*(val_max-val_min);
+
+   IntervalNode *initial_node = new IntervalNode(val_min, val_max);
+   SearchInterval *initial_interval = new SearchInterval(pos_range, 0,
+                                                         initial_node);
+
+   std::priority_queue<SearchInterval*,
+       std::vector<SearchInterval*>, IntervalCompareMax> pq;
+   pq.push(initial_interval);
+
+   real_t max_lower_bound = val_min;
+   real_t max_upper_bound = val_max;
+
+   while (!pq.empty())
+   {
+      SearchInterval *current = pq.top();
+      pq.pop();
+      int curr_depth = current->depth;
+
+      // Reached max depth or this interval cannot contain the global maximum.
+      if (current->node->val_max <= max_threshold || curr_depth >= max_depth)
+      {
+         delete current;
+         continue;
+      }
+
+      max_upper_bound = initial_node->GetChildMaxUpper();
+      if (max_upper_bound - max_lower_bound < abs_tol)
+      {
+         delete current;
+         break;
+      }
+
+      // Subdivide the interval and get bounds on it
+      GetElementBoundsAtControlPoints(elem, plb, current->ref_range,
+                                      vdim, lower, upper, cp_ref_loc);
+
+      // process the bounds and create sub-intervals
+      for (int k = 0; k < (dim == 3 ? ncp-1 : 1); k++)
+      {
+         for (int j = 0; j < (dim >= 2 ? ncp-1 : 1); j++)
+         {
+            for (int i = 0; i < ncp-1; i++)
+            {
+               real_t lv = 0.0, uv = 0.0;
+               if (dim == 1)
+               {
+                  lv = std::max(lower(i), lower(i+1));
+                  uv = std::max(upper(i), upper(i+1));
+               }
+               else if (dim == 2)
+               {
+                  lv = std::max({lower(i + j*ncp), lower((i+1) + j*ncp),
+                                 lower(i + (j+1)*ncp),
+                                 lower((i+1) + (j+1)*ncp)});
+                  uv = std::max({upper(i + j*ncp), upper((i+1) + j*ncp),
+                                 upper(i + (j+1)*ncp),
+                                 upper((i+1) + (j+1)*ncp)});
+               }
+               else if (dim == 3)
+               {
+                  lv = std::max({lower(i + j*ncp + k*ncp*ncp),
+                                 lower((i+1) + j*ncp + k*ncp*ncp),
+                                 lower(i + (j+1)*ncp + k*ncp*ncp),
+                                 lower((i+1) + (j+1)*ncp + k*ncp*ncp),
+                                 lower(i + j*ncp + (k+1)*ncp*ncp),
+                                 lower((i+1) + j*ncp + (k+1)*ncp*ncp),
+                                 lower(i + (j+1)*ncp + (k+1)*ncp*ncp),
+                                 lower((i+1) + (j+1)*ncp + (k+1)*ncp*ncp)});
+                  uv = std::max({upper(i + j*ncp + k*ncp*ncp),
+                                 upper((i+1) + j*ncp + k*ncp*ncp),
+                                 upper(i + (j+1)*ncp + k*ncp*ncp),
+                                 upper((i+1) + (j+1)*ncp + k*ncp*ncp),
+                                 upper(i + j*ncp + (k+1)*ncp*ncp),
+                                 upper((i+1) + j*ncp + (k+1)*ncp*ncp),
+                                 upper(i + (j+1)*ncp + (k+1)*ncp*ncp),
+                                 upper((i+1) + (j+1)*ncp + (k+1)*ncp*ncp)});
+               }
+               IntervalNode *child_node = new IntervalNode(lv, uv);
+               current->node->AddChild(child_node);
+
+               if (uv > max_threshold)
+               {
+                  max_lower_bound = std::max(max_lower_bound, lv);
+                  max_threshold = std::max(max_threshold, lv);
+                  if (curr_depth < max_depth)
+                  {
+                     pos_range(0) = cp_ref_loc(i);
+                     pos_range(0+dim) = cp_ref_loc(i+1);
+                     if (dim >= 2)
+                     {
+                        pos_range(1) = cp_ref_loc(ncp + j);
+                        pos_range(1+dim) = cp_ref_loc(ncp + j+1);
+                     }
+                     if (dim == 3)
+                     {
+                        pos_range(2) = cp_ref_loc(2*ncp + k);
+                        pos_range(2+dim) = cp_ref_loc(2*ncp + k+1);
+                     }
+                     SearchInterval *child_interval =
+                        new SearchInterval(pos_range, curr_depth + 1,
+                                           child_node);
+                     pq.push(child_interval);
+                  }
+               }
+            }
+         }
+      }
+      delete current;
+   }
+   // clean up remaining intervals in queue
+   while (!pq.empty())
+   {
+      delete pq.top();
+      pq.pop();
+   }
+
+   max_upper_bound = initial_node->GetChildMaxUpper();
+   initial_node->DeleteChildren();
+   delete initial_node;
+   max_threshold = std::max(max_threshold, max_upper_bound);
+
+   return std::make_pair(max_lower_bound, max_upper_bound);
+}
+
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMinimum(
+   const int vdim, const PLBound &plb, const int max_depth,
+   const real_t tol) const
+{
+   real_t global_min_lower = std::numeric_limits<real_t>::max();
+   real_t global_min_upper = std::numeric_limits<real_t>::max();
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      std::pair<real_t, real_t> min_pair =
+         EstimateFunctionMinimum(i, plb, vdim, max_depth, tol,
+                                 global_min_lower);
+      global_min_upper = std::min(global_min_upper, min_pair.second);
+   }
+   return std::make_pair(global_min_lower, global_min_upper);
+}
+
+std::pair<real_t, real_t> GridFunction::EstimateFunctionMaximum(
+   const int vdim, const PLBound &plb, const int max_depth,
+   const real_t tol) const
+{
+   real_t global_max_lower = std::numeric_limits<real_t>::lowest();
+   real_t global_max_upper = std::numeric_limits<real_t>::lowest();
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      std::pair<real_t, real_t> max_pair =
+         EstimateFunctionMaximum(i, plb, vdim, max_depth, tol,
+                                 global_max_upper);
+      global_max_lower = std::max(global_max_lower, max_pair.first);
+   }
+   return std::make_pair(global_max_lower, global_max_upper);
+}
+
+}

fem/gridfunc.hpp

@@ -23,6 +23,7 @@
 #include <limits>
 #include <ostream>
 #include <string>
+#include <variant>
 
 namespace mfem
 {
@@ -79,10 +80,18 @@ protected:
                         bool wcoef,
                         int subdomain);
 
-   /** Project a discontinuous vector coefficient in a continuous space and
-       return in dof_attr the maximal attribute of the elements containing each
-       degree of freedom. */
-   void ProjectDiscCoefficient(VectorCoefficient &coeff, Array<int> &dof_attr);
+   /** @brief Project a discontinuous (vector) coefficient as a grid function on
+       a continuous finite element space. Return in dof_attr the maximal
+       attribute of the elements containing each degree of freedom. */
+   virtual void ProjectDiscCoefficient(
+      std::variant<Coefficient*, VectorCoefficient*> coeff, Array<int> &dof_attr);
+
+   /** @brief Project a discontinuous (vector) coefficient as a grid function on
+       a continuous finite element space. The values in shared dofs are
+       determined from the element with maximal attribute. */
+   virtual void ProjectDiscCoefficient(
+      std::variant<Coefficient*, VectorCoefficient*> coeff)
+   { Array<int> dof_attr; ProjectDiscCoefficient(coeff, dof_attr); };
 
    /** Helper function for ProjectCoefficientElementL2 */
    void ProjectCoefficientElementL2_(Coefficient &coeff, Vector &sol, Vector &Va);
@@ -150,11 +159,13 @@ public:
 
    FiniteElementCollection *OwnFEC() { return fec_owned; }
 
-   /// Shortcut for calling FiniteElementSpace::GetVectorDim() on the underlying #fes
-   int VectorDim() const;
+   /** @brief Shortcut for calling FiniteElementSpace::GetVectorDim() on the
+       underlying #fes */
+   int VectorDim() const { return fes->GetVectorDim(); }
 
-   /// Shortcut for calling FiniteElementSpace::GetCurlDim() on the underlying #fes
-   int CurlDim() const;
+   /** @brief Shortcut for calling FiniteElementSpace::GetCurlDim() on the
+       underlying #fes */
+   int CurlDim() const { return fes->GetCurlDim(); }
 
    /// Read only access to the (optional) internal true-dof Vector.
    const Vector &GetTrueVector() const
@@ -513,10 +524,17 @@ public:
        but using an array of scalar coefficients for each component. */
    void ProjectCoefficient(Coefficient *coeff[]);
 
+   /** @brief Project a discontinuous coefficient as a grid function on
+       a continuous finite element space. The values in shared dofs are
+       determined from the element with maximal attribute. */
+   virtual void ProjectDiscCoefficient(Coefficient &coeff)
+   { ProjectDiscCoefficient(&coeff); }
+
    /** @brief Project a discontinuous vector coefficient as a grid function on
        a continuous finite element space. The values in shared dofs are
        determined from the element with maximal attribute. */
-   virtual void ProjectDiscCoefficient(VectorCoefficient &coeff);
+   virtual void ProjectDiscCoefficient(VectorCoefficient &coeff)
+   { ProjectDiscCoefficient(&coeff); }
 
    enum AvgType {ARITHMETIC, HARMONIC};
    /** @brief Projects a discontinuous coefficient so that the values in shared
@@ -532,6 +550,9 @@ public:
    std::unique_ptr<GridFunction> ProlongateToMaxOrder() const;
 
 protected:
+   void ProjectBdrCoefficientNormal(Coefficient *coeff, VectorCoefficient *vcoeff,
+                                    const Array<int> &attr);
+
    /** @brief Accumulates (depending on @a type) the values of @a coeff at all
        shared vdofs and counts in how many zones each vdof appears. */
    void AccumulateAndCountZones(Coefficient &coeff, AvgType type,
@@ -564,6 +585,70 @@ protected:
    /// P-refinement version of Update().
    void UpdatePRef();
 
+   /** @brief Estimate the minimum value of the GridFunction in element @a elem
+    *  if it is below a certain @a min_threshold.
+    *
+    *  @details For a given element \p elem and grid function component \p vdim
+    *  an estimate of the function minimum is the minimum of the piecewise
+    *  linear lower bound obtained using the given PLBound object. The actual
+    *  minimum is between [minimum lower bound, minimum upper bound]. We
+    *  improve the estimate of the function minimum by recursively
+    *  subdividing the interval with the lowest lower bound, and computing
+    *  bounds on the sub-intervals.
+    *  This process continues until (i) the maximum recursion depth is reached
+    *  or (ii) the difference between the minimum upper bound and minimum lower
+    *  bound is less than a certain tolerance (\p tol * [initial maximum
+    *  upper bound - initial minimum lower bound]).
+    *  The function also terminates if the lowest minima estimate is found
+    *  to be above the given threshold \p min_threshold. This is useful when
+    *  we are interested in computing the global minimum of the function
+    *  over all elements. In this case we can reject elements where the lowest
+    *  bound is above the current global minimum. In case the function
+    *  minimum on the element is below the global minimum, we update
+    *  \p min_threshold.
+    *
+    *  We return a pair of values that bracket the actual minimum, i.e.
+    *  [min_lower_bound, min_upper_bound].
+    */
+   std::pair<real_t,real_t> EstimateFunctionMinimum(const int elem,
+                                                    const PLBound &plb,
+                                                    const int vdim,
+                                                    const int max_depth,
+                                                    const real_t tol,
+                                                    real_t &min_threshold)const;
+
+   /** @brief Estimate the maximum value of the GridFunction in element @a elem
+    *  if it is below a certain @a max_threshold.
+    *
+    *  @details For a given element \p elem and grid function component \p vdim
+    *  an estimate of the function maximum is the maximum of the piecewise
+    *  linear upper bound obtained using the given PLBound object. The actual
+    *  maximum is between [maximum lower bound, maximum upper bound]. We
+    *  improve the estimate of the function maximum by recursively
+    *  subdividing the interval with the highest upper bound, and computing
+    *  bounds on the sub-intervals.
+    *  This process continues until (i) the maximum recursion depth is reached
+    *  or (ii) the difference between the maximum upper bound and maximum lower
+    *  bound is less than a certain tolerance (\p tol * [initial maximum
+    *  upper bound - initial maximum lower bound]).
+    *  The function also terminates if the highest maxima estimate is found
+    *  to be below the given threshold \p max_threshold. This is useful when
+    *  we are interested in computing the global maximum of the function
+    *  over all elements. In this case we can reject elements where the upper
+    *  bound is below the current global maximum. In case the function
+    *  maximum on the element is above the global maximum, we update
+    *  \p max_threshold.
+    *
+    *  We return a pair of values that bracket the actual maximum, i.e.
+    *  [max_lower_bound, max_upper_bound].
+    */
+   std::pair<real_t,real_t> EstimateFunctionMaximum(const int elem,
+                                                    const PLBound &plb,
+                                                    const int vdim,
+                                                    const int max_depth,
+                                                    const real_t tol,
+                                                    real_t &max_threshold)const;
+
 public:
    /** @brief For each vdof, counts how many elements contain the vdof,
        as containment is determined by FiniteElementSpace::GetElementVDofs(). */
@@ -592,15 +677,26 @@ public:
    virtual void ProjectBdrCoefficient(Coefficient *coeff[],
                                       const Array<int> &attr);
 
-   /** Project the normal component of the given VectorCoefficient on
-       the boundary. Only boundary attributes that are marked in
-       'bdr_attr' are projected. Assumes RT-type VectorFE GridFunction. */
+   /** @brief Project the normal component of the given VectorCoefficient on
+       the boundary. */
+   /** Only boundary attributes that are marked in @a bdr_attr are
+       projected. Assumes RT-type vector finite element GridFunction. */
    void ProjectBdrCoefficientNormal(VectorCoefficient &vcoeff,
-                                    const Array<int> &bdr_attr);
+                                    const Array<int> &bdr_attr)
+   { ProjectBdrCoefficientNormal(NULL, &vcoeff, bdr_attr); }
+
+   /** @brief Project the given Coefficient in the normal direction on the
+       boundary. */
+   /** Only boundary attributes that are marked in @a bdr_attr are projected.
+       Assumes RT-type vector finite element GridFunction. */
+   void ProjectBdrCoefficientNormal(Coefficient &coeff,
+                                    const Array<int> &bdr_attr)
+   { ProjectBdrCoefficientNormal(&coeff, NULL, bdr_attr); }
 
    /** @brief Project the tangential components of the given VectorCoefficient
-       on the boundary. Only boundary attributes that are marked in @a bdr_attr
-       are projected. Assumes ND-type VectorFE GridFunction. */
+       on the boundary. */
+   /** Only boundary attributes that are marked in @a bdr_attr
+       are projected. Assumes ND-type vector finite element GridFunction. */
    virtual void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                              const Array<int> &bdr_attr);
 
@@ -1662,21 +1758,21 @@ public:
     */
    ///@{
    /// Computes the \ref PLBound for the gridfunction with number of control
-   /// points based on @a ref_factor, and returns the overall bounds for each
-   /// vdim (across all elements) in @b lower and @b upper. We also return the
+   /// points based on \p ref_factor, and returns the overall bounds for each
+   /// vdim (across all elements) in \p lower and \p upper. We also return the
    /// PLBound object used to compute the bounds.
-   /// We compute the bounds for each vdim if @a vdim < 1.
+   /// We compute the bounds for each vdim if \p vdim < 1.
    /// Note: For most cases, this method/interface will be sufficient.
    virtual PLBound GetBounds(Vector &lower, Vector &upper,
                              const int ref_factor=1, const int vdim=-1) const;
 
    /// Computes the \ref PLBound for the gridfunction with number of control
    /// points based on @a ref_factor, and returns the bounds for each element
-   /// ordered byVDim:
+   /// ordered byNODES:
    /// lower_{0,0}, lower_{1,0}, ..., lower_{ne-1,0},
    /// lower_{0,1}, ..., lower_{ne-1,vdim-1}. We also return the
    /// PLBound object used to compute the bounds.
-   /// We compute the bounds for each vdim if @a vdim < 1.
+   /// We compute the bounds for each vdim if \p vdim < 1.
    PLBound GetElementBounds(Vector &lower, Vector &upper,
                             const int ref_factor=1, const int vdim=-1) const;
 
@@ -1687,6 +1783,18 @@ public:
                                         Vector &lower, Vector &upper,
                                         const int vdim = -1) const;
 
+   /** @brief Gets the bounds on given reference range inside an element.
+    *
+    *  @details @a ref_range is a vector of size 2*dim that specifies the
+    *  lower and upper limits in each dimension of the reference element.
+    *  For example, in 2D, ref_range = [rmin, smin, rmax, smax].
+    */
+   void GetElementBoundsAtControlPoints(const int elem, const PLBound &plb,
+                                        const Vector &ref_range,
+                                        const int vdim,
+                                        Vector &lower, Vector &upper,
+                                        Vector &control_pos) const;
+
    /// Compute bounds on the grid function for the given element.
    /// The bounds are stored in @b lower and @b upper.
    void GetElementBounds(const int elem, const PLBound &plb,
@@ -1694,11 +1802,45 @@ public:
                          const int vdim = -1) const;
 
    /// Compute bounds on the grid function for all the elements. The bounds
-   /// are returned in @b lower and @b upper, ordered byVDim:
+   /// are returned in @b lower and @b upper, ordered byNODES:
    /// lower_{0,0}, lower_{1,0}, ..., lower_{ne-1,0},
    /// lower_{0,1}, ..., lower_{ne-1,vdim-1}
    void GetElementBounds(const PLBound &plb, Vector &lower, Vector &upper,
                          const int vdim=-1) const;
+
+   /** @brief Estimate the minimum value of the GridFunction in element @a elem.
+    *
+    *  @details See the protected version of EstimateFunctionMinimum for
+    *  details.
+    */
+   std::pair<real_t, real_t> EstimateFunctionMinimum(const int elem,
+                                                     const PLBound &plb,
+                                                     const int vdim,
+                                                     const int max_depth,
+                                                     const real_t tol) const;
+
+   /** @brief Estimate the minimum value of the GridFunction in element @a elem.
+    *
+    *  @details See the protected version of EstimateFunctionMaximum for
+    *  details.
+    */
+   std::pair<real_t, real_t> EstimateFunctionMaximum(const int elem,
+                                                     const PLBound &plb,
+                                                     const int vdim,
+                                                     const int max_depth,
+                                                     const real_t tol) const;
+
+   /** @brief Estimate the GridFunction minimum across all elements. */
+   virtual std::pair<real_t,real_t> EstimateFunctionMinimum(const int vdim,
+                                                            const PLBound &plb,
+                                                            const int max_depth,
+                                                            const real_t tol) const;
+
+   /** @brief Estimate the GridFunction maximum across all elements. */
+   virtual std::pair<real_t,real_t> EstimateFunctionMaximum(const int vdim,
+                                                            const PLBound &plb,
+                                                            const int max_depth,
+                                                            const real_t tol) const;
    ///@}
 
    /// Destroys grid function.
@@ -1804,7 +1946,7 @@ real_t ComputeElementLpDistance(real_t p, int i,
                                 GridFunction& gf1, GridFunction& gf2);
 
 
-/// Class used for extruding scalar GridFunctions
+/// Class used for extruding a scalar coefficient
 class ExtrudeCoefficient : public Coefficient
 {
 private:
@@ -1812,13 +1954,53 @@ private:
    Mesh *mesh_in;
    Coefficient &sol_in;
 public:
+   /// Constructs an instance of VectorExtrudeCoefficient
+   /**
+    * @param m      1D mesh
+    * @param s      1D vector coefficient
+    * @param n_     number of transverse elements of the extruded mesh
+    */
    ExtrudeCoefficient(Mesh *m, Coefficient &s, int n_)
-      : n(n_), mesh_in(m), sol_in(s) { }
+      : n(n_), mesh_in(m), sol_in(s)
+   { MFEM_VERIFY(n > 0, "Number of transverse elements must be positive!"); }
+
    real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+
    virtual ~ExtrudeCoefficient() { }
 };
 
-/// Extrude a scalar 1D GridFunction, after extruding the mesh with Extrude1D.
+/// Class used for extruding a vector coefficient
+class VectorExtrudeCoefficient : public VectorCoefficient
+{
+private:
+   int n;
+   Mesh *mesh_in;
+   VectorCoefficient &sol_in;
+public:
+   /// Constructs an instance of VectorExtrudeCoefficient
+   /**
+    * @param m      1D mesh
+    * @param s      1D vector coefficient
+    * @param n_     number of transverse elements of the extruded mesh
+    */
+   VectorExtrudeCoefficient(Mesh *m, VectorCoefficient &s, int n_)
+      : VectorCoefficient(s.GetVDim()), n(n_), mesh_in(m), sol_in(s)
+   { MFEM_VERIFY(n > 0, "Number of transverse elements must be positive!"); }
+
+   void Eval(Vector &v, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
+   using VectorCoefficient::Eval;
+
+   virtual ~VectorExtrudeCoefficient() { }
+};
+
+/// Extrude a 1D GridFunction, after extruding the mesh with Extrude1D()
+/**
+ * @param mesh      1D mesh
+ * @param mesh2d    extruded mesh
+ * @param sol       grid function
+ * @param ny        number of transverse elements of the extruded mesh
+ */
 GridFunction *Extrude1DGridFunction(Mesh *mesh, Mesh *mesh2d,
                                     GridFunction *sol, const int ny);
 

fem/gslib.hpp

@@ -21,6 +21,45 @@
 
 #ifdef MFEM_USE_GSLIB
 
+/* gslib license and copyright statement for code adapted from gslib:
+
+Copyright (c) 2008-2024, UCHICAGO ARGONNE, LLC.
+
+The UChicago Argonne, LLC as Operator of Argonne National
+Laboratory holds copyright in the Software. The copyright holder
+reserves all rights except those expressly granted to licensees,
+and U.S. Government license rights.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the disclaimer below.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the disclaimer (as noted below)
+in the documentation and/or other materials provided with the
+distribution.
+
+3. Neither the name of ANL nor the names of its contributors
+may be used to endorse or promote products derived from this software
+without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+UCHICAGO ARGONNE, LLC, THE U.S. DEPARTMENT OF
+ENERGY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
 namespace gslib
 {
 struct comm;
@@ -86,7 +125,7 @@ protected:
    void *fdataD;
    struct gslib::crystal *cr;             // gslib's internal data
    struct gslib::comm *gsl_comm;          // gslib's internal data
-   int dim, points_cnt;                   // mesh dimension and number of points
+   int dim, spacedim, points_cnt;         // mesh dimension and number of points
    Array<unsigned int> gsl_code, gsl_proc, gsl_elem, gsl_mfem_elem;
    Vector gsl_mesh, gsl_ref, gsl_dist, gsl_mfem_ref;
    Array<unsigned int> recv_proc, recv_index; // data for custom interpolation
@@ -104,18 +143,23 @@ protected:
    bool       gpu_to_cpu_fallback = false;
 
    // Device specific data used for FindPoints
-   struct
+   struct DEV_STRUCT
    {
       bool setup_device = false;
       bool find_device  = false;
-      int local_hash_size, dof1d, dof1d_sol, h_o_size, h_nx;
+      int local_hash_size, dof1d, dof1d_sol, lh_nx, gh_nx;
       double newt_tol; // Tolerance specified during setup for Newton solve
       struct gslib::crystal *cr;
       struct gslib::hash_data_3 *hash3;
       struct gslib::hash_data_2 *hash2;
       mutable Vector bb, wtend, gll1d, lagcoeff, gll1d_sol, lagcoeff_sol;
-      mutable Array<unsigned int> loc_hash_offset;
-      mutable Vector loc_hash_min, loc_hash_fac;
+      mutable Array<unsigned int> lh_offset, gh_offset;
+      mutable Vector lh_min, lh_fac, gh_min, gh_fac;
+      // Tolerance to mark points found on the surface as CODE_INTERNAL
+      // or CODE_BORDER. This is needed because we cannot only use reference
+      // space coordinates to determine if a point is located inside the
+      // element or not.
+      mutable double surf_dist_tol;
    } DEV;
 
    /// Use GSLIB for communication and interpolation
@@ -127,88 +171,157 @@ protected:
                                    Vector &field_out,
                                    const int field_out_ordering);
 
-   /// Since GSLIB is designed to work with quads/hexes, we split every
-   /// triangle/tet/prism/pyramid element into quads/hexes.
+   /** @brief Since GSLIB is designed to work with quads/hexes, we split every
+    *  triangle/tet/prism/pyramid element into quads/hexes. */
    virtual void SetupSplitMeshes();
 
-   /// Setup integration points that will be used to interpolate the nodal
-   /// location at points expected by GSLIB.
+   /** @brief Setup integration points that will be used to interpolate the
+    *  nodal location at points expected by GSLIB. */
    virtual void SetupIntegrationRuleForSplitMesh(Mesh *mesh,
                                                  IntegrationRule *irule,
                                                  int order);
 
-   /// Helper function that calls \ref SetupSplitMeshes and
-   /// \ref SetupIntegrationRuleForSplitMesh.
+   /** @brief Helper function that calls \ref SetupSplitMeshes and
+    * \ref SetupIntegrationRuleForSplitMesh. */
    virtual void SetupSplitMeshesAndIntegrationRules(const int order);
 
    /// Get GridFunction value at the points expected by GSLIB.
    virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals) const;
 
-   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices,
-   /// find the original element number (that was split into micro quads/hexes)
-   /// during the setup phase.
+   /** @brief Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For
+    *  simplices, find the original element number (that was split into
+    *  micro quads/hexes) during the setup phase. */
    virtual void MapRefPosAndElemIndices();
 
-   // Device functions
-   // FindPoints locally on device for 3D.
+   /// FindPoints locally on device for 3D.
    void FindPointsLocal3(const Vector &point_pos, int point_pos_ordering,
                          Array<unsigned int> &gsl_code_dev_l,
                          Array<unsigned int> &gsl_elem_dev_l, Vector &gsl_ref_l,
                          Vector &gsl_dist_l, int npt);
 
-   // FindPoints locally on device for 2D.
+   /// FindPoints locally on device for 2D.
    void FindPointsLocal2(const Vector &point_pos, int point_pos_ordering,
                          Array<unsigned int> &gsl_code_dev_l,
                          Array<unsigned int> &gsl_elem_dev_l, Vector &gsl_ref_l,
                          Vector &gsl_dist_l, int npt);
 
-   // Interpolate on device for 3D.
+   /// FindPoints locally on device for 3D surface elements.
+   void FindPointsSurfLocal3(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// FindPoints locally on device for 3D edge elements.
+   void FindPointsEdgeLocal3(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// FindPoints locally on device for 2D edge elements.
+   void FindPointsEdgeLocal2(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// Interpolate on device for 3D.
    void InterpolateLocal3(const Vector &field_in,
                           Array<int> &gsl_elem_dev_l,
                           Vector &gsl_ref_l,
                           Vector &field_out,
                           int npt, int ncomp,
-                          int nel, int dof1dsol);
-   // Interpolate on device for 2D.
+                          int dof1dsol);
+
+   /// Interpolate on device for 2D.
    void InterpolateLocal2(const Vector &field_in,
                           Array<int> &gsl_elem_dev_l,
                           Vector &gsl_ref_l,
                           Vector &field_out,
                           int npt, int ncomp,
-                          int nel, int dof1dsol);
+                          int dof1dsol);
 
-   // Prepare data for device functions.
+   /// Interpolate on device for 1D.
+   void InterpolateLocal1(const Vector &field_in,
+                          Array<int> &gsl_elem_dev_l,
+                          Vector &gsl_ref_l,
+                          Vector &field_out,
+                          int npt, int ncomp, int dof1dsol);
+
+   /// Prepare data for device execution for volume meshes.
    void SetupDevice();
 
-   /** Searches positions given in physical space by @a point_pos.
+   /** @brief Searches positions given in physical space by @a point_pos.
        These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
        byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering. */
    void FindPointsOnDevice(const Vector &point_pos,
                            const int point_pos_ordering = Ordering::byNODES);
 
-   /** Interpolation of field values at prescribed reference space positions.
-       @param[in] field_in_evec E-vector of grid function to be interpolated.
-                                Assumed ordering is NDOFSxVDIMxNEL
-       @param[in] nel           Number of elements in the mesh.
-       @param[in] ncomp         Number of components in the field.
-       @param[in] dof1dsol      Number of degrees of freedom in each reference
-                                space direction.
-       @param[in] ordering      Ordering of the out field values: byNodes/byVDIM
-
-       @param[out] field_out  Interpolated values. For points that are not found
-                              the value is set to #default_interp_value. */
+   /** @brief Interpolation of field values at prescribed reference space
+    *         positions.
+    *  @param[in] field_in_evec E-vector of grid function to be interpolated.
+    *                           Assumed ordering is NDOFSxVDIMxNEL
+    *  @param[in] nel           Number of elements in the mesh.
+    *  @param[in] ncomp         Number of components in the field.
+    *  @param[in] dof1dsol      Number of degrees of freedom in each reference
+    *                           space direction.
+    *  @param[in] ordering      Ordering of the out field values: byNodes/byVDIM
+    *
+    *  @param[out] field_out    Interpolated values. For points that are not
+    *                           found the value is set to
+    *                           #default_interp_value. */
    void InterpolateOnDevice(const Vector &field_in_evec, Vector &field_out,
                             const int nel, const int ncomp,
                             const int dof1dsol, const int ordering);
 
+   /** @brief Interpolation of field values at prescribed reference space
+    *         positions for surface meshes. */
+   void InterpolateSurfBase(const Vector &field_in, Vector &field_out,
+                            const int nel, const int ncomp,
+                            const int dof1dsol, const int field_out_ordering);
+
+   /// Preprocess 2D surface mesh needed for FindPoints.
+   void findptsedge_setup_2(DEV_STRUCT &devs,
+                            const double *const elx[2],
+                            const unsigned n,
+                            const uint nel,
+                            const unsigned m,
+                            const double bbox_tol,
+                            const uint local_hash_size,
+                            const uint global_hash_size);
+
+   /// Preprocess 3D surface mesh needed for FindPoints.
+   void findptssurf_setup_3(DEV_STRUCT &devs,
+                            const double *const elx[3],
+                            const unsigned n,
+                            const uint nel,
+                            const unsigned m,
+                            const double bbox_tol,
+                            const uint local_hash_size,
+                            const uint global_hash_size,
+                            const int rD);
+
 public:
+   /// Serial constructor
    FindPointsGSLIB();
+
+   /// Serial constructor + setup with given Mesh (see \ref Setup)
    FindPointsGSLIB(Mesh &mesh_in, const double bb_t = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
 #ifdef MFEM_USE_MPI
+   /// Constructor for ParMesh
    FindPointsGSLIB(MPI_Comm comm_);
+
+   /// Constructor + setup with given ParMesh (see \ref Setup)
    FindPointsGSLIB(ParMesh &mesh_in, const double bb_t = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
@@ -218,8 +331,10 @@ public:
    FindPointsGSLIB(const FindPointsGSLIB&) = delete;
    FindPointsGSLIB& operator=(const FindPointsGSLIB&) = delete;
 
-   /** Initializes the internal mesh in gslib, by sending the positions of the
-       Gauss-Lobatto nodes of the input Mesh object \p m.
+   /** @brief Preprocess the internal mesh in gslib.
+
+       @details Initializes the internal mesh in gslib, by sending the
+       positions of the Gauss-Lobatto nodes of the input Mesh object \p m.
        Note: not tested with periodic (L2).
        Note: the input mesh \p m must have Nodes set.
 
@@ -230,13 +345,22 @@ public:
                             search methods.
        @param[in] npt_max   (Optional) Number of points for simultaneous
                             iteration. This alters performance and
-                            memory footprint.*/
-
+                            memory footprint.
+   */
    void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
               const int npt_max = 256);
-   /** Searches positions given in physical space by \p point_pos.
-       These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
+
+   /// Preprocess the surface mesh to compute data for FindPoints.
+   void SetupSurf(Mesh &m,
+                  const double bb_t = 0.1,
+                  const double newt_tol = 1.0e-12,
+                  const int npt_max = 256);
+
+   /** @brief Searches positions given in physical space by \p point_pos.
+
+       @details These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
        byVDim: (XYZ,XYZ,....XYZ) specified by \p point_pos_ordering.
+
        This function populates the following member variables:
        #gsl_code        Return codes for each point: inside element (0),
                         element boundary (1), not found (2).
@@ -255,19 +379,34 @@ public:
        #gsl_dist        Distance between the sought and the found point
                         in physical space. */
    void FindPoints(const Vector &point_pos,
-                   const int point_pos_ordering = Ordering::byNODES);
+                   int point_pos_ordering = Ordering::byNODES);
+
    /// Convenience function when point positions are in a ParticleVector
    void FindPoints(const ParticleVector &point_pos)
    {
       FindPoints(point_pos, point_pos.GetOrdering());
    }
+
+   /** @brief Searches positions given in physical space by \p point_pos on
+    *  surface mesh. */
+   void FindPointsSurf(const Vector &point_pos,
+                       int point_pos_ordering = Ordering::byNODES);
+
+   /// Convenience function when point positions are in a ParticleVector
+   void FindPointsSurf(const ParticleVector &point_pos)
+   {
+      FindPointsSurf(point_pos, point_pos.GetOrdering());
+   }
+
    /// Setup FindPoints and search positions
    void FindPoints(Mesh &m, const Vector &point_pos,
                    const int point_pos_ordering = Ordering::byNODES,
                    const double bb_t = 0.1, const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
-   /** Interpolation of field values at prescribed reference space positions.
+   /** @brief Interpolation of field values at prescribed reference space
+    *  positions.
+
        @param[in] field_in    Function values that will be interpolated on the
                               reference positions. Note: it is assumed that
                               \p field_in is in H1 and in the same space as the
@@ -276,19 +415,36 @@ public:
                               the value is set to #default_interp_value.
                               The output ordering is determined from field_in.*/
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
+
    /// Interpolation of field values, with output ordering specification.
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out,
                             const int field_out_ordering);
-   /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
-       the output values in \p field_out corresponds to the ordering used
-       in the input GridFunction \p field_in. */
+
+   /** @brief Same as Interpolate but for surface meshes */
+   virtual void InterpolateSurf(const GridFunction &field_in,
+                                Vector &field_out);
+
+   /** @brief Same as Interpolate but for surface meshes with specified output
+       ordering */
+   virtual void InterpolateSurf(const GridFunction &field_in,
+                                Vector &field_out,
+                                const int field_out_ordering);
+
+   /** @brief Search positions and interpolate.
+    *
+    *  @details The ordering (byNODES or byVDIM) of the output values in
+    *  \p field_out corresponds to the ordering used in the input
+    *  GridFunction \p field_in.
+    */
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                     Vector &field_out,
-                    const int point_pos_ordering = Ordering::byNODES);
+                    int point_pos_ordering = Ordering::byNODES);
+
    /// Search positions and interpolate with given point and output ordering.
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                     Vector &field_out, const int point_pos_ordering,
                     const int field_out_ordering);
+
    /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
        or byVDIM) of the output values in \p field_out corresponds to the
        ordering used in the input GridFunction \p field_in. */
@@ -296,32 +452,36 @@ public:
                     const GridFunction &field_in, Vector &field_out,
                     const int point_pos_ordering = Ordering::byNODES);
 
-   /// Average type to be used for L2 functions in-case a point is located at
-   /// an element boundary where the function might be multi-valued.
+   /** @brief Average type to be used for L2 functions in-case a point is
+    *  located at an element boundary where the function might be multi-valued.
+    */
    virtual void SetL2AvgType(AvgType avgtype_) { avgtype = avgtype_; }
 
-   /// Set the default interpolation value for points that are not found in the
-   /// mesh.
+   /** @brief Set the default interpolation value for points that are not found in the mesh. */
    virtual void SetDefaultInterpolationValue(double interp_value_)
    {
       default_interp_value = interp_value_;
    }
 
-   /// Set the tolerance for detecting points outside the 'curvilinear' boundary
-   /// that gslib may return as found on the boundary. Points found on boundary
-   /// with distance greater than @ bdr_tol are marked as not found.
+   /** @brief Tolerance for detecting points outside the 'curvilinear' boundary.
+    *
+    *  @details When using FindPoints, gslib may return points as found on the
+    *  boundary even when they are slightly outside the domain. This tolerance
+    *  is used to filter such points based on the distance^2 value and mark them
+    *  as not found.*/
    virtual void SetDistanceToleranceForPointsFoundOnBoundary(double bdr_tol_)
    {
       bdr_tol = bdr_tol_;
    }
 
-   /// Enable/Disable use of CPU functions for GPU data if the gslib version
-   /// is older.
+   /** @brief Enable/Disable use of CPU functions for GPU data if the gslib
+    *  version is older. */
    virtual void SetGPUtoCPUFallback(bool mode) { gpu_to_cpu_fallback = mode; }
 
-   /** Cleans up memory allocated internally by gslib.
-       Note that in parallel, this must be called before MPI_Finalize(), as it
-       calls MPI_Comm_free() for internal gslib communicators. FreeData is
+   /** @brief Cleans up memory allocated internally by gslib.
+
+       @details Note that in parallel, this must be called before MPI_Finalize,
+       as it calls MPI_Comm_free() for internal gslib communicators. FreeData is
        also called by the class destructor and there are no memory leaks if the
        destructor is called before MPI_Finalize(). If the destructor is called
        after MPI_Finalize(), there will be an error because gslib will try to
@@ -329,8 +489,8 @@ public:
    */
    virtual void FreeData();
 
-   /// Return code for each point searched by FindPoints: inside element (0), on
-   /// element boundary (1), or not found (2).
+   /** @brief Return code for each point searched by FindPoints:
+    *  inside element (0), element boundary (1), or not found (2). */
    virtual const Array<unsigned int> &GetCode() const { return gsl_code; }
    /// Return element number for each point found by FindPoints.
    virtual const Array<unsigned int> &GetElem() const { return gsl_mfem_elem; }
@@ -338,15 +498,15 @@ public:
    virtual const Array<unsigned int> &GetProc() const { return gsl_proc; }
    /// Return reference coordinates for each point found by FindPoints.
    virtual const Vector &GetReferencePosition() const { return gsl_mfem_ref;  }
-   /// Return distance between the sought and the found point in physical space,
-   /// for each point found by FindPoints.
+   /// Return distance between the sought and the found point in physical space.
    virtual const Vector &GetDist()              const { return gsl_dist; }
 
-   /// Return element number for each point found by FindPoints corresponding to
-   /// GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with simplices.
+   /** @brief Return element number for each point found by FindPoints
+    *  corresponding to GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with
+    *  simplices. */
    virtual const Array<unsigned int> &GetGSLIBElem() const { return gsl_elem; }
-   /// Return reference coordinates in [-1,1] (internal range in GSLIB) for each
-   /// point found by FindPoints.
+   /** @brief Return reference coordinates in [-1,1] (internal range in GSLIB)
+    *  for each point found by FindPoints. */
    virtual const Vector &GetGSLIBReferencePosition() const { return gsl_ref; }
 
    /// Get array of indices of not-found points.
@@ -389,7 +549,7 @@ public:
 
    /// Return the axis-aligned bounding boxes (AABB) computed during \ref Setup.
    /// The size of the returned vector is (nel x nverts x dim), where nel is the
-   /// number of elements (after splitting for simplcies), nverts is number of
+   /// number of elements (after splitting for simplicies), nverts is number of
    /// vertices (4 in 2D, 8 in 3D), and dim is the spatial dimension.
    void GetAxisAlignedBoundingBoxes(Vector &aabb) const;
 
@@ -403,6 +563,18 @@ public:
    /// \p obbV, a vector of size (nel x nverts x dim) .
    void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
                                  Vector &obbV) const;
+
+   /** @brief Return the bounding boxes as a mesh on rank 0.
+    *
+    *  @param[in] type  Bounding-box type: 0 - AABB, 1 - OBB.
+    *
+    *  @return On rank 0, returns a newly allocated mesh containing the
+    *  bounding boxes. The caller owns the returned pointer and is responsible
+    *  for deleting it. On other ranks, returns nullptr.
+    */
+   Mesh *GetBoundingBoxMesh(int type);
+
+   virtual const Vector &GetGLLMesh()           const { return gsl_mesh; }
 };
 
 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -530,6 +702,116 @@ public:
    void GS(Vector &senddata, GSOp op);
 };
 
+#if defined(MFEM_USE_MPI)
+/** \brief Class to map a point in physical space to candidate ranks.
+ *
+ *  This class builds a Cartesian-aligned tensor grid that covers the entire
+ *  domain and precomputes which ranks have elements intersecting each
+ *  grid cell. Given a point in physical space, the grid cell containing
+ *  the point is determined, and the list of candidate ranks whose
+ *  elements intersect that cell is returned. This yields a fast, conservative
+ *  point-to-rank candidate query. This is used internally by FindPointsGSLIB
+ *  to speed up point searches in parallel.
+ *
+ *  See Mittal et al., "General Field Evaluation in High-Order Meshes on GPUs".
+ *  (2025). Computers & Fluids. for technical details.
+ *
+ */
+class GlobalBBoxTensorGridMap
+{
+private:
+   struct gslib::crystal *cr = nullptr;               // gslib's internal data
+   struct gslib::comm *gsl_comm = nullptr;            // gslib's internal data
+   int sdim, n_local_cells, num_procs;
+   Array<int> gmap_n;
+   Vector gmap_bnd_min, gmap_bnd_max;
+   Vector gmap_fac;
+   Array<int> ggrid_map;
+
+   void SetupCrystal(const MPI_Comm &comm);
+public:
+   /// Constructor for a given mesh and number of tensor grid divisions
+   GlobalBBoxTensorGridMap(ParMesh &pmesh, int nx);
+
+   /** @brief Constructor for given element bounds and spatial dimension.
+    *
+    *  @details This constructor must be called collectively on \a comm.
+    *  Supports spatial dimensions 1, 2, and 3, and accepts nel == 0 on a rank.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+    *
+    *  When by_max_size=false, n gives the number of tensor-grid divisions in
+    *  each direction. When by_max_size=true, n is a per-rank size hint used to
+    *  derive a uniform global resolution. The communicator-wide sum of n is
+    *  converted to nx = ceil(pow(sum(n), 1./sdim)) in each direction, so n is
+    *  not a hard cap on ggrid_map.Size().
+    */
+   GlobalBBoxTensorGridMap(const MPI_Comm &comm, Vector &elmin,
+                           Vector &elmax, int nel, int sdim, int n,
+                           bool by_max_size);
+
+   /** @brief Constructor for given element bounds, spatial dimension, and
+    *  tensor-grid divisions in each direction.
+    *
+    *  @details This constructor must be called collectively on \a comm.
+    *  Supports spatial dimensions 1, 2, and 3, and accepts nel == 0 on a rank.
+    *  Requires nx.Size() == sdim and positive entries in nx.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+    */
+   GlobalBBoxTensorGridMap(const MPI_Comm &comm, Vector &elmin,
+                           Vector &elmax, int nel, int sdim, Array<int> &nx);
+
+   ~GlobalBBoxTensorGridMap();
+
+   /** @brief Get list of procs corresponding to the list of points.
+    *
+    *  @details This method must be called collectively on the communicator
+    *  used to construct the map. The input points can be ordered byNodes:
+    *  (XXX...,YYY...,ZZZ) or byVDIM: (XYZ,XYZ,...), as specified by
+    *  \a ordering.
+    *
+    *  The output map contains one entry for each input point, keyed by the
+    *  point's local index in \a xyz. Points with no candidate ranks, including
+    *  points outside the global bounding box, have an empty list of candidate
+    *  ranks.
+    */
+   void MapPointsToProcs(Vector &xyz, int ordering,
+                         std::map<int, std::vector<int>> &pt_to_procs) const;
+
+   // Some getters
+   const Array<int> &GetGridMap() const { return ggrid_map; }
+   const Vector &GetGridFac() const { return gmap_fac; }
+   const Vector &GetGridMin() const { return gmap_bnd_min; }
+   const Vector &GetGridMax() const { return gmap_bnd_max; }
+   const Array<int> &GetGridN() const { return gmap_n; }
+
+private:
+   /// Setup the map given element bounds and number of tensor grid divisions.
+   void Setup(const MPI_Comm &comm, Vector &elmin, Vector &elmax,
+              int nel, Array<int> &nx);
+
+   /// Get global hash cell index for a given point.
+   int GetGlobalGridCellFromPoint(Vector &xyz) const;
+
+   /** @brief Get owning proc and local index on that proc for given global
+    *  grid cell index. */
+   void GlobalGridCellToProcAndLocalIndex(int i, int &proc, int &idx) const;
+
+   /// Map a point to proc and local index of the corresponding grid cell
+   void GetProcAndLocalIndexFromPoint(Vector &xyz, int &proc, int &idx) const;
+
+   /// Given local cell index, return list of procs saved in the map
+   Array<int> MapCellToProcs(int l_idx) const;
+};
+#endif // MFEM_USE_MPI
+
 } // namespace mfem
 
 #endif // MFEM_USE_GSLIB

fem/gslib/findpts_local_2.cpp

@@ -254,7 +254,7 @@ get_edge(const double *elx[2], const double *wtend, int ei,
       edge.dxdn[d] = workspace + (2 + d) * pN; //dxdn and dydn at DOFs along edge
    }
 
-   if (side_init != (1u << ei))
+   if (static_cast<unsigned>(side_init) != (1u << ei))
    {
 #define ELX(d, j, k) elx[d][j + k * pN] // assumes lexicographic ordering
       for (int d = 0; d < 2; ++d)
@@ -562,7 +562,7 @@ newton_area_fin:
       int f = flags >> (2 * dd) & 3u;
       res->r[dd] = f == 0 ? r0[dd] + dr[dd] : (f == 1 ? -1 : 1);
    }
-   res->flags = flags | (p->flags << 5);
+   res->flags = flags | ((p->flags & FLAG_MASK) << 5);
 }
 
 // Full Newton solve on the face. One of r/s/t is constrained.
@@ -635,7 +635,8 @@ newton_edge_fin:
    res->r[de] = nr;
    res->r[dn]=p->r[dn];
    res->dist2p = -v;
-   res->flags = flags | new_flags | (p->flags << 5);
+   res->flags = flags | new_flags | ((p->flags & FLAG_MASK) << 5);
+#undef EVAL
 }
 
 // Find closest mesh node to the sought point.
@@ -714,7 +715,6 @@ static void FindPointsLocal2D_Kernel(const int npt,
                                      const double *lagcoeff,
                                      const int pN = 0)
 {
-#define MAX_CONST(a, b) (((a) > (b)) ? (a) : (b))
    const int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D = T_D1D ? T_D1D : pN;
    const int p_NE = D1D*D1D;
@@ -729,7 +729,7 @@ static void FindPointsLocal2D_Kernel(const int npt,
       // 3D1D for seed, 10D1D+6 for area, 3D1D+9 for edge
       constexpr int size1 = 10*MD1 + 6;
       constexpr int size2 = MD1*4;            // edge constraints
-      constexpr int size3 = MD1*MD1*MD1*DIM;  // local element coordinates
+      constexpr int size3 = MD1*MD1*DIM;  // local element coordinates
 
       MFEM_SHARED double r_workspace[size1];
       MFEM_SHARED findptsElementPoint_t el_pts[2];
@@ -1162,9 +1162,9 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
    auto pgslm = gsl_mesh.Read();
    auto pwt = DEV.wtend.Read();
    auto pbb = DEV.bb.Read();
-   auto plhm = DEV.loc_hash_min.Read();
-   auto plhf = DEV.loc_hash_fac.Read();
-   auto plho = DEV.loc_hash_offset.ReadWrite();
+   auto plhm = DEV.lh_min.Read();
+   auto plhf = DEV.lh_fac.Read();
+   auto plho = DEV.lh_offset.ReadWrite();
    auto pcode = code.Write();
    auto pelem = elem.Write();
    auto pref = ref.Write();
@@ -1177,30 +1177,32 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
       case 2:
          return FindPointsLocal2D_Kernel<2>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 3:
          return FindPointsLocal2D_Kernel<3>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 4:
          return FindPointsLocal2D_Kernel<4>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 5:
          return FindPointsLocal2D_Kernel<5>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       default:
          return FindPointsLocal2D_Kernel(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                         pgslm, NE_split_total, pwt, pbb, DEV.h_nx,
+                                         pgslm, NE_split_total, pwt, pbb, DEV.lh_nx,
                                          plhm, plhf, plho, pcode, pelem,
                                          pref, pdist, pgll1d, plc, DEV.dof1d);
    }
 }
+#undef DIM2
+#undef DIM
 #undef CODE_INTERNAL
 #undef CODE_BORDER
 #undef CODE_NOT_FOUND

fem/gslib/findpts_local_3.cpp

@@ -294,7 +294,7 @@ get_face(const double *elx[3], const double *wtend, int fi, double *workspace,
       face.dxdn[d] = workspace+(3+d)*p_Nfr;
    }
 
-   if (side_init != (1u << fi))
+   if (static_cast<unsigned>(side_init) != (1u << fi))
    {
       const int e_stride[3] = {1, pN, pN*pN};
 #define ELX(d, j, k, l) elx[d][j*e_stride[d1]+k*e_stride[d2]+l*e_stride[dn]]
@@ -342,7 +342,7 @@ get_edge(const double *elx[3], const double *wtend, int ei, double *workspace,
 
    if (jidx >= 3*pN) { return edge; }
 
-   if (side_init != (64u << ei))
+   if (static_cast<unsigned>(side_init) != (64u << ei))
    {
       const int e_stride[3] = {1, pN, pN*pN};
 #define ELX(d, j, k, l) elx[d][j*e_stride[de]+k*e_stride[dn1]+l*e_stride[dn2]]
@@ -706,7 +706,7 @@ newton_vol_fin:
       int f = flags >> (2*dd) & 3u;
       res->r[dd] = f == 0 ? r0[dd]+dr[dd] : (f == 1 ? -1 : 1);
    }
-   res->flags = flags | (p->flags << 7);
+   res->flags = flags | ((p->flags & FLAG_MASK) << 7);
 }
 
 // Full Newton solve on the face. One of r/s/t is constrained.
@@ -889,7 +889,7 @@ newton_face_fin:
    res->r[dn] = p->r[dn];
    res->r[d1] = r[0];
    res->r[d2] = r[1];
-   res->flags = new_flags | (p->flags << 7);
+   res->flags = new_flags | ((p->flags & FLAG_MASK) << 7);
 }
 
 // Full Newton solve on the edge. Two of r/s/t are constrained.
@@ -973,7 +973,8 @@ newton_edge_fin:
    res->r[dn1] = p->r[dn1];
    res->r[dn2] = p->r[dn2];
    res->dist2p = -v;
-   res->flags = flags | new_flags | (p->flags << 7);
+   res->flags = flags | new_flags | ((p->flags & FLAG_MASK) << 7);
+#undef EVAL
 }
 
 // Find closest mesh node to the sought point.
@@ -1252,7 +1253,6 @@ static void FindPointsLocal3DKernel(const int npt,
                      case 0: // findpt_vol
                      {
                         double *wtr = r_workspace_ptr;
-
                         double *resid = wtr+6*D1D;
                         double *jac = resid+3;
                         double *resid_temp = jac+9;
@@ -1503,7 +1503,7 @@ static void FindPointsLocal3DKernel(const int npt,
                               // Hes_T is transposed version (i.e. in col major)
                               // n1*[2, 1, 1, 0, 0]
                               // j==1 => wt_j = wt+n1
-                              double *wt_j = wt+D1D*(2-(row+1) / 2);
+                              double *wt_j = wt+D1D*(2 - (row+1)/2);
                               const double *x = e_x[row+1][d];
                               hes_T[j] = 0.0;
                               for (int k = 0; k < D1D; ++k)
@@ -1522,7 +1522,6 @@ static void FindPointsLocal3DKernel(const int npt,
                               hes[j] += resid[d]*hes_T[j*3+d];
                            }
                         }
-
                         MFEM_SYNC_THREAD;
 
                         MFEM_FOREACH_THREAD(l,x,1)
@@ -1780,6 +1779,7 @@ static void FindPointsLocal3DKernel(const int npt,
          } //findpts_local
       } //elp
    });
+#undef MAXC
 }
 
 void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
@@ -1796,9 +1796,9 @@ void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
    auto pgslm = gsl_mesh.Read();
    auto pwt = DEV.wtend.Read();
    auto pbb = DEV.bb.Read();
-   auto plhm = DEV.loc_hash_min.Read();
-   auto plhf = DEV.loc_hash_fac.Read();
-   auto plho = DEV.loc_hash_offset.ReadWrite();
+   auto plhm = DEV.lh_min.Read();
+   auto plhf = DEV.lh_fac.Read();
+   auto plho = DEV.lh_offset.ReadWrite();
    auto pcode = code.Write();
    auto pelem = elem.Write();
    auto pref = ref.Write();
@@ -1809,31 +1809,31 @@ void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
    {
       case 2:
          FindPointsLocal3DKernel<2>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 3:
          FindPointsLocal3DKernel<3>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 4:
          FindPointsLocal3DKernel<4>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 5:
          FindPointsLocal3DKernel<5>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       default:
          FindPointsLocal3DKernel(npt, DEV.newt_tol, pp, point_pos_ordering, pgslm,
-                                 NE_split_total, pwt, pbb, DEV.h_nx, plhm, plhf,
+                                 NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
                                  plho, pcode, pelem, pref, pdist, pgll1d, plc,
                                  DEV.dof1d);
    }

fem/gslib/findptsedge_local_2.cpp

@@ -0,0 +1,725 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+#define sDIM 2
+#define sDIM2 4
+#define rDIM 1
+
+struct findptsElementPoint_t
+{
+   double x[sDIM], r, oldr, dist2, dist2p, tr;
+   int flags;
+};
+
+struct findptsElementGEdge_t
+{
+   double *x[sDIM];
+};
+
+struct findptsElementGPT_t
+{
+   double x[sDIM], jac[sDIM*rDIM], hes[sDIM*rDIM];
+};
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+struct obbox_t
+{
+   double c0[sDIM], A[sDIM*sDIM];
+   dbl_range_t x[sDIM];
+};
+
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[sDIM];
+   double fac[sDIM];
+   unsigned int *offset;
+};
+
+static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
+                                                        int i, const double *z,
+                                                        const double *lCoeff,
+                                                        int pN)
+{
+   double u0 = 1, u1 = 0, u2 = 0;
+   for (int j = 0; j < pN; ++j)
+   {
+      if (i != j)
+      {
+         double d_j = 2 * (x-z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
+   p0[i] = lCoeff[i] * u0;
+   p1[i] = 2.0 * lCoeff[i] * u1;
+   p2[i] = 8.0 * lCoeff[i] * u2;
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
+                                                      const double x[sDIM])
+{
+   double b_d;
+   for (int d=0; d<sDIM; ++d)
+   {
+      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      if (b_d < 0)   // if outside in any dimension
+      {
+         return b_d;
+      }
+   }
+   return b_d;       // only positive if inside
+}
+
+/* positive when given point is possibly inside given obbox b */
+static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
+                                                 const double x[sDIM])
+{
+   const double bxyz = obbox_axis_test(b,x);
+   if (bxyz<0)   // test if point is in AABB
+   {
+      return bxyz;
+   }
+   else   // test OBB only if inside AABB
+   {
+      double dxyz[sDIM];
+      for (int d=0; d<sDIM; ++d)
+      {
+         dxyz[d] = x[d] - b->c0[d];
+      }
+      double test = 1;
+      for (int d=0; d<sDIM; ++d)
+      {
+         double rst = 0;
+         for (int e=0; e<sDIM; ++e)
+         {
+            rst += b->A[d*2 + e] * dxyz[e];
+         }
+         double brst = (rst+1)*(1-rst);
+         test = test<0 ? test : brst;
+      }
+      return test;
+   }
+}
+
+/* Hash index in the hash table to the elements that possibly contain the point x */
+static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
+                                              const double x[2])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d=sDIM-1; d>=0; --d)
+   {
+      sum *= n;
+      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
+      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
+   }
+   return sum;
+}
+
+static MFEM_HOST_DEVICE inline double l2norm2(const double x[2])
+{
+   return x[0] * x[0] + x[1] * x[1];
+}
+
+/* the bit structure of flags is CRR
+   the C bit --- 1<<2 --- is set when the point is converged
+   RR is 0 = 00b if r is unconstrained,
+         1 = 01b if r is constrained at -1, i.e., rmin
+         2 = 10b if r is constrained at +1, i.e., rmax
+*/
+
+#define CONVERGED_FLAG (1u<<2)
+#define FLAG_MASK 0x07u // = 111b
+
+/* returns 1 if r direction (the only free direction in 2D) is constrained.
+   returns 1 if either 1st or 2nd bit of flags is set.
+*/
+static MFEM_HOST_DEVICE inline int num_constrained(const int flags)
+{
+   return ((flags | flags>>1) & 1u);
+}
+
+/* pi=0, r=-1; pi=1, r=+1 */
+static MFEM_HOST_DEVICE inline int point_index(const int x)
+{
+   return ((x>>1) & 1u);
+}
+
+/* check reduction in objective against prediction, and adjust
+   trust region radius (p->tr) accordingly;
+   may reject the prior step, returning 1; otherwise returns 0
+   sets out->dist2, out->index, out->x, out->oldr in any event,
+   leaving out->r, out->dr, out->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+                                                 const double resid[2],
+                                                 const findptsElementPoint_t *p,
+                                                 const double tol)
+{
+   const double dist2 = l2norm2(resid);
+   const double decr = p->dist2 - dist2;
+   const double pred = p->dist2p;
+   out->x[0] = p->x[0];
+   out->x[1] = p->x[1];
+   out->oldr = p->r;
+   out->dist2 = dist2;
+   if (decr >= 0.01*pred)
+   {
+      if (decr >= 0.9*pred)   // very good iteration
+      {
+         out->tr = p->tr*2;
+      }
+      else                    // somewhat good iteration
+      {
+         out->tr = p->tr;
+      }
+      return false;
+   }
+   else
+   {
+      /* reject step; note: the point will pass through this routine
+         again, and we set things up here so it gets classed as a
+         "very good iteration" --- this doubles the trust radius,
+         which is why we divide by 4 below */
+      double v0 = fabs(p->r - p->oldr);
+      out->tr = v0/4.0;
+      out->dist2 = p->dist2;
+      out->r = p->oldr;
+      out->flags = p->flags>>3;
+      out->dist2p = -HUGE_VAL;
+      if (pred < dist2*tol)
+      {
+         out->flags |= CONVERGED_FLAG;
+      }
+      return true;
+   }
+}
+
+static MFEM_HOST_DEVICE inline void newton_edge( findptsElementPoint_t *const
+                                                 out,
+                                                 const double jac[2],
+                                                 const double rhess,
+                                                 const double resid[2],
+                                                 int flags,
+                                                 const findptsElementPoint_t *const p,
+                                                 const double tol )
+{
+   const double tr = p->tr;
+   const double A = jac[0] * jac[0] + jac[1] * jac[1] -
+                    rhess; // A = J^T J - resid_d H_d
+   const double y = jac[0]*resid[0] + jac[1]*resid[1];        // y = J^T resid
+
+   const double oldr = p->r;
+   double dr, newr, tdr, tnewr, v, tv;
+   int new_flags=0, tnew_flags=0;
+
+#define EVAL(dr) ( (dr*A - 2*y) * dr )
+   if (A>0)
+   {
+      dr = y/A;
+      if (fabs(dr)<tol)
+      {
+         dr=0.0;
+         newr = oldr;
+      }
+      else
+      {
+         newr = oldr+dr;
+      }
+
+      if (fabs(dr)<tr && fabs(newr)<1)
+      {
+         v = EVAL(dr);
+         goto newton_edge_fin;
+      }
+   }
+
+   if ((newr=oldr-tr) > -1)
+   {
+      dr = -tr;
+   }
+   else
+   {
+      newr = -1, dr = -1-oldr, new_flags = flags|1u;
+   }
+   v = EVAL(dr);
+
+   if ((tnewr=oldr+tr) < 1)
+   {
+      tdr = tr;
+   }
+   else
+   {
+      tnewr = 1, tdr = 1-oldr, tnew_flags = flags|2u;
+   }
+   tv = EVAL(tdr);
+
+   if (tv<v)
+   {
+      newr = tnewr, dr = tdr, v = tv, new_flags = tnew_flags;
+   }
+#undef EVAL
+
+newton_edge_fin:
+   // check convergence by testing if change in r is less than tol
+   if (fabs(dr)<tol)
+   {
+      new_flags |= CONVERGED_FLAG;
+   }
+   out->r = newr;
+   out->dist2p = -v;
+   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+}
+
+static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
+                                     const double x[sDIM],
+                                     const double *z,
+                                     double       *dist2,
+                                     double       *r,
+                                     const int    ir,
+                                     const int    pN )
+{
+   double dx[sDIM];
+   for (int d=0; d<sDIM; ++d)
+   {
+      dx[d] = x[d] - elx[d][ir];
+   }
+   dist2[ir] = HUGE_VAL;
+   const double dist2_rs = l2norm2(dx);
+   if (dist2[ir]>dist2_rs)
+   {
+      dist2[ir] = dist2_rs;
+      r[ir] = z[ir];
+   }
+}
+
+template<int T_D1D = 0>
+static void FindPointsEdgeLocal2D_Kernel( const int     npt,
+                                          const double  tol,
+                                          const double  dist2tol,
+                                          const double  *x,
+                                          const int     point_pos_ordering,
+                                          const double  *xElemCoord,
+                                          const int     nel,
+                                          const double  *wtend,
+                                          const double  *boxinfo,
+                                          const int     hash_n,
+                                          const double  *hashMin,
+                                          const double  *hashFac,
+                                          unsigned int  *hashOffset,
+                                          unsigned int *const code_base,
+                                          unsigned int *const el_base,
+                                          double *const r_base,
+                                          double *const dist2_base,
+                                          const double  *gll1D,
+                                          const double  *lagcoeff,
+                                          const int     pN = 0 )
+{
+   const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D   = T_D1D ? T_D1D : pN;
+   const int p_NEL = nel*D1D;
+   MFEM_VERIFY(MD1<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D!=0, "Polynomial order not specified.");
+   const int nThreads = D1D*sDIM;
+
+   mfem::forall_2D(npt, nThreads, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      // 2D1D for seed, 3D1D + 7 for edge
+      constexpr int size1 = 3*MD1 + 7;
+      // edge coordinates = D1D*2
+      constexpr int size2 = 2*MD1;
+      // local element coordinates in shared memory
+      constexpr int size3 = MD1*sDIM;
+
+      MFEM_SHARED findptsElementPoint_t el_pts[2];
+      MFEM_SHARED double r_workspace[size1];
+
+      MFEM_SHARED double constraint_workspace[size2];
+
+      MFEM_SHARED double elem_coords[MD1 <= 6 ? size3 : 1];
+
+      double *r_workspace_ptr = r_workspace;
+      findptsElementPoint_t *fpt, *tmp;
+      fpt = el_pts + 0;
+      tmp = el_pts + 1;
+
+      // x and y coord index within point_pos for point i
+      int id_x = point_pos_ordering == 0 ? i     : i*sDIM;
+      int id_y = point_pos_ordering == 0 ? i+npt : i*sDIM+1;
+      double x_i[2] = {x[id_x], x[id_y]};
+
+      unsigned int *code_i = code_base  + i;
+      double *dist2_i      = dist2_base + i;
+
+      //---------------- map_points_to_els --------------------
+      findptsLocalHashData_t hash;
+      for (int d=0; d<sDIM; ++d)
+      {
+         hash.bnd[d].min = hashMin[d];
+         hash.fac[d] = hashFac[d];
+      }
+      hash.hash_n = hash_n;
+      hash.offset = hashOffset;
+
+      const int hi                  = hash_index(&hash, x_i);
+      const unsigned int *elp       = hash.offset + hash.offset[hi];
+      const unsigned int *const ele = hash.offset + hash.offset[hi+1];
+      *code_i  = CODE_NOT_FOUND;
+      *dist2_i = HUGE_VAL;
+
+      for (; elp!=ele; ++elp)
+      {
+         const unsigned int el = *elp;
+
+         obbox_t box;
+         int n_box_ents = 3*sDIM + sDIM2;
+
+         for (int idx = 0; idx < sDIM; ++idx)
+         {
+            box.c0[idx] = boxinfo[n_box_ents*el + idx];
+            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+         }
+
+         for (int idx = 0; idx < sDIM2; ++idx)
+         {
+            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+         }
+
+         if (obbox_test(&box,x_i)>=0)
+         {
+            //------------ findpts_local ------------------
+            {
+               if (MD1 <= 6)
+               {
+                  MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
+                  {
+                     const int qp = j % D1D;
+                     const int d = j / D1D;
+                     elem_coords[qp + d*D1D] =
+                        xElemCoord[qp + el*D1D + d*p_NEL];
+                  }
+                  MFEM_SYNC_THREAD;
+               }
+
+               const double *elx[sDIM];
+               for (int d=0; d<sDIM; d++)
+               {
+                  elx[d] = MD1<= 6 ? &elem_coords[d*D1D] :
+                           xElemCoord + d*p_NEL + el*D1D;
+               }
+               MFEM_SYNC_THREAD;
+               //// findpts_el ////
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     fpt->dist2 = HUGE_VAL;
+                     fpt->dist2p = 0;
+                     fpt->tr = 1;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     fpt->x[j] = x_i[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  {
+                     double *dist2_temp = r_workspace_ptr;
+                     double *r_temp = dist2_temp + D1D;
+                     MFEM_FOREACH_THREAD(j,x,D1D)
+                     {
+                        seed_j(elx, x_i, gll1D, dist2_temp, r_temp, j, D1D);
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        for (int ir=0; ir<D1D; ++ir)
+                        {
+                           if (dist2_temp[ir]<fpt->dist2)
+                           {
+                              fpt->dist2 = dist2_temp[ir];
+                              fpt->r = r_temp[ir];
+                           }
+                        }
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //seed done
+
+                  // Initialize tmp struct with fpt values before starting Newton iterations
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     tmp->dist2 = HUGE_VAL;
+                     tmp->dist2p = 0;
+                     tmp->tr = 1;
+                     tmp->flags = 0;
+                     tmp->r = fpt->r;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     tmp->x[j] = fpt->x[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+
+                  for (int step=0; step<50; step++)
+                  {
+                     int nc = num_constrained(tmp->flags & FLAG_MASK);
+                     switch (nc)
+                     {
+                        case 0:
+                        {
+                           double *wt = r_workspace_ptr;
+                           double *resid = wt + 3*D1D;
+                           double *jac = resid + sDIM;
+                           double *hess = jac + sDIM*rDIM;
+
+                           findptsElementGEdge_t edge;
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 edge.x[d] = constraint_workspace + d*D1D;
+                                 edge.x[d][j] = elx[d][j];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           // compute basis function info upto 2nd derivative
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              lag_eval_second_der(wt, tmp->r, j, gll1D,
+                                                  lagcoeff, D1D);
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,sDIM)
+                           {
+                              resid[j] = tmp->x[j];
+                              jac[j] = 0.0;
+                              hess[j] = 0.0;
+                              for (int k=0; k<D1D; ++k)
+                              {
+                                 resid[j] -= wt[      k]*edge.x[j][k];
+                                 jac[j]   += wt[D1D+k]*edge.x[j][k];
+                                 hess[j]  += wt[2*D1D+k]*edge.x[j][k];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              hess[2] = resid[0]*hess[0] + resid[1]*hess[1];
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              if (!reject_prior_step_q(fpt, resid, tmp, tol))
+                              {
+                                 newton_edge(fpt, jac, hess[2], resid,
+                                             tmp->flags & FLAG_MASK, tmp, tol);
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        }
+                        case 1:    // r is constrained to either -1 or 1
+                        {
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              const int pi = point_index(tmp->flags &
+                                                         FLAG_MASK);
+                              const double *wt   = wtend + pi*3*D1D;
+                              findptsElementGPT_t gpt;
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 gpt.x[d] = elx[d][pi*(D1D-1)];
+                                 gpt.jac[d] = 0.0;
+                                 gpt.hes[d] = 0.0;
+                                 for (int k=0; k<D1D; ++k)
+                                 {
+                                    gpt.jac[d] += wt[D1D  +k]*elx[d][k];
+                                    gpt.hes[d] += wt[2*D1D+k]*elx[d][k];
+                                 }
+                              }
+
+                              const double *const pt_x = gpt.x;
+                              const double *const jac = gpt.jac;
+                              const double *const hes = gpt.hes;
+                              double resid[sDIM], steep, sr;
+                              resid[0] = fpt->x[0] - pt_x[0];
+                              resid[1] = fpt->x[1] - pt_x[1];
+                              steep = jac[0]*resid[0] + jac[1]*resid[1];
+                              sr = steep*tmp->r;
+                              if ( !reject_prior_step_q(fpt, resid, tmp, tol) )
+                              {
+                                 if (sr<0)
+                                 {
+                                    const double rhess = resid[0]*hes[0] +
+                                                         resid[1]*hes[1];
+                                    newton_edge(fpt, jac, rhess,
+                                                resid, 0, tmp, tol);
+                                 }
+                                 else // sr==0
+                                 {
+                                    fpt->r = tmp->r;
+                                    fpt->dist2p = 0;
+                                    fpt->flags = tmp->flags | CONVERGED_FLAG;
+                                 }
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        } // case 1
+                     } //switch
+                     if (fpt->flags & CONVERGED_FLAG)
+                     {
+                        break;
+                     }
+                     MFEM_SYNC_THREAD;
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        *tmp = *fpt;
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //for int step<50
+               } //findpts_el
+
+               bool converged_internal =
+                  ((fpt->flags&FLAG_MASK) == CONVERGED_FLAG) &&
+                  (fpt->dist2<dist2tol);
+
+               if (*code_i == CODE_NOT_FOUND || converged_internal ||
+                   fpt->dist2 < *dist2_i)
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     *(el_base+i) = el;
+                     *code_i = converged_internal ? CODE_INTERNAL : CODE_BORDER;
+                     *dist2_i = fpt->dist2;
+                     *(r_base+i) = fpt->r;
+                  }
+                  MFEM_SYNC_THREAD;
+                  if (converged_internal)
+                  {
+                     break;
+                  }
+               }
+            } //findpts_local
+         } //obbox_test
+      } //elp
+   });
+}
+
+void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt )
+{
+   if (npt==0)
+   {
+      return;
+   }
+   MFEM_VERIFY(dim==1 && spacedim==2,"Function for 2D edges only");
+   bool use_dev = point_pos.UseDevice();
+   auto pp = point_pos.Read(use_dev);
+   auto pgslm = gsl_mesh.Read(use_dev);
+   auto pwt = DEV.wtend.Read(use_dev);
+   auto pbb = DEV.bb.Read(use_dev);
+   auto plhm = DEV.lh_min.Read(use_dev);
+   auto plhf = DEV.lh_fac.Read(use_dev);
+   auto plho = DEV.lh_offset.ReadWrite(use_dev);
+   auto pcode = code.Write(use_dev);
+   auto pelem = elem.Write(use_dev);
+   auto pref = ref.Write(use_dev);
+   auto pdist = dist.Write(use_dev);
+   auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
+   auto plc = DEV.lagcoeff.Read(use_dev);
+   double dist2tol = DEV.surf_dist_tol;
+   switch (DEV.dof1d)
+   {
+      case 2:
+         return FindPointsEdgeLocal2D_Kernel<2>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 3:
+         return FindPointsEdgeLocal2D_Kernel<3>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 4:
+         return FindPointsEdgeLocal2D_Kernel<4>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      default:
+         return FindPointsEdgeLocal2D_Kernel(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+   }
+}
+#undef sDIM
+#undef rDIM
+#undef sDIM2
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt ) {} ;
+#endif
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/findptsedge_local_3.cpp

@@ -0,0 +1,733 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+#define sDIM 3
+#define rDIM 1
+#define sDIM2 (sDIM*sDIM)
+#define rDIM2 (rDIM*rDIM)
+
+struct findptsElementPoint_t
+{
+   double x[sDIM], r, oldr, dist2, dist2p, tr;
+   int flags;
+};
+
+struct findptsElementGEdge_t
+{
+   double *x[sDIM], *dxdn[sDIM], *d2xdn[sDIM];
+};
+
+struct findptsElementGPT_t
+{
+   double x[sDIM], jac[sDIM], hes[sDIM*(1+1)];
+};
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+struct obbox_t
+{
+   double c0[sDIM], A[sDIM*sDIM];
+   dbl_range_t x[sDIM];
+};
+
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[sDIM];
+   double fac[sDIM];
+   unsigned int *offset;
+};
+
+static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
+                                                        int i, const double *z,
+                                                        const double *lCoeff,
+                                                        int pN)
+{
+   double u0 = 1, u1 = 0, u2 = 0;
+   for (int j=0; j<pN; ++j)
+   {
+      if (i!=j)
+      {
+         double d_j = 2 * (x-z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
+   p0[i] = lCoeff[i] * u0;
+   p1[i] = 2.0 * lCoeff[i] * u1;
+   p2[i] = 8.0 * lCoeff[i] * u2;
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
+                                                      const double x[sDIM])
+{
+   double b_d;
+   for (int d=0; d<sDIM; ++d)
+   {
+      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      if (b_d < 0)   // if outside in any dimension
+      {
+         return b_d;
+      }
+   }
+   return b_d;       // only positive if inside in all dimensions
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
+                                                 const double x[sDIM])
+{
+   const double bxyz = obbox_axis_test(b, x);
+   if (bxyz<0)
+   {
+      return bxyz;
+   }
+   else
+   {
+      double dxyz[3];
+      // dxyz: distance of the point from the center of the OBB
+      for (int d=0; d<sDIM; ++d)
+      {
+         dxyz[d] = x[d] - b->c0[d];
+      }
+      // transform dxyz to the local coordinate system of the OBB,
+      // and check if the point is inside the OBB [-1,1]^sDIM
+      double test = 1;
+      for (int d=0; d<sDIM; ++d)
+      {
+         double rst = 0;
+         for (int e=0; e<sDIM; ++e)
+         {
+            rst += b->A[d*sDIM + e] * dxyz[e];
+         }
+         double brst = (rst+1)*(1-rst);
+         test = test<0 ? test : brst;
+      }
+      return test;
+   }
+}
+
+/* Hash index in the hash table to the elements that possibly contain the point x */
+static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
+                                              const double x[sDIM])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d=sDIM-1; d>=0; --d)
+   {
+      sum *= n;
+      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
+      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
+   }
+   return sum;
+}
+
+
+static MFEM_HOST_DEVICE inline double norm2(const double x[sDIM])
+{
+   return ( x[0]*x[0] + x[1]*x[1] + x[2]*x[2] );
+}
+
+/* the bit structure of flags is CRR
+   the C bit --- 1<<2 --- is set when the point is converged
+   RR is 0 = 00b if r is unconstrained,
+         1 = 01b if r is constrained at -1, i.e., rmin
+         2 = 10b if r is constrained at +1, i.e., rmax
+*/
+#define CONVERGED_FLAG (1u<<2)
+#define FLAG_MASK 0x07u
+
+/* returns the number of constrained reference coordinates, max 2
+*/
+static MFEM_HOST_DEVICE inline int num_constrained(const int flags)
+{
+   const int y = (flags | flags>>1);
+   return (y & 1u) + (y>>2 & 1u);
+}
+
+static MFEM_HOST_DEVICE inline int point_index(const int x)
+{
+   return ((x>>1)&1u) | ((x>>2)&2u);
+}
+
+/* check reduction in objective against prediction, and adjust
+   trust region radius (p->tr) accordingly;
+   may reject the prior step, returning 1; otherwise returns 0
+   sets out->dist2, out->index, out->x, out->oldr in any event,
+   leaving out->r, out->dr, out->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+                                                 const double resid[3],
+                                                 const findptsElementPoint_t *p,
+                                                 const double tol)
+{
+   const double dist2 = norm2(resid);
+   const double decr  = p->dist2 - dist2;
+   const double pred  = p->dist2p;
+   for (int d=0; d<sDIM; ++d)
+   {
+      out->x[d] = p->x[d];
+   }
+   out->oldr = p->r;
+   out->dist2 = dist2;
+   if (decr>=0.01*pred)
+   {
+      if (decr>=0.9*pred)   // very good iteration
+      {
+         out->tr = 2*p->tr;
+      }
+      else   // good iteration
+      {
+         out->tr = p->tr;
+      }
+      return false;
+   }
+   else   // if the iteration in not good
+   {
+      /* reject step; note: the point will pass through this routine
+         again, and we set things up here so it gets classed as a
+         "very good iteration" --- this doubles the trust radius,
+         which is why we divide by 4 below */
+      double v0 = fabs(p->r - p->oldr);
+      out->tr = v0/4.0;
+      out->dist2 = p->dist2;
+      out->r = p->oldr;
+      out->flags = p->flags>>3;
+      out->dist2p = -HUGE_VAL;
+      if (pred<dist2*tol)
+      {
+         out->flags |= CONVERGED_FLAG;
+      }
+      return true;
+   }
+}
+
+static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
+                                                out,
+                                                const double jac[sDIM*rDIM],
+                                                const double rhes,
+                                                const double resid[sDIM],
+                                                int flags,
+                                                const findptsElementPoint_t *const p,
+                                                const double tol)
+{
+   const double tr = p->tr;
+   /* A = J^T J - resid_d H_d */
+   const double A = jac[0]*jac[0]+ jac[1] * jac[1] + jac[2] * jac[2]
+                    - rhes;
+   /* y = J^T r */
+   const double y = jac[0]*resid[0] + jac[1]*resid[1] + jac[0+2]*resid[2];
+
+   const double oldr = p->r;
+   double dr, nr, tdr, tnr;
+   double v, tv;
+   int new_flags = 0, tnew_flags = 0;
+
+#define EVAL(dr) (dr*A - 2*y)*dr
+
+   /* if A is not SPD, quadratic model has no minimum */
+   if (A>0)
+   {
+      dr = y/A;
+
+      if (fabs(dr)<tol)
+      {
+         dr=0.0;
+         nr = oldr;
+      }
+      else
+      {
+         nr = oldr+dr;
+      }
+      if ( fabs(dr)<tr && fabs(nr)<1 )
+      {
+         v = EVAL(dr);
+         goto newton_edge_fin;
+      }
+   }
+
+   if ( (nr=oldr-tr)>-1 )
+   {
+      dr = -tr;
+   }
+   else
+   {
+      nr = -1, dr = -1-oldr, new_flags = flags | 1u;
+   }
+   v = EVAL(dr);
+
+   if ( (tnr = oldr+tr)<1 )
+   {
+      tdr = tr;
+   }
+   else
+   {
+      tnr = 1, tdr = 1-oldr, tnew_flags = flags | 2u;
+   }
+   tv = EVAL(tdr);
+
+   if (tv<v)
+   {
+      nr = tnr, dr = tdr, v = tv, new_flags = tnew_flags;
+   }
+
+newton_edge_fin:
+   /* check convergence */
+   if ( fabs(dr)<tol )
+   {
+      new_flags |= CONVERGED_FLAG;
+   }
+   out->r = nr;
+   out->dist2p = -v;
+   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+#undef EVAL
+}
+
+static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
+                                    const double x[sDIM],
+                                    const double *z,
+                                    double *dist2,
+                                    double *r,
+                                    const int ir,
+                                    const int pN)
+{
+   if (ir>=pN)
+   {
+      return;
+   }
+
+   double dx[sDIM];
+   for (int d=0; d<sDIM; ++d)
+   {
+      dx[d] = x[d] - elx[d][ir];
+   }
+   dist2[ir] = norm2(dx);;
+   r[ir] = z[ir];
+}
+
+template<int T_D1D = 0>
+static void FindPointsEdgeLocal3D_Kernel(const int npt,
+                                         const double tol,
+                                         const double dist2tol,
+                                         const double *x,
+                                         const int point_pos_ordering,
+                                         const double *xElemCoord,
+                                         const int nel,
+                                         const double *wtend,
+                                         const double *boxinfo,
+                                         const int hash_n,
+                                         const double *hashMin,
+                                         const double *hashFac,
+                                         unsigned int *hashOffset,
+                                         unsigned int *const code_base,
+                                         unsigned int *const el_base,
+                                         double *const r_base,
+                                         double *const dist2_base,
+                                         const double *gll1D,
+                                         const double *lagcoeff,
+                                         const int pN = 0)
+{
+   const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D   = T_D1D ? T_D1D : pN;
+   const int p_NEL = nel*D1D;
+   MFEM_VERIFY(MD1<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D!=0, "Polynomial order not specified.");
+   const int nThreads = D1D*sDIM;
+
+   mfem::forall_2D(npt, nThreads, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      constexpr int size1 = 3*MD1 + 13;
+      constexpr int size2 = 3*MD1;
+      constexpr int size3 = MD1*sDIM;
+
+      MFEM_SHARED findptsElementPoint_t el_pts[2];
+      MFEM_SHARED double r_workspace[size1];
+
+      MFEM_SHARED double constraint_workspace[size2];
+
+      MFEM_SHARED double elem_coords[MD1 <= 6 ? size3 : 1];
+
+      double *r_workspace_ptr = r_workspace;
+      findptsElementPoint_t *fpt, *tmp;
+      fpt = el_pts + 0;
+      tmp = el_pts + 1;
+
+      int id_x = point_pos_ordering==0 ?       i :   i*sDIM;
+      int id_y = point_pos_ordering==0 ?   npt+i : 1+i*sDIM;
+      int id_z = point_pos_ordering==0 ? 2*npt+i : 2+i*sDIM;
+      double x_i[3] = {x[id_x], x[id_y], x[id_z]};
+
+      unsigned int *code_i = code_base  + i;
+      double *dist2_i      = dist2_base + i;
+
+      //// map_points_to_els ////
+      findptsLocalHashData_t hash;
+      for (int d=0; d<sDIM; ++d)
+      {
+         hash.bnd[d].min = hashMin[d];
+         hash.fac[d]     = hashFac[d];
+      }
+      hash.hash_n = hash_n;
+      hash.offset = hashOffset;
+
+      const unsigned int hi   = hash_index(&hash, x_i);
+      const unsigned int *elp       = hash.offset + hash.offset[hi];
+      const unsigned int *const ele = hash.offset + hash.offset[hi+1];
+      *code_i  = CODE_NOT_FOUND;
+      *dist2_i = HUGE_VAL;
+
+      for (; elp!=ele; ++elp)
+      {
+         const unsigned int el = *elp;
+         obbox_t box;
+         int n_box_ents = 3*sDIM + sDIM2;
+
+         for (int idx = 0; idx < sDIM; ++idx)
+         {
+            box.c0[idx] = boxinfo[n_box_ents*el + idx];
+            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+         }
+         for (int idx = 0; idx < sDIM2; ++idx)
+         {
+            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+         }
+
+         if (obbox_test(&box, x_i)>=0)
+         {
+            //// findpts_local ////
+            {
+               if (MD1 <= 6)
+               {
+                  MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
+                  {
+                     const int qp = j % D1D;
+                     const int d = j / D1D;
+                     elem_coords[qp + d*D1D] =
+                        xElemCoord[qp + el*D1D + d*p_NEL];
+                  }
+                  MFEM_SYNC_THREAD;
+               }
+
+               const double *elx[sDIM];
+               for (int d=0; d<sDIM; d++)
+               {
+                  elx[d] = MD1<= 6 ? &elem_coords[d*D1D] :
+                           xElemCoord + d*p_NEL + el*D1D;
+               }
+               MFEM_SYNC_THREAD;
+               //// findpts_el ////
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     fpt->dist2 = HUGE_VAL;
+                     fpt->dist2p = 0;
+                     fpt->tr = 1.0;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     fpt->x[j] = x_i[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  //// seed ////
+                  {
+                     double *dist2_temp = r_workspace_ptr;
+                     double *r_temp = dist2_temp + D1D;
+                     MFEM_FOREACH_THREAD(j,x,nThreads)
+                     {
+                        seed_j(elx, x_i, gll1D, dist2_temp, r_temp, j, D1D);
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        fpt->dist2 = HUGE_VAL;
+                        for (int ir=0; ir<D1D; ++ir)
+                        {
+                           if (dist2_temp[ir] < fpt->dist2)
+                           {
+                              fpt->dist2 = dist2_temp[ir];
+                              fpt->r = r_temp[ir];
+                           }
+                        }
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //seed done
+
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     tmp->dist2 = HUGE_VAL;
+                     tmp->dist2p = 0;
+                     tmp->tr = 1;
+                     tmp->flags = 0;
+                     tmp->r = fpt->r;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     tmp->x[j] = fpt->x[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  for (int step=0; step<50; step++)
+                  {
+                     switch (num_constrained(tmp->flags & FLAG_MASK))
+                     {
+                        case 0:
+                        {
+                           double *wt = r_workspace_ptr;
+                           double *resid = wt + 3*D1D;
+                           double *jac = resid + sDIM;
+                           double *hess = jac + sDIM*rDIM;
+
+                           findptsElementGEdge_t edge;
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 edge.x[d] = constraint_workspace + d*D1D;
+                                 edge.x[d][j] = elx[d][j];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              lag_eval_second_der(wt, tmp->r, j, gll1D,
+                                                  lagcoeff, D1D);
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,sDIM)
+                           {
+                              resid[j] = tmp->x[j];
+                              jac[j] = 0.0;
+                              hess[j] = 0.0;
+                              for (int k=0; k<D1D; ++k)
+                              {
+                                 resid[j] -= wt[      k]*edge.x[j][k];
+                                 jac[j]   += wt[D1D+k]*edge.x[j][k];
+                                 hess[j]  += wt[2*D1D+k]*edge.x[j][k];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              hess[3] = resid[0]*hess[0] + resid[1]*hess[1] +
+                                        resid[2]*hess[2];
+                           }
+
+                           MFEM_FOREACH_THREAD(l,x,1)
+                           {
+                              if (!reject_prior_step_q(fpt,resid,tmp,tol))
+                              {
+                                 newton_edge(fpt,jac,hess[3],resid,
+                                             tmp->flags&FLAG_MASK,tmp,tol);
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        }
+                        case 1:
+                        {
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              const int pi = point_index(tmp->flags &
+                                                         FLAG_MASK);
+                              const double *wt = wtend + pi*3*D1D;
+                              findptsElementGPT_t gpt;
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 gpt.x[d] = elx[d][pi*(D1D-1)];
+                                 gpt.jac[d] = 0.0;
+                                 gpt.hes[d] = 0.0;
+                                 for (int k=0; k<D1D; ++k)
+                                 {
+                                    gpt.jac[d] += wt[D1D  +k]*elx[d][k];
+                                    gpt.hes[d] += wt[2*D1D+k]*elx[d][k];
+                                 }
+                              }
+
+                              const double *const pt_x = gpt.x;
+                              const double *const jac = gpt.jac;
+                              const double *const hes = gpt.hes;
+                              double resid[sDIM], steep, sr;
+                              resid[0] = fpt->x[0] - pt_x[0];
+                              resid[1] = fpt->x[1] - pt_x[1];
+                              resid[2] = fpt->x[2] - pt_x[2];
+                              steep = jac[0]*resid[0] + jac[1]*resid[1] +
+                                      jac[2]*resid[2];
+                              sr = steep*tmp->r;
+                              if (!reject_prior_step_q(fpt, resid, tmp, tol))
+                              {
+                                 if (sr<0)
+                                 {
+                                    const double rhess = resid[0]*hes[0] +
+                                                         resid[1]*hes[1] +
+                                                         resid[2]*hes[2];
+                                    newton_edge(fpt, jac, rhess,
+                                                resid, 0, tmp, tol);
+                                 }
+                                 else   // sr==0
+                                 {
+                                    fpt->r = tmp->r;
+                                    fpt->dist2p = 0;
+                                    fpt->flags = tmp->flags | CONVERGED_FLAG;
+                                 }
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        } // case 1
+                     } //switch
+                     if (fpt->flags & CONVERGED_FLAG)
+                     {
+                        break;
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        *tmp = *fpt;
+                     }
+                     MFEM_SYNC_THREAD;
+                  } // for step<50
+               } // findpts_el
+
+               bool converged_internal =
+                  ((fpt->flags&FLAG_MASK) == CONVERGED_FLAG) &&
+                  (fpt->dist2<dist2tol);
+               if (*code_i==CODE_NOT_FOUND || converged_internal ||
+                   fpt->dist2<*dist2_i)
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     *(el_base+i) = el;
+                     *code_i  = converged_internal?CODE_INTERNAL:CODE_BORDER;
+                     *dist2_i = fpt->dist2;
+                     *(r_base+i) = fpt->r;
+                  }
+                  MFEM_SYNC_THREAD;
+                  if (converged_internal)
+                  {
+                     break;
+                  }
+               }
+            } // findpts_local
+         } // obbox_test
+      } // elp
+   });
+}
+
+void FindPointsGSLIB::FindPointsEdgeLocal3(const Vector &point_pos,
+                                           int point_pos_ordering,
+                                           Array<unsigned int> &code,
+                                           Array<unsigned int> &elem,
+                                           Vector &ref,
+                                           Vector &dist,
+                                           int npt)
+{
+   if (npt == 0)
+   {
+      return;
+   }
+   MFEM_VERIFY(spacedim==3 && dim == 1,"Function for 3D edges only");
+   bool use_dev = point_pos.UseDevice();
+   auto pp = point_pos.Read(use_dev);
+   auto pgslm = gsl_mesh.Read(use_dev);
+   auto pwt = DEV.wtend.Read(use_dev);
+   auto pbb = DEV.bb.Read(use_dev);
+   auto plhm = DEV.lh_min.Read(use_dev);
+   auto plhf = DEV.lh_fac.Read(use_dev);
+   auto plho = DEV.lh_offset.ReadWrite(use_dev);
+   auto pcode = code.Write(use_dev);
+   auto pelem = elem.Write(use_dev);
+   auto pref = ref.Write(use_dev);
+   auto pdist = dist.Write(use_dev);
+   auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
+   auto plc = DEV.lagcoeff.Read(use_dev);
+   double dist2tol = DEV.surf_dist_tol;
+   switch (DEV.dof1d)
+   {
+      case 2:
+         return FindPointsEdgeLocal3D_Kernel<2>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 3:
+         return FindPointsEdgeLocal3D_Kernel<3>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 4:
+         return FindPointsEdgeLocal3D_Kernel<4>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      default:
+         return FindPointsEdgeLocal3D_Kernel(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+   }
+}
+#undef rDIM2
+#undef sDIM2
+#undef rDIM
+#undef sDIM
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::FindPointsEdgeLocal3( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt ) {} ;
+#endif
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/interpolate_local_1.cpp

@@ -0,0 +1,157 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/kernels.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+
+static MFEM_HOST_DEVICE void lagrange_eval(double *p0, double x,
+                                           int i, int p_Nq,
+                                           double *z, double *lagrangeCoeff)
+{
+   double p_i = (1 << (p_Nq - 1));
+   for (int j=0; j<p_Nq; ++j)
+   {
+      p_i *= j==i ? 1 : x-z[j];
+   }
+   p0[i] = lagrangeCoeff[i] * p_i;
+}
+
+template<int T_D1D = 0>
+static void InterpolateLocal1DKernel(const double *const gf_in,
+                                     int *const el,
+                                     double *const r,
+                                     double *const int_out,
+                                     const int npt,
+                                     const int nfields,
+                                     double *gll1D,
+                                     double *lagcoeff,
+                                     const int pN = 0)
+{
+   const int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D = T_D1D ? T_D1D : pN;
+   const int p_Nq = D1D;
+   MFEM_VERIFY(MD1 <= DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D != 0, "Polynomial order not specified.");
+   // for each point of the npt points, create a thread block of size dof1Dsol
+   mfem::forall_2D(npt, D1D, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      MFEM_SHARED double wtr[MD1];
+      MFEM_SHARED double sums[MD1];
+
+      // Evaluate basis functions at the reference space coordinates
+      MFEM_FOREACH_THREAD(j,x,D1D)
+      {
+         lagrange_eval(wtr, r[i], j, p_Nq, gll1D, lagcoeff);
+      }
+      MFEM_SYNC_THREAD;
+
+      for (int fld=0; fld<nfields; ++fld)
+      {
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Nq + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
+         const int elemOffset = el[i]*nfields*p_Nq + fld*p_Nq;
+         MFEM_FOREACH_THREAD(j,x,D1D)
+         {
+            sums[j] = wtr[j] * gf_in[elemOffset + j];
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(j,x,1)
+         {
+            double sumv = 0.0;
+            // sum the contributions of each lagrange polynomial
+            for (int jj=0; jj<D1D; ++jj)
+            {
+               sumv += sums[jj];
+            }
+            int_out[fld*npt + i] = sumv;
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+void FindPointsGSLIB::InterpolateLocal1( const Vector &field_in,
+                                         Array<int> &gsl_elem_dev_l,
+                                         Vector &gsl_ref_l,
+                                         Vector &field_out,
+                                         int npt,
+                                         int ncomp,
+                                         int dof1Dsol )
+{
+   MFEM_VERIFY(dim == 1, "Kernel for edges only.");
+   if (npt == 0) { return; }
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsl = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
+   switch (dof1Dsol)
+   {
+      case 2: return InterpolateLocal1DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 3: return InterpolateLocal1DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 4: return InterpolateLocal1DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 5: return InterpolateLocal1DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      default: return InterpolateLocal1DKernel(pfin, pgsl, pgslr, pfout,
+                                                  npt, ncomp,
+                                                  pgll, plcf, dof1Dsol);
+   }
+}
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::InterpolateLocal1(const Vector &field_in,
+                                        Array<int> &gsl_elem_dev_l,
+                                        Vector &gsl_ref_l,
+                                        Vector &field_out,
+                                        int npt, int ncomp,
+                                        int dof1Dsol) {};
+#endif
+
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/interpolate_local_2.cpp

@@ -52,8 +52,6 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
                                      double *const int_out,
                                      const int npt,
                                      const int ncomp,
-                                     const int nel,
-                                     const int gf_offset,
                                      double *gll1D,
                                      double *lagcoeff,
                                      const int pN = 0)
@@ -64,6 +62,8 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
    const int p_Np = D1D*D1D;
    MFEM_VERIFY(MD1 <= DofQuadLimits::MAX_D1D,
                "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
    MFEM_VERIFY(D1D != 0, "Polynomial order not specified.");
    mfem::forall_2D(npt, D1D, D1D, [=] MFEM_HOST_DEVICE (int i)
    {
@@ -82,9 +82,9 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
 
       for (int fld = 0; fld < Nfields; ++fld)
       {
-         // If using GetNodalValues, ordering is NDOFSxNELxVDIM
-         // const int elemOffset = el[i] * p_Np + fld * gf_offset;
-         //if using R->Mult for L -> E-Vec use below: NDOFSxVDIMxNEL
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Np + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
          const int elemOffset = el[i] * p_Np * Nfields + fld * p_Np;
          MFEM_FOREACH_THREAD(j,x,D1D)
          {
@@ -120,32 +120,32 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol)
+                                        int dof1Dsol)
 {
    if (npt == 0) { return; }
-   const int gf_offset = field_in.Size()/ncomp;
-   auto pfin = field_in.Read();
-   auto pgsl = gsl_elem_dev_l.ReadWrite();
-   auto pgslr = gsl_ref_l.ReadWrite();
-   auto pfout = field_out.Write();
-   auto pgll = DEV.gll1d_sol.ReadWrite();
-   auto plcf = DEV.lagcoeff_sol.ReadWrite();
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsl = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
       case 2: return InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 3: return InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 4: return InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 5: return InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       default: return InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
-                                                  npt, ncomp, nel, gf_offset,
+                                                  npt, ncomp,
                                                   pgll, plcf, dof1Dsol);
    }
 }
@@ -160,7 +160,7 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol) {};
+                                        int dof1Dsol) {};
 #endif
 } // namespace mfem
 

fem/gslib/interpolate_local_3.cpp

@@ -52,8 +52,6 @@ static void InterpolateLocal3DKernel(const double *const gf_in,
                                      double *const int_out,
                                      const int npt,
                                      const int ncomp,
-                                     const int nel,
-                                     const int gf_offset,
                                      double *gll1D,
                                      double *lagcoeff,
                                      const int pN = 0)
@@ -84,9 +82,9 @@ static void InterpolateLocal3DKernel(const double *const gf_in,
 
       for (int fld = 0; fld < Nfields; ++fld)
       {
-         // If using GetNodalValues, ordering is NDOFSxNELxVDIM
-         // const int elemOffset = el[i] * p_Np + fld * gf_offset;
-         //if using R->Mult for L -> E-Vec use below.
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Np + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
          const int elemOffset = el[i] * p_Np * Nfields + fld * p_Np;
          MFEM_FOREACH_THREAD(j,x,D1D)
          {
@@ -125,37 +123,38 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol)
+                                        int dof1Dsol)
 {
    if (npt == 0) { return; }
-   const int gf_offset = field_in.Size()/ncomp;
-   auto pfin = field_in.Read();
-   auto pgsle = gsl_elem_dev_l.ReadWrite();
-   auto pgslr = gsl_ref_l.ReadWrite();
-   auto pfout = field_out.Write();
-   auto pgll = DEV.gll1d_sol.ReadWrite();
-   auto plcf = DEV.lagcoeff_sol.ReadWrite();
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsle = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
       case 2: return InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 3: return InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 4: return InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 5: return InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       default: return InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
-                                                  npt, ncomp, nel, gf_offset,
+                                                  npt, ncomp,
                                                   pgll, plcf, dof1Dsol);
    }
 }
 
 
+#undef MAXC
 #undef CODE_INTERNAL
 #undef CODE_BORDER
 #undef CODE_NOT_FOUND
@@ -165,7 +164,7 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol) {};
+                                        int dof1Dsol) {};
 #endif
 } // namespace mfem
 

fem/integ/bilininteg_hdiv_ea.cpp

@@ -197,15 +197,21 @@ static void EAHdivAssemble3D(const int NE,
       // Assemble (one row per thread)
       MFEM_FOREACH_THREAD(idx_i, x, NDOF)
       {
+         // NOTE: due to an llvm backend bug, usage of the modulus operator
+         // has been removed from this foreach section.
          const int ic = idx_i / NDOF_C;
-         const int idx_ii = idx_i % NDOF_C;
+         const int idx_ii = idx_i - ic * NDOF_C; // idx_i % NDOF_C
 
          const int nx_i = (ic == 0) ? D1D : D1D-1;
          const int ny_i = (ic == 1) ? D1D : D1D-1;
 
-         const int ix = idx_ii % nx_i;
-         const int iy = (idx_ii / nx_i) % ny_i;
-         const int iz = (idx_ii / nx_i) / ny_i;
+         const int qx_i = idx_ii / nx_i;
+         const int ix = idx_ii - qx_i * nx_i; // idx_ii % nx_i
+
+         const int qy_i = qx_i / ny_i;
+         const int iy = qx_i - qy_i * ny_i; // (idx_ii / nx_i) % ny_i
+
+         const int iz = qy_i; // (idx_ii / nx_i) / ny_i
 
          const real_t (&Bi1)[MQ1][MD1] = (ic == 0) ? r_Bc : r_Bo;
          const real_t (&Bi2)[MQ1][MD1] = (ic == 1) ? r_Bc : r_Bo;
@@ -214,14 +220,18 @@ static void EAHdivAssemble3D(const int NE,
          for (int idx_j = 0; idx_j < NDOF; ++idx_j)
          {
             const int jc = idx_j / NDOF_C;
-            const int idx_jj = idx_j % NDOF_C;
+            const int idx_jj = idx_j - jc * NDOF_C; // idx_j % NDOF_C
 
             const int nx_j = (jc == 0) ? D1D : D1D-1;
             const int ny_j = (jc == 1) ? D1D : D1D-1;
 
-            const int jx = idx_jj % nx_j;
-            const int jy = (idx_jj / nx_j) % ny_j;
-            const int jz = (idx_jj / nx_j) / ny_j;
+            const int qx_j = idx_jj / nx_j;
+            const int jx = idx_jj - qx_j * nx_j; // idx_jj % nx_j
+
+            const int qy_j = qx_j / ny_j;
+            const int jy = qx_j - qy_j * ny_j; // (idx_jj / nx_j) % ny_j
+
+            const int jz = qy_j; // (idx_jj / nx_j) / ny_j
 
             const real_t (&Bj1)[MQ1][MD1] = (jc == 0) ? r_Bc : r_Bo;
             const real_t (&Bj2)[MQ1][MD1] = (jc == 1) ? r_Bc : r_Bo;

fem/integ/bilininteg_mass_kernels.hpp

@@ -181,6 +181,12 @@ constexpr int NBZ(int D1D)
 {
    return ipow(2, D(D1D) >= 0 ? D(D1D) : 0);
 }
+constexpr int NBZ3D(int MDQ)
+{
+   return MDQ > 0 ? std::min<int>(
+             (128 + MDQ * MDQ * MDQ - 1) / (MDQ * MDQ * MDQ), 64)
+          : 1;
+}
 }
 
 // Shared memory PA Mass Diagonal 2D kernel
@@ -804,19 +810,23 @@ void PAMassApply3D_Element(const int e,
    }
 }
 
-template<int T_D1D, int T_Q1D, bool ACCUMULATE = true>
-MFEM_HOST_DEVICE inline
-void SmemPAMassApply3D_Element(const int e,
-                               const int NE,
-                               const real_t *b_,
-                               const real_t *d_,
-                               const real_t *x_,
-                               real_t *y_,
-                               const int d1d = 0,
-                               const int q1d = 0)
+template <int T_D1D, int T_Q1D, int TBATCH, bool ACCUMULATE = true>
+MFEM_HOST_DEVICE inline void
+SmemPAMassApply3D_Element(const int e, const int NE, const real_t *b_,
+                          const real_t *d_, const real_t *x_, real_t *y_,
+                          int d1d = 0, int q1d = 0)
 {
-   constexpr int D1D = T_D1D ? T_D1D : d1d;
-   constexpr int Q1D = T_Q1D ? T_Q1D : q1d;
+   static_assert(TBATCH > 0, "TBATCH must be positive");
+#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
+   constexpr int tbatch = TBATCH;
+   const int tidz = MFEM_THREAD_ID(z);
+#else
+   // host always batch size 1
+   constexpr int tbatch = 1;
+   constexpr int tidz = 0;
+#endif
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
    constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
    constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
@@ -829,33 +839,37 @@ void SmemPAMassApply3D_Element(const int e,
    MFEM_SHARED real_t sDQ[MQ1*MD1];
    real_t (*B)[MD1] = (real_t (*)[MD1]) sDQ;
    real_t (*Bt)[MQ1] = (real_t (*)[MQ1]) sDQ;
-   MFEM_SHARED real_t sm0[MDQ*MDQ*MDQ];
-   MFEM_SHARED real_t sm1[MDQ*MDQ*MDQ];
-   real_t (*X)[MD1][MD1]   = (real_t (*)[MD1][MD1]) sm0;
-   real_t (*DDQ)[MD1][MQ1] = (real_t (*)[MD1][MQ1]) sm1;
-   real_t (*DQQ)[MQ1][MQ1] = (real_t (*)[MQ1][MQ1]) sm0;
-   real_t (*QQQ)[MQ1][MQ1] = (real_t (*)[MQ1][MQ1]) sm1;
-   real_t (*QQD)[MQ1][MD1] = (real_t (*)[MQ1][MD1]) sm0;
-   real_t (*QDD)[MD1][MD1] = (real_t (*)[MD1][MD1]) sm1;
-   MFEM_FOREACH_THREAD(dy,y,D1D)
+   MFEM_SHARED real_t sm0[tbatch][MDQ*MDQ*MDQ];
+   MFEM_SHARED real_t sm1[tbatch][MDQ*MDQ*MDQ];
+   real_t (*X)[MD1][MD1]   = (real_t (*)[MD1][MD1]) (sm0+tidz);
+   real_t (*DDQ)[MD1][MQ1] = (real_t (*)[MD1][MQ1]) (sm1+tidz);
+   real_t (*DQQ)[MQ1][MQ1] = (real_t (*)[MQ1][MQ1]) (sm0+tidz);
+   real_t (*QQQ)[MQ1][MQ1] = (real_t (*)[MQ1][MQ1]) (sm1+tidz);
+   real_t (*QQD)[MQ1][MD1] = (real_t (*)[MQ1][MD1]) (sm0+tidz);
+   real_t (*QDD)[MD1][MD1] = (real_t (*)[MD1][MD1]) (sm1+tidz);
+   MFEM_FOREACH_THREAD(dy, y, D1D)
    {
-      MFEM_FOREACH_THREAD(dx,x,D1D)
+      MFEM_FOREACH_THREAD(dx, x, D1D)
       {
          MFEM_UNROLL(MD1)
          for (int dz = 0; dz < D1D; ++dz)
          {
-            X[dz][dy][dx] = x(dx,dy,dz,e);
+            X[dz][dy][dx] = x(dx, dy, dz, e);
          }
       }
-      MFEM_FOREACH_THREAD(dx,x,Q1D)
+      MFEM_FOREACH_THREAD(dx, x, Q1D) { B[dx][dy] = b(dx, dy); }
+   }
+   if (tidz == 0)
+   {
+      MFEM_FOREACH_THREAD(dy, y, D1D)
       {
-         B[dx][dy] = b(dx,dy);
+         MFEM_FOREACH_THREAD(dx, x, Q1D) { B[dx][dy] = b(dx, dy); }
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(dy,y,D1D)
+   MFEM_FOREACH_THREAD(dy, y, D1D)
    {
-      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      MFEM_FOREACH_THREAD(qx, x, Q1D)
       {
          real_t u[D1D];
          MFEM_UNROLL(MD1)
@@ -880,9 +894,9 @@ void SmemPAMassApply3D_Element(const int e,
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   MFEM_FOREACH_THREAD(qy, y, Q1D)
    {
-      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      MFEM_FOREACH_THREAD(qx, x, Q1D)
       {
          real_t u[D1D];
          MFEM_UNROLL(MD1)
@@ -907,9 +921,9 @@ void SmemPAMassApply3D_Element(const int e,
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   MFEM_FOREACH_THREAD(qy, y, Q1D)
    {
-      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      MFEM_FOREACH_THREAD(qx, x, Q1D)
       {
          real_t u[Q1D];
          MFEM_UNROLL(MQ1)
@@ -929,22 +943,22 @@ void SmemPAMassApply3D_Element(const int e,
          MFEM_UNROLL(MQ1)
          for (int qz = 0; qz < Q1D; qz++)
          {
-            QQQ[qz][qy][qx] = u[qz] * d(qx,qy,qz,e);
+            QQQ[qz][qy][qx] = u[qz] * d(qx, qy, qz, e);
          }
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(di,y,D1D)
+   if (tidz == 0)
    {
-      MFEM_FOREACH_THREAD(q,x,Q1D)
+      MFEM_FOREACH_THREAD(di, y, D1D)
       {
-         Bt[di][q] = b(q,di);
+         MFEM_FOREACH_THREAD(q, x, Q1D) { Bt[di][q] = b(q, di); }
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   MFEM_FOREACH_THREAD(qy, y, Q1D)
    {
-      MFEM_FOREACH_THREAD(dx,x,D1D)
+      MFEM_FOREACH_THREAD(dx, x, D1D)
       {
          real_t u[Q1D];
          MFEM_UNROLL(MQ1)
@@ -969,9 +983,9 @@ void SmemPAMassApply3D_Element(const int e,
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(dy,y,D1D)
+   MFEM_FOREACH_THREAD(dy, y, D1D)
    {
-      MFEM_FOREACH_THREAD(dx,x,D1D)
+      MFEM_FOREACH_THREAD(dx, x, D1D)
       {
          real_t u[Q1D];
          MFEM_UNROLL(MQ1)
@@ -996,9 +1010,9 @@ void SmemPAMassApply3D_Element(const int e,
       }
    }
    MFEM_SYNC_THREAD;
-   MFEM_FOREACH_THREAD(dy,y,D1D)
+   MFEM_FOREACH_THREAD(dy, y, D1D)
    {
-      MFEM_FOREACH_THREAD(dx,x,D1D)
+      MFEM_FOREACH_THREAD(dx, x, D1D)
       {
          real_t u[D1D];
          MFEM_UNROLL(MD1)
@@ -1020,11 +1034,11 @@ void SmemPAMassApply3D_Element(const int e,
          {
             if (ACCUMULATE)
             {
-               y(dx,dy,dz,e) += u[dz];
+               y(dx, dy, dz, e) += u[dz];
             }
             else
             {
-               y(dx,dy,dz,e) = u[dz];
+               y(dx, dy, dz, e) = u[dz];
             }
          }
       }
@@ -1115,8 +1129,8 @@ inline void PAMassApply3D(const int NE,
    });
 }
 
-// Shared memory PA Mass Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
+// Shared memory PA Mass Apply 3D kernel
+template<int T_D1D = 0, int T_Q1D = 0, int TBATCH=1>
 inline void SmemPAMassApply3D(const int NE,
                               const Array<real_t> &b_,
                               const Array<real_t> &bt_,
@@ -1126,6 +1140,9 @@ inline void SmemPAMassApply3D(const int NE,
                               const int d1d = 0,
                               const int q1d = 0)
 {
+   static_assert(T_D1D > 0, "T_D1D must be positive");
+   static_assert(T_Q1D > 0, "T_Q1D must be positive");
+   static_assert(TBATCH > 0, "TBATCH must be positive");
    MFEM_CONTRACT_VAR(bt_);
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1137,9 +1154,11 @@ inline void SmemPAMassApply3D(const int NE,
    const auto d = d_.Read();
    const auto x = x_.Read();
    auto y = y_.ReadWrite();
-   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   mfem::forall_2D_batch<T_Q1D * T_Q1D * TBATCH>(NE, Q1D, Q1D, TBATCH,
+                                                 [=] MFEM_HOST_DEVICE(int e)
    {
-      internal::SmemPAMassApply3D_Element<T_D1D,T_Q1D>(e, NE, b, d, x, y, d1d, q1d);
+      internal::SmemPAMassApply3D_Element<T_D1D, T_Q1D, TBATCH>(e, NE, b, d, x,
+                                                                y, d1d, q1d);
    });
 }
 
@@ -1394,7 +1413,16 @@ ApplyKernelType MassIntegrator::ApplyPAKernels::Kernel()
 {
    if constexpr (DIM == 1) { return internal::PAMassApply1D; }
    else if constexpr (DIM == 2) { return internal::SmemPAMassApply2D<T_D1D,T_Q1D>; }
-   else if constexpr (DIM == 3) { return internal::SmemPAMassApply3D<T_D1D, T_Q1D>; }
+   else if constexpr (DIM == 3)
+   {
+      constexpr int MDQ = T_D1D >= T_Q1D ? T_D1D : T_Q1D;
+      // max 64 threads in z limit in cuda and hip
+      if constexpr (MDQ > 0)
+      {
+         return internal::SmemPAMassApply3D<T_D1D, T_Q1D,
+                internal::mass::NBZ3D(MDQ)>;
+      }
+   }
    MFEM_ABORT("");
 }
 

fem/integ/bilininteg_vecdiffusion_pa.hpp

@@ -171,15 +171,15 @@ template<int DIM, int T_SDIM, int T_D1D, int T_Q1D>
 VectorDiffusionIntegrator::ApplyKernelType
 VectorDiffusionIntegrator::ApplyPAKernels::Kernel()
 {
-   if (DIM == 2)
+   if constexpr (DIM == 2)
    {
       return internal::SmemPAVectorDiffusionApply2D<T_SDIM, T_D1D, T_Q1D>;
    }
-   else if (DIM == 3)
+   else if constexpr (DIM == 3)
    {
       return internal::SmemPAVectorDiffusionApply3D<T_SDIM, T_D1D, T_Q1D>;
    }
-   else { MFEM_ABORT("Unsupported kernel"); }
+   MFEM_ABORT("Unsupported kernel");
 }
 
 inline VectorDiffusionIntegrator::ApplyKernelType

fem/integ/bilininteg_vecmass_pa.hpp

@@ -182,15 +182,15 @@ template<int DIM, int T_D1D, int T_Q1D>
 VectorMassIntegrator::VectorMassAddMultPAType
 VectorMassIntegrator::VectorMassAddMultPA::Kernel()
 {
-   if (DIM == 2)
+   if constexpr (DIM == 2)
    {
       return internal::SmemPAVectorMassApply2D<T_D1D,T_Q1D>;
    }
-   else if (DIM == 3)
+   else if constexpr (DIM == 3)
    {
       return internal::SmemPAVectorMassApply3D<T_D1D, T_Q1D>;
    }
-   else { MFEM_ABORT("Unsupported kernel"); }
+   MFEM_ABORT("Unsupported kernel");
 }
 
 inline VectorMassIntegrator::VectorMassAddMultPAType

fem/integ/lininteg_domain_kernels.hpp

@@ -301,18 +301,14 @@ template <int DIM, int T_D1D, int T_Q1D>
 DomainLFIntegrator::AssembleKernelType
 DomainLFIntegrator::AssembleKernels::Kernel()
 {
-   switch (DIM)
-   {
-      case 1:
-         return DLFEvalAssemble1D<T_D1D, T_Q1D>;
-      case 2:
-         return DLFEvalAssemble2D<T_D1D, T_Q1D>;
-      case 3:
-         return DLFEvalAssemble3D<T_D1D, T_Q1D>;
-   }
+   if constexpr (DIM == 1) { return DLFEvalAssemble1D<T_D1D, T_Q1D>; }
+   if constexpr (DIM == 2) { return DLFEvalAssemble2D<T_D1D, T_Q1D>; }
+   if constexpr (DIM == 3) { return DLFEvalAssemble3D<T_D1D, T_Q1D>; }
    MFEM_ABORT("");
 }
+
 /// \endcond DO_NOT_DOCUMENT
 
 } // namespace mfem
-#endif
+
+#endif // MFEM_LININTEG_DOMAIN_KERNELS_HPP

fem/intrules.hpp

@@ -43,56 +43,52 @@ public:
       index = i;
    }
 
+   void Set3w(const real_t x1, const real_t x2, const real_t x3, const real_t w)
+   { x = x1; y = x2; z = x3; weight = w; }
+   void Set2w(const real_t x1, const real_t x2, const real_t w)
+   { x = x1; y = x2; weight = w; }
+   void Set1w(const real_t x1, const real_t w)
+   { x = x1; weight = w; }
+
+   void Set3w(const real_t *p) { Set3w(p[0], p[1], p[2], p[3]); }
+   void Set2w(const real_t *p) { Set2w(p[0], p[1], p[2]); }
+   void Set1w(const real_t *p) { Set1w(p[0], p[1]); }
+
+   void Set3(const real_t x1, const real_t x2, const real_t x3)
+   { x = x1; y = x2; z = x3; }
+   void Set2(const real_t x1, const real_t x2)
+   { x = x1; y = x2; }
+   void Set1(const real_t x1)
+   { x = x1; }
+
+   void Set3(const real_t *p) { Set3(p[0], p[1], p[2]); }
+   void Set2(const real_t *p) { Set2(p[0], p[1]); }
+   void Set1(const real_t *p) { Set1(p[0]); }
+
+   void Set(const real_t x1, const real_t x2, const real_t x3, const real_t w)
+   { Set3w(x1, x2, x3, w); }
+
    void Set(const real_t *p, const int dim)
    {
       MFEM_ASSERT(1 <= dim && dim <= 3, "invalid dim: " << dim);
-      x = p[0];
-      if (dim > 1)
+      switch (dim)
       {
-         y = p[1];
-         if (dim > 2)
-         {
-            z = p[2];
-         }
+         case 3: Set3(p); break;
+         case 2: Set2(p); break;
+         case 1: Set1(p); break;
       }
    }
 
    void Get(real_t *p, const int dim) const
    {
       MFEM_ASSERT(1 <= dim && dim <= 3, "invalid dim: " << dim);
-      p[0] = x;
-      if (dim > 1)
+      switch (dim)
       {
-         p[1] = y;
-         if (dim > 2)
-         {
-            p[2] = z;
-         }
+         case 3: p[2] = z;
+         case 2: p[1] = y;
+         case 1: p[0] = x;
       }
    }
-
-   void Set(const real_t x1, const real_t x2, const real_t x3, const real_t w)
-   { x = x1; y = x2; z = x3; weight = w; }
-
-   void Set3w(const real_t *p) { x = p[0]; y = p[1]; z = p[2]; weight = p[3]; }
-
-   void Set3(const real_t x1, const real_t x2, const real_t x3)
-   { x = x1; y = x2; z = x3; }
-
-   void Set3(const real_t *p) { x = p[0]; y = p[1]; z = p[2]; }
-
-   void Set2w(const real_t x1, const real_t x2, const real_t w)
-   { x = x1; y = x2; weight = w; }
-
-   void Set2w(const real_t *p) { x = p[0]; y = p[1]; weight = p[2]; }
-
-   void Set2(const real_t x1, const real_t x2) { x = x1; y = x2; }
-
-   void Set2(const real_t *p) { x = p[0]; y = p[1]; }
-
-   void Set1w(const real_t x1, const real_t w) { x = x1; weight = w; }
-
-   void Set1w(const real_t *p) { x = p[0]; weight = p[1]; }
 };
 
 /// Class for an integration rule - an Array of IntegrationPoint.
@@ -125,18 +121,6 @@ private:
    void AddTriPoints3b(const int off, const real_t b, const real_t weight)
    { AddTriPoints3(off, (1. - b)/2., b, weight); }
 
-   void AddTriPoints3R(const int off, const real_t a, const real_t b,
-                       const real_t c, const real_t weight)
-   {
-      IntPoint(off + 0).Set2w(a, b, weight);
-      IntPoint(off + 1).Set2w(c, a, weight);
-      IntPoint(off + 2).Set2w(b, c, weight);
-   }
-
-   void AddTriPoints3R(const int off, const real_t a, const real_t b,
-                       const real_t weight)
-   { AddTriPoints3R(off, a, b, 1. - a - b, weight); }
-
    void AddTriPoints6(const int off, const real_t a, const real_t b,
                       const real_t c, const real_t weight)
    {
@@ -183,14 +167,6 @@ private:
       AddTetPoints3(off + 1, a, 1. - 3.*a, weight);
    }
 
-   // given b, add the permutations of (a,a,a,b), where 3*a + b = 1
-   void AddTetPoints4b(const int off, const real_t b, const real_t weight)
-   {
-      const real_t a = (1. - b)/3.;
-      IntPoint(off).Set(a, a, a, weight);
-      AddTetPoints3(off + 1, a, b, weight);
-   }
-
    // add the permutations of (a,a,b,b), 2*(a + b) = 1
    void AddTetPoints6(const int off, const real_t a, const real_t weight)
    {
@@ -209,14 +185,37 @@ private:
       AddTetPoints6(off + 6, a, bc, cb, weight);
    }
 
-   // given (b,c), add the permutations of (a,a,b,c), 2*a + b + c = 1
-   void AddTetPoints12bc(const int off, const real_t b, const real_t c,
-                         const real_t weight)
+   // add all 24 permutations of (a,b,c,d) where a+b+c+d = 1, all distinct
+   void AddTetPoints24(const int off, const real_t a, const real_t b,
+                       const real_t c, const real_t weight)
    {
-      const real_t a = (1. - b - c)/2.;
-      AddTetPoints3(off,     a, b, weight);
-      AddTetPoints3(off + 3, a, c, weight);
-      AddTetPoints6(off + 6, a, b, c, weight);
+      const real_t d = 1. - a - b - c;
+      // all 24 permutations of 4 distinct barycentric coordinates
+      // permuting which coordinate goes to x, y, z (4th is 1-x-y-z)
+      IntPoint(off +  0).Set(a, b, c, weight);
+      IntPoint(off +  1).Set(a, b, d, weight);
+      IntPoint(off +  2).Set(a, c, b, weight);
+      IntPoint(off +  3).Set(a, c, d, weight);
+      IntPoint(off +  4).Set(a, d, b, weight);
+      IntPoint(off +  5).Set(a, d, c, weight);
+      IntPoint(off +  6).Set(b, a, c, weight);
+      IntPoint(off +  7).Set(b, a, d, weight);
+      IntPoint(off +  8).Set(b, c, a, weight);
+      IntPoint(off +  9).Set(b, c, d, weight);
+      IntPoint(off + 10).Set(b, d, a, weight);
+      IntPoint(off + 11).Set(b, d, c, weight);
+      IntPoint(off + 12).Set(c, a, b, weight);
+      IntPoint(off + 13).Set(c, a, d, weight);
+      IntPoint(off + 14).Set(c, b, a, weight);
+      IntPoint(off + 15).Set(c, b, d, weight);
+      IntPoint(off + 16).Set(c, d, a, weight);
+      IntPoint(off + 17).Set(c, d, b, weight);
+      IntPoint(off + 18).Set(d, a, b, weight);
+      IntPoint(off + 19).Set(d, a, c, weight);
+      IntPoint(off + 20).Set(d, b, a, weight);
+      IntPoint(off + 21).Set(d, b, c, weight);
+      IntPoint(off + 22).Set(d, c, a, weight);
+      IntPoint(off + 23).Set(d, c, b, weight);
    }
 
 public:

fem/linearform.cpp

@@ -297,7 +297,8 @@ void LinearForm::Assemble()
          tr = mesh->GetBdrFaceTransformations(i);
          if (tr != NULL)
          {
-            fes -> GetElementVDofs (tr -> Elem1No, vdofs);
+            mfem::DofTransformation doftrans;
+            fes -> GetElementVDofs (tr -> Elem1No, vdofs, doftrans);
             for (int k = 0; k < boundary_face_integs.Size(); k++)
             {
                if (boundary_face_integs_marker[k] &&
@@ -307,6 +308,7 @@ void LinearForm::Assemble()
                boundary_face_integs[k]->
                AssembleRHSElementVect(*fes->GetFE(tr->Elem1No),
                                       *tr, elemvect);
+               doftrans.TransformDual(elemvect);
                AddElementVector (vdofs, elemvect);
             }
          }

fem/lininteg.hpp

@@ -164,8 +164,8 @@ private:
 
 public:
    /// Constructs the domain integrator $ (Q, \nabla v) $
-   DomainLFGradIntegrator(VectorCoefficient &QF)
-      : DeltaLFIntegrator(QF), Q(QF) { }
+   DomainLFGradIntegrator(VectorCoefficient &QF, const IntegrationRule *ir = NULL)
+      : DeltaLFIntegrator(QF, ir), Q(QF) { }
 
    bool SupportsDevice() const override { return true; }
 

fem/lor/lor.cpp

@@ -158,15 +158,16 @@ void LORBase::ConstructLocalDofPermutation(Array<int> &perm_) const
                int i;
                i = dofmap_lor[off_lor + i1 + i2*2];
                int s1 = i < 0 ? -1 : 1;
-               int idof_lor = vdof_lor[absdof(i)];
+               int idof_lor = vdof_lor[UnsignIndex(i)];
                i = dofmap_ho[off_ho + i1*n1 + i2*n2];
                int s2 = i < 0 ? -1 : 1;
-               int idof_ho = vdof_ho[absdof(i)];
+               int idof_ho = vdof_ho[UnsignIndex(i)];
                int s3 = idof_lor < 0 ? -1 : 1;
                int s4 = idof_ho < 0 ? -1 : 1;
                int s = s1*s2*s3*s4;
-               i = absdof(idof_ho);
-               perm_[absdof(idof_lor)] = s < 0 ? -1-absdof(i) : absdof(i);
+               i = UnsignIndex(idof_ho);
+               perm_[UnsignIndex(idof_lor)] = s < 0 ? -1-UnsignIndex(i) :
+                                              UnsignIndex(i);
             }
          }
       };
@@ -232,7 +233,7 @@ void LORBase::ConstructDofPermutation() const
          int j = l_perm[i];
          int s = j < 0 ? -1 : 1;
          int t_i = pfes_lor->GetLocalTDofNumber(i);
-         int t_j = pfes_ho->GetLocalTDofNumber(absdof(j));
+         int t_j = pfes_ho->GetLocalTDofNumber(UnsignIndex(j));
          // Either t_i and t_j both -1, or both non-negative
          if ((t_i < 0 && t_j >=0) || (t_j < 0 && t_i >= 0))
          {

fem/lor/lor.hpp

@@ -57,8 +57,6 @@ private:
    /// values (after temporarily changing them for LOR assembly).
    void ResetIntegrationRules(GetIntegratorsFn get_integrators);
 
-   static inline int absdof(int i) { return i < 0 ? -1-i : i; }
-
 protected:
    enum FESpaceType { H1, ND, RT, L2, INVALID };
 

fem/pfespace.cpp

@@ -424,7 +424,7 @@ void ParFiniteElementSpace::GetGroupComm(
             {
                if (ind[l] < 0)
                {
-                  dofs[l] = m + (-1-ind[l]);
+                  dofs[l] = m + FlipIndexSign(ind[l]);
                   if (g_ldof_sign)
                   {
                      (*g_ldof_sign)[dofs[l]] = -1;
@@ -462,7 +462,7 @@ void ParFiniteElementSpace::GetGroupComm(
             {
                if (ind[l] < 0)
                {
-                  dofs[l] = m + (-1-ind[l]);
+                  dofs[l] = m + FlipIndexSign(ind[l]);
                   if (g_ldof_sign)
                   {
                      (*g_ldof_sign)[dofs[l]] = -1;
@@ -500,7 +500,7 @@ void ParFiniteElementSpace::GetGroupComm(
             {
                if (ind[l] < 0)
                {
-                  dofs[l] = m + (-1-ind[l]);
+                  dofs[l] = m + FlipIndexSign(ind[l]);
                   if (g_ldof_sign)
                   {
                      (*g_ldof_sign)[dofs[l]] = -1;
@@ -538,16 +538,16 @@ void ParFiniteElementSpace::ApplyLDofSigns(Array<int> &dofs) const
    {
       if (dofs[i] < 0)
       {
-         if (ldof_sign[-1-dofs[i]] < 0)
+         if (ldof_sign[FlipIndexSign(dofs[i])] < 0)
          {
-            dofs[i] = -1-dofs[i];
+            dofs[i] = FlipIndexSign(dofs[i]);
          }
       }
       else
       {
          if (ldof_sign[dofs[i]] < 0)
          {
-            dofs[i] = -1-dofs[i];
+            dofs[i] = FlipIndexSign(dofs[i]);
          }
       }
    }
@@ -699,7 +699,8 @@ void ParFiniteElementSpace::GetSharedEdgeDofs(
       for (int i = 0; i < dofs.Size(); i++)
       {
          const int di = dofs[i];
-         dofs[i] = (di >= 0) ? rdofs[di] : -1-rdofs[-1-di];
+         dofs[i] = di >= 0 ? rdofs[di] :
+                   FlipIndexSign(rdofs[FlipIndexSign(di)]);
       }
    }
 }
@@ -723,7 +724,8 @@ void ParFiniteElementSpace::GetSharedTriangleDofs(
       for (int i = 0; i < dofs.Size(); i++)
       {
          const int di = dofs[i];
-         dofs[i] = (di >= 0) ? rdofs[di] : -1-rdofs[-1-di];
+         dofs[i] = di >= 0 ? rdofs[di] :
+                   FlipIndexSign(rdofs[FlipIndexSign(di)]);
       }
    }
 }
@@ -747,7 +749,8 @@ void ParFiniteElementSpace::GetSharedQuadrilateralDofs(
       for (int i = 0; i < dofs.Size(); i++)
       {
          const int di = dofs[i];
-         dofs[i] = (di >= 0) ? rdofs[di] : -1-rdofs[-1-di];
+         dofs[i] = (di >= 0) ? rdofs[di] :
+                   FlipIndexSign(rdofs[FlipIndexSign(di)]);
       }
    }
 }
@@ -1487,7 +1490,7 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
          {
-            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+            int ldof = UnsignIndex(ldofs[j]);
 
             if (ldof_marker[ldof] != fn)
             {
@@ -1548,7 +1551,7 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
          {
-            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+            int ldof = UnsignIndex(ldofs[j]);
 
             if (ldof_marker[ldof] != fn)
             {
@@ -1573,14 +1576,15 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
 
       for (int i = 0; i < num_ldofs; i++)
       {
-         int ldof = (ldofs_fn[i] >= 0 ? ldofs_fn[i] : -1-ldofs_fn[i]);
+         int ldof = UnsignIndex(ldofs_fn[i]);
          ldof_marker[ldof] = i;
       }
 
       for ( ; j < j_end; j++)
       {
-         int ldof = (send_J[j] >= 0 ? send_J[j] : -1-send_J[j]);
-         send_J[j] = (send_J[j] >= 0 ? ldof_marker[ldof] : -1-ldof_marker[ldof]);
+         const int ldof = UnsignIndex(send_J[j]);
+         send_J[j] = (send_J[j] >= 0 ? ldof_marker[ldof] :
+                      FlipIndexSign(ldof_marker[ldof]));
       }
    }
 
@@ -1672,12 +1676,7 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
    {
       for (int j_end = face_nbr_ldof.GetI()[fn+1]; j < j_end; j++)
       {
-         int ldof = face_nbr_ldof.GetJ()[j];
-         if (ldof < 0)
-         {
-            ldof = -1-ldof;
-         }
-
+         const int ldof = UnsignIndex(face_nbr_ldof.GetJ()[j]);
          face_nbr_glob_dof_map[j] = dof_face_nbr_offsets[fn] + ldof;
       }
    }
@@ -1721,7 +1720,7 @@ void ParFiniteElementSpace::GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const
    MFEM_ASSERT(Nonconforming() && i >= pmesh->GetNumFaces(), "");
    int el1, el2, inf1, inf2;
    pmesh->GetFaceElements(i, &el1, &el2);
-   el2 = -1 - el2;
+   el2 = FlipIndexSign(el2);
    pmesh->GetFaceInfos(i, &inf1, &inf2);
    MFEM_ASSERT(0 <= el2 && el2 < face_nbr_element_dof.Size(), "");
    const int nd = face_nbr_element_dof.RowSize(el2);
@@ -1737,7 +1736,8 @@ void ParFiniteElementSpace::GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const
    for (int j = 0; j < vdofs.Size(); j++)
    {
       const int ldof = vdofs[j];
-      vdofs[j] = (ldof >= 0) ? vol_vdofs[ldof] : -1-vol_vdofs[-1-ldof];
+      vdofs[j] = (ldof >= 0) ? vol_vdofs[ldof] :
+                 FlipIndexSign(vol_vdofs[FlipIndexSign(ldof)]);
    }
 }
 
@@ -2061,8 +2061,8 @@ void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
 
          for (int j = 0; j < ne; j++)
          {
-            dofs[offset++] = (ind[j] >= 0) ? (first + ind[j])
-                             /*         */ : (-1 - (first + (-1 - ind[j])));
+            dofs[offset++] = (ind[j] >= 0) ? (first + ind[j]) :
+                             FlipIndexSign(first + FlipIndexSign(ind[j]));
          }
       }
       else
@@ -2072,8 +2072,8 @@ void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
          const int *ind = fec->DofOrderForOrientation(Geometry::SEGMENT, Eo[i]);
          for (int j = 0; j < ne; j++)
          {
-            dofs[offset++] = (ind[j] >= 0) ? (first + ind[j])
-                             /*         */ : (-1 - (first + (-1 - ind[j])));
+            dofs[offset++] = (ind[j] >= 0) ? (first + ind[j]) :
+                             FlipIndexSign(first + FlipIndexSign(ind[j]));
          }
       }
    }
@@ -2866,7 +2866,7 @@ void NeighborRowMessage::Encode(int rank)
 
             if (ind && (edof = ind[edof]) < 0)
             {
-               edof = -1 - edof;
+               edof = FlipIndexSign(edof);
                s = -1;
             }
 
@@ -3067,10 +3067,10 @@ void NeighborRowMessage::Decode(int rank)
 
          // If edof arrived with a negative index, flip it, and the scaling.
          real_t s = (edof < 0) ? -1.0 : 1.0;
-         edof = (edof < 0) ? -1 - edof : edof;
+         edof = UnsignIndex(edof);
          if (ind && (edof = ind[edof]) < 0)
          {
-            edof = -1 - edof;
+            edof = FlipIndexSign(edof);
             s *= -1.0;
          }
 
@@ -3121,10 +3121,10 @@ void NeighborRowMessage::Decode(int rank)
 
             // If edof arrived with a negative index, flip it, and the scaling.
             s = (edof < 0) ? -1.0 : 1.0;
-            edof = (edof < 0) ? -1 - edof : edof;
+            edof = UnsignIndex(edof);
             if (ind && (edof = ind[edof]) < 0)
             {
-               edof = -1 - edof;
+               edof = FlipIndexSign(edof);
                s *= -1.0;
             }
 
@@ -4405,12 +4405,9 @@ ParFiniteElementSpace::RebalanceMatrix(int old_ndofs,
          {
             for (int j = 0; j < dofs.Size(); j++)
             {
-               int row = DofToVDof(dofs[j], vd);
-               if (row < 0) { row = -1 - row; }
-
-               int col = DofToVDof(old_dofs[j], vd, old_ndofs);
-               if (col < 0) { col = -1 - col; }
-
+               const int row = UnsignIndex(DofToVDof(dofs[j], vd));
+               const int col = UnsignIndex(DofToVDof(old_dofs[j], vd,
+                                                     old_ndofs));
                i_diag[row] = col;
             }
          }
@@ -4435,9 +4432,7 @@ ParFiniteElementSpace::RebalanceMatrix(int old_ndofs,
       {
          for (int j = 0; j < dofs.Size(); j++)
          {
-            int row = DofToVDof(dofs[j], vd);
-            if (row < 0) { row = -1 - row; }
-
+            const int row = UnsignIndex(DofToVDof(dofs[j], vd));
             if (i_diag[row] == i_diag[row+1]) // diag row empty?
             {
                i_offd[row] = old_dofs[j + vd * dofs.Size()];
@@ -4546,9 +4541,9 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    {
       const Embedding &emb = dtrans.embeddings[k];
 
-      int fine_rank = old_ranks[k];
-      int coarse_rank = (emb.parent < 0) ? (-1 - emb.parent)
-                        : old_pncmesh->ElementRank(emb.parent);
+      const int fine_rank = old_ranks[k];
+      const int coarse_rank = (emb.parent < 0) ? FlipIndexSign(emb.parent)
+                              : old_pncmesh->ElementRank(emb.parent);
 
       if (coarse_rank != MyRank && fine_rank == MyRank)
       {
@@ -4636,8 +4631,8 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
             {
                if (!std::isfinite(lR(i, 0))) { continue; }
 
-               int r = DofToVDof(dofs[i], vd);
-               int m = (r >= 0) ? r : (-1 - r);
+               const int r = DofToVDof(dofs[i], vd);
+               const int m = UnsignIndex(r);
 
                if (is_dg || !mark[m])
                {
@@ -4686,8 +4681,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
             {
                if (!std::isfinite(lR(i, 0))) { continue; }
 
-               int r = DofToVDof(dofs[i], vd);
-               int m = (r >= 0) ? r : (-1 - r);
+               const int m = UnsignIndex(DofToVDof(dofs[i], vd));
 
                if (is_dg || !mark[m])
                {

fem/pgridfunc.cpp

@@ -545,6 +545,8 @@ void ParGridFunction::GetElementDofValues(int el, Vector &dof_vals) const
 
 void ParGridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
+   MFEM_VERIFY(VectorDim() == 1,
+               "Cannot project scalar coefficient onto vector ParGridFunction");
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
 
    if (delta_c == NULL)
@@ -715,7 +717,8 @@ void ParGridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
 }
 
 
-void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
+void ParGridFunction::ProjectDiscCoefficient(
+   std::variant<Coefficient*, VectorCoefficient*> coeff)
 {
    // local maximal element attribute for each dof
    Array<int> ldof_attr;
@@ -761,6 +764,9 @@ void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
 
 void ParGridFunction::ProjectDiscCoefficient(Coefficient &coeff, AvgType type)
 {
+   MFEM_VERIFY(
+      VectorDim() == 1,
+      "Cannot project scalar coefficient onto a vector ParGridFunction");
    // Harmonic  (x1 ... xn) = [ (1/x1 + ... + 1/xn) / n ]^-1.
    // Arithmetic(x1 ... xn) = (x1 + ... + xn) / n.
 
@@ -786,6 +792,8 @@ void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &vcoeff,
    // Harmonic  (x1 ... xn) = [ (1/x1 + ... + 1/xn) / n ]^-1.
    // Arithmetic(x1 ... xn) = (x1 + ... + xn) / n.
 
+   MFEM_VERIFY(VectorDim() == vcoeff.GetVDim(), "vcoeff vdim != VectorDim()");
+
    // Number of zones that contain a given dof.
    Array<int> zones_per_vdof;
    AccumulateAndCountZones(vcoeff, type, zones_per_vdof);
@@ -858,6 +866,12 @@ void ParGridFunction::ProjectBdrCoefficient(
 #endif
 }
 
+void ParGridFunction::ProjectBdrCoefficient(VectorCoefficient &vcoeff,
+                                            const Array<int> &attr)
+{
+   ProjectBdrCoefficient(NULL, &vcoeff, attr);
+}
+
 void ParGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                                    const Array<int> &bdr_attr)
 {
@@ -1568,6 +1582,39 @@ PLBound ParGridFunction::GetBounds(Vector &lower, Vector &upper,
    return plb;
 }
 
+std::pair<real_t, real_t> ParGridFunction::EstimateFunctionMinimum(
+   const int vdim, const PLBound &plb, const int max_depth,
+   const real_t tol) const
+{
+   std::pair<real_t, real_t> minmax =
+      GridFunction::EstimateFunctionMinimum(vdim, plb, max_depth, tol);
+
+   real_t glob_min_lower = minmax.first;
+   real_t glob_min_upper = minmax.second;
+   MPI_Allreduce(MPI_IN_PLACE, &glob_min_lower, 1,
+                 MFEM_MPI_REAL_T, MPI_MIN, pfes->GetComm());
+   MPI_Allreduce(MPI_IN_PLACE, &glob_min_upper, 1,
+                 MFEM_MPI_REAL_T, MPI_MIN, pfes->GetComm());
+
+   return std::make_pair(glob_min_lower, glob_min_upper);
+}
+
+std::pair<real_t, real_t> ParGridFunction::EstimateFunctionMaximum(
+   const int vdim, const PLBound &plb, const int max_depth,
+   const real_t tol) const
+{
+   std::pair<real_t, real_t> minmax =
+      GridFunction::EstimateFunctionMaximum(vdim, plb, max_depth, tol);
+
+   real_t glob_max_lower = minmax.first;
+   real_t glob_max_upper = minmax.second;
+   MPI_Allreduce(MPI_IN_PLACE, &glob_max_lower, 1,
+                 MFEM_MPI_REAL_T, MPI_MAX, pfes->GetComm());
+   MPI_Allreduce(MPI_IN_PLACE, &glob_max_upper, 1,
+                 MFEM_MPI_REAL_T, MPI_MAX, pfes->GetComm());
+   return std::make_pair(glob_max_lower, glob_max_upper);
+}
+
 } // namespace mfem
 
 #endif // MFEM_USE_MPI

fem/pgridfunc.hpp

@@ -63,6 +63,12 @@ protected:
    void ProjectBdrCoefficient(Coefficient *coeff[], VectorCoefficient *vcoeff,
                               const Array<int> &attr);
 
+   /** @brief Project a discontinuous (vector) coefficient as a grid function on
+       a continuous finite element space. The values in shared dofs are
+       determined from the element with maximal attribute. */
+   virtual void ProjectDiscCoefficient(
+      std::variant<Coefficient*, VectorCoefficient*> coeff) override;
+
 public:
    ParGridFunction() { pfes = NULL; }
 
@@ -268,11 +274,6 @@ public:
                            ProjectType type = ProjectType::DEFAULT) override;
 
    using GridFunction::ProjectDiscCoefficient;
-   /** @brief Project a discontinuous vector coefficient as a grid function on
-       a continuous finite element space. The values in shared dofs are
-       determined from the element with maximal attribute. */
-   void ProjectDiscCoefficient(VectorCoefficient &coeff) override;
-
    void ProjectDiscCoefficient(Coefficient &coeff, AvgType type) override;
 
    void ProjectDiscCoefficient(VectorCoefficient &vcoeff, AvgType type) override;
@@ -280,8 +281,7 @@ public:
    using GridFunction::ProjectBdrCoefficient;
 
    void ProjectBdrCoefficient(VectorCoefficient &vcoeff,
-                              const Array<int> &attr) override
-   { ProjectBdrCoefficient(NULL, &vcoeff, attr); }
+                              const Array<int> &attr) override;
 
    void ProjectBdrCoefficient(Coefficient *coeff[],
                               const Array<int> &attr) override
@@ -609,6 +609,18 @@ public:
    PLBound GetBounds(Vector &lower, Vector &upper,
                      const int ref_factor=1, const int vdim=-1) const override;
 
+   /** @brief Estimate the GridFunction minimum across all elements. */
+   std::pair<real_t, real_t> EstimateFunctionMinimum(const int vdim,
+                                                     const PLBound &plb,
+                                                     const int max_depth,
+                                                     const real_t tol) const override;
+
+   /** @brief Estimate the GridFunction maximum across all elements. */
+   std::pair<real_t, real_t> EstimateFunctionMaximum(const int vdim,
+                                                     const PLBound &plb,
+                                                     const int max_depth,
+                                                     const real_t tol) const override;
+
    /** Save the local portion of the ParGridFunction. This differs from the
        serial GridFunction::Save in that it takes into account the signs of
        the local dofs. */

fem/prestriction.cpp

@@ -321,12 +321,17 @@ void ParL2FaceRestriction::DoubleValuedConformingMult(
    const int vd = vdim;
    const bool t = byvdim;
    const int threshold = ndofs;
-   const int nsdofs = pfes.GetFaceNbrVSize();
+   const int nsdofs = pfes.GetFaceNbrVSize() / vd;
    auto d_indices1 = scatter_indices1.Read();
    auto d_indices2 = scatter_indices2.Read();
    auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
-   auto d_x_shared = Reshape(face_nbr_data.Read(),
-                             t?vd:nsdofs, t?nsdofs:vd);
+   const int ne_shared = nsdofs / elem_dofs;
+   const int nedof = elem_dofs;
+   // Note: the shape of face_nbr_data, as determined by
+   // ParFiniteElementSpace::ExchangeFaceNbrData, is (elem_dofs, vdim,
+   // ne_shared), independent of the ordering (byNODES or byVDIM) of the finite
+   // element space.
+   auto d_x_shared = Reshape(face_nbr_data.Read(), elem_dofs, vd, ne_shared);
    auto d_y = Reshape(y.Write(), nface_dofs, vd, 2, nf);
    mfem::forall(nfdofs, [=] MFEM_HOST_DEVICE (int i)
    {
@@ -346,8 +351,9 @@ void ParL2FaceRestriction::DoubleValuedConformingMult(
          }
          else if (idx2>=threshold) // shared boundary
          {
-            d_y(dof, c, 1, face) = d_x_shared(t?c:(idx2-threshold),
-                                              t?(idx2-threshold):c);
+            const int e_shared = (idx2 - threshold) / nedof;
+            const int i_shared = (idx2 - threshold) % nedof;
+            d_y(dof, c, 1, face) = d_x_shared(i_shared,c,e_shared);
          }
          else // true boundary
          {

fem/qfunction.hpp

@@ -271,10 +271,7 @@ inline void QuadratureFunction::GetValues(
    const int s_offset = qspace->Offset(idx);
    const int sl_size = qspace->Offset(idx + 1) - s_offset;
    // Make the values matrix memory an alias of the quadrature function memory
-   Memory<real_t> &values_mem = values.GetMemory();
-   values_mem.Delete();
-   values_mem.MakeAlias(GetMemory(), vdim*s_offset, vdim*sl_size);
-   values.SetSize(vdim, sl_size);
+   values.MakeRef(GetMemory(), vdim*s_offset, vdim, sl_size);
 }
 
 inline void QuadratureFunction::GetValues(

fem/qinterp/det.hpp

@@ -334,17 +334,16 @@ template<int DIM, int SDIM, int D1D, int Q1D>
 QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Kernel()
 {
-   if (DIM == 1)
+   if constexpr (DIM == 1)
    {
-      if (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
-      else if (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 2>; }
-      else if (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 3>; }
-      else { MFEM_ABORT(""); }
+      if constexpr (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
+      else if constexpr (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 2>; }
+      else if constexpr (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 3>; }
    }
-   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D<D1D, Q1D>; }
-   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface<D1D, Q1D>; }
-   else if (DIM == 3) { return internal::quadrature_interpolator::Det3D<D1D, Q1D>; }
-   else { MFEM_ABORT(""); }
+   else if constexpr (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D<D1D, Q1D>; }
+   else if constexpr (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface<D1D, Q1D>; }
+   else if constexpr (DIM == 3) { return internal::quadrature_interpolator::Det3D<D1D, Q1D>; }
+   MFEM_ABORT("");
 }
 
 /// @endcond

fem/qinterp/eval.hpp

@@ -203,10 +203,10 @@ template<int DIM, QVectorLayout Q_LAYOUT,
 QuadratureInterpolator::TensorEvalKernelType
 QuadratureInterpolator::TensorEvalKernels::Kernel()
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Values1D<Q_LAYOUT>; }
-   else if (DIM == 2) { return internal::quadrature_interpolator::Values2D<Q_LAYOUT, VDIM, D1D, Q1D, NBZ>; }
-   else if (DIM == 3) { return internal::quadrature_interpolator::Values3D<Q_LAYOUT, VDIM, D1D, Q1D>; }
-   else { MFEM_ABORT(""); }
+   if constexpr (DIM == 1) { return internal::quadrature_interpolator::Values1D<Q_LAYOUT>; }
+   else if constexpr (DIM == 2) { return internal::quadrature_interpolator::Values2D<Q_LAYOUT, VDIM, D1D, Q1D, NBZ>; }
+   else if constexpr (DIM == 3) { return internal::quadrature_interpolator::Values3D<Q_LAYOUT, VDIM, D1D, Q1D>; }
+   MFEM_ABORT("");
 }
 
 /// @endcond

fem/qinterp/eval_hdiv.hpp

@@ -453,8 +453,15 @@ QuadratureInterpolator::TensorEvalHDivKernels::Kernel()
 {
    using namespace internal::quadrature_interpolator;
    static_assert(DIM == 2 || DIM == 3, "only DIM=2 and DIM=3 are implemented!");
-   if (DIM == 2) { return EvalHDiv2D<Q_LAYOUT, FLAGS, D1D, Q1D>; }
-   return EvalHDiv3D<Q_LAYOUT, FLAGS, D1D, Q1D>;
+   if constexpr (DIM == 2)
+   {
+      return EvalHDiv2D<Q_LAYOUT, FLAGS, D1D, Q1D>;
+   }
+   else if constexpr (DIM == 3)
+   {
+      return EvalHDiv3D<Q_LAYOUT, FLAGS, D1D, Q1D>;
+   }
+   MFEM_ABORT("only DIM=2 and DIM=3 are implemented!");
 }
 
 /// @endcond

fem/qinterp/grad.hpp

@@ -592,10 +592,10 @@ template<int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int VDIM, int D1D,
 QuadratureInterpolator::GradKernelType
 QuadratureInterpolator::GradKernels::Kernel()
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Derivatives1D<Q_LAYOUT, GRAD_PHYS>; }
-   else if (DIM == 2) { return internal::quadrature_interpolator::Derivatives2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D, NBZ>; }
-   else if (DIM == 3) { return internal::quadrature_interpolator::Derivatives3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D>; }
-   else { MFEM_ABORT(""); }
+   if constexpr (DIM == 1) { return internal::quadrature_interpolator::Derivatives1D<Q_LAYOUT, GRAD_PHYS>; }
+   else if constexpr (DIM == 2) { return internal::quadrature_interpolator::Derivatives2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D, NBZ>; }
+   else if constexpr (DIM == 3) { return internal::quadrature_interpolator::Derivatives3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D>; }
+   MFEM_ABORT("");
 }
 
 template<int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int VDIM, int D1D,
@@ -603,10 +603,10 @@ template<int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int VDIM, int D1D,
 QuadratureInterpolator::CollocatedGradKernelType
 QuadratureInterpolator::CollocatedGradKernels::Kernel()
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::CollocatedDerivatives1D<Q_LAYOUT, GRAD_PHYS>; }
-   else if (DIM == 2) { return internal::quadrature_interpolator::CollocatedDerivatives2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, NBZ>; }
-   else if (DIM == 3) { return internal::quadrature_interpolator::CollocatedDerivatives3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D>; }
-   else { MFEM_ABORT(""); }
+   if constexpr (DIM == 1) { return internal::quadrature_interpolator::CollocatedDerivatives1D<Q_LAYOUT, GRAD_PHYS>; }
+   else if constexpr (DIM == 2) { return internal::quadrature_interpolator::CollocatedDerivatives2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, NBZ>; }
+   else if constexpr (DIM == 3) { return internal::quadrature_interpolator::CollocatedDerivatives3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D>; }
+   MFEM_ABORT("");
 }
 
 /// @endcond

fem/quadinterpolator.cpp

@@ -752,10 +752,10 @@ template <int DIM, int VDIM, int ND, int NQ>
 EvalKernel QuadratureInterpolator::EvalKernels::Kernel()
 {
    using namespace internal::quadrature_interpolator;
-   if (DIM == 1) { return Eval1D; }
-   else if (DIM == 2) { return Eval2D<VDIM,ND,NQ>; }
-   else if (DIM == 3) { return Eval3D<VDIM,ND,NQ>; }
-   else { MFEM_ABORT(""); }
+   if constexpr (DIM == 1) { return Eval1D; }
+   else if constexpr (DIM == 2) { return Eval2D<VDIM,ND,NQ>; }
+   else if constexpr (DIM == 3) { return Eval3D<VDIM,ND,NQ>; }
+   MFEM_ABORT("");
 }
 
 template <int DIM>

fem/restriction.cpp

@@ -844,8 +844,6 @@ void ConformingFaceRestriction::ComputeGatherIndices(
    gather_offsets[0] = 0;
 }
 
-static inline int absdof(int i) { return i < 0 ? -1-i : i; }
-
 void ConformingFaceRestriction::SetFaceDofsScatterIndices(
    const Mesh::FaceInformation &face,
    const int face_index,
@@ -868,9 +866,9 @@ void ConformingFaceRestriction::SetFaceDofsScatterIndices(
    {
       const int lex_volume_dof = face_map[face_dof];
       const int s_volume_dof = AsConst(vol_dof_map)[lex_volume_dof]; // signed
-      const int volume_dof = absdof(s_volume_dof);
+      const int volume_dof = UnsignIndex(s_volume_dof);
       const int s_global_dof = elem_map[elem_index*elem_dofs + volume_dof];
-      const int global_dof = absdof(s_global_dof);
+      const int global_dof = UnsignIndex(s_global_dof);
       const int restriction_dof = face_dofs*face_index + face_dof;
       scatter_indices[restriction_dof] = s_global_dof;
       ++gather_offsets[global_dof + 1];
@@ -897,10 +895,10 @@ void ConformingFaceRestriction::SetFaceDofsGatherIndices(
    {
       const int lex_volume_dof = face_map[face_dof];
       const int s_volume_dof = AsConst(vol_dof_map)[lex_volume_dof];
-      const int volume_dof = absdof(s_volume_dof);
+      const int volume_dof = UnsignIndex(s_volume_dof);
       const int s_global_dof = elem_map[elem_index*elem_dofs + volume_dof];
       const int sgn = (s_global_dof >= 0) ? 1 : -1;
-      const int global_dof = absdof(s_global_dof);
+      const int global_dof = UnsignIndex(s_global_dof);
       const int restriction_dof = face_dofs*face_index + face_dof;
       const int s_restriction_dof = (sgn >= 0) ? restriction_dof : -1 -
                                     restriction_dof;
@@ -1400,20 +1398,17 @@ void L2FaceRestriction::PermuteAndSetSharedFaceDofsScatterIndices2(
    const int dim = fes.GetMesh()->Dimension();
    const int dof1d = fes.GetTypicalFE()->GetOrder()+1;
    fes.GetTypicalFE()->GetFaceMap(face_id2, face_map);
-   Array<int> face_nbr_dofs;
-   const ParFiniteElementSpace &pfes =
-      static_cast<const ParFiniteElementSpace&>(this->fes);
-   pfes.GetFaceNbrElementVDofs(elem_index, face_nbr_dofs);
 
    for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
    {
       const int face_dof_elem2 = PermuteFaceL2(dim, face_id1, face_id2,
                                                orientation, dof1d, face_dof_elem1);
       const int volume_dof_elem2 = face_map[face_dof_elem2];
-      const int global_dof_elem2 = face_nbr_dofs[volume_dof_elem2];
+      // Encode the volume DOF index and element index
+      const int global_dof_elem2 = elem_index*elem_dofs + volume_dof_elem2;
       const int restriction_dof_elem2 = face_dofs*face_index + face_dof_elem1;
       // Trick to differentiate dof location inter/shared
-      scatter_indices2[restriction_dof_elem2] = ndofs+global_dof_elem2;
+      scatter_indices2[restriction_dof_elem2] = ndofs + global_dof_elem2;
    }
 #endif
 }

fem/tmop.cpp

@@ -3797,13 +3797,18 @@ void TMOP_Integrator::EnableLimiting(const GridFunction &n0, Coefficient &w0,
 
 void TMOP_Integrator::EnableAdaptiveLimiting(const GridFunction &z0,
                                              Coefficient &coeff,
-                                             AdaptivityEvaluator &ae)
+                                             AdaptivityEvaluator &ae,
+                                             real_t delta_max)
 {
+   MFEM_VERIFY(delta_max > 0.0,
+               "EnableAdaptiveLimiting requires delta_max > 0.0.");
+
    adapt_lim_gf0 = &z0;
    delete adapt_lim_gf;
    adapt_lim_gf   = new GridFunction(z0);
    adapt_lim_coeff = &coeff;
    adapt_lim_eval = &ae;
+   adapt_lim_delta_max = delta_max;
 
    adapt_lim_eval->SetSerialMetaInfo(*z0.FESpace()->GetMesh(),
                                      *z0.FESpace());
@@ -3814,14 +3819,19 @@ void TMOP_Integrator::EnableAdaptiveLimiting(const GridFunction &z0,
 #ifdef MFEM_USE_MPI
 void TMOP_Integrator::EnableAdaptiveLimiting(const ParGridFunction &z0,
                                              Coefficient &coeff,
-                                             AdaptivityEvaluator &ae)
+                                             AdaptivityEvaluator &ae,
+                                             real_t delta_max)
 {
+   MFEM_VERIFY(delta_max > 0.0,
+               "EnableAdaptiveLimiting requires delta_max > 0.0.");
+
    adapt_lim_gf0 = &z0;
    adapt_lim_pgf0 = &z0;
    delete adapt_lim_gf;
    adapt_lim_gf   = new GridFunction(z0);
    adapt_lim_coeff = &coeff;
    adapt_lim_eval = &ae;
+   adapt_lim_delta_max = delta_max;
 
    adapt_lim_eval->SetParMetaInfo(*z0.ParFESpace()->GetParMesh(),
                                   *z0.ParFESpace());
@@ -4102,8 +4112,11 @@ void TMOP_Integrator::GetSurfaceFittingErrors(const Vector &d_loc,
 #ifdef MFEM_USE_MPI
       // Don't count the overlapping DOFs in parallel.
       // The pfes might be ordered byVDIM, while the loop goes consecutively.
-      const int dof_i = pfes->DofToVDof(i, 0);
-      if (parallel && pfes->GetLocalTDofNumber(dof_i) < 0) { continue; }
+      if (parallel)
+      {
+         const int dof_i = pfes->DofToVDof(i, 0);
+         if (pfes->GetLocalTDofNumber(dof_i) < 0) { continue; }
+      }
 #endif
 
       dof_cnt++;
@@ -4294,7 +4307,8 @@ real_t TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       // Contribution from the adaptive limiting term.
       if (adaptive_limiting)
       {
-         const real_t diff = adapt_lim_gf_q(i) - adapt_lim_gf0_q(i);
+         const real_t diff = (adapt_lim_gf_q(i) - adapt_lim_gf0_q(i)) /
+                             adapt_lim_delta_max;
          val += adapt_lim_coeff->Eval(*Tpr, ip) * lim_normal * diff * diff;
       }
 
@@ -4845,14 +4859,16 @@ void TMOP_Integrator::AssembleElemVecAdaptLim(const FiniteElement &el,
    grad_phys.Mult(adapt_lim_gf_e, grad_ptr);
 
    Vector adapt_lim_gf_grad_q(dim);
-
    for (int q = 0; q < nqp; q++)
    {
       const IntegrationPoint &ip = ir.IntPoint(q);
       el.CalcShape(ip, shape);
+
       adapt_lim_gf_grad_e.MultTranspose(shape, adapt_lim_gf_grad_q);
-      adapt_lim_gf_grad_q *= 2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q));
+      adapt_lim_gf_grad_q *= 2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) /
+                             adapt_lim_delta_max / adapt_lim_delta_max;
       adapt_lim_gf_grad_q *= weights(q) * lim_normal * adapt_lim_coeff->Eval(Tpr, ip);
+
       AddMultVWt(shape, adapt_lim_gf_grad_q, mat);
    }
 }
@@ -4899,7 +4915,11 @@ void TMOP_Integrator::AssembleElemGradAdaptLim(const FiniteElement &el,
       Vector gg_ptr(adapt_lim_gf_hess_q.GetData(), dim*dim);
       adapt_lim_gf_hess_e.MultTranspose(shape, gg_ptr);
 
-      const real_t w = weights(q) * lim_normal * adapt_lim_coeff->Eval(Tpr, ip);
+      const real_t coeff = adapt_lim_coeff->Eval(Tpr, ip);
+      const real_t factor =
+         weights(q) * lim_normal * coeff * 2.0 /
+         (adapt_lim_delta_max * adapt_lim_delta_max);
+
       for (int i = 0; i < dof * dim; i++)
       {
          const int idof = i % dof, idim = i / dof;
@@ -4907,10 +4927,11 @@ void TMOP_Integrator::AssembleElemGradAdaptLim(const FiniteElement &el,
          {
             const int jdof = j % dof, jdim = j / dof;
             const real_t entry =
-               w * ( 2.0 * adapt_lim_gf_grad_q(idim) * shape(idof) *
-                     /* */ adapt_lim_gf_grad_q(jdim) * shape(jdof) +
-                     2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) *
-                     adapt_lim_gf_hess_q(idim, jdim) * shape(idof) * shape(jdof));
+               factor *
+               (adapt_lim_gf_grad_q(idim) * shape(idof) *
+                adapt_lim_gf_grad_q(jdim) * shape(jdof) +
+                (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) *
+                adapt_lim_gf_hess_q(idim, jdim) * shape(idof) * shape(jdof));
             mat(i, j) += entry;
             if (i != j) { mat(j, i) += entry; }
          }
@@ -5668,6 +5689,22 @@ UpdateAfterMeshPositionChange(const Vector &d, const FiniteElementSpace &d_fes)
    if (adapt_lim_gf)
    {
       adapt_lim_eval->ComputeAtNewPosition(x_loc, *adapt_lim_gf, ordering);
+      if (PA.enabled)
+      {
+         PA.AL_grads_assembled = false;
+
+         // Step 1 of PA.ALFmF0 update: subtract the old ALF.
+         PA.ALFmF0 -= PA.ALF;
+
+         // Refresh PA.ALF from the updated adapt_lim_gf.
+         const ElementDofOrdering ord = ElementDofOrdering::LEXICOGRAPHIC;
+         const Operator *alf_R =
+            adapt_lim_gf->FESpace()->GetElementRestriction(ord);
+         alf_R->Mult(*adapt_lim_gf, PA.ALF);
+
+         // Step 2 of PA.ALFmF0 update: add the new ALF.
+         PA.ALFmF0 += PA.ALF;
+      }
    }
 
    // Update surf_fit_gf (and optionally its gradients) if surface
@@ -5928,6 +5965,28 @@ void TMOPComboIntegrator::EnableLimiting(const GridFunction &n0,
    for (int i = 1; i < tmopi.Size(); i++) { tmopi[i]->DisableLimiting(); }
 }
 
+void TMOPComboIntegrator::EnableAdaptiveLimiting(const GridFunction &z0,
+                                                 Coefficient &coeff,
+                                                 AdaptivityEvaluator &ae,
+                                                 real_t delta_max)
+{
+   MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");
+
+   tmopi[0]->EnableAdaptiveLimiting(z0, coeff, ae, delta_max);
+}
+
+#ifdef MFEM_USE_MPI
+void TMOPComboIntegrator::EnableAdaptiveLimiting(const ParGridFunction &z0,
+                                                 Coefficient &coeff,
+                                                 AdaptivityEvaluator &ae,
+                                                 real_t delta_max)
+{
+   MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");
+
+   tmopi[0]->EnableAdaptiveLimiting(z0, coeff, ae, delta_max);
+}
+#endif
+
 void TMOPComboIntegrator::SetLimitingNodes(const GridFunction &n0)
 {
    MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");

fem/tmop.hpp

@@ -1440,6 +1440,7 @@ public:
    void Eval_d2(const Vector &x, const Vector &x0, real_t dist,
                 DenseMatrix &d2) const override
    {
+      MFEM_CONTRACT_VAR(x0);
       MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
 
       d2.Diag(1.0 / (dist * dist), x.Size());
@@ -2044,6 +2045,7 @@ protected:
    GridFunction *adapt_lim_gf;           // Owned. Updated by adapt_lim_eval.
    Coefficient *adapt_lim_coeff;         // Not owned.
    AdaptivityEvaluator *adapt_lim_eval;  // Not owned.
+   real_t adapt_lim_delta_max = 1.0;
 
    // Surface fitting.
    const Array<bool> *surf_fit_marker;      // Not owned. Nodes to fit.
@@ -2110,9 +2112,20 @@ protected:
    //     Updated by every call to PANonlinearFormExtension::GetGradient().
    // MC: Q-Vector for the metric Coefficient.
    //     Updated when the mesh nodes change.
+   // ALC:  Q-Vector for spatial weight used for the adaptive limiting term.
+   //       Updated when the mesh nodes change.
+   // ALF: E-Vector constructed using adaptive limiting GF zeta.
+   //      The zeta is remapped when the mesh nodes change.
+   // ALFmF0: E-Vector constructed using adaptive limiting GF zeta.
+   //         It stores difference zeta-zeta0, as all computations use this.
+   // ALFG: Q-Vector for gradient of ALF at quadrature points.
+   //       Updated by every call to PANonlinearFormExtension::GetGradient().
+   // ALFH: Q-Vector for Hessian of ALF at quadrature points.
+   //       Updated by every call to PANonlinearFormExtension::GetGradient().
    //
-   // maps:     Dof2Quad map for fes associated with the nodal coordinates.
-   // maps_lim: Dof2Quad map for fes associated with the limiting dist GridFunc.
+   // maps:       Dof2Quad map for fes associated with the nodal coordinates.
+   // maps_lim:   Dof2Quad map for fes associated with the limiting dist GF.
+   // maps_nodes: like maps, but the quad points are the FE nodes.
    //
    // Jtr_debug_grad
    //     We keep track if Jtr was set by AssembleGradPA() in Jtr_debug_grad: it
@@ -2131,9 +2144,13 @@ protected:
       mutable DenseTensor Jtr;
       mutable bool Jtr_needs_update;
       mutable bool Jtr_debug_grad;
-      mutable Vector E, O, X0, XL, H, C0, LD, H0, MC;
+      mutable Vector E, O, X0, XL, H, C0, LD, H0, MC, ALC,
+              ALF, ALFmF0, ALFG, ALFH;
+      mutable bool AL_grads_assembled;
+      real_t al_delta;
       const DofToQuad *maps;
       const DofToQuad *maps_lim = nullptr;
+      const DofToQuad *maps_nodes = nullptr;
       const GeometricFactors *geom;
       const FiniteElementSpace *fes;
       const IntegrationRule *ir;
@@ -2216,16 +2233,25 @@ protected:
       return EnergyIntegrationRule(el);
    }
 
+   //
    // Auxiliary PA methods
+   //
+
+   // PA quadrature data computation - metric term / limiting / adapt limiting.
    void AssembleGradPA_2D(const Vector&) const;
    void AssembleGradPA_3D(const Vector&) const;
    void AssembleGradPA_C0_2D(const Vector&) const;
    void AssembleGradPA_C0_3D(const Vector&) const;
+   void AssembleGradPA_AdaptLim_2D(const Vector&) const;
+   void AssembleGradPA_AdaptLim_3D(const Vector&) const;
 
+   // PA energy computation - metric term / limiting / adaptive limiting.
    void GetLocalStateEnergyPA_2D(const Vector &x, real_t &energy) const;
-   void GetLocalStateEnergyPA_3D(const Vector&, real_t &energy) const;
+   void GetLocalStateEnergyPA_3D(const Vector &x, real_t &energy) const;
    real_t GetLocalStateEnergyPA_C0_2D(const Vector&) const;
    real_t GetLocalStateEnergyPA_C0_3D(const Vector&) const;
+   real_t GetLocalStateEnergyPA_AdaptLim_2D() const;
+   real_t GetLocalStateEnergyPA_AdaptLim_3D() const;
    void GetLocalNormalizationEnergiesPA_2D(const Vector &x,
                                            real_t &met_energy,
                                            real_t &lim_energy) const;
@@ -2233,22 +2259,35 @@ protected:
                                            real_t &met_energy,
                                            real_t &lim_energy) const;
 
+   // PA gradient computation - metric term / limiting / adaptive limiting.
    void AddMultPA_2D(const Vector&, Vector&) const;
    void AddMultPA_3D(const Vector&, Vector&) const;
    void AddMultPA_C0_2D(const Vector&, Vector&) const;
    void AddMultPA_C0_3D(const Vector&, Vector&) const;
+   void AddMultPA_AdaptLim_2D(const Vector&, Vector&) const;
+   void AddMultPA_AdaptLim_3D(const Vector&, Vector&) const;
 
+   // PA Hessian AddMult - metric term / limiting / adaptive limiting.
    void AddMultGradPA_2D(const Vector&, Vector&) const;
    void AddMultGradPA_3D(const Vector&, Vector&) const;
    void AddMultGradPA_C0_2D(const Vector&, Vector&) const;
    void AddMultGradPA_C0_3D(const Vector&, Vector&) const;
+   void AddMultGradPA_AdaptLim_2D(const Vector&, Vector&) const;
+   void AddMultGradPA_AdaptLim_3D(const Vector&, Vector&) const;
 
+   // PA diagonal assemblies - metric term / limiting / adaptive limiting.
    void AssembleDiagonalPA_2D(Vector&) const;
    void AssembleDiagonalPA_3D(Vector&) const;
    void AssembleDiagonalPA_C0_2D(Vector&) const;
    void AssembleDiagonalPA_C0_3D(Vector&) const;
+   void AssembleDiagonalPA_AdaptLim_2D(Vector&) const;
+   void AssembleDiagonalPA_AdaptLim_3D(Vector&) const;
 
+   // Setup of PA data structures related to the limiting term.
    void AssemblePA_Limiting();
+   // Setup of PA data structures related to the adaptive limiting term.
+   void AssemblePA_AdaptLim();
+   // Compute reference->target Jacobians for all quad points.
    void ComputeAllElementTargets(const Vector &xe = Vector()) const;
    // Updates the Q-vectors for the metric_coeff and lim_coeff, based on the
    // new physical positions of the quadrature points.
@@ -2351,21 +2390,23 @@ public:
 
    /** @brief Restriction of the node positions to certain regions.
 
-       Adds the term $ \int c (z(x) - z_0(x_0))^2 $, where z0(x0) is a given
-       function on the starting mesh, and z(x) is its image on the new mesh.
-       Minimizing this term means that a node at x0 is allowed to move to a
-       position x(x0) only if z(x) ~ z0(x0).
+       Adds the term $ \int c (z(x) - z_0(x_0))^2 / delta_max^2 $, where z0(x0)
+       is a given function on the starting mesh, and z(x) is its image on the
+       new mesh. Minimizing this term means that a node at x0 is allowed to
+       move to a position x(x0) only if z(x) ~ z0(x0).
        Such term can be used for tangential mesh relaxation.
 
        @param[in] z0     Function z0 that controls the adaptive limiting.
        @param[in] coeff  Coefficient c for the above integral.
-       @param[in] ae     AdaptivityEvaluator to compute z(x) from z0(x0). */
+       @param[in] ae     AdaptivityEvaluator to compute z(x) from z0(x0).
+       @param[in] delta_max Controls the allowable deviation from z0.
+                            Smaller values activate the term faster. */
    void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff,
-                               AdaptivityEvaluator &ae);
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
 #ifdef MFEM_USE_MPI
    /// Parallel support for adaptive limiting.
    void EnableAdaptiveLimiting(const ParGridFunction &z0, Coefficient &coeff,
-                               AdaptivityEvaluator &ae);
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
 #endif
 
    /** @brief Fitting of certain DOFs to the zero level set of a function.
@@ -2588,6 +2629,16 @@ public:
    void EnableLimiting(const GridFunction &n0, Coefficient &w0,
                        TMOP_LimiterFunction *lfunc = NULL);
 
+   /// Adds the adaptive limiting term to the first integrator.
+   void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff,
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
+#ifdef MFEM_USE_MPI
+   /// Parallel support for adaptive limiting.
+   void EnableAdaptiveLimiting(const ParGridFunction &z0, Coefficient &coeff,
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
+#endif
+
+
    /// Update the original/reference nodes used for limiting.
    void SetLimitingNodes(const GridFunction &n0);
 

fem/tmop/assemble/diag2_limit.cpp

@@ -11,7 +11,9 @@
 
 #include "../pa.hpp"
 #include "../../tmop.hpp"
+#include "../../kernels.hpp"
 #include "../../../general/forall.hpp"
+#include "../../../linalg/kernels.hpp"
 
 namespace mfem
 {
@@ -64,6 +66,93 @@ void TMOP_AssembleDiagPA_C0_2D(const int NE,
    });
 }
 
+// Diagonal assembly for AdaptLim limiting (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleDiagPA_AdaptLim_2D(const real_t lim_normal,
+                                     const real_t adapt_lim_delta_max,
+                                     const bool const_coeff,
+                                     const DeviceTensor<3, const real_t> &ALC,
+                                     const int NE,
+                                     const DeviceTensor<5, const real_t> &J,
+                                     const ConstDeviceMatrix &W,
+                                     const real_t *b,
+                                     const DeviceTensor<4, const real_t> &ALF_grad,
+                                     const DeviceTensor<5, const real_t> &ALF_hess,
+                                     const ConstDeviceCube &ALFmF0,
+                                     DeviceTensor<4> &D,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      MFEM_SHARED real_t qd[MQ1 * MD1];
+      DeviceTensor<2, real_t> QD(qd, MQ1, MD1);
+
+      for (int v = 0; v < 2; v++)
+      {
+         // Contract in y.
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               QD(qx, dy) = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  const real_t By = sB[dy][qy];
+                  const real_t bb = By * By;
+
+                  const real_t *Jtr = &J(0, 0, qx, qy, e);
+                  const real_t detJtr = kernels::Det<2>(Jtr);
+                  const real_t weight = W(qx, qy) * detJtr;
+                  const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+                  const real_t factor = weight * coeff * normal_inv_delta_sq;
+
+                  const real_t diff = alf_quad(qy, qx);
+                  const real_t grad_v = ALF_grad(v, qx, qy, e);
+                  const real_t hess_vv = ALF_hess(v, v, qx, qy, e);
+                  const real_t hdiag = factor * (grad_v * grad_v + diff * hess_vv);
+
+                  QD(qx, dy) += bb * hdiag;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Contract in x.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               real_t d = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  const real_t Bx = sB[dx][qx];
+                  const real_t bb = Bx * Bx;
+                  d += bb * QD(qx, dy);
+               }
+               D(dx, dy, v, e) += d;
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagCoef2D, TMOP_AssembleDiagPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagCoef2D);
 
@@ -80,4 +169,34 @@ void TMOP_Integrator::AssembleDiagonalPA_C0_2D(Vector &diagonal) const
    TMOPAssembleDiagCoef2D::Run(d, q, NE, B, H0, D, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagAdaptLim2D,
+                       TMOP_AssembleDiagPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagAdaptLim2D);
+
+void TMOP_Integrator::AssembleDiagonalPA_AdaptLim_2D(Vector &diagonal) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto *B = PA.maps->B.Read();
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 2, 2, q, q, NE);
+   auto D = Reshape(diagonal.ReadWrite(), d, d, 2, NE);
+
+   TMOPAssembleDiagAdaptLim2D::Run(d, q, ln, delta_max, const_coeff, ALC, NE,
+                                   J, W, B, ALF_grad, ALF_hess, ALFmF0, D, d, q);
+}
+
 } // namespace mfem

fem/tmop/assemble/diag3_limit.cpp

@@ -13,6 +13,7 @@
 #include "../../tmop.hpp"
 #include "../../kernels.hpp"
 #include "../../../general/forall.hpp"
+#include "../../../linalg/kernels.hpp"
 
 namespace mfem
 {
@@ -128,4 +129,162 @@ void TMOP_Integrator::AssembleDiagonalPA_C0_3D(Vector &diagonal) const
    TMOPAssembleDiagCoef3D::Run(d, q, NE, B, H0, D, d, q);
 }
 
+// Diagonal assembly for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleDiagPA_AdaptLim_3D(const real_t lim_normal,
+                                     const real_t adapt_lim_delta_max,
+                                     const bool const_coeff,
+                                     const DeviceTensor<4, const real_t> &ALC,
+                                     const int NE,
+                                     const DeviceTensor<6, const real_t> &J,
+                                     const ConstDeviceCube &W,
+                                     const real_t *b,
+                                     const DeviceTensor<5, const real_t> &ALF_grad,
+                                     const DeviceTensor<6, const real_t> &ALF_hess,
+                                     const DeviceTensor<4, const real_t> &ALFmF0,
+                                     DeviceTensor<5> &D,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      kernels::internal::s_regs3d_t<MQ1> r0, r1;
+
+      for (int v = 0; v < 3; ++v)
+      {
+         // Contract in z.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     const real_t Bz = sB[dz][qz];
+                     const real_t bb = Bz * Bz;
+
+                     const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+                     const real_t detJtr = kernels::Det<3>(Jtr);
+                     const real_t weight = W(qx, qy, qz) * detJtr;
+                     const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+                     const real_t factor = weight * coeff * normal_inv_delta_sq;
+
+                     const real_t diff = alf_quad(qz, qy, qx);
+                     const real_t grad_v = ALF_grad(v, qx, qy, qz, e);
+                     const real_t hess_vv = ALF_hess(v, v, qx, qy, qz, e);
+                     const real_t hdiag = factor * (grad_v * grad_v + diff * hess_vv);
+
+                     u += bb * hdiag;
+                  }
+                  r0[dz][qy][qx] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Contract in y.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  smem[qy][qx] = r0[dz][qy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     const real_t By = sB[dy][qy];
+                     u += (By * By) * smem[qy][qx];
+                  }
+                  r1[dz][dy][qx] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Contract in x.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  smem[dy][qx] = r1[dz][dy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     const real_t Bx = sB[dx][qx];
+                     u += (Bx * Bx) * smem[dy][qx];
+                  }
+                  D(dx, dy, dz, v, e) += u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagAdaptLim3D,
+                       TMOP_AssembleDiagPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagAdaptLim3D);
+
+void TMOP_Integrator::AssembleDiagonalPA_AdaptLim_3D(Vector &diagonal) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto *B = PA.maps->B.Read();
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 3, 3, q, q, q, NE);
+   auto D = Reshape(diagonal.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPAssembleDiagAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE,
+                                   J, W, B, ALF_grad, ALF_hess, ALFmF0, D, d, q);
+}
+
 } // namespace mfem

fem/tmop/assemble/grad2_limit.cpp

@@ -113,6 +113,178 @@ void TMOP_AssembleGradPA_C0_2D(const real_t lim_normal,
    });
 }
 
+// Assemble gradient and Hessian of ALF field at quadrature points for AdaptLim (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleGradPA_AdaptLim_2D(const int NE,
+                                     const real_t *B_nodes,
+                                     const real_t *G_nodes,
+                                     const real_t *B,
+                                     const DeviceTensor<4, const real_t> &X,
+                                     const ConstDeviceCube &ALF,
+                                     DeviceTensor<4> &ALF_grad,
+                                     DeviceTensor<5> &ALF_hess,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      // MD1 x MD1 or MQ1 x MQ1 shared memory block.
+      MFEM_SHARED union { real_t d[MD1][MD1]; real_t q[MQ1][MQ1]; } smem;
+      MFEM_SHARED real_t sB_nodes[MD1][MD1], sG_nodes[MD1][MD1];
+      MFEM_SHARED real_t sB_q[MD1][MQ1];
+
+      kernels::internal::s_regs2d_t<MD1> grad_c;
+      kernels::internal::v_regs2d_t<2, MD1> hess_c;
+
+      // Maps nodes - nodes.
+      kernels::internal::LoadMatrix(D1D, D1D, B_nodes, sB_nodes);
+      kernels::internal::LoadMatrix(D1D, D1D, G_nodes, sG_nodes);
+      // Map nodes - quads.
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB_q);
+
+      // Compute the physical Jacobian at DOF nodes.
+      kernels::internal::vd_regs2d_t<2, 2, MD1> r_X, r_J;
+      kernels::internal::LoadDofs2d(e, D1D, X, r_X);
+      kernels::internal::Grad2d(D1D, D1D, smem.d, sB_nodes, sG_nodes, r_X, r_J);
+
+      // Compute the reference derivatives of ALF at DOF nodes.
+      kernels::internal::s_regs2d_t<MD1> alf_n, dalf_dx_n, dalf_dy_n;
+      kernels::internal::LoadDofs2d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                sG_nodes, sB_nodes,
+                                                alf_n, dalf_dx_n);
+      kernels::internal::LoadDofs2d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sG_nodes,
+                                                alf_n, dalf_dy_n);
+
+      // Interpolation workspaces.
+      kernels::internal::s_regs2d_t<MQ1> r0, r1;
+
+      // Precompute the inverse of the physical Jacobian.
+      kernels::internal::vd_regs2d_t<2, 2, MD1> Jpr_inv;
+      MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+         {
+            const real_t Jpr[4] =
+            {
+               r_J[0][0][dy][dx], r_J[1][0][dy][dx],
+               r_J[0][1][dy][dx], r_J[1][1][dy][dx]
+            };
+            real_t Jpri[4];
+            kernels::CalcInverse<2>(Jpr, Jpri);
+            Jpr_inv(0, 0, dx, dy) = Jpri[0];
+            Jpr_inv(1, 0, dx, dy) = Jpri[1];
+            Jpr_inv(0, 1, dx, dy) = Jpri[2];
+            Jpr_inv(1, 1, dx, dy) = Jpri[3];
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      // Compute/interpolate gradient and Hessian one vector component at a time.
+      for (int c = 0; c < 2; c++)
+      {
+         kernels::internal::s_regs2d_t<MD1> rgrad_nodes, ddalf_dx_n, ddalf_dy_n;
+
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               grad_c[dy][dx] =
+                  Jpr_inv(0, c, dx, dy) * dalf_dx_n[dy][dx] +
+                  Jpr_inv(1, c, dx, dy) * dalf_dy_n[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute ALF_grad with intermediate workspaces
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               r0[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Eval2d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               ALF_grad(c, qx, qy, e) = r1[qy][qx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute ddalf_dx_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               rgrad_nodes[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                   sG_nodes, sB_nodes,
+                                                   rgrad_nodes, ddalf_dx_n);
+         // Compute ddalf_dy_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               rgrad_nodes[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sG_nodes,
+                                                   rgrad_nodes, ddalf_dy_n);
+         // Compute hess_c with ddalf_[dx, dy]_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               const real_t ddalf_dx = ddalf_dx_n[dy][dx];
+               const real_t ddalf_dy = ddalf_dy_n[dy][dx];
+               const real_t ddx = Jpr_inv(0, 0, dy, dx) * ddalf_dx +
+                                  Jpr_inv(1, 0, dy, dx) * ddalf_dy;
+               const real_t ddy = Jpr_inv(0, 1, dy, dx) * ddalf_dx +
+                                  Jpr_inv(1, 1, dy, dx) * ddalf_dy;
+               hess_c[0][dy][dx] = ddx;
+               hess_c[1][dy][dx] = ddy;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         for (int j = 0; j < 2; j++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  r0[dy][dx] = hess_c[j][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+            kernels::internal::Eval2d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  ALF_hess(c, j, qx, qy, e) = r1[qy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradCoef2D, TMOP_AssembleGradPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradCoef2D);
 
@@ -142,4 +314,29 @@ void TMOP_Integrator::AssembleGradPA_C0_2D(const Vector &x) const
                                J, W, b, bld, XL, X, H0, exp_lim, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradAdaptLim2D,
+                       TMOP_AssembleGradPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradAdaptLim2D);
+
+void TMOP_Integrator::AssembleGradPA_AdaptLim_2D(const Vector &x) const
+{
+   if (PA.AL_grads_assembled) { return; }
+
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto *B_nodes = PA.maps_nodes->B.Read(),
+               *G_nodes = PA.maps_nodes->G.Read();
+   const auto *B = PA.maps->B.Read();
+   const auto X = Reshape(x.Read(), d, d, 2, NE);
+   const auto ALF = Reshape(PA.ALF.Read(), d, d, NE);
+   auto ALF_grad = Reshape(PA.ALFG.Write(), 2, q, q, NE);
+   auto ALF_hess = Reshape(PA.ALFH.Write(), 2, 2, q, q, NE);
+
+   TMOPAssembleGradAdaptLim2D::Run(d, q, NE, B_nodes, G_nodes, B, X, ALF,
+                                   ALF_grad, ALF_hess, d, q);
+   PA.AL_grads_assembled = true;
+}
+
 } // namespace mfem

fem/tmop/assemble/grad3_limit.cpp

@@ -164,4 +164,252 @@ void TMOP_Integrator::AssembleGradPA_C0_3D(const Vector &x) const
                                J, W, b, bld, XL, X, H0, exp_lim, d, q);
 }
 
+// Assemble gradient and Hessian of ALF field at quadrature points for AdaptLim (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleGradPA_AdaptLim_3D(const int NE,
+                                     const real_t *B_nodes,
+                                     const real_t *G_nodes,
+                                     const real_t *B,
+                                     const DeviceTensor<5, const real_t> &X,
+                                     const DeviceTensor<4, const real_t> &ALF,
+                                     DeviceTensor<5> &ALF_grad,
+                                     DeviceTensor<6> &ALF_hess,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      // MD1 x MD1 or MQ1 x MQ1 shared memory block.
+      MFEM_SHARED union { real_t d[MD1][MD1]; real_t q[MQ1][MQ1]; } smem;
+      MFEM_SHARED real_t sB_nodes[MD1][MD1], sG_nodes[MD1][MD1];
+      MFEM_SHARED real_t sB_q[MD1][MQ1];
+
+      kernels::internal::s_regs3d_t<MD1> grad_c;
+      kernels::internal::v_regs3d_t<3, MD1> hess_c;
+
+      // Maps nodes - nodes.
+      kernels::internal::LoadMatrix(D1D, D1D, B_nodes, sB_nodes);
+      kernels::internal::LoadMatrix(D1D, D1D, G_nodes, sG_nodes);
+      // Map nodes - quads.
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB_q);
+
+      // Compute the physical Jacobian at DOF nodes.
+      kernels::internal::vd_regs3d_t<3, 3, MD1> r_X, r_J;
+      kernels::internal::LoadDofs3d(e, D1D, X, r_X);
+      kernels::internal::Grad3d(D1D, D1D, smem.d, sB_nodes, sG_nodes, r_X, r_J);
+
+      // Compute the reference derivatives of ALF at DOF nodes.
+      kernels::internal::s_regs3d_t<MD1> alf_n, dalf_dxi_n, dalf_deta_n, dalf_dzeta_n;
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sG_nodes, sB_nodes, sB_nodes,
+                                                alf_n, dalf_dxi_n);
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sG_nodes, sB_nodes,
+                                                alf_n, dalf_deta_n);
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sB_nodes, sG_nodes,
+                                                alf_n, dalf_dzeta_n);
+
+      // Interpolation workspaces.
+      kernels::internal::s_regs3d_t<MQ1> r0, r1;
+
+      // Compute/interpolate gradient and Hessian one vector component at a time.
+      for (int c = 0; c < 3; c++)
+      {
+         kernels::internal::s_regs3d_t<MD1> rgrad_nodes, dd_dxi_n, dd_deta_n, dd_dzeta_n;
+
+         // Precompute the inverse of the physical Jacobian.
+         kernels::internal::vd_regs3d_t<3, 3, MD1> Jpr_inv;
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  const real_t Jpr[9] =
+                  {
+                     r_J[0][0][dz][dy][dx], r_J[1][0][dz][dy][dx], r_J[2][0][dz][dy][dx],
+                     r_J[0][1][dz][dy][dx], r_J[1][1][dz][dy][dx], r_J[2][1][dz][dy][dx],
+                     r_J[0][2][dz][dy][dx], r_J[1][2][dz][dy][dx], r_J[2][2][dz][dy][dx]
+                  };
+                  real_t Jpri[9];
+                  kernels::CalcInverse<3>(Jpr, Jpri);
+                  Jpr_inv(0, 0, dx, dy, dz) = Jpri[0];
+                  Jpr_inv(1, 0, dx, dy, dz) = Jpri[1];
+                  Jpr_inv(2, 0, dx, dy, dz) = Jpri[2];
+                  Jpr_inv(0, 1, dx, dy, dz) = Jpri[3];
+                  Jpr_inv(1, 1, dx, dy, dz) = Jpri[4];
+                  Jpr_inv(2, 1, dx, dy, dz) = Jpri[5];
+                  Jpr_inv(0, 2, dx, dy, dz) = Jpri[6];
+                  Jpr_inv(1, 2, dx, dy, dz) = Jpri[7];
+                  Jpr_inv(2, 2, dx, dy, dz) = Jpri[8];
+
+                  grad_c[dz][dy][dx] =
+                     Jpr_inv(0, c, dx, dy, dz) * dalf_dxi_n[dz][dy][dx] +
+                     Jpr_inv(1, c, dx, dy, dz) * dalf_deta_n[dz][dy][dx] +
+                     Jpr_inv(2, c, dx, dy, dz) * dalf_dzeta_n[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Compute ALF_grad with intermediate workspaces.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  r0[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Eval3d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  ALF_grad(c, qx, qy, qz, e) = r1[qz][qy][qx];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute dd_dxi_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sG_nodes, sB_nodes, sB_nodes,
+                                                   rgrad_nodes, dd_dxi_n);
+         // Compute dd_deta_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sG_nodes, sB_nodes,
+                                                   rgrad_nodes, dd_deta_n);
+         // Compute dd_dzeta_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sB_nodes, sG_nodes,
+                                                   rgrad_nodes, dd_dzeta_n);
+
+         // Compute hess_c with dd_[dxi, deta, dzeta]_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  const real_t dd_dxi   = dd_dxi_n[dz][dy][dx];
+                  const real_t dd_deta  = dd_deta_n[dz][dy][dx];
+                  const real_t dd_dzeta = dd_dzeta_n[dz][dy][dx];
+                  const real_t ddx = Jpr_inv(0, 0, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 0, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 0, dx, dy, dz) * dd_dzeta;
+                  const real_t ddy = Jpr_inv(0, 1, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 1, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 1, dx, dy, dz) * dd_dzeta;
+                  const real_t ddz = Jpr_inv(0, 2, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 2, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 2, dx, dy, dz) * dd_dzeta;
+                  hess_c[0][dz][dy][dx] = ddx;
+                  hess_c[1][dz][dy][dx] = ddy;
+                  hess_c[2][dz][dy][dx] = ddz;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         for (int j = 0; j < 3; j++)
+         {
+            for (int dz = 0; dz < D1D; dz++)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+               {
+                  MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+                  {
+                     r0[dz][dy][dx] = hess_c[j][dz][dy][dx];
+                  }
+               }
+               MFEM_SYNC_THREAD;
+            }
+            kernels::internal::Eval3d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+               {
+                  MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+                  {
+                     ALF_hess(c, j, qx, qy, qz, e) = r1[qz][qy][qx];
+                  }
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradAdaptLim3D,
+                       TMOP_AssembleGradPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradAdaptLim3D);
+
+void TMOP_Integrator::AssembleGradPA_AdaptLim_3D(const Vector &x) const
+{
+   if (PA.AL_grads_assembled) { return; }
+
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto *B_nodes = PA.maps_nodes->B.Read(),
+               *G_nodes = PA.maps_nodes->G.Read();
+   const auto *B = PA.maps->B.Read();
+   const auto X = Reshape(x.Read(), d, d, d, 3, NE);
+   const auto ALF = Reshape(PA.ALF.Read(), d, d, d, NE);
+   auto ALF_grad = Reshape(PA.ALFG.Write(), 3, q, q, q, NE);
+   auto ALF_hess = Reshape(PA.ALFH.Write(), 3, 3, q, q, q, NE);
+
+   TMOPAssembleGradAdaptLim3D::Run(d, q, NE, B_nodes, G_nodes, B, X, ALF,
+                                   ALF_grad, ALF_hess, d, q);
+   PA.AL_grads_assembled = true;
+}
+
 } // namespace mfem

fem/tmop/mult/grad2_limit.cpp

@@ -67,6 +67,96 @@ void TMOP_AddMultGradPA_C0_2D(const int NE,
    });
 }
 
+// Gradient action for AdaptLim limiting (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultGradPA_AdaptLim_2D(const real_t lim_normal,
+                                    const real_t adapt_lim_delta_max,
+                                    const bool const_coeff,
+                                    const DeviceTensor<3, const real_t> &ALC,
+                                    const int NE,
+                                    const DeviceTensor<5, const real_t> &J,
+                                    const ConstDeviceMatrix &W,
+                                    const real_t *b,
+                                    const DeviceTensor<4, const real_t> &R,
+                                    const DeviceTensor<4, const real_t> &ALF_grad,
+                                    const DeviceTensor<5, const real_t> &ALF_hess,
+                                    const ConstDeviceCube &ALFmF0,
+                                    DeviceTensor<4> &Y,
+                                    const int d1d,
+                                    const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      // Input vector R at quad points.
+      kernels::internal::v_regs2d_t<2,MQ1> r_R_dof, r_R_quad;
+      kernels::internal::LoadDofs2d(e, D1D, R, r_R_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, r_R_dof, r_R_quad);
+
+      kernels::internal::v_regs2d_t<2,MQ1> r00, r01;
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const real_t *Jtr = &J(0, 0, qx, qy, e);
+            const real_t detJtr = kernels::Det<2>(Jtr);
+            const real_t weight = W(qx, qy) * detJtr;
+            const real_t diff = alf_quad(qy, qx);
+
+            // Load precomputed gradient at this quad point.
+            real_t grad_alf[2] =
+            {
+               ALF_grad(0, qx, qy, e),
+               ALF_grad(1, qx, qy, e)
+            };
+
+            // Load precomputed Hessian at this quad point.
+            real_t hess_alf[2][2];
+            for (int i = 0; i < 2; i++)
+            {
+               for (int j = 0; j < 2; j++)
+               {
+                  hess_alf[i][j] = ALF_hess(i, j, qx, qy, e);
+               }
+            }
+
+            // Get input vector at this quad point.
+            const real_t R_q[2] = { r_R_quad(0, qy, qx), r_R_quad(1, qy, qx) };
+
+            // Hessian action:
+            // H = factor * (grad x grad + (gf - gf0) * hess)
+            const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+            const real_t factor = weight * coeff * normal_inv_delta_sq;
+            const real_t grad_dot_R = grad_alf[0] * R_q[0] + grad_alf[1] * R_q[1];
+            real_t hess_R[2];
+            hess_R[0] = hess_alf[0][0] * R_q[0] + hess_alf[0][1] * R_q[1];
+            hess_R[1] = hess_alf[1][0] * R_q[0] + hess_alf[1][1] * R_q[1];
+
+            r00(0, qy, qx) = factor * (grad_alf[0] * grad_dot_R + diff * hess_R[0]);
+            r00(1, qy, qx) = factor * (grad_alf[1] * grad_dot_R + diff * hess_R[1]);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs2d(e, D1D, r01, Y);
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPMultGradCoefKernels, TMOP_AddMultGradPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradCoefKernels);
 
@@ -85,4 +175,34 @@ void TMOP_Integrator::AddMultGradPA_C0_2D(const Vector &R, Vector &C) const
    TMOPMultGradCoefKernels::Run(d, q, NE, b, H0, X, Y, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPMultGradAdaptLim, TMOP_AddMultGradPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradAdaptLim);
+
+void TMOP_Integrator::AddMultGradPA_AdaptLim_2D(const Vector &R,
+                                                Vector &C) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto RR = Reshape(R.Read(), d, d, 2, NE);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 2, 2, q, q, NE);
+   auto Y = Reshape(C.ReadWrite(), d, d, 2, NE);
+
+   TMOPMultGradAdaptLim::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, B,
+                             RR, ALF_grad, ALF_hess, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/grad3_limit.cpp

@@ -98,4 +98,135 @@ void TMOP_Integrator::AddMultGradPA_C0_3D(const Vector &R, Vector &C) const
    TMOPMultGradCoefKernels3D::Run(d, q, NE, b, H0, X, Y, d, q);
 }
 
+// Gradient action for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultGradPA_AdaptLim_3D(const real_t lim_normal,
+                                    const real_t adapt_lim_delta_max,
+                                    const bool const_coeff,
+                                    const DeviceTensor<4, const real_t> &ALC,
+                                    const int NE,
+                                    const DeviceTensor<6, const real_t> &J,
+                                    const ConstDeviceCube &W,
+                                    const real_t *b,
+                                    const DeviceTensor<5, const real_t> &R,
+                                    const DeviceTensor<5, const real_t> &ALF_grad,
+                                    const DeviceTensor<6, const real_t> &ALF_hess,
+                                    const DeviceTensor<4, const real_t> &ALFmF0,
+                                    DeviceTensor<5> &Y,
+                                    const int d1d,
+                                    const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      // Input vector R at quad points.
+      kernels::internal::v_regs3d_t<3, MQ1> r_R_dof, r_R_quad;
+      kernels::internal::LoadDofs3d(e, D1D, R, r_R_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, r_R_dof, r_R_quad);
+
+      kernels::internal::v_regs3d_t<3, MQ1> r00, r01;
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+               const real_t detJtr = kernels::Det<3>(Jtr);
+               const real_t weight = W(qx, qy, qz) * detJtr;
+               const real_t diff = alf_quad(qz, qy, qx);
+
+               // Load precomputed gradient at this quad point.
+               const real_t grad_alf[3] =
+               {
+                  ALF_grad(0, qx, qy, qz, e),
+                  ALF_grad(1, qx, qy, qz, e),
+                  ALF_grad(2, qx, qy, qz, e)
+               };
+
+               // Get input vector at this quad point.
+               const real_t R_q[3] =
+               {
+                  r_R_quad(0, qz, qy, qx),
+                  r_R_quad(1, qz, qy, qx),
+                  r_R_quad(2, qz, qy, qx)
+               };
+
+               // Hessian action:
+               // H = factor * (grad x grad + (gf - gf0) * hess)
+               const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+               const real_t factor = weight * coeff * normal_inv_delta_sq;
+               const real_t grad_dot_R =
+                  grad_alf[0] * R_q[0] + grad_alf[1] * R_q[1] + grad_alf[2] * R_q[2];
+               real_t hess_R[3];
+               hess_R[0] =
+                  ALF_hess(0, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(0, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(0, 2, qx, qy, qz, e) * R_q[2];
+               hess_R[1] =
+                  ALF_hess(1, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(1, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(1, 2, qx, qy, qz, e) * R_q[2];
+               hess_R[2] =
+                  ALF_hess(2, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(2, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(2, 2, qx, qy, qz, e) * R_q[2];
+
+               r00(0, qz, qy, qx) = factor * (grad_alf[0] * grad_dot_R + diff * hess_R[0]);
+               r00(1, qz, qy, qx) = factor * (grad_alf[1] * grad_dot_R + diff * hess_R[1]);
+               r00(2, qz, qy, qx) = factor * (grad_alf[2] * grad_dot_R + diff * hess_R[2]);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs3d(e, D1D, r01, Y);
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPMultGradAdaptLim3D, TMOP_AddMultGradPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradAdaptLim3D);
+
+void TMOP_Integrator::AddMultGradPA_AdaptLim_3D(const Vector &R,
+                                                Vector &C) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto RR = Reshape(R.Read(), d, d, d, 3, NE);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 3, 3, q, q, q, NE);
+   auto Y = Reshape(C.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPMultGradAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, B,
+                               RR, ALF_grad, ALF_hess, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/mult2_limit.cpp

@@ -108,6 +108,64 @@ void TMOP_AddMultPA_C0_2D(const real_t lim_normal,
    });
 }
 
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultPA_AdaptLim_2D(const real_t lim_normal,
+                                const real_t adapt_lim_delta_max,
+                                const bool const_coeff,
+                                const DeviceTensor<3, const real_t> &ALC,
+                                const int NE,
+                                const DeviceTensor<5, const real_t> &J,
+                                const ConstDeviceMatrix &W,
+                                const real_t *b,
+                                const DeviceTensor<4, const real_t> &ALF_grad,
+                                const ConstDeviceCube &ALFmF0,
+                                DeviceTensor<4> &Y,
+                                const int d1d,
+                                const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Evaluate ALF and ALF0 at the quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB,
+                                alf_dof, alf_quad);
+
+      kernels::internal::v_regs2d_t<2,MQ1> r00, r01;
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const real_t *Jtr = &J(0, 0, qx, qy, e);
+            const real_t detJtr = kernels::Det<2>(Jtr);
+            const real_t weight = W(qx, qy) * detJtr;
+
+            const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+            const real_t factor = weight * coeff * normal_inv_delta_sq *
+                                  alf_quad(qy, qx);
+
+            r00(0, qy, qx) = factor * ALF_grad(0, qx, qy, e);
+            r00(1, qy, qx) = factor * ALF_grad(1, qx, qy, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs2d(e, D1D, r01, Y);
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPMultCoefKernels, TMOP_AddMultPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultCoefKernels);
 
@@ -140,4 +198,32 @@ void TMOP_Integrator::AddMultPA_C0_2D(const Vector &x, Vector &y) const
                             Y, exp_lim, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPMultAdaptLim, TMOP_AddMultPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultAdaptLim);
+
+void TMOP_Integrator::AddMultPA_AdaptLim_2D([[maybe_unused]] const Vector &x,
+                                            Vector &y) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   auto Y = Reshape(y.ReadWrite(), d, d, 2, NE);
+
+   TMOPMultAdaptLim::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W,
+                         B, ALF_grad, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/mult3_limit.cpp

@@ -148,4 +148,95 @@ void TMOP_Integrator::AddMultPA_C0_3D(const Vector &x, Vector &y) const
                               X, Y, exp_lim, d, q);
 }
 
+// Residual term for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultPA_AdaptLim_3D(const real_t lim_normal,
+                                const real_t adapt_lim_delta_max,
+                                const bool const_coeff,
+                                const DeviceTensor<4, const real_t> &ALC,
+                                const int NE,
+                                const DeviceTensor<6, const real_t> &J,
+                                const ConstDeviceCube &W,
+                                const real_t *b,
+                                const DeviceTensor<5, const real_t> &ALF_grad,
+                                const DeviceTensor<4, const real_t> &ALFmF0,
+                                DeviceTensor<5> &Y,
+                                const int d1d,
+                                const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Evaluate ALF and ALF0 at the quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      kernels::internal::v_regs3d_t<3, MQ1> r00, r01;
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+               const real_t detJtr = kernels::Det<3>(Jtr);
+               const real_t weight = W(qx, qy, qz) * detJtr;
+
+               const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+               const real_t factor = weight * coeff * normal_inv_delta_sq *
+                                     alf_quad(qz, qy, qx);
+
+               r00(0, qz, qy, qx) = factor * ALF_grad(0, qx, qy, qz, e);
+               r00(1, qz, qy, qx) = factor * ALF_grad(1, qx, qy, qz, e);
+               r00(2, qz, qy, qx) = factor * ALF_grad(2, qx, qy, qz, e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs3d(e, D1D, r01, Y);
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPMultAdaptLim3D, TMOP_AddMultPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultAdaptLim3D);
+
+void TMOP_Integrator::AddMultPA_AdaptLim_3D([[maybe_unused]] const Vector &x,
+                                            Vector &y) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   auto Y = Reshape(y.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPMultAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W,
+                           B, ALF_grad, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/pa.cpp

@@ -46,12 +46,14 @@ void TMOP_Integrator::AssembleGradPA(const Vector &de,
    {
       AssembleGradPA_2D(xe);
       if (lim_coeff) { AssembleGradPA_C0_2D(xe); }
+      if (adapt_lim_gf) { AssembleGradPA_AdaptLim_2D(xe); }
    }
 
    if (PA.dim == 3)
    {
       AssembleGradPA_3D(xe);
       if (lim_coeff) { AssembleGradPA_C0_3D(xe); }
+      if (adapt_lim_gf) { AssembleGradPA_AdaptLim_3D(xe); }
    }
 }
 
@@ -197,12 +199,14 @@ void TMOP_Integrator::UpdateCoefficientsPA(const Vector &d_loc)
       add(*x_0, d_loc, x_loc);
    }
 
-   // Both are constant or not specified.
-   if (PA.MC.Size() == 1 && PA.C0.Size() == 1) { return; }
+
+   // All are constant or not specified.
+   if (PA.MC.Size() == 1 && PA.C0.Size() <= 1 && PA.ALC.Size() <= 1) { return; }
 
    // Coefficients are always evaluated on the CPU for now.
    PA.MC.HostWrite();
    PA.C0.HostWrite();
+   PA.ALC.HostWrite();
 
    const IntegrationRule &ir = *PA.ir;
    auto T = new IsoparametricTransformation;
@@ -226,6 +230,14 @@ void TMOP_Integrator::UpdateCoefficientsPA(const Vector &d_loc)
             PA.C0(q + e * PA.nq) = lim_coeff->Eval(*T, ir.IntPoint(q));
          }
       }
+
+      if (PA.ALC.Size() > 1)
+      {
+         for (int q = 0; q < PA.nq; ++q)
+         {
+            PA.ALC(q + e * PA.nq) = adapt_lim_coeff->Eval(*T, ir.IntPoint(q));
+         }
+      }
    }
 
    delete T;
@@ -321,7 +333,93 @@ void TMOP_Integrator::AssemblePA(const FiniteElementSpace &fes)
    PA.Jtr_debug_grad = false;
 
    // Limiting: lim_coeff -> PA.C0, lim_nodes0 -> PA.XL, lim_dist -> PA.LD, PA.H0
-   if (lim_coeff) { AssemblePA_Limiting(); }
+   if (lim_coeff)    { AssemblePA_Limiting(); }
+   // Adaptive limiting: adapt_lim_coeff -> PA.ALC, adapt_lim_gf -> PA.ALF,
+   //                    adapt_lim_gf0 -> PA.ALF0, adapt_lim_delta_max -> PA.ALD
+   if (adapt_lim_gf) { AssemblePA_AdaptLim(); }
+}
+
+void TMOP_Integrator::AssemblePA_AdaptLim()
+{
+   const FiniteElementSpace *alfes = adapt_lim_gf->FESpace();
+
+   MFEM_VERIFY(strcmp(alfes->FEColl()->Name(), PA.fes->FEColl()->Name()) == 0 &&
+               alfes->FEColl()->GetOrder() == PA.fes->FEColl()->GetOrder(),
+               "The PA code assumes the same FE spaces for mesh and limiting.");
+
+   PA.AL_grads_assembled = false;
+
+   // adapt_lim_coeff -> PA.ALC (Q-vector).
+   PA.ALC.UseDevice(true);
+   if (auto *cQ = dynamic_cast<ConstantCoefficient *>(adapt_lim_coeff))
+   {
+      PA.ALC.SetSize(1, Device::GetMemoryType());
+      PA.ALC.HostWrite();
+      PA.ALC(0) = cQ->constant;
+   }
+   else
+   {
+      PA.ALC.SetSize(PA.nq * PA.ne, Device::GetMemoryType());
+      auto ALC = Reshape(PA.ALC.HostWrite(), PA.nq, PA.ne);
+      for (int e = 0; e < PA.ne; ++e)
+      {
+         ElementTransformation &T = *PA.fes->GetElementTransformation(e);
+         for (int q = 0; q < PA.ir->GetNPoints(); ++q)
+         {
+            ALC(q, e) = adapt_lim_coeff->Eval(T, PA.ir->IntPoint(q));
+         }
+      }
+   }
+
+   const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
+
+   const FiniteElement *fe_n = PA.fes->GetTypicalFE();
+   // GetNodes() for tensor H1 elements with H1_DOF_MAP is stored in NATIVE
+   // order (via dof_map), while DofToQuad::TENSOR assumes LEXICOGRAPHIC
+   // ordering of the integration points.
+   const IntegrationRule &nodes = fe_n->GetNodes();
+   const auto *nfe = dynamic_cast<const NodalFiniteElement *>(fe_n);
+   const Array<int> *lex = (nfe && nfe->GetLexicographicOrdering().Size() > 0)
+                           ? &nfe->GetLexicographicOrdering() : nullptr;
+   if (!lex)
+   {
+      PA.maps_nodes = &fe_n->GetDofToQuad(nodes, DofToQuad::TENSOR);
+   }
+   else
+   {
+      IntegrationRule lex_nodes(nodes.GetNPoints());
+      MFEM_VERIFY(lex->Size() == nodes.GetNPoints(), "");
+      for (int i = 0; i < nodes.GetNPoints(); i++)
+      {
+         lex_nodes.IntPoint(i) = nodes.IntPoint((*lex)[i]);
+      }
+      PA.maps_nodes = &fe_n->GetDofToQuad(lex_nodes, DofToQuad::TENSOR);
+   }
+
+   // adapt_lim_gf -> PA.ALF (E-vector, same pattern as LD).
+   const FiniteElement &fe = *alfes->GetTypicalFE();
+   PA.ALF.SetSize(PA.ne * fe.GetDof(), Device::GetMemoryType());
+   PA.ALF.UseDevice(true);
+   const Operator *alf_R = alfes->GetElementRestriction(ordering);
+   alf_R->Mult(*adapt_lim_gf, PA.ALF);
+   // adapt_lim_gf - adapt_lim_gf0 -> PA.ALFmF0
+   PA.ALFmF0.SetSize(PA.ne * fe.GetDof(), Device::GetMemoryType());
+   PA.ALFmF0.UseDevice(true);
+   alf_R->Mult(*adapt_lim_gf0, PA.ALFmF0);
+   PA.ALFmF0 *= -1.0;
+   PA.ALFmF0 += PA.ALF;
+
+   // adapt_lim_delta_max -> PA.al_delta.
+   PA.al_delta = adapt_lim_delta_max;
+
+   // Allocate storage for gradient and Hessian of ALF at quadrature points
+   // These will be filled during AssembleGradPA
+   const int dim = PA.dim;
+   PA.ALFG.UseDevice(true);
+   PA.ALFG.SetSize(dim * PA.nq * PA.ne, Device::GetMemoryType());
+   PA.ALFH.UseDevice(true);
+   PA.ALFH.SetSize(dim * dim * PA.nq * PA.ne, Device::GetMemoryType());
+
 }
 
 void TMOP_Integrator::AssembleGradDiagonalPA(Vector &de) const
@@ -341,12 +439,14 @@ void TMOP_Integrator::AssembleGradDiagonalPA(Vector &de) const
    {
       AssembleDiagonalPA_2D(de);
       if (lim_coeff) { AssembleDiagonalPA_C0_2D(de); }
+      if (adapt_lim_gf) { AssembleDiagonalPA_AdaptLim_2D(de); }
    }
 
    if (PA.dim == 3)
    {
       AssembleDiagonalPA_3D(de);
       if (lim_coeff) { AssembleDiagonalPA_C0_3D(de); }
+      if (adapt_lim_gf) { AssembleDiagonalPA_AdaptLim_3D(de); }
    }
 }
 
@@ -373,12 +473,26 @@ void TMOP_Integrator::AddMultPA(const Vector &de, Vector &ye) const
    {
       AddMultPA_2D(xe, ye);
       if (lim_coeff) { AddMultPA_C0_2D(xe, ye); }
+      if (adapt_lim_gf)
+      {
+         // AddMultPA_AdaptLim_2D uses the precomputed AdaptLim field gradient
+         // at quadrature points (PA.ALFG). Ensure it is up-to-date for the
+         // current mesh configuration.
+         AssembleGradPA_AdaptLim_2D(xe);
+         AddMultPA_AdaptLim_2D(xe, ye);
+      }
+
    }
 
    if (PA.dim == 3)
    {
       AddMultPA_3D(xe, ye);
       if (lim_coeff) { AddMultPA_C0_3D(xe, ye); }
+      if (adapt_lim_gf)
+      {
+         AssembleGradPA_AdaptLim_3D(xe);
+         AddMultPA_AdaptLim_3D(xe, ye);
+      }
    }
 }
 
@@ -399,12 +513,14 @@ void TMOP_Integrator::AddMultGradPA(const Vector &re, Vector &ce) const
    {
       AddMultGradPA_2D(re, ce);
       if (lim_coeff) { AddMultGradPA_C0_2D(re, ce); }
+      if (adapt_lim_gf) { AddMultGradPA_AdaptLim_2D(re, ce); }
    }
 
    if (PA.dim == 3)
    {
       AddMultGradPA_3D(re, ce);
       if (lim_coeff) { AddMultGradPA_C0_3D(re, ce); }
+      if (adapt_lim_gf) { AddMultGradPA_AdaptLim_3D(re, ce); }
    }
 }
 
@@ -433,12 +549,14 @@ real_t TMOP_Integrator::GetLocalStateEnergyPA(const Vector &de) const
    {
       GetLocalStateEnergyPA_2D(xe, energy);
       if (lim_coeff) { energy += GetLocalStateEnergyPA_C0_2D(xe); }
+      if (adapt_lim_gf) { energy += GetLocalStateEnergyPA_AdaptLim_2D(); }
    }
 
    if (PA.dim == 3)
    {
       GetLocalStateEnergyPA_3D(xe, energy);
       if (lim_coeff) { energy += GetLocalStateEnergyPA_C0_3D(xe); }
+      if (adapt_lim_gf) { energy += GetLocalStateEnergyPA_AdaptLim_3D(); }
    }
 
    return energy;