Update operator.hpp

ConstrainedOperator::AddMultTranspose()
Merge branch 'master' into vecmasspa
2026-07-01 12:08:07 -04:00 · 2026-07-01 11:38:30 -04:00 · 2026-06-10 17:02:05 -07:00 · 2026-06-09 17:55:16 -07:00 · 2026-06-09 12:53:57 -07:00 · 2026-06-09 12:14:02 -07:00
183 changed files with 17072 additions and 5050 deletions
@@ -25,7 +25,7 @@ runs:
  steps:
    - uses: ./.github/actions/sanitize/config

-    - uses: actions/cache@v4
+    - uses: actions/cache@v5
      if: ${{env.DEBUG == 'true'}}
      id: debug
      with:
@@ -53,7 +53,7 @@ runs:
      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
      shell: bash

-    - uses: mfem/github-actions/build-mfem@v2.5
+    - uses: mfem/github-actions/build-mfem@v2.6
      if: ${{steps.debug.outputs.cache-hit != 'true'}}
      env:
        CXXFLAGS: ${{env.CXXFLAGS}}
@@ -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
@@ -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
@@ -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}}
@@ -0,0 +1,42 @@
+# MFEM Pull Request Review Agent Guide
+
+## Purpose and scope
+Review MFEM PRs for correctness, maintainability, performance, portability, test coverage, and MFEM consistency. Use the diff and PR context; reference source files, tests, and CI results when available. Follow `CONTRIBUTING.md`, especially Developer Guidelines, PR rules, checklist, and testing.
+
+## Critical review pillars
+- Correctness and numerical behavior
+- API and user-facing impact
+- Performance implications
+- Maintainability and portability
+
+## Review workflow
+1. Read the PR description, linked issues, and intended behavior.
+2. Inspect the diff before commenting.
+3. Identify affected MFEM components, examples, tests, build or docs changes, and downstream APIs.
+4. Analyze the code against the critical review pillars.
+5. Compare the change against nearby code and MFEM patterns; flag unmotivated deviations.
+6. Check whether tests and documentation were updated appropriately.
+7. Review CI results and suggest actions.
+8. Produce a structured review with prioritized findings.
+9. Always limit conclusions to available evidence.
+
+## MFEM-specific review checklist
+- Component-aware scope: identify the touched subsystem (FEM, solvers, preconditioners, linear algebra, mesh, examples, miniapps, build, or docs) and assess its impact against the review pillars.
+- Numerical and algorithmic behavior: assess issues in convergence, stability, tolerances, precision, iteration limits, and failure handling. If clear opportunities exist to improve the algorithmic approach, call them out with expected impact.
+- API and user-facing impact: assess backward compatibility, user-visible behavior and default changes, migration impact, deprecations, and whether documentation clearly explains user-facing API changes.
+- Data structure and memory semantics: assess ownership, lifetime, aliasing, container behavior, and device-host synchronization.
+- Parallel and serial behavior: assess whether the change preserves equivalent semantics in serial and parallel modes where applicable; if logic is currently mode-specific, check whether extension to the other mode is straightforward (clear abstractions, no hard-wired assumptions), document constraints, and call out expected behavior differences explicitly.
+- Backend and portability impact: assess likely cross-backend risks in CPU, CUDA, HIP, OCCA, RAJA, partial assembly, fallback paths, compiler compatibility, and platform assumptions.
+- Build, dependency, and configuration impact: assess CMake or make changes, optional dependency behavior, and feature-flag interactions.
+- Tests and docs alignment: check available regression or unit coverage evidence for changed behavior, and ensure docs are updated for new flags, APIs, options, or behavior changes.
+- MFEM developer-guideline fit: keep code lean, simple, general, logically separated, and portable; suggest C++17 improvements when they clearly improve safety, clarity, or maintainability.
+- New source files, examples, or miniapps: if a PR adds source/header files, verify they are properly wired into the relevant `makefile` and `CMakeLists.txt`, referenced in docs where applicable (including `doc/CodeDocumentation.dox`), and added to top-level `.gitignore` only when generated artifacts require it.
+- Changelog: verify `CHANGELOG` is updated if the PR introduces significant new features or user-facing changes.
+- MFEM conventions: use `real_t`; use `mfem::out`/`mfem::err` instead of `std::cout`/`std::cerr` in library code; flag large/binary files; if AI assistance is apparent but undisclosed, suggest following `CONTRIBUTING.md`.
+- Edge cases: if the PR touches complex or error-prone areas, suggest additional tests for edge cases, failure modes, and parallel behavior.
+
+## Commenting guidelines
+- Keep comments concise, actionable, and grounded in the diff.
+- Focus on correctness, behavior changes, and user impact over style nits.
+- Be professional, concise, collaborative, technically precise, and avoid unsupported assumptions.
+
@@ -13,7 +13,7 @@ Note that some of these scripts use the shared MFEM GitHub Actions from the exte

  <https://github.com/mfem/github-actions>

-For a particular action, e.g. `mfem/github-actions/build-mfem@v2.5`, the `v2.5` suffix denotes the branch in the above from which the action is taken.
+For a particular action, e.g. `mfem/github-actions/build-mfem@v2.5`, the `v2.5` suffix denotes the branch (or tag) in the above from which the action is taken.

 The current CI workflows are:

@@ -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
@@ -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
@@ -225,14 +225,14 @@ 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

      - name: get hypre
        if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os != 'windows-latest'
-        uses: mfem/github-actions/build-hypre@v2.5
+        uses: mfem/github-actions/build-hypre@v2.6
        with:
          archive: ${{ env.HYPRE_ARCHIVE }}
          dir: ${{ env.HYPRE_TOP_DIR }}
@@ -242,7 +242,7 @@ jobs:

      - name: get hypre (Windows)
        if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os == 'windows-latest'
-        uses: mfem/github-actions/build-hypre@v2.5
+        uses: mfem/github-actions/build-hypre@v2.6
        with:
          archive: ${{ env.HYPRE_ARCHIVE }}
          dir: ${{ env.HYPRE_TOP_DIR }}
@@ -255,14 +255,14 @@ 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

      - name: install metis
        if: matrix.mpi == 'par' && matrix.os != 'windows-latest' && steps.metis-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.5
+        uses: mfem/github-actions/build-metis@v2.6
        with:
          archive: ${{ matrix.os != 'macos-latest' && env.METIS_ARCHIVE || env.METIS_ARCHIVE_MAC }}
          dir: ${{ env.METIS_TOP_DIR }}
@@ -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
@@ -303,7 +304,7 @@ jobs:

      # MFEM build and test
      - name: build
-        uses: mfem/github-actions/build-mfem@v2.5
+        uses: mfem/github-actions/build-mfem@v2.6
        env:
          VCPKG_DEFAULT_BINARY_CACHE: ${{ github.workspace }}/vcpkg_cache
        with:
@@ -374,8 +375,10 @@ jobs:
      # Code coverage (process and upload reports)
      - name: codecov
        if: matrix.codecov == 'YES'
-        uses: mfem/github-actions/upload-coverage@v2.5
+        uses: mfem/github-actions/upload-coverage@v2.6
        with:
-          name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}
+          name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}
          project_dir: ${{ env.MFEM_TOP_DIR }}
          directories: "fem general linalg mesh"
+        env:
+          CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
@@ -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
@@ -39,7 +39,7 @@ jobs:

    steps:
      - name: checkout MFEM
-        uses: actions/checkout@v4
+        uses: actions/checkout@v6
        with:
          path: mfem

@@ -50,14 +50,14 @@ 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

      - name: Get Hypre
        if: steps.hypre-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.5
+        uses: mfem/github-actions/build-hypre@v2.6
        with:
          archive: ${{ env.HYPRE_ARCHIVE }}
          dir: ${{ env.HYPRE_TOP_DIR }}
@@ -65,21 +65,21 @@ 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

      - name: Install Metis
        if: steps.metis-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.5
+        uses: mfem/github-actions/build-metis@v2.6
        with:
          archive: ${{ env.METIS_ARCHIVE }}
          dir: ${{ env.METIS_TOP_DIR }}

      # MFEM build and test
      - name: build-mfem
-        uses: mfem/github-actions/build-mfem@v2.5
+        uses: mfem/github-actions/build-mfem@v2.6
        with:
          os: ${{ runner.os }}
          target: opt
@@ -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

@@ -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
@@ -30,7 +30,7 @@ jobs:
        uses: ./.github/actions/sanitize/mpi
      - name: Build
        if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.5
+        uses: mfem/github-actions/build-hypre@v2.6
        with:
          archive: ${{env.HYPRE_TGZ}}
          dir: ${{env.HYPRE_DIR}}
@@ -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}}
@@ -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
@@ -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
@@ -30,7 +30,7 @@ jobs:
        uses: ./.github/actions/sanitize/mpi
      - name: Build
        if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.5
+        uses: mfem/github-actions/build-metis@v2.6
        with:
          archive: ${{env.METIS_TGZ}}
          dir: ${{env.METIS_DIR}}
@@ -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}}
@@ -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
@@ -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"
@@ -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"
@@ -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
@@ -11,8 +11,26 @@
 Version 4.9.1 (development)
 ===========================

+- Policy for AI-assisted contribution added to CONTRIBUTING.md
+
 Discretization improvements
 ---------------------------
+- Added NVIDIA cuDSS library interface. Implementation examples have been 
+  added to ex1 and ex1p. See https://developer.nvidia.com/cudss for more 
+  details. Supported versions >= 0.6.0.
+
+- 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.
@@ -25,11 +43,28 @@ Meshing improvements
 - Improved support for 1D NURBS meshes with variable order, including using
  the patches construct for 1D NURBS meshes.

+- Added the option to include material interfaces (faces separating elements
+  with different element attributes) as additional boundary elements, for
+  parallel visualization, e.g. with GLVis. This is supported by both the Print
+  and PrintAsOne methods of ParMesh. See ParMesh::SetPrintInterfaces().
+
 New and updated examples and miniapps
 -------------------------------------
 - Electromagnetics/lorentz miniapp has been updated to leverage the ParticleSet
  capability.

+GPU computing
+-------------
+- Allow specifying GPU kernel launch bounds for native and RAJA GPU backends.
+
+Miscellaneous
+-------------
+- Fixed signed DOF handling in parallel grid-function reading (read constructor)
+  and saving via ParGridFunction::SaveAsOne(). Simplified the process of
+  applying the DOF signs by using the new method ApplyDofSigns() in class
+  ParFiniteElementSpace -- the method will return immediately if no sign flips
+  are needed.
+

 Version 4.9, released on Dec 11, 2025
 =====================================
@@ -433,6 +433,15 @@ if (MFEM_USE_STRUMPACK)
  endif()
 endif()

+# cuDSS can only be enabled in CUDA
+if (MFEM_USE_CUDSS)
+  if (MFEM_USE_CUDA)
+    find_package(CUDSS REQUIRED)
+  else()
+    message(FATAL_ERROR " *** cuDSS requires that CUDA be enabled.")
+  endif()
+endif()
+
 # GnuTLS
 if (MFEM_USE_GNUTLS)
  find_package(_GnuTLS REQUIRED)
@@ -631,7 +640,7 @@ find_package(Threads REQUIRED)
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB HDF5
    NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
-    ADIOS2 MKL_CPARDISO MKL_PARDISO AMGX MAGMA CUSPARSE CUBLAS CALIPER CODIPACK
+    ADIOS2 MKL_CPARDISO MKL_PARDISO AMGX MAGMA CUSPARSE CUBLAS CUDSS CALIPER CODIPACK
    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPBLAS HIPSPARSE MOONOLITH BLITZ
    ALGOIM ENZYME CUDA::cudart)

@@ -3,12 +3,13 @@
 </p>

 <p align="center">
-<a href="https://github.com/mfem/mfem/blob/master/LICENSE"><img alt="License" src="https://img.shields.io/badge/License-BSD-brightgreen.svg"></a>
-<a href="https://github.com/mfem/mfem/actions?query=workflow%3Arepo-check+branch%3Amaster"><img alt="Repo check" src="https://github.com/mfem/mfem/actions/workflows/repo-check.yml/badge.svg?branch=master"></a>
-<a href="https://github.com/mfem/mfem/actions?query=workflow%3Abuild-analysis+branch%3Amaster"><img alt="Build Analysis" src="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml/badge.svg?branch=master"></a>
-<a href="https://github.com/mfem/mfem/actions?query=workflow%3Abuilds-and-tests+branch%3Amaster"><img alt="Builds and Tests" src="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml/badge.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/blob/master/LICENSE"><img alt="License" src="https://img.shields.io/badge/License-BSD-blue.svg"></a>
+<a href="https://github.com/mfem/mfem/releases/latest"><img alt="GitHub release" src="https://img.shields.io/github/v/release/mfem/mfem"></a>
+<a href="https://github.com/mfem/mfem/actions/workflows/repo-check.yml?query=branch%3Amaster"><img alt="Repo check" src="https://github.com/mfem/mfem/actions/workflows/repo-check.yml/badge.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml?query=branch%3Amaster"><img alt="Build Analysis" src="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml/badge.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml?query=branch%3Amaster"><img alt="Builds and Tests" src="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml/badge.svg?branch=master"></a>
 <a href="https://ci.appveyor.com/project/mfem/mfem"><img alt="Build Status" src="https://ci.appveyor.com/api/projects/status/19non9sqm6msi2wy?svg=true"></a>
-<a href="https://docs.mfem.org/html/index.html"><img alt="Doxygen" src="https://img.shields.io/badge/code-documented-brightgreen.svg"></a>
+<a href="https://docs.mfem.org/html/index.html"><img alt="Documentation" src="https://img.shields.io/badge/code-documented-brightgreen.svg"></a>
 </p>


@@ -24,6 +25,14 @@ 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
@@ -76,7 +85,7 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
  follow the [MFEM PR Rules](#mfem-pr-rules).
 - When your contribution is fully working and ready to be reviewed, add
  the `ready-for-review` label.
- PRs are treated similarly to journal submission with an "editor" assigning two
+- PRs are treated similarly to journal submission, with an "editor" assigning two
  reviewers to evaluate the changes.
 - The reviewers have 3 weeks to evaluate the PR and work with the author to
  fix issues and implement improvements.
@@ -117,7 +126,7 @@ The MFEM source code has the following structure:
  │   ├── petsc
  │   ├── pumi
  │   ├── sundials
-  |   └── superlu
+  │   └── superlu
  ├── fem
  │   ├── ceed
  │   ├── dfem
@@ -129,10 +138,6 @@ The MFEM source code has the following structure:
  │   ├── moonolith
  │   ├── qinterp
  │   └── tmop
-  │   |   ├── assemble
-  │   |   ├── metrics
-  │   |   ├── mult
-  │   |   └── tools
  ├── general
  ├── linalg
  │   ├── batched
@@ -145,11 +150,10 @@ The MFEM source code has the following structure:
  │   ├── common
  │   ├── contact
  │   ├── dfem
+  │   ├── diag-smoothers
  │   ├── dpg
  │   ├── electromagnetics
  │   ├── fluids
-  │   │   ├── navier
-  │   │   └── schrodinger-flow
  │   ├── gslib
  │   ├── hdiv-linear-solver
  │   ├── hooke
@@ -159,6 +163,7 @@ The MFEM source code has the following structure:
  │   ├── nurbs
  │   ├── parelag
  │   ├── performance
+  │   ├── plasma
  │   ├── shifted
  │   ├── solvers
  │   ├── spde
@@ -189,15 +194,15 @@ respectively.

 - The main finite element classes are:
  + [`FiniteElement`](https://docs.mfem.org/html/classmfem_1_1FiniteElement.html)
-  + [`FiniteElementCollection`](https://docs.mfem.org/html/classmfem_1_1FiniteElement.html)
+  + [`FiniteElementCollection`](https://docs.mfem.org/html/classmfem_1_1FiniteElementCollection.html)
  + [`FiniteElementSpace`](https://docs.mfem.org/html/classmfem_1_1FiniteElementSpace.html)
  + [`GridFunction`](https://docs.mfem.org/html/classmfem_1_1GridFunction.html)
  + [`BilinearFormIntegrator`](https://docs.mfem.org/html/classmfem_1_1BilinearFormIntegrator.html) and [`LinearFormIntegrator`](https://docs.mfem.org/html/classmfem_1_1LinearFormIntegrator.html)
-  + [`LinearForm`](https://docs.mfem.org/html/classmfem_1_1LinearFormIntegrator.html), [`BilinearForm`](https://docs.mfem.org/html/classmfem_1_1BilinearForm.html) and [`MixedBilinearForm`](https://docs.mfem.org/html/classmfem_1_1MixedBilinearForm.html)
+  + [`LinearForm`](https://docs.mfem.org/html/classmfem_1_1LinearForm.html), [`BilinearForm`](https://docs.mfem.org/html/classmfem_1_1BilinearForm.html) and [`MixedBilinearForm`](https://docs.mfem.org/html/classmfem_1_1MixedBilinearForm.html)

 - The main linear algebra classes and sources are
  + [`Operator`](https://docs.mfem.org/html/classmfem_1_1Operator.html) and [`BilinearForm`](https://docs.mfem.org/html/classmfem_1_1BilinearForm.html)
-  + [`Vector`](https://docs.mfem.org/html/classmfem_1_1BilinearForm.html) and [`LinearForm`](https://docs.mfem.org/html/classmfem_1_1LinearForm.html)
+  + [`Vector`](https://docs.mfem.org/html/classmfem_1_1Vector.html) and [`LinearForm`](https://docs.mfem.org/html/classmfem_1_1LinearForm.html)
  + [`DenseMatrix`](https://docs.mfem.org/html/classmfem_1_1DenseMatrix.html) and [`SparseMatrix`](https://docs.mfem.org/html/classmfem_1_1SparseMatrix.html)
  + Sparse [smoothers](https://docs.mfem.org/html/sparsesmoothers_8hpp.html) and linear [solvers](https://docs.mfem.org/html/solvers_8hpp.html)

@@ -209,8 +214,8 @@ shared geometric entities between different tasks. The parallel source files
 have a `p` prefix, e.g. `pmesh.cpp` vs. the serial `mesh.cpp`.

 - The main parallel classes are
-  + [`ParMesh`](https://docs.mfem.org/html/solvers_8hpp.html)
-  + [`ParNCMesh`](https://docs.mfem.org/html/classmfem_1_1ParMesh.html)
+  + [`ParMesh`](https://docs.mfem.org/html/classmfem_1_1ParMesh.html)
+  + [`ParNCMesh`](https://docs.mfem.org/html/classmfem_1_1ParNCMesh.html)
  + [`ParFiniteElementSpace`](https://docs.mfem.org/html/classmfem_1_1ParFiniteElementSpace.html)
  + [`ParGridFunction`](https://docs.mfem.org/html/classmfem_1_1ParGridFunction.html)
  + [`ParBilinearForm`](https://docs.mfem.org/html/classmfem_1_1ParBilinearForm.html) and [`ParLinearForm`](https://docs.mfem.org/html/classmfem_1_1ParLinearForm.html)
@@ -220,14 +225,14 @@ have a `p` prefix, e.g. `pmesh.cpp` vs. the serial `mesh.cpp`.
 #### GPU and general device support

 GPU and multi-core CPU support is based on device kernels supporting different
-backends (CUDA, OCCA, RAJA, OpenMP, etc.) and an internal lightweight
+backends (CUDA, HIP, OCCA, RAJA, OpenMP, etc.) and an internal lightweight
 device/host memory manager.

 - The main device-relevant classes and sources are:
  + [`Device`](https://docs.mfem.org/html/device_8hpp.html)
  + [`MemoryManager`](https://docs.mfem.org/html/mem_manager_8hpp.html)
  + the [`mfem::forall`](https://docs.mfem.org/html/forall_8hpp.html) function
-  + the [`cuda.hpp`](https://docs.mfem.org/html/cuda_8hpp.html) and [`occa.hpp`](https://docs.mfem.org/html/occa_8hpp.html) files
+  + the [`cuda.hpp`](https://docs.mfem.org/html/cuda_8hpp.html), [`hip.hpp`](https://docs.mfem.org/html/hip_8hpp.html) and [`occa.hpp`](https://docs.mfem.org/html/occa_8hpp.html) files

 #### Utilities, building and documentation
 - The `general/` directory contains C++ classes that serve as utilities for
@@ -241,8 +246,8 @@ device/host memory manager.
 - `examples` and `miniapps` respectively gather simple and more fully-featured
  demonstrations of the usage on MFEM. They both rely on `data/` for the
  collection of meshes.
- The `tests/` directory contains a unit test suite and will later contain more
-  tests that run example codes.
+- The `tests/` directory contains a unit test suite, additional tests, and
+  benchmarks.

 See also the [code overview](https://mfem.org/code-overview/) section on the MFEM
 website.
@@ -276,8 +281,8 @@ Before you can start, you need a GitHub account, here are a few suggestions:
  the top of https://github.com/mfem.
 - Consider making your membership public by going to https://github.com/orgs/mfem/people
  and clicking on the organization visibility drop box next to your name.
- Project discussions and announcements will be posted at
-  https://github.com/orgs/mfem/teams/everyone.
+- Project discussions and announcements will be posted at https://github.com/orgs/mfem/discussions,
+  tagging the `@mfem/everyone` team when appropriate.

 #### Structure
 - The MFEM source code is in the [mfem](https://github.com/mfem/mfem)
@@ -337,11 +342,12 @@ Before you can start, you need a GitHub account, here are a few suggestions:
  - Well-designed simple code is frequently more general and powerful.
  - Lean code base is easier to understand by new collaborators.
  - New features should be added only if they are necessary or generally useful.
-  - Introduction of language constructions not currently used in MFEM should be
+  - Introduction of language constructs not currently used in MFEM should be
    justified and generally avoided (to maintain portability to various systems
    and compilers, including early access hardware).
-  - We prefer basic C++ and the C++03 standard, to keep the code readable by
-    a large audience and to make sure it compiles anywhere.
+  - We prefer basic C++. Use C++17 features judiciously, prioritizing readability,
+    consistency with existing MFEM code, and portability to different systems,
+    compilers and device backends.

 - *Keep the code general and reasonably efficient*
  - The main goal is fast prototyping for research and application development.
@@ -384,7 +390,7 @@ Before you can start, you need a GitHub account, here are a few suggestions:
 - When your branch is ready for other developers to review / comment on
  the code, create a pull request towards `mfem:master`.

- Pull request typically have titles like:
+- Pull requests typically have titles like:

     `Description [new-feature-dev]`

@@ -405,12 +411,12 @@ Before you can start, you need a GitHub account, here are a few suggestions:
 - Add a description, appropriate labels and assign yourself to the PR. The MFEM
  team will add reviewers as appropriate.

- List outstanding TODO items in the description, see PR #222 for an example.
+- List outstanding TODO items in the description.

 - When your contribution is fully working and ready to be reviewed, add
-  the `ready-for-review` label.
+  or request the `ready-for-review` label.

- PRs are treated similarly to journal submission with an "editor" assigning
+- PRs are treated similarly to journal submission, with an "editor" assigning
  two reviewers to evaluate the changes. The reviewers have 3 weeks to evaluate
  the PR and work with the author to implement improvements and fix issues.

@@ -436,7 +442,7 @@ Before you can start, you need a GitHub account, here are a few suggestions:
  checks in GitHub Actions enforce MFEM-specific rules which are explained in
  the error messages and the `tests/scripts` directory.

- Also note that the tests `branch-history` and `repos-checks` found in GitHub
+- Also note that the tests `branch-history` and `repo-check` found in GitHub
  Actions can be triggered automatically before each push using git hooks. See
  the [git hooks README](config/githooks/README.md) for a detailed explanation.

@@ -493,15 +499,15 @@ Everyone on the MFEM team can be asked to serve as a reviewer on a PR in their a

 3. To ensure the quality of the PR by making sure that the code adheres to the [Developer Guidelines](#developer-guidelines), e.g. all methods, data members, and functions have documentation, including data ownership and lifetime, new examples/miniapps have a corresponding PR in mfem/web, major features have `CHANGELOG` entries, etc.

-3. To seek help from the editors in case of difficulties.
+4. To seek help from the editors in case of difficulties.

-4. To complete the review in a timely manner: 3 weeks from assignment.
+5. To complete the review in a timely manner: 3 weeks from assignment.

-5. To test the PR thoroughly before merging in *next*. The PR author is also encouraged to perform testing and inform the reviewers about the results.
+6. To test the PR thoroughly before merging in *next*. The PR author is also encouraged to perform testing and inform the reviewers about the results.

-6. To monitor the PR impact on the testing in the *next* branch and alert the editors that the PR is ready for merging in *master*.
+7. To monitor the PR impact on the testing in the *next* branch and alert the editors that the PR is ready for merging in *master*.

-7. The review of bugfixes should be expedited proportional to their importance. The review window can be much less than three weeks in such cases.
+8. The review of bugfixes should be expedited proportional to their importance. The review window can be much less than three weeks in such cases.

 #### Responsibilities of Authors

@@ -527,30 +533,30 @@ Before a PR can be merged, it should satisfy the following:
 - [ ] Code builds.
 - [ ] Code passes `make style`.
 - [ ] Update `CHANGELOG`:
-    - [ ] Is this a new feature users need to be aware of? New or updated example or miniapp?
-    - [ ] Does it make sense to create a new section in the `CHANGELOG` to group with other related features?
+   - [ ] Is this a new feature users need to be aware of? New or updated example or miniapp?
+   - [ ] Does it make sense to create a new section in the `CHANGELOG` to group with other related features?
 - [ ] Update `INSTALL`:
-    - [ ] Had a new optional library been added? If so, what range of versions of this library are required? (*Make sure the external library is compatible with our BSD license, e.g. it is not licensed under GPL!*)
-    - [ ] Have the version ranges for any required or optional libraries changed?
-    - [ ] Does `make` or `cmake` have a new target?
-    - [ ] Did the requirements or the installation process change? *(rare)*
+   - [ ] Has a new optional library been added? If so, what range of versions of this library are required? (*Make sure the external library is compatible with our BSD license, e.g. it is not licensed under GPL!*)
+   - [ ] Have the version ranges for any required or optional libraries changed?
+   - [ ] Does `make` or `cmake` have a new target?
+   - [ ] Did the requirements or the installation process change? *(rare)*
 - [ ] Update continuous integration server configurations if necessary (e.g. with new version requirements for each of MFEM's dependencies)
-    - [ ] `.github`
-    - [ ] `.appveyor.yml`
+   - [ ] `.github`
+   - [ ] `.appveyor.yml`
 - [ ] Update `.gitignore`:
-    - [ ] Check if `make distclean; git status` shows any files that were generated from the source by the project (not an IDE) but we don't want to track in the repository.
-    - [ ] Add new patterns (just for the new files above) and re-run the above test.
+   - [ ] Check if `make distclean; git status` shows any files that were generated from the source by the project (not an IDE) but we don't want to track in the repository.
+   - [ ] Add new patterns (just for the new files above) and re-run the above test.
 - [ ] New examples:
-    - [ ] All sample runs at the top of the example source file work.
-    - [ ] Update `examples/makefile`:
+   - [ ] All sample runs at the top of the example source file work.
+   - [ ] Update `examples/makefile`:
      - [ ] Add the example code to the appropriate `SEQ_EXAMPLES` and `PAR_EXAMPLES` variables.
      - [ ] Add any files generated by it to the `clean` target.
      - [ ] Add the example binary and any files generated by it to the top-level `.gitignore` file.
-    - [ ] Update `examples/CMakeLists.txt`:
+   - [ ] Update `examples/CMakeLists.txt`:
      - [ ] Add the example code to the `ALL_EXE_SRCS` variable.
      - [ ] Make sure `THIS_TEST_OPTIONS` is set correctly for the new example.
   - [ ] List the new example in `doc/CodeDocumentation.dox`.
-   - [ ] If new examples directory (e.g.`examples/pumi`), list it in `doc/CodeDocumentation.conf.in`
+   - [ ] If new examples directory (e.g. `examples/pumi`), list it in `doc/CodeDocumentation.conf.in`
   - [ ] Companion pull request for documentation in [mfem/web](https://github.com/mfem/web) repo:
      - [ ] Update or add example-specific documentation, see e.g. the `src/examples.md`.
      - [ ] Add the description, labels and screenshots in `src/examples.md` and `src/img`.
@@ -567,13 +573,13 @@ Before a PR can be merged, it should satisfy the following:
      - [ ] Add/update the `CMakeLists.txt` file in the new miniapp directory.
      - [ ] Consider adding a new test for the new miniapp.
   - [ ] List the new miniapp in `doc/CodeDocumentation.dox`
-   - [ ] If new miniapps directory (e.g.`miniapps/nurbs`), add it to `MINIAPP_SUBDIRS` in the `makefile`.
-   - [ ] If new miniapps directory (e.g.`miniapps/nurbs`), list it in `doc/CodeDocumentation.conf.in`
+   - [ ] If new miniapps directory (e.g. `miniapps/nurbs`), add it to `MINIAPP_SUBDIRS` in the `makefile`.
+   - [ ] If new miniapps directory (e.g. `miniapps/nurbs`), list it in `doc/CodeDocumentation.conf.in`
   - [ ] Companion pull request for documentation in [mfem/web](https://github.com/mfem/web) repo:
-     - [ ] Update or add miniapp-specific documentation, see e.g. the `src/meshing.md` and `src/electromagnetics.md` files.
-     - [ ] Add the description, labels and screenshots in `src/examples.md` and `src/img`.
-     - [ ] The miniapps go at the end of the page, and are usually listed only under a specific "Application (PDE)" category.
-     - [ ] Add a short description of the miniapp in the "Extensive Examples" section of `features.md`.
+      - [ ] Update or add miniapp-specific documentation, see e.g. the `src/meshing.md` and `src/electromagnetics.md` files.
+      - [ ] Add the description, labels and screenshots in `src/examples.md` and `src/img`.
+      - [ ] The miniapps go at the end of the page, and are usually listed only under a specific "Application (PDE)" category.
+      - [ ] Add a short description of the miniapp in the "Extensive Examples" section of `features.md`.
 - [ ] New capability:
   - [ ] All new public, protected, and private classes, methods, data members, and functions have full Doxygen-style documentation in source comments. Documentation should include descriptions of member data, function arguments and return values, template parameters, and prerequisites for calling new functions.
   - [ ] Pointer arguments and return values must specify whether ownership is being transferred or lent with the call.
@@ -675,7 +681,7 @@ MFEM uses a `master`/`next`-branch workflow as described below:
 - [ ] Update URL shortlinks:
    - [ ] Create a shortlink at [http://bit.ly/](http://bit.ly/) for the release tarball, e.g. https://mfem.github.io/releases/mfem-3.1.tgz.
    - [ ] (LLNL only) Add and commit the new shortlink in the `links` and `links-mfem` files of the internal `mfem/downloads` repo.
-    - [ ] Add the new shortlinks to the MFEM packages in `spack`, `homebrew/science`, `VisIt`, etc.
+    - [ ] Add the new shortlinks to the MFEM package in `spack`.
 - [ ] Update website in `mfem/web` repo:
    - Update version and shortlinks in `src/index.md` and `src/download.md`.
    -  Use [cloc-1.62.pl](http://cloc.sourceforge.net/) and `ls -lh` to estimate the SLOC and the tarball size in `src/download.md`.
@@ -727,22 +733,24 @@ commit or push, see the [README](config/githooks/README.md) in the `config/githo
 directory.


-### Linux and Mac smoke tests
+### GitHub Actions smoke tests
+
 We use GitHub Actions to drive the default tests on the `master` and `next`
 branches. See the `.github/workflows` files and the logs at
 [https://github.com/mfem/mfem/actions](https://github.com/mfem/mfem/actions).

-Testing using GitHub Actions should be kept lightweight, as there is a time
-constraint on jobs. Two virtual machines are configured - Mac (OS X) and Linux.
+GitHub Actions testing should be kept lightweight, as there is a time
+constraint on jobs. The current workflows cover Linux, macOS, and Windows
+configurations.

 - Tests on the `master` branch are triggered whenever a PR is issued on this branch.
 - Tests on the `next` branch are currently scheduled to run each night.

+### Additional Windows smoke test

-### Windows smoke test
-We use Appveyor to test building with the MS Visual C++ compiler in a Windows
-environment, as well as to test the CMake build. See the `.appveyor` file and the
-build logs at
+We also use Appveyor to test building with the MS Visual C++ compiler in a Windows
+environment, as well as to test the CMake build. See the `.appveyor.yml` file
+and the build logs at
 [https://ci.appveyor.com/project/mfem/mfem](https://ci.appveyor.com/project/mfem/mfem).

 CMake is used to generate the MSVC Project files and drive the build.  A release
@@ -38,14 +38,13 @@ the option MFEM_USE_METIS.
 MFEM also includes support for devices such as GPUs, and programming models such
 as CUDA, HIP, OCCA, OpenMP and RAJA.

- Starting with version 4.0, MFEM requires a C++11 compiler. We recommend using
-  a newer compiler, e.g. GCC version 4.9 or higher.
+- Starting with version 4.9, MFEM requires a C++17 compiler.

 - CUDA support requires an NVIDIA GPU and an installation of the CUDA Toolkit
  https://developer.nvidia.com/cuda-toolkit

 - HIP support requires an AMD GPU and an installation of the ROCm software stack
-  https://rocmdocs.amd.com
+  https://rocm.docs.amd.com

 - OCCA support requires the OCCA library
  https://libocca.org
@@ -83,9 +82,9 @@ Serial build:
 Parallel build:
   (download hypre and METIS 4 from above URLs)
   (build METIS 4 in ../metis-4.0 relative to mfem/)
+   (for METIS 5, see https://mfem.org/building/#parallel-build-using-metis-5)
   (build hypre in ../hypre relative to mfem/)
   make parallel -j 4
-(For METIS 5, see https://mfem.org/building/#parallel-build-using-metis-5)

 CUDA build:
   make cuda -j 4
@@ -115,14 +114,14 @@ Serial build:
 Parallel build:
   (download hypre and METIS 4 from above URLs)
   (build METIS 4 in ../metis-4.0 relative to mfem/)
+   (for METIS 5, see https://mfem.org/building/#parallel-build-using-metis-5)
   (build hypre in ../hypre relative to mfem/)
   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
   cmake <mfem-source-dir> -DMFEM_USE_MPI=YES
   make -j 4
-(For METIS 5, see https://mfem.org/building/#parallel-build-using-metis-5)

 Parallel build with fetching of hypre and METIS:
-   mkdir <mfem-buil-dir> ; cd <mfem-build-dir>
+   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
   cmake <mfem-source-dir> -DMFEM_USE_MPI=YES -DMFEM_FETCH_TPLS=YES
   make -j 4

@@ -134,7 +133,8 @@ CUDA build:

 HIP build:
   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
-   cmake <mfem-source-dir> -DMFEM_USE_HIP=YES -DHIP_ARCH=gfx942 -DCMAKE_CXX_COMPILER=amdclang++ -DCMAKE_HIP_COMPILER=amdclang++
+   cmake <mfem-source-dir> -DMFEM_USE_HIP=YES -DHIP_ARCH=gfx942 \
+         -DCMAKE_CXX_COMPILER=amdclang++ -DCMAKE_HIP_COMPILER=amdclang++
   make -j 4

 Example codes (serial/parallel, depending on the build):
@@ -269,6 +269,7 @@ Compilers:
   CXX      - C++ compiler, serial build
   MPICXX   - MPI C++ compiler, parallel build
   CUDA_CXX - The CUDA compiler, 'nvcc' or 'clang++'
+   HIP_CXX  - The HIP compiler, e.g. 'hipcc'

 Compiler options:
   OPTIM_FLAGS - Options for optimized build
@@ -395,6 +396,11 @@ MFEM_USE_STRUMPACK = YES/NO
   classes. When enabled, this option uses the STRUMPACK_* library options, see
   below.

+MFEM_USE_CUDSS = YES/NO
+   Enable MFEM functionality based on the cuDSS library. When using cuDSS, CUDA
+   support must be also enabled in MFEM, i.e. MFEM_USE_CUDA=YES must be set.
+   When enabled, this option uses the CUDSS_* library options, see below.
+
 MFEM_USE_GINKGO = YES/NO
   Enable MFEM functionality based on the Ginkgo library, which provides
   iterative linear solvers and preconditioners with OpenMP, CUDA backends, see
@@ -554,13 +560,13 @@ MFEM_USE_RAJA = YES/NO
 MFEM_USE_OCCA = YES/NO
   Enables support for the OCCA library in MFEM. OCCA is an open-source library
   which aims to make it easy to program different types of devices (e.g. CPU,
-   GPU, FPGA) by providing an unified API for interacting with JIT-compiled
+   GPU, FPGA) by providing a unified API for interacting with JIT-compiled
   backends. In order to use the OCCA CUDA backend, CUDA support must be enabled
   in MFEM as well, i.e. MFEM_USE_CUDA=YES must be set.

 MFEM_USE_GSLIB = YES/NO
   Enables MFEM functionality based on the GSLIB library, and specifically its
-   FindPoints component, which provides a robust algorithms to evaluate finite
+   FindPoints component, which provides robust algorithms to evaluate finite
   element functions in a collection of points in physical space. When enabled,
   the user can use the GSLIB-FindPoints methods as shown in miniapps/gslib.

@@ -719,9 +725,18 @@ The specific libraries and their options are:
  Options: STRUMPACK_OPT, STRUMPACK_LIB.
  Versions: STRUMPACK >= 3.0.0.

- Ginkgo (optional), used when MFEM_USE_GINKGO = YES. Note that Ginkgo needs a
-  C++ compiler that supports the C++-17 standard. For additional requirements
-  and dependencies of specific modules, see the Ginkgo webpage below.
+- CUDSS (optional), used when MFEM_USE_CUDSS = YES. Note that CUDSS requires 
+  CUDA 12.x toolkit and the cuDSS libraries. The supported communication backend
+  is OpenMPI 4.x (default), and OpenMPI 4.x or a later version must be pre-built.
+  The source files in the cuDSS tarball provide guidance for developing custom 
+  MPI implementations.
+  URL: https://developer.nvidia.com/cudss
+       https://docs.nvidia.com/cuda/cudss/advanced_features.html#communication-layer-library-in-cudss
+  Options: CUDSS_OPT, CUDSS_LIB.
+  Versions: cuDSS >= 0.6.0.
+
+- Ginkgo (optional), used when MFEM_USE_GINKGO = YES. Ginkgo may have additional
+  requirements and module-specific dependencies; see the webpage below.
  URL: https://ginkgo-project.github.io
  Options: GINKGO_OPT, GINKGO_LIB, GINKGO_DIR, GINKGO_BUILD_TYPE (Release or
           Debug).
@@ -793,7 +808,7 @@ The specific libraries and their options are:
  Options: CONDUIT_OPT, CONDUIT_LIB.
  Versions: Conduit >= 0.3.1.

- ADIOS2 (optional) used when MFEM_USE_ADIOS2 = YES.
+- ADIOS2 (optional), used when MFEM_USE_ADIOS2 = YES.
  URL: https://adios2.readthedocs.io/
  Versions: ADIOS >= 2.5.0.

@@ -869,7 +884,7 @@ The specific libraries and their options are:
  Options: RAJA_DIR, RAJA_OPT, RAJA_LIB.
  Versions: RAJA >= 2022.10.3.

- Moonolith (optional), use when MFEM_USE_MOONOLITH = YES.
+- Moonolith (optional), used when MFEM_USE_MOONOLITH = YES.
  URL: https://bitbucket.org/zulianp/par_moonolith
  Options: MOONOLITH_DIR
  Versions: MOONOLITH >= 1.1.0.
@@ -957,7 +972,7 @@ CMAKE_BUILD_TYPE which can be set to standard values like "Debug", and "Release"
 To use a specific generator use the "-G <generator>" option of cmake:

   cmake <mfem-source-dir> -G "Xcode"
-   cmake <mfem-source-dir> -G "Visual Studio 12 2013"
+   cmake <mfem-source-dir> -G "Visual Studio 17 2022"
   cmake <mfem-source-dir> -G "MinGW Makefiles"

 With CMake it is possible to build MFEM as a shared library using the standard
@@ -1202,7 +1217,7 @@ larger problems, there are two options:
 Specific options for HIP
 ========================
 MFEM expects the `ROCM_PATH` environment variable to be set to the path of the
-ROCM install, as well as having `$ROCM_PATH/bin` in `PATH`.
+ROCm install, as well as having `$ROCM_PATH/bin` in `PATH`.

 Specific options for RAJA+HIP+MPI
 =================================
@@ -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
@@ -35,6 +35,7 @@ set(MFEM_USE_SUITESPARSE @MFEM_USE_SUITESPARSE@)
 set(MFEM_USE_SUPERLU @MFEM_USE_SUPERLU@)
 set(MFEM_USE_MUMPS @MFEM_USE_MUMPS@)
 set(MFEM_USE_STRUMPACK @MFEM_USE_STRUMPACK@)
+set(MFEM_USE_CUDSS @MFEM_USE_CUDSS@)
 set(MFEM_USE_GINKGO @MFEM_USE_GINKGO@)
 set(MFEM_USE_AMGX @MFEM_USE_AMGX@)
 set(MFEM_USE_MAGMA @MFEM_USE_MAGMA@)
@@ -109,6 +110,14 @@ if (MFEM_USE_RAJA)
   find_dependency(RAJA)
 endif()

+if (MFEM_USE_CUDSS)
+  find_dependency(cudss)
+endif (MFEM_USE_CUDSS)
+
+if (MFEM_USE_UMPIRE)
+   find_dependency(umpire)
+endif()
+
 if (NOT TARGET mfem)
  include(${CMAKE_CURRENT_LIST_DIR}/MFEMTargets.cmake)
 endif (NOT TARGET mfem)
@@ -108,6 +108,15 @@
 // Enable MFEM functionality based on the STRUMPACK library.
 #cmakedefine MFEM_USE_STRUMPACK

+// Enable MFEM functionality based on the cuDSS library.
+#cmakedefine MFEM_USE_CUDSS
+
+// CUDSS communication layer library path
+#cmakedefine MFEM_CUDSS_COMM_LIB "@MFEM_CUDSS_COMM_LIB@"
+
+// CUDSS threading layer library path
+#cmakedefine MFEM_CUDSS_THREADING_LIB "@MFEM_CUDSS_THREADING_LIB@"
+
 // Enable functionality based on the Ginkgo library.
 #cmakedefine MFEM_USE_GINKGO

@@ -0,0 +1,68 @@
+if (NOT cudss_DIR AND CUDSS_DIR)
+  set(cudss_DIR ${CUDSS_DIR}/lib/cmake/cudss)
+endif()
+message(STATUS "Looking for CUDSS ...")
+message(STATUS "   in CUDSS_DIR = ${CUDSS_DIR}")
+message(STATUS "      cudss_DIR = ${cudss_DIR}")
+find_package(cudss)
+set(CUDSS_FOUND ${cudss_FOUND})
+set(CUDSS_LIBRARIES "cudss")
+if (CUDSS_FOUND)
+  message(STATUS
+    "Found CUDSS target: ${CUDSS_LIBRARIES} (version: ${cudss_VERSION})")
+else()
+  set(msg STATUS)
+  if (CUDSS_FIND_REQUIRED)
+    set(msg FATAL_ERROR)
+  endif()
+  message(${msg}
+    "CUDSS not found. Please set CUDSS_DIR to the install prefix.")
+endif()
+
+if(CUDSS_FOUND AND TARGET cudss)
+  get_target_property(CUDSS_LIBRARY_LOCATION cudss IMPORTED_LOCATION)
+  if(NOT CUDSS_LIBRARY_LOCATION)
+    get_target_property(CUDSS_LIBRARY_LOCATION cudss IMPORTED_LOCATION_RELEASE)
+  endif()
+  if(CUDSS_LIBRARY_LOCATION)
+    get_filename_component(CUDSS_LIBRARY_DIR "${CUDSS_LIBRARY_LOCATION}" DIRECTORY)
+  else()
+    message(WARNING "Could not determine the location of the cuDSS library.")
+  endif()
+else()
+    message(WARNING "cuDSS target not available; cannot determine library directory.")
+endif()
+
+# Set the full name of the cuDSS threading library if OpenMP is enabled.
+# The threading layer library (libcudss_mtlayer_gomp.so) is located under the
+# cuDSS library directory by default.
+if (MFEM_USE_OPENMP)
+  find_file(
+    CUDSS_THREADING_LIB
+    NAMES libcudss_mtlayer_gomp.so
+    PATHS ${CUDSS_LIBRARY_DIR}
+    NO_DEFAULT_PATH
+  )
+  if (NOT DEFINED MFEM_CUDSS_THREADING_LIB AND CUDSS_THREADING_LIB)
+    set(MFEM_CUDSS_THREADING_LIB "${CUDSS_THREADING_LIB}")
+  endif()
+  message(STATUS "CUDSS threading layer library: ${MFEM_CUDSS_THREADING_LIB}")
+endif()
+
+# Set the full name of the cuDSS communication library if MFEM use OpenMPI.
+# The communication layer library (libcudss_commlayer_mpi.so) is located under the
+# cuDSS library directory by default.
+# The communication layer library is used pre-built communication layers for OpenMPI 
+# by default.
+if (MFEM_USE_MPI)
+  find_file(
+    CUDSS_COMM_LIB
+    NAMES libcudss_commlayer_openmpi.so
+    PATHS ${CUDSS_LIBRARY_DIR}
+    NO_DEFAULT_PATH
+  )
+  if (NOT DEFINED MFEM_CUDSS_COMM_LIB AND CUDSS_COMM_LIB)
+    set(MFEM_CUDSS_COMM_LIB "${CUDSS_COMM_LIB}")
+  endif()
+  message(STATUS "CUDSS communication layer library: ${MFEM_CUDSS_COMM_LIB}")
+endif()
@@ -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")
@@ -157,4 +157,28 @@ constexpr real_t operator""_r(unsigned long long v)
 #endif
 #endif // MFEM_USE_MPI not defined

+#ifndef MFEM_USE_CUDA
+#ifdef MFEM_USE_CUDSS
+#error Building with cuDSS (MFEM_USE_CUDSS=YES) requires CUDA (MFEM_USE_CUDA=YES)
+#endif
+#endif // MFEM_USE_CUDSS not defined
+
+#ifdef NVTX_DBG_HPP
+#include NVTX_DBG_HPP // IWYU pragma: keep
+#else
+#define db1(...)
+#define dbg(...)
+#define dbl(...)
+#define dba(...)
+#define dbc(...)
+#define NVTX_MARK_FUNCTION
+#define NVTX_MARK_BEGIN(...)
+#define NVTX_MARK_INI(...)
+#define NVTX_MARK_END(...)
+#define NVTX_MARK(...)
+#define NVTX_INI(...)
+#define NVTX_END(...)
+#define NVTX(...)
+#endif
+
 #endif // MFEM_CONFIG_HPP
@@ -108,6 +108,15 @@
 // Enable MFEM functionality based on the STRUMPACK library.
 // #define MFEM_USE_STRUMPACK

+// Enable MFEM functionality based on the cuDSS library.
+// #define MFEM_USE_CUDSS
+
+// CUDSS communication layer library path
+// #define MFEM_CUDSS_COMM_LIB "@MFEM_CUDSS_COMM_LIB@"
+
+// CUDSS threading layer library path
+// #define MFEM_CUDSS_THREADING_LIB "@MFEM_CUDSS_THREADING_LIB@"
+
 // Enable MFEM features based on the Ginkgo library.
 // #define MFEM_USE_GINKGO

@@ -36,6 +36,9 @@ MFEM_USE_SUPERLU       = @MFEM_USE_SUPERLU@
 MFEM_USE_SUPERLU5      = @MFEM_USE_SUPERLU5@
 MFEM_USE_MUMPS         = @MFEM_USE_MUMPS@
 MFEM_USE_STRUMPACK     = @MFEM_USE_STRUMPACK@
+MFEM_USE_CUDSS         = @MFEM_USE_CUDSS@
+MFEM_CUDSS_COMM_LIB    = @MFEM_CUDSS_COMM_LIB@
+MFEM_CUDSS_THREADING_LIB = @MFEM_CUDSS_THREADING_LIB@
 MFEM_USE_GINKGO        = @MFEM_USE_GINKGO@
 MFEM_USE_AMGX          = @MFEM_USE_AMGX@
 MFEM_USE_MAGMA         = @MFEM_USE_MAGMA@
@@ -38,6 +38,7 @@ option(MFEM_USE_SUPERLU "Enable SuperLU_DIST usage" OFF)
 option(MFEM_USE_SUPERLU5 "Use the old SuperLU_DIST 5.1 version" OFF)
 option(MFEM_USE_MUMPS "Enable MUMPS usage" OFF)
 option(MFEM_USE_STRUMPACK "Enable STRUMPACK usage" OFF)
+option(MFEM_USE_CUDSS "Enable cuDSS usage" OFF)
 option(MFEM_USE_GINKGO "Enable Ginkgo usage" OFF)
 option(MFEM_USE_AMGX "Enable AmgX usage" OFF)
 option(MFEM_USE_MAGMA "Enable MAGMA usage" OFF)
@@ -153,6 +153,7 @@ MFEM_USE_SUPERLU       = NO
 MFEM_USE_SUPERLU5      = NO
 MFEM_USE_MUMPS         = NO
 MFEM_USE_STRUMPACK     = NO
+MFEM_USE_CUDSS         = NO
 MFEM_USE_GINKGO        = NO
 MFEM_USE_AMGX          = NO
 MFEM_USE_MAGMA         = NO
@@ -368,6 +369,19 @@ STRUMPACK_OPT = -I$(STRUMPACK_DIR)/include $(SCOTCH_OPT)
 STRUMPACK_LIB = -L$(STRUMPACK_DIR)/lib -lstrumpack $(MPI_FORTRAN_LIB)\
 $(SCOTCH_LIB) $(SCALAPACK_LIB)

+# CUDSS library configuration
+CUDSS_DIR         = @MFEM_DIR@/../cudss
+CUDSS_INCLUDE_DIR = $(CUDSS_DIR)/include
+CUDSS_LIBRARY_DIR = $(CUDSS_DIR)/lib
+CUDSS_OPT         = -I$(CUDSS_INCLUDE_DIR)
+CUDSS_LIB         = \
+ $(XLINKER)-rpath,$(CUDSS_LIBRARY_DIR) -L$(CUDSS_LIBRARY_DIR) -lcudss
+# The cuDSS communication and threading libraries. 
+MFEM_CUDSS_COMM_LIB = $(abspath $(wildcard $(or $(CUDSS_COMM_LIB),\
+   $(subst @MFEM_DIR@,$(MFEM_DIR), $(CUDSS_LIBRARY_DIR)/libcudss_commlayer_openmpi.so))))
+MFEM_CUDSS_THREADING_LIB = $(abspath $(wildcard $(or $(CUDSS_THREADING_LIB),\
+   $(subst @MFEM_DIR@,$(MFEM_DIR),$(CUDSS_LIBRARY_DIR)/libcudss_mtlayer_gomp.so))))
+
 # Ginkgo library configuration
 GINKGO_DIR = @MFEM_DIR@/../ginkgo/install
 GINKGO_SEARCH_DIR = $(subst @MFEM_DIR@,$(MFEM_DIR),$(GINKGO_DIR))
@@ -621,7 +635,7 @@ PARELAG_LIB = -L$(PARELAG_DIR)/build/src -lParELAG
 AXOM_DIR = @MFEM_DIR@/../axom
 TRIBOL_DIR = @MFEM_DIR@/../tribol
 TRIBOL_OPT = -I$(TRIBOL_DIR)/include -I$(AXOM_DIR)/include
-TRIBOL_LIB = -L$(TRIBOL_DIR)/lib -ltribol -lredecomp -L$(AXOM_DIR)/lib -laxom_mint\
+TRIBOL_LIB = -L$(TRIBOL_DIR)/lib -ltribol -ltribol_shared -lredecomp -L$(AXOM_DIR)/lib -laxom_mint\
   -laxom_slam -laxom_slic -laxom_core

 # Enzyme configuration
@@ -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()
@@ -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)
@@ -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.*
@@ -224,17 +224,29 @@ int main(int argc, char *argv[])
   // 11. Solve the linear system A X = B.
   if (!pa)
   {
-#ifndef MFEM_USE_SUITESPARSE
-      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
-      GSSmoother M((SparseMatrix&)(*A));
-      PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
-#else
-      // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
-      UMFPackSolver umf_solver;
-      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-      umf_solver.SetOperator(*A);
-      umf_solver.Mult(B, X);
+#ifdef MFEM_USE_CUDSS
+      if (Device::Allows(Backend::CUDA_MASK))
+      {
+         // Use cuDSS to solve the system.
+         CuDSSSolver cudss_solver;
+         cudss_solver.SetOperator(*A);
+         cudss_solver.Mult(B, X);
+      }
+      else
 #endif
+      {
+#ifndef MFEM_USE_SUITESPARSE
+         // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
+         GSSmoother M((SparseMatrix&)(*A));
+         PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
+#else
+         // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
+         UMFPackSolver umf_solver;
+         umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+         umf_solver.SetOperator(*A);
+         umf_solver.Mult(B, X);
+#endif
+      }
   }
   else
   {
@@ -273,7 +285,7 @@ int main(int argc, char *argv[])
   if (visualization)
   {
      char vishost[] = "localhost";
-      int  visport   = 19916;
+      int visport = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "solution\n" << mesh << x << flush;
@@ -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
@@ -83,6 +83,9 @@ int main(int argc, char *argv[])
   const char *device_config = "cpu";
   bool visualization = true;
   bool algebraic_ceed = false;
+#ifdef MFEM_USE_CUDSS
+   bool cudss_solver = false;
+#endif

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -102,6 +105,10 @@ int main(int argc, char *argv[])
   args.AddOption(&algebraic_ceed, "-a", "--algebraic",
                  "-no-a", "--no-algebraic",
                  "Use algebraic Ceed solver");
+#endif
+#ifdef MFEM_USE_CUDSS
+   args.AddOption(&cudss_solver, "-cudss", "--cudss-solver", "-no-cudss",
+                  "--no-cudss-solver", "Use the cuDSS Solver.");
 #endif
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
@@ -248,33 +255,51 @@ int main(int argc, char *argv[])
   // 13. Solve the linear system A X = B.
   //     * With full assembly, use the BoomerAMG preconditioner from hypre.
   //     * With partial assembly, use Jacobi smoothing, for now.
-   Solver *prec = NULL;
-   if (pa)
+#ifdef MFEM_USE_CUDSS
+   if (!pa && (Device::Allows(Backend::CUDA_MASK) && cudss_solver))
   {
-      if (UsesTensorBasis(fespace))
-      {
-         if (algebraic_ceed)
-         {
-            prec = new ceed::AlgebraicSolver(a, ess_tdof_list);
-         }
-         else
-         {
-            prec = new OperatorJacobiSmoother(a, ess_tdof_list);
-         }
-      }
+      // Solve using a direct solver with cuDSS
+      CuDSSSolver cudss_solver(MPI_COMM_WORLD);
+      cudss_solver.SetMatrixSymType(
+         CuDSSSolver::SYMMETRIC_POSITIVE_DEFINITE);
+      cudss_solver.SetMatrixViewType(CuDSSSolver::UPPER);
+      cudss_solver.SetOperator(*A);
+      cudss_solver.Mult(B, X);
   }
   else
+#endif
   {
-      prec = new HypreBoomerAMG;
+      Solver *prec = NULL;
+      if (pa)
+      {
+         if (UsesTensorBasis(fespace))
+         {
+            if (algebraic_ceed)
+            {
+               prec = new ceed::AlgebraicSolver(a, ess_tdof_list);
+            }
+            else
+            {
+               prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+            }
+         }
+      }
+      else
+      {
+         prec = new HypreBoomerAMG;
+      }
+      CGSolver cg(MPI_COMM_WORLD);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(2000);
+      cg.SetPrintLevel(1);
+      if (prec)
+      {
+         cg.SetPreconditioner(*prec);
+      }
+      cg.SetOperator(*A);
+      cg.Mult(B, X);
+      delete prec;
   }
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(1e-12);
-   cg.SetMaxIter(2000);
-   cg.SetPrintLevel(1);
-   if (prec) { cg.SetPreconditioner(*prec); }
-   cg.SetOperator(*A);
-   cg.Mult(B, X);
-   delete prec;

   // 14. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
@@ -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)
   {
@@ -95,6 +95,15 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

+   if (amg_elast && !static_cond && reorder_space)
+   {
+      if (myid == 0)
+         cerr << "\nThe AMG elasticity solver requires ordering byVDIM! "
+              << "Ignoring the specified option -nodes/--by-nodes.\n"
+              << endl;
+      reorder_space = false;
+   }
+
   // 3. Enable hardware devices such as GPUs, and programming models such as
   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
   Device device(device_config);
@@ -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);
@@ -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;
 }


@@ -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);
@@ -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.*
@@ -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
@@ -57,6 +57,8 @@ set(SRCS
  integ/lininteg_domain_grad.cpp
  integ/lininteg_domain_vectorfe.cpp
  integ/nonlininteg_vecconvection_pa.cpp
+  integ/nonlininteg_vecconvection_pa_diag.cpp
+  integ/nonlininteg_vecconvection_pa_grad.cpp
  integ/nonlininteg_vecconvection_mf.cpp
  coefficient.cpp
  complex_fem.cpp
@@ -171,8 +173,12 @@ 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
@@ -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);
            }
         }
@@ -2651,14 +2651,22 @@ public:
   void AddMultMF(const Vector &x, Vector &y) const override;
   bool SupportsCeed() const override { return DeviceCanUseCeed(); }

+   // PA AddMultPA kernels
   using VectorMassAddMultPAType =
      void(*)(const int,  const int,
              const Array<real_t>&, const Vector&,
              const Vector&, Vector&, const int, const int);
-
   MFEM_REGISTER_KERNELS(VectorMassAddMultPA,
                         VectorMassAddMultPAType,
                         (int, int, int));
+
+   // PA DiagonalPA kernels
+   using VectorMassAssembleDiagonalPAType =
+      void(*)(const int, const int, const int,
+              const real_t*, const real_t*, real_t*);
+   MFEM_REGISTER_KERNELS(VectorMassAssembleDiagonalPA,
+                         VectorMassAssembleDiagonalPAType,
+                         (int /*dim*/, int /*q1d*/));
 };


@@ -2710,7 +2718,7 @@ 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:
@@ -3060,6 +3068,24 @@ public:
   void AddMultPA(const Vector &x, Vector &y) const override;
   void AddMultTransposePA(const Vector &x, Vector &y) const override;

+   using VectorDivergenceAddMultPAType =
+      void (*)(const int ne,
+               const Array<real_t> &b, const Array<real_t> &g, const Array<real_t> &bt,
+               const Vector &op, const Vector &x, Vector &y,
+               const int tr_d1d, const int te_d1d, const int q1d);
+   MFEM_REGISTER_KERNELS(VectorDivergenceAddMultPA,
+                         VectorDivergenceAddMultPAType,
+                         (int, int, int, int));
+
+   using VectorDivergenceAddMultTransposePAType =
+      void (*)(const int ne,
+               const Array<real_t> &bt, const Array<real_t> &gt, const Array<real_t> &b,
+               const Vector &q, const Vector &x, Vector &y,
+               const int tr_d1d, const int te_d1d, const int q1d);
+   MFEM_REGISTER_KERNELS(VectorDivergenceAddMultTransposePA,
+                         VectorDivergenceAddMultTransposePAType,
+                         (int, int, int, int));
+
   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
                                         const FiniteElement &test_fe,
                                         const ElementTransformation &Trans);
@@ -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
@@ -830,15 +830,9 @@ ParComplexGridFunction::ParComplexGridFunction(ParMesh *m, std::istream &input)
      int vsize = pfes->GetVSize();
      Vector::Load(input, 2*vsize);

-      real_t *data_  = const_cast<real_t*>(HostRead());
-      for (int i = 0; i < vsize; i++)
-      {
-         if (pfes->GetDofSign(i) < 0)
-         {
-            data_[i] = -data_[i];
-            data_[i+vsize] = -data_[i+vsize];
-         }
-      }
+      real_t *h_data = HostReadWrite();
+      pfes->ApplyDofSigns(h_data);
+      pfes->ApplyDofSigns(h_data + vsize);


      // if the mesh is a legacy (v1.1) NC mesh, it has old vertex ordering
@@ -1051,15 +1045,14 @@ void ParComplexGridFunction::Save(std::ostream &os) const
   os << '\n';

   int vsize = pfes->GetVSize();
-   real_t *data_  = const_cast<real_t*>(HostRead());
-   for (int i = 0; i < vsize; i++)
-   {
-      if (pfes->GetDofSign(i) < 0)
-      {
-         data_[i] = -data_[i];
-         data_[i+vsize] = -data_[i+vsize];
-      }
-   }
+   // We use const_cast + HostRead (instead of HostReadWrite) because we only
+   // need to change the host data temporarily and this way we do not invalidate
+   // the data if it is on device. If we use HostReadWrite here, later calls to
+   // Read or ReadWrite will need to copy the data from host to device. With the
+   // approach used here, the host-to-device copy is avoided.
+   real_t *h_data = const_cast<real_t*>(HostRead());
+   pfes->ApplyDofSigns(h_data);
+   pfes->ApplyDofSigns(h_data + vsize);

   if (pfes->GetOrdering() == Ordering::byNODES)
   {
@@ -1070,14 +1063,8 @@ void ParComplexGridFunction::Save(std::ostream &os) const
      Vector::Print(os, pfes->GetVDim());
   }

-   for (int i = 0; i < vsize; i++)
-   {
-      if (pfes->GetDofSign(i) < 0)
-      {
-         data_[i] = -data_[i];
-         data_[i+vsize] = -data_[i+vsize];
-      }
-   }
+   pfes->ApplyDofSigns(h_data);
+   pfes->ApplyDofSigns(h_data + vsize);

   os.flush();
 }
@@ -114,6 +114,10 @@ void ConduitDataCollection::Save()
                                         n_mesh["fields"][name]);
   }

+   // TODO: in parallel, we need to call ParFiniteElementSpace::ApplyDofSigns
+   // for all ParGridFunction objects before and after saving, see
+   // ParGridFunction::Save.
+
   // save mesh data
   SaveMeshAndFields(myid,
                     n_mesh,
@@ -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";
@@ -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
      {
@@ -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
@@ -349,7 +349,7 @@ public:
       vector-valued finite elements, which is also the width of the
       DenseMatrix argument in
       CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape). */
-   int GetPhysRangeDim(int /* space_dim */) const { return vdim; }
+   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
@@ -360,7 +360,7 @@ public:
       finite elements, which is also the width of the DenseMatrix argument in
       CalcPhysCurlShape(ElementTransformation &Trans, DenseMatrix &curl_shape).
   */
-   int GetPhysCurlDim(int /* space_dim */) const { return cdim; }
+   virtual int GetPhysCurlDim(int /* space_dim */) const { return cdim; }

   /// Returns the Geometry::Type of the reference element.
   Geometry::Type GetGeomType() const { return geom_type; }
@@ -1017,7 +1017,7 @@ public:
   VectorFiniteElement(int D, Geometry::Type G, int Do, int O, int M,
                       int F = FunctionSpace::Pk);

-   int GetPhysRangeDim(int space_dim) const { return space_dim; }
+   int GetPhysRangeDim(int space_dim) const override { return space_dim; }
 };

 /// @brief Class for computing 1D special polynomials and their associated basis
@@ -663,8 +663,8 @@ public:
                         const int cb_type = BasisType::GaussLobatto,
                         const int ob_type = BasisType::GaussLegendre);

-   int GetPhysRangeDim(int space_dim) const { return 2; }
-   int GetPhysCurlDim(int space_dim) const { return 1; }
+   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;
@@ -708,8 +708,8 @@ private:
                           DenseMatrix &I) const;

 public:
-   int GetPhysRangeDim(int space_dim) const { return 3; }
-   int GetPhysCurlDim(int space_dim) const { return 3; }
+   int GetPhysRangeDim(int space_dim) const override { return 3; }
+   int GetPhysCurlDim(int space_dim) const override { return 3; }

   using FiniteElement::CalcVShape;
   using FiniteElement::CalcPhysCurlShape;
@@ -510,8 +510,8 @@ public:
   RT_R2D_SegmentElement(const int p,
                         const int ob_type = BasisType::GaussLegendre);

-   int GetPhysRangeDim(int space_dim) const { return 2; }
-   int GetPhysCurlDim(int space_dim) const { return 0; }
+   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;
@@ -550,8 +550,8 @@ private:
                           DenseMatrix &I) const;

 public:
-   int GetPhysRangeDim(int space_dim) const { return 3; }
-   int GetPhysCurlDim(int space_dim) const { return 0; }
+   int GetPhysRangeDim(int space_dim) const override { return 3; }
+   int GetPhysCurlDim(int space_dim) const override { return 0; }

   using FiniteElement::CalcVShape;

@@ -3934,6 +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");
@@ -3964,6 +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
 {
@@ -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;

@@ -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;
@@ -345,27 +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();
@@ -2050,6 +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;

@@ -2202,6 +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;
@@ -2355,6 +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;
@@ -2630,6 +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;
@@ -2945,6 +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;
@@ -2974,6 +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;
@@ -3030,9 +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;

@@ -3046,7 +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
@@ -3062,17 +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);

@@ -3082,6 +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);

@@ -3137,52 +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++)
   {
@@ -3198,15 +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(
@@ -5007,6 +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)
@@ -5057,10 +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);
@@ -5758,4 +5768,4 @@ std::pair<real_t, real_t> GridFunction::EstimateFunctionMaximum(
   return std::make_pair(global_max_lower, global_max_upper);
 }

-}
+}
@@ -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,
@@ -656,15 +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);

@@ -1735,8 +1767,8 @@ public:
                             const int ref_factor=1, const int vdim=-1) const;

   /// Computes the \ref PLBound for the gridfunction with number of control
-   /// points based on \p ref_factor, and returns the bounds for each element
-   /// ordered byNodes:
+   /// points based on @a ref_factor, and returns the bounds for each element
+   /// 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.
@@ -1770,7 +1802,7 @@ 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 byNodes:
+   /// 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,
@@ -1914,7 +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:
@@ -1922,13 +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);

@@ -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
@@ -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
@@ -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);
   }
@@ -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
@@ -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
@@ -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
@@ -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

@@ -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

@@ -91,15 +91,15 @@ void ElasticityAddMultPA(const int dim, const int nDofs,
 void ElasticityAssembleDiagonalPA(const int dim, const int nDofs,
                                  const CoefficientVector &lambda,
                                  const CoefficientVector &mu, const GeometricFactors &geom,
-                                  const DofToQuad &maps, QuadratureFunction &QVec, Vector &diag)
+                                  const DofToQuad &maps, const IntegrationRule &ir, Vector &diag)
 {
   switch (dim)
   {
      case 2:
-         ElasticityAssembleDiagonalPA_<2>(nDofs, lambda, mu, geom, maps, QVec, diag);
+         ElasticityAssembleDiagonalPA_<2>(nDofs, lambda, mu, geom, maps, ir, diag);
         break;
      case 3:
-         ElasticityAssembleDiagonalPA_<3>(nDofs, lambda, mu, geom, maps, QVec, diag);
+         ElasticityAssembleDiagonalPA_<3>(nDofs, lambda, mu, geom, maps, ir, diag);
         break;
      default:
         MFEM_ABORT("Only dimensions 2 and 3 supported.");
@@ -38,7 +38,6 @@
 #include "../../linalg/vector.hpp"
 #include "../../linalg/tensor.hpp"
 #include "../quadinterpolator.hpp"
-#include "../bilininteg.hpp"
 #include "../coefficient.hpp"
 #include "../qfunction.hpp"

@@ -133,12 +132,12 @@ void ElasticityAssembleEA(const int dim, const int i_block, const int j_block,
 /// @param[in] mu Quadrature function for second Lame param.
 /// @param[in] geom Geometric factors corresponding to fespace.
 /// @param[in] maps DofToQuad maps for one element (assume elements all same).
-/// @param QVec Scratch Q-Vector. nQuad x dim x dim x dim x dim x numEls.
+/// @param[in] ir Integration rule.
 /// @param[out] diag diagonal of A. nDofs x dim x numEls.
 void ElasticityAssembleDiagonalPA(const int dim, const int nDofs,
                                  const CoefficientVector &lambda,
                                  const CoefficientVector &mu, const GeometricFactors &geom,
-                                  const DofToQuad &maps, QuadratureFunction &QVec, Vector &diag);
+                                  const DofToQuad &maps, const IntegrationRule &ir, Vector &diag);

 /// Templated implementation of ElasticityAddMultPA.
 template<int dim, int i_block = -1, int j_block = -1>
@@ -280,77 +279,62 @@ void ElasticityAddMultPA_(const int nDofs, const FiniteElementSpace &fespace,
 template<int dim>
 void ElasticityAssembleDiagonalPA_(const int nDofs,
                                   const CoefficientVector &lambda,
-                                   const CoefficientVector &mu, const GeometricFactors &geom,
-                                   const DofToQuad &maps, QuadratureFunction &QVec, Vector &diag)
+                                   const CoefficientVector &mu,
+                                   const GeometricFactors &geom,
+                                   const DofToQuad &maps,
+                                   const IntegrationRule &ir,
+                                   Vector &diag)
 {
-   using future::tensor;
-   using future::make_tensor;
   using future::det;
   using future::inv;
+   using future::make_tensor;
+   using future::tensor;

   // Assuming all elements are the same
-   const auto &ir = QVec.GetIntRule(0);
   static constexpr int d = dim;
   const int numPoints = ir.GetNPoints();
-   const int numEls = lambda.Size()/numPoints;
+   const int numEls = lambda.Size() / numPoints;
+
   const auto lamDev = Reshape(lambda.Read(), numPoints, numEls);
   const auto muDev = Reshape(mu.Read(), numPoints, numEls);
   const auto J = Reshape(geom.J.Read(), numPoints, d, d, numEls);
-   auto Q = Reshape(QVec.ReadWrite(), numPoints, d,d, d, numEls);
   const real_t *ipWeights = ir.GetWeights().Read();
-   mfem::forall_2D(numEls, numPoints,1, [=] MFEM_HOST_DEVICE (int e)
-   {
-      MFEM_FOREACH_THREAD(p, x,numPoints)
-      {
-         auto invJ = inv(make_tensor<d, d>(
-         [&](int i, int j) { return J(p, i, j, e); }));
-         const real_t w = ipWeights[p] /det(invJ);
-         for (int n = 0; n < d; n++)
-         {
-            for (int m = 0; m < d; m++)
-            {
-               for (int q = 0; q < d; q++)
-               {
-                  // compute contraction of 4*sym(grad(u))sym(grad(v)) term.
-                  // this contraction could be made slightly cheaper using Voigt
-                  // notation, but repeated entries are summed for simplicity.
-                  real_t contraction = 0.;
-                  for (int a = 0; a < d; a++)
-                  {
-                     for (int b = 0; b < d; b++)
-                     {
-                        contraction += ((a == q)*invJ(m,b) + (b==q)*invJ(m,a))*((a == q)
-                                                                                *invJ(n, b) + (b==q)*invJ(n,a));
-                     }
-                  }
-                  // lambda*div(u)*div(v) + 2*mu*sym(grad(u))*sym(grad(v))
-                  // contraction = 4*sym(grad(u))sym(grad(v))
-                  Q(p,m,n,q,e) = w*(lamDev(p, e)*invJ(m,q)*invJ(n,q)
-                                    + 0.5*muDev(p, e)*contraction);
-               }
-            }
-         }
-      }
-   });
-
-   // Reduce quadrature function to an E-Vector
-   const auto QRead = Reshape(QVec.Read(), numPoints, d, d, d, numEls);
-   auto diagDev = Reshape(diag.Write(), nDofs, d, numEls);
   const auto G = Reshape(maps.G.Read(), numPoints, d, nDofs);
+   auto diagDev = Reshape(diag.Write(), nDofs, d, numEls);
+
   mfem::forall_2D(numEls, d, nDofs, [=] MFEM_HOST_DEVICE (int e)
   {
-      MFEM_FOREACH_THREAD(i, y, nDofs)
+      MFEM_FOREACH_THREAD_DIRECT(i, y, nDofs)
      {
-         MFEM_FOREACH_THREAD(q, x, d)
+         MFEM_FOREACH_THREAD_DIRECT(q, x, d)
         {
-            real_t sum = 0.;
-            for (int n = 0; n < d; n++)
+            real_t sum = 0.0;
+            for (int p = 0; p < numPoints; p++)
            {
-               for (int m = 0; m < d; m++)
+               auto invJ = inv(make_tensor<d, d>([&](int r, int c) { return J(p, r, c, e); }));
+               const real_t w = ipWeights[p] / det(invJ);
+
+               for (int n = 0; n < d; n++)
               {
-                  for (int p = 0; p < numPoints; p++ )
+                  for (int m = 0; m < d; m++)
                  {
-                     sum += QRead(p,m,n,q,e)*G(p,m,i)*G(p,n,i);
+                     // compute contraction of 4*sym(grad(u))sym(grad(v)) term.
+                     // this contraction could be made slightly cheaper using Voigt
+                     // notation, but repeated entries are summed for simplicity.
+                     real_t contraction = 0.;
+                     for (int a = 0; a < d; a++)
+                     {
+                        for (int b = 0; b < d; b++)
+                        {
+                           contraction += ((a == q) * invJ(m, b) + (b == q) * invJ(m, a)) *
+                                          ((a == q) * invJ(n, b) + (b == q) * invJ(n, a));
+                        }
+                     }
+                     // lambda*div(u)*div(v) + 2*mu*sym(grad(u))*sym(grad(v))
+                     // contraction = 4*sym(grad(u))sym(grad(v))
+                     const real_t Q = w *
+                                      (lamDev(p, e) * invJ(m, q) * invJ(n, q) + 0.5 * muDev(p, e) * contraction);
+                     sum += Q * G(p, m, i) * G(p, n, i);
                  }
               }
            }
@@ -10,7 +10,6 @@
 // CONTRIBUTING.md for details.

 #include "../bilininteg.hpp"
-#include "../gridfunc.hpp"
 #include "../qfunction.hpp"
 #include "bilininteg_elasticity_kernels.hpp"

@@ -59,9 +58,8 @@ void ElasticityIntegrator::AssemblePA(const FiniteElementSpace &fes)

 void ElasticityIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   q_vec->SetVDim(vdim*vdim*vdim*vdim);
   internal::ElasticityAssembleDiagonalPA(vdim, ndofs, *lambda_quad, *mu_quad,
-                                          *geom, *maps, *q_vec, diag);
+                                          *geom, *maps, *IntRule, diag);
 }

 void ElasticityIntegrator::AddMultPA(const Vector &x, Vector &y) const
@@ -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;
@@ -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("");
 }

@@ -205,157 +205,40 @@ void VectorMassIntegrator::AddMultPA(const Vector &x, Vector &y) const

 }

-template <const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal2D(const int NE,
-                                           const Array<real_t> &b,
-                                           const Vector &pa_data, Vector &diag,
-                                           const int d1d = 0, const int q1d = 0)
-{
-   constexpr int VDIM = 2;
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
-   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
-   const auto B = Reshape(b.Read(), Q1D, D1D);
-   const auto D = Reshape(pa_data.Read(), Q1D, Q1D, NE);
-   auto Y = Reshape(diag.ReadWrite(), D1D, D1D, VDIM, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE(int e)
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int max_D1D = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
-      constexpr int max_Q1D = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
-
-      real_t temp[max_Q1D][max_D1D];
-      for (int qx = 0; qx < Q1D; ++qx)
-      {
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            temp[qx][dy] = 0.0;
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               temp[qx][dy] += B(qy, dy) * B(qy, dy) * D(qx, qy, e);
-            }
-         }
-      }
-      for (int dy = 0; dy < D1D; ++dy)
-      {
-         for (int dx = 0; dx < D1D; ++dx)
-         {
-            real_t temp1 = 0.0;
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               temp1 += B(qx, dx) * B(qx, dx) * temp[qx][dy];
-            }
-            Y(dx, dy, 0, e) = temp1;
-            Y(dx, dy, 1, e) = temp1;
-         }
-      }
-   });
-}
-
-template <const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal3D(const int NE,
-                                           const Array<real_t> &B_,
-                                           const Vector &pa_data, Vector &diag,
-                                           const int d1d = 0, const int q1d = 0)
-{
-   constexpr int VDIM = 3;
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
-   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
-   const auto B = Reshape(B_.Read(), Q1D, D1D);
-   MFEM_VERIFY(pa_data.Size() == Q1D * Q1D * Q1D * NE, "pa_data size error");
-   const auto D = Reshape(pa_data.Read(), Q1D, Q1D, Q1D, NE);
-   auto Y = Reshape(diag.ReadWrite(), D1D, D1D, D1D, VDIM, NE);
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE(int e)
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      // the following variables are evaluated at compile time
-      constexpr int max_D1D = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
-      constexpr int max_Q1D = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
-
-      real_t temp[max_Q1D][max_Q1D][max_D1D];
-      for (int qx = 0; qx < Q1D; ++qx)
-      {
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               temp[qx][qy][dz] = 0.0;
-               for (int qz = 0; qz < Q1D; ++qz)
-               {
-                  temp[qx][qy][dz] +=
-                     B(qz, dz) * B(qz, dz) * D(qx, qy, qz, e);
-               }
-            }
-         }
-      }
-      real_t temp2[max_Q1D][max_D1D][max_D1D];
-      for (int qx = 0; qx < Q1D; ++qx)
-      {
-         for (int dz = 0; dz < D1D; ++dz)
-         {
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               temp2[qx][dy][dz] = 0.0;
-               for (int qy = 0; qy < Q1D; ++qy)
-               {
-                  temp2[qx][dy][dz] +=
-                     B(qy, dy) * B(qy, dy) * temp[qx][qy][dz];
-               }
-            }
-         }
-      }
-      for (int dz = 0; dz < D1D; ++dz)
-      {
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               real_t temp3 = 0.0;
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  temp3 += B(qx, dx) * B(qx, dx) * temp2[qx][dy][dz];
-               }
-               Y(dx, dy, dz, 0, e) = temp3;
-               Y(dx, dy, dz, 1, e) = temp3;
-               Y(dx, dy, dz, 2, e) = temp3;
-            }
-         }
-      }
-   });
-}
-
-static void PAVectorMassAssembleDiagonal(const int dim, const int D1D,
-                                         const int Q1D, const int NE,
-                                         const Array<real_t> &B,
-                                         const Vector &pa_data,
-                                         Vector &diag)
-{
-   if (dim == 2)
-   {
-      return PAVectorMassAssembleDiagonal2D(NE, B, pa_data, diag, D1D, Q1D);
-   }
-   else if (dim == 3)
-   {
-      return PAVectorMassAssembleDiagonal3D(NE, B, pa_data, diag, D1D, Q1D);
-   }
-   MFEM_ABORT("Dimension not implemented.");
-}
-
 void VectorMassIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   if (DeviceCanUseCeed()) { ceedOp->GetDiagonal(diag); }
-   else
-   {
-      MFEM_VERIFY(coeff_vdim == 1, "coeff_vdim != 1");
-      MFEM_VERIFY(!VQ && !MQ, "VQ and MQ not supported");
-      PAVectorMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data, diag);
-   }
+   if (DeviceCanUseCeed()) { return ceedOp->GetDiagonal(diag); }
+
+   MFEM_VERIFY(coeff_vdim == 1, "coeff_vdim != 1");
+   MFEM_VERIFY(!VQ && !MQ, "VQ and MQ not supported");
+
+   // Add the VectorMassAssembleDiagonalPA specializations
+   static const auto vector_mass_assemble_diagonal_kernel_specializations =
+      ( // 2D
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 2>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 3>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 4>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 5>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 6>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 7>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<2, 8>::Add(),
+         // 3D
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 2>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 3>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 4>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 5>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 6>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 7>::Add(),
+         VectorMassIntegrator::VectorMassAssembleDiagonalPA::Specialization<3, 8>::Add(),
+         true);
+   MFEM_CONTRACT_VAR(vector_mass_assemble_diagonal_kernel_specializations);
+
+   VectorMassAssembleDiagonalPA::Run(dim, quad1D, // templated arguments
+                                     ne, dofs1D, quad1D,
+                                     maps->B.Read(),
+                                     pa_data.Read(),
+                                     diag.ReadWrite());
+
 }

 } // namespace mfem
@@ -176,8 +176,145 @@ void SmemPAVectorMassApply3D(const int NE,
   });
 }

+template <int T_Q1D = 0, int T_MDQ = 16>
+static void SmemPAVectorMassAssembleDiagonal2D(const int ne,
+                                               const int d1d,
+                                               const int q1d,
+                                               const real_t *b_r,
+                                               const real_t *d_r,
+                                               real_t *y_rw)
+{
+   constexpr int VDIM = 2;
+
+   const int D1D = d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(Q1D <= T_MDQ && D1D <= Q1D, "");
+
+   const auto B = Reshape(b_r, Q1D, D1D);
+   const auto D = Reshape(d_r, Q1D, Q1D, ne);
+   auto Y = Reshape(y_rw, D1D, D1D, VDIM, ne);
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(
+      ne, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t sm[MQ1][MQ1];
+
+      MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            real_t u = 0.0;
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               u += B(qy, dy) * B(qy, dy) * D(qx, qy, e);
+            }
+            sm[qx][dy] = u;
+         }
+      }
+      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)
+            {
+               u += B(qx, dx) * B(qx, dx) * sm[qx][dy];
+            }
+            Y(dx, dy, 0, e) = u;
+            Y(dx, dy, 1, e) = u;
+         }
+      }
+   });
+}
+
+template <int T_Q1D = 0, int T_MDQ = 12>
+static void SmemPAVectorMassAssembleDiagonal3D(const int ne,
+                                               const int d1d,
+                                               const int q1d,
+                                               const real_t *b_r,
+                                               const real_t *d_r,
+                                               real_t *y_rw)
+{
+   constexpr int VDIM = 3;
+
+   const int D1D = d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(Q1D <= T_MDQ && D1D <= Q1D, "");
+
+   const auto B = Reshape(b_r, Q1D, D1D);
+   const auto D = Reshape(d_r, Q1D, Q1D, Q1D, ne);
+   auto Y = Reshape(y_rw, D1D, D1D, D1D, VDIM, ne);
+
+   mfem::forall_3D<T_Q1D*T_Q1D*T_Q1D>(
+      ne, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t sm[2][MQ1][MQ1][MQ1];
+
+      MFEM_FOREACH_THREAD_DIRECT(dz, z, D1D)
+      {
+         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)
+               {
+                  u += B(qz, dz) * B(qz, dz) * D(qx, qy, qz, e);
+               }
+               sm[0][dz][qy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD_DIRECT(dz, z, D1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               real_t u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += B(qy, dy) * B(qy, dy) * sm[0][dz][qy][qx];
+               }
+               sm[1][dz][dy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD_DIRECT(dz, z, D1D)
+      {
+         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)
+               {
+                  u += B(qx, dx) * B(qx, dx) * sm[1][dz][dy][qx];
+               }
+               Y(dx, dy, dz, 0, e) = u;
+               Y(dx, dy, dz, 1, e) = u;
+               Y(dx, dy, dz, 2, e) = u;
+            }
+         }
+      }
+   });
+}
+
 } // namespace internal

+// AddMultPA kernels
 template<int DIM, int T_D1D, int T_Q1D>
 VectorMassIntegrator::VectorMassAddMultPAType
 VectorMassIntegrator::VectorMassAddMultPA::Kernel()
@@ -190,11 +327,11 @@ VectorMassIntegrator::VectorMassAddMultPA::Kernel()
   {
      return internal::SmemPAVectorMassApply3D<T_D1D, T_Q1D>;
   }
-   MFEM_ABORT("Unsupported kernel");
+   else { MFEM_ABORT("Unsupported kernel"); }
 }

 inline VectorMassIntegrator::VectorMassAddMultPAType
-VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int d1d, int q1d)
+VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int, int)
 {
   if (dim == 2)
   {
@@ -207,6 +344,36 @@ VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int d1d, int q1d)
   else { MFEM_ABORT("Unsupported kernel"); }
 }

+// DiagonalPA kernels
+template<int DIM, int T_Q1D>
+VectorMassIntegrator::VectorMassAssembleDiagonalPAType
+VectorMassIntegrator::VectorMassAssembleDiagonalPA::Kernel()
+{
+   if constexpr (DIM == 2)
+   {
+      return internal::SmemPAVectorMassAssembleDiagonal2D<T_Q1D>;
+   }
+   else if constexpr (DIM == 3)
+   {
+      return internal::SmemPAVectorMassAssembleDiagonal3D<T_Q1D>;
+   }
+   else { MFEM_ABORT("Unsupported kernel"); }
+}
+
+inline VectorMassIntegrator::VectorMassAssembleDiagonalPAType
+VectorMassIntegrator::VectorMassAssembleDiagonalPA::Fallback(int dim, int)
+{
+   if (dim == 2)
+   {
+      return internal::SmemPAVectorMassAssembleDiagonal2D;
+   }
+   else if (dim == 3)
+   {
+      return internal::SmemPAVectorMassAssembleDiagonal3D;
+   }
+   else { MFEM_ABORT("Unsupported kernel"); }
+}
+
 /// \endcond DO_NOT_DOCUMENT

 } // namespace mfem
@@ -0,0 +1,351 @@
+// 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 <utility>
+
+#include "../kernels.hpp"
+#include "../nonlininteg.hpp"
+#include "../../general/forall.hpp"
+
+namespace mfem
+{
+
+template<int T_D1D = 0, int T_Q1D = 0, int T_MDQ = 16>
+static void SmemPAConvectionNLGradDiagonal2D(const int NE,
+                                             const real_t *b,
+                                             const real_t *g,
+                                             const real_t *a,
+                                             const real_t *u,
+                                             real_t *de,
+                                             const int d1d,
+                                             const int q1d)
+{
+   static constexpr int VDIM = 2, DIM = 2;
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, NE);
+   const auto U = Reshape(u, D1D, D1D, VDIM, NE);
+   auto D = Reshape(de, D1D, D1D, VDIM, NE);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MD1 = T_D1D ? T_D1D : T_MDQ;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t sM[3][MQ1][MQ1], sQ[3][MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::v_regs2d_t<VDIM, MQ1> r0, r1;
+      kernels::internal::vd_regs2d_t<VDIM, DIM, MQ1> g0, g1;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, g, sG);
+
+      kernels::internal::LoadDofs2d(e, D1D, U, r0);
+      kernels::internal::Eval2d(D1D, Q1D, sM[0], sB, r0, r1);
+
+      kernels::internal::LoadDofs2d(e, D1D, U, g0);
+      kernels::internal::Grad2d(D1D, Q1D, sM[0], sB, sG, g0, g1);
+
+      for (int v = 0; v < VDIM; ++v)
+      {
+         future::tensor<real_t, VDIM> e_v = {};
+         e_v[v] = real_t(1);
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               const future::tensor<real_t, VDIM> u_val =
+               {
+                  r1[0][qy][qx], r1[1][qy][qx]
+               };
+               const future::tensor<real_t, VDIM, DIM> Q_adj =
+               {
+                  {  { A(0, 0, qx, qy, e), A(1, 0, qx, qy, e) },
+                     { A(0, 1, qx, qy, e), A(1, 1, qx, qy, e) }
+                  }
+               };
+               const future::tensor<real_t, VDIM, DIM> grad_U =
+               {
+                  {  { g1[0][0][qy][qx], g1[1][0][qy][qx] },
+                     { g1[0][1][qy][qx], g1[1][1][qy][qx] }
+                  }
+               };
+               const auto one = Q_adj * u_val;
+               const auto two = transpose(grad_U) * (Q_adj * e_v);
+               sQ[0][qx][qy] = one[0];
+               sQ[1][qx][qy] = one[1];
+               sQ[2][qx][qy] = two[v];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               real_t s[3] = {};
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  const real_t By = sB[dy][qy], Gy = sG[dy][qy];
+                  s[0] += By * By * sQ[0][qx][qy];
+                  s[1] += Gy * By * sQ[1][qx][qy];
+                  s[2] += By * By * sQ[2][qx][qy];
+               }
+               sM[0][qx][dy] = s[0];
+               sM[1][qx][dy] = s[1];
+               sM[2][qx][dy] = s[2];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         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], Gx = sG[dx][qx];
+                  d += Gx * Bx * sM[0][qx][dy] +
+                       Bx * Bx * sM[1][qx][dy] +
+                       Bx * Bx * sM[2][qx][dy];
+               }
+               D(dx, dy, v, e) += d;
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0, int T_MDQ = 16>
+static void SmemPAConvectionNLGradDiagonal3D(const int NE,
+                                             const real_t *b,
+                                             const real_t *g,
+                                             const real_t *a,
+                                             const real_t *u,
+                                             real_t *de,
+                                             const int d1d,
+                                             const int q1d)
+{
+   static constexpr int VDIM = 3, DIM = 3;
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, Q1D, NE);
+   const auto U = Reshape(u, D1D, D1D, D1D, VDIM, NE);
+   auto D = Reshape(de, D1D, D1D, D1D, VDIM, NE);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MD1 = T_D1D ? T_D1D : T_MDQ;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t sM[4][MQ1][MQ1], sQ[4][MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::v_regs3d_t<VDIM, MQ1> r0, r1;
+      kernels::internal::vd_regs3d_t<VDIM, DIM, MQ1> g0, g1;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, g, sG);
+
+      kernels::internal::LoadDofs3d(e, D1D, U, r0);
+      kernels::internal::Eval3d(D1D, Q1D, sM[0], sB, r0, r1);
+
+      kernels::internal::LoadDofs3d(e, D1D, U, g0);
+      kernels::internal::Grad3d(D1D, Q1D, sM[0], sB, sG, g0, g1);
+
+      for (int v = 0; v < VDIM; ++v)
+      {
+         future::tensor<real_t, VDIM> e_v = {};
+         e_v[v] = real_t(1);
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t s[4] = {};
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     const future::tensor<real_t, VDIM> u_val =
+                     {
+                        r1[0][qz][qy][qx], r1[1][qz][qy][qx], r1[2][qz][qy][qx]
+                     };
+                     const future::tensor<real_t, VDIM, DIM> Q_adj = {{
+                           {A(0,0,qx,qy,qz,e), A(1,0,qx,qy,qz,e), A(2,0,qx,qy,qz,e)},
+                           {A(0,1,qx,qy,qz,e), A(1,1,qx,qy,qz,e), A(2,1,qx,qy,qz,e)},
+                           {A(0,2,qx,qy,qz,e), A(1,2,qx,qy,qz,e), A(2,2,qx,qy,qz,e)}
+                        }
+                     };
+                     const future::tensor<real_t, VDIM, DIM> grad_U = {{
+                           {g1[0][0][qz][qy][qx], g1[1][0][qz][qy][qx], g1[2][0][qz][qy][qx]},
+                           {g1[0][1][qz][qy][qx], g1[1][1][qz][qy][qx], g1[2][1][qz][qy][qx]},
+                           {g1[0][2][qz][qy][qx], g1[1][2][qz][qy][qx], g1[2][2][qz][qy][qx]}
+                        }
+                     };
+                     const auto one = Q_adj * u_val;
+                     const auto two = transpose(grad_U) * (Q_adj * e_v);
+
+                     const real_t Bz = sB[dz][qz], Gz = sG[dz][qz];
+                     s[0] += one[0] * Bz * Bz;
+                     s[1] += one[1] * Bz * Bz;
+                     s[2] += one[2] * Bz * Gz;
+                     s[3] += two[v] * Bz * Bz;
+                  }
+                  sQ[0][qx][qy] = s[0];
+                  sQ[1][qx][qy] = s[1];
+                  sQ[2][qx][qy] = s[2];
+                  sQ[3][qx][qy] = s[3];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t s[4] = {};
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     const real_t By = sB[dy][qy], Gy = sG[dy][qy];
+                     s[0] += By * By * sQ[0][qx][qy];
+                     s[1] += Gy * By * sQ[1][qx][qy];
+                     s[2] += By * By * sQ[2][qx][qy];
+                     s[3] += By * By * sQ[3][qx][qy];
+                  }
+                  sM[0][dy][qx] = s[0];
+                  sM[1][dy][qx] = s[1];
+                  sM[2][dy][qx] = s[2];
+                  sM[3][dy][qx] = s[3];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            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], Gx = sG[dx][qx];
+                     d += Gx * Bx * sM[0][dy][qx];
+                     d += Bx * Bx * sM[1][dy][qx];
+                     d += Bx * Bx * sM[2][dy][qx];
+                     d += Bx * Bx * sM[3][dy][qx];
+                  }
+                  D(dx, dy, dz, v, e) += d;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
+void VectorConvectionNLFIntegrator::AssembleGradDiagonalPA(Vector &de) const
+{
+   if (dim == 2)
+   {
+      if (static auto ini = false; !std::exchange(ini, true))
+      {
+         VectorConvectionNLFGradDiagPA2D::Specialization<2, 2>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<2, 3>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<3, 4>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<3, 5>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<4, 5>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<4, 6>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<5, 7>::Add();
+         VectorConvectionNLFGradDiagPA2D::Specialization<5, 8>::Add();
+      }
+      VectorConvectionNLFGradDiagPA2D::Run(d1d, q1d, ne,
+                                           maps->B.Read(),
+                                           maps->G.Read(),
+                                           pa_adj.Read(),
+                                           pa_u.Read(),
+                                           de.ReadWrite(),
+                                           d1d, q1d);
+   }
+   else if (dim == 3)
+   {
+      if (static auto ini = false; !std::exchange(ini, true))
+      {
+         VectorConvectionNLFGradDiagPA3D::Specialization<2, 3>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<2, 4>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<2, 5>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<3, 4>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<3, 5>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<3, 6>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<4, 6>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<4, 7>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<4, 8>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<5, 7>::Add();
+         VectorConvectionNLFGradDiagPA3D::Specialization<5, 8>::Add();
+      }
+      VectorConvectionNLFGradDiagPA3D::Run(d1d, q1d, ne,
+                                           maps->B.Read(),
+                                           maps->G.Read(),
+                                           pa_adj.Read(),
+                                           pa_u.Read(),
+                                           de.ReadWrite(),
+                                           d1d, q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+   }
+}
+
+/// \cond DO_NOT_DOCUMENT
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPA2D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return SmemPAConvectionNLGradDiagonal2D<T_D1D, T_Q1D>;
+}
+
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPA2D::Fallback
+(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= 16, "d1d > 16 is not supported");
+   MFEM_VERIFY(q1d <= 16, "q1d > 16 is not supported");
+   return SmemPAConvectionNLGradDiagonal2D<>;
+}
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPA3D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return SmemPAConvectionNLGradDiagonal3D<T_D1D, T_Q1D>;
+}
+
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFGradDiagPA3D::Fallback
+(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= 16, "d1d > 16 is not supported");
+   MFEM_VERIFY(q1d <= 16, "q1d > 16 is not supported");
+   return SmemPAConvectionNLGradDiagonal3D<>;
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem
@@ -0,0 +1,319 @@
+// 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 <utility>
+
+#include "../kernels.hpp"
+#include "../nonlininteg.hpp"
+#include "../../general/forall.hpp"
+
+namespace mfem
+{
+
+void VectorConvectionNLFIntegrator::AssembleGradPA(
+   const Vector &u, const FiniteElementSpace &fes)
+{
+   this->pa_u = u;
+   AssemblePA(fes);
+
+   if (static auto done = false; !std::exchange(done, true))
+   {
+      // 2D
+      VectorConvectionNLFAddMultGradPA2D::Specialization<2, 2>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<2, 3>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<3, 4>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<3, 5>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<4, 5>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<4, 6>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<5, 7>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<5, 8>::Add();
+      VectorConvectionNLFAddMultGradPA2D::Specialization<6, 8>::Add();
+      // 3D
+      VectorConvectionNLFAddMultGradPA3D::Specialization<2, 3>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<2, 4>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<2, 5>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<3, 4>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<3, 5>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<3, 6>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<4, 5>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<4, 6>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<5, 6>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<4, 7>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<4, 8>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<5, 7>::Add();
+      VectorConvectionNLFAddMultGradPA3D::Specialization<5, 8>::Add();
+   }
+}
+
+template<int T_D1D = 0, int T_Q1D = 0, int T_MDQ = 16>
+static void SmemPAConvectionNLGradApply2D(const int ne,
+                                          const real_t *b,
+                                          const real_t *g,
+                                          const real_t *a,
+                                          const real_t *u,
+                                          const real_t *du,
+                                          real_t *y,
+                                          const int d1d,
+                                          const int q1d)
+{
+   static constexpr int VDIM = 2, DIM = 2;
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, ne);
+   const auto U = Reshape(u, D1D, D1D, VDIM, ne);
+   const auto dU = Reshape(du, D1D, D1D, VDIM, ne);
+   auto Y = Reshape(y, D1D, D1D, VDIM, ne);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(ne, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MD1 = T_D1D ? T_D1D : T_MDQ;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::vd_regs2d_t<VDIM, DIM, MQ1> g0, g1, g2;
+      kernels::internal::v_regs2d_t<DIM, MQ1> r0, r1, r2;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, g, sG);
+
+      kernels::internal::LoadDofs2d(e, D1D, dU, g0);
+      kernels::internal::Grad2d(D1D, Q1D, smem, sB, sG, g0, g1); // δu gradient
+
+      kernels::internal::LoadDofs2d(e, D1D, U, r0);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, r0, r2); // u value
+
+      kernels::internal::LoadDofs2d(e, D1D, dU, r0);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, r0, r1); // δu value
+
+      kernels::internal::LoadDofs2d(e, D1D, U, g0);
+      kernels::internal::Grad2d(D1D, Q1D, smem, sB, sG, g0, g2); // u gradient
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            // First part of the Jacobian: u·∇δu
+            const future::tensor<real_t, DIM> u_val =
+            {
+               r2[0][qy][qx], r2[1][qy][qx]
+            };
+            const future::tensor<real_t, VDIM, DIM> Q_adj =
+            {
+               {  { A(0, 0, qx, qy, e), A(1, 0, qx, qy, e) },
+                  { A(0, 1, qx, qy, e), A(1, 1, qx, qy, e) }
+               }
+            };
+            const future::tensor<real_t, VDIM, DIM> grad_dU =
+            {
+               {  { g1[0][0][qy][qx], g1[1][0][qy][qx] },
+                  { g1[0][1][qy][qx], g1[1][1][qy][qx] }
+               }
+            };
+            const auto one = transpose(grad_dU) * (Q_adj * u_val);
+
+            // Second part of the Jacobian: δu·∇u
+            const future::tensor<real_t, DIM> du_val =
+            {
+               r1[0][qy][qx], r1[1][qy][qx]
+            };
+            const future::tensor<real_t, VDIM, DIM> grad_U =
+            {
+               {  { g2[0][0][qy][qx], g2[1][0][qy][qx] },
+                  { g2[0][1][qy][qx], g2[1][1][qy][qx] }
+               }
+            };
+            const auto two = transpose(grad_U) * (Q_adj * du_val);
+
+            // u⋅∇δu + δu⋅∇u
+            r0[0][qy][qx] = one[0] + two[0];
+            r0[1][qy][qx] = one[1] + two[1];
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, r0, r1);
+      kernels::internal::WriteDofs2d(e, D1D, r1, Y);
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0, int T_MDQ = 16>
+static void SmemPAConvectionNLGradApply3D(const int ne,
+                                          const real_t *b,
+                                          const real_t *g,
+                                          const real_t *a,
+                                          const real_t *u,
+                                          const real_t *du,
+                                          real_t *y,
+                                          const int d1d,
+                                          const int q1d)
+{
+   static constexpr int VDIM = 3, DIM = 3;
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, Q1D, ne);
+   const auto U = Reshape(u, D1D, D1D, D1D, VDIM, ne);
+   const auto dU = Reshape(du, D1D, D1D, D1D, VDIM, ne);
+   auto Y = Reshape(y, D1D, D1D, D1D, VDIM, ne);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(ne, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MD1 = T_D1D ? T_D1D : T_MDQ;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MDQ;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::v_regs3d_t<VDIM, MQ1> r0, r1, r2;
+      kernels::internal::vd_regs3d_t<VDIM, DIM, MQ1> g0, g1, g2;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, g, sG);
+
+      kernels::internal::LoadDofs3d(e, D1D, dU, g0);
+      kernels::internal::Grad3d(D1D, Q1D, smem, sB, sG, g0, g1); // δu gradient
+
+      kernels::internal::LoadDofs3d(e, D1D, U, r0);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, r0, r2); // u value
+
+      kernels::internal::LoadDofs3d(e, D1D, dU, r0);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, r0, r1); // δu value
+
+      kernels::internal::LoadDofs3d(e, D1D, U, g0);
+      kernels::internal::Grad3d(D1D, Q1D, smem, sB, sG, g0, g2); // u gradient
+
+      for (int qz = 0; qz < Q1D; qz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               // First part of the Jacobian: u·∇δu
+               const future::tensor<real_t, DIM> u_val =
+               {
+                  r2[0][qz][qy][qx],
+                  r2[1][qz][qy][qx],
+                  r2[2][qz][qy][qx]
+               };
+               const future::tensor<real_t, VDIM, DIM> Q_adj = {{
+                     {A(0,0,qx,qy,qz,e), A(1,0,qx,qy,qz,e), A(2,0,qx,qy,qz,e)},
+                     {A(0,1,qx,qy,qz,e), A(1,1,qx,qy,qz,e), A(2,1,qx,qy,qz,e)},
+                     {A(0,2,qx,qy,qz,e), A(1,2,qx,qy,qz,e), A(2,2,qx,qy,qz,e)}
+                  }
+               };
+               const future::tensor<real_t, DIM, DIM> grad_dU = {{
+                     {g1[0][0][qz][qy][qx], g1[1][0][qz][qy][qx], g1[2][0][qz][qy][qx]},
+                     {g1[0][1][qz][qy][qx], g1[1][1][qz][qy][qx], g1[2][1][qz][qy][qx]},
+                     {g1[0][2][qz][qy][qx], g1[1][2][qz][qy][qx], g1[2][2][qz][qy][qx]}
+                  }
+               };
+               const auto one = transpose(grad_dU) * (Q_adj * u_val);
+
+               // Second part of the Jacobian: δu·∇u
+               const future::tensor<real_t, DIM> du_val =
+               {
+                  r1[0][qz][qy][qx], r1[1][qz][qy][qx], r1[2][qz][qy][qx]
+               };
+               const future::tensor<real_t, VDIM, DIM> grad_U = {{
+                     {g2[0][0][qz][qy][qx], g2[1][0][qz][qy][qx], g2[2][0][qz][qy][qx]},
+                     {g2[0][1][qz][qy][qx], g2[1][1][qz][qy][qx], g2[2][1][qz][qy][qx]},
+                     {g2[0][2][qz][qy][qx], g2[1][2][qz][qy][qx], g2[2][2][qz][qy][qx]}
+                  }
+               };
+               const auto two = transpose(grad_U) * (Q_adj * du_val);
+
+               // u⋅∇δu + δu⋅∇u
+               r0[0][qz][qy][qx] = one[0] + two[0];
+               r0[1][qz][qy][qx] = one[1] + two[1];
+               r0[2][qz][qy][qx] = one[2] + two[2];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, r0, r1);
+      kernels::internal::WriteDofs3d(e, D1D, r1, Y);
+   });
+}
+
+void VectorConvectionNLFIntegrator::AddMultGradPA(const Vector &x,
+                                                  Vector &y) const
+{
+   if (dim == 2)
+   {
+      VectorConvectionNLFAddMultGradPA2D::Run(d1d, q1d, ne,
+                                              maps->B.Read(),
+                                              maps->G.Read(),
+                                              pa_adj.Read(),
+                                              pa_u.Read(),
+                                              x.Read(),
+                                              y.ReadWrite(),
+                                              d1d, q1d);
+   }
+   else if (dim == 3)
+   {
+      VectorConvectionNLFAddMultGradPA3D::Run(d1d, q1d, ne,
+                                              maps->B.Read(),
+                                              maps->G.Read(),
+                                              pa_adj.Read(),
+                                              pa_u.Read(),
+                                              x.Read(),
+                                              y.ReadWrite(),
+                                              d1d, q1d);
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported dimension");
+   }
+}
+
+/// \cond DO_NOT_DOCUMENT
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPA2D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return SmemPAConvectionNLGradApply2D<T_D1D, T_Q1D>;
+}
+
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPA2D::Fallback
+(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= 16, "d1d > 16 is not supported");
+   MFEM_VERIFY(q1d <= 16, "q1d > 16 is not supported");
+   return SmemPAConvectionNLGradApply2D<>;
+}
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPA3D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return SmemPAConvectionNLGradApply3D<T_D1D, T_Q1D>;
+}
+
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPAType
+VectorConvectionNLFIntegrator::VectorConvectionNLFAddMultGradPA3D::Fallback
+(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= 16, "d1d > 16 is not supported");
+   MFEM_VERIFY(q1d <= 16, "q1d > 16 is not supported");
+   return SmemPAConvectionNLGradApply3D<>;
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem
@@ -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:
@@ -83,7 +83,7 @@ constexpr int SetMaxOf(int n) { return NextMultipleOf<4>(n); }
 #endif // CUDA/HIP && DEVICE_COMPILE

 /// Load 2D matrix into shared memory
-template <int MQ1>
+template <int MQ1, bool TRANSPOSE = false>
 inline MFEM_HOST_DEVICE void LoadMatrix(const int d1d, const int q1d,
                                        const real_t *M, real_t (*N)[MQ1])
 {
@@ -91,7 +91,14 @@ inline MFEM_HOST_DEVICE void LoadMatrix(const int d1d, const int q1d,
   {
      MFEM_FOREACH_THREAD_DIRECT(qx, x, q1d)
      {
-         N[dy][qx] = M[dy * q1d + qx];
+         if constexpr (TRANSPOSE)
+         {
+            N[dy][qx] = M[qx * d1d + dy];
+         }
+         else
+         {
+            N[dy][qx] = M[dy * q1d + qx];
+         }
      }
   }
   MFEM_SYNC_THREAD;
@@ -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);
            }
         }
@@ -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; }

@@ -284,12 +284,12 @@ GeometricMultigrid::GeometricMultigrid(
   ownedProlongations.SetSize(nlevels - 1);
   ownedProlongations = have_ess_bdr;

-   if (have_ess_bdr)
+   essentialTrueDofs.SetSize(nlevels);
+   for (int level = 0; level < nlevels; ++level)
   {
-      essentialTrueDofs.SetSize(nlevels);
-      for (int level = 0; level < nlevels; ++level)
+      essentialTrueDofs[level] = new Array<int>;
+      if (have_ess_bdr)
      {
-         essentialTrueDofs[level] = new Array<int>;
         fespaces.GetFESpaceAtLevel(level).GetEssentialTrueDofs(
            ess_bdr, *essentialTrueDofs[level]);
      }
@@ -187,8 +187,7 @@ public:
   /// mesh boundary element attributes that define the essential DOFs.
   ///
   /// If @a ess_bdr is empty, or all its entries are 0, then no essential
-   /// boundary conditions are imposed and the protected array essentialTrueDofs
-   /// remains empty.
+   /// boundary conditions are imposed.
   GeometricMultigrid(const FiniteElementSpaceHierarchy& fespaces_,
                      const Array<int> &ess_bdr);

@@ -18,6 +18,7 @@
 #include "fespace.hpp"
 #include "ceed/interface/operator.hpp"
 #include "integrator.hpp"
+#include "kernel_dispatch.hpp"

 namespace mfem
 {
@@ -384,10 +385,10 @@ private:
   DenseMatrix dshape, dshapex, EF, gradEF, ELV, elmat_comp;
   Vector shape;
   // PA extension
-   Vector pa_data;
+   int dim, ne, nq, d1d, q1d;
+   Vector pa_adj, pa_u;
   const DofToQuad *maps;         ///< Not owned
   const GeometricFactors *geom;  ///< Not owned
-   int dim, ne, nq;

 public:
   VectorConvectionNLFIntegrator(Coefficient &q): Q(&q) { }
@@ -411,12 +412,51 @@ public:

   void AssemblePA(const FiniteElementSpace &fes) override;

-   void AssembleMF(const FiniteElementSpace &fes) override;
+   void AssembleGradPA(const Vector &x, const FiniteElementSpace &fes) override;

   void AddMultPA(const Vector &x, Vector &y) const override;

-   void AddMultMF(const Vector &x, Vector &y) const override;
+   using VectorConvectionNLFAddMultPAType =
+      void(*)(const int ne, const real_t *B, const real_t *G, const real_t *A,
+              const real_t *x, real_t *y,
+              const int d1d, const int q1d);
+   MFEM_REGISTER_KERNELS(VectorConvectionNLFAddMultPA,
+                         VectorConvectionNLFAddMultPAType,
+                         (int, int, int));

+   void AddMultGradPA(const Vector &x, Vector &y) const override;
+
+   using VectorConvectionNLFAddMultGradPAType =
+      void(*)(const int ne, const real_t *B, const real_t *G, const real_t *A,
+              const real_t *u, const real_t *x, real_t *y,
+              const int d1d, const int q1d);
+
+   MFEM_REGISTER_KERNELS(VectorConvectionNLFAddMultGradPA2D,
+                         VectorConvectionNLFAddMultGradPAType,
+                         (int, int));
+
+   MFEM_REGISTER_KERNELS(VectorConvectionNLFAddMultGradPA3D,
+                         VectorConvectionNLFAddMultGradPAType,
+                         (int, int));
+
+   void AssembleGradDiagonalPA(Vector &) const override;
+
+   using VectorConvectionNLFGradDiagPAType =
+      void (*)(const int ne, const real_t *B, const real_t *G, const real_t *A,
+               const real_t *u, real_t *y,
+               const int d1d, const int q1d);
+
+   MFEM_REGISTER_KERNELS(VectorConvectionNLFGradDiagPA2D,
+                         VectorConvectionNLFGradDiagPAType,
+                         (int, int));
+
+   MFEM_REGISTER_KERNELS(VectorConvectionNLFGradDiagPA3D,
+                         VectorConvectionNLFGradDiagPAType,
+                         (int, int));
+
+   void AssembleMF(const FiniteElementSpace &fes) override;
+
+   void AddMultMF(const Vector &x, Vector &y) const override;

 protected:
   const IntegrationRule* GetDefaultIntegrationRule(
@@ -349,6 +349,7 @@ void ParFiniteElementSpace::GetGroupComm(
      }
   }

+   bool have_sign_flips = false;
   if (g_ldof_sign)
   {
      g_ldof_sign->SetSize(GetNDofs());
@@ -428,6 +429,7 @@ void ParFiniteElementSpace::GetGroupComm(
                  if (g_ldof_sign)
                  {
                     (*g_ldof_sign)[dofs[l]] = -1;
+                     have_sign_flips = true;
                  }
               }
               else
@@ -466,6 +468,7 @@ void ParFiniteElementSpace::GetGroupComm(
                  if (g_ldof_sign)
                  {
                     (*g_ldof_sign)[dofs[l]] = -1;
+                     have_sign_flips = true;
                  }
               }
               else
@@ -504,6 +507,7 @@ void ParFiniteElementSpace::GetGroupComm(
                  if (g_ldof_sign)
                  {
                     (*g_ldof_sign)[dofs[l]] = -1;
+                     have_sign_flips = true;
                  }
               }
               else
@@ -527,12 +531,18 @@ void ParFiniteElementSpace::GetGroupComm(
      group_ldof.GetI()[gr+1] = group_ldof_counter;
   }

+   if (g_ldof_sign && have_sign_flips == false)
+   {
+      g_ldof_sign->DeleteAll();
+   }
+
   gc.Finalize();
 }

 void ParFiniteElementSpace::ApplyLDofSigns(Array<int> &dofs) const
 {
   MFEM_ASSERT(Conforming(), "wrong code path");
+   if (!HaveDofSigns()) { return; }

   for (int i = 0; i < dofs.Size(); i++)
   {
@@ -559,6 +569,24 @@ void ParFiniteElementSpace::ApplyLDofSigns(Table &el_dof) const
   ApplyLDofSigns(all_dofs);
 }

+void ParFiniteElementSpace::ApplyDofSigns(real_t *h_data) const
+{
+   if (!HaveDofSigns()) { return; }
+
+   const bool byvdim = (ordering == Ordering::byVDIM);
+   for (int i = 0; i < ndofs; i++)
+   {
+      if (ldof_sign[i] < 0)
+      {
+         for (int d = 0; d < vdim; d++)
+         {
+            const int idx = byvdim ? d+vdim*i : i+ndofs*d;
+            h_data[idx] = -h_data[idx];
+         }
+      }
+   }
+}
+
 void ParFiniteElementSpace::GetElementDofs(int i, Array<int> &dofs,
                                           DofTransformation &doftrans) const
 {
@@ -1193,15 +1221,15 @@ void ParFiniteElementSpace::GetEssentialTrueDofsVar(const Array<int>
   MFEM_VERIFY(IsVariableOrder() && R,
               "GetEssentialTrueDofsVar is only for variable-order spaces");

-   true_ess_dofs.SetSize(R->Height(), Device::GetDeviceMemoryType());
+   true_ess_dofs.SetSize(R->Height());
+   true_ess_dofs.HostWrite();
+   true_ess_dofs = 0;

   const int ntdofs = tdof2ldof.Size();
   MFEM_VERIFY(vdim * ntdofs == R->NumRows() &&
               vdim * ntdofs == true_ess_dofs.Size(), "");
   MFEM_VERIFY(ldof_ltdof.Size() == ndofs && ess_dofs.Size() == vdim * ndofs, "");

-   true_ess_dofs = 0;
-
   const bool bynodes = (ordering == Ordering::byNODES);
   const int vdim_factor = bynodes ? 1 : vdim;
   const int num_true_dofs = R->NumRows() / vdim;
@@ -340,8 +340,20 @@ public:

   inline ParMesh *GetParMesh() const { return pmesh; }

-   int GetDofSign(int i)
-   { return NURBSext || Nonconforming() ? 1 : ldof_sign[VDofToDof(i)]; }
+   /** @brief Return true if the parallel FE space has DOFs with signs opposite
+       of the DOFs in the respective serial FE space. */
+   bool HaveDofSigns() const { return ldof_sign.Size() != 0; }
+
+   /** @brief Apply the DOF signs to the given host data @a h_data which must be
+       of size GetVSize() if HaveDofSigns() is true. If HaveDofSigns() is false,
+       this method is no-op and returns immediately. */
+   void ApplyDofSigns(real_t *h_data) const;
+
+   /** @brief Return -1 if the given (vector) DOF @a i has a sign opposite of
+       the DOF in the respecive serial FE space. Otherwise, return 1. */
+   int GetDofSign(int i) const
+   { return !HaveDofSigns() ? 1 : ldof_sign[VDofToDof(i)]; }
+
   HYPRE_BigInt *GetDofOffsets()     const { return dof_offsets; }
   HYPRE_BigInt *GetTrueDofOffsets() const { return tdof_offsets; }
   HYPRE_BigInt GlobalVSize() const
@@ -80,6 +80,8 @@ ParGridFunction::ParGridFunction(ParMesh *pmesh, std::istream &input)
                                    fes->GetOrdering());
   delete fes;
   fes = pfes;
+
+   pfes->ApplyDofSigns(HostReadWrite());
 }

 void ParGridFunction::Update()
@@ -545,6 +547,8 @@ 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 +719,8 @@ 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 +766,9 @@ 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 +794,8 @@ 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 +868,12 @@ 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)
 {
@@ -1068,18 +1084,17 @@ real_t ParGridFunction::ComputeDGFaceJumpError(Coefficient *exsol,

 void ParGridFunction::Save(std::ostream &os) const
 {
-   real_t *data_  = const_cast<real_t*>(HostRead());
-   for (int i = 0; i < size; i++)
-   {
-      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
-   }
+   // We use const_cast + HostRead (instead of HostReadWrite) because we only
+   // need to change the host data temporarily and this way we do not invalidate
+   // the data if it is on device. If we use HostReadWrite here, later calls to
+   // Read or ReadWrite will need to copy the data from host to device. With the
+   // approach used here, the host-to-device copy is avoided.
+   real_t *h_data = const_cast<real_t*>(HostRead());
+   pfes->ApplyDofSigns(h_data);

   GridFunction::Save(os);

-   for (int i = 0; i < size; i++)
-   {
-      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
-   }
+   pfes->ApplyDofSigns(h_data);
 }

 void ParGridFunction::Save(const char *fname, int precision) const
@@ -1250,7 +1265,13 @@ void ParGridFunction::SaveAsOne(std::ostream &os) const
   int *nfdofs = new int[NRanks];
   int *nrdofs = new int[NRanks];

+   // We use const_cast + HostRead (instead of HostReadWrite) because we only
+   // need to change the host data temporarily and this way we do not invalidate
+   // the data if it is on device. If we use HostReadWrite here, later calls to
+   // Read or ReadWrite will need to copy the data from host to device. With the
+   // approach used here, the host-to-device copy is avoided.
   real_t * h_data = const_cast<real_t *>(this->HostRead());
+   pfes->ApplyDofSigns(h_data);  // temporarily flip the dof signs

   values[0] = h_data;
   nv[0]     = pfes -> GetVSize();
@@ -1357,6 +1378,8 @@ void ParGridFunction::SaveAsOne(std::ostream &os) const
      MPI_Send(h_data, nv[0], MPITypeMap<real_t>::mpi_type, 0, 460, MyComm);
   }

+   pfes->ApplyDofSigns(h_data);  // restore the original h_data
+
   delete [] values;
   delete [] nv;
   delete [] nvdofs;
@@ -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
@@ -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
         {
@@ -1398,20 +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
 }
@@ -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());
@@ -4297,7 +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;
      }

@@ -4848,14 +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);
   }
 }
@@ -4902,7 +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;
@@ -4910,10 +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; }
         }
@@ -5671,6 +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
@@ -5931,6 +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.");
@@ -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);

@@ -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
--- a/Show More
+++ b/Show More