Merge remote-tracking branch 'origin/master' into eqdsk-dev

# Conflicts:
#	makefile
#	miniapps/plasma/CMakeLists.txt
#	miniapps/plasma/makefile
#	miniapps/plasma/plasma.hpp

.github/actions/sanitize/config/action.yml

@@ -94,6 +94,16 @@ inputs:
     description: If true, do not set any CXXFLAGS or LDFLAGS.
     default: false
 
+  # Unfortunately, "uses:" fields cannot have references to variables like
+  # ${{env.MFEM_ACTIONS_VERSION}}, so the branch/tag name has to be hard coded.
+  # Therefore, in the future, when updating the version of the
+  # mfem/github-actions to use, we'll have to replace:
+  # - all definitions of MFEM_ACTIONS_VERSION and
+  # - all "uses:" fields that refer to mfem/github-actions.
+  MFEM_ACTIONS_VERSION:
+    description: Version (branch or tag) of the mfem/github-actions to use.
+    default: v2.7
+
 runs:
   using: 'composite'
   steps:
@@ -118,6 +128,7 @@ runs:
         echo UBSAN_LDFLAGS=${{inputs.UBSAN_LDFLAGS}} >> $GITHUB_ENV
         echo MSAN_CXXFLAGS=${{inputs.MSAN_CXXFLAGS}} >> $GITHUB_ENV
         echo MSAN_LDFLAGS=${{inputs.MSAN_LDFLAGS}} >> $GITHUB_ENV
+        echo MFEM_ACTIONS_VERSION=${{inputs.MFEM_ACTIONS_VERSION}} >> $GITHUB_ENV
       shell: bash
 
     - name: Env (dir)

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

@@ -53,7 +53,7 @@ runs:
       run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
       shell: bash
 
-    - uses: mfem/github-actions/build-mfem@v2.6
+    - uses: mfem/github-actions/build-mfem@v2.7
       if: ${{steps.debug.outputs.cache-hit != 'true'}}
       env:
         CXXFLAGS: ${{env.CXXFLAGS}}

.github/actions/sanitize/mpi/action.yml

@@ -12,6 +12,11 @@
 name: 'Install MPI'
 description: 'Installs MPI and set up its environment variables'
 
+inputs:
+  NO_FLAGS:
+    description: If true, do not set any CXXFLAGS or LDFLAGS.
+    default: false
+
 runs:
   using: 'composite'
   steps:
@@ -27,6 +32,7 @@ runs:
       shell: bash
 
     - name: Env (bis)
+      if: ${{ inputs.NO_FLAGS != 'true' }}
       run: |
         echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.MPI_INC}} >> $GITHUB_ENV
         echo LDFLAGS=${{env.LDFLAGS}} ${{env.MPI_LIB}} >> $GITHUB_ENV

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

@@ -37,14 +37,14 @@ runs:
       with:
         path: ${{env.HYPRE_DIR}}
         fail-on-cache-miss: true
-        key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
+        key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-${{env.MFEM_ACTIONS_VERSION}}
 
     - uses: actions/cache/restore@v5  # Cache for Metis
       if: ${{inputs.par == 'true'}}
       with:
         path: ${{env.METIS_DIR}}
         fail-on-cache-miss: true
-        key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
+        key: ${{runner.os}}-build-${{env.METIS_DIR}}-${{env.MFEM_ACTIONS_VERSION}}
 
     - name: Hypre/Metis links
       if: ${{inputs.par == 'true'}}

.github/workflows/README.md

@@ -29,16 +29,12 @@ Runs a number of static repository-level sanity checks.
 
 - `branch-history` guards against accidental commits of large files using the `--history` option of the `config/githooks/pre-push` script.
 
-## `mfem-analysis.yml` (`build-analysis`)
-
-Checks if the code builds and satisfies minimal requirements.
-
-- `gitignore` builds hypre, METIS, and MFEM using `mfem/github-actions/build-hypre`, `mfem/github-actions/build-metis`, and `mfem/github-actions/build-mfem` and checks for correct `.gitignore` settings by running the `tests/scripts/gitignore` script.
-
 ## `builds-and-tests.yml`
 
 Runs a matrix of builds and tests runs with different compilers, OS, mfem/hypre settings, etc. Also processes and upload Codecov reports.
 
+One matrix job runs `tests/scripts/gitignore` after `make test-noclean` to check generated artifacts against `.gitignore`.
+
 Uses the following GitHub Actions from <https://github.com/mfem/github-actions>:
 
 - `mfem/github-actions/build-hypre`

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

@@ -40,6 +40,7 @@ env:
   METIS_ARCHIVE_MAC: metis-4.0.3-mac.tgz
   METIS_TOP_DIR: metis-4.0.3
   MFEM_TOP_DIR: mfem
+  MFEM_ACTIONS_VERSION: v2.7
 
 # Note for future improvements:
 #
@@ -110,6 +111,7 @@ jobs:
             build-system: make
             hypre-target: int64
             precision: fp64
+            gitignore-check: YES
           - os: ubuntu-latest
             target: opt
             codecov: NO
@@ -140,6 +142,10 @@ jobs:
 
     continue-on-error: ${{ matrix.enzyme && true || false }}
 
+    # Enable ccache for all jobs except Windows (would need sccache).
+    env:
+      USE_CCACHE: ${{ matrix.os != 'windows-latest' }}
+
     steps:
       # Fix 'No space left on device' errors for Ubuntu builds.
       - name: Run Actions Cleaner
@@ -170,20 +176,6 @@ jobs:
           env
         shell: bash
 
-      # For info on Xcode see:
-      #  - https://github.com/actions/runner-images/issues/12541
-      #  - https://github.com/actions/runner-images/blob/releases/macos-15-arm64/20250811/images/macos/macos-15-arm64-Readme.md#xcode
-      - name: Xcode version setup (MacOS)
-        if: matrix.os == 'macos-latest'
-        run: |
-          XCODE_PATH="/Applications/Xcode_16.4.app"
-          echo "> sudo xcode-select -s ${XCODE_PATH}"
-          sudo xcode-select -s ${XCODE_PATH}
-          echo "> g++ -v"
-          g++ -v
-          echo "> clang++ -v"
-          clang++ -v
-
       # Only get MPI if defined for the job.
       # TODO: It would be nice to have only one step, e.g. with a dedicated
       # action, but I (@adrienbernede) don't see how at the moment.
@@ -228,11 +220,11 @@ jobs:
         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
+          key: ${{ runner.os }}-ompi-build-${{ env.HYPRE_TOP_DIR }}-${{ matrix.hypre-target }}-${{ matrix.precision }}-${{ env.MFEM_ACTIONS_VERSION }}
 
       - name: get hypre
         if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os != 'windows-latest'
-        uses: mfem/github-actions/build-hypre@v2.6
+        uses: mfem/github-actions/build-hypre@v2.7
         with:
           archive: ${{ env.HYPRE_ARCHIVE }}
           dir: ${{ env.HYPRE_TOP_DIR }}
@@ -242,7 +234,7 @@ 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@v2.6
+        uses: mfem/github-actions/build-hypre@v2.7
         with:
           archive: ${{ env.HYPRE_ARCHIVE }}
           dir: ${{ env.HYPRE_TOP_DIR }}
@@ -258,11 +250,11 @@ jobs:
         uses: actions/cache@v5
         with:
           path: ${{ env.METIS_TOP_DIR }}
-          key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.5
+          key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-${{ env.MFEM_ACTIONS_VERSION }}
 
       - name: install metis
         if: matrix.mpi == 'par' && matrix.os != 'windows-latest' && steps.metis-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.6
+        uses: mfem/github-actions/build-metis@v2.7
         with:
           archive: ${{ matrix.os != 'macos-latest' && env.METIS_ARCHIVE || env.METIS_ARCHIVE_MAC }}
           dir: ${{ env.METIS_TOP_DIR }}
@@ -302,9 +294,55 @@ jobs:
           echo "OMPI_CC=$LLVM_PREFIX/bin/clang" >> $GITHUB_ENV
           echo "OMPI_CXX=$LLVM_PREFIX/bin/clang++" >> $GITHUB_ENV
 
+      # Restore the compiler cache (ccache). The key embeds the run id, so new
+      # runs save a fresh snapshot; the restore-keys prefix warm-starts from the
+      # most recent prior run (incl. the base branch for PRs).
+      - name: cache ccache
+        if: ${{ env.USE_CCACHE == 'true' }}
+        uses: actions/cache@v5
+        with:
+          path: .ccache
+          key: ccache-${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}${{ matrix.enzyme && '-enzyme' || '' }}-${{ github.run_id }}
+          restore-keys: |
+            ccache-${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}${{ matrix.enzyme && '-enzyme' || '' }}-
+
+      # Configure ccache and select how it is injected into the MFEM build:
+      # - make:  set CXX="ccache g++"; for MPI, OMPI_CXX="ccache g++" so mpicxx
+      #          runs ccache around g++ (not ccache around the mpicxx wrapper).
+      # - cmake: set CMAKE_<LANG>_COMPILER_LAUNCHER=ccache.
+      # - enzyme: wrap the brew clang++ via OMPI_CXX.
+      # The chosen options are passed through build-mfem's 'config-options'
+      # input (see the build step below).
+      - name: configure ccache
+        if: ${{ env.USE_CCACHE == 'true' }}
+        run: |
+          command -v ccache >/dev/null 2>&1 || {
+            if [[ "${{ runner.os }}" == "Linux" ]]; then
+              sudo apt-get update && sudo apt-get install -y ccache
+            else
+              brew install ccache
+            fi
+          }
+          echo "CCACHE_DIR=${{ github.workspace }}/.ccache" >> $GITHUB_ENV
+          echo "CCACHE_MAXSIZE=1G" >> $GITHUB_ENV
+          echo "CCACHE_COMPILERCHECK=content" >> $GITHUB_ENV
+          # Ignore header timestamps (restamped by each checkout) so direct mode hits.
+          echo "CCACHE_SLOPPINESS=include_file_mtime,include_file_ctime,time_macros" >> $GITHUB_ENV
+          # Hash absolute paths relative to the workspace.
+          echo "CCACHE_BASEDIR=${{ github.workspace }}" >> $GITHUB_ENV
+          if [[ "${{ matrix.enzyme }}" == "true" ]]; then
+            echo "OMPI_CXX=ccache $LLVM_PREFIX/bin/clang++" >> $GITHUB_ENV
+          elif [[ "${{ matrix.build-system }}" == "cmake" ]]; then
+            echo 'CCACHE_CONFIG_OPTS=-DCMAKE_CXX_COMPILER_LAUNCHER=ccache -DCMAKE_C_COMPILER_LAUNCHER=ccache' >> $GITHUB_ENV
+          else
+            echo "OMPI_CXX=ccache g++" >> $GITHUB_ENV
+            echo 'CCACHE_CONFIG_OPTS=CXX="ccache g++" MPICXX="mpicxx"' >> $GITHUB_ENV
+          fi
+        shell: bash
+
       # MFEM build and test
       - name: build
-        uses: mfem/github-actions/build-mfem@v2.6
+        uses: mfem/github-actions/build-mfem@v2.7
         env:
           VCPKG_DEFAULT_BINARY_CACHE: ${{ github.workspace }}/vcpkg_cache
         with:
@@ -317,9 +355,14 @@ jobs:
           metis-dir: ${{ env.METIS_TOP_DIR }}
           mfem-dir: ${{ env.MFEM_TOP_DIR }}
           precision: ${{ matrix.precision }}
-          config-options: ${{ matrix.config-opts }}
+          config-options: ${{ matrix.config-opts }} ${{ env.CCACHE_CONFIG_OPTS }}
           library-only: ${{ matrix.target == 'dbg' && matrix.os != 'ubuntu-latest' }}
 
+      - name: ccache stats
+        if: ${{ env.USE_CCACHE == 'true' }}
+        run: ccache -s
+        shell: bash
+
       # Run checks (and only checks) on debug targets
       - name: checks
         if: matrix.build-system == 'make' && matrix.target == 'dbg'
@@ -330,7 +373,13 @@ jobs:
       - name: tests
         if: matrix.build-system == 'make' && (matrix.target == 'opt' || matrix.os == 'ubuntu-latest')
         run: |
-          cd ${{ env.MFEM_TOP_DIR }} && make test
+          cd ${{ env.MFEM_TOP_DIR }}
+          if [[ "${{ matrix.gitignore-check }}" == "YES" ]]; then
+            make test-noclean
+          else
+            make test
+          fi
+        shell: bash
 
       - name: cmake checks
         if: matrix.build-system == 'cmake' && matrix.target == 'dbg'
@@ -375,10 +424,16 @@ jobs:
       # Code coverage (process and upload reports)
       - name: codecov
         if: matrix.codecov == 'YES'
-        uses: mfem/github-actions/upload-coverage@v2.6
+        uses: mfem/github-actions/upload-coverage@v2.7
         with:
           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 }}
+
+      - name: gitignore
+        if: matrix.gitignore-check == 'YES'
+        run: |
+          cd ${{ env.MFEM_TOP_DIR }}/tests/scripts
+          ./runtest gitignore

.github/workflows/cleanup-pr-caches.yml

@@ -0,0 +1,42 @@
+# 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.
+---
+# A closed PR's caches can never be restored again, so delete them to free
+# space against the 10 GB per-repo cache limit.
+name: Cleanup PR caches
+
+on:
+  pull_request:
+    types: [closed]
+
+permissions:
+  actions: write
+
+jobs:
+  cleanup:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Delete caches for the closed PR
+        env:
+          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          GH_REPO: ${{ github.repository }}
+          PR_REF: refs/pull/${{ github.event.pull_request.number }}/merge
+        run: |
+          echo "Deleting caches for $PR_REF"
+          while :; do
+            ids=$(gh cache list --ref "$PR_REF" --limit 100 --json id --jq '.[].id')
+            [ -n "$ids" ] || break
+            echo "$ids" | while read -r id; do
+              [ -n "$id" ] || continue
+              echo "Deleting cache $id"
+              gh cache delete "$id" || echo "  (already gone)"
+            done
+          done

.github/workflows/codeql-analysis.yml

@@ -14,9 +14,19 @@ name: "Static Analysis"
 on:
   push:
     branches: ["master", "next"]
+    paths-ignore: &docs-only-paths
+      - "**/*.md"
+      - "doc/**"
+      - ".binder/**"
+      - "CITATION.cff"
+      - "LICENSE"
+      - "NOTICE"
+      - "CHANGELOG"
+      - "INSTALL"
   pull_request:
     # The branches below must be a subset of the branches above
     branches: ["master"]
+    paths-ignore: *docs-only-paths
 
 concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}

.github/workflows/mfem-analysis.yml

@@ -1,100 +0,0 @@
-# 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.
-
-name: "Build Analysis"
-
-permissions:
-  actions: write
-
-on:
-  push:
-    branches:
-      - master
-      - next
-  pull_request:
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref }}
-  cancel-in-progress: true
-
-env:
-  HYPRE_ARCHIVE: v2.19.0.tar.gz
-  HYPRE_TOP_DIR: hypre-2.19.0
-  METIS_ARCHIVE: metis-4.0.3.tar.gz
-  METIS_TOP_DIR: metis-4.0.3
-  COVERAGE_ENV: mfem-coverage
-
-jobs:
-  gitignore:
-    runs-on: ubuntu-latest
-
-    steps:
-      - name: checkout MFEM
-        uses: actions/checkout@v6
-        with:
-          path: mfem
-
-      - name: Get MPI (Linux)
-        run: |
-          sudo apt-get install openmpi-bin libopenmpi-dev
-          export OMPI_MCA_rmaps_base_oversubscribe=1
-
-      - name: Cache Hypre Install
-        id: hypre-cache
-        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@v2.6
-        with:
-          archive: ${{ env.HYPRE_ARCHIVE }}
-          dir: ${{ env.HYPRE_TOP_DIR }}
-          target: int32
-
-      - name: Cache Metis Install
-        id: metis-cache
-        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@v2.6
-        with:
-          archive: ${{ env.METIS_ARCHIVE }}
-          dir: ${{ env.METIS_TOP_DIR }}
-
-      # MFEM build and test
-      - name: build-mfem
-        uses: mfem/github-actions/build-mfem@v2.6
-        with:
-          os: ${{ runner.os }}
-          target: opt
-          codecov: NO
-          mpi: par
-          build-system: make
-          hypre-dir: ${{ env.HYPRE_TOP_DIR }}
-          metis-dir: ${{ env.METIS_TOP_DIR }}
-          mfem-dir: mfem
-
-      - name: test (no clean)
-        run: |
-          cd mfem && make test-noclean
-
-      - name: gitignore
-        run: |
-          cd mfem/tests/scripts
-          ./runtest gitignore

.github/workflows/repo-check.yml

@@ -13,6 +13,7 @@ name: "Checks"
 
 permissions:
   actions: write
+  pull-requests: read
 
 on:
   push:
@@ -29,6 +30,11 @@ concurrency:
 # by checking if the workflow trigger is 'push' ("github.event_name == 'push'")
 # and if we are in a fork ("github.event.pull_request.head.repo.full_name !=
 # github.repository").
+#
+# The logic for the branch-history check is slightly different, since that check
+# also inspects the PR's labels to allow for overriding failures. In this case,
+# we run on all 'pull_request' triggers, but only run for 'push' triggers that
+# do not correspond to any open PRs.
 
 jobs:
   file-headers-check:
@@ -128,10 +134,7 @@ jobs:
 
   branch-history:
     if: |
-      github.ref != 'refs/heads/next' &&
-      github.ref != 'refs/heads/master' &&
-      (github.event_name == 'push' ||
-       github.event.pull_request.head.repo.full_name != github.repository)
+      github.ref != 'refs/heads/next' && github.ref != 'refs/heads/master'
     runs-on: ubuntu-latest
     steps:
       - name: checkout mfem
@@ -139,7 +142,27 @@ jobs:
         with:
           fetch-depth: 0
 
+      - name: check for pull request
+        id: check_pr
+        if: github.event_name == 'push'
+        env:
+          GH_TOKEN: ${{ github.token }}
+        run: |
+          pr_exists=$(gh pr list --repo "$GITHUB_REPOSITORY" \
+            --head "$GITHUB_REF_NAME" \
+            --state open \
+            --json number \
+            --jq 'length > 0')
+          echo "pr_exists=$pr_exists" >> "$GITHUB_OUTPUT"
+
       - name: branch-history
+        id: branch_history
+        if: |
+          (github.event_name == 'pull_request' ||
+           github.event_name == 'workflow_dispatch' ||
+           steps.check_pr.outputs.pr_exists == 'false')
+        continue-on-error: ${{ contains(github.event.pull_request.labels.*.name,
+                                        'branch-history-override') }}
         run: |
           # We override origin to make sure we point to the main repo.
           # This is to have consistent test results on PRs from forks.
@@ -147,3 +170,9 @@ jobs:
           git remote add origin https://github.com/mfem/mfem.git
           git checkout -b gh-actions-branch-history
           ./config/githooks/pre-push --history
+
+      - name: report branch-history override
+        if: steps.branch_history.outcome == 'failure'
+        run: |
+          echo "::warning::branch-history check failed, but the" \
+            "'branch-history-override' label is set."

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

@@ -19,18 +19,22 @@ jobs:
     steps:
       - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
+        with:
+          NO_FLAGS: true
       - name: Cache
         id: cache
         uses: actions/cache@v5
         with:
           path: ${{env.HYPRE_DIR}}
-          key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
+          key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-${{ env.MFEM_ACTIONS_VERSION }}
       - name: Setup
         if: steps.cache.outputs.cache-hit != 'true'
         uses: ./.github/actions/sanitize/mpi
+        with:
+          NO_FLAGS: true
       - name: Build
         if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.6
+        uses: mfem/github-actions/build-hypre@v2.7
         with:
           archive: ${{env.HYPRE_TGZ}}
           dir: ${{env.HYPRE_DIR}}

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

@@ -19,18 +19,22 @@ jobs:
     steps:
       - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/config
+        with:
+          NO_FLAGS: true
       - name: Cache
         id: cache
         uses: actions/cache@v5
         with:
           path: ${{env.METIS_DIR}}
-          key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
+          key: ${{runner.os}}-build-${{env.METIS_DIR}}-${{env.MFEM_ACTIONS_VERSION}}
       - name: Setup
         if: steps.cache.outputs.cache-hit != 'true'
         uses: ./.github/actions/sanitize/mpi
+        with:
+          NO_FLAGS: true
       - name: Build
         if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.6
+        uses: mfem/github-actions/build-metis@v2.7
         with:
           archive: ${{env.METIS_TGZ}}
           dir: ${{env.METIS_DIR}}

.github/workflows/sanitizers.yml

@@ -17,7 +17,17 @@ permissions:
 on:
   push:
     branches: ["master", "next"]
+    paths-ignore: &docs-only-paths
+      - "**/*.md"
+      - "doc/**"
+      - ".binder/**"
+      - "CITATION.cff"
+      - "LICENSE"
+      - "NOTICE"
+      - "CHANGELOG"
+      - "INSTALL"
   pull_request:
+    paths-ignore: *docs-only-paths
   workflow_dispatch:
 
 concurrency:

.gitignore

@@ -260,6 +260,7 @@ miniapps/meshing/polar-nc
 miniapps/meshing/mesh-quality
 miniapps/meshing/hpref
 miniapps/meshing/phpref
+miniapps/meshing/pref321
 miniapps/meshing/mobius-strip.mesh
 miniapps/meshing/klein-bottle.mesh
 miniapps/meshing/toroid-*.mesh
@@ -355,6 +356,11 @@ miniapps/performance/refined.mesh
 miniapps/performance/mesh.*
 miniapps/performance/sol.*
 
+miniapps/plasma/g_eqdsk_viewer
+miniapps/plasma/gnuplot_eqdsk.*
+miniapps/plasma/G_EQDSK_Viewer*
+miniapps/plasma/ParaView
+
 miniapps/shifted/distance
 miniapps/shifted/ParaViewDistance
 miniapps/shifted/ParaViewLSF

.gitlab/dane-baseline.yml

@@ -102,12 +102,14 @@ report_baseline:
         mkdir -p ${MACHINE_NAME}
         rundir="${MACHINE_NAME}/$(date +%Y-%m-%d)-gitlab-${BASELINE_TEST}-${CI_COMMIT_REF_SLUG}"
         rundir=$(${CI_PROJECT_DIR}/.gitlab/scripts/safe_create_rundir ${rundir})
-        cp ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/* ${rundir}
+        status=0
+        cp ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/* ${rundir} || { status=1; }
         printf "%s\n" "" "Pipeline URL:" "$CI_PIPELINE_URL" \
           >> ${rundir}/pipeline.txt
         # We create an autotest-email.html file, because that's how we signal
         # that there was an error / diff (temporary).
-        if [[ -f ${rundir}/${BASELINE_TEST}.err ]] || \
+        if [[ $status -ne 0 ]] || \
+           [[ -f ${rundir}/${BASELINE_TEST}.err ]] || \
            [[ -f ${rundir}/${BASELINE_TEST}-${MACHINE_NAME}.diff ]]; then
           cp ${rundir}/pipeline.txt ${rundir}/autotest-email.html
         fi

CHANGELOG

@@ -11,35 +11,60 @@
 Version 4.9.1 (development)
 ===========================
 
-- Policy for AI-assisted contribution added to CONTRIBUTING.md
+- Added policy for AI-assisted contribution 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.
+- Improved FindPointsGSLIB surface mesh capability with support for simplices
+  and an option to specify axis-aligned bounding box padding for near-surface
+  point queries.
+
+- Added GPU-enabled partial assembly for simplicial Bernstein H1 basis based on
+  ragged tensor algorithms (see DOI: 10.1137/11082539X) for mass and diffusion
+  integrators.
+
+- 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 and Vincent, DOI: 10.1016/j.camwa.2015.03.017
+  * Tet rules (d=1-13): Witherden and  Vincent (same as above)
+  * Tet rules (d=14-20): Chuluunbaatar et al., DOI: 10.1016/j.camwa.2022.08.016
+
+- Added support for general 1D Gauss-Jacobi quadrature rules and Stroud conical
+  quadrature rules on triangles and tetrahedra.
+
+- Improved the GridFunction projection routines. Projections work for Scalar,
+  Vector and VectorFE, also NURBS versions. Optionally different types of
+  projections can be selected, default behavior has not changed.
+
+- Added GridFunction projection methods for trace spaces, i.e., project
+  coefficients on the mesh skeleton.
+
+- Added methods to estimate function extremum using piecewise linear bounds plus
+  recursive subdivision.
 
 - Extend FindPointsGSLIB to support surface meshes.
 
-- Replaced legacy simplex quadrature rules with symmetric positive-weight
-  rules for triangles (orders 0-25) and tetrahedra (orders 0-20). These
-  rules guarantee all-positive weights and interior quadrature points,
-  improving numerical stability. Higher orders fall back to Grundmann-Moller.
-  Triangle rules: Witherden & Vincent, Comput. Math. Appl. 69(10):1232-1241,
-  2015.
-  Tet rules (d=1-13): Witherden & Vincent (ibid).
-  Tet rules (d=14-20): Chuluunbaatar et al., Comput. Math. Appl. 124:89-97,
-  2022.
-
-- Improved the gridfunction projection routines. Projections work for Scalar,
-  Vector and VectorFE, also NURBS versions. Optionally different types of
-  projections can be selected, default behaviour has not changed.
-
-- Added methods to estimate function extremum using piecewise linear bounds +
-  recursive subdivision.
+- Added support for complex-valued mixed bilinear forms via the new classes
+  MixedSesquilinearForm and ParMixedSesquilinearForm, mirroring the existing
+  SesquilinearForm classes. Rectangular complex operators are now also
+  handled correctly by ComplexSparseMatrix::GetSystemMatrix and
+  ComplexHypreParMatrix::GetSystemMatrix, which previously assumed equal
+  trial and test spaces.
 
 Meshing improvements
 --------------------
+- Added support for nonuniform anisotropic mesh refinement on parallel quad/hex
+  meshes with arbitrary spacing in each direction. This enables in particular
+  3:1 refinement in parallel, as demonstrated in the new meshing miniapp pref321.
+
+- Added option to guarantee mesh validity during TMOP-based r-adaptivity, using
+  bounds on the determinant of the mesh transformation Jacobian.
+
+- Added PA support for TMOP's adaptive limiting functionality. Multiple
+  GridFunctions and Coefficients can be combined to form a composite term.
+
 - Improved support for 1D NURBS meshes with variable order, including using
   the patches construct for 1D NURBS meshes.
 
@@ -48,22 +73,50 @@ Meshing improvements
   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.
+Linear and nonlinear solvers
+----------------------------
+- Added support for trace spaces in PRefinementTransferOperator. This is used in
+  PRefinement multigrid methods for problems posed on trace spaces (see e.g. the
+  DPG miniapps).
 
 GPU computing
 -------------
+- Improved partial assembly for VectorDivergenceIntegrator with shared-memory
+  kernels, kernel registration, and transpose support.
+
+- Improved partial-assembly diagonal kernels for VectorMassIntegrator (shared-
+  memory specializations) and ElasticityIntegrator (no scratch Q-vector).
+
+- Added PA gradient and diagonal support for VectorConvectionNLFIntegrator
+ (AssembleGradPA, AddMultGradPA, AssembleGradDiagonalPA).
+
+- Added device assembly support for 3D H(curl) VectorFEDomainLFIntegrator.
+
+- 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.
+
 - Allow specifying GPU kernel launch bounds for native and RAJA GPU backends.
 
+- Changed VectorFEMassIntegrator to use kernel specialization dispatch for
+  partial assembly.
+
+- Added support for FiniteElement::MapType::INTEGRAL spaces to
+  QuadratureInterpolator.
+
+New and updated examples and miniapps
+-------------------------------------
+- The Lorentz miniapp (in miniapps/electromagnetics) has been updated to
+  leverage the ParticleSet capability.
+
+- Added (Complex)PRefinementMultigrid solver option in the DPG miniapps.
+
 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.
+- Fixed signed DOF handling in ParGridFunction reading (read constructor) and
+  saving via 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

CMakeLists.txt

@@ -239,6 +239,13 @@ else()
   set(MFEM_DEBUG OFF)
 endif()
 
+# Shadow warnings for clang only; GCC's -Wshadow flags more.
+if (CMAKE_CXX_COMPILER_ID MATCHES "Clang")
+  set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -pedantic -Wall -Wshadow")
+elseif (CMAKE_CXX_COMPILER_ID STREQUAL "GNU")
+  set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -pedantic -Wall")
+endif()
+
 # Shared build on Windows
 if (WIN32 AND BUILD_SHARED_LIBS)
   # CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS works only with MSVC?

CONTRIBUTING.md

@@ -6,7 +6,6 @@
 <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="Documentation" src="https://img.shields.io/badge/code-documented-brightgreen.svg"></a>

config/cmake/modules/FindGSLIB.cmake

@@ -18,19 +18,17 @@
 
 if (MFEM_FETCH_GSLIB OR MFEM_FETCH_TPLS)
   enable_language(C)
-  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
   set(GSLIB_FETCH_VERSION 1.0.9)
-  set(GSLIB_C_FLAGS ${CMAKE_C_FLAGS_${BUILD_TYPE}})
-  if (CMAKE_C_FLAGS)
-    set(GSLIB_C_FLAGS "${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
-  endif()
-  if (BUILD_SHARED_LIBS)
-    set(GSLIB_C_FLAGS "${GSLIB_C_FLAGS} -fPIC")
-  endif()
   add_library(GSLIB STATIC IMPORTED)
+  # set options (technically flags because GSLIB does not use cmake)
+  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
+  set(GSLIB_FLAGS "${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
+  if (BUILD_SHARED_LIBS)
+    set(GSLIB_FLAGS "${GSLIB_FLAGS} -fPIC")
+  endif()
   # define external project and create future include directory so it is present
   # to pass CMake checks at end of MFEM configuration step
-  message(STATUS "Will fetch GSLIB ${GSLIB_FETCH_VERSION} to be built with ${GSLIB_C_FLAGS}")
+  message(STATUS "Will fetch GSLIB ${GSLIB_FETCH_VERSION} to be built with ${GSLIB_FLAGS}")
   set(PREFIX ${CMAKE_BINARY_DIR}/fetch/gslib)
   include(ExternalProject)
   ExternalProject_Add(gslib
@@ -40,7 +38,7 @@ if (MFEM_FETCH_GSLIB OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     PREFIX ${PREFIX}
     CONFIGURE_COMMAND ""
-    BUILD_COMMAND cd ${PREFIX}/src/gslib && $(MAKE) clean && $(MAKE) DESTDIR=${PREFIX} MPI=$<BOOL:${MFEM_USE_MPI}> "CFLAGS= ${GSLIB_C_FLAGS}"
+    BUILD_COMMAND cd ${PREFIX}/src/gslib && $(MAKE) clean && $(MAKE) DESTDIR=${PREFIX} MPI=$<BOOL:${MFEM_USE_MPI}> "CFLAGS=${GSLIB_FLAGS}"
     INSTALL_COMMAND "")
   file(MAKE_DIRECTORY ${PREFIX}/include)
   # set imported library target properties

config/cmake/modules/FindHYPRE.cmake

@@ -44,6 +44,9 @@ if (MFEM_FETCH_HYPRE OR MFEM_FETCH_TPLS)
   # set options and associated dependencies
   set(HYPRE_CMAKE_OPTIONS "")
   list(APPEND HYPRE_CMAKE_OPTIONS -DCMAKE_BUILD_TYPE:STRING=${CMAKE_BUILD_TYPE})
+  if (BUILD_SHARED_LIBS)
+    list(APPEND HYPRE_CMAKE_OPTIONS -DCMAKE_POSITION_INDEPENDENT_CODE:BOOL=ON)
+  endif()
   # collect all HYPRE_ENABLE variables and pass them to hypre, assuming they are BOOL.
   get_cmake_property(all_vars VARIABLES)
   foreach(var ${all_vars})
@@ -95,7 +98,6 @@ if (MFEM_FETCH_HYPRE OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     SOURCE_SUBDIR src
     PREFIX ${HYPRE_INSTALL}
-    BUILD_COMMAND ${CMAKE_COMMAND} --build . -- -j${CMAKE_BUILD_PARALLEL_LEVEL}
     CMAKE_CACHE_ARGS -DCMAKE_INSTALL_PREFIX:PATH=${HYPRE_INSTALL} -DCMAKE_INSTALL_LIBDIR:PATH=lib ${HYPRE_CMAKE_OPTIONS})
   file(MAKE_DIRECTORY ${HYPRE_INSTALL}/include)
   # set imported library target properties

config/cmake/modules/FindMETIS.cmake

@@ -19,10 +19,18 @@
 #   - METIS_VERSION_5 (cache variable)
 
 if (MFEM_FETCH_METIS OR MFEM_FETCH_TPLS)
+  enable_language(C)
   set(METIS_FETCH_VERSION 4.0.3)
   add_library(METIS STATIC IMPORTED)
+  # set options (technically flags because METIS does not use cmake)
+  set(METIS_FLAGS "-Wno-implicit-int -Wno-incompatible-pointer-types")
+  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
+  set(METIS_FLAGS "${METIS_FLAGS} ${CMAKE_C_FLAGS} ${CMAKE_C_FLAGS_${BUILD_TYPE}}")
+  if (BUILD_SHARED_LIBS)
+    set(METIS_FLAGS "${METIS_FLAGS} -fPIC")
+  endif()
   # define external project
-  message(STATUS "Will fetch METIS ${METIS_FETCH_VERSION} to be built with default options")
+  message(STATUS "Will fetch METIS ${METIS_FETCH_VERSION} to be built with ${METIS_FLAGS}")
   set(PREFIX ${CMAKE_BINARY_DIR}/fetch/metis)
   include(ExternalProject)
   ExternalProject_Add(metis
@@ -32,7 +40,7 @@ if (MFEM_FETCH_METIS OR MFEM_FETCH_TPLS)
     UPDATE_DISCONNECTED TRUE
     PREFIX ${PREFIX}
     CONFIGURE_COMMAND tar -xzf ../metis/metis-${METIS_FETCH_VERSION}-mac.tgz --strip=1
-    BUILD_COMMAND $(MAKE) COPTIONS=-Wno-incompatible-pointer-types
+    BUILD_COMMAND $(MAKE) clean && $(MAKE) "OPTFLAGS=${METIS_FLAGS}"
     INSTALL_COMMAND mkdir -p ${PREFIX}/lib && cp libmetis.a ${PREFIX}/lib/)
   # set imported library target properties
   add_dependencies(METIS metis)

config/cmake/modules/FindSuiteSparse.cmake

@@ -22,15 +22,15 @@ include(MfemCmakeUtilities)
 mfem_find_package(SuiteSparse SuiteSparse SuiteSparse_DIR "" "" "" ""
   "Paths to headers required by SuiteSparse."
   "Libraries required by SuiteSparse."
-  ADD_COMPONENT "UMFPACK" "include;suitesparse" umfpack.h "lib" umfpack
-  ADD_COMPONENT "KLU" "include;suitesparse" klu.h "lib" klu
-  ADD_COMPONENT "AMD" "include;suitesparse" amd.h "lib" amd
-  ADD_COMPONENT "BTF" "include;suitesparse" btf.h "lib" btf
-  ADD_COMPONENT "CHOLMOD" "include;suitesparse" cholmod.h "lib" cholmod
-  ADD_COMPONENT "COLAMD" "include;suitesparse" colamd.h "lib" colamd
-  ADD_COMPONENT "CAMD" "include;suitesparse" camd.h "lib" camd
-  ADD_COMPONENT "CCOLAMD" "include;suitesparse" ccolamd.h "lib" ccolamd
-  ADD_COMPONENT "config" "include;suitesparse" SuiteSparse_config.h "lib"
+  ADD_COMPONENT "UMFPACK" "include;include/suitesparse;suitesparse" umfpack.h "lib" umfpack
+  ADD_COMPONENT "KLU" "include;include/suitesparse;suitesparse" klu.h "lib" klu
+  ADD_COMPONENT "AMD" "include;include/suitesparse;suitesparse" amd.h "lib" amd
+  ADD_COMPONENT "BTF" "include;include/suitesparse;suitesparse" btf.h "lib" btf
+  ADD_COMPONENT "CHOLMOD" "include;include/suitesparse;suitesparse" cholmod.h "lib" cholmod
+  ADD_COMPONENT "COLAMD" "include;include/suitesparse;suitesparse" colamd.h "lib" colamd
+  ADD_COMPONENT "CAMD" "include;include/suitesparse;suitesparse" camd.h "lib" camd
+  ADD_COMPONENT "CCOLAMD" "include;include/suitesparse;suitesparse" ccolamd.h "lib" ccolamd
+  ADD_COMPONENT "config" "include;include/suitesparse;suitesparse" SuiteSparse_config.h "lib"
     suitesparseconfig)
 
 if (SuiteSparse_FOUND AND METIS_VERSION_5)

config/defaults.mk

@@ -27,7 +27,13 @@ MPICXX = mpicxx
 
 BASE_FLAGS  = -std=c++17
 OPTIM_FLAGS = -O3 $(BASE_FLAGS)
-DEBUG_FLAGS = -g $(XCOMPILER)-Wall $(BASE_FLAGS)
+
+# Shadow warnings for clang only; GCC's -Wshadow flags more.
+SHADOW_WARNING_FLAG = $(if $(findstring clang,\
+ $(shell $(MFEM_HOST_CXX) --version 2>/dev/null)),-Wshadow,)
+WARNING_FLAGS = -pedantic -Wall $(SHADOW_WARNING_FLAG)
+
+DEBUG_FLAGS = $(strip -g $(addprefix $(XCOMPILER),$(WARNING_FLAGS)) $(BASE_FLAGS))
 
 # Prefixes for passing flags to the compiler and linker when using CXX or MPICXX
 CXX_XCOMPILER =

config/githooks/README.md

@@ -39,3 +39,8 @@ when a picture was added for documentation.
 If that is the case, make sure the failure is indeed justified, and rerun the
 push command with the `--no-verify` option. This will skip the hooks, allowing
 you to push those changes.
+
+The `branch-history` check is run automatically through GitHub Actions. If a
+branch is known to have a large number of changes that are legitimate, the
+check can be overridden by setting  the label 'branch-history-override' on the
+pull request.

data/tinyzoo-2d.mesh

@@ -0,0 +1,38 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+
+dimension
+2
+
+elements
+2
+1 3 0 1 4 3
+1 2 1 2 4
+
+boundary
+5
+1 1 0 1
+1 1 1 2
+1 1 2 4
+1 1 4 3
+1 1 3 0
+
+vertices
+5
+2
+0 0
+1 0
+2 0
+0 1
+1 1

doc/CodeDocumentation.dox

@@ -201,6 +201,7 @@ namespace mfem {
  * - <a class="el" href="nurbs__naca__cmesh_8cpp_source.html">NURBS NACA Mesher</a>: generate NURBS based mesh around a NACA foil
  * - <a class="el" href="nurbs__printfunc_8cpp_source.html">NURBS Printer</a>: print the NURBS-basis
  * - <a class="el" href="nurbs__mesh_info_8cpp_source.html">NURBS Mesh info</a>: print the info of a NURBS mesh
+ * - <a class="el" href="nurbs__surface_8cpp_source.html">NURBS Surface</a>: interpolate a 3D Surface in a NURBS Patch
  *
  * <H3>Miniapps</H3>
  * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
@@ -245,6 +246,9 @@ namespace mfem {
  * - <a class="el" href="pdiffusion_8cpp_source.html">DPG Diffusion example</a>: DPG formulation for the diffusion problem
  * - <a class="el" href="pmaxwell_8cpp_source.html">DPG Maxwell example</a>: DPG formulation for the indefinite Maxwell problem
  * - <a class="el" href="lor__elast_8cpp_source.html">LOR Elasticity</a>: solve linear elasticity with LOR preconditioning on GPUs
+ * - <a class="el" href="reflector_8cpp_source.html">Reflector Miniapp</a>: reflect a mesh about a plane
+ * - <a class="el" href="ref321_8cpp_source.html">3:1 Refinement Miniapp</a>: perform 3:1 anisotropic mesh refinements
+ * - <a class="el" href="pref321_8cpp_source.html">3:1 Refinement Miniapp</a>: parallel 3:1 anisotropic mesh refinements
  *
  * See also the <a class="el" href="https://mfem.org/examples/">examples documentation</a> online.
  */

examples/ex1.cpp

@@ -50,6 +50,10 @@
 //               ex1 -m ../data/beam-tet.mesh -pa -d ceed-cpu
 //               ex1 -m ../data/beam-tet.mesh -pa -d ceed-cuda:/gpu/cuda/ref
 //
+// Device simplices sample runs:
+//               ex1 -pa -d gpu -m ../data/inline-tet.mesh
+//               ex1 -pa -d gpu -m ../data/inline-tri.mesh
+//
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Poisson problem
 //               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
@@ -138,25 +142,25 @@ int main(int argc, char *argv[])
    }
 
    // 5. Define a finite element space on the mesh. Here we use continuous
-   //    Lagrange finite elements of the specified order. If order < 1, we
-   //    instead use an isoparametric/isogeometric space.
+   //    Lagrange finite elements of the specified order.
+   //    - If order < 1, we instead use an isoparametric/isogeometric space.
+   //    - If the mesh is simplicial and partial assembly is requested,
+   //      we use the positive basis, which supports device execution.
    FiniteElementCollection *fec;
-   bool delete_fec;
+   auto basis_type = (pa && mesh.IsSimplexMesh()) ?
+                     BasisType::Positive : BasisType::GaussLobatto;
    if (order > 0)
    {
-      fec = new H1_FECollection(order, dim);
-      delete_fec = true;
+      fec = new H1_FECollection(order, dim, basis_type);
    }
    else if (mesh.GetNodes())
    {
       fec = mesh.GetNodes()->OwnFEC();
-      delete_fec = false;
       cout << "Using isoparametric FEs: " << fec->Name() << endl;
    }
    else
    {
-      fec = new H1_FECollection(order = 1, dim);
-      delete_fec = true;
+      fec = new H1_FECollection(order = 1, dim, basis_type);
    }
    FiniteElementSpace fespace(&mesh, fec);
    cout << "Number of finite element unknowns: "
@@ -292,10 +296,7 @@ int main(int argc, char *argv[])
    }
 
    // 15. Free the used memory.
-   if (delete_fec)
-   {
-      delete fec;
-   }
+   if (order > 0) { delete fec; }
 
    return 0;
 }

examples/ex1p.cpp

@@ -42,7 +42,11 @@
 //               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
 //               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
 //               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
-//               mpirun -np 4 ex1p -m ../data/beam-tet.mesh -pa -d ceed-cpu
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/beam-tet.mesh
+//
+// Device simplices sample runs:
+//               mpirun -np 4 ex1p -pa -d gpu -m ../data/inline-tet.mesh
+//               mpirun -np 4 ex1p -pa -d gpu -m ../data/inline-tri.mesh
 //
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Poisson problem
@@ -165,19 +169,20 @@ int main(int argc, char *argv[])
    }
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
-   //    use continuous Lagrange finite elements of the specified order. If
-   //    order < 1, we instead use an isoparametric/isogeometric space.
+   //    use continuous Lagrange finite elements of the specified order.
+   //    - If order < 1, we instead use an isoparametric/isogeometric space.
+   //    - If the mesh is simplicial and partial assembly is requested,
+   //      we use the positive basis, which supports device execution.
    FiniteElementCollection *fec;
-   bool delete_fec;
+   auto basis_type = (pa && pmesh.IsSimplexMesh()) ?
+                     BasisType::Positive : BasisType::GaussLobatto;
    if (order > 0)
    {
-      fec = new H1_FECollection(order, dim);
-      delete_fec = true;
+      fec = new H1_FECollection(order, dim, basis_type);
    }
    else if (pmesh.GetNodes())
    {
       fec = pmesh.GetNodes()->OwnFEC();
-      delete_fec = false;
       if (myid == 0)
       {
          cout << "Using isoparametric FEs: " << fec->Name() << endl;
@@ -185,8 +190,7 @@ int main(int argc, char *argv[])
    }
    else
    {
-      fec = new H1_FECollection(order = 1, dim);
-      delete_fec = true;
+      fec = new H1_FECollection(order = 1, dim, basis_type);
    }
    ParFiniteElementSpace fespace(&pmesh, fec);
    HYPRE_BigInt size = fespace.GlobalTrueVSize();
@@ -333,10 +337,7 @@ int main(int argc, char *argv[])
    }
 
    // 17. Free the used memory.
-   if (delete_fec)
-   {
-      delete fec;
-   }
+   if (order > 0) { delete fec; }
 
    return 0;
 }

fem/CMakeLists.txt

@@ -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
@@ -133,7 +135,7 @@ set(SRCS
   tmop/assemble/diag2.cpp
   tmop/assemble/grad2_limit.cpp
   tmop/assemble/grad2.cpp
-  tmop/assemble/diag3_limit.cpp  
+  tmop/assemble/diag3_limit.cpp
   tmop/assemble/diag3.cpp
   tmop/assemble/grad3_limit.cpp
   tmop/assemble/grad3.cpp
@@ -195,14 +197,20 @@ set(HDRS
   integ/bilininteg_dgtrace_kernels.hpp
   integ/bilininteg_vecdiffusion_kernels.hpp
   integ/bilininteg_convection_kernels.hpp
+  integ/bilininteg_diffusion_pa_simplices.hpp
   integ/bilininteg_diffusion_kernels.hpp
   integ/bilininteg_elasticity_kernels.hpp
   integ/bilininteg_hcurl_kernels.hpp
   integ/bilininteg_hdiv_kernels.hpp
   integ/bilininteg_hcurlhdiv_kernels.hpp
   integ/bilininteg_mass_kernels.hpp
+  integ/bilininteg_mass_pa_simplices.hpp
   integ/bilininteg_vecdiffusion_pa.hpp
+  integ/bilininteg_vecdiv_pa.hpp
   integ/bilininteg_vecmass_pa.hpp
+  integ/nonlininteg_vecconvection_pa.hpp
+  integ/nonlininteg_vecconvection_pa_diag.hpp
+  integ/nonlininteg_vecconvection_pa_grad.hpp
   coefficient.hpp
   complex_fem.hpp
   convergence.hpp
@@ -309,6 +317,7 @@ set(HDRS
   tmop_tools.hpp
   tmop_amr.hpp
   gslib.hpp
+  gslib/gslib_kernel_helpers.hpp
   transfer.hpp
   hyperbolic.hpp
   integrator.hpp

fem/bilininteg.cpp

@@ -1345,7 +1345,8 @@ real_t DiffusionIntegrator::ComputeFluxEnergy
 }
 
 const IntegrationRule &DiffusionIntegrator::GetRule(
-   const FiniteElement &trial_fe, const FiniteElement &test_fe)
+   const FiniteElement &trial_fe, const FiniteElement &test_fe,
+   const bool stroud)
 {
    int order;
    if (trial_fe.Space() == FunctionSpace::Pk)
@@ -1362,7 +1363,15 @@ const IntegrationRule &DiffusionIntegrator::GetRule(
    {
       return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
    }
-   return IntRules.Get(trial_fe.GetGeomType(), order);
+
+   if (stroud)
+   {
+      return StroudIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   else
+   {
+      return IntRules.Get(trial_fe.GetGeomType(), order);
+   }
 }
 
 MassIntegrator::MassIntegrator(const IntegrationRule *ir)
@@ -1449,7 +1458,8 @@ void MassIntegrator::AssembleElementMatrix2(
 
 const IntegrationRule &MassIntegrator::GetRule(const FiniteElement &trial_fe,
                                                const FiniteElement &test_fe,
-                                               const ElementTransformation &Trans)
+                                               const ElementTransformation &Trans,
+                                               const bool stroud)
 {
    // int order = trial_fe.GetOrder() + test_fe.GetOrder();
    const int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW();
@@ -1458,7 +1468,15 @@ const IntegrationRule &MassIntegrator::GetRule(const FiniteElement &trial_fe,
    {
       return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
    }
-   return IntRules.Get(trial_fe.GetGeomType(), order);
+
+   if (stroud)
+   {
+      return StroudIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   else
+   {
+      return IntRules.Get(trial_fe.GetGeomType(), order);
+   }
 }
 
 

fem/bilininteg.hpp

@@ -2184,11 +2184,22 @@ public:
                                    const Vector&, const Vector&,
                                    Vector&, const int, const int);
 
+   using ApplySimplexKernelType = void(*)(const int, const bool, const Array<int>&,
+                                          const Array<int>&,
+                                          const Array<int>&, const Array<int>&, const Array<int>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Vector&, const Vector&,
+                                          Vector&, const int, const int);
+
    using DiagonalKernelType = void(*)(const int, const bool, const Array<real_t>&,
                                       const Array<real_t>&, const Vector&, Vector&,
                                       const int, const int);
 
    MFEM_REGISTER_KERNELS(ApplyPAKernels, ApplyKernelType, (int, int, int));
+   MFEM_REGISTER_KERNELS(ApplySimplexPAKernels, ApplySimplexKernelType, (int, int,
+                                                                         int));
    MFEM_REGISTER_KERNELS(DiagonalPAKernels, DiagonalKernelType, (int, int, int));
    struct Kernels { Kernels(); };
 
@@ -2341,7 +2352,8 @@ public:
    void AddMultPatchPA(const int patch, const Vector &x, Vector &y) const;
 
    static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
-                                         const FiniteElement &test_fe);
+                                         const FiniteElement &test_fe,
+                                         const bool stroud = false);
 
    bool SupportsCeed() const override { return DeviceCanUseCeed(); }
 
@@ -2352,6 +2364,13 @@ public:
    {
       ApplyPAKernels::Specialization<DIM,D1D,Q1D>::Add();
       DiagonalPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+      AddSimplexSpecialization<DIM,D1D,Q1D>();
+   }
+
+   template <int DIM, int D1D, int Q1D>
+   static void AddSimplexSpecialization()
+   {
+      ApplySimplexPAKernels::Specialization<DIM,D1D,Q1D>::Add();
    }
 protected:
    const IntegrationRule* GetDefaultIntegrationRule(
@@ -2388,11 +2407,22 @@ public:
                                    const Array<real_t>&, const Vector&,
                                    const Vector&, Vector&, const int, const int);
 
+   using ApplySimplexKernelType = void(*)(const int, const Array<int>&,
+                                          const Array<int>&,
+                                          const Array<int>&, const Array<int>&, const Array<int>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Array<real_t>&, const Array<real_t>&,
+                                          const Vector&, const Vector&, Vector&,
+                                          const int, const int);
+
    using DiagonalKernelType =  void(*)(const int, const Array<real_t>&,
                                        const Vector&, Vector&, const int,
                                        const int);
 
    MFEM_REGISTER_KERNELS(ApplyPAKernels, ApplyKernelType, (int, int, int));
+   MFEM_REGISTER_KERNELS(ApplySimplexPAKernels, ApplySimplexKernelType, (int, int,
+                                                                         int));
    MFEM_REGISTER_KERNELS(DiagonalPAKernels, DiagonalKernelType, (int, int, int));
    struct Kernels { Kernels(); };
 
@@ -2441,7 +2471,8 @@ public:
 
    static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
                                          const FiniteElement &test_fe,
-                                         const ElementTransformation &Trans);
+                                         const ElementTransformation &Trans,
+                                         const bool stroud = false);
 
    bool SupportsCeed() const override { return DeviceCanUseCeed(); }
 
@@ -2452,6 +2483,13 @@ public:
    {
       ApplyPAKernels::Specialization<DIM,D1D,Q1D>::Add();
       DiagonalPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+      AddSimplexSpecialization<DIM,D1D,Q1D>();
+   }
+
+   template <int DIM, int D1D, int Q1D>
+   static void AddSimplexSpecialization()
+   {
+      ApplySimplexPAKernels::Specialization<DIM,D1D,Q1D>::Add();
    }
 
 protected:
@@ -2651,14 +2689,22 @@ 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*/));
 };
 
 
@@ -2957,11 +3003,10 @@ public:
     vector (diagonal matrix), or matrix), trial function $u$ is in $H(curl$ or
     $H(div)$, and test function $v$ is in $H(curl$, $H(div)$, or $v=(v_1,\dots,v_n)$, where
     $v_i$ are in $H^1$. */
-class VectorFEMassIntegrator: public BilinearFormIntegrator
+class VectorFEMassIntegrator : public BilinearFormIntegrator
 {
 private:
-   void Init(Coefficient *q, DiagonalMatrixCoefficient *dq, MatrixCoefficient *mq)
-   { Q = q; DQ = dq; MQ = mq; }
+   void Init(Coefficient *q, DiagonalMatrixCoefficient *dq, MatrixCoefficient *mq);
 
 #ifndef MFEM_THREAD_SAFE
    Vector shape;
@@ -2984,7 +3029,8 @@ protected:
    const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
    const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
    const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, nq, dofs1D, dofs1Dtest, quad1D, trial_fetype, test_fetype;
+   int dim, ne, nq, dofs1D, dofs1Dtest, quad1D;
+   FiniteElement::DerivType trial_fetype, test_fetype;
    bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient
 
 public:
@@ -3015,6 +3061,29 @@ public:
                    const bool add) override;
 
    const Coefficient *GetCoefficient() const { return Q; }
+
+   using ApplyKernelType =
+      void (*)(const int NE, bool symmetric, const bool scalar_coeff,
+               const Array<real_t> &trialBO, const Array<real_t> &trialBC,
+               const Array<real_t> &testBOt, const Array<real_t> &testBCt,
+               const Vector &pa_data, const Vector &x, Vector &y,
+               const int triald1d, const int testd1d, const int q1d);
+
+   /// parameters: trial_fetype, test_fetype, ndims, trial_d1d, test_d1d, q1d
+   MFEM_REGISTER_KERNELS(ApplyPAKernels, ApplyKernelType,
+                         (FiniteElement::DerivType, FiniteElement::DerivType,
+                          int, int, int, int));
+
+   struct Kernels { Kernels(); };
+
+   template <FiniteElement::DerivType TrialType,
+             FiniteElement::DerivType TestType, int DIM, int TRIAL_D1D,
+             int TEST_D1D, int Q1D>
+   static void AddSpecialization()
+   {
+      ApplyPAKernels::Specialization<TrialType, TestType, DIM, TRIAL_D1D,
+                     TEST_D1D, Q1D>::Add();
+   }
 };
 
 /** Integrator for $(Q \nabla \cdot u, v)$ where $u=(u_1,\cdots,u_n)$ and all $u_i$ are in the same
@@ -3060,6 +3129,24 @@ 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);

fem/coefficient.cpp

@@ -54,6 +54,8 @@ void Coefficient::Project(QuadratureFunction &qf)
    QuadratureSpaceBase &qspace = *qf.GetSpace();
    const int ne = qspace.GetNE();
    Vector values;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);
@@ -327,6 +329,8 @@ void VectorCoefficient::Project(QuadratureFunction &qf)
    const int ne = qspace.GetNE();
    DenseMatrix values;
    Vector col;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);
@@ -695,6 +699,8 @@ void MatrixCoefficient::Project(QuadratureFunction &qf, bool transpose)
    QuadratureSpaceBase &qspace = *qf.GetSpace();
    const int ne = qspace.GetNE();
    DenseMatrix values, matrix;
+   // GetValues makes a reference, but we need it to be valid on Host
+   qf.HostWrite();
    for (int iel = 0; iel < ne; ++iel)
    {
       qf.GetValues(iel, values);

fem/complex_fem.cpp

@@ -237,6 +237,81 @@ ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
    gfi->SyncAliasMemory(*this);
 }
 
+real_t
+ComplexGridFunction::ComputeLpError(const real_t p,
+                                    Coefficient &exsolr,
+                                    Coefficient &exsoli,
+                                    Coefficient *weight,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   real_t error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Vector valsr;
+   Vector valsi;
+
+   const GridFunction& gf_r = real();
+   const GridFunction& gf_i = imag();
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      if (elems != NULL && (*elems)[i] == 0) { continue; }
+      fe = fes->GetFE(i);
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         int intorder = 2*fe->GetOrder() + 3;
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      real_t elem_error = 0.0;
+      gf_r.GetValues(i, *ir, valsr);
+      gf_i.GetValues(i, *ir, valsi);
+      T = fes->GetElementTransformation(i);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         T->SetIntPoint(&ip);
+         real_t diffr = valsr(j) - exsolr.Eval(*T, ip);
+         real_t diffi = valsi(j) - exsoli.Eval(*T, ip);
+         real_t diff = hypot(diffr, diffi);
+         if (p < infinity())
+         {
+            diff = pow(diff, p);
+            if (weight)
+            {
+               diff *= weight->Eval(*T, ip);
+            }
+            elem_error += ip.weight * T->Weight() * diff;
+         }
+         else
+         {
+            if (weight)
+            {
+               diff *= weight->Eval(*T, ip);
+            }
+            error = std::max(error, diff);
+         }
+      }
+      if (p < infinity())
+      {
+         // negative quadrature weights may cause the error to be negative
+         error += fabs(elem_error);
+      }
+   }
+
+   if (p < infinity())
+   {
+      error = pow(error, 1./p);
+   }
+
+   return error;
+}
+
 void ComplexGridFunction::Save(std::ostream &os) const
 {
    os << "ComplexGridFunction\n";
@@ -643,8 +718,8 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
 
    // A = A_r + i A_i
    A.Clear();
-   if ( A_r.Type() == Operator::MFEM_SPARSEMAT ||
-        A_i.Type() == Operator::MFEM_SPARSEMAT )
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
    {
       ComplexSparseMatrix * A_sp =
          new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
@@ -704,8 +779,8 @@ SesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
 
    // A = A_r + i A_i
    A.Clear();
-   if ( A_r.Type() == Operator::MFEM_SPARSEMAT ||
-        A_i.Type() == Operator::MFEM_SPARSEMAT )
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
    {
       ComplexSparseMatrix * A_sp =
          new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
@@ -768,6 +843,426 @@ SesquilinearForm::Update(FiniteElementSpace *nfes)
    if ( blfi ) { blfi->Update(nfes); }
 }
 
+bool
+MixedSesquilinearForm::RealInteg()
+{
+   int nint = mblfr->GetDBFI()->Size() + mblfr->GetBBFI()->Size() +
+              mblfr->GetFBFI()->Size() + mblfr->GetBFBFI()->Size() +
+              mblfr->GetTFBFI()->Size() + mblfr->GetBTFBFI()->Size();
+   return (nint != 0);
+}
+
+bool
+MixedSesquilinearForm::ImagInteg()
+{
+   int nint = mblfi->GetDBFI()->Size() + mblfi->GetBBFI()->Size() +
+              mblfi->GetFBFI()->Size() + mblfi->GetBFBFI()->Size() +
+              mblfi->GetTFBFI()->Size() + mblfi->GetBTFBFI()->Size();
+   return (nint != 0);
+}
+
+MixedSesquilinearForm::MixedSesquilinearForm(FiniteElementSpace * trial_fes,
+                                             FiniteElementSpace * test_fes,
+                                             ComplexOperator::Convention convention)
+   : conv(convention),
+     mblfr(new mfem::MixedBilinearForm(trial_fes, test_fes)),
+     mblfi(new mfem::MixedBilinearForm(trial_fes, test_fes))
+{
+}
+
+MixedSesquilinearForm::MixedSesquilinearForm(FiniteElementSpace * trial_fes,
+                                             FiniteElementSpace * test_fes,
+                                             MixedBilinearForm * bfr,
+                                             MixedBilinearForm * bfi,
+                                             ComplexOperator::Convention convention)
+   : conv(convention),
+     mblfr(new MixedBilinearForm(trial_fes, test_fes, bfr)),
+     mblfi(new MixedBilinearForm(trial_fes, test_fes, bfi))
+{
+}
+
+MixedSesquilinearForm::~MixedSesquilinearForm()
+{
+   delete mblfr;
+   delete mblfi;
+}
+
+void
+MixedSesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                                           BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddDomainIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddDomainIntegrator(bfi_imag);
+   }
+}
+
+void
+MixedSesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                                           BilinearFormIntegrator * bfi_imag,
+                                           Array<int> & elem_marker)
+{
+   if (bfi_real)
+   {
+      mblfr->AddDomainIntegrator(bfi_real, elem_marker);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddDomainIntegrator(bfi_imag, elem_marker);
+   }
+}
+
+void
+MixedSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                                             BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBoundaryIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBoundaryIntegrator(bfi_imag);
+   }
+}
+
+void
+MixedSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                                             BilinearFormIntegrator * bfi_imag,
+                                             Array<int> & bdr_marker)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBoundaryIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBoundaryIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void
+MixedSesquilinearForm::AddInteriorFaceIntegrator(BilinearFormIntegrator *
+                                                 bfi_real,
+                                                 BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddInteriorFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddInteriorFaceIntegrator(bfi_imag);
+   }
+}
+
+void
+MixedSesquilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                            BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBdrFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBdrFaceIntegrator(bfi_imag);
+   }
+}
+
+void
+MixedSesquilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                            BilinearFormIntegrator * bfi_imag,
+                                            Array<int> & bdr_marker)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBdrFaceIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBdrFaceIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void MixedSesquilinearForm::AddTraceFaceIntegrator(BilinearFormIntegrator *
+                                                   bfi_real,
+                                                   BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddTraceFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddTraceFaceIntegrator(bfi_imag);
+   }
+}
+
+void MixedSesquilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator
+                                                      *bfi_real,
+                                                      BilinearFormIntegrator *bfi_imag)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBdrTraceFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBdrTraceFaceIntegrator(bfi_imag);
+   }
+}
+
+void MixedSesquilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator
+                                                      *bfi_real,
+                                                      BilinearFormIntegrator *bfi_imag,
+                                                      Array<int> &bdr_marker)
+{
+   if (bfi_real)
+   {
+      mblfr->AddBdrTraceFaceIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      mblfi->AddBdrTraceFaceIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void
+MixedSesquilinearForm::Assemble(int skip_zeros)
+{
+   mblfr->Assemble(skip_zeros);
+   mblfi->Assemble(skip_zeros);
+}
+
+void
+MixedSesquilinearForm::Finalize(int skip_zeros)
+{
+   mblfr->Finalize(skip_zeros);
+   mblfi->Finalize(skip_zeros);
+}
+
+ComplexSparseMatrix *
+MixedSesquilinearForm::AssembleComplexSparseMatrix()
+{
+   return new mfem::ComplexSparseMatrix(
+             &mblfr->SpMat(), &mblfi->SpMat(), false, false, conv);
+}
+
+void
+MixedSesquilinearForm::FormRectangularLinearSystem(const Array<int> &
+                                                   ess_trial_tdof_list,
+                                                   const Array<int> & ess_test_tdof_list,
+                                                   Vector & x,
+                                                   Vector & b,
+                                                   OperatorHandle & A,
+                                                   Vector & X,
+                                                   Vector & B)
+{
+   FiniteElementSpace * fes_trial = mblfr->TrialFESpace();
+   FiniteElementSpace * fes_test = mblfr->TestFESpace();
+   const int vsize_trial = fes_trial->GetVSize();
+   const int vsize_test = fes_test->GetVSize();
+
+   // Allocate temporary Vector
+   Vector b_0;
+   b_0.UseDevice(true);
+   b_0.SetSize(vsize_test);
+   b_0 = 0.0;
+
+   // Extract the real and imaginary parts of the input Vectors
+   MFEM_ASSERT(x.Size() == 2 * vsize_trial,
+               "Input GridFunction of incorrect size!");
+   x.Read();
+   Vector x_r;
+   x_r.MakeRef(x, 0, vsize_trial);
+   Vector x_i;
+   x_i.MakeRef(x, vsize_trial, vsize_trial);
+
+   MFEM_ASSERT(b.Size() == 2 * vsize_test, "Input LinearForm of incorrect size!");
+   b.Read();
+   Vector b_r;
+   b_r.MakeRef(b, 0, vsize_test);
+   Vector b_i;
+   b_i.MakeRef(b, vsize_test, vsize_test);
+
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
+   {
+      b_i *= -1.0;
+   }
+
+   const int tvsize_trial = fes_trial->GetTrueVSize();
+   const int tvsize_test = fes_test->GetTrueVSize();
+   OperatorHandle A_r, A_i;
+
+   X.UseDevice(true);
+   X.SetSize(2 * tvsize_trial);
+   X = 0.0;
+
+   B.UseDevice(true);
+   B.SetSize(2 * tvsize_test);
+   B = 0.0;
+
+   Vector X_r;
+   X_r.MakeRef(X, 0, tvsize_trial);
+   Vector X_i;
+   X_i.MakeRef(X, tvsize_trial, tvsize_trial);
+   Vector B_r;
+   B_r.MakeRef(B, 0, tvsize_test);
+   Vector B_i;
+   B_i.MakeRef(B, tvsize_test, tvsize_test);
+
+   Vector X_0, B_0;
+
+   if (RealInteg())
+   {
+      b_0 = b_r;
+      mblfr->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_r, X_0, B_0);
+      X_r = X_0;
+      B_r = B_0;
+
+      b_0 = b_i;
+      mblfr->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_r, X_0, B_0);
+      X_i = X_0;
+      B_i = B_0;
+
+      if (ImagInteg())
+      {
+         b_0 = 0.0;
+         mblfi->FormRectangularLinearSystem(
+            ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_i, X_0, B_0);
+         B_r -= B_0;
+
+         b_0 = 0.0;
+         mblfi->FormRectangularLinearSystem(
+            ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_i, X_0, B_0);
+         B_i += B_0;
+      }
+   }
+   else if (ImagInteg())
+   {
+      b_0 = b_i;
+      mblfi->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_i, X_0, B_0);
+      X_r = X_0;
+      B_i = B_0;
+
+      b_0 = b_r;
+      b_0 *= -1.0;
+      mblfi->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_i, X_0, B_0);
+      X_i = X_0;
+      B_r = B_0;
+      B_r *= -1.0;
+   }
+   else
+   {
+      MFEM_ABORT("Real and Imaginary part of the Mixed Sesquilinear form are empty");
+   }
+
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
+   {
+      B_i *= -1.0;
+      b_i *= -1.0;
+   }
+
+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
+   b_r.SyncAliasMemory(b);
+   b_i.SyncAliasMemory(b);
+
+   X_r.SyncAliasMemory(X);
+   X_i.SyncAliasMemory(X);
+   B_r.SyncAliasMemory(B);
+   B_i.SyncAliasMemory(B);
+
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
+   {
+      ComplexSparseMatrix * A_hyp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op = new ComplexOperator(A_r.As<Operator>(),
+                                                   A_i.As<Operator>(),
+                                                   A_r.OwnsOperator(),
+                                                   A_i.OwnsOperator(),
+                                                   conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
+}
+
+void
+MixedSesquilinearForm::FormRectangularSystemMatrix(const mfem::Array<int> &
+                                                   ess_trial_tdof_list,
+                                                   const mfem::Array<int> & ess_test_tdof_list,
+                                                   mfem::OperatorHandle & A)
+{
+   OperatorHandle A_r, A_i;
+   if (RealInteg())
+   {
+      mblfr->FormRectangularSystemMatrix(ess_trial_tdof_list, ess_test_tdof_list,
+                                         A_r);
+   }
+   if (ImagInteg())
+   {
+      mblfi->FormRectangularSystemMatrix(ess_trial_tdof_list, ess_test_tdof_list,
+                                         A_i);
+   }
+   if (!RealInteg() && !ImagInteg())
+   {
+      MFEM_ABORT("Both Real and Imaginary part of the Mixed Sesquilinear form are empty");
+   }
+
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::MFEM_SPARSEMAT) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::MFEM_SPARSEMAT))
+   {
+      ComplexSparseMatrix * A_hyp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op = new ComplexOperator(A_r.As<Operator>(),
+                                                   A_i.As<Operator>(),
+                                                   A_r.OwnsOperator(),
+                                                   A_i.OwnsOperator(),
+                                                   conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
+}
+
+void
+MixedSesquilinearForm::Update()
+{
+   mblfr->Update();
+   mblfi->Update();
+}
+
 
 #ifdef MFEM_USE_MPI
 
@@ -1539,8 +2034,8 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
 
    // A = A_r + i A_i
    A.Clear();
-   if ( A_r.Type() == Operator::Hypre_ParCSR ||
-        A_i.Type() == Operator::Hypre_ParCSR )
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
    {
       ComplexHypreParMatrix * A_hyp =
          new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
@@ -1607,8 +2102,8 @@ ParSesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
 
    // A = A_r + i A_i
    A.Clear();
-   if ( A_r.Type() == Operator::Hypre_ParCSR ||
-        A_i.Type() == Operator::Hypre_ParCSR )
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
    {
       ComplexHypreParMatrix * A_hyp =
          new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
@@ -1666,6 +2161,434 @@ ParSesquilinearForm::Update(FiniteElementSpace *nfes)
    if ( pblfi ) { pblfi->Update(nfes); }
 }
 
+bool
+ParMixedSesquilinearForm::RealInteg()
+{
+   int nint = pmblfr->GetDBFI()->Size() + pmblfr->GetBBFI()->Size() +
+              pmblfr->GetFBFI()->Size() + pmblfr->GetBFBFI()->Size() +
+              pmblfr->GetTFBFI()->Size() + pmblfr->GetBTFBFI()->Size();
+   return (nint != 0);
+}
+
+bool
+ParMixedSesquilinearForm::ImagInteg()
+{
+   int nint = pmblfi->GetDBFI()->Size() + pmblfi->GetBBFI()->Size() +
+              pmblfi->GetFBFI()->Size() + pmblfi->GetBFBFI()->Size() +
+              pmblfi->GetTFBFI()->Size() + pmblfi->GetBTFBFI()->Size();
+   return (nint != 0);
+}
+
+ParMixedSesquilinearForm::ParMixedSesquilinearForm(ParFiniteElementSpace *
+                                                   trial_fes,
+                                                   ParFiniteElementSpace * test_fes,
+                                                   ComplexOperator::Convention convention)
+   : conv(convention),
+     pmblfr(new ParMixedBilinearForm(trial_fes, test_fes)),
+     pmblfi(new ParMixedBilinearForm(trial_fes, test_fes))
+{
+}
+
+ParMixedSesquilinearForm::ParMixedSesquilinearForm(ParFiniteElementSpace *
+                                                   trial_fes,
+                                                   ParFiniteElementSpace * test_fes,
+                                                   ParMixedBilinearForm * pbfr,
+                                                   ParMixedBilinearForm * pbfi,
+                                                   ComplexOperator::Convention convention)
+   : conv(convention),
+     pmblfr(new ParMixedBilinearForm(trial_fes, test_fes, pbfr)),
+     pmblfi(new ParMixedBilinearForm(trial_fes, test_fes, pbfi))
+{
+}
+
+ParMixedSesquilinearForm::~ParMixedSesquilinearForm()
+{
+   delete pmblfr;
+   delete pmblfi;
+}
+
+void
+ParMixedSesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                                              BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddDomainIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddDomainIntegrator(bfi_imag);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                                              BilinearFormIntegrator * bfi_imag,
+                                              Array<int> & elem_marker)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddDomainIntegrator(bfi_real, elem_marker);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddDomainIntegrator(bfi_imag, elem_marker);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *
+                                                bfi_real,
+                                                BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBoundaryIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBoundaryIntegrator(bfi_imag);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *
+                                                bfi_real,
+                                                BilinearFormIntegrator * bfi_imag,
+                                                Array<int> & bdr_marker)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBoundaryIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBoundaryIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddInteriorFaceIntegrator(BilinearFormIntegrator *
+                                                    bfi_real,
+                                                    BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddInteriorFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddInteriorFaceIntegrator(bfi_imag);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *
+                                               bfi_real,
+                                               BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBdrFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBdrFaceIntegrator(bfi_imag);
+   }
+}
+
+void
+ParMixedSesquilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *
+                                               bfi_real,
+                                               BilinearFormIntegrator * bfi_imag,
+                                               Array<int> & bdr_marker)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBdrFaceIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBdrFaceIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void ParMixedSesquilinearForm::AddTraceFaceIntegrator(BilinearFormIntegrator *
+                                                      bfi_real,
+                                                      BilinearFormIntegrator * bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddTraceFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddTraceFaceIntegrator(bfi_imag);
+   }
+}
+
+void ParMixedSesquilinearForm::AddBdrTraceFaceIntegrator(
+   BilinearFormIntegrator *bfi_real,
+   BilinearFormIntegrator *bfi_imag)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBdrTraceFaceIntegrator(bfi_real);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBdrTraceFaceIntegrator(bfi_imag);
+   }
+}
+
+void ParMixedSesquilinearForm::AddBdrTraceFaceIntegrator(
+   BilinearFormIntegrator *bfi_real,
+   BilinearFormIntegrator *bfi_imag,
+   Array<int> &bdr_marker)
+{
+   if (bfi_real)
+   {
+      pmblfr->AddBdrTraceFaceIntegrator(bfi_real, bdr_marker);
+   }
+   if (bfi_imag)
+   {
+      pmblfi->AddBdrTraceFaceIntegrator(bfi_imag, bdr_marker);
+   }
+}
+
+void
+ParMixedSesquilinearForm::Assemble(int skip_zeros)
+{
+   pmblfr->Assemble(skip_zeros);
+   pmblfi->Assemble(skip_zeros);
+}
+
+void
+ParMixedSesquilinearForm::Finalize(int skip_zeros)
+{
+   pmblfr->Finalize(skip_zeros);
+   pmblfi->Finalize(skip_zeros);
+}
+
+ComplexHypreParMatrix *
+ParMixedSesquilinearForm::ParallelAssemble()
+{
+   return new ComplexHypreParMatrix(
+             pmblfr->ParallelAssemble(), pmblfi->ParallelAssemble(), true, true, conv);
+}
+
+void
+ParMixedSesquilinearForm::FormRectangularLinearSystem(const Array<int> &
+                                                      ess_trial_tdof_list,
+                                                      const Array<int> & ess_test_tdof_list,
+                                                      Vector & x,
+                                                      Vector & b,
+                                                      OperatorHandle & A,
+                                                      Vector & X,
+                                                      Vector & B)
+{
+   FiniteElementSpace * pfes_trial = pmblfr->TrialFESpace();
+   FiniteElementSpace * pfes_test = pmblfr->TestFESpace();
+   const int vsize_trial = pfes_trial->GetVSize();
+   const int vsize_test = pfes_test->GetVSize();
+
+   // Allocate temporary Vector
+   Vector b_0;
+   b_0.UseDevice(true);
+   b_0.SetSize(vsize_test);
+   b_0 = 0.0;
+
+   // Extract the real and imaginary parts of the input Vectors
+   MFEM_ASSERT(x.Size() == 2 * vsize_trial,
+               "Input GridFunction of incorrect size!");
+   x.Read();
+   Vector x_r;
+   x_r.MakeRef(x, 0, vsize_trial);
+   Vector x_i;
+   x_i.MakeRef(x, vsize_trial, vsize_trial);
+
+   MFEM_ASSERT(b.Size() == 2 * vsize_test, "Input LinearForm of incorrect size!");
+   b.Read();
+   Vector b_r;
+   b_r.MakeRef(b, 0, vsize_test);
+   Vector b_i;
+   b_i.MakeRef(b, vsize_test, vsize_test);
+
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
+   {
+      b_i *= -1.0;
+   }
+
+   const int tvsize_trial = pfes_trial->GetTrueVSize();
+   const int tvsize_test = pfes_test->GetTrueVSize();
+   OperatorHandle A_r, A_i;
+
+   X.UseDevice(true);
+   X.SetSize(2 * tvsize_trial);
+   X = 0.0;
+
+   B.UseDevice(true);
+   B.SetSize(2 * tvsize_test);
+   B = 0.0;
+
+   Vector X_r;
+   X_r.MakeRef(X, 0, tvsize_trial);
+   Vector X_i;
+   X_i.MakeRef(X, tvsize_trial, tvsize_trial);
+   Vector B_r;
+   B_r.MakeRef(B, 0, tvsize_test);
+   Vector B_i;
+   B_i.MakeRef(B, tvsize_test, tvsize_test);
+
+   Vector X_0, B_0;
+
+   if (RealInteg())
+   {
+      b_0 = b_r;
+      pmblfr->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_r, X_0, B_0);
+      X_r = X_0;
+      B_r = B_0;
+
+      b_0 = b_i;
+      pmblfr->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_r, X_0, B_0);
+      X_i = X_0;
+      B_i = B_0;
+
+      if (ImagInteg())
+      {
+         b_0 = 0.0;
+         pmblfi->FormRectangularLinearSystem(
+            ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_i, X_0, B_0);
+         B_r -= B_0;
+
+         b_0 = 0.0;
+         pmblfi->FormRectangularLinearSystem(
+            ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_i, X_0, B_0);
+         B_i += B_0;
+      }
+   }
+   else if (ImagInteg())
+   {
+      b_0 = b_i;
+      pmblfi->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_r, b_0, A_i, X_0, B_0);
+      X_r = X_0;
+      B_i = B_0;
+
+      b_0 = b_r;
+      b_0 *= -1.0;
+      pmblfi->FormRectangularLinearSystem(
+         ess_trial_tdof_list, ess_test_tdof_list, x_i, b_0, A_i, X_0, B_0);
+      X_i = X_0;
+      B_r = B_0;
+      B_r *= -1.0;
+   }
+   else
+   {
+      MFEM_ABORT("Real and Imaginary part of the Mixed Sesquilinear form are empty");
+   }
+
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
+   {
+      B_i *= -1.0;
+      b_i *= -1.0;
+   }
+
+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
+   b_r.SyncAliasMemory(b);
+   b_i.SyncAliasMemory(b);
+
+   X_r.SyncAliasMemory(X);
+   X_i.SyncAliasMemory(X);
+   B_r.SyncAliasMemory(B);
+   B_i.SyncAliasMemory(B);
+
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
+   {
+      ComplexHypreParMatrix * A_hyp =
+         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
+                                   A_i.As<HypreParMatrix>(),
+                                   A_r.OwnsOperator(),
+                                   A_i.OwnsOperator(),
+                                   conv);
+      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op = new ComplexOperator(A_r.As<Operator>(),
+                                                   A_i.As<Operator>(),
+                                                   A_r.OwnsOperator(),
+                                                   A_i.OwnsOperator(),
+                                                   conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
+}
+
+void
+ParMixedSesquilinearForm::FormRectangularSystemMatrix(const Array<int> &
+                                                      ess_trial_tdof_list,
+                                                      const Array<int> & ess_test_tdof_list,
+                                                      OperatorHandle & A)
+{
+   OperatorHandle A_r, A_i;
+   if (RealInteg())
+   {
+      pmblfr->FormRectangularSystemMatrix(ess_trial_tdof_list, ess_test_tdof_list,
+                                          A_r);
+   }
+   if (ImagInteg())
+   {
+      pmblfi->FormRectangularSystemMatrix(ess_trial_tdof_list, ess_test_tdof_list,
+                                          A_i);
+   }
+   if (!RealInteg() && !ImagInteg())
+   {
+      MFEM_ABORT("Both Real and Imaginary part of the Mixed Sesquilinear form are empty");
+   }
+
+   // A = A_r + i A_i
+   A.Clear();
+   if ((!A_r.Ptr() || A_r.Type() == Operator::Hypre_ParCSR) &&
+       (!A_i.Ptr() || A_i.Type() == Operator::Hypre_ParCSR))
+   {
+      ComplexHypreParMatrix * A_hyp =
+         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
+                                   A_i.As<HypreParMatrix>(),
+                                   A_r.OwnsOperator(),
+                                   A_i.OwnsOperator(),
+                                   conv);
+      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op = new ComplexOperator(A_r.As<Operator>(),
+                                                   A_i.As<Operator>(),
+                                                   A_r.OwnsOperator(),
+                                                   A_i.OwnsOperator(),
+                                                   conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
+}
+
+void
+ParMixedSesquilinearForm::Update()
+{
+   pmblfr->Update();
+   pmblfi->Update();
+}
+
+
+
 #endif // MFEM_USE_MPI
 
 }

fem/complex_fem.hpp

@@ -166,6 +166,75 @@ public:
       return sqrt(err_r * err_r + err_i * err_i);
    }
 
+   /// @brief Returns Max|u_ex - u_h| error for complex-valued H1 or L2 elements
+   ///
+   /// Compute the $L_\infty$ error across the entire domain.
+   ///
+   /// @param[in] exsolr  Coefficient object reproducing the real part of the
+   ///                    anticipated values of the scalar field, Re(u_ex).
+   /// @param[in] exsoli  Coefficient object reproducing the imaginary part of
+   ///                    the anticipated values of the scalar field, Im(u_ex).
+   /// @param[in] irs        Optional pointer to an array of custom integration
+   ///                       rules e.g. higher order than the default rules. If
+   ///                       present the array will be indexed by
+   ///                       Geometry::Type.
+   ///
+   /// @note Uses ComputeLpError internally. See the ComputeLpError
+   ///       documentation for generalizations of this error computation.
+   ///
+   /// @note If an array of integration rules is provided through @a irs, be
+   ///       sure to include valid rules for each element type that may occur
+   ///       in the list of elements.
+   ///
+   virtual real_t ComputeMaxError(Coefficient &exsolr,
+                                  Coefficient &exsoli,
+                                  const IntegrationRule *irs[] = NULL) const
+   {
+      return ComputeLpError(infinity(), exsolr, exsoli, NULL, irs);
+   }
+
+   /// @brief Returns ||u_ex - u_h||_Lp for complex-valued H1 or L2 elements
+   ///
+   /// Computes:
+   ///    $$(\sum_{elems} \int_{elem} w \, |u_{ex} - u_h|^p)^{1/p}$$
+   /// Where:
+   ///    $$|u_{ex} - u_h| = \sqrt{Re(u_{ex} - u_h)^2 + Im(u_{ex} - u_h)^2}$$
+   ///
+   /// @param[in] p       Real value indicating the exponent of the $L^p$ norm.
+   ///                    To avoid domain errors p should have a positive value,
+   ///                    either finite or infinite.
+   /// @param[in] exsolr  Coefficient object reproducing the real part of the
+   ///                    anticipated values of the scalar field, Re(u_ex).
+   /// @param[in] exsoli  Coefficient object reproducing the imaginary part of
+   ///                    the anticipated values of the scalar field, Im(u_ex).
+   /// @param[in] weight  Optional pointer to a Coefficient object reproducing
+   ///                    a weighting function, w.
+   /// @param[in] irs     Optional pointer to an array of custom integration
+   ///                    rules e.g. higher order than the default rules. If
+   ///                    present the array will be indexed by Geometry::Type.
+   /// @param[in] elems   Optional pointer to a marker array, with a length
+   ///                    equal to the number of local elements, indicating
+   ///                    which elements to integrate over. Only those elements
+   ///                    corresponding to non-zero entries in @a elems will
+   ///                    contribute to the computed L2 error.
+   ///
+   /// @note If an array of integration rules is provided through @a irs, be
+   ///       sure to include valid rules for each element type that may occur
+   ///       in the list of elements.
+   ///
+   /// @note Quadratures with negative weights (as in some simplex integration
+   ///       rules in MFEM) can produce negative integrals even with
+   ///       non-negative integrands. To avoid returning negative errors this
+   ///       function uses the absolute values of the element-wise integrals.
+   ///       This may lead to results which are not entirely consistent with
+   ///       such integration rules.
+   virtual real_t ComputeLpError(const real_t p,
+                                 Coefficient &exsolr,
+                                 Coefficient &exsoli,
+                                 Coefficient *weight = NULL,
+                                 const IntegrationRule *irs[] = NULL,
+                                 const Array<int> *elems = NULL) const;
+
    /// Save the ComplexGridFunction to an output stream.
    virtual void Save(std::ostream &out) const;
 
@@ -436,6 +505,186 @@ public:
    virtual ~SesquilinearForm();
 };
 
+/** Class for a mixed sesquilinear form
+
+    A mixed sesquilinear form is a generalization of a mixed bilinear form to
+    complex-valued fields. Mixed sesquilinear forms are linear in the second
+    argument but the first argument involves a complex conjugate in the sense
+    that:
+
+                a(alpha u, beta v) = conj(alpha) beta a(u, v)
+
+    The @a convention argument in the class's constructor is documented in the
+    mfem::ComplexOperator class found in linalg/complex_operator.hpp.
+
+    When supplying integrators to the MixedSesquilinearForm either the real or
+    imaginary integrator can be NULL. This indicates that the corresponding
+    portion of the complex-valued material coefficient is equal to zero.
+*/
+class MixedSesquilinearForm
+{
+private:
+   ComplexOperator::Convention conv;
+
+   MixedBilinearForm * mblfr;
+   MixedBilinearForm * mblfi;
+
+   /* These methods check if the real/imag parts of the sesqulinear form are not
+      empty */
+   bool RealInteg();
+   bool ImagInteg();
+
+public:
+   MixedSesquilinearForm(
+      FiniteElementSpace * trial_fes,
+      FiniteElementSpace * test_fes,
+      ComplexOperator::Convention convention = ComplexOperator::HERMITIAN);
+
+   /** @brief Create a MixedSesquilinearForm on the given trial and test
+       FiniteElementSpaces, using the same integrators as the
+       MixedBilinearForms @a bfr and @a bfi.
+
+       The FiniteElementSpace pointers are not owned by the newly constructed
+       object.
+
+       The integrators are copied as pointers and they are not owned by the
+       newly constructed MixedSesquilinearForm. */
+   MixedSesquilinearForm(
+      FiniteElementSpace * trial_fes,
+      FiniteElementSpace * test_fes,
+      MixedBilinearForm * bfr,
+      MixedBilinearForm * bfi,
+      ComplexOperator::Convention convention = ComplexOperator::HERMITIAN);
+
+   ComplexOperator::Convention GetConvention() const { return conv; }
+   void SetConvention(const ComplexOperator::Convention & convention) { conv = convention; }
+
+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::LEGACY (default)
+       - AssemblyLevel::FULL
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      mblfr->SetAssemblyLevel(assembly_level);
+      mblfi->SetAssemblyLevel(assembly_level);
+   }
+
+   MixedBilinearForm & real() { return *mblfr; }
+   MixedBilinearForm & imag() { return *mblfi; }
+   const MixedBilinearForm & real() const { return *mblfr; }
+   const MixedBilinearForm & imag() const { return *mblfi; }
+
+   /// Adds new Domain Integrator.
+   void AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                            BilinearFormIntegrator * bfi_imag);
+
+   /// Adds new Domain Integrator, restricted to specific attributes.
+   void AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                            BilinearFormIntegrator * bfi_imag,
+                            Array<int> & elem_marker);
+
+   /// Adds new Boundary Integrator.
+   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                              BilinearFormIntegrator * bfi_imag);
+
+   /** @brief Adds new boundary Integrator, restricted to specific boundary
+       attributes.
+
+       Assumes ownership of @a bfi.
+
+       The mfem::array @a bdr_marker is stored internally as a pointer to the given
+       mfem::Array<int> object. */
+   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                              BilinearFormIntegrator * bfi_imag,
+                              Array<int> & bdr_marker);
+
+   /// Adds new interior Face Integrator. Assumes ownership of @a bfi.
+   void AddInteriorFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag);
+
+   /// Adds new boundary Face Integrator. Assumes ownership of @a bfi.
+   void AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                             BilinearFormIntegrator * bfi_imag);
+
+   /** @brief Adds new boundary Face Integrator, restricted to specific boundary
+       attributes.
+
+       Assumes ownership of @a bfi.
+
+       The mfem::array @a bdr_marker is stored internally as a pointer to the given
+       mfem::Array<int> object. */
+   void AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                             BilinearFormIntegrator * bfi_imag,
+                             Array<int> & bdr_marker);
+
+   /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
+
+       This type of integrator assembles terms over all faces of the mesh using
+       the face FE from the trial space and the two adjacent volume FEs from
+       the test space. */
+   void AddTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                               BilinearFormIntegrator * bfi_imag);
+
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag);
+
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag,
+                                  Array<int> &bdr_marker);
+
+   /// Assemble the local matrix
+   void Assemble(int skip_zeros = 1);
+
+   /// Finalizes the matrix initialization.
+   void Finalize(int skip_zeros = 1);
+
+   /// Updates the internal mixed forms with the new finite element space.
+   virtual void Update();
+
+   /** @brief Return a ComplexSparseMatrix wrapping the local (L-dof) real
+       and imaginary matrices of the form.
+
+       The returned wrapper has to be deleted by the caller, but it does not
+       own the wrapped real and imaginary matrices, which remain owned by
+       this form. */
+   ComplexSparseMatrix *AssembleComplexSparseMatrix();
+
+   /// Return the trial FE space associated with the MixedSesquilinearForm.
+   FiniteElementSpace *TrialFESpace() { return mblfr->TrialFESpace(); }
+
+   /// Read-only access to the associated trial FiniteElementSpace.
+   const FiniteElementSpace *TrialFESpace() const { return mblfr->TrialFESpace(); }
+
+   /// Return the test FE space associated with the MixedSesquilinearForm.
+   FiniteElementSpace *TestFESpace() { return mblfr->TestFESpace(); }
+
+   /// Read-only access to the associated test FiniteElementSpace.
+   const FiniteElementSpace *TestFESpace() const { return mblfr->TestFESpace(); }
+
+
+   void FormRectangularLinearSystem(const Array<int> & ess_trial_tdof_list,
+                                    const Array<int> & ess_test_tdof_list,
+                                    Vector & x,
+                                    Vector & b,
+                                    OperatorHandle & A,
+                                    Vector & X,
+                                    Vector & B);
+
+   void FormRectangularSystemMatrix(const Array<int> & ess_trial_tdof_list,
+                                    const Array<int> & ess_test_tdof_list,
+                                    OperatorHandle & A);
+
+   virtual ~MixedSesquilinearForm();
+};
+
 #ifdef MFEM_USE_MPI
 
 /// Class for parallel complex-valued grid function - real + imaginary part
@@ -852,6 +1101,169 @@ public:
    virtual ~ParSesquilinearForm();
 };
 
+/** Class for a parallel mixed sesquilinear form
+
+    A mixed sesquilinear form is a generalization of a mixed bilinear form to
+    complex-valued fields. Mixed sesquilinear forms are linear in the second
+    argument but the first argument involves a complex conjugate in the sense
+    that:
+
+                a(alpha u, beta v) = conj(alpha) beta a(u, v)
+
+    The @a convention argument in the class's constructor is documented in the
+    mfem::ComplexOperator class found in linalg/complex_operator.hpp.
+
+    When supplying integrators to the ParMixedSesquilinearForm either the real
+    or imaginary integrator can be NULL. This indicates that the corresponding
+    portion of the complex-valued material coefficient is equal to zero.
+*/
+class ParMixedSesquilinearForm
+{
+private:
+   ComplexOperator::Convention conv;
+
+   ParMixedBilinearForm * pmblfr;
+   ParMixedBilinearForm * pmblfi;
+
+   /* These methods check if the real/imag parts of the sesqulinear form are
+    not empty */
+   bool RealInteg();
+   bool ImagInteg();
+
+public:
+   ParMixedSesquilinearForm(
+      ParFiniteElementSpace * trial_fes,
+      ParFiniteElementSpace * test_fes,
+      ComplexOperator::Convention convention = ComplexOperator::HERMITIAN);
+
+   /** @brief Create a ParMixedSesquilinearForm on the given trial and test
+       ParFiniteElementSpaces, using the same integrators as the
+       ParMixedBilinearForms @a pbfr and @a pbfi.
+
+       The ParFiniteElementSpace pointers are not owned by the newly
+       constructed object.
+
+       The integrators are copied as pointers and they are not owned by the
+       newly constructed ParMixedSesquilinearForm. */
+   ParMixedSesquilinearForm(
+      ParFiniteElementSpace * trial_fes,
+      ParFiniteElementSpace * test_fes,
+      ParMixedBilinearForm * pbfr,
+      ParMixedBilinearForm * pbfi,
+      ComplexOperator::Convention convention = ComplexOperator::HERMITIAN);
+
+   ComplexOperator::Convention GetConvention() const { return conv; }
+   void SetConvention(const ComplexOperator::Convention & convention) { conv = convention; }
+
+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::LEGACY (default)
+       - AssemblyLevel::FULL
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      pmblfr->SetAssemblyLevel(assembly_level);
+      pmblfi->SetAssemblyLevel(assembly_level);
+   }
+
+   ParMixedBilinearForm & real() { return *pmblfr; }
+   ParMixedBilinearForm & imag() { return *pmblfi; }
+   const ParMixedBilinearForm & real() const { return *pmblfr; }
+   const ParMixedBilinearForm & imag() const { return *pmblfi; }
+
+   /// Adds new Domain Integrator.
+   void AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                            BilinearFormIntegrator * bfi_imag);
+
+   /// Adds new Domain Integrator, restricted to specific attributes.
+   void AddDomainIntegrator(BilinearFormIntegrator * bfi_real,
+                            BilinearFormIntegrator * bfi_imag,
+                            Array<int> & elem_marker);
+
+   /// Adds new Boundary Integrator.
+   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                              BilinearFormIntegrator * bfi_imag);
+
+   /** @brief Adds new boundary Integrator, restricted to specific boundary
+       attributes.
+
+       Assumes ownership of @a bfi.
+
+       The mfem::array @a bdr_marker is stored internally as a pointer to the given
+       mfem::Array<int> object. */
+   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi_real,
+                              BilinearFormIntegrator * bfi_imag,
+                              Array<int> & bdr_marker);
+
+   /// Adds new interior Face Integrator. Assumes ownership of @a bfi.
+   void AddInteriorFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag);
+
+   /// Adds new boundary Face Integrator. Assumes ownership of @a bfi.
+   void AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                             BilinearFormIntegrator * bfi_imag);
+
+   /** @brief Adds new boundary Face Integrator, restricted to specific boundary
+       attributes.
+
+       Assumes ownership of @a bfi.
+
+       The mfem::array @a bdr_marker is stored internally as a pointer to the given
+       mfem::Array<int> object. */
+   void AddBdrFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                             BilinearFormIntegrator * bfi_imag,
+                             Array<int> & bdr_marker);
+
+   /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
+
+      This type of integrator assembles terms over all faces of the mesh using
+      the face FE from the trial space and the two adjacent volume FEs from
+      the test space. */
+   void AddTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                               BilinearFormIntegrator * bfi_imag);
+
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag);
+
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi_real,
+                                  BilinearFormIntegrator * bfi_imag,
+                                  Array<int> &bdr_marker);
+
+   /// Assemble the local matrix
+   void Assemble(int skip_zeros = 1);
+
+   /// Finalizes the matrix initialization.
+   void Finalize(int skip_zeros = 1);
+
+   /// Updates the internal mixed forms with the new finite element space.
+   virtual void Update();
+
+   /// Returns the matrix assembled on the true dofs, i.e. P^t A P.
+   /** The returned matrix has to be deleted by the caller. */
+   ComplexHypreParMatrix * ParallelAssemble();
+
+   void FormRectangularLinearSystem(const Array<int> & ess_trial_tdof_list,
+                                    const Array<int> & ess_test_tdof_list,
+                                    Vector & x,
+                                    Vector & b,
+                                    OperatorHandle & A,
+                                    Vector & X,
+                                    Vector & B);
+
+   void FormRectangularSystemMatrix(const Array<int> & ess_trial_tdof_list,
+                                    const Array<int> & ess_test_tdof_list,
+                                    OperatorHandle & A);
+
+   virtual ~ParMixedSesquilinearForm();
+};
+
 #endif // MFEM_USE_MPI
 
 }

fem/datacollection.cpp

@@ -809,7 +809,7 @@ ParaViewDataCollectionBase::ParaViewDataCollectionBase(
 
 void ParaViewDataCollectionBase::SetLevelsOfDetail(int levels_of_detail_)
 {
-   levels_of_detail = levels_of_detail_;
+   levels_of_detail = std::max(levels_of_detail_, 1);
 }
 
 void ParaViewDataCollectionBase::SetHighOrderOutput(bool high_order_output_)
@@ -1181,12 +1181,14 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,
    DenseMatrix vval, pmat;
    std::vector<char> buf;
    int vec_dim = it->second->VectorDim();
+   int map_type = it->second->FESpace()->GetTypicalFE()->GetMapType();
    os << "<DataArray type=\"" << GetDataTypeString()
       << "\" Name=\"" << it->first
       << "\" NumberOfComponents=\"" << vec_dim << "\" "
       << VTKComponentLabels(vec_dim) << " "
       << "format=\"" << GetDataFormatString() << "\" >" << '\n';
-   if (vec_dim == 1)
+   if (vec_dim == 1 && (map_type == FiniteElement::VALUE ||
+                        map_type == FiniteElement::INTEGRAL))
    {
       for (int i = 0; i < mesh->GetNE(); i++)
       {

fem/fe/fe_base.hpp

@@ -167,7 +167,15 @@ public:
       /** @brief Full multidimensional representation which does not use tensor
           product structure. The ordering of the degrees of freedom is the
           same as TENSOR, but the sizes of B and G are the same as FULL.*/
-      LEXICOGRAPHIC_FULL
+      LEXICOGRAPHIC_FULL,
+
+      /** @brief Ragged tensor product representation using 1D matrices/tensors
+          with dimensions using 1D number of quadrature points and ragged tensor degrees of
+          freedom. */
+      /** Used only for partial assembly of the H1 positive basis. The
+          size of B is d1d x qnpt x dim. Since different Gauss-Jacobi quadrature rules
+          are employed in each dimension, we need to store dim arrays. */
+      RAGGED_TENSOR
    };
 
    /// Describes the contents of the #B, #Bt, #G, and #Gt arrays, see #Mode.
@@ -228,6 +236,39 @@ public:
       const Array<DofToQuad*> &dof2quad_array,
       const IntegrationRule &ir,
       DofToQuad::Mode mode);
+
+   virtual ~DofToQuad() = default;
+};
+
+/** @brief Structure representing the matrices/tensors needed to evaluate (in
+    reference space) the values, gradients, divergences, or curls of a positive
+    FiniteElement on simplices at the quadrature points of Stroud conical quadrature. */
+class RaggedDofToQuad : public DofToQuad
+{
+public:
+   /** @brief Special basis function structures for positive (Bernstein) basis with
+      partial assembly. The storage layout of Ba1 is ndof x nqpt for scalar elements.
+      The storage layout of Ba2 is ndof x ndof x nqpt. In particular, we have
+            Ba2(iqpt, a1, a2) = B^{p-a1}_{a2}(x_{iqpt}). */
+   Array<real_t> Ba1, Ba2, Ba3;
+   Array<real_t> Ba1t, Ba2t, Ba3t;
+
+   /** @brief Special structures for gradients of positive basis with partial assembly.
+      The gradient arrays exploit properties of the Bernstein basis which allow grad(B^p_alpha)
+      to be expressed as the sum of products of B^{p-1}_alpha and the barycentric coordinates.
+      Thus, Ga1 and Ga2 simply contain the ragged tensor product components of B^{p-1}_alpha */
+   Array<real_t> Ga1, Ga2, Ga3;
+   Array<real_t> Ga1t, Ga2t, Ga3t;
+
+   /** @brief Mapping from the Bernstein multi-index (a_1, ..., a_d) to the lexicographic
+       dof index. */
+   Array<int> lex_map;
+
+   Array<int> forward_map2d_diff, forward_map3d_diff;
+   Array<int> inverse_map2d_diff, inverse_map3d_diff;
+
+   Array<int> forward_map2d_mass, forward_map3d_mass;
+   Array<int> inverse_map2d_mass, inverse_map3d_mass;
 };
 
 /// Describes the function space on each element

fem/fe/fe_fixed_order.hpp

@@ -307,12 +307,12 @@ public:
 
    /** @brief virtual function which evaluates the values of all
        shape functions at a given point ip and stores
-       them in the vector shape of dimension Dof (4) */
+       them in the vector shape of dimension Dof (6) */
    void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
 
    /** @brief virtual function which evaluates the values of all
        partial derivatives of all shape functions at a given
-       point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
+       point ip and stores them in the matrix dshape (Dof x Dim) (6 x 3)
        so that each row contains the derivatives of one shape function */
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;
@@ -336,12 +336,12 @@ public:
 
    /** @brief virtual function which evaluates the values of all
        shape functions at a given point ip and stores
-       them in the vector shape of dimension Dof (4) */
+       them in the vector shape of dimension Dof (5) */
    void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
 
    /** @brief virtual function which evaluates the values of all
        partial derivatives of all shape functions at a given
-       point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
+       point ip and stores them in the matrix dshape (Dof x Dim) (5 x 3)
        so that each row contains the derivatives of one shape function */
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;

fem/fe/fe_h1.cpp

@@ -1757,22 +1757,45 @@ H1_BergotPyramidElement::H1_BergotPyramidElement(const int p, const int btype)
       real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
       real_t z = ip.z;
 
-      poly1d.CalcLegendre(p, x, shape_x.GetData());
-      poly1d.CalcLegendre(p, y, shape_y.GetData());
-
-      o = 0;
-      for (int i = 0; i <= p; i++)
+      if (std::abs(z - 1.0) < apex_tol)
       {
-         for (int j = 0; j <= p; j++)
-         {
-            int maxij = std::max(i, j);
-            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
-                                             z, 1.0, shape_z);
-
-            for (int k = 0; k <= p - maxij; k++)
+         // Compute the limit of the basis functions as z->1 with x and y on the
+         // line between the center of the base and the apex
+         o = 0;
+         for (int i = 0; i <= p; i++)
+            for (int j = 0; j <= p; j++)
             {
-               T(o++, m) = shape_x(i) * shape_y(j) * shape_z(k) *
-                           pow(1.0 - ip.z, maxij);
+               int maxij = std::max(i, j);
+               for (int k = 0; k <= p - maxij; k++)
+                  if (i == 0 && j == 0)
+                  {
+                     T(o++, m) = ((k + 3.) * k + 2.) / 2.;
+                  }
+                  else
+                  {
+                     T(o++, m) = 0.;
+                  }
+            }
+      }
+      else
+      {
+         poly1d.CalcLegendre(p, x, shape_x.GetData());
+         poly1d.CalcLegendre(p, y, shape_y.GetData());
+
+         o = 0;
+         for (int i = 0; i <= p; i++)
+         {
+            for (int j = 0; j <= p; j++)
+            {
+               int maxij = std::max(i, j);
+               FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                                z, 1.0, shape_z);
+
+               for (int k = 0; k <= p - maxij; k++)
+               {
+                  T(o++, m) = shape_x(i) * shape_y(j) * shape_z(k) *
+                              pow(1.0 - ip.z, maxij);
+               }
             }
          }
       }
@@ -1793,25 +1816,44 @@ void H1_BergotPyramidElement::CalcShape(const IntegrationPoint &ip,
    Vector u(dof);
 #endif
 
-   real_t x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
-   real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
-   real_t z = ip.z;
+   const real_t x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
+   const real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
+   const real_t z = ip.z;
 
-   poly1d.CalcLegendre(p, x, shape_x.GetData());
-   poly1d.CalcLegendre(p, y, shape_y.GetData());
-
-   int o = 0;
-   for (int i = 0; i <= p; i++)
-      for (int j = 0; j <= p; j++)
-      {
-         int maxij = std::max(i, j);
-         FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0), z, 1.0,
-                                          shape_z);
-         for (int k = 0; k <= p - maxij; k++)
-            u[o++] = shape_x(i) * shape_y(j) * shape_z(k) *
-                     pow(1.0 - ip.z, maxij);
-      }
+   if (std::abs(z - 1.0) < apex_tol)
+   {
+      // Compute the limit of the basis functions as z->1 with x and y on the
+      // line between the center of the base and the apex
+      u = 0.;
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
+         {
+            int maxij = std::max(i, j);
+            for (int k = 0; k <= p - maxij; k++, o++)
+               if (i == 0 && j == 0)
+               {
+                  u(o) = ((k + 3.) * k + 2.) / 2.;
+               }
+         }
+   }
+   else
+   {
+      poly1d.CalcLegendre(p, x, shape_x.GetData());
+      poly1d.CalcLegendre(p, y, shape_y.GetData());
 
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
+         {
+            int maxij = std::max(i, j);
+            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                             z, 1.0, shape_z);
+            for (int k = 0; k <= p - maxij; k++)
+               u[o++] = shape_x(i) * shape_y(j) * shape_z(k) *
+                        pow(1.0 - ip.z, maxij);
+         }
+   }
    Ti.Mult(u, shape);
 }
 
@@ -1830,37 +1872,68 @@ void H1_BergotPyramidElement::CalcDShape(const IntegrationPoint &ip,
    Vector dshape_z(order+1);
    Vector dshape_z_dt(order+1);
 #endif
-   real_t x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
-   real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
-   real_t z = ip.z;
+   const real_t x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
+   const real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
+   const real_t z = ip.z;
 
-   poly1d.CalcLegendre(p, x, shape_x.GetData(), dshape_x.GetData());
-   poly1d.CalcLegendre(p, y, shape_y.GetData(), dshape_y.GetData());
-
-   int o = 0;
-   for (int i = 0; i <= p; i++)
-      for (int j = 0; j <= p; j++)
-      {
-         int maxij = std::max(i, j);
-         FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0), z, 1.0,
-                                          shape_z, dshape_z, dshape_z_dt);
-
-         for (int k = 0; k <= p - maxij; k++, o++)
+   if (std::abs(z - 1.0) < apex_tol)
+   {
+      // Compute the limit of the gradients of the basis functions as
+      // z->1 with x and y on the line between the center of the base and the
+      // apex
+      du = 0.;
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
          {
-            du(o,0) = dshape_x(i) * shape_y(j) * shape_z(k) *
-                      pow(1.0 - ip.z, maxij - 1);
-            du(o,1) = shape_x(i) * dshape_y(j) * shape_z(k) *
-                      pow(1.0 - ip.z, maxij - 1);
-            du(o,2) = shape_x(i) * shape_y(j) * dshape_z(k) *
-                      pow(1.0 - ip.z, maxij) +
-                      (ip.x * dshape_x(i) * shape_y(j) +
-                       ip.y * shape_x(i) * dshape_y(j)) *
-                      shape_z(k) * pow(1.0 - ip.z, maxij - 2) -
-                      maxij * shape_x(i) * shape_y(j) * shape_z(k) *
-                      pow(1.0 - ip.z, maxij - 1);
+            int maxij = std::max(i, j);
+            for (int k = 0; k <= p - maxij; k++, o++)
+            {
+               if (i == 0 && j == 0)
+               {
+                  du(o,2) = (((k + 6.) * k + 11.) * k + 6.) * k / 6.;
+               }
+               else if (i == 1 && j == 0)
+               {
+                  du(o,0) = ((((k + 10.) * k + 35.) * k + 50.) * k + 24.) / 24.;
+               }
+               else if (i == 0 && j == 1)
+               {
+                  du(o,1) = ((((k + 10.) * k + 35.) * k + 50.) * k + 24.) / 24.;
+               }
+            }
          }
-      }
+   }
+   else
+   {
+      poly1d.CalcLegendre(p, x, shape_x.GetData(), dshape_x.GetData());
+      poly1d.CalcLegendre(p, y, shape_y.GetData(), dshape_y.GetData());
 
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
+         {
+            int maxij = std::max(i, j);
+            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                             z, 1.0,
+                                             shape_z, dshape_z, dshape_z_dt);
+
+            for (int k = 0; k <= p - maxij; k++, o++)
+            {
+               du(o,0) = dshape_x(i) * shape_y(j) * shape_z(k) *
+                         pow(1.0 - ip.z, maxij - 1);
+               du(o,1) = shape_x(i) * dshape_y(j) * shape_z(k) *
+                         pow(1.0 - ip.z, maxij - 1);
+               du(o,2) = shape_x(i) * shape_y(j) * dshape_z(k) *
+                         pow(1.0 - ip.z, maxij) +
+                         (ip.x * dshape_x(i) * shape_y(j) +
+                          ip.y * shape_x(i) * dshape_y(j)) *
+                         shape_z(k) * pow(1.0 - ip.z, maxij - 2) -
+                         maxij * shape_x(i) * shape_y(j) * shape_z(k) *
+                         (maxij > 0 ? pow(1.0 - ip.z, maxij - 1) : 0.0);
+            }
+         }
+   }
    Ti.Mult(du, dshape);
 }
 

fem/fe/fe_h1.hpp

@@ -208,6 +208,8 @@ private:
 #endif
    DenseMatrixInverse Ti;
 
+   static constexpr real_t apex_tol = 1e-8;
+
 public:
    H1_BergotPyramidElement(const int p,
                            const int btype = BasisType::GaussLobatto);

fem/fe/fe_l2.cpp

@@ -1106,9 +1106,16 @@ L2_BergotPyramidElement::L2_BergotPyramidElement(const int p, const int btype)
          {
             const real_t wik = op[i] + op[k] + op[p-i-k];
             const real_t w = wik * wjk * op[p-k];
-            Nodes.IntPoint(o++).Set3(op[i] * (op[j] + op[p-j-k]) / w,
-                                     op[j] * (op[j] + op[p-j-k]) / w,
-                                     op[k] * op[p-k] / w);
+            if (std::abs(w) < apex_tol)
+            {
+               Nodes.IntPoint(o++).Set3(0.,0.,1.);
+            }
+            else
+            {
+               Nodes.IntPoint(o++).Set3(op[i] * (op[j] + op[p-j-k]) / w,
+                                        op[j] * (op[i] + op[p-i-k]) / w,
+                                        op[k] * op[p-k] / w);
+            }
          }
       }
 
@@ -1125,22 +1132,45 @@ L2_BergotPyramidElement::L2_BergotPyramidElement(const int p, const int btype)
       const real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
       const real_t z = ip.z;
 
-      poly1d.CalcLegendre(p, x, shape_x.GetData());
-      poly1d.CalcLegendre(p, y, shape_y.GetData());
-
-      o = 0;
-      for (int i = 0; i <= p; i++)
+      if (std::abs(z - 1.0) < apex_tol)
       {
-         for (int j = 0; j <= p; j++)
-         {
-            int maxij = std::max(i, j);
-            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
-                                             z, 1.0, shape_z);
-
-            for (int k = 0; k <= p - maxij; k++)
+         // Compute the limit of the basis functions as z->1 with x and y on the
+         // line between the center of the base and the apex
+         o = 0;
+         for (int i = 0; i <= p; i++)
+            for (int j = 0; j <= p; j++)
             {
-               T(o++, m) = shape_x(i) * shape_y(j) * shape_z(k) *
-                           pow(1.0 - ip.z, maxij);
+               int maxij = std::max(i, j);
+               for (int k = 0; k <= p - maxij; k++)
+                  if (i == 0 && j == 0)
+                  {
+                     T(o++, m) = ((k + 3.) * k + 2.) / 2.;
+                  }
+                  else
+                  {
+                     T(o++, m) = 0.;
+                  }
+            }
+      }
+      else
+      {
+         poly1d.CalcLegendre(p, x, shape_x.GetData());
+         poly1d.CalcLegendre(p, y, shape_y.GetData());
+
+         o = 0;
+         for (int i = 0; i <= p; i++)
+         {
+            for (int j = 0; j <= p; j++)
+            {
+               int maxij = std::max(i, j);
+               FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                                z, 1.0, shape_z);
+
+               for (int k = 0; k <= p - maxij; k++)
+               {
+                  T(o++, m) = shape_x(i) * shape_y(j) * shape_z(k) *
+                              pow(1.0 - ip.z, maxij);
+               }
             }
          }
       }
@@ -1165,26 +1195,41 @@ void L2_BergotPyramidElement::CalcShape(const IntegrationPoint &ip,
    const real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
    const real_t z = ip.z;
 
-   poly1d.CalcLegendre(p, x, shape_x.GetData());
-   poly1d.CalcLegendre(p, y, shape_y.GetData());
-
-   int o = 0;
-   for (int i = 0; i <= p; i++)
+   if (std::abs(z - 1.0) < apex_tol)
    {
-      for (int j = 0; j <= p; j++)
-      {
-         int maxij = std::max(i, j);
-         FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0), z, 1.0,
-                                          shape_z);
-
-         for (int k = 0; k <= p - maxij; k++)
+      // Compute the limit of the basis functions as z->1 with x and y on the
+      // line between the center of the base and the apex
+      u = 0.;
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
          {
-            u[o++] = shape_x(i) * shape_y(j) * shape_z(k) *
-                     pow(1.0 - ip.z, maxij);
+            int maxij = std::max(i, j);
+            for (int k = 0; k <= p - maxij; k++, o++)
+               if (i == 0 && j == 0)
+               {
+                  u(o) = ((k + 3.) * k + 2.) / 2.;
+               }
          }
-      }
    }
+   else
+   {
+      poly1d.CalcLegendre(p, x, shape_x.GetData());
+      poly1d.CalcLegendre(p, y, shape_y.GetData());
 
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
+         {
+            int maxij = std::max(i, j);
+            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                             z, 1.0, shape_z);
+
+            for (int k = 0; k <= p - maxij; k++)
+               u[o++] = shape_x(i) * shape_y(j) * shape_z(k) *
+                        pow(1.0 - ip.z, maxij);
+         }
+   }
    Ti.Mult(u, shape);
 }
 
@@ -1208,35 +1253,64 @@ void L2_BergotPyramidElement::CalcDShape(const IntegrationPoint &ip,
    const real_t y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
    const real_t z = ip.z;
 
-   Poly_1D::CalcLegendre(p, x, shape_x.GetData(), dshape_x.GetData());
-   Poly_1D::CalcLegendre(p, y, shape_y.GetData(), dshape_y.GetData());
-
-   int o = 0;
-   for (int i = 0; i <= p; i++)
+   if (std::abs(z - 1.0) < apex_tol)
    {
-      for (int j = 0; j <= p; j++)
-      {
-         int maxij = std::max(i, j);
-         FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0), z, 1.0,
-                                          shape_z, dshape_z, dshape_z_dt);
-
-         for (int k = 0; k <= p - maxij; k++, o++)
+      // Compute the limit of the gradients of the basis functions as
+      // z->1 with x and y on the line between the center of the base and the
+      // apex
+      du = 0.;
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
          {
-            du(o,0) = dshape_x(i) * shape_y(j) * shape_z(k) *
-                      pow(1.0 - ip.z, maxij - 1);
-            du(o,1) = shape_x(i) * dshape_y(j) * shape_z(k) *
-                      pow(1.0 - ip.z, maxij - 1);
-            du(o,2) = shape_x(i) * shape_y(j) * dshape_z(k) *
-                      pow(1.0 - ip.z, maxij) +
-                      (ip.x * dshape_x(i) * shape_y(j) +
-                       ip.y * shape_x(i) * dshape_y(j)) *
-                      shape_z(k) * pow(1.0 - ip.z, maxij - 2) -
-                      ((maxij > 0) ? (maxij * shape_x(i) * shape_y(j) * shape_z(k) *
-                                      pow(1.0 - ip.z, maxij - 1)) : 0.0);
+            int maxij = std::max(i, j);
+            for (int k = 0; k <= p - maxij; k++, o++)
+            {
+               if (i == 0 && j == 0)
+               {
+                  du(o,2) = (((k + 6.) * k + 11.) * k + 6.) * k / 6.;
+               }
+               else if (i == 1 && j == 0)
+               {
+                  du(o,0) = ((((k + 10.) * k + 35.) * k + 50.) * k + 24.) / 24.;
+               }
+               else if (i == 0 && j == 1)
+               {
+                  du(o,1) = ((((k + 10.) * k + 35.) * k + 50.) * k + 24.) / 24.;
+               }
+            }
          }
-      }
    }
+   else
+   {
+      Poly_1D::CalcLegendre(p, x, shape_x.GetData(), dshape_x.GetData());
+      Poly_1D::CalcLegendre(p, y, shape_y.GetData(), dshape_y.GetData());
 
+      int o = 0;
+      for (int i = 0; i <= p; i++)
+         for (int j = 0; j <= p; j++)
+         {
+            int maxij = std::max(i, j);
+            FuentesPyramid::CalcScaledJacobi(p-maxij, 2.0 * (maxij + 1.0),
+                                             z, 1.0,
+                                             shape_z, dshape_z, dshape_z_dt);
+
+            for (int k = 0; k <= p - maxij; k++, o++)
+            {
+               du(o,0) = dshape_x(i) * shape_y(j) * shape_z(k) *
+                         pow(1.0 - ip.z, maxij - 1);
+               du(o,1) = shape_x(i) * dshape_y(j) * shape_z(k) *
+                         pow(1.0 - ip.z, maxij - 1);
+               du(o,2) = shape_x(i) * shape_y(j) * dshape_z(k) *
+                         pow(1.0 - ip.z, maxij) +
+                         (ip.x * dshape_x(i) * shape_y(j) +
+                          ip.y * shape_x(i) * dshape_y(j)) *
+                         shape_z(k) * pow(1.0 - ip.z, maxij - 2) -
+                         maxij * shape_x(i) * shape_y(j) * shape_z(k) *
+                         (maxij > 0 ? pow(1.0 - ip.z, maxij - 1) : 0.0);
+            }
+         }
+   }
    Ti.Mult(du, dshape);
 }
 

fem/fe/fe_l2.hpp

@@ -225,6 +225,8 @@ private:
 #endif
    DenseMatrixInverse Ti;
 
+   static constexpr real_t apex_tol = 1e-8;
+
 public:
    /// Construct the L2_PyramidElement of order @a p and BasisType @a btype
    L2_BergotPyramidElement(const int p,

fem/fe/fe_nd.cpp

@@ -1282,12 +1282,49 @@ ND_SegmentElement::ND_SegmentElement(const int p, const int ob_type)
    }
 }
 
+void ND_SegmentElement::CalcShape(const IntegrationPoint &ip,
+                                  Vector &shape) const
+{
+   if (obasis1d.IsIntegratedType()) { obasis1d.ScaleIntegrated(false); }
+   obasis1d.Eval(ip.x, shape);
+}
+
 void ND_SegmentElement::CalcVShape(const IntegrationPoint &ip,
                                    DenseMatrix &shape) const
 {
    Vector vshape(shape.Data(), dof);
 
-   obasis1d.Eval(ip.x, vshape);
+   CalcShape(ip, vshape);
+}
+
+void ND_SegmentElement::ProjectIntegrated(VectorCoefficient &vc,
+                                          ElementTransformation &Trans,
+                                          Vector &dofs) const
+{
+   MFEM_ASSERT(obasis1d.IsIntegratedType(), "Not integrated type");
+   real_t vk[Geometry::MaxDim];
+   Vector xk(vk, vc.GetVDim());
+
+   const real_t *cp = poly1d.ClosedPoints(dof, BasisType::GaussLobatto);
+   const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, dof);
+   IntegrationPoint ip;
+
+   for (int i = 0; i < dof; i++)
+   {
+      const real_t h = cp[i+1] - cp[i];
+      real_t val = 0.0;
+
+      for (int q = 0; q < ir.GetNPoints(); q++)
+      {
+         const IntegrationPoint &ip1d = ir.IntPoint(q);
+         ip.x = cp[i] + h*ip1d.x;
+         Trans.SetIntPoint(&ip);
+         vc.Eval(xk, Trans, ip);
+         val += ip1d.weight*Trans.Jacobian().InnerProduct(tk, vk);
+      }
+
+      dofs(i) = val*h;
+   }
 }
 
 const real_t ND_WedgeElement::tk[15] =

fem/fe/fe_nd.hpp

@@ -303,8 +303,7 @@ public:
    /** @brief Construct the ND_SegmentElement of order @a p and open
        BasisType @a ob_type */
    ND_SegmentElement(const int p, const int ob_type = BasisType::GaussLegendre);
-   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override
-   { obasis1d.Eval(ip.x, shape); }
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
    void CalcVShape(const IntegrationPoint &ip,
                    DenseMatrix &shape) const override;
    void CalcVShape(ElementTransformation &Trans,
@@ -325,7 +324,10 @@ public:
    using FiniteElement::Project;
    void Project(VectorCoefficient &vc,
                 ElementTransformation &Trans, Vector &dofs) const override
-   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+   {
+      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
+      else { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+   }
    void ProjectMatrixCoefficient(MatrixCoefficient &mc,
                                  ElementTransformation &T,
                                  Vector &dofs) const override
@@ -338,6 +340,11 @@ public:
                     ElementTransformation &Trans,
                     DenseMatrix &grad) const override
    { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
+
+protected:
+   void ProjectIntegrated(VectorCoefficient &vc,
+                          ElementTransformation &Trans,
+                          Vector &dofs) const;
 };
 
 class ND_WedgeElement : public VectorFiniteElement

fem/fe/fe_pos.cpp

@@ -557,6 +557,101 @@ H1Pos_TriangleElement::H1Pos_TriangleElement(const int p)
       }
 }
 
+const DofToQuad &H1Pos_TriangleElement::GetRaggedTensorDofToQuad(
+   const FiniteElement &fe, const IntegrationRule &ir,
+   DofToQuad::Mode mode,
+   Array<DofToQuad*> &dof2quad_array)
+{
+   DofToQuad *d2q = nullptr;
+   MFEM_VERIFY(mode == DofToQuad::RAGGED_TENSOR, "invalid mode requested");
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   #pragma omp critical (DofToQuad)
+#endif
+   {
+      for (int i = 0; i < dof2quad_array.Size(); i++)
+      {
+         d2q = dof2quad_array[i];
+         if (d2q->IntRule != &ir || d2q->mode != mode) { d2q = nullptr; }
+      }
+      if (!d2q)
+      {
+         d2q = new RaggedDofToQuad;
+         const int ndof = fe.GetOrder() + 1; // verify
+         const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/fe.GetDim()) + 0.5);
+         d2q->FE = &fe;
+         d2q->IntRule = &ir;
+         d2q->mode = mode;
+         d2q->ndof = ndof;
+         d2q->nqpt = nqpt;
+
+         RaggedDofToQuad *rd2q = static_cast<RaggedDofToQuad*>(d2q);
+         rd2q->Ba1.SetSize(nqpt*ndof);
+         // second component of ragged tensor basis, technically dof*(dof-1)/2 entries
+         rd2q->Ba2.SetSize((int)nqpt*ndof*ndof);
+         rd2q->Ba1t.SetSize(nqpt*ndof);
+         rd2q->Ba2t.SetSize((int)nqpt*ndof*ndof);
+         // stores first component of ragged tensor basis with order p-1, for gradients only
+         rd2q->Ga1.SetSize(nqpt*(ndof -1));
+         // stores second component of ragged tensor basis with order p-1
+         rd2q->Ga2.SetSize(nqpt*(ndof-1)*(ndof -1));
+         rd2q->Ga1t.SetSize(nqpt*(ndof -1));
+         rd2q->Ga2t.SetSize(nqpt*(ndof-1)*(ndof -1));
+         rd2q->lex_map.SetSize(ndof * ndof);
+         Vector shape_a1(ndof), shape_a2(ndof * ndof);
+         Vector shape_Ga1(ndof-1), shape_Ga2((ndof-1) * (ndof-1));
+         for (int i = 0; i < nqpt; i++)
+         {
+            // The first 'nqpt' points in the first dimension 'ir' have the same x-coordinates as those
+            // of the 1D rule (ie. (2,0) Gauss-Jacobi rule). The first 'nqpt' points in the second dimension
+            // 'ir' have the same y-coordinates as those of the 1D rule for second dimension (i.e. (1,0)
+            // Gauss-Jacobi rule). Additionally, the Bernstein PA algorithms expect evaluation of the
+            // component 1D bases at the Stroud nodes pulled back to the unit square, so perform the pullback
+            // on the fly.
+            const real_t x = ir.IntPoint(i).x;
+            const real_t y = ir.IntPoint(nqpt*i).y / (1.0 - ir.IntPoint(nqpt*i).x);
+
+            Poly_1D::CalcBernstein(ndof-1, x, shape_a1);
+            Poly_1D::CalcBernstein(ndof-2, x, shape_Ga1);
+            for (int j = 0; j < ndof; j++)
+            {
+               rd2q->Ba1t[i+nqpt*j] = rd2q->Ba1[j+ndof*i] = shape_a1(j);
+               if (j < ndof-1)
+               {
+                  rd2q->Ga1t[i+nqpt*j] = rd2q->Ga1[j+(ndof-1)*i] = shape_Ga1(j);
+                  Poly_1D::CalcBernstein(ndof-2-j, y, shape_Ga2);
+               }
+
+               Poly_1D::CalcBernstein(ndof-1-j, y, shape_a2);
+               for (int k = 0; k < ndof-j; k++)
+               {
+                  rd2q->Ba2t[i + nqpt*(j + ndof*k)] = rd2q->Ba2[k + ndof*(j + ndof*i)] = shape_a2(
+                                                                                            k);
+                  if (j < ndof-1 && k < ndof-j-1)
+                  {
+                     rd2q->Ga2t[i + nqpt*(j + (ndof-1)*k)] = rd2q->Ga2[k + (ndof-1)*(j +
+                                                                                     (ndof-1)*i)] = shape_Ga2(k);
+                  }
+               }
+            }
+         }
+
+         // stores the mapping from 2D Bernstein multi-index (i,j,p-i-j) to the
+         // lexicographic DOF ordering
+         for (int i = 0; i < ndof; i++)
+         {
+            for (int j = 0; j < ndof-i; j++)
+            {
+               int idx = ((2 * (ndof-1) + 3) - j) * j / 2 + i;
+               rd2q->lex_map[j + ndof*i] = idx;
+            }
+         }
+         dof2quad_array.Append(d2q);
+      }
+   }
+   return *d2q;
+}
+
 // static method
 void H1Pos_TriangleElement::CalcShape(
    const int p, const real_t l1, const real_t l2, real_t *shape)
@@ -749,6 +844,213 @@ H1Pos_TetrahedronElement::H1Pos_TetrahedronElement(const int p)
          }
 }
 
+const DofToQuad &H1Pos_TetrahedronElement::GetRaggedTensorDofToQuad(
+   const FiniteElement &fe, const IntegrationRule &ir,
+   DofToQuad::Mode mode,
+   Array<DofToQuad*> &dof2quad_array)
+{
+   DofToQuad *d2q = nullptr;
+   MFEM_VERIFY(mode == DofToQuad::RAGGED_TENSOR, "invalid mode requested");
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   #pragma omp critical (DofToQuad)
+#endif
+   {
+      for (int i = 0; i < dof2quad_array.Size(); i++)
+      {
+         d2q = dof2quad_array[i];
+         if (d2q->IntRule != &ir || d2q->mode != mode) { d2q = nullptr; }
+      }
+      if (!d2q)
+      {
+         d2q = new RaggedDofToQuad;
+         const int ndof = fe.GetOrder() + 1; // verify
+         const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/fe.GetDim()) + 0.5);
+         const int basis_dim2d = ndof*(ndof+1) / 2;
+         const int basis_dim3d = ndof*(ndof+1)*(ndof+2) / 6;
+         const int basis_dim2d_diff = (ndof-1)*(ndof) / 2;
+         const int basis_dim3d_diff = (ndof-1)*(ndof)*(ndof+1) / 6;
+         d2q->FE = &fe;
+         d2q->IntRule = &ir;
+         d2q->mode = mode;
+         d2q->ndof = ndof;
+         d2q->nqpt = nqpt;
+
+         RaggedDofToQuad *rd2q = static_cast<RaggedDofToQuad*>(d2q);
+         rd2q->Ba1.SetSize(nqpt * ndof);
+         // second component of ragged tensor basis, technically dof*(dof-1)/2 entries
+         rd2q->Ba2.SetSize(nqpt * basis_dim2d);
+         // third component of ragged tensor basis, technically dof*(dof-1)/2 entries
+         rd2q->Ba3.SetSize(nqpt * basis_dim3d);
+         rd2q->Ba1t.SetSize(nqpt * ndof);
+         rd2q->Ba2t.SetSize(nqpt * basis_dim2d);
+         rd2q->Ba3t.SetSize(nqpt * basis_dim3d);
+         // stores first component of ragged tensor basis with order p-1, for gradients only
+         rd2q->Ga1.SetSize(nqpt * (ndof-1));
+         // stores second component of ragged tensor basis with order p-1
+         rd2q->Ga2.SetSize(nqpt * basis_dim2d_diff);
+         // stores third component of ragged tensor basis with order p-1
+         rd2q->Ga3.SetSize(nqpt * basis_dim3d_diff);
+         rd2q->Ga1t.SetSize(nqpt * (ndof-1));
+         rd2q->Ga2t.SetSize(nqpt * basis_dim2d_diff);
+         rd2q->Ga3t.SetSize(nqpt * basis_dim3d_diff);
+         rd2q->lex_map.SetSize(ndof * ndof * ndof);
+
+         rd2q->forward_map2d_diff.SetSize((ndof-1) * (ndof-1));
+         rd2q->forward_map3d_diff.SetSize((ndof-1) * (ndof-1) * (ndof-1));
+         rd2q->inverse_map2d_diff.SetSize(2 * basis_dim2d_diff);
+         rd2q->inverse_map3d_diff.SetSize(3 * basis_dim3d_diff);
+
+         rd2q->forward_map2d_mass.SetSize(ndof * ndof);
+         rd2q->forward_map3d_mass.SetSize(ndof * ndof * ndof);
+         rd2q->inverse_map2d_mass.SetSize(2 * basis_dim2d);
+         rd2q->inverse_map3d_mass.SetSize(2 * basis_dim3d);
+
+         // forward and inverse maps for multi-index to collpased 1d index for diffusion, can combine
+         // these four loops, but need four idx's and clause for shorter diff loops
+         int idx = 0;
+         for (int i = 0; i < ndof-1; i++)
+         {
+            for (int j = 0; j < ndof-i-1; j++)
+            {
+               rd2q->forward_map2d_diff[j + (ndof-1)*i] = idx;
+               rd2q->inverse_map2d_diff[2*idx] = i;
+               rd2q->inverse_map2d_diff[1 + 2*idx] = j;
+               idx++;
+            }
+         }
+
+         idx = 0;
+         for (int k = 0; k < ndof-1; k++)
+         {
+            for (int j = 0; j < ndof-k-1; j++)
+            {
+               for (int i = 0; i < ndof-k-j-1; i++)
+               {
+                  rd2q->forward_map3d_diff[k + (ndof-1)*(j + (ndof-1)*i)] = idx;
+                  rd2q->inverse_map3d_diff[3*idx] = i;
+                  rd2q->inverse_map3d_diff[1 + 3*idx] = j;
+                  rd2q->inverse_map3d_diff[2 + 3*idx] = k;
+                  idx++;
+               }
+            }
+         }
+
+         // forward and inverse maps for multi-index to collpased 1d index for mass
+         idx = 0;
+         for (int j = 0; j < ndof; j++)
+         {
+            for (int i = 0; i < ndof-j; i++)
+            {
+               rd2q->forward_map2d_mass[j + ndof*i] = idx;
+               rd2q->inverse_map2d_mass[2*idx] = i;
+               rd2q->inverse_map2d_mass[1 + 2*idx] = j;
+               idx++;
+            }
+         }
+
+         idx = 0;
+         for (int k = 0; k < ndof; k++)
+         {
+            for (int j = 0; j < ndof-k; j++)
+            {
+               for (int i = 0; i < ndof-k-j; i++)
+               {
+                  rd2q->forward_map3d_mass[k + ndof*(j + ndof*i)] = idx;
+                  rd2q->inverse_map3d_mass[2*idx] = i;
+                  rd2q->inverse_map3d_mass[1 + 2*idx] = j;
+                  // d2q->inverse_map3d_mass[2 + 3*idx] = k;
+                  idx++;
+               }
+            }
+         }
+
+         Vector shape_a1(ndof), shape_a2(ndof * ndof), shape_a3(ndof * ndof * ndof);
+         Vector shape_Ga1(ndof-1), shape_Ga2(ndof-1), shape_Ga3(ndof-1);
+         for (int i = 0; i < nqpt; i++)
+         {
+            // The first 'nqpt' points in the first dimension 'ir' have the same x-coordinates as those
+            // of the 1D rule (ie. (2,0) Gauss-Jacobi rule). The first 'nqpt' points in the second dimension
+            // 'ir' have the same y-coordinates as those of the 1D rule for second dimension (i.e. (1,0)
+            // Gauss-Jacobi rule). The first 'nqpt' points in the third dimension have the same z-coordinates
+            // as those of the 1D rule for the third dimension (i.e. Gauss-Legendre rule). Additionally,
+            // the Bernstein PA algorithms expect evaluation of the component 1D bases at the Stroud nodes
+            // pulled back to the unit cube, so perform the pullback on the fly.
+            const real_t x = ir.IntPoint(i).x;
+            const real_t y = ir.IntPoint(nqpt*i).y / (1.0 - ir.IntPoint(nqpt*i).x);
+            const real_t z = ir.IntPoint(nqpt*nqpt*i).z / (1.0 - ir.IntPoint(
+                                                              nqpt*nqpt*i).x - ir.IntPoint(nqpt*nqpt*i).y);
+            Poly_1D::CalcBernstein(ndof-1, x, shape_a1);
+            Poly_1D::CalcBernstein(ndof-2, x, shape_Ga1);
+            for (int j = 0; j < ndof; j++)
+            {
+               rd2q->Ba1t[i+nqpt*j] = rd2q->Ba1[j+ndof*i] = shape_a1(j);
+               if (j < ndof-1)
+               {
+                  rd2q->Ga1t[i+nqpt*j] = rd2q->Ga1[j+(ndof-1)*i] = shape_Ga1(j);
+                  Poly_1D::CalcBernstein(ndof-2-j, y, shape_Ga2);
+               }
+
+               Poly_1D::CalcBernstein(ndof-1-j, y, shape_a2);
+               for (int k = 0; k < ndof-j; k++)
+               {
+                  const int a_2d_mass = rd2q->forward_map2d_mass[k + ndof*j];
+                  rd2q->Ba2t[i + nqpt*a_2d_mass] = rd2q->Ba2[a_2d_mass + basis_dim2d*i] =
+                                                      shape_a2(
+                                                         k);
+                  if (j < ndof-1 && k < ndof-j-1)
+                  {
+                     const int a_2d_diff = rd2q->forward_map2d_diff[k + (ndof-1)*j];
+                     rd2q->Ga2t[i + nqpt*a_2d_diff] = rd2q->Ga2[a_2d_diff + basis_dim2d_diff*i] =
+                                                         shape_Ga2(k);
+                     Poly_1D::CalcBernstein(ndof-2-j-k, z, shape_Ga3);
+                  }
+
+                  Poly_1D::CalcBernstein(ndof-1-j-k, z, shape_a3);
+                  for (int m = 0; m < ndof-j-k; m++)
+                  {
+                     const int a_3d_mass = rd2q->forward_map3d_mass[m + ndof*(k + ndof*j)];
+                     rd2q->Ba3t[i + nqpt*a_3d_mass] = rd2q->Ba3[a_3d_mass + basis_dim3d*i] =
+                                                         shape_a3(
+                                                            m);
+                     if (j < ndof-1 && k < ndof-j-1 && m < ndof-j-k-1)
+                     {
+                        // // collapsed 1D access
+                        // d2q->Ga3[i + nqpt*(m + d2q->offset3d[k + (ndof-1)*j])] = shape_Ga3(m);
+                        // collapsed 1D access with forward mapping
+                        const int a_3d_diff = rd2q->forward_map3d_diff[m + (ndof-1)*(k + (ndof-1)*j)];
+                        rd2q->Ga3t[i + nqpt*a_3d_diff] = rd2q->Ga3[a_3d_diff + basis_dim3d_diff*i] =
+                                                            shape_Ga3(m);
+                     }
+                  }
+               }
+            }
+         }
+
+         // stores the mapping from 3D Bernstein multi-index (i,j,k,p-i-j-k) to the
+         // lexicographic DOF ordering
+         int p = ndof - 1;
+         for (int i = 0; i < ndof; i++)
+         {
+            for (int j = 0; j < ndof-i; j++)
+            {
+               for (int k = 0; k < ndof-i-j; k++)
+               {
+                  int dof = (p+1)*(p+2)*(p+3) / 6;
+                  int tet = (p-k)*(p-k+1)*(p-k+2) / 6;
+                  int tri = (p+1-k-j)*(p+2-k-j)/2;
+                  int multi_idx = dof - tet - tri + i;
+                  rd2q->lex_map[k + ndof*(j + ndof*i)] = multi_idx;
+               }
+            }
+         }
+
+         dof2quad_array.Append(d2q);
+      }
+   }
+   return *d2q;
+}
+
 // static method
 void H1Pos_TetrahedronElement::CalcShape(
    const int p, const real_t l1, const real_t l2, const real_t l3,

fem/fe/fe_pos.hpp

@@ -191,6 +191,21 @@ public:
    /// Construct the H1Pos_TriangleElement of order @a p
    H1Pos_TriangleElement(const int p);
 
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const override
+   {
+      return (mode == DofToQuad::RAGGED_TENSOR) ?
+             GetRaggedTensorDofToQuad(*this, ir, mode, dof2quad_array) :
+             FiniteElement::GetDofToQuad(ir, mode);
+   }
+
+   static const DofToQuad &GetRaggedTensorDofToQuad(
+      const FiniteElement &fe, const IntegrationRule &ir,
+      DofToQuad::Mode mode,
+      Array<DofToQuad*> &dof2quad_array);
+
+   const Array<int> &GetDofMap() const { return dof_map; }
+
    // The size of shape is (p+1)(p+2)/2 (dof).
    static void CalcShape(const int p, const real_t x, const real_t y,
                          real_t *shape);
@@ -220,6 +235,21 @@ public:
    /// Construct the H1Pos_TetrahedronElement of order @a p
    H1Pos_TetrahedronElement(const int p);
 
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const override
+   {
+      return (mode == DofToQuad::RAGGED_TENSOR) ?
+             GetRaggedTensorDofToQuad(*this, ir, mode, dof2quad_array) :
+             FiniteElement::GetDofToQuad(ir, mode);
+   }
+
+   static const DofToQuad &GetRaggedTensorDofToQuad(
+      const FiniteElement &fe, const IntegrationRule &ir,
+      DofToQuad::Mode mode,
+      Array<DofToQuad*> &dof2quad_array);
+
+   const Array<int> &GetDofMap() const { return dof_map; }
+
    // The size of shape is (p+1)(p+2)(p+3)/6 (dof).
    static void CalcShape(const int p, const real_t x, const real_t y,
                          const real_t z, real_t *shape);

fem/fe/fe_pyramid.hpp

@@ -17,6 +17,12 @@
 namespace mfem
 {
 
+struct ScalarPyramid
+{
+   // Default basis type for H1 and L2 pyramids
+   static inline int DefaultType = 1; // Bergot(0) or Fuentes(1)
+};
+
 /** Base class for arbitrary order basis functions on pyramid-shaped elements
 
   This base class provides a common class to store temporary vectors,

fem/fe_coll.cpp

@@ -228,7 +228,19 @@ FiniteElementCollection *FiniteElementCollection::New(const char *name)
    }
    else if (!strncmp(name, "H1_", 3))
    {
-      fec = new H1_FECollection(atoi(name + 7), atoi(name + 3));
+      // Parse pyramid basis type if included in the name
+      const char *pyr = strstr(name, "Pyr");
+      if (pyr == NULL)
+      {
+         // Use default pyramid type elements
+         fec = new H1_FECollection(atoi(name + 7), atoi(name + 3));
+      }
+      else
+      {
+         // Use specific pyramid type elements
+         fec = new H1_FECollection(atoi(name + 7), atoi(name + 3),
+                                   BasisType::GaussLobatto, atoi(pyr + 3));
+      }
    }
    else if (!strncmp(name, "H1Pos_Trace_", 12))
    {
@@ -245,26 +257,44 @@ FiniteElementCollection *FiniteElementCollection::New(const char *name)
    }
    else if (!strncmp(name, "H1@", 3))
    {
-      fec = new H1_FECollection(atoi(name + 9), atoi(name + 5),
-                                BasisType::GetType(name[3]));
+      // Parse pyramid basis type if included in the name
+      const char *pyr = strstr(name, "Pyr");
+      if (pyr == NULL)
+      {
+         // Use default pyramid type elements
+         fec = new H1_FECollection(atoi(name + 9), atoi(name + 5),
+                                   BasisType::GetType(name[3]));
+      }
+      else
+      {
+         // Use specific pyramid type elements
+         fec = new H1_FECollection(atoi(name + 9), atoi(name + 5),
+                                   BasisType::GetType(name[3]),
+                                   atoi(pyr + 3));
+      }
    }
-   else if (!strncmp(name, "L2_T", 4))
-      fec = new L2_FECollection(atoi(name + 10), atoi(name + 6),
-                                atoi(name + 4));
-   else if (!strncmp(name, "L2_", 3))
+   else if (!strncmp(name, "L2", 2))
    {
-      fec = new L2_FECollection(atoi(name + 7), atoi(name + 3));
-   }
-   else if (!strncmp(name, "L2Int_T", 7))
-   {
-      fec = new L2_FECollection(atoi(name + 13), atoi(name + 9),
-                                atoi(name + 7), FiniteElement::INTEGRAL);
-   }
-   else if (!strncmp(name, "L2Int_", 6))
-   {
-      fec = new L2_FECollection(atoi(name + 10), atoi(name + 6),
-                                BasisType::GaussLegendre,
-                                FiniteElement::INTEGRAL);
+      // Parse Map Type
+      const int mtype = strstr(name, "Int") == NULL ?
+                        FiniteElement::VALUE : FiniteElement::INTEGRAL;
+
+      // Parse the base order
+      const int p = atoi(strstr(name, "_P") + 2);
+
+      // Parse the mesh dimension
+      const int dim = atoi(strstr(name, "D") - 1);
+
+      // Parse basis type if specified
+      const char *t = strstr(name, "_T");
+      const int btype = t == NULL ? BasisType::GaussLegendre : atoi(t + 2);
+
+      // Parse the pyramid type if specified
+      const char *pyr = strstr(name, "Pyr");
+      const int ptype = pyr == NULL ? 1 : atoi(pyr + 3);
+
+      // Create collection
+      fec = new L2_FECollection(p, dim, btype, mtype, ptype);
    }
    else if (!strncmp(name, "RT_Trace_", 9))
    {
@@ -1709,9 +1739,10 @@ const int *RT1_3DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
 
 
 H1_FECollection::H1_FECollection(const int p, const int dim, const int btype,
-                                 const int pyrtype)
+                                 const int pyr_type)
    : FiniteElementCollection(p)
    , dim(dim)
+   , p_type(pyr_type)
 {
    MFEM_VERIFY(p >= 1, "H1_FECollection requires order >= 1.");
    MFEM_VERIFY(dim >= 0 && dim <= 3, "H1_FECollection requires 0 <= dim <= 3.");
@@ -1724,7 +1755,14 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype,
    {
       case BasisType::GaussLobatto:
       {
-         snprintf(h1_name, 32, "H1_%dD_P%d", dim, p);
+         if (pyr_type == ScalarPyramid::DefaultType)
+         {
+            snprintf(h1_name, 32, "H1_%dD_P%d", dim, p);
+         }
+         else
+         {
+            snprintf(h1_name, 32, "H1_%dD_P%d_Pyr%d", dim, p, pyr_type);
+         }
          break;
       }
       case BasisType::Positive:
@@ -1910,11 +1948,11 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype,
          H1_dof[Geometry::TETRAHEDRON] = (TriDof*pm3)/3;
          H1_dof[Geometry::CUBE] = QuadDof*pm1;
          H1_dof[Geometry::PRISM] = TriDof*pm1;
-         if (pyrtype == 0 || b_type == BasisType::Positive)
+         if (pyr_type == 0 || b_type == BasisType::Positive)
          {
             H1_dof[Geometry::PYRAMID] = pm2*pm1*(2*p-3)/6; // Bergot (JSC)
          }
-         else if (pyrtype == 1)
+         else if (pyr_type == 1)
          {
             H1_dof[Geometry::PYRAMID] = pm1*pm1*pm1; // Fuentes
          }
@@ -1935,13 +1973,15 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype,
                new H1_TetrahedronElement(p, btype);
             H1_Elements[Geometry::CUBE] = new H1_HexahedronElement(p, btype);
             H1_Elements[Geometry::PRISM] = new H1_WedgeElement(p, btype);
-            if (pyrtype == 0)
+            if (pyr_type == 0)
             {
-               H1_Elements[Geometry::PYRAMID] = new H1_BergotPyramidElement(p, btype);
+               H1_Elements[Geometry::PYRAMID] =
+                  new H1_BergotPyramidElement(p, btype);
             }
             else
             {
-               H1_Elements[Geometry::PYRAMID] = new H1_FuentesPyramidElement(p, btype);
+               H1_Elements[Geometry::PYRAMID] =
+                  new H1_FuentesPyramidElement(p, btype);
             }
          }
 
@@ -2148,6 +2188,7 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
    : FiniteElementCollection(p)
    , dim(dim)
    , m_type(map_type)
+   , p_type(pyr_type)
 {
    MFEM_VERIFY(p >= 0, "L2_FECollection requires order >= 0.");
 
@@ -2163,10 +2204,25 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
    switch (btype)
    {
       case BasisType::GaussLegendre:
-         snprintf(d_name, 32, "%s_%dD_P%d", prefix, dim, p);
+         if (pyr_type == ScalarPyramid::DefaultType)
+         {
+            snprintf(d_name, 32, "%s_%dD_P%d", prefix, dim, p);
+         }
+         else
+         {
+            snprintf(d_name, 32, "%s_%dD_P%d_Pyr%d", prefix, dim, p, pyr_type);
+         }
          break;
       default:
-         snprintf(d_name, 32, "%s_T%d_%dD_P%d", prefix, btype, dim, p);
+         if (pyr_type == ScalarPyramid::DefaultType)
+         {
+            snprintf(d_name, 32, "%s_T%d_%dD_P%d", prefix, btype, dim, p);
+         }
+         else
+         {
+            snprintf(d_name, 32, "%s_T%d_%dD_P%d_Pyr%d",
+                     prefix, btype, dim, p, pyr_type);
+         }
    }
 
    for (int g = 0; g < Geometry::NumGeom; g++)
@@ -2285,11 +2341,13 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
          L2_Elements[Geometry::PRISM] = new L2_WedgeElement(p, btype);
          if (pyr_type == 0)
          {
-            L2_Elements[Geometry::PYRAMID] = new L2_BergotPyramidElement(p, btype);
+            L2_Elements[Geometry::PYRAMID] =
+               new L2_BergotPyramidElement(p, btype);
          }
          else
          {
-            L2_Elements[Geometry::PYRAMID] = new L2_FuentesPyramidElement(p, btype);
+            L2_Elements[Geometry::PYRAMID] =
+               new L2_FuentesPyramidElement(p, btype);
          }
       }
 

fem/fe_coll.hpp

@@ -100,6 +100,10 @@ public:
       return FiniteElementForGeometry(GeomType);
    }
 
+   /** @brief Returns a collection of the trace elements.
+
+       @note The collection is owned by the caller and is NOT deleted in the
+       destructor. */
    virtual FiniteElementCollection *GetTraceCollection() const;
 
    virtual ~FiniteElementCollection();
@@ -250,6 +254,14 @@ public:
        its GetOrder() method. */
    virtual FiniteElementCollection *Clone(int p) const;
 
+   /** @brief Return the order parameter used to construct this collection.
+    *  This differs from GetOrder() depending on the collection type. */
+   virtual int GetConstructorOrder() const
+   {
+      MFEM_ABORT("Collection " << Name() << " does not support GetConstructorOrder");
+      return -1;
+   }
+
 protected:
    const int base_p; ///< Order as returned by GetOrder().
 
@@ -278,7 +290,7 @@ protected:
 class H1_FECollection : public FiniteElementCollection
 {
 protected:
-   int dim, b_type;
+   int dim, b_type, p_type;
    char h1_name[32];
    FiniteElement *H1_Elements[Geometry::NumGeom];
    int H1_dof[Geometry::NumGeom];
@@ -287,7 +299,7 @@ protected:
 public:
    explicit H1_FECollection(const int p, const int dim = 3,
                             const int btype = BasisType::GaussLobatto,
-                            const int pyrtype = 1);
+                            const int pyr_type = ScalarPyramid::DefaultType);
 
    const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const override;
@@ -312,7 +324,10 @@ public:
    const int *GetDofMap(Geometry::Type GeomType, int p) const;
 
    FiniteElementCollection *Clone(int p) const override
-   { return new H1_FECollection(p, dim, b_type); }
+   { return new H1_FECollection(p, dim, b_type, p_type); }
+
+   int GetConstructorOrder() const override
+   { return base_p; }
 
    virtual ~H1_FECollection();
 };
@@ -343,6 +358,10 @@ class H1_Trace_FECollection : public H1_FECollection
 public:
    H1_Trace_FECollection(const int p, const int dim,
                          const int btype = BasisType::GaussLobatto);
+
+   FiniteElementCollection *Clone(int p) const override
+   { return new H1_Trace_FECollection(p, dim+1, b_type); }
+
 };
 
 /// Arbitrary order "L2-conforming" discontinuous finite elements.
@@ -352,6 +371,7 @@ private:
    int dim;
    int b_type; // BasisType
    int m_type; // map type
+   int p_type; // Pyramid type (0 -> Bergot, 1 -> Fuentes)
    char d_name[32];
    ScalarFiniteElement *L2_Elements[Geometry::NumGeom];
    ScalarFiniteElement *Tr_Elements[Geometry::NumGeom];
@@ -364,7 +384,7 @@ public:
    L2_FECollection(const int p, const int dim,
                    const int btype = BasisType::GaussLegendre,
                    const int map_type = FiniteElement::VALUE,
-                   const int pyrtype = 1);
+                   const int pyr_type = ScalarPyramid::DefaultType);
 
    const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const override;
@@ -394,7 +414,10 @@ public:
    int GetBasisType() const { return b_type; }
 
    FiniteElementCollection *Clone(int p) const override
-   { return new L2_FECollection(p, dim, b_type, m_type); }
+   { return new L2_FECollection(p, dim, b_type, m_type, p_type); }
+
+   int GetConstructorOrder() const override
+   { return base_p; }
 
    virtual ~L2_FECollection();
 };
@@ -456,6 +479,9 @@ public:
    FiniteElementCollection *Clone(int p) const override
    { return new RT_FECollection(p, dim, cb_type, ob_type); }
 
+   int GetConstructorOrder() const override
+   { return base_p-1; }
+
    virtual ~RT_FECollection();
 };
 
@@ -536,6 +562,9 @@ public:
    FiniteElementCollection *Clone(int p) const override
    { return new ND_FECollection(p, dim, cb_type, ob_type); }
 
+   int GetConstructorOrder() const override
+   { return dim>1 ? base_p : base_p+1; }
+
    virtual ~ND_FECollection();
 };
 
@@ -548,6 +577,9 @@ public:
    ND_Trace_FECollection(const int p, const int dim,
                          const int cb_type = BasisType::GaussLobatto,
                          const int ob_type = BasisType::GaussLegendre);
+
+   FiniteElementCollection *Clone(int p) const override
+   { return new ND_Trace_FECollection(p, dim+1, cb_type, ob_type); }
 };
 
 /// Arbitrary order 3D H(curl)-conforming Nedelec finite elements in 1D.

fem/fespace.cpp

@@ -4631,9 +4631,8 @@ FiniteElementCollection *FiniteElementSpace::Load(Mesh *m, std::istream &input)
 
 ElementDofOrdering GetEVectorOrdering(const FiniteElementSpace& fes)
 {
-   return UsesTensorBasis(fes)?
+   return (UsesTensorBasis(fes) || fes.UsesRaggedTensorBasis()) ?
           ElementDofOrdering::LEXICOGRAPHIC:
           ElementDofOrdering::NATIVE;
 }
-
 } // namespace mfem

fem/fespace.hpp

@@ -1514,6 +1514,18 @@ public:
       return dynamic_cast<const L2_FECollection*>(fec) != NULL;
    }
 
+   /// @brief Return true if the mesh contains only one topology, the elements are
+   /// all triangles or tetrahedrons, and the elements are ragged tensor elements
+   /// i.e. Bernstein/positive basis.
+   bool UsesRaggedTensorBasis() const
+   {
+      bool simplex = this->GetMesh()->IsSimplexMesh();
+      bool positive =
+         dynamic_cast<const mfem::H1Pos_TriangleElement *>(this->GetTypicalFE()) ||
+         dynamic_cast<const mfem::H1Pos_TetrahedronElement *>(this->GetTypicalFE());
+      return simplex && positive;
+   }
+
    /** In variable-order spaces on nonconforming (NC) meshes, this function
        controls whether strict conformity is enforced in cases where coarse
        edges/faces have higher polynomial order than their fine NC neighbors.

fem/gridfunc.cpp

@@ -2256,6 +2256,104 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
    }
 }
 
+void GridFunction::AccumulateAndCountTraceValues(
+   Coefficient *coeff[], VectorCoefficient *vcoeff,
+   Array<int> &values_counter)
+{
+   if (vcoeff)
+   {
+      MFEM_VERIFY(fes->GetVDim() == vcoeff->GetVDim(),
+                  "vcoeff vdim != fes VDim");
+      MFEM_VERIFY(fes->GetTypicalTraceElement()->GetMapType() ==
+                  FiniteElement::VALUE &&
+                  fes->GetTypicalTraceElement()->GetRangeType() ==
+                  FiniteElement::SCALAR,
+                  "Can only call ProjectTraceCoefficient on scalar value-type "
+                  "trace elements. "
+                  "Use ProjectTraceCoefficientNormal for RT and "
+                  "ProjectTraceCoefficientTangent for ND finite elements.");
+   }
+
+   Array<int> vdofs;
+   Vector vc;
+
+   values_counter.SetSize(Size());
+   values_counter = 0;
+
+   const int vdim = fes->GetVDim();
+   HostReadWrite();
+
+   for (int i = 0; i < fes->GetMesh()->GetNumFaces(); i++)
+   {
+
+      const FiniteElement *fe = fes->GetFaceElement(i);
+      const int fdof = fe->GetDof();
+      ElementTransformation *transf = fes->GetMesh()->GetFaceTransformation(i);
+      const IntegrationRule &ir = fe->GetNodes();
+      fes->GetFaceVDofs(i, vdofs);
+
+      for (int j = 0; j < fdof; j++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(j);
+         transf->SetIntPoint(&ip);
+         if (vcoeff) { vcoeff->Eval(vc, *transf, ip); }
+         for (int d = 0; d < vdim; d++)
+         {
+            if (!vcoeff && !coeff[d]) { continue; }
+
+            real_t val = vcoeff ? vc(d) : coeff[d]->Eval(*transf, ip);
+            int ind = vdofs[fdof*d+j];
+            if ( ind < 0 )
+            {
+               val = -val, ind = -1-ind;
+            }
+            if (++values_counter[ind] == 1)
+            {
+               (*this)(ind) = val;
+            }
+            else
+            {
+               (*this)(ind) += val;
+            }
+         }
+      }
+   }
+}
+
+void GridFunction::AccumulateAndCountTraceTangentValues(
+   VectorCoefficient &vcoeff, Array<int> &values_counter)
+{
+   MFEM_VERIFY(fes->GetVDim() == 1, "fespace VDim != 1");
+   MFEM_VERIFY(fes->GetTypicalTraceElement()
+               ->GetRangeType() == FiniteElement::VECTOR &&
+               fes->GetTypicalTraceElement()
+               ->GetMapType() == FiniteElement::H_CURL,
+               "Not an ND FE space!");
+   MFEM_VERIFY(fes->GetTypicalTraceElement()->GetPhysRangeDim(
+                  fes->GetMesh()->SpaceDimension()) == vcoeff.GetVDim(),
+               "vcoeff vdim != PhysRangeDim");
+
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Array<int> dofs;
+   Vector lvec;
+
+   values_counter.SetSize(Size());
+   values_counter = 0;
+
+   HostReadWrite();
+
+   for (int i = 0; i < fes->GetMesh()->GetNumFaces(); i++)
+   {
+      fe = fes->GetFaceElement(i);
+      T = fes->GetMesh()->GetFaceTransformation(i);
+      fes->GetFaceVDofs(i, dofs);
+      lvec.SetSize(fe->GetDof());
+      fe->Project(vcoeff, *T, lvec);
+      accumulate_dofs(dofs, lvec, *this, values_counter);
+   }
+}
+
 void GridFunction::ComputeMeans(AvgType type, Array<int> &zones_per_vdof)
 {
    switch (type)
@@ -2698,6 +2796,74 @@ void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
    }
 }
 
+void GridFunction::ProjectTraceCoefficient(Coefficient *coeff[])
+{
+   Array<int> values_counter;
+   AccumulateAndCountTraceValues(coeff, NULL, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+}
+
+void GridFunction::ProjectTraceCoefficient(Coefficient &coeff)
+{
+   MFEM_VERIFY(FESpace()->GetVDim() == 1, "ProjectTraceCoefficient(Coefficient&)"
+               "is only valid for scalar GridFunction");
+   Coefficient *coeff_p = &coeff;
+   ProjectTraceCoefficient(&coeff_p);
+}
+
+void GridFunction::ProjectTraceCoefficient(VectorCoefficient &vcoeff)
+{
+   MFEM_VERIFY(FESpace()->GetVDim() == vcoeff.GetVDim(),
+               "Incompatible vcoeff vdim and fes vdim");
+   Array<int> values_counter;
+   AccumulateAndCountTraceValues(NULL, &vcoeff, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+}
+
+void GridFunction::ProjectTraceCoefficientNormal(VectorCoefficient &vcoeff)
+{
+   MFEM_VERIFY(fes->GetVDim() == 1, "fespace VDim != 1");
+   MFEM_VERIFY(fes->GetTypicalTraceElement()->GetRangeType() ==
+               FiniteElement::SCALAR &&
+               fes->GetTypicalTraceElement()->GetMapType() ==
+               FiniteElement::INTEGRAL, "Not an RT FE space!");
+   MFEM_VERIFY(vcoeff.GetVDim() == fes->GetMesh()->SpaceDimension(),
+               "vcoeff vdim (" << vcoeff.GetVDim()
+               << ") != SpaceDimension ("
+               << fes->GetMesh()->SpaceDimension() << ")");
+
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Array<int> dofs;
+   int dim = vcoeff.GetVDim();
+   Vector vc(dim), nor(dim), lvec;
+
+   for (int i = 0; i < fes->GetMesh()->GetNumFaces(); i++)
+   {
+      fe = fes->GetFaceElement(i);
+      T = fes->GetMesh()->GetFaceTransformation(i);
+      const IntegrationRule &ir = fe->GetNodes();
+      lvec.SetSize(fe->GetDof());
+      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);
+         lvec(j) = (vc * nor);
+      }
+      fes->GetFaceVDofs(i, dofs);
+      SetSubVector(dofs, lvec);
+   }
+}
+
+void GridFunction::ProjectTraceCoefficientTangent(VectorCoefficient &vcoeff)
+{
+   Array<int> values_counter;
+   AccumulateAndCountTraceTangentValues(vcoeff, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+}
+
 void GridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
                                               real_t rtol, int iter)
 {
@@ -5286,6 +5452,7 @@ PLBound GridFunction::GetBounds(Vector &lower, Vector &upper,
 {
    int max_order = fes->GetMaxElementOrder();
    PLBound plb(fes, ref_factor*(max_order+1));
+
    Vector lel, uel;
    GetElementBounds(plb, lel, uel, vdim);
 

fem/gridfunc.hpp

@@ -578,6 +578,13 @@ protected:
                                            const Array<int> &bdr_attr,
                                            Array<int> &values_counter);
 
+   void AccumulateAndCountTraceValues(Coefficient *coeff[],
+                                      VectorCoefficient *vcoeff,
+                                      Array<int> &values_counter);
+
+   void AccumulateAndCountTraceTangentValues(VectorCoefficient &vcoeff,
+                                             Array<int> &values_counter);
+
    // Complete the computation of averages; called e.g. after
    // AccumulateAndCountZones().
    void ComputeMeans(AvgType type, Array<int> &zones_per_vdof);
@@ -663,6 +670,23 @@ public:
       ProjectBdrCoefficient(&coeff_p, attr);
    }
 
+   /// Project a Coefficient on a GridFunction defined on H1 trace space
+   void ProjectTraceCoefficient(Coefficient *coeff[]);
+   void ProjectTraceCoefficient(Coefficient &coeff);
+
+   /** @brief Project a VectorCoefficient @a vcoeff on a GridFunction
+       defined on a Vector H1 trace space. Note that this also works
+       for a scalar H1 trace space, where only the first component of
+       @a vcoeff is used. */
+   void ProjectTraceCoefficient(VectorCoefficient &vcoeff);
+   /** @brief Project a VectorCoefficient on a GridFunction
+       defined on an RT trace space */
+   void ProjectTraceCoefficientNormal(VectorCoefficient &vcoeff);
+   /** @brief Project a VectorCoefficient on a GridFunction
+       defined on an ND trace space */
+   void ProjectTraceCoefficientTangent(VectorCoefficient &vcoeff);
+
+
    /** @brief Project a VectorCoefficient on the GridFunction, modifying only
        DOFs on the boundary associated with the boundary attributes marked in
        the @a attr array. */

fem/gslib.hpp

@@ -12,6 +12,9 @@
 #ifndef MFEM_GSLIB
 #define MFEM_GSLIB
 
+#include <map>
+#include <vector>
+
 #include "../config/config.hpp"
 #ifdef MFEM_USE_MPI
 #include "pgridfunc.hpp"
@@ -119,6 +122,11 @@ protected:
    // IntegrationRules for simplex->Quad/Hex and to project to p_max in-case of
    // p-refinement.
    Array<IntegrationRule *> ir_split;
+   /// Integration rules built at the field polynomial order (only for surface
+   /// meshes when mesh order is not the same as gridfunction order).
+   Array<IntegrationRule *> ir_split_sol;
+   /// Order at which #ir_split_sol was built; -1 means not built.
+   int ir_split_sol_order = -1;
    Array<FiniteElementSpace *> fes_rst_map; //FESpaces to map Quad/Hex->Simplex
    Array<GridFunction *> gf_rst_map; // GridFunctions to map Quad/Hex->Simplex
    FiniteElementCollection *fec_map_lin;
@@ -134,6 +142,8 @@ protected:
    AvgType avgtype;             // average type used for L2 functions
    Array<int> split_element_map;
    Array<int> split_element_index;
+   // Geometry::Type (as int) of the original element for each split quad.
+   Array<int> split_element_geom;
    int        NE_split_total;   // total number of elements after mesh splitting
    int        mesh_points_cnt;  // number of mesh nodes
    // Tolerance to ignore points found beyond the mesh boundary.
@@ -141,6 +151,12 @@ protected:
    double     bdr_tol;
    // Use CPU functions for Mesh/GridFunction on device for gslib1.0.7
    bool       gpu_to_cpu_fallback = false;
+   // Check if a point is inside the oriented bounding box of an
+   // element before the Newton iteration.
+   // Note: only used in MFEM implementation (not in gslib) which currently
+   // supports GPU kernels for area meshes in 2D, volume meshes in 3D,
+   // and surface meshes in 1D/2D/3D.
+   bool       obb_check = true;
 
    // Device specific data used for FindPoints
    struct DEV_STRUCT
@@ -162,11 +178,16 @@ protected:
       mutable double surf_dist_tol;
    } DEV;
 
-   /// Use GSLIB for communication and interpolation
+   // Helper function to setup and free gslib's crystal router.
+   void SetupCrystal(); // Called inside Setup and SetupSurf_base
+   void FreeCrystal();  // Called inside FreeData
+
+   /// Use GSLIB for communication and interpolation. Updates field_out on
+   /// host.
    virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out,
                               const int field_out_ordering);
    /// Uses GSLIB Crystal Router for communication followed by MFEM's
-   /// interpolation functions
+   /// interpolation functions. Updates field_out on host.
    virtual void InterpolateGeneral(const GridFunction &field_in,
                                    Vector &field_out,
                                    const int field_out_ordering);
@@ -181,12 +202,26 @@ protected:
                                                  IntegrationRule *irule,
                                                  int order);
 
+   /** @brief Build integration rules at the given @a order for each split mesh
+    *  and store them in @a ir_out. Requires that \ref SetupSplitMeshes has
+    *  already been called. */
+   virtual void SetupIntegrationRules(const int order,
+                                      Array<IntegrationRule *> &ir_out);
+
    /** @brief Helper function that calls \ref SetupSplitMeshes and
-    * \ref SetupIntegrationRuleForSplitMesh. */
+    * \ref SetupIntegrationRules. */
    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;
+   /** @brief Get GridFunction value at the points expected by GSLIB.
+    *  @param[in]  gf_in       Grid function to evaluate.
+    *  @param[out] node_vals   Output values.
+    *  @param[in]  ir_in       If non-null, use these rules instead of #ir_split.
+    *  @param[in]  by_element  If true, output has element-major layout
+    *                          [nel][vdim][ndofs]; otherwise component-major
+    *                          layout [vdim][total_pts]. */
+   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals,
+                               const Array<IntegrationRule *> *ir_in = nullptr,
+                               bool by_element = false) const;
 
    /** @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
@@ -291,29 +326,60 @@ protected:
    void findptsedge_setup_2(DEV_STRUCT &devs,
                             const double *const elx[2],
                             const unsigned n,
-                            const uint nel,
+                            const unsigned int nel,
                             const unsigned m,
-                            const double bbox_tol,
-                            const uint local_hash_size,
-                            const uint global_hash_size);
+                            const double bbox_rel_size_inc,
+                            const unsigned int local_hash_size,
+                            const unsigned int global_hash_size,
+                            const Vector *aabb_sz_inc);
 
    /// 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 int nel,
                             const unsigned m,
-                            const double bbox_tol,
-                            const uint local_hash_size,
-                            const uint global_hash_size,
-                            const int rD);
+                            const double bbox_rel_size_inc,
+                            const unsigned int local_hash_size,
+                            const unsigned int global_hash_size,
+                            const int rD,
+                            const Vector *aabb_sz_inc);
 
+   /** @brief Shared implementation for the public surface-setup methods.
+    *
+    *  @details Initializes the surface-search data structures, builds the
+    *  split-element representation expected by gslib, and constructs the
+    *  element bounding boxes used by the MFEM surface kernels.
+    *
+    *  If @a aabb_sz_inc is null, the setup stores the default oriented
+    *  bounding boxes and uses @a bbox_rel_size_inc as their relative size
+    *  increase factor.
+    *
+    *  If @a aabb_sz_inc is non-null, the setup stores axis-aligned bounding
+    *  boxes only, applies the requested absolute AABB expansion in each
+    *  physical direction, and adjusts the tolerance @a bdr_tol so points
+    *  found in the expanded region are classified as border points.
+    *
+    *  @param[in] m                  Input surface mesh.
+    *  @param[in] bbox_rel_size_inc  Relative size increase applied when
+    *                                expanding each element bounding box during
+    *                                setup.
+    *  @param[in] aabb_sz_inc        Optional total absolute AABB expansion
+    *                                applied to the stored axis-aligned
+    *                                bounding boxes after construction.
+    *  @param[in] newt_tol           Newton tolerance for the point-search
+    *                                kernels.
+    */
+   void SetupSurf_Base(Mesh &m,
+                       const double bbox_rel_size_inc,
+                       const Vector *aabb_sz_inc,
+                       const double newt_tol);
 public:
    /// Serial constructor
    FindPointsGSLIB();
 
    /// Serial constructor + setup with given Mesh (see \ref Setup)
-   FindPointsGSLIB(Mesh &mesh_in, const double bb_t = 0.1,
+   FindPointsGSLIB(Mesh &mesh_in, const double bbox_rel_size_inc = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
@@ -322,7 +388,7 @@ public:
    FindPointsGSLIB(MPI_Comm comm_);
 
    /// Constructor + setup with given ParMesh (see \ref Setup)
-   FindPointsGSLIB(ParMesh &mesh_in, const double bb_t = 0.1,
+   FindPointsGSLIB(ParMesh &mesh_in, const double bbox_rel_size_inc = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 #endif
@@ -338,23 +404,59 @@ public:
        Note: not tested with periodic (L2).
        Note: the input mesh \p m must have Nodes set.
 
-       @param[in] m         Input mesh.
-       @param[in] bb_t      (Optional) Relative size of bounding box around
-                            each element.
-       @param[in] newt_tol  (Optional) Newton tolerance for the gslib
-                            search methods.
-       @param[in] npt_max   (Optional) Number of points for simultaneous
-                            iteration. This alters performance and
-                            memory footprint.
+       @param[in] m                  Input mesh.
+       @param[in] bbox_rel_size_inc  (Optional) Relative size increase applied
+                                     when expanding each element bounding box.
+       @param[in] newt_tol           (Optional) Newton tolerance for the gslib
+                                     search methods.
+       @param[in] npt_max            (Optional) Number of points for
+                                     simultaneous iteration. This alters
+                                     performance and memory footprint.
    */
-   void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+   void Setup(Mesh &m, const double bbox_rel_size_inc = 0.1,
+              const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
    /// 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);
+                  const double bbox_rel_size_inc = 0.1,
+                  const double newt_tol = 1.0e-12);
+
+   /** @brief Preprocess the surface mesh to compute data for FindPoints using
+    *  absolute AABB expansion.
+    *
+    *  @details This method computes only axis-aligned bounding boxes and
+    *  increases their total length by a user-specified amount in each
+    *  physical direction. The absolute AABB expansion is applied
+    *  symmetrically to the lower and upper bounds.
+    *
+    *  The size of @a aabb_sz_inc determines how the expansion values are
+    *  interpreted:
+    *  - `1`: one expansion value used in every direction for every element
+    *  - `NElements`: one expansion value per element, reused in x/y/z
+    *    directions
+    *  - `SpaceDim`: one expansion value per physical direction, reused for
+    *    every element
+    *  - `NElements*SpaceDim`: one expansion value per element and direction,
+    *    ordered as `(dx1,dy1,dz1, ... dxN,dyN,dzN)`
+    *
+    *  This method disables the oriented bounding-box precheck because the
+    *  stored boxes are modified only in their axis-aligned representation.
+    *
+    *  @param[in] m                  Input surface mesh.
+    *  @param[in] aabb_sz_inc        Total absolute AABB expansion applied in
+    *                                each physical direction to the stored
+    *                                axis-aligned bounding boxes.
+    *  @param[in] newt_tol           Newton tolerance for the point-search
+    *                                kernels.
+    *
+    *  @note We disable the oriented bounding box check with this setup.
+    *        @a bdr_tol is also adjusted so that all points in the AABBs can
+    *        be found.
+    */
+   void SetupSurfWithAABBExpansion(Mesh &m, const Vector &aabb_sz_inc,
+                                   const double newt_tol = 1.0e-12);
+
 
    /** @brief Searches positions given in physical space by \p point_pos.
 
@@ -401,7 +503,8 @@ public:
    /// 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 double bbox_rel_size_inc = 0.1,
+                   const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
    /** @brief Interpolation of field values at prescribed reference space
@@ -413,7 +516,11 @@ public:
                               mesh that was given to Setup().
        @param[out] field_out  Interpolated values. For points that are not found
                               the value is set to #default_interp_value.
-                              The output ordering is determined from field_in.*/
+                              The output ordering is determined from field_in.
+
+       @note: field_out is moved to device if field_in is on device. Otherwise,
+              field_out memory allocation is not changed.
+   */
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
 
    /// Interpolation of field values, with output ordering specification.
@@ -468,7 +575,12 @@ public:
     *  @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.*/
+    *  as not found.
+    *
+    *  @note When the SetupSurfWithAABBExpansion method is used for surface
+    *  meshes, this tolerance is automatically computed based on the size of
+    *  expanded AABBs. Using this method will override that computed tolerance.
+    *  */
    virtual void SetDistanceToleranceForPointsFoundOnBoundary(double bdr_tol_)
    {
       bdr_tol = bdr_tol_;
@@ -603,25 +715,28 @@ public:
        Note: not tested with periodic meshes (L2).
        Note: the input mesh \p m must have Nodes set.
 
-       @param[in] m         Input mesh.
-       @param[in] meshid    A unique # for each overlapping mesh. This id is
-                            used to make sure that points being searched are not
-                            looked for in the mesh that they belong to.
-       @param[in] gfmax     (Optional) GridFunction in H1 that is used as a
-                            discriminator when one point is located in multiple
-                            meshes. The mesh that maximizes gfmax is chosen.
-                            For example, using the distance field based on the
-                            overlapping boundaries is helpful for convergence
-                            during Schwarz iterations.
-       @param[in] bb_t      (Optional) Relative size of bounding box around
-                            each element.
-       @param[in] newt_tol  (Optional) Newton tolerance for the gslib
-                            search methods.
-       @param[in] npt_max   (Optional) Number of points for simultaneous
-                            iteration. This alters performance and
-                            memory footprint.*/
-   void Setup(Mesh &m, const int meshid, GridFunction *gfmax = NULL,
-              const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+       @param[in] m                  Input mesh.
+       @param[in] meshid             A unique # for each overlapping mesh.
+                                     This id is used to make sure that points
+                                     being searched are not looked for in the
+                                     mesh that they belong to.
+       @param[in] gfmax              (Optional) GridFunction in H1 that is used
+                                     as a discriminator when one point is
+                                     located in multiple meshes. The mesh that
+                                     maximizes gfmax is chosen. For example,
+                                     using the distance field based on the
+                                     overlapping boundaries is helpful for
+                                     convergence during Schwarz iterations.
+       @param[in] bbox_rel_size_inc  (Optional) Relative size increase applied
+                                     when expanding each element bounding box.
+       @param[in] newt_tol           (Optional) Newton tolerance for the gslib
+                                     search methods.
+       @param[in] npt_max            (Optional) Number of points for
+                                     simultaneous iteration. This alters
+                                     performance and memory footprint.*/
+   void Setup(Mesh &m, const int meshid, GridFunction *gfmax = nullptr,
+              const double bbox_rel_size_inc = 0.1,
+              const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
    /** Searches positions given in physical space by \p point_pos. All output
@@ -677,7 +792,7 @@ class GSOPGSLIB
 protected:
    struct gslib::crystal *cr;               // gslib's internal data
    struct gslib::comm *gsl_comm;            // gslib's internal data
-   struct gslib::gs_data *gsl_data = NULL;
+   struct gslib::gs_data *gsl_data = nullptr;
    int num_ids;
 
 public:

fem/gslib/findpts_local_2.cpp

@@ -11,7 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -27,8 +27,6 @@
 #pragma GCC diagnostic pop
 #endif
 
-#include <climits>
-
 namespace mfem
 {
 #if GSLIB_RELEASE_VERSION >= 10009
@@ -54,127 +52,14 @@ struct findptsElementGPT_t
    double x[DIM], jac[DIM * DIM], hes[4];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-struct obbox_t
-{
-   double c0[DIM], A[DIM * DIM];
-   dbl_range_t x[DIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[DIM];
-   double fac[DIM];
-   unsigned int *offset;
-   int max;
-};
-
-// Eval the ith Lagrange interpolant and its first derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
-                                                       int i, const double *z,
-                                                       const double *lCoeff,
-                                                       int pN)
-{
-   double u0 = 1, u1 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2 * (x - z[j]);
-         u1 = d_j * u1 + u0;
-         u0 = d_j * u0;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-}
-
-// Eval the ith Lagrange interpolant and its first and second derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-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;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-   p0[2*pN+i] = 8.0 * lCoeff[i] * u2;
-}
-
-// Axis-aligned bounding box test.
-static MFEM_HOST_DEVICE inline double AABB_test(const obbox_t *const b,
-                                                const double x[2])
-{
-   double test = 1;
-   for (int d = 0; d < 2; ++d)
-   {
-      double b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
-      test = test < 0 ? test : b_d;
-   }
-   return test;
-}
-
-// Axis-aligned bounding box test followed by oriented bounding-box test.
-static MFEM_HOST_DEVICE inline double bbox_test(const obbox_t *const b,
-                                                const double x[2])
-{
-   const double bxyz = AABB_test(b, x);
-   if (bxyz < 0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[2];
-      for (int d = 0; d < 2; ++d)
-      {
-         dxyz[d] = x[d] - b->c0[d];
-      }
-      double test = 1;
-      for (int d = 0; d < 2; ++d)
-      {
-         double rst = 0;
-         for (int e = 0; e < 2; ++e)
-         {
-            rst += b->A[d * 2 + e] * dxyz[e];
-         }
-         double brst = (rst + 1) * (1 - rst);
-         test = test < 0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-// Element index corresponding to hash mesh that the point is located in.
-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 = 2 - 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;
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<DIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<DIM>;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_first_der;
+using gslib::lag_eval_second_der;
 
 /*Solve Ax=y. A is row-major */
 static MFEM_HOST_DEVICE inline void lin_solve_2(double x[2], const double A[4],
@@ -185,12 +70,6 @@ static MFEM_HOST_DEVICE inline void lin_solve_2(double x[2], const double A[4],
    x[1] = idet*(A[0]*y[1] - A[2]*y[0]);
 }
 
-/* L2 norm squared. */
-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 CSSRR
    the C bit --- 1<<4 --- is set when the point is converged
    RR is 0 = 00b if r is unconstrained,
@@ -352,7 +231,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *res,
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<2>(resid);
    const double decr = p->dist2 - dist2;
    const double pred = p->dist2p;
    for (int d = 0; d < 2; ++d)
@@ -695,25 +574,25 @@ static MFEM_HOST_DEVICE double tensor_ig2_j(double *g_partials,
 }
 
 template<int T_D1D = 0>
-static void FindPointsLocal2D_Kernel(const int npt,
-                                     const double tol,
-                                     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)
+static void FindPointsLocal2DKernel(const int npt,
+                                    const double tol,
+                                    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;
@@ -1175,30 +1054,45 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsLocal2D_Kernel<2>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<2>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 3:
-         return FindPointsLocal2D_Kernel<3>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<3>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 4:
-         return FindPointsLocal2D_Kernel<4>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<4>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       case 5:
-         return FindPointsLocal2D_Kernel<5>(
-                   npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
-                   pgll1d, plc);
+         FindPointsLocal2DKernel<5>(npt, DEV.newt_tol, pp,
+                                    point_pos_ordering, pgslm,
+                                    NE_split_total, pwt, pbb,
+                                    DEV.lh_nx, plhm, plhf, plho,
+                                    pcode, pelem, pref, pdist,
+                                    pgll1d, plc);
+         break;
       default:
-         return FindPointsLocal2D_Kernel(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                         pgslm, NE_split_total, pwt, pbb, DEV.lh_nx,
-                                         plhm, plhf, plho, pcode, pelem,
-                                         pref, pdist, pgll1d, plc, DEV.dof1d);
+         FindPointsLocal2DKernel(npt, DEV.newt_tol, pp,
+                                 point_pos_ordering, pgslm,
+                                 NE_split_total, pwt, pbb,
+                                 DEV.lh_nx, plhm, plhf, plho,
+                                 pcode, pelem, pref, pdist,
+                                 pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef DIM2

fem/gslib/findpts_local_3.cpp

@@ -11,9 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
-
-#include <climits>
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -59,128 +57,15 @@ struct findptsElemPt
    double x[DIM], jac[DIM * DIM], hes[18];
 };
 
-struct dbl_range_t
-{
-   double min, max;
-};
-
-struct obbox_t
-{
-   double c0[DIM], A[DIM * DIM];
-   dbl_range_t x[DIM];
-};
-
-struct findptsLocalHashData_t
-{
-   int hash_n;
-   dbl_range_t bnd[DIM];
-   double fac[DIM];
-   unsigned int *offset;
-   // int max;
-};
-
-// Eval the ith Lagrange interpolant and its first derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-static MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
-                                                       int i, const double *z,
-                                                       const double *lCoeff,
-                                                       int pN)
-{
-   double u0 = 1, u1 = 0;
-   for (int j = 0; j < pN; ++j)
-   {
-      if (i != j)
-      {
-         double d_j = 2*(x-z[j]);
-         u1 = d_j*u1+u0;
-         u0 = d_j*u0;
-      }
-   }
-   p0[i] = lCoeff[i]*u0;
-   p0[pN+i] = 2.0*lCoeff[i]*u1;
-}
-
-// Eval the ith Lagrange interpolant and its first and second derivative at x.
-// Note: lCoeff stores pre-computed coefficients for fast evaluation.
-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;
-      }
-   }
-   p0[i] = lCoeff[i]*u0;
-   p0[pN+i] = 2.0*lCoeff[i]*u1;
-   p0[2*pN+i] = 8.0*lCoeff[i]*u2;
-}
-
-// Axis-aligned bounding box test.
-static MFEM_HOST_DEVICE inline double AABB_test(const obbox_t *const b,
-                                                const double x[3])
-{
-   double b_d;
-   for (int d = 0; d < 3; ++d)
-   {
-      b_d = (x[d]-b->x[d].min)*(b->x[d].max-x[d]);
-      if (b_d < 0) { return b_d; }
-   }
-   return b_d;
-}
-
-// Axis-aligned bounding box test followed by oriented bounding-box test.
-static MFEM_HOST_DEVICE inline double bbox_test(const obbox_t *const b,
-                                                const double x[3])
-{
-   const double bxyz = AABB_test(b, x);
-   if (bxyz < 0)
-   {
-      return bxyz;
-   }
-   else
-   {
-      double dxyz[3];
-      for (int d = 0; d < 3; ++d)
-      {
-         dxyz[d] = x[d]-b->c0[d];
-      }
-      double test = 1;
-      for (int d = 0; d < 3; ++d)
-      {
-         double rst = 0;
-         for (int e = 0; e < 3; ++e)
-         {
-            rst += b->A[d*3+e]*dxyz[e];
-         }
-         double brst = (rst+1)*(1-rst);
-         test = test < 0 ? test : brst;
-      }
-      return test;
-   }
-}
-
-// Element index corresponding to hash mesh that the point is located in.
-static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
-                                              const double x[3])
-{
-   const int n = p->hash_n;
-   int sum = 0;
-   for (int d = 3-1; 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;
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<DIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<DIM>;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_first_der;
+using gslib::lag_eval_second_der;
+using gslib::lin_solve_sym_2;
 
 // Solve Ax=y. A is row-major.
 static MFEM_HOST_DEVICE inline void lin_solve_3(double x[3], const double A[9],
@@ -199,22 +84,6 @@ static MFEM_HOST_DEVICE inline void lin_solve_3(double x[3], const double A[9],
    x[2] = idet*(inv6*y[0]+inv7*y[1]+inv8*y[2]);
 }
 
-// Solve Ax=y. A is a symmetric 2x2 matrix.
-static MFEM_HOST_DEVICE inline void lin_solve_sym_2(double x[2],
-                                                    const double A[3],
-                                                    const double y[2])
-{
-   const double idet = 1 / (A[0]*A[2]-A[1]*A[1]);
-   x[0] = idet*(A[2]*y[0]-A[1]*y[1]);
-   x[1] = idet*(A[0]*y[1]-A[1]*y[0]);
-}
-
-// L2 norm.
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[3])
-{
-   return x[0]*x[0]+x[1]*x[1]+x[2]*x[2];
-}
-
 /* the bit structure of flags is CTTSSRR
    the C bit --- 1<<6 --- is set when the point is converged
    RR is 0 = 00b if r is unconstrained,
@@ -459,7 +328,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsPt *res,
                                                  const findptsPt *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<3>(resid);
    const double decr = p->dist2-dist2;
    const double pred = p->dist2p;
    for (int d = 0; d < 3; ++d)
@@ -1809,33 +1678,36 @@ 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.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    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.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    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.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    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.lh_nx, plhm,
-                                    plhf, plho, pcode, pelem, pref, pdist, pgll1d,
-                                    plc);
+                                    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.lh_nx, plhm, plhf,
-                                 plho, pcode, pelem, pref, pdist, pgll1d, plc,
+         FindPointsLocal3DKernel(npt, DEV.newt_tol, pp,
+                                 point_pos_ordering, pgslm,
+                                 NE_split_total, pwt, pbb,
+                                 DEV.lh_nx, plhm, plhf, plho,
+                                 pcode, pelem, pref, pdist, pgll1d, plc,
                                  DEV.dof1d);
+         break;
    }
 }
 #undef pMax

fem/gslib/findptsedge_local_2.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -52,113 +53,14 @@ 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];
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
 
 /* the bit structure of flags is CRR
    the C bit --- 1<<2 --- is set when the point is converged
@@ -187,29 +89,29 @@ static MFEM_HOST_DEVICE inline int point_index(const int x)
 /* 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,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[2],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<2>(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;
+   out_pt->x[0] = p->x[0];
+   out_pt->x[1] = p->x[1];
+   out_pt->oldr = p->r;
+   out_pt->dist2 = dist2;
    if (decr >= 0.01*pred)
    {
       if (decr >= 0.9*pred)   // very good iteration
       {
-         out->tr = p->tr*2;
+         out_pt->tr = p->tr*2;
       }
       else                    // somewhat good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -220,21 +122,21 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          "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;
+      out_pt->tr = v0/4.0;
+      out_pt->dist2 = p->dist2;
+      out_pt->r = p->oldr;
+      out_pt->flags = p->flags>>3;
+      out_pt->dist2p = -HUGE_VAL;
       if (pred < dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge( findptsElementPoint_t *const
-                                                 out,
+                                                 out_pt,
                                                  const double jac[2],
                                                  const double rhess,
                                                  const double resid[2],
@@ -304,9 +206,9 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r = newr;
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+   out_pt->r = newr;
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
 }
 
 static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
@@ -332,26 +234,27 @@ static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
 }
 
 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 )
+static void FindPointsEdgeLocal2DKernel( 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 bool    obb_check,
+                                         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;
@@ -412,22 +315,34 @@ static void FindPointsEdgeLocal2D_Kernel( const int     npt,
       {
          const unsigned int el = *elp;
 
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            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 < 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];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
+         }
+         else
+         {
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         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)
+         if (pass_bb)
          {
             //------------ findpts_local ------------------
             {
@@ -516,11 +431,14 @@ static void FindPointsEdgeLocal2D_Kernel( const int     npt,
                            double *hess = jac + sDIM*rDIM;
 
                            findptsElementGEdge_t edge;
+                           for (int d=0; d<sDIM; ++d)
+                           {
+                              edge.x[d] = constraint_workspace + d*D1D;
+                           }
                            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];
                               }
                            }
@@ -681,28 +599,41 @@ void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
    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);
+         FindPointsEdgeLocal2DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal2DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal2DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal2DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef sDIM

fem/gslib/findptsedge_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -54,117 +55,14 @@ 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] );
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
 
 /* the bit structure of flags is CRR
    the C bit --- 1<<2 --- is set when the point is converged
@@ -175,47 +73,46 @@ static MFEM_HOST_DEVICE inline double norm2(const double x[sDIM])
 #define CONVERGED_FLAG (1u<<2)
 #define FLAG_MASK 0x07u
 
-/* returns the number of constrained reference coordinates, max 2
+/* returns the number of constrained reference coordinates, max 1
 */
 static MFEM_HOST_DEVICE inline int num_constrained(const int flags)
 {
-   const int y = (flags | flags>>1);
-   return (y & 1u) + (y>>2 & 1u);
+   return ((flags | flags>>1) & 1u);
 }
 
 static MFEM_HOST_DEVICE inline int point_index(const int x)
 {
-   return ((x>>1)&1u) | ((x>>2)&2u);
+   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,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[3],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = norm2(resid);
+   const double dist2 = l2norm2<sDIM>(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_pt->x[d] = p->x[d];
    }
-   out->oldr = p->r;
-   out->dist2 = dist2;
+   out_pt->oldr = p->r;
+   out_pt->dist2 = dist2;
    if (decr>=0.01*pred)
    {
       if (decr>=0.9*pred)   // very good iteration
       {
-         out->tr = 2*p->tr;
+         out_pt->tr = 2*p->tr;
       }
       else   // good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -226,21 +123,21 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          "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;
+      out_pt->tr = v0/4.0;
+      out_pt->dist2 = p->dist2;
+      out_pt->r = p->oldr;
+      out_pt->flags = p->flags>>3;
+      out_pt->dist2p = -HUGE_VAL;
       if (pred<dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
-                                                out,
+                                                out_pt,
                                                 const double jac[sDIM*rDIM],
                                                 const double rhes,
                                                 const double resid[sDIM],
@@ -314,9 +211,9 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r = nr;
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+   out_pt->r = nr;
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
 #undef EVAL
 }
 
@@ -338,31 +235,32 @@ static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
    {
       dx[d] = x[d] - elx[d][ir];
    }
-   dist2[ir] = norm2(dx);;
+   dist2[ir] = l2norm2(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)
+static void FindPointsEdgeLocal3DKernel(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 bool obb_check,
+                                        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;
@@ -419,21 +317,35 @@ static void FindPointsEdgeLocal3D_Kernel(const int npt,
       for (; elp!=ele; ++elp)
       {
          const unsigned int el = *elp;
+
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            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 < 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];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
          }
-         for (int idx = 0; idx < sDIM2; ++idx)
+         else
          {
-            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         if (obbox_test(&box, x_i)>=0)
+         if (pass_bb)
          {
             //// findpts_local ////
             {
@@ -521,11 +433,14 @@ static void FindPointsEdgeLocal3D_Kernel(const int npt,
                            double *hess = jac + sDIM*rDIM;
 
                            findptsElementGEdge_t edge;
+                           for (int d=0; d<sDIM; ++d)
+                           {
+                              edge.x[d] = constraint_workspace + d*D1D;
+                           }
                            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];
                               }
                            }
@@ -688,28 +603,41 @@ void FindPointsGSLIB::FindPointsEdgeLocal3(const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
    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);
+         FindPointsEdgeLocal3DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal3DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal3DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       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);
+         FindPointsEdgeLocal3DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 #undef rDIM2

fem/gslib/findptssurf_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 #ifdef MFEM_USE_GSLIB
 
 #ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
@@ -51,124 +52,15 @@ struct findptsElementGPT_t
    double x[sDIM], jac[sDIM*rDIM], hes[sDIM*(rDIM+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;
-      }
-   }
-   p0[i] = lCoeff[i] * u0;
-   p0[pN+i] = 2.0 * lCoeff[i] * u1;
-   p0[2*pN+i] = 8.0 * lCoeff[i] * u2;
-}
-
-/* positive when possibly inside */
-static MFEM_HOST_DEVICE inline double AABB_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 bbox_test(const obbox_t *const b,
-                                                const double x[sDIM])
-{
-   const double bxyz = AABB_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];
-      }
-      // tranform 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 void lin_solve_sym_2(double x[2],
-                                                    const double A[3],
-                                                    const double y[2])
-{
-   const double idet = 1 / (A[0] * A[2] - A[1] * A[1]);
-   x[0] = idet * (A[2] * y[0] - A[1] * y[1]);
-   x[1] = idet * (A[0] * y[1] - A[1] * y[0]);
-}
-
-static MFEM_HOST_DEVICE inline double l2norm2(const double x[sDIM])
-{
-   return ( x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
-}
+using dbl_range_t = gslib::dbl_range_t;
+using obbox_t = gslib::obbox_t<sDIM>;
+using findptsLocalHashData_t = gslib::findptsLocalHashData_t<sDIM>;
+using gslib::AABB_test;
+using gslib::bbox_test;
+using gslib::hash_index;
+using gslib::l2norm2;
+using gslib::lag_eval_second_der;
+using gslib::lin_solve_sym_2;
 
 /* the bit structure of flags is CSSRR
    the C bit --- 1<<4 --- is set when the point is converged
@@ -219,18 +111,10 @@ static MFEM_HOST_DEVICE inline int point_index(const int x)
    return ((x>>1)&1u) | ((x>>2)&2u);
 }
 
-static MFEM_HOST_DEVICE inline findptsElementGEdge_t
+static MFEM_HOST_DEVICE inline void
 get_edge(const double *elx[3], const double *wtend, int ei,
-         double *workspace, int &side_init, int jidx, int pN)
+         int &side_init, int jidx, int pN, findptsElementGEdge_t &edge)
 {
-   findptsElementGEdge_t edge;
-   for (int d=0; d<sDIM; ++d)
-   {
-      edge.x[d]     = workspace             + d*pN;
-      edge.dxdn[d]  = workspace +   sDIM*pN + d*pN;
-      edge.d2xdn[d] = workspace + 2*sDIM*pN + d*pN;
-   }
-
    // given edge index, compute normal and tangential directions
    const int dn = ei>>1, //0 for rmin/rmax, 1 for smin/smax
              de = plus_1_mod_2(dn); // 1 for rmin/rmax, 0 for smin/smax
@@ -256,7 +140,6 @@ get_edge(const double *elx[3], const double *wtend, int ei,
       edge.d2xdn[dd][jj] = sums_k[1];
 #undef ELX
    }
-   return edge;
 }
 
 static MFEM_HOST_DEVICE inline findptsElementGPT_t get_pt(const double *elx[3],
@@ -312,34 +195,34 @@ static MFEM_HOST_DEVICE inline findptsElementGPT_t get_pt(const double *elx[3],
 /* 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,
+   sets out_pt->dist2, out_pt->index, out_pt->x, out_pt->oldr in any event,
+   leaving out_pt->r, out_pt->dr, out_pt->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out_pt,
                                                  const double resid[3],
                                                  const findptsElementPoint_t *p,
                                                  const double tol)
 {
-   const double dist2 = l2norm2(resid);
+   const double dist2 = l2norm2<sDIM>(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_pt->x[d] = p->x[d];
    }
    for (int d=0; d<rDIM; ++d)
    {
-      out->oldr[d] = p->r[d];
+      out_pt->oldr[d] = p->r[d];
    }
-   out->dist2 = dist2;
+   out_pt->dist2 = dist2;
    if (decr>=0.01*pred)
    {
       if (decr>=0.9*pred)   // very good iteration
       {
-         out->tr = 2*p->tr;
+         out_pt->tr = 2*p->tr;
       }
       else   // good iteration
       {
-         out->tr = p->tr;
+         out_pt->tr = p->tr;
       }
       return false;
    }
@@ -351,17 +234,17 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
          which is why we divide by 4 below */
       double v0 = fabs(p->r[0] - p->oldr[0]),
              v1 = fabs(p->r[1] - p->oldr[1]);
-      out->tr     = ( v0>v1 ? v0 : v1 )/4;
-      out->dist2  = p->dist2;
-      out->flags   = p->flags >> 5;
-      out->dist2p = -HUGE_VAL;
+      out_pt->tr     = ( v0>v1 ? v0 : v1 )/4;
+      out_pt->dist2  = p->dist2;
+      out_pt->flags   = p->flags >> 5;
+      out_pt->dist2p = -HUGE_VAL;
       for (int d=0; d<rDIM; ++d)
       {
-         out->r[d] = p->oldr[d];
+         out_pt->r[d] = p->oldr[d];
       }
       if (pred<dist2*tol)
       {
-         out->flags |= CONVERGED_FLAG;
+         out_pt->flags |= CONVERGED_FLAG;
       }
       return true;
    }
@@ -369,7 +252,7 @@ static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
 
 /* minimize ||resid - jac * dr||_2, with |dr| <= tr, |r0+dr|<=1
    (exact solution of trust region problem) */
-static MFEM_HOST_DEVICE void newton_face( findptsElementPoint_t *const out,
+static MFEM_HOST_DEVICE void newton_face( findptsElementPoint_t *const out_pt,
                                           const double jac[sDIM*rDIM],
                                           const double rhes[3],
                                           const double resid[sDIM],
@@ -540,19 +423,19 @@ newton_face_constrained:
    }
 
 newton_face_fin:
-   out->dist2p = -2*v;
+   out_pt->dist2p = -2*v;
    dr[0] = r[0] - p->r[0];
    dr[1] = r[1] - p->r[1];
    if ( fabs(dr[0])+fabs(dr[1]) < tol)
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r[0] = r[0], out->r[1] = r[1];
-   out->flags = new_flags | ((p->flags & FLAG_MASK)<<5);
+   out_pt->r[0] = r[0], out_pt->r[1] = r[1];
+   out_pt->flags = new_flags | ((p->flags & FLAG_MASK)<<5);
 }
 
 static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
-                                                out,
+                                                out_pt,
                                                 const double jac[sDIM*rDIM],
                                                 const double rhes,
                                                 const double resid[sDIM],
@@ -637,10 +520,10 @@ newton_edge_fin:
    {
       new_flags |= CONVERGED_FLAG;
    }
-   out->r[de] = nr;
-   out->r[dn] = p->r[dn];
-   out->dist2p = -v;
-   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<5);
+   out_pt->r[de] = nr;
+   out_pt->r[dn] = p->r[dn];
+   out_pt->dist2p = -v;
+   out_pt->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<5);
 #undef EVAL
 }
 
@@ -676,26 +559,27 @@ static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
 // global memory access of element coordinates.
 // Are the structs being stored in "local memory" or registers?
 template<int T_D1D = 0>
-static void FindPointsSurfLocal3D_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)
+static void FindPointsSurfLocal3DKernel(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 bool obb_check,
+                                        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;
@@ -753,22 +637,36 @@ static void FindPointsSurfLocal3D_Kernel(const int npt,
       {
          const unsigned int el = *elp;
 
-         // construct obbox on the fly
+         const int n_box_ents = obb_check ? (3*sDIM + sDIM2) : (2*sDIM);
+         bool pass_bb = true;
          obbox_t box;
-         int n_box_ents = 3*sDIM + sDIM2;
-         for (int idx = 0; idx < sDIM; ++idx)
+         if (obb_check)
          {
-            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];
+            // construct obbox on the fly
+            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];
+            }
+            pass_bb = (bbox_test(&box, x_i) >= 0);
+         }
+         else
+         {
+            for (int d = 0; d < sDIM; ++d)
+            {
+               box.x[d].min = boxinfo[n_box_ents*el + d];
+               box.x[d].max = boxinfo[n_box_ents*el + sDIM + d];
+            }
+            pass_bb = (AABB_test(&box, x_i) >= 0);
          }
 
-         for (int idx = 0; idx < sDIM2; ++idx)
-         {
-            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
-         }
-
-         if (bbox_test(&box, x_i) < 0) { continue; }
+         if (!pass_bb) { continue; }
 
          //// findpts_local ////
          {
@@ -968,13 +866,19 @@ static void FindPointsSurfLocal3D_Kernel(const int npt,
                         double *hes_T = jac + sDIM*rDIM;
                         double *hes   = hes_T + hes_count*sDIM;
                         findptsElementGEdge_t edge;
+                        for (int d=0; d<sDIM; ++d)
+                        {
+                           edge.x[d]     = constraint_workspace + d*D1D;
+                           edge.dxdn[d]  = constraint_workspace + d*D1D
+                                           + sDIM*D1D;
+                           edge.d2xdn[d] = constraint_workspace + d*D1D
+                                           + 2*sDIM*D1D;
+                        }
 
                         MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
                         {
-                           // utilized first D1D threads
-                           edge = get_edge(elx, wtend, ei,
-                                           constraint_workspace, edge_init, j,
-                                           D1D);
+                           // One thread per physical component and edge DOF.
+                           get_edge(elx, wtend, ei, edge_init, j, D1D, edge);
                         }
                         MFEM_SYNC_THREAD;
 
@@ -1045,7 +949,15 @@ static void FindPointsSurfLocal3D_Kernel(const int npt,
                               steep *= tmp->r[dn];
                               if (steep<0)
                               {
-                                 newton_face( fpt,jac,hes,resid,tmp->flags&CONVERGED_FLAG,tmp,tol);
+                                 double face_hes[3] =
+                                 {
+                                    dn == 0 ? hes[2] : hes[0],
+                                    hes[1],
+                                    dn == 0 ? hes[0] : hes[2]
+                                 };
+                                 newton_face(fpt, jac, face_hes, resid,
+                                             tmp->flags & CONVERGED_FLAG,
+                                             tmp, tol);
                               }
                               else
                               {
@@ -1211,29 +1123,42 @@ void FindPointsGSLIB::FindPointsSurfLocal3(const Vector &point_pos,
    auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
    auto plc = DEV.lagcoeff.Read(use_dev);
    double dist2tol = DEV.surf_dist_tol;
+   const bool obb_chk = obb_check;
 
    switch (DEV.dof1d)
    {
       case 2:
-         return FindPointsSurfLocal3D_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);
+         FindPointsSurfLocal3DKernel<2>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 3:
-         return FindPointsSurfLocal3D_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);
+         FindPointsSurfLocal3DKernel<3>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       case 4:
-         return FindPointsSurfLocal3D_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);
+         FindPointsSurfLocal3DKernel<4>(npt, DEV.newt_tol, dist2tol,
+                                        pp, point_pos_ordering, pgslm,
+                                        NE_split_total, pwt, pbb, obb_chk,
+                                        DEV.lh_nx, plhm, plhf, plho,
+                                        pcode, pelem, pref, pdist,
+                                        pgll1d, plc);
+         break;
       default:
-         return FindPointsSurfLocal3D_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);
+         FindPointsSurfLocal3DKernel(npt, DEV.newt_tol, dist2tol, pp,
+                                     point_pos_ordering, pgslm,
+                                     NE_split_total, pwt, pbb, obb_chk,
+                                     DEV.lh_nx, plhm, plhf, plho,
+                                     pcode, pelem, pref, pdist,
+                                     pgll1d, plc, DEV.dof1d);
+         break;
    }
 }
 

fem/gslib/gslib_kernel_helpers.hpp

@@ -0,0 +1,190 @@
+#ifndef MFEM_GSLIB_KERNEL_HELPERS_HPP
+#define MFEM_GSLIB_KERNEL_HELPERS_HPP
+
+#include "../../config/config.hpp"
+
+#include <cmath>
+
+namespace mfem
+{
+
+namespace gslib
+{
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+template <int SDIM>
+struct obbox_t
+{
+   double c0[SDIM], A[SDIM * SDIM];
+   dbl_range_t x[SDIM];
+};
+
+template <int SDIM>
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[SDIM];
+   double fac[SDIM];
+   unsigned int *offset;
+};
+
+// Eval the ith Lagrange interpolant at x.
+MFEM_HOST_DEVICE inline 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)
+   {
+      const double d_j = x - z[j];
+      p_i *= j == i ? 1 : d_j;
+   }
+   p0[i] = lagrangeCoeff[i] * p_i;
+}
+
+// Eval the ith Lagrange interpolant and its first derivative at x.
+MFEM_HOST_DEVICE inline void lag_eval_first_der(double *p0, double x,
+                                                int i, const double *z,
+                                                const double *lCoeff,
+                                                int pN)
+{
+   double u0 = 1, u1 = 0;
+   for (int j = 0; j < pN; ++j)
+   {
+      if (i != j)
+      {
+         const double d_j = 2 * (x - z[j]);
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   p0[i] = lCoeff[i] * u0;
+   p0[pN + i] = 2.0 * lCoeff[i] * u1;
+}
+
+// Eval the ith Lagrange interpolant and its first and second derivative at x.
+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)
+      {
+         const double d_j = 2 * (x - z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   p0[i] = lCoeff[i] * u0;
+   p0[pN + i] = 2.0 * lCoeff[i] * u1;
+   p0[2 * pN + i] = 8.0 * lCoeff[i] * u2;
+}
+
+// Solve Ax=y where A is a symmetric 2x2 matrix packed as {a00, a01, a11}.
+MFEM_HOST_DEVICE inline void lin_solve_sym_2(double x[2],
+                                             const double A[3],
+                                             const double y[2])
+{
+   const double idet = 1 / (A[0] * A[2] - A[1] * A[1]);
+   x[0] = idet * (A[2] * y[0] - A[1] * y[1]);
+   x[1] = idet * (A[0] * y[1] - A[1] * y[0]);
+}
+
+// Positive when the point is inside the axis-aligned bounding box.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double AABB_test(const obbox_t<SDIM> *const b,
+                                         const double (&x)[SDIM])
+{
+   double test = 1.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      const double b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      test = test < 0.0 ? test : b_d;
+   }
+   return test;
+}
+
+// Positive when the point is inside the oriented bounding box.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double bbox_test(const obbox_t<SDIM> *const b,
+                                         const double (&x)[SDIM])
+{
+   const double bxyz = AABB_test(b, x);
+   if (bxyz < 0.0)
+   {
+      return bxyz;
+   }
+
+   double dxyz[SDIM];
+   for (int d = 0; d < SDIM; ++d)
+   {
+      dxyz[d] = x[d] - b->c0[d];
+   }
+
+   double test = 1.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      double rst = 0.0;
+      for (int e = 0; e < SDIM; ++e)
+      {
+         rst += b->A[d * SDIM + e] * dxyz[e];
+      }
+      const double brst = (rst + 1.0) * (1.0 - rst);
+      test = test < 0.0 ? test : brst;
+   }
+   return test;
+}
+
+// Hash index in the hash table for the point x.
+template <int SDIM>
+MFEM_HOST_DEVICE inline int hash_index(
+   const findptsLocalHashData_t<SDIM> *const p,
+   const double (&x)[SDIM])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d = SDIM - 1; d >= 0; --d)
+   {
+      sum *= n;
+      const 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;
+}
+
+// Squared Euclidean norm.
+template <int SDIM>
+MFEM_HOST_DEVICE inline double l2norm2(const double (&x)[SDIM])
+{
+   double sum = 0.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      sum += x[d] * x[d];
+   }
+   return sum;
+}
+
+template <int SDIM>
+MFEM_HOST_DEVICE inline double l2norm2(const double *x)
+{
+   double sum = 0.0;
+   for (int d = 0; d < SDIM; ++d)
+   {
+      sum += x[d] * x[d];
+   }
+   return sum;
+}
+
+} // namespace gslib
+
+} // namespace mfem
+
+#endif

fem/gslib/interpolate_local_1.cpp

@@ -11,7 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
-#include "../../linalg/kernels.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -33,17 +33,7 @@ namespace mfem
 #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;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal1DKernel(const double *const gf_in,
@@ -123,21 +113,26 @@ void FindPointsGSLIB::InterpolateLocal1( const Vector &field_in,
    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);
+      case 2:
+         InterpolateLocal1DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal1DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal1DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal1DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal1DKernel(pfin, pgsl, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 #undef CODE_INTERNAL

fem/gslib/interpolate_local_2.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -32,18 +33,7 @@ namespace mfem
 #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)
-   {
-      double d_j = x - z[j];
-      p_i *= j == i ? 1 : d_j;
-   }
-   p0[i] = lagrangeCoeff[i] * p_i;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal2DKernel(const double *const gf_in,
@@ -132,21 +122,26 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
    auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
-      case 2: return InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 3: return InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 4: return InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 5: return InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      default: return InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
-                                                  npt, ncomp,
-                                                  pgll, plcf, dof1Dsol);
+      case 2:
+         InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 

fem/gslib/interpolate_local_3.cpp

@@ -11,6 +11,7 @@
 
 #include "../gslib.hpp"
 #include "../../general/forall.hpp"
+#include "gslib_kernel_helpers.hpp"
 
 #ifdef MFEM_USE_GSLIB
 
@@ -32,18 +33,7 @@ namespace mfem
 #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)
-   {
-      double d_j = x - z[j];
-      p_i *= j == i ? 1 : d_j;
-   }
-   p0[i] = lagrangeCoeff[i] * p_i;
-}
+using gslib::lagrange_eval;
 
 template<int T_D1D = 0>
 static void InterpolateLocal3DKernel(const double *const gf_in,
@@ -135,21 +125,26 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
    auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
-      case 2: return InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 3: return InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 4: return InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      case 5: return InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp,
-                                                    pgll, plcf);
-      default: return InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
-                                                  npt, ncomp,
-                                                  pgll, plcf, dof1Dsol);
+      case 2:
+         InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 3:
+         InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 4:
+         InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      case 5:
+         InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
+                                     npt, ncomp, pgll, plcf);
+         break;
+      default:
+         InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
+                                  npt, ncomp, pgll, plcf, dof1Dsol);
+         break;
    }
 }
 

fem/integ/bilininteg_diffusion_kernels.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "bilininteg_diffusion_kernels.hpp"
+#include "bilininteg_diffusion_pa_simplices.hpp" // IWYU pragma: keep
 
 namespace mfem
 {
@@ -19,6 +20,13 @@ namespace mfem
 DiffusionIntegrator::Kernels::Kernels()
 {
    // 2D
+   // Q = P, only for simplex
+   DiffusionIntegrator::AddSimplexSpecialization<2,2,1>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,3,2>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,4,3>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,5,4>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,6,5>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,7,6>();
    // Q = P+1
    DiffusionIntegrator::AddSpecialization<2,1,1>();
    DiffusionIntegrator::AddSpecialization<2,2,2>();
@@ -40,7 +48,18 @@ DiffusionIntegrator::Kernels::Kernels()
    DiffusionIntegrator::AddSpecialization<2,8,9>();
    DiffusionIntegrator::AddSpecialization<2,9,10>();
    // others
+   DiffusionIntegrator::AddSimplexSpecialization<2,2,5>();
+   DiffusionIntegrator::AddSimplexSpecialization<2,3,6>();
+
    // 3D
+   // Q = P, only for simplex
+   DiffusionIntegrator::AddSimplexSpecialization<3,2,1>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,3,2>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,4,3>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,5,4>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,6,5>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,7,6>();
+   DiffusionIntegrator::AddSimplexSpecialization<3,8,7>();
    // Q = P+1
    DiffusionIntegrator::AddSpecialization<3,1,1>();
    DiffusionIntegrator::AddSpecialization<3,2,2>();

fem/integ/bilininteg_diffusion_kernels.hpp

@@ -12,7 +12,6 @@
 #ifndef MFEM_BILININTEG_DIFFUSION_KERNELS_HPP
 #define MFEM_BILININTEG_DIFFUSION_KERNELS_HPP
 
-#include "../kernel_dispatch.hpp"
 #include "../../config/config.hpp"
 #include "../../general/array.hpp"
 #include "../../general/forall.hpp"
@@ -20,6 +19,8 @@
 #include "../../linalg/vector.hpp"
 #include "../bilininteg.hpp"
 
+#include "bilininteg_diffusion_pa_simplices.hpp"
+
 namespace mfem
 {
 
@@ -637,8 +638,8 @@ inline void SmemPADiffusionApply2D(const int NE,
                                    const bool symmetric,
                                    const Array<real_t> &b_,
                                    const Array<real_t> &g_,
-                                   const Array<real_t> &bt_,
-                                   const Array<real_t> &gt_,
+                                   const Array<real_t> &,
+                                   const Array<real_t> &,
                                    const Vector &d_,
                                    const Vector &x_,
                                    Vector &y_,
@@ -1218,43 +1219,47 @@ inline void SmemPADiffusionApply3D(const int NE,
 namespace
 {
 using ApplyKernelType = DiffusionIntegrator::ApplyKernelType;
+using ApplySimplexKernelType = DiffusionIntegrator::ApplySimplexKernelType;
 using DiagonalKernelType = DiffusionIntegrator::DiagonalKernelType;
 }
 
-template<int DIM, int T_D1D, int T_Q1D>
+template<int DIM, int D1D, int Q1D>
 ApplyKernelType DiffusionIntegrator::ApplyPAKernels::Kernel()
 {
-   if constexpr (DIM == 2) { return internal::SmemPADiffusionApply2D<T_D1D,T_Q1D>; }
-   else if constexpr (DIM == 3) { return internal::SmemPADiffusionApply3D<T_D1D, T_Q1D>; }
-   MFEM_ABORT("");
+   if constexpr (DIM == 2) { return internal::SmemPADiffusionApply2D<D1D, Q1D>; }
+   else if constexpr (DIM == 3) { return internal::SmemPADiffusionApply3D<D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+   return nullptr;
 }
 
 inline
-ApplyKernelType DiffusionIntegrator::ApplyPAKernels::Fallback(int DIM, int, int)
+ApplyKernelType DiffusionIntegrator::ApplyPAKernels::Fallback(int dim, int, int)
 {
-   if (DIM == 2) { return internal::PADiffusionApply2D; }
-   else if (DIM == 3) { return internal::PADiffusionApply3D; }
+   if (dim == 2) { return internal::PADiffusionApply2D; }
+   else if (dim == 3) { return internal::PADiffusionApply3D; }
    else { MFEM_ABORT(""); }
 }
 
 template<int DIM, int D1D, int Q1D>
 DiagonalKernelType DiffusionIntegrator::DiagonalPAKernels::Kernel()
 {
-   if constexpr (DIM == 2) { return internal::SmemPADiffusionDiagonal2D<D1D,Q1D>; }
+   if constexpr (DIM == 2) { return internal::SmemPADiffusionDiagonal2D<D1D, Q1D>; }
    else if constexpr (DIM == 3) { return internal::SmemPADiffusionDiagonal3D<D1D, Q1D>; }
-   MFEM_ABORT("");
+   else { MFEM_ABORT(""); }
+   return nullptr;
 }
 
 inline DiagonalKernelType
-DiffusionIntegrator::DiagonalPAKernels::Fallback(int DIM, int, int)
+DiffusionIntegrator::DiagonalPAKernels::Fallback(int dim, int, int)
 {
-   if (DIM == 2) { return internal::PADiffusionDiagonal2D; }
-   else if (DIM == 3) { return internal::PADiffusionDiagonal3D; }
+   if (dim == 2) { return internal::PADiffusionDiagonal2D; }
+   else if (dim == 3) { return internal::PADiffusionDiagonal3D; }
    else { MFEM_ABORT(""); }
+   return nullptr;
 }
+
 /// \endcond DO_NOT_DOCUMENT
 
 } // namespace mfem
 
-
 #endif

fem/integ/bilininteg_diffusion_pa.cpp

@@ -15,6 +15,7 @@
 #include "../../mesh/nurbs.hpp"
 #include "../ceed/integrators/diffusion/diffusion.hpp"
 #include "bilininteg_diffusion_kernels.hpp"
+#include "bilininteg_diffusion_pa_simplices.hpp"
 
 namespace mfem
 {
@@ -68,6 +69,24 @@ void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
       }
 #endif // MFEM_USE_OCCA
 
+      if (fespace->UsesRaggedTensorBasis())
+      {
+         const auto *rmaps = static_cast<const RaggedDofToQuad*>(maps);
+         return ApplySimplexPAKernels::Run(dim, dofs1D, quad1D, ne, symmetric,
+                                           rmaps->lex_map,
+                                           rmaps->forward_map2d_diff,
+                                           rmaps->inverse_map2d_diff,
+                                           rmaps->forward_map3d_diff,
+                                           rmaps->inverse_map3d_diff,
+                                           rmaps->Ga1,
+                                           rmaps->Ga2,
+                                           rmaps->Ga3,
+                                           rmaps->Ga1t,
+                                           rmaps->Ga2t,
+                                           rmaps->Ga3t,
+                                           Dv, x, y, dofs1D, quad1D);
+      }
+
       ApplyPAKernels::Run(dim, dofs1D, quad1D, ne, symmetric, B, G, Bt,
                           Gt, Dv, x, y, dofs1D, quad1D);
    }
@@ -94,7 +113,8 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    fespace = &fes;
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
-   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
+   const bool stroud = fes.UsesRaggedTensorBasis();
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, stroud);
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
@@ -119,13 +139,22 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    dim = mesh->Dimension();
    ne = fes.GetNE();
    geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mt);
+   if (stroud)
+   {
+      maps = &el.GetDofToQuad(*ir, DofToQuad::RAGGED_TENSOR);
+   }
+   else
+   {
+      maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   }
    const int sdim = mesh->SpaceDimension();
-   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
 
    QuadratureSpace qs(*mesh, *ir);
    CoefficientVector coeff(qs, CoefficientStorage::COMPRESSED);
+   // QuadratureSpace expects ir defined in reference simplex for Bernstein
+   // elements with partial assembly
 
    if (MQ) { coeff.ProjectTranspose(*MQ); }
    else if (VQ) { coeff.Project(*VQ); }

fem/integ/bilininteg_elasticity_kernels.cpp

@@ -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.");

fem/integ/bilininteg_elasticity_kernels.hpp

@@ -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 +279,67 @@ 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++)
+               const auto invJ = inv(make_tensor<d, d>([&](int r, int c)
                {
-                  for (int p = 0; p < numPoints; p++ )
+                  return J(p, r, c, e);
+               }));
+               const real_t w = ipWeights[p] / det(invJ);
+
+               for (int n = 0; n < d; n++)
+               {
+                  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 = 0.0;
+                     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);
                   }
                }
             }

fem/integ/bilininteg_elasticity_pa.cpp

@@ -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

fem/integ/bilininteg_hcurl_kernels.cpp

@@ -147,18 +147,16 @@ void PAHcurlMassAssembleDiagonal3D(const int D1D,
    }); // end of element loop
 }
 
-void PAHcurlMassApply2D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const bool symmetric,
-                        const Array<real_t> &bo,
-                        const Array<real_t> &bc,
-                        const Array<real_t> &bot,
-                        const Array<real_t> &bct,
-                        const Vector &pa_data,
-                        const Vector &x,
-                        Vector &y)
+void PAHcurlMassApply2D(const int NE, const bool symmetric,
+                        [[maybe_unused]] const bool scalar_coeff,
+                        const Array<real_t> &bo, const Array<real_t> &bc,
+                        const Array<real_t> &bot, const Array<real_t> &bct,
+                        const Vector &pa_data, const Vector &x, Vector &y,
+                        const int D1D, [[maybe_unused]] const int TestD1D,
+                        const int Q1D)
 {
+   MFEM_ASSERT(D1D == TestD1D,
+               "Trial and Test space must have the same number of dofs");
    auto Bo = Reshape(bo.Read(), Q1D, D1D-1);
    auto Bc = Reshape(bc.Read(), Q1D, D1D);
    auto Bot = Reshape(bot.Read(), D1D-1, Q1D);
@@ -277,18 +275,16 @@ void PAHcurlMassApply2D(const int D1D,
    }); // end of element loop
 }
 
-void PAHcurlMassApply3D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const bool symmetric,
-                        const Array<real_t> &bo,
-                        const Array<real_t> &bc,
-                        const Array<real_t> &bot,
-                        const Array<real_t> &bct,
-                        const Vector &pa_data,
-                        const Vector &x,
-                        Vector &y)
+void PAHcurlMassApply3D(const int NE, const bool symmetric,
+                        [[maybe_unused]] const bool scalar_coeff,
+                        const Array<real_t> &bo, const Array<real_t> &bc,
+                        const Array<real_t> &bot, const Array<real_t> &bct,
+                        const Vector &pa_data, const Vector &x, Vector &y,
+                        const int D1D, [[maybe_unused]] const int TestD1D,
+                        const int Q1D)
 {
+   MFEM_VERIFY(D1D == TestD1D,
+               "Trial and test spaces must have same number of dofs");
    MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
                "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,

fem/integ/bilininteg_hcurl_kernels.hpp

@@ -181,228 +181,312 @@ inline void SmemPAHcurlMassAssembleDiagonal3D(const int d1d,
 }
 
 // PA H(curl) Mass Apply 2D kernel
-void PAHcurlMassApply2D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const bool symmetric,
-                        const Array<real_t> &bo,
-                        const Array<real_t> &bc,
-                        const Array<real_t> &bot,
-                        const Array<real_t> &bct,
-                        const Vector &pa_data,
-                        const Vector &x,
-                        Vector &y);
+void PAHcurlMassApply2D(const int NE, const bool symmetric,
+                        const bool scalar_coeff, const Array<real_t> &bo,
+                        const Array<real_t> &bc, const Array<real_t> &bot,
+                        const Array<real_t> &bct, const Vector &pa_data,
+                        const Vector &x, Vector &y, const int TrialD1D,
+                        const int TestD1D, const int Q1D);
 
 // PA H(curl) Mass Apply 3D kernel
-void PAHcurlMassApply3D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const bool symmetric,
-                        const Array<real_t> &bo,
-                        const Array<real_t> &bc,
-                        const Array<real_t> &bot,
-                        const Array<real_t> &bct,
-                        const Vector &pa_data,
-                        const Vector &x,
-                        Vector &y);
+void PAHcurlMassApply3D(const int NE, const bool symmetric,
+                        [[maybe_unused]] const bool scalar_coeff,
+                        const Array<real_t> &bo, const Array<real_t> &bc,
+                        const Array<real_t> &bot, const Array<real_t> &bct,
+                        const Vector &pa_data, const Vector &x, Vector &y,
+                        const int TrialD1D, [[maybe_unused]] const int TestD1D,
+                        const int Q1D);
 
 // Shared memory PA H(curl) Mass Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
-inline void SmemPAHcurlMassApply3D(const int d1d,
-                                   const int q1d,
-                                   const int NE,
-                                   const bool symmetric,
-                                   const Array<real_t> &bo,
-                                   const Array<real_t> &bc,
-                                   const Array<real_t> &bot,
-                                   const Array<real_t> &bct,
-                                   const Vector &pa_data,
-                                   const Vector &x,
-                                   Vector &y)
+template <int T_D1D = 0, int T_Q1D = 0, int TBATCH = 0, bool ACCUMULATE = true>
+inline void SmemPAHcurlMassApply3D(
+   const int NE, const bool symmetric, [[maybe_unused]] const bool scalar_coeff,
+   const Array<real_t> &bo, const Array<real_t> &bc,
+   [[maybe_unused]] const Array<real_t> &bot,
+   [[maybe_unused]] const Array<real_t> &bct, const Vector &pa_data,
+   const Vector &x, Vector &y, const int d1d = 0,
+   [[maybe_unused]] const int test_d1d = 0, const int q1d = 0)
 {
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
    MFEM_VERIFY(T_D1D || d1d <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
                "Error: d1d > HCURL_MAX_D1D");
    MFEM_VERIFY(T_Q1D || q1d <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,
                "Error: q1d > HCURL_MAX_Q1D");
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-
+   MFEM_ASSERT(Q1D >= D1D, "Expected Q1D >= D1D");
    const int dataSize = symmetric ? 6 : 9;
 
-   auto Bo = Reshape(bo.Read(), Q1D, D1D-1);
-   auto Bc = Reshape(bc.Read(), Q1D, D1D);
-   auto op = Reshape(pa_data.Read(), Q1D, Q1D, Q1D, dataSize, NE);
-   auto X = Reshape(x.Read(), 3*(D1D-1)*D1D*D1D, NE);
-   auto Y = Reshape(y.ReadWrite(), 3*(D1D-1)*D1D*D1D, NE);
+   // assume trial space == test space
+   auto Bo = bo.Read();
+   auto Bc = bc.Read();
+   auto op =
+      Reshape(pa_data.Read(), Q1D, Q1D, Q1D, dataSize, NE);
+   auto X_ = Reshape(x.Read(), 3 * (D1D - 1) * D1D * D1D, NE);
+   auto y_ = y.ReadWrite();
 
-   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   constexpr int MD_ = T_D1D ? T_D1D : DofQuadLimits::HCURL_MAX_D1D;
+   constexpr int MQ_ = T_Q1D ? T_Q1D : DofQuadLimits::HCURL_MAX_Q1D;
+   constexpr int MDQ_ = std::max(MD_, MQ_);
+   constexpr int MB_ = TBATCH ? TBATCH : 1;
+
+   mfem::forall_2D_batch<MDQ_ * MDQ_ * MDQ_ * MB_>(
+      NE, MDQ_ * MDQ_ * MDQ_, 1, MB_, [=] MFEM_HOST_DEVICE(int e)
    {
+#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
+      constexpr int nbz = TBATCH ? TBATCH : 1;
+      int tidz = MFEM_THREAD_ID(z);
+#else
+      constexpr int nbz = 1;
+      constexpr int tidz = 0;
+#endif
+
       constexpr int VDIM = 3;
       constexpr int MD1D = T_D1D ? T_D1D : DofQuadLimits::HCURL_MAX_D1D;
       constexpr int MQ1D = T_Q1D ? T_Q1D : DofQuadLimits::HCURL_MAX_Q1D;
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MDQ = std::max(MD1D, MQ1D);
 
-      MFEM_SHARED real_t sBo[MQ1D][MD1D];
-      MFEM_SHARED real_t sBc[MQ1D][MD1D];
+      // nvcc limit work-around: can't have Y_ be captured first in
+      // if constexpr, so capture y_ and construct Y_ locally
+      // only works on GPU
+      auto Y = Reshape(y_, VDIM * (D1D - 1) * D1D * D1D, NE);
 
-      real_t op9[9];
-      MFEM_SHARED real_t sop[9*MQ1D*MQ1D];
-      MFEM_SHARED real_t mass[MQ1D][MQ1D][3];
+      MFEM_SHARED real_t sBo[MDQ * (MD1D - 1)];
+      MFEM_SHARED real_t sBc[MDQ * MD1D];
+      auto BO = Reshape(sBo, Q1D, D1D - 1);
+      auto BC = Reshape(sBc, Q1D, D1D);
 
-      MFEM_SHARED real_t sX[MD1D][MD1D][MD1D];
+      MFEM_SHARED real_t sX[nbz * VDIM * (MD1D - 1) * MD1D * MD1D];
+      MFEM_SHARED real_t sm0[nbz * VDIM * MDQ * MDQ * MDQ];
+      MFEM_SHARED real_t sm1[nbz * VDIM * MDQ * MDQ * MDQ];
 
-      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      real_t(*X)[nbz][(MD1D - 1) * MD1D * MD1D] =
+         (real_t(*)[nbz][(MD1D - 1) * MD1D * MD1D])(sX);
+      // shapes of buffers always use MQ1D to mitigate shared memory bank
+      // conflicts
+      real_t(*DDQ)[nbz][MQ1D][MQ1D][MQ1D] =
+         (real_t(*)[nbz][MQ1D][MQ1D][MQ1D])(sm0);
+      real_t(*DQQ)[nbz][MQ1D][MQ1D][MQ1D] =
+         (real_t(*)[nbz][MQ1D][MQ1D][MQ1D])(sm1);
+      real_t(*QQQ)[nbz][MQ1D][MQ1D][MQ1D] =
+         (real_t(*)[nbz][MQ1D][MQ1D][MQ1D])(sm0);
+      real_t(*QQD)[nbz][MQ1D][MQ1D][MQ1D] =
+         (real_t(*)[nbz][MQ1D][MQ1D][MQ1D])(sm1);
+      real_t(*QDD)[nbz][MQ1D][MQ1D][MQ1D] =
+         (real_t(*)[nbz][MQ1D][MQ1D][MQ1D])(sm0);
+
+      // load dofs into smem
+      const int offset = (D1D - 1) * D1D * D1D;
+      MFEM_FOREACH_THREAD_DIRECT(ix, x, offset)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         for (int dim = 0; dim < VDIM; ++dim)
          {
-            MFEM_FOREACH_THREAD(qz,z,Q1D)
-            {
-               for (int i=0; i<dataSize; ++i)
-               {
-                  op9[i] = op(qx,qy,qz,i,e);
-               }
-            }
+            X[dim][tidz][ix] = X_(ix + dim * offset, e);
          }
       }
-
-      const int tidx = MFEM_THREAD_ID(x);
-      const int tidy = MFEM_THREAD_ID(y);
-      const int tidz = MFEM_THREAD_ID(z);
-
+      // load basis functions data
       if (tidz == 0)
       {
-         MFEM_FOREACH_THREAD(d,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(ix, x, D1D * Q1D) { sBc[ix] = Bc[ix]; }
+         MFEM_FOREACH_THREAD_DIRECT(ix, x, (D1D - 1) * Q1D)
          {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
+            sBo[ix] = Bo[ix];
+         }
+      }
+
+      for (int dim0 = 0; dim0 < VDIM; ++dim0)
+      {
+         MFEM_SYNC_THREAD;
+         // sum factor to QQQ = Q_{dim0,dim1} B X_{dim1}
+         for (int dim1 = 0; dim1 < VDIM; ++dim1)
+         {
+            const int D1Dz = (dim1 == 2) ? D1D - 1 : D1D;
+            const int D1Dy = (dim1 == 1) ? D1D - 1 : D1D;
+            const int D1Dx = (dim1 == 0) ? D1D - 1 : D1D;
+
+            // threads assigned to mitigate bank conflicts
+            MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, Q1D, D1Dy, D1Dz,
+                                                 Q1D, Q1D, Q1D)
             {
-               sBc[q][d] = Bc(q,d);
-               if (d < D1D-1)
+               real_t u = 0;
+               for (int dx = 0; dx < D1Dx; ++dx)
                {
-                  sBo[q][d] = Bo(q,d);
+                  real_t b;
+                  if (dim1 == 0)
+                  {
+                     b = BO(qx, dx);
+                  }
+                  else
+                  {
+                     b = BC(qx, dx);
+                  }
+                  u += X[dim1][tidz][dx + (dy + dz * D1Dy) * D1Dx] * b;
+               }
+               DDQ[dim1][tidz][dz][dy][qx] = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+         for (int dim1 = 0; dim1 < VDIM; ++dim1)
+         {
+            const int D1Dz = (dim1 == 2) ? D1D - 1 : D1D;
+            const int D1Dy = (dim1 == 1) ? D1D - 1 : D1D;
+            // const int D1Dx = (dim1 == 0) ? D1D - 1 : D1D;
+            // threads assigned to mitigate bank conflicts
+            MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, Q1D, Q1D, D1Dz,
+                                                 Q1D, Q1D, Q1D)
+            {
+               real_t u = 0;
+               for (int dy = 0; dy < D1Dy; ++dy)
+               {
+                  real_t b;
+                  if (dim1 == 1)
+                  {
+                     b = BO(qy, dy);
+                  }
+                  else
+                  {
+                     b = BC(qy, dy);
+                  }
+                  u += DDQ[dim1][tidz][dz][dy][qx] * b;
+               }
+               DQQ[dim1][tidz][dz][qy][qx] = u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+         for (int dim1 = 0; dim1 < VDIM; ++dim1)
+         {
+            const int D1Dz = (dim1 == 2) ? D1D - 1 : D1D;
+            // const int D1Dy = (dim1 == 1) ? D1D - 1 : D1D;
+            // const int D1Dx = (dim1 == 0) ? D1D - 1 : D1D;
+            MFEM_FOREACH_THREAD_DIRECT_3D(qx, qy, qz, x, Q1D, Q1D, Q1D)
+            {
+               real_t u = 0;
+               for (int dz = 0; dz < D1Dz; ++dz)
+               {
+                  real_t b;
+                  if (dim1 == 2)
+                  {
+                     b = BO(qz, dz);
+                  }
+                  else
+                  {
+                     b = BC(qz, dz);
+                  }
+                  u += DQQ[dim1][tidz][dz][qy][qx] * b;
+               }
+               // pa_data is row major
+               int idx;
+               if (symmetric)
+               {
+                  int row;
+                  int col;
+                  if (dim0 > dim1)
+                  {
+                     row = dim1;
+                     col = dim0;
+                  }
+                  else
+                  {
+                     row = dim0;
+                     col = dim1;
+                  }
+                  idx = col + VDIM * row - row * (row + 1) / 2;
+               }
+               else
+               {
+                  idx = dim0 * VDIM + dim1;
+               }
+               QQQ[dim1][tidz][qz][qy][qx] = op(qx, qy, qz, idx, e) * u;
+            }
+         }
+         MFEM_SYNC_THREAD;
+         // sum factor back to Y
+         // Assume bot and bct == bo^t and bc^t respectively (i.e. test ==
+         // trial functions), skip loading them again.
+         {
+            const int D1Dz = (dim0 == 2) ? D1D - 1 : D1D;
+            const int D1Dy = (dim0 == 1) ? D1D - 1 : D1D;
+            const int D1Dx = (dim0 == 0) ? D1D - 1 : D1D;
+            // threads assigned to mitigate bank conflicts
+            MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, D1Dz, Q1D, Q1D,
+                                                 Q1D, Q1D, Q1D)
+            {
+               for (int dim1 = 0; dim1 < VDIM; ++dim1)
+               {
+                  real_t u = 0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     real_t b = 0;
+                     if (dim0 == 2)
+                     {
+                        b = BO(qz, dz);
+                     }
+                     else
+                     {
+                        b = BC(qz, dz);
+                     }
+                     u += QQQ[dim1][tidz][qz][qy][qx] * b;
+                  }
+                  QQD[dim1][tidz][qy][qx][dz] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+            // threads assigned to mitigate bank conflicts
+            MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, D1Dy, D1Dz, Q1D,
+                                                 Q1D, Q1D, Q1D)
+            {
+               for (int dim1 = 0; dim1 < VDIM; ++dim1)
+               {
+                  real_t u = 0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     real_t b;
+                     if (dim0 == 1)
+                     {
+                        b = BO(qy, dy);
+                     }
+                     else
+                     {
+                        b = BC(qy, dy);
+                     }
+                     u += QQD[dim1][tidz][qy][qx][dz] * b;
+                  }
+                  QDD[dim1][tidz][qx][dz][dy] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT_3D(dx, dy, dz, x, D1Dx, D1Dy, D1Dz)
+            {
+               int ix = dx + D1Dx * (dy + D1Dy * dz);
+               real_t u = 0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  real_t b;
+                  if (dim0 == 0)
+                  {
+                     b = BO(qx, dx);
+                  }
+                  else
+                  {
+                     b = BC(qx, dx);
+                  }
+                  for (int dim1 = 0; dim1 < VDIM; ++dim1)
+                  {
+                     u += QDD[dim1][tidz][qx][dz][dy] * b;
+                  }
+               }
+               if constexpr (ACCUMULATE)
+               {
+                  Y(ix + dim0 * offset, e) += u;
+               }
+               else
+               {
+                  Y(ix + dim0 * offset, e) = u;
                }
             }
          }
       }
-      MFEM_SYNC_THREAD;
-
-      for (int qz=0; qz < Q1D; ++qz)
-      {
-         int osc = 0;
-         for (int c = 0; c < VDIM; ++c)  // loop over x, y, z components
-         {
-            const int D1Dz = (c == 2) ? D1D - 1 : D1D;
-            const int D1Dy = (c == 1) ? D1D - 1 : D1D;
-            const int D1Dx = (c == 0) ? D1D - 1 : D1D;
-
-            MFEM_FOREACH_THREAD(dz,z,D1Dz)
-            {
-               MFEM_FOREACH_THREAD(dy,y,D1Dy)
-               {
-                  MFEM_FOREACH_THREAD(dx,x,D1Dx)
-                  {
-                     sX[dz][dy][dx] = X(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e);
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-
-            if (tidz == qz)
-            {
-               for (int i=0; i<dataSize; ++i)
-               {
-                  sop[i + (dataSize*tidx) + (dataSize*Q1D*tidy)] = op9[i];
-               }
-
-               MFEM_FOREACH_THREAD(qy,y,Q1D)
-               {
-                  MFEM_FOREACH_THREAD(qx,x,Q1D)
-                  {
-                     real_t u = 0.0;
-
-                     for (int dz = 0; dz < D1Dz; ++dz)
-                     {
-                        const real_t wz = (c == 2) ? sBo[qz][dz] : sBc[qz][dz];
-                        for (int dy = 0; dy < D1Dy; ++dy)
-                        {
-                           const real_t wy = (c == 1) ? sBo[qy][dy] : sBc[qy][dy];
-                           for (int dx = 0; dx < D1Dx; ++dx)
-                           {
-                              const real_t t = sX[dz][dy][dx];
-                              const real_t wx = (c == 0) ? sBo[qx][dx] : sBc[qx][dx];
-                              u += t * wx * wy * wz;
-                           }
-                        }
-                     }
-
-                     mass[qy][qx][c] = u;
-                  } // qx
-               } // qy
-            } // tidz == qz
-
-            osc += D1Dx * D1Dy * D1Dz;
-            MFEM_SYNC_THREAD;
-         } // c
-
-         MFEM_SYNC_THREAD;  // Sync mass[qy][qx][d] and sop
-
-         osc = 0;
-         for (int c = 0; c < VDIM; ++c)  // loop over x, y, z components
-         {
-            const int D1Dz = (c == 2) ? D1D - 1 : D1D;
-            const int D1Dy = (c == 1) ? D1D - 1 : D1D;
-            const int D1Dx = (c == 0) ? D1D - 1 : D1D;
-
-            real_t dxyz = 0.0;
-
-            MFEM_FOREACH_THREAD(dz,z,D1Dz)
-            {
-               const real_t wz = (c == 2) ? sBo[qz][dz] : sBc[qz][dz];
-
-               MFEM_FOREACH_THREAD(dy,y,D1Dy)
-               {
-                  MFEM_FOREACH_THREAD(dx,x,D1Dx)
-                  {
-                     for (int qy = 0; qy < Q1D; ++qy)
-                     {
-                        const real_t wy = (c == 1) ? sBo[qy][dy] : sBc[qy][dy];
-                        for (int qx = 0; qx < Q1D; ++qx)
-                        {
-                           const int os = (dataSize*qx) + (dataSize*Q1D*qy);
-                           const int id1 = os + ((c == 0) ? 0 : ((c == 1) ? (symmetric ? 1 : 3) :
-                                                                 (symmetric ? 2 : 6))); // O11, O21, O31
-                           const int id2 = os + ((c == 0) ? 1 : ((c == 1) ? (symmetric ? 3 : 4) :
-                                                                 (symmetric ? 4 : 7))); // O12, O22, O32
-                           const int id3 = os + ((c == 0) ? 2 : ((c == 1) ? (symmetric ? 4 : 5) :
-                                                                 (symmetric ? 5 : 8))); // O13, O23, O33
-
-                           const real_t m_c = (sop[id1] * mass[qy][qx][0]) + (sop[id2] * mass[qy][qx][1]) +
-                                              (sop[id3] * mass[qy][qx][2]);
-
-                           const real_t wx = (c == 0) ? sBo[qx][dx] : sBc[qx][dx];
-                           dxyz += m_c * wx * wy * wz;
-                        }
-                     }
-                  }
-               }
-            }
-
-            MFEM_SYNC_THREAD;
-
-            MFEM_FOREACH_THREAD(dz,z,D1Dz)
-            {
-               MFEM_FOREACH_THREAD(dy,y,D1Dy)
-               {
-                  MFEM_FOREACH_THREAD(dx,x,D1Dx)
-                  {
-                     Y(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e) += dxyz;
-                  }
-               }
-            }
-
-            osc += D1Dx * D1Dy * D1Dz;
-         } // c loop
-      } // qz
    }); // end of element loop
 }
 

fem/integ/bilininteg_hcurlhdiv_kernels.hpp

@@ -62,6 +62,30 @@ void PAHcurlHdivMassApply2D(const int D1D,
                             const Vector &x_,
                             Vector &y_);
 
+/// H(curl) test, H(div) trial
+inline void
+PAHcurlHdivMassApply2D(const int NE, const bool, const bool scalarCoeff,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int D1Dtest, const int Q1D)
+{
+   return PAHcurlHdivMassApply2D(D1D, D1Dtest, Q1D, NE, scalarCoeff, false,
+                                 false, Bo_, Bc_, Bot_, Bct_, op_, x_, y_);
+}
+
+/// H(div) test, H(curl) trial
+inline void
+PAHdivHcurlMassApply2D(const int NE, const bool, const bool scalarCoeff,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int D1Dtest, const int Q1D)
+{
+   return PAHcurlHdivMassApply2D(D1D, D1Dtest, Q1D, NE, scalarCoeff, true,
+                                 false, Bo_, Bc_, Bot_, Bct_, op_, x_, y_);
+}
+
 // PA H(curl)-H(div) Mass Apply 3D kernel
 void PAHcurlHdivMassApply3D(const int D1D,
                             const int D1Dtest,
@@ -78,6 +102,30 @@ void PAHcurlHdivMassApply3D(const int D1D,
                             const Vector &x_,
                             Vector &y_);
 
+/// H(curl) test, H(div) trial
+inline void
+PAHcurlHdivMassApply3D(const int NE, const bool, const bool scalarCoeff,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int D1Dtest, const int Q1D)
+{
+   PAHcurlHdivMassApply3D(D1D, D1Dtest, Q1D, NE, scalarCoeff, false, false, Bo_,
+                          Bc_, Bot_, Bct_, op_, x_, y_);
+}
+
+/// H(div) test, H(curl) trial
+inline void
+PAHdivHcurlMassApply3D(const int NE, const bool, const bool scalarCoeff,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int D1Dtest, const int Q1D)
+{
+   PAHcurlHdivMassApply3D(D1D, D1Dtest, Q1D, NE, scalarCoeff, true, false, Bo_,
+                          Bc_, Bot_, Bct_, op_, x_, y_);
+}
+
 // PA H(curl)-H(div) Curl Apply 3D kernel
 template<int T_D1D = 0, int T_D1D_TEST = 0, int T_Q1D = 0>
 inline void PAHcurlHdivApply3D(const int d1d,

fem/integ/bilininteg_hdiv_kernels.cpp

@@ -294,61 +294,14 @@ void PAHdivMassAssembleDiagonal3D(const int D1D,
    }); // end of element loop
 }
 
-void PAHdivMassApply(const int dim,
-                     const int D1D,
-                     const int Q1D,
-                     const int NE,
-                     const bool symmetric,
-                     const Array<real_t> &Bo,
-                     const Array<real_t> &Bc,
-                     const Array<real_t> &Bot,
-                     const Array<real_t> &Bct,
-                     const Vector &op,
-                     const Vector &x,
-                     Vector &y)
-{
-   const int id = (D1D << 4) | Q1D;
-
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x22: return SmemPAHdivMassApply2D<2,2>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x33: return SmemPAHdivMassApply2D<3,3>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x44: return SmemPAHdivMassApply2D<4,4>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x55: return SmemPAHdivMassApply2D<5,5>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         default: // fallback
-            return PAHdivMassApply2D(D1D,Q1D,NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x23: return SmemPAHdivMassApply3D<2,3>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x34: return SmemPAHdivMassApply3D<3,4>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x45: return SmemPAHdivMassApply3D<4,5>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x56: return SmemPAHdivMassApply3D<5,6>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x67: return SmemPAHdivMassApply3D<6,7>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         case 0x78: return SmemPAHdivMassApply3D<7,8>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-         default: // fallback
-            return PAHdivMassApply3D(D1D,Q1D,NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
-      }
-   }
-}
-
-void PAHdivMassApply2D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const bool symmetric,
-                       const Array<real_t> &Bo_,
-                       const Array<real_t> &Bc_,
-                       const Array<real_t> &Bot_,
-                       const Array<real_t> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_)
+void PAHdivMassApply2D(const int NE, const bool symmetric, const bool,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int TestD1D, const int Q1D)
 {
+   MFEM_VERIFY(D1D == TestD1D,
+               "Trial and test spaces must have same number of dofs");
    auto Bo = Reshape(Bo_.Read(), Q1D, D1D-1);
    auto Bc = Reshape(Bc_.Read(), Q1D, D1D);
    auto Bot = Reshape(Bot_.Read(), D1D-1, Q1D);
@@ -468,18 +421,14 @@ void PAHdivMassApply2D(const int D1D,
    }); // end of element loop
 }
 
-void PAHdivMassApply3D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const bool symmetric,
-                       const Array<real_t> &Bo_,
-                       const Array<real_t> &Bc_,
-                       const Array<real_t> &Bot_,
-                       const Array<real_t> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_)
+void PAHdivMassApply3D(const int NE, const bool symmetric, const bool,
+                       const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                       const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                       const Vector &op_, const Vector &x_, Vector &y_,
+                       const int D1D, const int TestD1D, const int Q1D)
 {
+   MFEM_VERIFY(D1D == TestD1D,
+               "Trial and test spaces must have same number of dofs");
    MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
                "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,

fem/integ/bilininteg_hdiv_kernels.hpp

@@ -66,58 +66,29 @@ void PAHdivMassAssembleDiagonal3D(const int D1D,
                                   const Vector &op_,
                                   Vector &diag_);
 
-void PAHdivMassApply(const int dim,
-                     const int D1D,
-                     const int Q1D,
-                     const int NE,
-                     const bool symmetric,
-                     const Array<real_t> &Bo,
-                     const Array<real_t> &Bc,
-                     const Array<real_t> &Bot,
-                     const Array<real_t> &Bct,
-                     const Vector &op,
-                     const Vector &x,
-                     Vector &y);
-
 // PA H(div) Mass Apply 2D kernel
-void PAHdivMassApply2D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const bool symmetric,
-                       const Array<real_t> &Bo_,
-                       const Array<real_t> &Bc_,
-                       const Array<real_t> &Bot_,
-                       const Array<real_t> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_);
+void PAHdivMassApply2D(const int NE, const bool symmetric,
+                       const bool scalar_coeff, const Array<real_t> &Bo_,
+                       const Array<real_t> &Bc_, const Array<real_t> &Bot_,
+                       const Array<real_t> &Bct_, const Vector &op_,
+                       const Vector &x_, Vector &y_, const int D1D,
+                       const int TestD1D, const int Q1D);
 
 // PA H(div) Mass Apply 3D kernel
-void PAHdivMassApply3D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const bool symmetric,
-                       const Array<real_t> &Bo_,
-                       const Array<real_t> &Bc_,
-                       const Array<real_t> &Bot_,
-                       const Array<real_t> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_);
+void PAHdivMassApply3D(const int NE, const bool symmetric,
+                       const bool scalar_coeff, const Array<real_t> &Bo_,
+                       const Array<real_t> &Bc_, const Array<real_t> &Bot_,
+                       const Array<real_t> &Bct_, const Vector &op_,
+                       const Vector &x_, Vector &y_, const int D1D,
+                       const int TestD1D, const int Q1D);
 
 // Shared memory PA H(div) Mass Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
-inline void SmemPAHdivMassApply2D(const int NE,
-                                  const bool symmetric,
-                                  const Array<real_t> &Bo_,
-                                  const Array<real_t> &Bc_,
-                                  const Array<real_t> &Bot_,
-                                  const Array<real_t> &Bct_,
-                                  const Vector &op_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+template <int T_D1D = 0, int T_Q1D = 0>
+inline void SmemPAHdivMassApply2D(
+   const int NE, const bool symmetric, const bool, const Array<real_t> &Bo_,
+   const Array<real_t> &Bc_, const Array<real_t> &Bot_,
+   const Array<real_t> &Bct_, const Vector &op_, const Vector &x_, Vector &y_,
+   const int d1d = 0, const int = 0, const int q1d = 0)
 {
    MFEM_CONTRACT_VAR(Bot_);
    MFEM_CONTRACT_VAR(Bct_);
@@ -280,18 +251,13 @@ inline void SmemPAHdivMassApply2D(const int NE,
 }
 
 // Shared memory PA H(div) Mass Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
-inline void SmemPAHdivMassApply3D(const int NE,
-                                  const bool symmetric,
-                                  const Array<real_t> &Bo_,
-                                  const Array<real_t> &Bc_,
-                                  const Array<real_t> &Bot_,
-                                  const Array<real_t> &Bct_,
-                                  const Vector &op_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+template <int T_D1D = 0, int T_Q1D = 0>
+inline void
+SmemPAHdivMassApply3D(const int NE, const bool symmetric, const bool,
+                      const Array<real_t> &Bo_, const Array<real_t> &Bc_,
+                      const Array<real_t> &Bot_, const Array<real_t> &Bct_,
+                      const Vector &op_, const Vector &x_, Vector &y_,
+                      const int d1d = 0, const int = 0, const int q1d = 0)
 {
    MFEM_CONTRACT_VAR(Bot_);
    MFEM_CONTRACT_VAR(Bct_);

fem/integ/bilininteg_mass_kernels.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "bilininteg_mass_kernels.hpp"
+#include "bilininteg_mass_pa_simplices.hpp" // IWYU pragma: keep
 
 namespace mfem
 {
@@ -39,8 +40,10 @@ MassIntegrator::Kernels::Kernels()
    MassIntegrator::AddSpecialization<2,9,10>();
    // others
    MassIntegrator::AddSpecialization<2,2,4>();
+   MassIntegrator::AddSpecialization<2,2,5>();
    MassIntegrator::AddSpecialization<2,3,6>();
    MassIntegrator::AddSpecialization<2,4,6>();
+
    // 3D
    // Q=P+1
    MassIntegrator::AddSpecialization<3,1,1>();

fem/integ/bilininteg_mass_kernels.hpp

@@ -19,6 +19,8 @@
 #include "../../linalg/vector.hpp"
 #include "../bilininteg.hpp"
 
+#include "bilininteg_mass_pa_simplices.hpp"
+
 namespace mfem
 {
 
@@ -1408,51 +1410,57 @@ using ApplyKernelType = MassIntegrator::ApplyKernelType;
 using DiagonalKernelType = MassIntegrator::DiagonalKernelType;
 }
 
-template<int DIM, int T_D1D, int T_Q1D>
+template<int DIM, int D1D, int Q1D>
 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 == 2) { return internal::SmemPAMassApply2D<D1D, Q1D>; }
    else if constexpr (DIM == 3)
    {
-      constexpr int MDQ = T_D1D >= T_Q1D ? T_D1D : T_Q1D;
+      constexpr int MDQ = D1D >= Q1D ? D1D : Q1D;
       // max 64 threads in z limit in cuda and hip
       if constexpr (MDQ > 0)
       {
-         return internal::SmemPAMassApply3D<T_D1D, T_Q1D,
+         return internal::SmemPAMassApply3D<D1D, Q1D,
                 internal::mass::NBZ3D(MDQ)>;
       }
    }
-   MFEM_ABORT("");
+   else { MFEM_ABORT(""); }
+   return nullptr;
 }
 
 inline ApplyKernelType MassIntegrator::ApplyPAKernels::Fallback(
-   int DIM, int, int)
+   int dim, int, int)
 {
-   if (DIM == 1) { return internal::PAMassApply1D; }
-   else if (DIM == 2) { return internal::PAMassApply2D; }
-   else if (DIM == 3) { return internal::PAMassApply3D; }
+   if (dim == 1) { return internal::PAMassApply1D; }
+   else if (dim == 2) { return internal::PAMassApply2D; }
+   else if (dim == 3) { return internal::PAMassApply3D; }
    else { MFEM_ABORT(""); }
+   return nullptr;
 }
 
-template<int DIM, int T_D1D, int T_Q1D>
+template<int DIM, int D1D, int Q1D>
 DiagonalKernelType MassIntegrator::DiagonalPAKernels::Kernel()
 {
    if constexpr (DIM == 1) { return internal::PAMassAssembleDiagonal1D; }
-   else if constexpr (DIM == 2) { return internal::SmemPAMassAssembleDiagonal2D<T_D1D,T_Q1D>; }
-   else if constexpr (DIM == 3) { return internal::SmemPAMassAssembleDiagonal3D<T_D1D, T_Q1D>; }
-   MFEM_ABORT("");
+   else if constexpr (DIM == 2) { return internal::SmemPAMassAssembleDiagonal2D<D1D, Q1D>; }
+   else if constexpr (DIM == 3) { return internal::SmemPAMassAssembleDiagonal3D<D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+   return nullptr;
 }
 
 inline DiagonalKernelType MassIntegrator::DiagonalPAKernels::Fallback(
-   int DIM, int, int)
+   int dim, int, int)
 {
-   if (DIM == 1) { return internal::PAMassAssembleDiagonal1D; }
-   else if (DIM == 2) { return internal::PAMassAssembleDiagonal2D; }
-   else if (DIM == 3) { return internal::PAMassAssembleDiagonal3D; }
+   if (dim == 1) { return internal::PAMassAssembleDiagonal1D; }
+   else if (dim == 2) { return internal::PAMassAssembleDiagonal2D; }
+   else if (dim == 3) { return internal::PAMassAssembleDiagonal3D; }
    else { MFEM_ABORT(""); }
+   return nullptr;
 }
+
 /// \endcond DO_NOT_DOCUMENT
+
 } // namespace mfem
 
 #endif

fem/integ/bilininteg_mass_pa.cpp

@@ -15,6 +15,7 @@
 #include "../qfunction.hpp"
 #include "../ceed/integrators/mass/mass.hpp"
 #include "bilininteg_mass_kernels.hpp"
+#include "bilininteg_mass_pa_simplices.hpp"
 
 namespace mfem
 {
@@ -29,9 +30,11 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
    // Assuming the same element type
    fespace = &fes;
    Mesh *mesh = fes.GetMesh();
+   dim = mesh->Dimension();
    const FiniteElement &el = *fes.GetTypicalFE();
    ElementTransformation *T0 = mesh->GetTypicalElementTransformation();
-   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T0);
+   const bool stroud = fes.UsesRaggedTensorBasis();
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T0, stroud);
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
@@ -48,17 +51,25 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
       return;
    }
    int map_type = el.GetMapType();
-   dim = mesh->Dimension();
    ne = fes.GetMesh()->GetNE();
    nq = ir->GetNPoints();
    geom = mesh->GetGeometricFactors(*ir, GeometricFactors::DETERMINANTS, mt);
-   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   if (stroud)
+   {
+      maps = &el.GetDofToQuad(*ir, DofToQuad::RAGGED_TENSOR);
+   }
+   else
+   {
+      maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   }
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
    pa_data.SetSize(ne*nq, mt);
 
    QuadratureSpace qs(*mesh, *ir);
    CoefficientVector coeff(Q, qs, CoefficientStorage::COMPRESSED);
+   // QuadratureSpace expects ir defined in reference simplex for Bernstein
+   // elements with partial assembly
    {
       const int NE = ne;
       const int NQ = nq;
@@ -147,9 +158,10 @@ void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
    {
       const int D1D = dofs1D;
       const int Q1D = quad1D;
+      const Vector &D = pa_data;
       const Array<real_t> &B = maps->B;
       const Array<real_t> &Bt = maps->Bt;
-      const Vector &D = pa_data;
+
 #ifdef MFEM_USE_OCCA
       if (DeviceCanUseOcca())
       {
@@ -164,7 +176,31 @@ void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
          MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
       }
 #endif // MFEM_USE_OCCA
-      ApplyPAKernels::Run(dim, D1D, Q1D, ne, B, Bt, D, x, y, D1D, Q1D);
+
+      if (fespace->UsesRaggedTensorBasis())
+      {
+         const auto *rmaps = static_cast<const RaggedDofToQuad*>(maps);
+
+         const Array<real_t> &Ba1 = rmaps->Ba1;
+         const Array<real_t> &Ba2 = rmaps->Ba2;
+         const Array<real_t> &Ba3 = rmaps->Ba3;
+         const Array<real_t> &Ba1t = rmaps->Ba1t;
+         const Array<real_t> &Ba2t = rmaps->Ba2t;
+         const Array<real_t> &Ba3t = rmaps->Ba3t;
+         const Array<int> &lex_map = rmaps->lex_map;
+         const Array<int> &forward_map2d = rmaps->forward_map2d_mass;
+         const Array<int> &inverse_map2d = rmaps->inverse_map2d_mass;
+         const Array<int> &forward_map3d = rmaps->forward_map3d_mass;
+         const Array<int> &inverse_map3d = rmaps->inverse_map3d_mass;
+         ApplySimplexPAKernels::Run(dim, D1D, Q1D, ne, lex_map, forward_map2d,
+                                    inverse_map2d,
+                                    forward_map3d, inverse_map3d, Ba1, Ba2, Ba3, Ba1t, Ba2t, Ba3t,
+                                    D, x, y, D1D, Q1D);
+      }
+      else
+      {
+         ApplyPAKernels::Run(dim, D1D, Q1D, ne, B, Bt, D, x, y, D1D, Q1D);
+      }
    }
 }
 
@@ -177,6 +213,8 @@ void MassIntegrator::AddAbsMultPA(const Vector &x, Vector &y) const
    }
    else
    {
+      MFEM_VERIFY(!fespace->UsesRaggedTensorBasis(),
+                  "AbsMultPA not implemented for ragged tensor basis");
       Vector abs_pa_data(pa_data);
       abs_pa_data.Abs();
       Array<real_t> absB(maps->B);

fem/integ/bilininteg_vecdiv_pa.hpp

@@ -0,0 +1,365 @@
+// 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.
+#pragma once
+
+#include "../../config/config.hpp"
+#include "../../general/array.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../../linalg/vector.hpp"
+#include "../bilininteg.hpp"
+#include "../kernels.hpp"
+
+namespace mfem
+{
+
+/// \cond DO_NOT_DOCUMENT
+
+namespace internal
+{
+
+// Shared memory PA Divergence Apply 2D kernel
+template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
+inline void SmemPADivergenceApply2D(const int NE,
+                                    const Array<real_t> &b_,
+                                    const Array<real_t> &g_,
+                                    const Array<real_t> &bt_,
+                                    const Vector &q_,
+                                    const Vector &x_,
+                                    Vector &y_,
+                                    const int tr_d1d = 0,
+                                    const int te_d1d = 0,
+                                    const int q1d = 0)
+{
+   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
+   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(TR_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(TE_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto B = b_.Read(), G = g_.Read(), Bt = bt_.Read();
+   const auto Q = Reshape(q_.Read(), Q1D, Q1D, 2, 2, NE);
+   const auto X = Reshape(x_.Read(), TR_D1D, TR_D1D, 2, NE);
+   auto Y = Reshape(y_.ReadWrite(), TE_D1D, TE_D1D, 1, NE);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MQ1][MQ1], sG[MQ1][MQ1];
+
+      kernels::internal::vd_regs2d_t<2, 2, MQ1> g0, g1;
+      kernels::internal::v_regs2d_t<1, MQ1> r0, r1;
+
+      kernels::internal::LoadMatrix(TR_D1D, Q1D, B, sB);
+      kernels::internal::LoadMatrix(TR_D1D, Q1D, G, sG);
+
+      kernels::internal::LoadDofs2d(e, TR_D1D, X, g0);
+      kernels::internal::Grad2d(TR_D1D, Q1D, smem, sB, sG, g0, g1);
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            r0[0][qy][qx] =
+               g1[0][0][qy][qx] * Q(qx, qy, 0, 0, e) +
+               g1[0][1][qy][qx] * Q(qx, qy, 1, 0, e) +
+               g1[1][0][qy][qx] * Q(qx, qy, 0, 1, e) +
+               g1[1][1][qy][qx] * Q(qx, qy, 1, 1, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::LoadMatrix<MQ1,true>(TE_D1D, Q1D, Bt, sB);
+      kernels::internal::EvalTranspose2d(TE_D1D, Q1D, smem, sB, r0, r1);
+      kernels::internal::WriteDofs2d(e, TE_D1D, r1, Y);
+   });
+}
+
+// Shared memory PA Divergence Apply 2D kernel transpose
+template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
+inline void SmemPADivergenceApplyTranspose2D(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 = 0,
+                                             const int te_d1d = 0,
+                                             const int q1d = 0)
+{
+   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
+   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(TR_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(TE_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto Bt = bt.Read(), Gt = gt.Read(), B = b.Read();
+   const auto Q = Reshape(q_.Read(), Q1D, Q1D, 2, 2, NE);
+   const auto X  = Reshape(x_.Read(), TE_D1D, TE_D1D, 1, NE);
+   auto Y  = Reshape(y_.ReadWrite(), TR_D1D, TR_D1D, 2, NE);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MQ1][MQ1], sG[MQ1][MQ1];
+
+      kernels::internal::v_regs2d_t<1, MQ1> r0, r1;
+      kernels::internal::vd_regs2d_t<2, 2, MQ1> g0, g1;
+
+      kernels::internal::LoadMatrix(TE_D1D, Q1D, B, sB);
+      kernels::internal::LoadDofs2d(e, TE_D1D, X, r0);
+      kernels::internal::Eval2d(TE_D1D, Q1D, smem, sB, r0, r1);
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            g0[0][0][qy][qx] = r1[0][qy][qx] * Q(qx, qy, 0, 0, e);
+            g0[0][1][qy][qx] = r1[0][qy][qx] * Q(qx, qy, 1, 0, e);
+            g0[1][0][qy][qx] = r1[0][qy][qx] * Q(qx, qy, 0, 1, e);
+            g0[1][1][qy][qx] = r1[0][qy][qx] * Q(qx, qy, 1, 1, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::LoadMatrix<MQ1,true>(TR_D1D, Q1D, Bt, sB);
+      kernels::internal::LoadMatrix<MQ1,true>(TR_D1D, Q1D, Gt, sG);
+      kernels::internal::GradTranspose2d(TR_D1D, Q1D, smem, sB, sG, g0, g1);
+      kernels::internal::WriteDofs2d(e, TR_D1D, g1, Y);
+   });
+}
+
+// Shared memory PA Divergence Apply 3D kernel transpose
+template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
+inline void SmemPADivergenceApplyTranspose3D(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_,
+                                             int tr_d1d = 0,
+                                             int te_d1d = 0,
+                                             int q1d = 0)
+{
+   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
+   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(TR_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(TE_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto Bt = bt.Read(), Gt = gt.Read(), B = b.Read();
+   const auto Q = Reshape(q_.Read(), Q1D, Q1D, Q1D, 3, 3, NE);
+   const auto X = Reshape(x_.Read(), TE_D1D, TE_D1D, TE_D1D, 1, NE);
+   auto Y = Reshape(y_.ReadWrite(), TR_D1D, TR_D1D, TR_D1D, 3, NE);
+
+   mfem::forall_2D<T_Q1D * T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MQ1][MQ1], sG[MQ1][MQ1];
+
+      kernels::internal::v_regs3d_t<1, MQ1> r0, r1;
+      kernels::internal::vd_regs3d_t<3, 3, MQ1> g0, g1;
+
+      kernels::internal::LoadMatrix(TE_D1D, Q1D, B, sB);
+      kernels::internal::LoadDofs3d(e, TE_D1D, X, r0);
+      kernels::internal::Eval3d(TE_D1D, Q1D, smem, sB, r0, r1);
+
+      for (int qz = 0; qz < Q1D; qz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const auto r = r1[0][qz][qy][qx];
+               g0[0][0][qz][qy][qx] = r * Q(qx, qy, qz, 0, 0, e);
+               g0[0][1][qz][qy][qx] = r * Q(qx, qy, qz, 1, 0, e);
+               g0[0][2][qz][qy][qx] = r * Q(qx, qy, qz, 2, 0, e);
+
+               g0[1][0][qz][qy][qx] = r * Q(qx, qy, qz, 0, 1, e);
+               g0[1][1][qz][qy][qx] = r * Q(qx, qy, qz, 1, 1, e);
+               g0[1][2][qz][qy][qx] = r * Q(qx, qy, qz, 2, 1, e);
+
+               g0[2][0][qz][qy][qx] = r * Q(qx, qy, qz, 0, 2, e);
+               g0[2][1][qz][qy][qx] = r * Q(qx, qy, qz, 1, 2, e);
+               g0[2][2][qz][qy][qx] = r * Q(qx, qy, qz, 2, 2, e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::LoadMatrix<MQ1,true>(TR_D1D, Q1D, Bt, sB);
+      kernels::internal::LoadMatrix<MQ1,true>(TR_D1D, Q1D, Gt, sG);
+      kernels::internal::GradTranspose3d(TR_D1D, Q1D, smem, sB, sG, g0, g1);
+      kernels::internal::WriteDofs3d(e, TR_D1D, g1, Y);
+   });
+}
+
+// Shared memory PA Divergence Apply 3D kernel
+template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
+inline void SmemPADivergenceApply3D(const int NE,
+                                    const Array<real_t> &b_,
+                                    const Array<real_t> &g_,
+                                    const Array<real_t> &bt_,
+                                    const Vector &q_,
+                                    const Vector &x_,
+                                    Vector &y_,
+                                    const int tr_d1d = 0,
+                                    const int te_d1d = 0,
+                                    const int q1d = 0)
+{
+   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
+   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   MFEM_VERIFY(TR_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(TE_D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto B = b_.Read(), G = g_.Read(), Bt = bt_.Read();
+   const auto Q = Reshape(q_.Read(), Q1D, Q1D, Q1D, 3,3, NE);
+   const auto X = Reshape(x_.Read(), TR_D1D, TR_D1D, TR_D1D, 3, NE);
+   auto Y = Reshape(y_.ReadWrite(), TE_D1D, TE_D1D, TE_D1D, 1, NE);
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MQ1][MQ1], sG[MQ1][MQ1];
+
+      kernels::internal::vd_regs3d_t<3, 3, MQ1> g0, g1;
+      kernels::internal::v_regs3d_t<1, MQ1> r0, r1;
+
+      kernels::internal::LoadMatrix(TR_D1D, Q1D, B, sB);
+      kernels::internal::LoadMatrix(TR_D1D, Q1D, G, sG);
+
+      kernels::internal::LoadDofs3d(e, TR_D1D, X, g0);
+      kernels::internal::Grad3d(TR_D1D, Q1D, smem, sB, sG, g0, g1);
+
+      for (int qz = 0; qz < Q1D; qz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               r0[0][qz][qy][qx] =
+                  // c = 0
+                  g1[0][0][qz][qy][qx] * Q(qx, qy, qz, 0, 0, e) +
+                  g1[0][1][qz][qy][qx] * Q(qx, qy, qz, 1, 0, e) +
+                  g1[0][2][qz][qy][qx] * Q(qx, qy, qz, 2, 0, e) +
+                  // c = 1
+                  g1[1][0][qz][qy][qx] * Q(qx, qy, qz, 0, 1, e) +
+                  g1[1][1][qz][qy][qx] * Q(qx, qy, qz, 1, 1, e) +
+                  g1[1][2][qz][qy][qx] * Q(qx, qy, qz, 2, 1, e) +
+                  // c = 2
+                  g1[2][0][qz][qy][qx] * Q(qx, qy, qz, 0, 2, e) +
+                  g1[2][1][qz][qy][qx] * Q(qx, qy, qz, 1, 2, e) +
+                  g1[2][2][qz][qy][qx] * Q(qx, qy, qz, 2, 2, e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::LoadMatrix<MQ1, true>(TE_D1D, Q1D, Bt, sB);
+      kernels::internal::EvalTranspose3d(TE_D1D, Q1D, smem, sB, r0, r1);
+      kernels::internal::WriteDofs3d(e, TE_D1D, r1, Y);
+   });
+}
+
+} // namespace internal
+
+template<int DIM, int T_TR_D1D, int T_TE_D1D, int T_Q1D>
+VectorDivergenceIntegrator::VectorDivergenceAddMultPAType
+VectorDivergenceIntegrator::VectorDivergenceAddMultPA::Kernel()
+{
+   static_assert(T_TR_D1D <= T_Q1D && T_TE_D1D <= T_Q1D);
+   if constexpr (DIM == 2)
+   {
+      return internal::SmemPADivergenceApply2D<T_TR_D1D, T_TE_D1D, T_Q1D>;
+   }
+   else if constexpr (DIM == 3)
+   {
+      return internal::SmemPADivergenceApply3D<T_TR_D1D, T_TE_D1D, T_Q1D>;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+inline VectorDivergenceIntegrator::VectorDivergenceAddMultPAType
+VectorDivergenceIntegrator::VectorDivergenceAddMultPA::Fallback
+(int dim, int tr_d1d, int te_d1d, int q1d)
+{
+   MFEM_VERIFY(tr_d1d <= q1d && te_d1d <= q1d, "");
+   MFEM_VERIFY(tr_d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(te_d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   if (dim == 2)
+   {
+      return internal::SmemPADivergenceApply2D;
+   }
+   else if (dim == 3)
+   {
+      return internal::SmemPADivergenceApply3D;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+template<int DIM, int T_TR_D1D, int T_TE_D1D, int T_Q1D>
+VectorDivergenceIntegrator::VectorDivergenceAddMultTransposePAType
+VectorDivergenceIntegrator::VectorDivergenceAddMultTransposePA::Kernel()
+{
+   static_assert(T_TR_D1D <= T_Q1D && T_TE_D1D <= T_Q1D);
+   if constexpr (DIM == 2)
+   {
+      return internal::SmemPADivergenceApplyTranspose2D<T_TR_D1D, T_TE_D1D, T_Q1D>;
+   }
+   else if constexpr (DIM == 3)
+   {
+      return internal::SmemPADivergenceApplyTranspose3D<T_TR_D1D, T_TE_D1D, T_Q1D>;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+inline VectorDivergenceIntegrator::VectorDivergenceAddMultTransposePAType
+VectorDivergenceIntegrator::VectorDivergenceAddMultTransposePA::Fallback
+(int dim, int tr_d1d, int te_d1d, int q1d)
+{
+   MFEM_VERIFY(tr_d1d <= q1d && te_d1d <= q1d, "");
+   MFEM_VERIFY(tr_d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(te_d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   if (dim == 2)
+   {
+      return internal::SmemPADivergenceApplyTranspose2D;
+   }
+   else if (dim == 3)
+   {
+      return internal::SmemPADivergenceApplyTranspose3D;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/integ/bilininteg_vecmass_pa.cpp

@@ -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

fem/integ/bilininteg_vecmass_pa.hpp

@@ -176,8 +176,146 @@ 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;
+         }
+      }
+   });
+}
+
+// T_MDQ <= 10 so the Q1D^3 thread block stays within the 1024/block GPU limit
+template <int T_Q1D = 0, int T_MDQ = 10>
+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()
@@ -194,7 +332,7 @@ VectorMassIntegrator::VectorMassAddMultPA::Kernel()
 }
 
 inline VectorMassIntegrator::VectorMassAddMultPAType
-VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int d1d, int q1d)
+VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int, int)
 {
    if (dim == 2)
    {
@@ -204,7 +342,37 @@ VectorMassIntegrator::VectorMassAddMultPA::Fallback(int dim, int d1d, int q1d)
    {
       return internal::SmemPAVectorMassApply3D;
    }
-   else { MFEM_ABORT("Unsupported kernel"); }
+   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>;
+   }
+   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;
+   }
+   MFEM_ABORT("Unsupported kernel");
 }
 
 /// \endcond DO_NOT_DOCUMENT

fem/integ/bilininteg_vectorfemass_kernels.hpp

@@ -0,0 +1,113 @@
+// 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.
+
+#ifndef MFEM_BILININTEG_VECTORFEMASS_KERNELS_HPP
+#define MFEM_BILININTEG_VECTORFEMASS_KERNELS_HPP
+
+#include "../../config/config.hpp"
+#include "../bilininteg.hpp"
+
+#include "bilininteg_diffusion_kernels.hpp"
+#include "bilininteg_hcurl_kernels.hpp"
+#include "bilininteg_hdiv_kernels.hpp"
+#include "bilininteg_hcurlhdiv_kernels.hpp"
+
+namespace mfem
+{
+/// \cond DO_NOT_DOCUMENT
+namespace internal
+{
+namespace hcurlmass
+{
+constexpr int NBZ3D(int d1d, int q1d)
+{
+   if (d1d <= 1 || q1d <= 0)
+   {
+      return 1;
+   }
+   // assume q1d >= d1d
+   // z dimension is capped at 64 on nvidia and amd gpus
+   int tmp = std::min((128 + q1d * q1d * q1d - 1) / (q1d * q1d * q1d), 64);
+   int smem_req =
+      sizeof(mfem::real_t) *
+      (3 * ((d1d - 1) * d1d * d1d + 2 * q1d * q1d * q1d) * tmp +
+       q1d * (d1d - 1) + q1d * d1d);
+   // assume GPU has at least 48k shared memory
+   return std::max(std::min(tmp, (48 * 1024 + smem_req - 1) / smem_req), 1);
+}
+} // namespace hcurlmass
+} // namespace internal
+
+template <FiniteElement::DerivType TrialType, FiniteElement::DerivType TestType,
+          int DIM, int TrialD1D, int TestD1D, int Q1D>
+VectorFEMassIntegrator::ApplyKernelType
+VectorFEMassIntegrator::ApplyPAKernels::Kernel()
+{
+   constexpr bool trial_curl = (TrialType == mfem::FiniteElement::CURL);
+   constexpr bool trial_div = (TrialType == mfem::FiniteElement::DIV);
+   constexpr bool test_curl = (TestType == mfem::FiniteElement::CURL);
+   constexpr bool test_div = (TestType == mfem::FiniteElement::DIV);
+
+   if constexpr (DIM == 3)
+   {
+      if constexpr (trial_curl && test_curl)
+      {
+         if (Device::Allows(Backend::DEVICE_MASK))
+         {
+            // assume TrialD1D == TestD1D
+            return internal::SmemPAHcurlMassApply3D<
+                   TrialD1D, Q1D, internal::hcurlmass::NBZ3D(TrialD1D, Q1D)>;
+         }
+         else
+         {
+            return internal::PAHcurlMassApply3D;
+         }
+      }
+      else if constexpr (trial_div && test_div)
+      {
+         // assumes TrialD1D == TestD1D
+         return internal::SmemPAHdivMassApply3D<TrialD1D, Q1D>;
+      }
+      else if constexpr (trial_curl && test_div)
+      {
+         return internal::PAHdivHcurlMassApply3D;
+      }
+      else if constexpr (trial_div && test_curl)
+      {
+         return internal::PAHcurlHdivMassApply3D;
+      }
+   }
+   else if constexpr (DIM == 2) // 2D
+   {
+      if constexpr (trial_curl && test_curl)
+      {
+         return internal::PAHcurlMassApply2D;
+      }
+      else if constexpr (trial_div && test_div)
+      {
+         // assumes TrialD1D == TestD1D
+         return internal::SmemPAHdivMassApply2D<TrialD1D, Q1D>;
+      }
+      else if constexpr (trial_curl && test_div)
+      {
+         return internal::PAHdivHcurlMassApply2D;
+      }
+      else if constexpr (trial_div && test_curl)
+      {
+         return internal::PAHcurlHdivMassApply2D;
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+/// \endcond DO_NOT_DOCUMENT
+}
+
+#endif

fem/integ/bilininteg_vectorfemass_pa.cpp

@@ -10,15 +10,123 @@
 // CONTRIBUTING.md for details.
 
 #include "../bilininteg.hpp"
-#include "../gridfunc.hpp"
-#include "../qfunction.hpp"
-#include "bilininteg_diffusion_kernels.hpp"
-#include "bilininteg_hcurl_kernels.hpp"
-#include "bilininteg_hdiv_kernels.hpp"
-#include "bilininteg_hcurlhdiv_kernels.hpp"
+#include "bilininteg_vectorfemass_kernels.hpp"
 
 namespace mfem
 {
+/// \cond DO_NOT_DOCUMENT
+VectorFEMassIntegrator::ApplyKernelType
+VectorFEMassIntegrator::ApplyPAKernels::Fallback(
+   FiniteElement::DerivType TrialType, FiniteElement::DerivType TestType,
+   int dim, int, int, int)
+{
+   const bool trial_curl = (TrialType == mfem::FiniteElement::CURL);
+   const bool trial_div = (TrialType == mfem::FiniteElement::DIV);
+   const bool test_curl = (TestType == mfem::FiniteElement::CURL);
+   const bool test_div = (TestType == mfem::FiniteElement::DIV);
+
+   if (dim == 3)
+   {
+      if (trial_curl && test_curl)
+      {
+         return internal::PAHcurlMassApply3D;
+      }
+      else if (trial_div && test_div)
+      {
+         return internal::PAHdivMassApply3D;
+      }
+      else if (trial_curl && test_div)
+      {
+         return internal::PAHdivHcurlMassApply3D;
+      }
+      else if (trial_div && test_curl)
+      {
+         return internal::PAHcurlHdivMassApply3D;
+      }
+   }
+   else if (dim == 2) // 2D
+   {
+      if (trial_curl && test_curl)
+      {
+         return internal::PAHcurlMassApply2D;
+      }
+      else if (trial_div && test_div)
+      {
+         return internal::PAHdivMassApply2D;
+      }
+      else if (trial_curl && test_div)
+      {
+         return internal::PAHdivHcurlMassApply2D;
+      }
+      else if (trial_div && test_curl)
+      {
+         return internal::PAHcurlHdivMassApply2D;
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+/// \endcond DO_NOT_DOCUMENT
+
+VectorFEMassIntegrator::Kernels::Kernels()
+{
+   // h(curl), h(curl)
+   // Q = P + 1 (3D)
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 2, 2, 3>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 3, 3, 4>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 4, 4, 5>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 5, 5, 6>();
+   // Q = P + 2 (3D)
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 2, 2, 4>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 3, 3, 5>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 4, 4, 6>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 5, 5, 7>();
+   // Q = P + 4 (3D)
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 2, 2, 6>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 3, 3, 7>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 4, 4, 8>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::CURL,
+                          FiniteElement::CURL, 3, 5, 5, 9>();
+   // h(div), h(div)
+   // Q = P (2D)
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 2, 2, 2, 2>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 2, 3, 3, 3>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 2, 4, 4, 4>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 2, 5, 5, 5>();
+
+   // Q = P + 1 (3D)
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 3, 2, 2, 3>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 3, 3, 3, 4>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 3, 4, 4, 5>();
+   VectorFEMassIntegrator::AddSpecialization<FiniteElement::DIV,
+                          FiniteElement::DIV, 3, 5, 5, 6>();
+}
+
+void VectorFEMassIntegrator::Init(Coefficient *q, DiagonalMatrixCoefficient *dq,
+                                  MatrixCoefficient *mq)
+{
+   static Kernels kernels{};
+   Q = q;
+   DQ = dq;
+   MQ = mq;
+}
 
 void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
@@ -67,8 +175,8 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 
    MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
 
-   trial_fetype = trial_el->GetDerivType();
-   test_fetype = test_el->GetDerivType();
+   trial_fetype = static_cast<FiniteElement::DerivType>(trial_el->GetDerivType());
+   test_fetype = static_cast<FiniteElement::DerivType>(test_el->GetDerivType());
 
    const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
    const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
@@ -215,225 +323,34 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
 
 void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 {
-   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
-   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
-   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
-   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
-
-   if (dim == 3)
-   {
-      if (trial_curl && test_curl)
-      {
-         if (Device::Allows(Backend::DEVICE_MASK))
-         {
-            const int ID = (dofs1D << 4) | quad1D;
-            switch (ID)
-            {
-               case 0x23:
-                  return internal::SmemPAHcurlMassApply3D<2,3>(
-                            dofs1D, quad1D, ne, symmetric,
-                            mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-               case 0x34:
-                  return internal::SmemPAHcurlMassApply3D<3,4>(
-                            dofs1D, quad1D, ne, symmetric,
-                            mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-               case 0x45:
-                  return internal::SmemPAHcurlMassApply3D<4,5>(
-                            dofs1D, quad1D, ne, symmetric,
-                            mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-               case 0x56:
-                  return internal::SmemPAHcurlMassApply3D<5,6>(
-                            dofs1D, quad1D, ne, symmetric,
-                            mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-               default:
-                  return internal::SmemPAHcurlMassApply3D(
-                            dofs1D, quad1D, ne, symmetric,
-                            mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-            }
-         }
-         else
-         {
-            internal::PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
-                                         mapsO->Bt, mapsC->Bt, pa_data, x, y);
-         }
-      }
-      else if (trial_div && test_div)
-      {
-         internal::PAHdivMassApply(3, dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
-                                   mapsO->Bt, mapsC->Bt, pa_data, x, y);
-      }
-      else if (trial_curl && test_div)
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
-                                          true, false, mapsO->B, mapsC->B, mapsOtest->Bt,
-                                          mapsCtest->Bt, pa_data, x, y);
-      }
-      else if (trial_div && test_curl)
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
-                                          false, false, mapsO->B, mapsC->B, mapsOtest->Bt,
-                                          mapsCtest->Bt, pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-   else // 2D
-   {
-      if (trial_curl && test_curl)
-      {
-         internal::PAHcurlMassApply2D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
-                                      mapsO->Bt, mapsC->Bt, pa_data, x, y);
-      }
-      else if (trial_div && test_div)
-      {
-         internal::PAHdivMassApply(2, dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
-                                   mapsO->Bt,
-                                   mapsC->Bt, pa_data, x, y);
-      }
-      else if ((trial_curl && test_div) || (trial_div && test_curl))
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply2D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
-                                          trial_curl, false, mapsO->B, mapsC->B,
-                                          mapsOtest->Bt, mapsCtest->Bt, pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
+   const bool scalar_coeff = !(DQ || MQ);
+   ApplyPAKernels::Run(trial_fetype, test_fetype, dim, dofs1D, dofs1Dtest,
+                       quad1D, ne, symmetric, scalar_coeff, mapsO->B, mapsC->B,
+                       mapsOtest->Bt, mapsCtest->Bt, pa_data, x, y, dofs1D,
+                       dofs1Dtest, quad1D);
 }
 
 void VectorFEMassIntegrator::AddAbsMultPA(const Vector &x, Vector &y) const
 {
-   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
-   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
-   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
-   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
+   const bool scalar_coeff = !(DQ || MQ);
 
    Vector abs_pa_data(pa_data);
    abs_pa_data.Abs();
 
    Array<real_t> absBo(mapsO->B);
    Array<real_t> absBc(mapsC->B);
-   Array<real_t> absBto(mapsO->Bt);
-   Array<real_t> absBtc(mapsC->Bt);
    Array<real_t> absBto_t(mapsOtest->Bt);
    Array<real_t> absBtc_t(mapsCtest->Bt);
 
    absBo.Abs();
    absBc.Abs();
-   absBto.Abs();
-   absBtc.Abs();
    absBto_t.Abs();
    absBtc_t.Abs();
 
-   if (dim == 3)
-   {
-      if (trial_curl && test_curl)
-      {
-         if (Device::Allows(Backend::DEVICE_MASK))
-         {
-            const int ID = (dofs1D << 4) | quad1D;
-            switch (ID)
-            {
-               case 0x23:
-                  return internal::SmemPAHcurlMassApply3D<2,3>(
-                            dofs1D, quad1D, ne, symmetric,
-                            absBo, absBc, absBto, absBtc,
-                            abs_pa_data, x, y);
-               case 0x34:
-                  return internal::SmemPAHcurlMassApply3D<3,4>(
-                            dofs1D, quad1D, ne, symmetric,
-                            absBo, absBc, absBto, absBtc,
-                            abs_pa_data, x, y);
-               case 0x45:
-                  return internal::SmemPAHcurlMassApply3D<4,5>(
-                            dofs1D, quad1D, ne, symmetric,
-                            absBo, absBc, absBto, absBtc,
-                            abs_pa_data, x, y);
-               case 0x56:
-                  return internal::SmemPAHcurlMassApply3D<5,6>(
-                            dofs1D, quad1D, ne, symmetric,
-                            absBo, absBc, absBto, absBtc,
-                            abs_pa_data, x, y);
-               default:
-                  return internal::SmemPAHcurlMassApply3D(
-                            dofs1D, quad1D, ne, symmetric,
-                            absBo, absBc, absBto, absBtc,
-                            abs_pa_data, x, y);
-            }
-         }
-         else
-         {
-            internal::PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric,
-                                         absBo, absBc, absBto, absBtc,
-                                         abs_pa_data, x, y);
-         }
-      }
-      else if (trial_div && test_div)
-      {
-         internal::PAHdivMassApply(3, dofs1D, quad1D, ne, symmetric,
-                                   absBo, absBc, absBto, absBtc,
-                                   abs_pa_data, x, y);
-      }
-      else if (trial_curl && test_div)
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne,
-                                          scalarCoeff, true, false,
-                                          absBo, absBc, absBto_t, absBtc_t,
-                                          abs_pa_data, x, y);
-      }
-      else if (trial_div && test_curl)
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne,
-                                          scalarCoeff, false, false,
-                                          absBo, absBc, absBto_t, absBtc_t,
-                                          abs_pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-   else // 2D
-   {
-      if (trial_curl && test_curl)
-      {
-         internal::PAHcurlMassApply2D(dofs1D, quad1D, ne, symmetric,
-                                      absBo, absBc, absBto, absBtc,
-                                      abs_pa_data, x, y);
-      }
-      else if (trial_div && test_div)
-      {
-         internal::PAHdivMassApply(2, dofs1D, quad1D, ne, symmetric,
-                                   absBo, absBc, absBto, absBtc,
-                                   abs_pa_data, x, y);
-      }
-      else if ((trial_curl && test_div) || (trial_div && test_curl))
-      {
-         const bool scalarCoeff = !(DQ || MQ);
-         internal::PAHcurlHdivMassApply2D(dofs1D, dofs1Dtest, quad1D, ne,
-                                          scalarCoeff, trial_curl, false,
-                                          absBo, absBc, absBto_t, absBtc_t,
-                                          abs_pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
+   ApplyPAKernels::Run(trial_fetype, test_fetype, dim, dofs1D, dofs1Dtest,
+                       quad1D, ne, symmetric, scalar_coeff, absBo, absBc,
+                       absBto_t, absBtc_t, abs_pa_data, x, y, dofs1D,
+                       dofs1Dtest, quad1D);
 }
 
 void VectorFEMassIntegrator::AddMultTransposePA(const Vector &x,

fem/integ/lininteg_domain_kernels.hpp

@@ -307,6 +307,506 @@ DomainLFIntegrator::AssembleKernels::Kernel()
    MFEM_ABORT("");
 }
 
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HdivDLFAssemble2D(const int ne, const Array<int> &markers,
+                              const Vector &jac, const Array<real_t> &weights,
+                              const Array<real_t> &testBO,
+                              const Array<real_t> &testBC, const Vector &coeff,
+                              Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 2 * (d - 1) * d * ne, "");
+
+   constexpr int vdim = 2;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1) : Reshape(F,vdim,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int vdim = 2;
+      if (M[e] == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q*D];
+      MFEM_SHARED real_t sBct[Q*D];
+      MFEM_SHARED real_t sQQ[vdim*Q*Q];
+      MFEM_SHARED real_t sQD[vdim*Q*D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d-1, q);
+      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
+
+      const DeviceCube QQ(sQQ, q, q, vdim);
+      const DeviceCube QD(sQD, q, d, vdim);
+
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const real_t cst_val_0 = C(0,0,0,0);
+         const real_t cst_val_1 = C(1,0,0,0);
+         MFEM_FOREACH_THREAD(y,y,q)
+         {
+            MFEM_FOREACH_THREAD(x,x,q)
+            {
+               const real_t J0 = J(x,y,0,vd,e);
+               const real_t J1 = J(x,y,1,vd,e);
+               const real_t C0 = cst ? cst_val_0 : C(0,x,y,e);
+               const real_t C1 = cst ? cst_val_1 : C(1,x,y,e);
+               QQ(x,y,vd) = W(x,y)*(J0*C0 + J1*C1);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(qy,y,q)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t qd = 0.0;
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  qd += QQ(qx,qy,vd) * Btx(dx,qx);
+               }
+               QD(dx,qy,vd) = qd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
+         DeviceTensor<4> Yxy(Y, nx, ny, vdim, ne);
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t dd = 0.0;
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  dd += QD(dx,qy,vd) * Bty(dy,qy);
+               }
+               Yxy(dx,dy,vd,e) += dd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HdivDLFAssemble3D(const int ne, const Array<int> &markers,
+                              const Vector &jac, const Array<real_t> &weights,
+                              const Array<real_t> &testBO,
+                              const Array<real_t> &testBC, const Vector &coeff,
+                              Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 3 * (d - 1) * (d - 1) * d * ne, "y wrong length");
+
+   constexpr int vdim = 3;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int vdim = 3;
+      if (M[e] == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q*D];
+      MFEM_SHARED real_t sBct[Q*D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d-1, q);
+      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
+
+      MFEM_SHARED real_t sm0[vdim*Q*Q*Q];
+      MFEM_SHARED real_t sm1[vdim*Q*Q*Q];
+      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
+      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
+      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
+
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const real_t cst_val_0 = C(0,0,0,0,0);
+         const real_t cst_val_1 = C(1,0,0,0,0);
+         const real_t cst_val_2 = C(2,0,0,0,0);
+         MFEM_FOREACH_THREAD(y,y,q)
+         {
+            MFEM_FOREACH_THREAD(x,x,q)
+            {
+               for (int z = 0; z < q; ++z)
+               {
+                  const real_t J0 = J(x,y,z,0,vd,e);
+                  const real_t J1 = J(x,y,z,1,vd,e);
+                  const real_t J2 = J(x,y,z,2,vd,e);
+                  const real_t C0 = cst ? cst_val_0 : C(0,x,y,z,e);
+                  const real_t C1 = cst ? cst_val_1 : C(1,x,y,z,e);
+                  const real_t C2 = cst ? cst_val_2 : C(2,x,y,z,e);
+                  QQQ(x,y,z,vd) = W(x,y,z)*(J0*C0 + J1*C1 + J2*C2);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(qy,y,q)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += QQQ(qx,qy,qz,vd) * Btx(dx,qx);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { DQQ(dx,qy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += DQQ(dx,qy,qz,vd) * Bty(dy,qy);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz) { DDQ(dx,dy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,vdim)
+      {
+         const int nx = (vd == 0) ? d : d-1;
+         const int ny = (vd == 1) ? d : d-1;
+         const int nz = (vd == 2) ? d : d-1;
+         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
+         DeviceMatrix Btz = (vd == 2) ? Bct : Bot;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               real_t u[D];
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  MFEM_UNROLL(D)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += DDQ(dx,dy,qz,vd) * Btz(dz,qz);
+                  }
+               }
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz) { Yxyz(dx,dy,dz,vd,e) += u[dz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+/// @param ne number of elements
+/// @param markers array where entry markers[e] == 0 to skip assembly over
+/// element e element
+/// @param jac Spatial Jacobians evaluated at all quadrature points
+/// @param weights 1D quadrature weights
+/// @param testBO 1D open basis test functions
+/// @param testBC 1D closed basis test functions
+/// @param coeff coefficient values evaluated at quadrature points, possibly
+/// compressed.
+/// @param d number of 1D closed dofs
+/// @param q number of 1D quadrature points
+/// @tparam T_D1D maximum number of dofs along any direction, or 0
+/// @tparam T_Q1D maximum number of quadrature points along any direction, or 0
+template <int T_D1D = 0, int T_Q1D = 0>
+static void HcurlDLFAssemble3D(const int ne, const Array<int> &markers,
+                               const Vector &jac, const Array<real_t> &weights,
+                               const Array<real_t> &testBO,
+                               const Array<real_t> &testBC, const Vector &coeff,
+                               Vector &y, const int d, const int q)
+{
+   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
+               "Problem size too large.");
+   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,
+               "Problem size too large.");
+   MFEM_VERIFY(y.Size() == 3 * (d - 1) * d * d * ne, "y wrong length");
+
+   constexpr int vdim = 3;
+   const auto F = coeff.Read();
+   const auto M = markers.Read();
+   const auto BO = Reshape(testBO.Read(), q, d-1);
+   const auto BC = Reshape(testBC.Read(), q, d);
+   const auto J = Reshape(jac.Read(), q, q, q, vdim, vdim, ne);
+   const auto W = Reshape(weights.Read(), q, q, q);
+   const bool cst = coeff.Size() == vdim;
+   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
+   auto Y = y.ReadWrite();
+
+   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE(int e)
+   {
+      if (M[e] == 0)
+      {
+         // ignore
+         return;
+      }
+
+      constexpr int vdim = 3;
+      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HCURL_MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HCURL_MAX_D1D;
+
+      MFEM_SHARED real_t sBot[Q * D];
+      MFEM_SHARED real_t sBct[Q * D];
+
+      // Bo and Bc into shared memory
+      const DeviceMatrix Bot(sBot, d - 1, q);
+      kernels::internal::LoadB<D, Q>(d - 1, q, BO, sBot);
+      const DeviceMatrix Bct(sBct, d, q);
+      kernels::internal::LoadB<D, Q>(d, q, BC, sBct);
+
+      MFEM_SHARED real_t sm0[vdim * Q * Q * Q];
+      MFEM_SHARED real_t sm1[vdim * Q * Q * Q];
+      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
+      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
+      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
+
+      const real_t cst_val_0 = C(0, 0, 0, 0, 0);
+      const real_t cst_val_1 = C(1, 0, 0, 0, 0);
+      const real_t cst_val_2 = C(2, 0, 0, 0, 0);
+
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         MFEM_FOREACH_THREAD(y, y, q)
+         {
+            MFEM_FOREACH_THREAD(x, x, q)
+            {
+               for (int z = 0; z < q; ++z)
+               {
+                  real_t curr[3];
+                  curr[0] = cst ? cst_val_0 : C(0, x, y, z, e);
+                  curr[1] = cst ? cst_val_1 : C(1, x, y, z, e);
+                  curr[2] = cst ? cst_val_2 : C(2, x, y, z, e);
+
+                  const real_t J11 = J(x, y, z, 0, 0, e);
+                  const real_t J21 = J(x, y, z, 1, 0, e);
+                  const real_t J31 = J(x, y, z, 2, 0, e);
+                  const real_t J12 = J(x, y, z, 0, 1, e);
+                  const real_t J22 = J(x, y, z, 1, 1, e);
+                  const real_t J32 = J(x, y, z, 2, 1, e);
+                  const real_t J13 = J(x, y, z, 0, 2, e);
+                  const real_t J23 = J(x, y, z, 1, 2, e);
+                  const real_t J33 = J(x, y, z, 2, 2, e);
+                  // adj(J)
+                  const real_t A11 = (J22 * J33) - (J23 * J32);
+                  const real_t A12 = (J32 * J13) - (J12 * J33);
+                  const real_t A13 = (J12 * J23) - (J22 * J13);
+                  const real_t A21 = (J31 * J23) - (J21 * J33);
+                  const real_t A22 = (J11 * J33) - (J13 * J31);
+                  const real_t A23 = (J21 * J13) - (J11 * J23);
+                  const real_t A31 = (J21 * J32) - (J31 * J22);
+                  const real_t A32 = (J31 * J12) - (J11 * J32);
+                  const real_t A33 = (J11 * J22) - (J12 * J21);
+                  const real_t A[9] = {A11, A12, A13, A21, A22,
+                                       A23, A31, A32, A33
+                                      };
+                  QQQ(x, y, z, vd) = W(x, y, z) * (A[vd * vdim] * curr[0] +
+                                                   A[vd * vdim + 1] * curr[1] +
+                                                   A[vd * vdim + 2] * curr[2]);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         DeviceMatrix Btx = (vd == 0) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(qy, y, q)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  u[qz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qx = 0; qx < q; ++qx)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += QQQ(qx, qy, qz, vd) * Btx(dx, qx);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  DQQ(dx, qy, qz, vd) = u[qz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         const int ny = (vd == 1) ? d - 1 : d;
+         DeviceMatrix Bty = (vd == 1) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(dy, y, ny)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[Q];
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  u[qz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qy = 0; qy < q; ++qy)
+               {
+                  MFEM_UNROLL(Q)
+                  for (int qz = 0; qz < q; ++qz)
+                  {
+                     u[qz] += DQQ(dx, qy, qz, vd) * Bty(dy, qy);
+                  }
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  DDQ(dx, dy, qz, vd) = u[qz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd, z, vdim)
+      {
+         const int nx = (vd == 0) ? d - 1 : d;
+         const int ny = (vd == 1) ? d - 1 : d;
+         const int nz = (vd == 2) ? d - 1 : d;
+         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
+         DeviceMatrix Btz = (vd == 2) ? Bot : Bct;
+         MFEM_FOREACH_THREAD(dy, y, ny)
+         {
+            MFEM_FOREACH_THREAD(dx, x, nx)
+            {
+               real_t u[D];
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz)
+               {
+                  u[dz] = 0.0;
+               }
+               MFEM_UNROLL(Q)
+               for (int qz = 0; qz < q; ++qz)
+               {
+                  MFEM_UNROLL(D)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += DDQ(dx, dy, qz, vd) * Btz(dz, qz);
+                  }
+               }
+               MFEM_UNROLL(D)
+               for (int dz = 0; dz < nz; ++dz)
+               {
+                  Yxyz(dx, dy, dz, vd, e) += u[dz];
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+template <FiniteElement::DerivType TestType, int DIM, int TEST_D1D, int Q1D>
+VectorFEDomainLFIntegrator::AssembleKernelType
+VectorFEDomainLFIntegrator::AssembleKernels::Kernel()
+{
+   if constexpr (TestType == FiniteElement::DIV)
+   {
+      if constexpr (DIM == 2)
+      {
+         return HdivDLFAssemble2D<TEST_D1D, Q1D>;
+      }
+      if constexpr (DIM == 3)
+      {
+         return HdivDLFAssemble3D<TEST_D1D, Q1D>;
+      }
+   }
+   if constexpr (TestType == FiniteElement::CURL)
+   {
+      if constexpr (DIM == 3)
+      {
+         return HcurlDLFAssemble3D<TEST_D1D, Q1D>;
+      }
+   }
+   MFEM_ABORT("");
+}
+
 /// \endcond DO_NOT_DOCUMENT
 
 } // namespace mfem

fem/integ/lininteg_domain_vectorfe.cpp

@@ -13,317 +13,76 @@
 #include "../../fem/kernels.hpp"
 #include "../fem.hpp"
 
+#include "lininteg_domain_kernels.hpp"
+
 namespace mfem
 {
 
-template<int T_D1D = 0, int T_Q1D = 0>
-static void HdivDLFAssemble2D(
-   const int ne, const int d, const int q, const int *markers, const real_t *bo,
-   const real_t *bc, const real_t *j, const real_t *weights,
-   const Vector &coeff, real_t *y)
+VectorFEDomainLFIntegrator::Kernels::Kernels()
 {
-   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
-               "Problem size too large.");
-   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
-               "Problem size too large.");
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 2, 8, 8>();
 
-   static constexpr int vdim = 2;
-   const auto F = coeff.Read();
-   const auto M = Reshape(markers, ne);
-   const auto BO = Reshape(bo, q, d-1);
-   const auto BC = Reshape(bc, q, d);
-   const auto J = Reshape(j, q, q, vdim, vdim, ne);
-   const auto W = Reshape(weights, q, q);
-   const bool cst = coeff.Size() == vdim;
-   const auto C = cst ? Reshape(F,vdim,1,1,1) : Reshape(F,vdim,q,q,ne);
-   auto Y = Reshape(y, 2*(d-1)*d, ne);
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::DIV, 3, 8, 8>();
 
-   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
-   {
-      if (M(e) == 0) { return; } // ignore
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 1, 1>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 2, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 3, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 4, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 5, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 6, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 7, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 8, 8>();
 
-      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
-      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
-
-      MFEM_SHARED real_t sBot[Q*D];
-      MFEM_SHARED real_t sBct[Q*D];
-      MFEM_SHARED real_t sQQ[vdim*Q*Q];
-      MFEM_SHARED real_t sQD[vdim*Q*D];
-
-      // Bo and Bc into shared memory
-      const DeviceMatrix Bot(sBot, d-1, q);
-      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
-      const DeviceMatrix Bct(sBct, d, q);
-      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
-
-      const DeviceCube QQ(sQQ, q, q, vdim);
-      const DeviceCube QD(sQD, q, d, vdim);
-
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const real_t cst_val_0 = C(0,0,0,0);
-         const real_t cst_val_1 = C(1,0,0,0);
-         MFEM_FOREACH_THREAD(y,y,q)
-         {
-            MFEM_FOREACH_THREAD(x,x,q)
-            {
-               const real_t J0 = J(x,y,0,vd,e);
-               const real_t J1 = J(x,y,1,vd,e);
-               const real_t C0 = cst ? cst_val_0 : C(0,x,y,e);
-               const real_t C1 = cst ? cst_val_1 : C(1,x,y,e);
-               QQ(x,y,vd) = W(x,y)*(J0*C0 + J1*C1);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(qy,y,q)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t qd = 0.0;
-               for (int qx = 0; qx < q; ++qx)
-               {
-                  qd += QQ(qx,qy,vd) * Btx(dx,qx);
-               }
-               QD(dx,qy,vd) = qd;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
-         DeviceTensor<4> Yxy(Y, nx, ny, vdim, ne);
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t dd = 0.0;
-               for (int qy = 0; qy < q; ++qy)
-               {
-                  dd += QD(dx,qy,vd) * Bty(dy,qy);
-               }
-               Yxy(dx,dy,vd,e) += dd;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-   });
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 1, 2>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 2, 3>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 3, 4>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 4, 5>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 5, 6>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 6, 7>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 7, 8>();
+   VectorFEDomainLFIntegrator::AddSpecialization<FiniteElement::CURL, 3, 8, 9>();
 }
 
-template<int T_D1D = 0, int T_Q1D = 0>
-static void HdivDLFAssemble3D(
-   const int ne, const int d, const int q, const int *markers, const real_t *bo,
-   const real_t *bc, const real_t *j, const real_t *weights,
-   const Vector &coeff, real_t *y)
+/// \cond DO_NOT_DOCUMENT
+VectorFEDomainLFIntegrator::AssembleKernelType
+VectorFEDomainLFIntegrator::AssembleKernels::Fallback(
+   FiniteElement::DerivType TestType, int DIM, int, int)
 {
-   MFEM_VERIFY(T_D1D || d <= DeviceDofQuadLimits::Get().HDIV_MAX_D1D,
-               "Problem size too large.");
-   MFEM_VERIFY(T_Q1D || q <= DeviceDofQuadLimits::Get().HDIV_MAX_Q1D,
-               "Problem size too large.");
-
-   static constexpr int vdim = 3;
-   const auto F = coeff.Read();
-   const auto M = Reshape(markers, ne);
-   const auto BO = Reshape(bo, q, d-1);
-   const auto BC = Reshape(bc, q, d);
-   const auto J = Reshape(j, q, q, q, vdim, vdim, ne);
-   const auto W = Reshape(weights, q, q, q);
-   const bool cst = coeff.Size() == vdim;
-   const auto C = cst ? Reshape(F,vdim,1,1,1,1) : Reshape(F,vdim,q,q,q,ne);
-   auto Y = Reshape(y, 2*(d-1)*(d-1)*d, ne);
-
-   mfem::forall_3D(ne, q, q, vdim, [=] MFEM_HOST_DEVICE (int e)
+   if (TestType == FiniteElement::DIV)
    {
-      if (M(e) == 0) { return; } // ignore
-
-      constexpr int Q = T_Q1D ? T_Q1D : DofQuadLimits::HDIV_MAX_Q1D;
-      constexpr int D = T_D1D ? T_D1D : DofQuadLimits::HDIV_MAX_D1D;
-
-      MFEM_SHARED real_t sBot[Q*D];
-      MFEM_SHARED real_t sBct[Q*D];
-
-      // Bo and Bc into shared memory
-      const DeviceMatrix Bot(sBot, d-1, q);
-      kernels::internal::LoadB<D,Q>(d-1, q, BO, sBot);
-      const DeviceMatrix Bct(sBct, d, q);
-      kernels::internal::LoadB<D,Q>(d, q, BC, sBct);
-
-      MFEM_SHARED real_t sm0[vdim*Q*Q*Q];
-      MFEM_SHARED real_t sm1[vdim*Q*Q*Q];
-      DeviceTensor<4> QQQ(sm1, q, q, q, vdim);
-      DeviceTensor<4> DQQ(sm0, d, q, q, vdim);
-      DeviceTensor<4> DDQ(sm1, d, d, q, vdim);
-
-      MFEM_FOREACH_THREAD(vd,z,vdim)
+      if (DIM == 2)
       {
-         const real_t cst_val_0 = C(0,0,0,0,0);
-         const real_t cst_val_1 = C(1,0,0,0,0);
-         const real_t cst_val_2 = C(2,0,0,0,0);
-         MFEM_FOREACH_THREAD(y,y,q)
-         {
-            MFEM_FOREACH_THREAD(x,x,q)
-            {
-               for (int z = 0; z < q; ++z)
-               {
-                  const real_t J0 = J(x,y,z,0,vd,e);
-                  const real_t J1 = J(x,y,z,1,vd,e);
-                  const real_t J2 = J(x,y,z,2,vd,e);
-                  const real_t C0 = cst ? cst_val_0 : C(0,x,y,z,e);
-                  const real_t C1 = cst ? cst_val_1 : C(1,x,y,z,e);
-                  const real_t C2 = cst ? cst_val_2 : C(2,x,y,z,e);
-                  QQQ(x,y,z,vd) = W(x,y,z)*(J0*C0 + J1*C1 + J2*C2);
-               }
-            }
-         }
+         return HdivDLFAssemble2D<0, 0>;
       }
-      MFEM_SYNC_THREAD;
-      // Apply Bt operator
-      MFEM_FOREACH_THREAD(vd,z,vdim)
+      if (DIM == 3)
       {
-         const int nx = (vd == 0) ? d : d-1;
-         DeviceMatrix Btx = (vd == 0) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(qy,y,q)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[Q];
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qx = 0; qx < q; ++qx)
-               {
-                  MFEM_UNROLL(Q)
-                  for (int qz = 0; qz < q; ++qz)
-                  {
-                     u[qz] += QQQ(qx,qy,qz,vd) * Btx(dx,qx);
-                  }
-               }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { DQQ(dx,qy,qz,vd) = u[qz]; }
-            }
-         }
+         return HdivDLFAssemble3D<0, 0>;
       }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         DeviceMatrix Bty = (vd == 1) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[Q];
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { u[qz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qy = 0; qy < q; ++qy)
-               {
-                  MFEM_UNROLL(Q)
-                  for (int qz = 0; qz < q; ++qz)
-                  {
-                     u[qz] += DQQ(dx,qy,qz,vd) * Bty(dy,qy);
-                  }
-               }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz) { DDQ(dx,dy,qz,vd) = u[qz]; }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(vd,z,vdim)
-      {
-         const int nx = (vd == 0) ? d : d-1;
-         const int ny = (vd == 1) ? d : d-1;
-         const int nz = (vd == 2) ? d : d-1;
-         DeviceTensor<5> Yxyz(Y, nx, ny, nz, vdim, ne);
-         DeviceMatrix Btz = (vd == 2) ? Bct : Bot;
-         MFEM_FOREACH_THREAD(dy,y,ny)
-         {
-            MFEM_FOREACH_THREAD(dx,x,nx)
-            {
-               real_t u[D];
-               MFEM_UNROLL(D)
-               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
-               MFEM_UNROLL(Q)
-               for (int qz = 0; qz < q; ++qz)
-               {
-                  MFEM_UNROLL(D)
-                  for (int dz = 0; dz < nz; ++dz)
-                  {
-                     u[dz] += DDQ(dx,dy,qz,vd) * Btz(dz,qz);
-                  }
-               }
-               MFEM_UNROLL(D)
-               for (int dz = 0; dz < nz; ++dz) { Yxyz(dx,dy,dz,vd,e) += u[dz]; }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-   });
-}
-
-static void HdivDLFAssemble(const FiniteElementSpace &fes,
-                            const IntegrationRule *ir,
-                            const Array<int> &markers,
-                            const Vector &coeff,
-                            Vector &y)
-{
-   Mesh &mesh = *fes.GetMesh();
-   const int dim = mesh.Dimension();
-   const FiniteElement *el = fes.GetTypicalFE();
-   const auto *vel = dynamic_cast<const VectorTensorFiniteElement *>(el);
-   MFEM_VERIFY(vel != nullptr, "Must be VectorTensorFiniteElement");
-   const MemoryType mt = Device::GetDeviceMemoryType();
-   const DofToQuad &maps_o = vel->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   const DofToQuad &maps_c = vel->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int d = maps_c.ndof, q = maps_c.nqpt;
-   constexpr int flags = GeometricFactors::JACOBIANS;
-   const GeometricFactors *geom = mesh.GetGeometricFactors(*ir, flags, mt);
-   decltype(&HdivDLFAssemble2D<>) ker =
-      dim == 2 ? HdivDLFAssemble2D<> : HdivDLFAssemble3D<>;
-
-   if (dim==2)
-   {
-      if (d==1 && q==1) { ker=HdivDLFAssemble2D<1,1>; }
-      if (d==2 && q==2) { ker=HdivDLFAssemble2D<2,2>; }
-      if (d==3 && q==3) { ker=HdivDLFAssemble2D<3,3>; }
-      if (d==4 && q==4) { ker=HdivDLFAssemble2D<4,4>; }
-      if (d==5 && q==5) { ker=HdivDLFAssemble2D<5,5>; }
-      if (d==6 && q==6) { ker=HdivDLFAssemble2D<6,6>; }
-      if (d==7 && q==7) { ker=HdivDLFAssemble2D<7,7>; }
-      if (d==8 && q==8) { ker=HdivDLFAssemble2D<8,8>; }
    }
-
-   if (dim==3)
+   else if (TestType == FiniteElement::CURL)
    {
-      if (d==2 && q==2) { ker=HdivDLFAssemble3D<2,2>; }
-      if (d==3 && q==3) { ker=HdivDLFAssemble3D<3,3>; }
-      if (d==4 && q==4) { ker=HdivDLFAssemble3D<4,4>; }
-      if (d==5 && q==5) { ker=HdivDLFAssemble3D<5,5>; }
-      if (d==6 && q==6) { ker=HdivDLFAssemble3D<6,6>; }
-      if (d==7 && q==7) { ker=HdivDLFAssemble3D<7,7>; }
-      if (d==8 && q==8) { ker=HdivDLFAssemble3D<8,8>; }
+      if (DIM == 3)
+      {
+         return HcurlDLFAssemble3D<0, 0>;
+      }
    }
-
-   MFEM_VERIFY(ker, "No kernel ndof " << d << " nqpt " << q);
-
-   const int ne = mesh.GetNE();
-   const int *M = markers.Read();
-   const real_t *Bo = maps_o.B.Read();
-   const real_t *Bc = maps_c.B.Read();
-   const real_t *J = geom->J.Read();
-   const real_t *W = ir->GetWeights().Read();
-   real_t *Y = y.ReadWrite();
-   ker(ne, d, q, M, Bo, Bc, J, W, coeff, Y);
+   MFEM_ABORT("");
 }
+/// \endcond DO_NOT_DOCUMENT
 
 void VectorFEDomainLFIntegrator::AssembleDevice(const FiniteElementSpace &fes,
                                                 const Array<int> &markers,
@@ -337,15 +96,23 @@ void VectorFEDomainLFIntegrator::AssembleDevice(const FiniteElementSpace &fes,
    QuadratureSpace qs(*fes.GetMesh(), *ir);
    CoefficientVector coeff(QF, qs, CoefficientStorage::COMPRESSED);
 
-   const int fe_type = fe.GetDerivType();
-   if (fe_type == FiniteElement::DIV)
-   {
-      HdivDLFAssemble(fes, ir, markers, coeff, b);
-   }
-   else
-   {
-      MFEM_ABORT("Not implemented.");
-   }
+   const FiniteElement::DerivType fe_type =
+      static_cast<FiniteElement::DerivType>(fe.GetDerivType());
+
+   Mesh &mesh = *fes.GetMesh();
+   const int dim = mesh.Dimension();
+   const FiniteElement *el = fes.GetTypicalFE();
+   const auto *vel = dynamic_cast<const VectorTensorFiniteElement *>(el);
+   MFEM_VERIFY(vel != nullptr, "Must be VectorTensorFiniteElement");
+   const MemoryType mt = Device::GetDeviceMemoryType();
+   const DofToQuad &maps_o = vel->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   const DofToQuad &maps_c = vel->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   const int d = maps_c.ndof, q = maps_c.nqpt;
+   constexpr int flags = GeometricFactors::JACOBIANS;
+   const GeometricFactors *geom = mesh.GetGeometricFactors(*ir, flags, mt);
+
+   AssembleKernels::Run(fe_type, dim, d, q, mesh.GetNE(), markers, geom->J,
+                        ir->GetWeights(), maps_o.B, maps_c.B, coeff, b, d, q);
 }
 
 } // namespace mfem

fem/integ/nonlininteg_vecconvection_pa.cpp

@@ -9,21 +9,51 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "../../general/forall.hpp"
-#include "../nonlininteg.hpp"
 #include "../ceed/integrators/nlconvection/nlconvection.hpp"
+#include "./nonlininteg_vecconvection_pa.hpp" // IWYU pragma: keep
+#include "./nonlininteg_vecconvection_pa_grad.hpp" // IWYU pragma: keep
+#include "./nonlininteg_vecconvection_pa_diag.hpp" // IWYU pragma: keep
 
 namespace mfem
 {
 
+VectorConvectionNLFIntegrator::Kernels::Kernels()
+{
+   // 2D
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 2, 2>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 2, 3>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 3, 4>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 3, 5>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 4, 5>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 4, 6>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 5, 7>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 5, 8>();
+   VectorConvectionNLFIntegrator::AddSpecialization<2, 6, 8>();
+   // 3D
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 2, 3>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 2, 4>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 2, 5>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 3, 4>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 3, 5>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 3, 6>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 4, 5>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 4, 6>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 4, 7>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 4, 8>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 5, 6>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 5, 7>();
+   VectorConvectionNLFIntegrator::AddSpecialization<3, 5, 8>();
+}
+
 void VectorConvectionNLFIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    MFEM_ASSERT(fes.GetOrdering() == Ordering::byNODES,
                "PA Only supports Ordering::byNODES!");
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
-   ElementTransformation &T = *mesh->GetTypicalElementTransformation();
-   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, T);
+   ElementTransformation &Tr = *mesh->GetTypicalElementTransformation();
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, Tr);
+
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
@@ -39,769 +69,124 @@ void VectorConvectionNLFIntegrator::AssemblePA(const FiniteElementSpace &fes)
       }
       return;
    }
-   dim = mesh->Dimension();
-   ne = fes.GetMesh()->GetNE();
+
+   ne = mesh->GetNE();
    nq = ir->GetNPoints();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   dim = mesh->Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "Dimension not supported");
+
+   const MemoryType mt = pa_mt == MemoryType::DEFAULT
+                         ? Device::GetDeviceMemoryType()
+                         : pa_mt;
+   pa_adj.SetSize(ne * nq * dim * dim, mt);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mt);
    maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
-   pa_data.SetSize(ne * nq * dim * dim, Device::GetMemoryType());
-   real_t COEFF = 1.0;
-   if (Q)
-   {
-      ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient *>(Q);
-      MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
-      COEFF = cQ->constant;
-   }
-   const int NE = ne;
-   const int NQ = nq;
-   auto W = ir->GetWeights().Read();
-   if (dim == 1)
-   {
-      MFEM_ABORT("dim==1 not supported!");
-   }
+   d1d = maps->ndof;
+   q1d = maps->nqpt;
+
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::COMPRESSED);
+
+   const int nq1d = q1d * q1d * (dim==3 ? q1d : 1);
+   MFEM_VERIFY(coeff.Size() == 1 || coeff.Size() == nq1d*ne, "Invalid coeff");
+   MFEM_VERIFY(ir->GetWeights().Size() == nq1d, "Invalid weights size");
+
+   const auto w_r = ir->GetWeights().Read();
+   const bool const_coeff = coeff.Size() == 1;
+
    if (dim == 2)
    {
-      auto J = Reshape(geom->J.Read(), NQ, 2, 2, NE);
-      auto G = Reshape(pa_data.Write(), NQ, 2, 2, NE);
-      mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+      const int Q1D = q1d;
+      constexpr int VDIM = 2, DIM = 2;
+      const auto W = Reshape(w_r, Q1D, Q1D);
+      const auto C = const_coeff ?
+                     Reshape(coeff.Read(), 1, 1, 1) :
+                     Reshape(coeff.Read(), Q1D, Q1D, ne);
+      const auto J = Reshape(geom->J.Read(), Q1D, Q1D, VDIM, DIM, ne);
+      auto A = Reshape(pa_adj.Write(), VDIM, DIM, Q1D, Q1D, ne);
+
+      mfem::forall_2D(ne, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
          {
-            const real_t J11 = J(q, 0, 0, e);
-            const real_t J12 = J(q, 0, 1, e);
-            const real_t J21 = J(q, 1, 0, e);
-            const real_t J22 = J(q, 1, 1, e);
-            // Store wq * Q * adj(J)
-            G(q, 0, 0, e) = W[q] * COEFF * J22;  // 1,1
-            G(q, 0, 1, e) = W[q] * COEFF * -J12; // 1,2
-            G(q, 1, 0, e) = W[q] * COEFF * -J21; // 2,1
-            G(q, 1, 1, e) = W[q] * COEFF * J11;  // 2,2
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t J11 = J(qx, qy, 0, 0, e), J12 = J(qx, qy, 0, 1, e);
+               const real_t J21 = J(qx, qy, 1, 0, e), J22 = J(qx, qy, 1, 1, e);
+               // adj(J)
+               const real_t A11 = +J22, A12 = -J12;
+               const real_t A21 = -J21, A22 = +J11;
+               // Store w * coeff * adj(J)
+               const real_t w = W(qx, qy);
+               const real_t c = const_coeff ? C(0, 0, 0) : C(qx, qy, e);
+               A(0, 0, qx, qy, e) = w * c * A11;
+               A(1, 0, qx, qy, e) = w * c * A12;
+               A(0, 1, qx, qy, e) = w * c * A21;
+               A(1, 1, qx, qy, e) = w * c * A22;
+            }
          }
       });
    }
-   if (dim == 3)
+   else if (dim == 3)
    {
-      auto J = Reshape(geom->J.Read(), NQ, 3, 3, NE);
-      auto G = Reshape(pa_data.Write(), NQ, 3, 3, NE);
-      mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+      const int Q1D = q1d;
+      constexpr int VDIM = 3, DIM = 3;
+      const auto W = Reshape(w_r, Q1D, Q1D, Q1D);
+      const auto C = const_coeff ?
+                     Reshape(coeff.Read(), 1, 1, 1, 1) :
+                     Reshape(coeff.Read(), Q1D, Q1D, Q1D, ne);
+      const auto J = Reshape(geom->J.Read(), Q1D, Q1D, Q1D, VDIM, DIM, ne);
+      auto A = Reshape(pa_adj.Write(), VDIM, DIM, Q1D, Q1D, Q1D, ne);
+
+      mfem::forall_3D(ne, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD_DIRECT(qz, z, Q1D)
          {
-            const real_t J11 = J(q, 0, 0, e);
-            const real_t J21 = J(q, 1, 0, e);
-            const real_t J31 = J(q, 2, 0, e);
-            const real_t J12 = J(q, 0, 1, e);
-            const real_t J22 = J(q, 1, 1, e);
-            const real_t J32 = J(q, 2, 1, e);
-            const real_t J13 = J(q, 0, 2, e);
-            const real_t J23 = J(q, 1, 2, e);
-            const real_t J33 = J(q, 2, 2, e);
-            const real_t cw = W[q] * COEFF;
-            // adj(J)
-            const real_t A11 = (J22 * J33) - (J23 * J32);
-            const real_t A12 = (J32 * J13) - (J12 * J33);
-            const real_t A13 = (J12 * J23) - (J22 * J13);
-            const real_t A21 = (J31 * J23) - (J21 * J33);
-            const real_t A22 = (J11 * J33) - (J13 * J31);
-            const real_t A23 = (J21 * J13) - (J11 * J23);
-            const real_t A31 = (J21 * J32) - (J31 * J22);
-            const real_t A32 = (J31 * J12) - (J11 * J32);
-            const real_t A33 = (J11 * J22) - (J12 * J21);
-            // Store wq * Q * adj(J)
-            G(q, 0, 0, e) = cw * A11; // 1,1
-            G(q, 0, 1, e) = cw * A12; // 1,2
-            G(q, 0, 2, e) = cw * A13; // 1,3
-            G(q, 1, 0, e) = cw * A21; // 2,1
-            G(q, 1, 1, e) = cw * A22; // 2,2
-            G(q, 1, 2, e) = cw * A23; // 2,3
-            G(q, 2, 0, e) = cw * A31; // 3,1
-            G(q, 2, 1, e) = cw * A32; // 3,2
-            G(q, 2, 2, e) = cw * A33; // 3,3
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  const real_t J11 = J(qx, qy, qz, 0, 0, e),
+                               J12 = J(qx, qy, qz, 0, 1, e),
+                               J13 = J(qx, qy, qz, 0, 2, e);
+                  const real_t J21 = J(qx, qy, qz, 1, 0, e),
+                               J22 = J(qx, qy, qz, 1, 1, e),
+                               J23 = J(qx, qy, qz, 1, 2, e);
+                  const real_t J31 = J(qx, qy, qz, 2, 0, e),
+                               J32 = J(qx, qy, qz, 2, 1, e),
+                               J33 = J(qx, qy, qz, 2, 2, e);
+                  const real_t c =
+                     const_coeff ? C(0, 0, 0, 0) : C(qx, qy, qz, e);
+                  const real_t cw = W(qx, qy, qz) * c;
+                  // adj(J)
+                  const real_t A11 = (J22 * J33) - (J23 * J32);
+                  const real_t A12 = (J32 * J13) - (J12 * J33);
+                  const real_t A13 = (J12 * J23) - (J22 * J13);
+                  const real_t A21 = (J31 * J23) - (J21 * J33);
+                  const real_t A22 = (J11 * J33) - (J13 * J31);
+                  const real_t A23 = (J21 * J13) - (J11 * J23);
+                  const real_t A31 = (J21 * J32) - (J31 * J22);
+                  const real_t A32 = (J31 * J12) - (J11 * J32);
+                  const real_t A33 = (J11 * J22) - (J12 * J21);
+                  // Store wq * coeff * adj(J)
+                  A(0, 0, qx, qy, qz, e) = cw * A11;
+                  A(1, 0, qx, qy, qz, e) = cw * A12;
+                  A(2, 0, qx, qy, qz, e) = cw * A13;
+                  A(0, 1, qx, qy, qz, e) = cw * A21;
+                  A(1, 1, qx, qy, qz, e) = cw * A22;
+                  A(2, 1, qx, qy, qz, e) = cw * A23;
+                  A(0, 2, qx, qy, qz, e) = cw * A31;
+                  A(1, 2, qx, qy, qz, e) = cw * A32;
+                  A(2, 2, qx, qy, qz, e) = cw * A33;
+               }
+            }
          }
       });
    }
-}
-
-// PA Convection NL 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
-static void PAConvectionNLApply2D(const int NE,
-                                  const Array<real_t> &b,
-                                  const Array<real_t> &g,
-                                  const Array<real_t> &bt,
-                                  const Vector &q_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
-{
-   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, "");
-   auto B = Reshape(b.Read(), Q1D, D1D);
-   auto G = Reshape(g.Read(), Q1D, D1D);
-   auto Bt = Reshape(bt.Read(), D1D, Q1D);
-   auto Q = Reshape(q_.Read(), Q1D * Q1D, 2, 2, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, 2, NE);
-   auto y = Reshape(y_.ReadWrite(), D1D, D1D, 2, NE);
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   else
    {
-      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 data[max_Q1D][max_Q1D][2];
-      real_t grad0[max_Q1D][max_Q1D][2];
-      real_t grad1[max_Q1D][max_Q1D][2];
-      real_t Z[max_Q1D][max_Q1D][2];
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            data[qy][qx][0] = 0.0;
-            data[qy][qx][1] = 0.0;
-            grad0[qy][qx][0] = 0.0;
-            grad0[qy][qx][1] = 0.0;
-            grad1[qy][qx][0] = 0.0;
-            grad1[qy][qx][1] = 0.0;
-         }
-      }
-      for (int dy = 0; dy < D1D; ++dy)
-      {
-         real_t dataX[max_Q1D][2];
-         real_t gradX0[max_Q1D][2];
-         real_t gradX1[max_Q1D][2];
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            dataX[qx][0] = 0.0;
-            dataX[qx][1] = 0.0;
-            gradX0[qx][0] = 0.0;
-            gradX0[qx][1] = 0.0;
-            gradX1[qx][0] = 0.0;
-            gradX1[qx][1] = 0.0;
-         }
-         for (int dx = 0; dx < D1D; ++dx)
-         {
-            const real_t s0 = x(dx, dy, 0, e);
-            const real_t s1 = x(dx, dy, 1, e);
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               const real_t Bx = B(qx, dx);
-               const real_t Gx = G(qx, dx);
-               dataX[qx][0] += s0 * Bx;
-               dataX[qx][1] += s1 * Bx;
-               gradX0[qx][0] += s0 * Gx;
-               gradX0[qx][1] += s0 * Bx;
-               gradX1[qx][0] += s1 * Gx;
-               gradX1[qx][1] += s1 * Bx;
-            }
-         }
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            const real_t By = B(qy, dy);
-            const real_t Gy = G(qy, dy);
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               data[qy][qx][0] += dataX[qx][0] * By;
-               data[qy][qx][1] += dataX[qx][1] * By;
-               grad0[qy][qx][0] += gradX0[qx][0] * By;
-               grad0[qy][qx][1] += gradX0[qx][1] * Gy;
-               grad1[qy][qx][0] += gradX1[qx][0] * By;
-               grad1[qy][qx][1] += gradX1[qx][1] * Gy;
-            }
-         }
-      }
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            const int q = qx + qy * Q1D;
-            const real_t u1 = data[qy][qx][0];
-            const real_t u2 = data[qy][qx][1];
-            const real_t grad00 = grad0[qy][qx][0];
-            const real_t grad01 = grad0[qy][qx][1];
-            const real_t grad10 = grad1[qy][qx][0];
-            const real_t grad11 = grad1[qy][qx][1];
-            const real_t Dxu1 = grad00 * Q(q, 0, 0, e) + grad01 * Q(q, 1, 0, e);
-            const real_t Dyu1 = grad00 * Q(q, 0, 1, e) + grad01 * Q(q, 1, 1, e);
-            const real_t Dxu2 = grad10 * Q(q, 0, 0, e) + grad11 * Q(q, 1, 0, e);
-            const real_t Dyu2 = grad10 * Q(q, 0, 1, e) + grad11 * Q(q, 1, 1, e);
-            Z[qy][qx][0] = u1 * Dxu1 + u2 * Dyu1;
-            Z[qy][qx][1] = u1 * Dxu2 + u2 * Dyu2;
-         }
-      }
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         real_t Y[max_D1D][2];
-         for (int dx = 0; dx < D1D; ++dx)
-         {
-            Y[dx][0] = 0.0;
-            Y[dx][1] = 0.0;
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               const real_t Btx = Bt(dx, qx);
-               Y[dx][0] += Btx * Z[qy][qx][0];
-               Y[dx][1] += Btx * Z[qy][qx][1];
-            }
-         }
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               const real_t Bty = Bt(dy, qy);
-               y(dx, dy, 0, e) += Bty * Y[dx][0];
-               y(dx, dy, 1, e) += Bty * Y[dx][1];
-            }
-         }
-      }
-   });
-}
-
-// PA Convection NL 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0>
-static void PAConvectionNLApply3D(const int NE,
-                                  const Array<real_t> &b,
-                                  const Array<real_t> &g,
-                                  const Array<real_t> &bt,
-                                  const Vector &q_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  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, "");
-
-   auto B = Reshape(b.Read(), Q1D, D1D);
-   auto G = Reshape(g.Read(), Q1D, D1D);
-   auto Bt = Reshape(bt.Read(), D1D, Q1D);
-   auto Q = Reshape(q_.Read(), Q1D * Q1D * Q1D, VDIM, VDIM, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, D1D, VDIM, NE);
-   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, VDIM, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      constexpr int VDIM = 3;
-      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 data[max_Q1D][max_Q1D][max_Q1D][VDIM];
-      real_t grad0[max_Q1D][max_Q1D][max_Q1D][VDIM];
-      real_t grad1[max_Q1D][max_Q1D][max_Q1D][VDIM];
-      real_t grad2[max_Q1D][max_Q1D][max_Q1D][VDIM];
-      real_t Z[max_Q1D][max_Q1D][max_Q1D][VDIM];
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               data[qz][qy][qx][0] = 0.0;
-               data[qz][qy][qx][1] = 0.0;
-               data[qz][qy][qx][2] = 0.0;
-
-               grad0[qz][qy][qx][0] = 0.0;
-               grad0[qz][qy][qx][1] = 0.0;
-               grad0[qz][qy][qx][2] = 0.0;
-
-               grad1[qz][qy][qx][0] = 0.0;
-               grad1[qz][qy][qx][1] = 0.0;
-               grad1[qz][qy][qx][2] = 0.0;
-
-               grad2[qz][qy][qx][0] = 0.0;
-               grad2[qz][qy][qx][1] = 0.0;
-               grad2[qz][qy][qx][2] = 0.0;
-            }
-         }
-      }
-      for (int dz = 0; dz < D1D; ++dz)
-      {
-         real_t dataXY[max_Q1D][max_Q1D][VDIM];
-         real_t gradXY0[max_Q1D][max_Q1D][VDIM];
-         real_t gradXY1[max_Q1D][max_Q1D][VDIM];
-         real_t gradXY2[max_Q1D][max_Q1D][VDIM];
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               dataXY[qy][qx][0] = 0.0;
-               dataXY[qy][qx][1] = 0.0;
-               dataXY[qy][qx][2] = 0.0;
-
-               gradXY0[qy][qx][0] = 0.0;
-               gradXY0[qy][qx][1] = 0.0;
-               gradXY0[qy][qx][2] = 0.0;
-
-               gradXY1[qy][qx][0] = 0.0;
-               gradXY1[qy][qx][1] = 0.0;
-               gradXY1[qy][qx][2] = 0.0;
-
-               gradXY2[qy][qx][0] = 0.0;
-               gradXY2[qy][qx][1] = 0.0;
-               gradXY2[qy][qx][2] = 0.0;
-            }
-         }
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            real_t dataX[max_Q1D][VDIM];
-            real_t gradX0[max_Q1D][VDIM];
-            real_t gradX1[max_Q1D][VDIM];
-            real_t gradX2[max_Q1D][VDIM];
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               dataX[qx][0] = 0.0;
-               dataX[qx][1] = 0.0;
-               dataX[qx][2] = 0.0;
-
-               gradX0[qx][0] = 0.0;
-               gradX0[qx][1] = 0.0;
-               gradX0[qx][2] = 0.0;
-
-               gradX1[qx][0] = 0.0;
-               gradX1[qx][1] = 0.0;
-               gradX1[qx][2] = 0.0;
-
-               gradX2[qx][0] = 0.0;
-               gradX2[qx][1] = 0.0;
-               gradX2[qx][2] = 0.0;
-            }
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               const real_t s0 = x(dx, dy, dz, 0, e);
-               const real_t s1 = x(dx, dy, dz, 1, e);
-               const real_t s2 = x(dx, dy, dz, 2, e);
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  const real_t Bx = B(qx, dx);
-                  const real_t Gx = G(qx, dx);
-
-                  dataX[qx][0] += s0 * Bx;
-                  dataX[qx][1] += s1 * Bx;
-                  dataX[qx][2] += s2 * Bx;
-
-                  gradX0[qx][0] += s0 * Gx;
-                  gradX0[qx][1] += s0 * Bx;
-                  gradX0[qx][2] += s0 * Bx;
-
-                  gradX1[qx][0] += s1 * Gx;
-                  gradX1[qx][1] += s1 * Bx;
-                  gradX1[qx][2] += s1 * Bx;
-
-                  gradX2[qx][0] += s2 * Gx;
-                  gradX2[qx][1] += s2 * Bx;
-                  gradX2[qx][2] += s2 * Bx;
-               }
-            }
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               const real_t By = B(qy, dy);
-               const real_t Gy = G(qy, dy);
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  dataXY[qy][qx][0] += dataX[qx][0] * By;
-                  dataXY[qy][qx][1] += dataX[qx][1] * By;
-                  dataXY[qy][qx][2] += dataX[qx][2] * By;
-
-                  gradXY0[qy][qx][0] += gradX0[qx][0] * By;
-                  gradXY0[qy][qx][1] += gradX0[qx][1] * Gy;
-                  gradXY0[qy][qx][2] += gradX0[qx][2] * By;
-
-                  gradXY1[qy][qx][0] += gradX1[qx][0] * By;
-                  gradXY1[qy][qx][1] += gradX1[qx][1] * Gy;
-                  gradXY1[qy][qx][2] += gradX1[qx][2] * By;
-
-                  gradXY2[qy][qx][0] += gradX2[qx][0] * By;
-                  gradXY2[qy][qx][1] += gradX2[qx][1] * Gy;
-                  gradXY2[qy][qx][2] += gradX2[qx][2] * By;
-               }
-            }
-         }
-         for (int qz = 0; qz < Q1D; ++qz)
-         {
-            const real_t Bz = B(qz, dz);
-            const real_t Gz = G(qz, dz);
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  data[qz][qy][qx][0] += dataXY[qy][qx][0] * Bz;
-                  data[qz][qy][qx][1] += dataXY[qy][qx][1] * Bz;
-                  data[qz][qy][qx][2] += dataXY[qy][qx][2] * Bz;
-
-                  grad0[qz][qy][qx][0] += gradXY0[qy][qx][0] * Bz;
-                  grad0[qz][qy][qx][1] += gradXY0[qy][qx][1] * Bz;
-                  grad0[qz][qy][qx][2] += gradXY0[qy][qx][2] * Gz;
-
-                  grad1[qz][qy][qx][0] += gradXY1[qy][qx][0] * Bz;
-                  grad1[qz][qy][qx][1] += gradXY1[qy][qx][1] * Bz;
-                  grad1[qz][qy][qx][2] += gradXY1[qy][qx][2] * Gz;
-
-                  grad2[qz][qy][qx][0] += gradXY2[qy][qx][0] * Bz;
-                  grad2[qz][qy][qx][1] += gradXY2[qy][qx][1] * Bz;
-                  grad2[qz][qy][qx][2] += gradXY2[qy][qx][2] * Gz;
-               }
-            }
-         }
-      }
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               const int q = qx + Q1D * (qy + qz * Q1D);
-
-               const real_t u1 = data[qz][qy][qx][0];
-               const real_t u2 = data[qz][qy][qx][1];
-               const real_t u3 = data[qz][qy][qx][2];
-
-               const real_t grad00 = grad0[qz][qy][qx][0];
-               const real_t grad01 = grad0[qz][qy][qx][1];
-               const real_t grad02 = grad0[qz][qy][qx][2];
-
-               const real_t grad10 = grad1[qz][qy][qx][0];
-               const real_t grad11 = grad1[qz][qy][qx][1];
-               const real_t grad12 = grad1[qz][qy][qx][2];
-
-               const real_t grad20 = grad2[qz][qy][qx][0];
-               const real_t grad21 = grad2[qz][qy][qx][1];
-               const real_t grad22 = grad2[qz][qy][qx][2];
-
-               const real_t Dxu1 = grad00 * Q(q, 0, 0, e)
-                                   + grad01 * Q(q, 1, 0, e)
-                                   + grad02 * Q(q, 2, 0, e);
-               const real_t Dyu1 = grad00 * Q(q, 0, 1, e)
-                                   + grad01 * Q(q, 1, 1, e)
-                                   + grad02 * Q(q, 2, 1, e);
-               const real_t Dzu1 = grad00 * Q(q, 0, 2, e)
-                                   + grad01 * Q(q, 1, 2, e)
-                                   + grad02 * Q(q, 2, 2, e);
-
-               const real_t Dxu2 = grad10 * Q(q, 0, 0, e)
-                                   + grad11 * Q(q, 1, 0, e)
-                                   + grad12 * Q(q, 2, 0, e);
-               const real_t Dyu2 = grad10 * Q(q, 0, 1, e)
-                                   + grad11 * Q(q, 1, 1, e)
-                                   + grad12 * Q(q, 2, 1, e);
-               const real_t Dzu2 = grad10 * Q(q, 0, 2, e)
-                                   + grad11 * Q(q, 1, 2, e)
-                                   + grad12 * Q(q, 2, 2, e);
-
-               const real_t Dxu3 = grad20 * Q(q, 0, 0, e)
-                                   + grad21 * Q(q, 1, 0, e)
-                                   + grad22 * Q(q, 2, 0, e);
-               const real_t Dyu3 = grad20 * Q(q, 0, 1, e)
-                                   + grad21 * Q(q, 1, 1, e)
-                                   + grad22 * Q(q, 2, 1, e);
-               const real_t Dzu3 = grad20 * Q(q, 0, 2, e)
-                                   + grad21 * Q(q, 1, 2, e)
-                                   + grad22 * Q(q, 2, 2, e);
-
-               Z[qz][qy][qx][0] = u1 * Dxu1 + u2 * Dyu1 + u3 * Dzu1;
-               Z[qz][qy][qx][1] = u1 * Dxu2 + u2 * Dyu2 + u3 * Dzu2;
-               Z[qz][qy][qx][2] = u1 * Dxu3 + u2 * Dyu3 + u3 * Dzu3;
-            }
-         }
-      }
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         real_t opXY[max_D1D][max_D1D][VDIM];
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               opXY[dy][dx][0] = 0.0;
-               opXY[dy][dx][1] = 0.0;
-               opXY[dy][dx][2] = 0.0;
-            }
-         }
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            real_t opX[max_D1D][VDIM];
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               opX[dx][0] = 0.0;
-               opX[dx][1] = 0.0;
-               opX[dx][2] = 0.0;
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  const real_t Btx = Bt(dx, qx);
-                  opX[dx][0] += Btx * Z[qz][qy][qx][0];
-                  opX[dx][1] += Btx * Z[qz][qy][qx][1];
-                  opX[dx][2] += Btx * Z[qz][qy][qx][2];
-               }
-            }
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const real_t Bty = Bt(dy, qy);
-                  opXY[dy][dx][0] += Bty * opX[dx][0];
-                  opXY[dy][dx][1] += Bty * opX[dx][1];
-                  opXY[dy][dx][2] += Bty * opX[dx][2];
-               }
-            }
-         }
-         for (int dz = 0; dz < D1D; ++dz)
-         {
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const real_t Btz = Bt(dz, qz);
-                  y(dx, dy, dz, 0, e) += Btz * opXY[dy][dx][0];
-                  y(dx, dy, dz, 1, e) += Btz * opXY[dy][dx][1];
-                  y(dx, dy, dz, 2, e) += Btz * opXY[dy][dx][2];
-               }
-            }
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0, int T_MAX_D1D = 0, int T_MAX_Q1D = 0>
-static void SmemPAConvectionNLApply3D(const int NE,
-                                      const Array<real_t> &b_,
-                                      const Array<real_t> &g_,
-                                      const Vector &d_,
-                                      const Vector &x_,
-                                      Vector &y_,
-                                      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;
-   constexpr int MD1 = T_D1D ? T_D1D : T_MAX_D1D;
-   constexpr int MQ1 = T_Q1D ? T_Q1D : T_MAX_Q1D;
-   MFEM_VERIFY(D1D <= MD1, "");
-   MFEM_VERIFY(Q1D <= MQ1, "");
-
-   auto b = Reshape(b_.Read(), Q1D, D1D);
-   auto g = Reshape(g_.Read(), Q1D, D1D);
-   auto D = Reshape(d_.Read(), Q1D * Q1D * Q1D, VDIM, VDIM, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, D1D, VDIM, NE);
-   auto Y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, VDIM, NE);
-
-   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
-   {
-      const int tidz = MFEM_THREAD_ID(z);
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : T_MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MAX_Q1D;
-      MFEM_SHARED real_t BG[2][MQ1 * MD1];
-      real_t(*B)[MD1] = (real_t(*)[MD1])(BG + 0);
-      real_t(*G)[MD1] = (real_t(*)[MD1])(BG + 1);
-      real_t(*Bt)[MQ1] = (real_t(*)[MQ1])(BG + 0);
-      MFEM_SHARED real_t U[2][MQ1][MQ1][MQ1];
-      MFEM_SHARED real_t sm0[3][MQ1 * MQ1 * MQ1];
-      MFEM_SHARED real_t sm1[3][MQ1 * MQ1 * MQ1];
-      real_t(*DDQ0)[MD1][MQ1] = (real_t(*)[MD1][MQ1])(sm0 + 0);
-      real_t(*DDQ1)[MD1][MQ1] = (real_t(*)[MD1][MQ1])(sm0 + 1);
-      real_t(*X)[MD1][MD1] = (real_t(*)[MD1][MD1])(sm0 + 2);
-      real_t(*DQQ0)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm1 + 0);
-      real_t(*DQQ1)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm1 + 1);
-      real_t(*DQQ2)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm1 + 2);
-      real_t(*QQQ0)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm0 + 0);
-      real_t(*QQQ1)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm0 + 1);
-      real_t(*QQQ2)[MQ1][MQ1] = (real_t(*)[MQ1][MQ1])(sm0 + 2);
-      real_t(*QQD0)[MQ1][MD1] = (real_t(*)[MQ1][MD1])(sm1 + 0);
-      real_t(*QDD0)[MD1][MD1] = (real_t(*)[MD1][MD1])(sm0 + 0);
-      MFEM_SHARED real_t Z[MQ1][MQ1][MQ1];
-
-      for (int cy = 0; cy < VDIM; ++cy)
-      {
-         if (tidz == 0)
-         {
-            MFEM_FOREACH_THREAD(q, x, Q1D)
-            {
-               MFEM_FOREACH_THREAD(d, y, D1D)
-               {
-                  B[q][d] = b(q, d);
-                  G[q][d] = g(q, d);
-               }
-            }
-         }
-         MFEM_FOREACH_THREAD(qz, z, Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy, y, Q1D)
-            {
-               MFEM_FOREACH_THREAD(qx, x, Q1D) { Z[qz][qy][qx] = 0.0; }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         for (int c = 0; c < VDIM; ++c)
-         {
-            MFEM_FOREACH_THREAD(dz, z, D1D)
-            {
-               MFEM_FOREACH_THREAD(dy, y, D1D)
-               {
-                  MFEM_FOREACH_THREAD(dx, x, D1D)
-                  {
-                     X[dz][dy][dx] = x(dx, dy, dz, cy, e);
-                     U[0][dz][dy][dx] = x(dx, dy, dz, c, e);
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-            MFEM_FOREACH_THREAD(dz, z, D1D)
-            {
-               MFEM_FOREACH_THREAD(dy, y, D1D)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, Q1D)
-                  {
-                     real_t u = 0.0;
-                     real_t v = 0.0;
-                     real_t z = 0.0;
-                     for (int dx = 0; dx < D1D; ++dx)
-                     {
-                        const real_t coord = X[dz][dy][dx];
-                        const real_t value = U[0][dz][dy][dx];
-                        u += coord * B[qx][dx];
-                        v += coord * G[qx][dx];
-                        z += value * B[qx][dx];
-                     }
-                     DDQ0[dz][dy][qx] = u;
-                     DDQ1[dz][dy][qx] = v;
-                     U[1][dz][dy][qx] = z;
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-            MFEM_FOREACH_THREAD(dz, z, D1D)
-            {
-               MFEM_FOREACH_THREAD(qy, y, Q1D)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, Q1D)
-                  {
-                     real_t u = 0.0;
-                     real_t v = 0.0;
-                     real_t w = 0.0;
-                     real_t z = 0.0;
-                     for (int dy = 0; dy < D1D; ++dy)
-                     {
-                        u += DDQ1[dz][dy][qx] * B[qy][dy];
-                        v += DDQ0[dz][dy][qx] * G[qy][dy];
-                        w += DDQ0[dz][dy][qx] * B[qy][dy];
-                        z += U[1][dz][dy][qx] * B[qy][dy];
-                     }
-                     DQQ0[dz][qy][qx] = u;
-                     DQQ1[dz][qy][qx] = v;
-                     DQQ2[dz][qy][qx] = w;
-                     U[0][dz][qy][qx] = z;
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-            MFEM_FOREACH_THREAD(qz, z, Q1D)
-            {
-               MFEM_FOREACH_THREAD(qy, y, Q1D)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, Q1D)
-                  {
-                     real_t u = 0.0;
-                     real_t v = 0.0;
-                     real_t w = 0.0;
-                     real_t z = 0.0;
-                     for (int dz = 0; dz < D1D; ++dz)
-                     {
-                        u += DQQ0[dz][qy][qx] * B[qz][dz];
-                        v += DQQ1[dz][qy][qx] * B[qz][dz];
-                        w += DQQ2[dz][qy][qx] * G[qz][dz];
-                        z += U[0][dz][qy][qx] * B[qz][dz];
-                     }
-                     QQQ0[qz][qy][qx] = u;
-                     QQQ1[qz][qy][qx] = v;
-                     QQQ2[qz][qy][qx] = w;
-                     U[1][qz][qy][qx] = z;
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-            MFEM_FOREACH_THREAD(qz, z, Q1D)
-            {
-               MFEM_FOREACH_THREAD(qy, y, Q1D)
-               {
-                  MFEM_FOREACH_THREAD(qx, x, Q1D)
-                  {
-                     const int q = qx + (qy + qz * Q1D) * Q1D;
-                     const real_t z = U[1][qz][qy][qx];
-                     const real_t gX = QQQ0[qz][qy][qx];
-                     const real_t gY = QQQ1[qz][qy][qx];
-                     const real_t gZ = QQQ2[qz][qy][qx];
-                     const real_t d = gX * D(q, 0, c, e) + gY * D(q, 1, c, e)
-                                      + gZ * D(q, 2, c, e);
-                     Z[qz][qy][qx] += z * d;
-                  }
-               }
-            }
-            MFEM_SYNC_THREAD;
-         } // for each conv component
-         if (tidz == 0)
-         {
-            MFEM_FOREACH_THREAD(d, y, D1D)
-            {
-               MFEM_FOREACH_THREAD(q, x, Q1D) { Bt[d][q] = b(q, d); }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qz, z, Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy, y, Q1D)
-            {
-               MFEM_FOREACH_THREAD(dx, x, D1D)
-               {
-                  real_t u = 0.0;
-                  for (int qx = 0; qx < Q1D; ++qx)
-                  {
-                     u += Z[qz][qy][qx] * Bt[dx][qx];
-                  }
-                  QQD0[qz][qy][dx] = u;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qz, z, Q1D)
-         {
-            MFEM_FOREACH_THREAD(dy, y, D1D)
-            {
-               MFEM_FOREACH_THREAD(dx, x, D1D)
-               {
-                  real_t u = 0.0;
-                  for (int qy = 0; qy < Q1D; ++qy)
-                  {
-                     u += QQD0[qz][qy][dx] * Bt[dy][qy];
-                  }
-                  QDD0[qz][dy][dx] = u;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dz, z, D1D)
-         {
-            MFEM_FOREACH_THREAD(dy, y, D1D)
-            {
-               MFEM_FOREACH_THREAD(dx, x, D1D)
-               {
-                  real_t u = 0.0;
-                  for (int qz = 0; qz < Q1D; ++qz)
-                  {
-                     u += QDD0[qz][dy][dx] * Bt[dz][qz];
-                  }
-                  Y(dx, dy, dz, cy, e) += u;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
+      MFEM_ABORT("dim " << dim << " not supported!");
+   }
 }
 
 void VectorConvectionNLFIntegrator::AddMultPA(const Vector &x, Vector &y) const
@@ -812,26 +197,13 @@ void VectorConvectionNLFIntegrator::AddMultPA(const Vector &x, Vector &y) const
    }
    else
    {
-      const int NE = ne;
-      const int D1D = maps->ndof;
-      const int Q1D = maps->nqpt;
-      const Vector &QV = pa_data;
-      const Array<real_t> &B = maps->B;
-      const Array<real_t> &G = maps->G;
-      const Array<real_t> &Bt = maps->Bt;
-      if (dim == 2)
-      {
-         return PAConvectionNLApply2D(NE, B, G, Bt, QV, x, y, D1D, Q1D);
-      }
-      if (dim == 3)
-      {
-         constexpr int T_MAX_D1D = 8;
-         constexpr int T_MAX_Q1D = 8;
-         MFEM_VERIFY(D1D <= T_MAX_D1D && Q1D <= T_MAX_Q1D, "Not yet implemented!");
-         return SmemPAConvectionNLApply3D<0, 0, T_MAX_D1D, T_MAX_Q1D>
-                (NE, B, G, QV, x, y, D1D, Q1D);
-      }
-      MFEM_ABORT("Not yet implemented!");
+      AddMultPAKernels::Run(dim, d1d, q1d, ne,
+                            maps->B.Read(),
+                            maps->G.Read(),
+                            pa_adj.Read(),
+                            x.Read(),
+                            y.ReadWrite(),
+                            d1d, q1d);
    }
 }
 

fem/integ/nonlininteg_vecconvection_pa.hpp

@@ -0,0 +1,209 @@
+// 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.
+#pragma once
+
+#include "../../config/config.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../kernels.hpp"
+#include "../nonlininteg.hpp"
+
+namespace mfem
+{
+
+/// \cond DO_NOT_DOCUMENT
+
+namespace internal
+{
+
+// PA Convection NL 2D kernel
+template<int T_D1D = 0, int T_Q1D = 0>
+inline void SmemPAConvectionNLApply2D(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 = 0,
+                                      const int q1d = 0)
+{
+   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 B = Reshape(b, Q1D, D1D);
+   const auto G = Reshape(g, Q1D, D1D);
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, NE);
+   const auto X = Reshape(x, 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1], sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::vd_regs2d_t<VDIM, DIM, MQ1> g0, g1;
+      kernels::internal::v_regs2d_t<VDIM, MQ1> r0, r1;
+      kernels::internal::v_regs2d_t<VDIM, MQ1> s0, s1;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, G, sG);
+
+      kernels::internal::LoadDofs2d(e, D1D, X, r0);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, r0, r1); // u vector-value
+      kernels::internal::LoadDofs2d(e, D1D, X, g0);
+      kernels::internal::Grad2d(D1D, Q1D, smem, sB, sG, g0, g1); // u vector-gradient
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const future::tensor<real_t, 2> U =
+            {
+               r1[0][qy][qx], r1[1][qy][qx]
+            };
+            const future::tensor<real_t, 2,2> gradU = {{
+                  {g1[0][0][qy][qx], g1[1][0][qy][qx]},
+                  {g1[0][1][qy][qx], g1[1][1][qy][qx]},
+               }
+            };
+            const future::tensor<real_t, 2,2> Q = {{
+                  {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, 2> conv = transpose(gradU) * (Q * U);
+            s0[0][qy][qx] = conv[0];
+            s0[1][qy][qx] = conv[1];
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, s0, s1);
+      kernels::internal::WriteDofs2d(e, D1D, s1, Y);
+   });
+}
+
+// PA Convection NL 3D kernel
+template<int T_D1D = 0, int T_Q1D = 0>
+inline void SmemPAConvectionNLApply3D(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 = 0,
+                                      const int q1d = 0)
+{
+   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 B = Reshape(b, Q1D, D1D);
+   const auto G = Reshape(g, Q1D, D1D);
+   const auto A = Reshape(a, VDIM, DIM, Q1D, Q1D, Q1D, NE);
+   const auto X = Reshape(x, 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      MFEM_SHARED real_t smem[MQ1][MQ1], sB[MD1][MQ1], sG[MD1][MQ1];
+
+      kernels::internal::vd_regs3d_t<VDIM, DIM, MQ1> g0, g1;
+      kernels::internal::v_regs3d_t<VDIM, MQ1> r0, r1;
+      kernels::internal::v_regs3d_t<VDIM, MQ1> s0, s1;
+
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB);
+      kernels::internal::LoadMatrix(D1D, Q1D, G, sG);
+
+      kernels::internal::LoadDofs3d(e, D1D, X, r0);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, r0, r1); // u vector-value
+      kernels::internal::LoadDofs3d(e, D1D, X, g0);
+      kernels::internal::Grad3d(D1D, Q1D, smem, sB, sG, g0, g1); // u vector-gradient
+
+      for (int qz = 0; qz < Q1D; qz++)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const future::tensor<real_t, 3> U =
+               {
+                  r1[0][qz][qy][qx], r1[1][qz][qy][qx], r1[2][qz][qy][qx]
+               };
+               const future::tensor<real_t, 3,3> gradU = {{
+                     {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 future::tensor<real_t, 3,3> Q = {{
+                     {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, 3> conv = transpose(gradU) * (Q * U);
+               s0[0][qz][qy][qx] = conv[0];
+               s0[1][qz][qy][qx] = conv[1];
+               s0[2][qz][qy][qx] = conv[2];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, s0, s1);
+      kernels::internal::WriteDofs3d(e, D1D, s1, Y);
+   });
+}
+
+} // namespace internal
+
+template<int DIM, int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::AddMultPAType
+VectorConvectionNLFIntegrator::AddMultPAKernels::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   if constexpr (DIM == 2)
+   {
+      return internal::SmemPAConvectionNLApply2D<T_D1D, T_Q1D>;
+   }
+   else if constexpr (DIM == 3)
+   {
+      return internal::SmemPAConvectionNLApply3D<T_D1D, T_Q1D>;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+inline VectorConvectionNLFIntegrator::AddMultPAType
+VectorConvectionNLFIntegrator::AddMultPAKernels::Fallback
+(int dim, int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   if (dim == 2)
+   {
+      return internal::SmemPAConvectionNLApply2D<>;
+   }
+   else if (dim == 3)
+   {
+      return internal::SmemPAConvectionNLApply3D<>;
+   }
+   MFEM_ABORT("Unsupported kernel");
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/integ/nonlininteg_vecconvection_pa_diag.cpp

@@ -0,0 +1,50 @@
+// 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 "../ceed/interface/util.hpp"
+#include "./nonlininteg_vecconvection_pa_diag.hpp" // IWYU pragma: keep
+
+namespace mfem
+{
+
+void VectorConvectionNLFIntegrator::AssembleGradDiagonalPA(Vector &de) const
+{
+   MFEM_VERIFY(!DeviceCanUseCeed(),
+               "VectorConvectionNLFIntegrator PA gradients are not supported "
+               "with the libCEED backend");
+
+   if (dim == 2)
+   {
+      GradDiagPA2D::Run(d1d, q1d, ne,
+                        maps->B.Read(),
+                        maps->G.Read(),
+                        pa_adj.Read(),
+                        pa_u.Read(),
+                        de.ReadWrite(),
+                        d1d, q1d);
+   }
+   else if (dim == 3)
+   {
+      GradDiagPA3D::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");
+   }
+}
+
+} // namespace mfem

fem/integ/nonlininteg_vecconvection_pa_diag.hpp

@@ -0,0 +1,302 @@
+// 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.
+#pragma once
+
+#include "../../config/config.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../kernels.hpp"
+#include "../nonlininteg.hpp"
+
+namespace mfem
+{
+
+/// \cond DO_NOT_DOCUMENT
+
+namespace internal
+{
+
+template<int T_D1D = 0, int T_Q1D = 0>
+inline 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      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>
+inline 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      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;
+         }
+      }
+   });
+}
+
+} // namespace internal
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::GradDiagPAType
+VectorConvectionNLFIntegrator::GradDiagPA2D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return internal::SmemPAConvectionNLGradDiagonal2D<T_D1D, T_Q1D>;
+}
+
+inline VectorConvectionNLFIntegrator::GradDiagPAType
+VectorConvectionNLFIntegrator::GradDiagPA2D::Fallback(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   return internal::SmemPAConvectionNLGradDiagonal2D<>;
+}
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::GradDiagPAType
+VectorConvectionNLFIntegrator::GradDiagPA3D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return internal::SmemPAConvectionNLGradDiagonal3D<T_D1D, T_Q1D>;
+}
+
+inline VectorConvectionNLFIntegrator::GradDiagPAType
+VectorConvectionNLFIntegrator::GradDiagPA3D::Fallback(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   return internal::SmemPAConvectionNLGradDiagonal3D<>;
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/integ/nonlininteg_vecconvection_pa_grad.cpp

@@ -0,0 +1,64 @@
+// 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 "../ceed/interface/util.hpp"
+#include "./nonlininteg_vecconvection_pa_grad.hpp" // IWYU pragma: keep
+
+namespace mfem
+{
+
+void VectorConvectionNLFIntegrator::AssembleGradPA(
+   const Vector &u, const FiniteElementSpace &fes)
+{
+   MFEM_VERIFY(!DeviceCanUseCeed(),
+               "VectorConvectionNLFIntegrator PA gradients are not supported "
+               "with the libCEED backend");
+
+   this->pa_u = u;
+   AssemblePA(fes);
+}
+
+void VectorConvectionNLFIntegrator::AddMultGradPA(const Vector &x,
+                                                  Vector &y) const
+{
+   MFEM_VERIFY(!DeviceCanUseCeed(),
+               "VectorConvectionNLFIntegrator PA gradients are not supported "
+               "with the libCEED backend");
+
+   if (dim == 2)
+   {
+      AddMultGradPA2D::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)
+   {
+      AddMultGradPA3D::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");
+   }
+}
+
+} // namespace mfem

fem/integ/nonlininteg_vecconvection_pa_grad.hpp

@@ -0,0 +1,257 @@
+// 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.
+#pragma once
+
+#include "../../config/config.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../kernels.hpp"
+#include "../nonlininteg.hpp"
+
+namespace mfem
+{
+
+/// \cond DO_NOT_DOCUMENT
+
+namespace internal
+{
+
+template<int T_D1D = 0, int T_Q1D = 0>
+inline 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      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>
+inline 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 : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+
+      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);
+   });
+}
+
+} // namespace internal
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::AddMultGradPAType
+VectorConvectionNLFIntegrator::AddMultGradPA2D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return internal::SmemPAConvectionNLGradApply2D<T_D1D, T_Q1D>;
+}
+
+inline VectorConvectionNLFIntegrator::AddMultGradPAType
+VectorConvectionNLFIntegrator::AddMultGradPA2D::Fallback(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   return internal::SmemPAConvectionNLGradApply2D<>;
+}
+
+template<int T_D1D, int T_Q1D>
+VectorConvectionNLFIntegrator::AddMultGradPAType
+VectorConvectionNLFIntegrator::AddMultGradPA3D::Kernel()
+{
+   static_assert(T_D1D <= T_Q1D, "d1d > q1d is not supported");
+   return internal::SmemPAConvectionNLGradApply3D<T_D1D, T_Q1D>;
+}
+
+inline VectorConvectionNLFIntegrator::AddMultGradPAType
+VectorConvectionNLFIntegrator::AddMultGradPA3D::Fallback(int d1d, int q1d)
+{
+   MFEM_VERIFY(d1d <= q1d, "d1d > q1d is not supported");
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+   return internal::SmemPAConvectionNLGradApply3D<>;
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
+} // namespace mfem

fem/intrules.cpp

@@ -236,6 +236,58 @@ IntegrationRule::ApplyToKnotIntervals(KnotVector const& kv) const
    return kvir;
 }
 
+IntegrationRule IntegrationRule::Reorder(const Array<int> &ordering) const
+{
+   const int np = GetNPoints();
+   MFEM_VERIFY(np == ordering.Size(), "Invalid permutation size");
+   IntegrationRule ir(np);
+   ir.SetOrder(GetOrder());
+
+   for (int i = 0; i < np; i++)
+   {
+      IntegrationPoint &ip_new = ir.IntPoint(i);
+      const IntegrationPoint &ip_old = IntPoint(ordering[i]);
+      ip_new.Set(ip_old.x, ip_old.y, ip_old.z, ip_old.weight);
+   }
+
+   return ir;
+}
+
+IntegrationRule DuffyTrans(const IntegrationRule &ir, int dim)
+{
+   IntegrationRule ir_mapped(ir.GetNPoints());
+   ir_mapped.SetOrder(ir.GetOrder());
+
+   if (dim == 2)
+   {
+      for (int i = 0; i < ir.GetNPoints(); i++)
+      {
+         IntegrationPoint &ip_mapped = ir_mapped.IntPoint(i);
+         ip_mapped.y = ir.IntPoint(i).y * (1 - ir.IntPoint(i).x);
+         ip_mapped.x = ir.IntPoint(i).x;
+         ip_mapped.weight = ir.IntPoint(i).weight;
+      }
+      return ir_mapped;
+   }
+   else if (dim == 3)
+   {
+      for (int i = 0; i < ir.GetNPoints(); i++)
+      {
+         IntegrationPoint &ip_mapped = ir_mapped.IntPoint(i);
+         ip_mapped.z = ir.IntPoint(i).z * (1 - ir.IntPoint(i).x) * (1 - ir.IntPoint(
+                                                                       i).y);
+         ip_mapped.y = ir.IntPoint(i).y * (1 - ir.IntPoint(i).x);
+         ip_mapped.x = ir.IntPoint(i).x;
+         ip_mapped.weight = ir.IntPoint(i).weight;
+      }
+      return ir_mapped;
+   }
+   else
+   {
+      MFEM_ABORT("Duffy transformation not implemented for this dimension!");
+   }
+}
+
 #ifdef MFEM_USE_MPFR
 
 // Class for computing hi-precision (HP) quadrature in 1D
@@ -433,6 +485,138 @@ public:
 #endif // MFEM_USE_MPFR
 
 
+void QuadratureFunctions1D::GaussJacobi(const int np, const real_t alpha,
+                                        const real_t beta, IntegrationRule* ir)
+{
+   /* The np-point Gauss-Jacobi quadrature rule is exact for polynomials of
+      degree 2np - 1 with weight function w(x) = (1-x)^alpha * x^beta. The
+      nodes are the zeros of the Jacobi polynomial P_{np}^{alpha,beta} and
+      the weights are
+
+      w_i = C / [(1 - x_i^2) * P'_{np}^{alpha,beta}(x_i)^2]
+      C = 2^{alpha + beta + 1} * Gamma(np + alpha + 1) * Gamma(np + beta + 1)
+            / [Gamma(np + alpha + beta + 1) * Gamma(np + 1)].
+
+      The nodes are computed via nonlinear solve (Newton's method) with an
+      initial guess corresponding to Gatteschi's asymptotic expansions of the
+      Jacobi polynomial roots [1].
+
+      The current initial guess has been tested and performs well for
+      np <= 200 and -1 <= alpha, beta <= 4. For larger np, it may be necessary
+      utilize different initial guesses in the vicinity of x = -1,+1 [2].
+
+      [1] Gautschi, W., & Giordano, C. (2008). Luigi Gatteschi’s work on
+          asymptotics of special functions and their zeros. Numerical Algorithms,
+          49, 11-31.
+      [2] Hale, N., & Townsend, A. (2013). Fast and accurate computation of
+          Gauss--Legendre and Gauss--Jacobi quadrature nodes and weights.
+          SIAM Journal on Scientific Computing, 35(2), A652-A674.
+   */
+   ir->SetSize(np);
+   ir->SetPointIndices();
+   ir->SetOrder(2*np - 1);
+
+   if (alpha <= -1.0 || beta <= -1.0)
+   {
+      MFEM_ABORT("Gauss-Jacobi quadrature only defined for alpha > -1 and beta > -1");
+   }
+   // Jacobi weight function is undefined whenever alpha <= -1 or beta <= -1
+
+   if (alpha > 4.0 || beta > 4.0)
+   {
+      MFEM_ABORT("Current Gauss-Jacobi quadrature implementation only tested for alpha <= 4 and beta <= 4");
+   }
+   // current asymptotic expansions for initial guess may perform poorly for large alpha, beta
+
+   switch (np)
+   {
+      case 1:
+         real_t x = (beta - alpha) / (alpha + beta + 2);
+         real_t w = pow(2, alpha + beta + 1) * tgamma(alpha + 2) * tgamma(
+                       beta + 2) / (tgamma(alpha + beta + 2));
+         w = 0.5 * w / pow(2, alpha + beta);
+         // map weight to  to [0,1], with additional 1/(2^(alpha + beta)) factor coming from mapping
+         // the weight (1-x)^alpha * (1+x)^beta to [0,1] as well.
+         ir->IntPoint(0).Set1w(0.5 * x + 0.5,
+                               4.0 * w / ((1.0 - x*x) * (alpha + beta + 2) * (alpha + beta + 2)));
+         return;
+   }
+
+#ifdef MFEM_USE_MPFR
+   MFEM_WARNING("MPFR implementation of Gauss-Jacobi quadrature not implemented yet. Falling "
+                "back to double precision implementation...");
+#endif
+
+   const int n = np;
+   // common constants for Jacobi polynomials
+   real_t ab = alpha + beta;
+   real_t a2_minus_b2 = (alpha - beta) * (alpha + beta);
+
+   // roots of P^(alpha,beta)_n in the interval [-1,1]
+   for (int i = 1; i <= n; i++)
+   {
+      // rather than using Chebyshev points for initial guess, use Gatteschi's asymptotic expansion for roots of Jacobi
+      // polynomials
+      real_t n_ab_plus_1 = 2 * n + alpha + beta + 1;
+      real_t v = (2 * i + alpha - 0.5) * M_PI / n_ab_plus_1;
+      real_t theta = v + 1.0 / (n_ab_plus_1*n_ab_plus_1) * ((0.25 - alpha*alpha) *
+                                                            1.0/tan(0.5*v) - (0.25 - beta*beta) * tan(0.5*v));
+      real_t z = cos(theta);
+
+      real_t pp, p1, dz, xi = 0.;
+      bool done = false;
+      while (1)
+      {
+         real_t p2 = 1;
+         p1 = ((alpha-beta) + (alpha + beta + 2) * z) / 2;
+         for (int j = 1; j <= n-1; j++)
+         {
+            real_t p3 = p2;
+            p2 = p1;
+
+            real_t jx2_ab = 2 * j + ab;
+            real_t an = (jx2_ab) * (jx2_ab + 2);
+            real_t bn = a2_minus_b2;
+            real_t cn = 2 * (j + alpha) * (j + beta) * (jx2_ab + 2) / (jx2_ab + 1);
+
+            real_t D = (jx2_ab + 1) / (2 * (j + 1) * (j + ab + 1) * (jx2_ab));
+            p1 = ((an * z + bn) * p2 - cn * p3) * D;
+         }
+         // p1 is Jacobi polynomial
+         pp = n * (alpha - beta - (2 * n + ab) * z) * p1 + 2 * (n + alpha) *
+              (n + beta) * p2;
+         pp = pp / ((2 * n + ab) * (1 - z*z));
+         // derivative of the Jacobi polynomial
+         if (done) { break; }
+
+         dz = p1/pp;
+#ifdef MFEM_USE_SINGLE
+         if (std::abs(dz) < 1e-7)
+#elif defined MFEM_USE_DOUBLE
+         if (std::abs(dz) < std::numeric_limits<real_t>::epsilon())
+            // this seems to cause trouble if we try std::abs(dz) < 1e-16
+#else
+         MFEM_ABORT("Floating point type undefined");
+         // if (std::abs(dz) < 1e-16)
+#endif
+         {
+            done = true;
+            xi = z - dz;
+         }
+         z -= dz;
+      }
+      real_t c0 = exp(lgamma(n + alpha + 1) - lgamma(n + ab + 1)) * exp(lgamma(
+                                                                           n + beta + 1) - lgamma(n + 1));
+      // ratio of gamma functions prone to overflow for large n, so compute logarithms
+      // of Gamma function instead, i.e. Gamma(a)/Gamma(b) = exp(lgamma(a) - lgamma(b))
+      ir->IntPoint(n-i).x = 0.5 * xi + 0.5;
+      ir->IntPoint(n-i).weight = 0.5 * c0 * pow(2.0,
+                                                ab + 1) / ((1.0 - xi*xi)*pp*pp) / pow(2, ab);
+      // map nodes and weights to the interval [0,1]
+   }
+}
+
+
 void QuadratureFunctions1D::GaussLegendre(const int np, IntegrationRule* ir)
 {
    ir->SetSize(np);
@@ -2362,6 +2546,194 @@ IntegrationRule *IntegrationRules::CubeIntegrationRule(int Order)
    return CubeIntRules[Order];
 }
 
+StroudIntegrationRules StroudIntRules;
+
+StroudIntegrationRules::StroudIntegrationRules()
+{
+   const MemoryType h_mt = MemoryType::HOST;
+   SquareStroudIntRules.SetSize(32, h_mt);
+   SquareStroudIntRules = NULL;
+
+   TriangleStroudIntRules.SetSize(32, h_mt);
+   TriangleStroudIntRules = NULL;
+
+   CubeStroudIntRules.SetSize(32, h_mt);
+   CubeStroudIntRules = NULL;
+
+   TetrahedronStroudIntRules.SetSize(32, h_mt);
+   TetrahedronStroudIntRules = NULL;
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   IntRuleLocks.SetSize(Geometry::NUM_GEOMETRIES, h_mt);
+   for (int i = 0; i < Geometry::NUM_GEOMETRIES; i++)
+   {
+      omp_init_lock(&IntRuleLocks[i]);
+   }
+#endif
+}
+
+const IntegrationRule &StroudIntegrationRules::Get(int GeomType, int Order)
+{
+   Array<IntegrationRule *> *ir_array = NULL;
+
+   switch (GeomType)
+   {
+      case Geometry::TRIANGLE:    ir_array = &TriangleStroudIntRules; break;
+      case Geometry::TETRAHEDRON: ir_array = &TetrahedronStroudIntRules; break;
+      case Geometry::INVALID:
+      case Geometry::NUM_GEOMETRIES:
+         MFEM_ABORT("Unknown type of reference element!");
+      default:
+         MFEM_ABORT("Stroud rules only valid for triangular and tetrahedral elements!");
+   }
+
+   if (Order < 0)
+   {
+      Order = 0;
+   }
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   omp_set_lock(&IntRuleLocks[GeomType]);
+#endif
+
+   if (!HaveIntRule(*ir_array, Order))
+   {
+      IntegrationRule *ir = GenerateIntegrationRule(GeomType, Order);
+#ifdef MFEM_DEBUG
+      int RealOrder = Order;
+      while (RealOrder+1 < ir_array->Size() && (*ir_array)[RealOrder+1] == ir)
+      {
+         RealOrder++;
+      }
+      MFEM_VERIFY(RealOrder == ir->GetOrder(), "internal error");
+#else
+      MFEM_CONTRACT_VAR(ir);
+#endif
+   }
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   omp_unset_lock(&IntRuleLocks[GeomType]);
+#endif
+
+   return *(*ir_array)[Order];
+}
+
+void StroudIntegrationRules::DeleteIntRuleArray(
+   Array<IntegrationRule *> &ir_array) const
+{
+   // Many of the intrules have multiple contiguous copies in the ir_array
+   // so we have to be careful to not delete them twice.
+   IntegrationRule *ir = NULL;
+   for (int i = 0; i < ir_array.Size(); i++)
+   {
+      if (ir_array[i] != NULL && ir_array[i] != ir)
+      {
+         ir = ir_array[i];
+         delete ir;
+      }
+   }
+}
+
+StroudIntegrationRules::~StroudIntegrationRules()
+{
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   for (int i = 0; i < Geometry::NUM_GEOMETRIES; i++)
+   {
+      omp_destroy_lock(&IntRuleLocks[i]);
+   }
+#endif
+   DeleteIntRuleArray(SquareStroudIntRules);
+   DeleteIntRuleArray(TriangleStroudIntRules);
+   DeleteIntRuleArray(CubeStroudIntRules);
+   DeleteIntRuleArray(TetrahedronStroudIntRules);
+}
+
+
+IntegrationRule *StroudIntegrationRules::GenerateIntegrationRule(int GeomType,
+                                                                 int Order)
+{
+   switch (GeomType)
+   {
+      case Geometry::TRIANGLE:
+         return TriangleStroudIntegrationRule(Order);
+      case Geometry::TETRAHEDRON:
+         return TetrahedronStroudIntegrationRule(Order);
+      case Geometry::INVALID:
+      case Geometry::NUM_GEOMETRIES:
+         MFEM_ABORT("Unknown type of reference element!");
+      default:
+         MFEM_ABORT("Stroud rules only valid for triangular and tetrahedral elements!");
+   }
+   return NULL;
+}
+
+/* Integration rule in reference triangle according to tensor product Gauss-Jacobi rule.
+  The nodes and weights are used in the original form defined on the reference
+  square to evaluate the component 1D basis functions. Mapping to the reference
+  triangle via IntegrationRule::DuffyTrans() occurs only in evaluation of coefficient
+  vectors, see e.g. MassIntegrator::AssemblePASimplex. */
+IntegrationRule *StroudIntegrationRules::TriangleStroudIntegrationRule(
+   int Order)
+{
+   int RealOrder = GetSegmentRealOrder(Order);
+   // Order is one of {RealOrder-1,RealOrder}
+   // if (!HaveIntRule(SegmentIntRules, RealOrder))
+   // {
+   //    SegmentIntegrationRule(RealOrder);
+   // }
+   IntegrationRule ir_0_0;
+   // Gauss-Jacobi is exact for 2*n-1
+   int n = RealOrder/2 + 1;
+   QuadratureFunctions1D::GaussJacobi(n, 0.0, 0.0, &ir_0_0);
+
+   IntegrationRule ir_1_0;
+   QuadratureFunctions1D::GaussJacobi(n, 1.0, 0.0, &ir_1_0);
+
+   AllocIntRule(TriangleStroudIntRules, RealOrder); // RealOrder >= Order
+   // create rule in unit square
+   TriangleStroudIntRules[RealOrder-1] =
+      TriangleStroudIntRules[RealOrder] =
+         new IntegrationRule(ir_1_0, ir_0_0);
+   // map rule to reference triangle
+   // TriangleStroudIntRules[RealOrder-1]->DuffyTrans(2);
+   *TriangleStroudIntRules[RealOrder-1] =
+      DuffyTrans(*TriangleStroudIntRules[RealOrder-1], 2);
+   return TriangleStroudIntRules[Order];
+}
+
+/* Integration rule in reference tetrahedron according to tensor product Gauss-Jacobi rule.
+  The nodes and weights are used in the original form defined on the reference
+  square to evaluate the component 1D basis functions. Mapping to the reference
+  triangle via IntegrationRule::DuffyTrans() occurs only in evaluation of coefficient
+  vectors, see e.g. MassIntegrator::AssemblePASimplex. */
+IntegrationRule *StroudIntegrationRules::TetrahedronStroudIntegrationRule(
+   int Order)
+{
+   int RealOrder = GetSegmentRealOrder(Order);
+   // Order is one of {RealOrder-1,RealOrder}
+
+   IntegrationRule ir_0_0;
+   int n = RealOrder/2 + 1;
+   QuadratureFunctions1D::GaussJacobi(n, 0.0, 0.0, &ir_0_0);
+
+   IntegrationRule ir_1_0;
+   QuadratureFunctions1D::GaussJacobi(n, 1.0, 0.0, &ir_1_0);
+
+   IntegrationRule ir_2_0;
+   QuadratureFunctions1D::GaussJacobi(n, 2.0, 0.0, &ir_2_0);
+
+   AllocIntRule(TetrahedronStroudIntRules, RealOrder); // RealOrder >= Order
+   // create rule in unit cube
+   TetrahedronStroudIntRules[RealOrder-1] =
+      TetrahedronStroudIntRules[RealOrder] =
+         new IntegrationRule(ir_2_0, ir_1_0, ir_0_0);
+   // map rule to reference tetrahedron
+   // TetrahedronStroudIntRules[RealOrder-1]->DuffyTrans(3);
+   *TetrahedronStroudIntRules[RealOrder-1] =
+      DuffyTrans(*TetrahedronStroudIntRules[RealOrder-1], 3);
+   return TetrahedronStroudIntRules[Order];
+}
+
 IntegrationRule& NURBSMeshRules::GetElementRule(const int elem,
                                                 const int patch, const int *ijk,
                                                 Array<const KnotVector*> const& kv) const

fem/intrules.hpp

@@ -269,6 +269,13 @@ public:
    /// applying this rule on each knot interval.
    IntegrationRule* ApplyToKnotIntervals(KnotVector const& kv) const;
 
+   /** @brief  Returns an integration rule such that the new IntegrationPoints
+    *  are re-ordered based on @a ordering.
+    *
+    *  @details In the new integration rule, ip_new[i] = ip_old[ordering[i]]
+    */
+   IntegrationRule Reorder(const Array<int> &ordering) const;
+
    /// Destroys an IntegrationRule object
    ~IntegrationRule() { }
 };
@@ -378,6 +385,8 @@ public:
        These methods calculate the actual points and weights for the different
        types of quadrature rules. */
    ///@{
+   static void GaussJacobi(const int np, const real_t alpha, const real_t beta,
+                           IntegrationRule* ir);
    static void GaussLegendre(const int np, IntegrationRule* ir);
    static void GaussLobatto(const int np, IntegrationRule *ir);
    static void OpenUniform(const int np, IntegrationRule *ir);
@@ -487,12 +496,71 @@ public:
    ~IntegrationRules();
 };
 
+/// Container class for integration rules
+class StroudIntegrationRules
+{
+private:
+   Array<IntegrationRule *> SquareStroudIntRules;
+   Array<IntegrationRule *> TriangleStroudIntRules;
+   Array<IntegrationRule *> CubeStroudIntRules;
+   Array<IntegrationRule *> TetrahedronStroudIntRules;
+
+#if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
+   Array<omp_lock_t> IntRuleLocks;
+#endif
+
+   void AllocIntRule(Array<IntegrationRule *> &ir_array, int Order) const
+   {
+      if (ir_array.Size() <= Order)
+      {
+         ir_array.SetSize(Order + 1, NULL);
+      }
+   }
+   bool HaveIntRule(Array<IntegrationRule *> &ir_array, int Order) const
+   {
+      return (ir_array.Size() > Order && ir_array[Order] != NULL);
+   }
+   int GetSegmentRealOrder(int Order) const
+   {
+      return Order | 1; // valid for all quad_type's
+   }
+   void DeleteIntRuleArray(Array<IntegrationRule *> &ir_array) const;
+
+   /// The following methods allocate new IntegrationRule objects without
+   /// checking if they already exist.  To avoid memory leaks use
+   /// IntegrationRules::Get(int GeomType, int Order) instead.
+   IntegrationRule *GenerateIntegrationRule(int GeomType, int Order);
+   IntegrationRule *TriangleStroudIntegrationRule(int Order);
+   IntegrationRule *TetrahedronStroudIntegrationRule(int Order);
+
+public:
+   /// Sets initial sizes for the integration rule arrays, but rules
+   /// are defined the first time they are requested with the Get method.
+   explicit StroudIntegrationRules();
+
+   /// Returns a Stroud integration rule for given GeomType and Order.
+   const IntegrationRule &Get(int GeomType, int Order);
+
+   /// Destroys an StroudIntegrationRules object
+   ~StroudIntegrationRules();
+};
+
 /// A global object with all integration rules (defined in intrules.cpp)
 extern MFEM_EXPORT IntegrationRules IntRules;
 
 /// A global object with all refined integration rules
 extern MFEM_EXPORT IntegrationRules RefinedIntRules;
 
+/// A global object with all Stroud integration rules (defined in intrules.cpp)
+extern MFEM_EXPORT StroudIntegrationRules StroudIntRules;
+
+/// Duffy Transformation of 2D and 3D tensor product rules of the form
+/// $X(t) = \sum_{i=1}^{d+1} \lambda_i(t) * x_i$, where $x_i$ are the vertices
+/// of the simplex and $\lambda_i = t_i * (1-\lambda_1-...-\lambda_{i-1})$, with
+/// $t$ being the coordinates in the unit square/cube. This function is used only
+/// in the partial assembly of Bernstein elements on simplices and does NOT
+/// modify the quadrature weights.
+IntegrationRule DuffyTrans(const IntegrationRule &ir, int dim);
 }
 
 #endif

fem/kernel_dispatch.hpp

@@ -61,7 +61,7 @@ namespace mfem
 #define MFEM_REGISTER_KERNELS_1(KernelName, KernelType, Params)                \
    MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, (), Params)
 
-// Version of MFEM_REGISTER_KERNELS without any optional (non-dispatch)
+// Version of MFEM_REGISTER_KERNELS with optional (non-dispatch)
 // parameters (e.g. NBZ).
 #define MFEM_REGISTER_KERNELS_2(KernelName, KernelType, Params, OptParams)     \
    MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, OptParams,           \

fem/kernels.hpp

@@ -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;

fem/lininteg.cpp

@@ -471,6 +471,13 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    }
 }
 
+VectorFEDomainLFIntegrator::VectorFEDomainLFIntegrator(
+   VectorCoefficient &F, const IntegrationRule *ir)
+   : DeltaLFIntegrator(F, ir), QF(F)
+{
+   static Kernels kernels{};
+}
+
 void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {

fem/lininteg.hpp

@@ -369,8 +369,8 @@ private:
    Vector vec;
 
 public:
-   VectorFEDomainLFIntegrator(VectorCoefficient &F)
-      : DeltaLFIntegrator(F), QF(F) { }
+   VectorFEDomainLFIntegrator(VectorCoefficient &F,
+                              const IntegrationRule *ir = nullptr);
 
    void AssembleRHSElementVect(const FiniteElement &el,
                                ElementTransformation &Tr,
@@ -387,6 +387,40 @@ public:
                        Vector &b) override;
 
    using LinearFormIntegrator::AssembleRHSElementVect;
+
+   /// @param ne number of elements
+   /// @param markers array where entry markers[e] == 0 to skip assembly over
+   /// element e element
+   /// @param jac Spatial Jacobians evaluated at all quadrature points
+   /// @param weights 1D quadrature weights
+   /// @param testBO 1D open basis test functions
+   /// @param testBC 1D closed basis test functions
+   /// @param coeff coefficient values evaluated at quadrature points, possibly
+   /// compressed.
+   /// @param d number of 1D closed dofs
+   /// @param q number of 1D quadrature points
+   using AssembleKernelType = void (*)(const int NE, const Array<int> &markers,
+                                       const Vector &jac,
+                                       const Array<real_t> &weights,
+                                       const Array<real_t> &testBO,
+                                       const Array<real_t> &testBC,
+                                       const Vector &coeff, Vector &y,
+                                       const int testd1d, const int q1d);
+
+   /// parameters: test_fetype, ndims, test_d1d, q1d
+   MFEM_REGISTER_KERNELS(AssembleKernels, AssembleKernelType,
+                         (FiniteElement::DerivType, int, int, int));
+
+   struct Kernels
+   {
+      Kernels();
+   };
+
+   template <FiniteElement::DerivType TestType, int DIM, int TEST_D1D, int Q1D>
+   static void AddSpecialization()
+   {
+      AssembleKernels::Specialization<TestType, DIM, TEST_D1D, Q1D>::Add();
+   }
 };
 
 /// $ (Q, \mathrm{curl}(v))_{\Omega} $ for Nedelec Elements

fem/nonlinearform_ext.cpp

@@ -100,6 +100,17 @@ PANonlinearFormExtension::Gradient::Gradient(const PANonlinearFormExtension &e):
 
 void PANonlinearFormExtension::Gradient::AssembleGrad(const Vector &g)
 {
+   if (DeviceCanUseCeed())
+   {
+      for (int i = 0; i < ext.dnfi.Size(); ++i)
+      {
+         MFEM_VERIFY(dynamic_cast<VectorConvectionNLFIntegrator *>
+                     (ext.dnfi[i]) == nullptr,
+                     "VectorConvectionNLFIntegrator PA gradients are not supported "
+                     "with the libCEED backend");
+      }
+   }
+
    ext.elemR->Mult(g, ext.xe);
    for (int i = 0; i < ext.dnfi.Size(); ++i)
    {