clean up pass

MixedVector gradient partial assembly

.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

@@ -111,6 +111,7 @@ jobs:
             build-system: make
             hypre-target: int64
             precision: fp64
+            gitignore-check: YES
           - os: ubuntu-latest
             target: opt
             codecov: NO
@@ -141,6 +142,10 @@ jobs:
 
     continue-on-error: ${{ matrix.enzyme && true || false }}
 
+    # Enable ccache for all jobs except Windows (would need sccache).
+    env:
+      USE_CCACHE: ${{ matrix.os != 'windows-latest' }}
+
     steps:
       # Fix 'No space left on device' errors for Ubuntu builds.
       - name: Run Actions Cleaner
@@ -289,6 +294,52 @@ jobs:
           echo "OMPI_CC=$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@v2.7
@@ -304,9 +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'
@@ -317,7 +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'
@@ -369,3 +431,9 @@ jobs:
           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

@@ -1,102 +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
-  MFEM_ACTIONS_VERSION: v2.7
-
-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 }}-int32-fp64-${{ env.MFEM_ACTIONS_VERSION }}
-
-      - name: Get Hypre
-        if: steps.hypre-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.7
-        with:
-          archive: ${{ env.HYPRE_ARCHIVE }}
-          dir: ${{ env.HYPRE_TOP_DIR }}
-          target: int32
-          precision: fp64
-
-      - 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 }}-${{ env.MFEM_ACTIONS_VERSION }}
-
-      - name: Install Metis
-        if: steps.metis-cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.7
-        with:
-          archive: ${{ env.METIS_ARCHIVE }}
-          dir: ${{ env.METIS_TOP_DIR }}
-
-      # MFEM build and test
-      - name: build-mfem
-        uses: mfem/github-actions/build-mfem@v2.7
-        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/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

.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

@@ -15,6 +15,10 @@ Version 4.9.1 (development)
 
 Discretization improvements
 ---------------------------
+- 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.
@@ -42,8 +46,19 @@ Discretization improvements
 
 - Extend FindPointsGSLIB to support surface meshes.
 
+- 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.
 
@@ -64,14 +79,55 @@ Linear and nonlinear solvers
   PRefinement multigrid methods for problems posed on trace spaces (see e.g. the
   DPG miniapps).
 
+- Added new class MultiVector: an array of Vectors of different sizes where each
+  Vector can be allocated independently. Also, added associated methods in class
+  Operator: MultMV, MultTransposeMV, and GetGradientMV, that use MultiVector
+  objects for input and/or output parameters. [PR #5249]
+
 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 partial assembly support for MixedScalarWeakGradientIntegrator.
+
+- Added partial assembly support for MixedDotProductIntegrator.
+
+- Added partial assembly support for MixedScalarCrossProductIntegrator.
+
+- Added partial assembly support for MixedScalarWeakCrossProductIntegrator.
+
+- Added partial assembly support for MixedVectorGradientIntegrator for H1->RT.
+
+- Added support for device partial assembly CurlInterpolator.
+  This supports 2D and 3D variants:
+    2D H1 (out-of-plane) to RT (in-plane)
+    2D ND (in-plane) to Integral L2 (out-of-plane)
+    3D ND to RT
+
 - 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.
+
+- Added support for FiniteElement::MapType::INTEGRAL spaces to
+  MixedScalarCurlIntegrator.
+
 New and updated examples and miniapps
 -------------------------------------
 - The Lorentz miniapp (in miniapps/electromagnetics) has been updated to
@@ -86,6 +142,15 @@ Miscellaneous
   using the new method ApplyDofSigns() in class ParFiniteElementSpace: the
   method will return immediately if no sign flips are needed.
 
+- Added support for saving DataCollection output on the node-local storage,
+  instead of requiring that the filesystem is shared among all the ranks.
+
+API changes
+-----------
+- Removed ProjectGrad from 2D RT elements. Users should use ProjectCurl instead.
+  This also fixes a bug where ProjectCurl was returning the negative curl,
+  identical to ProjectGrad.
+
 
 Version 4.9, released on Dec 11, 2025
 =====================================

CMakeLists.txt

@@ -88,18 +88,9 @@ if (MFEM_USE_STRUMPACK OR MFEM_USE_MUMPS)
   # Just needed to find the MPI_Fortran libraries to link with
   set(XSDK_ENABLE_Fortran ON)
 endif()
-# Ginkgo requires C++17:
-if ((MFEM_USE_GINKGO) AND ("${CMAKE_CXX_STANDARD}" LESS "17"))
-  set(CMAKE_CXX_STANDARD 17 CACHE STRING "C++ standard to use." FORCE)
-# Google Benchmark, SUNDIALS, STRUMPACK, Tribol, RAJA and Umpire require C++14:
-elseif ((MFEM_USE_BENCHMARK OR
-         MFEM_USE_SUNDIALS OR
-         MFEM_USE_STRUMPACK OR
-         MFEM_USE_TRIBOL OR
-         MFEM_USE_RAJA OR
-         MFEM_USE_UMPIRE) AND
-    ("${CMAKE_CXX_STANDARD}" LESS "14"))
-  set(CMAKE_CXX_STANDARD 14 CACHE STRING "C++ standard to use." FORCE)
+# RAJA requires C++20:
+if ((MFEM_USE_UMPIRE OR MFEM_USE_RAJA) AND ("${CMAKE_CXX_STANDARD}" LESS "20"))
+  set(CMAKE_CXX_STANDARD 20 CACHE STRING "C++ standard to use." FORCE)
 endif()
 
 # Include xSDK default CMake file.
@@ -239,6 +230,13 @@ 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/cmake/modules/MfemCmakeUtilities.cmake

@@ -962,7 +962,7 @@ function(mfem_export_mk_files)
     set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} -I${dir}")
   endforeach()
   # TODO: MFEM_TPLFLAGS: add other TPL flags, in addition to the -I flags.
-  set(MFEM_INCFLAGS "-I\$(MFEM_INC_DIR) \$(MFEM_TPLFLAGS)")
+  set(MFEM_INCFLAGS "-I\$(MFEM_INC_DIR) -I\$(MFEM_SOURCE_DIR) \$(MFEM_TPLFLAGS)")
   set(MFEM_PICFLAG "")
   if (BUILD_SHARED_LIBS)
     set(MFEM_PICFLAG "${CMAKE_SHARED_LIBRARY_CXX_FLAGS}")
@@ -1098,6 +1098,7 @@ function(mfem_export_mk_files)
     "${INSTALL_LIB_DIR}" "${CMAKE_INSTALL_PREFIX}" MFEM_LIB_DIR)
   mfem_path_to_fullpath(
     "${INSTALL_SHARE_DIR}/mfem/test.mk" "${CMAKE_INSTALL_PREFIX}" MFEM_TEST_MK)
+  set(MFEM_INCFLAGS "-I\$(MFEM_INC_DIR) \$(MFEM_TPLFLAGS)")
   set(MFEM_CONFIG_EXTRA "")
 
   # Create the install-tree version of 'config.mk'

config/defaults.mk

@@ -27,7 +27,10 @@ MPICXX = mpicxx
 
 BASE_FLAGS  = -std=c++17
 OPTIM_FLAGS = -O3 $(BASE_FLAGS)
-DEBUG_FLAGS = -g $(XCOMPILER)-Wall $(BASE_FLAGS)
+
+# The variable WARNING_FLAGS depends on which compiler is used, and is defined
+# later in this file.
+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 =
@@ -46,6 +49,10 @@ SHARED = NO
 #
 # If you set MFEM_USE_ENZYME=YES, must use CUDA_CXX=clang++
 CUDA_CXX = nvcc
+# CUDA compute capability used during compilation, e.g. sm_60. Multiple
+# architectures can be requested as a comma-separated list, e.g. sm_70,sm_80.
+# A single value may also be one of the nvcc special values "all",
+# "all-major", or "native".
 CUDA_ARCH = sm_60
 # Base CUDA install directory, only needed if building with clang+cuda:
 # The default setting is:
@@ -54,11 +61,23 @@ CUDA_ARCH = sm_60
 # 3. Use /usr/local/cuda
 CUDA_DIR = $(or $(CUDA_HOME),$(patsubst %/,%,$(dir \
  $(patsubst %/,%,$(dir $(shell command -v nvcc))))),/usr/local/cuda)
+# Derive nvcc/clang architecture flags from CUDA_ARCH. A comma-separated list
+# expands into one -gencode / --cuda-gpu-arch flag per architecture; otherwise
+# use the -arch / --cuda-gpu-arch shorthand.
+MFEM_COMMA := ,
+CUDA_ARCH_NUMS = $(patsubst sm_%,%,$(subst $(MFEM_COMMA), ,$(CUDA_ARCH)))
+NVCC_ARCH_FLAGS = $(strip $(if $(findstring $(MFEM_COMMA),$(CUDA_ARCH)),\
+ $(foreach arch,$(CUDA_ARCH_NUMS),\
+ -gencode arch=compute_$(arch)$(MFEM_COMMA)code=sm_$(arch)),\
+ -arch=$(CUDA_ARCH)))
+CLANG_ARCH_FLAGS = $(strip $(if $(findstring $(MFEM_COMMA),$(CUDA_ARCH)),\
+ $(foreach arch,$(CUDA_ARCH_NUMS),--cuda-gpu-arch=sm_$(arch)),\
+ --cuda-gpu-arch=$(CUDA_ARCH)))
 # flags for clang+cuda
-CLANG_CUDA_FLAGS = -xcuda --cuda-path=$(CUDA_DIR) --cuda-gpu-arch=$(CUDA_ARCH)
+CLANG_CUDA_FLAGS = -xcuda --cuda-path=$(CUDA_DIR) $(CLANG_ARCH_FLAGS)
 # flags for nvcc
 NVCC_FLAGS = -x=cu --expt-extended-lambda --expt-relaxed-constexpr \
- -arch=$(CUDA_ARCH) -isystem "$(CUDA_DIR)/include"
+ $(NVCC_ARCH_FLAGS) -isystem "$(CUDA_DIR)/include"
 # Prefixes for passing flags to the host compiler and linker when using
 # CUDA_CXX=nvcc
 CUDA_XCOMPILER = -Xcompiler=
@@ -376,7 +395,7 @@ CUDSS_LIBRARY_DIR = $(CUDSS_DIR)/lib
 CUDSS_OPT         = -I$(CUDSS_INCLUDE_DIR)
 CUDSS_LIB         = \
  $(XLINKER)-rpath,$(CUDSS_LIBRARY_DIR) -L$(CUDSS_LIBRARY_DIR) -lcudss
-# The cuDSS communication and threading libraries. 
+# The cuDSS communication and threading libraries.
 MFEM_CUDSS_COMM_LIB = $(abspath $(wildcard $(or $(CUDSS_COMM_LIB),\
    $(subst @MFEM_DIR@,$(MFEM_DIR), $(CUDSS_LIBRARY_DIR)/libcudss_commlayer_openmpi.so))))
 MFEM_CUDSS_THREADING_LIB = $(abspath $(wildcard $(or $(CUDSS_THREADING_LIB),\
@@ -659,3 +678,15 @@ VERBOSE = NO
 
 # Optional build tag
 MFEM_BUILD_TAG = $(shell uname -snm)
+
+# Enable -pedantic flag only for gcc or clang. nvcc complains with -pedantic
+# because of line directives.
+PEDANTIC_FLAG = $(if \
+   $(findstring NVIDIA,$(shell $(MFEM_CXX) --version 2>&1)),, \
+   $(if $(or \
+      $(findstring gcc version,$(shell $(MFEM_CXX) -v 2>&1)), \
+      $(findstring clang version,$(shell $(MFEM_CXX) -v 2>&1))),-pedantic,))
+# Enable 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_FLAG) -Wall $(SHADOW_WARNING_FLAG)

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.conf.in

@@ -1083,7 +1083,8 @@ EXCLUDE_PATTERNS       =
 # ANamespace::AClass, ANamespace::*Test
 
 EXCLUDE_SYMBOLS        = mfem::internal \
-                         mfem::kernels::internal
+                         mfem::kernels::internal \
+                         mfem::future::detail
 
 # The EXAMPLE_PATH tag can be used to specify one or more files or directories
 # that contain example code fragments that are included (see the \include

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/CMakeLists.txt

@@ -262,3 +262,8 @@ endif()
 if(MFEM_USE_MOONOLITH)
   add_subdirectory(moonolith)
 endif()
+
+# Include the examples/magma directory if MAGMA is enabled.
+if (MFEM_USE_MAGMA)
+  add_subdirectory(magma)
+endif()

examples/magma/CMakeLists.txt

@@ -0,0 +1,27 @@
+# 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.
+
+set(MAGMA_EXAMPLES_SRCS)
+list(APPEND MAGMA_EXAMPLES_SRCS
+  batched_mass_bench.cpp
+  )
+
+# Include the source directory where mfem.hpp and mfem-performance.hpp are.
+include_directories(BEFORE ${PROJECT_BINARY_DIR})
+
+# Add "test_magma" target (build-only by default).
+add_custom_target(test_magma
+  COMMENT "Building MAGMA examples ...")
+
+# Add one executable per cpp file, adding "magma_" as prefix to avoid
+# collisions in a unified build tree.
+set(PFX magma_)
+add_mfem_examples(MAGMA_EXAMPLES_SRCS ${PFX} "" test_magma)

examples/magma/README

@@ -0,0 +1,12 @@
+This directory contains an MFEM example focused on benchmarking MAGMA batched
+element-mass-matrix inverses/solves on GPU backends (CUDA/HIP).
+
+- `batched_mass_bench.cpp`: Assemble packed element mass matrices and compare:
+  - MFEM tripack inverse apply (packed lower-triangular)
+  - MAGMA packed Cholesky factor + solve
+  - MAGMA full (dense) batched Cholesky factor + solve
+
+Build and run from this directory (after building MFEM with MAGMA enabled):
+
+- `make batched_mass_bench`
+- `./batched_mass_bench -m ../../data/beam-hex.mesh -o 3 -r 2 -d hip -reps 100`

examples/magma/batched_mass_bench.cpp

@@ -0,0 +1,798 @@
+//                    MFEM Batched Mass Benchmark
+//
+// Compile with: make batched_mass_bench
+//
+// Sample runs:  batched_mass_bench -m ../../data/beam-hex.mesh -o 3 -r 2 -d hip -reps 100
+//               batched_mass_bench -m ../../data/beam-hex.mesh -o 3 -r 3 -d cuda -reps 50
+//
+// Description:  This example isolates the element mass-matrix
+//               inverse paths used by element matrix kernels. It
+//               assembles packed lower-triangular L2 element mass matrices,
+//               then times repeated mass inverse applications using MFEM's
+//               tripack path and MAGMA (packed and full-matrix variants).
+
+#include "mfem.hpp"
+#include <cmath>
+#include <iomanip>
+#include <iostream>
+#include <limits>
+#include <memory>
+
+using namespace mfem;
+using namespace std;
+
+namespace
+{
+
+#ifdef MFEM_USE_MAGMA
+inline void MagmaSetPointer(float **output, float *input,
+                            magma_int_t inc, magma_int_t row, magma_int_t col,
+                            magma_int_t lda, magma_int_t batch_count,
+                            magma_queue_t queue)
+{
+   magma_sset_pointer(output, input, inc, row, col, lda, batch_count, queue);
+}
+
+inline void MagmaSetPointer(double **output, double *input,
+                            magma_int_t inc, magma_int_t row, magma_int_t col,
+                            magma_int_t lda, magma_int_t batch_count,
+                            magma_queue_t queue)
+{
+   magma_dset_pointer(output, input, inc, row, col, lda, batch_count, queue);
+}
+
+inline magma_int_t MagmaPotrfBatched(magma_uplo_t uplo, magma_int_t n,
+                                     float **dA, magma_int_t ldda,
+                                     magma_int_t *info, magma_int_t batch_count,
+                                     magma_queue_t queue)
+{
+   return magma_spotrf_batched(uplo, n, dA, ldda, info, batch_count, queue);
+}
+
+inline magma_int_t MagmaPotrfBatched(magma_uplo_t uplo, magma_int_t n,
+                                     double **dA, magma_int_t ldda,
+                                     magma_int_t *info, magma_int_t batch_count,
+                                     magma_queue_t queue)
+{
+   return magma_dpotrf_batched(uplo, n, dA, ldda, info, batch_count, queue);
+}
+
+inline magma_int_t MagmaPotrsBatched(magma_uplo_t uplo, magma_int_t n,
+                                     magma_int_t nrhs, float **dA,
+                                     magma_int_t ldda, float **dB,
+                                     magma_int_t lddb, magma_int_t batch_count,
+                                     magma_queue_t queue)
+{
+   return magma_spotrs_batched(uplo, n, nrhs, dA, ldda, dB, lddb,
+                              batch_count, queue);
+}
+
+inline magma_int_t MagmaPotrsBatched(magma_uplo_t uplo, magma_int_t n,
+                                     magma_int_t nrhs, double **dA,
+                                     magma_int_t ldda, double **dB,
+                                     magma_int_t lddb, magma_int_t batch_count,
+                                     magma_queue_t queue)
+{
+   return magma_dpotrs_batched(uplo, n, nrhs, dA, ldda, dB, lddb,
+                              batch_count, queue);
+}
+
+void PrintMagmaFasterCondition(const double eq_fixed_ms,
+                               const double eq_apply_ms,
+                               const double magma_fixed_ms,
+                               const double magma_apply_ms)
+{
+   cout << "MAGMA faster condition (assembly+setup+N applies): ";
+
+   if (magma_fixed_ms <= eq_fixed_ms && magma_apply_ms <= eq_apply_ms)
+   {
+      if (magma_fixed_ms == eq_fixed_ms && magma_apply_ms == eq_apply_ms)
+      {
+         cout << "modeled totals are equal for all positive integer N.\n";
+      }
+      else
+      {
+         cout << "faster for every positive integer N.\n";
+      }
+      return;
+   }
+
+   if (magma_fixed_ms >= eq_fixed_ms && magma_apply_ms >= eq_apply_ms)
+   {
+      cout << "not faster for any positive integer N.\n";
+      return;
+   }
+
+   if (magma_apply_ms > eq_apply_ms)
+   {
+      const double crossover =
+         (eq_fixed_ms - magma_fixed_ms)/(magma_apply_ms - eq_apply_ms);
+      if (crossover <= 1.0)
+      {
+         cout << "only for N < " << crossover
+              << ", so not for any positive integer N.\n";
+      }
+      else
+      {
+         const double last_n =
+            floor(nextafter(crossover, -numeric_limits<double>::infinity()));
+         cout << "faster for N < " << crossover
+              << " applies (positive integer N <= " << (long long)last_n
+              << "); eq-iter is faster above that.\n";
+      }
+   }
+   else
+   {
+      const double crossover =
+         (magma_fixed_ms - eq_fixed_ms)/(eq_apply_ms - magma_apply_ms);
+      const double first_n = floor(crossover) + 1.0;
+      cout << "faster for N > " << crossover
+           << " applies (positive integer N >= " << (long long)first_n
+           << "); eq-iter is faster below that.\n";
+	   }
+	}
+
+real_t **SetMagmaPackedPointerArray(Array<real_t *> &ptrs, real_t *data,
+                                    const int stride,
+                                    const int batch_size,
+                                    const magma_queue_t queue)
+{
+   if (ptrs.Size() != batch_size)
+   {
+      if (ptrs.Size() != 0) { magma_queue_sync(queue); }
+      ptrs.SetSize(batch_size, Device::GetDeviceMemoryType());
+   }
+
+   real_t **d_ptrs = ptrs.Write();
+   MagmaSetPointer(d_ptrs, data, 1, 0, 0, stride, batch_size, queue);
+   return d_ptrs;
+}
+
+void ComputeMagmaFullCholeskyLower(
+   const Vector &full,
+   const int n,
+   Vector &factor,
+   Array<real_t *> &factor_ptrs,
+   const magma_queue_t queue)
+{
+   const int batch_size = full.Size()/(n*n);
+   MFEM_VERIFY(full.Size() == batch_size*n*n, "Invalid full matrix storage.");
+
+   factor = full;
+
+   if (batch_size == 0) { return; }
+
+   real_t *factor_data = factor.ReadWrite();
+   real_t **dA = SetMagmaPackedPointerArray(factor_ptrs, factor_data, n*n,
+                                            batch_size, queue);
+
+   Array<magma_int_t> info_array(batch_size, Device::GetDeviceMemoryType());
+   magma_int_t *d_info = info_array.Write();
+   magma_memset(d_info, 0, batch_size*sizeof(magma_int_t));
+
+   const magma_int_t status =
+      MagmaPotrfBatched(MagmaLower, n, dA, n, d_info, batch_size, queue);
+   MFEM_VERIFY(status == MAGMA_SUCCESS, "MAGMA full potrf batched failed.");
+
+   magma_queue_sync(queue);
+   const magma_int_t *info = info_array.HostRead();
+   for (int e = 0; e < batch_size; ++e)
+   {
+      MFEM_VERIFY(info[e] == 0, "MAGMA full potrf failed on matrix " << e << '.');
+   }
+}
+
+void SolveMagmaFullCholeskyLowerInPlace(
+   const Vector &full_factor,
+   const int n,
+   const Array<real_t *> &factor_ptrs,
+   Array<real_t *> &rhs_ptrs,
+   Vector &rhs_sol,
+   const magma_queue_t queue)
+{
+   const int batch_size = rhs_sol.Size()/n;
+   MFEM_VERIFY(rhs_sol.Size() == batch_size*n, "Invalid RHS size.");
+   MFEM_VERIFY(factor_ptrs.Size() == batch_size,
+               "Factor pointer array has the wrong size.");
+
+   if (batch_size == 0) { return; }
+
+   real_t *factor_data = const_cast<real_t *>(full_factor.Read());
+   real_t **dA = const_cast<real_t **>(factor_ptrs.Read());
+   (void)factor_data; // Factor data is referenced by dA (for clarity).
+
+   real_t *rhs_data = rhs_sol.ReadWrite();
+   real_t **dB = SetMagmaPackedPointerArray(rhs_ptrs, rhs_data, n, batch_size,
+                                            queue);
+
+   const magma_int_t status =
+      MagmaPotrsBatched(MagmaLower, n, 1, dA, n, dB, n, batch_size, queue);
+   MFEM_VERIFY(status == MAGMA_SUCCESS, "MAGMA full potrs batched failed.");
+}
+#endif
+
+void FillRHS(Vector &rhs)
+{
+   rhs.UseDevice(true);
+   real_t *x = rhs.HostWrite();
+   for (int i = 0; i < rhs.Size(); ++i)
+   {
+      x[i] = 1.0 + real_t((13*i + 7) % 29)/real_t(29);
+   }
+}
+
+void ComputeLowerPackedResidual(
+   const TriPackLowerMatrix &lower,
+   const Vector &x,
+   const Vector &rhs,
+   double &l2_residual,
+   double &relative_l2_residual,
+   real_t &max_residual,
+   real_t &relative_max_residual)
+{
+   const int n = lower.GetNumRows();
+   const int batch_size = lower.GetNumMatrices();
+   const int packed_size = lower.GetPackedSize();
+   MFEM_VERIFY(x.Size() == batch_size*n, "Solution vector has the wrong size.");
+   MFEM_VERIFY(rhs.Size() == batch_size*n, "Right-hand side has the wrong size.");
+
+   const real_t *A = lower.Data().HostRead();
+   const real_t *X = x.HostRead();
+   const real_t *B = rhs.HostRead();
+
+   long double l2_sum = 0.0;
+   long double rhs_l2_sum = 0.0;
+   real_t max_abs = 0.0;
+   real_t rhs_max_abs = 0.0;
+
+   for (int e = 0; e < batch_size; ++e)
+   {
+      const real_t *Ae = A + e*packed_size;
+      const real_t *Xe = X + e*n;
+      const real_t *Be = B + e*n;
+      for (int i = 0; i < n; ++i)
+      {
+         long double ax = 0.0;
+         for (int j = 0; j < n; ++j)
+         {
+         const real_t aij =
+            (i >= j) ?
+               Ae[TriPackLowerMatrix::LowerIndex(i, j, n)] :
+               Ae[TriPackLowerMatrix::LowerIndex(j, i, n)];
+            ax += (long double)aij * (long double)Xe[j];
+         }
+         const long double residual = ax - (long double)Be[i];
+         l2_sum += residual*residual;
+         rhs_l2_sum += (long double)Be[i]*(long double)Be[i];
+         max_abs = max(max_abs, (real_t)fabs((double)residual));
+         rhs_max_abs = max(rhs_max_abs, fabs(Be[i]));
+      }
+   }
+
+   l2_residual = sqrt((double)l2_sum);
+   const double rhs_l2_norm = sqrt((double)rhs_l2_sum);
+   relative_l2_residual =
+      (rhs_l2_norm > 0.0) ? l2_residual/rhs_l2_norm : l2_residual;
+   max_residual = max_abs;
+   relative_max_residual =
+      (rhs_max_abs > 0.0) ? max_residual/rhs_max_abs : max_residual;
+}
+
+void ApplyLowerInverseInPlace(
+   const TriPackLowerMatrix &lower_inverse,
+   Vector &x,
+   Vector &work)
+{
+   const int n = lower_inverse.GetNumRows();
+   const int batch_size = lower_inverse.GetNumMatrices();
+   const int packed_size = lower_inverse.GetPackedSize();
+   MFEM_VERIFY(x.Size() == batch_size*n, "Input vector has the wrong size.");
+
+   work.SetSize(batch_size*n);
+   work.UseDevice(true);
+
+   const real_t *L = lower_inverse.Data().Read();
+   const real_t *X = x.Read();
+   real_t *T = work.Write();
+
+   mfem::forall(batch_size*n, [=] MFEM_HOST_DEVICE (int idx)
+   {
+      const int i = idx % n;
+      const int e = idx / n;
+      const real_t *Le = L + e*packed_size;
+      const real_t *Xe = X + e*n;
+      real_t sum = 0.0;
+      for (int j = 0; j <= i; ++j)
+      {
+         sum += Le[TriPackLowerMatrix::LowerIndex(i, j, n)]*Xe[j];
+      }
+      T[idx] = sum;
+   });
+
+   const real_t *T_in = work.Read();
+   real_t *Y = x.Write();
+   mfem::forall(batch_size*n, [=] MFEM_HOST_DEVICE (int idx)
+   {
+      const int i = idx % n;
+      const int e = idx / n;
+      const real_t *Le = L + e*packed_size;
+      const real_t *Te = T_in + e*n;
+      real_t sum = 0.0;
+      for (int j = i; j < n; ++j)
+      {
+         sum += Le[TriPackLowerMatrix::LowerIndex(j, i, n)]*Te[j];
+      }
+      Y[idx] = sum;
+   });
+}
+
+double TimeLowerInverseApply(
+   const TriPackLowerMatrix &inverse,
+   const Vector &rhs,
+   const int reps,
+   Vector &x,
+   Vector &work)
+{
+   StopWatch sw;
+
+   // Dry run to remove first-use kernel and workspace allocation costs.
+   x = rhs;
+   ApplyLowerInverseInPlace(inverse, x, work);
+   MFEM_DEVICE_SYNC;
+   sw.Start();
+   for (int r = 0; r < reps; ++r)
+   {
+      x = rhs;
+      ApplyLowerInverseInPlace(inverse, x, work);
+   }
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   return 1000.0*sw.RealTime()/reps;
+}
+
+#ifdef MFEM_USE_MAGMA
+double TimeMagmaSolve(
+   const TriPackLowerMatrix &lower_factor,
+   const Vector &rhs,
+   const int reps,
+   Vector &x,
+   MagmaPackedLowerCholesky &ws)
+{
+   StopWatch sw;
+
+   // Dry run to remove first-use MAGMA and RHS pointer-array setup costs.
+   x = rhs;
+   ws.SolveInPlace(lower_factor, x);
+   MFEM_DEVICE_SYNC;
+   sw.Start();
+   for (int r = 0; r < reps; ++r)
+   {
+      x = rhs;
+      ws.SolveInPlace(lower_factor, x);
+   }
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   return 1000.0*sw.RealTime()/reps;
+}
+
+double TimeMagmaInverseApply(
+   const TriPackLowerMatrix &lower_inverse,
+   const Vector &rhs,
+   const int reps,
+   Vector &x,
+   MagmaPackedLowerInverse &ws)
+{
+   StopWatch sw;
+
+   // Dry run to remove first-use MAGMA and RHS pointer-array setup costs.
+   x = rhs;
+   ws.ApplyInPlace(lower_inverse, x);
+   MFEM_DEVICE_SYNC;
+   sw.Start();
+   for (int r = 0; r < reps; ++r)
+   {
+      x = rhs;
+      ws.ApplyInPlace(lower_inverse, x);
+   }
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   return 1000.0*sw.RealTime()/reps;
+}
+
+double TimeMagmaFullSolve(
+   const Vector &full_factor,
+   const int n,
+   const Array<real_t *> &factor_ptrs,
+   const Vector &rhs,
+   const int reps,
+   Vector &x,
+   const magma_queue_t queue)
+{
+   StopWatch sw;
+   Array<real_t *> rhs_ptrs;
+
+   x = rhs;
+   SolveMagmaFullCholeskyLowerInPlace(full_factor, n, factor_ptrs, rhs_ptrs, x,
+                                      queue);
+   MFEM_DEVICE_SYNC;
+   sw.Start();
+   for (int r = 0; r < reps; ++r)
+   {
+      x = rhs;
+      SolveMagmaFullCholeskyLowerInPlace(full_factor, n, factor_ptrs, rhs_ptrs,
+                                         x, queue);
+   }
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   return 1000.0*sw.RealTime()/reps;
+}
+#endif
+
+} // namespace
+
+int main(int argc, char *argv[])
+{
+   const char *mesh_file = "../../data/beam-hex.mesh";
+   int order = 3;
+   int ref_levels = 1;
+   int reps = 100;
+   int setup_reps = 10;
+   const char *device_config = "cpu";
+   bool use_magma = true;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of uniform refinements.");
+   args.AddOption(&reps, "-reps", "--apply-repetitions",
+                  "Number of mass inverse applications to time.");
+   args.AddOption(&setup_reps, "-sreps", "--setup-repetitions",
+                  "Number of setup repetitions to time.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&use_magma, "-magma", "--magma-solve",
+                  "-no-magma", "--no-magma-solve",
+                  "Time the MAGMA packed Cholesky solve when available.");
+   args.ParseCheck();
+
+   MFEM_VERIFY(reps > 0, "The number of apply repetitions must be positive.");
+   MFEM_VERIFY(setup_reps > 0,
+               "The number of setup repetitions must be positive.");
+
+   Device device(device_config);
+   device.Print();
+
+#ifndef MFEM_USE_MAGMA
+   MFEM_VERIFY(!use_magma, "MFEM was built without MAGMA support.");
+#endif
+
+   Mesh mesh(mesh_file, 1, 1);
+   for (int l = 0; l < ref_levels; ++l)
+   {
+      mesh.UniformRefinement();
+   }
+
+   const int dim = mesh.Dimension();
+   L2_FECollection fec(order, dim, BasisType::Positive);
+   FiniteElementSpace fespace(&mesh, &fec);
+
+   MFEM_VERIFY(UsesTensorBasis(fespace),
+               "This example requires a tensor-product finite element space.");
+
+   const int ne = mesh.GetNE();
+   const int elem_dofs = fespace.GetTypicalFE()->GetDof();
+
+   MassIntegrator mass;
+   StopWatch sw;
+
+   // Dry run assembly before timing steady-state work.
+   TriPackLowerMatrix packed_ea;
+   mass.AssembleEATriangular(fespace, packed_ea, false);
+   MFEM_DEVICE_SYNC;
+
+   sw.Clear();
+   sw.Start();
+   mass.AssembleEATriangular(fespace, packed_ea, false);
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   const double assemble_ms = 1000.0*sw.RealTime();
+
+   TriPackLowerMatrix tripack_inverse;
+   // Dry run setup before timing steady-state setup work.
+   tripack::ComputeCholeskyLowerInverse(packed_ea, tripack_inverse);
+   MFEM_DEVICE_SYNC;
+
+   sw.Clear();
+   sw.Start();
+   for (int r = 0; r < setup_reps; ++r)
+   {
+      tripack::ComputeCholeskyLowerInverse(packed_ea, tripack_inverse);
+   }
+   MFEM_DEVICE_SYNC;
+   sw.Stop();
+   const double tripack_inverse_setup_ms = 1000.0*sw.RealTime()/setup_reps;
+
+#ifdef MFEM_USE_MAGMA
+   magma_queue_t magma_queue = nullptr;
+   if (use_magma) { magma_queue = Magma::Queue(); }
+
+   TriPackLowerMatrix magma_factor;
+   std::unique_ptr<MagmaPackedLowerCholesky> magma_chol_ws;
+   double magma_factor_ms = 0.0;
+
+   TriPackLowerMatrix magma_inverse;
+   std::unique_ptr<MagmaPackedLowerInverse> magma_inv_ws;
+   double magma_inverse_ms = 0.0;
+   bool magma_ppinv_enabled = false;
+   Vector magma_full_factor;
+   Array<real_t *> magma_full_factor_ptrs;
+   double magma_full_factor_ms = 0.0;
+
+   if (use_magma)
+   {
+      magma_chol_ws.reset(new MagmaPackedLowerCholesky());
+      magma_chol_ws->SetQueue(magma_queue);
+
+      // Dry run setup before timing steady-state setup work.
+      magma_chol_ws->Factor(packed_ea, magma_factor);
+      MFEM_DEVICE_SYNC;
+
+      sw.Clear();
+      sw.Start();
+      for (int r = 0; r < setup_reps; ++r)
+      {
+         magma_chol_ws->Factor(packed_ea, magma_factor);
+      }
+      MFEM_DEVICE_SYNC;
+      sw.Stop();
+      magma_factor_ms = 1000.0*sw.RealTime()/setup_reps;
+
+      // Benchmark packed inverse (ppinv) only for sizes supported by MAGMA's
+      // current packed-inverse apply kernel.
+      if (elem_dofs <= 64)
+      {
+         magma_ppinv_enabled = true;
+         magma_inv_ws.reset(new MagmaPackedLowerInverse());
+         magma_inv_ws->SetQueue(magma_queue);
+
+         // Dry run setup before timing steady-state setup work.
+         magma_inv_ws->Compute(packed_ea, magma_inverse);
+         MFEM_DEVICE_SYNC;
+
+         sw.Clear();
+         sw.Start();
+         for (int r = 0; r < setup_reps; ++r)
+         {
+            magma_inv_ws->Compute(packed_ea, magma_inverse);
+         }
+         MFEM_DEVICE_SYNC;
+         sw.Stop();
+         magma_inverse_ms = 1000.0*sw.RealTime()/setup_reps;
+      }
+
+      // Full (dense) batched Cholesky factorization for comparison.
+      Vector full_ea(ne*elem_dofs*elem_dofs);
+      full_ea.UseDevice(true);
+      mass.AssembleEA(fespace, full_ea, false);
+
+      magma_full_factor.SetSize(full_ea.Size(), Device::GetDeviceMemoryType());
+      magma_full_factor.UseDevice(true);
+
+      ComputeMagmaFullCholeskyLower(full_ea, elem_dofs, magma_full_factor,
+                                    magma_full_factor_ptrs, magma_queue);
+      MFEM_DEVICE_SYNC;
+
+      sw.Clear();
+      sw.Start();
+      for (int r = 0; r < setup_reps; ++r)
+      {
+         ComputeMagmaFullCholeskyLower(full_ea, elem_dofs, magma_full_factor,
+                                       magma_full_factor_ptrs, magma_queue);
+      }
+      MFEM_DEVICE_SYNC;
+      sw.Stop();
+      magma_full_factor_ms = 1000.0*sw.RealTime()/setup_reps;
+   }
+#endif
+
+   Vector rhs(ne*elem_dofs);
+   FillRHS(rhs);
+
+   Vector tripack_x(rhs.Size()), work;
+   tripack_x.UseDevice(true);
+
+   const double tripack_apply_ms =
+      TimeLowerInverseApply(tripack_inverse, rhs, reps, tripack_x, work);
+
+   double tripack_res_l2 = 0.0, tripack_rel_res_l2 = 0.0;
+   real_t tripack_res_max = 0.0, tripack_rel_res_max = 0.0;
+   ComputeLowerPackedResidual(packed_ea, tripack_x, rhs,
+                              tripack_res_l2, tripack_rel_res_l2,
+                              tripack_res_max, tripack_rel_res_max);
+
+#ifdef MFEM_USE_MAGMA
+   double magma_solve_ms = 0.0;
+   double magma_full_solve_ms = 0.0;
+   double magma_res_l2 = 0.0, magma_rel_res_l2 = 0.0;
+   real_t magma_res_max = 0.0, magma_rel_res_max = 0.0;
+   double magma_full_res_l2 = 0.0, magma_full_rel_res_l2 = 0.0;
+   real_t magma_full_res_max = 0.0, magma_full_rel_res_max = 0.0;
+   Vector magma_x;
+   Vector magma_full_x;
+   if (use_magma)
+   {
+      magma_x.SetSize(rhs.Size());
+      magma_x.UseDevice(true);
+      magma_solve_ms =
+         TimeMagmaSolve(magma_factor, rhs, reps, magma_x, *magma_chol_ws);
+      ComputeLowerPackedResidual(packed_ea, magma_x, rhs,
+                                 magma_res_l2, magma_rel_res_l2,
+                                 magma_res_max, magma_rel_res_max);
+
+      magma_full_x.SetSize(rhs.Size());
+      magma_full_x.UseDevice(true);
+      magma_full_solve_ms =
+         TimeMagmaFullSolve(magma_full_factor, elem_dofs,
+                            magma_full_factor_ptrs, rhs, reps, magma_full_x,
+                            magma_queue);
+      ComputeLowerPackedResidual(packed_ea, magma_full_x, rhs,
+                                 magma_full_res_l2, magma_full_rel_res_l2,
+                                 magma_full_res_max, magma_full_rel_res_max);
+   }
+
+   double magma_ppinv_apply_ms = 0.0;
+   double magma_ppinv_res_l2 = 0.0, magma_ppinv_rel_res_l2 = 0.0;
+   real_t magma_ppinv_res_max = 0.0, magma_ppinv_rel_res_max = 0.0;
+   Vector magma_ppinv_x;
+   if (use_magma && magma_ppinv_enabled)
+   {
+      magma_ppinv_x.SetSize(rhs.Size());
+      magma_ppinv_x.UseDevice(true);
+      magma_ppinv_apply_ms =
+         TimeMagmaInverseApply(magma_inverse, rhs, reps, magma_ppinv_x,
+                               *magma_inv_ws);
+      ComputeLowerPackedResidual(packed_ea, magma_ppinv_x, rhs,
+                                 magma_ppinv_res_l2, magma_ppinv_rel_res_l2,
+                                 magma_ppinv_res_max,
+                                 magma_ppinv_rel_res_max);
+   }
+#endif
+
+   cout << fixed << setprecision(6);
+   cout << "Mass matrix inverse microbenchmark" << '\n';
+   cout << "Mesh: " << mesh_file << '\n';
+   cout << "Dimension: " << dim << '\n';
+   cout << "Elements: " << ne << '\n';
+   cout << "Element dofs: " << elem_dofs << '\n';
+   cout << "Scalar element unknowns: " << ne*elem_dofs << '\n';
+   cout << "Apply repetitions: " << reps << '\n';
+   cout << "Setup repetitions: " << setup_reps << '\n';
+   cout << '\n';
+
+   cout << "Assembly packed EA (ms): " << assemble_ms << '\n';
+   cout << "Setup MFEM tripack inverse (ms): " << tripack_inverse_setup_ms
+        << '\n';
+#ifdef MFEM_USE_MAGMA
+   if (use_magma)
+   {
+      cout << "Setup MAGMA packed Cholesky factor (ms): " << magma_factor_ms
+           << '\n';
+      cout << "Setup MAGMA full Cholesky factor (ms): " << magma_full_factor_ms
+           << '\n';
+      if (magma_ppinv_enabled)
+      {
+         cout << "Setup MAGMA packed inverse (ppinv) (ms): " << magma_inverse_ms
+              << '\n';
+      }
+      else
+      {
+         cout << "Setup MAGMA packed inverse (ppinv) (ms): skipped "
+              << "(requires element dofs <= 64)\n";
+      }
+   }
+#endif
+   cout << '\n';
+
+   cout << "Apply MFEM tripack inverse (ms/apply): " << tripack_apply_ms
+        << '\n';
+#ifdef MFEM_USE_MAGMA
+   if (use_magma)
+   {
+      cout << "Apply MAGMA packed Cholesky solve (ms/apply): "
+           << magma_solve_ms << '\n';
+      cout << "Apply MAGMA full Cholesky solve (ms/apply): "
+           << magma_full_solve_ms << '\n';
+      cout << "MAGMA solve / MFEM tripack inverse apply: "
+           << magma_solve_ms/tripack_apply_ms << '\n';
+      cout << "MAGMA full solve / MFEM tripack inverse apply: "
+           << magma_full_solve_ms/tripack_apply_ms << '\n';
+
+      if (magma_ppinv_enabled)
+      {
+         cout << "Apply MAGMA packed inverse (ppinv) (ms/apply): "
+              << magma_ppinv_apply_ms << '\n';
+         cout << "MAGMA ppinv apply / MFEM tripack inverse apply: "
+              << magma_ppinv_apply_ms/tripack_apply_ms << '\n';
+      }
+      else
+      {
+         cout << "Apply MAGMA packed inverse (ppinv) (ms/apply): skipped "
+              << "(requires element dofs <= 64)\n";
+      }
+
+      const double tripack_fixed_ms = assemble_ms + tripack_inverse_setup_ms;
+      const double magma_fixed_ms = assemble_ms + magma_factor_ms;
+      const double magma_full_fixed_ms = assemble_ms + magma_full_factor_ms;
+      const double tripack_total_ms =
+         tripack_fixed_ms + reps*tripack_apply_ms;
+      const double magma_total_ms = magma_fixed_ms + reps*magma_solve_ms;
+      const double magma_full_total_ms =
+         magma_full_fixed_ms + reps*magma_full_solve_ms;
+      cout << "Total MFEM tripack inverse for current repetitions "
+           << "(assembly+setup+applies, ms): " << tripack_total_ms << '\n';
+      cout << "Total MAGMA packed Cholesky solve for current repetitions "
+           << "(assembly+setup+applies, ms): " << magma_total_ms << '\n';
+      cout << "Total MAGMA full Cholesky solve for current repetitions "
+           << "(assembly+setup+applies, ms): " << magma_full_total_ms << '\n';
+      cout << "Faster approach for current repetitions: "
+           << ((magma_total_ms < tripack_total_ms &&
+                magma_total_ms <= magma_full_total_ms) ? "MAGMA packed" :
+               ((magma_full_total_ms < tripack_total_ms &&
+                 magma_full_total_ms < magma_total_ms) ? "MAGMA full" :
+                ((tripack_total_ms < magma_total_ms &&
+                  tripack_total_ms <= magma_full_total_ms) ? "tripack" :
+                 "tie")))
+           << '\n';
+      PrintMagmaFasterCondition(tripack_fixed_ms, tripack_apply_ms,
+                                magma_fixed_ms, magma_solve_ms);
+      PrintMagmaFasterCondition(tripack_fixed_ms, tripack_apply_ms,
+                                magma_full_fixed_ms, magma_full_solve_ms);
+
+      if (magma_ppinv_enabled)
+      {
+         const double magma_ppinv_fixed_ms =
+            assemble_ms + magma_inverse_ms;
+         const double magma_ppinv_total_ms =
+            magma_ppinv_fixed_ms + reps*magma_ppinv_apply_ms;
+         cout << "Total MAGMA packed inverse (ppinv) for current "
+              << "repetitions (assembly+setup+applies, ms): "
+              << magma_ppinv_total_ms << '\n';
+      }
+   }
+#endif
+   cout << '\n';
+
+   cout << scientific << setprecision(12);
+   cout << "Residual, MFEM tripack inverse, max: "
+        << tripack_res_max << " (relative "
+        << tripack_rel_res_max << "), L2: "
+        << tripack_res_l2 << " (relative "
+        << tripack_rel_res_l2 << ")\n";
+#ifdef MFEM_USE_MAGMA
+   if (use_magma)
+   {
+      cout << "Residual, MAGMA packed Cholesky solve, max: "
+           << magma_res_max << " (relative "
+           << magma_rel_res_max << "), L2: "
+           << magma_res_l2 << " (relative "
+           << magma_rel_res_l2 << ")\n";
+      cout << "Residual, MAGMA full Cholesky solve, max: "
+           << magma_full_res_max << " (relative "
+           << magma_full_rel_res_max << "), L2: "
+           << magma_full_res_l2 << " (relative "
+           << magma_full_rel_res_l2 << ")\n";
+      if (magma_ppinv_enabled)
+      {
+         cout << "Residual, MAGMA packed inverse (ppinv), max: "
+              << magma_ppinv_res_max << " (relative "
+              << magma_ppinv_rel_res_max << "), L2: "
+              << magma_ppinv_res_l2 << " (relative "
+              << magma_ppinv_rel_res_l2 << ")\n";
+      }
+   }
+#endif
+
+   return 0;
+}

examples/magma/makefile

@@ -0,0 +1,55 @@
+# 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.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/magma/,)
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_EXAMPLES = batched_mass_bench
+EXAMPLES = $(SEQ_EXAMPLES)
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all clean clean-build
+
+# Remove built-in rule
+%: %.cpp
+
+# Replace the default implicit rule for *.cpp files
+%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+
+all: $(EXAMPLES)
+
+ifeq ($(MFEM_USE_MAGMA),NO)
+$(EXAMPLES):
+	$(error MFEM is not configured with MAGMA)
+endif
+
+MFEM_TESTS = EXAMPLES
+include $(MFEM_TEST_MK)
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean: clean-build
+
+clean-build:
+	rm -f *.o *~ $(SEQ_EXAMPLES)
+	rm -rf *.dSYM *.TVD.*breakpoints

examples/makefile

@@ -68,6 +68,9 @@ endif
 ifeq ($(MFEM_USE_CALIPER),YES)
    SUBDIRS += caliper
 endif
+ifeq ($(MFEM_USE_MAGMA),YES)
+   SUBDIRS += magma
+endif
 
 SUBDIRS_ALL = $(addsuffix /all,$(SUBDIRS))
 SUBDIRS_TEST = $(addsuffix /test,$(SUBDIRS))
@@ -84,7 +87,8 @@ SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))
 
 # Replace the default implicit rule for *.cpp files
 %: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $< -o $@.o
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) $@.o -o $@ $(MFEM_LIBS)
 
 all: $(EXAMPLES) $(SUBDIRS_ALL)
 

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
@@ -204,7 +206,11 @@ set(HDRS
   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
@@ -311,6 +317,7 @@ set(HDRS
   tmop_tools.hpp
   tmop_amr.hpp
   gslib.hpp
+  gslib/gslib_kernel_helpers.hpp
   transfer.hpp
   hyperbolic.hpp
   integrator.hpp

fem/bilinearform.cpp

@@ -1255,6 +1255,31 @@ void BilinearForm::Mult(const Vector &x, Vector &y) const
    }
 }
 
+void BilinearForm::AddMult(const Vector &x, Vector &y, const real_t a) const
+{
+   if (ext)
+   {
+      ext->AddMult(x, y, a);
+   }
+   else
+   {
+      mat->AddMult(x, y, a);
+   }
+}
+
+void BilinearForm::AddMultTranspose(const Vector &x, Vector &y,
+                                    const real_t a) const
+{
+   if (ext)
+   {
+      ext->AddMultTranspose(x, y, a);
+   }
+   else
+   {
+      mat->AddMultTranspose(x, y, a);
+   }
+}
+
 void BilinearForm::MultTranspose(const Vector & x, Vector & y) const
 {
    if (ext)

fem/bilinearform.hpp

@@ -307,8 +307,8 @@ public:
    { mat->Mult(x, y); mat_e->AddMult(x, y); }
 
    /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const override
-   { mat -> AddMult (x, y, a); }
+   void AddMult(const Vector &x, Vector &y,
+                const real_t a = 1.0) const override;
 
    /** @brief Add the original uneliminated matrix vector multiple to a vector.
        The original matrix is $ M + Me $ so we have:
@@ -318,8 +318,7 @@ public:
 
    /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
    void AddMultTranspose(const Vector & x, Vector & y,
-                         const real_t a = 1.0) const override
-   { mat->AddMultTranspose(x, y, a); }
+                         const real_t a = 1.0) const override;
 
    /** @brief Add the original uneliminated matrix transpose vector
        multiple to a vector. The original matrix is $ M + M_e $

fem/bilinearform_ext.cpp

@@ -1997,7 +1997,11 @@ void PADiscreteLinearOperatorExtension::Assemble()
    }
    else
    {
-      mfem_error("A real ElementRestriction is required in this setting!");
+      const L2ElementRestriction* l2_elem_restrict =
+         dynamic_cast<const L2ElementRestriction*>(elem_restrict_test);
+      MFEM_VERIFY(l2_elem_restrict,
+                  "A real ElementRestriction is required in this setting!");
+      test_multiplicity = 1.0;
    }
 
    auto tm = test_multiplicity.ReadWrite();
@@ -2036,7 +2040,13 @@ void PADiscreteLinearOperatorExtension::AddMult(
    }
    else
    {
-      mfem_error("In this setting you need a real ElementRestriction!");
+      const L2ElementRestriction* l2_elem_restrict =
+         dynamic_cast<const L2ElementRestriction*>(elem_restrict_test);
+      MFEM_VERIFY(l2_elem_restrict,
+                  "In this setting you need a real ElementRestriction!");
+      tempY.SetSize(y.Size());
+      l2_elem_restrict->MultTranspose(localTest, tempY);
+      y += tempY;
    }
 }
 

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/coefficient.hpp

@@ -1055,7 +1055,8 @@ public:
 
 typedef VectorCoefficient DiagonalMatrixCoefficient;
 
-/// Base class for Matrix Coefficients that optionally depend on time and space.
+/** Base class for matrix-valued coefficients that optionally depend on time
+    and space. */
 class MatrixCoefficient
 {
 protected:
@@ -1102,6 +1103,9 @@ public:
    /// the quadrature points. The matrix will be transposed or not according to
    /// the boolean argument @a transpose.
    ///
+   /// The stored entries use the same row/column convention as `Eval()`,
+   /// unless `transpose == true`, in which case `K^T` is stored instead.
+   ///
    /// The @a vdim of the QuadratureFunction should be equal to the height times
    /// the width of the matrix.
    virtual void Project(QuadratureFunction &qf, bool transpose=false);

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;
 
@@ -323,6 +392,9 @@ private:
    bool RealInteg();
    bool ImagInteg();
 
+   void BuildComplexOperator(OperatorHandle &A_r, OperatorHandle &A_i,
+                             OperatorHandle &A) const;
+
 public:
    SesquilinearForm(FiniteElementSpace *fes,
                     ComplexOperator::Convention
@@ -436,6 +508,186 @@ 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
@@ -737,6 +989,12 @@ private:
    bool RealInteg();
    bool ImagInteg();
 
+   void SetImaginaryEssentialDiagonalToZero(
+      const Array<int> &ess_tdof_list, OperatorHandle &A);
+
+   void BuildComplexOperator(OperatorHandle &A_r, OperatorHandle &A_i,
+                             OperatorHandle &A) const;
+
 public:
    ParSesquilinearForm(ParFiniteElementSpace *pf,
                        ComplexOperator::Convention
@@ -852,6 +1110,169 @@ 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

@@ -38,9 +38,24 @@ int DataCollection::create_directory(const std::string &dir_name,
    // create directories recursively
    const char path_delim = '/';
    std::string::size_type pos = 0;
-   int err_flag;
+   int err_flag = 0;
 #ifdef MFEM_USE_MPI
    const ParMesh *pmesh = dynamic_cast<const ParMesh*>(mesh);
+   // In addition to the global root, let the lowest rank on each shared-memory
+   // node create the directory too, so that node-local (non-shared) filesystems
+   // get it on every node rather than only where the global root lives. On a
+   // shared filesystem the extra mkdir() hits EEXIST and is tolerated below.
+   bool node_root = true;
+   if (pmesh)
+   {
+      MPI_Comm node_comm;
+      MPI_Comm_split_type(pmesh->GetComm(), MPI_COMM_TYPE_SHARED, myid,
+                          MPI_INFO_NULL, &node_comm);
+      int node_rank;
+      MPI_Comm_rank(node_comm, &node_rank);
+      node_root = (node_rank == 0);
+      MPI_Comm_free(&node_comm);
+   }
 #endif
 
    do
@@ -52,7 +67,7 @@ int DataCollection::create_directory(const std::string &dir_name,
       err_flag = mkdir(subdir.c_str(), 0777);
       err_flag = (err_flag && (errno != EEXIST)) ? 1 : 0;
 #else
-      if (myid == 0 || pmesh == NULL)
+      if (node_root || pmesh == NULL)
       {
          err_flag = mkdir(subdir.c_str(), 0777);
          err_flag = (err_flag && (errno != EEXIST)) ? 1 : 0;
@@ -64,7 +79,8 @@ int DataCollection::create_directory(const std::string &dir_name,
 #ifdef MFEM_USE_MPI
    if (pmesh)
    {
-      MPI_Bcast(&err_flag, 1, MPI_INT, 0, pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE, &err_flag, 1, MPI_INT, MPI_MAX,
+                    pmesh->GetComm());
    }
 #endif
 
@@ -809,7 +825,7 @@ 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 +1197,14 @@ 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/dfem/doperator.cpp

@@ -51,4 +51,52 @@ DifferentiableOperator::DifferentiableOperator(
    }
 }
 
+
+void FDJacobian::Mult(const Vector &v, Vector &y) const
+{
+   // See [1] for choice of eps.
+   //
+   // [1] Woodward, C.S., Gardner, D.J. and Evans, K.J., 2015. On the use of
+   // finite difference matrix-vector products in Newton-Krylov solvers for
+   // implicit climate dynamics with spectral elements. Procedia Computer
+   // Science, 51, pp.2036-2045.
+   real_t eps;
+   if (fixed_eps > 0.0)
+   {
+      eps = fixed_eps;
+   }
+   else
+   {
+      const real_t vnorm_local = v.Norml2();
+      real_t vnorm;
+      MPI_Allreduce(&vnorm_local, &vnorm, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
+                    MPI_COMM_WORLD);
+      eps = lambda * (lambda + xnorm / vnorm);
+   }
+
+   // x + eps * v
+   {
+      const auto d_v = v.Read();
+      const auto d_x = x.Read();
+      auto d_xpev = xpev.Write();
+      mfem::forall(x.Size(), [=] MFEM_HOST_DEVICE (int i)
+      {
+         d_xpev[i] = d_x[i] + eps * d_v[i];
+      });
+   }
+
+   // y = f(x + eps * v)
+   op.Mult(xpev, y);
+
+   // y = (f(x + eps * v) - f(x)) / eps
+   {
+      const auto d_f = f.Read();
+      auto d_y = y.ReadWrite();
+      mfem::forall(f.Size(), [=] MFEM_HOST_DEVICE (int i)
+      {
+         d_y[i] = (d_y[i] - d_f[i]) / eps;
+      });
+   }
+}
+
 #endif // MFEM_USE_MPI

fem/dfem/doperator.hpp

@@ -697,17 +697,18 @@ void DifferentiableOperator::AddIntegrator(
 
    // The explicit captures are necessary to avoid dependency on
    // the specific instance of this class (this pointer).
-   restriction_callback =
-      [=, solutions = this->solutions, parameters = this->parameters]
-      (std::vector<Vector> &sol,
-       const std::vector<Vector> &par,
-       std::vector<Vector> &f)
+   restriction_callback = [element_dof_ordering,
+                           solutions_ = this->solutions,
+                           parameters_ = this->parameters]
+   (std::vector<Vector> &sol,
+    const std::vector<Vector> &par,
+    std::vector<Vector> &f)
    {
-      restriction<entity_t>(solutions, sol, f,
+      restriction<entity_t>(solutions_, sol, f,
                             element_dof_ordering);
-      restriction<entity_t>(parameters, par, f,
+      restriction<entity_t>(parameters_, par, f,
                             element_dof_ordering,
-                            solutions.size());
+                            solutions_.size());
    };
 
    prolongation_transpose = get_prolongation_transpose(
@@ -835,19 +836,19 @@ void DifferentiableOperator::AddIntegrator(
 
          // capture by ref:
          &restriction_cb = this->restriction_callback,
-         &fields_e = this->fields_e,
-         &residual_e = this->residual_e,
-         &output_restriction_transpose = this->output_restriction_transpose
+         &fields_e_ = this->fields_e,
+         &residual_e_ = this->residual_e,
+         &output_restriction_transpose_ = this->output_restriction_transpose
       ]
       (std::vector<Vector> &sol, const std::vector<Vector> &par, Vector &res)
       mutable // mutable: needed to modify 'shmem_cache'
    {
-      restriction_cb(sol, par, fields_e);
+      restriction_cb(sol, par, fields_e_);
 
-      residual_e = 0.0;
-      auto ye = Reshape(residual_e.ReadWrite(), test_vdim, num_test_dof, num_entities);
+      residual_e_ = 0.0;
+      auto ye = Reshape(residual_e_.ReadWrite(), test_vdim, num_test_dof, num_entities);
 
-      auto wrapped_fields_e = wrap_fields(fields_e,
+      auto wrapped_fields_e = wrap_fields(fields_e_,
                                           action_shmem_info.field_sizes,
                                           num_entities);
 
@@ -878,7 +879,7 @@ void DifferentiableOperator::AddIntegrator(
             y, fhat, output_fop, output_dtq_shmem[0],
             scratch_shmem, dimension, use_sum_factorization);
       }, num_entities, thread_blocks, action_shmem_info.total_size, shmem_cache.ReadWrite());
-      output_restriction_transpose(residual_e, res);
+      output_restriction_transpose_(residual_e_, res);
    });
 
    // Without this compile-time check, some valid instantiations of this method
@@ -1193,7 +1194,7 @@ void DifferentiableOperator::AddIntegrator(
 
                // capture by ref:
                &qpdc_mem = derivative_qp_caches_ref,
-               &fields = fields_ref
+               &fields_ = fields_ref
             ](std::vector<Vector> &f_e, SparseMatrix *&A) mutable
          {
             auto wrapped_fields_e = wrap_fields(f_e, shmem_info.field_sizes,
@@ -1241,14 +1242,14 @@ void DifferentiableOperator::AddIntegrator(
             {
                if (input_is_dependent[s])
                {
-                  trial_field = &fields[input_to_field[s]];
+                  trial_field = &fields_[input_to_field[s]];
                }
             }
 
             auto trial_fes = *std::get_if<const ParFiniteElementSpace *>
                              (&trial_field->data);
             auto test_fes = *std::get_if<const ParFiniteElementSpace *>
-                            (&fields[output_to_field[0]].data);
+                            (&fields_[output_to_field[0]].data);
 
             A = new SparseMatrix(test_fes->GetVSize(), trial_fes->GetVSize());
 
@@ -1334,7 +1335,7 @@ void DifferentiableOperator::AddIntegrator(
                input_to_field,
                output_to_field,
                &spmatcb = assemble_derivative_sparsematrix_callbacks_ref,
-               &fields = fields_ref
+               &fields_ = fields_ref
             ](std::vector<Vector> &f_e, HypreParMatrix *&A) mutable
          {
             SparseMatrix *spmat = nullptr;
@@ -1366,14 +1367,14 @@ void DifferentiableOperator::AddIntegrator(
             {
                if (input_is_dependent[s])
                {
-                  trial_field = &fields[input_to_field[s]];
+                  trial_field = &fields_[input_to_field[s]];
                }
             }
 
             auto trial_fes = *std::get_if<const ParFiniteElementSpace *>
                              (&trial_field->data);
             auto test_fes = *std::get_if<const ParFiniteElementSpace *>
-                            (&fields[output_to_field[0]].data);
+                            (&fields_[output_to_field[0]].data);
 
             if (same_test_and_trial)
             {

fem/dfem/util.hpp

@@ -597,7 +597,7 @@ struct ThreadBlocks
    int z = 1;
 };
 
-#if defined(MFEM_USE_CUDA_OR_HIP)
+#if defined(MFEM_USE_CUDA_OR_HIP_LANG)
 template <typename func_t>
 __global__ void forall_kernel_shmem(func_t f, int n)
 {
@@ -617,10 +617,11 @@ void forall(func_t f,
             int num_shmem = 0,
             real_t *shmem = nullptr)
 {
-   if (Device::Allows(Backend::CUDA_MASK) ||
-       Device::Allows(Backend::HIP_MASK))
+   internal::RequireKernelCompilation();
+
+#if defined(MFEM_USE_CUDA_OR_HIP_LANG)
+   if (Device::Allows(Backend::CUDA_MASK | Backend::HIP_MASK))
    {
-#if defined(MFEM_USE_CUDA_OR_HIP)
       // int gridsize = (N + Z - 1) / Z;
       int num_bytes = num_shmem * sizeof(decltype(shmem));
       dim3 block_size(blocks.x, blocks.y, blocks.z);
@@ -631,9 +632,10 @@ void forall(func_t f,
       MFEM_GPU_CHECK(hipGetLastError());
 #endif
       MFEM_DEVICE_SYNC;
-#endif
+      return;
    }
-   else if (Device::Allows(Backend::CPU_MASK))
+#endif
+   if (Device::Allows(Backend::CPU_MASK))
    {
       MFEM_ASSERT(!((bool)num_shmem != (bool)shmem),
                   "Backend::CPU needs a pre-allocated shared memory block");
@@ -671,52 +673,7 @@ public:
                     MPI_COMM_WORLD);
    }
 
-   void Mult(const Vector &v, Vector &y) const override
-   {
-      // See [1] for choice of eps.
-      //
-      // [1] Woodward, C.S., Gardner, D.J. and Evans, K.J., 2015. On the use of
-      // finite difference matrix-vector products in Newton-Krylov solvers for
-      // implicit climate dynamics with spectral elements. Procedia Computer
-      // Science, 51, pp.2036-2045.
-      real_t eps;
-      if (fixed_eps > 0.0)
-      {
-         eps = fixed_eps;
-      }
-      else
-      {
-         const real_t vnorm_local = v.Norml2();
-         real_t vnorm;
-         MPI_Allreduce(&vnorm_local, &vnorm, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
-                       MPI_COMM_WORLD);
-         eps = lambda * (lambda + xnorm / vnorm);
-      }
-
-      // x + eps * v
-      {
-         const auto d_v = v.Read();
-         const auto d_x = x.Read();
-         auto d_xpev = xpev.Write();
-         mfem::forall(x.Size(), [=] MFEM_HOST_DEVICE (int i)
-         {
-            d_xpev[i] = d_x[i] + eps * d_v[i];
-         });
-      }
-
-      // y = f(x + eps * v)
-      op.Mult(xpev, y);
-
-      // y = (f(x + eps * v) - f(x)) / eps
-      {
-         const auto d_f = f.Read();
-         auto d_y = y.ReadWrite();
-         mfem::forall(f.Size(), [=] MFEM_HOST_DEVICE (int i)
-         {
-            d_y[i] = (d_y[i] - d_f[i]) / eps;
-         });
-      }
-   }
+   void Mult(const Vector &v, Vector &y) const override;
 
    virtual MemoryClass GetMemoryClass() const override
    {

fem/fe/fe_base.cpp

@@ -1316,13 +1316,14 @@ void VectorFiniteElement::Project_RT(
    }
 }
 
-void VectorFiniteElement::ProjectGrad_RT(
+void VectorFiniteElement::ProjectCurl2D_RT(
    const real_t *nk, const Array<int> &d2n, const FiniteElement &fe,
    ElementTransformation &Trans, DenseMatrix &grad) const
 {
+   // 2D "ProjectCurl_RT"
    if (dim != 2)
    {
-      mfem_error("VectorFiniteElement::ProjectGrad_RT works only in 2D!");
+      mfem_error("VectorFiniteElement::ProjectCurl2D_RT works only in 2D!");
    }
 
    DenseMatrix dshape(fe.GetDof(), fe.GetDim());
@@ -1333,8 +1334,8 @@ void VectorFiniteElement::ProjectGrad_RT(
    for (int k = 0; k < dof; k++)
    {
       fe.CalcDShape(Nodes.IntPoint(k), dshape);
-      tk[0] = nk[d2n[k]*dim+1];
-      tk[1] = -nk[d2n[k]*dim];
+      tk[0] = -nk[d2n[k]*dim+1];
+      tk[1] = nk[d2n[k]*dim];
       dshape.Mult(tk, grad_k);
       for (int j = 0; j < grad_k.Size(); j++)
       {
@@ -1381,7 +1382,7 @@ void VectorFiniteElement::ProjectCurl_ND(
    }
 }
 
-void VectorFiniteElement::ProjectCurl_RT(
+void VectorFiniteElement::ProjectCurl3D_RT(
    const real_t *nk, const Array<int> &d2n, const FiniteElement &fe,
    ElementTransformation &Trans, DenseMatrix &curl) const
 {

fem/fe/fe_base.hpp

@@ -957,10 +957,11 @@ protected:
                    const FiniteElement &fe, ElementTransformation &Trans,
                    DenseMatrix &I) const;
 
-   // rotated gradient in 2D
-   void ProjectGrad_RT(const real_t *nk, const Array<int> &d2n,
-                       const FiniteElement &fe, ElementTransformation &Trans,
-                       DenseMatrix &grad) const;
+   // Input is a scalar representing the Z (out of plane) component, Output is
+   // the X-Y (in-plane) RT curl
+   void ProjectCurl2D_RT(const real_t *nk, const Array<int> &d2n,
+                         const FiniteElement &fe, ElementTransformation &Trans,
+                         DenseMatrix &grad) const;
 
    // Compute the curl as a discrete operator from ND FE (fe) to ND FE (this).
    // The natural FE for the range is RT, so this is an approximation.
@@ -968,9 +969,9 @@ protected:
                        const FiniteElement &fe, ElementTransformation &Trans,
                        DenseMatrix &curl) const;
 
-   void ProjectCurl_RT(const real_t *nk, const Array<int> &d2n,
-                       const FiniteElement &fe, ElementTransformation &Trans,
-                       DenseMatrix &curl) const;
+   void ProjectCurl3D_RT(const real_t *nk, const Array<int> &d2n,
+                         const FiniteElement &fe, ElementTransformation &Trans,
+                         DenseMatrix &curl) const;
 
    /** @brief Project a vector coefficient onto the ND basis functions
        @param tk    Edge tangent vectors for this element type
@@ -1446,6 +1447,8 @@ public:
                                 dof2quad_array_open);
    }
 
+   const Poly_1D::Basis &GetOpenBasis1D() const { return obasis1d; }
+
    virtual ~VectorTensorFiniteElement();
 };
 

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_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/fe_rt.hpp

@@ -73,16 +73,11 @@ public:
    void Project(const FiniteElement &fe, ElementTransformation &Trans,
                 DenseMatrix &I) const override
    { Project_RT(nk, dof2nk, fe, Trans, I); }
-   // Gradient + rotation = Curl: H1 -> H(div)
-   void ProjectGrad(const FiniteElement &fe,
-                    ElementTransformation &Trans,
-                    DenseMatrix &grad) const override
-   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
    // Curl = Gradient + rotation: H1 -> H(div)
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl2D_RT(nk, dof2nk, fe, Trans, curl); }
 
    void GetFaceMap(const int face_id, Array<int> &face_map) const override;
 
@@ -148,7 +143,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
 
    /// @brief Return the mapping from lexicographically ordered face DOFs to
    /// lexicographically ordered element DOFs corresponding to local face
@@ -210,16 +205,11 @@ public:
    void Project(const FiniteElement &fe, ElementTransformation &Trans,
                 DenseMatrix &I) const override
    { Project_RT(nk, dof2nk, fe, Trans, I); }
-   // Gradient + rotation = Curl: H1 -> H(div)
-   void ProjectGrad(const FiniteElement &fe,
-                    ElementTransformation &Trans,
-                    DenseMatrix &grad) const override
-   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
    // Curl = Gradient + rotation: H1 -> H(div)
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl2D_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 
@@ -274,7 +264,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 class RT_WedgeElement : public VectorFiniteElement
@@ -332,7 +322,7 @@ public:
    void ProjectCurl(const FiniteElement &fe,
                     ElementTransformation &Trans,
                     DenseMatrix &curl) const override
-   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
 };
 
 /** Arbitrary order H(Div) basis functions defined on pyramid-shaped elements
@@ -428,7 +418,7 @@ public:
    virtual void ProjectCurl(const FiniteElement &fe,
                             ElementTransformation &Trans,
                             DenseMatrix &curl) const
-   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
+   { ProjectCurl3D_RT(nk, dof2nk, fe, Trans, curl); }
 
    void CalcRawVShape(const IntegrationPoint &ip,
                       DenseMatrix &shape) const;

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();
@@ -286,7 +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];
@@ -295,7 +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;
@@ -320,7 +324,7 @@ 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; }
@@ -367,6 +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];
@@ -379,7 +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;
@@ -409,7 +414,7 @@ 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; }

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_convection_pa.cpp

@@ -178,6 +178,8 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    // Assumes tensor-product elements
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
+   MFEM_VERIFY(el.GetMapType() == FiniteElement::VALUE,
+               "Only value map type currently supported");
    ElementTransformation &Trans = *mesh->GetTypicalElementTransformation();
    const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, Trans);
    if (DeviceCanUseCeed())

fem/integ/bilininteg_diffusion_kernels.hpp

@@ -19,6 +19,8 @@
 #include "../../linalg/vector.hpp"
 #include "../bilininteg.hpp"
 
+#include "bilininteg_diffusion_pa_simplices.hpp"
+
 namespace mfem
 {
 

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,
@@ -789,6 +785,23 @@ void PAHcurlL2Setup2D(const int Q1D,
    });
 }
 
+void PAHcurlL2IntSetup2D(const int Q1D, const int NE, const Array<real_t> &w,
+                         Vector &coeff, const Vector &detJ, Vector &op)
+{
+   const int NQ = Q1D*Q1D;
+   auto W = w.Read();
+   auto C = Reshape(coeff.Read(), NQ, NE);
+   auto J = Reshape(detJ.Read(), NQ, NE);
+   auto y = Reshape(op.Write(), NQ, NE);
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         y(q,e) = W[q] * C(q,e) / J(q,e);
+      }
+   });
+}
+
 void PAHcurlL2Setup3D(const int NQ,
                       const int coeffDim,
                       const int NE,

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
 }
 
@@ -1805,13 +1889,17 @@ inline void SmemPACurlCurlApply3D(const int d1d,
    ForallWrap<3>(true, NE, device_kernel, host_kernel, Q1D, Q1D, Q1D);
 }
 
-// PA H(curl)-L2 Assemble 2D kernel
+// PA H(curl)-L2 value Assemble 2D kernel
 void PAHcurlL2Setup2D(const int Q1D,
                       const int NE,
                       const Array<real_t> &w,
                       Vector &coeff,
                       Vector &op);
 
+// PA H(curl)-L2 integral Assemble 2D kernel
+void PAHcurlL2IntSetup2D(const int Q1D, const int NE, const Array<real_t> &w,
+                         Vector &coeff, const Vector &detJ, Vector &op);
+
 // PA H(curl)-L2 Assemble 3D kernel
 void PAHcurlL2Setup3D(const int NQ,
                       const int coeffDim,

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,
@@ -816,8 +864,656 @@ inline void PAHcurlHdivApplyTranspose3D(const int d1d,
    }); // end of element loop
 }
 
+namespace curlinterp
+{
+constexpr int NBZ3D(int ndof_o, int nquad_o, int mdq)
+{
+   if (ndof_o <= 0 || nquad_o <= 0)
+   {
+      return 1;
+   }
+   int ndof_c = ndof_o + 1;
+   int nquad_c = nquad_o + 1;
+   // z dimension is capped at 64 on nvidia and amd gpus
+   int tmp =
+      std::min((128 + mdq * mdq * (mdq - 1) - 1) / (mdq * mdq * (mdq - 1)), 64);
+   int smem_req =
+      sizeof(mfem::real_t) *
+      ((3 * ndof_c * ndof_c * ndof_o + 2 * 2 * mdq * mdq * mdq) * tmp +
+       ndof_c * nquad_o + ndof_c * nquad_c + ndof_o * nquad_o);
+   // assume GPU has at least 48k shared memory
+   return std::max(std::min(tmp, (48 * 1024 + smem_req - 1) / smem_req), 1);
+}
+}
+
+template <int T_NDOF_O, int T_NQUAD_O>
+void CurlInterpolatorApply3DSmem(const int ne, const int ndof_o,
+                                 const int nquad_o, const Vector &pa,
+                                 const Vector &x_, Vector &y_)
+{
+   constexpr int mnd_o = T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
+   constexpr int mnq_o =
+      T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
+   constexpr int mndq = std::max(mnd_o + 1, mnq_o + 1);
+   constexpr int tbatch = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, mndq);
+   MFEM_VERIFY(ndof_o <= mnd_o, "Error: H(curl) order larger than supported");
+   MFEM_VERIFY(nquad_o <= mnq_o, "Error: H(div) order larger than supported");
+   int mnq = std::max(ndof_o + 1, nquad_o + 1);
+   auto pa_data = pa.Read();
+   auto x_d = x_.Read();
+   auto y_d = y_.ReadWrite();
+   mfem::forall_2D_batch<mndq * mndq * (mndq - 1) * tbatch>(
+      ne, mnq * mnq * (mnq - 1), 1, tbatch, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MND_O =
+         T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
+      constexpr int MNQ_O =
+         T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
+      constexpr int MNDQ = std::max(MND_O + 1, MNQ_O + 1);
+#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
+      constexpr int nbz = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, MNDQ);
+      int tidz = MFEM_THREAD_ID(z);
+      // Make mnq a local variable since capturing would result in different
+      // captures between host/device versions, and spuriously fails
+      int mnq = std::max(ndof_o + 1, nquad_o + 1);
+#else
+      constexpr int nbz = 1;
+      constexpr int tidz = 0;
+#endif
+      const int NDOF_O = T_NDOF_O ? T_NDOF_O : ndof_o;
+      const int NQUAD_O = T_NQUAD_O ? T_NQUAD_O : nquad_o;
+      const int NDOF_C = NDOF_O + 1;
+      const int NQUAD_C = NQUAD_O + 1;
+      MFEM_SHARED real_t
+      sBG[(MND_O + 1) * MNQ_O + (MND_O + 1) * (MNQ_O + 1) + MND_O * MNQ_O];
+      auto X_ = Reshape(x_d, 3 * NDOF_C * NDOF_C * NDOF_O, ne);
+      auto Y = Reshape(y_d, 3 * NQUAD_C * NQUAD_O * NQUAD_O, ne);
+      auto Gco = Reshape(sBG, NQUAD_O, NDOF_C);
+      auto Bcc = Reshape(sBG + NDOF_C * NQUAD_O, NQUAD_C, NDOF_C);
+      auto Boo =
+         Reshape(sBG + NDOF_C * NQUAD_O + NDOF_C * NQUAD_C, NQUAD_O, NDOF_O);
+      MFEM_SHARED real_t X[3][nbz][MND_O * (MND_O + 1) * (MND_O + 1)];
+      MFEM_SHARED real_t sm0[nbz * 2 * MNDQ * MNDQ * MNDQ];
+      MFEM_SHARED real_t sm1[nbz * 2 * MNDQ * MNDQ * MNDQ];
+
+      // shapes of buffers always use MNDQ to mitigate shared memory bank
+      // conflicts
+      real_t(*DDQ)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
+      real_t(*DQQ)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm1);
+      real_t(*QQQ)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
+      const int offset = NDOF_O * NDOF_C * NDOF_C;
+      const int offsetq = NQUAD_C * NQUAD_O * NQUAD_O;
+      MFEM_FOREACH_THREAD_DIRECT(ix, x, offset)
+      {
+         for (int dim = 0; dim < 3; ++dim)
+         {
+            X[dim][tidz][ix] = X_(ix + dim * offset, e);
+         }
+      }
+      // load basis functions data
+      if (tidz == 0)
+      {
+         auto npts = NDOF_C * NQUAD_O + NDOF_C * NQUAD_C + NDOF_O * NQUAD_O;
+         MFEM_FOREACH_THREAD(ix, x, npts) { sBG[ix] = pa_data[ix]; }
+      }
+      MFEM_SYNC_THREAD;
+
+      // x: Vz Bcc Gco Boo - Vy Bcc Boo Gco
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_C, NDOF_C,
+                                           NDOF_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_C; ++dx)
+         {
+            u += X[2][tidz][dx + (dy + dz * NDOF_C) * NDOF_C] * Bcc(qx, dx);
+         }
+         DDQ[0][tidz][dz][dy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_C, NDOF_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_C; ++dx)
+         {
+            u += X[1][tidz][dx + (dy + dz * NDOF_O) * NDOF_C] * Bcc(qx, dx);
+         }
+         DDQ[1][tidz][dz][dy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_C, NQUAD_O,
+                                           NDOF_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_C; ++dy)
+         {
+            u += DDQ[0][tidz][dz][dy][qx] * Gco(qy, dy);
+         }
+         DQQ[0][tidz][dz][qy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_C, NQUAD_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_O; ++dy)
+         {
+            u += DDQ[1][tidz][dz][dy][qx] * Boo(qy, dy);
+         }
+         DQQ[1][tidz][dz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_C, NQUAD_O,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_O; ++dz)
+         {
+            u += DQQ[0][tidz][dz][qy][qx] * Boo(qz, dz);
+         }
+         QQQ[0][tidz][qz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_C, NQUAD_O,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_C; ++dz)
+         {
+            u += DQQ[1][tidz][dz][qy][qx] * Gco(qz, dz);
+         }
+         Y(qx + (qy + qz * NQUAD_O) * NQUAD_C, e) =
+            QQQ[0][tidz][qz][qy][qx] - u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // y: Vx Boo Bcc Gco - Vz Gco Bcc Boo
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
+                                           NDOF_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_O; ++dx)
+         {
+            u += X[0][tidz][dx + (dy + dz * NDOF_C) * NDOF_O] * Boo(qx, dx);
+         }
+         DDQ[0][tidz][dz][dy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
+                                           NDOF_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_C; ++dx)
+         {
+            u += X[2][tidz][dx + (dy + dz * NDOF_C) * NDOF_C] * Gco(qx, dx);
+         }
+         DDQ[1][tidz][dz][dy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_C,
+                                           NDOF_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_C; ++dy)
+         {
+            u += DDQ[0][tidz][dz][dy][qx] * Bcc(qy, dy);
+         }
+         DQQ[0][tidz][dz][qy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_C,
+                                           NDOF_O, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_C; ++dy)
+         {
+            u += DDQ[1][tidz][dz][dy][qx] * Bcc(qy, dy);
+         }
+         DQQ[1][tidz][dz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_C; ++dz)
+         {
+            u += DQQ[0][tidz][dz][qy][qx] * Gco(qz, dz);
+         }
+         QQQ[0][tidz][qz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_O; ++dz)
+         {
+            u += DQQ[1][tidz][dz][qy][qx] * Boo(qz, dz);
+         }
+         Y(qx + (qy + qz * NQUAD_C) * NQUAD_O + offsetq, e) =
+            QQQ[0][tidz][qz][qy][qx] - u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // z: Vy Gco Boo Bcc - Vx Boo Gco Bcc
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_C; ++dx)
+         {
+            u += X[1][tidz][dx + (dy + dz * NDOF_O) * NDOF_C] * Gco(qx, dx);
+         }
+         DDQ[0][tidz][dz][dy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, dy, dz, x, NQUAD_O, NDOF_C,
+                                           NDOF_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int dx = 0; dx < NDOF_O; ++dx)
+         {
+            u += X[0][tidz][dx + (dy + dz * NDOF_C) * NDOF_O] * Boo(qx, dx);
+         }
+         DDQ[1][tidz][dz][dy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_O; ++dy)
+         {
+            u += DDQ[0][tidz][dz][dy][qx] * Boo(qy, dy);
+         }
+         DQQ[0][tidz][dz][qy][qx] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, dz, x, NQUAD_O, NQUAD_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dy = 0; dy < NDOF_C; ++dy)
+         {
+            u += DDQ[1][tidz][dz][dy][qx] * Gco(qy, dy);
+         }
+         DQQ[1][tidz][dz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_O,
+                                           NQUAD_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_C; ++dz)
+         {
+            u += DQQ[0][tidz][dz][qy][qx] * Bcc(qz, dz);
+         }
+         QQQ[0][tidz][qz][qy][qx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(qx, qy, qz, x, NQUAD_O, NQUAD_O,
+                                           NQUAD_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int dz = 0; dz < NDOF_C; ++dz)
+         {
+            u += DQQ[1][tidz][dz][qy][qx] * Bcc(qz, dz);
+         }
+         Y(qx + (qy + qz * NQUAD_O) * NQUAD_O + 2 * offsetq, e) =
+            QQQ[0][tidz][qz][qy][qx] - u;
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+template <int T_NDOF_O, int T_NQUAD_O>
+void CurlInterpolatorTApply3DSmem(const int ne, const int ndof_o,
+                                  const int nquad_o, const Vector &pa,
+                                  const Vector &x_, Vector &y_)
+{
+   constexpr int mnd_o = T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
+   constexpr int mnq_o =
+      T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
+   constexpr int mndq = std::max(mnd_o + 1, mnq_o + 1);
+   constexpr int tbatch = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, mndq);
+   MFEM_VERIFY(ndof_o <= mnd_o, "Error: H(curl) order larger than supported");
+   MFEM_VERIFY(nquad_o <= mnq_o, "Error: H(div) order larger than supported");
+   int mnq = std::max(ndof_o + 1, nquad_o + 1);
+   auto pa_data = pa.Read();
+   auto x_d = x_.Read();
+   auto y_d = y_.ReadWrite();
+   mfem::forall_2D_batch<mndq * mndq * (mndq - 1) * tbatch>(
+      ne, mnq * mnq * (mnq - 1), 1, tbatch, [=] MFEM_HOST_DEVICE(int e)
+   {
+      constexpr int MND_O =
+         T_NDOF_O ? T_NDOF_O : DofQuadLimits::HCURL_MAX_D1D - 1;
+      constexpr int MNQ_O =
+         T_NQUAD_O ? T_NQUAD_O : DofQuadLimits::HDIV_MAX_D1D - 1;
+      constexpr int MNDQ = std::max(MND_O + 1, MNQ_O + 1);
+#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__)
+      constexpr int nbz = curlinterp::NBZ3D(T_NDOF_O, T_NQUAD_O, MNDQ);
+      int tidz = MFEM_THREAD_ID(z);
+      // Make mnq a local variable since capturing would result in different
+      // captures between host/device versions, and spuriously fails
+      int mnq = std::max(ndof_o + 1, nquad_o + 1);
+#else
+      constexpr int nbz = 1;
+      constexpr int tidz = 0;
+#endif
+      const int NDOF_O = T_NDOF_O ? T_NDOF_O : ndof_o;
+      const int NQUAD_O = T_NQUAD_O ? T_NQUAD_O : nquad_o;
+      const int NDOF_C = NDOF_O + 1;
+      const int NQUAD_C = NQUAD_O + 1;
+      MFEM_SHARED real_t
+      sBG[(MND_O + 1) * MNQ_O + (MND_O + 1) * (MNQ_O + 1) + MND_O * MNQ_O];
+      auto X_ = Reshape(x_d, 3 * NQUAD_C * NQUAD_O * NQUAD_O, ne);
+      auto Y = Reshape(y_d, 3 * NDOF_C * NDOF_C * NDOF_O, ne);
+      auto Gco = Reshape(sBG, NQUAD_O, NDOF_C);
+      auto Bcc = Reshape(sBG + NDOF_C * NQUAD_O, NQUAD_C, NDOF_C);
+      auto Boo =
+         Reshape(sBG + NDOF_C * NQUAD_O + NDOF_C * NQUAD_C, NQUAD_O, NDOF_O);
+      MFEM_SHARED real_t X[3][nbz][MNQ_O * MNQ_O * (MNQ_O + 1)];
+      MFEM_SHARED real_t sm0[nbz * 2 * MNDQ * MNDQ * MNDQ];
+      MFEM_SHARED real_t sm1[nbz * 2 * MNDQ * MNDQ * MNDQ];
+
+      // shapes of buffers always use MNDQ to mitigate shared memory bank
+      // conflicts
+      real_t(*QQD)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
+      real_t(*QDD)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm1);
+      real_t(*DDD)[nbz][MNDQ][MNDQ][MNDQ] =
+         (real_t(*)[nbz][MNDQ][MNDQ][MNDQ])(sm0);
+      const int offset = NDOF_O * NDOF_C * NDOF_C;
+      const int offsetq = NQUAD_C * NQUAD_O * NQUAD_O;
+      MFEM_FOREACH_THREAD_DIRECT(ix, x, offsetq)
+      {
+         for (int dim = 0; dim < 3; ++dim)
+         {
+            X[dim][tidz][ix] = X_(ix + dim * offsetq, e);
+         }
+      }
+      // load basis functions data
+      if (tidz == 0)
+      {
+         auto npts = NDOF_C * NQUAD_O + NDOF_C * NQUAD_C + NDOF_O * NQUAD_O;
+         MFEM_FOREACH_THREAD(ix, x, npts) { sBG[ix] = pa_data[ix]; }
+      }
+      MFEM_SYNC_THREAD;
+
+      // x: Vy Boo Bcc Gco - Vz Boo Gco Bcc
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
+                                           NQUAD_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_O; ++qz)
+         {
+            u += X[1][tidz][qx + (qy + qz * NQUAD_C) * NQUAD_O] * Gco(qz, dz);
+         }
+         QQD[0][tidz][qy][qx][dz] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_C; ++qz)
+         {
+            u += X[2][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_O] * Bcc(qz, dz);
+         }
+         QQD[1][tidz][qy][qx][dz] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_C; ++qy)
+         {
+            u += QQD[0][tidz][qy][qx][dz] * Bcc(qy, dy);
+         }
+         QDD[0][tidz][qx][dz][dy] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_O; ++qy)
+         {
+            u += QQD[1][tidz][qy][qx][dz] * Gco(qy, dy);
+         }
+         QDD[1][tidz][qx][dz][dy] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_O, NDOF_C,
+                                           NDOF_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_O; ++qx)
+         {
+            u += QDD[0][tidz][qx][dz][dy] * Boo(qx, dx);
+         }
+         DDD[0][tidz][dz][dy][dx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_O, NDOF_C,
+                                           NDOF_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_O; ++qx)
+         {
+            u += QDD[1][tidz][qx][dz][dy] * Boo(qx, dx);
+         }
+         Y(dx + (dy + dz * NDOF_C) * NDOF_O, e) =
+            DDD[0][tidz][dz][dy][dx] - u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // y: Vz Gco Boo Bcc - Vx Bcc Boo Gco
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_O,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_C; ++qz)
+         {
+            u += X[2][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_O] * Bcc(qz, dz);
+         }
+         QQD[0][tidz][qy][qx][dz] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_C, NQUAD_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_O; ++qz)
+         {
+            u += X[0][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_C] * Gco(qz, dz);
+         }
+         QQD[1][tidz][qy][qx][dz] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_O, NDOF_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_O; ++qy)
+         {
+            u += QQD[0][tidz][qy][qx][dz] * Boo(qy, dy);
+         }
+         QDD[0][tidz][qx][dz][dy] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_O, NDOF_C,
+                                           NQUAD_C, mnq - 1, mnq, mnq)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_O; ++qy)
+         {
+            u += QQD[1][tidz][qy][qx][dz] * Boo(qy, dy);
+         }
+         QDD[1][tidz][qx][dz][dy] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_O; ++qx)
+         {
+            u += QDD[0][tidz][qx][dz][dy] * Gco(qx, dx);
+         }
+         DDD[0][tidz][dz][dy][dx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_O,
+                                           NDOF_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_C; ++qx)
+         {
+            u += QDD[1][tidz][qx][dz][dy] * Bcc(qx, dx);
+         }
+         Y(dx + (dy + dz * NDOF_O) * NDOF_C + offset, e) =
+            DDD[0][tidz][dz][dy][dx] - u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // z: Vx Bcc Gco Boo - Vy Gco Bcc Boo
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_O, NQUAD_C,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_O; ++qz)
+         {
+            u += X[0][tidz][qx + (qy + qz * NQUAD_O) * NQUAD_C] * Boo(qz, dz);
+         }
+         QQD[0][tidz][qy][qx][dz] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dz, qx, qy, x, NDOF_O, NQUAD_O,
+                                           NQUAD_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int qz = 0; qz < NQUAD_O; ++qz)
+         {
+            u += X[1][tidz][qx + (qy + qz * NQUAD_C) * NQUAD_O] * Boo(qz, dz);
+         }
+         QQD[1][tidz][qy][qx][dz] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_O,
+                                           NQUAD_C, mnq, mnq - 1, mnq)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_O; ++qy)
+         {
+            u += QQD[0][tidz][qy][qx][dz] * Gco(qy, dy);
+         }
+         QDD[0][tidz][qx][dz][dy] = u;
+      }
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dy, dz, qx, x, NDOF_C, NDOF_O,
+                                           NQUAD_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qy = 0; qy < NQUAD_C; ++qy)
+         {
+            u += QQD[1][tidz][qy][qx][dz] * Bcc(qy, dy);
+         }
+         QDD[1][tidz][qx][dz][dy] = u;
+      }
+      MFEM_SYNC_THREAD;
+
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_C,
+                                           NDOF_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_C; ++qx)
+         {
+            u += QDD[0][tidz][qx][dz][dy] * Bcc(qx, dx);
+         }
+         DDD[0][tidz][dz][dy][dx] = u;
+      }
+      MFEM_SYNC_THREAD;
+      // threads assigned to mitigate bank conflicts
+      MFEM_FOREACH_THREAD_DIRECT_3D_OFFSET(dx, dy, dz, x, NDOF_C, NDOF_C,
+                                           NDOF_O, mnq, mnq, mnq - 1)
+      {
+         real_t u = 0;
+         for (int qx = 0; qx < NQUAD_O; ++qx)
+         {
+            u += QDD[1][tidz][qx][dz][dy] * Gco(qx, dx);
+         }
+         Y(dx + (dy + dz * NDOF_C) * NDOF_C + 2 * offset, e) =
+            DDD[0][tidz][dz][dy][dx] - u;
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
 } // namespace internal
 
+template <int DIM, int NDOF_O, int NQUAD_O>
+CurlInterpolator::ApplyKernelType
+CurlInterpolator::ApplyPAKernels::Kernel()
+{
+   if constexpr (DIM == 3)
+   {
+      return internal::CurlInterpolatorApply3DSmem<NDOF_O, NQUAD_O>;
+   }
+   MFEM_ABORT("Bad dimension!");
+}
+
+template <int DIM, int NDOF_O, int NQUAD_O>
+CurlInterpolator::ApplyKernelType
+CurlInterpolator::ApplyTPAKernels::Kernel()
+{
+   if constexpr (DIM == 3)
+   {
+      return internal::CurlInterpolatorTApply3DSmem<NDOF_O, NQUAD_O>;
+   }
+   MFEM_ABORT("Bad dimension!");
+}
+
 } // namespace mfem
 
 /// \endcond DO_NOT_DOCUMENT

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_interp_pa.cpp

@@ -14,9 +14,218 @@
 #include "../gridfunc.hpp"
 #include "../qfunction.hpp"
 
+#include "bilininteg_hcurlhdiv_kernels.hpp"
+
 namespace mfem
 {
 
+namespace
+{
+
+void PAHcurlApplyCurl2D(const int c_dofs1D,
+                        const int o_dofs1D,
+                        const int NE,
+                        const Array<real_t> &Bo_,
+                        const Array<real_t> &Gc_,
+                        const Vector &x_,
+                        Vector &y_)
+{
+   auto Bo = Reshape(Bo_.Read(), o_dofs1D, o_dofs1D);
+   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
+   auto X = Reshape(x_.Read(), 2 * c_dofs1D * o_dofs1D, NE);
+   auto Y = Reshape(y_.ReadWrite(), o_dofs1D, o_dofs1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int iy = 0; iy < c_dofs1D; ++iy)
+      {
+         for (int ix = 0; ix < o_dofs1D; ++ix)
+         {
+            const real_t xv = X(ix + iy * o_dofs1D, e);
+            for (int oy = 0; oy < o_dofs1D; ++oy)
+            {
+               const real_t gy = Gc(oy, iy);
+               for (int ox = 0; ox < o_dofs1D; ++ox)
+               {
+                  Y(ox, oy, e) -= Bo(ox, ix) * gy * xv;
+               }
+            }
+         }
+      }
+
+      const int y_nd = c_dofs1D * o_dofs1D;
+      for (int iy = 0; iy < o_dofs1D; ++iy)
+      {
+         for (int ix = 0; ix < c_dofs1D; ++ix)
+         {
+            const real_t xv = X(y_nd + ix + iy * c_dofs1D, e);
+            for (int oy = 0; oy < o_dofs1D; ++oy)
+            {
+               const real_t by = Bo(oy, iy);
+               for (int ox = 0; ox < o_dofs1D; ++ox)
+               {
+                  Y(ox, oy, e) += Gc(ox, ix) * by * xv;
+               }
+            }
+         }
+      }
+   });
+}
+
+void PAHcurlApplyCurlTranspose2D(const int c_dofs1D,
+                                 const int o_dofs1D,
+                                 const int NE,
+                                 const Array<real_t> &Bo_,
+                                 const Array<real_t> &Gc_,
+                                 const Vector &x_,
+                                 Vector &y_)
+{
+   auto Bo = Reshape(Bo_.Read(), o_dofs1D, o_dofs1D);
+   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
+   auto X = Reshape(x_.Read(), o_dofs1D, o_dofs1D, NE);
+   auto Y = Reshape(y_.ReadWrite(), 2 * c_dofs1D * o_dofs1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int dy = 0; dy < c_dofs1D; ++dy)
+      {
+         for (int dx = 0; dx < o_dofs1D; ++dx)
+         {
+            real_t sum = 0.0;
+            for (int oy = 0; oy < o_dofs1D; ++oy)
+            {
+               const real_t gy = Gc(oy, dy);
+               for (int ox = 0; ox < o_dofs1D; ++ox)
+               {
+                  sum -= Bo(ox, dx) * gy * X(ox, oy, e);
+               }
+            }
+            Y(dx + dy * o_dofs1D, e) += sum;
+         }
+      }
+
+      const int y_nd = c_dofs1D * o_dofs1D;
+      for (int dy = 0; dy < o_dofs1D; ++dy)
+      {
+         for (int dx = 0; dx < c_dofs1D; ++dx)
+         {
+            real_t sum = 0.0;
+            for (int oy = 0; oy < o_dofs1D; ++oy)
+            {
+               const real_t by = Bo(oy, dy);
+               for (int ox = 0; ox < o_dofs1D; ++ox)
+               {
+                  sum += Gc(ox, dx) * by * X(ox, oy, e);
+               }
+            }
+            Y(y_nd + dx + dy * c_dofs1D, e) += sum;
+         }
+      }
+   });
+}
+
+void PAHdivApplyCurl2D(const int c_dofs1D,
+                       const int o_dofs1D,
+                       const int NE,
+                       const Array<real_t> &Bc_,
+                       const Array<real_t> &Gc_,
+                       const Vector &x_,
+                       Vector &y_)
+{
+   auto Bc = Reshape(Bc_.Read(), c_dofs1D, c_dofs1D);
+   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
+   auto X = Reshape(x_.Read(), c_dofs1D, c_dofs1D, NE);
+   auto Y = Reshape(y_.ReadWrite(), 2 * c_dofs1D * o_dofs1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int iy = 0; iy < c_dofs1D; ++iy)
+      {
+         for (int ix = 0; ix < c_dofs1D; ++ix)
+         {
+            const real_t xv = X(ix, iy, e);
+            for (int oy = 0; oy < o_dofs1D; ++oy)
+            {
+               const real_t gy = Gc(oy, iy);
+               for (int ox = 0; ox < c_dofs1D; ++ox)
+               {
+                  Y(ox + oy * c_dofs1D, e) += Bc(ox, ix) * gy * xv;
+               }
+            }
+         }
+      }
+
+      const int y_nd = c_dofs1D * o_dofs1D;
+      for (int iy = 0; iy < c_dofs1D; ++iy)
+      {
+         for (int ix = 0; ix < c_dofs1D; ++ix)
+         {
+            const real_t xv = X(ix, iy, e);
+            for (int oy = 0; oy < c_dofs1D; ++oy)
+            {
+               const real_t by = Bc(oy, iy);
+               for (int ox = 0; ox < o_dofs1D; ++ox)
+               {
+                  Y(y_nd + ox + oy * o_dofs1D, e) -= Gc(ox, ix) * by * xv;
+               }
+            }
+         }
+      }
+   });
+}
+
+void PAHdivApplyCurlTranspose2D(const int c_dofs1D,
+                                const int o_dofs1D,
+                                const int NE,
+                                const Array<real_t> &Bc_,
+                                const Array<real_t> &Gc_,
+                                const Vector &x_,
+                                Vector &y_)
+{
+   auto Bc = Reshape(Bc_.Read(), c_dofs1D, c_dofs1D);
+   auto Gc = Reshape(Gc_.Read(), o_dofs1D, c_dofs1D);
+   auto X = Reshape(x_.Read(), 2 * c_dofs1D * o_dofs1D, NE);
+   auto Y = Reshape(y_.ReadWrite(), c_dofs1D, c_dofs1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int dy = 0; dy < o_dofs1D; ++dy)
+      {
+         for (int dx = 0; dx < c_dofs1D; ++dx)
+         {
+            const real_t xv = X(dx + dy * c_dofs1D, e);
+            for (int iy = 0; iy < c_dofs1D; ++iy)
+            {
+               const real_t gy = Gc(dy, iy);
+               for (int ix = 0; ix < c_dofs1D; ++ix)
+               {
+                  Y(ix, iy, e) += Bc(dx, ix) * gy * xv;
+               }
+            }
+         }
+      }
+
+      const int y_nd = c_dofs1D * o_dofs1D;
+      for (int dy = 0; dy < c_dofs1D; ++dy)
+      {
+         for (int dx = 0; dx < o_dofs1D; ++dx)
+         {
+            const real_t xv = X(y_nd + dx + dy * o_dofs1D, e);
+            for (int iy = 0; iy < c_dofs1D; ++iy)
+            {
+               const real_t by = Bc(dy, iy);
+               for (int ix = 0; ix < c_dofs1D; ++ix)
+               {
+                  Y(ix, iy, e) -= Gc(dx, ix) * by * xv;
+               }
+            }
+         }
+      }
+   });
+}
+
+}
+
 // Apply to x corresponding to DOFs in H^1 (domain) the (topological) gradient
 // to get a dof in H(curl) (range). You can think of the range as the "test" space
 // and the domain as the "trial" space, but there's no integration.
@@ -1950,4 +2159,266 @@ void IdentityInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
    }
 }
 
+void CurlInterpolator::AssemblePA(const FiniteElementSpace &dom_fes,
+                                  const FiniteElementSpace &ran_fes)
+{
+   Mesh *mesh = dom_fes.GetMesh();
+   dim = mesh->Dimension();
+   ne = dom_fes.GetNE();
+   pa_mode_2d = 0;
+   MFEM_VERIFY(ne == ran_fes.GetNE(),
+               "Different meshes for domain and range spaces");
+
+   if (dim == 2)
+   {
+      pa_data.SetSize(0);
+      const FiniteElement *dom_fel = dom_fes.GetTypicalFE();
+      const FiniteElement *ran_fel = ran_fes.GetTypicalFE();
+      const bool hcurl_to_scalar =
+         dynamic_cast<const VectorTensorFiniteElement*>(dom_fel) != NULL &&
+         dom_fel->GetDerivType() == FiniteElement::CURL &&
+         dynamic_cast<const TensorBasisElement*>(ran_fel) != NULL &&
+         ran_fel->GetRangeType() == FiniteElement::SCALAR;
+      const bool scalar_to_hdiv =
+         dynamic_cast<const TensorBasisElement*>(dom_fel) != NULL &&
+         dom_fel->GetRangeType() == FiniteElement::SCALAR &&
+         dynamic_cast<const VectorTensorFiniteElement*>(ran_fel) != NULL &&
+         ran_fel->GetDerivType() == FiniteElement::DIV;
+
+      MFEM_VERIFY(hcurl_to_scalar || scalar_to_hdiv,
+                  "2D CurlInterpolator PA supports H(curl)->scalar and scalar->H(div) only.");
+
+      int closed_basis_type = -1;
+      int open_basis_type = -1;
+      if (hcurl_to_scalar)
+      {
+         const auto *trial_fec = dynamic_cast<const ND_FECollection*>(dom_fes.FEColl());
+         const auto *range_fec = dynamic_cast<const L2_FECollection*>(ran_fes.FEColl());
+         MFEM_VERIFY(trial_fec != NULL, "H(curl) domain must use ND_FECollection.");
+         MFEM_VERIFY(range_fec != NULL, "Scalar range must use L2_FECollection.");
+         MFEM_VERIFY(ran_fel->GetMapType() == FiniteElement::INTEGRAL,
+                     "2D H(curl)->scalar CurlInterpolator PA supports integral-map scalar range spaces only.");
+         closed_basis_type = trial_fec->GetClosedBasisType();
+         open_basis_type = trial_fec->GetOpenBasisType();
+         MFEM_VERIFY(range_fec->GetBasisType() == open_basis_type,
+                     "Domain/range open basis types do not match.");
+         pa_mode_2d = 1;
+      }
+      else
+      {
+         const auto *trial_fec = dynamic_cast<const H1_FECollection*>(dom_fes.FEColl());
+         const auto *range_fec = dynamic_cast<const RT_FECollection*>(ran_fes.FEColl());
+         MFEM_VERIFY(trial_fec != NULL, "Scalar domain must use H1_FECollection.");
+         MFEM_VERIFY(range_fec != NULL, "H(div) range must use RT_FECollection.");
+         closed_basis_type = trial_fec->GetBasisType();
+         open_basis_type = range_fec->GetOpenBasisType();
+         MFEM_VERIFY(range_fec->GetClosedBasisType() == closed_basis_type,
+                     "Domain/range closed basis types do not match.");
+         pa_mode_2d = 2;
+      }
+
+      const int order = hcurl_to_scalar
+                        ? dynamic_cast<const VectorTensorFiniteElement*>(dom_fel)->GetOrder()
+                        : dynamic_cast<const NodalTensorFiniteElement*>(dom_fel)->GetOrder();
+      c_dofs1D = order + 1;
+      o_dofs1D = order;
+
+      closed_dofquad_fe.reset(new H1_SegmentElement(order, closed_basis_type));
+      open_dofquad_fe.reset(new L2_SegmentElement(order - 1, open_basis_type));
+
+      mfem::QuadratureFunctions1D qf1d;
+      mfem::IntegrationRule closed_ir;
+      closed_ir.SetSize(c_dofs1D);
+      qf1d.GaussLobatto(c_dofs1D, &closed_ir);
+
+      mfem::IntegrationRule open_ir;
+      open_ir.SetSize(o_dofs1D);
+      qf1d.GaussLegendre(o_dofs1D, &open_ir);
+
+      maps_C_C = &closed_dofquad_fe->GetDofToQuad(closed_ir, DofToQuad::TENSOR);
+      maps_O_C = &closed_dofquad_fe->GetDofToQuad(open_ir, DofToQuad::TENSOR);
+      maps_O_O = &open_dofquad_fe->GetDofToQuad(open_ir, DofToQuad::TENSOR);
+
+      MFEM_VERIFY(maps_C_C->ndof == c_dofs1D && maps_C_C->nqpt == c_dofs1D, "");
+      MFEM_VERIFY(maps_O_C->ndof == c_dofs1D && maps_O_C->nqpt == o_dofs1D, "");
+      MFEM_VERIFY(maps_O_O->ndof == o_dofs1D && maps_O_O->nqpt == o_dofs1D, "");
+      return;
+   }
+
+   closed_dofquad_fe.reset();
+   open_dofquad_fe.reset();
+   maps_C_C = nullptr;
+   maps_O_C = nullptr;
+   maps_O_O = nullptr;
+
+   const VectorTensorFiniteElement *dom_el =
+      dynamic_cast<const VectorTensorFiniteElement *>(dom_fes.GetTypicalFE());
+   const VectorTensorFiniteElement *ran_el =
+      dynamic_cast<const VectorTensorFiniteElement *>(ran_fes.GetTypicalFE());
+   MFEM_VERIFY(dom_el != NULL, "Only VectorTensorFiniteElement is supported!");
+   MFEM_VERIFY(ran_el != NULL, "Only VectorTensorFiniteElement is supported!");
+   MFEM_VERIFY(dom_el->GetDerivType() == FiniteElement::CURL,
+               "Domain space must be H(curl)");
+   MFEM_VERIFY(ran_el->GetDerivType() == FiniteElement::DIV,
+               "Range space must be H(div)");
+
+   const int dims = dom_el->GetDim();
+   MFEM_VERIFY(dims == 3, "");
+
+   ndof_o = dom_el->GetOrder();
+   int ndof_c = ndof_o + 1;
+   nquad_o = ran_el->GetOrder();
+   int nquad_c = nquad_o + 1;
+
+   // extract the tensor product range dof locations
+   std::vector<real_t> qc(nquad_c);
+   std::vector<real_t> qo(nquad_o);
+   {
+      const IntegrationRule &ran_nodes = ran_el->GetNodes();
+      const Array<int> &quad_map = ran_el->GetDofMap();
+      for (int i = 0; i < nquad_c; ++i)
+      {
+         int idx = UnsignIndex(quad_map[i]);
+         qc[i] = ran_nodes.IntPoint(idx).x;
+      }
+      int offset = ndof_c * ndof_o * ndof_o;
+      for (int i = 0; i < nquad_o; ++i)
+      {
+         int idx = UnsignIndex(quad_map[i + offset]);
+         qo[i] = ran_nodes.IntPoint(idx).x;
+      }
+   }
+
+   // evaluate closed/open 1D basis (and their derivatives) at closed and
+   // open quads
+   // storage order: GCO, BCC, BOO
+   pa_data.SetSize(ndof_c * nquad_o + ndof_c * nquad_c + ndof_o * nquad_o);
+   auto ptr = pa_data.HostWrite();
+   auto &cbasis1d = dom_el->GetBasis1D();
+   auto &obasis1d = dom_el->GetOpenBasis1D();
+   Vector b, g;
+   b.SetSize(ndof_c);
+   g.SetSize(ndof_c);
+   for (int j = 0; j < nquad_o; ++j)
+   {
+      cbasis1d.Eval(qo[j], b, g);
+      for (int i = 0; i < ndof_c; ++i)
+      {
+         ptr[j + i * nquad_o] = g[i];
+      }
+   }
+   ptr += nquad_o * ndof_c;
+
+   for (int j = 0; j < nquad_c; ++j)
+   {
+      cbasis1d.Eval(qc[j], b);
+      for (int i = 0; i < ndof_c; ++i)
+      {
+         ptr[j + i * nquad_c] = b[i];
+      }
+   }
+   ptr += ndof_c * nquad_c;
+
+   b.SetSize(ndof_o);
+   for (int j = 0; j < nquad_o; ++j)
+   {
+      obasis1d.Eval(qo[j], b);
+      for (int i = 0; i < ndof_o; ++i)
+      {
+         ptr[j + i * nquad_o] = b[i];
+      }
+   }
+}
+
+CurlInterpolator::Kernels::Kernels()
+{
+   CurlInterpolator::AddSpecialization<3, 1, 1>();
+   CurlInterpolator::AddSpecialization<3, 2, 2>();
+   CurlInterpolator::AddSpecialization<3, 3, 3>();
+   CurlInterpolator::AddSpecialization<3, 4, 4>();
+   CurlInterpolator::AddSpecialization<3, 5, 5>();
+}
+
+CurlInterpolator::CurlInterpolator() { static Kernels kernels{}; }
+
+void CurlInterpolator::AddMultPA(const Vector &x, Vector &y) const
+{
+   if (dim == 2)
+   {
+      MFEM_VERIFY(maps_C_C != nullptr && maps_O_C != nullptr,
+                  "2D CurlInterpolator PA data is not assembled.");
+      if (pa_mode_2d == 1)
+      {
+         MFEM_VERIFY(maps_O_O != nullptr,
+                     "2D CurlInterpolator scalar curl map is not assembled.");
+         PAHcurlApplyCurl2D(c_dofs1D, o_dofs1D, ne, maps_O_O->B, maps_O_C->G,
+                            x, y);
+      }
+      else if (pa_mode_2d == 2)
+      {
+         PAHdivApplyCurl2D(c_dofs1D, o_dofs1D, ne, maps_C_C->B, maps_O_C->G,
+                           x, y);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported 2D CurlInterpolator mode.");
+      }
+      return;
+   }
+
+   ApplyPAKernels::Run(dim, ndof_o, nquad_o, ne, ndof_o, nquad_o, pa_data, x, y);
+}
+
+void CurlInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
+{
+   if (dim == 2)
+   {
+      MFEM_VERIFY(maps_C_C != nullptr && maps_O_C != nullptr,
+                  "2D CurlInterpolator PA data is not assembled.");
+      if (pa_mode_2d == 1)
+      {
+         MFEM_VERIFY(maps_O_O != nullptr,
+                     "2D CurlInterpolator scalar curl map is not assembled.");
+         PAHcurlApplyCurlTranspose2D(c_dofs1D, o_dofs1D, ne, maps_O_O->B,
+                                     maps_O_C->G, x, y);
+      }
+      else if (pa_mode_2d == 2)
+      {
+         PAHdivApplyCurlTranspose2D(c_dofs1D, o_dofs1D, ne, maps_C_C->B,
+                                    maps_O_C->G, x, y);
+      }
+      else
+      {
+         MFEM_ABORT("Unsupported 2D CurlInterpolator mode.");
+      }
+      return;
+   }
+
+   ApplyTPAKernels::Run(dim, ndof_o, nquad_o, ne, ndof_o, nquad_o, pa_data, x, y);
+}
+
+/// \cond DO_NOT_DOCUMENT
+
+CurlInterpolator::ApplyKernelType
+CurlInterpolator::ApplyPAKernels::Fallback(int DIM, int, int)
+{
+   if (DIM == 3)
+   {
+      return internal::CurlInterpolatorApply3DSmem<0, 0>;
+   }
+   MFEM_ABORT("Bad dimension!");
+}
+
+CurlInterpolator::ApplyKernelType
+CurlInterpolator::ApplyTPAKernels::Fallback(int DIM, int, int)
+{
+   if (DIM == 3)
+   {
+      return internal::CurlInterpolatorTApply3DSmem<0, 0>;
+   }
+   MFEM_ABORT("Bad dimension!");
+}
+
+/// \endcond DO_NOT_DOCUMENT
+
 } // namespace mfem

fem/integ/bilininteg_mass_ea.cpp

@@ -16,6 +16,71 @@
 
 namespace mfem
 {
+namespace
+{
+
+void AssembleEATriangularImpl(const int dim, const int ne,
+                              const int dofs1D, const int quad1D,
+                              const Array<real_t> &B,
+                              const Vector &pa_data,
+                              Vector &data,
+                              const bool add)
+{
+   using internal::EAMassAssembleTriangular1DLower;
+   using internal::EAMassAssembleTriangular2DLower;
+   using internal::EAMassAssembleTriangular3DLower;
+
+   if (dim == 1)
+   {
+      auto kernel = EAMassAssembleTriangular1DLower<0,0>;
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: kernel = EAMassAssembleTriangular1DLower<2,2>; break;
+         case 0x33: kernel = EAMassAssembleTriangular1DLower<3,3>; break;
+         case 0x44: kernel = EAMassAssembleTriangular1DLower<4,4>; break;
+         case 0x55: kernel = EAMassAssembleTriangular1DLower<5,5>; break;
+         case 0x66: kernel = EAMassAssembleTriangular1DLower<6,6>; break;
+         case 0x77: kernel = EAMassAssembleTriangular1DLower<7,7>; break;
+         case 0x88: kernel = EAMassAssembleTriangular1DLower<8,8>; break;
+         case 0x99: kernel = EAMassAssembleTriangular1DLower<9,9>; break;
+      }
+      return kernel(ne, B, pa_data, data, add, dofs1D, quad1D);
+   }
+   else if (dim == 2)
+   {
+      auto kernel = EAMassAssembleTriangular2DLower<0,0>;
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: kernel = EAMassAssembleTriangular2DLower<2,2>; break;
+         case 0x33: kernel = EAMassAssembleTriangular2DLower<3,3>; break;
+         case 0x44: kernel = EAMassAssembleTriangular2DLower<4,4>; break;
+         case 0x55: kernel = EAMassAssembleTriangular2DLower<5,5>; break;
+         case 0x66: kernel = EAMassAssembleTriangular2DLower<6,6>; break;
+         case 0x77: kernel = EAMassAssembleTriangular2DLower<7,7>; break;
+         case 0x88: kernel = EAMassAssembleTriangular2DLower<8,8>; break;
+         case 0x99: kernel = EAMassAssembleTriangular2DLower<9,9>; break;
+      }
+      return kernel(ne, B, pa_data, data, add, dofs1D, quad1D);
+   }
+   else if (dim == 3)
+   {
+      auto kernel = EAMassAssembleTriangular3DLower<0,0>;
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23: kernel = EAMassAssembleTriangular3DLower<2,3>; break;
+         case 0x34: kernel = EAMassAssembleTriangular3DLower<3,4>; break;
+         case 0x45: kernel = EAMassAssembleTriangular3DLower<4,5>; break;
+         case 0x56: kernel = EAMassAssembleTriangular3DLower<5,6>; break;
+         case 0x67: kernel = EAMassAssembleTriangular3DLower<6,7>; break;
+         case 0x78: kernel = EAMassAssembleTriangular3DLower<7,8>; break;
+         case 0x89: kernel = EAMassAssembleTriangular3DLower<8,9>; break;
+      }
+      return kernel(ne, B, pa_data, data, add, dofs1D, quad1D);
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+}
 
 void MassIntegrator::AssembleEA_(Vector &ea_data,
                                  const bool add)
@@ -75,6 +140,16 @@ void MassIntegrator::AssembleEA_(Vector &ea_data,
    MFEM_ABORT("Unknown kernel.");
 }
 
+void MassIntegrator::AssembleEATriangular_(
+   TriPackLowerMatrix &ea_data,
+   const bool add)
+{
+   Vector &data = ea_data.Data();
+   const Array<real_t> &B = maps->B;
+   return AssembleEATriangularImpl(dim, ne, dofs1D, quad1D, B, pa_data, data,
+                                   add);
+}
+
 void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
                                 Vector &ea_data,
                                 const bool add)
@@ -83,6 +158,35 @@ void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
    if (ne > 0) { AssembleEA_(ea_data, add); }
 }
 
+void MassIntegrator::AssembleEATriangular(const FiniteElementSpace &fes,
+                                          TriPackLowerMatrix &ea_data,
+                                          const bool add)
+{
+   AssemblePA(fes);
+   if (ne == 0) { return; }
+
+   int elem_dofs = 1;
+   for (int d = 0; d < dim; ++d)
+   {
+      elem_dofs *= dofs1D;
+   }
+
+   if (add)
+   {
+      MFEM_VERIFY(ea_data.GetNumRows() == elem_dofs,
+                  "Invalid triangular EA element size.");
+      MFEM_VERIFY(ea_data.GetNumMatrices() == ne,
+                  "Invalid triangular EA element count.");
+   }
+   else
+   {
+      ea_data.SetSize(elem_dofs, ne);
+      ea_data.UseDevice(true);
+   }
+
+   AssembleEATriangular_(ea_data, add);
+}
+
 void MassIntegrator::AssembleEABoundary(const FiniteElementSpace &fes,
                                         Vector &ea_data,
                                         const bool add)

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
 {
 
@@ -1400,6 +1402,480 @@ inline void EAMassAssemble3D(const int NE,
    });
 }
 
+template <int T_D1D = 0, int T_Q1D = 0>
+inline void EAMassAssembleTriangular1DLower(const int NE,
+                                            const Array<real_t> &basis,
+                                            const Vector &padata,
+                                            Vector &eadata,
+                                            const bool add,
+                                            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(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, NE);
+   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(),
+                    TriPackLowerMatrix::PackedSize(D1D), 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;
+      for (int i1 = 0; i1 < D1D; ++i1)
+      {
+         for (int j1 = 0; j1 <= i1; ++j1)
+         {
+            real_t val = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val += B(k1, i1) * B(k1, j1) * D(k1, e);
+            }
+            const int idx = TriPackLowerMatrix::LowerIndex(i1, j1, D1D);
+            if (add)
+            {
+               M(idx, e) += val;
+            }
+            else
+            {
+               M(idx, e) = val;
+            }
+         }
+      }
+   });
+}
+
+template <int T_D1D = 0, int T_Q1D = 0>
+inline void EAMassAssembleTriangular2DLower(const int NE,
+                                            const Array<real_t> &basis,
+                                            const Vector &padata,
+                                            Vector &eadata,
+                                            const bool add,
+                                            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, "");
+   const int ndofs = D1D*D1D;
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, Q1D, NE);
+   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(),
+                    TriPackLowerMatrix::PackedSize(ndofs), NE);
+
+   mfem::forall_2D(NE, D1D, D1D, [=] MFEM_HOST_DEVICE (int e)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      const int ndofs = D1D*D1D;
+      real_t r_B[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+         }
+      }
+      MFEM_SHARED real_t s_D[MQ1][MQ1];
+      MFEM_FOREACH_THREAD(k1,x,Q1D)
+      {
+         MFEM_FOREACH_THREAD(k2,y,Q1D)
+         {
+            s_D[k1][k2] = D(k1,k2,e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            const int row = i1 + D1D*i2;
+            for (int j2 = 0; j2 < D1D; ++j2)
+            {
+               for (int j1 = 0; j1 < D1D; ++j1)
+               {
+                  const int col = j1 + D1D*j2;
+                  if (row < col)
+                  {
+                     continue;
+                  }
+                  real_t val = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        val += r_B[k1][i1] * r_B[k1][j1]
+                               * r_B[k2][i2] * r_B[k2][j2]
+                               * s_D[k1][k2];
+                     }
+                  }
+                  const int idx = TriPackLowerMatrix::LowerIndex(row, col, ndofs);
+                  if (add)
+                  {
+                     M(idx, e) += val;
+                  }
+                  else
+                  {
+                     M(idx, e) = val;
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
+template <int T_D1D, int T_Q1D, int T_COLB, int T_NT = 32>
+inline void EAMassAssembleTriangular3D_LowerBlockCols_Impl(
+   const int NE,
+   const Array<real_t> &basis,
+   const Vector &padata,
+   Vector &eadata,
+   const bool add,
+   const int,
+   const int)
+{
+   static_assert(T_D1D > 0 && T_Q1D > 0, "");
+   // Specialized packed lower-triangular hex mass assembly using block-column
+   // sum-factorization.
+   constexpr int D1D = T_D1D;
+   constexpr int Q1D = T_Q1D;
+   constexpr int COLB = T_COLB;
+   constexpr int NT = T_NT;
+   constexpr int ND = D1D*D1D*D1D;
+   constexpr int NQ = Q1D*Q1D*Q1D;
+
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, NE);
+   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(),
+                    TriPackLowerMatrix::PackedSize(ND), NE);
+
+   mfem::forall_3D_grid(NE, NT, 1, 1, 0, [=] MFEM_HOST_DEVICE (int e)
+   {
+      const int tid = MFEM_THREAD_ID(x);
+
+      MFEM_SHARED real_t s_B[Q1D][D1D];
+      MFEM_SHARED real_t uW[NQ*COLB];
+      MFEM_SHARED real_t t1[D1D*Q1D*Q1D*COLB];
+      MFEM_SHARED real_t t2[D1D*D1D*Q1D*COLB];
+
+      for (int qb = tid; qb < Q1D*D1D; qb += NT)
+      {
+         const int q = qb % Q1D;
+         const int d = qb / Q1D;
+         s_B[q][d] = B(q, d);
+      }
+      MFEM_SYNC_THREAD;
+
+      for (int j0 = 0; j0 < ND; j0 += COLB)
+      {
+         const int b = (j0 + COLB <= ND) ? COLB : (ND - j0);
+         int j1[COLB], j2[COLB], j3[COLB];
+         for (int c = 0; c < COLB; ++c)
+         {
+            if (c < b)
+            {
+               const int jj = j0 + c;
+               j1[c] = jj % D1D;
+               const int tmp = jj / D1D;
+               j2[c] = tmp % D1D;
+               j3[c] = tmp / D1D;
+            }
+         }
+
+         for (int q = tid; q < NQ; q += NT)
+         {
+            const int q1 = q % Q1D;
+            const int tmp = q / Q1D;
+            const int q2 = tmp % Q1D;
+            const int q3 = tmp / Q1D;
+            const real_t Dq = D(q1, q2, q3, e);
+
+            for (int c = 0; c < b; ++c)
+            {
+               uW[q + NQ*c] = s_B[q1][j1[c]] * s_B[q2][j2[c]]
+                              * s_B[q3][j3[c]] * Dq;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         constexpr int T1S = D1D*Q1D*Q1D;
+         for (int a = tid; a < T1S; a += NT)
+         {
+            const int i1 = a % D1D;
+            const int tmp = a / D1D;
+            const int q2 = tmp % Q1D;
+            const int q3 = tmp / Q1D;
+
+            for (int c = 0; c < b; ++c)
+            {
+               real_t sum = 0.0;
+               for (int q1 = 0; q1 < Q1D; ++q1)
+               {
+                  const int q = q1 + Q1D*(q2 + Q1D*q3);
+                  sum += s_B[q1][i1] * uW[q + NQ*c];
+               }
+               t1[a + T1S*c] = sum;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         constexpr int T2S = D1D*D1D*Q1D;
+         for (int a = tid; a < T2S; a += NT)
+         {
+            const int i1 = a % D1D;
+            const int tmp = a / D1D;
+            const int i2 = tmp % D1D;
+            const int q3 = tmp / D1D;
+
+            for (int c = 0; c < b; ++c)
+            {
+               real_t sum = 0.0;
+               for (int q2 = 0; q2 < Q1D; ++q2)
+               {
+                  const int a1 = i1 + D1D*(q2 + Q1D*q3);
+                  sum += s_B[q2][i2] * t1[a1 + T1S*c];
+               }
+               t2[a + T2S*c] = sum;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         for (int c = 0; c < b; ++c)
+         {
+            const int col = j0 + c;
+            const int jj1 = j1[c];
+            const int jj2 = j2[c];
+            const int jj3 = j3[c];
+
+            for (int i3 = jj3 + 1; i3 < D1D; ++i3)
+            {
+               for (int a = tid; a < D1D*D1D; a += NT)
+               {
+                  const int i1 = a % D1D;
+                  const int i2 = a / D1D;
+                  real_t sum = 0.0;
+                  for (int q3 = 0; q3 < Q1D; ++q3)
+                  {
+                     const int a2 = i1 + D1D*(i2 + D1D*q3);
+                     sum += s_B[q3][i3] * t2[a2 + T2S*c];
+                  }
+                  const int row = i1 + D1D*(i2 + D1D*i3);
+                  const int idx =
+                     TriPackLowerMatrix::LowerIndex(row, col, ND);
+                  if (add) { M(idx, e) += sum; }
+                  else { M(idx, e) = sum; }
+               }
+               MFEM_SYNC_THREAD;
+            }
+
+            for (int i2 = jj2 + 1; i2 < D1D; ++i2)
+            {
+               const int i3 = jj3;
+               for (int i1 = tid; i1 < D1D; i1 += NT)
+               {
+                  real_t sum = 0.0;
+                  for (int q3 = 0; q3 < Q1D; ++q3)
+                  {
+                     const int a2 = i1 + D1D*(i2 + D1D*q3);
+                     sum += s_B[q3][i3] * t2[a2 + T2S*c];
+                  }
+                  const int row = i1 + D1D*(i2 + D1D*i3);
+                  const int idx =
+                     TriPackLowerMatrix::LowerIndex(row, col, ND);
+                  if (add) { M(idx, e) += sum; }
+                  else { M(idx, e) = sum; }
+               }
+               MFEM_SYNC_THREAD;
+            }
+
+            {
+               const int i3 = jj3;
+               const int i2 = jj2;
+               for (int i1 = tid + jj1; i1 < D1D; i1 += NT)
+               {
+                  real_t sum = 0.0;
+                  for (int q3 = 0; q3 < Q1D; ++q3)
+                  {
+                     const int a2 = i1 + D1D*(i2 + D1D*q3);
+                     sum += s_B[q3][i3] * t2[a2 + T2S*c];
+                  }
+                  const int row = i1 + D1D*(i2 + D1D*i3);
+                  const int idx =
+                     TriPackLowerMatrix::LowerIndex(row, col, ND);
+                  if (add) { M(idx, e) += sum; }
+                  else { M(idx, e) = sum; }
+               }
+               MFEM_SYNC_THREAD;
+            }
+         }
+      }
+   });
+}
+
+template <int T_D1D, int T_Q1D, int T_NT = 32>
+inline void EAMassAssembleTriangular3D_LowerBlockCols(
+   const int NE,
+   const Array<real_t> &basis,
+   const Vector &padata,
+   Vector &eadata,
+   const bool add,
+   const int d1d = 0,
+   const int q1d = 0)
+{
+   static_assert(T_D1D > 0 && T_Q1D > 0, "");
+
+   constexpr int D1D = T_D1D;
+   constexpr int Q1D = T_Q1D;
+   constexpr int NQ = Q1D*Q1D*Q1D;
+   constexpr int SharedBytesPerCol =
+      sizeof(real_t)*(NQ + D1D*Q1D*Q1D + D1D*D1D*Q1D);
+   constexpr int SharedBytesBase = sizeof(real_t)*(Q1D*D1D);
+   constexpr int MaxSharedBytes = 48*1024;
+   constexpr int COLB =
+      (SharedBytesBase + 4*SharedBytesPerCol <= MaxSharedBytes) ? 4 :
+      (SharedBytesBase + 2*SharedBytesPerCol <= MaxSharedBytes) ? 2 : 1;
+
+   return EAMassAssembleTriangular3D_LowerBlockCols_Impl<T_D1D, T_Q1D, COLB, T_NT>(
+             NE, basis, padata, eadata, add, d1d, q1d);
+}
+
+template <int T_D1D = 0, int T_Q1D = 0>
+inline void EAMassAssembleTriangular3DLower(const int NE,
+                                            const Array<real_t> &basis,
+                                            const Vector &padata,
+                                            Vector &eadata,
+                                            const bool add,
+                                            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, "");
+   const int ndofs = D1D*D1D*D1D;
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, NE);
+   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(),
+                    TriPackLowerMatrix::PackedSize(ndofs), NE);
+
+   if constexpr (T_D1D > 0 && T_Q1D > 0)
+   {
+      // Use the sum-factorized packed paths when the tensor dimensions are
+      // known at compile time. The generic path below handles dynamic sizes.
+      return EAMassAssembleTriangular3D_LowerBlockCols<T_D1D, T_Q1D>(
+                NE, basis, padata, eadata, add, d1d, q1d);
+   }
+   mfem::forall_3D(NE, D1D, D1D, D1D, [=] MFEM_HOST_DEVICE (int e)
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      constexpr int DQ = T_D1D * T_Q1D;
+      const int ndofs = D1D*D1D*D1D;
+
+      constexpr bool USE_REG = DQ != 0 && DQ <= 12;
+      constexpr int MD1r = USE_REG ? MD1 : 1;
+      constexpr int MQ1r = USE_REG ? MQ1 : 1;
+      constexpr int MD1s = USE_REG ? 1 : MD1;
+      constexpr int MQ1s = USE_REG ? 1 : MQ1;
+
+      MFEM_SHARED real_t s_B[MQ1s][MD1s];
+      real_t r_B[MQ1r][MD1r];
+      real_t (*l_B)[MD1] = nullptr;
+      if (USE_REG)
+      {
+         for (int d = 0; d < D1D; d++)
+         {
+            for (int q = 0; q < Q1D; q++)
+            {
+               r_B[q][d] = B(q,d);
+            }
+         }
+         l_B = (real_t (*)[MD1])r_B;
+      }
+      else
+      {
+         if (MFEM_THREAD_ID(z) == 0)
+         {
+            MFEM_FOREACH_THREAD(d,x,D1D)
+            {
+               MFEM_FOREACH_THREAD(q,y,Q1D)
+               {
+                  s_B[q][d] = B(q,d);
+               }
+            }
+         }
+         l_B = (real_t (*)[MD1])s_B;
+      }
+
+      MFEM_SHARED real_t s_D[MQ1][MQ1][MQ1];
+      MFEM_FOREACH_THREAD(k1,x,Q1D)
+      {
+         MFEM_FOREACH_THREAD(k2,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(k3,z,Q1D)
+            {
+               s_D[k1][k2][k3] = D(k1,k2,k3,e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(i3,z,D1D)
+            {
+               const int row = i1 + D1D*(i2 + D1D*i3);
+               for (int j3 = 0; j3 < D1D; ++j3)
+               {
+                  for (int j2 = 0; j2 < D1D; ++j2)
+                  {
+                     for (int j1 = 0; j1 < D1D; ++j1)
+                     {
+                        const int col = j1 + D1D*(j2 + D1D*j3);
+                        if (row < col)
+                        {
+                           continue;
+                        }
+                        real_t val = 0.0;
+                        for (int k1 = 0; k1 < Q1D; ++k1)
+                        {
+                           for (int k2 = 0; k2 < Q1D; ++k2)
+                           {
+                              for (int k3 = 0; k3 < Q1D; ++k3)
+                              {
+                                 val += l_B[k1][i1] * l_B[k1][j1]
+                                        * l_B[k2][i2] * l_B[k2][j2]
+                                        * l_B[k3][i3] * l_B[k3][j3]
+                                        * s_D[k1][k2][k3];
+                              }
+                           }
+                        }
+                        const int idx = TriPackLowerMatrix::LowerIndex(row, col, ndofs);
+                        if (add)
+                        {
+                           M(idx, e) += val;
+                        }
+                        else
+                        {
+                           M(idx, e) = val;
+                        }
+                     }
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
 } // namespace internal
 
 namespace

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

@@ -22,6 +22,8 @@ void VectorMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalFE();
+   MFEM_VERIFY(el.GetMapType() == FiniteElement::VALUE,
+               "Only value map type supported");
    ElementTransformation &Trans = *mesh->GetTypicalElementTransformation();
    const auto *ir = IntRule ? IntRule : &MassIntegrator::GetRule(el, el, Trans);
 
@@ -205,157 +207,40 @@ 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

@@ -542,7 +542,10 @@ void QuadratureFunctions1D::GaussJacobi(const int np, const real_t alpha,
          return;
    }
 
-#ifndef MFEM_USE_MPFR
+#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
@@ -611,13 +614,6 @@ void QuadratureFunctions1D::GaussJacobi(const int np, const real_t alpha,
                                                 ab + 1) / ((1.0 - xi*xi)*pp*pp) / pow(2, ab);
       // map nodes and weights to the interval [0,1]
    }
-
-#else // MFEM_USE_MPFR is defined
-
-   MFEM_ABORT("MPFR implementation of Gauss-Jacobi quadrature not defined yet");
-
-#endif // MFEM_USE_MPFR
-
 }
 
 

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