Merge branch 'complex-coef-dev' of github.com:mfem/mfem into complex-coef-dev

NURBS surface interpolation minapp

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

@@ -0,0 +1,154 @@
+# 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: Sanitizer Config
+description: Sets up environment variables for MFEM sanitizer workflow
+
+inputs:
+  DEBUG:
+    description: If true, use intermediate caches to speed up the workflow
+                 by reusing previous builds.
+    default: false
+
+  REPOSITORY:
+    description: Repository to checkout
+    default: mfem/mfem
+
+  BRANCH:
+    description: Branch to checkout
+    default: ubsan
+
+  CLANG_VER:
+    description: CLANG version to use
+    default: 18
+
+  # https://github.com/llvm/llvm-project/releases
+  LLVM_VER:
+    description: LLVM version to use
+    default: 19.1.7
+
+  # https://github.com/hypre-space/hypre/releases
+  HYPRE_VER:
+    description: HYPRE version to use
+    default: 2.19.0
+
+  METIS_VER:
+    description: METIS version to use
+    default: 4.0.3
+
+  CTEST:
+    description: CTest command to use
+    default: ctest -j --test-load $(nproc)
+                      --schedule-random
+                      --stop-on-failure --output-on-failure
+                      --test-dir
+
+  # https://clang.llvm.org/docs/AddressSanitizer.html
+  ASAN_OPTIONS:
+    default: detect_leaks=1,
+             strict_init_order=1,
+             strict_string_checks=1,
+             check_initialization_order=1,
+             detect_stack_use_after_return=1
+  ASAN_CXXFLAGS:
+    default: -fsanitize=address
+             -fsanitize-address-use-after-scope
+  ASAN_LDFLAGS:
+    default: -fsanitize=address
+
+  # https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html
+  UBSAN_OPTIONS:
+    default: halt_on_error=1, print_stacktrace=1
+  UBSAN_CXXFLAGS:
+    default: -fsanitize=undefined
+  UBSAN_LDFLAGS:
+    default: -fsanitize=undefined
+
+  # https://clang.llvm.org/docs/MemorySanitizer.html
+  MSAN_OPTIONS:
+    default: "poison_in_dtor=1"
+  MSAN_CXXFLAGS:
+    default: -fsanitize=memory
+             -fsanitize-memory-track-origins
+             -fsanitize-memory-use-after-dtor
+  MSAN_LDFLAGS:
+    default: -fsanitize=memory
+
+  LSAN_DIR:
+    description: LSAN suppression directory
+    default: lsan
+
+  LSAN_FILE:
+    description: LSAN suppression file
+    default: lsan.supp
+
+  NO_FLAGS:
+    description: If true, do not set any CXXFLAGS or LDFLAGS.
+    default: false
+
+runs:
+  using: 'composite'
+  steps:
+    - name: Env (Inputs)
+      run: |
+        echo DEBUG=${{inputs.DEBUG}} >> $GITHUB_ENV
+        echo REPOSITORY=${{inputs.REPOSITORY}} >> $GITHUB_ENV
+        echo BRANCH=${{inputs.BRANCH}} >> $GITHUB_ENV
+        echo CLANG_VER=${{inputs.CLANG_VER}} >> $GITHUB_ENV
+        echo LLVM_VER=${{inputs.LLVM_VER}} >> $GITHUB_ENV
+        echo HYPRE_VER=${{inputs.HYPRE_VER}} >> $GITHUB_ENV
+        echo METIS_VER=${{inputs.METIS_VER}} >> $GITHUB_ENV
+        echo CTEST=${{inputs.CTEST}} >> $GITHUB_ENV
+        echo ASAN_OPTIONS=${{inputs.ASAN_OPTIONS}} >> $GITHUB_ENV
+        echo UBSAN_OPTIONS=${{inputs.UBSAN_OPTIONS}} >> $GITHUB_ENV
+        echo MSAN_OPTIONS=${{inputs.MSAN_OPTIONS}} >> $GITHUB_ENV
+        echo LSAN_DIR=${{inputs.LSAN_DIR}} >> $GITHUB_ENV
+        echo LSAN_FILE=${{inputs.LSAN_FILE}} >> $GITHUB_ENV
+        echo ASAN_CXXFLAGS=${{inputs.ASAN_CXXFLAGS}} >> $GITHUB_ENV
+        echo ASAN_LDFLAGS=${{inputs.ASAN_LDFLAGS}} >> $GITHUB_ENV
+        echo UBSAN_CXXFLAGS=${{inputs.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
+        echo UBSAN_LDFLAGS=${{inputs.UBSAN_LDFLAGS}} >> $GITHUB_ENV
+        echo MSAN_CXXFLAGS=${{inputs.MSAN_CXXFLAGS}} >> $GITHUB_ENV
+        echo MSAN_LDFLAGS=${{inputs.MSAN_LDFLAGS}} >> $GITHUB_ENV
+      shell: bash
+
+    - name: Env (dir)
+      run: |
+        echo LLVM_DIR=${{github.workspace}}/llvm >> $GITHUB_ENV
+        echo HYPRE_DIR=hypre-${{inputs.HYPRE_VER}} >> $GITHUB_ENV
+        echo METIS_DIR=metis-${{inputs.METIS_VER}} >> $GITHUB_ENV
+      shell: bash
+
+    - name: Env (bis)
+      run: |
+        echo CC=clang-${{inputs.CLANG_VER}} >> $GITHUB_ENV
+        echo CXX=clang++-${{inputs.CLANG_VER}} >> $GITHUB_ENV
+        echo LLVM_INC=${{env.LLVM_DIR}}/include/c++/v1 >> $GITHUB_ENV
+        echo LLVM_LIB=${{env.LLVM_DIR}}/lib >> $GITHUB_ENV
+        echo HYPRE_TGZ=v${{inputs.HYPRE_VER}}.tar.gz >> $GITHUB_ENV
+        echo METIS_TGZ=metis-${{inputs.METIS_VER}}.tar.gz >> $GITHUB_ENV
+        LSAN_SUPPRESSIONS="${{github.workspace}}/${{inputs.LSAN_DIR}}/${{inputs.LSAN_FILE}}"
+        echo "LSAN_OPTIONS=suppressions=$LSAN_SUPPRESSIONS" >> $GITHUB_ENV
+      shell: bash
+
+    - name: Env (ter)
+      if: ${{ inputs.NO_FLAGS != 'true' }}
+      run: |
+        echo LLVM_CXXFLAGS=-stdlib=libc++ -I${{env.LLVM_INC}} -Isystem${{env.LLVM_INC}} >> $GITHUB_ENV
+        echo LLVM_LDFLAGS=-L${{env.LLVM_LIB}} -lc++abi -Wl,-rpath,${{env.LLVM_LIB}} >> $GITHUB_ENV
+      shell: bash
+
+    - name: Env (quater)
+      if: ${{ inputs.NO_FLAGS != 'true' }}
+      run: |
+        echo CXXFLAGS=${{env.LLVM_CXXFLAGS}} >> $GITHUB_ENV
+        echo LDFLAGS=${{env.LLVM_LDFLAGS}} >> $GITHUB_ENV
+      shell: bash

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

@@ -0,0 +1,91 @@
+# 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: 'MFEM Compilation'
+description: 'MFEM Compilation'
+
+inputs:
+  par:
+    description: 'Whether to build for parallel (true/false)'
+    default: false
+  sanitizer:
+    description: 'Sanitizer to use (asan, msan, ubsan)'
+    default: asan
+
+runs:
+  using: 'composite'
+  steps:
+    - uses: ./.github/actions/sanitize/config
+
+    - uses: actions/cache@v4
+      if: ${{env.DEBUG == 'true'}}
+      id: debug
+      with:
+        path: mfem/build
+        key: build-${{inputs.par}}-${{inputs.sanitizer}}
+
+    - uses: ./.github/actions/sanitize/setup
+      if: ${{steps.debug.outputs.cache-hit != 'true'}}
+      with:
+        par: ${{inputs.par}}
+        sanitizer: ${{inputs.sanitizer}}
+
+    - name: Build with ASAN
+      if: inputs.sanitizer == 'asan'
+      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.ASAN_CXXFLAGS}} >> $GITHUB_ENV
+      shell: bash
+
+    - name: Build with MSAN
+      if: inputs.sanitizer == 'msan'
+      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.MSAN_CXXFLAGS}} >> $GITHUB_ENV
+      shell: bash
+
+    - name: Build with UBSAN
+      if: inputs.sanitizer == 'ubsan'
+      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
+      shell: bash
+
+    - uses: mfem/github-actions/build-mfem@v2.5
+      if: ${{steps.debug.outputs.cache-hit != 'true'}}
+      env:
+        CXXFLAGS: ${{env.CXXFLAGS}}
+        LDFLAGS: ${{env.LDFLAGS}}
+      with:
+        mpi: ${{inputs.par == 'false' && 'seq' || 'par'}}
+        mfem-dir: mfem
+        os: ${{runner.os}}
+        library-only: true
+        build-system: cmake
+        hypre-dir: ${{env.HYPRE_DIR}}
+        metis-dir: ${{env.METIS_DIR}}
+        config-options: >-
+          -GNinja
+          -DMPICXX=${{env.CXX}}
+          -DCMAKE_CXX_STANDARD=17
+          -DMFEM_USE_MEMALLOC=OFF
+          -DCMAKE_BUILD_TYPE=Release
+          -DCMAKE_VERBOSE_MAKEFILE=ON
+          -DCMAKE_CXX_COMPILER=${{env.CXX}}
+          -DCMAKE_CXX_FLAGS_RELEASE='-g -O1 -fno-omit-frame-pointer'
+
+    - name: Delete object files
+      if: ${{steps.debug.outputs.cache-hit != 'true'}}
+      working-directory: mfem/build
+      run: find . -type f -name '*.o' -delete
+      shell: bash
+
+    - uses: actions/upload-artifact@v4
+      with:
+        name: build-${{inputs.par}}-${{inputs.sanitizer}}
+        path: mfem/build
+        if-no-files-found: error
+        retention-days: 1
+        overwrite: false

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

@@ -0,0 +1,33 @@
+# 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: 'Install MPI'
+description: 'Installs MPI and set up its environment variables'
+
+runs:
+  using: 'composite'
+  steps:
+    - name: Install
+      run: sudo apt-get install openmpi-bin libopenmpi-dev
+      shell: bash
+
+    - name: Env
+      run: |
+        echo PRTE_MCA_rmaps_default_mapping_policy=:oversubscribe >> $GITHUB_ENV
+        echo MPI_INC=$(mpicxx --showme:compile) >> $GITHUB_ENV
+        echo MPI_LIB=$(mpicxx --showme:link) >> $GITHUB_ENV
+      shell: bash
+
+    - name: Env (bis)
+      run: |
+        echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.MPI_INC}} >> $GITHUB_ENV
+        echo LDFLAGS=${{env.LDFLAGS}} ${{env.MPI_LIB}} >> $GITHUB_ENV
+      shell: bash

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

@@ -0,0 +1,71 @@
+# 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: 'Restore state'
+description: 'Restore state to be able to run checks, tests'
+
+inputs:
+  par:
+    description: 'Whether to build for parallel (true/false)'
+    default: false
+  sanitizer:
+    description: 'Sanitizer to use (asan, msan, ubsan)'
+    default: asan
+  cache-path:
+    description: 'path to what needs to be restored'
+    default: none
+  cache-skip:
+    description: 'Skip cache restoration'
+    default: false
+
+outputs:
+  cache-hit:
+    description: 'Output from a specific step'
+    value: ${{steps.debug.outputs.cache-hit}}
+
+runs:
+  using: 'composite'
+  steps:
+    - uses: ./.github/actions/sanitize/config
+
+    - uses: actions/cache@v4
+      if: ${{env.DEBUG == 'true' && inputs.cache-skip != 'true'}}
+      id: debug
+      with:
+        path: ${{inputs.cache-path}}
+        key: ${{github.job}}-${{inputs.par}}-${{inputs.sanitizer}}
+
+    - uses: ./.github/actions/sanitize/setup
+      if: ${{steps.debug.outputs.cache-hit != 'true'}}
+      with:
+        par: ${{inputs.par}}
+        sanitizer: ${{inputs.sanitizer}}
+
+    - uses: actions/download-artifact@v4
+      with:
+        name: build-${{inputs.par}}-${{inputs.sanitizer}}
+        path: mfem/build
+
+    - name: Ninja Patch
+      working-directory: mfem/build
+      run: |
+        sed -i -e 's/CXX_STATIC_LIBRARY_LINKER__mfem_Release.*/CUSTOM_COMMAND/' build.ninja
+        sed -i -e '/build tests\/unit\/all:/ s/tests\/unit\/[^ ]*unit_tests[^ ]*//g' build.ninja
+        sed -i -e '/^add_test(\[=\[\(unit_tests\|punit_tests\)\]=\]/ s/)/ "--input-file .\/list-test-names-${{matrix.tag}}" "--min-duration 1")/' tests/unit/CTestTestfile.cmake
+      shell: bash
+
+    - name: Copy Data
+      if: ${{steps.debug.outputs.cache-hit != 'true'}}
+      working-directory: mfem/build
+      run: |
+        ninja cmake_object_order_depends_target_unit_tests
+        cp -pR ../tests/unit/data tests/unit
+      shell: bash

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

@@ -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.
+---
+name: 'Setup state'
+description: 'Sets up the state to be able to run build & run'
+
+inputs:
+  par:
+    description: 'Whether to build for parallel (true/false)'
+    default: false
+  sanitizer:
+    description: 'Sanitizer to use (asan, msan, ubsan)'
+    default: asan
+
+runs:
+  using: 'composite'
+  steps:
+    - uses: actions/cache/restore@v4  # Cache for LLVM libcxx
+      with:
+        path: ${{env.LLVM_DIR}}
+        fail-on-cache-miss: true
+        key: build-libcxx-${{env.LLVM_VER}}-${{inputs.sanitizer}}
+
+    - uses: ./.github/actions/sanitize/mpi
+      if: ${{inputs.par == 'true'}}
+
+    - uses: actions/cache/restore@v4  # Cache for Hypre
+      if: ${{inputs.par == 'true'}}
+      with:
+        path: ${{env.HYPRE_DIR}}
+        fail-on-cache-miss: true
+        key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
+
+    - uses: actions/cache/restore@v4  # Cache for Metis
+      if: ${{inputs.par == 'true'}}
+      with:
+        path: ${{env.METIS_DIR}}
+        fail-on-cache-miss: true
+        key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
+
+    - name: Hypre/Metis links
+      if: ${{inputs.par == 'true'}}
+      run: ln -s -f ${{env.HYPRE_DIR}} hypre && ln -s -f ${{env.METIS_DIR}} metis-4.0
+      shell: bash
+
+    - uses: actions/cache/restore@v4  # Cache for LSAN suppression file
+      with:
+        path: ${{env.LSAN_DIR}}
+        fail-on-cache-miss: true
+        key: build-lsan-suppression-file
+
+    - uses: actions/checkout@v4  # Checkout the repository
+      with:
+        path: mfem
+        # ref: ${{env.BRANCH}}
+        # repository: ${{env.REPOSITORY}}

.github/workflows/README.md

@@ -7,18 +7,17 @@
 
                                https://mfem.org
 
-
 This directory contains the GitHub CI scripts for MFEM.
 
 Note that some of these scripts use the shared MFEM GitHub Actions from the external mfem/github-actions repository:
 
-  https://github.com/mfem/github-actions
+  <https://github.com/mfem/github-actions>
 
-For a particular action, e.g. `mfem/github-actions/build-mfem@v2.1`, the `v2.1` suffix denotes the branch in the above from which the action is taken.
+For a particular action, e.g. `mfem/github-actions/build-mfem@v2.5`, the `v2.5` suffix denotes the branch in the above from which the action is taken.
 
 The current CI workflows are:
 
-### `repo-check.yml`
+## `repo-check.yml`
 
 Runs a number of static repository-level sanity checks.
 
@@ -30,19 +29,39 @@ 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`)
+## `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`
+## `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.
 
-Uses the following GitHub Actions from https://github.com/mfem/github-actions:
+Uses the following GitHub Actions from <https://github.com/mfem/github-actions>:
 
 - `mfem/github-actions/build-hypre`
 - `mfem/github-actions/build-metis`
 - `mfem/github-actions/build-mfem`
 - `mfem/github-actions/upload-coverage`
+
+## Sanitizer Workflow for MFEM Verification
+
+This workflow validates MFEM unit tests, examples, and miniapps using sanitizer tools.
+
+- `sanitizers.yml` orchestrates:
+  - Building and caching dependencies: HYPRE, METIS, LSAN suppression file, and LLVM libcxx.
+  - Launching fine-grained jobs for serial (ASAN, MSAN, UBSAN) and parallel (ASAN, UBSAN) sanitizers.
+- `sanitize-tests.yml` is a reusable workflow accepting `par` mode (`true` for parallel) and `sanitizer` (ASAN, MSAN, or UBSAN) as inputs. It executes the following jobs:
+  - **Build**: Compiles the MFEM library with specified parallel and sanitizer settings.
+  - **Check**: Runs verification checks.
+  - Parallel jobs to test the following: **Examples**, **Miniapps** and **Unit tests**
+
+The workflow leverages composite actions in `.github/actions/sanitize/`:
+
+- `config`: Centralizes settings for the sanitizer workflow.
+- `mfem`: Manages the MFEM library build process.
+- `mpi`: Installs MPI and applies additional compilation flags.
+- `restore`: Restores the testing environment state.
+- `setup`: Builds or restores cached dependencies.

.github/workflows/mfem-sanitizer.yml

@@ -1,69 +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: "Sanitizer"
-
-permissions:
-  actions: write
-
-on:
-  push:
-    branches:
-      - master
-      - next
-  pull_request:
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  Serial:
-    runs-on: ubuntu-24.04
-
-    steps:
-      - name: MFEM Checkout
-        uses: actions/checkout@v4
-        with:
-          path: mfem
-
-      - name: MFEM Build
-        uses: mfem/github-actions/build-mfem@v2.5
-        with:
-          os: ${{ runner.os }}
-          target: opt
-          mpi: seq
-          hypre-dir: unused-hypre-dir
-          metis-dir: unused-metis-dir
-          mfem-dir: mfem
-          build-system: make
-          library-only: false
-          config-options:
-            CXX="clang++-18"
-            CXXFLAGS="-g -O1 -std=c++17
-                      -fsanitize=address
-                      -fno-omit-frame-pointer
-                      -fsanitize-address-use-after-scope"
-
-      - name: MFEM Info
-        working-directory: mfem
-        run: make info
-
-      - name: MFEM Sanitize
-        working-directory: mfem
-        run:
-          ASAN_OPTIONS="detect_leaks=1,
-                        strict_init_order=1,
-                        strict_string_checks=1,
-                        check_initialization_order=1,
-                        detect_stack_use_after_return=1"
-          make test

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

@@ -0,0 +1,39 @@
+# 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-hypre
+on:
+  workflow_call:
+jobs:
+  build-hypre:
+    runs-on: ubuntu-latest
+    name: 2.19.0
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/config
+      - name: Cache
+        id: cache
+        uses: actions/cache@v4
+        with:
+          path: ${{env.HYPRE_DIR}}
+          key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
+      - name: Setup
+        if: steps.cache.outputs.cache-hit != 'true'
+        uses: ./.github/actions/sanitize/mpi
+      - name: Build
+        if: steps.cache.outputs.cache-hit != 'true'
+        uses: mfem/github-actions/build-hypre@v2.5
+        with:
+          archive: ${{env.HYPRE_TGZ}}
+          dir: ${{env.HYPRE_DIR}}
+          target: int32
+          precision: fp64
+          build-system: make

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

@@ -0,0 +1,76 @@
+# 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-libcxx
+on:
+  workflow_call:
+jobs:
+  build-llvm-libcxx:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        sanitizer: [asan, msan, ubsan]
+        include:
+          - sanitizer: asan
+            llvm_use_sanitizer: "Address"
+          - sanitizer: msan
+            llvm_use_sanitizer: "MemoryWithOrigins"
+          - sanitizer: ubsan
+            llvm_use_sanitizer: "Undefined"
+    name: ${{matrix.sanitizer}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/config
+        with:
+          NO_FLAGS: true
+      - name: Cache
+        id: cache
+        uses: actions/cache@v4
+        with:
+          path: ${{env.LLVM_DIR}}
+          key: build-libcxx-${{env.LLVM_VER}}-${{matrix.sanitizer}}
+      - name: Clone
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        run: >
+          git clone --filter=blob:none --depth=1
+          --branch llvmorg-${{env.LLVM_VER}}
+          --no-checkout https://github.com/llvm/llvm-project.git llvm-project
+      - name: Checkout
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        working-directory: llvm-project
+        run: |
+          git sparse-checkout set --cone
+          git checkout llvmorg-${{env.LLVM_VER}}
+          git sparse-checkout set cmake llvm/cmake runtimes libcxx libcxxabi
+      - name: Mkdir
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        run: mkdir ${{env.LLVM_DIR}}
+      - name: CMake
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        working-directory: ${{env.LLVM_DIR}}
+        run: >
+          VERBOSE=1
+          cmake -GNinja ../llvm-project/runtimes/
+          -DCMAKE_C_COMPILER=${{env.CC}}
+          -DCMAKE_CXX_COMPILER=${{env.CXX}}
+          -DCMAKE_BUILD_TYPE=RelWithDebInfo
+          -DCMAKE_INSTALL_PREFIX=/usr
+          -DLLVM_USE_SANITIZER=${{matrix.llvm_use_sanitizer}}
+          -DLLVM_BUILD_32_BITS=OFF
+          -DLIBCXXABI_USE_LLVM_UNWINDER=OFF
+          -DLLVM_INCLUDE_TESTS=OFF
+          -DLIBCXX_INCLUDE_TESTS=OFF
+          -DLIBCXX_INCLUDE_BENCHMARKS=OFF
+          -DLLVM_ENABLE_RUNTIMES='libcxx;libcxxabi'
+      - name: Build
+        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
+        working-directory: ${{env.LLVM_DIR}}
+        run: cmake --build . -- cxx cxxabi

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

@@ -0,0 +1,38 @@
+# 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-file-lsan
+on:
+  workflow_call:
+jobs:
+  build-file-lsan:
+    runs-on: ubuntu-latest
+    name: lsan.supp
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/config
+      - name: Cache
+        id: cache
+        uses: actions/cache@v4
+        with:
+          path: ${{env.LSAN_DIR}}
+          key: build-lsan-suppression-file
+      - name: Setup
+        if: steps.cache.outputs.cache-hit != 'true'
+        run: |
+          mkdir -p ${{env.LSAN_DIR}}
+          cat << EOF > ${{env.LSAN_DIR}}/${{env.LSAN_FILE}}
+          leak:libevent_core-2.1.so
+          leak:ompi_mpi_finalize
+          leak:ompi_mpi_init
+          leak:PMPI_Init
+          leak:strdup
+          EOF

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

@@ -0,0 +1,36 @@
+# 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-metis
+on:
+  workflow_call:
+jobs:
+  build-metis:
+    runs-on: ubuntu-latest
+    name: 4.0.3
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/config
+      - name: Cache
+        id: cache
+        uses: actions/cache@v4
+        with:
+          path: ${{env.METIS_DIR}}
+          key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
+      - name: Setup
+        if: steps.cache.outputs.cache-hit != 'true'
+        uses: ./.github/actions/sanitize/mpi
+      - name: Build
+        if: steps.cache.outputs.cache-hit != 'true'
+        uses: mfem/github-actions/build-metis@v2.5
+        with:
+          archive: ${{env.METIS_TGZ}}
+          dir: ${{env.METIS_DIR}}

.github/workflows/sanitize-tests.yml

@@ -0,0 +1,197 @@
+# 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: Sanitize
+on:
+  workflow_call:
+    inputs:
+      par:
+        description: 'Whether to build for parallel (true/false)'
+        required: false
+        default: false
+        type: boolean
+      sanitizer:
+        description: 'Sanitizer to use (asan, msan, ubsan)'
+        required: true
+        default: asan
+        type: string
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/mfem
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+
+  check:
+    needs: [build]
+    runs-on: ubuntu-latest
+    env:
+      ex: ${{inputs.par && 'ex1p' || 'ex1'}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/examples/${{env.ex}}
+      - name: MFEM Check
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: ninja -v check
+
+  examples:
+    needs: [check]
+    runs-on: ubuntu-latest
+    env:
+      exclude: ${{inputs.par && '-E "_ser"' || ''}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/examples/ex1
+      - name: Build Examples
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: ninja -v examples
+      - name: Test Examples
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: |
+          ${{env.CTEST}} examples ${{env.exclude}} --show-only
+          ${{env.CTEST}} examples ${{env.exclude}}
+
+  miniapps:
+    needs: [check]
+    runs-on: ubuntu-latest
+    env:
+      exclude: ${{inputs.par && '-E "_ser"' || ''}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/miniapps/meshing/minimal-surface
+      - name: Build Miniapps
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: ninja -v miniapps
+      - name: Test Miniapps
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: |
+          ${{env.CTEST}} miniapps ${{env.exclude}} --show-only
+          ${{env.CTEST}} miniapps ${{env.exclude}}
+
+  tests-miniapps:
+    needs: [check]
+    runs-on: ubuntu-latest
+    env:
+      run: ${{inputs.par && '-R "_cpu_np"' || ''}}
+      exclude: ${{inputs.par && '"unit_tests|debug"' || '"^unit_tests$|debug"'}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/tests/unit/sedov_tests_cpu
+      - name: Build Tests Unit Miniapps
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: ninja -v tests/unit/all
+      - name: Run Tests Unit Miniapps
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: |
+          ${{env.CTEST}} tests/unit -E ${{env.exclude}} ${{env.run}} --show-only
+          ${{env.CTEST}} tests/unit -E ${{env.exclude}} ${{env.run}}
+
+  tests-unit-build:
+    needs: [check]
+    runs-on: ubuntu-latest
+    env:
+      unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/tests/unit/${{env.unit_tests}}
+      - name: Build Unit Tests
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: ninja -v ${{env.unit_tests}}
+      - name: Delete object files
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build/tests/unit
+        run: find . -type f -name '*.o' -delete
+      - uses: actions/upload-artifact@v4
+        with:
+          name: tests-${{inputs.par}}-${{inputs.sanitizer}}
+          path: mfem/build/tests/unit/${{env.unit_tests}}
+          if-no-files-found: error
+          retention-days: 1
+          overwrite: false
+
+  tests-unit-run:
+    needs: [tests-unit-build]
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        tag: [0, 1, 2, 3]
+    name: tests-unit-run-${{matrix.tag}}
+    env:
+      unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
+      np: ${{inputs.par && '_np=2' || ''}}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/sanitize/restore
+        id: restore
+        with:
+          par: ${{inputs.par}}
+          sanitizer: ${{inputs.sanitizer}}
+          cache-path: mfem/build/tests/unit/${{env.unit_tests}}
+      - uses: actions/download-artifact@v4
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        with:
+          name: tests-${{inputs.par}}-${{inputs.sanitizer}}
+          path: mfem/build/tests/unit
+      - name: Split Unit Tests
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build/tests/unit
+        run: |
+          chmod 755 ${{env.unit_tests}}
+          ./${{env.unit_tests}} --list-test-names-only | tail -n +2 > list-test-names
+          shuf list-test-names -o list-test-names
+          split --verbose -n l/4 -d -a 1 list-test-names list-test-names-
+      - name: Cat Unit Tests ${{matrix.tag}}
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build/tests/unit
+        run: cat list-test-names-${{matrix.tag}}
+      - name: Run Unit Tests ${{matrix.tag}}
+        if: ${{steps.restore.outputs.cache-hit != 'true'}}
+        working-directory: mfem/build
+        run: |
+          ${{env.CTEST}} tests/unit -R "${{env.unit_tests}}${{env.np}}" --show-only
+          ${{env.CTEST}} tests/unit -R "${{env.unit_tests}}${{env.np}}"

.github/workflows/sanitizers.yml

@@ -0,0 +1,73 @@
+# 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: Sanitizers
+
+permissions:
+  actions: write
+
+on:
+  push:
+    branches: ["master", "next"]
+  pull_request:
+  workflow_dispatch:
+
+concurrency:
+  group: ${{github.workflow}}-${{github.ref}}
+  cancel-in-progress: true
+
+jobs:
+
+  # Build steps for dependencies
+  build-hypre:
+    uses: ./.github/workflows/sanitize-build-hypre.yml
+
+  build-metis:
+    uses: ./.github/workflows/sanitize-build-metis.yml
+
+  build-lsan:
+    uses: ./.github/workflows/sanitize-build-lsan.yml
+
+  build-libcxx:
+    uses: ./.github/workflows/sanitize-build-libcxx.yml
+
+  # Serial sanitizers: asan, msan, ubsan
+  seq-asan:
+    needs: [build-libcxx]
+    uses: ./.github/workflows/sanitize-tests.yml
+    with:
+      sanitizer: asan
+
+  seq-msan:
+    needs: [build-libcxx]
+    uses: ./.github/workflows/sanitize-tests.yml
+    with:
+      sanitizer: msan
+
+  seq-ubsan:
+    needs: [build-libcxx]
+    uses: ./.github/workflows/sanitize-tests.yml
+    with:
+      sanitizer: ubsan
+
+  # Parallel sanitizers: asan, ubsan
+  par-asan:
+    needs: [build-libcxx, build-hypre, build-metis]
+    uses: ./.github/workflows/sanitize-tests.yml
+    with:
+      par: true
+      sanitizer: asan
+  par-ubsan:
+    needs: [build-libcxx, build-hypre, build-metis]
+    uses: ./.github/workflows/sanitize-tests.yml
+    with:
+      par: true
+      sanitizer: ubsan

.gitignore

@@ -19,9 +19,6 @@ CMakeFiles/
 # Clangd server cache
 *.cache*
 
-# VSCode configuration
-/.vscode/
-
 # Backup files
 *~
 
@@ -303,6 +300,7 @@ miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
+miniapps/nurbs/nurbs_surface
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
 miniapps/nurbs/sol_?.gf
@@ -321,6 +319,7 @@ miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
 miniapps/nurbs/glvis_naca-cmesh.mesh
 miniapps/nurbs/Naca_cmesh
+miniapps/nurbs/*-Surface.mesh
 
 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -416,8 +415,8 @@ miniapps/diag-smoothers/mg-abs-l1-jacobi
 tests/unit/output_meshes
 tests/unit/unit_tests
 tests/unit/punit_tests
-tests/unit/cunit_tests
-tests/unit/pcunit_tests
+tests/unit/gpu_unit_tests
+tests/unit/pgpu_unit_tests
 tests/unit/sedov_tests_*
 tests/unit/psedov_tests_*
 tests/unit/tmop_pa_tests_*

CHANGELOG

@@ -29,9 +29,14 @@ Discretization improvements
 
 Meshing improvements
 --------------------
+
 - Added support for higher order meshes in Mesh::MakeSimplicial and
   ParMesh::MakeSimplicial.
 
+- Added a new miniapp for interpolating a surface grid of points in 3D using a
+  smooth NURBS surface, that can then be sampled at arbitrary resolution while
+  staying close to the original geometry. See miniapps/nurbs/nurbs_surface.
+
 GPU computing
 -------------
 - The function Vector::SetSubVector(const Array<int> &, const real_t) now
@@ -39,6 +44,8 @@ GPU computing
   set. This is most often used for setting constant essential boundary
   conditions. A new function Vector::SetSubVectorHost has been added in cases
   where host execution is always needed (e.g. when the DOFs array is small).
+- Introduced MFEM_FOREACH_THREAD_DIRECT, which directly maps loop tasks to GPU
+  threads, assigning one task per thread.
 
 New and updated examples and miniapps
 -------------------------------------
@@ -48,13 +55,26 @@ New and updated examples and miniapps
   operators as smoothers.
   These miniapps can be found in `miniapps/diag-smoothers`.
 
-API changes:
+API changes
 -----------
 - mfem::internal::tensor and mfem::internal::dual have been moved to
   mfem::future::tensor and mfem::future::dual.
 - API addition: in class `Operator`, added virtual functions: `AbsMult`, and
   `AbsMultTranspose`; in class `Vector`, added `Abs` and `Pow`.
 
+Miscellaneous
+-------------
+- Added the "gpu", "raja-gpu", and "ceed-gpu" backend aliases/shortcuts which
+  automatically select between CUDA or HIP.
+- The CUDA-specific names used by some of the unit tests like 'cunit_tests' and
+  'pcunit_tests' were replaced by names using 'gpu' instead of 'c' (short for
+  CUDA) or 'cuda'. These tests automatically run the CUDA/HIP tests based on the
+  MFEM build configuration.
+- Added the option to enable GPU-aware MPI in MFEM using the environment
+  variable 'MFEM_GPU_AWARE_MPI' set to any value. Setting this environment
+  variable is an alternative to calling 'Device::SetGPUAwareMPI(true)'.
+- Added parallel Address Sanitizer, serial and parallel Undefined Behavior
+  Sanitizer and serial Memory Sanitizer GitHub actions tests on Ubuntu.
 
 Version 4.8, released on Apr 9, 2025
 ====================================

examples/ex22.cpp

@@ -62,14 +62,9 @@ static real_t epsilon_ = 1.0;
 static real_t sigma_ = 20.0;
 static real_t omega_ = 10.0;
 
-real_t u0_real_exact(const Vector &);
-real_t u0_imag_exact(const Vector &);
-
-void u1_real_exact(const Vector &, Vector &);
-void u1_imag_exact(const Vector &, Vector &);
-
-void u2_real_exact(const Vector &, Vector &);
-void u2_imag_exact(const Vector &, Vector &);
+complex<real_t> u0_exact(const Vector &x);
+void u1_exact(const Vector &, ComplexVector &);
+void u2_exact(const Vector &, ComplexVector &);
 
 bool check_for_inline_mesh(const char * mesh_file);
 
@@ -215,54 +210,48 @@ int main(int argc, char *argv[])
    ComplexGridFunction * u_exact = NULL;
    if (exact_sol) { u_exact = new ComplexGridFunction(fespace); }
 
-   FunctionCoefficient u0_r(u0_real_exact);
-   FunctionCoefficient u0_i(u0_imag_exact);
-   VectorFunctionCoefficient u1_r(dim, u1_real_exact);
-   VectorFunctionCoefficient u1_i(dim, u1_imag_exact);
-   VectorFunctionCoefficient u2_r(dim, u2_real_exact);
-   VectorFunctionCoefficient u2_i(dim, u2_imag_exact);
+   ComplexFunctionCoefficient u0(u0_exact);
+   ComplexVectorFunctionCoefficient u1(dim, u1_exact);
+   ComplexVectorFunctionCoefficient u2(dim, u2_exact);
 
-   ConstantCoefficient zeroCoef(0.0);
-   ConstantCoefficient oneCoef(1.0);
+   ComplexConstantCoefficient oneCoef(1.0);
 
-   Vector zeroVec(dim); zeroVec = 0.0;
    Vector  oneVec(dim);  oneVec = 0.0; oneVec[(prob==2)?(dim-1):0] = 1.0;
-   VectorConstantCoefficient zeroVecCoef(zeroVec);
-   VectorConstantCoefficient oneVecCoef(oneVec);
+   ComplexVectorConstantCoefficient oneVecCoef(oneVec);
 
    switch (prob)
    {
       case 0:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficient(u0_r, u0_i, ess_bdr);
-            u_exact->ProjectCoefficient(u0_r, u0_i);
+            u.ProjectBdrCoefficient(u0, ess_bdr);
+            u_exact->ProjectCoefficient(u0);
          }
          else
          {
-            u.ProjectBdrCoefficient(oneCoef, zeroCoef, ess_bdr);
+            u.ProjectBdrCoefficient(oneCoef, ess_bdr);
          }
          break;
       case 1:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficientTangent(u1_r, u1_i, ess_bdr);
-            u_exact->ProjectCoefficient(u1_r, u1_i);
+            u.ProjectBdrCoefficientTangent(u1, ess_bdr);
+            u_exact->ProjectCoefficient(u1);
          }
          else
          {
-            u.ProjectBdrCoefficientTangent(oneVecCoef, zeroVecCoef, ess_bdr);
+            u.ProjectBdrCoefficientTangent(oneVecCoef, ess_bdr);
          }
          break;
       case 2:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficientNormal(u2_r, u2_i, ess_bdr);
-            u_exact->ProjectCoefficient(u2_r, u2_i);
+            u.ProjectBdrCoefficientNormal(u2, ess_bdr);
+            u_exact->ProjectCoefficient(u2);
          }
          else
          {
-            u.ProjectBdrCoefficientNormal(oneVecCoef, zeroVecCoef, ess_bdr);
+            u.ProjectBdrCoefficientNormal(oneVecCoef, ess_bdr);
          }
          break;
       default: break; // This should be unreachable
@@ -300,27 +289,24 @@ int main(int argc, char *argv[])
    ConstantCoefficient lossCoef(omega_ * sigma_);
    ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
 
+   ComplexConstantCoefficient complexMassCoef(-omega_ * omega_ * epsilon_,
+                                              omega_ * sigma_);
+
    SesquilinearForm *a = new SesquilinearForm(fespace, conv);
    if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    switch (prob)
    {
       case 0:
-         a->AddDomainIntegrator(new DiffusionIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new MassIntegrator(massCoef),
-                                new MassIntegrator(lossCoef));
+         a->AddDomainIntegrator<DiffusionIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<MassIntegrator>(complexMassCoef);
          break;
       case 1:
-         a->AddDomainIntegrator(new CurlCurlIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
+         a->AddDomainIntegrator<CurlCurlIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<VectorFEMassIntegrator>(complexMassCoef);
          break;
       case 2:
-         a->AddDomainIntegrator(new DivDivIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
+         a->AddDomainIntegrator<DivDivIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<VectorFEMassIntegrator>(complexMassCoef);
          break;
       default: break; // This should be unreachable
    }
@@ -436,29 +422,24 @@ int main(int argc, char *argv[])
 
    if (exact_sol)
    {
-      real_t err_r = -1.0;
-      real_t err_i = -1.0;
+      real_t err_u = -1.0;
 
       switch (prob)
       {
          case 0:
-            err_r = u.real().ComputeL2Error(u0_r);
-            err_i = u.imag().ComputeL2Error(u0_i);
+            err_u = u.ComputeL2Error(u0);
             break;
          case 1:
-            err_r = u.real().ComputeL2Error(u1_r);
-            err_i = u.imag().ComputeL2Error(u1_i);
+            err_u = u.ComputeL2Error(u1);
             break;
          case 2:
-            err_r = u.real().ComputeL2Error(u2_r);
-            err_i = u.imag().ComputeL2Error(u2_i);
+            err_u = u.ComputeL2Error(u2);
             break;
          default: break; // This should be unreachable
       }
 
       cout << endl;
-      cout << "|| Re (u_h - u) ||_{L^2} = " << err_r << endl;
-      cout << "|| Im (u_h - u) ||_{L^2} = " << err_i << endl;
+      cout << "|| u_h - u ||_{L^2} = " << err_u << endl;
       cout << endl;
    }
 
@@ -564,36 +545,14 @@ complex<real_t> u0_exact(const Vector &x)
    return std::exp(-i * kappa * x[dim - 1]);
 }
 
-real_t u0_real_exact(const Vector &x)
-{
-   return u0_exact(x).real();
-}
-
-real_t u0_imag_exact(const Vector &x)
-{
-   return u0_exact(x).imag();
-}
-
-void u1_real_exact(const Vector &x, Vector &v)
+void u1_exact(const Vector &x, ComplexVector &v)
 {
    int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_real_exact(x);
+   v.SetSize(dim); v = 0.0; v[0] = u0_exact(x);
 }
 
-void u1_imag_exact(const Vector &x, Vector &v)
+void u2_exact(const Vector &x, ComplexVector &v)
 {
    int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_imag_exact(x);
-}
-
-void u2_real_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_real_exact(x);
-}
-
-void u2_imag_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_imag_exact(x);
+   v.SetSize(dim); v = 0.0; v[dim-1] = u0_exact(x);
 }

examples/ex22p.cpp

@@ -62,6 +62,10 @@ static real_t epsilon_ = 1.0;
 static real_t sigma_ = 20.0;
 static real_t omega_ = 10.0;
 
+complex<real_t> u0_exact(const Vector &x);
+void u1_exact(const Vector &, ComplexVector &);
+void u2_exact(const Vector &, ComplexVector &);
+
 real_t u0_real_exact(const Vector &);
 real_t u0_imag_exact(const Vector &);
 
@@ -244,13 +248,22 @@ int main(int argc, char *argv[])
    ParComplexGridFunction * u_exact = NULL;
    if (exact_sol) { u_exact = new ParComplexGridFunction(fespace); }
 
+   ComplexFunctionCoefficient u0(u0_exact);
+   ComplexVectorFunctionCoefficient u1(dim, u1_exact);
+   ComplexVectorFunctionCoefficient u2(dim, u2_exact);
+
+   ComplexConstantCoefficient oneCoef(1.0);
+
+   Vector  oneVec(dim);  oneVec = 0.0; oneVec[(prob==2)?(dim-1):0] = 1.0;
+   ComplexVectorConstantCoefficient oneVecCoef(oneVec);
+
    FunctionCoefficient u0_r(u0_real_exact);
    FunctionCoefficient u0_i(u0_imag_exact);
    VectorFunctionCoefficient u1_r(dim, u1_real_exact);
    VectorFunctionCoefficient u1_i(dim, u1_imag_exact);
    VectorFunctionCoefficient u2_r(dim, u2_real_exact);
    VectorFunctionCoefficient u2_i(dim, u2_imag_exact);
-
+   /*
    ConstantCoefficient zeroCoef(0.0);
    ConstantCoefficient oneCoef(1.0);
 
@@ -258,40 +271,40 @@ int main(int argc, char *argv[])
    Vector  oneVec(dim);  oneVec = 0.0; oneVec[(prob==2)?(dim-1):0] = 1.0;
    VectorConstantCoefficient zeroVecCoef(zeroVec);
    VectorConstantCoefficient oneVecCoef(oneVec);
-
+   */
    switch (prob)
    {
       case 0:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficient(u0_r, u0_i, ess_bdr);
-            u_exact->ProjectCoefficient(u0_r, u0_i);
+            u.ProjectBdrCoefficient(u0, ess_bdr);
+            u_exact->ProjectCoefficient(u0);
          }
          else
          {
-            u.ProjectBdrCoefficient(oneCoef, zeroCoef, ess_bdr);
+            u.ProjectBdrCoefficient(oneCoef, ess_bdr);
          }
          break;
       case 1:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficientTangent(u1_r, u1_i, ess_bdr);
-            u_exact->ProjectCoefficient(u1_r, u1_i);
+            u.ProjectBdrCoefficientTangent(u1, ess_bdr);
+            u_exact->ProjectCoefficient(u1);
          }
          else
          {
-            u.ProjectBdrCoefficientTangent(oneVecCoef, zeroVecCoef, ess_bdr);
+            u.ProjectBdrCoefficientTangent(oneVecCoef, ess_bdr);
          }
          break;
       case 2:
          if (exact_sol)
          {
-            u.ProjectBdrCoefficientNormal(u2_r, u2_i, ess_bdr);
-            u_exact->ProjectCoefficient(u2_r, u2_i);
+            u.ProjectBdrCoefficientNormal(u2, ess_bdr);
+            u_exact->ProjectCoefficient(u2);
          }
          else
          {
-            u.ProjectBdrCoefficientNormal(oneVecCoef, zeroVecCoef, ess_bdr);
+            u.ProjectBdrCoefficientNormal(oneVecCoef, ess_bdr);
          }
          break;
       default: break; // This should be unreachable
@@ -331,27 +344,24 @@ int main(int argc, char *argv[])
    ConstantCoefficient lossCoef(omega_ * sigma_);
    ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
 
+   ComplexConstantCoefficient complexMassCoef(-omega_ * omega_ * epsilon_,
+                                              omega_ * sigma_);
+
    ParSesquilinearForm *a = new ParSesquilinearForm(fespace, conv);
    if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    switch (prob)
    {
       case 0:
-         a->AddDomainIntegrator(new DiffusionIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new MassIntegrator(massCoef),
-                                new MassIntegrator(lossCoef));
+         a->AddDomainIntegrator<DiffusionIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<MassIntegrator>(complexMassCoef);
          break;
       case 1:
-         a->AddDomainIntegrator(new CurlCurlIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
+         a->AddDomainIntegrator<CurlCurlIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<VectorFEMassIntegrator>(complexMassCoef);
          break;
       case 2:
-         a->AddDomainIntegrator(new DivDivIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
+         a->AddDomainIntegrator<DivDivIntegrator>(stiffnessCoef);
+         a->AddDomainIntegrator<VectorFEMassIntegrator>(complexMassCoef);
          break;
       default: break; // This should be unreachable
    }
@@ -475,22 +485,18 @@ int main(int argc, char *argv[])
 
    if (exact_sol)
    {
-      real_t err_r = -1.0;
-      real_t err_i = -1.0;
+      real_t err_u = -1.0;
 
       switch (prob)
       {
          case 0:
-            err_r = u.real().ComputeL2Error(u0_r);
-            err_i = u.imag().ComputeL2Error(u0_i);
+            err_u = u.ComputeL2Error(u0);
             break;
          case 1:
-            err_r = u.real().ComputeL2Error(u1_r);
-            err_i = u.imag().ComputeL2Error(u1_i);
+            err_u = u.ComputeL2Error(u1);
             break;
          case 2:
-            err_r = u.real().ComputeL2Error(u2_r);
-            err_i = u.imag().ComputeL2Error(u2_i);
+            err_u = u.ComputeL2Error(u2);
             break;
          default: break; // This should be unreachable
       }
@@ -498,8 +504,7 @@ int main(int argc, char *argv[])
       if ( myid == 0 )
       {
          cout << endl;
-         cout << "|| Re (u_h - u) ||_{L^2} = " << err_r << endl;
-         cout << "|| Im (u_h - u) ||_{L^2} = " << err_i << endl;
+         cout << "|| u_h - u ||_{L^2} = " << err_u << endl;
          cout << endl;
       }
    }
@@ -627,6 +632,12 @@ real_t u0_imag_exact(const Vector &x)
    return u0_exact(x).imag();
 }
 
+void u1_exact(const Vector &x, ComplexVector &v)
+{
+   int dim = x.Size();
+   v.SetSize(dim); v = 0.0; v[0] = u0_exact(x);
+}
+
 void u1_real_exact(const Vector &x, Vector &v)
 {
    int dim = x.Size();
@@ -639,6 +650,12 @@ void u1_imag_exact(const Vector &x, Vector &v)
    v.SetSize(dim); v = 0.0; v[0] = u0_imag_exact(x);
 }
 
+void u2_exact(const Vector &x, ComplexVector &v)
+{
+   int dim = x.Size();
+   v.SetSize(dim); v = 0.0; v[dim-1] = u0_exact(x);
+}
+
 void u2_real_exact(const Vector &x, Vector &v)
 {
    int dim = x.Size();

fem/CMakeLists.txt

@@ -59,6 +59,7 @@ set(SRCS
   integ/nonlininteg_vecconvection_pa.cpp
   integ/nonlininteg_vecconvection_mf.cpp
   coefficient.cpp
+  complex_coefficient.cpp
   complex_fem.cpp
   convergence.cpp
   datacollection.cpp
@@ -176,6 +177,7 @@ set(HDRS
   integ/bilininteg_hcurlhdiv_kernels.hpp
   integ/bilininteg_mass_kernels.hpp
   coefficient.hpp
+  complex_coefficient.hpp
   complex_fem.hpp
   convergence.hpp
   datacollection.hpp
@@ -247,6 +249,7 @@ set(HDRS
   nonlinearform_ext.hpp
   nonlininteg.hpp
   qfunction.hpp
+  qinterp/det.hpp
   qinterp/eval.hpp
   qinterp/eval_hdiv.hpp
   qinterp/grad.hpp

fem/batchitrans.cpp

@@ -515,6 +515,7 @@ struct InvTNewtonSolver<Geometry::SEGMENT, SDim, SType, max_team_x>
             phys_tol += pptr[idx + d * npts] * pptr[idx + d * npts];
          }
          phys_tol = fmax(phys_rtol * phys_rtol, phys_tol * phys_rtol * phys_rtol);
+         hit_bdr[0] = prev_hit_bdr[0] = false;
       }
       // for each iteration
       while (true)

fem/complex_coefficient.cpp

@@ -0,0 +1,217 @@
+// 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 "complex_fem.hpp"
+#include "../general/forall.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+real_t
+RealPartCoefficient::Eval(ElementTransformation &T,
+                          const IntegrationPoint &ip)
+{
+   complex_t val = complex_coef_.Eval(T, ip);
+   return val.real();
+}
+
+real_t
+ImagPartCoefficient::Eval(ElementTransformation &T,
+                          const IntegrationPoint &ip)
+{
+   complex_t val = complex_coef_.Eval(T, ip);
+   return val.imag();
+}
+
+RealPartVectorCoefficient::RealPartVectorCoefficient(ComplexVectorCoefficient &
+                                                     complex_vcoef)
+   : VectorCoefficient(complex_vcoef.GetVDim()),
+     complex_vcoef_(complex_vcoef),
+     val_(vdim)
+{}
+
+void
+RealPartVectorCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   complex_vcoef_.Eval(val_, T, ip);
+   V = val_.real();
+}
+
+ImagPartVectorCoefficient::ImagPartVectorCoefficient(ComplexVectorCoefficient &
+                                                     complex_vcoef)
+   : VectorCoefficient(complex_vcoef.GetVDim()),
+     complex_vcoef_(complex_vcoef),
+     val_(vdim)
+{}
+
+void
+ImagPartVectorCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   complex_vcoef_.Eval(val_, T, ip);
+   V = val_.imag();
+}
+
+RealPartMatrixCoefficient::RealPartMatrixCoefficient(ComplexMatrixCoefficient &
+                                                     complex_mcoef)
+   : MatrixCoefficient(complex_mcoef.GetHeight(), complex_mcoef.GetWidth()),
+     complex_mcoef_(complex_mcoef),
+     val_(height, width)
+{}
+
+void
+RealPartMatrixCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   complex_mcoef_.Eval(val_, T, ip);
+   M = val_.real();
+}
+
+ImagPartMatrixCoefficient::ImagPartMatrixCoefficient(ComplexMatrixCoefficient &
+                                                     complex_mcoef)
+   : MatrixCoefficient(complex_mcoef.GetHeight(), complex_mcoef.GetWidth()),
+     complex_mcoef_(complex_mcoef),
+     val_(height, width)
+{}
+
+void
+ImagPartMatrixCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   complex_mcoef_.Eval(val_, T, ip);
+   M = val_.imag();
+}
+
+ComplexCoefficient::ComplexCoefficient()
+   : time(0.),
+     re_part_coef_(*this), im_part_coef_(*this),
+     real_coef_(re_part_coef_), imag_coef_(im_part_coef_)
+{ }
+
+ComplexCoefficient::ComplexCoefficient(Coefficient &c_r,
+                                       Coefficient &c_i)
+   : time(c_r.GetTime()),
+     re_part_coef_(*this), im_part_coef_(*this),
+     real_coef_(c_r), imag_coef_(c_i)
+{
+   c_i.SetTime(time);
+}
+
+complex_t
+ComplexCoefficient::Eval(ElementTransformation &T,
+                         const IntegrationPoint &ip)
+{
+   // Avoid circular dependency
+   MFEM_VERIFY(std::addressof(real_coef_) != std::addressof(re_part_coef_) &&
+               std::addressof(imag_coef_) != std::addressof(im_part_coef_),
+               "Classes dervied from ComplexCoefficient must either "
+               "implement an Eval method or supply Coefficients "
+               "for both the real and imaginary parts of the field.");
+
+   return complex_t(real_coef_.Eval(T, ip), imag_coef_.Eval(T, ip));
+}
+
+ComplexVectorCoefficient::ComplexVectorCoefficient(VectorCoefficient &v_r,
+                                                   VectorCoefficient &v_i)
+   : vdim(v_r.GetVDim()), time(v_r.GetTime()),
+     re_part_vcoef_(*this), im_part_vcoef_(*this),
+     real_vcoef_(v_r), imag_vcoef_(v_i)
+{
+   MFEM_ASSERT(v_r.GetVDim() == v_i.GetVDim(), "ComplexVectorCoefficient"
+               " - incompatible vector dimensions of real and imaginary parts.");
+
+   v_i.SetTime(time);
+}
+
+void ComplexVectorCoefficient::Eval(ComplexVector &V, ElementTransformation &T,
+                                    const IntegrationPoint &ip)
+{
+   // Avoid circular dependency
+   MFEM_VERIFY(std::addressof(real_vcoef_) != std::addressof(re_part_vcoef_) &&
+               std::addressof(imag_vcoef_) != std::addressof(im_part_vcoef_),
+               "Classes dervied from ComplexVectorCoefficient must either "
+               "implement an Eval method or supply VectorCoefficients "
+               "for both the real and imaginary parts of the field.");
+
+   V_r_.SetSize(vdim);
+   V_i_.SetSize(vdim);
+
+   real_vcoef_.Eval(V_r_, T, ip);
+   imag_vcoef_.Eval(V_i_, T, ip);
+
+   V.Set(V_r_, V_i_);
+}
+
+ComplexConstantCoefficient::ComplexConstantCoefficient(
+   const complex_t z)
+   : val(z), real_coef(z.real()), imag_coef(z.imag())
+{
+   real_coef_ = real_coef;
+   imag_coef_ = imag_coef;
+}
+
+ComplexConstantCoefficient::ComplexConstantCoefficient(
+   real_t z_r, real_t z_i)
+   : real_coef(z_r), imag_coef(z_i)
+{
+   val = complex_t(z_r, z_i);
+
+   real_coef_ = real_coef;
+   imag_coef_ = imag_coef;
+}
+
+complex_t ComplexFunctionCoefficient::Eval(ElementTransformation & T,
+                                           const IntegrationPoint & ip)
+{
+   real_t x[3];
+   Vector transip(x, 3);
+
+   T.Transform(ip, transip);
+
+   if (Function)
+   {
+      return Function(transip);
+   }
+   else
+   {
+      return TDFunction(transip, GetTime());
+   }
+}
+
+void ComplexVectorFunctionCoefficient::Eval(ComplexVector &V,
+                                            ElementTransformation &T,
+                                            const IntegrationPoint &ip)
+{
+   real_t x[3];
+   Vector transip(x, 3);
+
+   T.Transform(ip, transip);
+
+   V.SetSize(vdim);
+   if (Function)
+   {
+      Function(transip, V);
+   }
+   else
+   {
+      TDFunction(transip, GetTime(), V);
+   }
+   if (Q)
+   {
+      V *= Q->Eval(T, ip, GetTime());
+   }
+}
+
+} // end namespace mfem
+

fem/complex_coefficient.hpp

@@ -0,0 +1,523 @@
+// 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_COMPLEX_COEFFICIENT
+#define MFEM_COMPLEX_COEFFICIENT
+
+#include "../config/config.hpp"
+#include "../linalg/linalg.hpp"
+#include "coefficient.hpp"
+#include "intrules.hpp"
+#include "eltrans.hpp"
+
+namespace mfem
+{
+
+class ComplexCoefficient;
+class ComplexVectorCoefficient;
+class ComplexMatrixCoefficient;
+
+/// Standard Coefficient which returns the real part of a ComplexCoefficient
+class RealPartCoefficient : public Coefficient
+{
+private:
+   ComplexCoefficient &complex_coef_;
+
+public:
+   RealPartCoefficient(ComplexCoefficient & complex_coef)
+      : complex_coef_(complex_coef) {}
+
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip);
+};
+
+/// Standard Coefficient which returns the imaginary part of a
+/// ComplexCoefficient
+class ImagPartCoefficient : public Coefficient
+{
+private:
+   ComplexCoefficient &complex_coef_;
+
+public:
+   ImagPartCoefficient(ComplexCoefficient & complex_coef)
+      : complex_coef_(complex_coef) {}
+
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip);
+};
+
+typedef ImagPartCoefficient ImaginaryPartCoefficient;
+
+class RealPartVectorCoefficient : public VectorCoefficient
+{
+private:
+   ComplexVectorCoefficient &complex_vcoef_;
+   mutable ComplexVector val_;
+
+public:
+   RealPartVectorCoefficient(ComplexVectorCoefficient & complex_vcoef);
+
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip);
+};
+
+class ImagPartVectorCoefficient : public VectorCoefficient
+{
+private:
+   ComplexVectorCoefficient &complex_vcoef_;
+   mutable ComplexVector val_;
+
+public:
+   ImagPartVectorCoefficient(ComplexVectorCoefficient & complex_vcoef);
+
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip);
+};
+
+typedef ImagPartVectorCoefficient ImaginaryPartVectorCoefficient;
+
+class RealPartMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   ComplexMatrixCoefficient &complex_mcoef_;
+   mutable ComplexTypeDenseMatrix val_;
+
+public:
+   RealPartMatrixCoefficient(ComplexMatrixCoefficient & complex_mcoef);
+
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip);
+};
+
+class ImagPartMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   ComplexMatrixCoefficient &complex_mcoef_;
+   mutable ComplexTypeDenseMatrix val_;
+
+public:
+   ImagPartMatrixCoefficient(ComplexMatrixCoefficient & complex_mcoef);
+
+   void Eval(DenseMatrix &V, ElementTransformation &T,
+             const IntegrationPoint &ip);
+};
+
+typedef ImagPartMatrixCoefficient ImaginaryPartMatrixCoefficient;
+
+/** @brief Base class ComplexCoefficients that optionally depend on space and
+    time. These are used by the SesquilinearForm, ComplexLinearForm, and
+    ComplexGridFunction classes to represent the physical coefficients in
+    the PDEs that are being discretized. This class can also be used in a more
+    general way to represent functions that don't necessarily belong to a FE
+    space, e.g., to project onto ComplexGridFunctions to use as initial
+    conditions, exact solutions, etc. See, e.g., ex22 for these uses. */
+class ComplexCoefficient
+{
+protected:
+   real_t time;
+
+private:
+   RealPartCoefficient re_part_coef_;
+   ImagPartCoefficient im_part_coef_;
+
+protected:
+   Coefficient &real_coef_;
+   Coefficient &imag_coef_;
+
+public:
+
+   ComplexCoefficient();
+   ComplexCoefficient(Coefficient &c_r, Coefficient &c_i);
+
+   /// Set the time for time dependent coefficients
+   virtual void SetTime(real_t t)
+   { time = t; real_coef_.SetTime(t); imag_coef_.SetTime(t); }
+
+   /// Get the time for time dependent coefficients
+   real_t GetTime() { return time; }
+
+   /** @brief Evaluate the coefficient in the element described by @a T at the
+       point @a ip. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
+   virtual complex_t Eval(ElementTransformation &T,
+                          const IntegrationPoint &ip);
+
+   /** @brief Evaluate the coefficient in the element described by @a T at the
+       point @a ip at time @a t. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
+   complex_t Eval(ElementTransformation &T,
+                  const IntegrationPoint &ip, real_t t)
+   {
+      SetTime(t);
+      return Eval(T, ip);
+   }
+
+   /** @brief Access a standard Coefficient object reproducing the real part of
+       the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its real part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual Coefficient & real() { return real_coef_; }
+
+   /** @brief Access a standard Coefficient object reproducing the imaginary
+       part of the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its imaginary part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual Coefficient & imag() { return imag_coef_; }
+
+   virtual ~ComplexCoefficient() { }
+};
+
+/** @brief Base class ComplexVectorCoefficients that optionally depend
+    on space and time. These are used by the SesquilinearForm,
+    ComplexLinearForm, and ComplexGridFunction classes to represent
+    the physical vector-valued coefficients in the PDEs that are being
+    discretized. This class can also be used in a more general way to
+    represent functions that don't necessarily belong to a FE space,
+    e.g., to project onto ComplexGridFunctions to use as initial
+    conditions, exact solutions, etc. See, e.g., ex22 for these
+    uses. */
+class ComplexVectorCoefficient
+{
+protected:
+   int vdim;
+   real_t time;
+
+private:
+   RealPartVectorCoefficient re_part_vcoef_;
+   ImagPartVectorCoefficient im_part_vcoef_;
+
+protected:
+   VectorCoefficient &real_vcoef_;
+   VectorCoefficient &imag_vcoef_;
+
+   mutable Vector V_r_;
+   mutable Vector V_i_;
+
+public:
+   ComplexVectorCoefficient(int vd)
+      : vdim(vd), time(0.),
+        re_part_vcoef_(*this), im_part_vcoef_(*this),
+        real_vcoef_(re_part_vcoef_), imag_vcoef_(im_part_vcoef_)
+   { }
+
+   ComplexVectorCoefficient(VectorCoefficient &v_r, VectorCoefficient &v_i);
+
+
+   /// Set the time for time dependent coefficients
+   virtual void SetTime(real_t t)
+   { time = t; real_vcoef_.SetTime(t); imag_vcoef_.SetTime(t); }
+
+   /// Get the time for time dependent coefficients
+   real_t GetTime() { return time; }
+
+   /// Returns dimension of the vector.
+   int GetVDim() { return vdim; }
+
+   /** @brief Evaluate the vector coefficient in the element described by @a T
+       at the point @a ip, storing the result in @a V. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
+   virtual void Eval(ComplexVector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+
+   /** @brief Evaluate the vector coefficient in the element described by @a T
+       at the point @a ip at time @a t, storing the result in @a V. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
+   void Eval(ComplexVector &V, ElementTransformation &T,
+             const IntegrationPoint &ip, real_t t)
+   {
+      SetTime(t);
+      Eval(V, T, ip);
+   }
+
+   /** @brief Access a standard Coefficient object reproducing the real part of
+       the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its real part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual VectorCoefficient & real() { return real_vcoef_; }
+
+   /** @brief Access a standard Coefficient object reproducing the imaginary
+       part of the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its imaginary part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual VectorCoefficient & imag() { return imag_vcoef_; }
+
+   virtual ~ComplexVectorCoefficient() { }
+};
+
+/** @brief Base class ComplexMatrixCoefficients that optionally depend
+    on space and time. These are used by the SesquilinearForm,
+    ComplexLinearForm, and ComplexGridFunction classes to represent
+    the physical matrix-valued coefficients in the PDEs that are being
+    discretized. This class can also be used in a more general way to
+    represent functions that don't necessarily belong to a FE space.
+    See, e.g., ex22 for these uses. */
+class ComplexMatrixCoefficient
+{
+protected:
+   int height, width;
+   real_t time;
+
+private:
+   RealPartMatrixCoefficient re_part_mcoef_;
+   ImagPartMatrixCoefficient im_part_mcoef_;
+
+protected:
+   MatrixCoefficient &real_mcoef_;
+   MatrixCoefficient &imag_mcoef_;
+
+   mutable DenseMatrix M_r_;
+   mutable DenseMatrix M_i_;
+
+public:
+   /// Construct a dim x dim matrix coefficient.
+   explicit ComplexMatrixCoefficient(int dim)
+      : height(dim), width(dim), time(0.),
+        re_part_mcoef_(*this), im_part_mcoef_(*this),
+        real_mcoef_(re_part_mcoef_), imag_mcoef_(im_part_mcoef_)
+   { }
+
+   /// Construct a h x w matrix coefficient.
+   ComplexMatrixCoefficient(int h, int w) :
+      height(h), width(w), time(0.),
+      re_part_mcoef_(*this), im_part_mcoef_(*this),
+      real_mcoef_(re_part_mcoef_), imag_mcoef_(im_part_mcoef_)
+   { }
+
+   /// Set the time for time dependent coefficients
+   virtual void SetTime(real_t t) { time = t; }
+
+   /// Get the time for time dependent coefficients
+   real_t GetTime() { return time; }
+
+   /// Get the height of the matrix.
+   int GetHeight() const { return height; }
+
+   /// Get the width of the matrix.
+   int GetWidth() const { return width; }
+
+   /// For backward compatibility get the width of the matrix.
+   int GetVDim() const { return width; }
+
+   /** @brief Evaluate the matrix coefficient in the element described by @a T
+       at the point @a ip, storing the result in @a K. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
+   virtual void Eval(ComplexTypeDenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip) = 0;
+
+   /** @brief Access a standard Coefficient object reproducing the real part of
+       the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its real part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual MatrixCoefficient & real() { return real_mcoef_; }
+
+   /** @brief Access a standard Coefficient object reproducing the imaginary
+       part of the complex-valued field */
+   /** @note By default this method returns an internal object which
+       computes the complex value using the above Eval method and
+       returns its imaginary part. Custom implementations may choose to
+       override this method with a more efficient real-valued
+       coefficient. */
+   virtual MatrixCoefficient & imag() { return imag_mcoef_; }
+
+   virtual ~ComplexMatrixCoefficient() { }
+};
+
+/// A complex-valued coefficient that is constant across space and time
+class ComplexConstantCoefficient : public ComplexCoefficient
+{
+private:
+   complex_t val;
+
+   ConstantCoefficient real_coef;
+   ConstantCoefficient imag_coef;
+
+public:
+   ComplexConstantCoefficient(const complex_t z);
+
+   ComplexConstantCoefficient(real_t z_r, real_t z_i = 0.);
+
+   complex_t Eval(ElementTransformation &T,
+                  const IntegrationPoint &ip) { return val; }
+};
+
+/// Complex-valued vector coefficient that is constant in space and time.
+class ComplexVectorConstantCoefficient : public ComplexVectorCoefficient
+{
+private:
+   ComplexVector vec;
+
+public:
+   /// Construct the coefficient with constant vector @a v.
+   ComplexVectorConstantCoefficient(const ComplexVector &v)
+      : ComplexVectorCoefficient(v.Size()), vec(v) { }
+
+   /// Construct the coefficient with constant vector @a v.
+   ComplexVectorConstantCoefficient(const Vector &v)
+      : ComplexVectorCoefficient(v.Size()), vec(v) { }
+
+   using ComplexVectorCoefficient::Eval;
+
+   ///  Evaluate the vector coefficient at @a ip.
+   void Eval(ComplexVector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override { V = vec; }
+
+   /// Return a reference to the constant vector in this class.
+   const ComplexVector& GetVec() const { return vec; }
+};
+
+/// Complex-valued vector coefficient that is constant in space and time.
+class ComplexMatrixConstantCoefficient : public ComplexMatrixCoefficient
+{
+private:
+   ComplexTypeDenseMatrix mat;
+
+public:
+   /// Construct the coefficient with constant vector @a v.
+   ComplexMatrixConstantCoefficient(const ComplexTypeDenseMatrix &m)
+      : ComplexMatrixCoefficient(m.Height(), m.Width()), mat(m) { }
+
+   /// Construct the coefficient with constant vector @a v.
+   ComplexMatrixConstantCoefficient(const DenseMatrix &m)
+      : ComplexMatrixCoefficient(m.Height(), m.Width()), mat(m) { }
+
+   using ComplexMatrixCoefficient::Eval;
+
+   ///  Evaluate the matrix coefficient at @a ip.
+   void Eval(ComplexTypeDenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override { M = mat; }
+
+   /// Return a reference to the constant matrix in this class.
+   const ComplexTypeDenseMatrix& GetMat() const { return mat; }
+};
+
+/// A general complex-valued function coefficient
+class ComplexFunctionCoefficient : public ComplexCoefficient
+{
+protected:
+   std::function<complex_t(const Vector &)> Function;
+   std::function<complex_t(const Vector &, real_t)> TDFunction;
+
+public:
+   /// Define a time-independent coefficient from a std function
+   /** \param F time-independent std::function */
+   ComplexFunctionCoefficient(std::function<complex_t
+                              (const Vector &)> F)
+      : Function(std::move(F))
+   { }
+
+   /// Define a time-dependent coefficient from a std function
+   /** \param TDF time-dependent function */
+   ComplexFunctionCoefficient(std::function<complex_t
+                              (const Vector &, real_t)> TDF)
+      : TDFunction(std::move(TDF))
+   { }
+
+   /// (DEPRECATED) Define a time-independent coefficient from a C-function
+   /** @deprecated Use the method where the C-function, @a f, uses a const
+       Vector argument instead of Vector. */
+   MFEM_DEPRECATED ComplexFunctionCoefficient(complex_t
+                                              (*f)(Vector &))
+   {
+      // Cast first to (void*) to suppress a warning from newer version of
+      // Clang when using -Wextra.
+      Function = reinterpret_cast<complex_t(*)
+                 (const Vector&)>((void*)f);
+      TDFunction = NULL;
+   }
+
+   /// (DEPRECATED) Define a time-dependent coefficient from a C-function
+   /** @deprecated Use the method where the C-function, @a tdf, uses a const
+       Vector argument instead of Vector. */
+   MFEM_DEPRECATED ComplexFunctionCoefficient(complex_t
+                                              (*tdf)(Vector &, real_t))
+   {
+      Function = NULL;
+      // Cast first to (void*) to suppress a warning from newer version of
+      // Clang when using -Wextra.
+      TDFunction =
+         reinterpret_cast<complex_t(*)(const Vector&,
+                                       real_t)>((void*)tdf);
+   }
+
+   /// Evaluate the coefficient at @a ip.
+   complex_t Eval(ElementTransformation &T,
+                  const IntegrationPoint &ip) override;
+};
+
+/// A general vector function coefficient
+class ComplexVectorFunctionCoefficient : public ComplexVectorCoefficient
+{
+private:
+   std::function<void(const Vector &, ComplexVector &)> Function;
+   std::function<void(const Vector &, real_t, ComplexVector &)> TDFunction;
+   ComplexCoefficient *Q;
+
+public:
+   /// Define a time-independent complex-valued vector coefficient
+   /// from a std function
+   /** \param dim - the size of the vector
+       \param F - time-independent function
+       \param q - optional scalar Coefficient to scale the vector coefficient */
+   ComplexVectorFunctionCoefficient(int dim,
+                                    std::function<void(const Vector &,
+                                                       ComplexVector &)> F,
+                                    ComplexCoefficient *q = nullptr)
+      : ComplexVectorCoefficient(dim), Function(std::move(F)), Q(q)
+   { }
+
+   /// Define a time-dependent complex-valued vector coefficient from
+   /// a std function
+   /** \param dim - the size of the vector
+       \param TDF - time-dependent function
+       \param q - optional scalar ComplexCoefficient to scale the vector coefficient */
+   ComplexVectorFunctionCoefficient(int dim,
+                                    std::function<void(const Vector &, real_t,
+                                                       ComplexVector &)> TDF,
+                                    ComplexCoefficient *q = nullptr)
+      : ComplexVectorCoefficient(dim), TDFunction(std::move(TDF)), Q(q)
+   { }
+
+   using ComplexVectorCoefficient::Eval;
+   /// Evaluate the vector coefficient at @a ip.
+   void Eval(ComplexVector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
+
+   virtual ~ComplexVectorFunctionCoefficient() { }
+};
+
+} // end namespace mfem
+
+#endif

fem/complex_fem.cpp

@@ -96,6 +96,23 @@ ComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
    gfi->SyncAliasMemory(*this);
 }
 
+void
+ComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff)
+{
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
+   gfr->ProjectCoefficient(real_coeff);
+   *gfi = 0.0;
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
+}
+
+void
+ComplexGridFunction::ProjectCoefficient(ComplexCoefficient &coeff)
+{
+   this->ProjectCoefficient(coeff.real(), coeff.imag());
+}
+
 void
 ComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
                                         VectorCoefficient &imag_vcoeff)
@@ -108,6 +125,23 @@ ComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
    gfi->SyncAliasMemory(*this);
 }
 
+void
+ComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff)
+{
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
+   gfr->ProjectCoefficient(real_vcoeff);
+   *gfi = 0.0;
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
+}
+
+void
+ComplexGridFunction::ProjectCoefficient(ComplexVectorCoefficient &vcoeff)
+{
+   this->ProjectCoefficient(vcoeff.real(), vcoeff.imag());
+}
+
 void
 ComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
                                            Coefficient &imag_coeff,
@@ -121,6 +155,26 @@ ComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
    gfi->SyncAliasMemory(*this);
 }
 
+void
+ComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
+                                           Array<int> &attr)
+{
+   ConstantCoefficient zero_coeff(0.0);
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
+   gfr->ProjectBdrCoefficient(real_coeff, attr);
+   gfi->ProjectBdrCoefficient(zero_coeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
+}
+
+void
+ComplexGridFunction::ProjectBdrCoefficient(ComplexCoefficient &coeff,
+                                           Array<int> &attr)
+{
+   this->ProjectBdrCoefficient(coeff.real(), coeff.imag(), attr);
+}
+
 void
 ComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient &real_vcoeff,
                                                  VectorCoefficient &imag_vcoeff,
@@ -134,6 +188,28 @@ ComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient &real_vcoeff,
    gfi->SyncAliasMemory(*this);
 }
 
+void
+ComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient &real_vcoeff,
+                                                 Array<int> &attr)
+{
+   Vector zero_vec(real_vcoeff.GetVDim()); zero_vec = 0.;
+   VectorConstantCoefficient zero_vcoeff(zero_vec);
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
+   gfr->ProjectBdrCoefficientNormal(real_vcoeff, attr);
+   gfi->ProjectBdrCoefficientNormal(zero_vcoeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
+}
+
+void
+ComplexGridFunction::ProjectBdrCoefficientNormal(
+   ComplexVectorCoefficient &vcoeff,
+   Array<int> &attr)
+{
+   this->ProjectBdrCoefficientNormal(vcoeff.real(), vcoeff.imag(), attr);
+}
+
 void
 ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
                                                   &real_vcoeff,
@@ -149,6 +225,80 @@ ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
    gfi->SyncAliasMemory(*this);
 }
 
+void
+ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
+                                                  &real_vcoeff,
+                                                  Array<int> &attr)
+{
+   Vector zero_vec(real_vcoeff.GetVDim()); zero_vec = 0.;
+   VectorConstantCoefficient zero_vcoeff(zero_vec);
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
+   gfr->ProjectBdrCoefficientTangent(real_vcoeff, attr);
+   gfi->ProjectBdrCoefficientTangent(zero_vcoeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
+}
+
+void
+ComplexGridFunction::ProjectBdrCoefficientTangent(
+   ComplexVectorCoefficient &vcoeff,
+   Array<int> &attr)
+{
+   this->ProjectBdrCoefficientTangent(vcoeff.real(), vcoeff.imag(), attr);
+}
+
+real_t
+ComplexGridFunction::ComputeL2Error(Coefficient &re_exsol,
+                                    Coefficient &im_exsol,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   real_t err_r = gfr->ComputeL2Error(re_exsol, irs, elems);
+   real_t err_i = gfi->ComputeL2Error(im_exsol, irs, elems);
+
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
+real_t
+ComplexGridFunction::ComputeL2Error(Coefficient &re_exsol,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   ConstantCoefficient zero_coef(0.0);
+
+   real_t err_r = gfr->ComputeL2Error(re_exsol, irs, elems);
+   real_t err_i = gfi->ComputeL2Error(zero_coef, irs, elems);
+
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
+real_t
+ComplexGridFunction::ComputeL2Error(VectorCoefficient &re_exsol,
+                                    VectorCoefficient &im_exsol,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   real_t err_r = gfr->ComputeL2Error(re_exsol, irs, elems);
+   real_t err_i = gfi->ComputeL2Error(im_exsol, irs, elems);
+
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
+real_t
+ComplexGridFunction::ComputeL2Error(VectorCoefficient &re_exsol,
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
+{
+   Vector zero_vec(re_exsol.GetVDim()); zero_vec = 0.0;
+   VectorConstantCoefficient zero_coef(zero_vec);
+
+   real_t err_r = gfr->ComputeL2Error(re_exsol, irs, elems);
+   real_t err_i = gfi->ComputeL2Error(zero_coef, irs, elems);
+
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
 
 ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *fes,
                                      ComplexOperator::Convention convention)
@@ -731,6 +881,17 @@ ParComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
    pgfi->SyncAliasMemory(*this);
 }
 
+void
+ParComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff)
+{
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
+   pgfr->ProjectCoefficient(real_coeff);
+   *pgfi = 0.0;
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+}
+
 void
 ParComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
                                            VectorCoefficient &imag_vcoeff)
@@ -743,6 +904,17 @@ ParComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
    pgfi->SyncAliasMemory(*this);
 }
 
+void
+ParComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff)
+{
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
+   pgfr->ProjectCoefficient(real_vcoeff);
+   *pgfi = 0.0;
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+}
+
 void
 ParComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
                                               Coefficient &imag_coeff,
@@ -756,6 +928,19 @@ ParComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
    pgfi->SyncAliasMemory(*this);
 }
 
+void
+ParComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
+                                              Array<int> &attr)
+{
+   ConstantCoefficient zero_coeff(0.0);
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
+   pgfr->ProjectBdrCoefficient(real_coeff, attr);
+   pgfi->ProjectBdrCoefficient(zero_coeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+}
+
 void
 ParComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient
                                                     &real_vcoeff,
@@ -771,6 +956,21 @@ ParComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient
    pgfi->SyncAliasMemory(*this);
 }
 
+void
+ParComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient
+                                                    &real_vcoeff,
+                                                    Array<int> &attr)
+{
+   Vector zero_vec(real_vcoeff.GetVDim()); zero_vec = 0.;
+   VectorConstantCoefficient zero_vcoeff(zero_vec);
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
+   pgfr->ProjectBdrCoefficientNormal(real_vcoeff, attr);
+   pgfi->ProjectBdrCoefficientNormal(zero_vcoeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+}
+
 void
 ParComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
                                                      &real_vcoeff,
@@ -786,6 +986,21 @@ ParComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
    pgfi->SyncAliasMemory(*this);
 }
 
+void
+ParComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
+                                                     &real_vcoeff,
+                                                     Array<int> &attr)
+{
+   Vector zero_vec(real_vcoeff.GetVDim()); zero_vec = 0.;
+   VectorConstantCoefficient zero_vcoeff(zero_vec);
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
+   pgfr->ProjectBdrCoefficientTangent(real_vcoeff, attr);
+   pgfi->ProjectBdrCoefficientTangent(zero_vcoeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+}
+
 void
 ParComplexGridFunction::Distribute(const Vector *tv)
 {
@@ -825,6 +1040,31 @@ ParComplexGridFunction::ParallelProject(Vector &tv) const
    tvi.SyncAliasMemory(tv);
 }
 
+real_t
+ParComplexGridFunction::ComputeL2Error(Coefficient &exsolr,
+                                       const IntegrationRule *irs[],
+                                       Array<int> *elems) const
+{
+   ConstantCoefficient zeroCoef(0.0);
+
+   real_t err_r = pgfr->ComputeL2Error(exsolr, irs, elems);
+   real_t err_i = pgfi->ComputeL2Error(zeroCoef, irs, elems);
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
+real_t
+ParComplexGridFunction::ComputeL2Error(VectorCoefficient &exsolr,
+                                       const IntegrationRule *irs[],
+                                       Array<int> *elems) const
+{
+   Vector zeroVec(exsolr.GetVDim()); zeroVec = 0.0;
+   VectorConstantCoefficient zeroCoef(zeroVec);
+
+   real_t err_r = pgfr->ComputeL2Error(exsolr, irs, elems);
+   real_t err_i = pgfi->ComputeL2Error(zeroCoef, irs, elems);
+   return sqrt(err_r * err_r + err_i * err_i);
+}
+
 
 ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
                                            ComplexOperator::Convention

fem/datacollection.cpp

@@ -764,9 +764,9 @@ ParaViewDataCollectionBase::ParaViewDataCollectionBase(
 {
    cycle = 0;
 #ifdef MFEM_USE_ZLIB
-   compression = true; // if we have zlib, enable compression
-#else
-   compression = false; // otherwise, disable compression
+   // If we have zlib, enable compression. Otherwise, compression is disabled in
+   // the DataCollection base class constructor.
+   compression = true;
 #endif
 }
 
@@ -784,13 +784,8 @@ void ParaViewDataCollectionBase::SetCompressionLevel(int compression_level_)
 {
    MFEM_ASSERT(compression_level_ >= -1 && compression_level_ <= 9,
                "Compression level must be between -1 and 9 (inclusive).");
+   if (compression_level_ != 0) { SetCompression(true);}
    compression_level = compression_level_;
-   compression = compression_level_ != 0;
-}
-
-void ParaViewDataCollectionBase::SetCompression(bool compression_)
-{
-   compression = compression_;
 }
 
 int ParaViewDataCollectionBase::GetCompressionLevel() const
@@ -1174,7 +1169,14 @@ const char *ParaViewDataCollection::GetDataTypeString() const
 ParaViewHDFDataCollection::ParaViewHDFDataCollection(
    const std::string &collection_name, Mesh *mesh)
    : ParaViewDataCollectionBase(collection_name, mesh)
-{ }
+{
+   compression = true;
+}
+
+void ParaViewHDFDataCollection::SetCompression(bool compression_)
+{
+   compression = compression_;
+}
 
 void ParaViewHDFDataCollection::EnsureVTKHDF()
 {

fem/datacollection.hpp

@@ -537,13 +537,6 @@ public:
    /// Any nonzero compression level will enable compression.
    void SetCompressionLevel(int compression_level_);
 
-   /// @brief Enable or disable zlib compression.
-   ///
-   /// If the input is true, use the default zlib compression level (unless the
-   /// compression level has previously been set by calling
-   /// SetCompressionLevel()).
-   void SetCompression(bool compression_) override;
-
    /// @brief Sets whether or not to output the data as high-order elements
    /// (false by default).
    ///
@@ -633,6 +626,12 @@ public:
    ParaViewHDFDataCollection(const std::string& collection_name,
                              Mesh *mesh_ = nullptr);
 
+   /// @brief Enable or disable compression.
+   ///
+   /// The compression level can be set with SetCompressionLevel()). VTKHDF
+   /// compression does not require MFEM to be compiled with zlib support.
+   void SetCompression(bool compression_) override;
+
    /// Save the collection.
    void Save() override;
 

fem/dfem/doperator.hpp

@@ -241,6 +241,7 @@ public:
    {
       MFEM_ASSERT(!action_callbacks.empty(), "no integrators have been set");
       prolongation(solutions, solutions_t, solutions_l);
+      residual_l = 0.0;
       for (auto &action : action_callbacks)
       {
          action(solutions_l, parameters_l, residual_l);

fem/dfem/util.hpp

@@ -987,7 +987,7 @@ get_restriction_transpose(
    {
       auto RT = [=](const Vector &v_e, Vector &v_l)
       {
-         v_l = v_e;
+         v_l += v_e;
       };
       return std::make_tuple(RT, 1);
    }
@@ -996,7 +996,7 @@ get_restriction_transpose(
       const Operator *R = get_restriction<entity_t>(f, o);
       std::function<void(const Vector&, Vector&)> RT = [=](const Vector &x, Vector &y)
       {
-         R->MultTranspose(x, y);
+         R->AddMultTranspose(x, y);
       };
       return std::make_tuple(RT, R->Height());
    }
@@ -1708,6 +1708,7 @@ std::array<DofToQuadMap, N> load_dtq_mem(
          const auto B = Reshape(&dtq[i].B[0], nqp_b, dim_b, ndof_b);
          auto mem_Bi = Reshape(reinterpret_cast<real_t *>(mem) + offset, nqp_b, dim_b,
                                ndof_b);
+
          MFEM_FOREACH_THREAD(q, x, nqp_b)
          {
             MFEM_FOREACH_THREAD(d, y, ndof_b)
@@ -2158,7 +2159,7 @@ template <
    std::size_t... Is>
 std::array<DofToQuadMap, N> create_dtq_maps_impl(
    field_operator_ts &fops,
-   std::vector<const DofToQuad*> dtqs,
+   std::vector<const DofToQuad*> &dtqs,
    const std::array<int, N> &field_map,
    std::index_sequence<Is...>)
 {
@@ -2243,7 +2244,7 @@ template <
    std::size_t num_fields>
 std::array<DofToQuadMap, num_fields> create_dtq_maps(
    field_operator_ts &fops,
-   std::vector<const DofToQuad*> dtqmaps,
+   std::vector<const DofToQuad*> &dtqmaps,
    const std::array<int, num_fields> &to_field_map)
 {
    return create_dtq_maps_impl<entity_t>(

fem/gridfunc.cpp

@@ -4334,7 +4334,7 @@ real_t LSZZErrorEstimator(BilinearFormIntegrator &blfi,  // input
          u.GetSubVector(udofs, ul);
          utrans.InvTransformPrimal(ul);
          Transf = ufes->GetElementTransformation(ielem);
-         FiniteElement *dummy = nullptr;
+         const auto *dummy = ufes->GetFE(ielem);
          blfi.ComputeElementFlux(*ufes->GetFE(ielem), *Transf, ul,
                                  *dummy, fl, with_coeff, ir);
 

fem/integ/bilininteg_diffusion_kernels.hpp

@@ -1009,6 +1009,7 @@ inline void SmemPADiffusionApply3D(const int NE,
    auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
    auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
    auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_VERIFY(D1D <= Q1D, "THREAD_DIRECT requires D1D <= Q1D");
    mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -1038,11 +1039,11 @@ inline void SmemPADiffusionApply3D(const int NE,
       real_t (*QDD0)[MD1][MD1] = (real_t (*)[MD1][MD1]) (sm0+0);
       real_t (*QDD1)[MD1][MD1] = (real_t (*)[MD1][MD1]) (sm0+1);
       real_t (*QDD2)[MD1][MD1] = (real_t (*)[MD1][MD1]) (sm0+2);
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD_DIRECT(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_FOREACH_THREAD_DIRECT(dx,x,D1D)
             {
                X[dz][dy][dx] = x(dx,dy,dz,e);
             }
@@ -1050,9 +1051,9 @@ inline void SmemPADiffusionApply3D(const int NE,
       }
       if (MFEM_THREAD_ID(z) == 0)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            MFEM_FOREACH_THREAD_DIRECT(qx,x,Q1D)
             {
                B[qx][dy] = b(qx,dy);
                G[qx][dy] = g(qx,dy);
@@ -1060,11 +1061,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD_DIRECT(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            MFEM_FOREACH_THREAD_DIRECT(qx,x,Q1D)
             {
                real_t u = 0.0, v = 0.0;
                MFEM_UNROLL(MD1)
@@ -1080,11 +1081,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD_DIRECT(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD_DIRECT(qy,y,Q1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            MFEM_FOREACH_THREAD_DIRECT(qx,x,Q1D)
             {
                real_t u = 0.0, v = 0.0, w = 0.0;
                MFEM_UNROLL(MD1)
@@ -1101,11 +1102,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD_DIRECT(qz,z,Q1D)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD_DIRECT(qy,y,Q1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            MFEM_FOREACH_THREAD_DIRECT(qx,x,Q1D)
             {
                real_t u = 0.0, v = 0.0, w = 0.0;
                MFEM_UNROLL(MD1)
@@ -1136,9 +1137,9 @@ inline void SmemPADiffusionApply3D(const int NE,
       MFEM_SYNC_THREAD;
       if (MFEM_THREAD_ID(z) == 0)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            MFEM_FOREACH_THREAD_DIRECT(qx,x,Q1D)
             {
                Bt[dy][qx] = b(qx,dy);
                Gt[dy][qx] = g(qx,dy);
@@ -1146,11 +1147,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD_DIRECT(qz,z,Q1D)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD_DIRECT(qy,y,Q1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_FOREACH_THREAD_DIRECT(dx,x,D1D)
             {
                real_t u = 0.0, v = 0.0, w = 0.0;
                MFEM_UNROLL(MQ1)
@@ -1167,11 +1168,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD_DIRECT(qz,z,Q1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_FOREACH_THREAD_DIRECT(dx,x,D1D)
             {
                real_t u = 0.0, v = 0.0, w = 0.0;
                MFEM_UNROLL(Q1D)
@@ -1188,11 +1189,11 @@ inline void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD_DIRECT(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD_DIRECT(dy,y,D1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_FOREACH_THREAD_DIRECT(dx,x,D1D)
             {
                real_t u = 0.0, v = 0.0, w = 0.0;
                MFEM_UNROLL(MQ1)

fem/integ/bilininteg_mass_pa.cpp

@@ -62,7 +62,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 
    const int NE = ne;
    const int Q1D = quad1D;
-   const int NQ = pow(Q1D, dim);
+   const int NQ = static_cast<int>(std::pow(Q1D, dim));
    const bool const_c = coeff.Size() == 1;
    const bool by_val = map_type == FiniteElement::VALUE;
    const auto W = Reshape(ir->GetWeights().Read(), NQ);

fem/lininteg.hpp

@@ -673,7 +673,7 @@ public:
       int myid;
       MPI_Comm_rank(comm, &myid);
 
-      int seed = (seed_ > 0) ? seed_ + myid : (int)time(0) + myid;
+      int seed = (seed_ > 0) ? seed_ + myid : time(nullptr) + myid;
       SetSeed(seed);
    }
 #else

fem/pfespace.cpp

@@ -5259,7 +5259,7 @@ DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(
       gc.GetNeighborLTDofTable(nbr_ltdof);
       const int nb_connections = nbr_ltdof.Size_of_connections();
       shr_ltdof.SetSize(nb_connections);
-      shr_ltdof.CopyFrom(nbr_ltdof.GetJ());
+      if (nb_connections > 0) { shr_ltdof.CopyFrom(nbr_ltdof.GetJ()); }
       shr_buf.SetSize(nb_connections);
       shr_buf.UseDevice(true);
       shr_buf_offsets = nbr_ltdof.GetIMemory();
@@ -5288,7 +5288,7 @@ DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(
       gc.GetNeighborLDofTable(nbr_ldof);
       const int nb_connections = nbr_ldof.Size_of_connections();
       ext_ldof.SetSize(nb_connections);
-      ext_ldof.CopyFrom(nbr_ldof.GetJ());
+      if (nb_connections > 0) { ext_ldof.CopyFrom(nbr_ldof.GetJ()); }
       ext_ldof.GetMemory().UseDevice(true);
       ext_buf.SetSize(nb_connections);
       ext_buf.UseDevice(true);

fem/qinterp/det.cpp

@@ -9,278 +9,16 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "../quadinterpolator.hpp"
-#include "../../general/forall.hpp"
-#include "../../linalg/dtensor.hpp"
-#include "../../fem/kernels.hpp"
-#include "../../linalg/kernels.hpp"
-
-using namespace mfem;
+#include "det.hpp"
 
 namespace mfem
 {
 
 namespace internal
 {
-
 namespace quadrature_interpolator
 {
 
-static void Det1D(const int NE,
-                  const real_t *b,
-                  const real_t *g,
-                  const real_t *x,
-                  real_t *y,
-                  const int d1d,
-                  const int q1d,
-                  Vector *d_buff = nullptr)
-{
-   MFEM_CONTRACT_VAR(b);
-   MFEM_CONTRACT_VAR(d_buff);
-   const auto G = Reshape(g, q1d, d1d);
-   const auto X = Reshape(x, d1d, NE);
-
-   auto Y = Reshape(y, q1d, NE);
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int q = 0; q < q1d; q++)
-      {
-         real_t u = 0.0;
-         for (int d = 0; d < d1d; d++)
-         {
-            u += G(q, d) * X(d, e);
-         }
-         Y(q, e) = u;
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void Det2D(const int NE,
-                  const real_t *b,
-                  const real_t *g,
-                  const real_t *x,
-                  real_t *y,
-                  const int d1d = 0,
-                  const int q1d = 0,
-                  Vector *d_buff = nullptr)
-{
-   MFEM_CONTRACT_VAR(d_buff);
-   static constexpr int SDIM = 2;
-   static constexpr int NBZ = 1;
-
-   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 X = Reshape(x,  D1D, D1D, SDIM, NE);
-   auto Y = Reshape(y, Q1D, Q1D, NE);
-
-   mfem::forall_2D_batch(NE, Q1D, Q1D, NBZ, [=] MFEM_HOST_DEVICE (int e)
-   {
-      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-
-      MFEM_SHARED real_t BG[2][MQ1*MD1];
-      MFEM_SHARED real_t XY[SDIM][NBZ][MD1*MD1];
-      MFEM_SHARED real_t DQ[2*SDIM][NBZ][MD1*MQ1];
-      MFEM_SHARED real_t QQ[2*SDIM][NBZ][MQ1*MQ1];
-
-      kernels::internal::LoadX<MD1,NBZ>(e,D1D,X,XY);
-      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
-
-      kernels::internal::GradX<MD1,MQ1,NBZ>(D1D,Q1D,BG,XY,DQ);
-      kernels::internal::GradY<MD1,MQ1,NBZ>(D1D,Q1D,BG,DQ,QQ);
-
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            real_t J[4];
-            kernels::internal::PullGrad<MQ1,NBZ>(Q1D,qx,qy,QQ,J);
-            Y(qx,qy,e) = kernels::Det<2>(J);
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void Det2DSurface(const int NE,
-                         const real_t *b,
-                         const real_t *g,
-                         const real_t *x,
-                         real_t *y,
-                         const int d1d = 0,
-                         const int q1d = 0,
-                         Vector *d_buff = nullptr)
-{
-   MFEM_CONTRACT_VAR(d_buff);
-
-   static constexpr int SDIM = 3;
-   static constexpr int NBZ = 1;
-
-   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 X = Reshape(x,  D1D, D1D, SDIM, NE);
-   auto Y = Reshape(y, Q1D, Q1D, NE);
-
-   mfem::forall_2D_batch(NE, Q1D, Q1D, NBZ, [=] MFEM_HOST_DEVICE (int e)
-   {
-      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int tidz = MFEM_THREAD_ID(z);
-
-      MFEM_SHARED real_t BG[2][MQ1*MD1];
-      MFEM_SHARED real_t XYZ[SDIM][NBZ][MD1*MD1];
-      MFEM_SHARED real_t DQ[2*SDIM][NBZ][MD1*MQ1];
-
-      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
-
-      // Load XYZ components
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            for (int d = 0; d < SDIM; ++d)
-            {
-               XYZ[d][tidz][dx + dy*D1D] = X(dx,dy,d,e);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-
-      ConstDeviceMatrix B_mat(BG[0], D1D, Q1D);
-      ConstDeviceMatrix G_mat(BG[1], D1D, Q1D);
-
-      // x contraction
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            for (int d = 0; d < SDIM; ++d)
-            {
-               real_t u = 0.0;
-               real_t v = 0.0;
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const real_t xval = XYZ[d][tidz][dx + dy*D1D];
-                  u += xval * G_mat(dx,qx);
-                  v += xval * B_mat(dx,qx);
-               }
-               DQ[d][tidz][dy + qx*D1D] = u;
-               DQ[3 + d][tidz][dy + qx*D1D] = v;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      // y contraction and determinant computation
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            real_t J_[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
-            for (int d = 0; d < SDIM; ++d)
-            {
-               for (int dy = 0; dy < D1D; ++dy)
-               {
-                  J_[d] += DQ[d][tidz][dy + qx*D1D] * B_mat(dy,qy);
-                  J_[3 + d] += DQ[3 + d][tidz][dy + qx*D1D] * G_mat(dy,qy);
-               }
-            }
-            DeviceTensor<2> J(J_, 3, 2);
-            const real_t E = J(0,0)*J(0,0) + J(1,0)*J(1,0) + J(2,0)*J(2,0);
-            const real_t F = J(0,0)*J(0,1) + J(1,0)*J(1,1) + J(2,0)*J(2,1);
-            const real_t G = J(0,1)*J(0,1) + J(1,1)*J(1,1) + J(2,1)*J(2,1);
-            Y(qx,qy,e) = std::sqrt(E*G - F*F);
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0, bool SMEM = true>
-static void Det3D(const int NE,
-                  const real_t *b,
-                  const real_t *g,
-                  const real_t *x,
-                  real_t *y,
-                  const int d1d = 0,
-                  const int q1d = 0,
-                  Vector *d_buff = nullptr) // used only with SMEM = false
-{
-   constexpr int DIM = 3;
-   static constexpr int GRID = SMEM ? 0 : 128;
-
-   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 X = Reshape(x, D1D, D1D, D1D, DIM, NE);
-   auto Y = Reshape(y, Q1D, Q1D, Q1D, NE);
-
-   real_t *GM = nullptr;
-   if (!SMEM)
-   {
-      const DeviceDofQuadLimits &limits = DeviceDofQuadLimits::Get();
-      const int max_q1d = T_Q1D ? T_Q1D : limits.MAX_Q1D;
-      const int max_d1d = T_D1D ? T_D1D : limits.MAX_D1D;
-      const int max_qd = std::max(max_q1d, max_d1d);
-      const int mem_size = max_qd * max_qd * max_qd * 9;
-      d_buff->SetSize(2*mem_size*GRID);
-      GM = d_buff->Write();
-   }
-
-   mfem::forall_3D_grid(NE, Q1D, Q1D, Q1D, GRID, [=] MFEM_HOST_DEVICE (int e)
-   {
-      static constexpr int MQ1 = T_Q1D ? T_Q1D :
-                                 (SMEM ? DofQuadLimits::MAX_DET_1D : DofQuadLimits::MAX_Q1D);
-      static constexpr int MD1 = T_D1D ? T_D1D :
-                                 (SMEM ? DofQuadLimits::MAX_DET_1D : DofQuadLimits::MAX_D1D);
-      static constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
-      static constexpr int MSZ = MDQ * MDQ * MDQ * 9;
-
-      const int bid = MFEM_BLOCK_ID(x);
-      MFEM_SHARED real_t BG[2][MQ1*MD1];
-      MFEM_SHARED real_t SM0[SMEM?MSZ:1];
-      MFEM_SHARED real_t SM1[SMEM?MSZ:1];
-      real_t *lm0 = SMEM ? SM0 : GM + MSZ*bid;
-      real_t *lm1 = SMEM ? SM1 : GM + MSZ*(GRID+bid);
-      real_t (*DDD)[MD1*MD1*MD1] = (real_t (*)[MD1*MD1*MD1]) (lm0);
-      real_t (*DDQ)[MD1*MD1*MQ1] = (real_t (*)[MD1*MD1*MQ1]) (lm1);
-      real_t (*DQQ)[MD1*MQ1*MQ1] = (real_t (*)[MD1*MQ1*MQ1]) (lm0);
-      real_t (*QQQ)[MQ1*MQ1*MQ1] = (real_t (*)[MQ1*MQ1*MQ1]) (lm1);
-
-      kernels::internal::LoadX<MD1>(e,D1D,X,DDD);
-      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
-
-      kernels::internal::GradX<MD1,MQ1>(D1D,Q1D,BG,DDD,DDQ);
-      kernels::internal::GradY<MD1,MQ1>(D1D,Q1D,BG,DDQ,DQQ);
-      kernels::internal::GradZ<MD1,MQ1>(D1D,Q1D,BG,DQQ,QQQ);
-
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               real_t J[9];
-               kernels::internal::PullGrad<MQ1>(Q1D, qx,qy,qz, QQQ, J);
-               Y(qx,qy,qz,e) = kernels::Det<3>(J);
-            }
-         }
-      }
-   });
-}
-
 void InitDetKernels()
 {
    using k = QuadratureInterpolator::DetKernels;
@@ -302,27 +40,12 @@ void InitDetKernels()
 }
 
 } // namespace quadrature_interpolator
-
 } // namespace internal
 
 /// @cond Suppress_Doxygen_warnings
 
-namespace
-{
-using DetKernel = QuadratureInterpolator::DetKernelType;
-}
-
-template<int DIM, int SDIM, int D1D, int Q1D>
-DetKernel QuadratureInterpolator::DetKernels::Kernel()
-{
-   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
-   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D<D1D, Q1D>; }
-   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface<D1D, Q1D>; }
-   else if (DIM == 3) { return internal::quadrature_interpolator::Det3D<D1D, Q1D>; }
-   else { MFEM_ABORT(""); }
-}
-
-DetKernel QuadratureInterpolator::DetKernels::Fallback(
+QuadratureInterpolator::DetKernelType
+QuadratureInterpolator::DetKernels::Fallback(
    int DIM, int SDIM, int D1D, int Q1D)
 {
    if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }

fem/qinterp/det.hpp

@@ -0,0 +1,304 @@
+// 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_QUADINTERP_DET_HPP
+#define MFEM_QUADINTERP_DET_HPP
+
+#include "../quadinterpolator.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/dtensor.hpp"
+#include "../../fem/kernels.hpp"
+#include "../../linalg/kernels.hpp"
+
+namespace mfem
+{
+
+namespace internal
+{
+namespace quadrature_interpolator
+{
+
+inline void Det1D(const int NE,
+                  const real_t *b,
+                  const real_t *g,
+                  const real_t *x,
+                  real_t *y,
+                  const int d1d,
+                  const int q1d,
+                  Vector *d_buff = nullptr)
+{
+   MFEM_CONTRACT_VAR(b);
+   MFEM_CONTRACT_VAR(d_buff);
+   const auto G = Reshape(g, q1d, d1d);
+   const auto X = Reshape(x, d1d, NE);
+
+   auto Y = Reshape(y, q1d, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int q = 0; q < q1d; q++)
+      {
+         real_t u = 0.0;
+         for (int d = 0; d < d1d; d++)
+         {
+            u += G(q, d) * X(d, e);
+         }
+         Y(q, e) = u;
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+inline void Det2D(const int NE,
+                  const real_t *b,
+                  const real_t *g,
+                  const real_t *x,
+                  real_t *y,
+                  const int d1d = 0,
+                  const int q1d = 0,
+                  Vector *d_buff = nullptr)
+{
+   MFEM_CONTRACT_VAR(d_buff);
+   static constexpr int SDIM = 2;
+   static constexpr int NBZ = 1;
+
+   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 X = Reshape(x,  D1D, D1D, SDIM, NE);
+   auto Y = Reshape(y, Q1D, Q1D, NE);
+
+   mfem::forall_2D_batch(NE, Q1D, Q1D, NBZ, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+      MFEM_SHARED real_t BG[2][MQ1*MD1];
+      MFEM_SHARED real_t XY[SDIM][NBZ][MD1*MD1];
+      MFEM_SHARED real_t DQ[2*SDIM][NBZ][MD1*MQ1];
+      MFEM_SHARED real_t QQ[2*SDIM][NBZ][MQ1*MQ1];
+
+      kernels::internal::LoadX<MD1,NBZ>(e,D1D,X,XY);
+      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
+
+      kernels::internal::GradX<MD1,MQ1,NBZ>(D1D,Q1D,BG,XY,DQ);
+      kernels::internal::GradY<MD1,MQ1,NBZ>(D1D,Q1D,BG,DQ,QQ);
+
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            real_t J[4];
+            kernels::internal::PullGrad<MQ1,NBZ>(Q1D,qx,qy,QQ,J);
+            Y(qx,qy,e) = kernels::Det<2>(J);
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+inline void Det2DSurface(const int NE,
+                         const real_t *b,
+                         const real_t *g,
+                         const real_t *x,
+                         real_t *y,
+                         const int d1d = 0,
+                         const int q1d = 0,
+                         Vector *d_buff = nullptr)
+{
+   MFEM_CONTRACT_VAR(d_buff);
+
+   static constexpr int SDIM = 3;
+   static constexpr int NBZ = 1;
+
+   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 X = Reshape(x,  D1D, D1D, SDIM, NE);
+   auto Y = Reshape(y, Q1D, Q1D, NE);
+
+   mfem::forall_2D_batch(NE, Q1D, Q1D, NBZ, [=] MFEM_HOST_DEVICE (int e)
+   {
+      constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      const int tidz = MFEM_THREAD_ID(z);
+
+      MFEM_SHARED real_t BG[2][MQ1*MD1];
+      MFEM_SHARED real_t XYZ[SDIM][NBZ][MD1*MD1];
+      MFEM_SHARED real_t DQ[2*SDIM][NBZ][MD1*MQ1];
+
+      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
+
+      // Load XYZ components
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            for (int d = 0; d < SDIM; ++d)
+            {
+               XYZ[d][tidz][dx + dy*D1D] = X(dx,dy,d,e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      ConstDeviceMatrix B_mat(BG[0], D1D, Q1D);
+      ConstDeviceMatrix G_mat(BG[1], D1D, Q1D);
+
+      // x contraction
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            for (int d = 0; d < SDIM; ++d)
+            {
+               real_t u = 0.0;
+               real_t v = 0.0;
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  const real_t xval = XYZ[d][tidz][dx + dy*D1D];
+                  u += xval * G_mat(dx,qx);
+                  v += xval * B_mat(dx,qx);
+               }
+               DQ[d][tidz][dy + qx*D1D] = u;
+               DQ[3 + d][tidz][dy + qx*D1D] = v;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // y contraction and determinant computation
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            real_t J_[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
+            for (int d = 0; d < SDIM; ++d)
+            {
+               for (int dy = 0; dy < D1D; ++dy)
+               {
+                  J_[d] += DQ[d][tidz][dy + qx*D1D] * B_mat(dy,qy);
+                  J_[3 + d] += DQ[3 + d][tidz][dy + qx*D1D] * G_mat(dy,qy);
+               }
+            }
+            DeviceTensor<2> J(J_, 3, 2);
+            const real_t E = J(0,0)*J(0,0) + J(1,0)*J(1,0) + J(2,0)*J(2,0);
+            const real_t F = J(0,0)*J(0,1) + J(1,0)*J(1,1) + J(2,0)*J(2,1);
+            const real_t G = J(0,1)*J(0,1) + J(1,1)*J(1,1) + J(2,1)*J(2,1);
+            Y(qx,qy,e) = std::sqrt(E*G - F*F);
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0, bool SMEM = true>
+inline void Det3D(const int NE,
+                  const real_t *b,
+                  const real_t *g,
+                  const real_t *x,
+                  real_t *y,
+                  const int d1d = 0,
+                  const int q1d = 0,
+                  Vector *d_buff = nullptr) // used only with SMEM = false
+{
+   constexpr int DIM = 3;
+   static constexpr int GRID = SMEM ? 0 : 128;
+
+   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 X = Reshape(x, D1D, D1D, D1D, DIM, NE);
+   auto Y = Reshape(y, Q1D, Q1D, Q1D, NE);
+
+   real_t *GM = nullptr;
+   if (!SMEM)
+   {
+      const DeviceDofQuadLimits &limits = DeviceDofQuadLimits::Get();
+      const int max_q1d = T_Q1D ? T_Q1D : limits.MAX_Q1D;
+      const int max_d1d = T_D1D ? T_D1D : limits.MAX_D1D;
+      const int max_qd = std::max(max_q1d, max_d1d);
+      const int mem_size = max_qd * max_qd * max_qd * 9;
+      d_buff->SetSize(2*mem_size*GRID);
+      GM = d_buff->Write();
+   }
+
+   mfem::forall_3D_grid(NE, Q1D, Q1D, Q1D, GRID, [=] MFEM_HOST_DEVICE (int e)
+   {
+      static constexpr int MQ1 = T_Q1D ? T_Q1D :
+                                 (SMEM ? DofQuadLimits::MAX_DET_1D : DofQuadLimits::MAX_Q1D);
+      static constexpr int MD1 = T_D1D ? T_D1D :
+                                 (SMEM ? DofQuadLimits::MAX_DET_1D : DofQuadLimits::MAX_D1D);
+      static constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
+      static constexpr int MSZ = MDQ * MDQ * MDQ * 9;
+
+      const int bid = MFEM_BLOCK_ID(x);
+      MFEM_SHARED real_t BG[2][MQ1*MD1];
+      MFEM_SHARED real_t SM0[SMEM?MSZ:1];
+      MFEM_SHARED real_t SM1[SMEM?MSZ:1];
+      real_t *lm0 = SMEM ? SM0 : GM + MSZ*bid;
+      real_t *lm1 = SMEM ? SM1 : GM + MSZ*(GRID+bid);
+      real_t (*DDD)[MD1*MD1*MD1] = (real_t (*)[MD1*MD1*MD1]) (lm0);
+      real_t (*DDQ)[MD1*MD1*MQ1] = (real_t (*)[MD1*MD1*MQ1]) (lm1);
+      real_t (*DQQ)[MD1*MQ1*MQ1] = (real_t (*)[MD1*MQ1*MQ1]) (lm0);
+      real_t (*QQQ)[MQ1*MQ1*MQ1] = (real_t (*)[MQ1*MQ1*MQ1]) (lm1);
+
+      kernels::internal::LoadX<MD1>(e,D1D,X,DDD);
+      kernels::internal::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
+
+      kernels::internal::GradX<MD1,MQ1>(D1D,Q1D,BG,DDD,DDQ);
+      kernels::internal::GradY<MD1,MQ1>(D1D,Q1D,BG,DDQ,DQQ);
+      kernels::internal::GradZ<MD1,MQ1>(D1D,Q1D,BG,DQQ,QQQ);
+
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               real_t J[9];
+               kernels::internal::PullGrad<MQ1>(Q1D, qx,qy,qz, QQQ, J);
+               Y(qx,qy,qz,e) = kernels::Det<3>(J);
+            }
+         }
+      }
+   });
+}
+
+} // namespace quadrature_interpolator
+} // namespace internal
+
+/// @cond Suppress_Doxygen_warnings
+
+template<int DIM, int SDIM, int D1D, int Q1D>
+QuadratureInterpolator::DetKernelType
+QuadratureInterpolator::DetKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D<D1D, Q1D>; }
+   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface<D1D, Q1D>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Det3D<D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+/// @endcond
+
+} // namespace mfem
+
+#endif // MFEM_QUADINTERP_DET_HPP

fem/tmop.cpp

@@ -5122,33 +5122,32 @@ real_t TMOP_Integrator::GetSurfaceFittingWeight()
 
 void TMOP_Integrator::EnableNormalization(const GridFunction &x)
 {
-   ComputeNormalizationEnergies(x, metric_normal, lim_normal, surf_fit_normal);
+   ComputeNormalizationEnergies(x, metric_normal, lim_normal);
    metric_normal = 1.0 / metric_normal;
    lim_normal = 1.0 / lim_normal;
-   //if (surf_fit_gf) { surf_fit_normal = 1.0 / surf_fit_normal; }
    if (surf_fit_gf || surf_fit_pos) { surf_fit_normal = lim_normal; }
 }
 
 #ifdef MFEM_USE_MPI
 void TMOP_Integrator::ParEnableNormalization(const ParGridFunction &x)
 {
-   real_t loc[3];
-   ComputeNormalizationEnergies(x, loc[0], loc[1], loc[2]);
-   real_t rdc[3];
-   MPI_Allreduce(loc, rdc, 3, MPITypeMap<real_t>::mpi_type, MPI_SUM,
+   real_t loc[2];
+   ComputeNormalizationEnergies(x, loc[0], loc[1]);
+   real_t rdc[2];
+   MPI_Allreduce(loc, rdc, 2, MPITypeMap<real_t>::mpi_type, MPI_SUM,
                  x.ParFESpace()->GetComm());
    metric_normal = 1.0 / rdc[0];
    lim_normal    = 1.0 / rdc[1];
-   // if (surf_fit_gf) { surf_fit_normal = 1.0 / rdc[2]; }
    if (surf_fit_gf || surf_fit_pos) { surf_fit_normal = lim_normal; }
 }
 #endif
 
 void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
                                                    real_t &metric_energy,
-                                                   real_t &lim_energy,
-                                                   real_t &surf_fit_gf_energy)
+                                                   real_t &lim_energy)
 {
+   metric_energy = 0.0;
+   lim_energy = 0.0;
    if (PA.enabled)
    {
       MFEM_VERIFY(PA.E.Size() > 0, "Must be called after AssemblePA!");
@@ -5191,9 +5190,6 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
    Jpr.SetSize(dim);
    Jpt.SetSize(dim);
 
-   metric_energy = 0.0;
-   lim_energy = 0.0;
-   surf_fit_gf_energy = 0.0;
    for (int i = 0; i < fes->GetNE(); i++)
    {
       const FiniteElement *fe = fes->GetFE(i);
@@ -5225,21 +5221,7 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
          lim_energy += weight;
       }
 
-      // Normalization of the surface fitting term.
-      if (surf_fit_gf)
-      {
-         Array<int> dofs;
-         Vector sigma_e;
-         surf_fit_gf->FESpace()->GetElementDofs(i, dofs);
-         surf_fit_gf->GetSubVector(dofs, sigma_e);
-         for (int s = 0; s < dofs.Size(); s++)
-         {
-            if ((*surf_fit_marker)[dofs[s]] == true)
-            {
-               surf_fit_gf_energy += sigma_e(s) * sigma_e(s);
-            }
-         }
-      }
+      // TODO: Normalization of the surface fitting term.
    }
 
    // Cases when integration is not over the target element, or when the

fem/tmop.hpp

@@ -2038,8 +2038,7 @@ protected:
    } PA;
 
    void ComputeNormalizationEnergies(const GridFunction &x,
-                                     real_t &metric_energy, real_t &lim_energy,
-                                     real_t &surf_fit_gf_energy);
+                                     real_t &metric_energy, real_t &lim_energy);
 
    void AssembleElementVectorExact(const FiniteElement &el,
                                    ElementTransformation &T,

general/CMakeLists.txt

@@ -39,6 +39,7 @@ list(APPEND HDRS
   arrays_by_name.hpp
   backends.hpp
   binaryio.hpp
+  complex_type.hpp
   cuda.hpp
   device.hpp
   error.hpp

general/array.hpp

@@ -326,7 +326,11 @@ public:
        the Size to match this Capacity after this.*/
    template <typename U>
    inline void CopyFrom(const U *src)
-   { std::memcpy(begin(), src, MemoryUsage()); }
+   {
+      if (!begin() || size == 0) { return; }
+      MFEM_ASSERT(begin() && src, "Error in Array::CopyFrom");
+      std::memcpy(begin(), src, MemoryUsage());
+   }
 
    /// STL-like begin.  Returns pointer to the first element of the array.
    inline T* begin() { return data; }

general/backends.hpp

@@ -62,6 +62,7 @@
 #define MFEM_THREAD_ID(k) 0
 #define MFEM_THREAD_SIZE(k) 1
 #define MFEM_FOREACH_THREAD(i,k,N) for(int i=0; i<N; i++)
+#define MFEM_FOREACH_THREAD_DIRECT(i,k,N) MFEM_FOREACH_THREAD(i,k,N)
 #endif
 
 // 'double' and 'float' atomicAdd implementation for previous versions of CUDA

general/complex_type.hpp

@@ -0,0 +1,125 @@
+// 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_COMPLEX_TYPE
+#define MFEM_COMPLEX_TYPE
+
+#include "../config/config.hpp"
+
+#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
+#include <complex>
+#include <utility>
+#endif
+
+#if defined(MFEM_USE_CUDA)
+#include <cuComplex.h>
+#endif
+
+#if defined(MFEM_USE_HIP)
+#include <hip/hip_complex.h>
+#endif
+
+
+namespace mfem
+{
+
+/// @brief Complex number type for device.
+#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
+
+#define zAbs std::abs
+#define zExp std::exp
+#define zNorm std::norm
+using complex_t = std::complex<real_t>;
+
+#else // CUDA or HIP
+
+#if defined(MFEM_USE_CUDA)
+using DoubleComplex_t = cuDoubleComplex;
+#endif
+
+#if defined(MFEM_USE_HIP)
+using DoubleComplex_t = hipDoubleComplex;
+#endif
+
+struct Complex : public DoubleComplex_t
+{
+   MFEM_HOST_DEVICE Complex() = default;
+   MFEM_HOST_DEVICE Complex(real_t r) { x = r, y = 0.0; }
+   MFEM_HOST_DEVICE Complex(real_t r, real_t i) { x = r, y = i; }
+   MFEM_HOST_DEVICE real_t real() const { return x; }
+   MFEM_HOST_DEVICE void real(real_t r) { x = r; }
+   MFEM_HOST_DEVICE real_t imag() const { return y; }
+   MFEM_HOST_DEVICE void imag(real_t i) { y = i; }
+
+   template <typename U>
+   MFEM_HOST_DEVICE inline Complex &operator*=(const U &z)
+   {
+      return *this = *this * z, *this;
+   }
+
+   template <typename U>
+   MFEM_HOST_DEVICE inline Complex &operator/=(const U &z)
+   {
+      return *this = *this / z, *this;
+   }
+};
+
+MFEM_HOST_DEVICE inline Complex operator*(const Complex &x, const real_t &y)
+{
+   return Complex(x.real() * y, x.imag() * y);
+}
+
+MFEM_HOST_DEVICE inline Complex operator+(const Complex &a, const Complex &b)
+{
+   return Complex(a.real() + b.real(), a.imag() + b.imag());
+}
+
+MFEM_HOST_DEVICE inline Complex operator*(const real_t d, const Complex &z)
+{
+   return Complex(z.real() * d, z.imag() * d);
+}
+
+MFEM_HOST_DEVICE inline Complex operator*(const Complex &a, const Complex &b)
+{
+   return Complex(a.real() * b.real() - a.imag() * b.imag(),
+                  a.real() * b.imag() + a.imag() * b.real());
+}
+
+MFEM_HOST_DEVICE inline Complex operator/(const Complex &z, const real_t &d)
+{
+   return Complex(z.real() / d, z.imag() / d);
+}
+
+MFEM_HOST_DEVICE inline real_t zAbs(const Complex &z)
+{
+   return std::hypot(z.real(), z.imag());
+}
+
+MFEM_HOST_DEVICE inline Complex zExp(const Complex &q)
+{
+   Complex z;
+   real_t s, c, e = std::exp(q.real());
+   sincos(q.imag(), &s, &c);
+   z.real(c * e), z.imag(s * e);
+   return z;
+}
+
+MFEM_HOST_DEVICE inline real_t zNorm(const Complex &z)
+{
+   return z.real() * z.real() + z.imag() * z.imag();
+}
+
+using complex_t = Complex;
+#endif // MFEM_USE_CUDA || MFEM_USE_HIP
+
+} // namespace mfem
+
+#endif // MFEM_COMPLEX_TYPE

general/cuda.hpp

@@ -47,6 +47,7 @@
 #define MFEM_THREAD_ID(k) threadIdx.k
 #define MFEM_THREAD_SIZE(k) blockDim.k
 #define MFEM_FOREACH_THREAD(i,k,N) for(int i=threadIdx.k; i<N; i+=blockDim.k)
+#define MFEM_FOREACH_THREAD_DIRECT(i,k,N) if(const int i=threadIdx.k; i<N)
 #endif
 
 namespace mfem

general/device.cpp

@@ -16,6 +16,7 @@
 #include "../fem/ceed/interface/util.hpp"
 #endif
 #ifdef MFEM_USE_MPI
+#include "communication.hpp"
 #include "../linalg/hypre.hpp"
 #endif
 
@@ -145,6 +146,11 @@ Device::Device()
       Configure(device);
       device_env = true;
    }
+
+   if (GetEnv("MFEM_GPU_AWARE_MPI"))
+   {
+      SetGPUAwareMPI(true);
+   }
 }
 
 Device::~Device()
@@ -196,6 +202,29 @@ void Device::Configure(const std::string &device, const int device_id)
    {
       bmap[internal::backend_name[i]] = internal::backend_list[i];
    }
+   // auto-detect GPU configurations
+   // assumes only one of HIP or CUDA are available
+#ifdef MFEM_USE_HIP
+   bmap["gpu"] = Backend::HIP;
+#ifdef MFEM_USE_RAJA
+   bmap["raja-gpu"] = Backend::RAJA_HIP;
+#endif
+#ifdef MFEM_USE_CEED
+   bmap["ceed-gpu"] = Backend::CEED_HIP;
+#endif
+   // no OCCA+HIP?
+#elif defined(MFEM_USE_CUDA)
+   bmap["gpu"] = Backend::CUDA;
+#ifdef MFEM_USE_RAJA
+   bmap["raja-gpu"] = Backend::RAJA_CUDA;
+#endif
+#ifdef MFEM_USE_CEED
+   bmap["ceed-gpu"] = Backend::CEED_CUDA;
+#endif
+#ifdef MFEM_USE_OCCA
+   bmap["occa-gpu"] = Backend::OCCA_CUDA;
+#endif
+#endif
    std::string device_option;
    std::string::size_type beg = 0, end;
    while (1)
@@ -313,6 +342,13 @@ void Device::Print(std::ostream &os)
    {
       os << ',' << MemoryTypeName[static_cast<int>(device_mem_type)];
    }
+#ifdef MFEM_USE_MPI
+   if (Allows(Backend::DEVICE_MASK) &&
+       Mpi::IsInitialized() && !Mpi::IsFinalized())
+   {
+      os << "\nUse GPU-aware MPI:    " << (GetGPUAwareMPI() ? "yes" : "no");
+   }
+#endif
    os << std::endl;
 }
 

general/device.hpp

@@ -198,6 +198,10 @@ public:
          'ceed-hip', 'hip', 'debug',
          'occa-omp', 'raja-omp', 'omp',
          'ceed-cpu', 'occa-cpu', 'raja-cpu', 'cpu'.
+       - The following backend aliases are also available: 'ceed-gpu',
+         'occa-gpu', 'raja-gpu', and 'gpu' where they alias their respective
+         '*-cuda' or '*-hip' backends depending on the MFEM build-time
+         configuration.
        - Multiple backends can be configured at the same time.
        - Only one 'occa-*' backend can be configured at a time.
        - The backend 'occa-cuda' enables the 'cuda' backend unless 'raja-cuda'

general/hip.hpp

@@ -47,7 +47,9 @@
 #define MFEM_THREAD_ID(k) hipThreadIdx_ ##k
 #define MFEM_THREAD_SIZE(k) hipBlockDim_ ##k
 #define MFEM_FOREACH_THREAD(i,k,N) \
-    for(int i=hipThreadIdx_ ##k; i<N; i+=hipBlockDim_ ##k)
+   for(int i=hipThreadIdx_ ##k; i<N; i+=hipBlockDim_ ##k)
+#define MFEM_FOREACH_THREAD_DIRECT(i,k,N) \
+   if(const int i=hipThreadIdx_ ##k; i<N)
 #endif
 
 namespace mfem

linalg/CMakeLists.txt

@@ -21,6 +21,7 @@ list(APPEND SRCS
   blockvector.cpp
   complex_densemat.cpp
   complex_operator.cpp
+  complex_vector.cpp
   constraints.cpp
   densemat.cpp
   symmat.cpp
@@ -47,6 +48,7 @@ list(APPEND HDRS
   blockvector.hpp
   complex_densemat.hpp
   complex_operator.hpp
+  complex_vector.hpp
   constraints.hpp
   densemat.hpp
   dinvariants.hpp

linalg/complex_densemat.cpp

@@ -9,6 +9,7 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
+#include "../general/forall.hpp"
 #include "complex_densemat.hpp"
 #include "lapack.hpp"
 #include <complex>
@@ -16,6 +17,8 @@
 namespace mfem
 {
 
+using namespace std;
+
 DenseMatrix & ComplexDenseMatrix::real()
 {
    MFEM_ASSERT(Op_Real_, "ComplexDenseMatrix has no real part!");
@@ -1017,4 +1020,303 @@ void ComplexCholeskyFactors::GetInverseMatrix(int m, real_t * X_r,
    delete [] X;
 }
 
+ComplexTypeDenseMatrix::ComplexTypeDenseMatrix()
+   : height(0), width(0)
+{}
+
+ComplexTypeDenseMatrix::ComplexTypeDenseMatrix(const ComplexTypeDenseMatrix &m)
+   : height(m.Height()), width(m.Width())
+{
+   const int hw = height * width;
+   if (hw > 0)
+   {
+      MFEM_ASSERT(m.data, "invalid source matrix");
+      data.New(hw);
+      std::memcpy(data, m.data, sizeof(complex_t)*hw);
+   }
+}
+
+ComplexTypeDenseMatrix::ComplexTypeDenseMatrix(const DenseMatrix &m)
+   : height(m.Height()), width(m.Width())
+{
+   const int hw = height * width;
+   if (hw > 0)
+   {
+      MFEM_ASSERT(m.data, "invalid source matrix");
+      data.New(hw);
+
+      for (int i = 0; i < hw; i++)
+      {
+         data[i] = m.data[i];
+      }
+   }
+}
+
+ComplexTypeDenseMatrix::ComplexTypeDenseMatrix(int s)
+   : height(s), width(s)
+{
+   MFEM_ASSERT(s >= 0, "invalid DenseMatrix size: " << s);
+   if (s > 0)
+   {
+      data.New(s*s);
+      *this = 0.0; // init with zeroes
+   }
+}
+
+ComplexTypeDenseMatrix::ComplexTypeDenseMatrix(int m, int n)
+   : height(m), width(n)
+{
+   MFEM_ASSERT(m >= 0 && n >= 0,
+               "invalid DenseMatrix size: " << m << " x " << n);
+   const int capacity = m*n;
+   if (capacity > 0)
+   {
+      data.New(capacity);
+      *this = 0.0; // init with zeroes
+   }
+}
+
+void ComplexTypeDenseMatrix::SetSize(int h, int w)
+{
+   MFEM_ASSERT(h >= 0 && w >= 0,
+               "invalid ComplexTypeDenseMatrix size: " << h << " x " << w);
+   if (Height() == h && Width() == w)
+   {
+      return;
+   }
+   height = h;
+   width = w;
+   const int hw = h*w;
+   if (hw > data.Capacity())
+   {
+      data.Delete();
+      data.New(hw);
+      *this = 0.0; // init with zeroes
+   }
+}
+
+/// Returns reference to a_{ij}.
+complex_t &ComplexTypeDenseMatrix::Elem(int i, int j)
+{
+   return (*this)(i,j);
+}
+
+/// Returns constant reference to a_{ij}.
+const complex_t &ComplexTypeDenseMatrix::Elem(int i, int j) const
+{
+   return (*this)(i,j);
+}
+
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=(real_t c)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = c;
+   }
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=(complex_t c)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = c;
+   }
+   return *this;
+}
+
+/// Copy the matrix entries from the given array
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=(const real_t *d)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = d[i];
+   }
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=
+(const complex_t *d)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = d[i];
+   }
+   return *this;
+}
+
+/// Sets the matrix size and elements equal to those of m
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=(const DenseMatrix &m)
+{
+   SetSize(m.height, m.width);
+
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] = m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator=
+(const ComplexTypeDenseMatrix &m)
+{
+   SetSize(m.height, m.width);
+
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] = m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator+=(const real_t *m)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] += m[i];
+   }
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator+=
+(const complex_t *m)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] += m[i];
+   }
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator+=(const DenseMatrix &m)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] += m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator+=
+(const ComplexTypeDenseMatrix &m)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] += m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator-=(const DenseMatrix &m)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] -= m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator-=
+(const ComplexTypeDenseMatrix &m)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] -= m.data[i];
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator*=(real_t c)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] *= c;
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::operator*=(complex_t c)
+{
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] *= c;
+   }
+
+   return *this;
+}
+
+ComplexTypeDenseMatrix &ComplexTypeDenseMatrix::Set(const DenseMatrix &Mr,
+                                                    const DenseMatrix &Mi)
+{
+   MFEM_ASSERT(height == Mr.Height() && height == Mi.Height() &&
+               width == Mr.Width() && width == Mi.Width(),
+               "incompatible Matrices!");
+
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] = complex_t(Mr.data[i], Mi.data[i]);
+   }
+
+   return *this;
+}
+
+void ComplexTypeDenseMatrix::Swap(ComplexTypeDenseMatrix &other)
+{
+   mfem::Swap(width, other.width);
+   mfem::Swap(height, other.height);
+   mfem::Swap(data, other.data);
+}
+
+ComplexTypeDenseMatrix::~ComplexTypeDenseMatrix()
+{
+   data.Delete();
+}
+
+const DenseMatrix &ComplexTypeDenseMatrix::real() const
+{
+   re_part.SetSize(height, width);
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      re_part.data[i] = data[i].real();
+   }
+
+   return re_part;
+}
+
+const DenseMatrix &ComplexTypeDenseMatrix::imag() const
+{
+   im_part.SetSize(height, width);
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      im_part.data[i] = data[i].imag();
+   }
+
+   return im_part;
+}
+
 } // mfem namespace

linalg/complex_densemat.hpp

@@ -13,6 +13,7 @@
 #define MFEM_COMPLEX_DENSEMAT
 
 #include "complex_operator.hpp"
+#include "../general/complex_type.hpp"
 #include <complex>
 
 namespace mfem
@@ -241,6 +242,220 @@ public:
 
 };
 
+class ComplexTypeDenseMatrix
+{
+protected:
+   int height; ///< Dimension of the output / number of rows in the matrix.
+   int width;  ///< Dimension of the input / number of columns in the matrix.
+
+private:
+   Memory<complex_t > data;
+
+   mutable DenseMatrix re_part;
+   mutable DenseMatrix im_part;
+
+public:
+   /** Default constructor for DenseMatrix.
+       Sets data = NULL and height = width = 0. */
+   ComplexTypeDenseMatrix();
+
+   /// Copy constructor
+   ComplexTypeDenseMatrix(const ComplexTypeDenseMatrix &);
+   ComplexTypeDenseMatrix(const DenseMatrix &);
+
+   /// Creates square matrix of size s.
+   explicit ComplexTypeDenseMatrix(int s);
+
+   /// Creates rectangular matrix of size m x n.
+   ComplexTypeDenseMatrix(int m, int n);
+
+   /// Construct a ComplexTypeDenseMatrix using an existing data array.
+   /** The ComplexTypeDenseMatrix does not assume ownership of the data array,
+       i.e. it will not delete the array. */
+   ComplexTypeDenseMatrix(complex_t *d, int h, int w)
+      : height(h), width(w) { UseExternalData(d, h, w); }
+
+   /// Create a dense matrix using a braced initializer list
+   /// The inner lists correspond to rows of the matrix
+   template <int M, int N, typename T = real_t>
+   explicit ComplexTypeDenseMatrix(const T (&values)[M][N]) :
+      ComplexTypeDenseMatrix(
+         M, N)
+   {
+      // DenseMatrix is column-major so copies have to be element-wise
+      for (int i = 0; i < M; i++)
+      {
+         for (int j = 0; j < N; j++)
+         {
+            (*this)(i,j) = values[i][j];
+         }
+      }
+   }
+
+   /// Change the data array and the size of the DenseMatrix.
+   /** The DenseMatrix does not assume ownership of the data array, i.e. it will
+       not delete the data array @a d. This method should not be used with
+       DenseMatrix that owns its current data array. */
+   void UseExternalData(complex_t *d, int h, int w)
+   {
+      data.Wrap(d, h*w, false);
+      height = h; width = w;
+   }
+
+   /// Change the data array and the size of the DenseMatrix.
+   /** The DenseMatrix does not assume ownership of the data array, i.e. it will
+       not delete the new array @a d. This method will delete the current data
+       array, if owned. */
+   void Reset(complex_t *d, int h, int w)
+   { if (OwnsData()) { data.Delete(); } UseExternalData(d, h, w); }
+
+   /** Clear the data array and the dimensions of the DenseMatrix. This method
+       should not be used with DenseMatrix that owns its current data array. */
+   void ClearExternalData() { data.Reset(); height = width = 0; }
+
+   /// Delete the matrix data array (if owned) and reset the matrix state.
+   void Clear()
+   { if (OwnsData()) { data.Delete(); } ClearExternalData(); }
+
+   /// Get the height (size of output) of the Operator. Synonym with NumRows().
+   inline int Height() const { return height; }
+   /** @brief Get the number of rows (size of output) of the Operator. Synonym
+       with Height(). */
+   inline int NumRows() const { return height; }
+
+   /// Get the width (size of input) of the Operator. Synonym with NumCols().
+   inline int Width() const { return width; }
+   /** @brief Get the number of columns (size of input) of the Operator. Synonym
+       with Width(). */
+   inline int NumCols() const { return width; }
+
+   /// For backward compatibility define Size to be synonym of Width()
+   int Size() const { return Width(); }
+
+   // Total size = width*height
+   int TotalSize() const { return width*height; }
+
+   /// Change the size of the DenseMatrix to s x s.
+   void SetSize(int s) { SetSize(s, s); }
+
+   /// Change the size of the DenseMatrix to h x w.
+   void SetSize(int h, int w);
+
+   /// Returns the matrix data array.
+   inline complex_t *Data() const
+   {
+      return const_cast<complex_t*>
+             ((const complex_t*)data);
+   }
+
+   /// Returns the matrix data array.
+   inline complex_t *GetData() const { return Data(); }
+
+   Memory<complex_t > &GetMemory() { return data; }
+   const Memory<complex_t > &GetMemory() const { return data; }
+
+   /// Return the DenseMatrix data (host pointer) ownership flag.
+   inline bool OwnsData() const { return data.OwnsHostPtr(); }
+
+   /// Returns reference to a_{ij}.
+   inline complex_t &operator()(int i, int j);
+
+   /// Returns constant reference to a_{ij}.
+   inline const complex_t &operator()(int i, int j) const;
+
+   /// Returns reference to a_{ij}.
+   complex_t &Elem(int i, int j);
+
+   /// Returns constant reference to a_{ij}.
+   const complex_t &Elem(int i, int j) const;
+
+   /// Sets the matrix elements equal to constant c
+   ComplexTypeDenseMatrix &operator=(real_t c);
+   ComplexTypeDenseMatrix &operator=(complex_t c);
+
+   /// Copy the matrix entries from the given array
+   ComplexTypeDenseMatrix &operator=(const real_t *d);
+   ComplexTypeDenseMatrix &operator=(const complex_t *d);
+
+   /// Sets the matrix size and elements equal to those of m
+   ComplexTypeDenseMatrix &operator=(const DenseMatrix &m);
+   ComplexTypeDenseMatrix &operator=(const ComplexTypeDenseMatrix &m);
+
+   ComplexTypeDenseMatrix &operator+=(const real_t *m);
+   ComplexTypeDenseMatrix &operator+=(const complex_t *m);
+   ComplexTypeDenseMatrix &operator+=(const DenseMatrix &m);
+   ComplexTypeDenseMatrix &operator+=(const ComplexTypeDenseMatrix &m);
+
+   ComplexTypeDenseMatrix &operator-=(const DenseMatrix &m);
+   ComplexTypeDenseMatrix &operator-=(const ComplexTypeDenseMatrix &m);
+
+   ComplexTypeDenseMatrix &operator*=(real_t c);
+   ComplexTypeDenseMatrix &operator*=(complex_t c);
+
+   /// (*this) = x + i * y
+   ComplexTypeDenseMatrix &Set(const DenseMatrix &x, const DenseMatrix &y);
+
+   std::size_t MemoryUsage() const
+   { return data.Capacity() * sizeof(complex_t); }
+
+   /// Shortcut for mfem::Read( GetMemory(), TotalSize(), on_dev).
+   const complex_t *Read(bool on_dev = true) const
+   { return mfem::Read(data, Height()*Width(), on_dev); }
+
+   /// Shortcut for mfem::Read(GetMemory(), TotalSize(), false).
+   const complex_t *HostRead() const
+   { return mfem::Read(data, Height()*Width(), false); }
+
+   /// Shortcut for mfem::Write(GetMemory(), TotalSize(), on_dev).
+   complex_t *Write(bool on_dev = true)
+   { return mfem::Write(data, Height()*Width(), on_dev); }
+
+   /// Shortcut for mfem::Write(GetMemory(), TotalSize(), false).
+   complex_t *HostWrite()
+   { return mfem::Write(data, Height()*Width(), false); }
+
+   /// Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), on_dev).
+   complex_t *ReadWrite(bool on_dev = true)
+   { return mfem::ReadWrite(data, Height()*Width(), on_dev); }
+
+   /// Shortcut for mfem::ReadWrite(GetMemory(), TotalSize(), false).
+   complex_t *HostReadWrite()
+   { return mfem::ReadWrite(data, Height()*Width(), false); }
+
+   void Swap(ComplexTypeDenseMatrix &other);
+
+   /// Return a reference to the real part of this matrix
+   const DenseMatrix &real() const;
+
+   /// Return a reference to the imaginary part of this matrix
+   const DenseMatrix &imag() const;
+
+   /// Destroys dense matrix.
+   virtual ~ComplexTypeDenseMatrix();
+};
+
+/// Specialization of the template function Swap<> for class ComplexTypeDenseMatrix
+template<> inline void Swap<ComplexTypeDenseMatrix>(ComplexTypeDenseMatrix &a,
+                                                    ComplexTypeDenseMatrix &b)
+{
+   a.Swap(b);
+}
+
+// Inline methods
+
+inline complex_t &ComplexTypeDenseMatrix::operator()(int i, int j)
+{
+   MFEM_ASSERT(data && i >= 0 && i < height && j >= 0 && j < width, "");
+   return data[i+j*height];
+}
+
+inline const complex_t &ComplexTypeDenseMatrix::operator()
+(int i, int j) const
+{
+   MFEM_ASSERT(data && i >= 0 && i < height && j >= 0 && j < width, "");
+   return data[i+j*height];
+}
+
 } // namespace mfem
 
 #endif // MFEM_COMPLEX_DENSEMAT

linalg/complex_vector.cpp

@@ -0,0 +1,424 @@
+// 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 "../general/forall.hpp"
+#include "../general/reducers.hpp"
+#include "complex_vector.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+ComplexVector::ComplexVector(const ComplexVector &v)
+{
+   const int s = v.Size();
+   size = s;
+   if (s > 0)
+   {
+      MFEM_ASSERT(!v.data.Empty(), "invalid source vector");
+      data.New(s, v.data.GetMemoryType());
+      data.CopyFrom(v.data, s);
+   }
+   UseDevice(v.UseDevice());
+}
+
+ComplexVector::ComplexVector(const Vector &v)
+{
+   const int s = v.Size();
+   size = s;
+   if (s > 0)
+   {
+      MFEM_ASSERT(!v.data.Empty(), "invalid source vector");
+      data.New(s, v.data.GetMemoryType());
+      MFEM_FORALL(i, size, data[i] = v.data[i]; );
+   }
+   UseDevice(v.UseDevice());
+}
+
+ComplexVector::ComplexVector(ComplexVector &&v)
+{
+   *this = std::move(v);
+}
+
+complex_t &ComplexVector::Elem(int i)
+{
+   return operator()(i);
+}
+
+const complex_t &ComplexVector::Elem(int i) const
+{
+   return operator()(i);
+}
+
+complex_t ComplexVector::operator*(const complex_t *v) const
+{
+   HostRead();
+   complex_t dot = 0.0;
+#ifdef MFEM_USE_LEGACY_OPENMP
+   #pragma omp parallel for reduction(+:dot)
+#endif
+   for (int i = 0; i < size; i++)
+   {
+      dot += data[i] * v[i];
+   }
+   return dot;
+}
+
+complex_t ComplexVector::operator*(const real_t *v) const
+{
+   HostRead();
+   complex_t dot = 0.0;
+#ifdef MFEM_USE_LEGACY_OPENMP
+   #pragma omp parallel for reduction(+:dot)
+#endif
+   for (int i = 0; i < size; i++)
+   {
+      dot += data[i] * v[i];
+   }
+   return dot;
+}
+
+complex_t ComplexVector::operator*(const ComplexVector &v) const
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   if (size == 0) { return 0.0; }
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const auto m_data = Read(use_dev), v_data = v.Read(use_dev);
+
+   // The standard way of computing the dot product is non-deterministic
+   complex_t prod = 0.0;
+   for (int i = 0; i < size; i++)
+   {
+      prod += m_data[i] * v_data[i];
+   }
+   return prod;
+}
+
+complex_t ComplexVector::operator*(const Vector &v) const
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   if (size == 0) { return 0.0; }
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const auto m_data = Read(use_dev);
+   const auto v_data = v.Read(use_dev);
+
+   // The standard way of computing the dot product is non-deterministic
+   complex_t prod = 0.0;
+   for (int i = 0; i < size; i++)
+   {
+      prod += m_data[i] * v_data[i];
+   }
+   return prod;
+}
+
+ComplexVector &ComplexVector::operator=(const complex_t *v)
+{
+   HostRead();
+   MFEM_FORALL(i, size, data[i] = v[i]; );
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(const real_t *v)
+{
+   HostRead();
+   MFEM_FORALL(i, size, data[i] = v[i]; );
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(const ComplexVector &v)
+{
+#if 0
+   SetSize(v.Size(), v.data.GetMemoryType());
+   data.CopyFrom(v.data, v.Size());
+   UseDevice(v.UseDevice());
+#else
+   SetSize(v.Size());
+   const bool vuse = v.UseDevice();
+   const bool use_dev = UseDevice() || vuse;
+   v.UseDevice(use_dev);
+   // keep 'data' where it is, unless 'use_dev' is true
+   if (use_dev) { Write(); }
+   data.CopyFrom(v.data, v.Size());
+   v.UseDevice(vuse);
+#endif
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(const Vector &v)
+{
+   SetSize(v.Size());
+   const bool vuse = v.UseDevice();
+   const bool use_dev = UseDevice() || vuse;
+   v.UseDevice(use_dev);
+   // keep 'data' where it is, unless 'use_dev' is true
+   if (use_dev) { Write(); }
+   MFEM_FORALL(i, size, data[i] = v[i]; );
+   v.UseDevice(vuse);
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(ComplexVector &&v)
+{
+   v.Swap(*this);
+   if (this != &v) { v.Destroy(); }
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(complex_t value)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = Write(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] = value; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator=(real_t value)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = Write(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] = value; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator*=(complex_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator*=(real_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator*=(const ComplexVector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator*=(const Vector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator/=(complex_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   const complex_t m = conj(c) / norm(c);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= m; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator/=(real_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   const real_t m = 1.0/c;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] *= m; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator/=(const ComplexVector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] /= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator/=(const Vector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] /= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator-=(complex_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] -= c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator-=(real_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] -= c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator-=(const ComplexVector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] -= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator-=(const Vector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] -= x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator+=(complex_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] += c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator+=(real_t c)
+{
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] += c; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator+=(const ComplexVector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] += x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::operator+=(const Vector &v)
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   const auto x = v.Read(use_dev);
+   auto y = ReadWrite(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] += x[i]; });
+   return *this;
+}
+
+ComplexVector &ComplexVector::Set(const Vector &Vr, const Vector &Vi)
+{
+   MFEM_ASSERT(size == Vr.size && size == Vi.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || Vr.UseDevice() || Vi.UseDevice();
+   const int N = size;
+   const auto x = Vr.Read(use_dev);
+   const auto y = Vi.Read(use_dev);
+   auto z = Write(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { z[i] = complex_t(x[i], y[i]); });
+   return *this;
+}
+
+const Vector &ComplexVector::real() const
+{
+   re_part.SetSize(size);
+   const bool use_dev = UseDevice();
+   const int N = size;
+   const auto z = Read(use_dev);
+   auto x = re_part.Write(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { x[i] = z[i].real(); });
+   return re_part;
+}
+
+const Vector &ComplexVector::imag() const
+{
+   im_part.SetSize(size);
+   const bool use_dev = UseDevice();
+   const int N = size;
+   const auto z = Read(use_dev);
+   auto y = im_part.Write(use_dev);
+   mfem::forall_switch(use_dev, N, [=] MFEM_HOST_DEVICE (int i)
+   { y[i] = z[i].imag(); });
+   return im_part;
+}
+
+}

linalg/complex_vector.hpp

@@ -0,0 +1,479 @@
+// 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_COMPLEX_VECTOR
+#define MFEM_COMPLEX_VECTOR
+
+#include "vector.hpp"
+#include "../general/complex_type.hpp"
+
+namespace mfem
+{
+
+class ComplexVector
+{
+private:
+
+   Memory<complex_t > data;
+   int size;
+
+   mutable Vector re_part;
+   mutable Vector im_part;
+
+public:
+
+   /// Default constructor for ComplexVector. Sets size = 0
+   ComplexVector() : size(0) { }
+
+   /// Copy constructor. Allocates a new data array and copies the data.
+   ComplexVector(const ComplexVector &);
+
+   /// Copy constructor. Allocates a new data array and copies the
+   /// data into real part of this vector.
+   ComplexVector(const Vector &);
+
+   /// Move constructor. "Steals" data from its argument.
+   ComplexVector(ComplexVector&& v);
+
+   /// @brief Creates vector of size s.
+   /// @warning Entries are not initialized to zero!
+   explicit ComplexVector(int s);
+
+   /// Creates a vector referencing an array of complex<doubles>,
+   /// owned by someone else.
+   /// The pointer @a data_ can be NULL. The data array can be replaced later
+   /// with SetData().
+   ComplexVector(complex_t *data_, int size_)
+   { data.Wrap(data_, size_, false); size = size_; }
+
+   /// @brief Create a ComplexVector referencing a sub-vector of the
+   //  ComplexVector @a base starting at the given offset, @a
+   //  base_offset, and size @a size_.
+   ComplexVector(ComplexVector &base, int base_offset, int size_)
+      : data(base.data, base_offset, size_), size(size_) { }
+
+   /// Create a ComplexVector of size @a size_ using MemoryType @a mt.
+   ComplexVector(int size_, MemoryType mt)
+      : data(size_, mt), size(size_) { }
+
+   /// @brief Create a ComplexVector of size @a size_ using host
+   /// MemoryType @a h_mt and device MemoryType @a d_mt.
+   ComplexVector(int size_, MemoryType h_mt, MemoryType d_mt)
+      : data(size_, h_mt, d_mt), size(size_) { }
+
+   /// Create a vector from a statically sized C-style array of convertible type
+   template <typename CT, int N>
+   explicit ComplexVector(const CT (&values)[N]) : ComplexVector(N)
+   { std::copy(values, values + N, begin()); }
+
+   /// Create a vector using a braced initializer list
+   template <typename CT, typename std::enable_if<
+                std::is_convertible<CT,complex_t >::value,bool>::type = true>
+   explicit ComplexVector(std::initializer_list<CT> values) : ComplexVector(
+         values.size())
+   { std::copy(values.begin(), values.end(), begin()); }
+
+   /// Enable execution of Vector operations using the mfem::Device.
+   /// The default is to use Backend::CPU (serial execution on each MPI rank),
+   /// regardless of the mfem::Device configuration.
+   ///
+   /// When appropriate, MFEM functions and class methods will enable the use
+   /// of the mfem::Device for their Vector parameters.
+   ///
+   /// Some derived classes, e.g. GridFunction, enable the use of the
+   /// mfem::Device by default.
+   virtual void UseDevice(bool use_dev) const { data.UseDevice(use_dev); }
+
+   /// Return the device flag of the Memory object used by the Vector
+   virtual bool UseDevice() const { return data.UseDevice(); }
+
+   /// @brief Resize the vector to size @a s.
+   /// If the new size is less than or equal to Capacity() then the internal
+   /// data array remains the same. Otherwise, the old array is deleted, if
+   /// owned, and a new array of size @a s is allocated without copying the
+   /// previous content of the ComplexVector.
+   /// @warning In the second case above (new size greater than current one),
+   /// the vector will allocate new data array, even if it did not own the
+   /// original data! Also, new entries are not initialized!
+   void SetSize(int s);
+
+   /// Resize the vector to size @a s using MemoryType @a mt.
+   void SetSize(int s, MemoryType mt);
+
+   /// Resize the vector to size @a s using the MemoryType of @a v.
+   void SetSize(int s, const ComplexVector &v)
+   { SetSize(s, v.GetMemory().GetMemoryType()); }
+
+   /// Resize the vector to size @a s using the MemoryType of @a v.
+   void SetSize(int s, const Vector &v)
+   { SetSize(s, v.GetMemory().GetMemoryType()); }
+
+   /// Set the Vector data.
+   /// @warning This method should be called only when OwnsData() is false.
+   void SetData(complex_t *d)
+   { data.Wrap(d, data.Capacity(), false); }
+
+   /// Set the Vector data and size.
+   /// The Vector does not assume ownership of the new data. The new size is
+   /// also used as the new Capacity().
+   /// @warning This method should be called only when OwnsData() is false.
+   /// @sa NewDataAndSize().
+   void SetDataAndSize(complex_t *d, int s)
+   { data.Wrap(d, s, false); size = s; }
+
+   /// Set the Vector data and size, deleting the old data, if owned.
+   /// The Vector does not assume ownership of the new data. The new size is
+   /// also used as the new Capacity().
+   /// @sa SetDataAndSize().
+   void NewDataAndSize(complex_t *d, int s)
+   {
+      data.Delete();
+      SetDataAndSize(d, s);
+   }
+
+   /// Reset the Vector to use the given external Memory @a mem and size @a s.
+   /// If @a own_mem is false, the Vector will not own any of the pointers of
+   /// @a mem.
+   ///
+   /// Note that when @a own_mem is true, the @a mem object can be destroyed
+   /// immediately by the caller but `mem.Delete()` should NOT be called since
+   /// the Vector object takes ownership of all pointers owned by @a mem.
+   ///
+   /// @sa NewDataAndSize().
+   inline void NewMemoryAndSize(const Memory<complex_t > &mem,
+                                int s, bool own_mem);
+
+   /// Reset the Vector to be a reference to a sub-vector of @a base.
+   inline void MakeRef(ComplexVector &base, int offset, int size);
+
+   /// @brief Reset the Vector to be a reference to a sub-vector of @a base
+   /// without changing its current size.
+   inline void MakeRef(ComplexVector &base, int offset);
+
+   /// Set the Vector data (host pointer) ownership flag.
+   void MakeDataOwner() const { data.SetHostPtrOwner(true); }
+
+   /// Destroy a vector
+   void Destroy();
+
+   /// @brief Delete the device pointer, if owned. If @a copy_to_host is true
+   /// and the data is valid only on device, move it to host before deleting.
+   /// Invalidates the device memory.
+   void DeleteDevice(bool copy_to_host = true)
+   { data.DeleteDevice(copy_to_host); }
+
+   /// Returns the size of the vector.
+   inline int Size() const { return size; }
+
+   /// Return the size of the currently allocated data array.
+   /// It is always true that Capacity() >= Size().
+   inline int Capacity() const { return data.Capacity(); }
+
+   /// Return a pointer to the beginning of the ComplexVector data.
+   /// @warning This method should be used with caution as it gives write access
+   /// to the data of const-qualified ComplexVector%s.
+   inline complex_t *GetData() const
+   { return const_cast<complex_t*>((const complex_t*)data); }
+
+   /// STL-like begin.
+   inline complex_t *begin() { return data; }
+
+   /// STL-like end.
+   inline complex_t *end() { return data + size; }
+
+   /// STL-like begin (const version).
+   inline const complex_t *begin() const { return data; }
+
+   /// STL-like end (const version).
+   inline const complex_t *end() const { return data + size; }
+
+   /// Return a reference to the Memory object used by the Vector.
+   Memory<complex_t > &GetMemory() { return data; }
+
+   /// @brief Return a reference to the Memory object used by the
+   /// ComplexVector, const version.
+   const Memory<complex_t > &GetMemory() const { return data; }
+
+   /// Update the memory location of the vector to match @a v.
+   void SyncMemory(const ComplexVector &v) const
+   { GetMemory().Sync(v.GetMemory()); }
+
+   /// Update the alias memory location of the vector to match @a v.
+   void SyncAliasMemory(const ComplexVector &v) const
+   { GetMemory().SyncAlias(v.GetMemory(),Size()); }
+
+   /// Read the Vector data (host pointer) ownership flag.
+   inline bool OwnsData() const { return data.OwnsHostPtr(); }
+
+   /// Changes the ownership of the data; after the call the Vector is empty
+   inline void StealData(complex_t **p)
+   { *p = data; data.Reset(); size = 0; }
+
+   /// Changes the ownership of the data; after the call the Vector is empty
+   inline complex_t *StealData()
+   { complex_t *p; StealData(&p); return p; }
+
+   /// Access Vector entries. Index i = 0 .. size-1.
+   complex_t &Elem(int i);
+
+   /// Read only access to Vector entries. Index i = 0 .. size-1.
+   const complex_t &Elem(int i) const;
+
+   /// Access Vector entries using () for 0-based indexing.
+   /// @note If MFEM_DEBUG is enabled, bounds checking is performed.
+   inline complex_t &operator()(int i);
+
+   /// Read only access to Vector entries using () for 0-based indexing.
+   /// @note If MFEM_DEBUG is enabled, bounds checking is performed.
+   inline const complex_t &operator()(int i) const;
+
+   /// Access Vector entries using [] for 0-based indexing.
+   /// @note If MFEM_DEBUG is enabled, bounds checking is performed.
+   inline complex_t &operator[](int i) { return (*this)(i); }
+
+   /// Read only access to Vector entries using [] for 0-based indexing.
+   /// @note If MFEM_DEBUG is enabled, bounds checking is performed.
+   inline const complex_t &operator[](int i) const
+   { return (*this)(i); }
+
+   /// Dot product with a `complex<double> *` array.
+   /// @note No complex conjugate is performed
+   complex_t operator*(const complex_t *v) const;
+   complex_t operator*(const real_t *v) const;
+
+   /// Return the inner-product.
+   /// @note No complex conjugate is performed
+   complex_t operator*(const ComplexVector &v) const;
+   complex_t operator*(const Vector &v) const;
+
+   /// Copy Size() entries from @a v.
+   ComplexVector &operator=(const complex_t *v);
+   ComplexVector &operator=(const real_t *v);
+
+   /// Copy assignment.
+   /// @note Defining this method overwrites the implicitly defined copy
+   /// assignment operator.
+   ComplexVector &operator=(const ComplexVector &v);
+   ComplexVector &operator=(const Vector &v);
+
+   /// Move assignment
+   ComplexVector &operator=(ComplexVector&& v);
+
+   /// Redefine '=' for vector = constant.
+   ComplexVector &operator=(complex_t value);
+   ComplexVector &operator=(real_t value);
+
+   /// Scale vector by a constant
+   ComplexVector &operator*=(complex_t c);
+   ComplexVector &operator*=(real_t c);
+
+   /// Component-wise scaling: (*this)(i) *= v(i)
+   ComplexVector &operator*=(const ComplexVector &v);
+   ComplexVector &operator*=(const Vector &v);
+
+   /// Divide vector by a consant
+   ComplexVector &operator/=(complex_t c);
+   ComplexVector &operator/=(real_t c);
+
+   /// Component-wise division: (*this)(i) /= v(i)
+   ComplexVector &operator/=(const ComplexVector &v);
+   ComplexVector &operator/=(const Vector &v);
+
+   /// Subtract a constant from this vector
+   ComplexVector &operator-=(complex_t c);
+   ComplexVector &operator-=(real_t c);
+
+   /// Subtract a vector from this vector
+   ComplexVector &operator-=(const ComplexVector &v);
+   ComplexVector &operator-=(const Vector &v);
+
+   /// Add a constant to this vector
+   ComplexVector &operator+=(complex_t c);
+   ComplexVector &operator+=(real_t c);
+
+   /// Add a vector to this vector
+   ComplexVector &operator+=(const ComplexVector &v);
+   ComplexVector &operator+=(const Vector &v);
+
+   /// (*this) = x + i * y
+   ComplexVector &Set(const Vector &x, const Vector &y);
+
+   /// Swap the contents of two Vectors
+   inline void Swap(ComplexVector &other);
+
+   /// Return a reference to the real part of this vector
+   const Vector &real() const;
+
+   /// Return a reference to the imaginary part of this vector
+   const Vector &imag() const;
+
+   /// Destroys vector.
+   virtual ~ComplexVector();
+
+   /// Shortcut for mfem::Read(vec.GetMemory(), vec.Size(), on_dev).
+   virtual const complex_t *Read(bool on_dev = true) const
+   { return mfem::Read(data, size, on_dev); }
+
+   /// Shortcut for mfem::Read(vec.GetMemory(), vec.Size(), false).
+   virtual const complex_t *HostRead() const
+   { return mfem::Read(data, size, false); }
+
+   /// Shortcut for mfem::Write(vec.GetMemory(), vec.Size(), on_dev).
+   virtual complex_t *Write(bool on_dev = true)
+   { return mfem::Write(data, size, on_dev); }
+
+   /// Shortcut for mfem::Write(vec.GetMemory(), vec.Size(), false).
+   virtual complex_t *HostWrite()
+   { return mfem::Write(data, size, false); }
+
+   /// Shortcut for mfem::ReadWrite(vec.GetMemory(), vec.Size(), on_dev).
+   virtual complex_t *ReadWrite(bool on_dev = true)
+   { return mfem::ReadWrite(data, size, on_dev); }
+
+   /// Shortcut for mfem::ReadWrite(vec.GetMemory(), vec.Size(), false).
+   virtual complex_t *HostReadWrite()
+   { return mfem::ReadWrite(data, size, false); }
+};
+
+inline ComplexVector::ComplexVector(int s)
+{
+   MFEM_ASSERT(s>=0,"Unexpected negative size.");
+   size = s;
+   if (s > 0)
+   {
+      data.New(s);
+   }
+}
+
+inline void ComplexVector::SetSize(int s)
+{
+   if (s == size)
+   {
+      return;
+   }
+   if (s <= data.Capacity())
+   {
+      size = s;
+      return;
+   }
+   // preserve a valid MemoryType and device flag
+   const MemoryType mt = data.GetMemoryType();
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   size = s;
+   data.New(s, mt);
+   data.UseDevice(use_dev);
+}
+
+inline void ComplexVector::SetSize(int s, MemoryType mt)
+{
+   if (mt == data.GetMemoryType())
+   {
+      if (s == size)
+      {
+         return;
+      }
+      if (s <= data.Capacity())
+      {
+         size = s;
+         return;
+      }
+   }
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   if (s > 0)
+   {
+      data.New(s, mt);
+      size = s;
+   }
+   else
+   {
+      data.Reset();
+      size = 0;
+   }
+   data.UseDevice(use_dev);
+}
+
+inline void ComplexVector::NewMemoryAndSize(
+   const Memory<complex_t > &mem,
+   int s,
+   bool own_mem)
+{
+   data.Delete();
+   size = s;
+   if (own_mem)
+   {
+      data = mem;
+   }
+   else
+   {
+      data.MakeAlias(mem, 0, s);
+   }
+}
+
+inline void ComplexVector::MakeRef(ComplexVector &base, int offset, int s)
+{
+   data.Delete();
+   size = s;
+   data.MakeAlias(base.GetMemory(), offset, s);
+}
+
+inline void ComplexVector::MakeRef(ComplexVector &base, int offset)
+{
+   data.Delete();
+   data.MakeAlias(base.GetMemory(), offset, size);
+}
+
+inline void ComplexVector::Destroy()
+{
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   size = 0;
+   data.Reset();
+   data.UseDevice(use_dev);
+}
+
+inline complex_t &ComplexVector::operator()(int i)
+{
+   MFEM_ASSERT(data && i >= 0 && i < size,
+               "index [" << i << "] is out of range [0," << size << ")");
+
+   return data[i];
+}
+
+inline const complex_t &ComplexVector::operator()(int i) const
+{
+   MFEM_ASSERT(data && i >= 0 && i < size,
+               "index [" << i << "] is out of range [0," << size << ")");
+
+   return data[i];
+}
+
+inline void ComplexVector::Swap(ComplexVector &other)
+{
+   mfem::Swap(data, other.data);
+   mfem::Swap(size, other.size);
+}
+
+/// Specialization of the template function Swap<> for class ComplexVector
+template<> inline void Swap<ComplexVector>(ComplexVector &a, ComplexVector &b)
+{
+   a.Swap(b);
+}
+
+inline ComplexVector::~ComplexVector()
+{
+   data.Delete();
+}
+
+} // namespace mfem
+
+#endif

linalg/densemat.cpp

@@ -4405,4 +4405,32 @@ void BatchLUSolve(const DenseTensor &Mlu, const Array<int> &P, Vector &X)
    BatchedLinAlg::LUSolve(Mlu, P, X);
 }
 
+#ifdef MFEM_USE_LAPACK
+void BandedSolve(int KL, int KU, DenseMatrix &AB, DenseMatrix &B,
+                 Array<int> &ipiv)
+{
+   int LDAB = (2*KL) + KU + 1;
+   int N = AB.NumCols();
+   int NRHS = B.NumCols();
+   int info;
+   ipiv.SetSize(N);
+   MFEM_LAPACK_PREFIX(gbsv_)(&N, &KL, &KU, &NRHS, AB.GetData(), &LDAB,
+                             ipiv.GetData(), B.GetData(), &N, &info);
+   MFEM_ASSERT(info == 0, "BandedSolve failed in LAPACK");
+}
+
+void BandedFactorizedSolve(int KL, int KU, DenseMatrix &AB, DenseMatrix &B,
+                           bool transpose, Array<int> &ipiv)
+{
+   int LDAB = (2*KL) + KU + 1;
+   int N = AB.NumCols();
+   int NRHS = B.NumCols();
+   char trans = transpose ? 'T' : 'N';
+   int info;
+   MFEM_LAPACK_PREFIX(gbtrs_)(&trans, &N, &KL, &KU, &NRHS, AB.GetData(), &LDAB,
+                              ipiv.GetData(), B.GetData(), &N, &info);
+   MFEM_ASSERT(info == 0, "BandedFactorizedSolve failed in LAPACK");
+}
+#endif
+
 } // namespace mfem

linalg/densemat.hpp

@@ -24,6 +24,7 @@ class DenseMatrix : public Matrix
 {
    friend class DenseTensor;
    friend class DenseMatrixInverse;
+   friend class ComplexTypeDenseMatrix;
 
 private:
    Memory<real_t> data;
@@ -1329,6 +1330,13 @@ void BatchLUFactor(DenseTensor &Mlu, Array<int> &P, const real_t TOL = 0.0);
     dimension m x n. */
 void BatchLUSolve(const DenseTensor &Mlu, const Array<int> &P, Vector &X);
 
+#ifdef MFEM_USE_LAPACK
+void BandedSolve(int KL, int KU, DenseMatrix &AB, DenseMatrix &B,
+                 Array<int> &ipiv);
+void BandedFactorizedSolve(int KL, int KU, DenseMatrix &AB, DenseMatrix &B,
+                           bool transpose, Array<int> &ipiv);
+#endif
+
 // Inline methods
 
 inline real_t &DenseMatrix::operator()(int i, int j)

linalg/hypre.cpp

@@ -2574,6 +2574,18 @@ void HypreParMatrix::EliminateBC(const Array<int> &ess_dofs,
 #if defined(HYPRE_USING_GPU)
       if (HypreUsingGPU())
       {
+#if defined(HYPRE_WITH_GPU_AWARE_MPI) || defined(HYPRE_USING_GPU_AWARE_MPI)
+         // hypre_GetGpuAwareMPI() was introduced in v2.31.0, however, its value
+         // is not checked in hypre_ParCSRCommHandleCreate_v2() before v2.33.0,
+         // instead only HYPRE_WITH_GPU_AWARE_MPI is checked.
+#if MFEM_HYPRE_VERSION >= 23300
+         if (hypre_GetGpuAwareMPI())
+#endif
+         {
+            // ensure int_buf_data has been computed before sending it
+            MFEM_STREAM_SYNC;
+         }
+#endif
          // Try to use device-aware MPI for the communication if available
          comm_handle = hypre_ParCSRCommHandleCreate_v2(
                           11, comm_pkg, HYPRE_MEMORY_DEVICE, int_buf_data,

linalg/lapack.hpp

@@ -42,6 +42,13 @@ extern "C" void
 MFEM_LAPACK_PREFIX(getri_)(int *N, real_t *A, int *LDA, int *IPIV, real_t *WORK,
                            int *LWORK, int *INFO);
 extern "C" void
+MFEM_LAPACK_PREFIX(gbsv_)(int *, int *, int *, int *, real_t *, int *, int *,
+                          real_t *, int *, int *);
+extern "C" void
+MFEM_LAPACK_PREFIX(gbtrs_)(char *, int *, int *, int *, int *, real_t *, int *,
+                           int *, real_t *, int *, int *);
+
+extern "C" void
 MFEM_LAPACK_PREFIX(syevr_)(char *JOBZ, char *RANGE, char *UPLO, int *N,
                            real_t *A, int *LDA, real_t *VL, real_t *VU, int *IL,
                            int *IU, real_t *ABSTOL, int *M, real_t *W,

linalg/vector.hpp

@@ -80,6 +80,8 @@ inline real_t rand_real()
 /// Vector data type.
 class Vector
 {
+   friend class ComplexVector;
+
 protected:
 
    Memory<real_t> data;

mesh/exodus_writer.cpp

@@ -26,6 +26,12 @@
    }\
 }
 
+#if defined(MFEM_USE_DOUBLE)
+#define MFEM_NETCDF_REAL_T NC_DOUBLE
+#elif defined(MFEM_USE_SINGLE)
+#define MFEM_NETCDF_REAL_T NC_FLOAT
+#endif
+
 namespace mfem
 {
 
@@ -135,18 +141,18 @@ public:
    /// @brief Writes the mesh to an ExodusII file.
    /// @param fpath The path to the file.
    /// @param flags NC_CLOBBER will overwrite existing file.
-   void PrintExodusII(std::string fpath, int flags = NC_CLOBBER);
+   void PrintExodusII(const std::string &fpath, int flags = NC_CLOBBER);
 
    /// @brief Static method for writing a mesh to an ExodusII file.
    /// @param mesh The mesh to write to the file.
    /// @param fpath The path to the file.
    /// @param flags NetCDF file flags.
-   static void PrintExodusII(Mesh & mesh, std::string fpath,
+   static void PrintExodusII(Mesh & mesh, const std::string &fpath,
                              int flags = NC_CLOBBER);
 
 protected:
    /// @brief Closes any open file and creates a NetCDF file using selected flags.
-   void OpenExodusII(std::string fpath, int flags);
+   void OpenExodusII(const std::string &fpath, int flags);
 
    /// @brief Closes any open file.
    void CloseExodusII();
@@ -167,9 +173,9 @@ protected:
    std::unordered_set<int> GenerateUniqueNodeIDs();
 
    /// @brief Populates vectors with x, y, z coordinates from mesh.
-   void ExtractVertexCoordinates(std::vector<double> & coordx,
-                                 std::vector<double> & coordy,
-                                 std::vector<double> & coordz);
+   void ExtractVertexCoordinates(std::vector<real_t> &coordx,
+                                 std::vector<real_t> &coordy,
+                                 std::vector<real_t> &coordz);
 
    /// @brief Writes node connectivity for a particular block.
    /// @param block_id The block to write to the file.
@@ -187,7 +193,7 @@ protected:
    /// @brief Writes the number of elements in the mesh.
    void WriteNumOfElements();
 
-   /// @brief Writes the floating-point word size (4 == float; 8 == double).
+   /// @brief Writes the floating-point word size (sizeof(real_t)).
    void WriteFloatingPointWordSize();
 
    /// @brief Writes the API version.
@@ -291,7 +297,7 @@ private:
    std::map<int, std::vector<int>> exodusII_side_ids_for_boundary_id;
 };
 
-void Mesh::PrintExodusII(const std::string fpath)
+void Mesh::PrintExodusII(const std::string &fpath)
 {
    ExodusIIWriter::PrintExodusII(*this, fpath);
 }
@@ -362,7 +368,7 @@ void ExodusIIWriter::WriteExodusIIMeshInformation()
    WriteNodeSets();
 }
 
-void ExodusIIWriter::PrintExodusII(std::string fpath, int flags)
+void ExodusIIWriter::PrintExodusII(const std::string &fpath, int flags)
 {
    OpenExodusII(fpath, flags);
 
@@ -374,7 +380,7 @@ void ExodusIIWriter::PrintExodusII(std::string fpath, int flags)
    mfem::out << "Mesh successfully written to Exodus II file" << std::endl;
 }
 
-void ExodusIIWriter::PrintExodusII(Mesh & mesh, std::string fpath,
+void ExodusIIWriter::PrintExodusII(Mesh &mesh, const std::string &fpath,
                                    int flags)
 {
    ExodusIIWriter writer(mesh);
@@ -382,7 +388,7 @@ void ExodusIIWriter::PrintExodusII(Mesh & mesh, std::string fpath,
    writer.PrintExodusII(fpath, flags);
 }
 
-void ExodusIIWriter::OpenExodusII(std::string fpath, int flags)
+void ExodusIIWriter::OpenExodusII(const std::string &fpath, int flags)
 {
    CloseExodusII();  // Close any open files.
 
@@ -422,7 +428,7 @@ void ExodusIIWriter::WriteNumOfElements()
 
 void ExodusIIWriter::WriteFloatingPointWordSize()
 {
-   const int word_size = 8;
+   const int word_size = sizeof(real_t);
    PutAtt(NC_GLOBAL, ExodusIILabels::EXODUS_FLOATING_POINT_WORD_SIZE_LABEL,
           NC_INT, 1,
           &word_size);
@@ -430,13 +436,15 @@ void ExodusIIWriter::WriteFloatingPointWordSize()
 
 void ExodusIIWriter::WriteAPIVersion()
 {
-   PutAtt(NC_GLOBAL, ExodusIILabels::EXODUS_API_VERSION_LABEL, NC_FLOAT, 1,
+   PutAtt(NC_GLOBAL, ExodusIILabels::EXODUS_API_VERSION_LABEL, MFEM_NETCDF_REAL_T,
+          1,
           &ExodusIILabels::EXODUS_API_VERSION);
 }
 
 void ExodusIIWriter::WriteDatabaseVersion()
 {
-   PutAtt(NC_GLOBAL, ExodusIILabels::EXODUS_DATABASE_VERSION_LABEL, NC_FLOAT, 1,
+   PutAtt(NC_GLOBAL, ExodusIILabels::EXODUS_DATABASE_VERSION_LABEL,
+          MFEM_NETCDF_REAL_T, 1,
           &ExodusIILabels::EXODUS_DATABASE_VERSION);
 }
 
@@ -607,25 +615,25 @@ void ExodusIIWriter::WriteNodalCoordinates()
    DefineDimension("num_nodes", num_nodes, &num_nodes_id);
 
    // 3. Extract the nodal coordinates.
-   // NB: assume doubles (could be floats!); ndims = 1 (vector).
+   // NB: writes in format real_t (double or float); ndims = 1 (vector).
    // https://docs.unidata.ucar.edu/netcdf-c/current/group__variables.html#gac7e8662c51f3bb07d1fc6d6c6d9052c8
-   std::vector<double> coordx(num_nodes);
-   std::vector<double> coordy(num_nodes);
-   std::vector<double> coordz(mesh.Dimension() == 3 ? num_nodes : 0);
+   std::vector<real_t> coordx(num_nodes);
+   std::vector<real_t> coordy(num_nodes);
+   std::vector<real_t> coordz(mesh.Dimension() == 3 ? num_nodes : 0);
 
    ExtractVertexCoordinates(coordx, coordy, coordz);
 
    // 4. Define and put the nodal coordinates.
-   DefineAndPutVar(ExodusIILabels::EXODUS_COORDX_LABEL, NC_DOUBLE, 1,
+   DefineAndPutVar(ExodusIILabels::EXODUS_COORDX_LABEL, MFEM_NETCDF_REAL_T, 1,
                    &num_nodes_id,
                    coordx.data());
-   DefineAndPutVar(ExodusIILabels::EXODUS_COORDY_LABEL, NC_DOUBLE, 1,
+   DefineAndPutVar(ExodusIILabels::EXODUS_COORDY_LABEL, MFEM_NETCDF_REAL_T, 1,
                    &num_nodes_id,
                    coordy.data());
 
    if (mesh.Dimension() == 3)
    {
-      DefineAndPutVar(ExodusIILabels::EXODUS_COORDZ_LABEL, NC_DOUBLE, 1,
+      DefineAndPutVar(ExodusIILabels::EXODUS_COORDZ_LABEL, MFEM_NETCDF_REAL_T, 1,
                       &num_nodes_id,
                       coordz.data());
    }
@@ -770,9 +778,9 @@ void ExodusIIWriter::WriteNodeConnectivityForBlock(const int block_id)
 }
 
 
-void ExodusIIWriter::ExtractVertexCoordinates(std::vector<double> & coordx,
-                                              std::vector<double> & coordy,
-                                              std::vector<double> & coordz)
+void ExodusIIWriter::ExtractVertexCoordinates(std::vector<real_t> & coordx,
+                                              std::vector<real_t> & coordy,
+                                              std::vector<real_t> & coordz)
 {
    if (mesh.GetNodes()) // Higher-order.
    {
@@ -782,7 +790,7 @@ void ExodusIIWriter::ExtractVertexCoordinates(std::vector<double> & coordx,
       sorted_node_ids.assign(unordered_node_ids.begin(), unordered_node_ids.end());
       std::sort(sorted_node_ids.begin(), sorted_node_ids.end());
 
-      double coordinates[3];
+      real_t coordinates[3];
       for (size_t i = 0; i < sorted_node_ids.size(); i++)
       {
          int node_id = sorted_node_ids[i];
@@ -802,7 +810,7 @@ void ExodusIIWriter::ExtractVertexCoordinates(std::vector<double> & coordx,
    {
       for (int ivertex = 0; ivertex < mesh.GetNV(); ivertex++)
       {
-         double * coordinates = mesh.GetVertex(ivertex);
+         real_t *coordinates = mesh.GetVertex(ivertex);
 
          coordx[ivertex] = coordinates[0];
          coordy[ivertex] = coordinates[1];
@@ -1080,4 +1088,4 @@ void ExodusIIWriter::CheckNodalFESpaceIsSecondOrderH1() const
 
 #endif
 
-}
+}

mesh/mesh.cpp

@@ -2994,6 +2994,7 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
    const int num_edge_dofs = old_dofs.Size();
 
    // Save the original nodes
+   Nodes->HostReadWrite(); // for "(*Nodes)() = "
    const Vector onodes = *Nodes;
 
    // vertex dofs do not need to be moved

mesh/mesh.hpp

@@ -588,9 +588,10 @@ protected:
    void Loader(std::istream &input, int generate_edges = 0,
                std::string parse_tag = "");
 
-   /** If NURBS mesh, write NURBS format. If NCMesh, write mfem v1.1 format.
-       If section_delimiter is empty, write mfem v1.0 format. Otherwise, write
-       mfem v1.2 format with the given section_delimiter at the end.
+   /** @brief If NURBS mesh, write NURBS format. If NCMesh, write mfem v1.1
+       format. If section_delimiter is empty, write mfem v1.0 format. Otherwise,
+       write mfem v1.2 format with the given section_delimiter at the end.
+
        If @a comments is non-empty, it will be printed after the first line of
        the file, and each line should begin with '#'. */
    void Printer(std::ostream &os = mfem::out,
@@ -2482,10 +2483,12 @@ public:
    /// Print the mesh to the given stream using Netgen/Truegrid format.
    virtual void PrintXG(std::ostream &os = mfem::out) const;
 
-   /// Print the mesh to the given stream using the default MFEM mesh format.
-   /// \see mfem::ofgzstream() for on-the-fly compression of ascii outputs. If
-   /// @a comments is non-empty, it will be printed after the first line of the
-   /// file, and each line should begin with '#'.
+   /** @brief Print the mesh to the given stream using the default MFEM mesh
+       format.
+
+       \see mfem::ofgzstream() for on-the-fly compression of ascii outputs. If
+       @a comments is non-empty, it will be printed after the first line of the
+       file, and each line should begin with '#'. */
    virtual void Print(std::ostream &os = mfem::out,
                       const std::string &comments = "") const
    { Printer(os, "", comments); }
@@ -2537,7 +2540,7 @@ public:
 
 #ifdef MFEM_USE_NETCDF
    /// @brief Export a mesh to an Exodus II file.
-   void PrintExodusII(const std::string fpath);
+   void PrintExodusII(const std::string &fpath);
 #endif
 
    /** @brief Prints the mesh with boundary elements given by the boundary of

mesh/mesh_readers.cpp

@@ -802,21 +802,11 @@ struct BufferReader : BufferReaderBase
       {
          // Each "data block" is preceded by a header that is either UInt32 or
          // UInt64. The rest of the data follows.
-         uint64_t data_size;
-         if (header_type == UINT32_HEADER)
-         {
-            uint32_t *data_size_32 = (uint32_t *)header_buf;
-            data_size = *data_size_32;
-         }
-         else
-         {
-            uint64_t *data_size_64 = (uint64_t *)header_buf;
-            data_size = *data_size_64;
-         }
-         MFEM_VERIFY(sizeof(F)*n == data_size, "AppendedData: wrong data size");
+         MFEM_VERIFY(sizeof(F)*n == ReadHeaderEntry(header_buf),
+                     "AppendedData: wrong data size");
       }
 
-      if (std::is_same<T, F>::value)
+      if (std::is_same_v<T, F>)
       {
          // Special case: no type conversions necessary, so can just memcpy
          memcpy(dest, buf, sizeof(T)*n);

mesh/nurbs.cpp

@@ -9,8 +9,13 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "mesh_headers.hpp"
-#include "../fem/fem.hpp"
+#include "nurbs.hpp"
+
+#include "point.hpp"
+#include "segment.hpp"
+#include "quadrilateral.hpp"
+#include "hexahedron.hpp"
+#include "../fem/gridfunc.hpp"
 #include "../general/text.hpp"
 
 #include <fstream>
@@ -33,6 +38,7 @@ KnotVector::KnotVector(istream &input)
 
    knot.Load(input, NumOfControlPoints + Order + 1);
    GetElements();
+   coarse = false;
 }
 
 KnotVector::KnotVector(int order, int NCP)
@@ -41,12 +47,13 @@ KnotVector::KnotVector(int order, int NCP)
    NumOfControlPoints = NCP;
    knot.SetSize(NumOfControlPoints + Order + 1);
    NumOfElements = 0;
+   coarse = false;
 
    knot = -1.;
 }
 
 KnotVector::KnotVector(int order, const Vector& intervals,
-                       const Array<int>& continuity )
+                       const Array<int>& continuity)
 {
    // NOTE: This may need to be generalized to support periodicity
    // in the future.
@@ -86,6 +93,7 @@ KnotVector::KnotVector(int order, const Vector& intervals,
          ++NumOfElements;
       }
    }
+   coarse = false;
 }
 
 KnotVector &KnotVector::operator=(const KnotVector &kv)
@@ -143,7 +151,7 @@ void KnotVector::UniformRefinement(Vector &newknots, int rf) const
       {
          for (int m = 1; m < rf; ++m)
          {
-            newknots(j) = m * h * (knot(i) + knot(i+1));
+            newknots(j) = ((1.0 - (m * h)) * knot(i)) + (m * h * knot(i+1));
             j++;
          }
       }
@@ -332,7 +340,7 @@ void KnotVector::PrintFunctions(std::ostream &os, int samples) const
    }
 }
 
-// Routine from "The NURBS book" - 2nd ed - Piegl and Tiller
+// Routine from "The NURBS Book" - 2nd ed - Piegl and Tiller
 // Algorithm A2.2 p. 70
 void KnotVector::CalcShape(Vector &shape, int i, real_t xi) const
 {
@@ -359,7 +367,7 @@ void KnotVector::CalcShape(Vector &shape, int i, real_t xi) const
    }
 }
 
-// Routine from "The NURBS book" - 2nd ed - Piegl and Tiller
+// Routine from "The NURBS Book" - 2nd ed - Piegl and Tiller
 // Algorithm A2.3 p. 72
 void KnotVector::CalcDShape(Vector &grad, int i, real_t xi) const
 {
@@ -417,7 +425,7 @@ void KnotVector::CalcDShape(Vector &grad, int i, real_t xi) const
    }
 }
 
-// Routine from "The NURBS book" - 2nd ed - Piegl and Tiller
+// Routine from "The NURBS Book" - 2nd ed - Piegl and Tiller
 // Algorithm A2.3 p. 72
 void KnotVector::CalcDnShape(Vector &gradn, int n, int i, real_t xi) const
 {
@@ -537,11 +545,11 @@ void KnotVector::FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const
          int i = j - d;
          if (isElement(i))
          {
-            arg1 = 1e-16;
+            arg1 = std::numeric_limits<real_t>::epsilon() / 2_r;
             CalcShape(shape, i, arg1);
             max1 = shape[d];
 
-            arg2 = 1-(1e-16);
+            arg2 = 1_r - arg1;
             CalcShape(shape, i, arg2);
             max2 = shape[d];
 
@@ -579,9 +587,9 @@ void KnotVector::FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const
    }
 }
 
-// Routine from "The NURBS book" - 2nd ed - Piegl and Tiller
+// Routine from "The NURBS Book" - 2nd ed - Piegl and Tiller
 // Algorithm A9.1 p. 369
-void KnotVector::FindInterpolant(Array<Vector*> &x)
+void KnotVector::FindInterpolant(Array<Vector*> &x, bool reuse_inverse)
 {
    int order = GetOrder();
    int ncp = GetNCP();
@@ -589,29 +597,93 @@ void KnotVector::FindInterpolant(Array<Vector*> &x)
    // Find interpolation points
    Vector xi_args, u_args;
    Array<int> i_args;
-   FindMaxima(i_args,xi_args, u_args);
+   FindMaxima(i_args, xi_args, u_args);
 
    // Assemble collocation matrix
-   Vector shape(order+1);
-   DenseMatrix A(ncp,ncp);
-   A = 0.0;
+#ifdef MFEM_USE_LAPACK
+   // If using LAPACK, we use banded matrix storage (order + 1 nonzeros per row).
+   // Find banded structure of matrix.
+   int KL = 0; // Number of subdiagonals
+   int KU = 0; // Number of superdiagonals
    for (int i = 0; i < ncp; i++)
    {
-      CalcShape(shape, i_args[i], xi_args[i]);
       for (int p = 0; p < order+1; p++)
       {
-         A(i,i_args[i] + p) =  shape[p];
+         const int col = i_args[i] + p;
+         if (col < i)
+         {
+            KL = std::max(KL, i - col);
+         }
+         else if (i < col)
+         {
+            KU = std::max(KU, col - i);
+         }
       }
    }
 
-   // Solve problems
-   A.Invert();
+   const int LDAB = (2*KL) + KU + 1;
+   const int N = ncp;
+
+   fact_AB.SetSize(LDAB, N);
+#else
+   // Without LAPACK, we store and invert a DenseMatrix (inefficient).
+   if (!reuse_inverse)
+   {
+      A_coll_inv.SetSize(ncp, ncp);
+      A_coll_inv = 0.0;
+   }
+#endif
+
+   Vector shape(order+1);
+
+   if (!reuse_inverse) // Set collocation matrix entries
+   {
+      for (int i = 0; i < ncp; i++)
+      {
+         CalcShape(shape, i_args[i], xi_args[i]);
+         for (int p = 0; p < order+1; p++)
+         {
+            const int j = i_args[i] + p;
+#ifdef MFEM_USE_LAPACK
+            fact_AB(KL+KU+i-j,j) = shape[p];
+#else
+            A_coll_inv(i,j) = shape[p];
+#endif
+         }
+      }
+   }
+
+   // Solve the system
+#ifdef MFEM_USE_LAPACK
+   const int NRHS = x.Size();
+   DenseMatrix B(N, NRHS);
+   for (int j=0; j<NRHS; ++j)
+   {
+      for (int i=0; i<N; ++i) { B(i, j) = (*x[j])[i]; }
+   }
+
+   if (reuse_inverse)
+   {
+      BandedFactorizedSolve(KL, KU, fact_AB, B, false, fact_ipiv);
+   }
+   else
+   {
+      BandedSolve(KL, KU, fact_AB, B, fact_ipiv);
+   }
+
+   for (int j=0; j<NRHS; ++j)
+   {
+      for (int i=0; i<N; ++i) { (*x[j])[i] = B(i, j); }
+   }
+#else
+   if (!reuse_inverse) { A_coll_inv.Invert(); }
    Vector tmp;
-   for (int i= 0; i < x.Size(); i++)
+   for (int i = 0; i < x.Size(); i++)
    {
       tmp = *x[i];
-      A.Mult(tmp,*x[i]);
+      A_coll_inv.Mult(tmp, *x[i]);
    }
+#endif
 }
 
 int KnotVector::findKnotSpan(real_t u) const
@@ -1413,7 +1485,7 @@ void NURBSPatch::DegreeElevate(int t)
    }
 }
 
-// Routine from "The NURBS book" - 2nd ed - Piegl and Tiller
+// Routine from "The NURBS Book" - 2nd ed - Piegl and Tiller
 void NURBSPatch::DegreeElevate(int dir, int t)
 {
    if (dir >= kv.Size() || dir < 0)
@@ -1431,8 +1503,8 @@ void NURBSPatch::DegreeElevate(int dir, int t)
    KnotVector &oldkv = *kv[dir];
    oldkv.GetElements();
 
-   NURBSPatch *newpatch = new NURBSPatch(this, dir, oldkv.GetOrder() + t,
-                                         oldkv.GetNCP() + oldkv.GetNE()*t);
+   auto *newpatch = new NURBSPatch(this, dir, oldkv.GetOrder() + t,
+                                   oldkv.GetNCP() + oldkv.GetNE()*t);
    NURBSPatch &newp  = *newpatch;
    KnotVector &newkv = *newp.GetKV(dir);
 
@@ -2377,7 +2449,7 @@ NURBSExtension::NURBSExtension(Mesh *mesh_array[], int num_pieces)
 }
 
 NURBSExtension::NURBSExtension(const Mesh *patch_topology,
-                               const Array<const NURBSPatch*> patches_)
+                               const Array<const NURBSPatch*> &patches_)
 {
    // Basic topology checks
    MFEM_VERIFY(patches_.Size() > 0, "Must have at least one patch");
@@ -4587,7 +4659,7 @@ void NURBSExtension::KnotInsert(Array<Vector *> &kv)
 
             // Flip vector
             int size = pkvc[d]->Size();
-            int ns = ceil(size/2.0);
+            int ns = static_cast<int>(ceil(size/2.0));
             for (int j = 0; j < ns; j++)
             {
                real_t tmp = apb - pkvc[d]->Elem(j);
@@ -4647,7 +4719,7 @@ void NURBSExtension::KnotRemove(Array<Vector *> &kv, real_t tol)
 
             // Flip vector
             int size = pkvc[d]->Size();
-            int ns = ceil(size/2.0);
+            int ns = static_cast<int>(ceil(size/2.0));
             for (int j = 0; j < ns; j++)
             {
                real_t tmp = apb - pkvc[d]->Elem(j);

mesh/nurbs.hpp

@@ -22,7 +22,6 @@
 #include "../general/communication.hpp"
 #endif
 #include <iostream>
-#include <set>
 
 namespace mfem
 {
@@ -55,7 +54,7 @@ protected:
 
 public:
    /// Create an empty KnotVector.
-   KnotVector() { }
+   KnotVector() = default;
 
    /** @brief Create a KnotVector by reading data from stream @a input. Two
        integers are read, for order and number of control points. */
@@ -74,7 +73,7 @@ public:
        polynomial degree). Periodicity is not supported.
    */
    KnotVector(int order, const Vector& intervals,
-              const Array<int>& continuity );
+              const Array<int>& continuity);
 
    /// Copy constructor.
    KnotVector(const KnotVector &kv) { (*this) = kv; }
@@ -144,8 +143,13 @@ public:
    /** @brief Global curve interpolation through the points @a x (overwritten).
        @a x is an array with the length of the spatial dimension containing
        vectors with spatial coordinates. The control points of the interpolated
-       curve are returned in @a x in the same form. */
-   void FindInterpolant(Array<Vector*> &x);
+       curve are returned in @a x in the same form.
+
+       The inverse of the collocation matrix, used in the interpolation, is
+       stored for repeated calls and used if @a reuse_inverse is true. Reuse is
+       valid only if this KnotVector has not changed since the initial call with
+       @a reuse_inverse false. */
+   void FindInterpolant(Array<Vector*> &x, bool reuse_inverse = false);
 
    /** Set @a diff, comprised of knots in @a kv not contained in this KnotVector.
        @a kv must be of the same order as this KnotVector. The current
@@ -203,6 +207,14 @@ public:
    /** Flag to indicate whether the KnotVector has been coarsened, which means
        it is ready for non-nested refinement. */
    bool coarse;
+
+#ifdef MFEM_USE_LAPACK
+   // Data for reusing banded matrix factorization in FindInterpolant().
+   DenseMatrix fact_AB; /// Banded matrix factorization
+   Array<int> fact_ipiv; /// Row pivot indices
+#else
+   DenseMatrix A_coll_inv; /// Collocation matrix inverse
+#endif
 };
 
 
@@ -286,7 +298,7 @@ public:
        includes the weight. The array of control point coordinates stores each
        point's coordinates contiguously, and points are ordered in a standard
        ijk grid ordering. */
-   NURBSPatch(Array<const KnotVector *> &kv_,  int dim_,
+   NURBSPatch(Array<const KnotVector *> &kv_, int dim_,
               const real_t* control_points);
 
    /// Constructor for a patch of dimension equal to the size of @a kv.
@@ -701,7 +713,8 @@ public:
 
    NURBSExtension(Mesh *mesh_array[], int num_pieces);
 
-   NURBSExtension(const Mesh *patch_topology, const Array<const NURBSPatch*> p);
+   NURBSExtension(const Mesh *patch_topology,
+                  const Array<const NURBSPatch*> &patches_);
 
    /// Copy assignment not supported.
    NURBSExtension& operator=(const NURBSExtension&) = delete;

mesh/pmesh.cpp

@@ -3132,11 +3132,12 @@ void ParMesh::GetFaceNbrElementTransformation(
          pNodes->ParFESpace()->GetFaceNbrElementVDofs(FaceNo, vdofs);
          int n = vdofs.Size()/spaceDim;
          pointmat.SetSize(spaceDim, n);
+         pNodes->FaceNbrData().HostRead();
          for (int k = 0; k < spaceDim; k++)
          {
             for (int j = 0; j < n; j++)
             {
-               pointmat(k,j) = (pNodes->FaceNbrData())(vdofs[n*k+j]);
+               pointmat(k,j) = AsConst(pNodes->FaceNbrData())(vdofs[n*k+j]);
             }
          }
 

mesh/submesh/submesh_utils.cpp

@@ -257,15 +257,7 @@ template <typename SubMeshT>
 void AddBoundaryElements(SubMeshT &mesh,
                          const std::unordered_map<int,int> &lface_to_boundary_attribute)
 {
-   mesh.Dimension();
-   const int num_codim_1 = [&mesh]()
-   {
-      auto Dim = mesh.Dimension();
-      if (Dim == 1) { return mesh.GetNV(); }
-      else if (Dim == 2) { return mesh.GetNEdges(); }
-      else if (Dim == 3) { return mesh.GetNFaces(); }
-      else { MFEM_ABORT("Invalid dimension."); return -1; }
-   }();
+   const int num_codim_1 = mesh.GetNumFaces();
 
    if (mesh.Dimension() == 3)
    {

mesh/vtkhdf.cpp

@@ -84,7 +84,7 @@ void VTKHDF::EnsureSteps()
 }
 
 hid_t VTKHDF::EnsureDataset(hid_t f, const std::string &name, hid_t type,
-                            int ndims)
+                            Dims &dims)
 {
    const char *name_c = name.c_str();
 
@@ -94,20 +94,23 @@ hid_t VTKHDF::EnsureDataset(hid_t f, const std::string &name, hid_t type,
    if (status == 0)
    {
       // Dataset does not exist, create it.
-      Dims dims(ndims);
-      Dims maxdims(ndims, H5S_UNLIMITED);
-      const hid_t fspace = H5Screate_simple(ndims, dims, maxdims);
+      const int ndims = dims.ndims;
+      // The dataset is allowed to grow in the first dimension, but is fixed
+      // in size in all other dimesions; the maximum dataset size is same as
+      // dims, but unlimited in first dimension.
+      Dims max_dims = dims;
+      max_dims[0] = H5S_UNLIMITED;
+      const hid_t fspace = H5Screate_simple(ndims, dims, max_dims);
 
       Dims chunk(ndims);
       size_t chunk_size_bytes = 1024 * 1024 / 2; // 0.5 MB
       const size_t t_bytes = H5Tget_size(type);
       for (int i = 1; i < ndims; ++i)
       {
-         chunk[i] = 16;
-         chunk_size_bytes /= 16;
+         chunk[i] = dims[i];
+         chunk_size_bytes /= dims[i];
       }
       chunk[0] = chunk_size_bytes / t_bytes;
-      for (int i = 1; i < ndims; ++i) { chunk[i] = 16; }
       const hid_t dcpl = H5Pcreate(H5P_DATASET_CREATE);
       H5Pset_chunk(dcpl, ndims, chunk);
       if (compression_level >= 0)
@@ -124,7 +127,19 @@ hid_t VTKHDF::EnsureDataset(hid_t f, const std::string &name, hid_t type,
    else if (status > 0)
    {
       // Dataset exists, open it.
-      return H5Dopen2(f, name_c, H5P_DEFAULT);
+      const hid_t d = H5Dopen2(f, name_c, H5P_DEFAULT);
+
+      // Resize the dataset, set dims to its new size.
+      Dims old_dims(dims.ndims);
+      const hid_t dspace = H5Dget_space(d);
+      const int ndims_dset = H5Sget_simple_extent_ndims(dspace);
+      MFEM_VERIFY(ndims_dset == dims.ndims, "");
+      H5Sget_simple_extent_dims(dspace, old_dims, NULL);
+      H5Sclose(dspace);
+      dims[0] += old_dims[0];
+      H5Dset_extent(d, dims);
+
+      return d;
    }
    else
    {
@@ -160,27 +175,13 @@ void VTKHDF::AppendParData(hid_t f, const std::string &name, hsize_t locsize,
                            hsize_t offset, Dims globsize, T *data)
 {
    const int ndims = globsize.ndims;
-   const hid_t d = EnsureDataset(f, name, GetTypeID<T>(), ndims);
-
-   // Resize the dataset, set dims to its new size.
-   hsize_t old_size;
-   Dims dims(ndims);
-   {
-      const hid_t dspace = H5Dget_space(d);
-      const int ndims_dset = H5Sget_simple_extent_ndims(dspace);
-      MFEM_VERIFY(ndims_dset == ndims, "");
-      H5Sget_simple_extent_dims(dspace, dims, NULL);
-      H5Sclose(dspace);
-      old_size = dims[0];
-      dims[0] += globsize[0];
-      for (int i = 1; i < ndims; ++i) { dims[i] = globsize[i]; }
-      H5Dset_extent(d, dims);
-   }
+   Dims dims = globsize;
+   const hid_t d = EnsureDataset(f, name, GetTypeID<T>(), dims);
 
    // Write the new entry.
    const hid_t dspace = H5Dget_space(d);
    Dims start(ndims);
-   start[0] = old_size + offset;
+   start[0] = dims[0] - globsize[0] + offset;
    Dims count(ndims);
    count[0] = locsize;
    for (int i = 1; i < ndims; ++i) { count[i] = globsize[i]; }
@@ -334,14 +335,14 @@ void VTKHDF::Truncate(const real_t t)
    }
 
    // Index of found time index (may be 'one-past-the-end' if not found)
-   const int i = std::distance(tvals.begin(), it);
+   const ptrdiff_t i = std::distance(tvals.begin(), it);
 
    // Only truncate if needed
    const bool truncate = it != tvals.end();
 
    // Number of steps we are keeping
    nsteps = i;
-   H5LTset_attribute_int(vtk, "Steps", "NSteps", &nsteps, 1);
+   H5LTset_attribute_ulong(vtk, "Steps", "NSteps", &nsteps, 1);
 
    // We want to continue writing immediately after step 'i - 1'. If i = 0,
    // then this is at the beginning of the file, and the offsets do not need
@@ -509,7 +510,7 @@ void VTKHDF::UpdateSteps(real_t t)
 
    // Set the NSteps attribute
    ++nsteps;
-   H5LTset_attribute_int(steps, ".", "NSteps", &nsteps, 1);
+   H5LTset_attribute_ulong(steps, ".", "NSteps", &nsteps, 1);
 
    AppendValue(steps, "Values", t);
    AppendValue(steps, "PartOffsets", part_offset);
@@ -618,16 +619,16 @@ void VTKHDF::SaveMesh(const Mesh &mesh, bool high_order, int ref)
 
          for (int i = 0; i < pmat.Width(); i++)
          {
-            points.push_back(pmat(0,i));
-            if (pmat.Height() > 1) { points.push_back(pmat(1,i)); }
+            points.push_back(FP_T(pmat(0,i)));
+            if (pmat.Height() > 1) { points.push_back(FP_T(pmat(1,i))); }
             else { points.push_back(0.0); }
-            if (pmat.Height() > 2) { points.push_back(pmat(2,i)); }
+            if (pmat.Height() > 2) { points.push_back(FP_T(pmat(2,i))); }
             else { points.push_back(0.0); }
          }
       }
    }
 
-   const hsize_t ne_0 = mesh.GetNE();
+   const int ne_0 = mesh.GetNE();
    const hsize_t ne = high_order ? ne_0 : ne_ref;
 
    AppendParData(vtk, "NumberOfPoints", 1, mpi_rank, mpi_dims, &np);
@@ -657,7 +658,7 @@ void VTKHDF::SaveMesh(const Mesh &mesh, bool high_order, int ref)
          if (high_order)
          {
             Array<int> local_connectivity;
-            for (size_t e = 0; e < ne; ++e)
+            for (int e = 0; e < int(ne); ++e)
             {
                offsets[e] = off;
                const Geometry::Type geom = mesh.GetElementGeometry(e);
@@ -675,7 +676,7 @@ void VTKHDF::SaveMesh(const Mesh &mesh, bool high_order, int ref)
          {
             int off_0 = 0;
             int e_ref = 0;
-            for (hsize_t e = 0; e < ne_0; ++e)
+            for (int e = 0; e < ne_0; ++e)
             {
                const Geometry::Type geom = mesh.GetElementGeometry(e);
                const int nv = get_nv(e);
@@ -714,12 +715,13 @@ void VTKHDF::SaveMesh(const Mesh &mesh, bool high_order, int ref)
          const int *vtk_geom_map =
             high_order ? VTKGeometry::HighOrderMap : VTKGeometry::Map;
          int e_ref = 0;
-         for (hsize_t e = 0; e < ne_0; ++e)
+         for (int e = 0; e < ne_0; ++e)
          {
-            const int ne_ref = get_ne_ref(e, ref_0);
-            for (int i = 0; i < ne_ref; ++i, ++e_ref)
+            const int ne_ref_e = get_ne_ref(e, ref_0);
+            for (int i = 0; i < ne_ref_e; ++i, ++e_ref)
             {
-               cell_types[e_ref] = vtk_geom_map[mesh.GetElementGeometry(e)];
+               cell_types[e_ref] = static_cast<unsigned char>(
+                                      vtk_geom_map[mesh.GetElementGeometry(e)]);
             }
          }
          AppendParData(vtk, "Types", ne, e_offset, Dims({ne_total}),
@@ -732,11 +734,11 @@ void VTKHDF::SaveMesh(const Mesh &mesh, bool high_order, int ref)
          EnsureGroup("CellData", cell_data);
          std::vector<int> attributes(ne);
          hsize_t e_ref = 0;
-         for (hsize_t e = 0; e < ne_0; ++e)
+         for (int e = 0; e < ne_0; ++e)
          {
             const int attr = mesh.GetAttribute(e);
-            const int ne_ref = get_ne_ref(e, ref_0);
-            for (int i = 0; i < ne_ref; ++i, ++e_ref)
+            const int ne_ref_e = get_ne_ref(e, ref_0);
+            for (int i = 0; i < ne_ref_e; ++i, ++e_ref)
             {
                attributes[e_ref] = attr;
             }
@@ -772,7 +774,7 @@ void VTKHDF::SaveGridFunction(const GridFunction &gf, const std::string &name)
       {
          for (int vd = 0; vd < vdim; ++vd)
          {
-            point_values[off] = vec_val(vd, i);
+            point_values[off] = FP_T(vec_val(vd, i));
             ++off;
          }
       }

mesh/vtkhdf.hpp

@@ -76,14 +76,14 @@ private:
    /// Wrapper for storing dataset dimensions (max ndims is 2D in VTKHDF).
    struct Dims
    {
-      static constexpr int MAX_NDIMS = 2;
+      static constexpr size_t MAX_NDIMS = 2;
       std::array<hsize_t, MAX_NDIMS> data = { }; // Zero initialized
       int ndims = 0;
       Dims() = default;
       Dims(int ndims_) : ndims(ndims_) { MFEM_ASSERT(ndims <= MAX_NDIMS, ""); }
       Dims(int ndims_, hsize_t val) : Dims(ndims_) { data.fill(val); }
       template <typename T>
-      Dims(std::initializer_list<T> data_) : Dims(data_.size())
+      Dims(std::initializer_list<T> data_) : Dims(int(data_.size()))
       { std::copy(data_.begin(), data_.end(), data.begin()); }
       operator hsize_t*() { return data.data(); }
       hsize_t &operator[](int i) { return data[i]; }
@@ -97,7 +97,7 @@ private:
    hid_t steps = H5I_INVALID_HID;
 
    /// Number of time steps saved.
-   int nsteps = 0;
+   unsigned long nsteps = 0;
 
    /// Keep track of the offsets into the data arrays at each time step.
    struct Offsets
@@ -123,8 +123,8 @@ private:
    class MeshId
    {
       const Mesh *mesh_ptr = nullptr;
-      int sequence = -1;
-      int nodes_sequence = -1;
+      long sequence = -1;
+      long nodes_sequence = -1;
       bool high_order = true;
       int ref = -1;
    public:
@@ -187,8 +187,10 @@ private:
    /// The rank (number of dimensions) of the dataset is given by @a ndims and
    /// its data type is given by @a type.
    ///
-   /// The dataset will initially have zero size and unlimited maximum size.
-   hid_t EnsureDataset(hid_t f, const std::string &name, hid_t type, int ndims);
+   /// If the dataset does not exist, it will initially have size @a dims.
+   /// Otherwise, it will be resized to append data of size @a dims, and @a dims
+   /// will be set to the new total size.
+   hid_t EnsureDataset(hid_t f, const std::string &name, hid_t type, Dims &dims);
 
    /// @brief Ensure the named group is open, creating it if needed. Set @a
    /// group to the ID.

miniapps/meshing/fit-node-position.cpp

@@ -224,5 +224,6 @@ int main (int argc, char *argv[])
    }
 
    delete metric;
+   delete fec_mesh;
    return 0;
 }

miniapps/navier/CMakeLists.txt

@@ -52,20 +52,6 @@ if (MFEM_USE_MPI)
     ${NAVIER_COMMON_FILES}
     LIBRARIES mfem)
 
-  add_mfem_miniapp(incompressible_navier_dfem
-    MAIN incompressible_navier_dfem.cpp
-    EXTRA_HEADERS incompressible_navier_nvtx.hpp
-    LIBRARIES mfem)
-
-  add_mfem_miniapp(incompNS_2Dtest
-    MAIN incompNS_2Dtest.cpp
-    EXTRA_SOURCES incompressible_navier_solver.cpp
-                  incompressible_navier_tests.cpp
-    EXTRA_HEADERS incompressible_navier_solver.hpp
-                  incompressible_navier_nvtx.hpp
-    EXTRA_DEFINES MFEM_USE_CMAKE_TESTS
-    LIBRARIES mfem)
-
   add_mfem_miniapp(navier_turbchan
     MAIN navier_turbchan.cpp
     ${NAVIER_COMMON_FILES}
@@ -98,4 +84,4 @@ if (MFEM_USE_MPI)
         ${MPIEXEC_POSTFLAGS})
     endforeach()
 endif()
-endif()
+endif ()

miniapps/navier/incompNS_2Dtest.cpp

@@ -1,205 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-// 3D flow over a cylinder benchmark example
-
-#include "incompressible_navier_solver.hpp"
-
-#define NVTX_COLOR ::gpu::nvtx::kLawnGreen
-#include "incompressible_navier_nvtx.hpp"
-
-using namespace mfem;
-using namespace incompressible_navier;
-
-void vel(const Vector &x, real_t t, Vector &u)
-{
-   // real_t xi = x(0), yi = x(1);
-   u = 0.0;
-}
-
-void vel_inlet(const Vector &x, real_t t, Vector &u)
-{
-   u = 0.0;
-   if (x(0) < 0.001) { u(0) = -0.001 * (std::pow(x(1) - 0.5, 2.0) - 0.25); }
-}
-
-MFEM_EXPORT int navier(int argc, char *argv[], double &u, double &p, double &Ψ)
-{
-   dbg();
-   static mfem::MPI_Session mpi(argc, argv);
-   const int myid = mpi.WorldRank();
-   Hypre::Init();
-
-   const char *device_config = "cpu";
-   int serial_refinements = 1;
-   int nx = 90, ny = 30;
-   int v_order = 2;
-   int p_order = 1;
-   int t_order = 1;
-   real_t kin_vis = 20.0;
-   real_t dt = 1e-2;
-   real_t t = 0.0;
-   real_t t_final = 1.0;
-   bool last_step = false;
-   bool visualization = true;
-   bool use_paraview = false;
-   bool pa = false;
-   int vis_steps = 100;
-   int max_tsteps = -1;
-
-   constexpr int precision = 8;
-   std::cout.precision(precision);
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&serial_refinements, "-sr", "--serial-refinements",
-                  "Number serial refinements.");
-   args.AddOption(&nx, "-nx", "--nx", "Number of elements in X.");
-   args.AddOption(&ny, "-ny", "--ny", "Number of elements in Y.");
-   args.AddOption(&v_order, "-vo", "--vo", "Order.");
-   args.AddOption(&p_order, "-po", "--po", "Order.");
-   args.AddOption(&t_order, "-to", "--to", "Order.");
-   args.AddOption(&kin_vis, "-kv", "--kin-vis",
-                  "Kineic viscosity coefficient.");
-   args.AddOption(&dt, "-dt", "--time-step", "Initial time step size.");
-   args.AddOption(&t_final, "-tf", "--t-final", "Final time; start time is 0.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
-                  "--no-partial-assembly",
-                  "Enable or disable partial assembly.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
-   args.AddOption(&use_paraview, "-pv", "--paraview", "-no-pv", "--no-paraview",
-                  "Use ParaView.");
-   args.AddOption(&vis_steps, "-vs", "--visualization-steps",
-                  "Visualize every n-th timestep.");
-   args.AddOption(&max_tsteps, "-ms", "--max-steps",
-                  "Maximum number of steps (negative means no restriction).");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0) { args.PrintUsage(mfem::out); }
-      return EXIT_FAILURE;
-   }
-   if (myid == 0) { args.PrintOptions(mfem::out); }
-
-   // Mesh *mesh = new Mesh("box-cylinder.mesh");
-   const real_t sx = 3.0, sy = 1.0;
-   const bool generate_edges = true;
-   const auto QUAD = Element::QUADRILATERAL;
-   Mesh mesh = Mesh::MakeCartesian2D(nx, ny, QUAD, generate_edges, sx, sy);
-
-   for (int i = 0; i < serial_refinements; ++i) { mesh.UniformRefinement(); }
-
-   if (Mpi::Root())
-   {
-      std::cout << "Number of elements: " << mesh.GetNE() << std::endl;
-   }
-
-   auto *pmesh = new ParMesh(MPI_COMM_WORLD, mesh);
-
-   // Create the flow solver.
-   IncompressibleNavierSolver flowsolver(pmesh, v_order, p_order, t_order,
-                                         kin_vis);
-   flowsolver.EnablePA(pa);
-
-   // // Set the initial condition.
-   // ParGridFunction *u_ic = flowsolver.GetCurrentVelocity();
-   // VectorFunctionCoefficient u_excoeff(pmesh->Dimension(), vel);
-   // u_ic->ProjectCoefficient(u_excoeff);
-
-   // Add Dirichlet boundary conditions to velocity space restricted to
-   // selected attributes on the mesh.
-   Array<int> attr(pmesh->bdr_attributes.Max());
-   attr = 0;
-   Array<int> attr_inlet(pmesh->bdr_attributes.Max());
-   attr_inlet = 0;
-   // Inlet is attribute 1.
-   attr[0] = 1;
-   // Walls is attribute 3.
-   attr[2] = 1;
-   flowsolver.AddVelDirichletBC(vel, attr);
-
-   attr_inlet[3] = 1;
-   flowsolver.AddVelDirichletBC(vel_inlet, attr_inlet);
-
-   flowsolver.Setup(dt);
-
-   ParGridFunction *u_gf = flowsolver.GetCurrentVelocity();
-   ParGridFunction *p_gf = flowsolver.GetCurrentPressure();
-   ParGridFunction *psi_gf = flowsolver.GetCurrentPsi();
-
-   ParaViewDataCollection pvdc("3dfoc", pmesh);
-   if (use_paraview)
-   {
-      pvdc.SetDataFormat(VTKFormat::BINARY32);
-      // pvdc.SetHighOrderOutput(true);
-      pvdc.SetCycle(0);
-      pvdc.SetTime(t);
-      pvdc.RegisterField("velocity", u_gf);
-      pvdc.RegisterField("pressure", p_gf);
-      pvdc.RegisterField("psi", psi_gf);
-      pvdc.Save();
-   }
-
-   for (int step = 0; !last_step; ++step)
-   {
-      if (step == max_tsteps) { last_step = true; }
-      if (t + dt >= t_final - dt / 2) { last_step = true; }
-      const bool vis_step = last_step || (step % vis_steps) == 0;
-
-      flowsolver.Step(t, dt, step, vis_step);
-
-      if (vis_step)
-      {
-         if (Mpi::Root() && vis_steps)
-         {
-            printf("%11s %11s\n", "Time", "dt");
-            printf("%.5E %.5E\n", t, dt);
-         }
-         if (use_paraview)
-         {
-            pvdc.SetCycle(step);
-            pvdc.SetTime(t);
-            pvdc.Save();
-         }
-      }
-   }
-
-   // flowsolver.PrintTimingData();
-
-   auto reduce = [](ParGridFunction *gf) -> real_t { return (*gf) * (*gf); };
-   // auto reduce = [](ParGridFunction *gf) -> real_t { return gf->Norml2(); };
-   u = reduce(u_gf), p = reduce(p_gf), Ψ = reduce(psi_gf);
-
-   fflush(stdout);
-   delete pmesh;
-
-   return EXIT_SUCCESS;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-#ifndef MFEM_USE_CMAKE_TESTS
-int main(int argc, char *argv[])
-try
-{
-   dbg();
-   double u, p, Ψ; // unused
-   return navier(argc, argv, u, p, Ψ);
-}
-catch (std::exception &e)
-{
-   std::cerr << "\033[31m..xxxXXX[ERROR]XXXxxx.." << std::endl;
-   std::cerr << "\033[31m{}" << e.what() << std::endl;
-   return EXIT_FAILURE;
-}
-#endif // MFEM_USE_CMAKE_TESTS

miniapps/navier/incompressible_navier_dfem.cpp

@@ -1,397 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "mfem.hpp"
-using namespace mfem;
-using namespace mfem::future;
-
-#include "linalg/tensor.hpp"
-using mfem::future::tensor;
-
-#define NVTX_COLOR ::gpu::nvtx::kOrchid
-#include "incompressible_navier_nvtx.hpp"
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-void DiffusionSetup(const ParFiniteElementSpace &sfes,
-                    const IntegrationRule &ir,
-                    const Array<int> &domain_attributes,
-                    ParameterFunction &qdata)
-{
-   NVTX_MARK_FUNCTION;
-   auto pmesh = sfes.GetParMesh();
-   auto nodes = static_cast<ParGridFunction *>(pmesh->GetNodes());
-   auto mfes = nodes->ParFESpace();
-
-   constexpr int U = 0, Ξ = 1, Δ = 2;
-
-   DifferentiableOperator dop(
-   {{ U, &sfes }},
-   {
-      {  { Ξ, mfes },
-         { Δ, &qdata.GetParameterSpace() }
-      }
-   },
-   *pmesh);
-   const auto qfunc =
-      [] MFEM_HOST_DEVICE(const tensor<real_t, DIM, DIM> &J,
-                          const real_t &w)
-   {
-      auto invJ = inv(J);
-      tensor<real_t, DIM, DIM> C{};
-      C(0, 0) = M_PI;
-      C(0, 1) = 0, C(1, 0) = 0;
-      assert(C(0, 1) == 0 && C(1, 0) == 0); // diff otherwise
-      C(1, 1) = 1.0 / M_PI;
-      return tuple{ C * invJ * transpose(invJ) * det(J) * w };
-   };
-   dop.AddDomainIntegrator(qfunc,
-                           tuple{ Gradient<Ξ>{}, Weight{} }, // inputs
-                           tuple{ Identity<Δ>{} },           // outputs
-                           ir, domain_attributes);
-   dop.SetParameters({ nodes, &qdata });
-
-   Vector unused(sfes.GetTrueVSize());
-   dop.Mult(unused, qdata);
-   qdata.HostRead();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-void DiffusionApply(const ParFiniteElementSpace &sfes,
-                    const IntegrationRule &ir,
-                    const Array<int> &domain_attributes,
-                    ParameterFunction &qdata,
-                    const Vector &x, Vector &y)
-{
-   NVTX_MARK_FUNCTION;
-   auto pmesh = sfes.GetParMesh();
-   constexpr int U = 0, Q = 1;
-   auto qd_ps = &qdata.GetParameterSpace();
-   DifferentiableOperator dop({ { U, &sfes } }, { { Q, qd_ps } }, *pmesh);
-   const auto qfunc =[] MFEM_HOST_DEVICE(const tensor<real_t, DIM> &∇u,
-                                         const tensor<real_t, DIM, DIM> &Q)
-   {
-      return tuple{ Q * ∇u };
-   };
-   dop.AddDomainIntegrator(
-      qfunc,
-      tuple{ Gradient<U>{}, Identity<Q>{} },
-      tuple{ Gradient<U>{} },
-      ir, domain_attributes);
-   dop.SetParameters({ &qdata });
-   dop.Mult(x, y);
-   y.HostRead();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-int DiffVerification(ParFiniteElementSpace &h1fes,
-                     const IntegrationRule &ir,
-                     const Vector &qdata,
-                     const Vector &x, const Vector &y)
-{
-   NVTX_MARK_FUNCTION;
-   constexpr real_t ϵ = 1e-12;
-
-   MatrixFunctionCoefficient matrix_coeff(
-      DIM, [](const Vector &, DenseMatrix &C)
-   {
-      C.SetSize(DIM);
-      C(0, 0) = M_PI;
-      C(0, 1) = 0, C(1, 0) = 0;
-      assert(C(0, 1) == 0 && C(1, 0) == 0); // diff otherwise
-      C(1, 1) = 1.0 / M_PI;
-   });
-
-   ParBilinearForm a(&h1fes);
-
-   auto diff_integ = new DiffusionIntegrator(matrix_coeff);
-   diff_integ->SetIntRule(&ir);
-   a.AddDomainIntegrator(diff_integ);
-   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   OperatorPtr A;
-   a.Assemble(), a.Finalize();
-   a.FormSystemMatrix(Array<int> {}, A);
-
-   Vector y2(h1fes.TrueVSize());
-   y2 = 0.0;
-   A->Mult(x, y2);
-   y2.HostRead();
-
-   Vector diff(y2);
-   diff -= y;
-   const auto diff_norm = diff.Norml2();
-   if (diff_norm > ϵ)
-   {
-      dbg("\x1B[31m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-      return EXIT_FAILURE;
-   }
-
-   dbg("\x1B[32m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-   return EXIT_SUCCESS;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-void MassApply(const ParFiniteElementSpace &sfes,
-               const IntegrationRule &ir,
-               const Array<int> &domain_attributes,
-               const Vector &x, Vector &y)
-{
-   dbg();
-   auto &pmesh = *sfes.GetParMesh();
-   auto *nodes = static_cast<ParGridFunction *>(pmesh.GetNodes());
-   auto *mfes = nodes->ParFESpace();
-   constexpr int U = 0, Coords = 1;
-   DifferentiableOperator dop({{ U, &sfes }}, {{ Coords, mfes }}, pmesh);
-   const auto mf_mass_qf =
-      [](const real_t &dudxi,
-         const tensor<real_t, DIM, DIM> &J,
-         const real_t &w)
-   {
-      return tuple{ dudxi * w * det(J) };
-   };
-   dop.AddDomainIntegrator(
-      mf_mass_qf,
-      tuple{ Value<U>{}, Gradient<Coords>{}, Weight{} },
-      tuple{ Value<U>{} },
-      ir, domain_attributes);
-   dop.SetParameters({ nodes });
-   // Vector X(sfes.GetTrueVSize()), Y(sfes.GetTrueVSize());
-   // sfes.GetRestrictionMatrix()->Mult(x, X);
-   // dop.Mult(X, Y);
-   dop.Mult(x, y);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-int MassVerification(ParFiniteElementSpace &h1fes,
-                     const IntegrationRule &ir,
-                     const Vector &x, Vector &y)
-{
-   ParBilinearForm a(&h1fes);
-   auto mass_integ = new MassIntegrator;
-   mass_integ->SetIntRule(&ir);
-   a.AddDomainIntegrator(mass_integ);
-   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   a.Assemble(), a.Finalize();
-   Vector y2(h1fes.TrueVSize());
-   a.Mult(x, y2);
-   y2.HostRead();
-
-   Vector diff(y2);
-   diff -= y;
-
-   const auto diff_norm = diff.Norml2();
-   constexpr real_t ϵ = 1e-12;
-   if (diff_norm > ϵ)
-   {
-      dbg("\x1B[31m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-      return EXIT_FAILURE;
-   }
-   dbg("\x1B[32m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-   return EXIT_SUCCESS;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM>
-void VectorDiffApply(const ParFiniteElementSpace &vfes,
-                     const IntegrationRule &ir,
-                     const Array<int> &domain_attributes,
-                     const Vector &x,
-                     Vector &y)
-{
-   NVTX_MARK_FUNCTION;
-   auto pmesh = vfes.GetParMesh();
-   auto nodes = static_cast<ParGridFunction *>(pmesh->GetNodes());
-   auto mfes = nodes->ParFESpace();
-   constexpr int U = 0, Coords = 1;
-   DifferentiableOperator dop({{ U, &vfes }}, {{ Coords, mfes }}, *pmesh);
-   const auto qfunc =
-      [] MFEM_HOST_DEVICE(const tensor<real_t, DIM, DIM> &∇u,
-                          const tensor<real_t, DIM, DIM> &J, const real_t &w)
-   {
-      return tuple{ ∇u * inv(J) * det(J) * w * transpose(inv(J)) };
-   };
-   dop.AddDomainIntegrator(qfunc,
-                           tuple{ Gradient<U>{}, Gradient<Coords>{}, Weight{} },
-                           tuple{ Gradient<U>{} },
-                           ir, domain_attributes);
-   dop.SetParameters({ nodes });
-   dop.Mult(x, y);
-   y.HostRead();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-template <int DIM, int VDIM = DIM>
-int VectorDiffVerif(ParFiniteElementSpace &h1fes,
-                    const IntegrationRule &ir, const Vector &x,
-                    Vector &y)
-{
-   NVTX_MARK_FUNCTION;
-   ParBilinearForm a(&h1fes);
-   auto A_integ = new VectorDiffusionIntegrator(VDIM);
-   A_integ->SetIntRule(&ir);
-   a.AddDomainIntegrator(A_integ);
-   a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   a.Assemble(), a.Finalize();
-   Vector y2(h1fes.TrueVSize());
-   a.Mult(x, y2);
-   y2.HostRead();
-
-   Vector diff(y2);
-   diff -= y;
-
-   const auto diff_norm = diff.Norml2();
-   constexpr real_t ϵ = 1e-12;
-   if (diff_norm > ϵ)
-   {
-      dbg("\x1B[31m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-      return EXIT_FAILURE;
-   }
-   dbg("\x1B[32m||dFdu_FD u^* - ex||_l2 = {}", diff_norm);
-   return EXIT_SUCCESS;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-int main(int argc, char *argv[]) try
-{
-   NVTX_MARK_FUNCTION;
-   constexpr int DIM = 2, VDIM = DIM;
-
-   static mfem::MPI_Session mpi(argc, argv);
-   const int myid = mpi.WorldRank();
-   Hypre::Init();
-
-   const char *device_config = "cpu";
-   const char *mesh_file = "none";
-   int serial_refinements = 0;
-   int nx = 1, ny = 1;
-   int p = 1;
-   bool visualization = false;
-   bool pa = false;
-
-   std::cout.precision(8);
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
-   args.AddOption(&p, "-o", "--order", "Finite element order.");
-   args.AddOption(&serial_refinements, "-sr", "--serial-refinements",
-                  "Number serial refinements.");
-   args.AddOption(&nx, "-nx", "--nx", "Number of elements in X.");
-   args.AddOption(&ny, "-ny", "--ny", "Number of elements in Y.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
-                  "--no-partial-assembly",
-                  "Enable or disable partial assembly.");
-   args.AddOption(&device_config, "-d", "--device",
-                  "Device configuration string, see Device::Configure().");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0) { args.PrintUsage(mfem::out); }
-      return EXIT_FAILURE;
-   }
-   if (myid == 0) { args.PrintOptions(mfem::out); }
-
-   Mesh smesh;
-   if (std::string(mesh_file) != "none")
-   {
-      smesh = Mesh(mesh_file);
-   }
-   else
-   {
-      const real_t sx = 3.0, sy = 1.0;
-      const bool generate_edges = true;
-      const auto QUAD = Element::QUADRILATERAL;
-      smesh = Mesh::MakeCartesian2D(nx, ny, QUAD, generate_edges, sx, sy);
-   }
-   MFEM_ASSERT(smesh.Dimension() == 2, "2D mesh required!");
-
-   for (int i = 0; i < serial_refinements; ++i) { smesh.UniformRefinement(); }
-
-   dbg("Number of elements: {}", smesh.GetNE());
-   ParMesh pmesh(MPI_COMM_WORLD, smesh);
-   smesh.Clear();
-
-   pmesh.EnsureNodes();
-   pmesh.SetCurvature(p);
-   assert(DIM == pmesh.Dimension());
-
-   Array<int> domain_attributes;
-   if (pmesh.attributes.Size() > 0)
-   {
-      domain_attributes.SetSize(pmesh.attributes.Max());
-      domain_attributes = 1;
-   }
-
-   H1_FECollection fec(p, DIM);
-   ParFiniteElementSpace fes(&pmesh, &fec), vfes(&pmesh, &fec, VDIM);
-   dbg("#dofs:{} ", fes.GetTrueVSize());
-
-   const auto &fe = *fes.GetFE(0);
-   const auto &ir =
-      IntRules.Get(fe.GetGeomType(), fe.GetOrder() + fe.GetOrder() + fe.GetDim() - 1);
-
-   dbg("#ndof per el = {}", fe.GetDof());
-   dbg("#nqp = {}", ir.GetNPoints());
-   dbg("#q1d = {}", (int)floor(pow(ir.GetNPoints(), 1.0 / DIM) + 0.5));
-
-   ParGridFunction f1_gf(&fes);
-
-   auto f1 = [](const Vector &coords)
-   {
-      assert(DIM == 2);
-      const double x = coords(0), y = coords(1);
-      return M_PI + x + x * x + x * y + y;
-   };
-   FunctionCoefficient f1_c(f1);
-   f1_gf.ProjectCoefficient(f1_c);
-
-   Vector x(f1_gf), y(fes.GetTrueVSize());
-
-   UniformParameterSpace qd_ps(pmesh, ir, DIM * DIM);
-   ParameterFunction qdata(qd_ps);
-
-   dbg("Diffusion setup, apply & verification");
-   DiffusionSetup<DIM>(fes, ir, domain_attributes, qdata);
-   DiffusionApply<DIM>(fes, ir, domain_attributes, qdata, x, y);
-   if (DiffVerification<DIM>(fes, ir, qdata, x, y) != EXIT_SUCCESS) { return EXIT_FAILURE; }
-
-   dbg("Mass apply & verification");
-   MassApply<DIM>(fes, ir, domain_attributes, x, y);
-   if (MassVerification<DIM>(fes, ir, x, y) != EXIT_SUCCESS) { return EXIT_FAILURE; }
-
-   dbg("Vector diffusion apply");
-   VectorFunctionCoefficient vf1_c(VDIM, [](const Vector &coords, Vector &u)
-   {
-      assert(DIM == 2);
-      const double x = coords(0), y = coords(1);
-      u(0) = M_PI + 0.25 * x * x * y + y * y * x;
-      u(1) = M_PI - 0.25 * x * y * y + y * x * x;
-   });
-   ParGridFunction vf1_gf(&vfes);
-   vf1_gf.ProjectCoefficient(vf1_c);
-   Vector vx(vf1_gf), vy(vfes.GetTrueVSize());
-   VectorDiffApply<DIM>(vfes, ir, domain_attributes, vx, vy);
-   if (VectorDiffVerif<DIM>(vfes, ir, vx, vy) != EXIT_SUCCESS) { return EXIT_FAILURE; }
-
-   return EXIT_SUCCESS;
-}
-catch (std::exception &e)
-{
-   std::cerr << "\033[31m..xxxXXX[ERROR]XXXxxx.." << std::endl;
-   std::cerr << "\033[31m{}" << e.what() << std::endl;
-   return EXIT_FAILURE;
-}

miniapps/navier/incompressible_navier_nvtx.hpp

@@ -1,478 +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.
-#pragma once
-
-#define FMT_HEADER_ONLY
-#include <fmt/format.h>
-
-#include <array>
-#include <cassert>
-#include <cstddef>
-#include <cstdint>
-#include <iomanip>
-#include <iostream>
-#include <memory>
-#include <mutex>
-#include <stack>
-#include <string>
-
-#ifdef MFEM_USE_CALIPER
-#include <caliper/cali.h>
-#endif
-
-#ifdef MFEM_USE_CUDA
-#include <cudaProfiler.h>
-#include <cuda_runtime_api.h>
-#include <nvToolsExt.h>
-#else
-struct nvtxEventAttributes_t
-{
-   int version;
-   int size;
-   int category;
-   int colorType;
-   uint32_t color;
-   int payloadType;
-   uint64_t payload;
-   int messageType;
-   struct
-   {
-      std::string ascii;
-   } message;
-};
-#define NVTX_VERSION 1
-#define NVTX_EVENT_ATTRIB_STRUCT_SIZE 256
-#define NVTX_COLOR_ARGB 0
-#define NVTX_MESSAGE_TYPE_ASCII 0
-#define nvtxRangePushEx(...)
-#define nvtxRangePop(...)
-#define cudaStreamSynchronize(...)
-#endif
-
-namespace gpu::nvtx
-{
-
-///////////////////////////////////////////////////////////////////////////////
-// https://en.wikipedia.org/wiki/Web_colors#Extended_colors
-// http://www.calmar.ws/vim/256-xterm-24bit-rgb-color-chart.html
-// clang-format off
-enum color_names
-{
-   kBlack = 0, kNavyBlue, kDarkBlue, kMediumBlue, kBlue, kDarkGreen, kWebGreen, kTeal,
-   kDarkCyan, kDeepSkyBlue, kDarkTurquoise, kMediumSpringGreen, kGreen, kLime,
-   kSpringGreen, kAqua, kCyan, kMidnightBlue, kDodgerBlue, kLightSeaGreen, kForestGreen,
-   kSeaGreen, kDarkSlateGray, kLimeGreen, kMediumSeaGreen, kTurquoise, kRoyalBlue,
-   kSteelBlue, kDarkSlateBlue, kMediumTurquoise, kIndigo, kDarkOliveGreen, kCadetBlue,
-   kCornflower, kRebeccaPurple, kMediumAquamarine, kDimGray, kSlateBlue, kOliveDrab,
-   kSlateGray, kLightSlateGray, kMediumSlateBlue, kLawnGreen, kWebMaroon, kWebPurple,
-   kChartreuse, kAquamarine, kOlive, kWebGray, kSkyBlue, kLightSkyBlue, kBlueViolet,
-   kDarkRed, kDarkMagenta, kSaddleBrown, kDarkSeaGreen, kLightGreen, kMediumPurple,
-   kDarkViolet, kPaleGreen, kDarkOrchid, kYellowGreen, kPurple, kSienna, kBrown,
-   kDarkGray, kLightBlue, kGreenYellow, kPaleTurquoise, kMaroon, kLightSteelBlue,
-   kPowderBlue, kFirebrick, kDarkGoldenrod, kMediumOrchid, kRosyBrown, kDarkKhaki,
-   kGray, kSilver, kMediumVioletRed, kIndianRed, kPeru, kChocolate, kTan, kLightGray,
-   kThistle, kOrchid, kGoldenrod, kPaleVioletRed, kCrimson, kGainsboro, kPlum, kBurlywood,
-   kLightCyan, kLavender, kDarkSalmon, kViolet, kPaleGoldenrod, kLightCoral, kKhaki,
-   kAliceBlue, kHoneydew, kAzure, kSandyBrown, kWheat, kBeige, kWhiteSmoke, kMintCream,
-   kGhostWhite, kSalmon, kAntiqueWhite, kLinen, kLightGoldenrod, kOldLace, kRed,
-   kFuchsia, kMagenta, kDeepPink, kOrangeRed, kTomato, kHotPink, kCoral, kDarkOrange,
-   kLightSalmon, kOrange, kLightPink, kPink, kGold, kPeachPuff, kNavajoWhite, kMoccasin,
-   kBisque, kMistyRose, kBlanchedAlmond, kPapayaWhip, kLavenderBlush, kSeashell,
-   kCornsilk, kLemonChiffon, kFloralWhite, kSnow, kYellow, kLightYellow, kIvory, kWhite,
-   kNvidia
-};
-// clang-format on
-
-static constexpr int kNumHexColors = 146;
-static constexpr std::array<uint32_t, kNumHexColors> kHexColors =
-{
-   {
-      0x000000, 0x000080, 0x00008B, 0x0000CD, 0x0000FF, 0x006400, 0x008000,
-      0x008080, 0x008B8B, 0x00BFFF, 0x00CED1, 0x00FA9A, 0x00FF00, 0x00FF00,
-      0x00FF7F, 0x00FFFF, 0x00FFFF, 0x191970, 0x1E90FF, 0x20B2AA, 0x228B22,
-      0x2E8B57, 0x2F4F4F, 0x32CD32, 0x3CB371, 0x40E0D0, 0x4169E1, 0x4682B4,
-      0x483D8B, 0x48D1CC, 0x4B0082, 0x556B2F, 0x5F9EA0, 0x6495ED, 0x663399,
-      0x66CDAA, 0x696969, 0x6A5ACD, 0x6B8E23, 0x708090, 0x778899, 0x7B68EE,
-      0x7CFC00, 0x7F0000, 0x7F007F, 0x7FFF00, 0x7FFFD4, 0x808000, 0x808080,
-      0x87CEEB, 0x87CEFA, 0x8A2BE2, 0x8B0000, 0x8B008B, 0x8B4513, 0x8FBC8F,
-      0x90EE90, 0x9370DB, 0x9400D3, 0x98FB98, 0x9932CC, 0x9ACD32, 0xA020F0,
-      0xA0522D, 0xA52A2A, 0xA9A9A9, 0xADD8E6, 0xADFF2F, 0xAFEEEE, 0xB03060,
-      0xB0C4DE, 0xB0E0E6, 0xB22222, 0xB8860B, 0xBA55D3, 0xBC8F8F, 0xBDB76B,
-      0xBEBEBE, 0xC0C0C0, 0xC71585, 0xCD5C5C, 0xCD853F, 0xD2691E, 0xD2B48C,
-      0xD3D3D3, 0xD8BFD8, 0xDA70D6, 0xDAA520, 0xDB7093, 0xDC143C, 0xDCDCDC,
-      0xDDA0DD, 0xDEB887, 0xE0FFFF, 0xE6E6FA, 0xE9967A, 0xEE82EE, 0xEEE8AA,
-      0xF08080, 0xF0E68C, 0xF0F8FF, 0xF0FFF0, 0xF0FFFF, 0xF4A460, 0xF5DEB3,
-      0xF5F5DC, 0xF5F5F5, 0xF5FFFA, 0xF8F8FF, 0xFA8072, 0xFAEBD7, 0xFAF0E6,
-      0xFAFAD2, 0xFDF5E6, 0xFF0000, 0xFF00FF, 0xFF00FF, 0xFF1493, 0xFF4500,
-      0xFF6347, 0xFF69B4, 0xFF7F50, 0xFF8C00, 0xFFA07A, 0xFFA500, 0xFFB6C1,
-      0xFFC0CB, 0xFFD700, 0xFFDAB9, 0xFFDEAD, 0xFFE4B5, 0xFFE4C4, 0xFFE4E1,
-      0xFFEBCD, 0xFFEFD5, 0xFFF0F5, 0xFFF5EE, 0xFFF8DC, 0xFFFACD, 0xFFFAF0,
-      0xFFFAFA, 0xFFFF00, 0xFFFFE0, 0xFFFFF0, 0xFFFFFF, 0x76B900
-   }
-};
-
-///////////////////////////////////////////////////////////////////////////////
-constexpr size_t static_strlen(const char *str)
-{
-   return *str == '\0' ? 0 : static_strlen(str + 1) + 1;
-}
-
-constexpr uint8_t static_checksum8(const char *bfr)
-{
-   unsigned int chk = 0;
-   size_t len = static_strlen(bfr);
-   for (; len; len--, bfr++) { chk += static_cast<unsigned int>(*bfr); }
-   return static_cast<uint8_t>(chk);
-}
-
-constexpr char *static_strrnchr(const char *str, const char c, int n)
-{
-   size_t len = static_strlen(str);
-   char *p = const_cast<char *>(str) + len - 1;
-   for (; n; n--, p--, len--)
-   {
-      for (; len; p--, len--)
-      {
-         if (*p == c) { break; }
-      }
-      if (!len) { return nullptr; }
-      if (n == 1) { return p; }
-   }
-   return nullptr;
-}
-
-inline uint32_t static_color(const uint8_t COLOR, const int RANK,
-                             const char *FILE)
-{
-   constexpr auto kMpiColorShift = 1;
-   const auto rank_shift = kMpiColorShift * RANK;
-   if (COLOR > 0) { return kHexColors[COLOR + rank_shift]; }
-   const auto file_color = static_checksum8(FILE);
-   return kHexColors[(file_color + rank_shift) % kNumHexColors];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// Helpers to generate unique variable names
-#define NVTX_FLF __FILE__, __LINE__, __FUNCTION__
-#define NVTX_PRIVATE_NAME(prefix) NVTX_PRIVATE_CONCAT(prefix, __LINE__)
-#define NVTX_PRIVATE_CONCAT(a, b) NVTX_PRIVATE_CONCAT2(a, b)
-#define NVTX_PRIVATE_CONCAT2(a, b) a##b
-
-#ifndef NVTX_COLOR
-#define NVTX_COLOR ::gpu::nvtx::kBlack
-#endif
-
-///////////////////////////////////////////////////////////////////////////////
-struct Debug
-{
-   const bool debug = false, end = true;
-
-   inline Debug() = default;
-
-   inline Debug(const int RANK, const char *FILE, const int LINE,
-                const char *FUNC, uint8_t COLOR, bool ini = true,
-                bool END = true): debug(true), end(END)
-   {
-      const char *base = static_strrnchr(FILE, '/', 2);
-      const char *file = base ? base + 1 : FILE;
-      const uint32_t rgb = static_color(COLOR, RANK, FILE);
-      const uint8_t r = (rgb >> 16) & 0xFF, g = (rgb >> 8) & 0xFF,
-                    b = rgb & 0xFF;
-      std::cout << "\033[38;2;";
-      std::cout << std::to_string(r) << ";";
-      std::cout << std::to_string(g) << ";";
-      std::cout << std::to_string(b) << "m";
-      if (ini)
-      {
-         std::cout << RANK << std::setw(64) << file << ":";
-         std::cout << "\033[2m" << std::setw(4) << std::left << LINE
-                   << "\033[22m: ";
-         if (FUNC) { std::cout << "[" << FUNC << "] "; }
-      }
-      std::cout << std::right << "\033[1m";
-   }
-
-   inline ~Debug()
-   {
-      if (debug) { std::cout << "\033[m" << (end ? "\n" : "") << std::flush; }
-   }
-
-   template <typename T>
-   inline void operator<<(const T &arg) const noexcept
-   {
-      if (debug) { std::cout << arg; }
-   }
-
-   template <typename T>
-   inline void operator()(const T &arg) const noexcept
-   {
-      if (debug) { this->operator<<(arg); }
-   }
-
-   template <typename... Args>
-   inline void operator()(const char *fmt, Args &&...args) const noexcept
-   {
-      if (debug) { std::cout << fmt::format(fmt, std::forward<Args>(args)...); }
-   }
-
-   inline void operator()() const noexcept {}
-
-   static Debug Set(const char *FILE, const int LINE, const char *FUNC,
-                    uint8_t COLOR, bool INI = true, bool END = true)
-   {
-      static int mpi_rank = 0, dbg_mpi_rank = 0;
-      static bool env_mpi = false, env_dbg = false;
-      if (static bool ini = false; !std::exchange(ini, true))
-      {
-         env_dbg = (getenv("MFEM_DEBUG") != nullptr);
-         env_mpi = getenv("MFEM_DEBUG_MPI") != nullptr;
-         // int mpi_flag = 0;
-         // MPI_Initialized(&mpi_flag);
-         // if (mpi_flag) { MPI_Comm_rank(MPI_COMM_WORLD, &mpi_rank); }
-         dbg_mpi_rank = atoi(env_mpi ? getenv("MFEM_DEBUG_MPI") : "0");
-      }
-      const bool debug = (env_dbg && (!env_mpi || (dbg_mpi_rank == mpi_rank)));
-      return debug ? Debug(mpi_rank, FILE, LINE, FUNC, COLOR, INI, END)
-             : Debug();
-   }
-};
-
-// Debug console traces, unnamed
-#define NVTX_DEBUG(...)                                                  \
-   ::gpu::nvtx::Debug::Set(NVTX_FLF, NVTX_COLOR).operator()(__VA_ARGS__)
-
-#define NVTX_DEBUG_NO_INI(...)                                \
-   ::gpu::nvtx::Debug::Set(NVTX_FLF, NVTX_COLOR, false, true) \
-      .operator()(__VA_ARGS__)
-
-#define NVTX_DEBUG_APPEND(...)                                 \
-   ::gpu::nvtx::Debug::Set(NVTX_FLF, NVTX_COLOR, false, false) \
-      .operator()(__VA_ARGS__)
-
-#define NVTX_DEBUG_NO_END(...)                                \
-   ::gpu::nvtx::Debug::Set(NVTX_FLF, NVTX_COLOR, true, false) \
-      .operator()(__VA_ARGS__)
-
-///////////////////////////////////////////////////////////////////////////////
-struct Nvtx
-{
-   const bool nvtx = false, enforce_kernel_sync = false;
-   const char *base, *file;
-   const uint32_t color = kBlack;
-   mutable std::string ascii;
-   mutable nvtxEventAttributes_t event;
-   mutable bool pushed = false;
-
-   inline Nvtx() = default;
-
-   Nvtx(bool enforce_kernel_sync, const char *FILE, const int LINE,
-        const char *FUNC, uint8_t COLOR):
-      nvtx(true), enforce_kernel_sync(enforce_kernel_sync),
-      base(static_strrnchr(FILE, '/', 2)), file(base ? base + 1 : FILE),
-      color(COLOR), ascii(file), event({})
-   {
-      event.version = NVTX_VERSION;
-      event.size = NVTX_EVENT_ATTRIB_STRUCT_SIZE;
-      event.colorType = NVTX_COLOR_ARGB;
-      event.color = static_color(COLOR, 0, FILE);
-      event.messageType = NVTX_MESSAGE_TYPE_ASCII;
-
-      ascii += ":";
-      ascii += std::to_string(LINE);
-      ascii += ":[";
-      ascii += FUNC;
-      ascii += "] ";
-
-      pushed = false;
-   }
-
-   explicit Nvtx(const char *title, uint8_t color = kWheat,
-                 bool enforce_kernel_sync = true):
-      nvtx(true), enforce_kernel_sync(enforce_kernel_sync), color(color),
-      ascii(title), event({})
-   {
-      event.version = NVTX_VERSION;
-      event.size = NVTX_EVENT_ATTRIB_STRUCT_SIZE;
-      event.colorType = NVTX_COLOR_ARGB;
-      event.color = static_color(color, 0, "");
-      event.messageType = NVTX_MESSAGE_TYPE_ASCII;
-      event.message.ascii = ascii.c_str();
-      nvtxRangePushEx(&event);
-      pushed = true;
-   }
-
-   inline void operator()() const
-   {
-      if (!nvtx) { return; }
-      event.message.ascii = ascii.c_str();
-      assert(!pushed);
-      nvtxRangePushEx(&event);
-      pushed = true;
-   }
-
-   template <typename T>
-   inline void operator()(const T &arg) const
-   {
-      if (!nvtx) { return; }
-      this->operator<<(arg);
-      event.message.ascii = ascii.c_str();
-      assert(!pushed);
-      nvtxRangePushEx(&event);
-      pushed = true;
-   }
-
-   template <typename... Args>
-   inline void operator()(fmt::format_string<Args...> fmt, Args &&...args) const
-   {
-      if (!nvtx) { return; }
-      ascii += fmt::format(fmt, std::forward<Args>(args)...);
-      event.message.ascii = ascii.c_str();
-      assert(!pushed);
-      nvtxRangePushEx(&event);
-      pushed = true;
-   }
-
-   template <typename T>
-   inline void operator<<(const T &arg) const
-   {
-      if (nvtx) { ascii += arg; }
-   }
-
-   inline ~Nvtx()
-   {
-      if (!nvtx) { return; }
-      if (enforce_kernel_sync)
-      {
-         nvtxEventAttributes_t eks = {};
-         eks.version = NVTX_VERSION;
-         eks.size = NVTX_EVENT_ATTRIB_STRUCT_SIZE;
-         eks.category = 0; // user value
-         eks.colorType = NVTX_COLOR_ARGB;
-         eks.messageType = NVTX_MESSAGE_TYPE_ASCII;
-         eks.message.ascii = "!"; // enforce kernel synchronization
-         eks.color = kHexColors[kYellow];
-         nvtxRangePushEx(&eks);
-         cudaStreamSynchronize(nullptr);
-         nvtxRangePop(/*eks*/);
-      }
-      assert(pushed);
-      nvtxRangePop(/*event*/);
-   }
-
-   using nvtx_ptr = std::unique_ptr<Nvtx>;
-   using nvtx_stack_t = std::stack<nvtx_ptr>;
-
-   static nvtx_ptr Set(const char *FILE, const int LINE, const char *FUNC,
-                       uint8_t COLOR)
-   {
-      static bool nvtx = false, eks = false;
-      if (static bool ini = false; !std::exchange(ini, true))
-      {
-         eks = getenv("MFEM_EKS") != nullptr;
-         nvtx = getenv("MFEM_NVTX") != nullptr;
-         Nvtx force_first_eks("Init EKS", kYellow, true);
-      }
-      return nvtx_ptr(nvtx ? new Nvtx(eks, FILE, LINE, FUNC, COLOR)
-                      : new Nvtx());
-   }
-
-   static nvtx_stack_t &Stack()
-   {
-      auto nvtx_events = []() -> nvtx_stack_t &
-      {
-         static nvtx_stack_t events;
-         return events;
-      };
-      static std::once_flag ready;
-      // one touch to guarantee the object is ready
-      std::call_once(ready, [&] { nvtx_events(); });
-      return nvtx_events();
-   }
-};
-
-// Temporary object only alive for the current statement
-#define NVTX_(COLOR, ...)                                       \
-   NVTX_DEBUG(__VA_ARGS__);                                     \
-   std::unique_ptr<::gpu::nvtx::Nvtx> NVTX_PRIVATE_NAME(nvtx) = \
-      ::gpu::nvtx::Nvtx::Set(NVTX_FLF, COLOR);                  \
-   NVTX_PRIVATE_NAME(nvtx)->operator()(__VA_ARGS__)
-
-// Temporary object only alive for the current statement
-#define NVTX(...) NVTX_(NVTX_COLOR, __VA_ARGS__)
-
-// Begin(with color)/End NVTX event traces
-#define NVTX_BEGIN_(COLOR, ...)                                              \
-   NVTX_DEBUG(__VA_ARGS__);                                                  \
-   ::gpu::nvtx::Nvtx::Stack().push(::gpu::nvtx::Nvtx::Set(NVTX_FLF, COLOR)); \
-   ::gpu::nvtx::Nvtx::Stack().top()->operator()(__VA_ARGS__)
-
-// Begin/End NVTX event traces
-#define NVTX_BEGIN(...) NVTX_BEGIN_(NVTX_COLOR, __VA_ARGS__);
-
-#define NVTX_END(...)                        \
-   ::gpu::nvtx::Nvtx::Stack().top().reset(); \
-   ::gpu::nvtx::Nvtx::Stack().pop()
-
-#ifdef USE_CALIPER
-// CALIPER & NVTX marks
-#define NVTX_MARK_FUNCTION                                            \
-      NVTX();                                                            \
-      std::unique_ptr<cali::Function> __cali_ann##__func__;              \
-      __cali_ann##__func__ = std::make_unique<cali::Function>(__func__);
-
-#define NVTX_MARK(...)                                                   \
-      NVTX(__VA_ARGS__);                                                    \
-      std::unique_ptr<cali::Function> __cali_ann##__func__;                 \
-      __cali_ann##__func__ = std::make_unique<cali::Function>(__VA_ARGS__);
-
-#define NVTX_MARK_FUNCTION_NAME(STR_NAME)                                \
-      NVTX(STR_NAME);                                                       \
-      std::unique_ptr<cali::Function> __cali_ann##__func__;                 \
-      if (g_caliper)                                                        \
-      {                                                                     \
-         __cali_ann##__func__ = std::make_unique<cali::Function>(STR_NAME); \
-      }
-
-#define NVTX_MARK_BEGIN(...)     \
-      CALI_MARK_BEGIN(__VA_ARGS__); \
-      NVTX_BEGIN(__VA_ARGS__);
-
-#define NVTX_MARK_END(...)     \
-      NVTX_END(__VA_ARGS__);      \
-      CALI_MARK_END(__VA_ARGS__);
-#else
-#define NVTX_MARK_FUNCTION NVTX()
-#define NVTX_MARK(...) NVTX(__VA_ARGS__)
-#define NVTX_MARK_FUNCTION_NAME(...) NVTX(__VA_ARGS__)
-#define NVTX_MARK_BEGIN(...) NVTX_BEGIN(__VA_ARGS__)
-#define NVTX_MARK_END(...) NVTX_END(__VA_ARGS__)
-#endif
-
-} // namespace gpu::nvtx
-
-// Debug console traces, unnamed
-#if 1
-#define dbg(...) NVTX_DEBUG(__VA_ARGS__)
-#define dbl(...) NVTX_DEBUG_NO_END(__VA_ARGS__)
-#define dba(...) NVTX_DEBUG_APPEND(__VA_ARGS__)
-#define dbc(...) NVTX_DEBUG_NO_INI(__VA_ARGS__)
-#else
-#define dbg(...)
-#define dbl(...) (void)0
-#define dba(...)
-#define dbc(...)
-#endif
-
-inline bool ClearScreen()
-{
-   dbg("\x1B[2J\x1B[3J\x1B[H");
-   return true;
-}

miniapps/navier/incompressible_navier_solver.cpp

@@ -1,490 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "incompressible_navier_solver.hpp"
-
-#define NVTX_COLOR ::gpu::nvtx::kCyan
-#include "incompressible_navier_nvtx.hpp"
-
-using namespace mfem;
-using namespace incompressible_navier;
-
-IncompressibleNavierSolver::IncompressibleNavierSolver(ParMesh *mesh,
-                                                       int velorder, int porder,
-                                                       int torder,
-                                                       real_t kin_vis):
-   pmesh(mesh), velorder(velorder), porder(porder), torder(torder),
-   kin_vis(kin_vis), gll_rules(0, Quadrature1D::GaussLobatto),
-   vfec(new H1_FECollection(velorder, pmesh->Dimension())),
-   psifec(new H1_FECollection(porder)), pfec(new H1_FECollection(porder)),
-   vfes(new ParFiniteElementSpace(pmesh, vfec, pmesh->Dimension())),
-   psifes(new ParFiniteElementSpace(pmesh, pfec)),
-   pfes(new ParFiniteElementSpace(pmesh, pfec)),
-
-   velGF(torder + 1, nullptr), pGF(torder + 1, nullptr)
-{
-   NVTX();
-   // Check if fully periodic mesh
-   if (!(pmesh->bdr_attributes.Size() == 0))
-   {
-      vel_ess_attr.SetSize(pmesh->bdr_attributes.Max());
-      vel_ess_attr = 0;
-
-      pres_ess_attr.SetSize(pmesh->bdr_attributes.Max());
-      pres_ess_attr = 0;
-   }
-
-   for (int i = 0; i < torder + 1; i++)
-   {
-      velGF[i] = new ParGridFunction(vfes);
-      *velGF[i] = 0.0;
-      pGF[i] = new ParGridFunction(pfes);
-      *pGF[i] = 0.0;
-   }
-
-   psiGF.SetSpace(psifes);
-   DvGF.SetSpace(vfes);
-   divVelGF.SetSpace(pfes);
-   pRHS.SetSpace(pfes);
-}
-
-void IncompressibleNavierSolver::Setup(real_t dt)
-{
-   if (verbose && pmesh->GetMyRank() == 0)
-   {
-      mfem::out << "Setup" << std::endl;
-      if (partial_assembly)
-      {
-         mfem::out << "Using Partial Assembly" << std::endl;
-      }
-      else { mfem::out << "Using Full Assembly" << std::endl; }
-   }
-
-   this->Setup_velocity(dt);
-
-   this->Setup_auxiliary(dt);
-
-   this->Setup_pressure(dt);
-}
-
-void IncompressibleNavierSolver::Setup_velocity(real_t dt)
-{
-   // GLL integration rule (Numerical Integration)
-   const IntegrationRule &ir_ni =
-      gll_rules.Get(vfes->GetFE(0)->GetGeomType(), 2 * velorder - 1);
-
-   vfes->GetEssentialTrueDofs(vel_ess_attr, vel_ess_tdof);
-
-   //-------------------------------------------------------------------------
-
-   // Setup of coefficient for mass term of Eq(13)
-   dtCoeff = new ConstantCoefficient(1.0 / dt);
-   auto *vmass_blfi = new VectorMassIntegrator(*dtCoeff);
-
-   // Setup of coefficient for stiffness term of Eq(13)
-   kinvisCoeff = new ConstantCoefficient(kin_vis);
-   auto *vdiff_blfi = new VectorDiffusionIntegrator(*kinvisCoeff);
-
-   // setup of Bilinear form of Eq(13)
-   velBForm = new ParBilinearForm(vfes);
-   if (numerical_integ)
-   {
-      vmass_blfi->SetIntRule(&ir_ni);
-      vdiff_blfi->SetIntRule(&ir_ni);
-   }
-   velBForm->AddDomainIntegrator(vmass_blfi);
-   velBForm->AddDomainIntegrator(vdiff_blfi);
-   if (partial_assembly) { velBForm->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-
-   velBForm->Assemble();
-   velBForm->FormSystemMatrix(vel_ess_tdof, vOp);
-
-   //-------------------------------------------------------------------------
-
-   // Setup of coefficient for Eq(18)
-   pUnitVectorCoeff = new UnitVectorGridFunctionCoeff(pmesh->Dimension());
-   auto *pvel_lfi = new VectorDomainLFGradIntegrator(*pUnitVectorCoeff);
-
-   // Setup of coefficient for Eq(20)
-   nonlinTermCoeff = new NonLinTermVectorGridFunctionCoeff(pmesh->Dimension());
-   auto *p_nonlintermlfi = new VectorDomainLFIntegrator(*nonlinTermCoeff);
-
-   // Setup of coefficient for Eq(21)
-   prevVelLoadCoeff = new PrevVelVectorGridFunctionCoeff(pmesh->Dimension());
-   auto *prevVelLoadLFi = new VectorDomainLFIntegrator(*prevVelLoadCoeff);
-
-   // Setup of linear form of Eq(13)
-   velLForm = new ParLinearForm(vfes);
-   if (numerical_integ)
-   {
-      prevVelLoadLFi->SetIntRule(&ir_ni);
-      pvel_lfi->SetIntRule(&ir_ni);
-      p_nonlintermlfi->SetIntRule(&ir_ni);
-   }
-   velLForm->AddDomainIntegrator(prevVelLoadLFi);
-   velLForm->AddDomainIntegrator(pvel_lfi);
-   velLForm->AddDomainIntegrator(p_nonlintermlfi);
-
-   //-------------------------------------------------------------------------
-
-   if (partial_assembly)
-   {
-      Vector diag_pa(vfes->GetTrueVSize());
-      velBForm->AssembleDiagonal(diag_pa);
-      velInvPC = new OperatorJacobiSmoother(diag_pa, vel_ess_tdof);
-   }
-   else
-   {
-      velInvPC = new HypreSmoother(*vOp.As<HypreParMatrix>());
-      dynamic_cast<HypreSmoother *>(velInvPC)->SetType(HypreSmoother::Jacobi,
-                                                       1);
-   }
-
-   velInv = new CGSolver(vfes->GetComm());
-   velInv->iterative_mode = true;
-   velInv->SetOperator(*vOp);
-   velInv->SetPreconditioner(*velInvPC);
-   velInv->SetPrintLevel(pl_velsolve);
-   velInv->SetRelTol(rtol_velsolve);
-   velInv->SetAbsTol(0.0);
-   velInv->SetMaxIter(1200);
-}
-
-void IncompressibleNavierSolver::Setup_auxiliary(real_t dt)
-{
-   // GLL integration rule (Numerical Integration)
-   const IntegrationRule &ir_ni =
-      gll_rules.Get(vfes->GetFE(0)->GetGeomType(), 2 * velorder - 1);
-   Array<int> empty;
-
-   // setup of Bilinear form of Eq(14)
-   psiBForm = new ParBilinearForm(psifes);
-   auto *psidiff_blfi = new DiffusionIntegrator;
-
-   if (numerical_integ) { psidiff_blfi->SetIntRule(&ir_ni); }
-   psiBForm->AddDomainIntegrator(psidiff_blfi);
-   if (partial_assembly) { psiBForm->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-
-   psiBForm->Assemble();
-   psiBForm->FormSystemMatrix(empty, psiOp);
-
-   //-------------------------------------------------------------------------
-
-   // Setup of coefficient for linear form in Eq(14)
-   DvelCoeff = new VectorGridFunctionCoefficient;
-   auto *Dvel_lfi = new DomainLFGradIntegrator(*DvelCoeff);
-
-   // Setup of linear form of Eq(14)
-   psiLForm = new ParLinearForm(psifes);
-
-   if (numerical_integ) { Dvel_lfi->SetIntRule(&ir_ni); }
-   psiLForm->AddDomainIntegrator(Dvel_lfi);
-
-   //-------------------------------------------------------------------------
-   if (partial_assembly)
-   {
-      int psifes_truevsize = psifes->GetTrueVSize();
-      mfem::Vector psin(psifes_truevsize);
-      psin = 0.0;
-      mfem::Vector respsi(psifes_truevsize);
-      respsi = 0.0;
-
-      lor = new ParLORDiscretization(*psiBForm, empty);
-      psiInvPC = new HypreBoomerAMG(lor->GetAssembledMatrix());
-      psiInvPC->SetPrintLevel(0);
-      psiInvPC->Mult(respsi, psin);
-      SpInvOrthoPC = new OrthoSolver(psifes->GetComm());
-      SpInvOrthoPC->SetSolver(*psiInvPC);
-   }
-   else
-   {
-      psiInvPC = new HypreBoomerAMG(*psiOp.As<HypreParMatrix>());
-      psiInvPC->SetPrintLevel(0);
-      SpInvOrthoPC = new OrthoSolver(psifes->GetComm());
-      SpInvOrthoPC->SetSolver(*psiInvPC);
-   }
-
-   psiInv = new CGSolver(psifes->GetComm());
-   psiInv->iterative_mode = true;
-   psiInv->SetOperator(*psiOp);
-   psiInv->SetPreconditioner(*SpInvOrthoPC);
-   psiInv->SetPrintLevel(pl_psisolve);
-   psiInv->SetRelTol(rtol_psisolve);
-   psiInv->SetAbsTol(0.0);
-   psiInv->SetMaxIter(1000);
-}
-
-void IncompressibleNavierSolver::Setup_pressure(real_t dt)
-{
-   // GLL integration rule (Numerical Integration)
-   const IntegrationRule &ir_ni =
-      gll_rules.Get(vfes->GetFE(0)->GetGeomType(), 2 * velorder - 1);
-   Array<int> empty;
-
-   //-------------------------------------------------------------------------
-
-   // setup of Bilinear form of Eq(15)
-   pBForm = new ParBilinearForm(pfes);
-   auto *pmass_blfi = new MassIntegrator;
-
-   if (numerical_integ) { pmass_blfi->SetIntRule(&ir_ni); }
-   pBForm->AddDomainIntegrator(pmass_blfi);
-   if (partial_assembly) { pBForm->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-
-   pBForm->Assemble();
-   pBForm->FormSystemMatrix(empty, pOp);
-
-   //-------------------------------------------------------------------------
-
-   // Setup of divergence of velocity coefficient for linear form in Eq(15)
-   divVelCoeff = new DivergenceGridFunctionCoefficient(velGF[0]);
-
-   // Setup of coefficient for linear form in Eq(14)
-   pRHSCoeff = new GridFunctionCoefficient(&pRHS);
-   auto *p_lfi = new DomainLFIntegrator(*pRHSCoeff);
-
-   // Setup of linear form of Eq(15)
-   pLForm = new ParLinearForm(pfes);
-   if (numerical_integ) { p_lfi->SetIntRule(&ir_ni); }
-   pLForm->AddDomainIntegrator(p_lfi);
-
-   //-------------------------------------------------------------------------
-   if (partial_assembly)
-   {
-      Vector diag_pa(pfes->GetTrueVSize());
-      pBForm->AssembleDiagonal(diag_pa);
-      pInvPC = new OperatorJacobiSmoother(diag_pa, empty);
-   }
-   else
-   {
-      pInvPC = new HypreSmoother(*pOp.As<HypreParMatrix>());
-      dynamic_cast<HypreSmoother *>(pInvPC)->SetType(HypreSmoother::Jacobi, 1);
-   }
-
-   pInv = new CGSolver(pfes->GetComm());
-   pInv->iterative_mode = true;
-   pInv->SetOperator(*pOp);
-   pInv->SetPreconditioner(*pInvPC);
-   pInv->SetPrintLevel(pl_psolve);
-   pInv->SetRelTol(rtol_psolve);
-   pInv->SetAbsTol(0.0);
-   pInv->SetMaxIter(1000);
-}
-
-void IncompressibleNavierSolver::UpdateTimestepHistory(real_t dt) {}
-
-void IncompressibleNavierSolver::Step(real_t &time, real_t dt, int current_step,
-                                      const bool vis_step)
-{
-   this->Step_velocity(time, dt, current_step);
-
-   this->Step_auxiliary(time, dt, current_step);
-
-   this->Step_pressure(time, dt, current_step);
-
-   *velGF[1] = *velGF[0];
-   *pGF[1] = *pGF[0];
-
-   if (vis_step)
-   {
-      mfem::out << "It: " << iter << " | Iter_U: " << iter_vsolve
-                << " | Iter_Psi: " << iter_psisolve
-                << " | Iter_P: " << iter_psolve << "\n";
-      mfem::out << "It: " << iter << " | Resid_U: " << res_vsolve
-                << " | Resid_Psi: " << res_psisolve
-                << " | Resid_P: " << res_psisolve << "\n";
-   }
-
-   time += dt;
-   iter++;
-}
-
-void IncompressibleNavierSolver::Step_velocity(real_t &time, real_t dt,
-                                               int current_step)
-{
-   for (auto &vel_dbc : vel_dbcs)
-   {
-      velGF[0]->ProjectBdrCoefficient(*vel_dbc.coeff, vel_dbc.attr);
-      velGF[1]->ProjectBdrCoefficient(*vel_dbc.coeff, vel_dbc.attr);
-   }
-
-   // Update state in coefficient for Eq(18)
-   pUnitVectorCoeff->SetGridFunction(pGF[1]);
-
-   // Update state in coefficient for Eq(20)
-   nonlinTermCoeff->SetGridFunction(velGF[1]);
-
-   // Update state in coefficient for Eq(21)
-   prevVelLoadCoeff->SetGridFunction(velGF[1], dt);
-
-   velLForm->Assemble();
-   velLForm->ParallelAssemble(velLF);
-
-   Vector X1, B1;
-
-   if (partial_assembly)
-   {
-      auto *vpC = vOp.As<ConstrainedOperator>();
-      EliminateRHS(*velBForm, *vpC, vel_ess_tdof, *velGF[0], velLF, X1, B1, 1);
-   }
-   else
-   {
-      velBForm->FormLinearSystem(vel_ess_tdof, *velGF[0], velLF, vOp, X1, B1,
-                                 1);
-   }
-
-   velInv->Mult(B1, X1);
-   iter_vsolve = velInv->GetNumIterations();
-   res_vsolve = velInv->GetFinalNorm();
-   velBForm->RecoverFEMSolution(X1, velLF, *velGF[0]);
-}
-
-void IncompressibleNavierSolver::Step_auxiliary(real_t &time, real_t dt,
-                                                int current_step)
-{
-   // Compute new increment GF for LF of Eq(14)  and update state in coefficient
-   subtract(1.0 / dt, *velGF[0], *velGF[1], DvGF);
-   DvelCoeff->SetGridFunction(&DvGF);
-
-   psiLForm->Assemble();
-   psiLForm->ParallelAssemble(psiLF);
-
-   Vector X2, B2;
-   Array<int> empty;
-   if (partial_assembly)
-   {
-      auto *psipC = psiOp.As<ConstrainedOperator>();
-      EliminateRHS(*psiBForm, *psipC, empty, psiGF, psiLF, X2, B2, 1);
-   }
-   else { psiBForm->FormLinearSystem(empty, psiGF, psiLF, psiOp, X2, B2, 1); }
-
-   psiInv->Mult(B2, X2);
-   iter_psisolve = psiInv->GetNumIterations();
-   res_psisolve = psiInv->GetFinalNorm();
-   psiBForm->RecoverFEMSolution(X2, psiLF, psiGF);
-}
-
-void IncompressibleNavierSolver::Step_pressure(real_t &time, real_t dt,
-                                               int current_step)
-{
-   Array<int> empty;
-
-   // Compute new GF for LF of Eq(15) and update state in coefficient
-   divVelCoeff->SetGridFunction(velGF[0]);
-   divVelGF.ProjectCoefficient(*divVelCoeff);
-
-   add(*pGF[1], psiGF, pRHS);
-   add(pRHS, -1.0 * kin_vis, divVelGF, pRHS);
-   pRHSCoeff->SetGridFunction(&pRHS);
-
-   pLForm->Assemble();
-   pLForm->ParallelAssemble(pLF);
-
-   Vector X3, B3;
-
-   if (partial_assembly)
-   {
-      auto *ppC = pOp.As<ConstrainedOperator>();
-      EliminateRHS(*pBForm, *ppC, empty, *pGF[0], pLF, X3, B3, 1);
-   }
-   else { pBForm->FormLinearSystem(empty, *pGF[0], pLF, pOp, X3, B3, 1); }
-
-   pInv->Mult(B3, X3);
-   iter_psolve = pInv->GetNumIterations();
-   res_psisolve = pInv->GetFinalNorm();
-   pBForm->RecoverFEMSolution(X3, pLF, *pGF[0]);
-}
-
-void IncompressibleNavierSolver::EliminateRHS(Operator &A,
-                                              ConstrainedOperator &constrainedA,
-                                              const Array<int> &ess_tdof_list,
-                                              Vector &x, Vector &b, Vector &X,
-                                              Vector &B, int copy_interior)
-{
-   const Operator *Po = A.GetOutputProlongation();
-   const Operator *Pi = A.GetProlongation();
-   const Operator *Ri = A.GetRestriction();
-   A.InitTVectors(Po, Ri, Pi, x, b, X, B);
-   if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
-   constrainedA.EliminateRHS(X, B);
-}
-
-real_t IncompressibleNavierSolver::ComputeCFL(ParGridFunction &u, real_t dt)
-{
-   return 0;
-}
-
-void IncompressibleNavierSolver::AddVelDirichletBC(VectorCoefficient *coeff,
-                                                   Array<int> &attr)
-{
-   vel_dbcs.emplace_back(attr, coeff);
-
-   if (verbose && pmesh->GetMyRank() == 0)
-   {
-      mfem::out << "Adding Velocity Dirichlet BC to attributes ";
-      for (int i = 0; i < attr.Size(); ++i)
-      {
-         if (attr[i] == 1) { mfem::out << i << " "; }
-      }
-      mfem::out << std::endl;
-   }
-
-   for (int i = 0; i < attr.Size(); ++i)
-   {
-      MFEM_ASSERT((vel_ess_attr[i] && attr[i]) == 0,
-                  "Duplicate boundary definition deteceted.");
-      if (attr[i] == 1) { vel_ess_attr[i] = 1; }
-   }
-}
-
-void IncompressibleNavierSolver::AddVelDirichletBC(VecFuncT *f,
-                                                   Array<int> &attr)
-{
-   AddVelDirichletBC(new VectorFunctionCoefficient(pmesh->Dimension(), f),
-                     attr);
-}
-
-IncompressibleNavierSolver::~IncompressibleNavierSolver()
-{
-   delete velBForm;
-   delete psiBForm;
-   delete pBForm;
-
-   delete kinvisCoeff;
-   delete dtCoeff;
-
-   for (int i = 0; i < torder + 1; i++)
-   {
-      delete velGF[i];
-      delete pGF[i];
-   }
-
-   delete DvelCoeff;
-   delete divVelCoeff;
-   delete pRHSCoeff;
-   delete pUnitVectorCoeff;
-
-   delete velInv;
-   delete velInvPC;
-   delete psiInv;
-   delete SpInvOrthoPC;
-   delete psiInvPC;
-   delete lor;
-   delete pInv;
-   delete pInvPC;
-
-   delete vfec;
-   delete psifec;
-   delete pfec;
-   delete vfes;
-   delete psifes;
-   delete pfes;
-}

miniapps/navier/incompressible_navier_solver.hpp

@@ -1,338 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#pragma once
-
-#define INCOMP_NAVIER_VERSION 0.1
-
-#include "mfem.hpp"
-
-namespace mfem::incompressible_navier
-{
-
-using VecFuncT = void(const Vector &x, real_t t, Vector &u);
-using ScalarFuncT = real_t(const Vector &x, real_t t);
-
-// Coefficient which computed contribution of Eq(18)
-class UnitVectorGridFunctionCoeff : public VectorCoefficient
-{
-public:
-   UnitVectorGridFunctionCoeff(int dim): VectorCoefficient(dim * dim) {}
-
-   void Eval(Vector &V, ElementTransformation &T,
-             const IntegrationPoint &ip) override
-   {
-      real_t coeffVal = gridfunc_->GetValue(T, ip);
-
-      V.SetSize(vdim);
-      V = 0.0; // FIXME
-      V[0] = coeffVal;
-      V[3] = coeffVal;
-   }
-
-   void SetGridFunction(GridFunction *gridfunc) { gridfunc_ = gridfunc; }
-
-   GridFunction *gridfunc_ = nullptr;
-};
-
-// Coefficient which computed contribution of Eq(21)
-class PrevVelVectorGridFunctionCoeff : public VectorCoefficient
-{
-public:
-   PrevVelVectorGridFunctionCoeff(int dim): VectorCoefficient(dim) {}
-
-   void Eval(Vector &V, ElementTransformation &T, const IntegrationPoint &ip)
-   {
-      V.SetSize(vdim);
-      gridFuncCoeff->Eval(V, T, ip);
-
-      V *= 1.0 / dt_;
-   }
-
-   void SetGridFunction(GridFunction *gridfunc, real_t dt)
-   {
-      gridfunc_ = gridfunc;
-      dt_ = dt;
-      delete gridFuncCoeff;
-      gridFuncCoeff = new VectorGridFunctionCoefficient(gridfunc);
-   }
-
-   GridFunction *gridfunc_ = nullptr;
-   VectorGridFunctionCoefficient *gridFuncCoeff = nullptr;
-   real_t dt_;
-};
-
-// Coefficient which computed contribution of Eq(20)
-class NonLinTermVectorGridFunctionCoeff : public VectorCoefficient
-{
-public:
-   NonLinTermVectorGridFunctionCoeff(int dim): VectorCoefficient(dim) {}
-
-   void Eval(Vector &V, ElementTransformation &T, const IntegrationPoint &ip)
-   {
-      Vector val(vdim);
-      Vector resultVal(vdim);
-      DenseMatrix vecGrad;
-      V.SetSize(vdim);
-      gridFuncCoeff->Eval(val, T, ip);
-
-      gridfunc_->GetVectorGradient(T, vecGrad);
-
-      vecGrad.MultTranspose(val, V);
-
-      V *= -1.0;
-   }
-
-   void SetGridFunction(ParGridFunction *gridfunc)
-   {
-      delete gridFuncCoeff;
-      gridfunc_ = gridfunc;
-      gridFuncCoeff = new VectorGridFunctionCoefficient(gridfunc);
-   }
-
-   VectorGridFunctionCoefficient *gridFuncCoeff = nullptr;
-   ParGridFunction *gridfunc_ = nullptr;
-};
-
-/// Container for a Dirichlet boundary condition of the velocity field.
-class VelDirichletBC_T
-{
-public:
-   VelDirichletBC_T(Array<int> attr, VectorCoefficient *coeff):
-      attr(attr), coeff(coeff)
-   {
-   }
-
-   VelDirichletBC_T(VelDirichletBC_T &&obj)
-   {
-      // Deep copy the attribute array
-      this->attr = obj.attr;
-
-      // Move the coefficient pointer
-      this->coeff = obj.coeff;
-      obj.coeff = nullptr;
-   }
-
-   ~VelDirichletBC_T() { delete coeff; }
-
-   Array<int> attr;
-   VectorCoefficient *coeff;
-};
-
-/// Transient incompressible Navier Stokes solver in a split scheme formulation.
-/**
- * This implementation of a transient incompressible Navier Stokes solver uses
- * the non-dimensionalized formulation. The coupled momentum and
- * incompressibility equations are decoupled using the split scheme described in
- * [1]. This leads to three solving steps.
- *
- */
-class IncompressibleNavierSolver
-{
-public:
-   /// Initialize data structures, set FE space order and kinematic viscosity.
-   /**
-    * The ParMesh @a mesh can be a linear or curved parallel mesh. The @a order
-    * of the finite element spaces is
-    */
-   IncompressibleNavierSolver(ParMesh *mesh, int velorder, int porder,
-                              int tOrder, real_t kin_vis);
-
-   /// Initialize forms, solvers and preconditioners.
-   void Setup(real_t dt);
-
-   void Setup_velocity(real_t dt);
-
-   void Setup_auxiliary(real_t dt);
-
-   void Setup_pressure(real_t dt);
-
-   /// Compute solution at the next time step t+dt.
-   /**
-    * This method can
-    */
-   void Step(real_t &time, real_t dt, int cur_step, bool vis_step);
-
-   void Step_velocity(real_t &time, real_t dt, int cur_step);
-
-   void Step_auxiliary(real_t &time, real_t dt, int cur_step);
-
-   void Step_pressure(real_t &time, real_t dt, int cur_step);
-
-   /// Return a pointer to the provisional velocity ParGridFunction.
-   ParGridFunction *GetProvisionalVelocity() { return velGF[1]; }
-
-   /// Return a pointer to the current velocity ParGridFunction.
-   ParGridFunction *GetCurrentVelocity() { return velGF[0]; }
-
-   /// Return a pointer to the current pressure ParGridFunction.
-   ParGridFunction *GetCurrentPressure() { return pGF[0]; }
-
-   /// Return a pointer to the current pressure ParGridFunction.
-   ParGridFunction *GetCurrentPsi() { return &psiGF; }
-
-   /// Add a Dirichlet boundary condition to the velocity field.
-   void AddVelDirichletBC(VectorCoefficient *coeff, Array<int> &attr);
-
-   void AddVelDirichletBC(VecFuncT *f, Array<int> &attr);
-
-   /// Add a Dirichlet boundary condition to the pressure field.
-   // void AddPresDirichletBC(Coefficient *coeff, Array<int> &attr);
-
-   // void AddPresDirichletBC(ScalarFuncT *f, Array<int> &attr);
-
-   /// Enable partial assembly for every operator.
-   void EnablePA(bool pa) { partial_assembly = pa; }
-
-   /// Enable numerical integration rules. This means collocated quadrature at
-   /// the nodal points.
-   void EnableNI(bool ni) { numerical_integ = ni; }
-
-   /// Print timing summary of the solving routine.
-   void PrintTimingData();
-
-   ~IncompressibleNavierSolver();
-
-   /// Rotate entries in the time step and solution history arrays.
-   void UpdateTimestepHistory(real_t dt);
-
-   /// Compute CFL
-   real_t ComputeCFL(ParGridFunction &u, real_t dt);
-
-protected:
-   /// Eliminate essential BCs in an Operator and apply to RHS.
-   void EliminateRHS(Operator &A, ConstrainedOperator &constrainedA,
-                     const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                     Vector &X, Vector &B, int copy_interior = 0);
-
-   /// Enable/disable debug output.
-   bool debug = false;
-
-   /// Enable/disable verbose output.
-   bool verbose = true;
-
-   /// Enable/disable partial assembly of forms.
-   bool partial_assembly = false;
-
-   /// Enable/disable numerical integration rules of forms.
-   bool numerical_integ = false;
-
-   /// The parallel mesh.
-   ParMesh *pmesh = nullptr;
-
-   /// The order of the velocity and pressure space.
-   const int velorder;
-   const int porder;
-   const int torder;
-
-   /// Kinematic viscosity (dimensionless).
-   const real_t kin_vis;
-   Coefficient *kinvisCoeff = nullptr;
-
-   Coefficient *dtCoeff = nullptr;
-
-   IntegrationRules gll_rules;
-
-   /// Velocity $H^1$ finite element collection.
-   FiniteElementCollection *vfec = nullptr;
-
-   /// Psi $H^1$ finite element collection.
-   FiniteElementCollection *psifec = nullptr;
-
-   /// Pressure $H^1$ finite element collection.
-   FiniteElementCollection *pfec = nullptr;
-
-   /// Velocity $(H^1)^d$ finite element space.
-   ParFiniteElementSpace *vfes = nullptr;
-
-   /// Psi $(H^1)^d$ finite element space.
-   ParFiniteElementSpace *psifes = nullptr;
-
-   /// Pressure $H^1$ finite element space.
-   ParFiniteElementSpace *pfes = nullptr;
-
-   ParBilinearForm *velBForm = nullptr; // vmass + vdiff
-   ParBilinearForm *psiBForm = nullptr; // diffusion
-   ParBilinearForm *pBForm = nullptr;   // mass
-
-   ParLinearForm *velLForm = nullptr; // vLF + vLFGrad + vLF
-   ParLinearForm *psiLForm = nullptr; // LFGrad
-   ParLinearForm *pLForm = nullptr;   // LF
-
-   // current (0) and provisional (1) velocity
-   std::vector<ParGridFunction *> velGF;
-
-   // current (0) pressure ParGridFunction.
-   std::vector<ParGridFunction *> pGF;
-   ParGridFunction psiGF;
-
-   ParGridFunction DvGF, divVelGF, pRHS;
-   VectorGridFunctionCoefficient *DvelCoeff = nullptr;
-   DivergenceGridFunctionCoefficient *divVelCoeff = nullptr;
-   GridFunctionCoefficient *pRHSCoeff = nullptr;
-   UnitVectorGridFunctionCoeff *pUnitVectorCoeff = nullptr;
-   NonLinTermVectorGridFunctionCoeff *nonlinTermCoeff = nullptr;
-   PrevVelVectorGridFunctionCoeff *prevVelLoadCoeff = nullptr;
-
-   OperatorHandle vOp;
-   OperatorHandle psiOp;
-   OperatorHandle pOp;
-
-   Solver *velInvPC = nullptr;
-   CGSolver *velInv = nullptr;
-
-   ParLORDiscretization *lor = nullptr;
-   HypreBoomerAMG *psiInvPC = nullptr;
-   OrthoSolver *SpInvOrthoPC = nullptr;
-   CGSolver *psiInv = nullptr;
-
-   Solver *pInvPC = nullptr;
-   CGSolver *pInv = nullptr;
-
-   Vector velLF, psiLF, pLF;
-
-   // All essential attributes.
-   Array<int> vel_ess_attr;
-   Array<int> pres_ess_attr;
-
-   // All essential true dofs.
-   Array<int> vel_ess_tdof;
-   Array<int> pres_ess_tdof;
-
-   // Bookkeeping for velocity dirichlet bcs.
-   std::vector<VelDirichletBC_T> vel_dbcs;
-
-   // Print levels.
-   int pl_psolve = 0;
-   int pl_psisolve = 0;
-   int pl_velsolve = 0;
-   int pl_amg = 0;
-
-#if defined(MFEM_USE_DOUBLE)
-   real_t rtol_psolve = 1e-12;
-   real_t rtol_psisolve = 1e-12;
-   real_t rtol_velsolve = 1e-12;
-#elif defined(MFEM_USE_SINGLE)
-   real_t rtol_psolve = 1e-9;
-   real_t rtol_psisolve = 1e-5;
-   real_t rtol_velsolve = 1e-7;
-#else
-   #error "Only single and double precision are supported!"
-#endif
-
-   // Iteration counts.
-   int iter = 1, iter_vsolve = 0, iter_psolve = 0, iter_psisolve = 0;
-
-   // Residuals.
-   real_t res_vsolve = 0.0, res_psolve = 0.0, res_psisolve = 0.0;
-};
-
-} // namespace mfem::incompressible_navier

miniapps/navier/incompressible_navier_tests.cpp

@@ -1,206 +0,0 @@
-#include <algorithm>
-#include <iostream>
-#include <memory>
-#include <sstream>
-#include <unistd.h>
-
-#define NVTX_COLOR ::gpu::nvtx::kMagenta
-#include "incompressible_navier_nvtx.hpp"
-
-///////////////////////////////////////////////////////////////////////////////
-int navier(int argc, char *argv[], double &u, double &p, double &Ψ);
-
-///////////////////////////////////////////////////////////////////////////////
-template <class T>
-std::enable_if_t<!std::numeric_limits<T>::is_integer, bool>
-AlmostEq(T x, T y, T tolerance = 100.0 * std::numeric_limits<T>::epsilon())
-{
-   const T neg = std::abs(x - y);
-   constexpr T min = std::numeric_limits<T>::min();
-   constexpr T eps = std::numeric_limits<T>::epsilon();
-   const T min_abs = std::min(std::abs(x), std::abs(y));
-   if (std::abs(min_abs) == 0.0) { return neg < eps; }
-   return (neg / (1.0 + std::max(min, min_abs))) < tolerance;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-using char_uptr = std::unique_ptr<char[]>;
-using args_ptr_t = std::vector<char_uptr>;
-using args_t = std::vector<char *>;
-
-///////////////////////////////////////////////////////////////////////////////
-struct Results
-{
-   double u{}, p{}, Ψ {};
-};
-
-///////////////////////////////////////////////////////////////////////////////
-struct Test
-{
-   static constexpr const char *binary = "incompNS_2Dtest ";
-   static constexpr const char *common = "-no-vis -no-pv";
-   const std::string options;
-   const Results results;
-   Test(const char *args, const Results &res):
-      options(std::string(args) + " " + common), results(res)
-   {
-      dbg("options: {}", options.c_str());
-      dbg("results: U={:.15e}, P={:.15e}, Ψ={:.15e}",
-          results.u, results.p, results.Ψ);
-   }
-   std::string Command() const { return binary + options; }
-};
-
-///////////////////////////////////////////////////////////////////////////////
-#if 1 // dot product reduction (miniapps/navier/incompNS_2Dtest.cpp#L182)
-static const Test gold[] =
-{
-   {
-      "-nx 9 -ny 3 -sr 0",
-      { 3.056430866716070e-06, 1.504027632950462e-01, 7.132601171183242e-08 }
-   },
-   {
-      "-nx 16 -ny 8 -sr 0",
-      { 1.409287729554512e-05, 5.718053801962010e-01, 1.904938419441012e-07 }
-   },
-   // {
-   //    "-nx 9 -ny 3 -sr 1",
-   //    { 1.23258426138828e-05, 5.18207619597952e-01, 1.956175418199867e-07 }
-   // },
-   // {
-   //    "-nx 9 -ny 3 -sr 2",
-   //    { 4.74381190869396e-05, 1.80653923294262e+00, 5.90778654333642e-07 }
-   // },
-};
-#else // Norml2 reduction
-///////////////////////////////////////////////////////////////////////////////
-const Test runs[] =
-{
-   {
-      "-nx 9 -ny 3 -sr 0",
-      { 1.746844586767688e-03, 3.874421956807944e-01, 2.670296315544763e-04 }
-   },
-   // 1.748265101955712e-03, 3.878179512284757e-01, 2.670693013280680e-04 //
-   // Release { "-nx 9 -ny 3 -sr 1",
-   //  { 1.232584261388279e-05, 5.182076195979519e-01, 1.956175418199866e-07 }
-   //  },
-   // { "-nx 9 -ny 3 -sr 2",
-   //  { 4.743811908693962e-05, 1.806539232942622e+00, 5.907786543336419e-07 }
-   //  },
-};
-#endif
-
-///////////////////////////////////////////////////////////////////////////////
-int NavierTest(const int k, const Test &run)
-{
-   dbg();
-   static args_ptr_t args_ptr;
-   args_t args;
-
-   std::istringstream iss(run.Command());
-
-   auto add_arg = [&](std::string token) -> char_uptr
-   {
-      auto arg_ptr = std::make_unique<char[]>(token.size() + 1);
-      std::memcpy(arg_ptr.get(), token.c_str(), token.size() + 1);
-      arg_ptr[token.size()] = '\0';
-      return arg_ptr;
-   };
-
-   std::string token;
-   while (iss >> token)
-   {
-      auto arg_ptr = add_arg(token);
-      args.push_back(arg_ptr.get());
-      args_ptr.emplace_back(std::move(arg_ptr));
-   }
-   args.push_back(nullptr);
-
-   auto launch = [&args, &run, &k]() -> int
-   {
-      // dbg("Launching test #{}: \x1B[33m{}\x1B[m", k, gold.Command().c_str());
-      Results res{};
-      navier(args.size() - 1, args.data(), res.u, res.p, res.Ψ);
-      // dbg("Results: U={:.15e}, P={:.15e}, Ψ={:.15e}", res.u, res.p, res.Ψ);
-
-      const bool u = AlmostEq(res.u, run.results.u);
-      const bool p = AlmostEq(res.p, run.results.p);
-      const bool Ψ = AlmostEq(res.Ψ, run.results.Ψ);
-
-      constexpr auto ok = [](bool ok) -> int { return ok ? 32 : 31; };
-      constexpr auto to_string = [](args_t &args) -> std::string
-      {
-         std::string args_str;
-         for (auto &arg : args)
-         {
-            if (!arg) { break; }
-            args_str += std::string(arg) + " ";
-         }
-         return args_str;
-      };
-
-      dbg("#{} \x1B[33m{}\x1B[m", k, to_string(args).c_str());
-      dbg("U: \x1B[33m{:.15e} \x1B[{}m{:.15e}", run.results.u, ok(u), res.u );
-      dbg("P: \x1B[33m{:.15e} \x1B[{}m{:.15e}", run.results.p, ok(p), res.p);
-      dbg("Ψ: \x1B[33m{:.15e} \x1B[{}m{:.15e}", run.results.Ψ, ok(Ψ), res.Ψ);
-
-      if (u && p && Ψ) { return std::cout << "✅" << std::endl, EXIT_SUCCESS; }
-      else { return std::cout << "❌" << std::endl, EXIT_FAILURE; }
-   };
-
-   // first launch with default arguments
-   if (launch() != EXIT_SUCCESS) { return EXIT_FAILURE; }
-
-   // second launch with the same arguments, but with -pa
-   args.pop_back(); // nullptr
-   auto arg_pa_ptr = add_arg("-pa");
-   args.push_back(arg_pa_ptr.get());
-   args_ptr.emplace_back(std::move(arg_pa_ptr));
-   args.push_back(nullptr);
-   if (launch() != EXIT_SUCCESS) { return EXIT_FAILURE; }
-
-   return EXIT_SUCCESS;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-int main(int argc, char *argv[])
-try
-{
-   dbg();
-
-   int opt;
-   int test = -1;
-   auto show_usage = [](const int ret = EXIT_FAILURE)
-   {
-      printf("Usage: program [-a <arg>] [-b <arg>] [-h]\n");
-      printf("  -t <test>  Optional test number \n");
-      printf("  -h         Show this help message\n");
-      exit(ret);
-   };
-
-   while ((opt = getopt(argc, argv, "t:h")) != -1)
-   {
-      switch (opt)
-      {
-         case 't': test = std::atoi(optarg); break;
-         case 'h': show_usage(EXIT_SUCCESS);
-         default:  show_usage(EXIT_FAILURE);
-      }
-   }
-
-   constexpr int N_TESTS = sizeof(gold) / sizeof(Test);
-   if (test >= 0 && test < N_TESTS) { return NavierTest(test, gold[test]); }
-
-   int k = 0;
-   for (auto &run : gold)
-   {
-      if (NavierTest(k++, run) != EXIT_SUCCESS) { return EXIT_FAILURE; }
-   }
-   return EXIT_SUCCESS;
-}
-catch (std::exception &e)
-{
-   std::cerr << "\033[31m..xxxXXX[ERROR]XXXxxx.." << std::endl;
-   std::cerr << "\033[31m{}" << e.what() << std::endl;
-   return EXIT_FAILURE;
-}

miniapps/nurbs/CMakeLists.txt

@@ -80,6 +80,10 @@ add_mfem_miniapp(nurbs_solenoidal
   LIBRARIES mfem)
   add_dependencies(nurbs_solenoidal copy_miniapps_nurbs_data)
 
+add_mfem_miniapp(nurbs_surface
+  MAIN nurbs_surface.cpp
+  LIBRARIES mfem)
+
 if (MFEM_ENABLE_TESTING)
   add_test(NAME nurbs_ex1_1d_r1_o2_ser
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
@@ -247,6 +251,14 @@ if (MFEM_ENABLE_TESTING)
     COMMAND $<TARGET_FILE:nurbs_solenoidal> -no-vis
         -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2)
 
+  add_test(NAME nurbs_surface_10_10_10_10_ex1_o3_ser
+    COMMAND $<TARGET_FILE:nurbs_surface> -no-vis
+        -o 3 -nx 10 -ny 10 -fnx 10 -fny 10 -ex 1 -orig)
+
+  add_test(NAME nurbs_surface_10_10_40_40_ex1_o3_ser
+    COMMAND $<TARGET_FILE:nurbs_surface> -no-vis
+        -o 3 -nx 10 -ny 10 -fnx 40 -fny 14 -ex 1)
+
 endif()
 
 if (MFEM_USE_MPI)

miniapps/nurbs/makefile

@@ -21,7 +21,7 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_MINIAPPS = nurbs_ex1 nurbs_patch_ex1 nurbs_ex3 nurbs_ex5 nurbs_ex24 \
-   nurbs_curveint nurbs_printfunc nurbs_solenoidal nurbs_naca_cmesh
+   nurbs_curveint nurbs_printfunc nurbs_solenoidal nurbs_naca_cmesh nurbs_surface
 PAR_MINIAPPS = nurbs_ex1p nurbs_ex11p
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -158,6 +158,13 @@ nurbs_naca_cmesh-test-seq: nurbs_naca_cmesh
 nurbs_printfunc-test-seq: nurbs_printfunc
 	@$(call mfem-test,$<,, NURBS miniapp)
 
+SURF_ARGS_1 := -o 3 -nx 10 -ny 10 -fnx 10 -fny 10 -ex 1 -orig
+SURF_ARGS_2 := -o 3 -nx 10 -ny 10 -fnx 40 -fny 40 -ex 1
+
+nurbs_surface-test-seq: nurbs_surface
+	@$(call mfem-test,$<,, NURBS miniapp,$(SURF_ARGS_1))
+	@$(call mfem-test,$<,, NURBS miniapp,$(SURF_ARGS_2))
+
 EX1P_ARGS_1 :=
 EX1P_ARGS_2 := -m ../../data/pipe-nurbs-2d.mesh -o 2 -no-ibp
 EX1P_ARGS_3 := -m ../../data/ball-nurbs.mesh -o 2 --weak-bc -r 0
@@ -192,6 +199,6 @@ clean-build:
 
 clean-exec:
 	@rm -f refined.mesh sin-fit.mesh ex5.mesh exsol.mesh mesh.* sol.* mode_*
-	@rm -f naca-cmesh.mesh sol_?.gf
+	@rm -f naca-cmesh.mesh sol_?.gf *-Surface.mesh
 	@rm -rf Example1* Example3* Example5* Solenoidal_* ParaView
 	@rm -rf CurveInt Naca_cmesh glvis_naca-cmesh.mesh solution.dat

miniapps/nurbs/nurbs_surface.cpp

@@ -0,0 +1,655 @@
+// 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.
+//
+//          --------------------------------------------------------
+//          NURBS Surface: Interpolate a 3D Surface in a NURBS Patch
+//          --------------------------------------------------------
+//
+// Compile with: make nurbs_surface
+//
+// Sample runs:  nurbs_surface -o 3 -nx 10 -ny 10 -fnx 10 -fny 10 -ex 1 -orig
+//               nurbs_surface -o 3 -nx 10 -ny 10 -fnx 40 -fny 40 -ex 1
+//               nurbs_surface -o 3 -nx 20 -ny 20 -fnx 10 -fny 10 -ex 1
+//               nurbs_surface -o 3 -nx 20 -ny 20 -fnx 40 -fny 40 -ex 1 -j 0.5
+//               nurbs_surface -o 3 -nx 10 -ny 10 -fnx 10 -fny 10 -ex 2 -orig
+//               nurbs_surface -o 3 -nx 10 -ny 10 -fnx 40 -fny 40 -ex 2
+//               nurbs_surface -o 3 -nx 20 -ny 20 -fnx 10 -fny 10 -ex 2
+//               nurbs_surface -o 3 -nx 10 -ny 10 -fnx 10 -fny 10 -ex 3 -orig
+//               nurbs_surface -o 3 -nx 10 -ny 10 -fnx 40 -fny 40 -ex 3
+//               nurbs_surface -o 3 -nx 20 -ny 20 -fnx 10 -fny 10 -ex 3
+//               nurbs_surface -o 3 -nx 20 -ny 10 -fnx 20 -fny 10 -ex 4 -orig
+//             * nurbs_surface -o 3 -nx 20 -ny 10 -fnx 80 -fny 40 -ex 4
+//             * nurbs_surface -o 3 -nx 40 -ny 20 -fnx 20 -fny 10 -ex 4
+//             * nurbs_surface -o 3 -nx 100 -ny 100 -fnx 100 -fny 100 -ex 5 -orig
+//             * nurbs_surface -o 3 -nx 100 -ny 100 -fnx 400 -fny 400 -ex 5
+//             * nurbs_surface -o 3 -nx 200 -ny 200 -fnx 100 -fny 100 -ex 5
+//
+// Description:  This example demonstrates the use of MFEM to interpolate an
+//               input surface point grid in 3D using a NURBS surface. The NURBS
+//               surface can then be sampled to generate an output mesh of
+//               arbitrary resolution while staying close to the input geometry.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Example data for 3D point grid on surface, given by an analytic function.
+void SurfaceGridExample(int example, int nx, int ny, Array3D<real_t> &vertices,
+                        real_t jitter);
+
+// Write a linear surface mesh with given vertex positions in v.
+void WriteLinearMesh(int nx, int ny, const Array3D<real_t> &v,
+                     const std::string &basename, bool visualization = false,
+                     int x = 0, int y = 0, int w = 500, int h = 500);
+
+// Given an input grid of 3D points on a surface, this class computes a NURBS
+// surface of given order that interpolates the vertices of the input grid.
+class SurfaceInterpolator
+{
+public:
+   /// Constructor for a given 2D point grid size and NURBS order.
+   SurfaceInterpolator(int num_elem_x, int num_elem_y, int order);
+
+   /// Create a surface interpolating the 2D grid of 3D points in @a input3D.
+   void CreateSurface(const Array3D<real_t> &input3D);
+
+   /// Sample the surface with the given grid size, storing points in
+   /// @a output3D.
+   void SampleSurface(int num_elem_x, int num_elem_y, bool compareOriginal,
+                      Array3D<real_t> &output3D);
+
+   /** @brief Write the NURBS surface mesh to file, defined coordinate-wise by
+       the entries of @a cmesh. */
+   void WriteNURBSMesh(const std::string &basename, bool visualization = false,
+                       int x = 0, int y = 0, int w = 500, int h = 500);
+
+protected:
+   /** @brief Compute the NURBS mesh interpolating the given coordinate of the
+       grid of 3D points in @a input3D. */
+   void ComputeNURBS(int coordinate, const Array3D<real_t> &input3D);
+
+private:
+   int nx, ny; // Number of elements in two directions of the surface grid
+   int orderNURBS; // NURBS degree
+   real_t hx, hy, hz; // Grid size in reference space
+
+   Array3D<real_t> initial3D; // Initial grid of points
+
+   static constexpr int dim = 3;
+   Array<int> ncp; // Number of control points in each direction
+   Array<int> nks; // Number of knot-spans in each direction
+
+   std::vector<Vector> ugrid; // Parameter space [0,1]^2 grid point coordinates
+
+   std::vector<KnotVector> kv; // KnotVectors in each direction
+
+   std::unique_ptr<NURBSPatch> patch; // Pointer to the only patch in the mesh
+
+   Mesh mesh; // NURBS mesh representing the surface
+   std::vector<Mesh> cmesh; // NURBS meshes representing point components
+};
+
+
+int main(int argc, char *argv[])
+{
+   // Parse command-line options
+   int nx = 4;
+   int ny = 4;
+   int fnx = 40;
+   int fny = 40;
+   int order = 3;
+   int example = 1;
+   bool visualization = true;
+   bool compareOriginal = false;
+   real_t jitter = 0.0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&example, "-ex", "--example",
+                  "Example data");
+   args.AddOption(&nx, "-nx", "--nx",
+                  "Number of elements in x");
+   args.AddOption(&ny, "-ny", "--ny",
+                  "Number of elements in y");
+   args.AddOption(&fnx, "-fnx", "--fnx",
+                  "Number of resampled elements in x");
+   args.AddOption(&fny, "-fny", "--fny",
+                  "Number of resampled elements in y");
+   args.AddOption(&order, "-o", "--order",
+                  "NURBS finite element order (polynomial degree)");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&compareOriginal, "-orig", "--compare-original", "-no-orig",
+                  "--no-compare-original",
+                  "Compare to the original mesh?");
+   args.AddOption(&jitter, "-j", "--jitter",
+                  "Relative jittering in (0,1) to add to the input point "
+                  "coordinates on a uniform nx x ny grid (0 by default)");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   if (compareOriginal && (fnx != nx || fny != ny))
+   {
+      cout << "Comparing to the original mesh requires the same number of "
+           << "samples!\n";
+      return 1;
+   }
+
+   // Dimensions of the 3 surfaces (Input, NURBS, Output)
+   cout << "Input Surface:  " << nx << " x " << ny << " linear elements\n";
+   cout << "NURBS Surface:  " << nx + 1 - order << " x " << ny + 1 - order
+        << " knot elements of order " << order << "\n";
+   cout << "Output Surface: " << fnx << " x " << fny << " linear elements\n";
+
+   // Set the vertex coordinates of the initial linear mesh
+   constexpr int dim = 3;
+   Array3D<real_t> input3D(nx + 1, ny + 1, dim);
+   SurfaceGridExample(example, nx, ny, input3D, jitter);
+
+   // Create a NURBS surface for the given nx, ny and order parameters that
+   // interpolates the input vertex coordinates
+   SurfaceInterpolator surf(nx, ny, order);
+   surf.CreateSurface(input3D);
+
+   // Compute the vertex coordinates of the output linear mesh by sampling the
+   // values from the NURBS surface
+   Array3D<real_t> output3D(fnx + 1, fny + 1, dim);
+   surf.SampleSurface(fnx, fny, compareOriginal, output3D);
+
+   // Save and optionally visualize the 3 surfaces (Input, NURBS, Output)
+   WriteLinearMesh(nx, ny, input3D, "Input-Surface", visualization, 0, 0);
+   surf.WriteNURBSMesh("NURBS-Surface", visualization, 502, 0);
+   WriteLinearMesh(fnx, fny, output3D, "Output-Surface", visualization, 1004, 0);
+
+   return 0;
+}
+
+// f(x,y) = sin(2 * pi * x) * sin(2 * pi * y)
+void Function1(real_t u, real_t v, real_t &x, real_t &y, real_t &z)
+{
+   x = u;
+   y = v;
+   z = sin(2.0 * M_PI * u) * sin(2.0 * M_PI * v);
+}
+
+// Part of the parametric surface of a sphere, using spherical coordinates.
+void Function2(real_t u, real_t v, real_t &x, real_t &y, real_t &z)
+{
+   constexpr real_t r = 1.0;
+   constexpr real_t pi_4 = M_PI * 0.25;
+   constexpr real_t phi0 = -3*pi_4;
+   constexpr real_t phi1 = 3*pi_4;
+   constexpr real_t theta0 = pi_4;
+   constexpr real_t theta1 = 3 * pi_4;
+
+   const real_t phi = (phi0 * (1.0 - v)) + (phi1 * v);
+   const real_t theta = (theta0 * (1.0 - u)) + (theta1 * u);
+   x = r * sin(theta) * cos(phi);
+   y = r * sin(theta) * sin(phi);
+   z = r * cos(theta);
+}
+
+// Helicoid surface
+void Function3(real_t u, real_t v, real_t &x, real_t &y, real_t &z)
+{
+   x = u * cos(2.0 * M_PI * v);
+   y = u * sin(2.0 * M_PI * v);
+   z = v;
+}
+
+// Mobius strip
+void Function4(real_t u, real_t v, real_t &x, real_t &y, real_t &z)
+{
+   constexpr int twists = 1;
+   const real_t a = 1.0 + 0.5 * ((2.0 * v) - 1.0) * cos(2.0 * M_PI * twists * u);
+   x = a * cos(2.0 * M_PI * u);
+   y = a * sin(2.0 * M_PI * u);
+   z = 0.5 * (2.0 * v - 1.0) * sin(2.0 * M_PI * twists * u);
+}
+
+// Breather surface
+void Function5(real_t u, real_t v, real_t &x, real_t &y, real_t &z)
+{
+   const real_t m = 13.2 * ((2.0 * u) - 1.0);
+   const real_t n = 37.4 * ((2.0 * v) - 1.0);
+   constexpr real_t b = 0.4;
+   constexpr real_t r = 1.0 - (b*b);
+   const real_t w = sqrt(r);
+   const real_t denom = b * (pow(w*cosh(b*m),2) + pow(b*sin(w*n),2));
+   x = -m + (2*r*cosh(b*m)*sinh(b*m)) / denom;
+   y = (2*w*cosh(b*m)*(-(w*cos(n)*cos(w*n)) - sin(n)*sin(w*n))) / denom;
+   z = (2*w*cosh(b*m)*(-(w*sin(n)*cos(w*n)) + cos(n)*sin(w*n))) / denom;
+}
+
+void SurfaceFunction(int example, real_t u, real_t v,
+                     real_t &x, real_t &y, real_t &z)
+{
+   switch (example)
+   {
+      case 1:
+         Function1(u, v, x, y, z);
+         break;
+      case 2:
+         Function2(u, v, x, y, z);
+         break;
+      case 3:
+         Function3(u, v, x, y, z);
+         break;
+      case 4:
+         Function4(u, v, x, y, z);
+         break;
+      default:
+         Function5(u, v, x, y, z);
+   };
+}
+
+// Example data for 3D point grid on surface, given by an analytic function.
+void SurfaceExample(int example, const std::vector<Vector> &grid,
+                    Array3D<real_t> &v3D, real_t jitter)
+{
+   int seed = (int)time(0);
+   srand((unsigned)seed);
+
+   real_t h0 = grid[0][1]-grid[0][0], h1 = grid[1][1]-grid[1][0];
+   for (int i = 0; i < grid[0].Size(); i++)
+   {
+      for (int j = 0; j < grid[1].Size(); j++)
+      {
+         if (i != 0 && i != grid[0].Size()-1 && j != 0 && j != grid[1].Size()-1)
+         {
+            SurfaceFunction(example, grid[0][i] + rand_real()*h0*jitter,
+                            grid[1][j] + rand_real()*h1*jitter,
+                            v3D(i, j, 0), v3D(i, j, 1), v3D(i, j, 2));
+         }
+         else
+         {
+            SurfaceFunction(example, grid[0][i], grid[1][j],
+                            v3D(i, j, 0), v3D(i, j, 1), v3D(i, j, 2));
+         }
+      }
+   }
+}
+
+void SurfaceGridExample(int example, int nx, int ny, Array3D<real_t> &vertices,
+                        real_t jitter = 0)
+{
+   // Define a uniform grid of the reference parameter space [0,1]^2
+   std::vector<Vector> uniformGrid(2);
+   for (int i = 0; i < 2; ++i)
+   {
+      const int n = (i == 0) ? nx : ny;
+      const real_t h = 1.0 / n;
+      uniformGrid[i].SetSize(n + 1);
+      for (int j = 0; j <= n; ++j) { uniformGrid[i][j] = j * h; }
+   }
+
+   SurfaceExample(example, uniformGrid, vertices, jitter);
+}
+
+// Write a linear surface mesh with given vertex positions in v.
+void WriteLinearMesh(int nx, int ny, const Array3D<real_t> &v,
+                     const std::string &basename, bool visualization,
+                     int x, int y, int w, int h)
+{
+   const int nv = (nx + 1) * (ny + 1);
+   const int nelem = nx * ny;
+   constexpr int dim = 3; // Spatial dimension
+
+   Mesh lmesh(2, nv, nelem, 0, dim);
+   Vector vertex(dim);
+
+   for (int i = 0; i <= nx; ++i)
+   {
+      for (int j = 0; j <= ny; ++j)
+      {
+         for (int k = 0; k < dim; ++k) { vertex[k] = v(i, j, k); }
+         lmesh.AddVertex(vertex);
+      }
+   }
+
+   Array<int> verts(4);
+
+   auto vID = [&](int i, int j)
+   {
+      return j + (i * (ny + 1));
+   };
+
+   for (int i = 0; i < nx; ++i)
+   {
+      for (int j = 0; j < ny; ++j)
+      {
+         verts[0] = vID(i, j);
+         verts[1] = vID(i+1, j);
+         verts[2] = vID(i+1, j+1);
+         verts[3] = vID(i, j+1);
+
+         Element* el = lmesh.NewElement(Element::QUADRILATERAL);
+         el->SetVertices(verts);
+         lmesh.AddElement(el);
+      }
+   }
+
+   lmesh.FinalizeTopology();
+
+   ofstream mesh_ofs(basename + ".mesh");
+   mesh_ofs.precision(8);
+   lmesh.Print(mesh_ofs);
+
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      constexpr int visport = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "mesh\n" << lmesh
+               << "window_title '" << basename << "'"
+               << "window_geometry "
+               << x << " " << y << " " << w << " " << h << "\n"
+               << "keys PPPPPPPPAattttt******\n"
+               << flush;
+   }
+}
+
+
+// Compute error of interpolation with respect to an input grid of point data.
+void CheckError(const Array3D<real_t> &a, const Array3D<real_t> &b, int c,
+                int nx, int ny)
+{
+   real_t maxErr = 0.0;
+   for (int i = 0; i <= nx; ++i)
+   {
+      for (int j = 0; j <= ny; ++j)
+      {
+         const real_t err_ij = std::abs(a(i, j, c) - b(i, j, 2));
+         maxErr = std::max(maxErr, err_ij);
+      }
+   }
+
+   cout << "Max error: " << maxErr << " for coordinate " << c << endl;
+}
+
+
+// Sample a NURBS mesh to generate a first-order mesh.
+void SampleNURBS(bool uniform, int nx, int ny, const Mesh &mesh,
+                 const Array<int> &nks, const std::vector<Vector> &ugrid,
+                 Array3D<real_t> &vpos)
+{
+   const GridFunction *nodes = mesh.GetNodes();
+
+   const real_t hx = 1.0 / (real_t) nx;
+   const real_t hy = 1.0 / (real_t) ny;
+
+   const real_t hxks = 1.0 / (real_t) nks[0];
+   const real_t hyks = 1.0 / (real_t) nks[1];
+
+   Vector vertex;
+   IntegrationPoint ip;
+
+   ip.z = 1.0;
+   for (int i = 0; i <= nx; ++i)
+   {
+      const real_t xref = uniform ? i * hx : ugrid[0][i];
+      const int nurbsElem0 = std::min((int) (xref / hxks), nks[0] - 1);
+      const real_t ipx = (xref - (nurbsElem0 * hxks)) / hxks;
+      ip.x = ipx;
+
+      for (int j = 0; j <= ny; ++j)
+      {
+         const real_t yref = uniform ? j * hy : ugrid[1][j];
+         const int nurbsElem1 = std::min((int) (yref / hyks), nks[1] - 1);
+         const real_t ipy = (yref - (nurbsElem1 * hyks)) / hyks;
+         ip.y = ipy;
+
+         const int nurbsElem = nurbsElem0 + (nurbsElem1 * nks[0]);
+         nodes->GetVectorValue(nurbsElem, ip, vertex);
+
+         for (int k = 0; k < 3; ++k)
+         {
+            vpos(i, j, k) = vertex[k];
+         }
+      }
+   }
+}
+
+
+SurfaceInterpolator::SurfaceInterpolator(int num_elem_x, int num_elem_y,
+                                         int order) :
+   nx(num_elem_x), ny(num_elem_y), orderNURBS(order),
+   ncp(dim), nks(dim), ugrid(dim - 1)
+{
+   ncp[0] = nx + 1;
+   ncp[1] = ny + 1;
+   ncp[2] = order + 1;
+
+   for (int i = 0; i < dim; ++i)
+   {
+      nks[i] = ncp[i] - order;
+
+      Vector intervals(nks[i]);
+      Array<int> continuity(nks[i] + 1);
+
+      intervals = 1.0 / (real_t) nks[i];
+      continuity = order - 1;
+      continuity[0] = -1;
+      continuity[nks[i]] = -1;
+
+      kv.emplace_back(order, intervals, continuity);
+   }
+
+   patch.reset(new NURBSPatch(&kv[0], &kv[1], &kv[2], dim + 1));
+
+   hx = 1.0 / (real_t) (ncp[0] - 1);
+   hy = 1.0 / (real_t) (ncp[1] - 1);
+   hz = 1.0 / (real_t) (ncp[2] - 1);
+
+   Vector xi_args;
+   Array<int> i_args;
+   for (int i = 0; i < 2; ++i)
+   {
+      kv[i].FindMaxima(i_args, xi_args, ugrid[i]);
+   }
+}
+
+void SurfaceInterpolator::CreateSurface(const Array3D<real_t> &input3D)
+{
+   cmesh.clear();
+   for (int c = 0; c < dim; ++c) // Loop over coordinates
+   {
+      ComputeNURBS(c, input3D);
+      cmesh.emplace_back(mesh);
+   }
+
+   initial3D = input3D;
+}
+
+void SurfaceInterpolator::SampleSurface(int num_elem_x, int num_elem_y,
+                                        bool compareOriginal,
+                                        Array3D<real_t> &output3D)
+{
+   Array3D<real_t> vpos(num_elem_x + 1, num_elem_y + 1, dim);
+   for (int c = 0; c < dim; ++c) // Loop over coordinates
+   {
+      SampleNURBS(true, num_elem_x, num_elem_y, cmesh[c], nks, ugrid, vpos);
+
+      if (compareOriginal)
+      {
+         SampleNURBS(false, num_elem_x, num_elem_y, cmesh[c], nks, ugrid, vpos);
+         CheckError(initial3D, vpos, c, nx, ny);
+      }
+
+      for (int i = 0; i <= num_elem_x; ++i)
+      {
+         for (int j = 0; j <= num_elem_y; ++j)
+         {
+            output3D(i,j,c) = vpos(i,j,2);
+         }
+      }
+   }
+}
+
+void SurfaceInterpolator::ComputeNURBS(int coordinate,
+                                       const Array3D<real_t> &input3D)
+{
+   Array<Vector*> x;
+   for (int i = 0; i < dim; ++i) { x.Append(new Vector(ncp[0])); }
+
+   for (int k = 0; k < ncp[2]; ++k)
+   {
+      const real_t z = k * hz;
+
+      // For each horizontal slice (fixed k), interpolate a 2D surface by
+      // sweeping curve interpolations in each direction. See Algorithm A9.4 of
+      // "The NURBS Book" - 2nd ed - Piegl and Tiller.
+
+      // Resize for sweep in first direction
+      for (int i = 0; i < dim; ++i) { x[i]->SetSize(ncp[0]); }
+
+      // Sweep in the first direction
+      for (int j = 0; j < ncp[1]; ++j)
+      {
+         for (int i = 0; i < ncp[0]; i++)
+         {
+            (*x[0])[i] = ugrid[0][i];
+            (*x[1])[i] = ugrid[1][j];
+
+            const real_t s_ij = input3D(i, j, coordinate);
+            (*x[2])[i] = -1.0 + z + s_ij;
+         }
+
+         const bool reuse_factorization = j > 0;
+         kv[0].FindInterpolant(x, reuse_factorization);
+
+         for (int i = 0; i < ncp[0]; i++)
+         {
+            (*patch)(i,j,k,0) = (*x[0])[i];
+            (*patch)(i,j,k,1) = (*x[1])[i];
+            (*patch)(i,j,k,2) = (*x[2])[i];
+            (*patch)(i,j,k,3) = 1.0; // weight
+         }
+      }
+
+      // Resize for sweep in second direction
+      for (int i = 0; i < dim; ++i) { x[i]->SetSize(ncp[1]); }
+
+      // Do another sweep in the second direction
+      for (int i = 0; i < ncp[0]; i++)
+      {
+         for (int j = 0; j < ncp[1]; ++j)
+         {
+            (*x[0])[j] = (*patch)(i,j,k,0);
+            (*x[1])[j] = (*patch)(i,j,k,1);
+            (*x[2])[j] = (*patch)(i,j,k,2);
+         }
+
+         const bool reuse_factorization = i > 0;
+         kv[1].FindInterpolant(x, reuse_factorization);
+
+         for (int j = 0; j < ncp[1]; ++j)
+         {
+            (*patch)(i,j,k,0) = (*x[0])[j];
+            (*patch)(i,j,k,1) = (*x[1])[j];
+            (*patch)(i,j,k,2) = (*x[2])[j];
+         }
+      }
+   }
+
+   for (auto p : x) { delete p; }
+
+   Array<const NURBSPatch*> patches(1);
+   patches[0] = patch.get();
+   Mesh patch_topology = Mesh::MakeCartesian3D(1, 1, 1, Element::HEXAHEDRON);
+   NURBSExtension nurbsExt(&patch_topology, patches);
+
+   mesh = Mesh(nurbsExt);
+}
+
+void SurfaceInterpolator::WriteNURBSMesh(const std::string &basename,
+                                         bool visualization,
+                                         int x, int y, int w, int h)
+{
+   GridFunction *nodes = cmesh[0].GetNodes();
+   NURBSPatch patch2D(&kv[0], &kv[1], dim);
+   Array<const NURBSPatch*> patches(1);
+   patches[0] = &patch2D;
+   Mesh patch_topology = Mesh::MakeCartesian2D(1, 1, Element::QUADRILATERAL);
+   Array<int> dofs;
+   cmesh[0].NURBSext->GetPatchDofs(0, dofs);
+
+   MFEM_VERIFY(dofs.Size() == (nx + 1) * (ny + 1) * (orderNURBS + 1), "");
+
+   for (int j = 0; j < ncp[1]; ++j)
+   {
+      for (int i = 0; i < ncp[0]; i++)
+      {
+         const int dof = dofs[i + (ncp[0] * (j + (ncp[1] * orderNURBS)))];
+         for (int k = 0; k < 2; ++k) { patch2D(i,j,k) = (*nodes)[dim*dof + k]; }
+         patch2D(i,j,2) = 1.0; // weight
+      }
+   }
+
+   NURBSExtension nurbsExt(&patch_topology, patches);
+   Mesh mesh2D(nurbsExt);
+
+   FiniteElementCollection *fec = nodes->OwnFEC();
+   FiniteElementSpace fespace(&mesh2D, fec, dim, Ordering::byVDIM);
+   GridFunction nodes2D(&fespace);
+
+   const int n = mesh2D.GetNodes()->Size() / (dim - 1);
+   MFEM_VERIFY((dim - 1) * n == mesh2D.GetNodes()->Size(), "");
+   MFEM_VERIFY(dim * n == nodes2D.Size(), "");
+
+   Array<int> dofs2D;
+   mesh2D.NURBSext->GetPatchDofs(0, dofs2D);
+
+   for (int k = 0; k < dim; ++k)
+   {
+      const GridFunction &nodes_k = *cmesh[k].GetNodes();
+
+      for (int j = 0; j < ncp[1]; ++j)
+      {
+         for (int i = 0; i < ncp[0]; i++)
+         {
+            const int dof = dofs[i + (ncp[0] * (j + (ncp[1] * orderNURBS)))];
+            const int dof2D = dofs2D[i + (ncp[0] * j)];
+            nodes2D[(dim*dof2D) + k] = nodes_k[dim*dof + 2];
+         }
+      }
+   }
+
+   // Make mesh2D into a surface mesh with nodes given by nodes2D
+   mesh2D.NewNodes(nodes2D);
+
+   ofstream mesh_ofs(basename + ".mesh");
+   mesh_ofs.precision(8);
+   mesh2D.Print(mesh_ofs);
+
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      constexpr int visport = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "mesh\n" << mesh2D
+               << "window_title '" << basename << "'"
+               << "window_geometry "
+               << x << " " << y << " " << w << " " << h << "\n"
+               << "keys PPPPPPPPAattttt******\n"
+               << flush;
+   }
+}

miniapps/solvers/block-solvers.cpp

@@ -52,12 +52,13 @@
 //        (respectively 0), essential (respectively natural) boundary condition
 //        will be imposed on boundary with the i-th attribute.
 
+#include <fstream>
+#include <iostream>
+#include <functional>
+
 #include "mfem.hpp"
 #include "bramble_pasciak.hpp"
 #include "div_free_solver.hpp"
-#include <fstream>
-#include <iostream>
-#include <memory>
 
 using namespace std;
 using namespace mfem;
@@ -83,48 +84,54 @@ real_t natural_bc(const Vector & x);
        D: subset of the boundary where natural boundary condition is imposed. */
 class DarcyProblem
 {
-   OperatorPtr M_;
-   OperatorPtr B_;
-   Vector rhs_;
-   Vector ess_data_;
-   ParGridFunction u_;
-   ParGridFunction p_;
+   OperatorPtr M_, B_;
+   Vector rhs_, ess_data_;
+   ParGridFunction u_, p_;
    ParMesh mesh_;
-   ParBilinearForm *mVarf_;
-   ParMixedBilinearForm *bVarf_;
+   DFSSpaces dfs_spaces_;
+   std::function<bool (int)> refine_fn = [&](int num_refs)
+   {
+      for (int l = 0; l < num_refs; l++)
+      {
+         mesh_.UniformRefinement();
+         dfs_spaces_.CollectDFSData();
+      }
+      return true;
+   };
+   const bool dfs_refine_;
+   ParBilinearForm mVarf_;
+   ParMixedBilinearForm bVarf_;
    VectorFunctionCoefficient ucoeff_;
    FunctionCoefficient pcoeff_;
-   DFSSpaces dfs_spaces_;
    PWConstCoefficient mass_coeff;
    const IntegrationRule *irs_[Geometry::NumGeom];
 public:
    DarcyProblem(Mesh &mesh, int num_refines, int order, const char *coef_file,
                 Array<int> &ess_bdr, DFSParameters param);
 
-   HypreParMatrix& GetM() { return *M_.As<HypreParMatrix>(); }
-   HypreParMatrix& GetB() { return *B_.As<HypreParMatrix>(); }
+   const HypreParMatrix& GetM() const { return *M_.As<HypreParMatrix>(); }
+   const HypreParMatrix& GetB() const { return *B_.As<HypreParMatrix>(); }
    const Vector& GetRHS() { return rhs_; }
    const Vector& GetEssentialBC() { return ess_data_; }
    const DFSData& GetDFSData() const { return dfs_spaces_.GetDFSData(); }
    void ShowError(const Vector &sol, bool verbose);
    void VisualizeSolution(const Vector &sol, std::string tag, int visport = 19916);
-   ParBilinearForm* GetMform() const { return mVarf_; }
-   ParMixedBilinearForm* GetBform() const { return bVarf_; }
+   ParBilinearForm& GetMform() { return mVarf_; }
+   ParMixedBilinearForm& GetBform() { return bVarf_; }
 };
 
 DarcyProblem::DarcyProblem(Mesh &mesh, int num_refs, int order,
                            const char *coef_file, Array<int> &ess_bdr,
                            DFSParameters dfs_param)
-   : mesh_(MPI_COMM_WORLD, mesh), ucoeff_(mesh.Dimension(), u_exact),
-     pcoeff_(p_exact), dfs_spaces_(order, num_refs, &mesh_, ess_bdr, dfs_param),
+   : mesh_(MPI_COMM_WORLD, mesh),
+     dfs_spaces_(order, num_refs, &mesh_, ess_bdr, dfs_param),
+     dfs_refine_(refine_fn(num_refs)),
+     mVarf_(dfs_spaces_.GetHdivFES()),
+     bVarf_(dfs_spaces_.GetHdivFES(), dfs_spaces_.GetL2FES()),
+     ucoeff_(mesh.Dimension(), u_exact),
+     pcoeff_(p_exact),
      mass_coeff()
 {
-   for (int l = 0; l < num_refs; l++)
-   {
-      mesh_.UniformRefinement();
-      dfs_spaces_.CollectDFSData();
-   }
-
    Vector coef_vector(mesh.GetNE());
    coef_vector = 1.0;
    if (std::strcmp(coef_file, ""))
@@ -153,24 +160,20 @@ DarcyProblem::DarcyProblem(Mesh &mesh, int num_refs, int order,
    gform.AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
    gform.Assemble();
 
-   mVarf_ = new ParBilinearForm(dfs_spaces_.GetHdivFES());
-   bVarf_ = new ParMixedBilinearForm(dfs_spaces_.GetHdivFES(),
-                                     dfs_spaces_.GetL2FES());
+   mVarf_.AddDomainIntegrator(new VectorFEMassIntegrator(mass_coeff));
+   mVarf_.ComputeElementMatrices();
+   mVarf_.Assemble();
+   mVarf_.EliminateEssentialBC(ess_bdr, u_, fform);
 
-   mVarf_->AddDomainIntegrator(new VectorFEMassIntegrator(mass_coeff));
-   mVarf_->ComputeElementMatrices();
-   mVarf_->Assemble();
-   mVarf_->EliminateEssentialBC(ess_bdr, u_, fform);
+   mVarf_.Finalize();
+   M_.Reset(mVarf_.ParallelAssemble());
 
-   mVarf_->Finalize();
-   M_.Reset(mVarf_->ParallelAssemble());
-
-   bVarf_->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
-   bVarf_->Assemble();
-   bVarf_->SpMat() *= -1.0;
-   bVarf_->EliminateTrialEssentialBC(ess_bdr, u_, gform);
-   bVarf_->Finalize();
-   B_.Reset(bVarf_->ParallelAssemble());
+   bVarf_.AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+   bVarf_.Assemble();
+   bVarf_.SpMat() *= -1.0;
+   bVarf_.EliminateTrialEssentialBC(ess_bdr, u_, gform);
+   bVarf_.Finalize();
+   B_.Reset(bVarf_.ParallelAssemble());
 
    rhs_.SetSize(M_->NumRows() + B_->NumRows());
    Vector rhs_block0(rhs_.GetData(), M_->NumRows());
@@ -341,8 +344,8 @@ int main(int argc, char *argv[])
 
    // Generate components of the saddle point problem
    DarcyProblem darcy(*mesh, par_ref_levels, order, coef_file, ess_bdr, param);
-   HypreParMatrix& M = darcy.GetM();
-   HypreParMatrix& B = darcy.GetB();
+   const HypreParMatrix &M = darcy.GetM();
+   const HypreParMatrix &B = darcy.GetB();
    const DFSData& DFS_data = darcy.GetDFSData();
    delete mesh;
 

miniapps/solvers/block_fespace_operator.cpp

@@ -14,29 +14,27 @@
 namespace mfem
 {
 
-BlockFESpaceOperator::BlockFESpaceOperator(const
-                                           std::vector<const FiniteElementSpace*> &fespaces):
+BlockFESpaceOperator::BlockFESpaceOperator(const FESVector &fespaces):
    Operator(GetHeight(fespaces)),
    offsets(GetBlockOffsets(fespaces)),
    prolongColOffsets(GetProColBlockOffsets(fespaces)),
    restrictRowOffsets(GetResRowBlockOffsets(fespaces)),
    A(offsets),
-   prolongation(offsets,prolongColOffsets),
+   prolongation(offsets, prolongColOffsets),
    restriction(restrictRowOffsets, offsets)
 {
    for (size_t i = 0; i <fespaces.size(); i++)
    {
       // Since const_cast is required here, be sure to avoid using
       // BlockOperator::GetBlock on restriction or prolongation.
-      prolongation.SetDiagonalBlock(i,
-                                    const_cast<Operator *>(fespaces[i]->GetProlongationMatrix()));
-      restriction.SetDiagonalBlock(i,
-                                   const_cast<Operator *>(fespaces[i]->GetRestrictionOperator()));
+      auto prolongation_matrix = fespaces[i]->GetProlongationMatrix();
+      auto restriction_matrix = fespaces[i]->GetRestrictionOperator();
+      prolongation.SetDiagonalBlock(i, const_cast<Operator *>(prolongation_matrix));
+      restriction.SetDiagonalBlock(i, const_cast<Operator *>(restriction_matrix));
    }
 }
 
-int BlockFESpaceOperator::GetHeight(const std::vector<const FiniteElementSpace*>
-                                    &fespaces)
+int BlockFESpaceOperator::GetHeight(const FESVector &fespaces)
 {
    int height = 0;
    for (size_t i = 0; i < fespaces.size(); i++)
@@ -46,8 +44,7 @@ int BlockFESpaceOperator::GetHeight(const std::vector<const FiniteElementSpace*>
    return height;
 }
 
-Array<int> BlockFESpaceOperator::GetBlockOffsets(const
-                                                 std::vector<const FiniteElementSpace*> &fespaces)
+Array<int> BlockFESpaceOperator::GetBlockOffsets(const FESVector &fespaces)
 {
    Array<int> offsets(fespaces.size()+1);
    offsets[0] = 0;
@@ -60,8 +57,8 @@ Array<int> BlockFESpaceOperator::GetBlockOffsets(const
    return offsets;
 }
 
-Array<int> BlockFESpaceOperator::GetProColBlockOffsets(const
-                                                       std::vector<const FiniteElementSpace*> &fespaces)
+Array<int> BlockFESpaceOperator::GetProColBlockOffsets(const FESVector
+                                                       &fespaces)
 {
    Array<int> offsets(fespaces.size()+1);
    offsets[0] = 0;
@@ -83,8 +80,8 @@ Array<int> BlockFESpaceOperator::GetProColBlockOffsets(const
    return offsets;
 }
 
-Array<int> BlockFESpaceOperator::GetResRowBlockOffsets(const
-                                                       std::vector<const FiniteElementSpace*> &fespaces)
+Array<int> BlockFESpaceOperator::GetResRowBlockOffsets(const FESVector
+                                                       &fespaces)
 {
    Array<int> offsets(fespaces.size()+1);
    std::cout << "fespaces.size() = " << fespaces.size() << std::endl;

miniapps/solvers/block_fespace_operator.hpp

@@ -25,7 +25,8 @@ namespace mfem
 ///        L-Vectors. For example, a block may be a BilinearForm.
 class BlockFESpaceOperator : public Operator
 {
-private:
+   using FESVector = std::vector<const FiniteElementSpace*>;
+
    /// Offsets for the square "A" operator.
    Array<int> offsets;
    /// Column offsets for the prolongation operator.
@@ -39,33 +40,27 @@ private:
    /// Maps true dofs of each block to local dofs.
    BlockOperator restriction;
    /// Computes height for parent operator.
-   static int GetHeight(const std::vector<const FiniteElementSpace*>
-                        &fespaces);
+   static int GetHeight(const FESVector &fespaces);
    /// Computes offsets for A BlockOperator.
-   static Array<int> GetBlockOffsets(const std::vector<const FiniteElementSpace*>
-                                     &fespaces);
+   static Array<int> GetBlockOffsets(const FESVector &fespaces);
    /// Computes col_offsets for prolongation operator.
-   static Array<int> GetProColBlockOffsets(const
-                                           std::vector<const FiniteElementSpace*> &fespaces);
+   static Array<int> GetProColBlockOffsets(const FESVector &fespaces);
    /// Computes row_offsets for restriction operator.
-   static Array<int> GetResRowBlockOffsets(const
-                                           std::vector<const FiniteElementSpace*> &fespaces);
+   static Array<int> GetResRowBlockOffsets(const FESVector &fespaces);
+
 public:
    /// @brief Constructor for BlockFESpaceOperator.
    /// @param[in] fespaces Finite element spaces for diagonal blocks. Spaces are not owned.
-   BlockFESpaceOperator(const std::vector<const FiniteElementSpace*> &fespaces);
+   BlockFESpaceOperator(const FESVector &fespaces);
    const Operator* GetProlongation () const override;
    const Operator* GetRestriction () const override;
    void Mult(const Vector &x, Vector &y) const override {A.Mult(x,y);};
    /// @brief Wraps BlockOperator::SetBlock. Eventually would like this class to inherit
    /// from BlockOperator instead, but can't easily due to ownership of offset data
    /// in BlockOperator being by reference.
-   void SetBlock( int   iRow,
-                  int   iCol,
-                  Operator *  op,
-                  real_t   c = 1.0) {A.SetBlock(iRow, iCol, op, c);};
+   void SetBlock(int iRow, int iCol, Operator *op, real_t c = 1.0) { A.SetBlock(iRow, iCol, op, c); };
 };
 
 } // namespace mfem
 
-#endif
+#endif // MFEM_BLOCK_FESPACE_OPERATOR

miniapps/solvers/bramble_pasciak.cpp

@@ -9,70 +9,65 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-
 #include "bramble_pasciak.hpp"
 
 using namespace std;
 
-namespace mfem
-{
-namespace blocksolvers
+namespace mfem::blocksolvers
 {
+
 /// Bramble-Pasciak Solver
-BramblePasciakSolver::BramblePasciakSolver(
-   ParBilinearForm *mVarf,
-   ParMixedBilinearForm *bVarf,
-   const BPSParameters &param)
-   : DarcySolver(mVarf->ParFESpace()->GetTrueVSize(),
-                 bVarf->TestFESpace()->GetTrueVSize())
+BramblePasciakSolver::BramblePasciakSolver(ParBilinearForm &mVarf,
+                                           ParMixedBilinearForm &bVarf,
+                                           const BPSParameters &param)
+   : DarcySolver(mVarf.ParFESpace()->GetTrueVSize(),
+                 bVarf.TestFESpace()->GetTrueVSize())
 {
-   M_.reset(mVarf->ParallelAssemble());
-   B_.reset(bVarf->ParallelAssemble());
-   Q_.reset(ConstructMassPreconditioner(*mVarf, param.q_scaling));
+   M_.reset(mVarf.ParallelAssemble());
+   B_.reset(bVarf.ParallelAssemble());
+   Q_.reset(ConstructMassPreconditioner(mVarf, param.q_scaling));
 
    Vector diagM;
    M_->GetDiag(diagM);
-   auto BT = B_->Transpose();
-   auto invDBt = new HypreParMatrix(*BT);
+   std::unique_ptr<HypreParMatrix> invDBt(B_->Transpose());
    invDBt->InvScaleRows(diagM);
-   auto S = ParMult(B_.get(), invDBt);
+   S_.reset(ParMult(B_.get(), invDBt.get(), true));
    M0_.Reset(new HypreDiagScale(*M_));
-   M1_.Reset(new HypreBoomerAMG(*S));
+   M1_.Reset(new HypreBoomerAMG(*S_));
    M1_.As<HypreBoomerAMG>()->SetPrintLevel(0);
 
    Init(*M_, *B_, *Q_, *M0_.As<Solver>(), *M1_.As<Solver>(), param);
 }
 
-BramblePasciakSolver::BramblePasciakSolver(
-   HypreParMatrix &M, HypreParMatrix &B, HypreParMatrix &Q,
-   Solver &M0, Solver &M1,
-   const BPSParameters &param)
+BramblePasciakSolver::BramblePasciakSolver(HypreParMatrix &M,
+                                           HypreParMatrix &B,
+                                           HypreParMatrix &Q,
+                                           Solver &M0, Solver &M1,
+                                           const BPSParameters &param)
    : DarcySolver(M.NumRows(), B.NumRows())
 {
    Init(M, B, Q, M0, M1, param);
 }
 
-void BramblePasciakSolver::Init(
-   HypreParMatrix &M, HypreParMatrix &B, HypreParMatrix &Q,
-   Solver &M0, Solver &M1,
-   const BPSParameters &param)
+void BramblePasciakSolver::Init(HypreParMatrix &M,
+                                HypreParMatrix &B,
+                                HypreParMatrix &Q,
+                                Solver &M0, Solver &M1,
+                                const BPSParameters &param)
 {
-   auto Bt = new TransposeOperator(&B);
+   Bt_ = std::make_unique<TransposeOperator>(&B);
    auto invQ = new HypreDiagScale(Q);
 
    use_bpcg = param.use_bpcg;
 
    if (use_bpcg)
    {
-      oop_ = new BlockOperator(offsets_);
-      oop_->owns_blocks = false;
+      oop_ = std::make_unique<BlockOperator>(offsets_);
       oop_->SetBlock(0, 0, &M);
-      oop_->SetBlock(0, 1, Bt);
+      oop_->SetBlock(0, 1, Bt_.get());
       oop_->SetBlock(1, 0, &B);
-
       // cpc_ unused in bpcg
       auto temp_cpc = new BlockDiagonalPreconditioner(offsets_);
-      temp_cpc->owns_blocks = true;
       temp_cpc->SetDiagonalBlock(0, invQ);
       temp_cpc->SetDiagonalBlock(1, &M1);
       // tri(1,0) = B M0 = B invQ
@@ -81,51 +76,48 @@ void BramblePasciakSolver::Init(
       auto BinvQ = new ProductOperator(&B, invQ, false, false);
       // tri
       auto temp_tri = new BlockOperator(offsets_);
-      temp_tri->owns_blocks = true;
       temp_tri->SetBlock(0, 0, id_m);
       temp_tri->SetBlock(1, 1, id_b, -1.0);
       temp_tri->SetBlock(1, 0, BinvQ);
+      temp_tri->owns_blocks = 1;
 
-      ppc_ = new ProductOperator(temp_cpc, temp_tri, true, true);
+      ppc_ = std::make_unique<ProductOperator>(temp_cpc, temp_tri, true, true);
 
-      ipc_ = new BlockOperator(offsets_);
-      ipc_->owns_blocks = false;
+      ipc_ = std::make_unique<BlockOperator>(offsets_);
       ipc_->SetDiagonalBlock(0, invQ);
+      ipc_->owns_blocks = 1;
 
       // bpcg
-      solver_.reset(new BPCGSolver(M.GetComm(), *ipc_, *ppc_));
+      solver_ = std::make_unique<BPCGSolver>(M.GetComm(), ipc_.get(), ppc_.get());
       solver_->SetOperator(*oop_);
    }
    else
    {
       // oop_ unused in cg
       auto temp_oop = new BlockOperator(offsets_);
-      temp_oop->owns_blocks = false;
       temp_oop->SetBlock(0, 0, &M);
-      temp_oop->SetBlock(0, 1, Bt);
+      temp_oop->SetBlock(0, 1, Bt_.get());
       temp_oop->SetBlock(1, 0, &B);
 
       // ipc_ unused in cg
       auto temp_ipc = new BlockOperator(offsets_);
-      temp_ipc->owns_blocks = false;
       temp_ipc->SetDiagonalBlock(0, invQ);
+      temp_ipc->owns_blocks = 1;
 
       // temp_AN = temp_oop * temp_ipc
       auto temp_AN = new ProductOperator(temp_oop, temp_ipc, true, true);
 
       // Required for updating the RHS
       auto id = new IdentityOperator(M.NumRows()+B.NumRows());
-      map_ = new SumOperator(temp_AN, 1.0, id, -1.0, true, true);
+      map_ = std::make_unique<SumOperator>(temp_AN, 1.0, id, -1.0, true, true);
+      mop_ = std::make_unique<ProductOperator>(map_.get(), temp_oop, false, false);
 
-      mop_ = new ProductOperator(map_, temp_oop, false, true);
-
-      cpc_ = new BlockDiagonalPreconditioner(offsets_);
-      cpc_->owns_blocks = true;
+      cpc_ = std::make_unique<BlockDiagonalPreconditioner>(offsets_);
       cpc_->SetDiagonalBlock(0, &M0);
       cpc_->SetDiagonalBlock(1, &M1);
 
       // (P)CG
-      solver_.reset(new CGSolver(M.GetComm()));
+      solver_ = std::make_unique<CGSolver>(M.GetComm());
       solver_->SetOperator(*mop_);
       solver_->SetPreconditioner(*cpc_);
    }
@@ -133,7 +125,7 @@ void BramblePasciakSolver::Init(
 }
 
 HypreParMatrix *BramblePasciakSolver::ConstructMassPreconditioner(
-   ParBilinearForm &mVarf, real_t q_scaling)
+   const ParBilinearForm &mVarf, real_t q_scaling)
 {
    MFEM_ASSERT((q_scaling > 0.0) && (q_scaling < 1.0),
                "Invalid Q-scaling factor: q_scaling = " << q_scaling );
@@ -167,7 +159,7 @@ HypreParMatrix *BramblePasciakSolver::ConstructMassPreconditioner(
       Vector x(M_i.Height()), Mx(M_i.Height()), diff(M_i.Height());
       real_t eval_prev = 0.0;
       int iter = 0;
-      x.Randomize(696383552+779345*i);
+      x.Randomize(static_cast<int>(696383552LL+779345LL*i));
 #if defined(MFEM_USE_DOUBLE)
       const real_t rel_tol = 1e-12;
 #elif defined(MFEM_USE_SINGLE)
@@ -400,5 +392,5 @@ void BPCGSolver::Mult(const Vector &b, Vector &x) const
    final_norm = sqrt(delta);
    Monitor(final_iter, final_norm, r, x, true);
 }
-} // namespace blocksolvers
-} // namespace mfem
+
+} // namespace mfem::blocksolvers

miniapps/solvers/bramble_pasciak.hpp

@@ -49,9 +49,7 @@
 #include "darcy_solver.hpp"
 #include <memory>
 
-namespace mfem
-{
-namespace blocksolvers
+namespace mfem::blocksolvers
 {
 
 /// Parameters for the BramblePasciakSolver method
@@ -70,11 +68,11 @@ protected:
    void UpdateVectors();
 
 public:
-   BPCGSolver(const Operator &ipc, const Operator &ppc) { pprec = &ppc; iprec = &ipc; }
+   BPCGSolver(const Operator *ipc, const Operator *ppc): iprec(ipc), pprec(ppc) {}
 
 #ifdef MFEM_USE_MPI
-   BPCGSolver(MPI_Comm comm_, const Operator &ipc, const Operator &ppc)
-      : IterativeSolver(comm_) { pprec = &ppc; iprec = &ipc; }
+   BPCGSolver(MPI_Comm comm_, const Operator *ipc, const Operator *ppc)
+      : IterativeSolver(comm_), iprec(ipc), pprec(ppc) { }
 #endif
 
    void SetOperator(const Operator &op) override
@@ -83,11 +81,9 @@ public:
    void SetPreconditioner(Solver &pc) override
    { if (Mpi::Root()) { MFEM_WARNING("SetPreconditioner has no effect on BPCGSolver.\n"); } }
 
-   virtual void SetIncompletePreconditioner(const Operator &ipc)
-   { iprec = &ipc; }
+   virtual void SetIncompletePreconditioner(const Operator *ipc) { iprec = ipc; }
 
-   virtual void SetParticularPreconditioner(const Operator &ppc)
-   { pprec = &ppc; }
+   virtual void SetParticularPreconditioner(const Operator *ppc) { pprec = ppc; }
 
    void Mult(const Vector &b, Vector &x) const override;
 };
@@ -116,23 +112,20 @@ public:
     1. P. Vassilevski, Multilevel Block Factorization Preconditioners (Appendix
        F.3), Springer, 2008.
 
-    2. J. Bramble and J. Pasciak.  A Preconditioning Technique for Indefinite
+    2. J. Bramble and J. Pasciak. A Preconditioning Technique for Indefinite
        Systems Resulting From Mixed Approximations of Elliptic Problems,
        Mathematics of Computation, 50:1-17, 1988. */
 class BramblePasciakSolver : public DarcySolver
 {
    mutable bool use_bpcg;
    std::unique_ptr<IterativeSolver> solver_;
-   BlockOperator *oop_, *ipc_;
-   ProductOperator *mop_;
-   SumOperator *map_;
-   ProductOperator *ppc_;
-   BlockDiagonalPreconditioner *cpc_;
-   std::unique_ptr<HypreParMatrix> M_;
-   std::unique_ptr<HypreParMatrix> B_;
-   std::unique_ptr<HypreParMatrix> Q_;
-   OperatorPtr M0_;
-   OperatorPtr M1_;
+   std::unique_ptr<BlockOperator> oop_, ipc_;
+   std::unique_ptr<ProductOperator> mop_, ppc_;
+   std::unique_ptr<SumOperator> map_;
+   std::unique_ptr<BlockDiagonalPreconditioner> cpc_;
+   std::unique_ptr<HypreParMatrix> M_, B_, Q_, S_;
+   std::unique_ptr<TransposeOperator> Bt_;
+   OperatorPtr M0_, M1_;
    Array<int> ess_zero_dofs_;
 
    void Init(HypreParMatrix &M, HypreParMatrix &B,
@@ -142,8 +135,8 @@ class BramblePasciakSolver : public DarcySolver
 public:
    /// System and mass preconditioner are constructed from bilinear forms
    BramblePasciakSolver(
-      ParBilinearForm *mVarf,
-      ParMixedBilinearForm *bVarf,
+      ParBilinearForm &mVarf,
+      ParMixedBilinearForm &bVarf,
       const BPSParameters &param);
 
    /// System and mass preconditioner are user-provided
@@ -158,8 +151,8 @@ public:
        element T:
                                 M_T x_T = lambda_T diag(M_T) x_T.
        We set Q_T = alpha * min(lambda_T) * diag(M_T), 0 < alpha < 1. */
-   static HypreParMatrix *ConstructMassPreconditioner(ParBilinearForm &mVarf,
-                                                      real_t alpha = 0.5);
+   static HypreParMatrix *ConstructMassPreconditioner(const ParBilinearForm &mVarf,
+                                                      const real_t alpha = 0.5);
 
    void Mult(const Vector &x, Vector &y) const override;
    void SetOperator(const Operator &op) override { }
@@ -167,7 +160,6 @@ public:
    int GetNumIterations() const override { return solver_->GetNumIterations(); }
 };
 
-} // namespace blocksolvers
-} // namespace mfem
+} // namespace mfem::blocksolvers
 
 #endif // MFEM_BP_SOLVER_HPP

miniapps/solvers/darcy_solver.cpp

@@ -13,10 +13,9 @@
 
 using namespace std;
 
-namespace mfem
-{
-namespace blocksolvers
+namespace mfem::blocksolvers
 {
+
 void SetOptions(IterativeSolver& solver, const IterSolveParameters& param)
 {
    solver.SetPrintLevel(param.print_level);
@@ -49,7 +48,7 @@ BDPMinresSolver::BDPMinresSolver(const HypreParMatrix& M,
    prec_.SetDiagonalBlock(0, new HypreDiagScale(M));
    prec_.SetDiagonalBlock(1, new HypreBoomerAMG(*S_.As<HypreParMatrix>()));
    static_cast<HypreBoomerAMG&>(prec_.GetDiagonalBlock(1)).SetPrintLevel(0);
-   prec_.owns_blocks = true;
+   prec_.owns_blocks = 1;
 
    SetOptions(solver_, param);
    solver_.SetOperator(op_);
@@ -61,5 +60,5 @@ void BDPMinresSolver::Mult(const Vector & x, Vector & y) const
    solver_.Mult(x, y);
    for (int dof : ess_zero_dofs_) { y[dof] = 0.0; }
 }
-} // namespace blocksolvers
-} // namespace mfem
+
+} // namespace mfem::blocksolvers

miniapps/solvers/darcy_solver.hpp

@@ -13,13 +13,10 @@
 #define MFEM_DARCY_SOLVER_HPP
 
 #include "mfem.hpp"
-#include <memory>
-#include <vector>
 
-namespace mfem
-{
-namespace blocksolvers
+namespace mfem::blocksolvers
 {
+
 struct IterSolveParameters
 {
    int print_level = 0;
@@ -32,8 +29,6 @@ struct IterSolveParameters
    real_t rel_tol = 1e-5;
 #else
 #error "Only single and double precision are supported!"
-   real_t abs_tol = 1e-12;
-   real_t rel_tol = 1e-9;
 #endif
 };
 
@@ -68,7 +63,7 @@ public:
    void SetEssZeroDofs(const Array<int>& dofs) { dofs.Copy(ess_zero_dofs_); }
    int GetNumIterations() const override { return solver_.GetNumIterations(); }
 };
-} // namespace blocksolvers
-} // namespace mfem
+
+} // namespace mfem::blocksolvers
 
 #endif // MFEM_DARCY_SOLVER_HPP

miniapps/solvers/div_free_solver.cpp

@@ -13,16 +13,16 @@
 
 using namespace std;
 
-namespace mfem
+namespace mfem::blocksolvers
 {
-namespace blocksolvers
+
+static HypreParMatrix* TwoStepsRAP(const HypreParMatrix *Rt,
+                                   const HypreParMatrix *A,
+                                   const HypreParMatrix *P)
 {
-HypreParMatrix* TwoStepsRAP(const HypreParMatrix& Rt, const HypreParMatrix& A,
-                            const HypreParMatrix& P)
-{
-   OperatorPtr R(Rt.Transpose());
-   OperatorPtr RA(ParMult(R.As<HypreParMatrix>(), &A));
-   return ParMult(RA.As<HypreParMatrix>(), &P, true);
+   OperatorPtr R(Rt->Transpose());
+   OperatorPtr RA(ParMult(R.As<HypreParMatrix>(), A));
+   return ParMult(RA.As<HypreParMatrix>(), P, true);
 }
 
 void GetRowColumnsRef(const SparseMatrix& A, int row, Array<int>& cols)
@@ -59,34 +59,36 @@ DFSSpaces::DFSSpaces(int order, int num_refine, ParMesh *mesh,
 
    if (mesh->Dimension() == 3)
    {
-      hcurl_fec_.reset(new ND_FECollection(order+1, mesh->Dimension()));
+      hcurl_fec_ = std::make_unique<ND_FECollection>(order+1, mesh->Dimension());
    }
    else
    {
-      hcurl_fec_.reset(new H1_FECollection(order+1, mesh->Dimension()));
+      hcurl_fec_ = std::make_unique<H1_FECollection>(order+1, mesh->Dimension());
    }
 
    all_bdr_attr_.SetSize(ess_attr.Size(), 1);
-   hdiv_fes_.reset(new ParFiniteElementSpace(mesh, &hdiv_fec_));
-   l2_fes_.reset(new ParFiniteElementSpace(mesh, &l2_fec_));
-   coarse_hdiv_fes_.reset(new ParFiniteElementSpace(*hdiv_fes_));
-   coarse_l2_fes_.reset(new ParFiniteElementSpace(*l2_fes_));
-   l2_0_fes_.reset(new ParFiniteElementSpace(mesh, &l2_0_fec_));
+   hdiv_fes_ = std::make_unique<ParFiniteElementSpace>(mesh, &hdiv_fec_);
+   l2_fes_ = std::make_unique<ParFiniteElementSpace>(mesh, &l2_fec_);
+   coarse_hdiv_fes_ = std::make_unique<ParFiniteElementSpace>(*hdiv_fes_);
+   coarse_l2_fes_ = std::make_unique<ParFiniteElementSpace>(*l2_fes_);
+   l2_0_fes_ = std::make_unique<ParFiniteElementSpace>(mesh, &l2_0_fec_);
    l2_0_fes_->SetUpdateOperatorType(Operator::MFEM_SPARSEMAT);
    el_l2dof_.reserve(num_refine+1);
    el_l2dof_.push_back(ElemToDof(*coarse_l2_fes_));
 
    data_.agg_hdivdof.resize(num_refine);
    data_.agg_l2dof.resize(num_refine);
-   data_.P_hdiv.resize(num_refine, OperatorPtr(Operator::Hypre_ParCSR));
-   data_.P_l2.resize(num_refine, OperatorPtr(Operator::Hypre_ParCSR));
+   data_.P_hdiv.resize(num_refine);
+   data_.P_l2.resize(num_refine);
+
    data_.Q_l2.resize(num_refine);
    hdiv_fes_->GetEssentialTrueDofs(ess_attr, data_.coarsest_ess_hdivdofs);
    data_.C.resize(num_refine+1);
+   data_.Ae.resize(num_refine+1);
 
-   hcurl_fes_.reset(new ParFiniteElementSpace(mesh, hcurl_fec_.get()));
-   coarse_hcurl_fes_.reset(new ParFiniteElementSpace(*hcurl_fes_));
-   data_.P_hcurl.resize(num_refine, OperatorPtr(Operator::Hypre_ParCSR));
+   hcurl_fes_ = std::make_unique<ParFiniteElementSpace>(mesh, hcurl_fec_.get());
+   coarse_hcurl_fes_ = std::make_unique<ParFiniteElementSpace>(*hcurl_fes_);
+   data_.P_hcurl.resize(num_refine);
 }
 
 SparseMatrix* AggToInteriorDof(const Array<int>& bdr_truedofs,
@@ -104,8 +106,8 @@ SparseMatrix* AggToInteriorDof(const Array<int>& bdr_truedofs,
    agg_tdof_T.As<HypreParMatrix>()->GetDiag(tdof_agg);
    agg_tdof_T.As<HypreParMatrix>()->GetOffd(is_shared, trash);
 
-   int * I = new int [tdof_agg.NumRows()+1]();
-   int * J = new int[tdof_agg.NumNonZeroElems()];
+   int *I = new int[tdof_agg.NumRows()+1]();
+   int *J = new int[tdof_agg.NumNonZeroElems()];
 
    Array<int> is_bdr;
    FiniteElementSpace::ListToMarker(bdr_truedofs, tdof_agg.NumRows(), is_bdr);
@@ -119,7 +121,7 @@ SparseMatrix* AggToInteriorDof(const Array<int>& bdr_truedofs,
       J[counter++] = tdof_agg.GetRowColumns(i)[0];
    }
 
-   real_t * D = new real_t[I[tdof_agg.NumRows()]];
+   auto *D = new real_t[I[tdof_agg.NumRows()]];
    std::fill_n(D, I[tdof_agg.NumRows()], 1.0);
 
    SparseMatrix intdof_agg(I, J, D, tdof_agg.NumRows(), tdof_agg.NumCols());
@@ -146,20 +148,21 @@ void DFSSpaces::MakeDofRelationTables(int level)
 
 void DFSSpaces::CollectDFSData()
 {
-   auto GetP = [this](OperatorPtr& P, unique_ptr<ParFiniteElementSpace>& cfes,
-                      ParFiniteElementSpace& fes, bool remove_zero)
+   auto GetP = [&](std::unique_ptr<OperatorPtr> &P,
+                   std::unique_ptr<ParFiniteElementSpace> &cfes,
+                   ParFiniteElementSpace& fes, const bool remove_zero)
    {
       fes.Update();
-      fes.GetTrueTransferOperator(*cfes, P);
-      if (remove_zero)
-      {
-         P.As<HypreParMatrix>()->DropSmallEntries(1e-16);
-      }
+      auto T = new OperatorHandle(Operator::Hypre_ParCSR);
+      fes.GetTrueTransferOperator(*cfes, *T);
+      P.reset(T);
+      if (remove_zero) { P->As<HypreParMatrix>()->DropSmallEntries(1e-16); }
       (level_ < (int)data_.P_l2.size()-1) ? cfes->Update() : cfes.reset();
    };
 
    GetP(data_.P_hdiv[level_], coarse_hdiv_fes_, *hdiv_fes_, true);
    GetP(data_.P_l2[level_], coarse_l2_fes_, *l2_fes_, false);
+
    MakeDofRelationTables(level_);
 
    GetP(data_.P_hcurl[level_], coarse_hcurl_fes_, *hcurl_fes_, true);
@@ -171,7 +174,9 @@ void DFSSpaces::CollectDFSData()
    data_.C[level_+1].Reset(curl.ParallelAssemble());
    mfem::Array<int> ess_hcurl_tdof;
    hcurl_fes_->GetEssentialTrueDofs(ess_bdr_attr_, ess_hcurl_tdof);
-   data_.C[level_+1].As<HypreParMatrix>()->EliminateCols(ess_hcurl_tdof);
+   data_.Ae[level_+1].reset(
+      data_.C[level_+1].As<HypreParMatrix>()
+      ->EliminateCols(ess_hcurl_tdof));
 
    ++level_;
 
@@ -189,7 +194,7 @@ void DFSSpaces::DataFinalize()
    SparseMatrix P_l2;
    for (int l = (int)data_.P_l2.size()-1; l >= 0; --l)
    {
-      data_.P_l2[l].As<HypreParMatrix>()->GetDiag(P_l2);
+      data_.P_l2[l]->As<HypreParMatrix>()->GetDiag(P_l2);
       OperatorPtr PT_l2(Transpose(P_l2));
       auto PTW = Mult(*PT_l2.As<SparseMatrix>(), *W.As<SparseMatrix>());
       auto cW = Mult(*PTW, P_l2);
@@ -245,7 +250,7 @@ SaddleSchwarzSmoother::SaddleSchwarzSmoother(const HypreParMatrix& M,
                                              const SparseMatrix& agg_hdivdof,
                                              const SparseMatrix& agg_l2dof,
                                              const HypreParMatrix& P_l2,
-                                             const HypreParMatrix& Q_l2)
+                                             const ProductOperator& Q_l2)
    : Solver(M.NumRows() + B.NumRows()), agg_hdivdof_(agg_hdivdof),
      agg_l2dof_(agg_l2dof), solvers_loc_(agg_l2dof.NumRows())
 {
@@ -312,23 +317,27 @@ void SaddleSchwarzSmoother::Mult(const Vector & x, Vector & y) const
    blk_y.GetBlock(1) -= coarse_l2_projection;
 }
 
-DivFreeSolver::DivFreeSolver(const HypreParMatrix &M, const HypreParMatrix& B,
+DivFreeSolver::DivFreeSolver(const HypreParMatrix &M,
+                             const HypreParMatrix &B,
                              const DFSData& data)
    : DarcySolver(M.NumRows(), B.NumRows()), data_(data), param_(data.param),
-     BT_(B.Transpose()), BBT_solver_(B, param_.BBT_solve_param),
-     ops_offsets_(data.P_l2.size()+1), ops_(ops_offsets_.size()),
-     blk_Ps_(ops_.Size()-1), smoothers_(ops_.Size())
+     BT_(B.Transpose()),
+     BBT_solver_(B, param_.BBT_solve_param),
+     ops_offsets_(data.P_l2.size()+1),
+     ops_(ops_offsets_.size()),
+     blk_Ps_(ops_.size()-1),
+     smoothers_(ops_.size())
 {
    ops_offsets_.back().MakeRef(DarcySolver::offsets_);
-   ops_.Last() = new BlockOperator(ops_offsets_.back());
-   ops_.Last()->SetBlock(0, 0, const_cast<HypreParMatrix*>(&M));
-   ops_.Last()->SetBlock(1, 0, const_cast<HypreParMatrix*>(&B));
-   ops_.Last()->SetBlock(0, 1, BT_.Ptr());
+   ops_.back() = std::make_unique<BlockOperator>(ops_offsets_.back());
+   ops_.back()->SetBlock(0, 0, const_cast<HypreParMatrix*>(&M));
+   ops_.back()->SetBlock(1, 0, const_cast<HypreParMatrix*>(&B));
+   ops_.back()->SetBlock(0, 1, BT_.Ptr());
 
    for (int l = data.P_l2.size(); l >= 0; --l)
    {
-      auto& M_f = static_cast<const HypreParMatrix&>(ops_[l]->GetBlock(0, 0));
-      auto& B_f = static_cast<const HypreParMatrix&>(ops_[l]->GetBlock(1, 0));
+      auto &M_f = static_cast<const HypreParMatrix&>(ops_[l]->GetBlock(0, 0));
+      auto &B_f = static_cast<const HypreParMatrix&>(ops_[l]->GetBlock(1, 0));
 
       if (l == 0)
       {
@@ -343,123 +352,112 @@ DivFreeSolver::DivFreeSolver(const HypreParMatrix &M, const HypreParMatrix& B,
 
          const IterSolveParameters& param = param_.coarse_solve_param;
          auto coarse_solver = new BDPMinresSolver(M_f, B_f, param);
-         if (ops_.Size() > 1)
+         if (ops_.size() > 1)
          {
             coarse_solver->SetEssZeroDofs(data.coarsest_ess_hdivdofs);
          }
-         smoothers_[l] = coarse_solver;
+         smoothers_[l].reset(coarse_solver);
          continue;
       }
 
-      HypreParMatrix& P_hdiv_l = *data.P_hdiv[l-1].As<HypreParMatrix>();
-      HypreParMatrix& P_l2_l = *data.P_l2[l-1].As<HypreParMatrix>();
+      auto P_hdiv_l = data.P_hdiv[l-1]->As<HypreParMatrix>();
+      auto P_l2_l = data.P_l2[l-1]->As<HypreParMatrix>();
       SparseMatrix& agg_hdivdof_l = *data.agg_hdivdof[l-1].As<SparseMatrix>();
       SparseMatrix& agg_l2dof_l = *data.agg_l2dof[l-1].As<SparseMatrix>();
-      HypreParMatrix& Q_l2_l = *data.Q_l2[l-1].As<HypreParMatrix>();
-      HypreParMatrix* C_l = data.C[l].As<HypreParMatrix>();
+      ProductOperator& Q_l2_l = *data.Q_l2[l-1].As<ProductOperator>();
+      auto* C_l = data.C[l].As<HypreParMatrix>();
 
       auto S0 = new SaddleSchwarzSmoother(M_f, B_f, agg_hdivdof_l,
-                                          agg_l2dof_l, P_l2_l, Q_l2_l);
+                                          agg_l2dof_l, *P_l2_l, Q_l2_l);
       if (param_.coupled_solve)
       {
          auto S1 = new BlockDiagonalPreconditioner(ops_offsets_[l]);
          S1->SetDiagonalBlock(0, new AuxSpaceSmoother(M_f, C_l));
-         S1->owns_blocks = true;
-         smoothers_[l] = new ProductSolver(ops_[l], S0, S1, false, true, true);
+         S1->owns_blocks = 1;
+         smoothers_[l] =
+            std::make_unique<ProductSolver>(ops_[l].get(), S0, S1, false, true, true);
       }
       else
       {
-         smoothers_[l] = S0;
+         smoothers_[l].reset(S0);
       }
 
-      HypreParMatrix* M_c = TwoStepsRAP(P_hdiv_l, M_f, P_hdiv_l);
-      HypreParMatrix* B_c = TwoStepsRAP(P_l2_l, B_f, P_hdiv_l);
+      HypreParMatrix* M_c = TwoStepsRAP(P_hdiv_l, &M_f, P_hdiv_l);
+      HypreParMatrix* B_c = TwoStepsRAP(P_l2_l, &B_f, P_hdiv_l);
 
       ops_offsets_[l-1].SetSize(3, 0);
       ops_offsets_[l-1][1] = M_c->NumRows();
       ops_offsets_[l-1][2] = M_c->NumRows() + B_c->NumRows();
 
-      blk_Ps_[l-1] = new BlockOperator(ops_offsets_[l], ops_offsets_[l-1]);
-      blk_Ps_[l-1]->SetBlock(0, 0, &P_hdiv_l);
-      blk_Ps_[l-1]->SetBlock(1, 1, &P_l2_l);
+      blk_Ps_[l-1] =
+         std::make_unique<BlockOperator>(ops_offsets_[l], ops_offsets_[l-1]);
+      blk_Ps_[l-1]->SetBlock(0, 0, P_hdiv_l);
+      blk_Ps_[l-1]->SetBlock(1, 1, P_l2_l);
 
-      ops_[l-1] = new BlockOperator(ops_offsets_[l-1]);
+      ops_[l-1] =
+         std::make_unique<BlockOperator>(ops_offsets_[l-1]);
       ops_[l-1]->SetBlock(0, 0, M_c);
       ops_[l-1]->SetBlock(1, 0, B_c);
       ops_[l-1]->SetBlock(0, 1, B_c->Transpose());
-      ops_[l-1]->owns_blocks = true;
+      ops_[l-1]->owns_blocks = 1;
    }
 
-   Array<bool> own_ops(ops_.Size());
-   Array<bool> own_smoothers(smoothers_.Size());
-   Array<bool> own_Ps(blk_Ps_.Size());
-   own_ops = true;
-   own_smoothers = true;
-   own_Ps = true;
-
    if (data_.P_l2.size() == 0) { return; }
 
+   Array<bool> own_ops(ops_.size());
+   Array<bool> own_smoothers(smoothers_.size());
+   Array<bool> own_blk_Ps(blk_Ps_.size());
+   own_ops = false, own_smoothers = false, own_blk_Ps = false;
+
+   Array<Solver*> smoothers(smoothers_.size());
+
    if (param_.coupled_solve)
    {
       solver_.Reset(new GMRESSolver(B.GetComm()));
-      solver_.As<GMRESSolver>()->SetOperator(*(ops_.Last()));
-      prec_.Reset(new Multigrid(ops_, smoothers_, blk_Ps_,
-                                own_ops, own_smoothers, own_Ps));
+      solver_.As<GMRESSolver>()->SetOperator(*(ops_.back()));
+      Array<BlockOperator*> ops(ops_.size()), blk_Ps(blk_Ps_.size());
+      for (size_t i = 0; i < ops_.size(); ++i) { ops[i] = ops_[i].get(); }
+      for (size_t i = 0; i < blk_Ps_.size(); ++i) { blk_Ps[i] = blk_Ps_[i].get(); }
+      for (size_t i = 0; i < smoothers_.size(); ++i) { smoothers[i] = smoothers_[i].get(); }
+      prec_.Reset(new Multigrid(ops, smoothers, blk_Ps,
+                                own_ops, own_smoothers, own_blk_Ps));
    }
    else
    {
       Array<HypreParMatrix*> ops(data_.P_hcurl.size()+1);
-      Array<Solver*> smoothers(ops.Size());
       Array<HypreParMatrix*> Ps(data_.P_hcurl.size());
-      own_Ps = false;
-
-      HypreParMatrix& C_finest = *data.C.back().As<HypreParMatrix>();
-      ops.Last() = TwoStepsRAP(C_finest, M, C_finest);
+      auto C_finest = data.C.back().As<HypreParMatrix>();
+      ops.Last() = TwoStepsRAP(C_finest, &M, C_finest);
       ops.Last()->EliminateZeroRows();
       ops.Last()->DropSmallEntries(1e-14);
-
       solver_.Reset(new CGSolver(B.GetComm()));
       solver_.As<CGSolver>()->SetOperator(*ops.Last());
       smoothers.Last() = new HypreSmoother(*ops.Last());
       static_cast<HypreSmoother*>(smoothers.Last())->SetOperatorSymmetry(true);
-
       for (int l = Ps.Size()-1; l >= 0; --l)
       {
-         Ps[l] = data_.P_hcurl[l].As<HypreParMatrix>();
-         ops[l] = TwoStepsRAP(*Ps[l], *ops[l+1], *Ps[l]);
+         Ps[l] = data_.P_hcurl[l]->As<HypreParMatrix>();
+         ops[l] = TwoStepsRAP(Ps[l], ops[l+1], Ps[l]);
          ops[l]->DropSmallEntries(1e-14);
          smoothers[l] = new HypreSmoother(*ops[l]);
          static_cast<HypreSmoother*>(smoothers[l])->SetOperatorSymmetry(true);
       }
-
-      prec_.Reset(new Multigrid(ops, smoothers, Ps, own_ops, own_smoothers, own_Ps));
+      own_ops = true, own_smoothers = true;
+      prec_.Reset(new Multigrid(ops, smoothers, Ps,
+                                own_ops, own_smoothers, own_blk_Ps));
    }
 
    solver_.As<IterativeSolver>()->SetPreconditioner(*prec_.As<Solver>());
    SetOptions(*solver_.As<IterativeSolver>(), param_);
 }
 
-DivFreeSolver::~DivFreeSolver()
-{
-   if (param_.coupled_solve) { return; }
-   for (int i = 0; i < ops_.Size(); ++i)
-   {
-      delete ops_[i];
-      delete smoothers_[i];
-      if (i == ops_.Size() - 1) { break; }
-      delete blk_Ps_[i];
-   }
-}
-
 void DivFreeSolver::SolveParticular(const Vector& rhs, Vector& sol) const
 {
-   std::vector<Vector> rhss(smoothers_.Size());
-   std::vector<Vector> sols(smoothers_.Size());
-
+   std::vector<Vector> rhss(smoothers_.size()), sols(smoothers_.size());
    rhss.back().SetDataAndSize(const_cast<real_t*>(rhs.HostRead()), rhs.Size());
    sols.back().SetDataAndSize(sol.HostWrite(), sol.Size());
 
-   for (int l = blk_Ps_.Size()-1; l >= 0; --l)
+   for (int l = blk_Ps_.size()-1; l >= 0; --l)
    {
       rhss[l].SetSize(blk_Ps_[l]->NumCols());
       sols[l].SetSize(blk_Ps_[l]->NumCols());
@@ -470,12 +468,12 @@ void DivFreeSolver::SolveParticular(const Vector& rhs, Vector& sol) const
       blk_Ps_[l]->MultTranspose(rhss[l+1], rhss[l]);
    }
 
-   for (int l = 0; l < smoothers_.Size(); ++l)
+   for (size_t l = 0; l < smoothers_.size(); ++l)
    {
       smoothers_[l]->Mult(rhss[l], sols[l]);
    }
 
-   for (int l = 0; l < blk_Ps_.Size(); ++l)
+   for (size_t l = 0; l < blk_Ps_.size(); ++l)
    {
       Vector P_sol(blk_Ps_[l]->NumRows());
       blk_Ps_[l]->Mult(sols[l], P_sol);
@@ -507,12 +505,12 @@ void DivFreeSolver::Mult(const Vector & x, Vector & y) const
    MFEM_VERIFY(x.Size() == offsets_[2], "MLDivFreeSolver: x size is invalid");
    MFEM_VERIFY(y.Size() == offsets_[2], "MLDivFreeSolver: y size is invalid");
 
-   if (ops_.Size() == 1) { smoothers_[0]->Mult(x, y); return; }
+   if (ops_.size() == 1) { smoothers_[0]->Mult(x, y); return; }
 
    BlockVector blk_y(y, offsets_);
 
    BlockVector resid(offsets_);
-   ops_.Last()->Mult(y, resid);
+   ops_.back()->Mult(y, resid);
    add(1.0, x, -1.0, resid, resid);
 
    BlockVector correction(offsets_);
@@ -539,7 +537,7 @@ void DivFreeSolver::Mult(const Vector & x, Vector & y) const
       ch.Clear();
       ch.Start();
 
-      ops_.Last()->Mult(y, resid);
+      ops_.back()->Mult(y, resid);
       add(1.0, x, -1.0, resid, resid);
 
       SolveDivFree(resid.GetBlock(0), correction.GetBlock(0));
@@ -553,7 +551,7 @@ void DivFreeSolver::Mult(const Vector & x, Vector & y) const
       ch.Clear();
       ch.Start();
 
-      auto& M = dynamic_cast<const HypreParMatrix&>(ops_.Last()->GetBlock(0, 0));
+      auto& M = dynamic_cast<const HypreParMatrix&>(ops_.back()->GetBlock(0, 0));
       M.Mult(-1.0, correction.GetBlock(0), 1.0, resid.GetBlock(0));
       SolvePotential(resid.GetBlock(0), correction.GetBlock(1));
       blk_y.GetBlock(1) += correction.GetBlock(1);
@@ -567,11 +565,12 @@ void DivFreeSolver::Mult(const Vector & x, Vector & y) const
 
 int DivFreeSolver::GetNumIterations() const
 {
-   if (ops_.Size() == 1)
+   if (ops_.size() == 1)
    {
-      return static_cast<BDPMinresSolver*>(smoothers_[0])->GetNumIterations();
+      return static_cast<BDPMinresSolver*>
+             (smoothers_.at(0).get())->GetNumIterations();
    }
    return solver_.As<IterativeSolver>()->GetNumIterations();
 }
-} // namespace blocksolvers
-} // namespace mfem
+
+} // namespace mfem::blocksolvers

miniapps/solvers/div_free_solver.hpp

@@ -13,11 +13,11 @@
 #define MFEM_DIVFREE_SOLVER_HPP
 
 #include "darcy_solver.hpp"
+#include <memory>
 
-namespace mfem
-{
-namespace blocksolvers
+namespace mfem::blocksolvers
 {
+
 /// Parameters for the divergence free solver
 struct DFSParameters : IterSolveParameters
 {
@@ -35,14 +35,18 @@ struct DFSParameters : IterSolveParameters
 /// Data for the divergence free solver
 struct DFSData
 {
-   std::vector<OperatorPtr> agg_hdivdof;  // agglomerates to H(div) dofs table
-   std::vector<OperatorPtr> agg_l2dof;    // agglomerates to L2 dofs table
-   std::vector<OperatorPtr> P_hdiv;   // Interpolation matrix for H(div) space
-   std::vector<OperatorPtr> P_l2;     // Interpolation matrix for L2 space
-   std::vector<OperatorPtr> P_hcurl;  // Interpolation for kernel space of div
-   std::vector<OperatorPtr> Q_l2;     // Q_l2[l] = (W_{l+1})^{-1} P_l2[l]^T W_l
-   Array<int> coarsest_ess_hdivdofs;  // coarsest level essential H(div) dofs
-   std::vector<OperatorPtr> C;        // discrete curl: ND -> RT, map to Null(B)
+   using UniqueOperatorPtr = std::unique_ptr<OperatorPtr>;
+   using UniqueHypreParMatrix = std::unique_ptr<HypreParMatrix>;
+
+   std::vector<OperatorPtr> agg_hdivdof; // agglomerates to H(div) dofs table
+   std::vector<OperatorPtr> agg_l2dof; // agglomerates to L2 dofs table
+   std::vector<UniqueOperatorPtr> P_hdiv; // Interpolation matrix for H(div) space
+   std::vector<UniqueOperatorPtr> P_l2; // Interpolation matrix for L2 space
+   std::vector<UniqueOperatorPtr> P_hcurl; // Interpolation for kernel space of div
+   std::vector<OperatorPtr> Q_l2; // Q_l2[l] = (W_{l+1})^{-1} P_l2[l]^T W_l
+   Array<int> coarsest_ess_hdivdofs; // coarsest level essential H(div) dofs
+   std::vector<OperatorPtr> C; // discrete curl: ND -> RT, map to Null(B)
+   std::vector<UniqueHypreParMatrix> Ae;
    DFSParameters param;
 };
 
@@ -92,8 +96,7 @@ public:
 /// Compute the product B * B^T and solve it with CG preconditioned by BoomerAMG
 class BBTSolver : public Solver
 {
-   OperatorPtr BBT_;
-   OperatorPtr BBT_prec_;
+   OperatorPtr BBT_, BBT_prec_;
    CGSolver BBT_solver_;
 public:
    BBTSolver(const HypreParMatrix &B, IterSolveParameters param);
@@ -115,14 +118,11 @@ public:
 ///                      [ B   0  ]
 class SaddleSchwarzSmoother : public Solver
 {
-   const SparseMatrix& agg_hdivdof_;
-   const SparseMatrix& agg_l2dof_;
+   const SparseMatrix &agg_hdivdof_, &agg_l2dof_;
    OperatorPtr coarse_l2_projector_;
 
    Array<int> offsets_;
-   mutable Array<int> offsets_loc_;
-   mutable Array<int> hdivdofs_loc_;
-   mutable Array<int> l2dofs_loc_;
+   mutable Array<int> offsets_loc_, hdivdofs_loc_, l2dofs_loc_;
    std::vector<OperatorPtr> solvers_loc_;
 public:
    /** SaddleSchwarzSmoother solves local saddle point problems defined on a
@@ -140,7 +140,7 @@ public:
                          const SparseMatrix& agg_hdivdof,
                          const SparseMatrix& agg_l2dof,
                          const HypreParMatrix& P_l2,
-                         const HypreParMatrix& Q_l2);
+                         const ProductOperator& Q_l2);
    void Mult(const Vector &x, Vector &y) const override;
    void MultTranspose(const Vector &x, Vector &y) const override { Mult(x, y); }
    void SetOperator(const Operator &op) override { }
@@ -178,11 +178,10 @@ class DivFreeSolver : public DarcySolver
    OperatorPtr BT_;
    BBTSolver BBT_solver_;
    std::vector<Array<int>> ops_offsets_;
-   Array<BlockOperator*> ops_;
-   Array<BlockOperator*> blk_Ps_;
-   Array<Solver*> smoothers_;
-   OperatorPtr prec_;
-   OperatorPtr solver_;
+   std::vector<std::unique_ptr<BlockOperator>> ops_;
+   std::vector<std::unique_ptr<BlockOperator>> blk_Ps_;
+   std::vector<std::unique_ptr<Solver>> smoothers_;
+   OperatorPtr prec_, solver_;
 
    void SolveParticular(const Vector& rhs, Vector& sol) const;
    void SolveDivFree(const Vector& rhs, Vector& sol) const;
@@ -190,14 +189,11 @@ class DivFreeSolver : public DarcySolver
 public:
    DivFreeSolver(const HypreParMatrix& M, const HypreParMatrix &B,
                  const DFSData& data);
-   ~DivFreeSolver();
    void Mult(const Vector &x, Vector &y) const override;
    void SetOperator(const Operator &op) override { }
    int GetNumIterations() const override;
 };
 
-} // namespace blocksolvers
-
-} // namespace mfem
+} // namespace mfem::blocksolvers
 
 #endif // MFEM_DIVFREE_SOLVER_HPP

miniapps/spde/generate_random_field.cpp

@@ -33,8 +33,6 @@
 //     (2D random field with anisotropy)
 //     mpirun -np 4 generate_random_field -o 1 -r 3 -rp 3 -nu 4 -l1 0.09 -l2 0.03 -l3 0.05 -s 0.01 -t 0.08 -top 1 -no-rs -m ../../data/ref-square.mesh
 
-#include <math.h>
-#include <fstream>
 #include <iostream>
 #include <string>
 #include "mfem.hpp"
@@ -260,7 +258,8 @@ int main(int argc, char *argv[])
    // III.3 Solve the SPDE problem
    spde::SPDESolver solver(nu, bc, &fespace, l1, l2, l3, e1, e2,
                            e3);
-   const int seed = (random_seed) ? 0 : std::numeric_limits<int>::max();
+   const int seed = (random_seed) ? 0 :
+                    std::numeric_limits<int>::max() - Mpi::WorldRank();
    solver.SetupRandomFieldGenerator(seed);
    solver.GenerateRandomField(u);
 

miniapps/toys/lissajous.cpp

@@ -133,8 +133,11 @@ int main(int argc, char *argv[])
       u.Save(sol_ofs);
    }
 
-   soutv << "keys '.0" << std::string((int)b, '0') << "'\n" << flush;
-   south << "keys '.0" << std::string((int)a, '0') << "'\n" << flush;
+   if (visualization)
+   {
+      soutv << "keys '.0" << std::string((int)b, '0') << "'\n" << flush;
+      south << "keys '.0" << std::string((int)a, '0') << "'\n" << flush;
+   }
 
    cout << "Which direction(s) are the two curves spinning in?\n";
 

tests/unit/CMakeLists.txt

@@ -32,6 +32,7 @@ set(UNIT_TESTS_SRCS
   linalg/test_chebyshev.cpp
   linalg/test_complex_dense_matrix.cpp
   linalg/test_complex_operator.cpp
+  linalg/test_complex_vector.cpp
   linalg/test_constrainedsolver.cpp
   linalg/test_direct_solvers.cpp
   linalg/test_hypre_ilu.cpp
@@ -179,25 +180,42 @@ if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
 endif()
 
 #-----------------------------------------------------------
-# SERIAL CUDA TESTS: cunit_tests
+# SERIAL CUDA TESTS: gpu_unit_tests
 #-----------------------------------------------------------
-# Create CUDA 'cunit_tests' executable and test
+# Create CUDA executable and test
 if (MFEM_USE_CUDA)
-   set(CUNIT_TESTS_SRCS cunit_test_main.cpp)
-   set_property(SOURCE ${CUNIT_TESTS_SRCS} PROPERTY LANGUAGE CUDA)
-   mfem_add_executable(cunit_tests ${CUNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
-   target_link_libraries(cunit_tests mfem)
-   add_dependencies(cunit_tests copy_data)
-   add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} cunit_tests)
+   # gpu_unit_tests
+   set(GPU_UNIT_TESTS_SRCS gpu_unit_test_main.cpp)
+   set_property(SOURCE ${GPU_UNIT_TESTS_SRCS} PROPERTY LANGUAGE CUDA)
+   mfem_add_executable(gpu_unit_tests ${GPU_UNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
+   target_link_libraries(gpu_unit_tests mfem)
+   add_dependencies(gpu_unit_tests copy_data)
+   add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} gpu_unit_tests)
    if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
-      add_test(NAME cunit_tests COMMAND cunit_tests)
+      add_test(NAME gpu_unit_tests COMMAND gpu_unit_tests)
+   endif()
+endif()
+
+#-----------------------------------------------------------
+# SERIAL HIP TESTS: gpu_unit_tests
+#-----------------------------------------------------------
+# Create HIP 'gpu_unit_tests' executable and test
+if (MFEM_USE_HIP)
+   # gpu_unit_tests
+   set(GPU_UNIT_TESTS_SRCS gpu_unit_test_main.cpp)
+   mfem_add_executable(gpu_unit_tests ${GPU_UNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
+   target_link_libraries(gpu_unit_tests mfem)
+   add_dependencies(gpu_unit_tests copy_data)
+   add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} gpu_unit_tests)
+   if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
+      add_test(NAME gpu_unit_tests COMMAND gpu_unit_tests)
    endif()
 endif()
 
 #-----------------------------------------------------------
 # SERIAL SEDOV + TMOP TESTS:
-#   sedov_tests_{cpu,debug,cuda,cuda_uvm}
-#   tmop_pa_tests_{cpu,debug,cuda}
+#   sedov_tests_{cpu,debug,gpu,gpu_uvm}
+#   tmop_pa_tests_{cpu,debug,gpu}
 #-----------------------------------------------------------
 # Function to add one device serial test from the tests/unit/miniapp directory.
 # All device unit tests are built into a separate executable, in order to be
@@ -226,27 +244,27 @@ function(add_serial_miniapp_test name test_uvm)
         add_test(NAME ${name}_tests_debug COMMAND ${name}_tests_debug)
     endif()
 
-    if (MFEM_USE_CUDA)
-       mfem_add_executable(${name}_tests_cuda ${${NAME}_TESTS_SRCS})
-       target_compile_definitions(${name}_tests_cuda PUBLIC MFEM_${NAME}_DEVICE="cuda")
-       target_link_libraries(${name}_tests_cuda mfem)
-       add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} ${name}_tests_cuda)
+    if (MFEM_USE_CUDA OR MFEM_USE_HIP)
+       mfem_add_executable(${name}_tests_gpu ${${NAME}_TESTS_SRCS})
+       target_compile_definitions(${name}_tests_gpu PUBLIC MFEM_${NAME}_DEVICE="gpu")
+       target_link_libraries(${name}_tests_gpu mfem)
+       add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} ${name}_tests_gpu)
        if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
-           add_test(NAME ${name}_tests_cuda COMMAND ${name}_tests_cuda)
+           add_test(NAME ${name}_tests_gpu COMMAND ${name}_tests_gpu)
        endif()
 
        if (test_uvm)
-           mfem_add_executable(${name}_tests_cuda_uvm ${${NAME}_TESTS_SRCS})
-           target_compile_definitions(${name}_tests_cuda_uvm PUBLIC
-               MFEM_${NAME}_DEVICE="cuda:uvm")
-           target_link_libraries(${name}_tests_cuda_uvm mfem)
+           mfem_add_executable(${name}_tests_gpu_uvm ${${NAME}_TESTS_SRCS})
+           target_compile_definitions(${name}_tests_gpu_uvm PUBLIC
+               MFEM_${NAME}_DEVICE="gpu:uvm")
+           target_link_libraries(${name}_tests_gpu_uvm mfem)
            add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME}
-               ${name}_tests_cuda_uvm)
+               ${name}_tests_gpu_uvm)
            if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
-               add_test(NAME ${name}_tests_cuda_uvm COMMAND ${name}_tests_cuda_uvm)
+               add_test(NAME ${name}_tests_gpu_uvm COMMAND ${name}_tests_gpu_uvm)
            endif()
        endif()
-    endif(MFEM_USE_CUDA)
+    endif()
 endfunction(add_serial_miniapp_test)
 
 add_serial_miniapp_test(sedov ON)  # UVM ON
@@ -282,10 +300,11 @@ if (MFEM_USE_CEED)
 endif()
 
 #-----------------------------------------------------------
-# PARALLEL CPU AND CUDA TESTS: {p,pc}unit_tests
+# PARALLEL CPU AND CUDA TESTS: {p,pc}unit_tests and pgpu_unit_tests
 #-----------------------------------------------------------
-# Define executables and tests 'punit_tests' and 'pcunit_tests'
+# Define executables and tests
 if (MFEM_USE_MPI)
+   # punit_tests
    if (MFEM_USE_CUDA)
       set_property(SOURCE punit_test_main.cpp PROPERTY LANGUAGE CUDA)
    endif()
@@ -301,27 +320,44 @@ if (MFEM_USE_MPI)
       endif()
    endforeach()
    if (MFEM_USE_CUDA)
-      set(PCUNIT_TESTS_SRCS pcunit_test_main.cpp)
-      set_property(SOURCE ${PCUNIT_TESTS_SRCS} PROPERTY LANGUAGE CUDA)
-      mfem_add_executable(pcunit_tests ${PCUNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
-      add_dependencies(pcunit_tests copy_data)
-      target_link_libraries(pcunit_tests mfem)
-      add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} pcunit_tests)
-      foreach(np 1 ${MFEM_MPI_NP})
-         if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
-            add_test(NAME pcunit_tests_np=${np}
-                     COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${np}
-                     ${MPIEXEC_PREFLAGS} $<TARGET_FILE:pcunit_tests>
-                     ${MPIEXEC_POSTFLAGS})
-         endif()
-      endforeach()
+       # pgpu_unit_tests
+       set(PGPU_UNIT_TESTS_SRCS pgpu_unit_test_main.cpp)
+       set_property(SOURCE ${PGPU_UNIT_TESTS_SRCS} PROPERTY LANGUAGE CUDA)
+       mfem_add_executable(pgpu_unit_tests ${PGPU_UNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
+       add_dependencies(pgpu_unit_tests copy_data)
+       target_link_libraries(pgpu_unit_tests mfem)
+       add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} pgpu_unit_tests)
+       foreach(np 1 ${MFEM_MPI_NP})
+          if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
+             add_test(NAME pgpu_unit_tests_np=${np}
+                      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${np}
+                      ${MPIEXEC_PREFLAGS} $<TARGET_FILE:pgpu_unit_tests>
+                      ${MPIEXEC_POSTFLAGS})
+          endif()
+       endforeach()
+    endif()
+    if (MFEM_USE_HIP)
+       # pgpu_unit_tests
+       set(PGPU_UNIT_TESTS_SRCS pgpu_unit_test_main.cpp)
+       mfem_add_executable(pgpu_unit_tests ${PGPU_UNIT_TESTS_SRCS} ${UNIT_TESTS_SRCS})
+       add_dependencies(pgpu_unit_tests copy_data)
+       target_link_libraries(pgpu_unit_tests mfem)
+       add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} pgpu_unit_tests)
+       foreach(np 1 ${MFEM_MPI_NP})
+          if (MFEM_USE_DOUBLE) # otherwise returns MFEM_SKIP_RETURN_VALUE
+             add_test(NAME pgpu_unit_tests_np=${np}
+                      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${np}
+                      ${MPIEXEC_PREFLAGS} $<TARGET_FILE:pgpu_unit_tests>
+                      ${MPIEXEC_POSTFLAGS})
+          endif()
+       endforeach()
    endif()
 endif(MFEM_USE_MPI)
 
 #-----------------------------------------------------------
 # PARALLEL SEDOV + TMOP TESTS:
-#   psedov_tests_{cpu,debug,cuda,cuda_uvm}
-#   ptmop_pa_tests_{cpu,cuda}
+#   psedov_tests_{cpu,debug,gpu,gpu_uvm}
+#   ptmop_pa_tests_{cpu,gpu}
 #-----------------------------------------------------------
 # Function to add one MPI executable for a test.
 function(add_mpi_executable_test name dev)
@@ -371,10 +407,10 @@ function(add_parallel_miniapp_test name HYPRE_MM)
             list(APPEND backends debug)
         endif()
     endif()
-    if (MFEM_USE_CUDA)
-        list(APPEND backends cuda)
+    if (MFEM_USE_CUDA OR MFEM_USE_HIP)
+        list(APPEND backends gpu)
         if (HYPRE_MM)
-            list(APPEND backends cuda_uvm)
+            list(APPEND backends gpu_uvm)
         endif()
     endif()
 

tests/unit/README.md

@@ -8,10 +8,10 @@ This directory contains MFEM's suite of unit tests, using the
 MFEM's unit test suite includes a number of executables:
 
 * `unit_tests`
-* `cunit_tests` if MFEM is compiled with CUDA support
-* `sedov_tests_cpu`, `sedov_tests_debug` (and `sedov_tests_cuda` and
-  `sedov_tests_cuda_uvm` if CUDA is enabled), testing a Sedov hydrodynamics case
-* `tmop_pa_tests_cpu`, `tmop_pa_tests_debug` (and `tmop_pa_tests_cuda` if CUDA
+* `gpu_unit_tests` if MFEM is compiled with CUDA/HIP support
+* `sedov_tests_cpu`, `sedov_tests_debug` (and `sedov_tests_gpu` and
+  `sedov_tests_gpu_uvm` if GPU is enabled), testing a Sedov hydrodynamics case
+* `tmop_pa_tests_cpu`, `tmop_pa_tests_debug` (and `tmop_pa_tests_gpu` if GPU
   is enabled), testing TMOP with partial assembly
 
 There are also parallel versions of these executables (prefixed with `p`), which
@@ -67,11 +67,11 @@ and those are:
   serial test executables, and will only be tested with the parallel executable
   (e.g. `punit_tests`). `punit_tests` will only run tests marked with
   `[Parallel]`.
-* `[CUDA]`, which indicates that a test will be tested with the CUDA executables
-  (e.g. `cunit_tests`). These tests will still be run by the standard (CPU)
-  executables. `cunit_tests` will only run tests marked with `[CUDA]`, and its
-  parallel version `pcunit_tests` will only run tests marked with _both_
-  `[CUDA]` and `[Parallel]`.
+* `[GPU]`, which indicates that a test will be tested with the GPU executables
+  (e.g. `gpu_unit_tests`). These tests will still be run by the standard (CPU)
+  executables. `gpu_unit_tests` will only run tests marked with `[GPU]`, and its
+  parallel version `pgpu_unit_tests` will only run tests marked with _both_
+  `[GPU]` and `[Parallel]`.
 * `[MFEMData]`, which indicates that a test requires access to a clone of the
   MFEM data repository (see the `--data` flag below), in order to run tests on
   some larger mesh files. By default, tests tagged with this tag are skipped,

tests/unit/fem/test_assemblediagonalpa.cpp

@@ -185,7 +185,7 @@ TEST_CASE("Diffusion Diagonal PA", "[PartialAssembly][AssembleDiagonal]")
    {
       for (int ne = 1; ne < 3; ++ne)
       {
-         const int n_elements = pow(ne, dimension);
+         const int n_elements = static_cast<int>(pow(ne, dimension));
          CAPTURE(dimension, n_elements);
 
          for (int order = 1; order < 5; ++order)
@@ -359,7 +359,7 @@ TEST_CASE("Vector Diffusion Diagonal PA",
 }
 
 TEST_CASE("Hcurl/Hdiv diagonal PA",
-          "[CUDA][PartialAssembly][AssembleDiagonal]")
+          "[GPU][PartialAssembly][AssembleDiagonal]")
 {
    for (int dimension = 2; dimension < 4; ++dimension)
    {
@@ -404,7 +404,7 @@ TEST_CASE("Hcurl/Hdiv diagonal PA",
             {
                for (int ne = 1; ne < 3; ++ne)
                {
-                  const int n_elements = std::pow(ne, dimension);
+                  const int n_elements = static_cast<int>(std::pow(ne, dimension));
                   CAPTURE(dimension, spaceType, integrator, coeffType, n_elements);
 
                   int max_order = (dimension == 3) ? 2 : 3;

tests/unit/fem/test_assembly_levels.cpp

@@ -195,7 +195,7 @@ void test_assembly_level(const char *meshname,
    REQUIRE(y_test.Norml2() < 1.e-12);
 }
 
-TEST_CASE("H1 Assembly Levels", "[AssemblyLevel], [PartialAssembly], [CUDA]")
+TEST_CASE("H1 Assembly Levels", "[AssemblyLevel], [PartialAssembly], [GPU]")
 {
    const bool all_tests = launch_all_non_regression_tests;
 
@@ -251,7 +251,7 @@ TEST_CASE("H1 Assembly Levels", "[AssemblyLevel], [PartialAssembly], [CUDA]")
    }
 } // H1 Assembly Levels test case
 
-TEST_CASE("H(div) Element Assembly", "[AssemblyLevel][CUDA]")
+TEST_CASE("H(div) Element Assembly", "[AssemblyLevel][GPU]")
 {
    const auto fname = GENERATE(
                          "../../data/inline-quad.mesh",
@@ -316,7 +316,7 @@ TEST_CASE("H(div) Element Assembly", "[AssemblyLevel][CUDA]")
    }
 }
 
-TEST_CASE("NormalTraceJumpIntegrator Element Assembly", "[AssemblyLevel][CUDA]")
+TEST_CASE("NormalTraceJumpIntegrator Element Assembly", "[AssemblyLevel][GPU]")
 {
    const auto fname = GENERATE(
                          "../../data/inline-quad.mesh",
@@ -387,7 +387,7 @@ TEST_CASE("NormalTraceJumpIntegrator Element Assembly", "[AssemblyLevel][CUDA]")
    }
 }
 
-TEST_CASE("L2 Assembly Levels", "[AssemblyLevel], [PartialAssembly], [CUDA]")
+TEST_CASE("L2 Assembly Levels", "[AssemblyLevel], [PartialAssembly], [GPU]")
 {
    const bool dg = true;
    auto pb = GENERATE(Problem::Mass, Problem::Convection);
@@ -454,7 +454,16 @@ void CompareMatricesNonZeros(SparseMatrix &A1, const SparseMatrix &A2,
                              HYPRE_BigInt *cmap1=nullptr,
                              std::unordered_map<HYPRE_BigInt,int> *cmap2inv=nullptr)
 {
-   REQUIRE(A1.Height() == A2.Height());
+   bool A1_Heigh_equals_A2_Height = A1.Height() == A2.Height();
+#ifdef MFEM_USE_MPI
+   if (Mpi::IsInitialized() && !Mpi::IsFinalized())
+   {
+      const bool in = A1_Heigh_equals_A2_Height;
+      MPI_Allreduce(&in, &A1_Heigh_equals_A2_Height, 1, MPI_C_BOOL, MPI_LAND,
+                    MPI_COMM_WORLD);
+   }
+#endif
+   REQUIRE(A1_Heigh_equals_A2_Height);
    int n = A1.Height();
 
    const int *I1 = A1.HostReadI();
@@ -488,6 +497,14 @@ void CompareMatricesNonZeros(SparseMatrix &A1, const SparseMatrix &A2,
       }
    }
 
+#ifdef MFEM_USE_MPI
+   if (Mpi::IsInitialized() && !Mpi::IsFinalized())
+   {
+      const real_t in = error;
+      MPI_Allreduce(&in, &error, 1, MPITypeMap<real_t>::mpi_type, MPI_MAX,
+                    MPI_COMM_WORLD);
+   }
+#endif
    REQUIRE(error == MFEM_Approx(0.0, 1e-10));
 }
 
@@ -559,7 +576,7 @@ void TestH1FullAssembly(Mesh &mesh, int order)
    REQUIRE(B1.Normlinf() == MFEM_Approx(0.0));
 }
 
-TEST_CASE("Serial H1 Full Assembly", "[AssemblyLevel], [CUDA]")
+TEST_CASE("Serial H1 Full Assembly", "[AssemblyLevel], [GPU]")
 {
    auto order = GENERATE(1, 2, 3);
    auto mesh_fname = GENERATE(
@@ -570,7 +587,7 @@ TEST_CASE("Serial H1 Full Assembly", "[AssemblyLevel], [CUDA]")
    TestH1FullAssembly(mesh, order);
 }
 
-TEST_CASE("Full Assembly Connectivity", "[AssemblyLevel], [CUDA]")
+TEST_CASE("Full Assembly Connectivity", "[AssemblyLevel], [GPU]")
 {
    const int order = GENERATE(1, 2, 3);
    const int ne = GENERATE(4, 8, 16, 32);
@@ -638,7 +655,7 @@ void TestSameHypreMatrices(OperatorHandle &A1, OperatorHandle &A2)
    CompareMatricesNonZeros(*M2, *M1);
 }
 
-TEST_CASE("Parallel H1 Full Assembly", "[AssemblyLevel], [Parallel], [CUDA]")
+TEST_CASE("Parallel H1 Full Assembly", "[AssemblyLevel], [Parallel], [GPU]")
 {
    auto order = GENERATE(1, 2, 3);
    auto mesh_fname = GENERATE(
@@ -646,6 +663,8 @@ TEST_CASE("Parallel H1 Full Assembly", "[AssemblyLevel], [Parallel], [CUDA]")
                         "../../data/fichera.mesh"
                      );
 
+   // CAPTURE(order, mesh_fname);
+
    Mesh serial_mesh(mesh_fname);
    ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
    serial_mesh.Clear();
@@ -675,17 +694,25 @@ TEST_CASE("Parallel H1 Full Assembly", "[AssemblyLevel], [Parallel], [CUDA]")
 
    OperatorHandle A_fa, A_legacy;
 
-   // Test that ParallelAssemble gives the same result
-   A_fa.Reset(a_fa.ParallelAssemble());
-   A_legacy.Reset(a_legacy.ParallelAssemble());
+   DYNAMIC_SECTION("[order: " << order << ", dim: " << dim
+                   << "]: (1) ParallelAssemble")
+   {
+      // Test that ParallelAssemble gives the same result
+      A_fa.Reset(a_fa.ParallelAssemble());
+      A_legacy.Reset(a_legacy.ParallelAssemble());
 
-   TestSameHypreMatrices(A_fa, A_legacy);
+      TestSameHypreMatrices(A_fa, A_legacy);
+   }
 
-   // Test that FormSystemMatrix gives the same result
-   a_fa.FormSystemMatrix(ess_tdof_list, A_fa);
-   a_legacy.FormSystemMatrix(ess_tdof_list, A_legacy);
+   DYNAMIC_SECTION("[order: " << order << ", dim: " << dim
+                   << "]: (2) FormSystemMatrix")
+   {
+      // Test that FormSystemMatrix gives the same result
+      a_fa.FormSystemMatrix(ess_tdof_list, A_fa);
+      a_legacy.FormSystemMatrix(ess_tdof_list, A_legacy);
 
-   TestSameHypreMatrices(A_fa, A_legacy);
+      TestSameHypreMatrices(A_fa, A_legacy);
+   }
 
    // Test that FormLinearSystem gives the same result
    ParGridFunction x1(&fespace);
@@ -701,13 +728,23 @@ TEST_CASE("Parallel H1 Full Assembly", "[AssemblyLevel], [Parallel], [CUDA]")
 
    a_fa.Assemble();
 
-   a_fa.FormLinearSystem(ess_tdof_list, x1, b1, A_fa, X1, B1);
-   a_legacy.FormLinearSystem(ess_tdof_list, x2, b2, A_legacy, X2, B2);
+   DYNAMIC_SECTION("[order: " << order << ", dim: " << dim
+                   << "]: (3) FormLinearSystem")
+   {
+      a_fa.FormLinearSystem(ess_tdof_list, x1, b1, A_fa, X1, B1);
+      a_legacy.FormLinearSystem(ess_tdof_list, x2, b2, A_legacy, X2, B2);
 
-   TestSameHypreMatrices(A_fa, A_legacy);
+      TestSameHypreMatrices(A_fa, A_legacy);
+   }
 
-   B1 -= B2;
-   REQUIRE(B1.Normlinf() == MFEM_Approx(0.0));
+   DYNAMIC_SECTION("[order: " << order << ", dim: " << dim
+                   << "]: (4) FormLinearSystem - RHS")
+   {
+      B1 -= B2;
+      const real_t B_err = GlobalLpNorm(infinity(), B1.Normlinf(),
+                                        MPI_COMM_WORLD);
+      REQUIRE(B_err == MFEM_Approx(0.0));
+   }
 }
 
 #endif

tests/unit/fem/test_bilinearform.cpp

@@ -69,7 +69,7 @@ TEST_CASE("Test order of boundary integrators",
 
 TEST_CASE("FormLinearSystem/SolutionScope",
           "[BilinearForm]"
-          "[CUDA]")
+          "[GPU]")
 {
    // Create a simple mesh and FE space
    int dim = 2, nx = 2, ny = 2, order = 2;

tests/unit/fem/test_block_operators.cpp

@@ -14,7 +14,7 @@
 
 using namespace mfem;
 
-TEST_CASE("BlockOperators", "[BlockOperators], [CUDA]")
+TEST_CASE("BlockOperators", "[BlockOperators], [GPU]")
 {
    const int dim = 2, nx = 3, ny = 3, order = 2;
    Element::Type e_type = Element::QUADRILATERAL;

tests/unit/fem/test_calccurlshape.cpp

@@ -231,7 +231,7 @@ void TestFDCalcCurlShape(FiniteElement* fe, ElementTransformation * T,
       IntegrationPoint pt = ir->IntPoint(i);
       fe->CalcCurlShape(pt, dshape);
 
-      CAPTURE(pt.x, pt.y, pt.z);
+      CAPTURE(pt.x, pt.y, dim == 3 ? pt.z : 0_r);
 
       fdshape = 0.0;
       for (int d=0; d<dim; d++)

tests/unit/fem/test_calcdivshape.cpp

@@ -94,7 +94,7 @@ void TestCalcDivShape(FiniteElement* fe, ElementTransformation * T, int res)
          if (fe->GetGeomType() == Geometry::PYRAMID &&
              (ip.z >= 1.0 || ip.y > 1.0 - ip.z || ip.x > 1.0 - ip.z)) { continue; }
 
-         CAPTURE(ip.x, ip.y, ip.z);
+         CAPTURE(ip.x, ip.y, dim == 3 ? ip.z : 0_r);
 
          fe->CalcDivShape(ip, weights);
 
@@ -215,7 +215,7 @@ void TestFDCalcDivShape(FiniteElement* fe, ElementTransformation * T, int order)
       IntegrationPoint pt = ir->IntPoint(i);
       fe->CalcDivShape(pt, dshape);
 
-      CAPTURE(pt.x, pt.y, pt.z);
+      CAPTURE(pt.x, pt.y, dim == 3 ? pt.z : 0_r);
 
       fdshape = 0.0;
       for (int d=0; d<dim; d++)

tests/unit/fem/test_dgmassinv.cpp

@@ -14,7 +14,7 @@
 
 using namespace mfem;
 
-TEST_CASE("DG Mass Inverse", "[CUDA]")
+TEST_CASE("DG Mass Inverse", "[GPU]")
 {
    auto mesh_filename = GENERATE(
                            "../../data/inline-segment.mesh",

tests/unit/fem/test_fa_determinism.cpp

@@ -14,7 +14,7 @@
 
 using namespace mfem;
 
-TEST_CASE("FA Determinism", "[PartialAssembly][CUDA]")
+TEST_CASE("FA Determinism", "[PartialAssembly][GPU]")
 {
    const int order = 3;
    const char *mesh_filename = "../../data/star-q3.mesh";

tests/unit/fem/test_fe_symmetry.cpp

@@ -221,7 +221,8 @@ TEST_CASE("FE Symmetry",
          const int ne = order; // Num DoFs per edge
          const int nt = order * (order - 1); // Num DoF per tri face
          const int nq = 2 * nt; // Num DoF per quad face
-         const int ni = order * pow(order - 1, 2); // Num DoF per interior dir
+         // Num DoF per interior dir
+         const int ni = order * (static_cast<int>(pow(order-1, 2)));
          const int oq = 8 * ne; // Offset to first quad DoF
          const int ot = oq + nq; // Offset to first tri DoF
          const int oi = ot + 4 * nt; // Offset to first interior DoF

tests/unit/fem/test_inversetransform.cpp

@@ -190,7 +190,7 @@ TEST_CASE("InverseElementTransformation",
 }
 
 TEST_CASE("BatchInverseElementTransformation",
-          "[InverseElementTransformation], [CUDA]")
+          "[InverseElementTransformation], [GPU]")
 {
    const real_t tol = 4e-13;
 
@@ -268,13 +268,14 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts] -
-                                            orig_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts] -
+                                   orig_ref_space[i + d * npts]));
             }
          }
       }
@@ -369,13 +370,14 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts] -
-                                            orig_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts] -
+                                   orig_ref_space[i + d * npts]));
             }
          }
       }
@@ -471,13 +473,14 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts] -
-                                            orig_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts] -
+                                   orig_ref_space[i + d * npts]));
             }
          }
       }
@@ -575,13 +578,14 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts] -
-                                            orig_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts] -
+                                   orig_ref_space[i + d * npts]));
             }
          }
       }
@@ -675,13 +679,14 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts] -
-                                            orig_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts] -
+                                   orig_ref_space[i + d * npts]));
             }
          }
       }
@@ -758,12 +763,13 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts]));
             }
          }
       }
@@ -846,12 +852,13 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts]));
             }
          }
       }
@@ -925,12 +932,13 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts]));
             }
          }
       }
@@ -1010,12 +1018,13 @@ TEST_CASE("BatchInverseElementTransformation",
       real_t max_err = 0;
       for (int i = 0; i < npts; ++i)
       {
-         if (res_type[i] == InverseElementTransformation::Inside)
+         if (AsConst(res_type)[i] == InverseElementTransformation::Inside)
          {
             ++pts_found;
             for (int d = 0; d < dim; ++d)
             {
-               max_err = fmax(max_err, fabs(res_ref_space[i + d * npts]));
+               max_err = fmax(max_err,
+                              fabs(AsConst(res_ref_space)[i + d * npts]));
             }
          }
       }

tests/unit/fem/test_linearform_ext.cpp

@@ -201,7 +201,7 @@ struct LinearFormExtTest
    }
 };
 
-TEST_CASE("Linear Form Extension", "[LinearFormExtension], [CUDA]")
+TEST_CASE("Linear Form Extension", "[LinearFormExtension], [GPU]")
 {
    const bool all = launch_all_non_regression_tests;
 
@@ -328,7 +328,7 @@ TEST_CASE("Linear Form Extension", "[LinearFormExtension], [CUDA]")
    }
 }
 
-TEST_CASE("H(div) Linear Form Extension", "[LinearFormExtension], [CUDA]")
+TEST_CASE("H(div) Linear Form Extension", "[LinearFormExtension], [GPU]")
 {
    const bool all = launch_all_non_regression_tests;
 

tests/unit/fem/test_lor_batched.cpp

@@ -140,17 +140,17 @@ void TestBatchedLOR()
    TestSameMatrices(A2, A1);
 }
 
-TEST_CASE("LOR Batched H1", "[LOR][BatchedLOR][CUDA]")
+TEST_CASE("LOR Batched H1", "[LOR][BatchedLOR][GPU]")
 {
    TestBatchedLOR<H1_FECollection,MassIntegrator,DiffusionIntegrator>();
 }
 
-TEST_CASE("LOR Batched ND", "[LOR][BatchedLOR][CUDA]")
+TEST_CASE("LOR Batched ND", "[LOR][BatchedLOR][GPU]")
 {
    TestBatchedLOR<ND_FECollection,VectorFEMassIntegrator,CurlCurlIntegrator>();
 }
 
-TEST_CASE("LOR Batched RT", "[LOR][BatchedLOR][CUDA]")
+TEST_CASE("LOR Batched RT", "[LOR][BatchedLOR][GPU]")
 {
    TestBatchedLOR<RT_FECollection,VectorFEMassIntegrator,DivDivIntegrator>();
 }
@@ -192,6 +192,8 @@ void ParTestBatchedLOR()
                               "../../data/fichera-q3.mesh"
                            );
 
+   CAPTURE(order, mesh_fname);
+
    Mesh serial_mesh = Mesh::LoadFromFile(mesh_fname);
 
    ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
@@ -226,22 +228,22 @@ void ParTestBatchedLOR()
    TestSameMatrices(A2, A1);
 }
 
-TEST_CASE("Parallel LOR Batched H1", "[LOR][BatchedLOR][Parallel][CUDA]")
+TEST_CASE("Parallel LOR Batched H1", "[LOR][BatchedLOR][Parallel][GPU]")
 {
    ParTestBatchedLOR<H1_FECollection,MassIntegrator,DiffusionIntegrator>();
 }
 
-TEST_CASE("Parallel LOR Batched ND", "[LOR][BatchedLOR][Parallel][CUDA]")
+TEST_CASE("Parallel LOR Batched ND", "[LOR][BatchedLOR][Parallel][GPU]")
 {
    ParTestBatchedLOR<ND_FECollection,VectorFEMassIntegrator,CurlCurlIntegrator>();
 }
 
-TEST_CASE("Parallel LOR Batched RT", "[LOR][BatchedLOR][Parallel][CUDA]")
+TEST_CASE("Parallel LOR Batched RT", "[LOR][BatchedLOR][Parallel][GPU]")
 {
    ParTestBatchedLOR<RT_FECollection,VectorFEMassIntegrator,DivDivIntegrator>();
 }
 
-TEST_CASE("LOR AMS", "[LOR][BatchedLOR][AMS][Parallel][CUDA]")
+TEST_CASE("LOR AMS", "[LOR][BatchedLOR][AMS][Parallel][GPU]")
 {
    enum SpaceType { ND, RT };
    auto space_type = GENERATE(ND, RT);
@@ -313,7 +315,7 @@ TEST_CASE("LOR AMS", "[LOR][BatchedLOR][AMS][Parallel][CUDA]")
    }
 }
 
-TEST_CASE("LOR ADS", "[LOR][BatchedLOR][ADS][Parallel][CUDA]")
+TEST_CASE("LOR ADS", "[LOR][BatchedLOR][ADS][Parallel][GPU]")
 {
    // Only need to test ADS in 3D
    auto mesh_fname = GENERATE("../../data/fichera-q3.mesh");