- added 3D cyclone particle tracker

A few small fixes and feature additions

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

@@ -25,7 +25,7 @@ runs:
   steps:
     - uses: ./.github/actions/sanitize/config
 
-    - uses: actions/cache@v4
+    - uses: actions/cache@v5
       if: ${{env.DEBUG == 'true'}}
       id: debug
       with:

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

@@ -36,7 +36,7 @@ runs:
   steps:
     - uses: ./.github/actions/sanitize/config
 
-    - uses: actions/cache@v4
+    - uses: actions/cache@v5
       if: ${{env.DEBUG == 'true' && inputs.cache-skip != 'true'}}
       id: debug
       with:

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

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

.github/workflows/build-container.yml

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

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

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

.github/workflows/codeql-analysis.yml

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

.github/workflows/mfem-analysis.yml

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

.github/workflows/repo-check.yml

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

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

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

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

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

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

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

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

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

.github/workflows/sanitize-tests.yml

@@ -28,7 +28,7 @@ jobs:
   build:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/mfem
         with:
           par: ${{inputs.par}}
@@ -40,7 +40,7 @@ jobs:
     env:
       ex: ${{inputs.par && 'ex1p' || 'ex1'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -58,7 +58,7 @@ jobs:
     env:
       exclude: ${{inputs.par && '-E "_ser"' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -82,7 +82,7 @@ jobs:
     env:
       exclude: ${{inputs.par && '-E "_ser"' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -107,7 +107,7 @@ jobs:
       run: ${{inputs.par && '-R "_cpu_np"' || ''}}
       exclude: ${{inputs.par && '"unit_tests|debug"' || '"^unit_tests$|debug"'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -131,7 +131,7 @@ jobs:
     env:
       unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:
@@ -165,7 +165,7 @@ jobs:
       unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
       np: ${{inputs.par && '_np=2' || ''}}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: ./.github/actions/sanitize/restore
         id: restore
         with:

.gitignore

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

CHANGELOG

@@ -8,6 +8,22 @@
                                https://mfem.org
 
 
+Version 4.10 (development)
+==========================
+
+Discretization improvements
+---------------------------
+- Replaced legacy simplex quadrature rules with symmetric positive-weight
+  rules for triangles (orders 0-25) and tetrahedra (orders 0-20). These
+  rules guarantee all-positive weights and interior quadrature points,
+  improving numerical stability. Higher orders fall back to Grundmann-Moller.
+  Triangle rules: Witherden & Vincent, Comput. Math. Appl. 69(10):1232-1241,
+  2015.
+  Tet rules (d=1-13): Witherden & Vincent (ibid).
+  Tet rules (d=14-20): Chuluunbaatar et al., Comput. Math. Appl. 124:89-97,
+  2022.
+
+
 Version 4.9.1 (development)
 ===========================
 
@@ -17,6 +33,9 @@ Discretization improvements
   Vector and VectorFE, also NURBS versions. Optionally different types of
   projections can be selected, default behaviour has not changed.
 
+- Added methods to estimate function extremum using piecewise linear bounds +
+  recursive subdivision.
+
 Meshing improvements
 --------------------
 - Improved support for 1D NURBS meshes with variable order, including using

CMakeLists.txt

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

config/cmake/MFEMConfig.cmake.in

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

config/cmake/modules/FindUMPIRE.cmake

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

config/cmake/modules/MfemCmakeUtilities.cmake

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

examples/ex12p.cpp

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

examples/ex22p.cpp

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

examples/ex37.cpp

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

examples/ex37.hpp

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

examples/ex37p.cpp

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

examples/makefile

@@ -157,6 +157,8 @@ ex37-test-seq: ex37
 	@$(call mfem-test,$<,, Serial example,-mi 3)
 ex37p-test-par: ex37p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-mi 3)
+ex39-test-seq: ex39
+	@$(call mfem-test,$<,, Serial example,-m ../data/compass.mesh)
 ex41-test-seq: ex41
 	@$(call mfem-test,$<,, Serial example,-tf 1.0)
 ex41p-test-par: ex41p

fem/bilinearform.cpp

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

fem/bilininteg.hpp

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

fem/bounds.cpp

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

fem/bounds.hpp

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

fem/coefficient.hpp

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

fem/complex_fem.hpp

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

fem/dfem/integrate.hpp

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

fem/estimators.hpp

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

fem/fe/fe_base.cpp

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

fem/fe/fe_base.hpp

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

fem/fe/fe_h1.cpp

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

fem/fe/fe_nd.cpp

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

fem/fe/fe_nd.hpp

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

fem/fe/fe_rt.cpp

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

fem/fe/fe_rt.hpp

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

fem/fespace.cpp

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

fem/fespace.hpp

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

fem/gridfunc.cpp

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

fem/gridfunc.hpp

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

fem/gslib.hpp

@@ -202,13 +202,19 @@ protected:
                             const int dof1dsol, const int ordering);
 
 public:
+   /// Serial constructor
    FindPointsGSLIB();
+
+   /// Serial constructor + setup with given Mesh (see \ref Setup)
    FindPointsGSLIB(Mesh &mesh_in, const double bb_t = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
 #ifdef MFEM_USE_MPI
+   /// Constructor for ParMesh
    FindPointsGSLIB(MPI_Comm comm_);
+
+   /// Constructor + setup with given ParMesh (see \ref Setup)
    FindPointsGSLIB(ParMesh &mesh_in, const double bb_t = 0.1,
                    const double newt_tol = 1.0e-12,
                    const int npt_max = 256);

fem/integ/bilininteg_hdiv_ea.cpp

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

fem/integ/bilininteg_vecdiffusion_pa.hpp

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

fem/integ/bilininteg_vecmass_pa.hpp

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

fem/integ/lininteg_domain_kernels.hpp

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

fem/intrules.hpp

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

fem/linearform.cpp

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

fem/lininteg.hpp

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

fem/lor/lor.cpp

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

fem/lor/lor.hpp

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

fem/pfespace.cpp

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

fem/pgridfunc.cpp

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

fem/pgridfunc.hpp

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

fem/prestriction.cpp

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

fem/qfunction.hpp

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

fem/qinterp/det.hpp

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

fem/qinterp/eval.hpp

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

fem/qinterp/eval_hdiv.hpp

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

fem/qinterp/grad.hpp

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

fem/quadinterpolator.cpp

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

fem/restriction.cpp

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

fem/tmop.cpp

@@ -4102,8 +4102,11 @@ void TMOP_Integrator::GetSurfaceFittingErrors(const Vector &d_loc,
 #ifdef MFEM_USE_MPI
       // Don't count the overlapping DOFs in parallel.
       // The pfes might be ordered byVDIM, while the loop goes consecutively.
-      const int dof_i = pfes->DofToVDof(i, 0);
-      if (parallel && pfes->GetLocalTDofNumber(dof_i) < 0) { continue; }
+      if (parallel)
+      {
+         const int dof_i = pfes->DofToVDof(i, 0);
+         if (pfes->GetLocalTDofNumber(dof_i) < 0) { continue; }
+      }
 #endif
 
       dof_cnt++;

general/array.hpp

@@ -114,10 +114,22 @@ public:
    Array<T> &operator=(const Array<T> &src) { src.Copy(*this); return *this; }
 
    /// Move assignment operator
+   /** If *this is a non-owning view (e.g., from MakeRef()), the data is copied
+       so that the base is also modified. */
    Array<T> &operator=(Array<T> &&src)
    {
       if (this == &src) { return *this; }
-      Swap(src);  // Swap does not use move assignment!
+      // If *this is a non-owning view (alias), and its capacity is sufficient
+      // to contain src, then copy into *this so that the alias's base memory is
+      // modified.
+      if (!OwnsData() && Capacity() >= src.Size())
+      {
+         *this = src; // Copy assignment.
+      }
+      else
+      {
+         Swap(src); // Swap the pointers only.
+      }
       src.DeleteAll();
       return *this;
    }
@@ -251,6 +263,9 @@ public:
    /// Make this Array a reference to 'master'.
    inline void MakeRef(const Array &master);
 
+   /// Make this Array a reference to the given sub-Memory of @a base.
+   inline void MakeRef(Memory<T> &base, int offset, int size_);
+
    /// Reset the Array to use the given external Memory @a mem and size @a s.
    /** If @a own_mem is false, the Array will not own any of the pointers of
        @a mem.
@@ -1073,6 +1088,14 @@ inline void Array<T>::MakeRef(const Array &master)
    data.MakeAlias(master.GetMemory(), 0, size);
 }
 
+template <class T>
+inline void Array<T>::MakeRef(Memory<T> &base, int offset, int size_)
+{
+   data.Delete();
+   size = size_;
+   data.MakeAlias(base, offset, size_);
+}
+
 template <class T>
 inline void Array<T>::NewMemoryAndSize(
    const Memory<T> &mem, int s, bool own_mem)

general/arrays_by_name.hpp

@@ -14,6 +14,7 @@
 
 #include "../config/config.hpp"
 #include "array.hpp"
+#include "text.hpp"
 
 #include <iostream>
 #include <map>
@@ -247,7 +248,8 @@ inline void ArraysByName<T>::Print(std::ostream &os, int width) const
    os << data.size() << '\n';
    for (auto const &it : data)
    {
-      os << '"' << it.first << '"' << '\n' << it.second.Size() << '\n';
+      // Note: The method Load() can read any string formatted with std::quoted.
+      os << std::quoted(it.first) << '\n' << it.second.Size() << '\n';
       it.second.Print(os, width > 0 ? width : it.second.Size());
    }
 }
@@ -258,31 +260,36 @@ void ArraysByName<T>::Load(std::istream &in)
    int NumArrays;
    in >> NumArrays;
 
-   std::string ArrayLine, ArrayName;
-   for (int i=0; i < NumArrays; i++)
+   for (int i = 0; i < NumArrays; i++)
    {
       in >> std::ws;
-      getline(in, ArrayLine);
-
-      std::size_t q0 = ArrayLine.find('"');
-      std::size_t q1 = ArrayLine.rfind('"');
-
-      if (q0 != std::string::npos && q1 > q0)
+      // Read the name:
+      // - If the stream 'in' starts with " then parse it with the function
+      //   parse_quoted_string() from text.hpp. In this case, the name can be
+      //   empty. Note: this case allows for reading any string formatted using
+      //   std::quoted, e.g. as in the method Print().
+      // - If the name does not start with " then the name ends with the first
+      //   white space character (and the white space character is not included
+      //   in the name). Since white space characters are skipped before reading
+      //   the name, there will be at least one non-white-space character in the
+      //   name in this case.
+      std::string ArrayName;
+      if (in.peek() == '"')
       {
-         // Locate set name between first and last double quote
-         ArrayName = ArrayLine.substr(q0+1,q1-q0-1);
+         if (parse_quoted_string(ArrayName, in) != 0)
+         {
+            MFEM_ABORT("error parsing input!");
+         }
       }
       else
       {
-         // If no double quotes found locate set name using white space
-         q1 = ArrayLine.find(' ');
-         ArrayName = ArrayLine.substr(0,q1-1);
+         in >> ArrayName;
+         MFEM_VERIFY(in.good(), "error parsing input!");
       }
 
-      // Ignore the remainder of the line which may contain explanatory comments
-      data[ArrayName].Load(in, 0);
+      // Read the array
+      data[ArrayName].Load(in);
    }
-
 }
 
 }

general/device.cpp

@@ -726,16 +726,16 @@ std::string Device::GetUUID(const int device_id)
    MFEM_GPU_CHECK(cudaGetDeviceProperties(&prop, device_id));
    for (int i = 0; i < 16; ++i)
    {
-      res << std::setfill('0') << std::setw(2) << std::hex
-          << static_cast<unsigned>(prop.uuid.bytes[i]);
+      const unsigned b = static_cast<unsigned char>(prop.uuid.bytes[i]);
+      res << std::setfill('0') << std::setw(2) << std::hex << b;
    }
 #elif defined(MFEM_USE_HIP)
    hipUUID uuid;
    MFEM_GPU_CHECK(hipDeviceGetUuid(&uuid, device_id));
    for (int i = 0; i < 16; ++i)
    {
-      res << std::setfill('0') << std::setw(2) << std::hex
-          << static_cast<unsigned>(uuid.bytes[i]);
+      const unsigned b = static_cast<unsigned char>(uuid.bytes[i]);
+      res << std::setfill('0') << std::setw(2) << std::hex << b;
    }
 #endif
    return res.str();

general/globals.hpp

@@ -113,6 +113,10 @@ void SetGlobalMPI_Comm(MPI_Comm comm);
 /// to suppress the warning.
 const char* GetEnv(const char* name);
 
+/// Signed indices i -> -1 - i are used as a convention to encode orientation.
+inline MFEM_HOST_DEVICE int FlipIndexSign(int i) { return -1 - i; }
+inline MFEM_HOST_DEVICE int UnsignIndex(int i) { return i < 0 ? -1 - i : i; }
+
 } // namespace mfem
 
 #endif

general/mem_manager.cpp

@@ -759,7 +759,9 @@ private:
    {
       switch (mt)
       {
-         case MT::HOST_DEBUG: return new MmuHostMemorySpace();
+         case MT::HOST_DEBUG:
+            if (GetEnv("MFEM_MMU_STD")) { return new StdHostMemorySpace(); }
+            return new MmuHostMemorySpace();
 #ifdef MFEM_USE_UMPIRE
          case MT::HOST_UMPIRE:
             return new UmpireHostMemorySpace(
@@ -788,7 +790,9 @@ private:
          case MT::DEVICE_UMPIRE: return new NoDeviceMemorySpace();
          case MT::DEVICE_UMPIRE_2: return new NoDeviceMemorySpace();
 #endif
-         case MT::DEVICE_DEBUG: return new MmuDeviceMemorySpace();
+         case MT::DEVICE_DEBUG:
+            if (GetEnv("MFEM_MMU_STD")) { return new StdDeviceMemorySpace(); }
+            return new MmuDeviceMemorySpace();
          case MT::DEVICE:
          {
 #if defined(MFEM_USE_CUDA)

general/text.hpp

@@ -50,6 +50,48 @@ inline void filter_dos(std::string &line)
    }
 }
 
+/** @brief Read a string formatted using std::quoted. Return nonzero on error.
+
+    The stream @a in must begin with @a delim. After clearing @a result and
+    extracting the opening @a delim, characters are extracted from @a in and
+    processed as follows:
+    - if the character is @a delim, return 0;
+    - if the character is different from @a escape, it is appended to @a result;
+    - if the character is @a escape, the next character from @a in is extracted
+      and if it is one of @a delim or @a escape, it is appended to @a result;
+      otherwise, both @a escape and the character after it are appended to
+      @a result; note that the latter case is not possible if the input was
+      formatted with std::quoted with the same @a delim and @a escape
+      characters.
+
+    If the stream @a in does not begin with @a delim, error code 1 is returned.
+    If reading the stream fails, error code 2 is returned. On success, zero is
+    returned and the closing @a delim character is the last character extracted
+    from @a in. */
+inline int parse_quoted_string(std::string &result, std::istream &in,
+                               char delim = '"', char escape = '\\')
+{
+   using tt = std::string::traits_type;  // std::char_traits<char>
+   auto equal = [](tt::int_type c1, tt::char_type c2) -> bool
+   {
+      return tt::eq_int_type(c1, tt::to_int_type(c2));
+   };
+   result.clear();
+   if (!equal(in.peek(), delim)) { return 1; }
+   in.get();  // extract delim
+   for (auto c = in.get(); !equal(c, delim); c = in.get())
+   {
+      if (equal(c, escape))
+      {
+         c = in.get();
+         if (!equal(c, escape) && !equal(c, delim)) { result += escape; }
+      }
+      if (!in) { return 2; }
+      result += tt::to_char_type(c);
+   }
+   return 0;
+}
+
 /// Convert an integer to a 0-padded string with the given number of @a digits
 inline std::string to_padded_string(int i, int digits)
 {

linalg/densemat.hpp

@@ -82,6 +82,15 @@ public:
       }
    }
 
+   /// Make the DenseMatrix to reference the given sub-Memory of @a base.
+   /** The DenseMatrix does not assume ownership of the data array, i.e. it will
+       not delete the @a base Memory. */
+   void MakeRef(Memory<real_t> &base, int offset, int h, int w)
+   {
+      data.MakeRef(base, offset, h*w);
+      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 data array @a d. */

linalg/hypre.cpp

@@ -317,6 +317,9 @@ void HypreParVector::WrapHypreParVector(hypre_ParVector *y, bool owner)
 
 Vector * HypreParVector::GlobalVector() const
 {
+   MFEM_VERIFY(size > 0,
+               "GlobalVector method can only be called on vectors wherein each "
+               "process owns one or more entries");
    hypre_Vector *hv = hypre_ParVectorToVectorAll(*this);
    Vector *v = new Vector(hv->data, internal::to_int(hv->size));
    v->MakeDataOwner();

linalg/petsc.cpp

@@ -38,6 +38,13 @@
 #if PETSC_VERSION_LT(3,19,0)
 #define PETSC_SUCCESS 0
 #endif
+#if PETSC_VERSION_LT(3,23,0)
+#define PetscContainerSetCtxDestroy(A,B) PetscContainerSetUserDestroy(A,B)
+typedef PetscErrorCode (PetscCtxDestroyFn)(void**);
+#endif
+#if PETSC_VERSION_LT(3,24,0)
+typedef PetscErrorCode KSPMonitorFn(KSP,PetscInt,PetscReal,void*);
+#endif
 
 #include <fstream>
 #include <iomanip>
@@ -77,13 +84,17 @@ static PetscErrorCode __mfem_mat_shell_apply_transpose(Mat,Vec,Vec);
 static PetscErrorCode __mfem_mat_shell_destroy(Mat);
 static PetscErrorCode __mfem_mat_shell_copy(Mat,Mat,MatStructure);
 #if PETSC_VERSION_LT(3,23,0)
-static PetscErrorCode __mfem_array_container_destroy(void*);
-static PetscErrorCode __mfem_matarray_container_destroy(void *);
-#else
-static PetscErrorCode __mfem_array_container_destroy(void**);
-static PetscErrorCode __mfem_matarray_container_destroy(void**);
+typedef void *PetscCtxRt;
+#elif PETSC_VERSION_LT(3,25,0)
+typedef void **PetscCtxRt;
 #endif
+static PetscErrorCode __mfem_array_container_destroy(PetscCtxRt);
+static PetscErrorCode __mfem_matarray_container_destroy(PetscCtxRt);
+#if PETSC_VERSION_LT(3,23,0)
 static PetscErrorCode __mfem_monitor_ctx_destroy(void**);
+#else
+static PetscErrorCode __mfem_monitor_ctx_destroy(PetscCtxRt);
+#endif
 
 // auxiliary functions
 static PetscErrorCode Convert_Array_IS(MPI_Comm,bool,const mfem::Array<int>*,
@@ -1317,11 +1328,7 @@ BlockDiagonalConstructor(MPI_Comm comm,
 
          ierr = PetscContainerCreate(comm,&c); CCHKERRQ(comm,ierr);
          ierr = PetscContainerSetPointer(c,ptrs[i]); CCHKERRQ(comm,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
          CCHKERRQ(comm,ierr);
          ierr = PetscObjectCompose((PetscObject)A,names[i],(PetscObject)c);
          CCHKERRQ(comm,ierr);
@@ -1648,11 +1655,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
          PetscContainer c;
          ierr = PetscContainerCreate(comm,&c); CCHKERRQ(comm,ierr);
          ierr = PetscContainerSetPointer(c,vmatsl2l); PCHKERRQ(c,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_matarray_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_matarray_container_destroy);
-#endif
          PCHKERRQ(c,ierr);
          ierr = PetscObjectCompose((PetscObject)(*A),"_MatIS_PtAP_l2l",(PetscObject)c);
          PCHKERRQ((*A),ierr);
@@ -1748,11 +1751,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
 
             ierr = PetscContainerCreate(PETSC_COMM_SELF,&c); PCHKERRQ(B,ierr);
             ierr = PetscContainerSetPointer(c,ptrs[i]); PCHKERRQ(B,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-            ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
             ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
             PCHKERRQ(B,ierr);
             ierr = PetscObjectCompose((PetscObject)(B),names[i],(PetscObject)c);
             PCHKERRQ(B,ierr);
@@ -2198,11 +2197,7 @@ PetscParMatrix * RAP(PetscParMatrix *Rt, PetscParMatrix *A, PetscParMatrix *P)
          ierr = PetscContainerCreate(PetscObjectComm((PetscObject)B),&c);
          PCHKERRQ(B,ierr);
          ierr = PetscContainerSetPointer(c,vmatsl2l); PCHKERRQ(c,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_matarray_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_matarray_container_destroy);
-#endif
          PCHKERRQ(c,ierr);
          ierr = PetscObjectCompose((PetscObject)B,"_MatIS_PtAP_l2l",(PetscObject)c);
          PCHKERRQ(B,ierr);
@@ -2485,7 +2480,6 @@ void PetscSolver::SetMaxIter(int max_iter)
 
 void PetscSolver::SetPrintLevel(int plev)
 {
-   typedef PetscErrorCode (*myPetscFunc)(void**);
    PetscViewerAndFormat *vf = NULL;
    PetscViewer viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm(obj));
 
@@ -2498,7 +2492,6 @@ void PetscSolver::SetPrintLevel(int plev)
    {
       // there are many other options, see the function KSPSetFromOptions() in
       // src/ksp/ksp/interface/itcl.c
-      typedef PetscErrorCode (*myMonitor)(KSP,PetscInt,PetscReal,void*);
       KSP ksp = (KSP)obj;
       if (plev >= 0)
       {
@@ -2507,29 +2500,29 @@ void PetscSolver::SetPrintLevel(int plev)
       if (plev == 1)
       {
 #if PETSC_VERSION_LT(3,15,0)
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorDefault,vf,
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorDefault,vf,
 #else
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorResidual,vf,
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorResidual,vf,
 #endif
-                              (myPetscFunc)PetscViewerAndFormatDestroy);
+                              (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(ksp,ierr);
       }
       else if (plev > 1)
       {
          ierr = KSPSetComputeSingularValues(ksp,PETSC_TRUE); PCHKERRQ(ksp,ierr);
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorSingularValue,vf,
-                              (myPetscFunc)PetscViewerAndFormatDestroy);
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorSingularValue,vf,
+                              (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(ksp,ierr);
          if (plev > 2)
          {
             ierr = PetscViewerAndFormatCreate(viewer,PETSC_VIEWER_DEFAULT,&vf);
             PCHKERRQ(viewer,ierr);
 #if PETSC_VERSION_LT(3,15,0)
-            ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorTrueResidualNorm,vf,
+            ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorTrueResidualNorm,vf,
 #else
-            ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorTrueResidual,vf,
+            ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorTrueResidual,vf,
 #endif
-                                 (myPetscFunc)PetscViewerAndFormatDestroy);
+                                 (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
             PCHKERRQ(ksp,ierr);
          }
       }
@@ -2545,7 +2538,7 @@ void PetscSolver::SetPrintLevel(int plev)
       if (plev > 0)
       {
          ierr = SNESMonitorSet(snes,(myMonitor)SNESMonitorDefault,vf,
-                               (myPetscFunc)PetscViewerAndFormatDestroy);
+                               (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(snes,ierr);
       }
    }
@@ -4163,20 +4156,31 @@ void PetscNonlinearSolver::SetUpdate(void (*update)(Operator *,int,
 void PetscNonlinearSolver::Mult(const Vector &b, Vector &x) const
 {
    SNES snes = (SNES)obj;
+   MPI_Comm comm = PetscObjectComm(obj);
 
-   bool b_nonempty = b.Size();
-   if (!B) { B = new PetscParVector(PetscObjectComm(obj), *this, true); }
-   if (!X) { X = new PetscParVector(PetscObjectComm(obj), *this, false, false); }
+   // Reduction needed: some processes may have null local size while others don't,
+   // and VecPlaceArray (used by PlaceMemory) is a logically collective operation.
+   PetscBool b_nonempty = b.Size() ? PETSC_TRUE : PETSC_FALSE;
+#if PETSC_VERSION_LT(3,24,0)
+   mpiierr = MPI_Allreduce(MPI_IN_PLACE,&b_nonempty,1,MPIU_BOOL,MPI_LOR,comm);
+#else
+   mpiierr = MPI_Allreduce(MPI_IN_PLACE,&b_nonempty,1,MPI_C_BOOL,MPI_LOR,comm);
+#endif
+   CCHKERRQ(comm,mpiierr);
+
+   // Always create B with allocate=false so that PlaceMemory can be called on
+   // it regardless of whether b was empty on a previous call.
+   if (!B) { B = new PetscParVector(comm, *this, true, false); }
+   if (!X) { X = new PetscParVector(comm, *this, false, false); }
    X->PlaceMemory(x.GetMemory(),iterative_mode);
    if (b_nonempty) { B->PlaceMemory(b.GetMemory()); }
-   else { *B = 0.0; }
 
    Customize();
 
    if (!iterative_mode) { *X = 0.; }
 
-   // Solve the system.
-   ierr = SNESSolve(snes, B->x, X->x); PCHKERRQ(snes, ierr);
+   // Solve the system. Pass nullptr for b when empty (PETSc treats it as zero RHS).
+   ierr = SNESSolve(snes, b_nonempty ? B->x : nullptr, X->x); PCHKERRQ(snes, ierr);
    X->ResetMemory();
    if (b_nonempty) { B->ResetMemory(); }
 }
@@ -5329,21 +5333,27 @@ static PetscErrorCode __mfem_pc_shell_destroy(PC pc)
    PetscFunctionReturn(PETSC_SUCCESS);
 }
 
+static PetscErrorCode __mfem_array_container_destroy(PetscCtxRt ptr)
+{
+   PetscErrorCode ierr;
+
+   PetscFunctionBeginUser;
 #if PETSC_VERSION_LT(3,23,0)
-
-static PetscErrorCode __mfem_array_container_destroy(void *ptr)
-{
-   PetscErrorCode ierr;
-
-   PetscFunctionBeginUser;
    ierr = PetscFree(ptr); CHKERRQ(ierr);
+#else
+   ierr = PetscFree(*(void**)ptr); CHKERRQ(ierr);
+#endif
    PetscFunctionReturn(PETSC_SUCCESS);
 }
 
-static PetscErrorCode __mfem_matarray_container_destroy(void *ptr)
+static PetscErrorCode __mfem_matarray_container_destroy(PetscCtxRt ptr)
 {
+#if PETSC_VERSION_LT(3,23,0)
    mfem::Array<Mat> *a = (mfem::Array<Mat>*)ptr;
-   PetscErrorCode   ierr;
+#else
+   mfem::Array<Mat> *a = *(mfem::Array<Mat>**)ptr;
+#endif
+   PetscErrorCode ierr;
 
    PetscFunctionBeginUser;
    for (int i=0; i<a->Size(); i++)
@@ -5356,41 +5366,16 @@ static PetscErrorCode __mfem_matarray_container_destroy(void *ptr)
    PetscFunctionReturn(PETSC_SUCCESS);
 }
 
+#if PETSC_VERSION_LT(3,23,0)
+static PetscErrorCode __mfem_monitor_ctx_destroy(void **ctx)
 #else
-
-static PetscErrorCode __mfem_array_container_destroy(void **ptr)
+static PetscErrorCode __mfem_monitor_ctx_destroy(PetscCtxRt ctx)
+#endif
 {
    PetscErrorCode ierr;
 
    PetscFunctionBeginUser;
-   ierr = PetscFree(*ptr); CHKERRQ(ierr);
-   PetscFunctionReturn(PETSC_SUCCESS);
-}
-
-static PetscErrorCode __mfem_matarray_container_destroy(void **ptr)
-{
-   mfem::Array<Mat> *a = (mfem::Array<Mat>*)*ptr;
-   PetscErrorCode   ierr;
-
-   PetscFunctionBeginUser;
-   for (int i=0; i<a->Size(); i++)
-   {
-      Mat M = (*a)[i];
-      MPI_Comm comm = PetscObjectComm((PetscObject)M);
-      ierr = MatDestroy(&M); CCHKERRQ(comm,ierr);
-   }
-   delete a;
-   PetscFunctionReturn(PETSC_SUCCESS);
-}
-
-#endif
-
-static PetscErrorCode __mfem_monitor_ctx_destroy(void **ctx)
-{
-   PetscErrorCode  ierr;
-
-   PetscFunctionBeginUser;
-   ierr = PetscFree(*ctx); CHKERRQ(ierr);
+   ierr = PetscFree(*(void**)ctx); CHKERRQ(ierr);
    PetscFunctionReturn(PETSC_SUCCESS);
 }
 
@@ -5635,11 +5620,7 @@ static PetscErrorCode MatConvert_hypreParCSR_AIJ(hypre_ParCSRMatrix* hA,Mat* pA)
 
       ierr = PetscContainerCreate(comm,&c); CHKERRQ(ierr);
       ierr = PetscContainerSetPointer(c,ptrs[i]); CHKERRQ(ierr);
-#if PETSC_VERSION_LT(3,23,0)
-      ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
       ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
       CHKERRQ(ierr);
       ierr = PetscObjectCompose((PetscObject)(*pA),names[i],(PetscObject)c);
       CHKERRQ(ierr);
@@ -5733,11 +5714,7 @@ static PetscErrorCode MatConvert_hypreParCSR_IS(hypre_ParCSRMatrix* hA,Mat* pA)
 
       ierr = PetscContainerCreate(PETSC_COMM_SELF,&c); CHKERRQ(ierr);
       ierr = PetscContainerSetPointer(c,ptrs[i]); CHKERRQ(ierr);
-#if PETSC_VERSION_LT(3,23,0)
-      ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
       ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
       CHKERRQ(ierr);
       ierr = PetscObjectCompose((PetscObject)lA,names[i],(PetscObject)c);
       CHKERRQ(ierr);

makefile

@@ -126,11 +126,11 @@ EXAMPLE_TEST_DIRS := examples
 MINIAPP_SUBDIRS = common electromagnetics meshing performance tools \
  toys nurbs gslib adjoint solvers shifted mtop parelag tribol autodiff dfem \
  hooke multidomain dpg hdiv-linear-solver spde diag-smoothers contact \
- fluids/navier fluids/schrodinger-flow
+ fluids/navier fluids/schrodinger-flow plasma plasma/pic
 MINIAPP_DIRS := $(addprefix miniapps/,$(MINIAPP_SUBDIRS))
 MINIAPP_TEST_DIRS := $(filter-out %/common,$(MINIAPP_DIRS))
 MINIAPP_USE_COMMON := $(addprefix miniapps/,electromagnetics meshing tools \
- toys shifted dpg diag-smoothers fluids/navier)
+ toys shifted dpg diag-smoothers fluids/navier plasma plasma/pic)
 
 EM_DIRS = $(EXAMPLE_DIRS) $(MINIAPP_DIRS)
 

mesh/mesh.cpp

@@ -493,8 +493,7 @@ void Mesh::GetBdrElementTransformation(int i,
          {
             for (int j = 0; j < n; j++)
             {
-               int idx = vdofs[n*k+j];
-               pm(k,j) = nodes((idx<0)? -1-idx:idx);
+               pm(k,j) = nodes(UnsignIndex(vdofs[n*k+j]));
             }
          }
          ElTr->SetFE(bdr_el);
@@ -1356,7 +1355,7 @@ Mesh::FaceInformation Mesh::GetFaceInformation(int f) const
                face.element[0].conformity = ElementConformity::Coincident;
                face.element[1].conformity = ElementConformity::Coincident;
                face.element[1].location = ElementLocation::FaceNbr;
-               face.element[1].index = -1 - e2;
+               face.element[1].index = FlipIndexSign(e2);
                face.element[1].orientation = inf2%64;
             }
          }
@@ -1379,7 +1378,7 @@ Mesh::FaceInformation Mesh::GetFaceInformation(int f) const
                face.element[1].location = ElementLocation::FaceNbr;
                face.element[0].conformity = ElementConformity::Coincident;
                face.element[1].conformity = ElementConformity::Superset;
-               face.element[1].index = -1 - e2;
+               face.element[1].index = FlipIndexSign(e2);
                face.element[1].orientation = inf2%64;
             }
             face.point_matrix = nc_faces_info[ncface].PointMatrix;
@@ -1405,7 +1404,7 @@ Mesh::FaceInformation Mesh::GetFaceInformation(int f) const
          face.element[1].location = ElementLocation::FaceNbr;
          face.element[0].conformity = ElementConformity::Superset;
          face.element[1].conformity = ElementConformity::Coincident;
-         face.element[1].index = -1 - e2;
+         face.element[1].index = FlipIndexSign(e2);
          face.element[1].orientation = inf2%64;
          face.point_matrix = nc_faces_info[ncface].PointMatrix;
       }
@@ -1438,7 +1437,7 @@ Mesh::FaceInformation::operator Mesh::FaceInfo() const
          break;
       case FaceInfoTag::SharedConforming:
          res.Elem1No = element[0].index;
-         res.Elem2No = -1 - element[1].index;
+         res.Elem2No = FlipIndexSign(element[1].index);
          res.Elem1Inf = element[0].orientation + element[0].local_face_id*64;
          res.Elem2Inf = element[1].orientation + element[1].local_face_id*64;
          break;
@@ -1448,7 +1447,7 @@ Mesh::FaceInformation::operator Mesh::FaceInfo() const
          break;
       case FaceInfoTag::SharedSlaveNonconforming:
          res.Elem1No = element[0].index;
-         res.Elem2No = -1 - element[1].index;
+         res.Elem2No = FlipIndexSign(element[1].index);
          res.Elem1Inf = element[0].orientation + element[0].local_face_id*64;
          res.Elem2Inf = element[1].orientation + element[1].local_face_id*64;
          break;
@@ -1456,7 +1455,7 @@ Mesh::FaceInformation::operator Mesh::FaceInfo() const
          break;
       case FaceInfoTag::GhostSlave:
          res.Elem1No = element[0].index;
-         res.Elem2No = -1 - element[1].index;
+         res.Elem2No = FlipIndexSign(element[1].index);
          res.Elem1Inf = element[0].orientation + element[0].local_face_id*64;
          res.Elem2Inf = element[1].orientation + element[1].local_face_id*64;
          break;
@@ -1617,7 +1616,9 @@ Element::Type Mesh::GetFaceElementType(int Face) const
 
 Array<int> Mesh::GetFaceToBdrElMap() const
 {
-   Array<int> face_to_be(Dim == 2 ? NumOfEdges : NumOfFaces);
+   Array<int> face_to_be(Dim == 1 ? NumOfVertices :
+                         Dim == 2 ? NumOfEdges :
+                         Dim == 3 ? NumOfFaces : 0);
    face_to_be = -1;
    for (int i = 0; i < NumOfBdrElements; i++)
    {
@@ -6514,7 +6515,7 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_ukv)
          input >> edge_to_ukv[j] >> v[0] >> v[1];
          if (v[0] > v[1])
          {
-            edge_to_ukv[j] = -1 - edge_to_ukv[j];
+            edge_to_ukv[j] = FlipIndexSign(edge_to_ukv[j]);
          }
       }
    }
@@ -6551,9 +6552,6 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
    const int NP = NumOfElements; // number of patches
    const int NPKV = NP * dim;    // number of patch knotvectors
    constexpr int notset = -9999999;
-   // Sign convention
-   auto flipSign = [](int i) { return -1 - i; };
-   auto unSign = [](int i) { return (i < 0) ? -1 - i : i; };
    // Local edge index -> dimension convention
    auto edge_to_dim = [](int i) { return (i < 8) ? ((i & 1) ? 1 : 0) : 2; };
 
@@ -6569,7 +6567,7 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
       {
          GetElementVertices(i, v);
          // Sign is based on the edge's vertex indices
-         edge_to_ukv[i] = (v[1] > v[0]) ? i : flipSign(i);
+         edge_to_ukv[i] = (v[1] > v[0]) ? i : FlipIndexSign(i);
          ukv_to_rpkv[i] = i;
       }
       return;
@@ -6619,14 +6617,14 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
          // We've set this edge already - link this index to it
          if (edge_to_pkv[edge] != notset)
          {
-            const int pkv_other = unSign(edge_to_pkv[edge]);
+            const int pkv_other = UnsignIndex(edge_to_pkv[edge]);
             unite(pkv, pkv_other);
          }
          else
          {
             GetEdgeVertices(edge, v);
             // Sign is based on the edge's vertex indices
-            edge_to_pkv[edge] = (v[1] > v[0]) ? pkv : flipSign(pkv);
+            edge_to_pkv[edge] = (v[1] > v[0]) ? pkv : FlipIndexSign(pkv);
          }
       }
    }
@@ -6653,10 +6651,10 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
    edge_to_ukv.SetSize(NumOfEdges);
    for (int i = 0; i < NumOfEdges; i++)
    {
-      const int pkv = unSign(edge_to_pkv[i]);
+      const int pkv = UnsignIndex(edge_to_pkv[i]);
       const int rpkv = pkv_to_rpkv[pkv];
       const int ukv = rpkv_to_ukv[rpkv];
-      edge_to_ukv[i] = (edge_to_pkv[i] < 0) ? flipSign(ukv) : ukv;
+      edge_to_ukv[i] = (edge_to_pkv[i] < 0) ? FlipIndexSign(ukv) : ukv;
    }
 
    CorrectPatchTopoOrientations(edge_to_ukv);
@@ -6667,9 +6665,6 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
    const int dim = Dimension(); // Topological (not physical) dimension
    if (dim == 1) { return; }
 
-   // Sign convention
-   auto flipSign = [](int i) { return -1 - i; };
-
    const Table *face2elem = GetFaceToElementTable();
    Array<int> pfaces, orient;
    Array<int> fe, feo;
@@ -6688,7 +6683,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
          for (auto e : fe)
          {
             const int skv = edge_to_ukv[e];
-            if (skv == kv || flipSign(skv) == kv) { hasKV = true; }
+            if (skv == kv || FlipIndexSign(skv) == kv) { hasKV = true; }
          }
          if (hasKV)
          {
@@ -6718,7 +6713,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       };
    }
 
-   Array<int> ukvs((dim==2) ? 4 : 12);
+   Array<int> ukvs((dim == 2) ? 4 : 12);
    Array<int> pe, oe;
    bool initKV = false;
 
@@ -6732,7 +6727,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       for (int i = 0; i < pe.Size(); i++)
       {
          ukvs[i] = edge_to_ukv[pe[i]];
-         ukvs[i] = (oe[i] < 0) ? flipSign(ukvs[i]) : ukvs[i];
+         ukvs[i] = (oe[i] < 0) ? FlipIndexSign(ukvs[i]) : ukvs[i];
       }
 
       // Find the direction with this kv.
@@ -6740,12 +6735,19 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       for (int d=0; d<dim; ++d) // Loop over directions.
       {
          const int skv = edge_to_ukv[pe[dir_edges[d][0]]];
-         if (skv == kv || flipSign(skv) == kv)
+         if (skv == kv || FlipIndexSign(skv) == kv)
          {
-            thisDir = d;
+            for (auto e : dir_edges[d])
+               if (!edgeSet[pe[e]])
+               {
+                  thisDir = d;
+               }
          }
       }
-      MFEM_VERIFY(thisDir >= 0, "");
+      if (thisDir == -1)
+      {
+         return false;
+      }
 
       // For this direction, find any edge already set. If no edge is set, we
       // arbitrarily take the first.
@@ -6777,12 +6779,12 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
          }
 
          const int edge = pe[i];
-         if ((dim == 2 && ukvs[i] != flipSign(ukvs[ref_edge0])) ||
-             (dim == 3 && ukvs[i] == flipSign(ukvs[ref_edge0])))
+         if ((dim == 2 && ukvs[i] != FlipIndexSign(ukvs[ref_edge0])) ||
+             (dim == 3 && ukvs[i] == FlipIndexSign(ukvs[ref_edge0])))
          {
             // Flip the sign of this edge
-            MFEM_VERIFY(!edgeSet[edge], "");
-            edge_to_ukv[edge] = flipSign(edge_to_ukv[edge]);
+            MFEM_ASSERT(!edgeSet[edge], "");
+            edge_to_ukv[edge] = FlipIndexSign(edge_to_ukv[edge]);
          }
 
          edgeSet[edge] = true;
@@ -6827,10 +6829,11 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       int unsetDim = -1;
       for (int d=0; d<dim; ++d) // Loop over dimensions.
       {
-         if (!edgeSet[pe[dir_edges[d][0]]])
-         {
-            unsetDim = d;
-         }
+         for (auto e : dir_edges[d])
+            if (!edgeSet[pe[e]])
+            {
+               unsetDim = d;
+            }
       }
 
       if (unsetDim == -1)
@@ -6839,9 +6842,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
          continue;
       }
 
-      const int kv_signed = edge_to_ukv[pe[dir_edges[unsetDim][0]]];
-      const int kv = kv_signed < 0 ? flipSign(kv_signed) : kv_signed;
-      MFEM_VERIFY(!edgeSet[pe[dir_edges[unsetDim][0]]], "");
+      const int kv = UnsignIndex(edge_to_ukv[pe[dir_edges[unsetDim][0]]]);
 
       initKV = false;
 
@@ -6891,6 +6892,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       }
    }
 
+#ifdef MFEM_DEBUG
    bool allSet = true;
    for (auto eset : edgeSet)
    {
@@ -6899,7 +6901,8 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
          allSet = false;
       }
    }
-   MFEM_VERIFY(allSet && unset.size() == 0, "Some edge is not set");
+   MFEM_ASSERT(allSet && unset.size() == 0, "Some edge is not set");
+#endif
 
    delete face2elem;
 }
@@ -6941,7 +6944,7 @@ void Mesh::LoadNonconformingPatchTopo(std::istream &input,
 
       if (v[0] > v[1])
       {
-         ukv = -1 - ukv;
+         ukv = FlipIndexSign(ukv);
       }
       edge_to_ukv[j] = ukv;
    }
@@ -12438,11 +12441,7 @@ void Mesh::PrintTopoEdges(std::ostream &os, const Array<int> &e_to_k,
    for (int i = 0; i < NumOfEdges; i++)
    {
       edge_vertex->GetRow(i, vert);
-      int ki = e_to_k[i];
-      if (ki < 0)
-      {
-         ki = -1 - ki;
-      }
+      const int ki = UnsignIndex(e_to_k[i]);
 
       if (vmap)
       {
@@ -15751,9 +15750,18 @@ Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
 {
    MFEM_VERIFY(dim > 1, "Not implemented for 1D meshes.");
 
-   auto factor = [&](int N)
+   // Closest int divisor to the cubit root, going down.
+   auto factor3 = [](int N)
    {
-      for (int i = static_cast<int>(sqrt(N)); i > 0; i--)
+      for (int i = static_cast<int>(round(cbrt(N))); i > 0; i--)
+      {  if (N % i == 0) { return i; } }
+      return 1;
+   };
+
+   // Closest int divisor to the square root, going down.
+   auto factor2 = [](int N)
+   {
+      for (int i = static_cast<int>(round(sqrt(N))); i > 0; i--)
       { if (N % i == 0) { return i; } }
       return 1;
    };
@@ -15777,22 +15785,22 @@ Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
    int el0_x, el0_y, el0_z;
    if (dim == 2)
    {
-      mpi_x = factor(mpi_cnt);
+      mpi_x = factor2(mpi_cnt);
       mpi_y = mpi_cnt / mpi_x;
 
       // Switch order for better balance.
-      el0_y = factor(el0);
+      el0_y = factor2(el0);
       el0_x = el0 / el0_y;
    }
    else
    {
-      mpi_x = factor(mpi_cnt);
-      mpi_y = factor(mpi_cnt / mpi_x);
+      mpi_x = factor3(mpi_cnt);
+      mpi_y = factor2(mpi_cnt / mpi_x);
       mpi_z = mpi_cnt / mpi_x / mpi_y;
 
       // Switch order for better balance.
-      el0_z = factor(el0);
-      el0_y = factor(el0 / el0_z);
+      el0_z = factor3(el0);
+      el0_y = factor2(el0 / el0_z);
       el0_x = el0 / el0_y / el0_z;
    }
 

mesh/mesh.hpp

@@ -3206,10 +3206,22 @@ public:
 
 
 /// Extrude a 1D mesh
+/**
+ * @param mesh      1D mesh
+ * @param ny        number of transverse elements of the extruded mesh
+ * @param sy        physical size in the direction of extrusion
+ * @param closed    if false, only the original boundaries are extruded,
+ *                  otherwise boundaries are generated all around the domain
+ */
 Mesh *Extrude1D(Mesh *mesh, const int ny, const real_t sy,
                 const bool closed = false);
 
 /// Extrude a 2D mesh
+/**
+ * @param mesh      2D mesh
+ * @param nz        number of transverse elements of the extruded mesh
+ * @param sz        physical size in the direction of extrusion
+ */
 Mesh *Extrude2D(Mesh *mesh, const int nz, const real_t sz);
 
 /** @brief Constructs the smallest possible [0,1]^dim serial mesh that can be

mesh/mesh_operators.cpp

@@ -63,7 +63,6 @@ ThresholdRefiner::ThresholdRefiner(ErrorEstimator &est)
 
    threshold = 0.0;
    num_marked_elements = 0LL;
-   current_sequence = -1;
 
    non_conforming = -1;
    nc_limit = 0;
@@ -87,7 +86,6 @@ int ThresholdRefiner::MarkWithoutRefining(Mesh & mesh,
    threshold = 0.0;
    num_marked_elements = 0LL;
    refinements.SetSize(0);
-   current_sequence = mesh.GetSequence();
 
    const long long num_elements = mesh.GetGlobalNE();
    if (num_elements >= max_elements) { return STOP; }
@@ -143,13 +141,12 @@ int ThresholdRefiner::ApplyImpl(Mesh &mesh)
    if (num_marked_elements == 0LL) { return STOP; }
 
    mesh.GeneralRefinement(marked_elements, non_conforming, nc_limit);
-   return CONTINUE + REFINED;
+   return static_cast<int>(CONTINUE) + static_cast<int>(REFINED);
 }
 
 void ThresholdRefiner::Reset()
 {
    estimator.Reset();
-   current_sequence = -1;
    num_marked_elements = 0LL;
    // marked_elements.SetSize(0); // not necessary
 }
@@ -162,7 +159,7 @@ int ThresholdDerefiner::ApplyImpl(Mesh &mesh)
    const Vector &local_err = estimator.GetLocalErrors();
    bool derefs = mesh.DerefineByError(local_err, threshold, nc_limit, op);
 
-   return derefs ? CONTINUE + DEREFINED : NONE;
+   return derefs ? static_cast<int>(CONTINUE) + static_cast<int>(DEREFINED) : NONE;
 }
 
 
@@ -290,7 +287,7 @@ int CoefficientRefiner::PreprocessMesh(Mesh &mesh, int max_it)
    }
    delete l2fes;
    delete gf;
-   return CONTINUE + REFINED;
+   return static_cast<int>(CONTINUE) + static_cast<int>(REFINED);
 
 }
 
@@ -310,7 +307,7 @@ int Rebalancer::ApplyImpl(Mesh &mesh)
    if (pmesh && pmesh->Nonconforming())
    {
       pmesh->Rebalance();
-      return CONTINUE + REBALANCED;
+      return static_cast<int>(CONTINUE) + static_cast<int>(REBALANCED);
    }
 #endif
    return NONE;

mesh/mesh_operators.hpp

@@ -188,7 +188,6 @@ protected:
    long long num_marked_elements;
 
    Array<Refinement> marked_elements;
-   long current_sequence;
 
    int non_conforming;
    int nc_limit;

mesh/mesh_readers.cpp

@@ -1516,12 +1516,15 @@ void Mesh::ReadInlineMesh(std::istream &input, bool generate_edges)
 void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
 {
    string buff;
-   real_t version;
+   string version;
    int binary, dsize;
    input >> version >> binary >> dsize;
-   if (version < 2.2)
+   if (version != "2.2")
    {
-      MFEM_ABORT("Gmsh file version < 2.2");
+      MFEM_ABORT("Gmsh file version must be 2.2, found version "
+                 << version << ".\n"
+                 "To convert your mesh to the required format, use:\n"
+                 "  gmsh -format msh22 -save -o output.msh input.msh");
    }
    if (dsize != sizeof(double))
    {

mesh/ncmesh.cpp

@@ -3542,7 +3542,7 @@ void NCMesh::TraverseQuadFace(int vn0, int vn1, int vn2, int vn3,
 
             // create a slave face record with a degenerate point matrix
             face_list.slaves.Append(
-               Slave(-1 - enode.edge_index,
+               Slave(FlipIndexSign(enode.edge_index),
                      eid[0].element, eid[0].local, Geometry::SQUARE));
             Slave &sl = face_list.slaves.Last();
 
@@ -3589,7 +3589,7 @@ void NCMesh::TraverseTetEdge(int vn0, int vn1, const Point &p0, const Point &p1,
          // non-slave edge is really a (face-)slave itself.
          const MeshId &eid = *eid_and_type.id;
          face_list.slaves.Append(
-            Slave(-1 - eid.index, eid.element, eid.local, Geometry::TRIANGLE));
+            Slave(FlipIndexSign(eid.index), eid.element, eid.local, Geometry::TRIANGLE));
 
          int v0index = nodes[vn0].vert_index;
          int v1index = nodes[vn1].vert_index;

mesh/ncnurbs.cpp

@@ -93,7 +93,7 @@ void NCNURBSExtension::GetMasterEdgeEntities(
       }
       else
       {
-         const int auxEdge = -1 - edge_i;
+         const int auxEdge = FlipIndexSign(edge_i);
          GetAuxEdgeVertices(auxEdge, sverts);
       }
 
@@ -159,7 +159,7 @@ void NCNURBSExtension::FindAdditionalFacesSA(
             {
                if (edge < 0)
                {
-                  sideAuxEdges[s].Append(-1 - edge);
+                  sideAuxEdges[s].Append(FlipIndexSign(edge));
                }
                else
                {
@@ -456,7 +456,7 @@ void NCNURBSExtension::FindAdditionalFacesSA(
                                        == afverts[j], "");
                         }
 
-                        ori_f2 = -1 - ori_f2;
+                        ori_f2 = FlipIndexSign(ori_f2);
                      }
                      else
                      {
@@ -468,7 +468,7 @@ void NCNURBSExtension::FindAdditionalFacesSA(
                      }
 
                      facePairs.emplace_back(FacePairInfo{fverts[vMinID], f,
-                     SlaveFaceInfo{-1 - afid, ori_f2,
+                     SlaveFaceInfo{FlipIndexSign(afid), ori_f2,
                         {fki(vMinID,0), fki(vMinID,1)},
                         {
                            fki((vMinID + 2) % 4,0) - fki(vMinID,0),
@@ -509,7 +509,7 @@ void NCNURBSExtension::FindAdditionalFacesSA(
                      auxFaces.push_back(auxFace);
 
                      facePairs.emplace_back(FacePairInfo{fverts[vMinID], f,
-                     SlaveFaceInfo{-1 - auxFaceId, ori_f,
+                     SlaveFaceInfo{FlipIndexSign(auxFaceId), ori_f,
                         {fki(vMinID,0), fki(vMinID,1)},
                         {
                            fki((vMinID + 2) % 4,0) - fki(vMinID,0),
@@ -622,7 +622,7 @@ void NCNURBSExtension::GetAuxFaceEdges(int auxFace, Array<int> &edges) const
       }
       else // Auxiliary edge
       {
-         edges[i] = -1 - auxv2e.at(edge_v);
+         edges[i] = FlipIndexSign(auxv2e.at(edge_v));
       }
    }
 }
@@ -633,7 +633,7 @@ int OffsetHelper(int i, int j, const Array<int> &a, const Array<int> &b)
 {
    if (i < 0)
    {
-      return b[-1 - i + j];
+      return b[FlipIndexSign(i) + j];
    }
    else if (i + j < a.Size())
    {
@@ -679,7 +679,7 @@ void NCNURBSExtension::GetMasterEdgeDofs(bool dof, int me,
       }
       else // Auxiliary edge
       {
-         GetAuxEdgeVertices(-1 - slaveId, svert);
+         GetAuxEdgeVertices(FlipIndexSign(slaveId), svert);
       }
 
       bool reverse = false;
@@ -872,7 +872,7 @@ void ReorderArray2D(int i0, int j0, const Array2D<int> &a,
 // Set a quadrilateral vertex index permutation for a given orientation.
 void GetVertexOrdering(int ori, std::array<int, 4> &perm)
 {
-   const int oriAbs = ori < 0 ? -1 - ori : ori;
+   const int oriAbs = UnsignIndex(ori);
 
    for (int i=0; i<4; ++i)
    {
@@ -1094,7 +1094,7 @@ void NCNURBSExtension::GetMasterFaceDofs(bool dof, int mf,
       if (slaveId < 0)
       {
          // Auxiliary face
-         const int auxFace = -1 - slaveId;
+         const int auxFace = FlipIndexSign(slaveId);
 
          // Set slave face entity dimensions.
          if (dof)
@@ -1171,7 +1171,7 @@ void NCNURBSExtension::GetMasterFaceDofs(bool dof, int mf,
             }
             else
             {
-               const int auxEdge = -1 - edge;
+               const int auxEdge = FlipIndexSign(edge);
                GetAuxEdgeVertices(auxEdge, evert);
             }
             MFEM_ASSERT(evert[0] == vstart || evert[1] == vstart, "");
@@ -1184,7 +1184,7 @@ void NCNURBSExtension::GetMasterFaceDofs(bool dof, int mf,
          // dimensions of the master face, by using ori.
          int e1 = -1, e2 = -1;
          {
-            const int aori = ori < 0 ? -1 - ori : ori;
+            const int aori = UnsignIndex(ori);
             if (aori % 2 == 0)
             {
                e1 = 0;
@@ -1416,14 +1416,15 @@ void NCNURBSExtension::ProcessVertexToKnot2D(const VertexToKnotSpan &v2k,
          {
             // Create a new auxiliary edge
             auxv2e[childPair] = auxEdges.size();
-            auxEdges.emplace_back(AuxiliaryEdge{pv[0] < pv[1] ?
-                                                parentEdge : -1 - parentEdge,
+            auxEdges.emplace_back(AuxiliaryEdge{pv[0] < pv[1] ? parentEdge :
+                                                FlipIndexSign(parentEdge),
             {childPair.first, childPair.second},
             {newParentEdge ? 0 : prevKI, ks}});
          }
       }
 
-      const int childEdge = childPairTopo ? v2e[childPair] : -1 - auxv2e[childPair];
+      const int childEdge = childPairTopo ? v2e[childPair] :
+                            FlipIndexSign(auxv2e[childPair]);
 
       // Check whether this is the final vertex in this parent edge. Note that
       // the logic for comparing (pv[0],pv[1]) to the next parents assumes the
@@ -1460,14 +1461,15 @@ void NCNURBSExtension::ProcessVertexToKnot2D(const VertexToKnotSpan &v2k,
 
                // -1 denotes `ne` at endpoint
                auxEdges.emplace_back(AuxiliaryEdge{pv[0] < pv[1] ?
-                                                   -1 - parentEdge : parentEdge,
+                                                   FlipIndexSign(parentEdge) :
+                                                   parentEdge,
                {finalChildPair.first, finalChildPair.second},
                {ks, -1}});
             }
          }
 
          const int finalChildEdge = finalChildPairTopo ? v2e[finalChildPair] :
-                                    -1 - auxv2e[finalChildPair];
+                                    FlipIndexSign(auxv2e[finalChildPair]);
          edgePairs.emplace_back(-1, -1, finalChildEdge, parentEdge);
       }
 
@@ -1805,7 +1807,7 @@ void NCNURBSExtension::ProcessVertexToKnot3D(
                   auxFaces.push_back(auxFace);
                   facePairs.emplace_back(
                      FacePairInfo{cv[0], parentFace,
-                                  SlaveFaceInfo{-1 - auxv2f[childPair],
+                                  SlaveFaceInfo{FlipIndexSign(auxv2f[childPair]),
                                                 0, {i0, j0}, {d0, d1}}});
                }
             }
@@ -2111,7 +2113,7 @@ void NCNURBSExtension::ProcessVertexToKnot3D(
                      auxv2e[childPair] = auxEdges.size();
                      auxEdges.emplace_back(AuxiliaryEdge{pv0 < pv1 ?
                                                          parentEdge :
-                                                         -1 - parentEdge,
+                                                         FlipIndexSign(parentEdge),
                      {childPair.first, childPair.second},
                      {knotIndex0, knotIndex1}});
                   }
@@ -2131,7 +2133,8 @@ void NCNURBSExtension::ProcessVertexToKnot3D(
 
                   const EdgePairInfo ep_e((e_idx == n_d - de) ? -1 : tv,
                                           (e_idx == n_d - de) ? -1 : tvki,
-                                          -1 - auxv2e[childPair], parentEdge);
+                                          FlipIndexSign(auxv2e[childPair]),
+                                          parentEdge);
 
                   const bool unset = !edgePairs[edgePairOS[parentEdge] + e_idx].isSet;
                   if (unset)
@@ -2226,7 +2229,7 @@ void NCNURBSExtension::GetAuxFaceToPatchTable(Array2D<int> &auxface2patch)
                if (s < 0)
                {
                   // Auxiliary face.
-                  const int aux = -1 - s;
+                  const int aux = FlipIndexSign(s);
                   if (auxface2patch(aux, 0) >= 0)
                   {
                      if (auxface2patch(aux, 1) != -1) { consistent = false; }
@@ -2316,7 +2319,7 @@ void NCNURBSExtension::UpdateAuxiliaryKnotSpans(const Array<int> &rf)
    for (auto auxEdge : auxEdges)
    {
       const int p = auxEdge.parent;
-      const int parent = p < 0 ? -1 - p : p;
+      const int parent = UnsignIndex(p);
       const int kv = KnotInd(parent);
       for (int i=0; i<2; ++i)
       {
@@ -2382,14 +2385,8 @@ int NCNURBSExtension::AuxiliaryEdgeNE(int aux_edge)
    const int signedParentEdge = auxEdges[aux_edge].parent;
    const int ki0 = auxEdges[aux_edge].ksi[0];
    const int ki1raw = auxEdges[aux_edge].ksi[1];
-   int ki1 = ki1raw;
-   if (ki1raw == -1)
-   {
-      const bool rev = signedParentEdge < 0;
-      const int parentEdge = rev ? -1 - signedParentEdge : signedParentEdge;
-      ki1 = KnotVec(parentEdge)->GetNE();
-   }
-
+   const int ki1 = ki1raw == -1 ? KnotVec(UnsignIndex(signedParentEdge))->GetNE()
+                   : ki1raw;
    return ki1 - ki0;
 }
 
@@ -2403,7 +2400,7 @@ void NCNURBSExtension::SlaveEdgeToParent(int se, int parent,
    Array<int> sev(2);
    if (se < 0) // Auxiliary edge
    {
-      for (int i=0; i<2; ++i) { sev[i] = auxEdges[-1 - se].v[i]; }
+      for (int i=0; i<2; ++i) { sev[i] = auxEdges[FlipIndexSign(se)].v[i]; }
    }
    else
    {
@@ -2459,7 +2456,7 @@ void NCNURBSExtension::GetMasterEdgePieceOffsets(int mid, Array<int> &os)
       }
       else
       {
-         nes = AuxiliaryEdgeNE(-1 - s);
+         nes = AuxiliaryEdgeNE(FlipIndexSign(s));
       }
 
       os[i+1] = os[i] + nes;
@@ -2565,7 +2562,7 @@ int NCNURBSExtension::SetPatchFactors(int p)
                }
                else // Aux edge
                {
-                  const int aux_edge = -1 - s;
+                  const int aux_edge = FlipIndexSign(s);
                   if (auxef[aux_edge].Size() == 0)
                   {
                      auxef[aux_edge].SetSize(AuxiliaryEdgeNE(aux_edge));
@@ -2611,7 +2608,7 @@ int NCNURBSExtension::SetPatchFactors(int p)
    }
 
    MFEM_VERIFY(consistent, "");
-   return partialChange ? -1 - dirSet : dirSet;
+   return partialChange ? FlipIndexSign(dirSet) : dirSet;
 }
 
 void NCNURBSExtension::PropagateFactorsForKV(int rf_default)
@@ -2715,7 +2712,7 @@ void NCNURBSExtension::PropagateFactorsForKV(int rf_default)
                if (s < 0)
                {
                   // Auxiliary face.
-                  const int aux = -1 - s;
+                  const int aux = FlipIndexSign(s);
                   for (int i=0; i<2; ++i)
                   {
                      const int patch = auxface2patch(aux, i);
@@ -2763,7 +2760,7 @@ void NCNURBSExtension::PropagateFactorsForKV(int rf_default)
 
          const int dirSetSigned = SetPatchFactors(p);
          const bool partialChange = dirSetSigned < 0;
-         const int dirSet = partialChange ? -1 - dirSetSigned : dirSetSigned;
+         const int dirSet = UnsignIndex(dirSetSigned);
          const bool changed = (patchState[p] != dirSet) || partialChange;
          patchState[p] = dirSet;
 
@@ -2806,8 +2803,8 @@ void NCNURBSExtension::PropagateFactorsForKV(int rf_default)
             {
                const int dirSetSigned_i = SetPatchFactors(i);
                const bool partialChange_i = dirSetSigned_i < 0;
-               const int dirSet_i = partialChange_i ? -1 - dirSetSigned_i :
-                                    dirSetSigned_i;
+               const int dirSet_i = partialChange_i ?
+                                    FlipIndexSign(dirSetSigned_i) : dirSetSigned_i;
                const bool changed_i = (patchState[i] != dirSet_i) ||
                                       partialChange_i;
                patchState[p] = dirSet_i;
@@ -3027,7 +3024,7 @@ int GetFaceOrientation(const Mesh *mesh, const int face,
 
    // Check whether ordering is reversed.
    const bool rev = verts[(s + 1) % 4] != fverts[1];
-   if (rev) { s = -1 - s; } // Reversed order is encoded by the sign.
+   if (rev) { s = FlipIndexSign(s); } // Reversed order is encoded by the sign.
    return s;
 }
 
@@ -3040,7 +3037,7 @@ int GetFaceOrientation(const Mesh *mesh, const int face,
 // see GetFaceOrientation.
 bool Reorder2D(int ori, std::array<int, 2> &s0)
 {
-   const int shift = ori < 0 ? -1 - ori : ori;
+   const int shift = UnsignIndex(ori);
 
    // Shift is an F1 index in the counter-clockwise ordering of 4 quad vertices.
    // Now find the (i,j) indices of this index, with i,j in {0,1}.
@@ -3064,7 +3061,7 @@ void GetInverseShiftedDimensions2D(int signedShift, int sm, int sn, int &m,
                                    int &n)
 {
    const bool rev = (signedShift < 0);
-   const int shift = rev ? -1 - signedShift : signedShift;
+   const int shift = UnsignIndex(signedShift);
    MFEM_ASSERT(0 <= shift && shift < 4, "");
 
    // We consider 8 cases for the possible values of rev and shift.
@@ -3136,7 +3133,7 @@ void GetShiftedGridPoints2D(int m, int n, int i, int j, int signedShift,
                             int& sm, int& sn, int& si, int& sj)
 {
    const bool rev = (signedShift < 0);
-   const int shift = rev ? -1 - signedShift : signedShift;
+   const int shift = UnsignIndex(signedShift);
    MFEM_ASSERT(0 <= shift && shift < 4, "");
 
    // (0,0) <= (i,j) < (m,n) are old indices, and old vertex [shift] maps
@@ -3798,8 +3795,7 @@ void NCNURBSExtension::GenerateOffsets()
       const int signedParentEdge = auxEdges[e].parent;
       const int ki0 = auxEdges[e].ksi[0];
       const int ki1raw = auxEdges[e].ksi[1];
-      const bool rev = signedParentEdge < 0;
-      const int parentEdge = rev ? -1 - signedParentEdge : signedParentEdge;
+      const int parentEdge = UnsignIndex(signedParentEdge);
       const int masterNE = KnotVec(parentEdge)->GetNE();
       const int ki1 = ki1raw == -1 ? masterNE : ki1raw;
       const int perEdgeCP = GetNCPperEdge(KnotVec(e));

mesh/nurbs.cpp

@@ -3723,10 +3723,7 @@ bool NURBSExtension::CheckPatches()
       for (int i = 0; i < edges.Size(); i++)
       {
          edges[i] = edge_to_ukv[edges[i]];
-         if (oedge[i] < 0)
-         {
-            edges[i] = -1 - edges[i];
-         }
+         if (oedge[i] < 0) { edges[i] = FlipIndexSign(edges[i]); }
       }
 
       // In 2d - opposite edges must be same knotvector with opposite sign.
@@ -3740,7 +3737,7 @@ bool NURBSExtension::CheckPatches()
       // {7, 6}, {4, 7}, {0, 4}, {1, 5}, {2, 6}, {3, 7} for Geometry::CUBE in 3D
       // See fem/geom.cpp for these definitions.
       if ((dim == 2 &&
-           (edges[0] != -1 - edges[2] || edges[1] != -1 - edges[3])) ||
+           (edges[0] != FlipIndexSign(edges[2]) || edges[1] != FlipIndexSign(edges[3]))) ||
 
           (dim == 3 &&
            (edges[0] != edges[2] || edges[0] != edges[4] ||
@@ -3769,7 +3766,7 @@ void NURBSExtension::CheckBdrPatches()
          edges[i] = edge_to_ukv[edges[i]];
          if (oedge[i] < 0)
          {
-            edges[i] = -1 - edges[i];
+            edges[i] = FlipIndexSign(edges[i]);
          }
       }
 
@@ -4766,14 +4763,13 @@ void NURBSExtension::GenerateBdrElementDofTable()
    SetPatchToBdrElements();
 
    int *dof = bel_dof->GetJ();
-   int ndof = bel_dof->Size_of_connections();
+   const int ndof = bel_dof->Size_of_connections();
    for (int i = 0; i < ndof; i++)
    {
-      int idx = dof[i];
+      const int idx = dof[i];
       if (idx < 0)
       {
-         dof[i] = -1 - (activeDof[-1-idx] - 1);
-         dof[i] = -activeDof[-1-idx];
+         dof[i] = -activeDof[FlipIndexSign(idx)];
       }
       else
       {
@@ -4858,12 +4854,12 @@ void NURBSExtension::Generate2DBdrElementDofTable()
                   for (int ii = 0; ii <= ord0; ii++)
                   {
                      conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
-                     if (s == -1) { conn.to = -1 -conn.to; }
+                     if (s == -1) { conn.to = FlipIndexSign(conn.to); }
                      bel_dof_list.Append(conn);
                   }
                }
                bel_to_patch[lbe] = b;
-               bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : (-1-i);
+               bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : FlipIndexSign(i);
                lbe++;
             }
             gbe++;
@@ -4936,14 +4932,14 @@ void NURBSExtension::Generate3DBdrElementDofTable()
                            {
                               const int ii_ = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
                               conn.to = DofMap(p2g(ii_, jj_));
-                              if (s == -1) { conn.to = -1 -conn.to; }
+                              if (s == -1) { conn.to = FlipIndexSign(conn.to); }
                               bel_dof_list.Append(conn);
                            }
                         }
                      }
                      bel_to_patch[lbe] = b;
-                     bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : (-1-i);
-                     bel_to_IJK(lbe,1) = (okv[1] >= 0) ? j : (-1-j);
+                     bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : FlipIndexSign(i);
+                     bel_to_IJK(lbe,1) = (okv[1] >= 0) ? j : FlipIndexSign(j);
                      lbe++;
                   }
                   gbe++;

mesh/nurbs.hpp

@@ -220,7 +220,7 @@ public:
        @a u.
        The main purpose of this function is its use in FindInterpolant.
        Use GetBotella instead for each shape function separately, perhaps in
-       conjuction with GetSpan and GetRefPoint.*/
+       conjunction with GetSpan and GetRefPoint.*/
    MFEM_DEPRECATED void FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const;
 
    /** @brief Global curve interpolation through the points @a x (overwritten).
@@ -1398,8 +1398,7 @@ inline const real_t &NURBSPatch::operator()(int i, int j, int k, int l) const
 
 inline int NURBSExtension::KnotInd(int edge) const
 {
-   const int kv = edge_to_ukv[edge];
-   return kv >= 0 ? kv : -1 - kv;
+   return UnsignIndex(edge_to_ukv[edge]);
 }
 
 inline int NURBSExtension::KnotSign(int edge) const
@@ -1429,7 +1428,7 @@ const
    else
    {
       *okv = -oedge;
-      return knotVectors[-1-kv];
+      return knotVectors[FlipIndexSign(kv)];
    }
 }
 

mesh/pmesh.cpp

@@ -5639,6 +5639,12 @@ Mesh ParMesh::GetSerialMesh(int save_rank) const
       }
    }
 
+   if (MyRank == save_rank)
+   {
+      attribute_sets.Copy(serialmesh.attribute_sets);
+      bdr_attribute_sets.Copy(serialmesh.bdr_attribute_sets);
+   }
+
    MPI_Barrier(MyComm);
    return serialmesh;
 }

mesh/pncmesh.cpp

@@ -400,7 +400,7 @@ void ParNCMesh::MakeSharedList(const NCList &list, NCList &shared)
          }
          else // special case: prism edge-face constraint
          {
-            if (entity_owner[1][-1-si] != MyRank)
+            if (entity_owner[1][FlipIndexSign(si)] != MyRank)
             {
                master_flag |= 0x2;
             }
@@ -571,9 +571,10 @@ void ParNCMesh::CalculatePMatrixGroups()
       ranks.SetSize(0);
       for (int j = master_face.slaves_begin; j < master_face.slaves_end; j++)
       {
-         int si = face_list.slaves[j].index;
-         int owner = (si >= 0) ? entity_owner[2][si] // standard face dependency
-                     /*     */ : entity_owner[1][-1 - si]; // prism edge-face dep
+         const int si = face_list.slaves[j].index;
+         const int owner =
+            (si >= 0) ? entity_owner[2][si] : // standard face dependency
+            entity_owner[1][FlipIndexSign(si)]; // prism edge-face dep
          ranks.Append(groups[owner][0]);
       }
       ranks.Sort();
@@ -1181,7 +1182,7 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
       if (e[0]->rank == MyRank) { std::swap(e[0], e[1]); }
 
       Mesh::FaceInfo &fi = pmesh.faces_info[cf.index];
-      fi.Elem2No = -1 - fnbr_index[e[0]->index - NElements];
+      fi.Elem2No = FlipIndexSign(fnbr_index[e[0]->index - NElements]);
 
       if (Dim == 3)
       {
@@ -1270,7 +1271,7 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
                // In other words, side 1 IS the side that generated the face.
             }
             MFEM_ASSERT(fi.Elem2No >= NElements, "");
-            fi.Elem2No = -1 - fnbr_index[fi.Elem2No - NElements];
+            fi.Elem2No = FlipIndexSign(fnbr_index[fi.Elem2No - NElements]);
 
             const DenseMatrix* pm = full_list.point_matrices[sf.geom][sf.matrix];
             if (!sloc && Dim == 3)
@@ -2286,7 +2287,7 @@ void ParNCMesh::Derefine(const Array<int> &derefs)
       if (element_type[index] == 0)
       {
          // this coarse element will get pruned, encode who owns it now
-         index = -1 - elements[coarse[i]].rank;
+         index = FlipIndexSign(elements[coarse[i]].rank);
       }
       transforms.embeddings[i].parent = index;
    }

mesh/submesh/psubmesh.hpp

@@ -227,15 +227,29 @@ public:
                                            const ParGridFunction &dst);
 
    /**
-   * @brief Check if ParMesh @a m is a ParSubMesh.
+   * @brief Check if Mesh @a m is a ParSubMesh.
    *
-   * @param m The input ParMesh
+   * @param m The input Mesh
    */
-   static bool IsParSubMesh(const ParMesh *m)
+   static bool IsParSubMesh(const Mesh *m)
    {
       return dynamic_cast<const ParSubMesh *>(m) != nullptr;
    }
 
+   /**
+   * @brief Check if Mesh @a sub is a ParSubMesh of Mesh @a parent.
+   *
+   * @param sub The potential submesh Mesh
+   * @param parent The potential parent Mesh
+   */
+   static bool IsParSubMesh(const Mesh* sub, const Mesh* parent)
+   {
+      while (IsParSubMesh(sub) &&
+             (sub = static_cast<const ParSubMesh *>(sub)->GetParent()) &&
+             sub != parent);
+      return sub == parent;
+   }
+
 private:
    ParSubMesh(const ParMesh &parent, SubMesh::From from,
               const Array<int> &attributes);

mesh/submesh/submesh.hpp

@@ -225,6 +225,20 @@ public:
       return dynamic_cast<const SubMesh *>(m) != nullptr;
    }
 
+   /**
+   * @brief Check if Mesh @a sub is a SubMesh of Mesh @a parent.
+   *
+   * @param sub The potential submesh Mesh
+   * @param parent The potential parent Mesh
+   */
+   static bool IsSubMesh(const Mesh* sub, const Mesh* parent)
+   {
+      while (IsSubMesh(sub) &&
+             (sub = static_cast<const SubMesh *>(sub)->GetParent()) &&
+             sub != parent);
+      return sub == parent;
+   }
+
 private:
    /// Private constructor
    SubMesh(const Mesh &parent, From from, const Array<int> &attributes);

miniapps/CMakeLists.txt

@@ -35,6 +35,7 @@ add_subdirectory(multidomain)
 add_subdirectory(nurbs)
 add_subdirectory(parelag)
 add_subdirectory(performance)
+add_subdirectory(plasma)
 add_subdirectory(shifted)
 add_subdirectory(solvers)
 add_subdirectory(spde)

miniapps/fluids/navier/CMakeLists.txt

@@ -17,9 +17,13 @@ if (MFEM_USE_MPI)
 
   if(MFEM_USE_GSLIB)
     list(APPEND NAVIER_COMMON_SOURCES
-      navier_particles.cpp)
+      navier_particles.cpp
+      navier_tools.cpp
+      ascii.cpp)
     list(APPEND NAVIER_COMMON_HEADERS
-      navier_particles.hpp)
+      navier_particles.hpp
+      navier_tools.hpp
+      ascii.hpp)
   endif()
 
   convert_filenames_to_full_paths(NAVIER_COMMON_SOURCES)
@@ -71,11 +75,17 @@ if (MFEM_USE_MPI)
     COMMENT "Copying navier miniapps data files ...")
   add_custom_target(copy_miniapps_navier_data DEPENDS data_is_copied)
 
-  add_mfem_miniapp(navier_bifurcation
-    MAIN navier_bifurcation.cpp
+#  add_mfem_miniapp(navier_bifurcation
+#    MAIN navier_bifurcation.cpp
+#    ${NAVIER_COMMON_FILES}
+#    LIBRARIES mfem-common)
+#add_dependencies(navier_bifurcation copy_miniapps_navier_data)
+
+  add_mfem_miniapp(cyclone_particle
+    MAIN cyclone_particle.cpp
     ${NAVIER_COMMON_FILES}
     LIBRARIES mfem-common)
-add_dependencies(navier_bifurcation copy_miniapps_navier_data)
+add_dependencies(cyclone_particle copy_miniapps_navier_data)
 
   if (MFEM_USE_GSLIB)
     add_mfem_miniapp(navier_cht

miniapps/fluids/navier/ascii.cpp

@@ -0,0 +1,213 @@
+// Copyright (c) 2010-2021, 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 <fstream>
+#include <iostream>
+
+#include "ascii.hpp"
+#include "mfem.hpp"
+
+
+namespace mfem
+{
+
+//------------------------------------------------------------------------------
+
+bool
+file_exists( const std::string & aPath )
+{
+    // test if file exists
+    std::ifstream tFile( aPath );
+
+    // save result into output variable
+    bool aFileExists;
+
+    if ( tFile )
+    {
+        // close file
+        tFile.close();
+        aFileExists = true;
+    }
+    else
+    {
+        aFileExists = false;
+    }
+
+    return aFileExists;
+}
+
+//------------------------------------------------------------------------------
+
+std::vector<std::string> split_string(
+    const std::string  & aString,
+    const std::string  & aDelim)
+{
+    // create empty cell of strings
+    std::vector<std::string> VectorOfStrings;
+
+    size_t start;
+    size_t end = 0;
+
+    while ((start = aString.find_first_not_of(aDelim, end)) != std::string::npos)
+    {
+        end = aString.find(aDelim, start);
+        VectorOfStrings.push_back(aString.substr(start, end - start));
+    }
+
+    return VectorOfStrings;
+}
+
+//------------------------------------------------------------------------------
+
+Ascii::Ascii( const std::string & aPath, const FileMode & aMode ) :
+    mMode( aMode )
+{
+    // test if path is absolute
+    if ( aPath.substr( 0,1 ) == "/" )
+    {
+        mPath = aPath;
+    }
+    // test if path is relative
+    else if ( aPath.substr( 0,2 ) == "./" )
+    {
+        mPath = aPath;
+    }
+    else
+    {
+        MFEM_ASSERT( false, "");
+        //mPath = std::sprint( "%s/%s", std::getenv( "PWD" ), aPath.c_str() );
+    }
+
+    switch ( aMode )
+    {
+        case ( FileMode::OPEN_RDONLY ) :
+        {
+            this->load_buffer();
+            break;
+        }
+        case ( FileMode::NEW ) :
+        {
+            mBuffer.clear();
+            break;
+        }
+        default:
+        {
+            MFEM_ASSERT( false, "Unknown file mode for ASCII file" );
+        }
+    }
+}
+
+//------------------------------------------------------------------------------
+
+Ascii::~Ascii()
+{
+    MFEM_ASSERT( ! mChangedSinceLastSave, "File  was changed but never saved." );
+
+    mBuffer.clear();
+}
+//------------------------------------------------------------------------------
+
+bool Ascii::save()
+{
+    MFEM_ASSERT( mMode != FileMode::OPEN_RDONLY,
+                 "File can't be saved since it is opened in write protected mode." );
+
+    // open file
+    std::ofstream tFile( mPath.c_str(),  std::ofstream::trunc );
+
+    if ( tFile )
+    {
+        // save buffer to file
+        for ( std::string & tLine : mBuffer )
+        {
+            tFile << tLine << std::endl;
+        }
+
+        tFile.close();
+    }
+    else
+    {
+        MFEM_ASSERT( false,
+                     "Something went wrong while trying to save." );
+    }
+
+    mChangedSinceLastSave = false;
+
+    return mChangedSinceLastSave;
+}
+
+//------------------------------------------------------------------------------
+
+int Ascii::length() const
+{
+    return mBuffer.size();
+}
+
+//------------------------------------------------------------------------------
+
+std::string & Ascii::line( const int aLineNumber )
+{
+    return mBuffer[aLineNumber];
+}
+
+//------------------------------------------------------------------------------
+
+const std::string & Ascii::line( const int aLineNumber ) const
+{
+    return mBuffer[aLineNumber];
+}
+
+//------------------------------------------------------------------------------
+
+void Ascii::print( const std::string & aLine )
+{
+    mBuffer.push_back( aLine );
+
+    mChangedSinceLastSave = true;
+}
+
+//------------------------------------------------------------------------------
+
+void Ascii::load_buffer()
+{
+    // tidy up buffer
+    mBuffer.clear();
+
+    // make sure that file exists
+    MFEM_ASSERT( file_exists( mPath ),
+                 "File does not exist." );
+
+    // open file
+    std::ifstream tFile( mPath );
+
+    // test if file can be opened
+    if ( tFile )
+    {
+        // temporary container for string
+        std::string tLine;
+
+        while ( std::getline( tFile, tLine ) )
+        {
+            mBuffer.push_back( tLine );
+        }
+
+        // close file
+        tFile.close();
+    }
+    else
+    {
+        MFEM_ASSERT( false, "Someting went wrong while opening file\n " );
+    }
+}
+
+//------------------------------------------------------------------------------
+
+}

miniapps/fluids/navier/ascii.hpp

@@ -0,0 +1,147 @@
+// Copyright (c) 2010-2021, 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 PROJECTS_ASCII_HPP_
+#define PROJECTS_ASCII_HPP_
+
+#include <vector>
+#include <iomanip>
+#include <iostream>
+#include <sstream>
+
+
+
+namespace mfem
+{
+//------------------------------------------------------------------------------
+
+enum class FileMode
+{
+    NEW,
+    OPEN_RDONLY,
+    OPEN_RDWR
+};
+
+//------------------------------------------------------------------------------
+
+/**
+ * this function tests if a file exists
+ * @param aPath
+ * @return
+ */
+bool file_exists( const std::string & aPath );
+
+
+std::vector<std::string> split_string(
+    const std::string  & aString,
+    const std::string  & aDelim);
+
+class Ascii
+{
+    //------------------------------------------------------------------------------
+protected:
+    //------------------------------------------------------------------------------
+
+    std::string          mPath;
+    const FileMode       mMode;
+    std::vector< std::string >       mBuffer;
+
+    bool                 mChangedSinceLastSave = false;
+
+    //------------------------------------------------------------------------------
+public:
+    //------------------------------------------------------------------------------
+
+    Ascii(
+        const std::string   & aPath,
+        const enum FileMode & aMode );
+
+    //------------------------------------------------------------------------------
+
+    ~Ascii();
+
+    //------------------------------------------------------------------------------
+
+    // save the buffer to the file
+    bool save();
+
+    //------------------------------------------------------------------------------
+
+    void print( const std::string & aLine );
+
+    //------------------------------------------------------------------------------
+
+    /**
+     * return the number of lines
+     */
+    int length() const;
+
+    //------------------------------------------------------------------------------
+
+    std::string & line( const int aLineNumber );
+
+    //------------------------------------------------------------------------------
+
+    const std::string & line( const int aLineNumber ) const;
+
+    //------------------------------------------------------------------------------
+private:
+    //------------------------------------------------------------------------------
+
+    void load_buffer();
+
+    //------------------------------------------------------------------------------
+};
+
+//------------------------------------------------------------------------------
+
+template<typename T>
+inline std::string stringify(T aValue)
+{
+    std::ostringstream out;
+    out << aValue;
+    return out.str();
+}
+
+template<>
+inline std::string stringify<bool>(bool aValue)
+{
+    std::ostringstream out;
+    out << std::boolalpha << aValue;
+    return out.str();
+}
+
+template<>
+inline std::string stringify<double>(double aValue)
+{
+    std::ostringstream out;
+    out << std::setprecision(14) << std::scientific << aValue;
+    return out.str();
+}
+
+template<>
+inline std::string stringify<long double>(long double aValue)
+{
+    std::ostringstream out;
+    out << std::setprecision(14) << std::scientific << aValue;
+    return out.str();
+}
+
+template<>
+inline std::string stringify<float>(float aValue)
+{
+    std::ostringstream out;
+    out << std::setprecision(14) << std::scientific << aValue;
+    return out.str();
+}
+}
+
+#endif /* PROJECTS_ASCII_HPP_ */

miniapps/fluids/navier/cyclone_particle.cpp

@@ -0,0 +1,470 @@
+// 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.
+//
+//   ---------------------------------------------------------------------
+//   Navier Bifurcation: Tracer Particles in a 2D Bifurcating Channel Flow
+//   ---------------------------------------------------------------------
+//
+// Note: MFEM must be compiled with GSLIB for this miniapp to include
+//       particles - otherwise, it will just compute the fluid flow.
+//
+// This miniapp demonstrates the usage of tracer particles (i.e. one-way
+// coupled) in fluid flow. The fluid flow is computed with NavierSolver and
+// the particles are advected with NavierParticles. Particles are injected
+// periodically at random locations along the inlet boundary. Reflection
+// boundary conditions are used on the channel walls.
+//
+// Sample run:
+// * mpirun -np 10 particles_cyclone -rs 3 -npt 100 -nt 4e5 -traj 10
+
+
+#include "navier_particles.hpp"
+#include "navier_tools.hpp"
+#include "ascii.hpp"
+
+#include "../../common/pfem_extras.hpp"
+#include "../../common/particles_extras.hpp"
+#include "../../../general/text.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+using namespace navier;
+using namespace mfem::common;
+
+struct flow_context
+{
+   // common
+   real_t dt = 2e-4;
+   real_t nt = 10000;
+
+   // fluid
+   int rs_levels = 0;
+   int order = 1;
+   real_t Re = 1000;             // Reynolds number
+   int paraview_freq = 500;      // frequency of ParaView output
+
+   // particle
+   int add_particles_freq = 1; // frequency of particle injection
+   int num_add_particles = 400;  // total particles added each injection
+   real_t kappa_min = 1.0;       // drag property min
+   real_t kappa_max = 10.0;      // drag property max
+   real_t gamma = 5e2;           // gravity property
+   real_t zeta = 0.19;           // lift property
+   int print_csv_freq = 1;     // frequency of particle CSV outputting
+
+   // GLVis visualization for solution and (optionally) particles
+   bool visualization = true;
+   // Particle trajectory visualization [visualization must be set to true]
+   // traj_len_update_freq = 0 means no trajectory visualization.
+   // traj_len_update_freq > 0 means update trajectory every
+   // traj_len_update_freq time steps. This is useful for long simulations
+   // with small time-steps.
+   int traj_len_update_freq = 1;
+} ctx;
+
+#ifdef MFEM_USE_GSLIB
+// Set properties for injected particles. The location is set randomly to be
+// on the inlet boundary (x=0), velocity is initialized to 0, and
+// kappa (drag property) is set randomly in [kappa_min, kappa_max]
+// using kappa_seed.
+void SetInjectedParticles(NavierParticles &particle_solver,
+                          const Array<int> &p_idxs,
+                          real_t kappa_min, real_t kappa_max, int kappa_seed,
+                          real_t zeta, real_t gamma, int step);
+#endif
+
+int main(int argc, char *argv[])
+{
+   // Initialize MPI and HYPRE.
+   Mpi::Init(argc, argv);
+   int rank = Mpi::WorldRank();
+   Hypre::Init();
+
+   // Parse command line arguments
+   OptionsParser args(argc, argv);
+   args.AddOption(&ctx.dt, "-dt", "--time-step", "Time step.");
+   args.AddOption(&ctx.nt, "-nt", "--num-timesteps", "Number of time steps.");
+   args.AddOption(&ctx.rs_levels, "-rs", "--refine-serial",
+                  "Number of times to refine the mesh in serial.");
+   args.AddOption(&ctx.order, "-o", "--order",
+                  "Order (degree) of the finite elements.");
+   args.AddOption(&ctx.Re, "-Re", "--reynolds-number", "Reynolds number.");
+   args.AddOption(&ctx.paraview_freq, "-pv", "--paraview-freq",
+                  "ParaView data collection write frequency. 0 to disable.");
+   args.AddOption(&ctx.visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&ctx.add_particles_freq, "-ipf", "--inject-particles-freq",
+                  "Frequency of particle injection at domain inlet.");
+   args.AddOption(&ctx.num_add_particles, "-npt", "--num-particles-inject",
+                  "Number of particles to add each injection.");
+   args.AddOption(&ctx.kappa_min, "-kmin", "--kappa-min",
+                  "Kappa constant minimum.");
+   args.AddOption(&ctx.kappa_max, "-kmax", "--kappa-max",
+                  "Kappa constant maximum.");
+   args.AddOption(&ctx.gamma, "-g", "--gamma", "Gamma constant.");
+   args.AddOption(&ctx.zeta, "-z", "--zeta", "Zeta constant.");
+   args.AddOption(&ctx.print_csv_freq, "-csv", "--csv-freq",
+                  "Frequency of particle CSV outputting. 0 to disable.");
+   args.AddOption(&ctx.traj_len_update_freq, "-traj", "--traj-freq",
+                  "Frequency of particle trajectory update. 0 to disable.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   if (rank == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // Load mesh + complete any serial refinements
+   Mesh mesh("./good_mesh.e");
+   for (int lev = 0; lev < ctx.rs_levels; lev++)
+   {
+      mesh.UniformRefinement();
+   }
+
+   // Parallel decompose mesh
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   pmesh.EnsureNodes();
+   mesh.Clear();
+
+   real_t time = 0.0;
+
+   std::cout<<"mesh done"<<std::endl;
+
+   // Diffusion Solver -------------------------------------
+   int diffOrder = 1;
+   ConstantCoefficient oneCoeff(1.0);
+   ConstantCoefficient zeroCoeff(0.0);
+   mfem::navier::DiffusionSolver_particle * diffusionSolver = new mfem::navier::DiffusionSolver_particle();
+   diffusionSolver->SetMesh(&pmesh);
+   diffusionSolver->SetOrder(diffOrder);
+   diffusionSolver->SetDiffusionCoefficient(&oneCoeff);
+   diffusionSolver->SetMassCoefficient(&zeroCoeff);
+   Array<int> ess_bdr_filter;
+   if (mesh.bdr_attributes.Size())
+   {
+      ess_bdr_filter.SetSize(mesh.bdr_attributes.Max());
+      ess_bdr_filter = 0;
+   }
+   diffusionSolver->SetEssentialBoundary(ess_bdr_filter);
+   diffusionSolver->SetupFEM();
+   diffusionSolver->AssembleDiffusionBilinear();
+
+   diffusionSolver->SetRHSCoefficient(&oneCoeff);
+   diffusionSolver->Solve();
+   ParGridFunction dist_field = *diffusionSolver->GetParFEMSolution();
+
+   std::cout<<"diffusion solve done"<<std::endl;
+   // Verlocity reader -------------------------------------
+
+   int dim = pmesh.Dimension();
+   H1_FECollection fec(ctx.order, dim);
+   ParFiniteElementSpace pfes_vector(&pmesh, &fec, dim);
+   ParFiniteElementSpace pfes_scalar(&pmesh, &fec, 1);
+
+   ParGridFunction u_gf(&pfes_vector); u_gf = 0.0;
+   ParGridFunction w_gf(&pfes_vector); w_gf = 0.0;
+
+   u_gf.SetTrueVector();
+   mfem::Vector & true_u_gf = u_gf.GetTrueVector();
+
+   if (true)
+   {
+      std::string velReader = "./Cosre_cyclone.txt";
+      mfem::Ascii tAsciiReader( velReader, mfem::FileMode::OPEN_RDONLY );
+
+      int tNumLines = tAsciiReader.length();
+
+      std::vector<std::vector<std::string>> splitString(tNumLines);
+
+      for ( int Ik = 0; Ik < tNumLines; Ik++ )
+      {
+         const std::string & tFileLine = tAsciiReader.line( Ik );
+
+         splitString[Ik] = split_string( tFileLine, " ");
+
+         // mfem::mfem_error("break here!!!!!!!!!!");
+      }
+
+      int numNodes   = true_u_gf.Size() / dim;
+      mfem::Vector locationVector(dim);
+
+      real_t epsilon = 1e-2;
+
+      for ( int Ak = 0; Ak < numNodes; Ak++)
+      {
+        pmesh.GetNode(Ak, &locationVector[0]);
+        //const double * pCoords(locationVector.GetData());
+
+         for ( int Ik = 0; Ik < tNumLines; Ik++ )
+         {
+            if( std::abs(locationVector[0] - std::stod(splitString[Ik][0])) < epsilon &&
+                std::abs(locationVector[1] - std::stod(splitString[Ik][1])) < epsilon &&
+                std::abs(locationVector[2] - std::stod(splitString[Ik][2])) < epsilon )
+            {
+               true_u_gf[ Ak ] = std::stod(splitString[Ik][6]);
+               true_u_gf[ Ak +numNodes ] = std::stod(splitString[Ik][7]);
+               true_u_gf[ Ak +2*numNodes] = std::stod(splitString[Ik][8]);
+               break;
+            }         
+         }
+      }
+      u_gf.SetFromTrueVector();
+   }
+
+   ComputeCurl3D_particle(u_gf, w_gf);
+
+   GradientGridFunctionCoefficient gradcoeff(&dist_field);
+   ParGridFunction gradDistField(&pfes_vector);
+   gradDistField.ProjectCoefficient(gradcoeff);
+
+
+   std::cout<<"read velocity done"<<std::endl;
+
+#ifdef MFEM_USE_GSLIB
+   // Create the particle solver
+   NavierParticles particle_solver(MPI_COMM_WORLD, 0, pmesh);
+   int nparticles = (ctx.nt/ctx.add_particles_freq) *
+                    ctx.num_add_particles / Mpi::WorldSize();
+
+   particle_solver.GetParticles().Reserve(nparticles);
+#endif
+
+   // Set up solution and particle visualization
+   char vishost[] = "localhost";
+   int visport = 19916;
+   socketstream vis_sol;
+   int Ww = 500, Wh = 500; // window size
+   int Wx = 10, Wy = 0; // window position
+   char keys[] = "mAcRjlmm]]]]]]]]]";
+   std::unique_ptr<ParticleTrajectories> traj_vis;
+   // Extract boundary mesh for particle visualization
+   int nattr = pmesh.bdr_attributes.Max();
+   std::cout<<"nattr "<<nattr<<std::endl;
+   Array<int> subdomain_attributes(nattr);
+   for (int i = 0; i < nattr; i++)
+   {
+      subdomain_attributes[i] = i+1;
+   }
+   auto psubmesh = std::unique_ptr<ParMesh>(new ParMesh(
+                                               ParSubMesh::CreateFromBoundary(pmesh, subdomain_attributes)));
+
+   if (ctx.visualization)
+   {
+      VisualizeField(vis_sol, vishost, visport, u_gf, "Velocity",
+                     Wx, Wy, Ww, Wh, keys);
+#ifdef MFEM_USE_GSLIB
+      if (ctx.traj_len_update_freq > 0)
+      {
+         int traj_length = 1; // length of trajectory in number of segments
+         traj_vis = std::make_unique<ParticleTrajectories>(
+                       particle_solver.GetParticles(),
+                       traj_length, vishost, visport,
+                       "Particle Trajectories",
+                       Ww+Wx, Wy, Ww, Wh, "bbm");
+         //traj_vis->AddMeshForVisualization(psubmesh.get());
+         traj_vis->Visualize();
+      }
+#endif
+   }
+
+   // Initialize ParaView DC (if freq != 0)
+   std::unique_ptr<ParaViewDataCollection> pvdc;
+   if (ctx.paraview_freq > 0)
+   {
+      pvdc = std::make_unique<ParaViewDataCollection>("cyclone_particle", &pmesh);
+      pvdc->SetPrefixPath("ParaView_cyclone");
+      pvdc->SetLevelsOfDetail(ctx.order);
+      pvdc->SetDataFormat(VTKFormat::BINARY);
+      pvdc->SetHighOrderOutput(true);
+      pvdc->RegisterField("Velocity",&u_gf);
+      pvdc->RegisterField("Vorticity",&w_gf);
+      pvdc->RegisterField("Distance",&dist_field);
+      pvdc->SetTime(time);
+      pvdc->SetCycle(0);
+      pvdc->Save();
+   }
+
+      std::cout<<"vis output mesh done"<<std::endl;
+#ifdef MFEM_USE_GSLIB
+   std::string csv_prefix = "Cyclone_particles_";
+   // Setup arrays to indicate what to print.
+   // Particle id, rank, and coordinates are included by default. We also
+   // include the first field (i.e. \kappa with index 0 inside the ParticleSet)
+   Array<int> print_field_idxs({0});
+   // Print the first tag for each particle.
+   Array<int> print_tag_idxs({0});
+   if (ctx.print_csv_freq > 0)
+   {
+      std::string file_name = csv_prefix +
+                              mfem::to_padded_string(0, 6) + ".csv";
+      particle_solver.GetParticles().PrintCSV(file_name.c_str(),
+                                              print_field_idxs,
+                                              print_tag_idxs);
+   }
+   particle_solver.Setup(ctx.dt);
+#endif
+
+   int vis_count = 1;
+
+   Array<int> add_particle_idxs;
+   real_t cfl;
+   for (int step = 1; step <= ctx.nt; step++)
+   {
+#ifdef MFEM_USE_GSLIB
+      // Inject particles at inlet and initialize their properties
+      //if (step % ctx.add_particles_freq == 0)
+      if (step == 1)
+      {
+         int size = Mpi::WorldSize();
+         int rank_num_particles = ctx.num_add_particles/size +
+                                  (rank < (ctx.num_add_particles % size) ?
+                                   1 : 0);
+         // Add particles to the ParticleSet
+               std::cout<<"rank_num_particles "<<rank_num_particles<<std::endl;
+         particle_solver.GetParticles().AddParticles(rank_num_particles,
+                                                     &add_particle_idxs);
+         // Initialize properties of the new particles
+         SetInjectedParticles(particle_solver, add_particle_idxs,
+                              ctx.kappa_min, ctx.kappa_max,
+                              (rank+1)*step, ctx.zeta, ctx.gamma, step);
+      }
+      // Step the particles
+      particle_solver.Step(ctx.dt, u_gf, w_gf, dist_field, gradDistField);
+
+      // Output particle data to csv
+      if (ctx.print_csv_freq > 0 && step % ctx.print_csv_freq == 0)
+      {
+         vis_count++;
+         std::string file_name = csv_prefix +
+                                 mfem::to_padded_string(step, 6) + ".csv";
+         particle_solver.GetParticles().PrintCSV(file_name.c_str(),
+                                                 print_field_idxs,
+                                                 print_tag_idxs);
+      }
+#endif
+
+      // Output flow data for ParaView
+      if (ctx.paraview_freq > 0 && step % ctx.paraview_freq == 0)
+      {
+         pvdc->SetTime(vis_count);
+         pvdc->SetCycle(step);
+         pvdc->Save();
+      }
+
+      // GLVis visualization
+      if (ctx.visualization)
+      {
+         VisualizeField(vis_sol, vishost, visport, u_gf,
+                        "Velocity", Wx, Wy, Ww, Wh, keys);
+#ifdef MFEM_USE_GSLIB
+         if (ctx.traj_len_update_freq > 0 &&
+             step % ctx.traj_len_update_freq == 0)
+         {
+            traj_vis->Visualize();
+         }
+#endif
+      }
+
+#ifdef MFEM_USE_GSLIB
+      auto global_np =  particle_solver.GetParticles().GetGlobalNParticles();
+      auto inactive_global_np =
+         particle_solver.GetInactiveParticles().GetGlobalNParticles();
+#endif
+      if (rank == 0)
+      {
+         printf("\n%-11s %-11s %-11s %-11s\n", "Step", "Time", "dt", "CFL");
+         printf("%-11i %-11.5E %-11.5E %-11.5E\n", step, time, ctx.dt, cfl);
+#ifdef MFEM_USE_GSLIB
+         printf("\n%16s: %-9llu\n", "Active Particles", global_np);
+         printf("%16s: %-9llu\n", "Lost Particles", inactive_global_np);
+#endif
+         printf("-----------------------------------------------\n");
+         fflush(stdout);
+      }
+   }
+   return 0;
+}
+
+#ifdef MFEM_USE_GSLIB
+void SetInjectedParticles(NavierParticles &particle_solver,
+                          const Array<int> &p_idxs, real_t kappa_min,
+                          real_t kappa_max, int kappa_seed,
+                          real_t zeta, real_t gamma, int step)
+{
+   // Set initial conditions for new particles.
+   MPI_Comm comm = particle_solver.GetParticles().GetComm();
+   int my_rank;
+   MPI_Comm_rank(comm, &my_rank);
+   Vector rand_init_xloc(p_idxs.Size());
+   Vector rand_init_yloc(p_idxs.Size());
+   Vector rand_init_zloc(p_idxs.Size());
+   rand_init_xloc.Randomize(my_rank + step);
+   rand_init_yloc.Randomize(my_rank + step+999);
+   rand_init_zloc.Randomize(my_rank + step+777);
+   rand_init_xloc *= 0.03;
+   rand_init_xloc -= 0.015;
+   rand_init_yloc *= 0.03;
+   rand_init_yloc -= 0.015;
+   rand_init_zloc *= 0.03;
+   rand_init_zloc -= 0.015;
+   std::cout<< "p_idxs.Size() "<< p_idxs.Size()<<std::endl;
+   for (int i = 0; i < p_idxs.Size(); i++)
+   {
+      int idx = p_idxs[i];
+
+      for (int j = 0; j < 4; j++)
+      {
+         if (j == 0)
+         {
+            // Set position randomly along inlet
+            real_t xval = -0.225 + rand_init_xloc(i);
+            real_t yval =  0.05471 + rand_init_yloc(i);
+            real_t zval = -0.01935 + rand_init_zloc(i);
+            if(i<200)
+            {
+               xval+=0.021;
+            }
+            particle_solver.X().SetValues(idx, Vector({xval, yval, zval}));
+         }
+         else
+         {
+            // Zero-out position history
+            particle_solver.X(j).SetValues(idx, Vector({0.0, 0.0, 0.0}));
+         }
+
+         // Zero-out particle velocities, fluid velocities, and fluid vorticities
+         particle_solver.V(j).SetValues(idx, Vector({17.0, 0.0, 0.0}));
+         particle_solver.U(j).SetValues(idx, Vector({17.0, 0.0, 0.0}));
+         particle_solver.W(j).SetValues(idx, Vector({ 0.0, 0.0, 0.0}));
+
+         // Set Kappa, Zeta, Gamma
+         std::mt19937 gen(kappa_seed);
+         std::uniform_real_distribution<> real_dist(0.0,1.0);
+         particle_solver.Kappa()[idx] = kappa_min + real_dist(gen)*
+                                        (kappa_max - kappa_min);
+         particle_solver.Zeta()[idx] = zeta;
+         particle_solver.Gamma()[idx] = gamma;
+         particle_solver.Status()[idx] = 0.0;
+      }
+
+      // Set order to 0
+      particle_solver.Order()[idx] = 0;
+   }
+}
+#endif
+
+
+
+
+

miniapps/fluids/navier/navier_particles.cpp

@@ -133,6 +133,76 @@ void NavierParticles::ParticleStep2D(const real_t &dt, int p)
    xpn *= 1.0/beta[0];
 }
 
+void NavierParticles::ParticleStep3D(const real_t &dt, int p)
+{
+   Vector w_n_ext(3);  w_n_ext = 0.0;
+
+   int order_idx = Order()[p] - 1;
+   const Array<real_t> &beta = beta_k[order_idx];
+   const Array<real_t> &alpha = alpha_k[order_idx];
+
+   const real_t &kappa = Kappa()[p];
+   const real_t &zeta = Zeta()[p];
+   const real_t &gamma = Gamma()[p];
+
+   // Extrapolate particle vorticity using EXTk (w_n is new vorticity at old
+   // particle loc)
+   // w_n_ext = alpha1*w_nm1 + alpha2*w_nm2 + alpha3*w_nm3
+   for (int j = 1; j <= 3; j++)
+   {
+      w_n_ext(0) += alpha[j-1]*W(j)(p, 0);
+      w_n_ext(1) += alpha[j-1]*W(j)(p, 1);
+      w_n_ext(2) += alpha[j-1]*W(j)(p, 2);
+   }
+
+   // Assemble the 3D matrix B with implicit terms
+   DenseMatrix B({{ beta[0]+dt*kappa  ,  zeta*dt*w_n_ext(2), -zeta*dt*w_n_ext(1)},
+                  {-zeta*dt*w_n_ext(2),  beta[0]+dt*kappa  ,  zeta*dt*w_n_ext(0)},
+                  { zeta*dt*w_n_ext(1), -zeta*dt*w_n_ext(0),  beta[0]+dt*kappa  }});
+
+   // Assemble the RHS with BDF and EXT terms
+   r = 0.0;
+   for (int j = 1; j <= 3; j++)
+   {
+      U(j).GetValuesRef(p, up);
+      V(j).GetValuesRef(p, vp);
+
+      // Add particle velocity component
+      add(r, -beta[j], vp, r);
+
+      // Create C
+      C = up;
+      C *= kappa;
+      add(C, -gamma, Vector({0.0, 0.0, 1.0}), C);
+      add(C, zeta, Vector({ up[1]*w_n_ext[2] - up[2]*w_n_ext[1],
+                            up[2]*w_n_ext[0] - up[0]*w_n_ext[2],
+                            up[0]*w_n_ext[1] - up[1]*w_n_ext[0]}), C);
+
+      // Add C
+      add(r, dt*alpha[j-1], C, r);
+   }
+
+   // Solve for particle velocity
+   DenseMatrixInverse B_inv(B);
+   V(0).GetValuesRef(p, vp);
+   B_inv.Mult(r, vp);
+
+   // Compute updated particle position
+   X(0).GetValuesRef(p, xpn);
+   xpn = 0.0;
+   for (int j = 1; j <= 3; j++)
+   {
+      X(j).GetValuesRef(p, xp);
+      add(xpn, -beta[j], xp, xpn);
+   }
+   V(0).GetValuesRef(p, vp);
+   add(xpn, dt, vp, xpn);
+   xpn *= 1.0/beta[0];
+
+   //vp.Print();
+   //xpn.Print();
+}
+
 void NavierParticles::Get2DNormal(const Vector &p1, const Vector &p2,
                                   bool inv_normal, Vector &normal)
 {
@@ -312,7 +382,79 @@ void NavierParticles::ApplyBCs()
             Apply2DRecirculationBC(bc);
          }
       },bc_v);
+   }
+}
 
+void NavierParticles::ApplyBCs3D(const ParGridFunction &T_gf, const ParGridFunction &Tgrad_gf)
+{
+   finder.FindPoints(X());
+   finder.Interpolate(T_gf, T(), T().GetOrdering());
+   finder.Interpolate(Tgrad_gf, nablaT(), nablaT().GetOrdering());
+
+   for (int i = 0; i < fluid_particles.GetNParticles(); i++)
+   {
+      const real_t &distance = T()[i];
+      nablaT().GetValuesRef(i, surfNormal);
+      mfem::Vector SurNorm(3); SurNorm= surfNormal;
+      SurNorm /= SurNorm.Norml2();
+      V(0).GetValuesRef(i, vp);
+      Vector p_xn(3);
+      X().GetValuesRef(i, p_xn);
+      Array<int> inactive_idxs(1);
+
+      if(p_xn[2] <= -0.38)
+      {
+         Status()[i] = 1.0;
+
+         inactive_idxs[0] = i;
+         fluid_particles.RemoveParticles(inactive_idxs);
+      }
+
+      if(p_xn[2] >= 0.041)
+      {
+         Status()[i] = 2.0;
+
+         inactive_idxs[0] = i;
+         fluid_particles.RemoveParticles(inactive_idxs);
+      }
+
+      if(distance <= 3e-5)
+      {
+         //get normal of surface
+         Vector normal({ vp[1]*SurNorm[2] - vp[2]*SurNorm[1],
+                         vp[2]*SurNorm[0] - vp[0]*SurNorm[2],
+                         vp[0]*SurNorm[1] - vp[1]*SurNorm[0]});
+
+         normal /= normal.Norml2();
+
+         Vector tangential({ normal[1]*SurNorm[2] - normal[2]*SurNorm[1],
+                             normal[2]*SurNorm[0] - normal[0]*SurNorm[2],
+                             normal[0]*SurNorm[1] - normal[1]*SurNorm[0]});
+
+         tangential /= tangential.Norml2();
+
+         DenseMatrix B({{ SurNorm[0], tangential[0], normal[0]},
+                        { SurNorm[1], tangential[1], normal[1]},
+                        { SurNorm[2], tangential[2], normal[2]}});
+
+         Vector vpCoordWall(3);
+         Vector vpPostWall(3);
+
+         DenseMatrixInverse B_inv(B);
+         B_inv.Mult(vp, vpCoordWall);
+
+         vpPostWall = vpCoordWall;
+         vpPostWall[0] = -vpCoordWall[0];
+
+         //vpCoordWall.Print();
+         //vpPostWall.Print();
+
+         B.Mult(vpPostWall, vp);
+         //vp.Print();
+
+         // Set order to 0, to avoid re-computing x history as well
+         Order()[i] = 0;
+      }
    }
 }
 
@@ -321,7 +463,6 @@ NavierParticles::NavierParticles(MPI_Comm comm, int num_particles, Mesh &m)
      inactive_fluid_particles(comm, 0, m.SpaceDimension()),
      finder(comm)
 {
-
    for (int o = 0; o < 3; o++)
    {
       beta_k[o].SetSize(4);
@@ -338,6 +479,9 @@ NavierParticles::NavierParticles(MPI_Comm comm, int num_particles, Mesh &m)
    fp_idx.field.kappa = fluid_particles.AddField(1, Ordering::byVDIM, "kappa");
    fp_idx.field.zeta = fluid_particles.AddField(1, Ordering::byVDIM, "zeta");
    fp_idx.field.gamma = fluid_particles.AddNamedField(1, "gamma");
+   fp_idx.field.dist = fluid_particles.AddNamedField(1, "dist");
+   fp_idx.field.grad_dist = fluid_particles.AddNamedField(dim, "nabla_dist");
+   fp_idx.field.status = fluid_particles.AddNamedField(1, "status");
 
    inactive_fluid_particles.AddField(1);
    inactive_fluid_particles.AddField(1);
@@ -367,7 +511,7 @@ NavierParticles::NavierParticles(MPI_Comm comm, int num_particles, Mesh &m)
 }
 
 void NavierParticles::Step(const real_t dt, const ParGridFunction &u_gf,
-                           const ParGridFunction &w_gf)
+                           const ParGridFunction &w_gf, const ParGridFunction &T_gf, const ParGridFunction &gradT_gf)
 {
    // Shift fluid velocity, fluid vorticity, particle velocity, and particle position
    for (int i = N_HIST-1; i > 0; i--)
@@ -384,6 +528,8 @@ void NavierParticles::Step(const real_t dt, const ParGridFunction &u_gf,
 
    SetTimeIntegrationCoefficients();
 
+   bool reflect = false;       //FIXME
+
    if (fluid_particles.GetDim() == 2)
    {
       for (int i = 0; i < fluid_particles.GetNParticles(); i++)
@@ -399,11 +545,87 @@ void NavierParticles::Step(const real_t dt, const ParGridFunction &u_gf,
    }
    else
    {
-      MFEM_ABORT("3D particles not yet implemented.");
+      for (int i = 0; i < fluid_particles.GetNParticles(); i++)
+      {
+         // Increment particle order
+         int &order = Order()[i];
+         if (order < 3)
+         {
+            order++;
+         }
+         ParticleStep3D(dt, i);
+      }
+
+      double scaling = 1.0;
+      int counter = 0;
+
+
+      while(true)
+      {
+         finder.FindPoints(X());
+         const Array<unsigned int> lost_idxs = finder.GetPointsNotFoundIndices();
+
+         if( lost_idxs.Size() == 0 || counter == 5)
+         {
+            if(counter == 5)
+            {
+              std::cout<<"LINE SEARCH NOT CONVERGED"<<std::endl;
+            }
+            break;
+         }
+         
+         for (int j = 0; j < lost_idxs.Size(); j++)
+         {
+            unsigned int index = lost_idxs[j];
+
+            Vector p_xn(3), p_xnm1(3),p_xdiff(3) ;
+            X().GetValuesRef(index, p_xn);
+            X(1).GetValuesRef(index, p_xnm1);
+
+            p_xdiff = p_xn;
+            p_xdiff -= p_xnm1;
+
+            p_xdiff /=2.0;
+
+            p_xn = p_xnm1;
+            p_xn += p_xdiff;
+         }
+
+         // Set order to 0 (so that it becomes 1 on next iteration)
+         //Order()[index] = 0;
+
+
+         // for (int j = 0; j < lost_idxs.Size(); j++)
+         // {
+         //    unsigned int index = lost_idxs[j];
+
+         //    //Order()[index] = 0;
+
+         //    Vector p_xn(3), p_xnm1(3) ;
+         //    X().GetValuesRef(index, p_xn);
+         //    X(1).GetValuesRef(index, p_xnm1);
+         //    // p_xn.Print();
+         //    p_xnm1.Print();
+         //    p_xn = p_xnm1;
+
+         //    ParticleStep3D(dt / scaling, index);
+
+         //    finder.FindPoints(X());
+         //    finder.Interpolate(T_gf, T(), T().GetOrdering());
+         //    const real_t &distance = T()[index];
+
+         //    std::cout<<"distance: "<<distance <<std::endl;
+
+         // }
+
+         counter++;
+      }
    }
 
    // Apply any BCs
-   ApplyBCs();
+   ApplyBCs3D(T_gf, gradT_gf);
+
+   //ApplyBCs();
 
    // Re-interpolate fluid velocity + vorticity onto particles' new location
    InterpolateUW(u_gf, w_gf);

miniapps/fluids/navier/navier_particles.hpp

@@ -77,7 +77,7 @@ protected:
    {
       struct FieldIndices
       {
-         int kappa, zeta, gamma;
+         int kappa, zeta, gamma, dist, grad_dist, status;
          int u[N_HIST];
          int v[N_HIST];
          int w[N_HIST];
@@ -121,6 +121,9 @@ protected:
    /// 2D particle step for particle at index \p p
    void ParticleStep2D(const real_t &dt, int p);
 
+   /// 3D particle step for particle at index \p p
+   void ParticleStep3D(const real_t &dt, int p);
+
    /** @brief Given two 2D points, get the unit normal to the line
     *  connecting them.
     *
@@ -166,6 +169,8 @@ protected:
    /// Apply all BCs in \ref bcs
    void ApplyBCs();
 
+   void ApplyBCs3D(const ParGridFunction &T_gf, const ParGridFunction &Tgrad_gf);
+
    /** @brief Move any particles that have left the domain to the
     *  inactive ParticleSet.
     *
@@ -179,7 +184,7 @@ protected:
    void DeactivateLostParticles(bool findpts);
 
    // Temporary vectors for particle computation
-   mutable Vector up, vp, xpn, xp;
+   mutable Vector up, vp, xpn, xp, surfNormal;
    mutable Vector r, C;
 
 public:
@@ -197,7 +202,7 @@ public:
     *  @param[in] w_gf     Fluid vorticity on fluid mesh.
     */
    void Step(const real_t dt, const ParGridFunction &u_gf,
-             const ParGridFunction &w_gf);
+             const ParGridFunction &w_gf, const ParGridFunction &T_gf, const ParGridFunction &gradT_gf);
 
    /** @brief Interpolate fluid velocity and vorticity onto current particles'
     *  location.
@@ -213,6 +218,11 @@ public:
    /// Get reference to the inactive ParticleSet.
    ParticleSet& GetInactiveParticles() { return inactive_fluid_particles; }
 
+   ParticleVector& Status()
+   {
+      return fluid_particles.Field(fp_idx.field.status);
+   }
+
    /// Get reference to the κ ParticleVector.
    ParticleVector& Kappa()
    {
@@ -231,6 +241,16 @@ public:
       return fluid_particles.Field(fp_idx.field.gamma);
    }
 
+   ParticleVector& T()
+   {
+      return fluid_particles.Field(fp_idx.field.dist);
+   }
+
+   ParticleVector& nablaT()
+   {
+      return fluid_particles.Field(fp_idx.field.grad_dist);
+   }
+
    /** @brief Get reference to the fluid velocity-interpolated ParticleVector at
     *  time n - \p nm .
     */

miniapps/fluids/navier/navier_tools.cpp

@@ -0,0 +1,335 @@
+// 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 "navier_tools.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+using namespace std;
+
+namespace mfem
+{
+namespace navier
+{
+
+      void ComputeCurl3D_particle(ParGridFunction &u, ParGridFunction &cu)
+{
+   FiniteElementSpace *fes = u.FESpace();
+
+   // AccumulateAndCountZones.
+   Array<int> zones_per_vdof;
+   zones_per_vdof.SetSize(fes->GetVSize());
+   zones_per_vdof = 0;
+
+   cu = 0.0;
+
+   // Local interpolation.
+   int elndofs;
+   Array<int> vdofs;
+   Vector vals;
+   Vector loc_data;
+   int vdim = fes->GetVDim();
+   DenseMatrix grad_hat;
+   DenseMatrix dshape;
+   DenseMatrix grad;
+   Vector curl;
+
+   for (int e = 0; e < fes->GetNE(); ++e)
+   {
+      fes->GetElementVDofs(e, vdofs);
+      u.GetSubVector(vdofs, loc_data);
+      vals.SetSize(vdofs.Size());
+      ElementTransformation *tr = fes->GetElementTransformation(e);
+      const FiniteElement *el = fes->GetFE(e);
+      elndofs = el->GetDof();
+      int dim = el->GetDim();
+      dshape.SetSize(elndofs, dim);
+
+      for (int dof = 0; dof < elndofs; ++dof)
+      {
+         // Project.
+         const IntegrationPoint &ip = el->GetNodes().IntPoint(dof);
+         tr->SetIntPoint(&ip);
+
+         // Eval and GetVectorGradientHat.
+         el->CalcDShape(tr->GetIntPoint(), dshape);
+         grad_hat.SetSize(vdim, dim);
+         DenseMatrix loc_data_mat(loc_data.GetData(), elndofs, vdim);
+         MultAtB(loc_data_mat, dshape, grad_hat);
+
+         const DenseMatrix &Jinv = tr->InverseJacobian();
+         grad.SetSize(grad_hat.Height(), Jinv.Width());
+         Mult(grad_hat, Jinv, grad);
+
+         curl.SetSize(3);
+         curl(0) = grad(2, 1) - grad(1, 2);
+         curl(1) = grad(0, 2) - grad(2, 0);
+         curl(2) = grad(1, 0) - grad(0, 1);
+
+         for (int j = 0; j < curl.Size(); ++j)
+         {
+            vals(elndofs * j + dof) = curl(j);
+         }
+      }
+
+      // Accumulate values in all dofs, count the zones.
+      for (int j = 0; j < vdofs.Size(); j++)
+      {
+         int ldof = vdofs[j];
+         cu(ldof) += vals[j];
+         zones_per_vdof[ldof]++;
+      }
+   }
+
+   // Communication
+
+   // Count the zones globally.
+   GroupCommunicator &gcomm = u.ParFESpace()->GroupComm();
+   gcomm.Reduce<int>(zones_per_vdof, GroupCommunicator::Sum);
+   gcomm.Bcast(zones_per_vdof);
+
+   // Accumulate for all vdofs.
+   gcomm.Reduce<real_t>(cu.GetData(), GroupCommunicator::Sum);
+   gcomm.Bcast<real_t>(cu.GetData());
+
+   // Compute means.
+   for (int i = 0; i < cu.Size(); i++)
+   {
+      const int nz = zones_per_vdof[i];
+      if (nz)
+      {
+         cu(i) /= nz;
+      }
+   }
+}
+
+DiffusionSolver_particle::DiffusionSolver_particle(Mesh * mesh_, int order_,
+                                 Coefficient * diffcf_, Coefficient * rhscf_)
+   : mesh(mesh_), order(order_), diffcf(diffcf_), rhscf(rhscf_)
+{
+
+#ifdef MFEM_USE_MPI
+   pmesh = dynamic_cast<ParMesh *>(mesh);
+   if (pmesh) { parallel = true; }
+#endif
+
+   SetupFEM();
+}
+
+void DiffusionSolver_particle::SetupFEM()
+{
+   dim = mesh->Dimension();
+   fec = new H1_FECollection(order, dim);
+
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      pfes = new ParFiniteElementSpace(pmesh, fec);
+      u = new ParGridFunction(pfes);
+      b = new ParLinearForm(pfes);
+   }
+   else
+   {
+      fes = new FiniteElementSpace(mesh, fec);
+      u = new GridFunction(fes);
+      b = new LinearForm(fes);
+   }
+#else
+   fes = new FiniteElementSpace(mesh, fec);
+   u = new GridFunction(fes);
+   b = new LinearForm(fes);
+#endif
+   *u=0.0;
+
+   if (!ess_bdr.Size())
+   {
+      if (mesh->bdr_attributes.Size())
+      {
+         ess_bdr.SetSize(mesh->bdr_attributes.Max());
+         ess_bdr = 1;
+      }
+   }
+}
+
+void DiffusionSolver_particle::UpdateEssentialTDofs()
+{
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      pfes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
+   }
+   else
+   {
+      fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
+   }
+#else
+   fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
+#endif
+}
+
+void DiffusionSolver_particle::AssembleDiffusionBilinear(bool update_ess_tdofs)
+{
+   if (update_ess_tdofs)
+   {
+      UpdateEssentialTDofs();
+   }
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      a = new ParBilinearForm(pfes);
+   }
+   else
+   {
+      a = new BilinearForm(fes);
+   }
+#else
+   a = new BilinearForm(fes);
+#endif
+   a->AddDomainIntegrator(new DiffusionIntegrator(*diffcf));
+   if (masscf)
+   {
+      a->AddDomainIntegrator(new MassIntegrator(*masscf));
+   }
+   a->Assemble();
+   a->FormSystemMatrix(ess_tdof_list, A);
+}
+
+void DiffusionSolver_particle::Solve()
+{
+   Vector B, X;
+
+   if (b)
+   {
+      delete b;
+#ifdef MFEM_USE_MPI
+      if (parallel)
+      {
+         b = new ParLinearForm(pfes);
+      }
+      else
+      {
+         b = new LinearForm(fes);
+      }
+#else
+      b = new LinearForm(fes);
+#endif
+   }
+   if (rhscf)
+   {
+      b->AddDomainIntegrator(new DomainLFIntegrator(*rhscf));
+   }
+   if (neumann_cf)
+   {
+      MFEM_VERIFY(neumann_bdr.Size(), "neumann_bdr attributes not provided");
+      b->AddBoundaryIntegrator(new BoundaryLFIntegrator(*neumann_cf),neumann_bdr);
+   }
+   else if (gradient_cf)
+   {
+      MFEM_VERIFY(neumann_bdr.Size(), "neumann_bdr attributes not provided");
+      b->AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(*gradient_cf),
+                               neumann_bdr);
+   }
+
+   b->Assemble();
+
+   *u=0.0;
+   if (essbdr_cf)
+   {
+      u->ProjectBdrCoefficient(*essbdr_cf,ess_bdr);
+   }
+
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      X.SetSize(pfes->TrueVSize());
+      B.SetSize(pfes->TrueVSize());
+      dynamic_cast<ParGridFunction*>(u)->ParallelAssemble(X);
+      dynamic_cast<ParLinearForm*>(b)->ParallelAssemble(B);
+      dynamic_cast<ParBilinearForm*>(a)->ParallelEliminateTDofsInRHS(
+         ess_tdof_list, X, B);
+   }
+   else
+   {
+      X.NewDataAndSize(u->GetData(), u->Size());
+      B.NewDataAndSize(b->GetData(), b->Size());
+      a->EliminateVDofsInRHS(ess_tdof_list, X, B);
+   }
+#else
+   X.NewDataAndSize(u->GetData(), u->Size());
+   B.NewDataAndSize(b->GetData(), b->Size());
+   a->EliminateVDofsInRHS(ess_tdof_list, X, B);
+#endif
+
+   CGSolver * cg = nullptr;
+   Solver * M = nullptr;
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      M = new HypreBoomerAMG;
+      dynamic_cast<HypreBoomerAMG*>(M)->SetPrintLevel(0);
+      cg = new CGSolver(pmesh->GetComm());
+   }
+   else
+   {
+      M = new GSSmoother((SparseMatrix&)(*A));
+      cg = new CGSolver;
+   }
+#else
+   M = new GSSmoother((SparseMatrix&)(*A));
+   cg = new CGSolver;
+#endif
+   cg->SetRelTol(1e-12);
+   cg->SetMaxIter(10000);
+   cg->SetPrintLevel(0);
+   cg->SetPreconditioner(*M);
+   cg->SetOperator(*A);
+   cg->Mult(B, X);
+   delete M;
+   delete cg;
+   a->RecoverFEMSolution(X, *b, *u);
+}
+
+GridFunction * DiffusionSolver_particle::GetFEMSolution()
+{
+   return u;
+}
+
+#ifdef MFEM_USE_MPI
+ParGridFunction * DiffusionSolver_particle::GetParFEMSolution()
+{
+   if (parallel)
+   {
+      return dynamic_cast<ParGridFunction*>(u);
+   }
+   else
+   {
+      MFEM_ABORT("Wrong code path. Call GetFEMSolution");
+      return nullptr;
+   }
+}
+#endif
+
+DiffusionSolver_particle::~DiffusionSolver_particle()
+{
+   delete u; u = nullptr;
+   delete fes; fes = nullptr;
+#ifdef MFEM_USE_MPI
+   delete pfes; pfes=nullptr;
+#endif
+   delete fec; fec = nullptr;
+   delete b;
+   A.Clear();
+   delete a;
+}
+
+} // namespace navier
+} // namespace mfem
+#endif // MFEM_USE_GSLIB

miniapps/fluids/navier/navier_tools.hpp

@@ -0,0 +1,122 @@
+// 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_NAVIER_TOOLS_HPP
+#define MFEM_NAVIER_TOOLS_HPP
+
+#include "mfem.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+#include <vector>
+#include <type_traits>
+
+namespace mfem
+{
+namespace navier
+{
+   void ComputeCurl3D_particle(ParGridFunction &u, ParGridFunction &cu);
+
+   /**
+ * @brief Class for solving Poisson's equation:
+ *
+ *       - ∇ ⋅(κ ∇ u) = f  in Ω
+ *
+ */
+class DiffusionSolver_particle
+{
+private:
+   Mesh * mesh = nullptr;
+   int order = 1;
+   // diffusion coefficient
+   Coefficient * diffcf = nullptr;
+   // mass coefficient
+   Coefficient * masscf = nullptr;
+   Coefficient * rhscf = nullptr;
+   Coefficient * essbdr_cf = nullptr;
+   Coefficient * neumann_cf = nullptr;
+   VectorCoefficient * gradient_cf = nullptr;
+
+   // FEM solver
+   int dim;
+   FiniteElementCollection * fec = nullptr;
+   FiniteElementSpace * fes = nullptr;
+   Array<int> ess_bdr;
+   Array<int> ess_tdof_list;
+   Array<int> neumann_bdr;
+   GridFunction * u = nullptr;
+   LinearForm * b = nullptr;
+   BilinearForm * a = nullptr;
+   OperatorPtr A;
+   bool parallel;
+#ifdef MFEM_USE_MPI
+   ParMesh * pmesh = nullptr;
+   ParFiniteElementSpace * pfes = nullptr;
+#endif
+
+public:
+   DiffusionSolver_particle() { }
+   DiffusionSolver_particle(Mesh * mesh_, int order_, Coefficient * diffcf_,
+                   Coefficient * cf_);
+
+   void SetMesh(Mesh * mesh_)
+   {
+      mesh = mesh_;
+      parallel = false;
+#ifdef MFEM_USE_MPI
+      pmesh = dynamic_cast<ParMesh *>(mesh);
+      if (pmesh) { parallel = true; }
+#endif
+   }
+   void SetOrder(int order_) { order = order_ ; }
+   void SetDiffusionCoefficient(Coefficient * diffcf_) { diffcf = diffcf_; }
+   void SetMassCoefficient(Coefficient * masscf_) { masscf = masscf_; }
+   void SetRHSCoefficient(Coefficient * rhscf_) { rhscf = rhscf_; }
+   void SetEssentialBoundary(const Array<int> & ess_bdr_) { ess_bdr = ess_bdr_;};
+   void SetNeumannBoundary(const Array<int> & neumann_bdr_) { neumann_bdr = neumann_bdr_;};
+   void SetNeumannData(Coefficient * neumann_cf_) {neumann_cf = neumann_cf_;}
+   void SetEssBdrData(Coefficient * essbdr_cf_) {essbdr_cf = essbdr_cf_;}
+   void SetGradientData(VectorCoefficient * gradient_cf_) {gradient_cf = gradient_cf_;}
+
+   void ResetFEM();
+   void SetupFEM();
+
+   void UpdateEssentialTDofs();
+   void AssembleDiffusionBilinear(bool update_ess_tdofs=true);
+   void Solve();
+   GridFunction * GetFEMSolution();
+   LinearForm * GetLinearForm() {return b;}
+#ifdef MFEM_USE_MPI
+   ParGridFunction * GetParFEMSolution();
+   ParLinearForm * GetParLinearForm()
+   {
+      if (parallel)
+      {
+         return dynamic_cast<ParLinearForm *>(b);
+      }
+      else
+      {
+         MFEM_ABORT("Wrong code path. Call GetLinearForm");
+         return nullptr;
+      }
+   }
+#endif
+
+   ~DiffusionSolver_particle();
+};
+
+} // namespace navier
+
+} // namespace mfem
+
+#endif // MFEM_USE_GSLIB
+
+#endif // MFEM_NAVIER_PARTICLES_HPP

miniapps/hdiv-linear-solver/change_basis.cpp

@@ -22,7 +22,7 @@ void ComputeInverse(const Array<real_t> &A, Array<real_t> &Ainv)
 {
    Array<real_t> A2 = A;
    const int n2 = A.Size();
-   const int n = static_cast<const int>(sqrt(n2));
+   const int n = static_cast<int>(sqrt(n2));
    Array<int> ipiv(n);
    LUFactors lu(A2.GetData(), ipiv.GetData());
    lu.Factor(n);
@@ -58,7 +58,7 @@ void SubcellIntegrals(int n, const Poly_1D::Basis &basis, Array<real_t> &B)
 
 void Transpose(const Array<real_t> &B, Array<real_t> &Bt)
 {
-   const int n = static_cast<const int>(sqrt(B.Size()));
+   const int n = static_cast<int>(sqrt(B.Size()));
    Bt.SetSize(n*n);
    for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) { Bt[i+j*n] = B[j+i*n]; }
 }