Silenced tee.

Range and curl dimension in physical space

CHANGELOG

@@ -17,6 +17,9 @@ 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/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/ex1p.cpp

@@ -66,6 +66,26 @@
 using namespace std;
 using namespace mfem;
 
+class VisServer
+{
+   const char *path{};
+   int port{-1};
+
+   struct Deleter { void operator()(FILE *); };
+   std::unique_ptr<FILE, Deleter> fglvis;
+
+   void Open();
+public:
+   VisServer(const char *path_, int port_ = 19916)
+      : path(path_), port(port_) { Open(); }
+
+   explicit VisServer() = default;
+
+   inline const char *GetPath() const { return path; }
+   inline int GetPort() const { return port; }
+   inline bool IsOpen() const { return (fglvis != nullptr); }
+};
+
 int main(int argc, char *argv[])
 {
    // 1. Initialize MPI and HYPRE.
@@ -82,6 +102,7 @@ int main(int argc, char *argv[])
    bool fa = false;
    const char *device_config = "cpu";
    bool visualization = true;
+   const char *visserver = "";
    bool algebraic_ceed = false;
 
    OptionsParser args(argc, argv);
@@ -106,6 +127,8 @@ int main(int argc, char *argv[])
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
+   args.AddOption(&visserver, "-vs", "--visualization-server",
+                  "Path to GLVis binary to start own server.");
    args.Parse();
    if (!args.Good())
    {
@@ -301,6 +324,14 @@ int main(int argc, char *argv[])
    {
       char vishost[] = "localhost";
       int  visport   = 19916;
+
+      VisServer server;
+      if (strlen(visserver) > 0)
+      {
+         server = VisServer(visserver, visport);
+         visport = server.GetPort();
+      }
+
       socketstream sol_sock(vishost, visport);
       sol_sock << "parallel " << num_procs << " " << myid << "\n";
       sol_sock.precision(8);
@@ -315,3 +346,66 @@ int main(int argc, char *argv[])
 
    return 0;
 }
+
+void VisServer::Open()
+{
+   if (!path || strlen(path) <= 0) { return; }
+
+#ifdef MFEM_USE_MPI
+   if (Mpi::Root())
+#endif // MFEM_USE_MPI
+   {
+      // Open a log file
+      FILE *ftmp = popen("mktemp --tmpdir glvis-log.XXXXXX", "r");
+      constexpr size_t ssize = 256;
+      char stmp[ssize];
+      fgets(stmp, ssize, ftmp);
+      pclose(ftmp);
+      int len = strlen(stmp);
+      if (len > 0 && stmp[len-1] == '\n') { stmp[--len] = '\0'; }
+      std::cout << "Starting GLVis log in: " << stmp << std::endl;
+
+      // Start the server
+      std::stringstream ss;
+      ss << "trap '' SIGPIPE && " << path <<
+         " -no-pr -no-ex 2>&1 | tee \"" << stmp <<
+         "\" 2> /dev/null | grep -m 1 ^GLVIS_SERVER_PORT";
+      fglvis.reset(popen(ss.str().c_str(), "r"));
+
+      // Capture the port number
+      char line[ssize];
+      bool captured = false;
+      while (fgets(line, ssize, fglvis.get()))
+      {
+         if (strncmp(line, "GLVIS_SERVER_PORT=", 18) == 0)
+         {
+            sscanf(line, "GLVIS_SERVER_PORT=%d", &port);
+            captured = true;
+            break;
+         }
+      }
+      if (captured)
+      {
+         std::cout << "Started GLVis server at port: " << port << std::endl;
+      }
+      else
+      {
+         std::cerr << "GLVis server did not start normally." << std::endl;
+      }
+   }
+#ifdef MFEM_USE_MPI
+   MPI_Bcast(&port, 1, MPI_INT, 0, MPI_COMM_WORLD);
+#endif // MFEM_USE_MPI
+}
+
+void VisServer::Deleter::operator()(FILE *f)
+{
+   if (f != nullptr)
+   {
+      int ierr = pclose(f);
+      if (ierr != 0)
+      {
+         std::cerr << "GLVis server pclose() returns: " << ierr << std::endl;
+      }
+   }
+}

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/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/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). */
+   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).
+   */
+   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 { 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 { return 2; }
+   int GetPhysCurlDim(int space_dim) const { 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 { return 3; }
+   int GetPhysCurlDim(int space_dim) const { 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 { return 2; }
+   int GetPhysCurlDim(int space_dim) const { 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 { return 3; }
+   int GetPhysCurlDim(int space_dim) const { 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)];
             }
          }
 

fem/fespace.hpp

@@ -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)

fem/gridfunc.cpp

@@ -30,6 +30,7 @@
 #include <cmath>
 #include <iostream>
 #include <algorithm>
+#include <queue>
 
 namespace mfem
 {
@@ -5117,6 +5118,103 @@ 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 +5295,467 @@ 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

@@ -564,6 +564,70 @@ 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(). */
@@ -1662,21 +1726,21 @@ 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 +1751,18 @@ 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 +1770,45 @@ 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.

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/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

@@ -1568,6 +1568,39 @@ 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

@@ -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/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;

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/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)

linalg/CMakeLists.txt

@@ -55,7 +55,6 @@ list(APPEND HDRS
   dinvariants.hpp
   dtensor.hpp
   dual.hpp
-  eigensolver.hpp
   filteredsolver.hpp
   handle.hpp
   invariants.hpp

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/eigensolver.hpp

@@ -1,203 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-/**
- * @file eigensolver.hpp
- *
- * @brief This file contains a common interface for all eigensolver classes
- */
-
-#ifndef MFEM_EIGENSOLVER
-#define MFEM_EIGENSOLVER
-
-#ifdef MFEM_HYPRE
-#include "hypre.hpp"
-#endif
-
-#ifdef MFEM_SLEPC
-#include "slepc.hpp"
-#endif
-
-namespace mfem
-{
-
-enum class EigenSolverType
-{
-   HYPRE,
-   SLEPC,
-   INVALID_TYPE
-};
-
-/// Provides base class for MFEM Eigensolvers
-class EigenSolverBase
-{
-public:
-   EigenSolverBase() {}
-
-   /// Destructor
-   virtual ~EigenSolverBase() = default;
-
-   /// Solves the eigenvalue problem
-   virtual void Solve() = 0;
-
-   /// Set the required number of modes
-   virtual void SetNumModes(int num_Modes)
-   {
-      numModes=num_Modes;
-   }
-
-   /// @brief  Set the operator to the eigenvalue problem
-   /// @param A - operator
-   virtual void SetOperator(Operator& A) = 0;
-
-   /// @brief Sets operators for the generalized eigenvalue problem
-   /// @param A - operator
-   /// @param M - mass matrix
-   virtual void SetOperator(Operator& A, Operator& M)
-   {
-      MFEM_ABORT("Generalized eigensolver is not supported!");
-   }
-
-   /// Optional method - sets preconditioner for the
-   /// eigenvalue solver.
-   virtual void SetPreconditioner(Solver& precond)
-   {
-      MFEM_ABORT("Preconditioner is not supported!");
-   }
-
-   /// Returns the converged eigenvalues
-   virtual void GetEigenvalues(Array<real_t>& eigen_vals) = 0;
-
-   /// Returns the vec_index eigenvector.
-   virtual void GetEigenvector(int vec_index, Vector& vector) = 0;
-
-   /// Returns the eigensolver type.
-   EigenSolverType GetSolverType() { return eigSolverType; }
-
-protected:
-   int numModes = 0;
-   EigenSolverType eigSolverType = EigenSolverType::INVALID_TYPE;
-};
-
-#ifdef MFEM_HYPRE
-class EigenSolverHypreLOBPCG : public EigenSolverBase
-{
-public:
-   EigenSolverHypreLOBPCG(MPI_Comm comm)
-   {
-      eigenSolver = std::make_unique<HypreLOBPCG>(comm);
-      eigSolverType = EigenSolverType::HYPRE;
-   }
-
-   ~EigenSolverHypreLOBPCG() {}
-
-   void Solve() override { eigenSolver->Solve(); }
-   void SetNumModes(int num_Modes) override
-   {
-      eigenSolver->SetNumModes(num_Modes);
-      numModes = num_Modes;
-   }
-
-   void SetOperator(Operator& A) override { eigenSolver->SetOperator(A); }
-
-   void SetOperator(Operator& A, Operator& M) override
-   {
-      eigenSolver->SetOperator(A);
-      eigenSolver->SetMassMatrix(M);
-   }
-
-   void SetPreconditioner(Solver& precond) override { eigenSolver->SetPreconditioner(precond); }
-   void GetEigenvalues(Array<real_t>& eigen_vals) override { eigenSolver->GetEigenvalues(eigen_vals); }
-   void GetEigenvector(int vec_index, Vector& vector) override
-   {
-      const HypreParVector& eigenvec = eigenSolver->GetEigenvector(vec_index);
-      vector = eigenvec;
-   }
-
-   void SetTol(real_t tol) { eigenSolver->SetTol(tol); }
-   void SetRelTol(real_t rel_tol) { eigenSolver->SetRelTol(rel_tol); }
-   void SetMaxIter(int max_iter) { eigenSolver->SetMaxIter(max_iter); }
-   void SetPrintLevel(int logging) { eigenSolver->SetPrintLevel(logging); }
-   void SetRandomSeed(int seed) { eigenSolver->SetRandomSeed(seed); }
-   void SetPrecondUsageMode(int usage_mode) { eigenSolver->SetPrecondUsageMode(usage_mode); }
-
-private:
-   std::unique_ptr<HypreLOBPCG> eigenSolver = nullptr;
-};
-#endif
-
-#ifdef MFEM_SLEPC
-class EigenSolverSlepc : public EigenSolverBase
-{
-public:
-   EigenSolverSlepc(MPI_Comm comm)
-   {
-      eigSolverType = EigenSolverType::SLEPC;
-      eigenSolver = std::make_unique<SlepcEigenSolver>(comm);
-
-      eigenSolver->SetWhichEigenpairs(SlepcEigenSolver::TARGET_REAL);
-      eigenSolver->SetTarget(0.0);
-      eigenSolver->SetSpectralTransformation(SlepcEigenSolver::SHIFT_INVERT);
-   }
-
-   ~EigenSolverSlepc() {}
-
-   void Solve() override { eigenSolver->Solve(); }
-   void SetNumModes(int num_Modes) override
-   {
-      eigenSolver->SetNumModes(num_Modes);
-      numModes = num_Modes;
-   }
-   /// @brief  Set the operator to the slepc eigenvalue problem. This method deep copies data to create a PetscParMatrix
-   /// @param A - operator, must be of type HypreParMatrix.
-   void SetOperator(Operator& A) override
-   {
-      petscMatA = std::make_unique<PetscParMatrix>
-                  (dynamic_cast<HypreParMatrix*>(&A));
-      eigenSolver->SetOperator(*petscMatA);
-   }
-   /// @brief  Set the operators to the slepc eigenvalue problem. This method deep copies data to create a PetscParMatrix
-   /// @param A - operator, must be of type HypreParMatrix.
-   /// @param M - operator, must be of type HypreParMatrix.
-   void SetOperator(Operator& A, Operator& M) override
-   {
-      petscMatA = std::make_unique<PetscParMatrix>
-                  (dynamic_cast<const HypreParMatrix*>(&A));
-      petscMatM = std::make_unique<PetscParMatrix>
-                  (dynamic_cast<const HypreParMatrix*>(&M));
-
-      eigenSolver->SetOperators(*petscMatA, *petscMatM);
-   }
-   void SetPreconditioner([[maybe_unused]] Solver& precond) override {}
-   void GetEigenvalues(Array<real_t>& eigen_vals) override
-   {
-      eigen_vals.SetSize(numModes);
-      for (int ik = 0; ik < numModes; ik++)
-      {
-         eigenSolver->GetEigenvalue(static_cast<unsigned int>(ik), eigen_vals[ik]);
-      }
-   }
-   void GetEigenvector( int vec_index, Vector& vector) override
-   { eigenSolver->GetEigenvector(vec_index, vector); }
-
-   void SetTol(real_t tol) { eigenSolver->SetTol(tol); }
-   void SetMaxIter(int max_iter) { eigenSolver->SetMaxIter(max_iter); }
-
-private:
-   std::unique_ptr<SlepcEigenSolver> eigenSolver = nullptr;
-   std::unique_ptr<PetscParMatrix> petscMatA = nullptr;
-   std::unique_ptr<PetscParMatrix> petscMatM = nullptr;
-};
-#endif
-
-}  // namespace mfem
-
-#endif

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);
       }
    }
@@ -5329,21 +5322,27 @@ 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 +5355,16 @@ 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 +5609,7 @@ 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 +5703,7 @@ 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
 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)
 
 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;
@@ -6514,7 +6513,7 @@ 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 +6550,6 @@ 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 +6565,7 @@ 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 +6615,14 @@ 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 +6649,10 @@ 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 +6663,6 @@ 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 +6681,7 @@ 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 +6711,7 @@ 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 +6725,7 @@ 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 +6733,19 @@ 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 +6777,12 @@ 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 +6827,11 @@ 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 +6840,7 @@ 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 +6890,7 @@ void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
       }
    }
 
+#ifdef MFEM_DEBUG
    bool allSet = true;
    for (auto eset : edgeSet)
    {
@@ -6899,7 +6899,8 @@ 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 +6942,7 @@ void Mesh::LoadNonconformingPatchTopo(std::istream &input,
 
       if (v[0] > v[1])
       {
-         ukv = -1 - ukv;
+         ukv = FlipIndexSign(ukv);
       }
       edge_to_ukv[j] = ukv;
    }
@@ -12438,11 +12439,7 @@ 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 +15748,18 @@ 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 +15783,22 @@ 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_operators.cpp

@@ -143,7 +143,7 @@ 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()
@@ -162,7 +162,7 @@ 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 +290,7 @@ 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 +310,7 @@ 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/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/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;
    }

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/nurbs/nurbs_ex10p.cpp

@@ -264,7 +264,7 @@ int main(int argc, char *argv[])
    //    parallel degrees of freedom, with offsets given by array true_offset.
    FiniteElementCollection *fec = nullptr;
    NURBSExtension *NURBSext = nullptr;
-   if (mesh->NURBSext)
+   if (pmesh->NURBSext)
    {
       NURBSext = new NURBSExtension(pmesh->NURBSext, order);
       fec = new NURBSFECollection(order);

miniapps/plasma/CMakeLists.txt

@@ -0,0 +1,25 @@
+# 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.
+
+if (MFEM_USE_MPI)
+  list(APPEND PLASMA_COMMON_SOURCES)
+
+  list(APPEND PLASMA_COMMON_HEADERS
+  plasma.hpp)
+
+  convert_filenames_to_full_paths(PLASMA_COMMON_SOURCES)
+  convert_filenames_to_full_paths(PLASMA_COMMON_HEADERS)
+
+  set(PLASMA_COMMON_FILES
+      EXTRA_SOURCES ${PLASMA_COMMON_SOURCES}
+      EXTRA_HEADERS ${PLASMA_COMMON_HEADERS})
+
+endif()

miniapps/plasma/makefile

@@ -0,0 +1,85 @@
+# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/plasma/,)
+CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+# Use the MFEM install directory
+# MFEM_INSTALL_DIR = ../../mfem
+# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_MINIAPPS = 
+PAR_MINIAPPS = 
+ifeq ($(MFEM_USE_MPI),NO)
+   MINIAPPS = $(SEQ_MINIAPPS)
+else
+   MINIAPPS = $(PAR_MINIAPPS) $(SEQ_MINIAPPS)
+endif
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all lib-common clean clean-build clean-exec
+.PRECIOUS: %.o
+
+COMMON_LIB = -L$(MFEM_BUILD_DIR)/miniapps/common -lmfem-common
+
+# If MFEM_SHARED is set, add the ../common rpath
+COMMON_LIB += $(if $(MFEM_SHARED:YES=),,\
+   $(if $(MFEM_USE_CUDA:YES=),$(CXX_XLINKER),$(CUDA_XLINKER))-rpath,$(abspath\
+   $(MFEM_BUILD_DIR)/miniapps/common))
+
+COMMON_O=
+
+# Remove built-in rules
+%: %.cpp
+%.o: %.cpp
+
+all: $(MINIAPPS)
+
+# Rules for building the miniapps
+%: $(SRC)%.cpp $(COMMON_O) $(MFEM_LIB_FILE) $(CONFIG_MK) | lib-common
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) $< -o $@ $(COMMON_O) $(COMMON_LIB) \
+        $(MFEM_LIBS)
+
+# Rules for compiling miniapp dependencies
+$(COMMON_O) $(addsuffix _solver.o,$(MINIAPPS)): \
+%.o: $(SRC)%.cpp $(SRC)%.hpp $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<) -o $(@)
+
+# Rule for building lib-common
+lib-common:
+	$(MAKE) -C $(MFEM_BUILD_DIR)/miniapps/common
+
+MFEM_TESTS = MINIAPPS
+include $(MFEM_TEST_MK)
+
+# Testing: Specific execution options
+RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
+
+# Testing: "test" target and mfem-test* variables are defined in config/test.mk
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean: clean-build clean-exec
+
+clean-build:
+	rm -f *.o *~ $(SEQ_MINIAPPS) $(PAR_MINIAPPS)
+	rm -rf *.dSYM *.TVD.*breakpoints
+
+clean-exec:
+

miniapps/plasma/plasma.hpp

@@ -0,0 +1,62 @@
+// 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_PLASMA_HPP
+#define MFEM_PLASMA_HPP
+
+#include <cmath>
+#include <complex>
+
+namespace mfem
+{
+
+namespace plasma
+{
+
+// Physical Constants
+
+// Permittivity of Free Space (units F/m)
+static const real_t epsilon0_ = 8.8541878176e-12;
+
+// Permeability of Free Space (units H/m)
+static const real_t mu0_ = 4.0e-7 * M_PI;
+
+// Speed of light in Free Space (units m/s)
+static const real_t c0_ = 1.0 / sqrt(epsilon0_ * mu0_);
+
+// Impedance of Free Space (units Ohm)
+static const real_t Z0_ = sqrt(mu0_ / epsilon0_);
+
+static const real_t q_     = 1.602176634e-19; // Elementary charge in coulombs
+static const real_t eV_    = 1.602176634e-19; // 1 eV in Joules
+static const real_t amu_   = 1.660539040e-27; // Atomic mass unit in kilograms
+static const real_t me_kg_ = 9.10938356e-31;  // Mass of electron in kilograms
+static const real_t me_u_  = 5.4857990907e-4; // Mass of electron in a.m.u
+
+/**
+   Returns the cyclotron frequency in radians/second
+   m is the mass in a.m.u
+   q is the charge in units of elementary electric charge
+   B is the magnetic field magnitude in tesla
+ */
+inline real_t cyclotronFrequency(real_t B, real_t m, real_t q)
+{
+   return fabs(q * q_ * B / (m * amu_));
+}
+
+typedef std::complex<real_t> complex_t;
+
+} // namespace plasma
+
+} // namespace mfem
+
+#endif // MFEM_PLASMA_HPP
+

miniapps/tools/gridfunction-bounds.cpp

@@ -23,6 +23,8 @@
 // (2) Dzanic et al., "A method for bounding high-order finite element
 //     functions: Applications to mesh validity and bounds-preserving limiters".
 //
+// We also use a recursive subdivision strategy to compute tighter estimate of
+// the function extremum.
 //
 // Compile with: make gridfunction-bounds
 //
@@ -31,9 +33,6 @@
 //  mpirun -np 4 gridfunction-bounds -nb 100 -ref 5 -bt 2 -l2
 
 #include "mfem.hpp"
-#include <memory>
-#include <iostream>
-#include <fstream>
 
 using namespace mfem;
 using namespace std;
@@ -56,6 +55,8 @@ int main (int argc, char *argv[])
    int  b_type           = -1;
    bool continuous       = true;
    int  nbrute           = 0;
+   int  rec_depth        = 4;
+   real_t rel_tol        = 1e-4;
 
    // Parse command-line options.
    OptionsParser args(argc, argv);
@@ -83,6 +84,12 @@ int main (int argc, char *argv[])
    args.AddOption(&nbrute, "-nb", "--nbrute",
                   "Brute force search for minimum in an array of nxnxn points "
                   "in each element.");
+   args.AddOption(&rec_depth, "-rd", "--rec-depth",
+                  "Maximum depth for recursive subdivision to compute function "
+                  "extremum.");
+   args.AddOption(&rel_tol, "-rt", "--rel-tol",
+                  "Relative tolerance for termination of recursive "
+                  "subdivision.");
    args.ParseCheck();
 
    Mesh mesh(mesh_file, 1, 1, false);
@@ -151,7 +158,19 @@ int main (int argc, char *argv[])
    ParGridFunction lowerb(&fes_pc), upperb(&fes_pc);
 
    // Compute bounds
-   pfunc_proj->GetElementBounds(lowerb, upperb, ref);
+   PLBound plb = pfunc_proj->GetElementBounds(lowerb, upperb, ref);
+
+   // Compute minimum and maximum bounds via recursion
+   Vector bound_rec_min(vdim), bound_rec_max(vdim);
+   for (int d = 0; d < vdim; d++)
+   {
+      auto min_interval = pfunc_proj->EstimateFunctionMinimum(d, plb, rec_depth,
+                                                              rel_tol);
+      auto max_interval = pfunc_proj->EstimateFunctionMaximum(d, plb, rec_depth,
+                                                              rel_tol);
+      bound_rec_min(d) = min_interval.first;
+      bound_rec_max(d) = max_interval.second;
+   }
 
    Vector bound_min(vdim), bound_max(vdim);
    for (int d = 0; d < vdim; d++)
@@ -236,17 +255,31 @@ int main (int argc, char *argv[])
       {
          for (int d = 0; d < vdim; d++)
          {
-            cout << "Brute force and bounding comparison for component " <<
+            cout << "Compare function extremum for component " <<
                  d << endl;
-            cout << "Brute force minimum and minimum bound: " << global_min(d)
-                 << " " <<  bound_min(d) << endl;
-
-            cout << "Brute force maximum and maximum bound: " << global_max(d)
-                 << " " <<  bound_max(d) << endl;
-
-            cout << "The difference in bounds is: " <<
-                 global_min(d)-bound_min(d) << " " <<
-                 bound_max(d)-global_max(d) << endl;
+            constexpr int w = 20;
+            cout << left << setw(w) << " "
+                 << setw(w)  << "Brute force"
+                 << setw(w) << "PL Bound"
+                 << setw(w) << "PL Bound + recursion" << endl
+                 << left << setw(w) << "Minimum: "
+                 << setw(w) << global_min(d)
+                 << setw(w) << bound_min(d)
+                 << setw(w) << bound_rec_min(d) << endl
+                 << left << setw(w) << "Difference: "
+                 << setw(w) << "-"
+                 << setw(w) << global_min(d)-bound_min(d)
+                 << setw(w) << global_min(d)-bound_rec_min(d) << endl;
+            cout << endl
+                 << left << setw(w) << "Maximum: "
+                 << setw(w) << global_max(d)
+                 << setw(w) << bound_max(d)
+                 << setw(w) << bound_rec_max(d) << endl
+                 << left << setw(w) << "Difference: "
+                 << setw(w) << "-"
+                 << setw(w) << bound_max(d)-global_max(d)
+                 << setw(w) << bound_rec_max(d)-global_max(d) << endl;
+            cout << endl;
          }
       }
    }
@@ -255,10 +288,19 @@ int main (int argc, char *argv[])
    {
       for (int d = 0; d < vdim; d++)
       {
-         cout << "Minimum bound for component " << d << " is " <<
-              bound_min(d) << endl;
-         cout << "Maximum bound for component " << d << " is " <<
-              bound_max(d) << endl;
+         cout << "Compare function extremum for component " <<
+              d << endl;
+         constexpr int w = 20;
+         cout << left << setw(w) << " "
+              << setw(w) << "PL Bound"
+              << setw(w) << "PL Bound + recursion" << endl
+              << left << setw(w) << "Minimum: "
+              << setw(w) << bound_min(d)
+              << setw(w) << bound_rec_min(d) << endl;
+         cout << endl
+              << left << setw(w) << "Maximum: "
+              << setw(w) << bound_max(d)
+              << setw(w) << bound_rec_max(d) << endl;
       }
    }
 

tests/unit/catch.hpp

@@ -295,8 +295,13 @@ namespace Catch {
 // Otherwise all supported compilers support COUNTER macro,
 // but user still might want to turn it off
 #if ( !defined(__JETBRAINS_IDE__) || __JETBRAINS_IDE__ >= 20170300L )
+#if ( !(defined(__clang__) && __clang_major__ >= 22 ) )
+// don't use __COUNTER__ if compiling with clang 22+ to avoid compiler warning
+// https://github.com/llvm/llvm-project/pull/162662
+// TODO: can enable if building with C2y
     #define CATCH_INTERNAL_CONFIG_COUNTER
 #endif
+#endif
 
 ////////////////////////////////////////////////////////////////////////////////
 

tests/unit/fem/test_col_lag_der.cpp

@@ -151,6 +151,8 @@ TEST_CASE("Collocated Derivative Kernels", "[QuadratureInterpolator]")
       auto L = GENERATE(QVectorLayout::byNODES, QVectorLayout::byVDIM);
       auto P = GENERATE(true, false);
 
+      CAPTURE(L, P);
+
       const int nd = maps.ndof;
       const int nq = maps.nqpt;
 
@@ -163,7 +165,15 @@ TEST_CASE("Collocated Derivative Kernels", "[QuadratureInterpolator]")
       CGK::Run(dim, L, P, vdim, nd, nelem, maps.G.Read(), geom->J.Read(),
                evec_values.Read(), col_der.Write(), sdim, vdim, nd);
 
+      const real_t max_norm = qp_der.Normlinf();
+
       qp_der -= col_der;
-      REQUIRE(qp_der.Normlinf() == MFEM_Approx(0.0, 1e-10, 1e-10));
+
+      const real_t abs_err = qp_der.Normlinf();
+      const real_t rel_err = max_norm > 0_r ?
+                             abs_err/max_norm :
+                             abs_err > 0_r ? mfem::infinity() : 0_r;
+      CAPTURE(rel_err, max_norm);
+      CHECK(rel_err <= 1e-13);
    }
 }

tests/unit/fem/test_fe.cpp

@@ -281,8 +281,10 @@ TEST_CASE("Nedelec Segment Finite Element",
             REQUIRE( fe.GetRangeType()      == (int) FiniteElement::VECTOR  );
             REQUIRE( fe.GetMapType()        == (int) FiniteElement::H_CURL  );
             REQUIRE( fe.GetDerivType()      == (int) FiniteElement::NONE    );
-            REQUIRE( fe.GetDerivRangeType() == (int) FiniteElement::SCALAR  );
-            REQUIRE( fe.GetDerivMapType()   == (int) FiniteElement::INTEGRAL);
+            REQUIRE( fe.GetDerivRangeType() ==
+                     (int) FiniteElement::UNKNOWN_RANGE_TYPE);
+            REQUIRE( fe.GetDerivMapType()   ==
+                     (int) FiniteElement::UNKNOWN_MAP_TYPE);
          }
       }
       SECTION("Sizes for p = " + std::to_string(p))

tests/unit/general/test_array.cpp

@@ -125,6 +125,59 @@ TEST_CASE("Array stl-interactions", "[Array]")
    }
 }
 
+
+TEST_CASE("Array move assignment to view (MakeRef)", "[Array]")
+{
+   constexpr int n = 5;
+
+   // Helper function that returns an Array by value (rvalue)
+   auto make_sequence_array = [](int n)
+   {
+      Array<int> arr(n);
+      for (int i = 0; i < n; i++)
+      {
+         arr[i] = i + 1;  // 1, 2, 3, ...
+      }
+      return arr;
+   };
+
+   // Create backing storage
+   Array<int> backing1(n), backing2(n);
+   backing1 = 0.0; backing2 = 0.0;
+
+   // Create a view into the backing storage
+   Array<int> view1, view2;
+   view1.MakeRef(backing1);
+   view2.MakeRef(backing2);
+
+   auto seq_array = make_sequence_array(n);
+   view1 = seq_array; // copy assign
+   view2 = std::move(seq_array); // move assign
+
+   CHECK(seq_array.Size() == 0); // seq_array is invalidated by the move
+
+   // Both assignments should be semantically equivalent.
+   for (int i = 0; i < n; i++)
+   {
+      CHECK(backing1[i] == backing2[i]);
+   }
+
+   // Create backing storage as raw array
+   int backing3[n] = {0, 0, 0, 0, 0};
+
+   // Create a view into the backing storage
+   Array<int> view3;
+   view3.MakeRef(backing3, n);
+
+   // Assign from rvalue
+   view3 = std::move(view2);
+
+   for (int i = 0; i < n; i++)
+   {
+      CHECK(backing3[i] == backing1[i]);
+   }
+}
+
 TEST_CASE("Array delete at indices", "[Array],[GPU]")
 {
    for (int use_dev = 0; use_dev < 2; use_dev++)

tests/unit/linalg/test_matrix_dense.cpp

@@ -961,3 +961,38 @@ TEST_CASE("NNLS", "[DenseMatrix]")
 }
 
 #endif // if MFEM_USE_LAPACK
+
+TEST_CASE("DenseTensor slice copy and move assign equivalency",
+          "[DenseMatrix][DenseTensor]")
+{
+   auto fill_matrix = [](int n)
+   {
+      DenseMatrix M(n, n);
+      M = 0.0;
+      for (int i = 0; i < n; i++)
+         for (int j = 0; j < n; j++)
+         {
+            M(i, j) = i+j*n+1;
+         }
+      return M;
+   };
+
+   constexpr int n = 3;
+   constexpr int k = 2;
+
+   DenseTensor tensor1(n, n, k), tensor2(n, n, k);
+   tensor1 = 0.0; tensor2 = 0.0;
+
+   DenseMatrix temp = fill_matrix(n);
+   tensor1(0) = temp; // copy assign
+   tensor2(0) = std::move(temp); // move assign
+
+   // Check that the tensor was actually updated
+   for (int i = 0; i < n; i++)
+   {
+      for (int j = 0; j < n; j++)
+      {
+         CHECK(tensor1(i, j, 0) == tensor2(i, j, 0));
+      }
+   }
+}

tests/unit/mesh/test_nurbs.cpp

@@ -222,13 +222,13 @@ TEST_CASE("Greville, Botella and Demko points", "[NURBS]")
       mfem::out<<"Knotvector : "; kvp.Print(mfem::out);
 
       kvp.GetGreville(xi);
-      mfem::out<<"Greville points : "; xi.Print(std::cout,999);
+      mfem::out<<"Greville points : "; xi.Print(mfem::out,999);
 
       kvp.GetBotella(xi);
-      mfem::out<<"Botella  points : "; xi.Print(std::cout,999);
+      mfem::out<<"Botella  points : "; xi.Print(mfem::out,999);
 
       kvp.GetDemko(xi);
-      mfem::out<<"Demko    points : "; xi.Print(std::cout,999);
+      mfem::out<<"Demko    points : "; xi.Print(mfem::out,999);
    }
 
    KnotVector kv(3, Vector({0.0, 0.3, 0.3, 0.3, 0.6, 1.0}));