Fix style error

Credit to William Moses.

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

fem/CMakeLists.txt

@@ -213,6 +213,7 @@ set(HDRS
   dfem/qfunction_apply.hpp
   dfem/qfunction_transform.hpp
   dfem/tuple.hpp
+  dfem/univarsolvers.hpp
   dfem/util.hpp
   eltrans.hpp
   estimators.hpp

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/dfem/univarsolvers.hpp

@@ -0,0 +1,263 @@
+// 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 univarsolvers.hpp
+ *
+ * @brief Solvers of functions of a single variable suitable for use in ∂FEM q-functions.
+ */
+
+#ifndef MFEM_UNIVARSOLVERS
+#define MFEM_UNIVARSOLVERS
+
+#include <cmath>
+#include <limits>
+
+#include "../../config/config.hpp"
+#include "../../general/enzyme.hpp"
+#include "../../general/error.hpp"
+
+#ifdef MFEM_USE_ENZYME
+
+// Currently needed to work around a bug in LLVM
+extern void __enzyme_double(void*, size_t);
+
+namespace mfem
+{
+
+namespace future
+{
+/// Representation of root search bounds
+struct Bounds
+{
+   real_t lower, upper;
+};
+
+
+/// Settings for univariate solver
+struct SolverSettings
+{
+   real_t residual_abs_tol; ///< Tolerance for convergence check on absolute value of residual
+   real_t residual_rel_tol; ///< Tolerance for convergence check on absolute value of current residual relative to absolute value of residual at initial guess
+   Bounds bounds; ///< Bounds on root
+   int max_iters = 50;
+};
+} // namespace future
+
+namespace internal
+{
+/// @cond DO_NOT_DOCUMENT
+
+using future::SolverSettings;
+
+// The noinline attribute is neccessary for Enzyme. If this function were to be
+//  inlined in the calling function, The custom derivative rules would not be
+// found (since the function they refer to would no longer exist).
+template <auto f, typename T>
+__attribute__((noinline))
+MFEM_HOST_DEVICE void SolveNewtonBisection_impl(const real_t* x0_ptr,
+                                                const T* p_ptr, const SolverSettings* settings_ptr, real_t* x_ptr)
+{
+   int max_iters = settings_ptr->max_iters;
+
+   const real_t& x0 = *x0_ptr;
+   const T& p = *p_ptr;
+   const SolverSettings& settings = *settings_ptr;
+   const real_t& left_bracket = settings.bounds.lower;
+   const real_t& right_bracket = settings.bounds.upper;
+   real_t& x = *x_ptr;
+   using std::abs;
+
+   auto fprime = [&p](real_t x)
+   {
+      real_t x_dot = 1.0;
+      return __enzyme_fwddiff<real_t>((void*)+f, enzyme_dup, x, x_dot, enzyme_const,
+                                      p);
+   };
+
+   real_t fl = f(left_bracket, p);
+   real_t fh = f(right_bracket, p);
+
+   // handle corner cases where one of the brackets is the root
+   if (abs(fl) < settings.residual_abs_tol)
+   {
+      x = left_bracket;
+      return;
+   }
+   else if (abs(fh) < settings.residual_abs_tol)
+   {
+      x = right_bracket;
+      return;
+   }
+
+   if (fl * fh > 0)
+   {
+      MFEM_WARNING("Root is not bracketed, solver may diverge.");
+   }
+
+   // clamp initial guess within root brackets
+   x = x0 > right_bracket? right_bracket : x0 < left_bracket? left_bracket : x0;
+
+   // Orient search so that f(xl) < 0
+   real_t xl = left_bracket;
+   real_t xh = right_bracket;
+   if (fl > 0.0)
+   {
+      xl = right_bracket;
+      xh = left_bracket;
+      real_t tmp = fl;
+      fl = fh;
+      fh = tmp;
+   }
+
+   real_t dx_old = abs(right_bracket - left_bracket);
+   real_t dx = dx_old;
+   x = x0;
+   real_t r = f(x, p);
+   real_t dr_dx = fprime(x);
+   real_t r0 = r;
+   for (int i = 0; i < max_iters; i++)
+   {
+      if ((((x - xh) * dr_dx - r)*((x - xl)*dr_dx - r) >= 0.0) ||
+          // Newton out of range
+          (std::abs(2.0*r) > std::abs(
+              dx_old*dr_dx)))              // Newton decreasing bracket slower than bisection
+      {
+         // Take bisection step
+         dx_old = dx;
+         dx = 0.5*(xh - xl);
+         real_t x_old = x;
+         x = xl + dx;
+         if (x == x_old) { return; }
+      }
+      else
+      {
+         // Take Newton step
+         dx_old = dx;
+         dx = -r/dr_dx;
+         real_t x_old = x;
+         x += dx;
+         if (x == x_old) { return; }
+      }
+
+      // update residual and jacobian
+      r = f(x, p);
+      dr_dx = fprime(x);
+
+      // Check convergence
+      if (abs(r) < settings.residual_rel_tol*r0 ||
+          abs(r) < settings.residual_abs_tol)
+      {
+         return;
+      }
+
+      // Update bracket
+      if (r < 0.0)
+      {
+         xl = x;
+         fl = r;
+      }
+      else
+      {
+         xh = x;
+         fh = r;
+      }
+   }
+   MFEM_ABORT("Univariate solve did not converge.");
+}
+
+template <auto f, typename T>
+void SolveNewtonBisection_impl_fwddiff(const real_t* x0,
+                                       const real_t* /* unused shadow */,
+                                       const T* p, const T* dp,
+                                       const SolverSettings* settings, const SolverSettings* /* unused shadow */,
+                                       real_t* x, real_t* dx)
+{
+   SolveNewtonBisection_impl<f>(x0, p, settings, x);
+   real_t dfdx = __enzyme_fwddiff<real_t>((void*)+f, enzyme_dup, *x, 1.0,
+                                          enzyme_const, *p);
+   real_t dfdp = __enzyme_fwddiff<real_t>((void*)+f, enzyme_const, *x, enzyme_dup,
+                                          *p, *dp);
+   *dx = -dfdp/dfdx;
+}
+
+
+template<auto f, typename T>
+void SolveNewtonBisection_impl_aug(const real_t* x0, real_t* x0_bar,
+                                   const T* p, T* p_bar,
+                                   const SolverSettings* settings, SolverSettings* settings_bar,
+                                   real_t* x, real_t* x_bar)
+{
+   SolveNewtonBisection_impl<f>(x0, p, settings, x);
+}
+
+// Change the residual function to return-by-reference so that there is a
+// slot to provide the downstream cotangent (ie the shadow for y)
+// in the reverse mode call.
+template<auto f, typename T>
+void rbr_wrapper(real_t x, T& p, real_t& y)
+{
+   y = f(x, p);
+}
+
+template<auto f, typename T>
+void SolveNewtonBisection_impl_rev(const real_t* x0, real_t* x0_bar,
+                                   const T* p, T* p_bar,
+                                   const SolverSettings* settings, SolverSettings* settings_bar,
+                                   real_t* x, real_t* x_bar)
+{
+   real_t drdx = __enzyme_fwddiff<real_t>((void*)+f, enzyme_dup, *x, 1.0,
+                                          enzyme_const, *p);
+   real_t lambda = -(*x_bar / drdx);
+   real_t r;
+   __enzyme_autodiff<void>((void*)rbr_wrapper<f, T>, enzyme_const, *x, enzyme_dup,
+                           p, p_bar, enzyme_dupnoneed, &r, &lambda);
+
+   // These are logically constants, the root has no sensitivity to these
+   *x0_bar = 0.0;
+   *settings_bar = SolverSettings{};
+}
+
+/// @endcond
+} // namespace internal
+
+
+namespace future
+{
+
+/**
+ * @brief Find the root of a univariate funtion
+ */
+template<auto f, typename T>
+MFEM_HOST_DEVICE __attribute__((always_inline)) real_t SolveNewtonBisection(
+   real_t x0, T p, SolverSettings settings)
+{
+   // We need to tell Enzyme how much memory in the SolverSettings object is
+   // used by active variables (in the sense of Enzyme activity analysis).
+   // Without this, it seems that a bug in LLVM causes this information to
+   // be lost during some optimization pass, and the Enzyme pass fails in
+   // Release builds.
+   // There are 4 real_t members in settings, which is what Enzyme will
+   // consider active.
+   // TODO: File an issue on Enzyme to remind Bill to fix this in LLVM.
+   __enzyme_double((void*)&settings, sizeof(real_t)*4);
+
+   real_t x;
+   internal::SolveNewtonBisection_impl<f>(&x0, &p, &settings, &x);
+   return x;
+}
+
+
+} // namespace future
+} // namespace mfem
+
+#endif // MFEM_USE_ENZYME
+#endif // MFEM_UNIVARSOLVERS

fem/fe/fe_base.cpp

@@ -1044,9 +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)
@@ -1064,13 +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_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/fem.hpp

@@ -53,6 +53,7 @@
 #include "particleset.hpp"
 
 #include "dfem/doperator.hpp"
+#include "dfem/univarsolvers.hpp"
 
 #ifdef MFEM_USE_MPI
 #include "pfespace.hpp"

fem/prestriction.cpp

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

fem/restriction.cpp

@@ -1398,20 +1398,17 @@ void L2FaceRestriction::PermuteAndSetSharedFaceDofsScatterIndices2(
    const int dim = fes.GetMesh()->Dimension();
    const int dof1d = fes.GetTypicalFE()->GetOrder()+1;
    fes.GetTypicalFE()->GetFaceMap(face_id2, face_map);
-   Array<int> face_nbr_dofs;
-   const ParFiniteElementSpace &pfes =
-      static_cast<const ParFiniteElementSpace&>(this->fes);
-   pfes.GetFaceNbrElementVDofs(elem_index, face_nbr_dofs);
 
    for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
    {
       const int face_dof_elem2 = PermuteFaceL2(dim, face_id1, face_id2,
                                                orientation, dof1d, face_dof_elem1);
       const int volume_dof_elem2 = face_map[face_dof_elem2];
-      const int global_dof_elem2 = face_nbr_dofs[volume_dof_elem2];
+      // Encode the volume DOF index and element index
+      const int global_dof_elem2 = elem_index*elem_dofs + volume_dof_elem2;
       const int restriction_dof_elem2 = face_dofs*face_index + face_dof_elem1;
       // Trick to differentiate dof location inter/shared
-      scatter_indices2[restriction_dof_elem2] = ndofs+global_dof_elem2;
+      scatter_indices2[restriction_dof_elem2] = ndofs + global_dof_elem2;
    }
 #endif
 }

linalg/hypre.cpp

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

linalg/petsc.cpp

@@ -38,6 +38,13 @@
 #if PETSC_VERSION_LT(3,19,0)
 #define PETSC_SUCCESS 0
 #endif
+#if PETSC_VERSION_LT(3,23,0)
+#define PetscContainerSetCtxDestroy(A,B) PetscContainerSetUserDestroy(A,B)
+typedef PetscErrorCode (PetscCtxDestroyFn)(void**);
+#endif
+#if PETSC_VERSION_LT(3,24,0)
+typedef PetscErrorCode KSPMonitorFn(KSP,PetscInt,PetscReal,void*);
+#endif
 
 #include <fstream>
 #include <iomanip>
@@ -77,13 +84,17 @@ static PetscErrorCode __mfem_mat_shell_apply_transpose(Mat,Vec,Vec);
 static PetscErrorCode __mfem_mat_shell_destroy(Mat);
 static PetscErrorCode __mfem_mat_shell_copy(Mat,Mat,MatStructure);
 #if PETSC_VERSION_LT(3,23,0)
-static PetscErrorCode __mfem_array_container_destroy(void*);
-static PetscErrorCode __mfem_matarray_container_destroy(void *);
-#else
-static PetscErrorCode __mfem_array_container_destroy(void**);
-static PetscErrorCode __mfem_matarray_container_destroy(void**);
+typedef void *PetscCtxRt;
+#elif PETSC_VERSION_LT(3,25,0)
+typedef void **PetscCtxRt;
 #endif
+static PetscErrorCode __mfem_array_container_destroy(PetscCtxRt);
+static PetscErrorCode __mfem_matarray_container_destroy(PetscCtxRt);
+#if PETSC_VERSION_LT(3,23,0)
 static PetscErrorCode __mfem_monitor_ctx_destroy(void**);
+#else
+static PetscErrorCode __mfem_monitor_ctx_destroy(PetscCtxRt);
+#endif
 
 // auxiliary functions
 static PetscErrorCode Convert_Array_IS(MPI_Comm,bool,const mfem::Array<int>*,
@@ -1317,11 +1328,7 @@ BlockDiagonalConstructor(MPI_Comm comm,
 
          ierr = PetscContainerCreate(comm,&c); CCHKERRQ(comm,ierr);
          ierr = PetscContainerSetPointer(c,ptrs[i]); CCHKERRQ(comm,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
          CCHKERRQ(comm,ierr);
          ierr = PetscObjectCompose((PetscObject)A,names[i],(PetscObject)c);
          CCHKERRQ(comm,ierr);
@@ -1648,11 +1655,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
          PetscContainer c;
          ierr = PetscContainerCreate(comm,&c); CCHKERRQ(comm,ierr);
          ierr = PetscContainerSetPointer(c,vmatsl2l); PCHKERRQ(c,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_matarray_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_matarray_container_destroy);
-#endif
          PCHKERRQ(c,ierr);
          ierr = PetscObjectCompose((PetscObject)(*A),"_MatIS_PtAP_l2l",(PetscObject)c);
          PCHKERRQ((*A),ierr);
@@ -1748,11 +1751,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
 
             ierr = PetscContainerCreate(PETSC_COMM_SELF,&c); PCHKERRQ(B,ierr);
             ierr = PetscContainerSetPointer(c,ptrs[i]); PCHKERRQ(B,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-            ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
-#else
             ierr = PetscContainerSetCtxDestroy(c,__mfem_array_container_destroy);
-#endif
             PCHKERRQ(B,ierr);
             ierr = PetscObjectCompose((PetscObject)(B),names[i],(PetscObject)c);
             PCHKERRQ(B,ierr);
@@ -2198,11 +2197,7 @@ PetscParMatrix * RAP(PetscParMatrix *Rt, PetscParMatrix *A, PetscParMatrix *P)
          ierr = PetscContainerCreate(PetscObjectComm((PetscObject)B),&c);
          PCHKERRQ(B,ierr);
          ierr = PetscContainerSetPointer(c,vmatsl2l); PCHKERRQ(c,ierr);
-#if PETSC_VERSION_LT(3,23,0)
-         ierr = PetscContainerSetUserDestroy(c,__mfem_matarray_container_destroy);
-#else
          ierr = PetscContainerSetCtxDestroy(c,__mfem_matarray_container_destroy);
-#endif
          PCHKERRQ(c,ierr);
          ierr = PetscObjectCompose((PetscObject)B,"_MatIS_PtAP_l2l",(PetscObject)c);
          PCHKERRQ(B,ierr);
@@ -2485,7 +2480,6 @@ void PetscSolver::SetMaxIter(int max_iter)
 
 void PetscSolver::SetPrintLevel(int plev)
 {
-   typedef PetscErrorCode (*myPetscFunc)(void**);
    PetscViewerAndFormat *vf = NULL;
    PetscViewer viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm(obj));
 
@@ -2498,7 +2492,6 @@ void PetscSolver::SetPrintLevel(int plev)
    {
       // there are many other options, see the function KSPSetFromOptions() in
       // src/ksp/ksp/interface/itcl.c
-      typedef PetscErrorCode (*myMonitor)(KSP,PetscInt,PetscReal,void*);
       KSP ksp = (KSP)obj;
       if (plev >= 0)
       {
@@ -2507,29 +2500,29 @@ void PetscSolver::SetPrintLevel(int plev)
       if (plev == 1)
       {
 #if PETSC_VERSION_LT(3,15,0)
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorDefault,vf,
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorDefault,vf,
 #else
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorResidual,vf,
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorResidual,vf,
 #endif
-                              (myPetscFunc)PetscViewerAndFormatDestroy);
+                              (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(ksp,ierr);
       }
       else if (plev > 1)
       {
          ierr = KSPSetComputeSingularValues(ksp,PETSC_TRUE); PCHKERRQ(ksp,ierr);
-         ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorSingularValue,vf,
-                              (myPetscFunc)PetscViewerAndFormatDestroy);
+         ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorSingularValue,vf,
+                              (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(ksp,ierr);
          if (plev > 2)
          {
             ierr = PetscViewerAndFormatCreate(viewer,PETSC_VIEWER_DEFAULT,&vf);
             PCHKERRQ(viewer,ierr);
 #if PETSC_VERSION_LT(3,15,0)
-            ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorTrueResidualNorm,vf,
+            ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorTrueResidualNorm,vf,
 #else
-            ierr = KSPMonitorSet(ksp,(myMonitor)KSPMonitorTrueResidual,vf,
+            ierr = KSPMonitorSet(ksp,(KSPMonitorFn *)KSPMonitorTrueResidual,vf,
 #endif
-                                 (myPetscFunc)PetscViewerAndFormatDestroy);
+                                 (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
             PCHKERRQ(ksp,ierr);
          }
       }
@@ -2545,7 +2538,7 @@ void PetscSolver::SetPrintLevel(int plev)
       if (plev > 0)
       {
          ierr = SNESMonitorSet(snes,(myMonitor)SNESMonitorDefault,vf,
-                               (myPetscFunc)PetscViewerAndFormatDestroy);
+                               (PetscCtxDestroyFn *)PetscViewerAndFormatDestroy);
          PCHKERRQ(snes,ierr);
       }
    }
@@ -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)
 

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/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
+

tests/unit/CMakeLists.txt

@@ -39,6 +39,7 @@ set(UNIT_TESTS_SRCS
   dfem/test_divergence.cpp
   dfem/test_lvector_interface.cpp
   dfem/test_mass.cpp
+  dfem/test_univarsolver.cpp
   general/test_array.cpp
   general/test_scan.cpp
   general/test_arrays_by_name.cpp

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/dfem/test_univarsolver.cpp

@@ -0,0 +1,359 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include <algorithm>
+#include <cmath>
+
+#include "mfem.hpp"
+#include "unit_tests.hpp"
+
+#ifdef MFEM_USE_ENZYME
+
+using mfem::real_t;
+using namespace mfem::future;
+
+MFEM_HOST_DEVICE inline real_t FlowResistance(real_t eqps, real_t sigma_y, real_t n, real_t ep_0)
+{
+    return sigma_y*(1.0 + std::pow((eqps)/ep_0, n));
+}
+
+using J2PlasticityParameters = tuple<real_t, real_t, real_t, real_t, real_t, real_t>;
+
+// Residual function that is solved in the plasticity model.
+// Made a free function to facilitate Enzyme differentiation.
+real_t J2PlasticityResidual(real_t delta_eqps, J2PlasticityParameters p)
+{
+    auto [eqps, q, G, sigma_y, n, ep_0] = p;
+    return q - 3.0*G*delta_eqps - FlowResistance(eqps + delta_eqps, sigma_y, n, ep_0);
+}
+
+struct J2Plasticity {
+  static constexpr int dim = 3;  ///< spatial dimension
+  static constexpr int N_INTERNAL_STATES = 10;
+  static constexpr real_t tol = 1e-10;  ///< relative tolerance on residual mag to judge convergence of return map
+
+  real_t E;        ///< Young's modulus
+  real_t nu;       ///< Poisson's ratio
+  real_t sigma_y;  ///< Yield strength
+  real_t n;        ///< Hardening index
+  real_t ep_0;     ///< Reference plastic strain
+  
+  /// @brief variables required to characterize the hysteresis response
+  struct InternalState {
+    tensor<real_t, dim, dim> plastic_strain;
+    real_t accumulated_plastic_strain;
+  };
+
+  /// Internal state variables in a flattened array for storing in a global field
+  using PackedInternalState = mfem::future::tensor<real_t, N_INTERNAL_STATES>;
+
+  // Unflatten internal state variables
+  MFEM_HOST_DEVICE static inline InternalState unpack_internal_state(
+      const mfem::future::tensor<real_t, N_INTERNAL_STATES>& packed_state)
+  {
+    auto plastic_strain =
+        mfem::future::make_tensor<dim, dim>([&packed_state](int i, int j) { return packed_state[dim * i + j]; });
+    real_t accumulated_plastic_strain = packed_state[N_INTERNAL_STATES - 1];
+    return {plastic_strain, accumulated_plastic_strain};
+  }
+
+  // Flatten internal state variables (for repacking into global field)
+  MFEM_HOST_DEVICE static inline PackedInternalState pack_internal_state(
+      const mfem::future::tensor<real_t, dim, dim>& plastic_strain, real_t accumulated_plastic_strain)
+  {
+    PackedInternalState packed_state{};
+    for (int i = 0, ij = 0; i < dim; i++) {
+      for (int j = 0; j < dim; j++, ij++) {
+        packed_state[ij] = plastic_strain[i][j];
+      }
+    }
+    packed_state[N_INTERNAL_STATES - 1] = accumulated_plastic_strain;
+    return packed_state;
+  }
+
+  // Compute the new stress and the internal state variables
+  MFEM_HOST_DEVICE inline tuple<tensor<real_t, dim, dim>, PackedInternalState>
+  update(tensor<real_t, dim, dim> dudxi,
+         PackedInternalState internal_state,
+         tensor<real_t, dim, dim> J,
+         real_t w) const
+  {
+    auto invJ = inv(J);
+    const auto dudX = dudxi * invJ;
+    auto I = IdentityMatrix<dim>();
+    const real_t K = E / (3.0 * (1.0 - 2.0 * nu));
+    const real_t G = 0.5 * E / (1.0 + nu);
+
+    auto [plastic_strain, accumulated_plastic_strain] = unpack_internal_state(internal_state);
+    
+    auto el_strain = sym(dudX) - plastic_strain;
+    auto p = K * tr(el_strain);
+    auto s = 2.0 * G * dev(el_strain);
+    auto q = std::sqrt(1.5) * norm(s);
+    real_t denom = q > 0.0? q : 1.0;
+    auto Np = 1.5 * s / denom;
+
+    if (q > FlowResistance(accumulated_plastic_strain, sigma_y, n, ep_0)) {
+        real_t lb = 0.0;
+        real_t ub = (q - FlowResistance(accumulated_plastic_strain, sigma_y, n, ep_0))/(3*G);
+        SolverSettings settings{1e-10*sigma_y, 1e-10, {lb, ub}};
+        // Use the differentiable univariate root finder.
+        // This has custom derivatives, so it's ok to differentiate this enclosing function.
+        real_t delta_eqps = SolveNewtonBisection<J2PlasticityResidual>(
+            0.5*(lb + ub), make_tuple(accumulated_plastic_strain, q, G, sigma_y, n, ep_0), settings);
+        accumulated_plastic_strain += delta_eqps;
+        plastic_strain += delta_eqps * Np;
+        s -= 2.0 * G * delta_eqps * Np;
+    }
+    auto Q_new = pack_internal_state(plastic_strain, accumulated_plastic_strain);
+    auto stress = s + p * I;
+    const real_t dV = det(J)*w;
+    return {stress*transpose(invJ)*dV, Q_new};
+  }
+  
+  MFEM_HOST_DEVICE inline tensor<real_t, dim, dim>
+  stress(tensor<real_t, dim, dim> dudxi,
+         PackedInternalState internal_state,
+         tensor<real_t, dim, dim> J,
+         real_t w) const
+  {
+    auto [stress, internal_state_new] = update(dudxi, internal_state, J, w);
+    return stress;
+  }
+
+  MFEM_HOST_DEVICE inline PackedInternalState
+  internal_state_new(tensor<real_t, dim, dim> dudxi,
+                     PackedInternalState internal_state,
+                     tensor<real_t, dim, dim> J,
+                     real_t w) const
+  {
+    auto [stress, internal_state_new] = update(dudxi, internal_state, J, w);
+    return internal_state_new;
+  }
+};
+
+
+// Register the custom derivatives for the solver.
+// This needs to be done for every residual function that the solver is applied on,
+// since the SolveNewtonBisection_impl is a function template, and we need a real
+// function with an address to specify the custom derivative.
+
+// Forward mode
+__attribute__((used))
+void *  __enzyme_register_derivative_newton_bisection_on_j2[2] = {
+  (void*) mfem::internal::SolveNewtonBisection_impl<J2PlasticityResidual, J2PlasticityParameters>,
+  (void*) mfem::internal::SolveNewtonBisection_impl_fwddiff<J2PlasticityResidual, J2PlasticityParameters>
+};
+
+ // Reverse mode
+__attribute__((used))
+void* __enzyme_register_gradient_SolveNewtonBisectionJ2[3] = {
+  (void*)mfem::internal::SolveNewtonBisection_impl<J2PlasticityResidual, J2PlasticityParameters>,
+  (void*)mfem::internal::SolveNewtonBisection_impl_aug<J2PlasticityResidual, J2PlasticityParameters>,
+  (void*)mfem::internal::SolveNewtonBisection_impl_rev<J2PlasticityResidual, J2PlasticityParameters>
+};
+
+// Create free functions for Enzyme to differentiate in the tests
+// Return by value version
+tensor<real_t, 3, 3> ComputeStress(
+    J2Plasticity* material, tensor<real_t, 3, 3> dudxi, 
+    J2Plasticity::PackedInternalState Q, tensor<real_t, 3, 3> J, real_t w)
+{
+    return material->stress(dudxi, Q, J, w);
+}
+
+// Return by reference version
+void ComputeStressRef(const J2Plasticity* material, const tensor<real_t, 3, 3>& dudxi,
+                      const J2Plasticity::PackedInternalState& Q,
+                      const tensor<real_t, 3, 3>& J, real_t w,
+                      tensor<real_t, 3, 3>& sigma)
+{
+  sigma = material->stress(dudxi, Q, J, w);
+}
+
+template <int dim>
+real_t elementwise_max_norm(tensor<real_t, dim, dim> A) {
+  real_t maxval = 0;
+  for (int i = 0; i < dim; i++) {
+    for (int j = 0; j < dim; j++) {
+      maxval = std::max(std::abs(A[i][j]), maxval);
+    }
+  }
+  return maxval;
+}
+
+
+TEST_CASE("Univariate function solver in a qfunction", "[univar]")
+{
+    J2Plasticity material{70.0e3, 0.34, 240.0, 0.15, 1e-3};
+    tensor<real_t, 3, 3> H{{{0.947667  , 0.9785799 , 0.33229148},
+                            {0.46866846, 0.5698887 , 0.16550303},
+                            {0.3101946 , 0.68948054, 0.74676657}}};
+    J2Plasticity::PackedInternalState Q{};
+    const tensor<real_t, 3, 3> J = IdentityMatrix<3>();
+    const real_t w = 1.0;
+
+    SECTION("Correctness")
+    {
+      // Checks that stress after update is on the yield surface.
+      auto [stress, Q_new] = material.update(H, Q, IdentityMatrix<3>(), 1.0);
+      real_t mises = std::sqrt(1.5)*norm(dev(stress));
+      real_t eqps = Q_new[9];
+      // This test only makes sense if the displacement gradient is big enough to 
+      // cuase yielding.
+      REQUIRE(eqps > 1e-9);
+      real_t Y = FlowResistance(eqps, material.sigma_y, material.n, material.ep_0);
+      CHECK(mises == MFEM_Approx(Y, 0.0, 1e-8));
+    }
+
+    SECTION("JVP")
+    {
+      // Compare forward mode derivative to finite difference approximation
+
+      tensor<real_t, 3, 3> H_dot{{{1.0, 0.0 , 0.0},
+                                  {0.0, 0.0 , 0.0},
+                                  {0.0, 0.0 , 0.0}}};
+
+      // Enzyme directional derivative (uses custom derivative of solver)
+      auto sigma_dot = __enzyme_fwddiff<tensor<real_t, 3, 3>>((void*)ComputeStress, 
+                                                              enzyme_const, &material,
+                                                              enzyme_dup, H, H_dot,
+                                                              enzyme_const, Q,
+                                                              enzyme_const, J,
+                                                              enzyme_const, w);
+      // sigma_dot = ∂sigma / ∂H[0, 0]
+      REQUIRE(sigma_dot[0][0] > 0.0);
+
+      // Finite difference derivative approximation
+      constexpr int dim = 3;
+      real_t eps = 1e-5;
+      tensor<real_t, 3, 3> sigma = ComputeStress(&material, H, Q, J, w);
+      tensor<real_t, 3, 3> sigma_p = ComputeStress(&material, H + eps*H_dot, Q, J, w);
+      tensor<real_t, 3, 3> sigma_dot_h = (1.0/eps)*(sigma_p - sigma);
+
+      tensor<real_t, 3, 3> rel_error = sigma_dot - sigma_dot_h;
+      for (int i = 0; i < dim; i++) {
+        for (int j = 0; j < dim; j++) {
+          real_t denom = sigma[i][j] != 0? sigma[i][j] : 1.0;
+          rel_error[i][j] /= denom;
+        }
+      }
+
+      CHECK(elementwise_max_norm(rel_error) < 1e-5);
+    }
+
+    SECTION("VJP")
+    {
+      // compare reverse mode derivative to finite differences
+
+      tensor<real_t, 3, 3> sigma;
+      ComputeStressRef(&material, H, Q, J, w, sigma);
+      double epsilon = 1e-6;
+      tensor<real_t, 3, 3> dH{{{1.0, 0.0, 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}}};
+      auto H_p = H + epsilon*dH;
+      tensor<real_t, 3, 3> sigma_p;
+      ComputeStressRef(&material, H_p, Q, J, w, sigma_p);
+      auto sigma_dot_h = (sigma_p - sigma)/epsilon;
+      // Note: sigma_dot_h[i,j] = ∂sigma[i,j]/∂H[0,0]
+
+      tensor<real_t, 3, 3> sigma_bar{{{1.0, 0.0, 0.0},
+                                      {0.0, 0.0, 0.0},
+                                      {0.0, 0.0, 0.0}}};
+
+      tensor<real_t, 3, 3> H_bar{};
+      J2Plasticity::PackedInternalState Q_bar{};
+      tensor<real_t, 3, 3> J_bar{};
+      __enzyme_autodiff<void>(
+        (void*)ComputeStressRef,  enzyme_const, &material, enzyme_dup, &H, &H_bar,
+        enzyme_dup, &Q, &Q_bar, enzyme_dup, &J, &J_bar, enzyme_const, w,
+        enzyme_dup, &sigma, &sigma_bar);
+
+      // H_bar[ij] = ∂sigma[0,0]/∂H[i,j]
+      // For this model, we expect the major symmetries in the tangent operator.
+      // Hence H_bar \approx sigma_dot_h
+
+      const double abs_tol = 1e-12;
+      const double rel_tol = 5e-6;
+      for (int i = 0; i < 3; i++) {
+        for (int j = 0; j < 3; j++) {
+          CHECK(H_bar[i][j] == MFEM_Approx(sigma_dot_h[i][j], abs_tol, rel_tol));
+        }
+      }
+    }
+}
+
+
+real_t nthroot_res(real_t x, tuple<real_t, real_t> p)
+{
+    auto [index, radicand] = p;
+    return std::pow(x, index) - radicand;
+}
+
+__attribute__((used))
+void* __enzyme_register_gradient_solver[3] = {
+  (void*)mfem::internal::SolveNewtonBisection_impl<nthroot_res, tuple<real_t, real_t>>,
+  (void*)mfem::internal::SolveNewtonBisection_impl_aug<nthroot_res, tuple<real_t, real_t>>,
+  (void*)mfem::internal::SolveNewtonBisection_impl_rev<nthroot_res, tuple<real_t, real_t>>
+};
+
+TEST_CASE("Univariate solver reverse mode derivative", "[univar]")
+{
+  auto mysqrt = [](real_t x) -> real_t
+    {
+      real_t x0 = x;
+      real_t index = 2.0;
+      real_t ub = std::max(1.0, x);
+      SolverSettings settings{1e-12, 1e-12, {0, ub}};
+      return SolveNewtonBisection<nthroot_res>(x0, make_tuple(index, x), settings);
+    };
+
+  real_t x = 2.0;
+  real_t dydx = __enzyme_autodiff<real_t>((void*)+mysqrt, enzyme_out, x);
+  CHECK(dydx == MFEM_Approx(0.5/std::sqrt(2.0)));
+}
+
+TEST_CASE("Univariate function solver robustness", "[univar]")
+{
+  SolverSettings settings{1e-12, 1e-12};
+
+  SECTION("Simple case")
+  {
+      auto Nthroot = [&settings](real_t x, real_t n) {
+          real_t x0 = std::max(x, 1.0);
+          settings.bounds = {0.0, x0};
+          return SolveNewtonBisection<nthroot_res>(x0, make_tuple(n, x), settings);
+      };
+      real_t x = 8.0;
+      real_t y = Nthroot(x, 3.0);
+      CHECK(y == MFEM_Approx(2.0));
+  }
+
+    SECTION("Stiff problem")
+    {
+        auto f = [](real_t x, real_t p) { return std::pow(x, p) - 1.0; };
+        real_t x0 = 0.1;
+        real_t p = 50;
+        settings.bounds = {0.0, 5.1};
+        real_t x = SolveNewtonBisection<+f>(x0, p, settings);
+        CHECK(x == MFEM_Approx(1.0));
+    }
+
+    SECTION("Works where Newton diverges")
+    {
+        auto f = [](double x, int) { return std::atan(x); };
+        real_t x0 = 1.5;
+        settings.bounds = {0.0, 2.0};
+        real_t x = SolveNewtonBisection<+f>(x0, int{}, settings);
+        CHECK(std::abs(x) == MFEM_Approx(0.0));
+    }
+}
+
+#endif // MFEM_USE_ENZYME

tests/unit/fem/test_face_restriction.cpp

@@ -117,3 +117,52 @@ TEST_CASE("Vector FE Face Restriction", "[FaceRestriction]")
    gf2 -= gf;
    REQUIRE(gf2.Normlinf() == MFEM_Approx(0.0));
 }
+
+#ifdef MFEM_USE_MPI
+
+TEST_CASE("L2 Face Restriction", "[FaceRestriction][Parallel]")
+{
+   const int dim = GENERATE(2, 3);
+   constexpr int nx = 3;
+   constexpr int order = 2;
+   constexpr int vdim = 2;
+   const Ordering::Type ordering = GENERATE(Ordering::byNODES, Ordering::byVDIM);
+
+   Mesh serial_mesh = MakeCartesianMesh(nx, dim);
+   ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
+
+   L2_FECollection fec(order, dim, BasisType::GaussLobatto);
+   ParFiniteElementSpace fes(&mesh, &fec, vdim, ordering);
+
+   auto *R = fes.GetFaceRestriction(ElementDofOrdering::LEXICOGRAPHIC,
+                                    FaceType::Interior);
+
+   Vector vals({1.0, 2.0});
+   VectorConstantCoefficient coeff(vals);
+
+   ParGridFunction gf(&fes);
+   gf.ProjectCoefficient(coeff);
+
+   Vector face_vec(R->Height());
+   R->Mult(gf, face_vec);
+
+   const int nf = mesh.GetNFbyType(FaceType::Interior);
+   const int face_dofs = fes.GetTypicalTraceElement()->GetDof();
+   auto h_face_vec = Reshape(face_vec.HostRead(), face_dofs, vdim, 2, nf);
+
+   for (int f = 0; f < nf; ++f)
+   {
+      for (int m = 0; m < 2; ++m)
+      {
+         for (int c = 0; c < vdim; ++c)
+         {
+            for (int i = 0; i < face_dofs; ++i)
+            {
+               REQUIRE(h_face_vec(i, c, m, f) == vals[c]);
+            }
+         }
+      }
+   }
+}
+
+#endif

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))