style

Merge branch 'master' into eigenSolverInterface
Merge branch 'master' of https://github.com/mfem/mfem
2026-02-10 12:48:56 -08:00 · 2026-02-10 10:47:01 -08:00 · 2026-02-10 10:46:20 -08:00 · 2026-02-10 10:45:28 -08:00 · 2026-02-07 13:14:15 -08:00 · 2026-02-07 13:14:00 -08:00
126 changed files with 9928 additions and 2177 deletions
@@ -313,6 +313,8 @@ miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
 miniapps/nurbs/nurbs_ex3
 miniapps/nurbs/nurbs_ex5
+miniapps/nurbs/nurbs_ex10
+miniapps/nurbs/nurbs_ex10p
 miniapps/nurbs/nurbs_ex11p
 miniapps/nurbs/nurbs_ex24
 miniapps/nurbs/nurbs_solenoidal
@@ -338,7 +340,14 @@ miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
 miniapps/nurbs/glvis_naca-cmesh.mesh
 miniapps/nurbs/Naca_cmesh
+miniapps/nurbs/nurbs_mesh_info
+miniapps/nurbs/k*_*.dat
 miniapps/nurbs/*-Surface.mesh
+miniapps/nurbs/*.mesh
+miniapps/nurbs/*.sol
+miniapps/nurbs/deformed.*
+miniapps/nurbs/elastic_energy.*
+miniapps/nurbs/velocity.*

 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -360,6 +369,7 @@ miniapps/shifted/lsf_integral
 miniapps/tools/display-basis
 miniapps/tools/load-dc
 miniapps/tools/convert-dc
+miniapps/tools/compare-dc
 miniapps/tools/gridfunction-bounds
 miniapps/tools/lor-transfer
 miniapps/tools/plor-transfer
@@ -11,6 +11,22 @@
 Version 4.9.1 (development)
 ===========================

+Discretization improvements
+---------------------------
+- Improved the gridfunction projection routines. Projections work for Scalar,
+  Vector and VectorFE, also NURBS versions. Optionally different types of
+  projections can be selected, default behaviour has not changed.
+
+Meshing improvements
+--------------------
+- Improved support for 1D NURBS meshes with variable order, including using
+  the patches construct for 1D NURBS meshes.
+
+New and updated examples and miniapps
+-------------------------------------
+- Electromagnetics/lorentz miniapp has been updated to leverage the ParticleSet
+  capability.
+

 Version 4.9, released on Dec 11, 2025
 =====================================
@@ -95,6 +111,23 @@ Linear and nonlinear solvers
  Filtering (AMGF), providing robust preconditioning for linear systems arising
  in constrained optimization problems such as frictionless contact.

+  Added 'GetResiduals' and 'GetFinalAbsResidualNorm' to 'HyprePCG',
+  'HypreGMRES', and 'HypreFGMRES' to get 'r' and '|r|_p'. Note that the latter
+  computes '|r|_p' from 'r' instead of returning a cached value like the
+  relative 'GetFinalResidualNorm'. These require Hypre >= 2.15.0.
+
+  Changed the default solver parameters for 'HyprePCG' to 'tol=1e-6' and
+  'max_iter=1000'. This matches the default parameters in Hypre 3.0.
+
+  Added various helper functions for querying/modifying Hypre solvers:
+  'HypreSmoother::GetType', 'HypreSmoother::GetSOROptions',
+  'HypreSmoother::GetPolyOptions', 'HypreSmoother::GetWindowParameters',
+  'HypreSmoother::IsOperatorSymmetric', 'HyprePCG::GetTol',
+  'HyprePCG::GetAbsTol', 'HyprePCG::GetMaxIter', 'HyprePCG::SetUseTwoNorm',
+  'HypreGMRES::GetTol', 'HypreGMRES::GetAbsTol', 'HypreGMRES::GetMaxIter',
+  'HypreGMRES::GetKDim', 'HypreFGMRES::GetTol', 'HypreFGMRES::GetMaxIter',
+  'HypreFGMRES::GetKDim', and 'HypreBoomerAMG::GetMaxIter'.
+
 GPU computing
 -------------
 - Added the 'gpu', 'raja-gpu', and 'ceed-gpu' backend aliases/shortcuts which
@@ -870,11 +870,12 @@ add_dependencies(exec
 #  - https://cmake.org/Bug/view.php?id=8438

 # Add a target to copy the mfem data directory to the build directory
-add_custom_command(OUTPUT data_is_copied
-  COMMAND ${CMAKE_COMMAND} -E copy_directory ${PROJECT_SOURCE_DIR}/data data
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying the data directory ...")
-add_custom_target(copy_data DEPENDS data_is_copied)
+# Implementable as a single copy_directory_if_different command w/ CMake >= 3.26
+file(GLOB DATA_FILES CONFIGURE_DEPENDS ${PROJECT_SOURCE_DIR}/data/*)
+add_custom_target(copy_data
+  COMMAND ${CMAKE_COMMAND} -E make_directory data
+  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${DATA_FILES} data
+  COMMENT "Syncing the data directory ...")
 # Add 'copy_data' as a prerequisite for all executables, if the source and the
 # build directories are not the same.
 if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
@@ -1006,6 +1007,10 @@ install(FILES
 install(EXPORT ${PROJECT_NAME_UC}Targets
    DESTINATION ${INSTALL_CMAKE_DIR})

+# Install the data directory if present, i.e. if the copy_data target is built
+install(DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/data
+  DESTINATION ${MFEM_INSTALL_DIR} OPTIONAL)
+
 #-------------------------------------------------------------------------------
 # Create 'config.mk' from 'config.mk.in' for the build and install locations and
 # define install rules for 'config.mk' and 'test.mk'
@@ -18,6 +18,7 @@
 # Some choices below are based on the OS type:
 NOTMAC := $(subst Darwin,,$(shell uname -s))

+ASTYLE_BIN = astyle
 ETAGS_BIN = $(shell command -v etags 2> /dev/null)
 EGREP_BIN = $(shell command -v egrep 2> /dev/null)

@@ -0,0 +1,86 @@
+MFEM NURBS mesh v1.0
+
+dimension
+1
+
+# Four segments with different NURBS orders, described via patches.
+elements
+4
+1 1 0 1
+2 1 2 3
+3 1 4 5
+4 1 6 7
+
+boundary
+0
+
+edges
+4
+0 0 1
+1 2 3
+2 4 5
+3 6 7
+
+vertices
+8
+
+patches
+
+# Patch 0: linear (order 1, 3 spans)
+knotvectors
+1
+1 4  0 0  .4 .6 1 1
+
+dimension
+2
+
+controlpoints
+0.0  0.0  1.0
+0.6  0.4  1.0
+0.4  0.6  1.0
+1.0  1.0  1.0
+
+# Patch 1: quadratic (order 2, 2 spans)
+knotvectors
+1
+2 4  0 0 0  .5 1 1 1
+
+dimension
+2
+
+controlpoints
+1.0  0.0  1.0
+1.9  0.0  1.21
+2.0  0.9  1.22
+2.0  1.0  1.0
+
+# Patch 2: cubic (order 3, 3 spans)
+knotvectors
+1
+3 6  0 0 0 0 .33 .66 1 1 1 1
+
+dimension
+2
+
+controlpoints
+2.0   0.0  1.0
+2.1   0.2  1.31
+3.5   0.4  1.32
+2.5   0.6  1.33
+2.9   1.0  1.34
+3.0   1.0  1.0
+
+# Patch 3: quartic (order 4, 1 span)
+knotvectors
+1
+4 5  0 0 0 0 0 1 1 1 1 1
+
+dimension
+2
+
+controlpoints
+3.0    0.0  1.0
+3.45   0.5  1.41
+3.50   1.0  1.42
+3.75   0.8  1.43
+4.0    0.0  1.0
@@ -0,0 +1,79 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+# Three segments with different NURBS orders, described via patches.
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+patches
+
+# Patch 0: linear (order 1, 2 control points)
+knotvectors
+1
+1 2  0 0  1 1
+
+dimension
+2
+
+controlpoints
+0.0  0.0  1.0
+1.0  1.0  1.0
+
+# Patch 1: quadratic (order 2, 3 control points)
+knotvectors
+1
+2 3  0 0 0  1 1 1
+
+dimension
+2
+
+controlpoints
+1.0  0.0   1.0
+1.02 1.02  1.2
+2.0  1.0   1.0
+
+# Patch 2: cubic (order 3, 4 control points)
+knotvectors
+1
+3 4  0 0 0 0  1 1 1 1
+
+dimension
+2
+
+controlpoints
+2.0   0.0   1.0
+2.03  0.83  1.31
+2.33  1.03  1.32
+3.0   1.0   1.0
+
@@ -0,0 +1,72 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+# Edge 0: linear (order 1, 2 control points)
+# Edge 1: quadratic (order 2, 3 control points)
+# Edge 2: cubic (order 3, 4 control points)
+knotvectors
+3
+1 2  0 0  1 1
+2 3  0 0 0  1 1 1
+3 4  0 0 0 0  1 1 1 1
+
+# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
+weights
+1
+1
+1
+1
+1
+1
+1.2
+1.31
+1.32
+
+FiniteElementSpace
+FiniteElementCollection: NURBS
+VDim: 2
+Ordering: 1
+
+0.0  0.0
+1.0  1.0
+1.0  0.0
+2.0  1.0
+2.0  0.0
+3.0  1.0
+1.02 1.02
+2.03 0.83
+2.33 1.03
@@ -0,0 +1,79 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+# Three segments with different NURBS orders, described via patches.
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+patches
+
+# Patch 0: linear (order 1, 2 control points)
+knotvectors
+1
+1 2  0 0  1 1
+
+dimension
+3
+
+controlpoints
+0.0  0.0  0.01 1.0
+1.0  1.0  1.01 1.0
+
+# Patch 1: quadratic (order 2, 3 control points)
+knotvectors
+1
+2 3  0 0 0  1 1 1
+
+dimension
+3
+
+controlpoints
+1.0  0.0   0.02 1.0
+1.02 1.02  0.52 1.2
+2.0  1.0   1.02 1.0
+
+# Patch 2: cubic (order 3, 4 control points)
+knotvectors
+1
+3 4  0 0 0 0  1 1 1 1
+
+dimension
+3
+
+controlpoints
+2.0   0.0   0.03 1.0
+2.03  0.83  0.33 1.31
+2.33  1.03  0.63 1.32
+3.0   1.0   1.03 1.0
+
@@ -0,0 +1,72 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+# Edge 0: linear (order 1, 2 control points)
+# Edge 1: quadratic (order 2, 3 control points)
+# Edge 2: cubic (order 3, 4 control points)
+knotvectors
+3
+1 2  0 0  1 1
+2 3  0 0 0  1 1 1
+3 4  0 0 0 0  1 1 1 1
+
+# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
+weights
+1
+1
+1
+1
+1
+1
+1.2
+1.31
+1.32
+
+FiniteElementSpace
+FiniteElementCollection: NURBS
+VDim: 3
+Ordering: 1
+
+0.0  0.0   0.01
+1.0  1.0   1.01
+1.0  0.0   0.02
+2.0  1.0   1.02
+2.0  0.0   0.03
+3.0  1.0   1.03
+1.02 1.02  0.52
+2.03 0.83  0.33
+2.33 1.03  0.63
@@ -190,6 +190,8 @@ namespace mfem {
 *  <a class="el" href="nurbs__ex1p_8cpp_source.html">1p</a>,
 *  <a class="el" href="nurbs__ex3_8cpp_source.html">3</a>,
 *  <a class="el" href="nurbs__ex5_8cpp_source.html">5</a>,
+ *  <a class="el" href="nurbs__ex10_8cpp_source.html">10</a>,
+ *  <a class="el" href="nurbs__ex10p_8cpp_source.html">10p</a>,
 *  <a class="el" href="nurbs__ex11p_8cpp_source.html">11p</a>, and
 *  <a class="el" href="nurbs__ex24_8cpp_source.html">24</a>,
 *   demonstrating howto perform NURBS-based Isogeometric Analysis.
@@ -198,6 +200,7 @@ namespace mfem {
 * - <a class="el" href="nurbs__curveint_8cpp_source.html">NURBS Interpolation</a>: NURBS interpolation of given geometry
 * - <a class="el" href="nurbs__naca__cmesh_8cpp_source.html">NURBS NACA Mesher</a>: generate NURBS based mesh around a NACA foil
 * - <a class="el" href="nurbs__printfunc_8cpp_source.html">NURBS Printer</a>: print the NURBS-basis
+ * - <a class="el" href="nurbs__mesh_info_8cpp_source.html">NURBS Mesh info</a>: print the info of a NURBS mesh
 *
 * <H3>Miniapps</H3>
 * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
@@ -119,7 +119,7 @@ int main(int argc, char *argv[])
   }

   LinearForm b(&fespace);
-   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));

   // 6. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the linear elasticity integrator with piece-wise
@@ -140,7 +140,7 @@ int main(int argc, char *argv[])
   }

   ParLinearForm b(&fespace);
-   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));

   // 6. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the linear elasticity integrator with piece-wise
@@ -9,6 +9,7 @@
 //               ex4 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex4 -m ../data/escher.mesh
 //               ex4 -m ../data/fichera.mesh -o 2 -hb
+//               ex4 -m ../data/fichera.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-q2.vtk
 //               ex4 -m ../data/fichera-q3.mesh -o 2 -sc
 //               ex4 -m ../data/square-disc-nurbs.mesh
@@ -18,6 +19,7 @@
 //               ex4 -m ../data/amr-quad.mesh
 //               ex4 -m ../data/amr-hex.mesh
 //               ex4 -m ../data/amr-hex.mesh -o 2 -hb
+//               ex4 -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
 //               ex4 -m ../data/ref-prism.mesh -o 1
 //               ex4 -m ../data/octahedron.mesh -o 1
@@ -25,6 +27,8 @@
 //
 // Device sample runs:
 //               ex4 -m ../data/star.mesh -pa -d cuda
+//               ex4 -m ../data/star.mesh -hb -ea -d cuda
+//               ex4 -m ../data/amr-quad.mesh -hb -ea -d cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-omp
 //               ex4 -m ../data/beam-hex.mesh -pa -d cuda
@@ -193,7 +197,7 @@ int main(int argc, char *argv[])
   cout << "Size of linear system: " << A->Height() << endl;

   // 11. Solve the linear system A X = B.
-   if (!pa)
+   if (!pa && (!ea || hybridization))
   {
 #ifndef MFEM_USE_SUITESPARSE
      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
@@ -9,6 +9,7 @@
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex4p -m ../data/escher.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb
+//               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/fichera-q2.vtk
 //               mpirun -np 4 ex4p -m ../data/fichera-q3.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/square-disc-nurbs.mesh -o 3
@@ -17,14 +18,18 @@
 //               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
 //               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
+//               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
+//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/ref-prism.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
 // Device sample runs:
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d cuda
+//               mpirun -np 4 ex4p -m ../data/star.mesh -ea -hb -d cuda
+//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -ea -hb -d cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-omp
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -pa -d cuda
@@ -230,7 +235,7 @@ int main(int argc, char *argv[])
   pcg->SetMaxIter(2000);
   pcg->SetPrintLevel(1);
   if (hybridization) { prec = new HypreBoomerAMG(*A.As<HypreParMatrix>()); }
-   else if (pa) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
+   else if (pa || ea) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
   else
   {
      ParFiniteElementSpace *prec_fespace =
@@ -825,14 +825,46 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
                                    Vector &b, OperatorHandle &A, Vector &X,
                                    Vector &B, int copy_interior)
 {
+   const SparseMatrix *P = fes->GetConformingProlongation();
+   const SparseMatrix *R = fes->GetConformingRestriction();
   if (ext)
   {
      if (hybridization)
      {
         FormSystemMatrix(ess_tdof_list, A);
-         ConstrainedOperator A_constrained(this, ess_tdof_list);
-         A_constrained.EliminateRHS(x, b);
-         hybridization->ReduceRHS(b, B);
+
+         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
+         {
+            Operator *op;
+            Operator::FormSystemOperator(ess_tdof_list, op);
+            return dynamic_cast<ConstrainedOperator*>(op);
+         }());
+         MFEM_ASSERT(A_constrained != nullptr, "");
+
+         Vector conf_b, conf_x;
+         if (P)
+         {
+            // Nonconforming
+            conf_b.SetSize(P->Width());
+            conf_x.SetSize(P->Width());
+            P->MultTranspose(b, conf_b);
+            R->Mult(x, conf_x);
+         }
+         else
+         {
+            // Conforming
+            conf_b.MakeRef(b, 0, b.Size());
+            conf_x.MakeRef(x, 0, x.Size());
+         }
+
+         A_constrained->EliminateRHS(conf_x, conf_b);
+
+         if (P)
+         {
+            R->MultTranspose(conf_b, b); // store eliminated rhs in b
+         }
+
+         hybridization->ReduceRHS(conf_b, B);
         X.SetSize(B.Size());
         X = 0.0;
      }
@@ -842,7 +874,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      }
      return;
   }
-   const SparseMatrix *P = fes->GetConformingProlongation();
   FormSystemMatrix(ess_tdof_list, A);

   // Transform the system and perform the elimination in B, based on the
@@ -878,7 +909,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      if (hybridization)
      {
         // Reduction to the Lagrange multipliers system
-         const SparseMatrix *R = fes->GetConformingRestriction();
         Vector conf_b(P->Width()), conf_x(P->Width());
         P->MultTranspose(b, conf_b);
         R->Mult(x, conf_x);
@@ -891,7 +921,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      else
      {
         // Variational restriction with P
-         const SparseMatrix *R = fes->GetConformingRestriction();
         B.SetSize(P->Width());
         P->MultTranspose(b, B);
         X.SetSize(R->Height());
@@ -1302,6 +1302,73 @@ real_t TraceCoefficient::Eval(ElementTransformation &T,
   return ma.Trace();
 }

+VectorComponentCoefficient::VectorComponentCoefficient(VectorCoefficient &A,
+                                                       int c)
+   : a(&A), va(A.GetVDim())
+{
+   SetComponent(c);
+}
+
+void VectorComponentCoefficient::SetComponent(int c)
+{
+   MFEM_ASSERT(c < a->GetVDim() && c >= 0,
+               "VectorComponentCoefficient:  "
+               "Index not in range.");
+
+   component = c;
+}
+
+void VectorComponentCoefficient::SetTime(real_t t)
+{
+   if (a) { a->SetTime(t); }
+   this->Coefficient::SetTime(t);
+}
+
+real_t VectorComponentCoefficient::Eval(ElementTransformation &T,
+                                        const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   return va[component];
+}
+
+MatrixComponentCoefficient::MatrixComponentCoefficient(MatrixCoefficient &A,
+                                                       int ri, int ci)
+   : a(&A), ma(A.GetHeight(), A.GetWidth())
+{
+   SetRowIndex(ri);
+   SetColumnIndex(ci);
+}
+
+void MatrixComponentCoefficient::SetRowIndex(int ri)
+{
+   MFEM_ASSERT(ri < a->GetHeight() && ri >= 0,
+               "MatrixComponentCoefficient:  "
+               "Row index not in range.");
+
+   row_idx = ri;
+}
+
+void MatrixComponentCoefficient::SetColumnIndex(int ci)
+{
+   MFEM_ASSERT(ci < a->GetWidth() && ci >= 0,
+               "MatrixComponentCoefficient:  "
+               "Column index not in range.");
+   col_idx = ci;
+}
+
+void MatrixComponentCoefficient::SetTime(real_t t)
+{
+   if (a) { a->SetTime(t); }
+   this->Coefficient::SetTime(t);
+}
+
+real_t MatrixComponentCoefficient::Eval(ElementTransformation &T,
+                                        const IntegrationPoint &ip)
+{
+   a->Eval(ma, T, ip);
+   return ma(row_idx,col_idx);
+}
+
 VectorSumCoefficient::VectorSumCoefficient(int dim)
   : VectorCoefficient(dim),
     ACoef(NULL), BCoef(NULL),
@@ -114,11 +114,10 @@ public:
   /// Construct the constant coefficient using a vector of constants.
   /** @a c should be a vector defined by attributes, so for region with
       attribute @a i @a c[i-1] is the coefficient in that region */
-   PWConstCoefficient(Vector &c)
-   { constants.SetSize(c.Size()); constants=c; }
+   PWConstCoefficient(const Vector &c) { UpdateConstants(c); }

   /// Update the constants with vector @a c.
-   void UpdateConstants(Vector &c) { constants.SetSize(c.Size()); constants=c; }
+   void UpdateConstants(const Vector &c) { constants = c; }

   /// Return a reference to the i-th constant
   real_t &operator()(int i) { return constants(i-1); }
@@ -1332,8 +1331,8 @@ public:
   /// Get the coefficient located at (i,j) in the matrix.
   Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }

-   /** @brief Set the coefficient located at (i,j) in the matrix.  By default by
-       default this will take ownership of the Coefficient passed in, but this
+   /** @brief Set the coefficient located at (i,j) in the matrix.  By default
+       this will take ownership of the Coefficient passed in, but this
       can be overridden with the @a own parameter. */
   void Set(int i, int j, Coefficient * c, bool own=true);

@@ -1873,6 +1872,85 @@ public:
               const IntegrationPoint &ip) override;
 };

+/// Scalar coefficient defined as component of a vector coefficient
+class VectorComponentCoefficient : public Coefficient
+{
+private:
+   VectorCoefficient *a = nullptr;
+
+   mutable Vector va;
+   int component;
+
+public:
+   /// Construct with a vector coefficient.
+   VectorComponentCoefficient(VectorCoefficient &A)
+      : a(&A), va(A.GetVDim()), component(0) {};
+
+   VectorComponentCoefficient(VectorCoefficient &A, int c);
+
+   /// Set the time for internally stored coefficients
+   void SetTime(real_t t) override;
+
+   /// Reset the vector coefficient
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+
+   /// Return the vector coefficient
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Set the component
+   void SetComponent(int c);
+
+   /// Return the component
+   int GetComponent() const { return component; }
+
+   /// Evaluate the trace coefficient at @a ip.
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
+};
+
+/// Scalar coefficient defined as component of a matrix coefficient
+class MatrixComponentCoefficient : public Coefficient
+{
+private:
+   MatrixCoefficient *a = nullptr;
+
+   mutable DenseMatrix ma;
+   int row_idx,col_idx;
+
+public:
+   MatrixComponentCoefficient(MatrixCoefficient &A)
+      : a(&A), ma(A.GetHeight(), A.GetWidth()), row_idx(0), col_idx(0) {};
+
+   /// Construct with the matrix coefficient.
+   MatrixComponentCoefficient(MatrixCoefficient &A, int ri, int ci);
+
+   /// Set the time for internally stored coefficients
+   void SetTime(real_t t) override;
+
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
+   /// Reset the index
+   void SetRowIndex(int ri);
+
+   /// Return the index
+   int GetRowIndex() const { return row_idx; }
+
+   /// Reset the index
+   void SetColumnIndex(int ci);
+
+   /// Return the index
+   int GetColumnIndex() const { return col_idx; }
+
+
+   /// Evaluate the trace coefficient at @a ip.
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
+};
+
 /// Vector coefficient defined as the linear combination of two vectors
 class VectorSumCoefficient : public VectorCoefficient
 {
@@ -12,7 +12,6 @@
 #include "dgmassinv.hpp"
 #include "bilinearform.hpp"
 #include "dgmassinv_kernels.hpp"
-#include "../general/forall.hpp"

 namespace mfem
 {
@@ -119,151 +118,6 @@ void DGMassInverse::Update()

 DGMassInverse::~DGMassInverse() = default;

-template<int DIM, int D1D, int Q1D>
-void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
-{
-   using namespace internal; // host/device kernel functions
-
-   const int NE = fes.GetNE();
-   const int d1d = m->dofs1D;
-   const int q1d = m->quad1D;
-
-   const int ND = static_cast<int>(pow(d1d, DIM));
-
-   const auto B = m->maps->B.Read();
-   const auto Bt = m->maps->Bt.Read();
-   const auto pa_data = m->pa_data.Read();
-   const auto dinv = diag_inv.Read();
-   auto r = r_.Write();
-   auto d = d_.Write();
-   auto z = z_.Write();
-   auto u = u_.ReadWrite();
-
-   const real_t RELTOL = rel_tol;
-   const real_t ABSTOL = abs_tol;
-   const int MAXIT = max_iter;
-   const bool IT_MODE = iterative_mode;
-   const bool CHANGE_BASIS = (d2q != nullptr);
-
-   // b is the right-hand side (if no change of basis, this just points to the
-   // incoming RHS vector, if we have to change basis, this points to the
-   // internal b2 vector where we put the transformed RHS)
-   const real_t *b;
-   // the following are non-null if we have to change basis
-   real_t *b2 = nullptr; // non-const access to b2
-   const real_t *b_orig = nullptr; // RHS vector in "original" basis
-   const real_t *d2q_B = nullptr; // matrix to transform initial guess
-   const real_t *q2d_B = nullptr; // matrix to transform solution
-   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
-   if (CHANGE_BASIS)
-   {
-      d2q_B = d2q->B.Read();
-      q2d_B = B_.Read();
-      q2d_Bt = Bt_.Read();
-
-      b2 = b2_.Write();
-      b_orig = b_.Read();
-      b = b2;
-   }
-   else
-   {
-      b = b_.Read();
-   }
-
-   static constexpr int NB = Q1D ? Q1D : 1; // block size
-
-   mfem::forall_2D(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
-   {
-      // Perform change of basis if needed
-      if (CHANGE_BASIS)
-      {
-         // Transform RHS
-         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
-         if (IT_MODE)
-         {
-            // Transform initial guess
-            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
-         }
-      }
-
-      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
-
-      // Compute first residual
-      if (IT_MODE)
-      {
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
-         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
-      }
-      else
-      {
-         // if not in iterative mode, use zero initial guess
-         const int BX = MFEM_THREAD_SIZE(x);
-         const int BY = MFEM_THREAD_SIZE(y);
-         const int bxy = BX*BY;
-         const auto B = ConstDeviceMatrix(b, ND, NE);
-         auto U = DeviceMatrix(u, ND, NE);
-         auto R = DeviceMatrix(r, ND, NE);
-         for (int i = tid; i < ND; i += bxy)
-         {
-            U(i, e) = 0.0;
-            R(i, e) = B(i, e);
-         }
-         MFEM_SYNC_THREAD;
-      }
-
-      DGMassPreconditioner(e, NE, ND, dinv, r, z);
-      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
-
-      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
-      if (nom < 0.0) { return; /* Not positive definite */ }
-      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
-      if (nom <= r0) { return; /* Converged */ }
-
-      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
-      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
-      if (den <= 0.0)
-      {
-         DGMassDot<NB>(e, NE, ND, d, d);
-         // d2 > 0 => not positive definite
-         if (den == 0.0) { return; }
-      }
-
-      // start iteration
-      int i = 1;
-      while (true)
-      {
-         const real_t alpha = nom/den;
-         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
-         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
-
-         DGMassPreconditioner(e, NE, ND, dinv, r, z);
-
-         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
-         if (betanom < 0.0) { return; /* Not positive definite */ }
-         if (betanom <= r0) { break; /* Converged */ }
-
-         if (++i > MAXIT) { break; }
-
-         const real_t beta = betanom/nom;
-         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
-         den = DGMassDot<NB>(e, NE, ND, d, z);
-         if (den <= 0.0)
-         {
-            DGMassDot<NB>(e, NE, ND, d, d);
-            // d2 > 0 => not positive definite
-            if (den == 0.0) { break; }
-         }
-         nom = betanom;
-      }
-
-      if (CHANGE_BASIS)
-      {
-         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
-      }
-   });
-}
-
 void DGMassInverse::Mult(const Vector &Mu, Vector &u) const
 {
   // Dispatch to templated version based on dim, d1d, and q1d.
@@ -306,23 +160,4 @@ DGMassInvKernels::DGMassInvKernels()
   k::Specialization<3,6,7>::Add();
 }

-/// @cond Suppress_Doxygen_warnings
-
-template <int DIM, int D1D, int Q1D>
-DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
-{
-   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
-}
-
-DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
-   int dim, int, int)
-{
-   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
-   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
-   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
-   else { MFEM_ABORT("Unsupported dimension."); }
-}
-
-/// @endcond
-
 } // namespace mfem
@@ -15,6 +15,7 @@
 #include "../linalg/kernels.hpp"
 #include "kernels.hpp"
 #include "integ/bilininteg_mass_kernels.hpp"
+#include "dgmassinv.hpp"

 namespace mfem
 {
@@ -333,6 +334,170 @@ void DGMassBasis(const int e,

 } // namespace internal

+template<int DIM, int D1D, int Q1D>
+void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
+{
+   using namespace internal; // host/device kernel functions
+
+   const int NE = fes.GetNE();
+   const int d1d = m->dofs1D;
+   const int q1d = m->quad1D;
+
+   const int ND = static_cast<int>(pow(d1d, DIM));
+
+   const auto B = m->maps->B.Read();
+   const auto Bt = m->maps->Bt.Read();
+   const auto pa_data = m->pa_data.Read();
+   const auto dinv = diag_inv.Read();
+   auto r = r_.Write();
+   auto d = d_.Write();
+   auto z = z_.Write();
+   auto u = u_.ReadWrite();
+
+   const real_t RELTOL = rel_tol;
+   const real_t ABSTOL = abs_tol;
+   const int MAXIT = max_iter;
+   const bool IT_MODE = iterative_mode;
+   const bool CHANGE_BASIS = (d2q != nullptr);
+
+   // b is the right-hand side (if no change of basis, this just points to the
+   // incoming RHS vector, if we have to change basis, this points to the
+   // internal b2 vector where we put the transformed RHS)
+   const real_t *b;
+   // the following are non-null if we have to change basis
+   real_t *b2 = nullptr; // non-const access to b2
+   const real_t *b_orig = nullptr; // RHS vector in "original" basis
+   const real_t *d2q_B = nullptr; // matrix to transform initial guess
+   const real_t *q2d_B = nullptr; // matrix to transform solution
+   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
+   if (CHANGE_BASIS)
+   {
+      d2q_B = d2q->B.Read();
+      q2d_B = B_.Read();
+      q2d_Bt = Bt_.Read();
+
+      b2 = b2_.Write();
+      b_orig = b_.Read();
+      b = b2;
+   }
+   else
+   {
+      b = b_.Read();
+   }
+
+   static constexpr int NB = Q1D ? Q1D : 1; // block size
+
+   mfem::forall_2D<NB*NB>(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
+   {
+      // Perform change of basis if needed
+      if (CHANGE_BASIS)
+      {
+         // Transform RHS
+         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
+         if (IT_MODE)
+         {
+            // Transform initial guess
+            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
+         }
+      }
+
+      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
+
+      // Compute first residual
+      if (IT_MODE)
+      {
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
+         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
+      }
+      else
+      {
+         // if not in iterative mode, use zero initial guess
+         const int BX = MFEM_THREAD_SIZE(x);
+         const int BY = MFEM_THREAD_SIZE(y);
+         const int bxy = BX*BY;
+         const auto B = ConstDeviceMatrix(b, ND, NE);
+         auto U = DeviceMatrix(u, ND, NE);
+         auto R = DeviceMatrix(r, ND, NE);
+         for (int i = tid; i < ND; i += bxy)
+         {
+            U(i, e) = 0.0;
+            R(i, e) = B(i, e);
+         }
+         MFEM_SYNC_THREAD;
+      }
+
+      DGMassPreconditioner(e, NE, ND, dinv, r, z);
+      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
+
+      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
+      if (nom < 0.0) { return; /* Not positive definite */ }
+      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
+      if (nom <= r0) { return; /* Converged */ }
+
+      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
+      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
+      if (den <= 0.0)
+      {
+         DGMassDot<NB>(e, NE, ND, d, d);
+         // d2 > 0 => not positive definite
+         if (den == 0.0) { return; }
+      }
+
+      // start iteration
+      int i = 1;
+      while (true)
+      {
+         const real_t alpha = nom/den;
+         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
+         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
+
+         DGMassPreconditioner(e, NE, ND, dinv, r, z);
+
+         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
+         if (betanom < 0.0) { return; /* Not positive definite */ }
+         if (betanom <= r0) { break; /* Converged */ }
+
+         if (++i > MAXIT) { break; }
+
+         const real_t beta = betanom/nom;
+         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
+         den = DGMassDot<NB>(e, NE, ND, d, z);
+         if (den <= 0.0)
+         {
+            DGMassDot<NB>(e, NE, ND, d, d);
+            // d2 > 0 => not positive definite
+            if (den == 0.0) { break; }
+         }
+         nom = betanom;
+      }
+
+      if (CHANGE_BASIS)
+      {
+         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
+      }
+   });
+}
+
+/// @cond Suppress_Doxygen_warnings
+
+template <int DIM, int D1D, int Q1D>
+inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
+{
+   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
+}
+
+inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
+   int dim, int, int)
+{
+   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
+   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
+   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
+   else { MFEM_ABORT("Unsupported dimension."); }
+}
+
+/// @endcond
+
 } // namespace mfem

 #endif
@@ -69,9 +69,9 @@ inline int ToLexOrdering2D(const int face_id, const int size1d, const int i)
 }

 /// @brief Given a face DOF index on a shared face, ordered lexicographically
-/// relative to element the element (where the local face is face_id), and
-/// return the corresponding face DOF index ordered lexicographically relative
-/// to the face itself.
+/// relative to the element (where the local face is face_id), return the
+/// corresponding face DOF index ordered lexicographically relative to the face
+/// itself.
 MFEM_HOST_DEVICE
 inline int PermuteFace2D(const int face_id, const int orientation,
                         const int size1d, const int index)
@@ -231,7 +231,7 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
   {
      for (int nd = 0; nd < dof; nd++)
      {
-         Laplacian[nd] = hess(nd,0) + hess(nd,4) + hess(nd,5);
+         Laplacian[nd] = hess(nd,0) + hess(nd,3) + hess(nd,5);
      }
   }
   else if (dim == 2)
@@ -268,11 +268,9 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
      scale[0] =   Gij(0,0);
      scale[1] = 2*Gij(0,1);
      scale[2] = 2*Gij(0,2);
-
-      scale[3] = 2*Gij(1,2);
-      scale[4] =   Gij(2,2);
-
-      scale[5] =   Gij(1,1);
+      scale[3] =   Gij(1,1);
+      scale[4] = 2*Gij(1,2);
+      scale[5] =   Gij(2,2);
   }
   else if (dim == 2)
   {
@@ -309,12 +307,12 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
      map[2] = 2;

      map[3] = 1;
-      map[4] = 5;
-      map[5] = 3;
+      map[4] = 3;
+      map[5] = 4;

      map[6] = 2;
-      map[7] = 3;
-      map[8] = 4;
+      map[7] = 4;
+      map[8] = 5;
   }
   else if (dim == 2)
   {
@@ -382,11 +380,7 @@ const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &ir,
   #pragma omp critical (DofToQuad)
 #endif
   {
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         d2q = dof2quad_array[i];
-         if (d2q->IntRule != &ir || d2q->mode != mode) { d2q = nullptr; }
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
      if (!d2q)
      {
 #ifdef MFEM_THREAD_SAFE
@@ -661,14 +655,22 @@ void ScalarFiniteElement::ScalarLocalL2Restriction(
 void NodalFiniteElement::CreateLexicographicFullMap(const IntegrationRule &ir)
 const
 {
+   // Get the FULL version of the map. This call contains omp critical region,
+   // so it is done before the critical region below.
+   auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);

 #if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
   #pragma omp critical (DofToQuad)
 #endif
   {
-      // Get the FULL version of the map.
-      auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);
-      //Undo the native ordering which is what FiniteElement::GetDofToQuad returns.
+      // If the new Dof2Quad is already present, e.g. added in a previous call
+      // or added by another omp thread, return.
+      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();
@@ -724,13 +726,7 @@ const DofToQuad &NodalFiniteElement::GetDofToQuad(const IntegrationRule &ir,
   #pragma omp critical (DofToQuad)
 #endif
   {
-      //Should make this loop a function of FiniteElement
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         d2q = dof2quad_array[i];
-         if (d2q->IntRule == &ir && d2q->mode == mode) { break; }
-         d2q = nullptr;
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
   }
   if (d2q) { return *d2q; }
   if (mode != DofToQuad::LEXICOGRAPHIC_FULL)
@@ -2631,15 +2627,7 @@ const DofToQuad &TensorBasisElement::GetTensorDofToQuad(
   #pragma omp critical (DofToQuad)
 #endif
   {
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         auto* d2q_ = dof2quad_array[i];
-         if (d2q_->IntRule == &ir && d2q_->mode == mode)
-         {
-            d2q = d2q_;
-            break;
-         }
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
      if (!d2q)
      {
         d2q = new DofToQuad;
@@ -44,7 +44,7 @@ public:
      NumBasisTypes   = 9   /**< Keep track of maximum types to prevent
                                 hard-coding */
   };
-   /** @brief If the input does not represents a valid BasisType, abort with an
+   /** @brief If the input does not represent a valid BasisType, abort with an
       error; otherwise return the input. */
   static int Check(int b_type)
   {
@@ -52,7 +52,7 @@ public:
                  "unknown BasisType: " << b_type);
      return b_type;
   }
-   /** @brief If the input does not represents a valid nodal BasisType, abort
+   /** @brief If the input does not represent a valid nodal BasisType, abort
       with an error; otherwise return the input. */
   static int CheckNodal(int b_type)
   {
@@ -222,6 +222,12 @@ public:

   /// Returns absolute value of the maps
   DofToQuad Abs() const;
+
+   /// Auxiliary function for searching DofToQuad arrays.
+   static inline DofToQuad *SearchArray(
+      const Array<DofToQuad*> &dof2quad_array,
+      const IntegrationRule &ir,
+      DofToQuad::Mode mode);
 };

 /// Describes the function space on each element
@@ -407,6 +413,7 @@ public:
   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
       part of the Hessian of one shape function.
       The order in 2D is {u_xx, u_xy, u_yy}.
+       The order in 3D is {u_xx, u_xy, u_xz, u_yy, u_yz, u_zz}.
       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &Hessian) const;
@@ -1120,7 +1127,7 @@ public:
      return GetPoints(p, btype, on_device);
   }

-   /// Get coordinates of a closed (GaussLegendre) set of points if degree @a p
+   /// Get coordinates of a closed (GaussLobatto) set of points if degree @a p
   const real_t *ClosedPoints(const int p,
                              const int btype = BasisType::GaussLobatto,
                              bool on_device = false)
@@ -1376,6 +1383,21 @@ public:
 void InvertLinearTrans(ElementTransformation &trans,
                       const IntegrationPoint &pt, Vector &x);

+
+// static inline method
+inline DofToQuad *DofToQuad::SearchArray(
+   const Array<DofToQuad*> &dof2quad_array,
+   const IntegrationRule &ir,
+   DofToQuad::Mode mode)
+{
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      DofToQuad *d2q = dof2quad_array[i];
+      if (d2q->IntRule == &ir && d2q->mode == mode) { return d2q; }
+   }
+   return nullptr;
+}
+
 } // namespace mfem

 #endif
@@ -60,6 +60,12 @@ void Linear1DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(1,0) =  1.;
 }

+void Linear1DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}
+
 Linear2DFiniteElement::Linear2DFiniteElement()
   : NodalFiniteElement(2, Geometry::TRIANGLE, 3, 1)
 {
@@ -87,6 +93,11 @@ void Linear2DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(2,0) =  0.; dshape(2,1) =  1.;
 }

+void Linear2DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}

 BiLinear2DFiniteElement::BiLinear2DFiniteElement()
   : NodalFiniteElement(2, Geometry::SQUARE, 4, 1, FunctionSpace::Qk)
@@ -1256,6 +1267,12 @@ void Linear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   }
 }

+void Linear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}
+
 void Linear3DFiniteElement::GetFaceDofs (int face, int **dofs, int *ndofs)
 const
 {
@@ -1632,6 +1649,37 @@ void TriLinear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
   dshape(7,2) =   ox *  y;
 }

+void TriLinear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                           DenseMatrix &h) const
+{
+   real_t x = ip.x, y = ip.y, z = ip.z;
+   real_t ox = 1.-x, oy = 1.-y, oz = 1.-z;
+
+   h(0,0) = 0.;   h(0,1) =  oz;   h(0,2) = oy;
+   h(0,3) = 0.;   h(0,4) =  ox;   h(0,5) = 0.;
+
+   h(1,0) = 0.;   h(1,1) = -oz;   h(1,2) = -oy;
+   h(1,3) = 0.;   h(1,4) =  x;    h(1,5) = 0.;
+
+   h(2,0) = 0.;   h(2,1) =  oz;   h(2,2) = -y;
+   h(2,3) = 0.;   h(2,4) =  -x;   h(2,5) = 0.;
+
+   h(3,0) = 0.;   h(3,1) = -oz;   h(3,2) = y;
+   h(3,3) = 0.;   h(3,4) = -ox;   h(3,5) = 0.;
+
+   h(4,0) = 0.;   h(4,1) =  z;    h(4,2) = -oy;
+   h(4,3) = 0.;   h(4,4) = -ox;   h(4,5) = 0.;
+
+   h(5,0) = 0.;   h(5,1) = -z;    h(5,2) = oy;
+   h(5,3) = 0.;   h(5,4) = -x;    h(5,5) = 0.;
+
+   h(6,0) = 0.;   h(6,1) =  z;    h(6,2) = y;
+   h(6,3) = 0.;   h(6,4) =  x;    h(6,5) = 0.;
+
+   h(7,0) = 0.;   h(7,1) = -z;    h(7,2) = -y;
+   h(7,3) = 0.;   h(7,4) = ox;    h(7,5) = 0.;
+}
+

 P0SegmentFiniteElement::P0SegmentFiniteElement(int Ord)
   : NodalFiniteElement(1, Geometry::SEGMENT, 1, Ord)   // default Ord = 0
@@ -50,6 +50,8 @@ public:
       contains the derivative of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
 };

 /// A 2D linear element on triangle with nodes at the vertices of the triangle
@@ -70,6 +72,8 @@ public:
       so that each row contains the derivatives of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }
 };
@@ -404,6 +408,9 @@ public:
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;

+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
+
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }

@@ -445,7 +452,8 @@ public:
       so that each row contains the derivatives of one shape function */
   void CalcDShape(const IntegrationPoint &ip,
                   DenseMatrix &dshape) const override;
-
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.0; dofs(vertex) = 1.0; }
 };
@@ -84,6 +84,46 @@ void NURBS1DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   add(1.0, hess, (-d2sum + 2*dsum*dsum*sum)*sum*sum, shape_x, hess);
 }

+void NURBS1DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+
+   for (int i = 0; i <= order; i++)
+   {
+      real_t kx = kv[0]->GetBotella(ijk[0] + i);
+      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
+      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
+
+      Trans.SetIntPoint(&ip);
+      dofs(i) = coeff.Eval(Trans, ip);
+   }
+}
+
+void NURBS1DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+
+   for (int i = 0; i <= order; i++)
+   {
+      real_t kx = kv[0]->GetBotella(ijk[0] + i);
+      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
+      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
+
+      Trans.SetIntPoint(&ip);
+      vc.Eval(x, Trans, ip);
+      for (int j = 0; j < x.Size(); j++)
+      {
+         dofs(dof*j+i) = x(j);
+      }
+   }
+}
+

 void NURBS2DFiniteElement::SetOrder() const
 {
@@ -215,6 +255,63 @@ void NURBS2DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   }
 }

+void NURBS2DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+   for (int o = 0, j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         dofs(o) = coeff.Eval(Trans, ip);
+      }
+   }
+}
+
+void NURBS2DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+   for (int o = 0, j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+         for (int v = 0; v < x.Size(); v++)
+         {
+            dofs(dof*v+o) = x(v);
+         }
+      }
+   }
+}

 void NURBS3DFiniteElement::SetOrder() const
 {
@@ -348,11 +445,10 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
            d2sum[0] += ( hessian(o,0) = d2sx*sy*sz*weights(o) );
            d2sum[1] += ( hessian(o,1) = dsx*dsy*sz*weights(o) );
            d2sum[2] += ( hessian(o,2) = dsx*sy*dsz*weights(o) );
+            d2sum[3] += ( hessian(o,3) = sx*d2sy*sz*weights(o) );
+            d2sum[4] += ( hessian(o,4) = sx*dsy*dsz*weights(o) );
+            d2sum[5] += ( hessian(o,5) = sx*sy*d2sz*weights(o) );

-            d2sum[3] += ( hessian(o,3) = sx*dsy*dsz*weights(o) );
-
-            d2sum[4] += ( hessian(o,4) = sx*sy*d2sz*weights(o) );
-            d2sum[5] += ( hessian(o,5) = sx*d2sy*sz*weights(o) );
         }
      }
   }
@@ -401,6 +497,85 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
   }
 }

+void NURBS3DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+
+   for (int o = 0, k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            dofs(o) = coeff.Eval(Trans, ip);
+         }
+      }
+   }
+}
+
+void NURBS3DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+
+   for (int o = 0, k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+            for (int v = 0; v < x.Size(); v++)
+            {
+               dofs(dof*v+o) = x(v);
+            }
+         }
+      }
+   }
+}

 void NURBS_HDiv2DFiniteElement::SetOrder() const
 {
@@ -517,6 +692,63 @@ void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
   }
 }

+void NURBS_HDiv2DFiniteElement::Project(VectorCoefficient &vc,
+                                        ElementTransformation &Trans,
+                                        Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 2, "");
+   Vector x(2), mx(2);
+   IntegrationPoint ip;
+   int o = 0;
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 2;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.AdjugateJacobian().Mult(x,mx);
+         dofs(o) = mx(0);
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.AdjugateJacobian().Mult(x,mx);
+         dofs(o) = mx(1);
+      }
+   }
+}
+
 NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -696,6 +928,120 @@ void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
   }
 }

+
+void NURBS_HDiv3DFiniteElement::Project(VectorCoefficient &vc,
+                                        ElementTransformation &Trans,
+                                        Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 3, "");
+   Vector x(2), mx(3);
+   IntegrationPoint ip;
+
+   int o = 0;
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 2)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(0);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(1);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(2);
+         }
+      }
+   }
+
+}
+
+
 NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -817,13 +1163,68 @@ void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
   }
 }

+void NURBS_HCurl2DFiniteElement::Project(VectorCoefficient &vc,
+                                         ElementTransformation &Trans,
+                                         Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 2, "");
+   Vector x(2), xm(2);
+   IntegrationPoint ip;
+   int i, j, o;
+   for (o = 0, j = 0; j <= orders[1]+1; j++)
+   {
+      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+      for (i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.Jacobian().MultTranspose(x,xm);
+         dofs(o) = xm(0);
+      }
+   }
+
+   for (j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 2;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (i = 0; i <= orders[0]+1; i++, o++)
+      {
+         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.Jacobian().MultTranspose(x,xm);
+         dofs(o) = xm(1);
+      }
+   }
+}
+
 NURBS_HCurl2DFiniteElement::~NURBS_HCurl2DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
   if (kv1[1]) { delete kv1[1]; }
 }

-
 void NURBS_HCurl3DFiniteElement::SetOrder() const
 {
   orders[0] = kv[0]->GetOrder();
@@ -1003,11 +1404,124 @@ void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
            curl_shape(o,0) = shape1_x(i)*dsy1_sz;
            curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
            curl_shape(o,2) = 0.0;
+
         }
      }
   }
 }

+void NURBS_HCurl3DFiniteElement::Project(VectorCoefficient &vc,
+                                         ElementTransformation &Trans,
+                                         Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 3, "");
+   Vector x(3), xm(3);
+   IntegrationPoint ip;
+
+   int o = 0;
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 1)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(0);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 2)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(1);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 2)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(2);
+         }
+      }
+   }
+
+}
+
+
 NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
 {
   if (kv1[0]) { delete kv1[0]; }
@@ -86,6 +86,18 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };

 /// An arbitrary order 2D NURBS element on a square
@@ -121,6 +133,18 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };

 /// An arbitrary order 3D NURBS element on a cube
@@ -161,6 +185,18 @@ public:
                   DenseMatrix &dshape) const override;
   void CalcHessian (const IntegrationPoint &ip,
                     DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };


@@ -242,6 +278,13 @@ public:
   void CalcDivShape(const IntegrationPoint &ip,
                     Vector &divshape) const override;

+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
   ~NURBS_HDiv2DFiniteElement();
 };

@@ -336,6 +379,13 @@ public:
   void CalcDivShape(const IntegrationPoint &ip,
                     Vector &divshape) const override;

+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
   ~NURBS_HDiv3DFiniteElement();
 };

@@ -415,6 +465,13 @@ public:
   void CalcCurlShape(const IntegrationPoint &ip,
                      DenseMatrix &curl_shape) const override;

+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
   ~NURBS_HCurl2DFiniteElement();
 };

@@ -506,6 +563,13 @@ public:
   void CalcCurlShape(const IntegrationPoint &ip,
                      DenseMatrix &curl_shape) const override;

+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
   ~NURBS_HCurl3DFiniteElement();
 };

@@ -111,36 +111,36 @@ public:
   | :------: | :---: | :---: | :-------: | :-----: | :---: |
   | H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
   | H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
-   | H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
+   | H1Pos_[DIM]_[ORDER] | H1 | * | 2 | VALUE | H1 nodal elements |
   | H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
   | H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
   | ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
   | ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
-   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
-   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
+   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
+   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * / * | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
   | ND_R1D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
   | ND_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
   | ND_R2D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
   | ND_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
   | RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
   | RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
-   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
   | RT_R1D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
   | RT_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
   | RT_R2D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
   | RT_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
-   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
+   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | VALUE | Discontinuous L2 elements |
   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
-   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
+   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | INTEGRAL | Discontinuous L2 elements |
   | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | * | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
   | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | * | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
   | NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
   | LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
   | CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
@@ -172,7 +172,7 @@ public:
   | :------: | :--------: |
   | [DIM]    | Dimension of the elements (1D, 2D, 3D) |
   | [ORDER]  | Approximation order of the elements (P0, P1, P2, ...) |
-   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
+   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1-GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform 6-Serendipity 7-ClosedGL 8-IntegratedGLL) |
   | [OBTYPE] | Open BasisType of the element for elements which have both types |
   | [CBTYPE] | Closed BasisType of the element for elements which have both types |

@@ -1516,36 +1516,76 @@ const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
   const bool is_dg_space = IsDGSpace();
   const L2FaceValues m = (is_dg_space && mul==L2FaceValues::DoubleValued) ?
                          L2FaceValues::DoubleValued : L2FaceValues::SingleValued;
-   key_face key = std::make_tuple(is_dg_space, f_ordering, type, m);
+   auto key = std::make_tuple(is_dg_space, f_ordering, type, m);
   auto itr = L2F.find(key);
   if (itr != L2F.end())
   {
-      return itr->second;
+      return itr->second.get();
   }
   else
   {
-      FaceRestriction *res;
+      std::unique_ptr<FaceRestriction> res;
      if (is_dg_space)
      {
         if (Conforming())
         {
-            res = new L2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new L2FaceRestriction(*this, f_ordering, type, m));
         }
         else
         {
-            res = new NCL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new NCL2FaceRestriction(*this, f_ordering, type, m));
         }
      }
      else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
      {
-         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
+         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
      }
      else
      {
-         res = new ConformingFaceRestriction(*this, f_ordering, type);
+         res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
      }
-      L2F[key] = res;
-      return res;
+      return L2F.emplace(key, std::move(res)).first->second.get();
+   }
+}
+
+const InterpolationManager &FiniteElementSpace::GetInterpolationManager(
+   ElementDofOrdering f_ordering, FaceType type) const
+{
+   const auto key = make_tuple(f_ordering, type);
+
+   auto it = interpolations.find(key);
+   if (it != interpolations.end())
+   {
+      return *it->second;
+   }
+   else
+   {
+      auto interp = make_unique<InterpolationManager>(*this, f_ordering, type);
+
+      int face_idx = 0;
+      for (int f = 0; f < mesh->GetNumFacesWithGhost(); ++f)
+      {
+         Mesh::FaceInformation face = mesh->GetFaceInformation(f);
+         if (!face.IsOfFaceType(type) || face.IsNonconformingCoarse())
+         {
+            continue;
+         }
+         if (face.IsConforming() || face.IsBoundary())
+         {
+            interp->RegisterFaceConformingInterpolation(face, face_idx);
+         }
+         else
+         {
+            interp->RegisterFaceCoarseToFineInterpolation(face, face_idx);
+         }
+         ++face_idx;
+      }
+
+      // Transform the interpolation matrix map into contiguous memory.
+      interp->LinearizeInterpolatorMapIntoVector();
+      interp->InitializeNCInterpConfig();
+
+      return *interpolations.emplace(key, std::move(interp)).first->second;
   }
 }

@@ -3969,11 +4009,8 @@ void FiniteElementSpace::Destroy()
      delete E2Q_array[i];
   }
   E2Q_array.SetSize(0);
-   for (auto &x : L2F)
-   {
-      delete x.second;
-   }
   L2F.clear();
+   interpolations.clear();
   for (int i = 0; i < E2IFQ_array.Size(); i++)
   {
      delete E2IFQ_array[i];
@@ -13,6 +13,7 @@
 #define MFEM_FESPACE

 #include "../config/config.hpp"
+#include "../general/hash_util.hpp"
 #include "../linalg/ordering.hpp"
 #include "../linalg/sparsemat.hpp"
 #include "../mesh/mesh.hpp"
@@ -320,18 +321,11 @@ protected:
   mutable OperatorHandle L2E_nat, L2E_lex;
   /// The face restriction operators, see GetFaceRestriction().
   using key_face = std::tuple<bool, ElementDofOrdering, FaceType, L2FaceValues>;
-   struct key_hash
-   {
-      std::size_t operator()(const key_face& k) const
-      {
-         return std::get<0>(k)
-                + 2 * (int)std::get<1>(k)
-                + 4 * (int)std::get<2>(k)
-                + 8 * (int)std::get<3>(k);
-      }
-   };
-   using map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>;
-   mutable map_L2F L2F;
+   mutable std::unordered_map<key_face,std::unique_ptr<FaceRestriction>,
+           TupleHasher> L2F;
+
+   mutable std::unordered_map<std::tuple<ElementDofOrdering,FaceType>,
+           std::unique_ptr<InterpolationManager>, TupleHasher> interpolations;

   mutable Array<QuadratureInterpolator*> E2Q_array;
   mutable Array<FaceQuadratureInterpolator*> E2IFQ_array;
@@ -751,6 +745,9 @@ public:
      ElementDofOrdering f_ordering, FaceType,
      L2FaceValues mul = L2FaceValues::DoubleValued) const;

+   const InterpolationManager &GetInterpolationManager(
+      ElementDofOrdering f_ordering, FaceType type) const;
+
   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
       quadrature point values and/or derivatives (Q-vectors). */
   /** An E-vector represents the element-wise discontinuous version of the FE
@@ -2352,52 +2352,83 @@ void GridFunction::ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
   }
 }

-void GridFunction::ProjectCoefficient(Coefficient &coeff)
+void GridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
   DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
   DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector vals;

   if (delta_c == NULL)
   {
      if (fes->GetNURBSext() == NULL)
      {
-         Array<int> vdofs;
-         Vector vals;
-
-         for (int i = 0; i < fes->GetNE(); i++)
+         switch (type)
         {
-            fes->GetElementVDofs(i, vdofs, doftrans);
-            vals.SetSize(vdofs.Size());
-            fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
-            doftrans.TransformPrimal(vals);
-            SetSubVector(vdofs, vals);
+            case ProjectType::ELEMENT_L2:
+               ProjectCoefficientElementL2(coeff);
+               return;
+            case ProjectType::GLOBAL_L2:
+               ProjectCoefficientGlobalL2(coeff);
+               return;
+            default:
+               for (int i = 0; i < fes->GetNE(); i++)
+               {
+                  fes->GetElementVDofs(i, vdofs, doftrans);
+                  vals.SetSize(vdofs.Size());
+                  fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+                  doftrans.TransformPrimal(vals);
+                  SetSubVector(vdofs, vals);
+               }
         }
      }
      else
      {
-         // Define and assemble linear form
-         LinearForm b(fes);
-         b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
-         b.Assemble();
+         switch (type)
+         {
+            case ProjectType::DEFAULT:
+            case ProjectType::ELEMENT_L2:
+               ProjectCoefficientElementL2(coeff);
+               return;
+            case ProjectType::GLOBAL_L2:
+               ProjectCoefficientGlobalL2(coeff);
+               return;
+            case ProjectType::ELEMENT:
+               constexpr real_t signal = std::numeric_limits<real_t>::min();

-         // Define and assemble bilinear form
-         BilinearForm a(fes);
-         a.AddDomainIntegrator(new MassIntegrator());
-         a.Assemble();
+               for (int i = 0; i < fes->GetNE(); i++)
+               {
+                  fes->GetElementVDofs(i, vdofs, doftrans);
+                  vals.SetSize(vdofs.Size());
+                  vals = signal;

-         // Set solver and preconditioner
-         SparseMatrix A(a.SpMat());
-         GSSmoother  prec(A);
-         CGSolver cg;
-         cg.SetOperator(A);
-         cg.SetPreconditioner(prec);
-         cg.SetRelTol(1e-12);
-         cg.SetMaxIter(1000);
-         cg.SetPrintLevel(0);
+                  fes->GetFE(i)->Project(coeff,
+                                         *fes->GetElementTransformation(i),
+                                         vals);
+                  doftrans.TransformPrimal(vals);

-         // Solve and get solution
-         *this = 0.0;
-         cg.Mult(b,*this);
+                  // Remove undefined dofs
+                  // The knot location (either Botella, Demko or Greville point)
+                  // where the NURBS dof are evaluated might fall outside of the
+                  // domain of the element. In that case the value is not set, and
+                  // the value remains the signal value.
+                  int s = 0;
+                  for (int ii = 0; ii < vals.Size(); ii++)
+                  {
+                     if (vals[ii] != signal)
+                     {
+                        vdofs[s] = vdofs[ii];
+                        vals(s) = vals(ii);
+                        s++;
+                     }
+                  }
+                  vdofs.SetSize(s);
+                  vals.SetSize(s);
+
+                  // Add reduced dofs to global vector
+                  SetSubVector(vdofs, vals);
+               }
+         }
      }
   }
   else
@@ -2410,6 +2441,167 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff)
   }
 }

+void GridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff, real_t rtol,
+                                              int iter)
+{
+   // Define and assemble linear form
+   LinearForm b(fes);
+   b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+   b.Assemble();
+
+   // Define and assemble bilinear form
+   BilinearForm a(fes);
+   a.AddDomainIntegrator(new MassIntegrator());
+   a.Assemble();
+
+   // Set solver and preconditioner
+   SparseMatrix A(a.SpMat());
+   GSSmoother  prec(A);
+   CGSolver cg;
+   cg.SetOperator(A);
+   cg.SetPreconditioner(prec);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+
+   // Solve and get solution
+   *this = 0.0;
+   cg.Mult(b,*this);
+}
+
+void GridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
+{
+   Vector Va;
+   ProjectCoefficientElementL2_(coeff, *this, Va);
+   (*this) /= Va;
+}
+
+void GridFunction::ProjectCoefficientElementL2_(Coefficient &coeff,
+                                                Vector &x, Vector &Va)
+{
+   DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector shape,shape2, elvect, elwght;
+   DenseMatrix elmat;
+   Va.SetSize(fes->GetNDofs() );
+   x.SetSize(fes->GetNDofs() );
+   Va = 0.0;
+   x = 0.0;
+
+   if (fes->GetNURBSext() == NULL)
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         shape.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            real_t val = coeff.Eval(tr, ip);
+
+            el.CalcPhysShape(tr, shape);
+
+            elvect.Add(wght * val, shape);
+            elwght.Add(wght, shape);
+            AddMult_a_VVt(wght, shape, elmat);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add reduced dofs to global vector
+         x.AddElementVector(vdofs, elvect);
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+   else
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetDim();
+         int p = el.GetOrder();
+         L2_FECollection fe_coll(p,  dim);
+         //H1_FECollection fe_coll(p,  dim, BasisType::Positive);
+         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
+         MFEM_ASSERT(el2.GetDof() == dof, "Element dofs do not match.");
+
+         shape.SetSize(dof);
+         shape2.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            real_t val = coeff.Eval(tr, ip);
+            el.CalcPhysShape(tr, shape);
+            el2.CalcPhysShape(tr, shape2);
+
+            elvect.Add(wght * val, shape2);
+            elwght.Add(wght, shape);
+            AddMult_a_VVt(wght, shape2, elmat);
+         }
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix 2");
+         }
+         // Map to NURBS
+         DenseMatrix I;
+         el2.Project(el,tr,I);
+         if (!LinearSolve(I, elvect.GetData(),1e-32))
+         {
+            MFEM_WARNING("Error in inverting element local matrix 3");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add reduced dofs to global vector
+         x.AddElementVector(vdofs, elvect);
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+}
+
 void GridFunction::ProjectCoefficient(
   Coefficient &coeff, Array<int> &dofs, int vd)
 {
@@ -2434,49 +2626,318 @@ void GridFunction::ProjectCoefficient(
   }
 }

-void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
+void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
+                                      ProjectType type)
 {
+   Array<int> vdofs;
+   Vector vals;
   DofTransformation doftrans;
+
   if (fes->GetNURBSext() == NULL)
   {
-      int i;
-      Array<int> vdofs;
-      Vector vals;
-
-      for (i = 0; i < fes->GetNE(); i++)
+      switch (type)
      {
-         fes->GetElementVDofs(i, vdofs, doftrans);
-         vals.SetSize(vdofs.Size());
-         fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-         doftrans.TransformPrimal(vals);
-         SetSubVector(vdofs, vals);
+         case ProjectType::ELEMENT_L2:
+            ProjectCoefficientElementL2(vcoeff);
+            return;
+         case ProjectType::GLOBAL_L2:
+            ProjectCoefficientGlobalL2(vcoeff);
+            return;
+         default:
+            for (int i = 0; i < fes->GetNE(); i++)
+            {
+               fes->GetElementVDofs(i, vdofs, doftrans);
+               vals.SetSize(vdofs.Size());
+               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+               doftrans.TransformPrimal(vals);
+               SetSubVector(vdofs, vals);
+            }
      }
   }
   else
   {
-      // Define and assemble linear form
-      LinearForm b(fes);
+      switch (type)
+      {
+         case ProjectType::DEFAULT:
+         case ProjectType::ELEMENT_L2:
+            ProjectCoefficientElementL2(vcoeff);
+            return;
+         case ProjectType::GLOBAL_L2:
+            ProjectCoefficientGlobalL2(vcoeff);
+            return;
+         case ProjectType::ELEMENT:
+            constexpr real_t signal = std::numeric_limits<real_t>::min();
+            for (int i = 0; i < fes->GetNE(); i++)
+            {
+               fes->GetElementVDofs(i, vdofs, doftrans);
+               vals.SetSize(vdofs.Size());
+               vals = signal;
+               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+               doftrans.TransformPrimal(vals);
+               // Remove undefined dofs
+               // The knot location (either Botella, Demko or Greville point)
+               // where the NURBS dof are evaluated might fall outside of the
+               // domain of the element. In that case the value is not set, and
+               // the value remains the signal value.
+               int s = 0;
+               for (int ii = 0; ii < vals.Size(); ii++)
+               {
+                  if (vals[ii] != signal)
+                  {
+                     vdofs[s] = vdofs[ii];
+                     vals(s) = vals(ii);
+                     s++;
+                  }
+               }
+               vdofs.SetSize(s);
+               vals.SetSize(s);
+
+               // Add reduced dofs to global vector
+               SetSubVector(vdofs, vals);
+            }
+      }
+   }
+}
+
+void GridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                              real_t rtol, int iter)
+{
+   // Define and assemble linear form
+   LinearForm b(fes);
+   BilinearForm a(fes);
+
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
-      b.Assemble();
-
-      // Define and assemble bilinear form
-      BilinearForm a(fes);
      a.AddDomainIntegrator(new VectorFEMassIntegrator());
-      a.Assemble();
+   }
+   else
+   {
+      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorMassIntegrator());
+   }
+   a.Assemble();
+   b.Assemble();

-      // Set solver and preconditioner
-      SparseMatrix A(a.SpMat());
-      GSSmoother  prec(A);
-      CGSolver cg;
-      cg.SetOperator(A);
-      cg.SetPreconditioner(prec);
-      cg.SetRelTol(1e-12);
-      cg.SetMaxIter(1000);
-      cg.SetPrintLevel(0);
+   // Set solver and preconditioner
+   SparseMatrix A(a.SpMat());
+   GSSmoother  prec(A);
+   CGSolver cg;
+   cg.SetOperator(A);
+   cg.SetPreconditioner(prec);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);

-      // Solve and get solution
-      *this = 0.0;
-      cg.Mult(b,*this);
+   // Solve and get solution
+   *this = 0.0;
+   cg.Mult(b,*this);
+}
+
+void GridFunction::ProjectCoefficientElementL2_(VectorCoefficient &vcoeff,
+                                                Vector &x, Vector &Va)
+{
+   DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector shapel2, elvect, elwght, val;
+   DenseMatrix  shape, elmat;
+   Va.SetSize(Size());
+   x.SetSize(Size());
+   Va = 0.0;
+   x = 0.0;
+
+   if (fes->GetNURBSext() == NULL)
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementVDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetRangeDim();
+         shape.SetSize(dof,dim);
+         shapel2.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            vcoeff.Eval(val, tr, ip);
+            val *= wght;
+
+            el.CalcPhysVShape(tr, shape);
+
+            shape.AddMult (val, elvect);
+            AddMult_a_AAt(wght, shape, elmat);
+
+            shape.GetRowl2(shapel2);
+            elwght.Add(wght, shapel2);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add to global vector
+         x.AddElementVector(vdofs, elvect);
+
+         // Add to weight vector -- no need for an orientation
+         for (int i = 0; i < vdofs.Size(); i++)
+         {
+            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
+         }
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+   else
+   {
+      DenseMatrix partelmat;
+      Vector shape2;
+
+      if (fes->GetTypicalFE()->GetOrder() >= 6 )
+      {
+         MFEM_WARNING("This project is not stable for"
+                      "NURBS VectorFE with order >= 5");
+      }
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementVDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetRangeDim();
+         int p = el.GetOrder();
+         L2_FECollection fe_coll(p,  dim);
+         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
+         int dof2 = el2.GetDof();
+         MFEM_ASSERT(dof2*dim >= dof, "Element dofs do not match.");
+         shape2.SetSize(dof2);
+         shape.SetSize(dof,dim);
+         shapel2.SetSize(dof);
+         elvect.SetSize(dof2*dim);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof2*dim,dof2*dim);
+         partelmat.SetSize(dof2,dof2);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            vcoeff.Eval(val, tr, ip);
+            val *= wght;
+
+            el2.CalcPhysShape(tr, shape2);
+            el.CalcPhysVShape(tr, shape);
+
+            for (int k = 0; k < dim; k++)
+            {
+               for (int s = 0; s < dof2; s++)
+               {
+                  elvect(dof2*k+s) += val(k) * shape2(s);
+               }
+            }
+
+            MultVVt(shape2, partelmat);
+            partelmat *= wght;
+            for (int k = 0; k < dim; k++)
+            {
+               elmat.AddMatrix(partelmat, dof2*k, dof2*k);
+            }
+
+            shape.GetRowl2(shapel2);
+            elwght.Add(wght, shapel2);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData()))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Map to NURBS
+         DenseMatrix I;
+         el2.Project(el,tr,I);
+
+         // LSQ solve
+         // For higher order NURBS solving this non-square matrix causes issues.
+         // For Order <=4 the routine seems to work fine.
+         Vector vec(dof);
+         DenseMatrix mat(dof, dof);
+         I.Transpose();
+         I.Mult(elvect, vec);
+         MultAAt(I, mat);
+         if (!LinearSolve(mat, vec.GetData(), 1e-24))
+         {
+            mat.TestInversion();
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+         elvect = vec;
+
+         // Scale
+         elvect *= elwght;
+
+         // Add to global vector
+         x.AddElementVector(vdofs, elvect);
+
+         // Add to weight vector -- no need for an orientation
+         for (int i = 0; i < vdofs.Size(); i++)
+         {
+            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
+         }
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+}
+
+void GridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
+{
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
+      Vector Va;
+      ProjectCoefficientElementL2_(vcoeff, *this, Va);
+      (*this) /= Va;
+   }
+   else
+   {
+      Array<int> vdofs(fes->GetNDofs());
+      Vector x, Va;
+      VectorComponentCoefficient coeff(vcoeff,
+                                       0);  // 0  to ensure we have a valid object
+
+      for (int v = 0; v < VectorDim(); v++)
+      {
+         coeff.SetComponent(v);
+         ProjectCoefficientElementL2_(coeff, x, Va);
+         x /= Va;
+         fes->GetVDofs(v, vdofs);
+         SetSubVector(vdofs, x);
+      }
   }
 }

@@ -27,6 +27,24 @@
 namespace mfem
 {

+/** This enumerated type describes the three main projection types:
+    - ELEMENT, assigns the degree of freedom per element, as specified in the
+      specific element
+    - GLOBAL_L2, solves a global L2 projection
+    - ELEMENT_L2, solves a element level L2 projection. Inter element
+      connectivity is dealt with similar as in:
+      Bezier-Projection : A unified approach for local projection and
+      quadrature-free refinement and coarsening of NURBS and T-splines with
+      particular application to isogeometric design and analysis
+      [CMAME (284) 2015 pg 55-105]
+    - DEFAULT, for NURBS spaces this is ELEMENT_L2, while for all other spaces
+      this ELEMENT.
+   Note 1: ELEMENT_L2 also works for non NURBS elements
+   Note 2: For NURBS elements the ELEMENT projection gives results without
+   over and undershoots. However, the gradient near the boundary does not
+   converge.*/
+enum class ProjectType { DEFAULT, ELEMENT, GLOBAL_L2, ELEMENT_L2 };
+
 /// Class for grid function - Vector with associated FE space.
 class GridFunction : public Vector
 {
@@ -66,13 +84,17 @@ protected:
       degree of freedom. */
   void ProjectDiscCoefficient(VectorCoefficient &coeff, Array<int> &dof_attr);

+   /** Helper function for ProjectCoefficientElementL2 */
+   void ProjectCoefficientElementL2_(Coefficient &coeff, Vector &sol, Vector &Va);
+   void ProjectCoefficientElementL2_(VectorCoefficient &vcoeff, Vector &sol,
+                                     Vector &Va);
+
   /// Loading helper.
   void LegacyNCReorder();

   void Destroy();

 public:
-
   GridFunction() { fes = NULL; fec_owned = NULL; fes_sequence = 0; UseDevice(true); }

   /// Copy constructor. The internal true-dof vector #t_vec is not copied.
@@ -84,6 +106,10 @@ public:
   GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }

+   /// Same as above but specify the memory type
+   GridFunction(FiniteElementSpace *f, MemoryType mt) : Vector(f->GetVSize(), mt)
+   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
+
   /// Construct a GridFunction using previously allocated array @a data.
   /** The GridFunction does not assume ownership of @a data which is assumed to
       be of size at least `f->GetVSize()`. Similar to the Vector constructor
@@ -420,9 +446,30 @@ public:
   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
       projection computation depends on the choice of the FiniteElementSpace
       #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). For NURBS spaces these degrees of
-       freedom are not available and L2 projection is resorted to as fallback. */
-   virtual void ProjectCoefficient(Coefficient &coeff);
+       in each element (not L2 projection). For elements without a projection
+       member function one could use ProjectCoefficientGlobalL2 instead.
+       NOTE: For parallel simulations with NURBS elements some dofs might
+       not be defined, if the evaluation point does not reside on this rank.
+       If that is the case it is defined on another rank, and the issue is
+       rectified with the appropriate communication, see in ParGridFunction.
+       */
+   virtual void ProjectCoefficient(Coefficient &coeff,
+                                   ProjectType type = ProjectType::DEFAULT);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                           real_t rtol = 1e-12,
+                                           int iter = 1000);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is an element local L2 projection, with an appropriate
+       weighting for Dofs that are shared between elements. Inspired on
+       Bezier-Projection [CMAME (284) 2015 pg 55-105]
+       This routine can be used a fallback for elements without a projection
+       member function.*/
+   virtual void ProjectCoefficientElementL2(Coefficient &coeff);

   /** @brief Project @a coeff Coefficient to @a this GridFunction, using one
       element for each degree of freedom in @a dofs and nodal interpolation on
@@ -432,9 +479,26 @@ public:
   /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction. The
       projection computation depends on the choice of the FiniteElementSpace
       #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). For NURBS spaces these degrees of
-       freedom are not available and L2 projection is resorted to as fallback. */
-   void ProjectCoefficient(VectorCoefficient &vcoeff);
+       in each element (not L2 projection). For elements without a projection
+       member function one could use ProjectCoefficientGlobalL2 instead.
+       NOTE: For parallel simulations with NURBS elements some dofs might
+       not be defined, if the evaluation point does not reside on this rank.
+       If that is the case it is defined on another rank, and the issue is
+       rectified with the appropriate communication, see in ParGridFunction.*/
+   virtual void ProjectCoefficient(VectorCoefficient &vcoeff,
+                                   ProjectType type = ProjectType::DEFAULT);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                           real_t rtol = 1e-12,
+                                           int iter = 1000);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientElementL2(VectorCoefficient &vcoeff);

   /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction, using
       one element for each degree of freedom in @a dofs and nodal interpolation
@@ -234,7 +234,7 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
 }

 void FindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                 int point_pos_ordering)
+                                 const int point_pos_ordering)
 {
   MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
   bool dev_mode = (point_pos.UseDevice() && Device::IsEnabled());
@@ -482,7 +482,7 @@ void FindPointsGSLIB::SetupDevice()
 }

 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         int point_pos_ordering)
+                                         const int point_pos_ordering)
 {
   if (!DEV.setup_device)
   {
@@ -505,13 +505,13 @@ void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,

   if (dim == 2)
   {
-      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
-                       gsl_dist, points_cnt);
+      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem,
+                       gsl_ref, gsl_dist, points_cnt);
   }
   else
   {
-      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
-                       gsl_dist, points_cnt);
+      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem,
+                       gsl_ref, gsl_dist, points_cnt);
   }

   // Sync from device to host
@@ -1085,7 +1085,7 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #else
 void FindPointsGSLIB::SetupDevice() {};
 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         int point_pos_ordering) {};
+                                         const int point_pos_ordering) {};
 void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
                                          Vector &field_out,
                                          const int nel, const int ncomp,
@@ -1094,7 +1094,8 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #endif

 void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
-                                 int point_pos_ordering, const double bb_t,
+                                 const int point_pos_ordering,
+                                 const double bb_t,
                                 const double newt_tol, const int npt_max)
 {
   if (!setupflag || (mesh != &m) )
@@ -1105,16 +1106,28 @@ void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
 }

 void FindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out,
-                                  int point_pos_ordering)
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering)
 {
   FindPoints(point_pos, point_pos_ordering);
   Interpolate(field_in, field_out);
 }

+void FindPointsGSLIB::Interpolate(const Vector &point_pos,
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering,
+                                  const int field_out_ordering)
+{
+   FindPoints(point_pos, point_pos_ordering);
+   Interpolate(field_in, field_out, field_out_ordering);
+}
+
 void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out,
-                                  int point_pos_ordering)
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering)
 {
   FindPoints(m, point_pos, point_pos_ordering);
   Interpolate(field_in, field_out);
@@ -1470,7 +1483,7 @@ void FindPointsGSLIB::SetupSplitMeshesAndIntegrationRules(const int order)
 }

 void FindPointsGSLIB::GetNodalValues(const GridFunction *gf_in,
-                                     Vector &node_vals)
+                                     Vector &node_vals) const
 {
   const GridFunction *nodes     = gf_in;
   const FiniteElementSpace *fes = nodes->FESpace();
@@ -1758,6 +1771,13 @@ void FindPointsGSLIB::MapRefPosAndElemIndices()

 void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
                                  Vector &field_out)
+{
+   Interpolate(field_in, field_out, field_in.FESpace()->GetOrdering());
+}
+
+void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int field_out_ordering)
 {
   const int  gf_order   = field_in.FESpace()->GetMaxElementOrder(),
              mesh_order = mesh->GetNodalFESpace()->GetMaxElementOrder();
@@ -1800,7 +1820,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
      const int maxOrder = field_in.FESpace()->GetMaxElementOrder();

      InterpolateOnDevice(node_vals, field_out, NE_split_total, ncomp,
-                          maxOrder+1, field_in.FESpace()->GetOrdering());
+                          maxOrder+1, field_out_ordering);
      return;
 #endif
   }
@@ -1812,12 +1832,13 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
       field_in.FESpace()->IsVariableOrder() ==
       mesh->GetNodalFESpace()->IsVariableOrder())
   {
-      InterpolateH1(field_in, field_out);
+      InterpolateH1(field_in, field_out, field_out_ordering);
      return;
   }
   else
   {
-      InterpolateGeneral(field_in, field_out);
+      InterpolateGeneral(field_in, field_out,
+                         field_out_ordering);
      if (!fec_l2 || avgtype == AvgType::NONE) { return; }
   }

@@ -1861,11 +1882,11 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,

      if (gf_order_h1 == mesh_order) // basis is GaussLobatto by default
      {
-         InterpolateH1(field_in_h1, field_out_l2);
+         InterpolateH1(field_in_h1, field_out_l2, field_out_ordering);
      }
      else
      {
-         InterpolateGeneral(field_in_h1, field_out_l2);
+         InterpolateGeneral(field_in_h1, field_out_l2, field_out_ordering);
      }

      // Copy interpolated values for the points on element border
@@ -1873,7 +1894,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
      {
         for (int i = 0; i < indl2.Size(); i++)
         {
-            int idx = field_in_h1.FESpace()->GetOrdering() == Ordering::byNODES?
+            int idx = field_out_ordering == Ordering::byNODES?
                      indl2[i] + j*points_cnt:
                      indl2[i]*ncomp + j;
            field_out(idx) = field_out_l2(idx);
@@ -1883,7 +1904,8 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
 }

 void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
-                                    Vector &field_out)
+                                    Vector &field_out,
+                                    const int field_out_ordering)
 {
   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
   if (field_in.FESpace()->IsVariableOrder())
@@ -1913,7 +1935,8 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                dataptrout = i*points_cnt;
      if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
      {
-         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
+         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin,
+                                        points_fld);
      }
      else
      {
@@ -1945,7 +1968,7 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                        (gslib::findpts_data_3 *)this->fdataD);
      }
   }
-   if (field_in.FESpace()->GetOrdering() == Ordering::byVDIM)
+   if (field_out_ordering == Ordering::byVDIM)
   {
      Vector field_out_temp = field_out;
      for (int i = 0; i < ncomp; i++)
@@ -1959,7 +1982,8 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
 }

 void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
-                                         Vector &field_out)
+                                         Vector &field_out,
+                                         const int field_out_ordering)
 {
   int ncomp   = field_in.VectorDim(),
       nptorig = points_cnt,
@@ -1979,7 +2003,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
         if (dim == 3) { ip.z = gsl_mfem_ref(index*dim + 2); }
         Vector localval(ncomp);
         field_in.GetVectorValue(gsl_mfem_elem[index], ip, localval);
-         if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
+         if (field_out_ordering == Ordering::byNODES)
         {
            for (int i = 0; i < ncomp; i++)
            {
@@ -2014,7 +2038,10 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
      for (int index = 0; index < npt; index++)
      {
         if (gsl_code[index] == 2) { continue; }
-         for (int d = 0; d < dim; ++d) { pt->r[d]= gsl_mfem_ref(index*dim + d); }
+         for (int d = 0; d < dim; ++d)
+         {
+            pt->r[d]= gsl_mfem_ref(index*dim + d);
+         }
         pt->index = index;
         pt->proc  = gsl_proc[index];
         pt->el    = gsl_mfem_elem[index];
@@ -2104,7 +2131,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
            sdpt = (struct send_pt *)sendpt->ptr;
            for (int index = 0; index < static_cast<int>(sendpt->n); index++)
            {
-               int idx = field_in.FESpace()->GetOrdering() == Ordering::byNODES ?
+               int idx = field_out_ordering == Ordering::byNODES ?
                         sdpt->index + j*nptorig :
                         sdpt->index*ncomp + j;
               field_out(idx) = sdpt->ival;
@@ -2246,7 +2273,7 @@ void FindPointsGSLIB::DistributeInterpolatedValues(const Vector &int_vals,
   }
 }

-void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb)
+void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb) const
 {
   MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
   auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2317,7 +2344,7 @@ void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb)
 }

 void FindPointsGSLIB::GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
-                                               Vector &obbV)
+                                               Vector &obbV) const
 {
   MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
   auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2502,8 +2529,8 @@ void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
 }

 void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                        Array<unsigned int> &point_id,
-                                        int point_pos_ordering)
+                                        const Array<unsigned int> &point_id,
+                                        const int point_pos_ordering)
 {
   MFEM_VERIFY(setupflag, "Use OversetFindPointsGSLIB::Setup before "
               "finding points.");
@@ -2582,10 +2609,10 @@ void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
 }

 void OversetFindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                         Array<unsigned int> &point_id,
+                                         const Array<unsigned int> &point_id,
                                         const GridFunction &field_in,
                                         Vector &field_out,
-                                         int point_pos_ordering)
+                                         const int point_pos_ordering)
 {
   FindPoints(point_pos, point_id, point_pos_ordering);
   Interpolate(field_in, field_out);
@@ -119,11 +119,13 @@ protected:
   } DEV;

   /// Use GSLIB for communication and interpolation
-   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out);
+   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out,
+                              const int field_out_ordering);
   /// Uses GSLIB Crystal Router for communication followed by MFEM's
   /// interpolation functions
   virtual void InterpolateGeneral(const GridFunction &field_in,
-                                   Vector &field_out);
+                                   Vector &field_out,
+                                   const int field_out_ordering);

   /// Since GSLIB is designed to work with quads/hexes, we split every
   /// triangle/tet/prism/pyramid element into quads/hexes.
@@ -140,7 +142,7 @@ protected:
   virtual void SetupSplitMeshesAndIntegrationRules(const int order);

   /// Get GridFunction value at the points expected by GSLIB.
-   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals);
+   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals) const;

   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices,
   /// find the original element number (that was split into micro quads/hexes)
@@ -182,7 +184,7 @@ protected:
       These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
       byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering. */
   void FindPointsOnDevice(const Vector &point_pos,
-                           int point_pos_ordering = Ordering::byNODES);
+                           const int point_pos_ordering = Ordering::byNODES);

   /** Interpolation of field values at prescribed reference space positions.
       @param[in] field_in_evec E-vector of grid function to be interpolated.
@@ -253,10 +255,15 @@ public:
       #gsl_dist        Distance between the sought and the found point
                        in physical space. */
   void FindPoints(const Vector &point_pos,
-                   int point_pos_ordering = Ordering::byNODES);
+                   const int point_pos_ordering = Ordering::byNODES);
+   /// Convenience function when point positions are in a ParticleVector
+   void FindPoints(const ParticleVector &point_pos)
+   {
+      FindPoints(point_pos, point_pos.GetOrdering());
+   }
   /// Setup FindPoints and search positions
   void FindPoints(Mesh &m, const Vector &point_pos,
-                   int point_pos_ordering = Ordering::byNODES,
+                   const int point_pos_ordering = Ordering::byNODES,
                   const double bb_t = 0.1, const double newt_tol = 1.0e-12,
                   const int npt_max = 256);

@@ -266,20 +273,28 @@ public:
                              \p field_in is in H1 and in the same space as the
                              mesh that was given to Setup().
       @param[out] field_out  Interpolated values. For points that are not found
-                              the value is set to #default_interp_value. */
+                              the value is set to #default_interp_value.
+                              The output ordering is determined from field_in.*/
   virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
+   /// Interpolation of field values, with output ordering specification.
+   virtual void Interpolate(const GridFunction &field_in, Vector &field_out,
+                            const int field_out_ordering);
   /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
       the output values in \p field_out corresponds to the ordering used
       in the input GridFunction \p field_in. */
   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                    Vector &field_out,
-                    int point_pos_ordering = Ordering::byNODES);
+                    const int point_pos_ordering = Ordering::byNODES);
+   /// Search positions and interpolate with given point and output ordering.
+   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
+                    Vector &field_out, const int point_pos_ordering,
+                    const int field_out_ordering);
   /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
       or byVDIM) of the output values in \p field_out corresponds to the
       ordering used in the input GridFunction \p field_in. */
   void Interpolate(Mesh &m, const Vector &point_pos,
                    const GridFunction &field_in, Vector &field_out,
-                    int point_pos_ordering = Ordering::byNODES);
+                    const int point_pos_ordering = Ordering::byNODES);

   /// Average type to be used for L2 functions in-case a point is located at
   /// an element boundary where the function might be multi-valued.
@@ -376,7 +391,7 @@ public:
   /// The size of the returned vector is (nel x nverts x dim), where nel is the
   /// number of elements (after splitting for simplcies), nverts is number of
   /// vertices (4 in 2D, 8 in 3D), and dim is the spatial dimension.
-   void GetAxisAlignedBoundingBoxes(Vector &aabb);
+   void GetAxisAlignedBoundingBoxes(Vector &aabb) const;

   /// Return the oriented bounding boxes (OBB) computed during \ref Setup.
   /// Each OBB is represented using the inverse transformation (A^{-1}) and
@@ -386,7 +401,8 @@ public:
   /// size (dim x dim x nel), and the OBB centers are returned in \p obbC,
   /// a vector of size (nel x dim). The vertices of the OBBs are returned in
   /// \p obbV, a vector of size (nel x nverts x dim) .
-   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC, Vector &obbV);
+   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
+                                 Vector &obbV) const;
 };

 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -446,13 +462,14 @@ public:
                                       byNodes: (XXX...,YYY...,ZZZ) or
                                       byVDim: (XYZ,XYZ,....XYZ) */
   void FindPoints(const Vector &point_pos,
-                   Array<unsigned int> &point_id,
-                   int point_pos_ordering = Ordering::byNODES);
+                   const Array<unsigned int> &point_id,
+                   const int point_pos_ordering = Ordering::byNODES);

   /** Search positions and interpolate */
-   void Interpolate(const Vector &point_pos, Array<unsigned int> &point_id,
+   void Interpolate(const Vector &point_pos,
+                    const Array<unsigned int> &point_id,
                    const GridFunction &field_in, Vector &field_out,
-                    int point_pos_ordering = Ordering::byNODES);
+                    const int point_pos_ordering = Ordering::byNODES);
   using FindPointsGSLIB::Interpolate;
 };

@@ -789,7 +789,6 @@ void Hybridization::ComputeH()
   }
   else
   {
-      // TODO: add ones on the diagonal of zero rows
      V->Finalize();
      Array<HYPRE_BigInt> V_J(V->NumNonZeroElems());
      MFEM_ASSERT(c_pfes, "");
@@ -823,6 +822,13 @@ void Hybridization::ComputeH()
      MFEM_VERIFY(pH.Type() != Operator::PETSC_MATIS, "To be implemented");
      pH.MakePtAP(plpH, pP);
      delete lpH;
+
+      HypreParMatrix *hH = pH.As<HypreParMatrix>();
+      MFEM_ASSERT(hH, "");
+
+      SparseMatrix H_diag;
+      hH->GetDiag(H_diag);
+      H_diag.SetDiagIdentity();
   }
 #endif
 }
@@ -14,8 +14,11 @@

 #include "../config/config.hpp"
 #include "../general/array.hpp"
+#include "../linalg/operator.hpp"
 #include "../linalg/vector.hpp"

+#include <memory>
+
 namespace mfem
 {

@@ -45,15 +48,30 @@ protected:
   Array<int> hat_dof_gather_map;
   Array<DofType> hat_dof_marker;

-   Array<int> el_to_face;
-   Array<int> face_to_el;
+   Array<int> el_to_face; ///< Element to face connectivity.
+   Array<int> el_face_offsets; ///< Per-element offsets into @a el_to_face.
+   Array<int> face_to_el; ///< Face-to-element connectivity.
+   Array<int> face_face_offsets; ///< Face-to-face offsets.
+
+   int n_el_face; ///< Total number of element-to-face connections.
+   int n_face_face; ///< Total number of face-to-face connections.
+
   Vector Ct_mat; ///< Constraint matrix (transposed) stored element-wise.

+   /// @name For parallel non-conforming meshes
+   ///@{
+   std::unique_ptr<Operator> P_pc; ///< Partially conforming prolongation.
+   std::unique_ptr<Operator> P_nbr; ///< Face-neighbor prolongation.
+   ///@}
+
   Array<int> idofs, bdofs;

   Vector Ahat, Ahat_ii, Ahat_ib, Ahat_bi, Ahat_bb;
   Array<int> Ahat_ii_piv, Ahat_bb_piv;

+   /// Return the (partially) conforming prolongation on the constraint space.
+   const Operator &GetProlongation() const;
+
 public:
   /// Construct the constraint matrix.
   void ConstructC();
@@ -1004,13 +1004,16 @@ inline void SmemPADiffusionApply3D(const int NE,
   const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
   MFEM_VERIFY(D1D <= max_d1d, "");
   MFEM_VERIFY(Q1D <= max_q1d, "");
-   auto b = Reshape(b_.Read(), Q1D, D1D);
-   auto g = Reshape(g_.Read(), Q1D, D1D);
-   auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
+   const auto b = Reshape(b_.Read(), Q1D, D1D);
+   const auto g = Reshape(g_.Read(), Q1D, D1D);
+   const auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
+   const auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
   MFEM_VERIFY(D1D <= Q1D, "THREAD_DIRECT requires D1D <= Q1D");
-   mfem::forall_3D(NE, Q1D, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+
+   mfem::forall_3D<T_Q1D*T_Q1D*T_Q1D>(NE,
+                                      Q1D, Q1D, Q1D,
+                                      [=] MFEM_HOST_DEVICE (int e)
   {
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1133,11 +1133,11 @@ inline void SmemPAMassApply3D(const int NE,
   const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
   MFEM_VERIFY(D1D <= max_d1d, "");
   MFEM_VERIFY(Q1D <= max_q1d, "");
-   auto b = b_.Read();
-   auto d = d_.Read();
-   auto x = x_.Read();
+   const auto b = b_.Read();
+   const auto d = d_.Read();
+   const auto x = x_.Read();
   auto y = y_.ReadWrite();
-   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE (int e)
   {
      internal::SmemPAMassApply3D_Element<T_D1D,T_Q1D>(e, NE, b, d, x, y, d1d, q1d);
   });
@@ -1156,8 +1156,8 @@ inline void EAMassAssemble1D(const int NE,
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
-   auto B = Reshape(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, NE);
+   const auto B = Reshape(basis.Read(), Q1D, D1D);
+   const auto D = Reshape(padata.Read(), Q1D, NE);
   auto M = Reshape(add ? eadata.ReadWrite() : eadata.Write(), D1D, D1D, NE);
   mfem::forall_2D(NE, D1D, D1D, [=] MFEM_HOST_DEVICE (int e)
   {
@@ -28,7 +28,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   const FaceType ftype = FaceType::Interior;
   const int nf = mesh.GetNFbyType(ftype);

-   const Geometry::Type geom = mesh.GetFaceGeometry(0);
+   const Geometry::Type geom = mesh.GetTypicalFaceGeometry();
   const int trial_order = trial_fes.GetMaxElementOrder();
   const int test_order = test_fes.GetMaxElementOrder();
   const int qorder = test_order + trial_order - 1;
@@ -47,7 +47,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      });
   }

-   const FiniteElement &trial_face_el = *trial_fes.GetFaceElement(0);
+   const FiniteElement &trial_face_el = *trial_fes.GetTypicalTraceElement();
   const auto maps = &trial_face_el.GetDofToQuad(ir, DofToQuad::TENSOR);
   const int ndof_face = trial_face_el.GetDof();

@@ -72,7 +72,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      MFEM_ABORT("Unknown kernel.");
   }

-   const FiniteElement &test_el = *test_fes.GetFE(0);
+   const FiniteElement &test_el = *test_fes.GetTypicalFE();
   const int n_faces_per_el = 2*dim; // assuming tensor product
   // Get all the local face maps (mapping from lexicographic face index to
   // lexicographic volume index, depending on the local face index).
@@ -90,10 +90,10 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   Array<int> face_info(nf * 4);
   {
      int fidx = 0;
-      for (int f = 0; f < mesh.GetNumFaces(); ++f)
+      for (int f = 0; f < mesh.GetNumFacesWithGhost(); ++f)
      {
         Mesh::FaceInformation finfo = mesh.GetFaceInformation(f);
-         if (!finfo.IsInterior()) { continue; }
+         if (!finfo.IsInterior() || finfo.IsNonconformingCoarse()) { continue; }
         face_info[0 + fidx*4] = finfo.element[0].local_face_id;
         face_info[1 + fidx*4] = finfo.element[0].orientation;
         face_info[2 + fidx*4] = finfo.element[1].local_face_id;
@@ -114,7 +114,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
   else
   {
      d_emat = emat.Write();
-      mfem::forall(emat.Size(), [=] MFEM_HOST_DEVICE (int i) { d_emat[i] = 0.0; });
+      emat = 0.0; // Will execute on device, since Write() sets the device flag
   }

   const auto face_mats = Reshape(mass_emat.Read(), ndof_face, ndof_face, nf);
@@ -133,26 +133,104 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
      }
   };

-   mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
+   auto permute_face_2 = [=] MFEM_HOST_DEVICE(int local_face_1, int local_face_2,
+                                              int orient, int size1d, int index)
   {
-      MFEM_FOREACH_THREAD(el_i, z, 2)
+      if (dim == 2)
      {
-         const int lf_i = d_face_info(0, el_i, f);
-         const int orient = d_face_info(1, el_i, f);
-         // Loop over face indices in "native ordering"
-         MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
+         return internal::PermuteFace2D(local_face_1, local_face_2, orient,
+                                        size1d, index);
+      }
+      else // dim == 3
+      {
+         return internal::PermuteFace3D(local_face_1, local_face_2, orient,
+                                        size1d, index);
+      }
+   };
+
+   if (mesh.Conforming())
+   {
+      mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
+      {
+         MFEM_FOREACH_THREAD(el_i, z, 2)
         {
-            // Convert to lexicographic relative to the face itself
-            const int i_face = permute_face(lf_i, orient, d1d, i_lex);
-            // Convert from lexicographic face DOF to volume DOF
-            const int i = d_face_maps(i_lex, lf_i);
-            MFEM_FOREACH_THREAD(j, y, ndof_face)
+            const int lf_i = d_face_info(0, el_i, f);
+            const int orient = d_face_info(1, el_i, f);
+            // Loop over face indices in "native ordering"
+            MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
            {
-               el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
+               // Convert to lexicographic relative to the face itself
+               const int i_face = permute_face(lf_i, orient, d1d, i_lex);
+               // Convert from lexicographic face DOF to volume DOF
+               const int i = d_face_maps(i_lex, lf_i);
+               MFEM_FOREACH_THREAD(j, y, ndof_face)
+               {
+                  el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
+               }
            }
         }
-      }
-   });
+      });
+   }
+   else
+   {
+      const InterpolationManager &interp =
+         test_fes.GetInterpolationManager(ElementDofOrdering::LEXICOGRAPHIC, ftype);
+
+      auto interp_configs = interp.GetFaceInterpConfig().Read();
+      const int nc_size = interp.GetNumInterpolators();
+      auto d_interp = Reshape(interp.GetInterpolators().Read(),
+                              ndof_face, ndof_face, nc_size);
+
+      mfem::forall(nf, [=] MFEM_HOST_DEVICE (int f)
+      {
+         const InterpConfig conf = interp_configs[f];
+         const int master_side = conf.master_side;
+         const int interp_index = conf.index;
+
+         const int lf_0 = d_face_info(0, 0, f);
+
+         for (int el_i = 0; el_i < 2; ++el_i)
+         {
+            const int lf_i = d_face_info(0, el_i, f);
+            const int orient = d_face_info(1, el_i, f);
+
+            for (int j = 0; j < ndof_face; j++)
+            {
+               for (int i_lex = 0; i_lex < ndof_face; i_lex++)
+               {
+                  real_t val = 0.0;
+                  if (conf.is_non_conforming && el_i == master_side)
+                  {
+                     // Interpolate from el_i (coarse element) to the fine face.
+                     // The mapping is given by d_interp, which uses indices
+                     // relative to element 0.
+
+                     // i0 is lexicographic relative to element 0
+                     const int i0 = permute_face_2(lf_i, lf_0, orient, d1d, i_lex);
+
+                     // k0 is lexicographic relative to element 0
+                     for (int k0 = 0; k0 < ndof_face; k0++)
+                     {
+                        // k is relative to the face itself
+                        const int k = permute_face(lf_0, orient, d1d, k0);
+                        val += d_interp(k0, i0, interp_index)
+                               * face_mats(k, j, f);
+                     }
+                  }
+                  else
+                  {
+                     // Convert to lexicographic relative to the face itself
+                     const int i_face = permute_face(lf_i, orient, d1d, i_lex);
+                     val = face_mats(i_face, j, f);
+                  }
+                  // Convert from lexicographic face DOF to volume DOF
+                  const int i = d_face_maps(i_lex, lf_i);
+                  el_mats(i, j, el_i, f) += val;
+               }
+            }
+         }
+      });
+   }
 }

 }
@@ -54,7 +54,7 @@ void SmemPAVectorDiffusionApply2D(const int NE,
   const auto XE = Reshape(x.Read(), D1D, D1D, SDIM, NE);
   auto YE = Reshape(y.ReadWrite(), D1D, D1D, SDIM, NE);

-   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -120,7 +120,7 @@ void SmemPAVectorDiffusionApply3D(const int NE,
   const auto XE = Reshape(x.Read(), D1D, D1D, D1D, SDIM, NE);
   auto YE = Reshape(y.ReadWrite(), D1D, D1D, D1D, SDIM, NE);

-   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -51,7 +51,7 @@ void SmemPAVectorMassApply2D(const int NE,
   const auto X = Reshape(x.Read(), D1D, D1D, VDIM, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, VDIM, NE);

-   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -119,7 +119,7 @@ void SmemPAVectorMassApply3D(const int NE,
   const auto X = Reshape(x.Read(), D1D, D1D, D1D, VDIM, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, D1D, VDIM, NE);

-   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
   {
      constexpr int MD1 = T_D1D > 0 ? SetMaxOf(T_D1D) : DofQuadLimits::MAX_T1D;
      constexpr int MQ1 = T_Q1D > 0 ? SetMaxOf(T_Q1D) : DofQuadLimits::MAX_T1D;
@@ -14,6 +14,7 @@

 #include "../config/config.hpp"
 #include "kernel_reporter.hpp"
+#include "../general/hash_util.hpp"
 #include <unordered_map>
 #include <tuple>
 #include <type_traits>
@@ -86,35 +87,6 @@ namespace mfem
    }                                                                          \
  }

-/// @brief Hashes variadic packs for which each type contained in the variadic
-/// pack has a specialization of `std::hash` available.
-///
-/// For example, packs containing int, bool, enum values, etc.
-template<typename ...KernelParameters>
-struct KernelDispatchKeyHash
-{
-private:
-   template<int N>
-   size_t operator()(std::tuple<KernelParameters...> value) const { return 0; }
-
-   // The hashing formula here is taken directly from the Boost library, with
-   // the magic number 0x9e3779b9 chosen to minimize hashing collisions.
-   template<std::size_t N, typename THead, typename... TTail>
-   size_t operator()(std::tuple<KernelParameters...> value) const
-   {
-      constexpr int Index = N - sizeof...(TTail) - 1;
-      auto lhs_hash = std::hash<THead>()(std::get<Index>(value));
-      auto rhs_hash = operator()<N, TTail...>(value);
-      return lhs_hash^(rhs_hash + 0x9e3779b9 + (lhs_hash<<6) + (lhs_hash>>2));
-   }
-public:
-   /// Returns the hash of the given @a value.
-   size_t operator()(std::tuple<KernelParameters...> value) const
-   {
-      return operator()<sizeof...(KernelParameters),KernelParameters...>(value);
-   }
-};
-
 namespace internal { template<typename... Types> struct KernelTypeList { }; }

 template<typename... T> class KernelDispatchTable { };
@@ -128,8 +100,8 @@ class KernelDispatchTable<Kernels,
         internal::KernelTypeList<Params...>,
         internal::KernelTypeList<OptParams...>>
 {
-   using TableType = std::unordered_map<std::tuple<Params...>,
-         Signature, KernelDispatchKeyHash<Params...>>;
+   using TableType =
+      std::unordered_map<std::tuple<Params...>, Signature, TupleHasher>;
   TableType table;

   /// @brief Call function @a f with arguments @a args (perfect forwaring).
@@ -78,10 +78,7 @@ template <int Dim>
 void BuildBoxes(const Mesh &mesh,
                std::vector<::moonolith::AABB<Dim, double>> &element_boxes)
 {
-#ifndef NDEBUG
-   const int dim = mesh.Dimension();
-   assert(dim == Dim);
-#endif
+   MFEM_ASSERT(mesh.Dimension() == Dim, "Mesh and box dimensions mismatched");
   element_boxes.resize(mesh.GetNE());

   DenseMatrix pts;
@@ -488,10 +488,16 @@ void ParBilinearForm::FormLinearSystem(
         R.Mult(x, true_X);

         FormSystemMatrix(ess_tdof_list, A);
-         ConstrainedOperator *A_constrained;
-         Operator::FormConstrainedSystemOperator(ess_tdof_list, A_constrained);
+
+         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
+         {
+            Operator *op;
+            Operator::FormSystemOperator(ess_tdof_list, op);
+            return dynamic_cast<ConstrainedOperator*>(op);
+         }());
+         MFEM_ASSERT(A_constrained != nullptr, "");
+
         A_constrained->EliminateRHS(true_X, true_B);
-         delete A_constrained;
         R.MultTranspose(true_B, b);
         hybridization->ReduceRHS(true_B, B);
         X.SetSize(B.Size());
@@ -646,39 +646,38 @@ const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
   auto itr = L2F.find(key);
   if (itr != L2F.end())
   {
-      return itr->second;
+      return itr->second.get();
   }
   else
   {
-      FaceRestriction *res;
+      std::unique_ptr<FaceRestriction> res;
      if (is_dg_space)
      {
         if (Conforming())
         {
-            res = new ParL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new ParL2FaceRestriction(*this, f_ordering, type, m));
         }
         else
         {
-            res = new ParNCL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new ParNCL2FaceRestriction(*this, f_ordering, type, m));
         }
      }
      else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
      {
-         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
+         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
      }
      else
      {
         if (Conforming())
         {
-            res = new ConformingFaceRestriction(*this, f_ordering, type);
+            res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
         }
         else
         {
-            res = new ParNCH1FaceRestriction(*this, f_ordering, type);
+            res.reset(new ParNCH1FaceRestriction(*this, f_ordering, type));
         }
      }
-      L2F[key] = res;
-      return res;
+      return L2F.emplace(key, std::move(res)).first->second.get();
   }
 }

@@ -483,6 +483,8 @@ public:
   const FiniteElement *GetFaceNbrFaceFE(int i) const;
   const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() { return face_nbr_glob_dof_map; }
   const HYPRE_BigInt *GetFaceNbrGlobalDofMap() { return face_nbr_glob_dof_map; }
+   const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() const
+   { return face_nbr_glob_dof_map; }
   ElementTransformation *GetFaceNbrElementTransformation(int i) const
   { return pmesh->GetFaceNbrElementTransformation(i); }

@@ -543,13 +543,22 @@ void ParGridFunction::GetElementDofValues(int el, Vector &dof_vals) const
   }
 }

-void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
+void ParGridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
   DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);

   if (delta_c == NULL)
   {
-      GridFunction::ProjectCoefficient(coeff);
+      (*this) = std::numeric_limits<real_t>::min();
+      GridFunction::ProjectCoefficient(coeff,type);
+
+      // Accumulate for all vdofs.
+      if (pfes->GetNURBSext())
+      {
+         GroupCommunicator &gcomm = pfes->GroupComm();
+         gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
+         gcomm.Bcast<real_t>(data);
+      }
   }
   else
   {
@@ -565,6 +574,147 @@ void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
   }
 }

+void ParGridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
+                                         ProjectType type)
+{
+   GridFunction::ProjectCoefficient(vcoeff, type);
+
+   // Accumulate for all vdofs.
+   if (pfes->GetNURBSext())
+   {
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
+      gcomm.Bcast<real_t>(data);
+   }
+}
+
+void ParGridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                                 real_t rtol,
+                                                 int iter)
+{
+   // Define and assemble linear form
+   ParLinearForm b(pfes);
+   b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+   b.Assemble();
+
+   // Define and assemble bilinear form
+   ParBilinearForm a(pfes);
+   a.AddDomainIntegrator(new MassIntegrator());
+   a.Assemble();
+
+   // Configure solver
+   OperatorPtr A;
+   Vector B, X, x(*this);
+   Array<int> ess_tdof_list;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+   Solver *prec = new HypreBoomerAMG;
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+   cg.SetPreconditioner(*prec);
+   cg.SetOperator(*A);
+   cg.Mult(B, X);
+   a.RecoverFEMSolution(X, b, x);
+   delete prec;
+}
+
+void ParGridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
+{
+   Vector Va;
+   ProjectCoefficientElementL2_(coeff, *this, Va);
+
+   GroupCommunicator &gcomm = pfes->GroupComm();
+   gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+   gcomm.Bcast<real_t>(GetData());
+
+   gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
+   gcomm.Bcast<real_t>(Va.GetData());
+   (*this)/=Va;
+}
+
+void ParGridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                                 real_t rtol, int iter)
+{
+   // Define and assemble linear form
+   ParLinearForm b(pfes);
+   ParBilinearForm a(pfes);
+
+   // Dimension argument to GetRangeType is arbitrary to be 3, could also be 2.
+   if (fes->FEColl()->GetRangeType(3)  == mfem::FiniteElement::VECTOR)
+   {
+      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorFEMassIntegrator());
+   }
+   else
+   {
+      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorMassIntegrator());
+   }
+   b.Assemble();
+   a.Assemble();
+
+   // Configure solver
+   OperatorPtr A;
+   Vector B, X, x(*this);
+   x = 0.0;
+   Array<int> ess_tdof_list;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+   Solver *prec = new HypreBoomerAMG;
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+   cg.SetPreconditioner(*prec);
+   cg.SetOperator(*A);
+   cg.Mult(B, X);
+   a.RecoverFEMSolution(X, b, x);
+   x.Print();
+   delete prec;
+}
+
+void ParGridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
+{
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
+      Vector Va;
+      ProjectCoefficientElementL2_(vcoeff, *this, Va);
+
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(GetData());
+
+      gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(Va.GetData());
+      (*this)/=Va;
+   }
+   else
+   {
+      Array<int> vdofs(fes->GetNDofs());
+      Vector x, Va, gVa(Size());
+      VectorComponentCoefficient coeff(vcoeff,0);
+      *this = 0.0;
+      gVa = 0.0;
+      for (int v = 0; v < VectorDim(); v++)
+      {
+         coeff.SetComponent(v);
+         ProjectCoefficientElementL2_(coeff, x, Va);
+         fes->GetVDofs(v, vdofs);
+         SetSubVector(vdofs, x);
+         gVa.SetSubVector(vdofs, Va);
+      }
+
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(GetData());
+
+      gcomm.Reduce<real_t>(gVa.GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(gVa.GetData());
+      *this /= gVa;
+   }
+}
+
+
 void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
 {
   // local maximal element attribute for each dof
@@ -72,6 +72,10 @@ public:

   ParGridFunction(ParFiniteElementSpace *pf) : GridFunction(pf), pfes(pf) { }

+   /// Same as above but specify the device memory type
+   ParGridFunction(ParFiniteElementSpace *pf, MemoryType mt) :
+      GridFunction(pf, mt), pfes(pf) { }
+
   /// Construct a ParGridFunction using previously allocated array @a data.
   /** The ParGridFunction does not assume ownership of @a data which is assumed
       to be of size at least `pf->GetVSize()`. Similar to the GridFunction and
@@ -257,7 +261,11 @@ public:
   void GetElementDofValues(int el, Vector &dof_vals) const override;

   using GridFunction::ProjectCoefficient;
-   void ProjectCoefficient(Coefficient &coeff) override;
+   void ProjectCoefficient(Coefficient &coeff,
+                           ProjectType type = ProjectType::DEFAULT) override;
+
+   void ProjectCoefficient(VectorCoefficient &vcoeff,
+                           ProjectType type = ProjectType::DEFAULT) override;

   using GridFunction::ProjectDiscCoefficient;
   /** @brief Project a discontinuous vector coefficient as a grid function on
@@ -282,6 +290,18 @@ public:
   void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                     const Array<int> &bdr_attr) override;

+   void ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                   real_t rtol = 1e-12,
+                                   int iter = 1000) override;
+
+   void ProjectCoefficientElementL2(Coefficient &coeff) override;
+
+   void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                   real_t rtol = 1e-12,
+                                   int iter = 1000) override;
+
+   void ProjectCoefficientElementL2(VectorCoefficient &vcoeff) override;
+
   /// @brief Returns ||u_ex - u_h||_L1 in parallel for H1 or L2 elements
   ///
   /// @see GridFunction::ComputeL1Error(Coefficient *exsol[],
@@ -994,7 +994,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
      {
         if ( face.IsConforming() )
         {
-            interpolations.RegisterFaceConformingInterpolation(face,f_ind);
            SetFaceDofsScatterIndices1(face,f_ind);
            if ( m==L2FaceValues::DoubleValued )
            {
@@ -1010,7 +1009,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
         }
         else // Non-conforming face
         {
-            interpolations.RegisterFaceCoarseToFineInterpolation(face,f_ind);
            SetFaceDofsScatterIndices1(face,f_ind);
            if ( m==L2FaceValues::DoubleValued )
            {
@@ -1028,7 +1026,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
      }
      else if (type==FaceType::Boundary && face.IsBoundary())
      {
-         interpolations.RegisterFaceConformingInterpolation(face,f_ind);
         SetFaceDofsScatterIndices1(face,f_ind);
         if ( m==L2FaceValues::DoubleValued )
         {
@@ -1046,10 +1043,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
   {
      gather_offsets[i] += gather_offsets[i - 1];
   }
-
-   // Transform the interpolation matrix map into a contiguous memory structure.
-   interpolations.LinearizeInterpolatorMapIntoVector();
-   interpolations.InitializeNCInterpConfig();
 }

 void ParNCL2FaceRestriction::ComputeGatherIndices()
@@ -326,9 +326,7 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
   void FillI(SparseMatrix &mat,
              const bool keep_nbr_block = false) const override;

@@ -364,9 +362,7 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
   void FillJAndData(const Vector &fea_data,
                     SparseMatrix &mat,
                     const bool keep_nbr_block = false) const override;
@@ -50,7 +50,13 @@ QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Fallback(
   int DIM, int SDIM, int D1D, int Q1D)
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   if (DIM == 1)
+   {
+      if (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
+      else if (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<0,0,2>; }
+      else if (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<0,0,3>; }
+      else { MFEM_ABORT(""); }
+   }
   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D; }
   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface; }
   else if (DIM == 3)
@@ -56,6 +56,50 @@ inline void Det1D(const int NE,
   });
 }

+template<int T_D1D = 0, int T_Q1D = 0, int T_SDIM = 3>
+inline void Det1DSurface(const int NE,
+                         const real_t *b,
+                         const real_t *g,
+                         const real_t *x,
+                         real_t *y,
+                         const int d1d = 0,
+                         const int q1d = 0,
+                         Vector *d_buff = nullptr)
+{
+   MFEM_CONTRACT_VAR(b);
+   MFEM_CONTRACT_VAR(d_buff);
+
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto G = Reshape(g, Q1D, D1D);
+   const auto X = Reshape(x, D1D, T_SDIM, NE);
+   auto Y = Reshape(y, Q1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int q = 0; q < Q1D; q++)
+      {
+         real_t grad[T_SDIM];
+         for (int s = 0; s < T_SDIM; s++) { grad[s] = 0.0; }
+         for (int d = 0; d < D1D; d++)
+         {
+            const real_t gval = G(q, d);
+            for (int s = 0; s < T_SDIM; s++)
+            {
+               grad[s] += gval * X(d, s, e);
+            }
+         }
+         real_t norm2 = 0.0;
+         for (int s = 0; s < T_SDIM; s++)
+         {
+            norm2 += grad[s] * grad[s];
+         }
+         Y(q, e) = std::sqrt(norm2);
+      }
+   });
+}
+
 template<int T_D1D = 0, int T_Q1D = 0>
 inline void Det2D(const int NE,
                  const real_t *b,
@@ -290,7 +334,13 @@ template<int DIM, int SDIM, int D1D, int Q1D>
 QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Kernel()
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   if (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(""); }
+   }
   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>; }
@@ -542,7 +542,8 @@ void QuadratureInterpolator::Mult(const Vector &e_vec,
   }

   MFEM_ASSERT(!(eval_flags & DETERMINANTS) || dim == vdim ||
-               (dim == 2 && vdim == 3), "Invalid dimensions for determinants.");
+               (dim == 2 && vdim == 3) || (dim == 1 && vdim == 2) ||
+               (dim == 1 && vdim == 3), "Invalid dimensions for determinants.");
   MFEM_ASSERT(fespace->GetMesh()->GetNumGeometries(
                  fespace->GetMesh()->Dimension()) == 1,
               "mixed meshes are not supported");
@@ -1506,12 +1506,12 @@ void L2FaceRestriction::EnsureNormalDerivativeRestriction() const
   }
 }

-InterpolationManager::InterpolationManager(const FiniteElementSpace &fes,
-                                           ElementDofOrdering ordering,
+InterpolationManager::InterpolationManager(const FiniteElementSpace &fes_,
+                                           ElementDofOrdering ordering_,
                                           FaceType type)
-   : fes(fes),
-     ordering(ordering),
-     interp_config( fes.GetNFbyType(type) ),
+   : fes(fes_),
+     ordering(ordering_),
+     interp_config(fes.GetNFbyType(type)),
     nc_cpt(0)
 { }

@@ -1536,7 +1536,8 @@ void InterpolationManager::RegisterFaceCoarseToFineInterpolation(
                        face.element[0].local_face_id +
                        6*face.element[1].local_face_id +
                        36*face.element[1].orientation ;
-   // Unfortunately we can't trust unicity of the ptMat to identify the transformation.
+   // Unfortunately we can't trust uniqueness of the ptMat to identify the
+   // transformation.
   Key key(ptMat, face_key);
   auto itr = interp_map.find(key);
   if ( itr == interp_map.end() )
@@ -1583,17 +1584,27 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
   IsoparametricTransformation isotr;
   isotr.SetIdentityTransformation(trace_fe->GetGeomType());
   isotr.SetPointMat(*ptMat);
-   DenseMatrix& trans_pt_mat = isotr.GetPointMat();
-   // PointMatrix needs to be flipped in 2D
-   if ( trace_fe->GetGeomType()==Geometry::SEGMENT && !is_ghost_slave )
-   {
-      std::swap(trans_pt_mat(0,0),trans_pt_mat(0,1));
-   }
   DenseMatrix native_interpolator(face_dofs,face_dofs);
   trace_fe->GetLocalInterpolation(isotr, native_interpolator);
+
+   if (trace_fe->GetMapType() == FiniteElement::INTEGRAL)
+   {
+      // Handle potentially inverted Jacobian matrix
+      isotr.SetIntPoint(&Geometries.GetCenter(trace_fe->GetGeomType()));
+      native_interpolator *= (isotr.Weight() >= 0) ? 1.0 : -1.0;
+   }
+
   const int dim = trace_fe->GetDim()+1;
   const int dof1d = trace_fe->GetOrder()+1;
-   const int orientation = face.element[1].orientation;
+   int orientation_i = face.element[1].orientation;
+   const int orientation_j = face.element[1].orientation;
+
+   // In 2D, need to flip orientation of the segments`
+   if (trace_fe->GetGeomType() == Geometry::SEGMENT && !is_ghost_slave)
+   {
+      orientation_i = 1;
+   }
+
   for (int i = 0; i < face_dofs; i++)
   {
      const int ni = (dof_map.Size()==0) ? i : dof_map[i];
@@ -1602,7 +1613,7 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
      {
         // master side is elem 2, so we permute to order dofs as elem 1.
         li = PermuteFaceL2(dim, face_id2, face_id1,
-                            orientation, dof1d, li);
+                            orientation_i, dof1d, li);
      }
      for (int j = 0; j < face_dofs; j++)
      {
@@ -1611,7 +1622,7 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
         {
            // master side is elem 2, so we permute to order dofs as elem 1.
            lj = PermuteFaceL2(dim, face_id2, face_id1,
-                               orientation, dof1d, lj);
+                               orientation_j, dof1d, lj);
         }
         const int nj = (dof_map.Size()==0) ? j : dof_map[j];
         (*interpolator)(li,lj) = native_interpolator(ni,nj);
@@ -1676,7 +1687,7 @@ NCL2FaceRestriction::NCL2FaceRestriction(const FiniteElementSpace &fes,
                                         const L2FaceValues m,
                                         bool build)
   : L2FaceRestriction(fes, f_ordering, type, m, false),
-     interpolations(fes, f_ordering, type)
+     interpolations(fes.GetInterpolationManager(ordering, type))
 {
   if (!build) { return; }
   x_interp.UseDevice(true);
@@ -2202,14 +2213,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
         {
            PermuteAndSetFaceDofsScatterIndices2(face,f_ind);
         }
-         if ( face.IsConforming() )
-         {
-            interpolations.RegisterFaceConformingInterpolation(face,f_ind);
-         }
-         else // Non-conforming face
-         {
-            interpolations.RegisterFaceCoarseToFineInterpolation(face,f_ind);
-         }
         f_ind++;
      }
      else if ( type==FaceType::Boundary && face.IsBoundary() )
@@ -2219,7 +2222,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
         {
            SetBoundaryDofsScatterIndices2(face,f_ind);
         }
-         interpolations.RegisterFaceConformingInterpolation(face,f_ind);
         f_ind++;
      }
   }
@@ -2232,10 +2234,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
   {
      gather_offsets[i] += gather_offsets[i - 1];
   }
-
-   // Transform the interpolation matrix map into a contiguous memory structure.
-   interpolations.LinearizeInterpolatorMapIntoVector();
-   interpolations.InitializeNCInterpConfig();
 }

 void NCL2FaceRestriction::ComputeGatherIndices()
@@ -2278,6 +2276,18 @@ void NCL2FaceRestriction::ComputeGatherIndices()
   gather_offsets[0] = 0;
 }

+static int GetSharedVSize(const FiniteElementSpace &fes)
+{
+#ifdef MFEM_USE_MPI
+   if (auto pfes = dynamic_cast<const ParFiniteElementSpace*>(&fes))
+   {
+      const_cast<ParFiniteElementSpace*>(pfes)->ExchangeFaceNbrData();
+      return pfes->GetFaceNbrVSize();
+   }
+#endif
+   return 0;
+}
+
 L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(
   const FiniteElementSpace& fes_,
   const ElementDofOrdering ordering_,
@@ -2288,25 +2298,54 @@ L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(
     nfaces(fes.GetNFbyType(type)),
     vdim(fes.GetVDim()),
     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     face_dofs(nfaces > 0 ? fes.GetFaceElement(0)->GetDof() : 0),
+     face_dofs(fes.GetTypicalTraceElement()->GetDof()),
     nfdofs(face_dofs*nfaces),
-     ndofs(fes.GetNDofs())
+     ndofs(fes.GetNDofs()),
+     nsdofs(GetSharedVSize(fes))
 {
   height = nfdofs;
   width = ndofs;

+#ifdef MFEM_USE_MPI
+   auto pfes = dynamic_cast<const ParFiniteElementSpace*>(&fes);
+#endif
+
   const Table &face2dof = fes.GetFaceToDofTable();

   const Mesh &mesh = *fes.GetMesh();
   int face_idx = 0;
-   gather_map.SetSize(nfdofs);
-   for (int f = 0; f < mesh.GetNumFaces(); ++f)
+   scatter_map.SetSize(nfdofs);
+   gather_map.SetSize(ndofs + nsdofs);
+   gather_map = -1;
+
+   Array<int> dofs;
+   for (int f = 0; f < mesh.GetNumFacesWithGhost(); ++f)
   {
      Mesh::FaceInformation face = mesh.GetFaceInformation(f);
-      if (!face.IsOfFaceType(type)) { continue; }
-      for (int i = 0; i < face_dofs; ++i)
+      if (!face.IsOfFaceType(type) || face.IsNonconformingCoarse()) { continue; }
+
+      if (f < mesh.GetNumFaces())
      {
-         gather_map[i + face_idx*face_dofs] = face2dof.GetJ()[i + f*face_dofs];
+         // Local face
+         face2dof.GetRow(f, dofs);
+         for (int i = 0; i < face_dofs; ++i)
+         {
+            scatter_map[i + face_idx*face_dofs] = dofs[i];
+            gather_map[dofs[i]] = i + face_idx*face_dofs;
+         }
+      }
+      else
+      {
+         // Shared (non-conforming) ghost face
+#ifdef MFEM_USE_MPI
+         MFEM_ASSERT(pfes != nullptr, "");
+         pfes->GetFaceNbrFaceVDofs(f, dofs);
+         for (int i = 0; i < face_dofs; ++i)
+         {
+            scatter_map[i + face_idx*face_dofs] = ndofs + dofs[i];
+            gather_map[ndofs + dofs[i]] = i + face_idx*face_dofs;
+         }
+#endif
      }
      ++face_idx;
   }
@@ -2314,13 +2353,19 @@ L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(

 void L2InterfaceFaceRestriction::Mult(const Vector &x, Vector &y) const
 {
+   const int NDOFS = ndofs;
   const int nd = face_dofs;
   const int nf = nfaces;
   const int vd = vdim;
   const bool t = byvdim;
-   const int *map = gather_map.Read();
+   const int *map = scatter_map.Read();
+
+   Vector face_nbr_data = GetLVectorFaceNbrData(fes, x, type);
+   MFEM_ASSERT(face_nbr_data.Size() / vd == nsdofs, "");

   const auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   const auto d_x_shared = Reshape(face_nbr_data.Read(),
+                                   t?vd:nsdofs, t?nsdofs:vd);
   auto d_y = Reshape(y.Write(), nd, vd, nf);

   mfem::forall(nd*nf, [=] MFEM_HOST_DEVICE (int i)
@@ -2328,7 +2373,8 @@ void L2InterfaceFaceRestriction::Mult(const Vector &x, Vector &y) const
      const int j = map[i];
      for (int c = 0; c < vd; ++c)
      {
-         d_y(i % nd, c, i / nd) = d_x(t?c:j, t?j:c);
+         if (j < NDOFS) { d_y(i % nd, c, i / nd) = d_x(t?c:j, t?j:c); }
+         else { d_y(i % nd, c, i / nd) = d_x_shared(t?c:(j-NDOFS), t?(j-NDOFS):c); }
      }
   });
 }
@@ -2343,15 +2389,39 @@ void L2InterfaceFaceRestriction::AddMultTranspose(
   const int *map = gather_map.Read();

   const auto d_x = Reshape(x.Read(), nd, vd, nf);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.ReadWrite(), t?vd:ndofs, t?ndofs:vd);

-   mfem::forall(ndofs, [=] MFEM_HOST_DEVICE (int i) { d_y[i] = 0.0; });
-   mfem::forall(nd*nf, [=] MFEM_HOST_DEVICE (int i)
+   mfem::forall(ndofs, [=] MFEM_HOST_DEVICE (int i)
   {
      const int j = map[i];
+      if (j < 0) { return; }
      for (int c = 0; c < vd; ++c)
      {
-         d_y(t?c:j, t?j:c) = d_x(i % nd, c, i / nd);
+         d_y(t?c:i, t?i:c) += a*d_x(j % nd, c, j / nd);
+      }
+   });
+}
+
+void L2InterfaceFaceRestriction::MultTransposeShared(
+   const Vector &x, Vector &y) const
+{
+   const int nd = face_dofs;
+   const int nf = nfaces;
+   const int vd = vdim;
+   const bool t = byvdim;
+   const int *map = gather_map.Read();
+
+   const auto d_x = Reshape(x.Read(), nd, vd, nf);
+   auto d_y = Reshape(y.Write(), t?vd:(ndofs+nsdofs), t?(ndofs+nsdofs):vd);
+   y = 0.0;
+
+   mfem::forall(ndofs + nsdofs, [=] MFEM_HOST_DEVICE (int i)
+   {
+      const int j = map[i];
+      if (j < 0) { return; }
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(t?c:i, t?i:c) = d_x(j % nd, c, j / nd);
      }
   });
 }
@@ -2361,6 +2431,11 @@ const Array<int> &L2InterfaceFaceRestriction::GatherMap() const
   return gather_map;
 }

+const Array<int> &L2InterfaceFaceRestriction::ScatterMap() const
+{
+   return scatter_map;
+}
+
 Vector GetLVectorFaceNbrData(
   const FiniteElementSpace &fes, const Vector &x, FaceType ftype)
 {
@@ -2382,6 +2457,7 @@ Vector GetLVectorFaceNbrData(
         {
            ParGridFunction gf(pfes, const_cast<Vector&>(x));
            gf.ExchangeFaceNbrData();
+            x.SyncMemory(gf);
            return std::move(gf.FaceNbrData());
         }
      }
@@ -812,13 +812,12 @@ protected:
       PointMatrix and a local face identifier. */
   using Key = std::pair<const DenseMatrix*,int>;
   /// The temporary map used to store the different interpolators.
-   using Map = std::map<Key, std::pair<int,const DenseMatrix*>>;
+   using Map =
+      std::unordered_map<Key, std::pair<int,const DenseMatrix*>, PairHasher>;
   Map interp_map; // The temporary map that stores the interpolators.

 public:
-   InterpolationManager() = delete;
-
-   /** @brief main constructor.
+   /** @brief Constructor.

       @param[in] fes      The FiniteElementSpace on which this operates
       @param[in] ordering Request a specific element ordering.
@@ -909,7 +908,7 @@ private:
 class NCL2FaceRestriction : virtual public L2FaceRestriction
 {
 protected:
-   InterpolationManager interpolations;
+   const InterpolationManager &interpolations;
   mutable Vector x_interp;

   /** @brief Constructs an NCL2FaceRestriction, this is a specialization of a
@@ -996,9 +995,7 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
   void FillI(SparseMatrix &mat,
              const bool keep_nbr_block = false) const override;

@@ -1016,9 +1013,7 @@ public:
       @param[in] keep_nbr_block When set to true the SparseMatrix will
                                 include the rows (in addition to the columns)
                                 corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
   void FillJAndData(const Vector &fea_data,
                     SparseMatrix &mat,
                     const bool keep_nbr_block = false) const override;
@@ -1036,9 +1031,7 @@ public:
                              added the face contributions.
                              The format is: dofs x dofs x ne, where dofs is the
                              number of dofs per element and ne the number of
-                              elements.
-
-       @warning This method is not implemented yet. */
+                              elements. */
   void AddFaceMatricesToElementMatrices(const Vector &fea_data,
                                         Vector &ea_data) const override;

@@ -1130,7 +1123,9 @@ protected:
   const int face_dofs; ///< Number of dofs on each face
   const int nfdofs; ///< Total number of dofs on the faces (E-vector size)
   const int ndofs; ///< Number of dofs in the space (L-vector size)
+   const int nsdofs; ///< Number of shared face neighbor (ghost) dofs
   Array<int> gather_map; ///< Gather map
+   Array<int> scatter_map; ///< Scatter map

 public:
   /** @brief Constructs an L2InterfaceFaceRestriction.
@@ -1168,7 +1163,24 @@ public:
   void AddMultTranspose(const Vector &x, Vector &y,
                         const real_t a = 1.0) const override;

+   /// @brief Gather degrees of freedom, from face E-vector to L-vector and
+   /// shared (ghost) DOFs.
+   ///
+   /// @param[in]     x The face E-Vector degrees of freedom with size
+   ///                  (face_dofs, vdim, nf), where nf is the number of
+   ///                  interior or boundary faces requested by @a type in the
+   ///                  constructor. The face_dofs should be ordered according
+   ///                  to the given ElementDofOrdering
+   /// @param[out]    y Vector of length vsize + face neighbor vsize
+   void MultTransposeShared(const Vector &x, Vector &y) const;
+
   const Array<int> &GatherMap() const override;
+
+   /// @brief Return the low-level mapping from L-dofs to E-dofs.
+   ///
+   /// L-dofs that do not correspond to an E-dof (e.g. that lie on a face of a
+   /// different type) are given index -1.
+   const Array<int> &ScatterMap() const;
 };

 /** @brief Convert a dof face index from Native ordering to lexicographic
@@ -333,6 +333,12 @@ void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
   int nel_ho = mesh_ho->GetNE();
   int nel_lor = mesh_lor->GetNE();

+   if (nel_ho == 0)
+   {
+      M_LH.SetSize(0);
+      return;
+   }
+
   const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();

   int nref_max = 0;
@@ -831,11 +837,17 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::Mult(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMult(
   const Vector &x, Vector &y) const
 {
+   const int nel_ho = fes_ho.GetMesh()->GetNE();
+
+   if (nel_ho == 0)
+   {
+      return;
+   }
+
   const int iho = 0;
   const int nref = ho2lor.RowSize(iho);
   const int ndof_ho = fes_ho.GetFE(iho)->GetDof();
   const int ndof_lor = fes_lor.GetFE(ho2lor.GetRow(iho)[0])->GetDof();
-   const int nel_ho = fes_ho.GetMesh()->GetNE();

   DenseTensor R_dt;
   R_dt.NewMemoryAndSize(R.GetMemory(), ndof_lor*nref, ndof_ho, nel_ho, false);
@@ -887,11 +899,17 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::MultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMultTranspose(
   const Vector &x, Vector &y) const
 {
+   const int nel_ho = fes_ho.GetMesh()->GetNE();
+
+   if (nel_ho == 0)
+   {
+      return;
+   }
+
   const int iho = 0;
   const int nref = ho2lor.RowSize(iho);
   const int ndof_ho = fes_ho.GetFE(iho)->GetDof();
   const int ndof_lor = fes_lor.GetFE(ho2lor.GetRow(iho)[0])->GetDof();
-   const int nel_ho = fes_ho.GetMesh()->GetNE();

   DenseTensor R_dt;
   R_dt.NewMemoryAndSize(R.GetMemory(), ndof_lor*nref, ndof_ho, nel_ho, false);
@@ -901,7 +919,6 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::Prolongate(
   const Vector &x, Vector &y) const
 {
-
   if (fes_ho.GetNE() == 0) { return; }

   if (use_ea)
@@ -960,14 +977,13 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAProlongate(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::ProlongateTranspose(
   const Vector &x, Vector &y) const
 {
+   if (fes_ho.GetNE() == 0) { return; }

   if (use_ea)
   {
      return EAProlongateTranspose(x,y);
   }

-
-   if (fes_ho.GetNE() == 0) { return; }
   MFEM_VERIFY(P.Size() > 0, "Prolongation not supported for these spaces.")
   int vdim = fes_ho.GetVDim();
   Array<int> vdofs;
@@ -1244,13 +1260,6 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space
   int ndof_ho = pfes_ho.GetNDofs();
   int ndof_lor = pfes_lor.GetNDofs();

-
-   // If the local mesh is empty, skip all computations
-   if (nel_ho == 0)
-   {
-      return;
-   }
-
   const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();

   int nref_max = 0;
@@ -1860,6 +1869,11 @@ L2ProjectionGridTransfer::H1SpaceMixedMassOperator::H1SpaceMixedMassOperator(
 void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::Mult(const Vector &x,
                                                              Vector &y) const
 {
+   if (fes_ho->GetNE() == 0)
+   {
+      return;
+   }
+
   const Operator* elem_restrict_ho = fes_ho->GetElementRestriction(
                                         ElementDofOrdering::NATIVE);
   const Operator* elem_restrict_lor = fes_lor->GetElementRestriction(
@@ -1906,6 +1920,11 @@ void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::Mult(const Vector &x,
 void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::MultTranspose(
   const Vector &x, Vector &y) const
 {
+   if (fes_ho->GetNE() == 0)
+   {
+      return;
+   }
+
   const Operator* elem_restrict_ho = fes_ho->GetElementRestriction(
                                         ElementDofOrdering::NATIVE);
   const Operator* elem_restrict_lor = fes_lor->GetElementRestriction(
@@ -18,6 +18,7 @@ list(APPEND SRCS
  gecko.cpp
  globals.cpp
  hash.cpp
+  hash_util.cpp
  isockstream.cpp
  mem_manager.cpp
  occa.cpp
@@ -46,6 +47,7 @@ list(APPEND HDRS
  globals.hpp
  zstr.hpp
  hash.hpp
+  hash_util.hpp
  isockstream.hpp
  kdtree.hpp
  mem_alloc.hpp
@@ -44,6 +44,7 @@
 #endif

 #if !defined(MFEM_USE_CUDA_OR_HIP)
+constexpr bool mfem_use_gpu = false;
 #define MFEM_DEVICE
 #define MFEM_HOST
 #define MFEM_LAMBDA
@@ -52,6 +53,7 @@
 #define MFEM_DEVICE_SYNC
 // MFEM_STREAM_SYNC is used for UVM and MPI GPU-Aware kernels
 #define MFEM_STREAM_SYNC
+#define MFEM_LAUNCH_BOUNDS(...)
 #endif

 #if !((defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__)) || \
@@ -20,9 +20,11 @@

 #if defined(MFEM_USE_CUDA) && defined(__CUDACC__)
 #define MFEM_USE_CUDA_OR_HIP
+constexpr bool mfem_use_gpu = true;
 #define MFEM_DEVICE __device__
 #define MFEM_HOST __host__
 #define MFEM_LAMBDA __host__
+#define MFEM_LAUNCH_BOUNDS __launch_bounds__
 // #define MFEM_HOST_DEVICE __host__ __device__ // defined in config/config.hpp
 #define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(cudaDeviceSynchronize())
 #define MFEM_STREAM_SYNC MFEM_GPU_CHECK(cudaStreamSynchronize(0))
@@ -295,11 +295,12 @@ using hip_threads_z =
 #endif

 #if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_CUDA) && defined(__CUDACC__)
-template <const int BLOCKS = MFEM_CUDA_BLOCKS, typename DBODY>
+template <typename DBODY>
 void RajaCuWrap1D(const int N, DBODY &&d_body)
 {
   //true denotes asynchronous kernel
-   RAJA::forall<RAJA::cuda_exec<BLOCKS,true>>(RAJA::RangeSegment(0,N),d_body);
+   RAJA::forall<RAJA::cuda_exec<MFEM_CUDA_BLOCKS,true>>(RAJA::RangeSegment(0,N),
+                                                        d_body);
 }

 template <typename DBODY>
@@ -362,18 +363,18 @@ struct RajaCuWrap;
 template <>
 struct RajaCuWrap<1>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
-      RajaCuWrap1D<BLCK>(N, d_body);
+      RajaCuWrap1D(N, d_body);
   }
 };

 template <>
 struct RajaCuWrap<2>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -384,7 +385,7 @@ struct RajaCuWrap<2>
 template <>
 struct RajaCuWrap<3>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -395,11 +396,12 @@ struct RajaCuWrap<3>
 #endif

 #if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_HIP) && defined(__HIP__)
-template <const int BLOCKS = MFEM_HIP_BLOCKS, typename DBODY>
+template <typename DBODY>
 void RajaHipWrap1D(const int N, DBODY &&d_body)
 {
   //true denotes asynchronous kernel
-   RAJA::forall<RAJA::hip_exec<BLOCKS,true>>(RAJA::RangeSegment(0,N),d_body);
+   RAJA::forall<RAJA::hip_exec<MFEM_HIP_BLOCKS,true>>(RAJA::RangeSegment(0,N),
+                                                      d_body);
 }

 template <typename DBODY>
@@ -462,18 +464,18 @@ struct RajaHipWrap;
 template <>
 struct RajaHipWrap<1>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
-      RajaHipWrap1D<BLCK>(N, d_body);
+      RajaHipWrap1D(N, d_body);
   }
 };

 template <>
 struct RajaHipWrap<2>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -484,7 +486,7 @@ struct RajaHipWrap<2>
 template <>
 struct RajaHipWrap<3>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -584,12 +586,31 @@ void CuKernel2D(const int N, BODY body)
   body(k);
 }

+// __launch_bounds__ second argument is omitted to get the default behavior
+template <int MAX_THREADS_PER_BLOCK, typename BODY>
+__global__
+MFEM_LAUNCH_BOUNDS(MAX_THREADS_PER_BLOCK)
+static void CuKernel2DLaunchBounds(const int N, BODY body)
+{
+   const int k = blockIdx.x*blockDim.z + threadIdx.z;
+   if (k >= N) { return; }
+   body(k);
+}
+
 template <typename BODY> __global__ static
 void CuKernel3D(const int N, BODY body)
 {
   for (int k = blockIdx.x; k < N; k += gridDim.x) { body(k); }
 }

+template <int MAX_THREADS_PER_BLOCK, typename BODY>
+__global__
+MFEM_LAUNCH_BOUNDS(MAX_THREADS_PER_BLOCK)
+static void CuKernel3DLaunchBounds(const int N, BODY body)
+{
+   for (int k = blockIdx.x; k < N; k += gridDim.x) { body(k); }
+}
+
 template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
 void CuWrap1D(const int N, DBODY &&d_body)
 {
@@ -604,6 +625,8 @@ void CuWrap2D(const int N, DBODY &&d_body,
              const int X, const int Y, const int BZ)
 {
   if (N==0) { return; }
+   // required for optimized GCC/NVCC builds to prevent runtime
+   // ODR/linkage violations of inlined templated kernel helpers
   MFEM_VERIFY(BZ>0, "");
   const int GRID = (N+BZ-1)/BZ;
   const dim3 BLCK(X,Y,BZ);
@@ -611,6 +634,19 @@ void CuWrap2D(const int N, DBODY &&d_body,
   MFEM_GPU_CHECK(cudaGetLastError());
 }

+template <int MAX_THREADS_PER_BLOCK, typename DBODY>
+void CuWrap2DLaunchBounds(const int N, DBODY &&d_body,
+                          const int X, const int Y, const int BZ)
+{
+   if (N==0) { return; }
+   MFEM_VERIFY(BZ>0, "");
+   const int GRID = (N+BZ-1)/BZ;
+   const dim3 BLCK(X,Y,BZ);
+   static_assert(MAX_THREADS_PER_BLOCK > 0);
+   CuKernel2DLaunchBounds<MAX_THREADS_PER_BLOCK><<<GRID,BLCK>>>(N, d_body);
+   MFEM_GPU_CHECK(cudaGetLastError());
+}
+
 template <typename DBODY>
 void CuWrap3D(const int N, DBODY &&d_body,
              const int X, const int Y, const int Z, const int G)
@@ -622,24 +658,35 @@ void CuWrap3D(const int N, DBODY &&d_body,
   MFEM_GPU_CHECK(cudaGetLastError());
 }

-template <int Dim>
-struct CuWrap;
-
-template <>
-struct CuWrap<1>
+template <int MAX_THREADS_PER_BLOCK, typename DBODY>
+void CuWrap3DLaunchBounds(const int N, DBODY &&d_body,
+                          const int X, const int Y, const int Z, const int G)
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   if (N==0) { return; }
+   const int GRID = G == 0 ? N : G;
+   const dim3 BLCK(X,Y,Z);
+   static_assert(MAX_THREADS_PER_BLOCK > 0);
+   CuKernel3DLaunchBounds<MAX_THREADS_PER_BLOCK><<<GRID, BLCK>>>(N, d_body);
+   MFEM_GPU_CHECK(cudaGetLastError());
+}
+
+template <int Dim, int MAX_THREADS_PER_BLOCK> struct CuWrap;
+
+template <int MAX_THREADS_PER_BLOCK>
+struct CuWrap<1, MAX_THREADS_PER_BLOCK>
+{
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
-      CuWrap1D<BLCK>(N, d_body);
+      CuWrap1D<MFEM_CUDA_BLOCKS>(N, d_body);
   }
 };

 template <>
-struct CuWrap<2>
+struct CuWrap<2, 0>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -647,10 +694,22 @@ struct CuWrap<2>
   }
 };

-template <>
-struct CuWrap<3>
+template <int MAX_THREADS_PER_BLOCK>
+struct CuWrap<2, MAX_THREADS_PER_BLOCK>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
+   static void run(const int N, DBODY &&d_body,
+                   const int X, const int Y, const int Z, const int G)
+   {
+      static_assert(MAX_THREADS_PER_BLOCK > 0);
+      CuWrap2DLaunchBounds<MAX_THREADS_PER_BLOCK>(N, d_body, X, Y, Z);
+   }
+};
+
+template <>
+struct CuWrap<3, 0>
+{
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -658,6 +717,17 @@ struct CuWrap<3>
   }
 };

+template <int MAX_THREADS_PER_BLOCK>
+struct CuWrap<3, MAX_THREADS_PER_BLOCK>
+{
+   template <typename DBODY>
+   static void run(const int N, DBODY &&d_body,
+                   const int X, const int Y, const int Z, const int G)
+   {
+      CuWrap3DLaunchBounds<MAX_THREADS_PER_BLOCK>(N, d_body, X, Y, Z, G);
+   }
+};
+
 #endif // defined(MFEM_USE_CUDA) && defined(__CUDACC__)


@@ -680,13 +750,31 @@ void HipKernel2D(const int N, BODY body)
   body(k);
 }

+template <int MAX_THREADS_PER_BLOCK, typename BODY>
+__global__
+MFEM_LAUNCH_BOUNDS(MAX_THREADS_PER_BLOCK)
+static void HipKernel2DLaunchBounds(const int N, BODY body)
+{
+   const int k = hipBlockIdx_x*hipBlockDim_z + hipThreadIdx_z;
+   if (k >= N) { return; }
+   body(k);
+}
+
 template <typename BODY> __global__ static
 void HipKernel3D(const int N, BODY body)
 {
   for (int k = hipBlockIdx_x; k < N; k += hipGridDim_x) { body(k); }
 }

-template <const int BLCK = MFEM_HIP_BLOCKS, typename DBODY>
+template <int MAX_THREADS_PER_BLOCK, typename BODY>
+__global__
+MFEM_LAUNCH_BOUNDS(MAX_THREADS_PER_BLOCK)
+static void HipKernel3DLaunchBounds(const int N, BODY body)
+{
+   for (int k = hipBlockIdx_x; k < N; k += hipGridDim_x) { body(k); }
+}
+
+template <int BLCK = MFEM_HIP_BLOCKS, typename DBODY>
 void HipWrap1D(const int N, DBODY &&d_body)
 {
   if (N==0) { return; }
@@ -700,12 +788,27 @@ void HipWrap2D(const int N, DBODY &&d_body,
               const int X, const int Y, const int BZ)
 {
   if (N==0) { return; }
+   MFEM_VERIFY(BZ>0, "");
   const int GRID = (N+BZ-1)/BZ;
   const dim3 BLCK(X,Y,BZ);
   hipLaunchKernelGGL(HipKernel2D,GRID,BLCK,0,nullptr,N,d_body);
   MFEM_GPU_CHECK(hipGetLastError());
 }

+template <int MAX_THREADS_PER_BLOCK, typename DBODY>
+void HipWrap2DLaunchBounds(const int N, DBODY &&d_body,
+                           const int X, const int Y, const int BZ)
+{
+   if (N==0) { return; }
+   MFEM_VERIFY(BZ>0, "");
+   const int GRID = (N+BZ-1)/BZ;
+   const dim3 BLCK(X,Y,BZ);
+   static_assert(MAX_THREADS_PER_BLOCK > 0);
+   HipKernel2DLaunchBounds<MAX_THREADS_PER_BLOCK><<<dim3(GRID), dim3(BLCK), 0, 0>>>
+   (N, d_body);
+   MFEM_GPU_CHECK(hipGetLastError());
+}
+
 template <typename DBODY>
 void HipWrap3D(const int N, DBODY &&d_body,
               const int X, const int Y, const int Z, const int G)
@@ -717,24 +820,36 @@ void HipWrap3D(const int N, DBODY &&d_body,
   MFEM_GPU_CHECK(hipGetLastError());
 }

-template <int Dim>
-struct HipWrap;
-
-template <>
-struct HipWrap<1>
+template <int MAX_THREADS_PER_BLOCK, typename DBODY>
+void HipWrap3DLaunchBounds(const int N, DBODY &&d_body,
+                           const int X, const int Y, const int Z, const int G)
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   if (N==0) { return; }
+   const int GRID = G == 0 ? N : G;
+   const dim3 BLCK(X,Y,Z);
+   static_assert(MAX_THREADS_PER_BLOCK > 0);
+   HipKernel3DLaunchBounds<MAX_THREADS_PER_BLOCK><<<dim3(GRID), dim3(BLCK), 0, 0>>>
+   (N, d_body);
+   MFEM_GPU_CHECK(hipGetLastError());
+}
+
+template <int Dim, int MAX_THREADS_PER_BLOCK> struct HipWrap;
+
+template <int MAX_THREADS_PER_BLOCK>
+struct HipWrap<1, MAX_THREADS_PER_BLOCK>
+{
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
-      HipWrap1D<BLCK>(N, d_body);
+      HipWrap1D<MFEM_HIP_BLOCKS>(N, d_body);
   }
 };

 template <>
-struct HipWrap<2>
+struct HipWrap<2, 0>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -742,10 +857,21 @@ struct HipWrap<2>
   }
 };

-template <>
-struct HipWrap<3>
+template <int MAX_THREADS_PER_BLOCK>
+struct HipWrap<2, MAX_THREADS_PER_BLOCK>
 {
-   template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+   template <typename DBODY>
+   static void run(const int N, DBODY &&d_body,
+                   const int X, const int Y, const int Z, const int G)
+   {
+      HipWrap2DLaunchBounds<MAX_THREADS_PER_BLOCK>(N, d_body, X, Y, Z);
+   }
+};
+
+template <>
+struct HipWrap<3, 0>
+{
+   template <typename DBODY>
   static void run(const int N, DBODY &&d_body,
                   const int X, const int Y, const int Z, const int G)
   {
@@ -753,11 +879,24 @@ struct HipWrap<3>
   }
 };

+template <int MAX_THREADS_PER_BLOCK>
+struct HipWrap<3, MAX_THREADS_PER_BLOCK>
+{
+   template <typename DBODY>
+   static void run(const int N, DBODY &&d_body,
+                   const int X, const int Y, const int Z, const int G)
+   {
+      HipWrap3DLaunchBounds<MAX_THREADS_PER_BLOCK>(N, d_body, X, Y, Z, G);
+   }
+};
+
 #endif // defined(MFEM_USE_HIP) && defined(__HIP__)


-/// The forall kernel body wrapper
-template <const int DIM, typename d_lambda, typename h_lambda>
+///////////////////////////////////////////////////////////////////////////////
+/// Forall host & device kernel dispatch
+template <int DIM, int MAX_THREADS_PER_BLOCK = 0,
+          typename d_lambda, typename h_lambda>
 inline void ForallWrap(const bool use_dev, const int N,
                       d_lambda &&d_body, h_lambda &&h_body,
                       const int X=0, const int Y=0, const int Z=0,
@@ -790,7 +929,7 @@ inline void ForallWrap(const bool use_dev, const int N,
   // If Backend::CUDA is allowed, use it
   if (Device::Allows(Backend::CUDA))
   {
-      return CuWrap<DIM>::run(N, d_body, X, Y, Z, G);
+      return CuWrap<DIM, MAX_THREADS_PER_BLOCK>::run(N, d_body, X, Y, Z, G);
   }
 #endif

@@ -798,7 +937,7 @@ inline void ForallWrap(const bool use_dev, const int N,
   // If Backend::HIP is allowed, use it
   if (Device::Allows(Backend::HIP))
   {
-      return HipWrap<DIM>::run(N, d_body, X, Y, Z, G);
+      return HipWrap<DIM, MAX_THREADS_PER_BLOCK>::run(N, d_body, X, Y, Z, G);
   }
 #endif

@@ -827,7 +966,9 @@ backend_cpu:
   for (int k = 0; k < N; k++) { h_body(k); }
 }

-template <const int DIM, typename lambda>
+///////////////////////////////////////////////////////////////////////////////
+/// Forall host & device kernel wrappers
+template <int DIM, typename lambda>
 inline void ForallWrap(const bool use_dev, const int N, lambda &&body,
                       const int X=0, const int Y=0, const int Z=0,
                       const int G=0)
@@ -835,6 +976,16 @@ inline void ForallWrap(const bool use_dev, const int N, lambda &&body,
   ForallWrap<DIM>(use_dev, N, body, body, X, Y, Z, G);
 }

+template <int DIM, int MAX_THREADS_PER_BLOCK, typename lambda>
+inline void ForallWrap(const bool use_dev, const int N, lambda &&body,
+                       const int X=0, const int Y=0, const int Z=0,
+                       const int G=0)
+{
+   ForallWrap<DIM, MAX_THREADS_PER_BLOCK>(use_dev, N, body, body, X, Y, Z, G);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// forall interfaces
 template<typename lambda>
 inline void forall(int N, lambda &&body) { ForallWrap<1>(true, N, body); }

@@ -843,7 +994,7 @@ inline void forall(int Nx, int Ny, lambda &&body)
 {
   if (Device::Allows(Backend::DEVICE_MASK))
   {
-      forall(Nx * Ny, [=] MFEM_HOST_DEVICE(int idx)
+      mfem::forall(Nx * Ny, [=] MFEM_HOST_DEVICE(int idx)
      {
         int j = idx / Nx;
         int i = idx % Nx;
@@ -879,7 +1030,7 @@ inline void forall(int Nx, int Ny, int Nz, lambda &&body)
 {
   if (Device::Allows(Backend::DEVICE_MASK))
   {
-      forall(Nx * Ny * Nz, [=] MFEM_HOST_DEVICE(int idx)
+      mfem::forall(Nx * Ny * Nz, [=] MFEM_HOST_DEVICE(int idx)
      {
         int i = idx % Nx;
         int j = idx / Nx;
@@ -927,6 +1078,12 @@ inline void forall_2D(int N, int X, int Y, lambda &&body)
   ForallWrap<2>(true, N, body, X, Y, 1);
 }

+template<int MAX_THREADS_PER_BLOCK, typename lambda>
+inline void forall_2D(int N, int X, int Y, lambda &&body)
+{
+   ForallWrap<2, MAX_THREADS_PER_BLOCK>(true, N, body, X, Y, 1);
+}
+
 template<typename lambda>
 inline void forall_2D_batch(int N, int X, int Y, int BZ, lambda &&body)
 {
@@ -939,6 +1096,12 @@ inline void forall_3D(int N, int X, int Y, int Z, lambda &&body)
   ForallWrap<3>(true, N, body, X, Y, Z, 0);
 }

+template<int MAX_THREADS_PER_BLOCK, typename lambda>
+inline void forall_3D(int N, int X, int Y, int Z, lambda &&body)
+{
+   ForallWrap<3, MAX_THREADS_PER_BLOCK>(true, N, body, X, Y, Z, 0);
+}
+
 template<typename lambda>
 inline void forall_3D_grid(int N, int X, int Y, int Z, int G, lambda &&body)
 {
@@ -80,159 +80,4 @@ std::string HashFunction::GetHash() const
   return hash;
 }

-constexpr static uint64_t rotl64(uint64_t x, int r)
-{
-   return (x << r) | (x >> (64 - r));
-}
-
-void Hasher::init(uint64_t seed)
-{
-   data[0] = seed;
-   data[1] = seed;
-   nbytes = 0;
-}
-
-void Hasher::add_block(uint64_t k1, uint64_t k2)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] = rotl64(data[0], 27);
-   data[0] += data[1];
-   data[0] = data[0] * 5 + 0x52dce729ull;
-
-   k2 *= c2;
-   k2 = rotl64(k2, 33);
-   k2 *= c1;
-   data[1] ^= k2;
-
-   data[1] = rotl64(data[1], 31);
-   data[1] += data[0];
-   data[1] = data[1] * 5 + 0x38495ab5ull;
-}
-
-static uint64_t fmix64(uint64_t k)
-{
-   // http://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html
-   // mix13
-   k ^= k >> 30;
-   k *= 0xbf58476d1ce4e5b9ull;
-   k ^= k >> 27;
-   k *= 0x94d049bb133111ebull;
-   k ^= k >> 31;
-   return k;
-}
-
-void Hasher::append(const uint8_t *vs, uint64_t bytes)
-{
-   if (bytes == 0)
-   {
-      return;
-   }
-   auto rem = nbytes % 16;
-   nbytes += bytes;
-   uint8_t *tmp = reinterpret_cast<uint8_t *>(buf_);
-   while (true)
-   {
-      if (bytes + rem >= 16)
-      {
-         std::copy(vs, vs + 16 - rem, tmp + rem);
-         add_block(buf_[0], buf_[1]);
-         vs += (16 - rem);
-         bytes -= (16 - rem);
-         rem = 0;
-      }
-      else
-      {
-         std::copy(vs, vs + bytes, tmp + rem);
-         return;
-      }
-   }
-}
-
-void Hasher::finalize()
-{
-   auto rem = nbytes % 16;
-   if (rem > 0)
-   {
-      nbytes -= rem;
-      if (rem <= 8)
-      {
-         finalize(buf_[0], rem);
-      }
-      else
-      {
-         finalize(buf_[0], buf_[1], rem);
-      }
-      return;
-   }
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
-void Hasher::finalize(uint64_t k1, int num)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-   nbytes += num;
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
-void Hasher::finalize(uint64_t k1, uint64_t k2, int num)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-   nbytes += num;
-   k2 *= c2;
-   k2 = rotl64(k2, 33);
-   k2 *= c1;
-   data[1] ^= k2;
-
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
 } // namespace mfem
@@ -15,8 +15,8 @@
 #include "../config/config.hpp"
 #include "array.hpp"
 #include "globals.hpp"
+#include "hash_util.hpp"

-#include <array>
 #include <cstdint>
 #include <type_traits>
 #include <utility>
@@ -457,75 +457,6 @@ protected:
   int BinSize(int idx) const;
 };

-///
-/// @brief streaming implementation for murmurhash3 128 (x64).
-/// Constructs the hash in 3 stages: init, append, finalize.
-///
-struct Hasher
-{
-   /// where the final hash result is stored after finalize. Use data[1] when
-   /// only 64 bits are required.
-   uint64_t data[2] = {0, 0};
-
-private:
-   uint64_t nbytes = 0;
-
-   uint64_t buf_[2] = {0, 0};
-
-public:
-
-   /// resets this hasher back to an initial seed
-   void init(uint64_t seed = 0);
-   void append(const uint8_t *vs, uint64_t bytes);
-
-   void finalize();
-
-private:
-   // add 16 bytes
-   void add_block(uint64_t k1, uint64_t k2);
-
-   // add [1-8] more bytes, then finalize
-   void finalize(uint64_t k1, int num);
-
-   // add [1-15] more bytes, then finalize
-   // 0 < num < 16
-   void finalize(uint64_t k1, uint64_t k2, int num);
-};
-
-/// Helper class for hashing std::pair. Usable in place of std::hash<std::pair<T,U>>
-struct PairHasher
-{
-   template <class T, class V>
-   size_t operator()(const std::pair<T, V> &v) const noexcept
-   {
-      Hasher hash;
-      // chosen randomly with a 2^64-sided dice
-      hash.init(0xfebd1fe69813c14full);
-      hash.append(reinterpret_cast<const uint8_t *>(&v.first), sizeof(T));
-      hash.append(reinterpret_cast<const uint8_t *>(&v.second), sizeof(V));
-      hash.finalize();
-      return hash.data[1];
-   }
-};
-
-/// Helper class for hashing std::array. Usable in place of std::hash<std::array<T,N>>
-struct ArrayHasher
-{
-   template <class T, size_t N>
-   size_t operator()(const std::array<T, N> &v) const noexcept
-   {
-      Hasher hash;
-      // chosen randomly with a 2^64-sided dice
-      hash.init(0xfebd1fe69813c14full);
-      for (size_t i = 0; i < N; ++i)
-      {
-         hash.append(reinterpret_cast<const uint8_t *>(&v[i]), sizeof(T));
-      }
-      hash.finalize();
-      return hash.data[1];
-   }
-};
-
 /// Hash function for data sequences.
 /** Depends on GnuTLS for SHA-256 hashing. */
 class HashFunction
@@ -0,0 +1,172 @@
+// 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 "hash_util.hpp"
+
+namespace mfem
+{
+
+constexpr static uint64_t rotl64(uint64_t x, int r)
+{
+   return (x << r) | (x >> (64 - r));
+}
+
+void Hasher::init(uint64_t seed)
+{
+   data[0] = seed;
+   data[1] = seed;
+   nbytes = 0;
+}
+
+void Hasher::add_block(uint64_t k1, uint64_t k2)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] = rotl64(data[0], 27);
+   data[0] += data[1];
+   data[0] = data[0] * 5 + 0x52dce729ull;
+
+   k2 *= c2;
+   k2 = rotl64(k2, 33);
+   k2 *= c1;
+   data[1] ^= k2;
+
+   data[1] = rotl64(data[1], 31);
+   data[1] += data[0];
+   data[1] = data[1] * 5 + 0x38495ab5ull;
+}
+
+static uint64_t fmix64(uint64_t k)
+{
+   // http://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html
+   // mix13
+   k ^= k >> 30;
+   k *= 0xbf58476d1ce4e5b9ull;
+   k ^= k >> 27;
+   k *= 0x94d049bb133111ebull;
+   k ^= k >> 31;
+   return k;
+}
+
+void Hasher::append(const std::byte *vs, uint64_t bytes)
+{
+   if (bytes == 0)
+   {
+      return;
+   }
+   auto rem = nbytes % 16;
+   nbytes += bytes;
+   std::byte *tmp = reinterpret_cast<std::byte *>(buf_);
+   while (true)
+   {
+      if (bytes + rem >= 16)
+      {
+         std::copy(vs, vs + 16 - rem, tmp + rem);
+         add_block(buf_[0], buf_[1]);
+         vs += (16 - rem);
+         bytes -= (16 - rem);
+         rem = 0;
+      }
+      else
+      {
+         std::copy(vs, vs + bytes, tmp + rem);
+         return;
+      }
+   }
+}
+
+void Hasher::finalize()
+{
+   auto rem = nbytes % 16;
+   if (rem > 0)
+   {
+      nbytes -= rem;
+      if (rem <= 8)
+      {
+         finalize(buf_[0], rem);
+      }
+      else
+      {
+         finalize(buf_[0], buf_[1], rem);
+      }
+      return;
+   }
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+void Hasher::finalize(uint64_t k1, int num)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+   nbytes += num;
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+void Hasher::finalize(uint64_t k1, uint64_t k2, int num)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+   nbytes += num;
+   k2 *= c2;
+   k2 = rotl64(k2, 33);
+   k2 *= c1;
+   data[1] ^= k2;
+
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+}
@@ -0,0 +1,172 @@
+// 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_HASH_UTIL_HPP
+#define MFEM_HASH_UTIL_HPP
+
+#include <array>
+#include <cstddef>
+#include <tuple>
+#include <functional>
+#include <utility>
+#include <cstdint>
+
+namespace mfem
+{
+
+/// @brief streaming implementation for murmurhash3 128 (x64).
+///
+/// Constructs the hash in 3 stages: init, append, finalize.
+struct Hasher
+{
+   /// @brief Storage for the final hash result after finalize() is called.
+   ///
+   /// Use data[1] when only 64 bits are required.
+   uint64_t data[2] = {0, 0};
+
+private:
+   uint64_t nbytes = 0;
+   uint64_t buf_[2] = {0, 0};
+
+public:
+
+   /// Resets the Hasher back to an initial seed
+   void init(uint64_t seed = 0);
+
+   /// Append data @a vs of size @a bytes.
+   void append(const std::byte *vs, uint64_t bytes);
+
+   void finalize();
+
+private:
+   /// Add a block of 16 bytes.
+   void add_block(uint64_t k1, uint64_t k2);
+
+   /// @brief Add [1-8] more bytes, then finalize.
+   ///
+   /// @a num must satisfy 0 < num < 9.
+   void finalize(uint64_t k1, int num);
+
+   /// @brief Add [1-15] more bytes, then finalize.
+   ///
+   /// @a num must satisfy 0 < num < 16.
+   void finalize(uint64_t k1, uint64_t k2, int num);
+};
+
+template <class T> struct ChainedHasher
+{
+   static void Append(Hasher &hasher, const T &value)
+   {
+      if constexpr (std::is_fundamental_v<T> || std::is_pointer_v<T>)
+      {
+         hasher.append(reinterpret_cast<const std::byte *>(&value), sizeof(T));
+      }
+      else
+      {
+         std::hash<T> h;
+         auto v = h(value);
+         hasher.append(reinterpret_cast<std::byte *>(&v), sizeof(v));
+      }
+   }
+};
+
+template <class T, class V> struct ChainedHasher<std::pair<T, V>>
+{
+   static void Append(Hasher &hasher, const std::pair<T, V> &value)
+   {
+      ChainedHasher<T>::Append(hasher, value.first);
+      ChainedHasher<V>::Append(hasher, value.second);
+   }
+};
+
+template <class T, size_t N> struct ChainedHasher<std::array<T, N>>
+{
+   static void Append(Hasher &hasher, const std::array<T, N> &value)
+   {
+      for (size_t i = 0; i < N; ++i)
+      {
+         ChainedHasher<T>::Append(hasher, value[i]);
+      }
+   }
+};
+
+template<class... Ts> struct ChainedHasher<std::tuple<Ts...>>
+{
+private:
+   template <size_t N>
+   static void AppendImpl(Hasher &hasher, const std::tuple<Ts...> &value)
+   {
+      ChainedHasher<std::decay_t<decltype(std::get<N>(value))>>::Append(
+                                                                hasher, std::get<N>(value));
+      if constexpr (N + 1 < sizeof...(Ts))
+      {
+         AppendImpl<N + 1>(hasher, value);
+      }
+   }
+
+public:
+   static void Append(Hasher &hasher, const std::tuple<Ts...> &value)
+   {
+      if constexpr (sizeof...(Ts))
+      {
+         AppendImpl<0>(hasher, value);
+      }
+   }
+};
+
+/// Helper class for hashing std::pair of hashable types.
+struct PairHasher
+{
+   template <class T, class V>
+   size_t operator()(const std::pair<T, V> &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<std::pair<T, V>>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+/// Helper class for hashing std::array of a hashable type.
+struct ArrayHasher
+{
+   template <class T, size_t N>
+   size_t operator()(const std::array<T, N> &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<std::array<T, N>>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+/// Helper class for hashing std::tuple of hashable types.
+struct TupleHasher
+{
+   template <class T>
+   size_t operator()(const T &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<T>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+} // namespace mfem
+
+#endif
@@ -20,9 +20,11 @@

 #if defined(MFEM_USE_HIP) && defined(__HIP__)
 #define MFEM_USE_CUDA_OR_HIP
+constexpr bool mfem_use_gpu = true;
 #define MFEM_DEVICE __device__
 #define MFEM_HOST __host__
 #define MFEM_LAMBDA __host__ __device__
+#define MFEM_LAUNCH_BOUNDS __launch_bounds__
 // #define MFEM_HOST_DEVICE __host__ __device__ // defined in config/config.hpp
 #define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(hipDeviceSynchronize())
 #define MFEM_STREAM_SYNC MFEM_GPU_CHECK(hipStreamSynchronize(0))
@@ -55,6 +55,7 @@ list(APPEND HDRS
  dinvariants.hpp
  dtensor.hpp
  dual.hpp
+  eigensolver.hpp
  filteredsolver.hpp
  handle.hpp
  invariants.hpp
@@ -1370,6 +1370,35 @@ void DenseMatrix::Getl1Diag(Vector &l) const
      }
 }

+void DenseMatrix::GetRowl1(Vector &l) const
+{
+   l.SetSize(height);
+   l = 0.0;
+
+   for (int j = 0; j < width; ++j)
+      for (int i = 0; i < height; ++i)
+      {
+         l(i) += fabs((*this)(i,j));
+      }
+}
+
+void DenseMatrix::GetRowl2(Vector &l) const
+{
+   l.SetSize(height);
+   l = 0.0;
+
+   for (int j = 0; j < width; ++j)
+      for (int i = 0; i < height; ++i)
+      {
+         l[i] += operator()(i,j)*operator()(i,j);
+      }
+
+   for (int i = 0; i < height; ++i)
+   {
+      l[i] = sqrt(l[i]);
+   }
+}
+
 void DenseMatrix::GetRowSums(Vector &l) const
 {
   l.SetSize(height);
@@ -346,8 +346,12 @@ public:
   /// Returns the diagonal of the matrix
   void GetDiag(Vector &d) const;
   /// Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|
-   void Getl1Diag(Vector &l) const;
-   /// Compute the row sums of the DenseMatrix
+   MFEM_DEPRECATED void Getl1Diag(Vector &l) const;
+   /// Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|
+   void GetRowl1(Vector &l) const;
+   /// Returns the l2norm of the rows of the DenseMatrix
+   void GetRowl2(Vector &l) const;
+   /// Returns the row sums of the DenseMatrix
   void GetRowSums(Vector &l) const;

   /// Creates n x n diagonal matrix with diagonal elements c
@@ -0,0 +1,203 @@
+// 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
@@ -3634,12 +3634,25 @@ void HypreSmoother::SetType(HypreSmoother::Type type_, int relax_times_)
   relax_times = relax_times_;
 }

+void HypreSmoother::GetType(HypreSmoother::Type &type_, int &relax_times_) const
+{
+   type_ = static_cast<HypreSmoother::Type>(type);
+   relax_times_ = relax_times;
+}
+
 void HypreSmoother::SetSOROptions(real_t relax_weight_, real_t omega_)
 {
   relax_weight = relax_weight_;
   omega = omega_;
 }

+void HypreSmoother::GetSOROptions(real_t &relax_weight_, real_t &omega_) const
+{
+   // TODO: are these used for all smoother types?
+   relax_weight_ = relax_weight;
+   omega_ = omega;
+}
+
 void HypreSmoother::SetPolyOptions(int poly_order_, real_t poly_fraction_,
                                   int eig_est_cg_iter_)
 {
@@ -3648,6 +3661,15 @@ void HypreSmoother::SetPolyOptions(int poly_order_, real_t poly_fraction_,
   eig_est_cg_iter = eig_est_cg_iter_;
 }

+void HypreSmoother::GetPolyOptions(int &poly_order_, real_t &poly_fraction_,
+                                   int &eig_est_cg_iter_) const
+{
+   // TODO: are these used for all smoother types?
+   poly_order_ = poly_order;
+   poly_fraction_ = poly_fraction;
+   eig_est_cg_iter_ = eig_est_cg_iter;
+}
+
 void HypreSmoother::SetTaubinOptions(real_t lambda_, real_t mu_,
                                     int taubin_iter_)
 {
@@ -3656,6 +3678,14 @@ void HypreSmoother::SetTaubinOptions(real_t lambda_, real_t mu_,
   taubin_iter = taubin_iter_;
 }

+void HypreSmoother::GetTaubinOptions(real_t &lambda_, real_t &mu_,
+                                     int &taubin_iter_) const
+{
+   lambda_ = lambda;
+   mu_ = mu;
+   taubin_iter_ = taubin_iter;
+}
+
 void HypreSmoother::SetWindowByName(const char* name)
 {
   real_t a = -1, b, c;
@@ -3678,6 +3708,13 @@ void HypreSmoother::SetWindowParameters(real_t a, real_t b, real_t c)
   window_params[2] = c;
 }

+void HypreSmoother::GetWindowParameters(real_t &a, real_t &b, real_t &c) const
+{
+   a = window_params[0];
+   b = window_params[1];
+   c = window_params[2];
+}
+
 void HypreSmoother::SetOperator(const Operator &op)
 {
   A = const_cast<HypreParMatrix *>(dynamic_cast<const HypreParMatrix *>(&op));
@@ -4173,12 +4210,20 @@ HypreSolver::~HypreSolver()
   auxX.Delete();
 }

+void HyprePCG::SetDefaultOptions()
+{
+   // Explicitly set just in case past/future versions of hypre change the
+   // defaults
+   SetTol(1e-6);
+   SetMaxIter(1000);
+}

 HyprePCG::HyprePCG(MPI_Comm comm) : precond(NULL)
 {
   iterative_mode = true;

   HYPRE_ParCSRPCGCreate(comm, &pcg_solver);
+   SetDefaultOptions();
 }

 HyprePCG::HyprePCG(const HypreParMatrix &A_) : HypreSolver(&A_), precond(NULL)
@@ -4190,6 +4235,7 @@ HyprePCG::HyprePCG(const HypreParMatrix &A_) : HypreSolver(&A_), precond(NULL)
   HYPRE_ParCSRMatrixGetComm(*A, &comm);

   HYPRE_ParCSRPCGCreate(comm, &pcg_solver);
+   SetDefaultOptions();
 }

 void HyprePCG::SetOperator(const Operator &op)
@@ -4214,21 +4260,54 @@ void HyprePCG::SetOperator(const Operator &op)
   auxX.Delete(); auxX.Reset();
 }

+void HyprePCG::SetUseTwoNorm(bool val)
+{
+   HYPRE_PCGSetTwoNorm(pcg_solver, val);
+}
+
+bool HyprePCG::GetUseTwoNorm() const
+{
+   HYPRE_Int val;
+   HYPRE_PCGGetTwoNorm(pcg_solver, &val);
+   return val != 0;
+}
+
 void HyprePCG::SetTol(real_t tol)
 {
   HYPRE_PCGSetTol(pcg_solver, tol);
 }

+real_t HyprePCG::GetTol() const
+{
+   HYPRE_Real tol;
+   HYPRE_PCGGetTol(pcg_solver, &tol);
+   return tol;
+}
+
 void HyprePCG::SetAbsTol(real_t atol)
 {
   HYPRE_PCGSetAbsoluteTol(pcg_solver, atol);
 }

+real_t HyprePCG::GetAbsTol() const
+{
+   HYPRE_Real atol;
+   hypre_PCGGetAbsoluteTol(pcg_solver, &atol);
+   return atol;
+}
+
 void HyprePCG::SetMaxIter(int max_iter)
 {
   HYPRE_PCGSetMaxIter(pcg_solver, max_iter);
 }

+int HyprePCG::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_PCGGetMaxIter(pcg_solver, &max_iter);
+   return max_iter;
+}
+
 void HyprePCG::SetLogging(int logging)
 {
   HYPRE_PCGSetLogging(pcg_solver, logging);
@@ -4344,6 +4423,20 @@ HyprePCG::~HyprePCG()
   HYPRE_ParCSRPCGDestroy(pcg_solver);
 }

+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HyprePCG::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRPCGGetResidual(pcg_solver, &r);
+   return HypreParVector(r);
+}
+
+void HyprePCG::GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif

 HypreGMRES::HypreGMRES(MPI_Comm comm) : precond(NULL)
 {
@@ -4399,26 +4492,69 @@ void HypreGMRES::SetOperator(const Operator &op)
   auxX.Delete(); auxX.Reset();
 }

+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HypreGMRES::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRGMRESGetResidual(gmres_solver, &r);
+   return HypreParVector(r);
+}
+
+void HypreGMRES::GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif
+
 void HypreGMRES::SetTol(real_t tol)
 {
   HYPRE_GMRESSetTol(gmres_solver, tol);
 }

+real_t HypreGMRES::GetTol()const
+{
+   HYPRE_Real tol;
+   HYPRE_GMRESGetTol(gmres_solver, &tol);
+   return tol;
+}
+
 void HypreGMRES::SetAbsTol(real_t tol)
 {
   HYPRE_GMRESSetAbsoluteTol(gmres_solver, tol);
 }

+real_t HypreGMRES::GetAbsTol() const
+{
+   HYPRE_Real atol;
+   HYPRE_GMRESGetAbsoluteTol(gmres_solver, &atol);
+   return atol;
+}
+
 void HypreGMRES::SetMaxIter(int max_iter)
 {
   HYPRE_GMRESSetMaxIter(gmres_solver, max_iter);
 }

+int HypreGMRES::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_GMRESGetMaxIter(gmres_solver, &max_iter);
+   return max_iter;
+}
+
 void HypreGMRES::SetKDim(int k_dim)
 {
   HYPRE_GMRESSetKDim(gmres_solver, k_dim);
 }

+int HypreGMRES::GetKDim() const
+{
+   HYPRE_Int k_dim;
+   HYPRE_GMRESGetKDim(gmres_solver, &k_dim);
+   return k_dim;
+}
+
 void HypreGMRES::SetLogging(int logging)
 {
   HYPRE_GMRESSetLogging(gmres_solver, logging);
@@ -4576,16 +4712,37 @@ void HypreFGMRES::SetTol(real_t tol)
   HYPRE_ParCSRFlexGMRESSetTol(fgmres_solver, tol);
 }

+real_t HypreFGMRES::GetTol() const
+{
+   HYPRE_Real tol;
+   HYPRE_FlexGMRESGetTol(fgmres_solver, &tol);
+   return tol;
+}
+
 void HypreFGMRES::SetMaxIter(int max_iter)
 {
   HYPRE_ParCSRFlexGMRESSetMaxIter(fgmres_solver, max_iter);
 }

+int HypreFGMRES::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_FlexGMRESGetMaxIter(fgmres_solver, &max_iter);
+   return max_iter;
+}
+
 void HypreFGMRES::SetKDim(int k_dim)
 {
   HYPRE_ParCSRFlexGMRESSetKDim(fgmres_solver, k_dim);
 }

+int HypreFGMRES::GetKDim() const
+{
+   HYPRE_Int k_dim;
+   HYPRE_FlexGMRESGetKDim(fgmres_solver, &k_dim);
+   return k_dim;
+}
+
 void HypreFGMRES::SetLogging(int logging)
 {
   HYPRE_ParCSRFlexGMRESSetLogging(fgmres_solver, logging);
@@ -4682,6 +4839,21 @@ HypreFGMRES::~HypreFGMRES()
   HYPRE_ParCSRFlexGMRESDestroy(fgmres_solver);
 }

+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HypreFGMRES::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRFlexGMRESGetResidual(fgmres_solver, &r);
+   return HypreParVector(r);
+}
+
+void HypreFGMRES::GetFinalAbsResidualNorm(real_t &final_res_norm,
+                                          real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif

 void HypreDiagScale::SetOperator(const Operator &op)
 {
@@ -5170,6 +5342,13 @@ void HypreBoomerAMG::ResetAMGPrecond()
   }
 }

+int HypreBoomerAMG::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_BoomerAMGGetMaxIter(amg_precond, &max_iter);
+   return max_iter;
+}
+
 void HypreBoomerAMG::SetOperator(const Operator &op)
 {
   const HypreParMatrix *new_A = dynamic_cast<const HypreParMatrix *>(&op);
@@ -1160,6 +1160,15 @@ public:
      return HypreUsingGPU() ? l1Jacobi : l1GS;
   }

+   /// Default solver settings:
+   /// type = DefaultType()
+   /// relax_times = 1
+   /// omega = 1.0
+   /// poly_order = 2
+   /// poly_fraction = 0.3
+   /// lambda = 0.5
+   /// mu = -0.5
+   /// taubin_iter = 40
   HypreSmoother();

   HypreSmoother(const HypreParMatrix &A_, int type = DefaultType(),
@@ -1169,20 +1178,28 @@ public:

   /// Set the relaxation type and number of sweeps
   void SetType(HypreSmoother::Type type, int relax_times = 1);
+   using Operator::GetType;
+   void GetType(HypreSmoother::Type &type, int &relax_times) const;
   /// Set SOR-related parameters
   void SetSOROptions(real_t relax_weight, real_t omega);
+   void GetSOROptions(real_t &relax_weight, real_t &omega) const;
+
   /// Set parameters for polynomial smoothing
   /** By default, 10 iterations of CG are used to estimate the eigenvalues.
       Setting eig_est_cg_iter = 0 uses hypre's hypre_ParCSRMaxEigEstimate() instead. */
   void SetPolyOptions(int poly_order, real_t poly_fraction,
                       int eig_est_cg_iter = 10);
+   void GetPolyOptions(int &poly_order, real_t &poly_fraction,
+                       int &eig_est_cg_iter) const;
   /// Set parameters for Taubin's lambda-mu method
   void SetTaubinOptions(real_t lambda, real_t mu, int iter);
+   void GetTaubinOptions(real_t &lambda, real_t &mu, int &iter) const;

   /// Convenience function for setting canonical windowing parameters
   void SetWindowByName(const char* window_name);
   /// Set parameters for windowing function for FIR smoother.
   void SetWindowParameters(real_t a, real_t b, real_t c);
+   void GetWindowParameters(real_t &a, real_t &b, real_t &c) const;
   /// Compute window and Chebyshev coefficients for given polynomial order.
   void SetFIRCoefficients(real_t max_eig);

@@ -1190,12 +1207,15 @@ public:
   /** By default, the l1-norms take their sign from the corresponding diagonal
       entries in the associated matrix. */
   void SetPositiveDiagonal(bool pos = true) { pos_l1_norms = pos; }
+   bool IsPositiveDiagonal() const { return pos_l1_norms; };

   /** Explicitly indicate whether the linear system matrix A is symmetric. If A
       is symmetric, the smoother will also be symmetric. In this case, calling
       MultTranspose will be redirected to Mult. (This is also done if the
       smoother is diagonal.) By default, A is assumed to be nonsymmetric. */
   void SetOperatorSymmetry(bool is_sym) { A_is_symmetric = is_sym; }
+   /// @return true if the smoother assumes A is symmetric, false otherwise
+   bool IsOperatorSymmetric() const { return A_is_symmetric; }

   /** Set/update the associated operator. Must be called after setting the
       HypreSmoother type and options. */
@@ -1327,6 +1347,7 @@ public:
 #endif

 /// PCG solver in hypre
+/// Defaults to (relative) tol=1e-6, atol=0, max_iter=1000
 class HyprePCG : public HypreSolver
 {
 private:
@@ -1334,6 +1355,9 @@ private:

   HypreSolver * precond;

+   /// Default PCG options
+   void SetDefaultOptions();
+
 public:
   HyprePCG(MPI_Comm comm);

@@ -1342,8 +1366,11 @@ public:
   void SetOperator(const Operator &op) override;

   void SetTol(real_t tol);
+   real_t GetTol() const;
   void SetAbsTol(real_t atol);
+   real_t GetAbsTol() const;
   void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
   void SetLogging(int logging);
   void SetPrintLevel(int print_lvl);

@@ -1368,12 +1395,32 @@ public:
      num_iterations = internal::to_int(num_it);
   }

+   /// Gets the relative residual norm
   void GetFinalResidualNorm(real_t &final_res_norm) const
   {
      HYPRE_ParCSRPCGGetFinalRelativeResidualNorm(pcg_solver,
                                                  &final_res_norm);
   }

+   /// @param[in] use
+   ///   Convergence criterion:
+   ///   - when true: (r, r) < max(r_tol^2 (b, b), a_tol^2)
+   ///   - when false: (r, A r) < max(r_tol^2 (b, A b), a_tol^2)
+   /// @sa HYPRE_PCGSetTwoNorm
+   void SetUseTwoNorm(bool use);
+
+   /// @sa HYPRE_PCGGetTwoNorm
+   bool GetUseTwoNorm() const;
+
+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRPCGGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
   /// The typecast to HYPRE_Solver returns the internal pcg_solver
   operator HYPRE_Solver() const override { return pcg_solver; }

@@ -1391,7 +1438,8 @@ public:
   virtual ~HyprePCG();
 };

-/// GMRES solver in hypre
+/// GMRES solver in hypre.
+/// Defaults to k=50, (relative) tol=1e-6, atol=0, max_iter=100.
 class HypreGMRES : public HypreSolver
 {
 private:
@@ -1410,9 +1458,13 @@ public:
   void SetOperator(const Operator &op) override;

   void SetTol(real_t tol);
+   real_t GetTol() const;
   void SetAbsTol(real_t tol);
+   real_t GetAbsTol() const;
   void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
   void SetKDim(int dim);
+   int GetKDim() const;
   void SetLogging(int logging);
   void SetPrintLevel(int print_lvl);

@@ -1432,12 +1484,22 @@ public:
      num_iterations = internal::to_int(num_it);
   }

+   /// Gets the relative residual norm
   void GetFinalResidualNorm(real_t &final_res_norm) const
   {
      HYPRE_ParCSRGMRESGetFinalRelativeResidualNorm(gmres_solver,
                                                    &final_res_norm);
   }

+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRGMRESGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
   /// The typecast to HYPRE_Solver returns the internal gmres_solver
   operator HYPRE_Solver() const override { return gmres_solver; }

@@ -1455,7 +1517,8 @@ public:
   virtual ~HypreGMRES();
 };

-/// Flexible GMRES solver in hypre
+/// Flexible GMRES solver in hypre.
+/// Defaults to k=50, (relative) tol=1e-6, max_iter=100.
 class HypreFGMRES : public HypreSolver
 {
 private:
@@ -1474,8 +1537,11 @@ public:
   void SetOperator(const Operator &op) override;

   void SetTol(real_t tol);
+   real_t GetTol() const;
   void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
   void SetKDim(int dim);
+   int GetKDim() const;
   void SetLogging(int logging);
   void SetPrintLevel(int print_lvl);

@@ -1495,12 +1561,22 @@ public:
      num_iterations = internal::to_int(num_it);
   }

+   /// Gets the relative residual norm
   void GetFinalResidualNorm(real_t &final_res_norm) const
   {
      HYPRE_ParCSRFlexGMRESGetFinalRelativeResidualNorm(fgmres_solver,
                                                        &final_res_norm);
   }

+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRFlexGMRESGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
   /// The typecast to HYPRE_Solver returns the internal fgmres_solver
   operator HYPRE_Solver() const override { return fgmres_solver; }

@@ -1556,7 +1632,8 @@ public:
   virtual ~HypreDiagScale() { }
 };

-/// The ParaSails preconditioner in hypre
+/// The ParaSails preconditioner in hypre.
+/// See SetDefaultOptions() for default solver options.
 class HypreParaSails : public HypreSolver
 {
 private:
@@ -1685,10 +1762,14 @@ public:
 /**
@brief Wrapper for Hypre's native parallel ILU preconditioner.

-The default ILU factorization type is ILU(k).  If you need to change this, or
-any other option, you can use the HYPRE_Solver method to cast the object for use
-with Hypre's native functions. For example, if want to use natural ordering
-rather than RCM reordering, you can use the following approach:
+Default parameters: ILU(k) factorization type, tol=0.0 (for use as a
+preconditioner), fill level = 1 (for ILU(k)), reverse Cuthill-McKee (RCM)
+re-ordering.
+
+If you need to change this, or any other option, you can use the HYPRE_Solver
+method to cast the object for use with Hypre's native functions. For example, if
+want to use natural ordering rather than RCM reordering, you can use the
+following approach:

@code
 mfem::HypreILU ilu();
@@ -1829,6 +1910,7 @@ public:

   void SetMaxIter(int max_iter)
   { HYPRE_BoomerAMGSetMaxIter(amg_precond, max_iter); }
+   int GetMaxIter() const;

   /// Expert option - consult hypre documentation/team
   void SetMaxLevels(int max_levels)
@@ -1853,6 +1935,8 @@ public:
   /// Expert option - consult hypre documentation/team
   void SetRelaxType(int relax_type)
   { HYPRE_BoomerAMGSetRelaxType(amg_precond, relax_type); }
+   // not implemented in hypre
+   // int GetRelaxType() const;

   /// Expert option - consult hypre documentation/team
   void SetCycleType(int cycle_type)
@@ -2153,8 +2237,14 @@ public:
   ~HypreLOBPCG();

   void SetTol(real_t tol);
+   // not implemented in HYPRE
+   // real_t GetTol() const;
   void SetRelTol(real_t rel_tol);
+   // not implemented in HYPRE
+   // real_t GetRelTol() const;
   void SetMaxIter(int max_iter);
+   // not implemented in HYPRE
+   // int GetMaxIter() const;
   void SetPrintLevel(int logging);
   void SetNumModes(int num_eigs) { nev = num_eigs; }
   void SetPrecondUsageMode(int pcg_mode);
@@ -3639,12 +3639,20 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
      // make sure ess/nat_dof have been collectively set
      PetscBool lpr = PETSC_FALSE,pr;
      if (opts.ess_dof) { lpr = PETSC_TRUE; }
+#if PETSC_VERSION_LT(3,24,0)
      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPIU_BOOL,MPI_LOR,comm);
+#else
+      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPI_C_BOOL,MPI_LOR,comm);
+#endif
      CCHKERRQ(comm,mpiierr);
      MFEM_VERIFY(lpr == pr,"ess_dof should be collectively set");
      lpr = PETSC_FALSE;
      if (opts.nat_dof) { lpr = PETSC_TRUE; }
+#if PETSC_VERSION_LT(3,24,0)
      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPIU_BOOL,MPI_LOR,comm);
+#else
+      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPI_C_BOOL,MPI_LOR,comm);
+#endif
      CCHKERRQ(comm,mpiierr);
      MFEM_VERIFY(lpr == pr,"nat_dof should be collectively set");
      // make sure fields have been collectively set
@@ -4058,8 +4066,13 @@ void PetscNonlinearSolver::SetOperator(const Operator &op)
      ls = (PetscBool)(height == op.Height() && width  == op.Width() &&
                       (void*)&op == fctx &&
                       (void*)&op == jctx);
+#if PETSC_VERSION_LT(3,24,0)
      mpiierr = MPI_Allreduce(&ls,&gs,1,MPIU_BOOL,MPI_LAND,
                              PetscObjectComm((PetscObject)snes));
+#else
+      mpiierr = MPI_Allreduce(&ls,&gs,1,MPI_C_BOOL,MPI_LAND,
+                              PetscObjectComm((PetscObject)snes));
+#endif
      CCHKERRQ(PetscObjectComm((PetscObject)snes),mpiierr);
      if (!gs)
      {
@@ -1066,6 +1066,11 @@ void SparseMatrix::BooleanMultTranspose(const Array<int> &x,
   y.SetSize(Width());
   y = 0;

+   HostReadI();
+   HostReadJ();
+   x.HostRead();
+   y.HostReadWrite();
+
   for (int i = 0; i < Height(); i++)
   {
      if (x[i])
@@ -363,14 +363,19 @@ void SuperLUSolver::Init(MPI_Comm comm)
   // Set default options:
   //    options.Fact = DOFACT;
   //    options.Equil = YES;
+   //    options.ParSymbFact = NO;
   //    options.ColPerm = METIS_AT_PLUS_A;
   //    options.RowPerm = LargeDiag_MC64;
   //    options.ReplaceTinyPivot = NO;
-   //    options.Trans = NOTRANS;
   //    options.IterRefine = SLU_DOUBLE;
+   //    options.Trans = NOTRANS;
   //    options.SolveInitialized = NO;
   //    options.RefineInitialized = NO;
   //    options.PrintStat = YES;
+   //    options.lookahead_etree = NO;
+   //    options.num_lookaheads = 10;
+   //    options.superlu_acc_offload = 1;
+   //    options.SymPattern = NO;
   superlu_dist_options_t *options = (superlu_dist_options_t *)optionsPtr_;
   set_default_options_dist(options);
 #if SUPERLU_DIST_MAJOR_VERSION > 7 || \
@@ -472,6 +477,12 @@ void SuperLUSolver::SetFact(superlu::Fact fact)
   options->Fact = opt;
 }

+void SuperLUSolver::SetDeviceOffload(bool offload)
+{
+   superlu_dist_options_t *options = (superlu_dist_options_t *)optionsPtr_;
+   options->superlu_acc_offload = offload;
+}
+
 void SuperLUSolver::SetOperator(const Operator &op)
 {
   // Verify that we have a compatible operator
@@ -250,7 +250,8 @@ public:
       work (default false) */
   void SetSymmetricPattern(bool sym);

-   /** @brief Specify whether to perform parallel symbolic factorization.
+   /** @brief Specify whether to perform parallel symbolic factorization
+       (default false)
       @note If true SuperLU will use superlu::PARMETIS for the Column
       Permutation regardless of the setting */
   void SetParSymbFact(bool par);
@@ -263,6 +264,10 @@ public:
       superlu::FACTORED*/
   void SetFact(superlu::Fact fact);

+   /** @brief Specify whether to offload numerical factorization onto the device
+       (default true if SuperLU_DIST has been compiled with GPU support) */
+   void SetDeviceOffload(bool offload);
+
   // Processor grid for SuperLU_DIST.
   const int nprow_, npcol_, npdep_;

@@ -794,7 +794,6 @@ status info:
 	$(info MFEM_MPI_NP            = $(MFEM_MPI_NP))
 	@true

-ASTYLE_BIN = astyle
 ASTYLE = $(ASTYLE_BIN) --options=$(SRC)config/mfem.astylerc
 ASTYLE_VER = "Artistic Style Version 3.1"
 FORMAT_FILES = $(foreach dir,$(DIRS) $(EM_DIRS) config,$(dir)/*.?pp)
@@ -113,13 +113,13 @@ AttributeSets::GetAttributeSetMarker(const std::string & set_name) const

 Array<int> AttributeSets::AttrToMarker(int max_attr, const Array<int> &attrs)
 {
-   MFEM_ASSERT(attrs.Max() <= max_attr, "Invalid attribute number present.");
+   MFEM_VERIFY(attrs.Min() >= 1, "Found attribute less than one")
+   MFEM_ASSERT(attrs.Max() <= max_attr, "Found attribute greater than max_attr")

   Array<int> marker(max_attr);
   marker = 0;
   for (auto const &attr : attrs)
   {
-      MFEM_VERIFY(attr > 0, "Attribute number less than one!");
      marker[attr-1] = 1;
   }
   return marker;
@@ -4792,11 +4792,12 @@ Mesh::Mesh(const NURBSExtension& ext)
   if (NURBSext->HavePatches())
   {
      NURBSFECollection  *fec = new NURBSFECollection(NURBSext->GetOrder());
-      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, Dim,
+      const int vdim = NURBSext->GetPatchSpaceDimension();
+      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, vdim,
                                                       Ordering::byVDIM);
      Nodes = new GridFunction(fes);
      Nodes->MakeOwner(fec);
-      NURBSext->SetCoordsFromPatches(*Nodes);
+      NURBSext->SetCoordsFromPatches(*Nodes, vdim);
      own_nodes = 1;
      spaceDim = Nodes->VectorDim();
      for (int i = 0; i < spaceDim; i++)
@@ -6410,7 +6411,7 @@ void Mesh::UpdateNURBS()
   NURBSext->SetKnotsFromPatches();

   Dim = NURBSext->Dimension();
-   spaceDim = Dim;
+   spaceDim = Nodes->FESpace()->GetVDim();

   if (NumOfElements != NURBSext->GetNE())
   {
@@ -6435,7 +6436,8 @@ void Mesh::UpdateNURBS()
   Nodes->FESpace()->Update();
   Nodes->Update();
   NodesUpdated();
-   NURBSext->SetCoordsFromPatches(*Nodes);
+   const int vdim = Nodes->FESpace()->GetVDim();
+   NURBSext->SetCoordsFromPatches(*Nodes, vdim);

   if (NumOfVertices != NURBSext->GetNV())
   {
@@ -7834,6 +7836,17 @@ bool Mesh::IsMixedMesh() const

 void Mesh::GetElementEdges(int i, Array<int> &edges, Array<int> &cor) const
 {
+   if (Dim == 1)
+   {
+      // In 1D, elements are segments and can be treated as edges.
+      edges.SetSize(1);
+      cor.SetSize(1);
+      edges[0] = i;
+      const int *v = elements[i]->GetVertices();
+      cor[0] = (v[0] < v[1]) ? (1) : (-1);
+      return;
+   }
+
   if (el_to_edge)
   {
      el_to_edge->GetRow(i, edges);
@@ -12389,6 +12402,38 @@ void Mesh::PrintTopoEdges(std::ostream &os, const Array<int> &e_to_k,
 {
   Array<int> vert;

+   // In 1D patch-topology NURBS meshes, knotvector orientation is stored in the
+   // file's `edges` section, but the topological 1D mesh has NumOfEdges == 0
+   // (its "faces" are vertices). When a valid edge->knotvector map is provided,
+   // print a pseudo-edge list derived from the 1D elements so external tools
+   // (e.g. VisIt) can consume the mapping.
+   if (Dim == 1 && NumOfEdges == 0 && e_to_k.Size() == NumOfElements)
+   {
+      const int ne = NumOfElements;
+      os << "\nedges\n" << ne << '\n';
+      for (int i = 0; i < ne; i++)
+      {
+         const int *v = elements[i]->GetVertices();
+         int v0 = v[0], v1 = v[1];
+
+         int ki = e_to_k[i];
+         const bool flip = (ki < 0); // desired output vertex order: descending
+         if (flip) { ki = -1 - ki; } // print the unsigned knotvector index
+
+         // Encode the sign of e_to_k in the vertex ordering, consistent with
+         // Mesh::LoadPatchTopo(): v0 > v1 => negative sign.
+         if ((v0 > v1) != flip) { std::swap(v0, v1); }
+
+         os << ki << ' ' << v0 << ' ' << v1 << '\n';
+      }
+
+      if (!vmap)
+      {
+         os << "\nvertices\n" << NumOfVertices << '\n';
+      }
+      return;
+   }
+
   os << "\nedges\n" << NumOfEdges << '\n';
   for (int i = 0; i < NumOfEdges; i++)
   {
@@ -15701,6 +15746,128 @@ Mesh *Extrude2D(Mesh *mesh, const int nz, const real_t sz)
   return mesh3d;
 }

+Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
+                  int &par_ref, Array<int> &partitioning)
+{
+   MFEM_VERIFY(dim > 1, "Not implemented for 1D meshes.");
+
+   auto factor = [&](int N)
+   {
+      for (int i = static_cast<int>(sqrt(N)); i > 0; i--)
+      { if (N % i == 0) { return i; } }
+      return 1;
+   };
+
+   par_ref = 0;
+   const int ref_factor = (dim == 2) ? 4 : 8;
+
+   // Elements per task before performing parallel refinements.
+   // This will be used to form the serial mesh.
+   int el0 = elem_per_mpi;
+   while (el0 % ref_factor == 0)
+   {
+      el0 /= ref_factor;
+      par_ref++;
+   }
+
+   // In the serial mesh we have:
+   // The number of MPI blocks is mpi_cnt = mp_x.mpy_y.mpy_z.
+   // The size of each MPI block is el0 = el0_x.el0_y.el0_z.
+   int mpi_x, mpi_y, mpi_z;
+   int el0_x, el0_y, el0_z;
+   if (dim == 2)
+   {
+      mpi_x = factor(mpi_cnt);
+      mpi_y = mpi_cnt / mpi_x;
+
+      // Switch order for better balance.
+      el0_y = factor(el0);
+      el0_x = el0 / el0_y;
+   }
+   else
+   {
+      mpi_x = factor(mpi_cnt);
+      mpi_y = factor(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_x = el0 / el0_y / el0_z;
+   }
+
+   if (print && dim == 2)
+   {
+      int elem_par_x = mpi_x * el0_x * pow(2, par_ref),
+          elem_par_y = mpi_y * el0_y * pow(2, par_ref);
+
+      mfem::out << "--- Mesh generation: \n";
+      mfem::out << "Par mesh:    " << elem_par_x << " x " << elem_par_y
+                << " (" << elem_par_x * elem_par_y << " elements)\n"
+                << "Elem / task: "
+                << el0_x * pow(2, par_ref) << " x "
+                << el0_y * pow(2, par_ref)
+                << " (" << el0_x * pow(2, 2*par_ref) * el0_y << " elements)\n"
+                << "MPI blocks:  " << mpi_x << " x " << mpi_y
+                << " (" << mpi_x * mpi_y << " mpi tasks)\n" << "-\n"
+                << "Serial mesh: "
+                << mpi_x * el0_x << " x " << mpi_y * el0_y
+                << " (" << mpi_x * el0_x * mpi_y * el0_y << " elements)\n"
+                << "Elem / task: " << el0_x << " x " << el0_y << std::endl
+                << "Par refine:  " << par_ref << std::endl;
+      mfem::out << "--- \n";
+   }
+
+   if (print && dim == 3)
+   {
+      int elem_par_x = mpi_x * el0_x * pow(2, par_ref),
+          elem_par_y = mpi_y * el0_y * pow(2, par_ref),
+          elem_par_z = mpi_z * el0_z * pow(2, par_ref);
+
+      mfem::out << "--- Mesh generation: \n";
+      mfem::out << "Par mesh:    "
+                << elem_par_x << " x " << elem_par_y << " x " << elem_par_z
+                << " (" << elem_par_x*elem_par_y*elem_par_z << " elements)\n"
+                << "Elem / task: "
+                << el0_x * pow(2, par_ref) << " x "
+                << el0_y * pow(2, par_ref) << " x "
+                << el0_z * pow(2, par_ref)
+                << " (" << el0_x*pow(2, 3*par_ref)*el0_y*el0_z << " elements)\n"
+                << "MPI blocks:  " << mpi_x << " x " << mpi_y << " x " << mpi_z
+                << " (" << mpi_x * mpi_y * mpi_z << " mpi tasks)\n" << "-\n"
+                << "Serial mesh: "
+                << mpi_x*el0_x << " x " << mpi_y*el0_y << " x " << mpi_z*el0_z
+                << " (" << mpi_x*el0_x*mpi_y*el0_y*mpi_z*el0_z << " elements)\n"
+                << "Elem / task: "
+                << el0_x << " x " << el0_y << " x " << el0_z  << std::endl
+                << "Par refine:  " << par_ref << std::endl;
+      mfem::out << "--- \n";
+   }
+
+   Mesh mesh;
+   int nxyz[3];
+   if (dim == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(mpi_x * el0_x,
+                                   mpi_y * el0_y, Element::QUADRILATERAL, true);
+      nxyz[0] = mpi_x; nxyz[1] = mpi_y;
+   }
+   else
+   {
+      mesh = Mesh::MakeCartesian3D(mpi_x * el0_x,
+                                   mpi_y * el0_y,
+                                   mpi_z * el0_z, Element::HEXAHEDRON, true);
+      nxyz[0] = mpi_x; nxyz[1] = mpi_y; nxyz[2] = mpi_z;
+   }
+
+   const int NE = mesh.GetNE();
+   partitioning.SetSize(NE);
+   std::unique_ptr<int[]> p_raw(mesh.CartesianPartitioning(nxyz));
+   std::copy(p_raw.get(), p_raw.get() + NE, partitioning.GetData());
+
+   return mesh;
+}
+
 bool Mesh::Conforming() const
 {
   if (NURBSext)
@@ -2078,12 +2078,13 @@ public:
       contrary to the ones obtained through Mesh::GetFacesElements and can
       directly be used, e.g., Elem1 and Elem2 indices.
       Likewise the orientations for Elem1 and Elem2 already take into account
-       special cases and can be used as is.
-   */
+       special cases and can be used as is. */
   struct FaceInformation
   {
+      /// The face topology (boundary, conforming, or nonconforming).
      FaceTopology topology;

+      /// Information about the adjacent elements.
      struct
      {
         ElementLocation location;
@@ -2093,8 +2094,13 @@ public:
         int orientation;
      } element[2];

+      /// Detailed face information (see FaceInfoTag).
      FaceInfoTag tag;
+
+      /// If the face is nonconforming, the index of the NC face. -1 otherwise.
      int ncface;
+
+      /// The point matrix for nonconforming faces.
      const DenseMatrix* point_matrix;

      /** @brief Return true if the face is a local interior face which is NOT
@@ -2113,21 +2119,20 @@ public:

      /** @brief return true if the face is an interior face to the computation
          domain, either a local or shared interior face (not a boundary face)
-          which is NOT a master nonconforming face.
-       */
+          which is NOT a master nonconforming face. */
      bool IsInterior() const
      {
         return topology == FaceTopology::Conforming ||
                topology == FaceTopology::Nonconforming;
      }

-      /** @brief Return true if the face is a boundary face. */
+      /// Return true if the face is a boundary face.
      bool IsBoundary() const
      {
         return topology == FaceTopology::Boundary;
      }

-      /// @brief Return true if the face is of the same type as @a type.
+      /// Return true if the face is of the same type as @a type.
      bool IsOfFaceType(FaceType type) const
      {
         switch (type)
@@ -2141,13 +2146,13 @@ public:
         }
      }

-      /// @brief Return true if the face is a conforming face.
+      /// Return true if the face is a conforming face.
      bool IsConforming() const
      {
         return topology == FaceTopology::Conforming;
      }

-      /// @brief Return true if the face is a nonconforming fine face.
+      /// Return true if the face is a nonconforming fine face.
      bool IsNonconformingFine() const
      {
         return topology == FaceTopology::Nonconforming &&
@@ -2155,7 +2160,7 @@ public:
                 element[1].conformity == ElementConformity::Superset);
      }

-      /// @brief Return true if the face is a nonconforming coarse face.
+      /// Return true if the face is a nonconforming coarse face.
      /** Note that ghost nonconforming master faces cannot be clearly
          identified as such with the currently available information, so this
          method will return false for such faces. */
@@ -2165,7 +2170,7 @@ public:
                element[1].conformity == ElementConformity::Subset;
      }

-      /// @brief cast operator from FaceInformation to FaceInfo.
+      /// cast operator from FaceInformation to FaceInfo.
      operator Mesh::FaceInfo() const;
   };

@@ -3207,6 +3212,28 @@ Mesh *Extrude1D(Mesh *mesh, const int ny, const real_t sy,
 /// Extrude a 2D mesh
 Mesh *Extrude2D(Mesh *mesh, const int nz, const real_t sz);

+/** @brief Constructs the smallest possible [0,1]^dim serial mesh that can be
+    used later to obtain a ParMesh with @a elem_per_mpi elements, with the same
+    topology, for each of the @a mpi_cnt MPI tasks. For quads and hexes.
+
+    The serial mesh has the smallest possible number of elements. The parallel
+    mesh will be obtained by parallel refinements. Each MPI task will have
+    elements with the same topology (same number, same connectivity).
+
+    @param[in]  dim          dimension (2 or 3).
+    @param[in]  mpi_cnt      number of MPI tasks.
+    @param[in]  elem_per_mpi number of elements per MPI task.
+    @param[in]  print        shows meshing info in the terminal.
+    @param[out] par_ref      number of parallel refinement needed afterwards.
+    @param[out] partitioning partitioning to create the desired ParMesh.
+
+    Usual use case:
+    Mesh mesh = PartitionMPI(dim, mpi_cnt, elem_per_mpi, print, par_ref, par);
+    ParMesh pmesh(MPI_COMM_WORLD, mesh, par.GetData());
+    for (int lev = 0; lev < par_ref; lev++) { pmesh.UniformRefinement(); }   */
+Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
+                  int &par_ref, Array<int> &partitioning);
+
 // shift cyclically 3 integers left-to-right
 inline void ShiftRight(int &a, int &b, int &c)
 {
@@ -1328,11 +1328,12 @@ void Mesh::ReadNURBSMesh(std::istream &input, int &curved, int &read_gf,
   if (NURBSext->HavePatches())
   {
      NURBSFECollection  *fec = new NURBSFECollection(NURBSext->GetOrder());
-      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, Dim,
+      const int vdim = NURBSext->GetPatchSpaceDimension();
+      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, vdim,
                                                       Ordering::byVDIM);
      Nodes = new GridFunction(fes);
      Nodes->MakeOwner(fec);
-      NURBSext->SetCoordsFromPatches(*Nodes);
+      NURBSext->SetCoordsFromPatches(*Nodes, vdim);
      own_nodes = 1;
      read_gf = 0;
      spaceDim = Nodes->VectorDim();
@@ -51,6 +51,21 @@ protected:
   /// Number of elements, defined by distinct knots.
   int NumOfElements;

+   // Stores the demko points
+   mutable Vector demko;
+
+   /// Compute all the Demko points
+   void ComputeDemko() const;
+
+#ifdef MFEM_USE_LAPACK
+   // Data for reusing banded matrix factorization in FindInterpolant().
+   mutable DenseMatrix fact_AB; /// Banded matrix factorization
+   mutable Array<int> fact_ipiv; /// Row pivot indices
+#else
+   mutable DenseMatrix A_coll_inv; /// Collocation matrix inverse
+#endif
+
+
 public:
   /// Create an empty KnotVector.
   KnotVector() = default;
@@ -59,18 +74,28 @@ public:
       integers are read, for order and number of control points. */
   KnotVector(std::istream &input);

-   /** @brief Create a KnotVector with undefined knots (initialized to -1) of
-       order @a order and number of control points @a NCP. */
-   KnotVector(int order, int NCP);
+   /** @brief Create a KnotVector with order @a order.
+       When @a NCP is not provided  the number of control points is set to
+       @a order + 1, and the first @a order + 1 knots are set to 0 and last
+       @a order + 1 knots are set to 1.
+       When @a NCP is given number of control points is @a NCP and
+       the knots are initialized to -1) */
+   KnotVector(int order, int NCP = -1);
+
+   /** @brief Create a KnotVector with order @a order and knots @a knot.
+       If @a k has the correct number of repeated knots at the begin and end,
+       then this constructor will copy the knots as provided.
+       Otherwise, the knot vector will be extended by repeating the end knots
+       (order + 1) times. Internal knots will retain the multiplicity as given
+       in the input. */
+   KnotVector(int order, const Vector &k);

   /** @brief Create a KnotVector by passing in a degree, a Vector of interval
       lengths of length n, and a list of continuity of length n + 1.
-
       The intervals refer to spans between unique knot values (not counting
       zero-size intervals at repeated knots), and the continuity values should
       be >= -1 (discontinuous) and <= order-1 (maximally-smooth for the given
-       polynomial degree). Periodicity is not supported.
-   */
+       polynomial degree). Periodicity is not supported.*/
   KnotVector(int order, const Vector& intervals,
              const Array<int>& continuity);

@@ -103,13 +128,69 @@ public:
       with @a isElement for non-empty knot spans (elements). */
   int GetNKS() const { return NumOfControlPoints - Order; }

-   /** @brief Return the parameter for element reference coordinate @a xi
-       in [0,1], for the element beginning at knot @a ni. */
-   real_t getKnotLocation(real_t xi, int ni) const
-   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); }
+   /// Return whether knot location @a u is in a given span @a ni.
+   bool inSpan(real_t u, int ni) const
+   {
+      if ((u < knot(ni)) || (u > knot(ni+1))) { return false; }
+      return true;
+   }

   /// Return the index of the knot span containing parameter @a u.
-   int findKnotSpan(real_t u) const;
+   int GetSpan(real_t u) const;
+
+   /** @brief Return the reference coordinate in [0,1] for parameter @a u
+       in the element beginning at knot @a ni. */
+   real_t GetRefPoint(real_t u, int ni) const
+   { return (u-knot(ni))/(knot(ni+1)-knot(ni)); };
+
+   /** @brief Return the knot location for element reference coordinate @a xi
+       in [0,1], for the element beginning at knot @a ni. */
+   real_t GetKnotLocation(real_t xi, int ni) const
+   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); }
+
+   /** @brief Return the parameter for element reference coordinate @a xi
+       in [0,1], for the element beginning at knot @a ni. */
+   MFEM_DEPRECATED real_t getKnotLocation(real_t xi, int ni) const
+   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); } // Use GetKnotLocation instead
+
+   /// Return the index of the knot span containing parameter @a u.
+   MFEM_DEPRECATED int findKnotSpan(real_t u) const;  // Use GetSpan instead
+
+   /** Gives the @a i average knot location. Average is taken over @a Order
+       number of knots.*/
+   real_t GetGreville(int i) const;
+
+   void GetGreville(Vector &xi) const;
+
+   /** Gives the knot location where the @a i shape function is maximum.
+       Reverts to the Greville point if knot is repeated @a Order +1 times.
+       For background see:
+
+       Olivier Botella and Karim Shariff.
+       "B-spline methods in fluid dynamics."
+       International Journal of Computational Fluid Dynamics 17.2 (2003): 133-149.
+
+       Points are found using Newton iteration, with the Greville point as the
+       starting value. */
+   real_t GetBotella(int i) const;
+
+   void GetBotella(Vector &xi) const;
+
+   /** Gives the knot location of the @a i extremum of the Chebyshev spline.
+       For background see:
+
+       Stephen Demko
+       "On the existence of interpolating projections onto spline spaces."
+       Journal of approximation theory 43.2 (1985): 151-156.
+
+       Points are found using Remez iteration:
+        - Find interpolant, given by a, through given points, given by Demko
+        - Find extrema of this polynomial and update Demko points
+        - Repeat until converged
+        - Use the Greville point as starting point */
+   real_t GetDemko(int i) const;
+
+   void GetDemko(Vector &xi) const;

   // The following functions evaluate shape functions, which are B-spline basis
   // functions.
@@ -136,19 +217,32 @@ public:
   /** @brief Gives the locations of the maxima of the KnotVector in reference
       space. The function gives the knot span @a ks, the coordinate in the
       knot span @a xi, and the coordinate of the maximum in parameter space
-       @a u. */
-   void FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const;
+       @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.*/
+   MFEM_DEPRECATED void FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const;

   /** @brief Global curve interpolation through the points @a x (overwritten).
       @a x is an array with the length of the spatial dimension containing
       vectors with spatial coordinates. The control points of the interpolated
       curve are returned in @a x in the same form.
+       Use GetInterpolant instead. For the knot location one can use either
+       GetBotella, GetDemko or GetGreville. FindInterpolant uses the Botella
+       points, however, the Demko points might be more appropriate. */
+   MFEM_DEPRECATED void FindInterpolant(Array<Vector*> &x, bool reuse_inverse);

-       The inverse of the collocation matrix, used in the interpolation, is
-       stored for repeated calls and used if @a reuse_inverse is true. Reuse is
-       valid only if this KnotVector has not changed since the initial call with
-       @a reuse_inverse false. */
-   void FindInterpolant(Array<Vector*> &x, bool reuse_inverse = false);
+   /** @brief Global curve interpolation through the points @a x (overwritten)
+       at the knot location @a u. The control points of the
+       interpolated curve are returned in @a x in the same form.
+       For the knot location one can use  for instance GetBotella, GetDemko or
+       GetGreville. The Demko points might be most appropriate.*/
+   void GetInterpolant(Array<Vector*> &x, const Vector &u,
+                       bool reuse_inverse = false) const;
+
+   /// Different interface to same routine
+   void GetInterpolant(const Vector &x, const Vector &u,
+                       Vector &a, bool reuse_inverse = false) const;

   /** Set @a diff, comprised of knots in @a kv not contained in this KnotVector.
       @a kv must be of the same order as this KnotVector. The current
@@ -191,6 +285,18 @@ public:
       number of samples of the shape functions per element.*/
   void PrintFunctions(std::ostream &os, int samples=11) const;

+   /** Prints the function with basis function coefficient @a a, and its first
+       and second derivatives associated with the KnotVector per element.
+       Use GetElements() to count the elements before using this function.
+       @a samples is the number of samples of the shape functions per element.*/
+   void PrintFunction(std::ostream &os, const Vector &a, int samples=11) const;
+
+   /** Prints the @a i-th function and its first and second
+       derivatives associated with the KnotVector per element. Use GetElements()
+       to count the elements before using this function. @a samples is the
+       number of samples of the shape functions per element.*/
+   void PrintFunction(std::ostream &os, int i, int samples=11) const;
+
   /// Destroys KnotVector
   ~KnotVector() { }

@@ -209,14 +315,6 @@ public:
   /** @brief Flag to indicate whether the KnotVector has been coarsened, which
       means it is ready for non-nested refinement. */
   bool coarse;
-
-#ifdef MFEM_USE_LAPACK
-   // Data for reusing banded matrix factorization in FindInterpolant().
-   DenseMatrix fact_AB; /// Banded matrix factorization
-   Array<int> fact_ipiv; /// Row pivot indices
-#else
-   DenseMatrix A_coll_inv; /// Collocation matrix inverse
-#endif
 };


@@ -599,22 +697,26 @@ protected:
   /// Throw an error if any boundary patch has invalid KnotVector orientation.
   MFEM_DEPRECATED void CheckBdrPatches();

+   /// Return the patch-topology edge indices that define the KnotVectors for
+   /// patch @a p in each parametric direction.
+   void GetPatchDirectionEdges(int p, Array<int> &edges);
+
   /** @brief Return the directions in @a kvdir of the KnotVectors in patch @a p
       based on the patch edge orientations. Each entry of @a kvdir is -1 if the
       KnotVector direction is flipped, +1 otherwise. */
   void CheckKVDirection(int p, Array <int> &kvdir);

-   /**  @brief Create the comprehensive set of KnotVectors. In 1D, this set is
-    identical to the unique set of KnotVectors. */
+   /** @brief Create the comprehensive set of KnotVectors, one per patch and
+       parametric direction, accounting for the edge orientations. */
   void CreateComprehensiveKV();

-   /**  Update the unique set of KnotVectors. In 1D, this set is identical to
-    the comprehensive set of KnotVectors. */
+   /** @brief Update the unique set of KnotVectors from the comprehensive set
+       of KnotVectors. */
   void UpdateUniqueKV();

   /** @brief Check if the comprehensive array of KnotVectors agrees with the
       unique set of KnotVectors, on each patch. Return false if there is a
-       difference, true otherwise. This function throws an error in 1D. */
+       difference, true otherwise. */
   bool ConsistentKVSets();

   /// Return KnotVectors in @a kv in each dimension for patch @a p.
@@ -820,6 +922,13 @@ public:
   /// Return the dimension of the reference space (not physical space).
   int Dimension() const { return patchTopo->Dimension(); }

+   /** @brief Return the physical dimension of the NURBS geometry
+
+       The physical dimension is inferred from the first patch,
+       i.e. number of coordinates per control point minus one (for the weight).
+       This method requires patch data to be present, i.e. HavePatches() == true */
+   int GetPatchSpaceDimension() const;
+
   /// Return the number of patches.
   int GetNP()     const { return patchTopo->GetNE(); }

@@ -933,9 +1042,9 @@ public:
   void ConvertToPatches(const Vector &Nodes);
   /// Set KnotVectors from @a patches and construct mesh and space data.
   void SetKnotsFromPatches();
-   /** @brief Set FE coordinates in @a Nodes, using data from @a patches, and
-       erase @a patches. */
-   void SetCoordsFromPatches(Vector &Nodes);
+   /** @brief Set FE coordinates in @a Nodes, using data from @a patches,
+       with physical vector dimension @a vdim, and erase @a patches. */
+   void SetCoordsFromPatches(Vector &Nodes, int vdim);

   /** @brief Read a GridFunction @a sol from stream @a input, written
       patch-by-patch, e.g. with PrintSolution(). */
@@ -3041,7 +3041,7 @@ void ParMesh::GetSharedFaceTransformationsByLocalIndex(
   // for ghost faces we need a special version of GetFaceTransformation
   if (is_ghost)
   {
-      GetGhostFaceTransformation(FElTr, face_type, face_geom);
+      GetGhostFaceTransformation(FaceNo, FElTr);
      mask |= FaceElementTransformations::HAVE_FACE;
   }

@@ -3064,19 +3064,29 @@ void ParMesh::GetSharedFaceTransformationsByLocalIndex(
 }

 void ParMesh::GetGhostFaceTransformation(
-   FaceElementTransformations &FElTr, Element::Type face_type,
-   Geometry::Type face_geom) const
+   int FaceNo, FaceElementTransformations &FElTr) const
 {
+   MFEM_ASSERT(FaceNo >= GetNumFaces(), "Not a ghost face.");
+
+   // use the local face data
+   const int LocFaceNo = nc_faces_info[faces_info[FaceNo].NCFace].MasterFace;
+   FElTr.Attribute = (Dim == 1) ? 1 : faces[LocFaceNo]->GetAttribute();
+   FElTr.ElementNo = FaceNo;
+   FElTr.ElementType = ElementTransformation::FACE;
+   FElTr.mesh = this;
+
   // calculate composition of FElTr.Loc1 and FElTr.Elem1
   DenseMatrix &face_pm = FElTr.GetPointMat();
   FElTr.Reset();
   if (Nodes == NULL)
   {
+      const Element::Type face_type = GetFaceElementType(LocFaceNo);
      FElTr.Elem1->Transform(FElTr.Loc1.Transf.GetPointMat(), face_pm);
      FElTr.SetFE(GetTransformationFEforElementType(face_type));
   }
   else
   {
+      const Geometry::Type face_geom = GetFaceGeometry(LocFaceNo);
      const FiniteElement* face_el =
         Nodes->FESpace()->GetTraceElement(FElTr.Elem1No, face_geom);
      MFEM_VERIFY(dynamic_cast<const NodalFiniteElement*>(face_el),
@@ -150,15 +150,7 @@ protected:
                    int elem, int start, int end, const int fverts[][N]);

   void GetGhostFaceTransformation(
-      FaceElementTransformations &FElTr, Element::Type face_type,
-      Geometry::Type face_geom) const;
-   void GetGhostFaceTransformation(
-      FaceElementTransformations *FElTr, Element::Type face_type,
-      Geometry::Type face_geom) const
-   {
-      MFEM_ASSERT(FElTr, "Missing FaceElementTransformations object!");
-      GetGhostFaceTransformation(*FElTr, face_type, face_geom);
-   }
+      int FaceNo, FaceElementTransformations &FElTr) const;

   /// Update the groups after triangle refinement
   void RefineGroups(const DSTable &v_to_v, int *middle);
@@ -1195,14 +1195,22 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
      }
   }

-   // If there are shared slaves, they will also need to be updated.
+   // If there are shared slaves, they will also need to be updated. First,
+   // check whether the update has already been done.
+   bool sharedUpdated = false;
   if (shared.slaves.Size())
+   {
+      int nfaces = NFaces, nghosts = NGhostFaces;
+      if (Dim <= 2) { nfaces = NEdges, nghosts = NGhostEdges; }
+      sharedUpdated = (pmesh.faces_info.Size() == nfaces + nghosts);
+   }
+
+   if (shared.slaves.Size() && !sharedUpdated)
   {
      int nfaces = NFaces, nghosts = NGhostFaces;
      if (Dim <= 2) { nfaces = NEdges, nghosts = NGhostEdges; }

      // enlarge Mesh::faces_info for ghost slaves
-      MFEM_ASSERT(pmesh.faces_info.Size() == nfaces, "");
      MFEM_ASSERT(pmesh.GetNumFaces() == nfaces, "");
      pmesh.faces_info.SetSize(nfaces + nghosts);
      for (int i = nfaces; i < pmesh.faces_info.Size(); i++)
@@ -1303,14 +1311,12 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
               // Mesh::ApplyLocalSlaveTransformation.
            }

-            MFEM_ASSERT(fi.NCFace < 0, "fi.NCFace = " << fi.NCFace);
            fi.NCFace = pmesh.nc_faces_info.Size();
            pmesh.nc_faces_info.Append(Mesh::NCFaceInfo(true, sf.master, pm));
         }
      }
   }

-
   // In 3D some extra orientation data structures can be needed.
   if (Dim == 3)
   {
@@ -34,14 +34,16 @@ class ParNCSubMesh;
 * subset of the parent Mesh and reuses the parallel distribution.
 *
 * The attributes are taken from the parent. That means if a volume is extracted
- * from a volume, it has the same domain attribute as the parent. Its boundary
- * attributes are generated (there will be one boundary attribute 1 for all of
- * the boundaries).
+ * from a volume, it has the same domain attribute as the parent. Its new
+ * boundary attributes are, for any boundary common to the parent and the new
+ * submesh, the boundary attribute of the parent; and, for all new boundaries,
+ * a single, generated, common attribute equal to one plus the largest boundary
+ * attribute of the parent.
 *
 * If a surface is extracted from a volume, the boundary attribute from the
- * parent is assigned to be the new domain attribute. Its boundary attributes
- * are generated (there will be one boundary attribute 1 for all of the
- * boundaries).
+ * parent is assigned to be the new domain attribute. Its new boundary attribute
+ * is a single, generated, common attribute equal to one plus the largest
+ * boundary attribute of the parent.
 *
 * For more customized boundary attributes, the resulting ParSubMesh has to be
 * postprocessed.
@@ -28,14 +28,16 @@ class NCSubMesh;
 * subset of the parents Mesh and reuses the parallel distribution.
 *
 * The attributes are taken from the parent. That means if a volume is extracted
- * from a volume, it has the same domain attribute as the parent. Its boundary
- * attributes are generated (there will be one boundary attribute 1 for all of
- * the boundaries).
+ * from a volume, it has the same domain attribute as the parent. Its new
+ * boundary attributes are, for any boundary common to the parent and the new
+ * submesh, the boundary attribute of the parent; and, for all new boundaries,
+ * a single, generated, common attribute equal to one plus the largest boundary
+ * attribute of the parent.
 *
 * If a surface is extracted from a volume, the boundary attribute from the
- * parent is assigned to be the new domain attribute. Its boundary attributes
- * are generated (there will be one boundary attribute 1 for all of the
- * boundaries).
+ * parent is assigned to be the new domain attribute. Its new boundary attribute
+ * is a single, generated, common attribute equal to one plus the largest
+ * boundary attribute of the parent.
 *
 * For more customized boundary attributes, the resulting SubMesh has to be
 * postprocessed.
@@ -232,27 +232,6 @@ MergeMeshNodes(Mesh * mesh, int logging)
   }
 }

-void AttrToMarker(int max_attr, const Array<int> &attrs, Array<int> &marker)
-{
-   MFEM_ASSERT(attrs.Max() <= max_attr, "Invalid attribute number present.");
-
-   marker.SetSize(max_attr);
-   if (attrs.Size() == 1 && attrs[0] == -1)
-   {
-      marker = 1;
-   }
-   else
-   {
-      marker = 0;
-      for (int j=0; j<attrs.Size(); j++)
-      {
-         int attr = attrs[j];
-         MFEM_VERIFY(attr > 0, "Attribute number less than one!");
-         marker[attr-1] = 1;
-      }
-   }
-}
-
 void AffineTransformation::Eval(Vector &V, ElementTransformation &T,
                                const IntegrationPoint &ip)
 {
@@ -33,9 +33,14 @@ void MergeMeshNodes(Mesh * mesh, int logging);
 /// Convert a set of attribute numbers to a marker array
 /** The marker array will be of size max_attr and it will contain only zeroes
    and ones. Ones indicate which attribute numbers are present in the attrs
-    array. In the special case when attrs has a single entry equal to -1 the
-    marker array will contain all ones. */
-void AttrToMarker(int max_attr, const Array<int> &attrs, Array<int> &marker);
+    array. In the special case when attrs has an entry equal to -1 the marker
+    array will contain all ones. */
+inline
+void AttrToMarker(int max_attr, const Array<int> &attrs, Array<int> &marker)
+{
+   if (attrs.Find(-1) != -1) { (marker = Array<int>(max_attr)) = 1; }
+   else { marker = AttributeSets::AttrToMarker(max_attr, attrs); }
+}

 /// Transform a mesh according to an arbitrary affine transformation
 ///    y = A x + b
@@ -174,7 +174,6 @@ ParticleTrajectories::ParticleTrajectories(const ParticleSet &particles,

 void ParticleTrajectories::AddSegmentStart()
 {
-   if (!pset.GetNParticles()) { return; }
   // Create a new mesh for all particle segments for this timestep
   segment_meshes.emplace_front(1, pset.GetNParticles()*2,
                                pset.GetNParticles(),
@@ -200,11 +199,10 @@ void ParticleTrajectories::AddSegmentStart()

 void ParticleTrajectories::SetSegmentEnd()
 {
-   if (segment_meshes.empty()) { return; } // no segments to end
-
   const Array<ParticleSet::IDType> &end_ids = pset.GetIDs();

-   // Add all endpoint vertices + segments for all particles
+   // Add all endpoint vertices + segments for all particles that were in
+   // SetSegmentStart
   int num_start = segment_ids.front().Size();
   for (int i = 0; i < num_start; i++)
   {
@@ -230,11 +228,6 @@ void ParticleTrajectories::SetSegmentEnd()
 void ParticleTrajectories::Visualize()
 {
   SetSegmentEnd();
-   if (segment_meshes.empty() && !mesh)
-   {
-      AddSegmentStart();
-      return;
-   }

   // Create a mesh of all the trajectory segments
   std::vector<Mesh*> all_meshes;
@@ -246,8 +239,23 @@ void ParticleTrajectories::Visualize()
   {
      all_meshes.push_back(mesh);
   }
+   if (mesh_bb)
+   {
+      all_meshes.push_back(mesh_bb);
+   }

   Mesh trajectories(all_meshes.data(), all_meshes.size());
+   bool vis = trajectories.GetNE() > 0;
+#ifdef MFEM_USE_MPI
+   MPI_Allreduce(MPI_IN_PLACE, &vis, 1, MFEM_MPI_CXX_BOOL,
+                 MPI_LOR, pset.GetComm());
+#endif // MFEM_USE_MPI
+   if (!vis) // if all rank have 0 elements, skip visualization
+   {
+      AddSegmentStart();
+      return;
+   }
+

 #ifdef MFEM_USE_MPI
   VisualizeMesh(sock, vishost, visport, trajectories, comm,
@@ -260,5 +268,97 @@ void ParticleTrajectories::Visualize()
   AddSegmentStart();
 }

+void ParticleTrajectories::SetVisualizationBoundingBox(const Vector &xmin,
+                                                       const Vector &xmax)
+{
+   MFEM_VERIFY(xmin.Size() == pset.GetDim() &&
+               xmax.Size() == pset.GetDim(),
+               "Bounding box dimension must match ParticleSet dimension.");
+
+   // Create a box mesh for visualization
+   if (mesh_bb)
+   {
+      delete mesh_bb;
+      mesh_bb = nullptr;
+   }
+
+   if (pset.GetDim() == 2)
+   {
+      int dim = 2;
+      int nvert = 4;
+      int nelem = 4;
+      mesh_bb = new Mesh(1, nvert, nelem, 0, dim);
+      Vector v0(dim), v1(dim), v2(dim), v3(dim);
+      v0 = xmin;
+      v1 = xmax;
+      v2[0] = xmax[0]; v2[1] = xmin[1];
+      v3[0] = xmin[0]; v3[1] = xmax[1];
+
+      mesh_bb->AddVertex(v0);
+      mesh_bb->AddVertex(v1);
+      mesh_bb->AddVertex(v2);
+      mesh_bb->AddVertex(v3);
+
+      int vi[2] = {0,1};
+      mesh_bb->AddSegment(vi);
+      vi[0] = 1; vi[1] = 2;
+      mesh_bb->AddSegment(vi);
+      vi[0] = 2; vi[1] = 3;
+      mesh_bb->AddSegment(vi);
+      vi[0] = 3; vi[1] = 0;
+      mesh_bb->AddSegment(vi);
+      mesh_bb->FinalizeMesh();
+   }
+   else // dim == 3
+   {
+      int dim = 3;
+      int nvert = 8;
+      int nelem = 12;
+      mesh_bb = new Mesh(1, nvert, nelem, 0, dim);
+      Vector v(dim);
+
+      // Vertices
+      v[0] = xmin[0]; v[1] = xmin[1]; v[2] = xmin[2];
+      mesh_bb->AddVertex(v); // 0: 000
+      v[0] = xmax[0]; v[1] = xmin[1]; v[2] = xmin[2];
+      mesh_bb->AddVertex(v); // 1: 100
+      v[0] = xmax[0]; v[1] = xmax[1]; v[2] = xmin[2];
+      mesh_bb->AddVertex(v); // 2: 110
+      v[0] = xmin[0]; v[1] = xmax[1]; v[2] = xmin[2];
+      mesh_bb->AddVertex(v); // 3: 010
+
+      v[0] = xmin[0]; v[1] = xmin[1]; v[2] = xmax[2];
+      mesh_bb->AddVertex(v); // 4: 001
+      v[0] = xmax[0]; v[1] = xmin[1]; v[2] = xmax[2];
+      mesh_bb->AddVertex(v); // 5: 101
+      v[0] = xmax[0]; v[1] = xmax[1]; v[2] = xmax[2];
+      mesh_bb->AddVertex(v); // 6: 111
+      v[0] = xmin[0]; v[1] = xmax[1]; v[2] = xmax[2];
+      mesh_bb->AddVertex(v); // 7: 011
+
+      // Segments
+      int vi[2];
+      // Bottom face
+      vi[0] = 0; vi[1] = 1; mesh_bb->AddSegment(vi);
+      vi[0] = 1; vi[1] = 2; mesh_bb->AddSegment(vi);
+      vi[0] = 2; vi[1] = 3; mesh_bb->AddSegment(vi);
+      vi[0] = 3; vi[1] = 0; mesh_bb->AddSegment(vi);
+
+      // Top face
+      vi[0] = 4; vi[1] = 5; mesh_bb->AddSegment(vi);
+      vi[0] = 5; vi[1] = 6; mesh_bb->AddSegment(vi);
+      vi[0] = 6; vi[1] = 7; mesh_bb->AddSegment(vi);
+      vi[0] = 7; vi[1] = 4; mesh_bb->AddSegment(vi);
+
+      // Vertical edges
+      vi[0] = 0; vi[1] = 4; mesh_bb->AddSegment(vi);
+      vi[0] = 1; vi[1] = 5; mesh_bb->AddSegment(vi);
+      vi[0] = 2; vi[1] = 6; mesh_bb->AddSegment(vi);
+      vi[0] = 3; vi[1] = 7; mesh_bb->AddSegment(vi);
+
+      mesh_bb->FinalizeMesh();
+   }
+}
+
 } // namespace common
 } // namespace mfem
@@ -46,7 +46,8 @@ class ParticleTrajectories
 {
 protected:
   const ParticleSet &pset;
-   Mesh *mesh = nullptr;
+   Mesh *mesh = nullptr; // optional edge mesh to visualize along with particles
+   Mesh *mesh_bb = nullptr; // optional bounding box mesh for visualization

   socketstream sock;
   /// Track particle IDs that exist at the segment start.
@@ -90,10 +91,24 @@ public:
                        const char *keys_=nullptr);

   /// Add a mesh to be visualized along with the particle trajectories.
-   void AddMeshForVisualization(Mesh *mesh_) { mesh = mesh_; }
+   void AddMeshForVisualization(Mesh *mesh_)
+   {
+      MFEM_VERIFY(mesh_->Dimension() == 1,
+                  "Mesh dimension must be 1 to match the particle trajectory.");
+      mesh = mesh_;
+   }

   /// Visualize the particle trajectories (and mesh if provided).
   void Visualize();
+
+   /// Set the bounding box for visualization.
+   void SetVisualizationBoundingBox(const Vector &xmin, const Vector &xmax);
+
+   /// Destructor
+   ~ParticleTrajectories()
+   {
+      delete mesh_bb;
+   }
 };


@@ -34,11 +34,13 @@ if (MFEM_USE_MPI)
   EXTRA_HEADERS maxwell_solver.hpp ${MFEM_MINIAPPS_COMMON_HEADERS}
   LIBRARIES mfem-common)

- add_mfem_miniapp(lorentz
-   MAIN lorentz.cpp
-   EXTRA_HEADERS ${MFEM_MINIAPPS_COMMON_HEADERS}
-   LIBRARIES mfem-common)
-
+ if (MFEM_USE_GSLIB)
+  add_mfem_miniapp(lorentz
+    MAIN lorentz.cpp
+    EXTRA_HEADERS ${MFEM_MINIAPPS_COMMON_HEADERS}
+    LIBRARIES mfem-common)
+endif()
+  
  # Add the corresponding tests to the "test" target
  if (MFEM_ENABLE_TESTING)
    add_test(NAME tesla_np=4
@@ -21,7 +21,10 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

 SEQ_MINIAPPS =
-PAR_MINIAPPS = volta tesla maxwell joule lorentz
+PAR_MINIAPPS = volta tesla maxwell joule
+ifeq ($(MFEM_USE_GSLIB), YES)
+   PAR_MINIAPPS += lorentz
+endif
 ifeq ($(MFEM_USE_MPI),NO)
   MINIAPPS = $(SEQ_MINIAPPS)
 else
@@ -51,9 +54,11 @@ all: $(MINIAPPS)
 	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $@_solver.o $(COMMON_LIB) \
 	  $(MFEM_LIBS)

+ifeq ($(MFEM_USE_MPI),YES)
 lorentz: %: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK) | lib-common
 	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<)
 	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $(COMMON_LIB) $(MFEM_LIBS)
+endif

 # Rules for compiling miniapp dependencies
 $(addsuffix _solver.o,$(MINIAPPS)): \
@@ -112,10 +117,10 @@ joule-test-par: joule
 lorentz-test-par: lorentz-test-1 lorentz-test-2
 lorentz-test-1: lorentz volta-test-3
 	@$(call mfem-test,$<, $(RUN_MPI), Electromagnetic miniapp,\
-	-er Volta-AMR-Parallel -ec 2 -x0 '0.5 0.5 0.9' -p0 '1 0 0')
+	-er Volta-AMR-Parallel -ec 2 -npt 100 -xmin '0.0 0.0 0.0' -xmax '1.0 1.0 1.0' -pmin '1 0 0' -pmax '1 0 0' -rdf 0 -vt 0 -nt 100')
 lorentz-test-2: lorentz tesla-test-2
 	@$(call mfem-test,$<, $(RUN_MPI), Electromagnetic miniapp,\
-	-br Tesla-AMR-Parallel -bc 2 -x0 '0.1 0.5 0.1' -p0 '0 0.4 0.1' -tf 9)
+	-br Tesla-AMR-Parallel -bc 2 -br Tesla-AMR-Parallel -npt 10 -xmin '0.0 0.0 0.0' -xmax '1.0 1.0 1.0' -pmin '0 0.1 0.05' -pmax '0 0.4 0.1' -nt 1000 -rdf 0 -vt 0)

 # Testing: "test" target and mfem-test* variables are defined in config/test.mk

@@ -421,22 +421,18 @@ void NavierParticles::Step(const real_t dt, const ParGridFunction &u_gf,
 void NavierParticles::InterpolateUW(const ParGridFunction &u_gf,
                                    const ParGridFunction &w_gf)
 {
-   finder.FindPoints(X(), X().GetOrdering());
+   finder.FindPoints(X());

-   finder.Interpolate(u_gf, U());
-   Ordering::Reorder(U(), U().GetVDim(), u_gf.ParFESpace()->GetOrdering(),
-                     U().GetOrdering());
+   finder.Interpolate(u_gf, U(), U().GetOrdering());

-   finder.Interpolate(w_gf, W());
-   Ordering::Reorder(W(), W().GetVDim(), w_gf.ParFESpace()->GetOrdering(),
-                     W().GetOrdering());
+   finder.Interpolate(w_gf, W(), W().GetOrdering());
 }

 void NavierParticles::DeactivateLostParticles(bool findpts)
 {
   if (findpts)
   {
-      finder.FindPoints(X(), X().GetOrdering());
+      finder.FindPoints(X());
   }

   const Array<unsigned int> lost_idxs = finder.GetPointsNotFoundIndices();
@@ -15,16 +15,14 @@ set(MESH_GF_FILES
    triple-pt-1.gf
    triple-pt-2.gf
 )
-
+# add target which keeps required mesh files in sync
 set(SRC_MESH_GF_FILES)
 foreach(MESH_GF_FILE ${MESH_GF_FILES})
  list(APPEND SRC_MESH_GF_FILES ${CMAKE_CURRENT_SOURCE_DIR}/${MESH_GF_FILE})
 endforeach()
-add_custom_command(OUTPUT data_is_copied
+add_custom_target(copy_miniapps_gslib_data
  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_GF_FILES} .
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying gslib miniapps data files ...")
-add_custom_target(copy_miniapps_gslib_data DEPENDS data_is_copied)
+  COMMENT "Syncing gslib miniapps data files ...")

 if (MFEM_USE_GSLIB)
  add_mfem_miniapp(schwarz_ex1
@@ -27,11 +27,9 @@ set(SRC_MESH_FILES)
 foreach(MESH_FILE ${MESH_FILES})
  list(APPEND SRC_MESH_FILES ${CMAKE_CURRENT_SOURCE_DIR}/${MESH_FILE})
 endforeach()
-add_custom_command(OUTPUT data_is_copied
+add_custom_target(copy_miniapps_meshing_data
  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} .
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying meshing miniapps data files ...")
-add_custom_target(copy_miniapps_meshing_data DEPENDS data_is_copied)
+  COMMENT "Syncing meshing miniapps data files ...")

 add_mfem_miniapp(klein-bottle
  MAIN klein-bottle.cpp
@@ -19,11 +19,9 @@ set(SRC_MESH_FILES)
 foreach(MESH_FILE ${MESH_FILES})
  list(APPEND SRC_MESH_FILES ${CMAKE_CURRENT_SOURCE_DIR}/${MESH_FILE})
 endforeach()
-add_custom_command(OUTPUT data_is_copied
+add_custom_target(copy_miniapps_multidomain_data
  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} .
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying multidomain miniapps data files ...")
-add_custom_target(copy_miniapps_multidomain_data DEPENDS data_is_copied)
+  COMMENT "Syncing multidomain miniapps data files ...")

 # Parallel apps.
 if (MFEM_USE_MPI)
@@ -9,33 +9,12 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-set(MESH_FILES
-  cube-nurbs.mesh
-  ijk-hex-nurbs.mesh
-  plus-nurbs-permuted.mesh
-  plus-nurbs.mesh
-  square-nurbs.mesh
-  two-cubes-nurbs-autoedge.mesh
-  two-cubes-nurbs-rot.mesh
-  two-cubes-nurbs.mesh
-  two-squares-nurbs-autoedge.mesh
-  two-squares-nurbs-rot.mesh
-  two-squares-nurbs.mesh
-  3patch-nurbs.mesh
-  3patch-nurbs-flipedge.mesh
-)
-# Add a target to copy the mesh files from the source directory; used by sample
-# runs.
-set(SRC_MESH_FILES)
-foreach(MESH_FILE ${MESH_FILES})
-  list(APPEND SRC_MESH_FILES ${CMAKE_CURRENT_SOURCE_DIR}/meshes/${MESH_FILE})
-endforeach()
-add_custom_command(OUTPUT data_is_copied
+# add target which keeps required mesh files in sync
+file(GLOB SRC_MESH_FILES CONFIGURE_DEPENDS ${CMAKE_CURRENT_SOURCE_DIR}/meshes/*)
+add_custom_target(copy_miniapps_nurbs_data
  COMMAND ${CMAKE_COMMAND} -E make_directory meshes
-  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} meshes/
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying nurbs miniapps data files ...")
-add_custom_target(copy_miniapps_nurbs_data DEPENDS data_is_copied)
+  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} meshes
+  COMMENT "Syncing nurbs miniapps data directory ...")

 add_mfem_miniapp(nurbs_ex1
  MAIN nurbs_ex1.cpp
@@ -52,6 +31,11 @@ add_mfem_miniapp(nurbs_ex5
  LIBRARIES mfem)
  add_dependencies(nurbs_ex5 copy_miniapps_nurbs_data)

+add_mfem_miniapp(nurbs_ex10
+  MAIN nurbs_ex10.cpp
+  LIBRARIES mfem)
+  add_dependencies(nurbs_ex10 copy_miniapps_nurbs_data)
+
 add_mfem_miniapp(nurbs_ex24
  MAIN nurbs_ex24.cpp
  LIBRARIES mfem)
@@ -72,6 +56,10 @@ add_mfem_miniapp(nurbs_printfunc
  LIBRARIES mfem)
  add_dependencies(nurbs_printfunc copy_miniapps_nurbs_data)

+add_mfem_miniapp(nurbs_mesh_info
+  MAIN nurbs_mesh_info.cpp
+  LIBRARIES mfem)
+
 add_mfem_miniapp(nurbs_patch_ex1
  MAIN nurbs_patch_ex1.cpp
  LIBRARIES mfem)
@@ -269,6 +257,11 @@ if (MFEM_USE_MPI)
    LIBRARIES mfem)
    add_dependencies(nurbs_ex1p copy_miniapps_nurbs_data)

+  add_mfem_miniapp(nurbs_ex10p
+    MAIN nurbs_ex10p.cpp
+    LIBRARIES mfem)
+    add_dependencies(nurbs_ex10p copy_miniapps_nurbs_data)
+
  add_mfem_miniapp(nurbs_ex11p
    MAIN nurbs_ex11p.cpp
    LIBRARIES mfem)
@@ -20,9 +20,11 @@ CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

-SEQ_MINIAPPS = nurbs_ex1 nurbs_patch_ex1 nurbs_ex3 nurbs_ex5 nurbs_ex24 \
-   nurbs_curveint nurbs_printfunc nurbs_solenoidal nurbs_naca_cmesh nurbs_surface
-PAR_MINIAPPS = nurbs_ex1p nurbs_ex11p
+SEQ_MINIAPPS = nurbs_ex1 nurbs_patch_ex1 nurbs_ex3 nurbs_ex5 nurbs_ex10 \
+   nurbs_ex24 nurbs_curveint nurbs_printfunc nurbs_solenoidal nurbs_naca_cmesh \
+   nurbs_mesh_info
+PAR_MINIAPPS = nurbs_ex1p nurbs_ex10p nurbs_ex11p
+
 ifeq ($(MFEM_USE_MPI),NO)
   MINIAPPS = $(SEQ_MINIAPPS)
 else
@@ -199,6 +201,7 @@ clean-build:

 clean-exec:
 	@rm -f refined.mesh sin-fit.mesh ex5.mesh exsol.mesh mesh.* sol.* mode_*
-	@rm -f naca-cmesh.mesh sol_?.gf *-Surface.mesh
+	@rm -f naca-cmesh.mesh sol_?.gf k?_*.dat *-Surface.mesh
 	@rm -rf Example1* Example3* Example5* Solenoidal_* ParaView
 	@rm -rf CurveInt Naca_cmesh glvis_naca-cmesh.mesh solution.dat
+	@rm -rf velocity.* elastic_energy.* deformed.*
--- a/Show More
+++ b/Show More