make style

2. Add _USE_MATH_DEFINES to CmakeLists.txt (without this change VS doesn't "see" this preprocessor in config.hpp)
3. Remove asm definition - asm is not allowed in VS anymore
4. Convert "const double Epsilon" to constexpr (fixes CUDA compilation error)

.gitlab-ci.yml

@@ -50,6 +50,7 @@ variables:
   AUTOTEST_REPO: ssh://git@mybitbucket.llnl.gov:7999/mfem/autotest.git
   MFEM_DATA_REPO: https://github.com/mfem/data.git
   ARTIFACTS_DIR: artifacts
+  SLURM_OVERLAP: 1
 
 # The pipeline is divided into stages. Usually, jobs in a given stage wait for
 # the preceding stages to complete before to start. However, we sometimes use

CHANGELOG

@@ -12,6 +12,21 @@ Version 4.3.1 (development)
 ===========================
 - Added support for hr-adaptivity using TMOP-based error estimator.
 
+- Adding lowest order Nedelec and Raviart-Thomas basis functions on wedge
+  shaped elements.
+
+- Added initial support for meshes with pyramidal elements, including several
+  pyramidal meshes in the data/ directory and support for the lowest order H1,
+  Nedelec, Raviart-Thomas, and L2 basis functions on pyramids.
+
+- Updated the hypre interface according to changes in hypre-2.22.1. The ADS
+  solver is now fully working on GPUs.
+
+- Tetrahedral meshes no longer need to be reordered to support high order
+  Nedelec basis functions. This will allow future support for Nedelec basis
+  functions on wedges and pyramids which are not amenable to reordering. The
+  ReorientTetMesh method of the Mesh and ParMesh classes has been deprecated.
+
 
 Version 4.3, released on July 29, 2021
 ======================================

CITATION.cff

@@ -0,0 +1,66 @@
+cff-version: 1.2.0
+message: "If you use MFEM, please cite it as follows."
+authors:
+- family-names: "MFEM Team"
+title: "MFEM: Modular Finite Element Methods [Software]"
+doi: 10.11578/dc.20171025.1248
+url: "https://mfem.org"
+preferred-citation:
+  type: article
+  authors:
+  - family-names: "Anderson"
+    given-names: "Robert"
+    orcid: "https://orcid.org/0000-0002-3508-9944"
+  - family-names: "Andrej"
+    given-names: "Julian"
+    orcid: "https://orcid.org/0000-0001-7661-4840"
+  - family-names: "Barker"
+    given-names: "Andrew"
+    orcid: "https://orcid.org/0000-0003-3572-911X"
+  - family-names: "Bramwell"
+    given-names: "Jamie"
+  - family-names: "Camier"
+    given-names: "Jean-Sylvain"
+    orcid: "https://orcid.org/0000-0003-2421-1999"
+  - family-names: "Cerveny"
+    given-names: "Jakub"
+    orcid: "https://orcid.org/0000-0003-4231-2531"
+  - family-names: "Dobrev"
+    given-names: "Veselin"
+    orcid: "https://orcid.org/0000-0003-1793-5622"
+  - family-names: "Dudouit"
+    given-names: "Yohann"
+    orcid: "https://orcid.org/0000-0001-5831-561X"
+  - family-names: "Fisher"
+    given-names: "Aaron"
+  - family-names: "Kolev"
+    given-names: "Tzanio"
+    orcid: "https://orcid.org/0000-0002-2810-3090"
+  - family-names: "Pazner"
+    given-names: "Will"
+    orcid: "https://orcid.org/0000-0003-4885-2934"
+  - family-names: "Stowell"
+    given-names: "Mark"
+    orcid: "https://orcid.org/0000-0002-5389-7435"
+  - family-names: "Tomov"
+    given-names: "Vladimir"
+    orcid: "https://orcid.org/0000-0002-1846-6816"
+  - family-names: "Akkerman"
+    given-names: "Ido"
+    orcid: "https://orcid.org/0000-0002-5937-0300"
+  - family-names: "Dahm"
+    given-names: "Johann"
+    orcid: "https://orcid.org/0000-0001-9657-3564"
+  - family-names: "Medina"
+    given-names: "David"
+  - family-names: "Zampini"
+    given-names: "Stefano"
+    orcid: "https://orcid.org/0000-0002-0435-0433"
+  doi: "10.1016/j.camwa.2020.06.009"
+  journal: "Computers \\& Mathematics with Applications"
+  month: 1
+  start: 42 # First page number
+  end: 74 # Last page number
+  title: "MFEM: A Modular Finite Element Methods Library"
+  volume: 81
+  year: 2021

CMakeLists.txt

@@ -175,6 +175,10 @@ else()
   set(MFEM_DEBUG OFF)
 endif()
 
+if (WIN32)
+	add_definitions(-D_USE_MATH_DEFINES)
+endif()
+
 # MPI -> hypre; PETSc (optional)
 if (MFEM_USE_MPI)
   find_package(MPI REQUIRED)

INSTALL

@@ -549,7 +549,7 @@ The specific libraries and their options are:
   Options: HYPRE_OPT, HYPRE_LIB.
   Versions: HYPRE >= 2.10.0b  (HYPRE built without CUDA)
             HYPRE >= 2.20.0   (HYPRE built with '--enable-mixedint')
-            HYPRE >= 2.22.0   (HYPRE built with CUDA)
+            HYPRE >= 2.22.1   (HYPRE built with CUDA)
 
 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
   MFEM_USE_METIS_5 = YES (default is to use METIS 4).

data/inline-pyramid.mesh

@@ -0,0 +1,9 @@
+MFEM INLINE mesh v1.0
+
+type = pyramid
+nx = 4
+ny = 4
+nz = 4
+sx = 1.0
+sy = 1.0
+sz = 1.0

data/octahedron.mesh

@@ -0,0 +1,43 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+#
+
+dimension
+3
+
+elements
+2
+1 7 4 3 2 1 0
+1 7 1 2 3 4 5
+
+boundary
+8
+1 2 0 2 1
+2 2 0 3 2
+3 2 0 4 3
+4 2 0 1 4
+5 2 1 2 5
+6 2 2 3 5
+7 2 3 4 5
+8 2 4 1 5
+
+vertices
+6
+3
+0 0 -1
+1 0 0
+0 1 0
+-1 0 0
+0 -1 0
+0 0 1

data/ref-pyramid.mesh

@@ -0,0 +1,38 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+#
+
+dimension
+3
+
+elements
+1
+1 7 0 1 2 3 4
+
+boundary
+5
+1 3 3 2 1 0
+2 2 0 1 4
+3 2 1 2 4
+4 2 2 3 4
+5 2 3 0 4
+
+vertices
+5
+3
+0 0 0
+1 0 0
+1 1 0
+0 1 0
+0 0 1

examples/caliper/ex1.cpp

@@ -206,9 +206,9 @@ int main(int argc, char *argv[])
    cout << "Size of linear system: " << A->Height() << endl;
 
    // 11. Solve the linear system A X = B.
-   MFEM_PERF_BEGIN("Solve A X=B");
    if (!pa)
    {
+      MFEM_PERF_SCOPE("Solve A X=B (FA)");
 #ifndef MFEM_USE_SUITESPARSE
       // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
       GSSmoother M((SparseMatrix&)(*A));
@@ -223,6 +223,7 @@ int main(int argc, char *argv[])
    }
    else // Jacobi preconditioning in partial assembly mode
    {
+      MFEM_PERF_SCOPE("Solve A X=B (PA)");
       if (UsesTensorBasis(fespace))
       {
          OperatorJacobiSmoother M(a, ess_tdof_list);
@@ -233,7 +234,6 @@ int main(int argc, char *argv[])
          CG(*A, B, X, 1, 400, 1e-12, 0.0);
       }
    }
-   MFEM_PERF_END("Solve A X=B");
    // 12. Recover the solution as a finite element grid function.
    a.RecoverFEMSolution(X, b, x);
 

examples/caliper/ex1p.cpp

@@ -231,28 +231,29 @@ int main(int argc, char *argv[])
    // 13. Solve the linear system A X = B.
    //     * With full assembly, use the BoomerAMG preconditioner from hypre.
    //     * With partial assembly, use Jacobi smoothing, for now.
-   MFEM_PERF_BEGIN("Solve A X = B");
-   Solver *prec = NULL;
-   if (pa)
    {
-      if (UsesTensorBasis(fespace))
+      MFEM_PERF_SCOPE("Solve A X=B");
+      Solver *prec = NULL;
+      if (pa)
       {
-         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+         if (UsesTensorBasis(fespace))
+         {
+            prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+         }
       }
+      else
+      {
+         prec = new HypreBoomerAMG;
+      }
+      CGSolver cg(MPI_COMM_WORLD);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(2000);
+      cg.SetPrintLevel(1);
+      if (prec) { cg.SetPreconditioner(*prec); }
+      cg.SetOperator(*A);
+      cg.Mult(B, X);
+      delete prec;
    }
-   else
-   {
-      prec = new HypreBoomerAMG;
-   }
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(1e-12);
-   cg.SetMaxIter(2000);
-   cg.SetPrintLevel(1);
-   if (prec) { cg.SetPreconditioner(*prec); }
-   cg.SetOperator(*A);
-   cg.Mult(B, X);
-   delete prec;
-   MFEM_PERF_END("Solve A X = B");
    // 14. Recover the parallel grid function corresponding to X. This is the
    //     local finite element solution on each processor.
    a.RecoverFEMSolution(X, b, x);

examples/ex1.cpp

@@ -9,6 +9,7 @@
 //               ex1 -m ../data/fichera.mesh
 //               ex1 -m ../data/fichera-mixed.mesh
 //               ex1 -m ../data/toroid-wedge.mesh
+//               ex1 -m ../data/octahedron.mesh -o 1
 //               ex1 -m ../data/periodic-annulus-sector.msh
 //               ex1 -m ../data/periodic-torus-sector.msh
 //               ex1 -m ../data/square-disc-p2.vtk -o 2

examples/ex13p.cpp

@@ -118,7 +118,6 @@ int main(int argc, char *argv[])
    {
       pmesh->UniformRefinement();
    }
-   pmesh->ReorientTetMesh();
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Nedelec finite elements of the specified order.

examples/ex16.cpp

@@ -24,7 +24,10 @@
 //               class ConductionOperator defining C(u)), as well as their
 //               implicit time integration. Note that implementing the method
 //               ConductionOperator::ImplicitSolve is the only requirement for
-//               high-order implicit (SDIRK) time integration.
+//               high-order implicit (SDIRK) time integration. In this example,
+//               the diffusion operator is linearized by evaluating with the
+//               lagged solution from the previous timestep, so there is only
+//               a linear solve.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -326,8 +329,8 @@ ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
    // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
+   //    du_dt = M^{-1}*-Ku
+   // for du_dt, where K is linearized by using u from the previous timestep
    Kmat.Mult(u, z);
    z.Neg(); // z = -z
    M_solver.Mult(z, du_dt);
@@ -338,7 +341,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
    // Solve the equation:
    //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
+   // for du_dt, where K is linearized by using u from the previous timestep
    if (!T)
    {
       T = Add(1.0, Mmat, dt, Kmat);

examples/ex16p.cpp

@@ -24,8 +24,11 @@
 //               class ConductionOperator defining C(u)), as well as their
 //               implicit time integration. Note that implementing the method
 //               ConductionOperator::ImplicitSolve is the only requirement for
-//               high-order implicit (SDIRK) time integration. Optional saving
-//               with ADIOS2 (adios2.readthedocs.io) is also illustrated.
+//               high-order implicit (SDIRK) time integration. In this example,
+//               the diffusion operator is linearized by evaluating with the
+//               lagged solution from the previous timestep, so there is only
+//               a linear solve. Optional saving with ADIOS2
+//               (adios2.readthedocs.io) is also illustrated.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -420,8 +423,8 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
    // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
+   //    du_dt = M^{-1}*-Ku
+   // for du_dt, where K is linearized by using u from the previous timestep
    Kmat.Mult(u, z);
    z.Neg(); // z = -z
    M_solver.Mult(z, du_dt);
@@ -432,7 +435,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
    // Solve the equation:
    //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
+   // for du_dt, where K is linearized by using u from the previous timestep
    if (!T)
    {
       T = Add(1.0, Mmat, dt, Kmat);

examples/ex1p.cpp

@@ -9,6 +9,7 @@
 //               mpirun -np 4 ex1p -m ../data/fichera.mesh
 //               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
 //               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex1p -m ../data/periodic-annulus-sector.msh
 //               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
 //               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2

examples/ex22.cpp

@@ -13,6 +13,8 @@
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 1
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa
+//               ex22 -m ../data/inline-wedge.mesh -o 1
+//               ex22 -m ../data/inline-pyramid.mesh -o 1
 //               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0
 //
 // Device sample runs:

examples/ex22p.cpp

@@ -13,6 +13,8 @@
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 1
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 2
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa
+//               mpirun -np 4 ex22p -m ../data/inline-wedge.mesh -o 1
+//               mpirun -np 4 ex22p -m ../data/inline-pyramid.mesh -o 1
 //               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0
 //
 // Device sample runs:

examples/ex24.cpp

@@ -113,7 +113,6 @@ int main(int argc, char *argv[])
          mesh->UniformRefinement();
       }
    }
-   mesh->ReorientTetMesh();
 
    // 5. Define a finite element space on the mesh. Here we use Nedelec or
    //    Raviart-Thomas finite elements of the specified order.

examples/ex24p.cpp

@@ -141,7 +141,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use Nedelec or Raviart-Thomas finite elements of the specified order.

examples/ex25.cpp

@@ -92,7 +92,7 @@ class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
    CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , Vector &);
+   void (*Function)(const Vector &, CartesianPML *, Vector &);
 public:
    PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
                                               Vector &),
@@ -277,10 +277,8 @@ int main(int argc, char *argv[])
       mesh->UniformRefinement();
    }
 
-   // 6. Reorient mesh in case of a tet mesh
-   mesh->ReorientTetMesh();
-
-   // Set element attributes in order to distinguish elements in the PML region
+   // 6. Set element attributes in order to distinguish elements in the
+   //    PML region
    pml->SetAttributes(mesh);
 
    // 7. Define a finite element space on the mesh. Here we use the Nedelec

examples/ex25p.cpp

@@ -92,7 +92,7 @@ class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
    CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , Vector &);
+   void (*Function)(const Vector &, CartesianPML *, Vector &);
 public:
    PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
                                               Vector &),
@@ -316,9 +316,6 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 7a. Reorient mesh in case of a tet mesh
-   pmesh->ReorientTetMesh();
-
    // 8. Set element attributes in order to distinguish elements in the PML
    pml->SetAttributes(pmesh);
 

examples/ex3.cpp

@@ -16,6 +16,8 @@
 //               ex3 -m ../data/beam-hex-nurbs.mesh
 //               ex3 -m ../data/amr-hex.mesh
 //               ex3 -m ../data/fichera-amr.mesh
+//               ex3 -m ../data/ref-prism.mesh -o 1
+//               ex3 -m ../data/octahedron.mesh -o 1
 //               ex3 -m ../data/star-surf.mesh -o 1
 //               ex3 -m ../data/mobius-strip.mesh -f 0.1
 //               ex3 -m ../data/klein-bottle.mesh -f 0.1
@@ -113,7 +115,6 @@ int main(int argc, char *argv[])
          mesh->UniformRefinement();
       }
    }
-   mesh->ReorientTetMesh();
 
    // 5. Define a finite element space on the mesh. Here we use the Nedelec
    //    finite elements of the specified order.

examples/ex3p.cpp

@@ -16,6 +16,8 @@
 //               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
 //               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
 //               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/ref-prism.mesh -o 1
+//               mpirun -np 4 ex3p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
 //               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
 //               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
@@ -139,9 +141,7 @@ int main(int argc, char *argv[])
 
    // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them.
+   //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
    {
@@ -151,7 +151,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Nedelec finite elements of the specified order.

examples/ex4.cpp

@@ -19,6 +19,8 @@
 //               ex4 -m ../data/amr-hex.mesh
 //               ex4 -m ../data/amr-hex.mesh -o 2 -hb
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
+//               ex4 -m ../data/ref-prism.mesh -o 1
+//               ex4 -m ../data/octahedron.mesh -o 1
 //               ex4 -m ../data/star-surf.mesh -o 1
 //
 // Device sample runs:

examples/ex4p.cpp

@@ -19,6 +19,8 @@
 //               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
 //               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/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:
@@ -135,9 +137,7 @@ int main(int argc, char *argv[])
 
    // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them (this is needed in the ADS solver below).
+   //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
    {
@@ -147,7 +147,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Raviart-Thomas finite elements of the specified order.

examples/ex8p.cpp

@@ -106,7 +106,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 6. Define the trial, interfacial (trace) and test DPG spaces:
    //    - The trial space, x0_space, contains the non-interfacial unknowns and

examples/petsc/ex3p.cpp

@@ -121,9 +121,7 @@ int main(int argc, char *argv[])
 
    // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them.
+   //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
    {
@@ -133,7 +131,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 6. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Nedelec finite elements of the specified order.

examples/petsc/ex4p.cpp

@@ -122,9 +122,7 @@ int main(int argc, char *argv[])
 
    // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them (this is needed in the ADS solver below).
+   //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
    {
@@ -134,7 +132,6 @@ int main(int argc, char *argv[])
          pmesh->UniformRefinement();
       }
    }
-   pmesh->ReorientTetMesh();
 
    // 6. Define a parallel finite element space on the parallel mesh. Here we
    //    use the Raviart-Thomas finite elements of the specified order.

fem/CMakeLists.txt

@@ -39,6 +39,7 @@ set(SRCS
   complex_fem.cpp
   convergence.cpp
   datacollection.cpp
+  doftrans.cpp
   eltrans.cpp
   estimators.cpp
   fe.cpp
@@ -119,6 +120,7 @@ set(HDRS
   complex_fem.hpp
   convergence.hpp
   datacollection.hpp
+  doftrans.hpp
   eltrans.hpp
   estimators.hpp
   fe.hpp

fem/bilinearform.cpp

@@ -391,6 +391,7 @@ void BilinearForm::Assemble(int skip_zeros)
    }
 
    ElementTransformation *eltrans;
+   DofTransformation * doftrans;
    Mesh *mesh = fes -> GetMesh();
    DenseMatrix elmat, *elmat_p;
 
@@ -424,7 +425,7 @@ void BilinearForm::Assemble(int skip_zeros)
       for (int i = 0; i < fes -> GetNE(); i++)
       {
          int elem_attr = fes->GetMesh()->GetAttribute(i);
-         fes->GetElementVDofs(i, vdofs);
+         doftrans = fes->GetElementVDofs(i, vdofs);
          if (element_matrices)
          {
             elmat_p = &(*element_matrices)(i);
@@ -458,6 +459,11 @@ void BilinearForm::Assemble(int skip_zeros)
             {
                elmat_p = &elmat;
             }
+            if (doftrans)
+            {
+               doftrans->TransformDual(elmat);
+            }
+            elmat_p = &elmat;
          }
          if (static_cond)
          {
@@ -503,7 +509,7 @@ void BilinearForm::Assemble(int skip_zeros)
          if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
 
          const FiniteElement &be = *fes->GetBE(i);
-         fes -> GetBdrElementVDofs (i, vdofs);
+         doftrans = fes -> GetBdrElementVDofs (i, vdofs);
          eltrans = fes -> GetBdrElementTransformation (i);
          int k = 0;
          for (; k < boundary_integs.Size(); k++)
@@ -523,17 +529,22 @@ void BilinearForm::Assemble(int skip_zeros)
             boundary_integs[k]->AssembleElementMatrix(be, *eltrans, elemmat);
             elmat += elemmat;
          }
+         if (doftrans)
+         {
+            doftrans->TransformDual(elmat);
+         }
+         elmat_p = &elmat;
          if (!static_cond)
          {
-            mat->AddSubMatrix(vdofs, vdofs, elmat, skip_zeros);
+            mat->AddSubMatrix(vdofs, vdofs, *elmat_p, skip_zeros);
             if (hybridization)
             {
-               hybridization->AssembleBdrMatrix(i, elmat);
+               hybridization->AssembleBdrMatrix(i, *elmat_p);
             }
          }
          else
          {
-            static_cond->AssembleBdrMatrix(i, elmat);
+            static_cond->AssembleBdrMatrix(i, *elmat_p);
          }
       }
    }
@@ -1318,9 +1329,10 @@ void MixedBilinearForm::Assemble (int skip_zeros)
       return;
    }
 
-   Array<int> tr_vdofs, te_vdofs;
    ElementTransformation *eltrans;
-   DenseMatrix elemmat;
+   DofTransformation * dom_dof_trans;
+   DofTransformation * ran_dof_trans;
+   DenseMatrix elmat;
 
    Mesh *mesh = test_fes -> GetMesh();
 
@@ -1333,16 +1345,24 @@ void MixedBilinearForm::Assemble (int skip_zeros)
    {
       for (int i = 0; i < test_fes -> GetNE(); i++)
       {
-         trial_fes -> GetElementVDofs (i, tr_vdofs);
-         test_fes  -> GetElementVDofs (i, te_vdofs);
+         dom_dof_trans = trial_fes -> GetElementVDofs (i, trial_vdofs);
+         ran_dof_trans = test_fes  -> GetElementVDofs (i, test_vdofs);
          eltrans = test_fes -> GetElementTransformation (i);
+
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
          for (int k = 0; k < domain_integs.Size(); k++)
          {
             domain_integs[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
                                                         *test_fes  -> GetFE(i),
                                                         *eltrans, elemmat);
-            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            elmat += elemmat;
          }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformDual(ran_dof_trans, dom_dof_trans, elmat);
+         }
+         mat -> AddSubMatrix (test_vdofs, trial_vdofs, elmat, skip_zeros);
       }
    }
 
@@ -1374,9 +1394,12 @@ void MixedBilinearForm::Assemble (int skip_zeros)
          const int bdr_attr = mesh->GetBdrAttribute(i);
          if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
 
-         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
-         test_fes  -> GetBdrElementVDofs (i, te_vdofs);
+         dom_dof_trans = trial_fes -> GetBdrElementVDofs (i, trial_vdofs);
+         ran_dof_trans = test_fes  -> GetBdrElementVDofs (i, test_vdofs);
          eltrans = test_fes -> GetBdrElementTransformation (i);
+
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
          for (int k = 0; k < boundary_integs.Size(); k++)
          {
             if (boundary_integs_marker[k] &&
@@ -1385,29 +1408,34 @@ void MixedBilinearForm::Assemble (int skip_zeros)
             boundary_integs[k]->AssembleElementMatrix2 (*trial_fes -> GetBE(i),
                                                         *test_fes  -> GetBE(i),
                                                         *eltrans, elemmat);
-            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            elmat += elemmat;
          }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformDual(ran_dof_trans, dom_dof_trans, elmat);
+         }
+         mat -> AddSubMatrix (test_vdofs, trial_vdofs, elmat, skip_zeros);
       }
    }
 
    if (trace_face_integs.Size())
    {
       FaceElementTransformations *ftr;
-      Array<int> te_vdofs2;
+      Array<int> test_vdofs2;
       const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
 
       int nfaces = mesh->GetNumFaces();
       for (int i = 0; i < nfaces; i++)
       {
          ftr = mesh->GetFaceElementTransformations(i);
-         trial_fes->GetFaceVDofs(i, tr_vdofs);
-         test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
+         trial_fes->GetFaceVDofs(i, trial_vdofs);
+         test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
          trial_face_fe = trial_fes->GetFaceElement(i);
          test_fe1 = test_fes->GetFE(ftr->Elem1No);
          if (ftr->Elem2No >= 0)
          {
-            test_fes->GetElementVDofs(ftr->Elem2No, te_vdofs2);
-            te_vdofs.Append(te_vdofs2);
+            test_fes->GetElementVDofs(ftr->Elem2No, test_vdofs2);
+            test_vdofs.Append(test_vdofs2);
             test_fe2 = test_fes->GetFE(ftr->Elem2No);
          }
          else
@@ -1421,7 +1449,7 @@ void MixedBilinearForm::Assemble (int skip_zeros)
          {
             trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
                                                      *test_fe2, *ftr, elemmat);
-            mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
          }
       }
    }
@@ -1461,8 +1489,8 @@ void MixedBilinearForm::Assemble (int skip_zeros)
          ftr = mesh->GetBdrFaceTransformations(i);
          if (ftr)
          {
-            trial_fes->GetFaceVDofs(ftr->ElementNo, tr_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
+            trial_fes->GetFaceVDofs(ftr->ElementNo, trial_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
             trial_face_fe = trial_fes->GetFaceElement(ftr->ElementNo);
             test_fe1 = test_fes->GetFE(ftr->Elem1No);
             // The test_fe2 object is really a dummy and not used on the
@@ -1479,7 +1507,7 @@ void MixedBilinearForm::Assemble (int skip_zeros)
                                                                  *test_fe1,
                                                                  *test_fe2,
                                                                  *ftr, elemmat);
-               mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
+               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
             }
          }
       }
@@ -1841,6 +1869,8 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
 
    Array<int> dom_vdofs, ran_vdofs;
    ElementTransformation *T;
+   DofTransformation * dom_dof_trans;
+   DofTransformation * ran_dof_trans;
    const FiniteElement *dom_fe, *ran_fe;
    DenseMatrix totelmat, elmat;
 
@@ -1853,8 +1883,8 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
    {
       for (int i = 0; i < test_fes->GetNE(); i++)
       {
-         trial_fes->GetElementVDofs(i, dom_vdofs);
-         test_fes->GetElementVDofs(i, ran_vdofs);
+         dom_dof_trans = trial_fes->GetElementVDofs(i, dom_vdofs);
+         ran_dof_trans = test_fes->GetElementVDofs(i, ran_vdofs);
          T = test_fes->GetElementTransformation(i);
          dom_fe = trial_fes->GetFE(i);
          ran_fe = test_fes->GetFE(i);
@@ -1867,6 +1897,10 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
                                                      elmat);
             totelmat += elmat;
          }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformPrimal(ran_dof_trans, dom_dof_trans, totelmat);
+         }
          mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
       }
    }

fem/bilininteg_convection_ea.cpp

@@ -17,14 +17,14 @@ namespace mfem
 {
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble1D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble1D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -69,14 +69,14 @@ static void EAConvectionAssemble1D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble2D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble2D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -146,14 +146,14 @@ static void EAConvectionAssemble2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble3D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble3D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/bilininteg_convection_pa.cpp

@@ -21,13 +21,13 @@ namespace mfem
 // PA Convection Integrator
 
 // PA Convection Assemble 2D kernel
-static void PAConvectionSetup2D(const int NQ,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const Vector &vel,
-                                const double alpha,
-                                Vector &op)
+void PAConvectionSetup2D(const int NQ,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const Vector &vel,
+                         const double alpha,
+                         Vector &op)
 {
    constexpr int DIM = 2;
 
@@ -60,13 +60,13 @@ static void PAConvectionSetup2D(const int NQ,
 }
 
 // PA Convection Assemble 3D kernel
-static void PAConvectionSetup3D(const int NQ,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const Vector &vel,
-                                const double alpha,
-                                Vector &op)
+void PAConvectionSetup3D(const int NQ,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const Vector &vel,
+                         const double alpha,
+                         Vector &op)
 {
    constexpr int DIM = 3;
    constexpr int SDIM = DIM;
@@ -135,7 +135,7 @@ static void PAConvectionSetup(const int dim,
 }
 
 // PA Convection Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PAConvectionApply2D(const int ne,
                          const Array<double> &b,
                          const Array<double> &g,
@@ -254,7 +254,7 @@ void PAConvectionApply2D(const int ne,
 }
 
 // Optimized PA Convection Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPAConvectionApply2D(const int ne,
                              const Array<double> &b,
                              const Array<double> &g,
@@ -382,7 +382,7 @@ void SmemPAConvectionApply2D(const int ne,
 }
 
 // PA Convection Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PAConvectionApply3D(const int ne,
                          const Array<double> &b,
                          const Array<double> &g,
@@ -563,7 +563,7 @@ void PAConvectionApply3D(const int ne,
 }
 
 // Optimized PA Convection Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void SmemPAConvectionApply3D(const int ne,
                              const Array<double> &b,
                              const Array<double> &g,

fem/bilininteg_dgtrace_ea.cpp

@@ -16,12 +16,12 @@
 namespace mfem
 {
 
-static void EADGTraceAssemble1DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add)
+void EADGTraceAssemble1DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add)
 {
    auto D = Reshape(padata.Read(), 2, 2, NF);
    auto A_int = Reshape(eadata_int.ReadWrite(), 2, NF);
@@ -50,11 +50,11 @@ static void EADGTraceAssemble1DInt(const int NF,
    });
 }
 
-static void EADGTraceAssemble1DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add)
+void EADGTraceAssemble1DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add)
 {
    auto D = Reshape(padata.Read(), 2, 2, NF);
    auto A_bdr = Reshape(eadata_bdr.ReadWrite(), NF);
@@ -72,14 +72,14 @@ static void EADGTraceAssemble1DBdr(const int NF,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble2DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -128,13 +128,13 @@ static void EADGTraceAssemble2DInt(const int NF,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble2DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -170,14 +170,14 @@ static void EADGTraceAssemble2DBdr(const int NF,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble3DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -268,13 +268,13 @@ static void EADGTraceAssemble3DInt(const int NF,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble3DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/bilininteg_dgtrace_pa.cpp

@@ -19,16 +19,16 @@ using namespace std;
 namespace mfem
 {
 // PA DG Trace Integrator
-static void PADGTraceSetup2D(const int Q1D,
-                             const int NF,
-                             const Array<double> &w,
-                             const Vector &det,
-                             const Vector &nor,
-                             const Vector &rho,
-                             const Vector &vel,
-                             const double alpha,
-                             const double beta,
-                             Vector &op)
+void PADGTraceSetup2D(const int Q1D,
+                      const int NF,
+                      const Array<double> &w,
+                      const Vector &det,
+                      const Vector &nor,
+                      const Vector &rho,
+                      const Vector &vel,
+                      const double alpha,
+                      const double beta,
+                      Vector &op)
 {
    const int VDIM = 2;
 
@@ -61,16 +61,16 @@ static void PADGTraceSetup2D(const int Q1D,
    });
 }
 
-static void PADGTraceSetup3D(const int Q1D,
-                             const int NF,
-                             const Array<double> &w,
-                             const Vector &det,
-                             const Vector &nor,
-                             const Vector &rho,
-                             const Vector &vel,
-                             const double alpha,
-                             const double beta,
-                             Vector &op)
+void PADGTraceSetup3D(const int Q1D,
+                      const int NF,
+                      const Array<double> &w,
+                      const Vector &det,
+                      const Vector &nor,
+                      const Vector &rho,
+                      const Vector &vel,
+                      const double alpha,
+                      const double beta,
+                      Vector &op)
 {
    const int VDIM = 3;
 
@@ -301,7 +301,7 @@ void DGTraceIntegrator::AssemblePABoundaryFaces(const FiniteElementSpace& fes)
 }
 
 // PA DGTrace Apply 2D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApply2D(const int NF,
                       const Array<double> &b,
                       const Array<double> &bt,
@@ -392,7 +392,7 @@ void PADGTraceApply2D(const int NF,
 }
 
 // PA DGTrace Apply 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApply3D(const int NF,
                       const Array<double> &b,
                       const Array<double> &bt,
@@ -537,7 +537,7 @@ void PADGTraceApply3D(const int NF,
 }
 
 // Optimized PA DGTrace Apply 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPADGTraceApply3D(const int NF,
                           const Array<double> &b,
                           const Array<double> &bt,
@@ -701,7 +701,7 @@ static void PADGTraceApply(const int dim,
 }
 
 // PA DGTrace Apply 2D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApplyTranspose2D(const int NF,
                                const Array<double> &b,
                                const Array<double> &bt,
@@ -797,7 +797,7 @@ void PADGTraceApplyTranspose2D(const int NF,
 }
 
 // PA DGTrace Apply Transpose 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApplyTranspose3D(const int NF,
                                const Array<double> &b,
                                const Array<double> &bt,
@@ -953,7 +953,7 @@ void PADGTraceApplyTranspose3D(const int NF,
 }
 
 // Optimized PA DGTrace Apply Transpose 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPADGTraceApplyTranspose3D(const int NF,
                                    const Array<double> &b,
                                    const Array<double> &bt,

fem/bilininteg_diffusion_ea.cpp

@@ -17,14 +17,14 @@ namespace mfem
 {
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble1D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble1D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -68,14 +68,14 @@ static void EADiffusionAssemble1D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble2D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble2D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -145,14 +145,14 @@ static void EADiffusionAssemble2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble3D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble3D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/bilininteg_diffusion_pa.cpp

@@ -496,14 +496,14 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionDiagonal2D(const int NE,
-                                  const bool symmetric,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &d,
-                                  Vector &y,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PADiffusionDiagonal2D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &d,
+                           Vector &y,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -562,14 +562,14 @@ static void PADiffusionDiagonal2D(const int NE,
 
 // Shared memory PA Diffusion Diagonal 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPADiffusionDiagonal2D(const int NE,
-                                      const bool symmetric,
-                                      const Array<double> &b_,
-                                      const Array<double> &g_,
-                                      const Vector &d_,
-                                      Vector &y_,
-                                      const int d1d = 0,
-                                      const int q1d = 0)
+void SmemPADiffusionDiagonal2D(const int NE,
+                               const bool symmetric,
+                               const Array<double> &b_,
+                               const Array<double> &g_,
+                               const Vector &d_,
+                               Vector &y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -656,14 +656,14 @@ static void SmemPADiffusionDiagonal2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionDiagonal3D(const int NE,
-                                  const bool symmetric,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &d,
-                                  Vector &y,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PADiffusionDiagonal3D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &d,
+                           Vector &y,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    constexpr int DIM = 3;
    const int D1D = T_D1D ? T_D1D : d1d;
@@ -757,14 +757,14 @@ static void PADiffusionDiagonal3D(const int NE,
 
 // Shared memory PA Diffusion Diagonal 3D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPADiffusionDiagonal3D(const int NE,
-                                      const bool symmetric,
-                                      const Array<double> &b_,
-                                      const Array<double> &g_,
-                                      const Vector &d_,
-                                      Vector &y_,
-                                      const int d1d = 0,
-                                      const int q1d = 0)
+void SmemPADiffusionDiagonal3D(const int NE,
+                               const bool symmetric,
+                               const Array<double> &b_,
+                               const Array<double> &g_,
+                               const Vector &d_,
+                               Vector &y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
 {
    constexpr int DIM = 3;
    const int D1D = T_D1D ? T_D1D : d1d;
@@ -1034,17 +1034,17 @@ static void OccaPADiffusionApply3D(const int D1D,
 
 // PA Diffusion Apply 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionApply2D(const int NE,
-                               const bool symmetric,
-                               const Array<double> &b_,
-                               const Array<double> &g_,
-                               const Array<double> &bt_,
-                               const Array<double> &gt_,
-                               const Vector &d_,
-                               const Vector &x_,
-                               Vector &y_,
-                               const int d1d = 0,
-                               const int q1d = 0)
+void PADiffusionApply2D(const int NE,
+                        const bool symmetric,
+                        const Array<double> &b_,
+                        const Array<double> &g_,
+                        const Array<double> &bt_,
+                        const Array<double> &gt_,
+                        const Vector &d_,
+                        const Vector &x_,
+                        Vector &y_,
+                        const int d1d = 0,
+                        const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1156,15 +1156,15 @@ static void PADiffusionApply2D(const int NE,
 
 // Shared memory PA Diffusion Apply 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPADiffusionApply2D(const int NE,
-                                   const bool symmetric,
-                                   const Array<double> &b_,
-                                   const Array<double> &g_,
-                                   const Vector &d_,
-                                   const Vector &x_,
-                                   Vector &y_,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void SmemPADiffusionApply2D(const int NE,
+                            const bool symmetric,
+                            const Array<double> &b_,
+                            const Array<double> &g_,
+                            const Vector &d_,
+                            const Vector &x_,
+                            Vector &y_,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1314,16 +1314,16 @@ static void SmemPADiffusionApply2D(const int NE,
 
 // PA Diffusion Apply 3D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionApply3D(const int NE,
-                               const bool symmetric,
-                               const Array<double> &b,
-                               const Array<double> &g,
-                               const Array<double> &bt,
-                               const Array<double> &gt,
-                               const Vector &d_,
-                               const Vector &x_,
-                               Vector &y_,
-                               int d1d = 0, int q1d = 0)
+void PADiffusionApply3D(const int NE,
+                        const bool symmetric,
+                        const Array<double> &b,
+                        const Array<double> &g,
+                        const Array<double> &bt,
+                        const Array<double> &gt,
+                        const Vector &d_,
+                        const Vector &x_,
+                        Vector &y_,
+                        int d1d = 0, int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1533,15 +1533,15 @@ static MFEM_HOST_DEVICE inline double sign(const int q, const int d)
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPADiffusionApply3D(const int NE,
-                                   const bool symmetric,
-                                   const Array<double> &b_,
-                                   const Array<double> &g_,
-                                   const Vector &d_,
-                                   const Vector &x_,
-                                   Vector &y_,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void SmemPADiffusionApply3D(const int NE,
+                            const bool symmetric,
+                            const Array<double> &b_,
+                            const Array<double> &g_,
+                            const Vector &d_,
+                            const Vector &x_,
+                            Vector &y_,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/bilininteg_divergence.cpp

@@ -21,12 +21,12 @@ namespace mfem
 // PA Divergence Integrator
 
 // PA Divergence Assemble 2D kernel
-static void PADivergenceSetup2D(const int Q1D,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const double COEFF,
-                                Vector &op)
+void PADivergenceSetup2D(const int Q1D,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const double COEFF,
+                         Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -51,12 +51,12 @@ static void PADivergenceSetup2D(const int Q1D,
 }
 
 // PA Divergence Assemble 3D kernel
-static void PADivergenceSetup3D(const int Q1D,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const double COEFF,
-                                Vector &op)
+void PADivergenceSetup3D(const int Q1D,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const double COEFF,
+                         Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -160,16 +160,16 @@ void VectorDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 
 // PA Divergence Apply 2D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApply2D(const int NE,
-                                const Array<double> &b,
-                                const Array<double> &g,
-                                const Array<double> &bt,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int tr_d1d = 0,
-                                const int te_d1d = 0,
-                                const int q1d = 0)
+void PADivergenceApply2D(const int NE,
+                         const Array<double> &b,
+                         const Array<double> &g,
+                         const Array<double> &bt,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int tr_d1d = 0,
+                         const int te_d1d = 0,
+                         const int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -281,16 +281,16 @@ static void PADivergenceApply2D(const int NE,
 // Shared memory PA Divergence Apply 2D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0,
          const int T_NBZ = 0>
-static void SmemPADivergenceApply2D(const int NE,
-                                    const Array<double> &b_,
-                                    const Array<double> &g_,
-                                    const Array<double> &bt_,
-                                    const Vector &op_,
-                                    const Vector &x_,
-                                    Vector &y_,
-                                    const int tr_d1d = 0,
-                                    const int te_d1d = 0,
-                                    const int q1d = 0)
+void SmemPADivergenceApply2D(const int NE,
+                             const Array<double> &b_,
+                             const Array<double> &g_,
+                             const Array<double> &bt_,
+                             const Vector &op_,
+                             const Vector &x_,
+                             Vector &y_,
+                             const int tr_d1d = 0,
+                             const int te_d1d = 0,
+                             const int q1d = 0)
 {
    // TODO
    MFEM_ASSERT(false, "SHARED MEM NOT PROGRAMMED YET");
@@ -298,16 +298,16 @@ static void SmemPADivergenceApply2D(const int NE,
 
 // PA Divergence Apply 2D kernel transpose
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApplyTranspose2D(const int NE,
-                                         const Array<double> &bt,
-                                         const Array<double> &gt,
-                                         const Array<double> &b,
-                                         const Vector &op_,
-                                         const Vector &x_,
-                                         Vector &y_,
-                                         const int tr_d1d = 0,
-                                         const int te_d1d = 0,
-                                         const int q1d = 0)
+void PADivergenceApplyTranspose2D(const int NE,
+                                  const Array<double> &bt,
+                                  const Array<double> &gt,
+                                  const Array<double> &b,
+                                  const Vector &op_,
+                                  const Vector &x_,
+                                  Vector &y_,
+                                  const int tr_d1d = 0,
+                                  const int te_d1d = 0,
+                                  const int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -414,16 +414,16 @@ static void PADivergenceApplyTranspose2D(const int NE,
 
 // PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApply3D(const int NE,
-                                const Array<double> &b,
-                                const Array<double> &g,
-                                const Array<double> &bt,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                int tr_d1d = 0,
-                                int te_d1d = 0,
-                                int q1d = 0)
+void PADivergenceApply3D(const int NE,
+                         const Array<double> &b,
+                         const Array<double> &g,
+                         const Array<double> &bt,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         int tr_d1d = 0,
+                         int te_d1d = 0,
+                         int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -597,16 +597,16 @@ static void PADivergenceApply3D(const int NE,
 
 // PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApplyTranspose3D(const int NE,
-                                         const Array<double> &bt,
-                                         const Array<double> &gt,
-                                         const Array<double> &b,
-                                         const Vector &op_,
-                                         const Vector &x_,
-                                         Vector &y_,
-                                         int tr_d1d = 0,
-                                         int te_d1d = 0,
-                                         int q1d = 0)
+void PADivergenceApplyTranspose3D(const int NE,
+                                  const Array<double> &bt,
+                                  const Array<double> &gt,
+                                  const Array<double> &b,
+                                  const Vector &op_,
+                                  const Vector &x_,
+                                  Vector &y_,
+                                  int tr_d1d = 0,
+                                  int te_d1d = 0,
+                                  int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -775,16 +775,16 @@ static void PADivergenceApplyTranspose3D(const int NE,
 
 // Shared memory PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void SmemPADivergenceApply3D(const int NE,
-                                    const Array<double> &b_,
-                                    const Array<double> &g_,
-                                    const Array<double> &bt_,
-                                    const Vector &q_,
-                                    const Vector &x_,
-                                    Vector &y_,
-                                    const int tr_d1d = 0,
-                                    const int te_d1d = 0,
-                                    const int q1d = 0)
+void SmemPADivergenceApply3D(const int NE,
+                             const Array<double> &b_,
+                             const Array<double> &g_,
+                             const Array<double> &bt_,
+                             const Vector &q_,
+                             const Vector &x_,
+                             Vector &y_,
+                             const int tr_d1d = 0,
+                             const int te_d1d = 0,
+                             const int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;

fem/bilininteg_gradient.cpp

@@ -70,12 +70,12 @@ namespace mfem
    the \b MFEM_SHARED keyword for local arrays. */
 
 // PA Gradient Assemble 2D kernel
-static void PAGradientSetup2D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const Vector &c,
-                              Vector &op)
+void PAGradientSetup2D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       const Vector &c,
+                       Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -105,12 +105,12 @@ static void PAGradientSetup2D(const int Q1D,
 }
 
 // PA Gradient Assemble 3D kernel
-static void PAGradientSetup3D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const Vector &c,
-                              Vector &op)
+void PAGradientSetup3D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       const Vector &c,
+                       Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -254,16 +254,16 @@ void GradientIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 
 // PA Gradient Apply 2D kernel
 template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
-static void PAGradientApply2D(const int NE,
-                              const Array<double> &b,
-                              const Array<double> &g,
-                              const Array<double> &bt,
-                              const Vector &op_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int tr_d1d = 0,
-                              const int te_d1d = 0,
-                              const int q1d = 0)
+void PAGradientApply2D(const int NE,
+                       const Array<double> &b,
+                       const Array<double> &g,
+                       const Array<double> &bt,
+                       const Vector &op_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int tr_d1d = 0,
+                       const int te_d1d = 0,
+                       const int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -384,16 +384,16 @@ static void PAGradientApplyTranspose2D(const int NE,
 
 // PA Gradient Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PAGradientApply3D(const int NE,
-                              const Array<double> &b,
-                              const Array<double> &g,
-                              const Array<double> &bt,
-                              const Vector &op_,
-                              const Vector &x_,
-                              Vector &y_,
-                              int tr_d1d = 0,
-                              int te_d1d = 0,
-                              int q1d = 0)
+void PAGradientApply3D(const int NE,
+                       const Array<double> &b,
+                       const Array<double> &g,
+                       const Array<double> &bt,
+                       const Vector &op_,
+                       const Vector &x_,
+                       Vector &y_,
+                       int tr_d1d = 0,
+                       int te_d1d = 0,
+                       int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -579,16 +579,16 @@ static void PAGradientApplyTranspose3D(const int NE,
 
 // Shared memory PA Gradient Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void SmemPAGradientApply3D(const int NE,
-                                  const Array<double> &b_,
-                                  const Array<double> &g_,
-                                  const Array<double> &bt_,
-                                  const Vector &d_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int tr_d1d = 0,
-                                  const int te_d1d = 0,
-                                  const int q1d = 0)
+void SmemPAGradientApply3D(const int NE,
+                           const Array<double> &b_,
+                           const Array<double> &g_,
+                           const Array<double> &bt_,
+                           const Vector &d_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int tr_d1d = 0,
+                           const int te_d1d = 0,
+                           const int q1d = 0)
 {
    const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
    const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;

fem/bilininteg_hcurl.cpp

@@ -791,12 +791,12 @@ void SmemPAHcurlMassApply3D(const int D1D,
 }
 
 // PA H(curl) curl-curl assemble 2D kernel
-static void PACurlCurlSetup2D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              Vector &coeff,
-                              Vector &op)
+void PACurlCurlSetup2D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       Vector &coeff,
+                       Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -818,13 +818,13 @@ static void PACurlCurlSetup2D(const int Q1D,
 }
 
 // PA H(curl) curl-curl assemble 3D kernel
-static void PACurlCurlSetup3D(const int Q1D,
-                              const int coeffDim,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              Vector &coeff,
-                              Vector &op)
+void PACurlCurlSetup3D(const int Q1D,
+                       const int coeffDim,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       Vector &coeff,
+                       Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    const bool symmetric = (coeffDim != 9);
@@ -1045,16 +1045,16 @@ void CurlCurlIntegrator::AssemblePA(const FiniteElementSpace &fes)
    }
 }
 
-static void PACurlCurlApply2D(const int D1D,
-                              const int Q1D,
-                              const int NE,
-                              const Array<double> &bo,
-                              const Array<double> &bot,
-                              const Array<double> &gc,
-                              const Array<double> &gct,
-                              const Vector &pa_data,
-                              const Vector &x,
-                              Vector &y)
+void PACurlCurlApply2D(const int D1D,
+                       const int Q1D,
+                       const int NE,
+                       const Array<double> &bo,
+                       const Array<double> &bot,
+                       const Array<double> &gc,
+                       const Array<double> &gct,
+                       const Vector &pa_data,
+                       const Vector &x,
+                       Vector &y)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_D1D = HCURL_MAX_D1D;
@@ -1166,19 +1166,19 @@ static void PACurlCurlApply2D(const int D1D,
 }
 
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PACurlCurlApply3D(const int D1D,
-                              const int Q1D,
-                              const bool symmetric,
-                              const int NE,
-                              const Array<double> &bo,
-                              const Array<double> &bc,
-                              const Array<double> &bot,
-                              const Array<double> &bct,
-                              const Array<double> &gc,
-                              const Array<double> &gct,
-                              const Vector &pa_data,
-                              const Vector &x,
-                              Vector &y)
+void PACurlCurlApply3D(const int D1D,
+                       const int Q1D,
+                       const bool symmetric,
+                       const int NE,
+                       const Array<double> &bo,
+                       const Array<double> &bc,
+                       const Array<double> &bot,
+                       const Array<double> &bct,
+                       const Array<double> &gc,
+                       const Array<double> &gct,
+                       const Vector &pa_data,
+                       const Vector &x,
+                       Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -1677,19 +1677,19 @@ static void PACurlCurlApply3D(const int D1D,
 }
 
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPACurlCurlApply3D(const int D1D,
-                                  const int Q1D,
-                                  const bool symmetric,
-                                  const int NE,
-                                  const Array<double> &bo,
-                                  const Array<double> &bc,
-                                  const Array<double> &bot,
-                                  const Array<double> &bct,
-                                  const Array<double> &gc,
-                                  const Array<double> &gct,
-                                  const Vector &pa_data,
-                                  const Vector &x,
-                                  Vector &y)
+void SmemPACurlCurlApply3D(const int D1D,
+                           const int Q1D,
+                           const bool symmetric,
+                           const int NE,
+                           const Array<double> &bo,
+                           const Array<double> &bc,
+                           const Array<double> &bot,
+                           const Array<double> &bct,
+                           const Array<double> &gc,
+                           const Array<double> &gct,
+                           const Vector &pa_data,
+                           const Vector &x,
+                           Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -2032,13 +2032,13 @@ void CurlCurlIntegrator::AddMultPA(const Vector &x, Vector &y) const
    }
 }
 
-static void PACurlCurlAssembleDiagonal2D(const int D1D,
-                                         const int Q1D,
-                                         const int NE,
-                                         const Array<double> &bo,
-                                         const Array<double> &gc,
-                                         const Vector &pa_data,
-                                         Vector &diag)
+void PACurlCurlAssembleDiagonal2D(const int D1D,
+                                  const int Q1D,
+                                  const int NE,
+                                  const Array<double> &bo,
+                                  const Array<double> &gc,
+                                  const Vector &pa_data,
+                                  Vector &diag)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
@@ -2087,16 +2087,16 @@ static void PACurlCurlAssembleDiagonal2D(const int D1D,
 }
 
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PACurlCurlAssembleDiagonal3D(const int D1D,
-                                         const int Q1D,
-                                         const bool symmetric,
-                                         const int NE,
-                                         const Array<double> &bo,
-                                         const Array<double> &bc,
-                                         const Array<double> &go,
-                                         const Array<double> &gc,
-                                         const Vector &pa_data,
-                                         Vector &diag)
+void PACurlCurlAssembleDiagonal3D(const int D1D,
+                                  const int Q1D,
+                                  const bool symmetric,
+                                  const int NE,
+                                  const Array<double> &bo,
+                                  const Array<double> &bc,
+                                  const Array<double> &go,
+                                  const Array<double> &gc,
+                                  const Vector &pa_data,
+                                  Vector &diag)
 {
    constexpr static int VDIM = 3;
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
@@ -2273,16 +2273,16 @@ static void PACurlCurlAssembleDiagonal3D(const int D1D,
 }
 
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPACurlCurlAssembleDiagonal3D(const int D1D,
-                                             const int Q1D,
-                                             const bool symmetric,
-                                             const int NE,
-                                             const Array<double> &bo,
-                                             const Array<double> &bc,
-                                             const Array<double> &go,
-                                             const Array<double> &gc,
-                                             const Vector &pa_data,
-                                             Vector &diag)
+void SmemPACurlCurlAssembleDiagonal3D(const int D1D,
+                                      const int Q1D,
+                                      const bool symmetric,
+                                      const int NE,
+                                      const Array<double> &bo,
+                                      const Array<double> &bc,
+                                      const Array<double> &go,
+                                      const Array<double> &gc,
+                                      const Vector &pa_data,
+                                      Vector &diag)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -2955,18 +2955,18 @@ void MixedVectorCurlIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 // Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
 // integrated against H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlL2Apply3D(const int D1D,
-                             const int Q1D,
-                             const int coeffDim,
-                             const int NE,
-                             const Array<double> &bo,
-                             const Array<double> &bc,
-                             const Array<double> &bot,
-                             const Array<double> &bct,
-                             const Array<double> &gc,
-                             const Vector &pa_data,
-                             const Vector &x,
-                             Vector &y)
+void PAHcurlL2Apply3D(const int D1D,
+                      const int Q1D,
+                      const int coeffDim,
+                      const int NE,
+                      const Array<double> &bo,
+                      const Array<double> &bc,
+                      const Array<double> &bot,
+                      const Array<double> &bct,
+                      const Array<double> &gc,
+                      const Vector &pa_data,
+                      const Vector &x,
+                      Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3297,16 +3297,16 @@ static void PAHcurlL2Apply3D(const int D1D,
 // Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
 // integrated against H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPAHcurlL2Apply3D(const int D1D,
-                                 const int Q1D,
-                                 const int coeffDim,
-                                 const int NE,
-                                 const Array<double> &bo,
-                                 const Array<double> &bc,
-                                 const Array<double> &gc,
-                                 const Vector &pa_data,
-                                 const Vector &x,
-                                 Vector &y)
+void SmemPAHcurlL2Apply3D(const int D1D,
+                          const int Q1D,
+                          const int coeffDim,
+                          const int NE,
+                          const Array<double> &bo,
+                          const Array<double> &bc,
+                          const Array<double> &gc,
+                          const Vector &pa_data,
+                          const Vector &x,
+                          Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3585,18 +3585,18 @@ static void SmemPAHcurlL2Apply3D(const int D1D,
 // Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
 // integrated against H(div) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlHdivApply3D(const int D1D,
-                               const int D1Dtest,
-                               const int Q1D,
-                               const int NE,
-                               const Array<double> &bo,
-                               const Array<double> &bc,
-                               const Array<double> &bot,
-                               const Array<double> &bct,
-                               const Array<double> &gc,
-                               const Vector &pa_data,
-                               const Vector &x,
-                               Vector &y)
+void PAHcurlHdivApply3D(const int D1D,
+                        const int D1Dtest,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &bo,
+                        const Array<double> &bc,
+                        const Array<double> &bot,
+                        const Array<double> &bct,
+                        const Array<double> &gc,
+                        const Vector &pa_data,
+                        const Vector &x,
+                        Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -4071,18 +4071,18 @@ void MixedVectorWeakCurlIntegrator::AssemblePA(const FiniteElementSpace
 // Apply to x corresponding to DOF's in H(curl) (trial), integrated against curl
 // of H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlL2Apply3DTranspose(const int D1D,
-                                      const int Q1D,
-                                      const int coeffDim,
-                                      const int NE,
-                                      const Array<double> &bo,
-                                      const Array<double> &bc,
-                                      const Array<double> &bot,
-                                      const Array<double> &bct,
-                                      const Array<double> &gct,
-                                      const Vector &pa_data,
-                                      const Vector &x,
-                                      Vector &y)
+void PAHcurlL2Apply3DTranspose(const int D1D,
+                               const int Q1D,
+                               const int coeffDim,
+                               const int NE,
+                               const Array<double> &bo,
+                               const Array<double> &bc,
+                               const Array<double> &bot,
+                               const Array<double> &bct,
+                               const Array<double> &gct,
+                               const Vector &pa_data,
+                               const Vector &x,
+                               Vector &y)
 {
    // See PAHcurlL2Apply3D for comments.
 
@@ -4413,16 +4413,16 @@ static void PAHcurlL2Apply3DTranspose(const int D1D,
 }
 
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPAHcurlL2Apply3DTranspose(const int D1D,
-                                          const int Q1D,
-                                          const int coeffDim,
-                                          const int NE,
-                                          const Array<double> &bo,
-                                          const Array<double> &bc,
-                                          const Array<double> &gc,
-                                          const Vector &pa_data,
-                                          const Vector &x,
-                                          Vector &y)
+void SmemPAHcurlL2Apply3DTranspose(const int D1D,
+                                   const int Q1D,
+                                   const int coeffDim,
+                                   const int NE,
+                                   const Array<double> &bo,
+                                   const Array<double> &bc,
+                                   const Array<double> &gc,
+                                   const Vector &pa_data,
+                                   const Vector &x,
+                                   Vector &y)
 {
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -4675,13 +4675,13 @@ void MixedVectorWeakCurlIntegrator::AddMultPA(const Vector &x, Vector &y) const
 // Apply to x corresponding to DOFs in H^1 (domain) the (topological) gradient
 // to get a dof in H(curl) (range). You can think of the range as the "test" space
 // and the domain as the "trial" space, but there's no integration.
-static void PAHcurlApplyGradient2D(const int c_dofs1D,
-                                   const int o_dofs1D,
-                                   const int NE,
-                                   const Array<double> &B_,
-                                   const Array<double> &G_,
-                                   const Vector &x_,
-                                   Vector &y_)
+void PAHcurlApplyGradient2D(const int c_dofs1D,
+                            const int o_dofs1D,
+                            const int NE,
+                            const Array<double> &B_,
+                            const Array<double> &G_,
+                            const Vector &x_,
+                            Vector &y_)
 {
    auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
    auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -4753,12 +4753,12 @@ static void PAHcurlApplyGradient2D(const int c_dofs1D,
 }
 
 // Specialization of PAHcurlApplyGradient2D to the case where B is identity
-static void PAHcurlApplyGradient2DBId(const int c_dofs1D,
-                                      const int o_dofs1D,
-                                      const int NE,
-                                      const Array<double> &G_,
-                                      const Vector &x_,
-                                      Vector &y_)
+void PAHcurlApplyGradient2DBId(const int c_dofs1D,
+                               const int o_dofs1D,
+                               const int NE,
+                               const Array<double> &G_,
+                               const Vector &x_,
+                               Vector &y_)
 {
    auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
 
@@ -4822,7 +4822,7 @@ static void PAHcurlApplyGradient2DBId(const int c_dofs1D,
    });
 }
 
-static void PAHcurlApplyGradientTranspose2D(
+void PAHcurlApplyGradientTranspose2D(
    const int c_dofs1D, const int o_dofs1D, const int NE,
    const Array<double> &B_, const Array<double> &G_,
    const Vector &x_, Vector &y_)
@@ -4898,7 +4898,7 @@ static void PAHcurlApplyGradientTranspose2D(
 
 // Specialization of PAHcurlApplyGradientTranspose2D to the case where
 // B is identity
-static void PAHcurlApplyGradientTranspose2DBId(
+void PAHcurlApplyGradientTranspose2DBId(
    const int c_dofs1D, const int o_dofs1D, const int NE,
    const Array<double> &G_,
    const Vector &x_, Vector &y_)
@@ -4965,13 +4965,13 @@ static void PAHcurlApplyGradientTranspose2DBId(
    });
 }
 
-static void PAHcurlApplyGradient3D(const int c_dofs1D,
-                                   const int o_dofs1D,
-                                   const int NE,
-                                   const Array<double> &B_,
-                                   const Array<double> &G_,
-                                   const Vector &x_,
-                                   Vector &y_)
+void PAHcurlApplyGradient3D(const int c_dofs1D,
+                            const int o_dofs1D,
+                            const int NE,
+                            const Array<double> &B_,
+                            const Array<double> &G_,
+                            const Vector &x_,
+                            Vector &y_)
 {
    auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
    auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -5154,12 +5154,12 @@ static void PAHcurlApplyGradient3D(const int c_dofs1D,
 }
 
 // Specialization of PAHcurlApplyGradient3D to the case where
-static void PAHcurlApplyGradient3DBId(const int c_dofs1D,
-                                      const int o_dofs1D,
-                                      const int NE,
-                                      const Array<double> &G_,
-                                      const Vector &x_,
-                                      Vector &y_)
+void PAHcurlApplyGradient3DBId(const int c_dofs1D,
+                               const int o_dofs1D,
+                               const int NE,
+                               const Array<double> &G_,
+                               const Vector &x_,
+                               Vector &y_)
 {
    auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
 
@@ -5322,7 +5322,7 @@ static void PAHcurlApplyGradient3DBId(const int c_dofs1D,
    });
 }
 
-static void PAHcurlApplyGradientTranspose3D(
+void PAHcurlApplyGradientTranspose3D(
    const int c_dofs1D, const int o_dofs1D, const int NE,
    const Array<double> &B_, const Array<double> &G_,
    const Vector &x_, Vector &y_)
@@ -5507,7 +5507,7 @@ static void PAHcurlApplyGradientTranspose3D(
 }
 
 // Specialization of PAHcurlApplyGradientTranspose3D to the case where
-static void PAHcurlApplyGradientTranspose3DBId(
+void PAHcurlApplyGradientTranspose3DBId(
    const int c_dofs1D, const int o_dofs1D, const int NE,
    const Array<double> &G_,
    const Vector &x_, Vector &y_)
@@ -5789,14 +5789,14 @@ void GradientInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
    }
 }
 
-static void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
-                                        const int o_dofs1D,
-                                        const int NE,
-                                        const Array<double> &Bclosed,
-                                        const Array<double> &Bopen,
-                                        const Vector &pa_data,
-                                        const Vector &x_,
-                                        Vector &y_)
+void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
+                                 const int o_dofs1D,
+                                 const int NE,
+                                 const Array<double> &Bclosed,
+                                 const Array<double> &Bopen,
+                                 const Vector &pa_data,
+                                 const Vector &x_,
+                                 Vector &y_)
 {
    auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
    auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6002,14 +6002,14 @@ static void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
    });
 }
 
-static void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
-                                                 const int o_dofs1D,
-                                                 const int NE,
-                                                 const Array<double> &Bclosed,
-                                                 const Array<double> &Bopen,
-                                                 const Vector &pa_data,
-                                                 const Vector &x_,
-                                                 Vector &y_)
+void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
+                                          const int o_dofs1D,
+                                          const int NE,
+                                          const Array<double> &Bclosed,
+                                          const Array<double> &Bopen,
+                                          const Vector &pa_data,
+                                          const Vector &x_,
+                                          Vector &y_)
 {
    auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
    auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6228,14 +6228,14 @@ static void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
    });
 }
 
-static void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
-                                        const int o_dofs1D,
-                                        const int NE,
-                                        const Array<double> &Bclosed,
-                                        const Array<double> &Bopen,
-                                        const Vector &pa_data,
-                                        const Vector &x_,
-                                        Vector &y_)
+void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
+                                 const int o_dofs1D,
+                                 const int NE,
+                                 const Array<double> &Bclosed,
+                                 const Array<double> &Bopen,
+                                 const Vector &pa_data,
+                                 const Vector &x_,
+                                 Vector &y_)
 {
    auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
    auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6327,14 +6327,14 @@ static void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
    });
 }
 
-static void PAHcurlVecH1IdentityApplyTranspose2D(const int c_dofs1D,
-                                                 const int o_dofs1D,
-                                                 const int NE,
-                                                 const Array<double> &Bclosed,
-                                                 const Array<double> &Bopen,
-                                                 const Vector &pa_data,
-                                                 const Vector &x_,
-                                                 Vector &y_)
+void PAHcurlVecH1IdentityApplyTranspose2D(const int c_dofs1D,
+                                          const int o_dofs1D,
+                                          const int NE,
+                                          const Array<double> &Bclosed,
+                                          const Array<double> &Bopen,
+                                          const Vector &pa_data,
+                                          const Vector &x_,
+                                          Vector &y_)
 {
    auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
    auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);

fem/bilininteg_hdiv.cpp

@@ -539,12 +539,12 @@ void PAHdivMassApply3D(const int D1D,
 
 // PA H(div) div-div assemble 2D kernel
 // NOTE: this is identical to PACurlCurlSetup3D
-static void PADivDivSetup2D(const int Q1D,
-                            const int NE,
-                            const Array<double> &w,
-                            const Vector &j,
-                            Vector &coeff_,
-                            Vector &op)
+void PADivDivSetup2D(const int Q1D,
+                     const int NE,
+                     const Array<double> &w,
+                     const Vector &j,
+                     Vector &coeff_,
+                     Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -565,12 +565,12 @@ static void PADivDivSetup2D(const int Q1D,
    });
 }
 
-static void PADivDivSetup3D(const int Q1D,
-                            const int NE,
-                            const Array<double> &w,
-                            const Vector &j,
-                            Vector &coeff_,
-                            Vector &op)
+void PADivDivSetup3D(const int Q1D,
+                     const int NE,
+                     const Array<double> &w,
+                     const Vector &j,
+                     Vector &coeff_,
+                     Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -599,16 +599,16 @@ static void PADivDivSetup3D(const int Q1D,
    });
 }
 
-static void PADivDivApply2D(const int D1D,
-                            const int Q1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &Bot_,
-                            const Array<double> &Gct_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PADivDivApply2D(const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &Bot_,
+                     const Array<double> &Gct_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -718,16 +718,16 @@ static void PADivDivApply2D(const int D1D,
    }); // end of element loop
 }
 
-static void PADivDivApply3D(const int D1D,
-                            const int Q1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &Bot_,
-                            const Array<double> &Gct_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PADivDivApply3D(const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &Bot_,
+                     const Array<double> &Gct_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
    MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -967,13 +967,13 @@ void DivDivIntegrator::AddMultPA(const Vector &x, Vector &y) const
    }
 }
 
-static void PADivDivAssembleDiagonal2D(const int D1D,
-                                       const int Q1D,
-                                       const int NE,
-                                       const Array<double> &Bo_,
-                                       const Array<double> &Gc_,
-                                       const Vector &op_,
-                                       Vector &diag_)
+void PADivDivAssembleDiagonal2D(const int D1D,
+                                const int Q1D,
+                                const int NE,
+                                const Array<double> &Bo_,
+                                const Array<double> &Gc_,
+                                const Vector &op_,
+                                Vector &diag_)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
@@ -1023,13 +1023,13 @@ static void PADivDivAssembleDiagonal2D(const int D1D,
    });
 }
 
-static void PADivDivAssembleDiagonal3D(const int D1D,
-                                       const int Q1D,
-                                       const int NE,
-                                       const Array<double> &Bo_,
-                                       const Array<double> &Gc_,
-                                       const Vector &op_,
-                                       Vector &diag_)
+void PADivDivAssembleDiagonal3D(const int D1D,
+                                const int Q1D,
+                                const int NE,
+                                const Array<double> &Bo_,
+                                const Array<double> &Gc_,
+                                const Vector &op_,
+                                Vector &diag_)
 {
    MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1104,11 +1104,11 @@ void DivDivIntegrator::AssembleDiagonalPA(Vector& diag)
 }
 
 // PA H(div)-L2 (div u, p) assemble 2D kernel
-static void PADivL2Setup2D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           Vector &coeff_,
-                           Vector &op)
+void PADivL2Setup2D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &coeff_,
+                    Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -1123,11 +1123,11 @@ static void PADivL2Setup2D(const int Q1D,
    });
 }
 
-static void PADivL2Setup3D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           Vector &coeff_,
-                           Vector &op)
+void PADivL2Setup3D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &coeff_,
+                    Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -1225,16 +1225,16 @@ VectorFEDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 
 // Apply to x corresponding to DOF's in H(div) (trial), whose divergence is
 // integrated against L_2 test functions corresponding to y.
-static void PAHdivL2Apply3D(const int D1D,
-                            const int Q1D,
-                            const int L2D1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &L2Bot_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PAHdivL2Apply3D(const int D1D,
+                     const int Q1D,
+                     const int L2D1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &L2Bot_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
    MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1388,16 +1388,16 @@ static void PAHdivL2Apply3D(const int D1D,
 
 // Apply to x corresponding to DOF's in H(div) (trial), whose divergence is
 // integrated against L_2 test functions corresponding to y.
-static void PAHdivL2Apply2D(const int D1D,
-                            const int Q1D,
-                            const int L2D1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &L2Bot_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PAHdivL2Apply2D(const int D1D,
+                     const int Q1D,
+                     const int L2D1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &L2Bot_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1494,16 +1494,16 @@ static void PAHdivL2Apply2D(const int D1D,
    }); // end of element loop
 }
 
-static void PAHdivL2ApplyTranspose3D(const int D1D,
-                                     const int Q1D,
-                                     const int L2D1D,
-                                     const int NE,
-                                     const Array<double> &L2Bo_,
-                                     const Array<double> &Gct_,
-                                     const Array<double> &Bot_,
-                                     const Vector &op_,
-                                     const Vector &x_,
-                                     Vector &y_)
+void PAHdivL2ApplyTranspose3D(const int D1D,
+                              const int Q1D,
+                              const int L2D1D,
+                              const int NE,
+                              const Array<double> &L2Bo_,
+                              const Array<double> &Gct_,
+                              const Array<double> &Bot_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_)
 {
    MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1656,16 +1656,16 @@ static void PAHdivL2ApplyTranspose3D(const int D1D,
    }); // end of element loop
 }
 
-static void PAHdivL2ApplyTranspose2D(const int D1D,
-                                     const int Q1D,
-                                     const int L2D1D,
-                                     const int NE,
-                                     const Array<double> &L2Bo_,
-                                     const Array<double> &Gct_,
-                                     const Array<double> &Bot_,
-                                     const Vector &op_,
-                                     const Vector &x_,
-                                     Vector &y_)
+void PAHdivL2ApplyTranspose2D(const int D1D,
+                              const int Q1D,
+                              const int L2D1D,
+                              const int NE,
+                              const Array<double> &L2Bo_,
+                              const Array<double> &Gct_,
+                              const Array<double> &Bot_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_)
 {
    constexpr static int VDIM = 2;
    constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1791,16 +1791,16 @@ void VectorFEDivergenceIntegrator::AddMultTransposePA(const Vector &x,
    }
 }
 
-static void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
-                                             const int Q1D,
-                                             const int L2D1D,
-                                             const int NE,
-                                             const Array<double> &L2Bo_,
-                                             const Array<double> &Gct_,
-                                             const Array<double> &Bot_,
-                                             const Vector &op_,
-                                             const Vector &D_,
-                                             Vector &diag_)
+void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
+                                      const int Q1D,
+                                      const int L2D1D,
+                                      const int NE,
+                                      const Array<double> &L2Bo_,
+                                      const Array<double> &Gct_,
+                                      const Array<double> &Bot_,
+                                      const Vector &op_,
+                                      const Vector &D_,
+                                      Vector &diag_)
 {
    MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
    MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1916,16 +1916,16 @@ static void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
    }); // end of element loop
 }
 
-static void PAHdivL2AssembleDiagonal_ADAt_2D(const int D1D,
-                                             const int Q1D,
-                                             const int L2D1D,
-                                             const int NE,
-                                             const Array<double> &L2Bo_,
-                                             const Array<double> &Gct_,
-                                             const Array<double> &Bot_,
-                                             const Vector &op_,
-                                             const Vector &D_,
-                                             Vector &diag_)
+void PAHdivL2AssembleDiagonal_ADAt_2D(const int D1D,
+                                      const int Q1D,
+                                      const int L2D1D,
+                                      const int NE,
+                                      const Array<double> &L2Bo_,
+                                      const Array<double> &Gct_,
+                                      const Array<double> &Bot_,
+                                      const Vector &op_,
+                                      const Vector &D_,
+                                      Vector &diag_)
 {
    constexpr static int VDIM = 2;
 

fem/bilininteg_mass_ea.cpp

@@ -17,13 +17,13 @@ namespace mfem
 {
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble1D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble1D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -67,13 +67,13 @@ static void EAMassAssemble1D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble2D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble2D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -139,13 +139,13 @@ static void EAMassAssemble2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble3D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble3D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/bilininteg_mass_pa.cpp

@@ -155,12 +155,12 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassAssembleDiagonal2D(const int NE,
-                                     const Array<double> &b,
-                                     const Vector &d,
-                                     Vector &y,
-                                     const int d1d = 0,
-                                     const int q1d = 0)
+void PAMassAssembleDiagonal2D(const int NE,
+                              const Array<double> &b,
+                              const Vector &d,
+                              Vector &y,
+                              const int d1d = 0,
+                              const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -201,12 +201,12 @@ static void PAMassAssembleDiagonal2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPAMassAssembleDiagonal2D(const int NE,
-                                         const Array<double> &b_,
-                                         const Vector &d_,
-                                         Vector &y_,
-                                         const int d1d = 0,
-                                         const int q1d = 0)
+void SmemPAMassAssembleDiagonal2D(const int NE,
+                                  const Array<double> &b_,
+                                  const Vector &d_,
+                                  Vector &y_,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -267,12 +267,12 @@ static void SmemPAMassAssembleDiagonal2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassAssembleDiagonal3D(const int NE,
-                                     const Array<double> &b,
-                                     const Vector &d,
-                                     Vector &y,
-                                     const int d1d = 0,
-                                     const int q1d = 0)
+void PAMassAssembleDiagonal3D(const int NE,
+                              const Array<double> &b,
+                              const Vector &d,
+                              Vector &y,
+                              const int d1d = 0,
+                              const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -336,12 +336,12 @@ static void PAMassAssembleDiagonal3D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPAMassAssembleDiagonal3D(const int NE,
-                                         const Array<double> &b_,
-                                         const Vector &d_,
-                                         Vector &y_,
-                                         const int d1d = 0,
-                                         const int q1d = 0)
+void SmemPAMassAssembleDiagonal3D(const int NE,
+                                  const Array<double> &b_,
+                                  const Vector &d_,
+                                  Vector &y_,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -569,14 +569,14 @@ static void OccaPAMassApply3D(const int D1D,
 #endif // MFEM_USE_OCCA
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassApply2D(const int NE,
-                          const Array<double> &b_,
-                          const Array<double> &bt_,
-                          const Vector &d_,
-                          const Vector &x_,
-                          Vector &y_,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void PAMassApply2D(const int NE,
+                   const Array<double> &b_,
+                   const Array<double> &bt_,
+                   const Vector &d_,
+                   const Vector &x_,
+                   Vector &y_,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -661,14 +661,14 @@ static void PAMassApply2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPAMassApply2D(const int NE,
-                              const Array<double> &b_,
-                              const Array<double> &bt_,
-                              const Vector &d_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int d1d = 0,
-                              const int q1d = 0)
+void SmemPAMassApply2D(const int NE,
+                       const Array<double> &b_,
+                       const Array<double> &bt_,
+                       const Vector &d_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int d1d = 0,
+                       const int q1d = 0)
 {
    MFEM_CONTRACT_VAR(bt_);
    const int D1D = T_D1D ? T_D1D : d1d;
@@ -784,14 +784,14 @@ static void SmemPAMassApply2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassApply3D(const int NE,
-                          const Array<double> &b_,
-                          const Array<double> &bt_,
-                          const Vector &d_,
-                          const Vector &x_,
-                          Vector &y_,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void PAMassApply3D(const int NE,
+                   const Array<double> &b_,
+                   const Array<double> &bt_,
+                   const Vector &d_,
+                   const Vector &x_,
+                   Vector &y_,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -925,14 +925,14 @@ static void PAMassApply3D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPAMassApply3D(const int NE,
-                              const Array<double> &b_,
-                              const Array<double> &bt_,
-                              const Vector &d_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int d1d = 0,
-                              const int q1d = 0)
+void SmemPAMassApply3D(const int NE,
+                       const Array<double> &b_,
+                       const Array<double> &bt_,
+                       const Vector &d_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int d1d = 0,
+                       const int q1d = 0)
 {
    MFEM_CONTRACT_VAR(bt_);
    const int D1D = T_D1D ? T_D1D : d1d;

fem/bilininteg_vecdiffusion.cpp

@@ -22,12 +22,12 @@ namespace mfem
 // PA Vector Diffusion Integrator
 
 // PA Diffusion Assemble 2D kernel
-static void PAVectorDiffusionSetup2D(const int Q1D,
-                                     const int NE,
-                                     const Array<double> &w,
-                                     const Vector &j,
-                                     const Vector &c,
-                                     Vector &op)
+void PAVectorDiffusionSetup2D(const int Q1D,
+                              const int NE,
+                              const Array<double> &w,
+                              const Vector &j,
+                              const Vector &c,
+                              Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -59,12 +59,12 @@ static void PAVectorDiffusionSetup2D(const int Q1D,
 }
 
 // PA Diffusion Assemble 3D kernel
-static void PAVectorDiffusionSetup3D(const int Q1D,
-                                     const int NE,
-                                     const Array<double> &w,
-                                     const Vector &j,
-                                     const Vector &c,
-                                     Vector &op)
+void PAVectorDiffusionSetup3D(const int Q1D,
+                              const int NE,
+                              const Array<double> &w,
+                              const Vector &j,
+                              const Vector &c,
+                              Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -251,7 +251,7 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }
 
 // PA Diffusion Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0>
 void PAVectorDiffusionApply2D(const int NE,
                               const Array<double> &b,
                               const Array<double> &g,
@@ -374,7 +374,7 @@ void PAVectorDiffusionApply2D(const int NE,
 
 // PA Diffusion Apply 3D kernel
 template<const int T_D1D = 0,
-         const int T_Q1D = 0> static
+         const int T_Q1D = 0>
 void PAVectorDiffusionApply3D(const int NE,
                               const Array<double> &b,
                               const Array<double> &g,
@@ -606,13 +606,13 @@ void VectorDiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAVectorDiffusionDiagonal2D(const int NE,
-                                        const Array<double> &b,
-                                        const Array<double> &g,
-                                        const Vector &d,
-                                        Vector &y,
-                                        const int d1d = 0,
-                                        const int q1d = 0)
+void PAVectorDiffusionDiagonal2D(const int NE,
+                                 const Array<double> &b,
+                                 const Array<double> &g,
+                                 const Vector &d,
+                                 Vector &y,
+                                 const int d1d = 0,
+                                 const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -673,13 +673,13 @@ static void PAVectorDiffusionDiagonal2D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAVectorDiffusionDiagonal3D(const int NE,
-                                        const Array<double> &b,
-                                        const Array<double> &g,
-                                        const Vector &d,
-                                        Vector &y,
-                                        const int d1d = 0,
-                                        const int q1d = 0)
+void PAVectorDiffusionDiagonal3D(const int NE,
+                                 const Array<double> &b,
+                                 const Array<double> &g,
+                                 const Vector &d,
+                                 Vector &y,
+                                 const int d1d = 0,
+                                 const int q1d = 0)
 {
    constexpr int DIM = 3;
    const int D1D = T_D1D ? T_D1D : d1d;

fem/bilininteg_vecmass.cpp

@@ -104,14 +104,14 @@ void VectorMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 
 template<const int T_D1D = 0,
          const int T_Q1D = 0>
-static void PAVectorMassApply2D(const int NE,
-                                const Array<double> &B_,
-                                const Array<double> &Bt_,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int d1d = 0,
-                                const int q1d = 0)
+void PAVectorMassApply2D(const int NE,
+                         const Array<double> &B_,
+                         const Array<double> &Bt_,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int d1d = 0,
+                         const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -201,14 +201,14 @@ static void PAVectorMassApply2D(const int NE,
 
 template<const int T_D1D = 0,
          const int T_Q1D = 0>
-static void PAVectorMassApply3D(const int NE,
-                                const Array<double> &B_,
-                                const Array<double> &Bt_,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int d1d = 0,
-                                const int q1d = 0)
+void PAVectorMassApply3D(const int NE,
+                         const Array<double> &B_,
+                         const Array<double> &Bt_,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int d1d = 0,
+                         const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -379,13 +379,13 @@ void VectorMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 }
 
 template<const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal2D(const int NE,
-                                           const Array<double> &B_,
-                                           const Array<double> &Bt_,
-                                           const Vector &op_,
-                                           Vector &diag_,
-                                           const int d1d = 0,
-                                           const int q1d = 0)
+void PAVectorMassAssembleDiagonal2D(const int NE,
+                                    const Array<double> &B_,
+                                    const Array<double> &Bt_,
+                                    const Vector &op_,
+                                    Vector &diag_,
+                                    const int d1d = 0,
+                                    const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -431,13 +431,13 @@ static void PAVectorMassAssembleDiagonal2D(const int NE,
 }
 
 template<const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal3D(const int NE,
-                                           const Array<double> &B_,
-                                           const Array<double> &Bt_,
-                                           const Vector &op_,
-                                           Vector &diag_,
-                                           const int d1d = 0,
-                                           const int q1d = 0)
+void PAVectorMassAssembleDiagonal3D(const int NE,
+                                    const Array<double> &B_,
+                                    const Array<double> &Bt_,
+                                    const Vector &op_,
+                                    Vector &diag_,
+                                    const int d1d = 0,
+                                    const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/doftrans.cpp

@@ -0,0 +1,358 @@
+// Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "fem.hpp"
+
+namespace mfem
+{
+
+void DofTransformation::TransformPrimal(Vector &v) const
+{
+   TransformPrimal(v.GetData());
+}
+
+void DofTransformation::TransformPrimalCols(DenseMatrix &V) const
+{
+   for (int c=0; c<V.Width(); c++)
+   {
+      TransformPrimal(V.GetColumn(c));
+   }
+}
+
+void DofTransformation::TransformDual(Vector &v) const
+{
+   TransformDual(v.GetData());
+}
+
+void DofTransformation::TransformDual(DenseMatrix &V) const
+{
+   TransformDualCols(V);
+   TransformDualRows(V);
+}
+
+void DofTransformation::TransformDualRows(DenseMatrix &V) const
+{
+   Vector row;
+   for (int r=0; r<V.Height(); r++)
+   {
+      V.GetRow(r, row);
+      TransformDual(row);
+      V.SetRow(r, row);
+   }
+}
+
+void DofTransformation::TransformDualCols(DenseMatrix &V) const
+{
+   for (int c=0; c<V.Width(); c++)
+   {
+      TransformDual(V.GetColumn(c));
+   }
+}
+
+void DofTransformation::InvTransformPrimal(Vector &v) const
+{
+   InvTransformPrimal(v.GetData());
+}
+
+void TransformPrimal(const DofTransformation *ran_dof_trans,
+                     const DofTransformation *dom_dof_trans,
+                     DenseMatrix &elmat)
+{
+   if (ran_dof_trans && dom_dof_trans)
+   {
+      ran_dof_trans->TransformPrimalCols(elmat);
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else if (ran_dof_trans)
+   {
+      ran_dof_trans->TransformPrimalCols(elmat);
+   }
+   else if (dom_dof_trans)
+   {
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else
+   {
+      // If both transformations are NULL this function should not be called
+   }
+}
+
+void TransformDual(const DofTransformation *ran_dof_trans,
+                   const DofTransformation *dom_dof_trans,
+                   DenseMatrix &elmat)
+{
+   if (ran_dof_trans && dom_dof_trans)
+   {
+      ran_dof_trans->TransformDualCols(elmat);
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else if (ran_dof_trans)
+   {
+      ran_dof_trans->TransformDualCols(elmat);
+   }
+   else if (dom_dof_trans)
+   {
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else
+   {
+      // If both transformations are NULL this function should not be called
+   }
+}
+
+void VDofTransformation::TransformPrimal(double *v) const
+{
+   int size = doftrans_->Size();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES || vdim_ == 1)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->TransformPrimal(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->TransformPrimal(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+void VDofTransformation::InvTransformPrimal(double *v) const
+{
+   int size = doftrans_->Height();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->InvTransformPrimal(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->InvTransformPrimal(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+void VDofTransformation::TransformDual(double *v) const
+{
+   int size = doftrans_->Size();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->TransformDual(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->TransformDual(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+const double ND_DofTransformation::T_data[24] =
+{
+   1.0,  0.0,  0.0,  1.0,
+   -1.0, -1.0,  0.0,  1.0,
+   0.0,  1.0, -1.0, -1.0,
+   1.0,  0.0, -1.0, -1.0,
+   -1.0, -1.0,  1.0,  0.0,
+   0.0,  1.0,  1.0,  0.0
+};
+
+const DenseTensor ND_DofTransformation
+::T(const_cast<double*>(ND_DofTransformation::T_data), 2, 2, 6);
+
+const double ND_DofTransformation::TInv_data[24] =
+{
+   1.0,  0.0,  0.0,  1.0,
+   -1.0, -1.0,  0.0,  1.0,
+   -1.0, -1.0,  1.0,  0.0,
+   1.0,  0.0, -1.0, -1.0,
+   0.0,  1.0, -1.0, -1.0,
+   0.0,  1.0,  1.0,  0.0
+};
+
+const DenseTensor ND_DofTransformation
+::TInv(const_cast<double*>(TInv_data), 2, 2, 6);
+
+ND_DofTransformation::ND_DofTransformation(int size, int p)
+   : DofTransformation(size),
+     order(p)
+{
+}
+
+ND_TriDofTransformation::ND_TriDofTransformation(int p)
+   : ND_DofTransformation(p*(p + 2), p)
+{
+}
+
+void ND_TriDofTransformation::TransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         T(Fo[f]).Mult(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TriDofTransformation::InvTransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).Mult(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TriDofTransformation::TransformDual(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).MultTranspose(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+ND_TetDofTransformation::ND_TetDofTransformation(int p)
+   : ND_DofTransformation(p*(p + 2)*(p + 3)/2, p)
+{
+}
+
+void ND_TetDofTransformation::TransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         T(Fo[f]).Mult(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TetDofTransformation::InvTransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).Mult(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TetDofTransformation::TransformDual(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).MultTranspose(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+} // namespace mfem

fem/doftrans.hpp

@@ -0,0 +1,277 @@
+// Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_DOFTRANSFORM
+#define MFEM_DOFTRANSFORM
+
+#include "../config/config.hpp"
+#include "../linalg/linalg.hpp"
+#include "intrules.hpp"
+#include "fe.hpp"
+
+namespace mfem
+{
+
+/** The DofTransformation class is an abstract base class for a family of
+    transformations that map local degrees of freedom (DoFs), contained within
+    individual elements, to global degrees of freedom, stored within
+    GridFunction objects. These transformations are necessary to ensure that
+    basis functions in neighboring elements align correctly. Closely related but
+    complementary transformations are required for the entries stored in
+    LinearForm and BilinearForm objects. The DofTransformation class is designed
+    to apply the action of both of these types of DoF transformations.
+
+    Let the "primal transformation" be given by the operator T. This means that
+    given a local element vector v the data that must be placed into a
+    GridFunction object is v_t = T * v.
+
+    We also need the inverse of the primal transformation T^{-1} so that we can
+    recover the local element vector from data read out of a GridFunction
+    e.g. v = T^{-1} * v_t.
+
+    We need to preserve the action of our linear forms applied to primal
+    vectors. In other words, if f is the local vector computed by a linear
+    form then f * v = f_t * v_t (where "*" represents an inner product of
+    vectors). This requires that f_t = T^{-T} * f i.e. the "dual transform" is
+    given by the transpose of the inverse of the primal transformation.
+
+    For bilinear forms we require that v^T * A * v = v_t^T * A_t * v_t. This
+    implies that A_t = T^{-T} * A * T^{-1}. This can be accomplished by
+    performing dual transformations of the rows and columns of the matrix A.
+
+    For discrete linear operators the range must be modified with the primal
+    transformation rather than the dual transformation because the result is a
+    primal vector rather than a dual vector. This leads to the transformation
+    D_t = T * D * T^{-1}. This can be accomplished by using a primal
+    transformation on the columns of D and a dual transformation on its rows.
+*/
+class DofTransformation
+{
+protected:
+   int size_;
+
+   Array<int> Fo;
+
+   DofTransformation(int size)
+      : size_(size) {}
+
+public:
+
+   inline int Size() const { return size_; }
+   inline int Height() const { return size_; }
+   inline int NumRows() const { return size_; }
+   inline int Width() const { return size_; }
+   inline int NumCols() const { return size_; }
+
+   /** @brief Configure the transformation using face orientations for the
+       current element. */
+   /// The face_orientation array can be obtained from Mesh::GetElementFaces.
+   inline void SetFaceOrientations(const Array<int> & face_orientation)
+   { Fo = face_orientation; }
+
+   inline const Array<int> & GetFaceOrientations() const { return Fo; }
+
+   /** Transform local DoFs to align with the global DoFs. For example, this
+       transformation can be used to map the local vector computed by
+       FiniteElement::Project() to the transformed vector stored within a
+       GridFunction object. */
+   virtual void TransformPrimal(double *v) const = 0;
+   virtual void TransformPrimal(Vector &v) const;
+
+   /// Transform groups of DoFs stored as dense matrices
+   virtual void TransformPrimalCols(DenseMatrix &V) const;
+
+   /** Inverse transform local DoFs. Used to transform DoFs from a global vector
+       back to their element-local form. For example, this must be used to
+       transform the vector obtained using GridFunction::GetSubVector before it
+       can be used to compute a local interpolation.
+   */
+   virtual void InvTransformPrimal(double *v) const = 0;
+   virtual void InvTransformPrimal(Vector &v) const;
+
+   /** Transform dual DoFs as computed by a LinearFormIntegrator before summing
+       into a LinearForm object. */
+   virtual void TransformDual(double *v) const = 0;
+   virtual void TransformDual(Vector &v) const;
+
+   /** Transform a matrix of dual DoFs entries as computed by a
+       BilinearFormIntegrator before summing into a BilinearForm object. */
+   virtual void TransformDual(DenseMatrix &V) const;
+
+   /// Transform groups of dual DoFs stored as dense matrices
+   virtual void TransformDualRows(DenseMatrix &V) const;
+   virtual void TransformDualCols(DenseMatrix &V) const;
+
+   virtual ~DofTransformation() {}
+};
+
+/** Transform a matrix of DoFs entries from different finite element spaces as
+    computed by a DiscreteInterpolator before copying into a
+    DiscreteLinearOperator.
+*/
+void TransformPrimal(const DofTransformation *ran_dof_trans,
+                     const DofTransformation *dom_dof_trans,
+                     DenseMatrix &elmat);
+
+/** Transform a matrix of dual DoFs entries from different finite element spaces
+    as computed by a BilinearFormIntegrator before summing into a
+    MixedBilinearForm object.
+*/
+void TransformDual(const DofTransformation *ran_dof_trans,
+                   const DofTransformation *dom_dof_trans,
+                   DenseMatrix &elmat);
+
+/** The VDofTransformation class implements a nested transformation where an
+    arbitrary DofTransformation is replicated with a vdim >= 1.
+*/
+class VDofTransformation : public DofTransformation
+{
+private:
+   int vdim_;
+   int ordering_;
+   DofTransformation * doftrans_;
+
+public:
+   /** @brief Default constructor which requires that SetDofTransformation be
+       called before use. */
+   VDofTransformation(int vdim = 1, int ordering = 0)
+      : DofTransformation(0),
+        vdim_(vdim), ordering_(ordering),
+        doftrans_(NULL) {}
+
+   /// Constructor with a known DofTransformation
+   VDofTransformation(DofTransformation & doftrans, int vdim = 1,
+                      int ordering = 0)
+      : DofTransformation(vdim * doftrans.Size()),
+        vdim_(vdim), ordering_(ordering),
+        doftrans_(&doftrans) {}
+
+   /// Set or change the vdim parameter
+   inline void SetVDim(int vdim)
+   {
+      vdim_ = vdim;
+      if (doftrans_)
+      {
+         size_ = vdim_ * doftrans_->Size();
+      }
+   }
+
+   /// Return the current vdim value
+   inline int GetVDim() const { return vdim_; }
+
+   /// Set or change the nested DofTransformation object
+   inline void SetDofTransformation(DofTransformation & doftrans)
+   {
+      size_ = vdim_ * doftrans.Size();
+      doftrans_ = &doftrans;
+   }
+
+   /// Return the nested DofTransformation object
+   inline DofTransformation * GetDofTransformation() const { return doftrans_; }
+
+   inline void SetFaceOrientation(const Array<int> & face_orientation)
+   { Fo = face_orientation; doftrans_->SetFaceOrientations(face_orientation); }
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+   void InvTransformPrimal(double *v) const;
+   void TransformDual(double *v) const;
+};
+
+/** Abstract base class for high-order Nedelec spaces on elements with
+    triangular faces.
+
+    The Nedelec DoFs on the interior of triangular faces come in pairs which
+    share an interpolation point but have different vector directions. These
+    directions depend on the orientation of the face and can therefore differ in
+    neighboring elements. The mapping required to transform these DoFs can be
+    implemented as series of 2x2 linear transformations. The raw data for these
+    linear transformations is stored in the T_data and TInv_data arrays and can
+    be accessed as DenseMatrices using the GetFaceTransform() and
+    GetFaceInverseTransform() methods.
+*/
+class ND_DofTransformation : public DofTransformation
+{
+protected:
+   static const double T_data[24];
+   static const double TInv_data[24];
+   static const DenseTensor T, TInv;
+   int order;
+
+   ND_DofTransformation(int size, int order);
+
+public:
+   // Return the 2x2 transformation operator for the given face orientation
+   static const DenseMatrix & GetFaceTransform(int ori) { return T(ori); }
+
+   // Return the 2x2 inverse transformation operator
+   static const DenseMatrix & GetFaceInverseTransform(int ori)
+   { return TInv(ori); }
+};
+
+/// DoF transformation implementation for the Nedelec basis on triangles
+class ND_TriDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_TriDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+/// DoF transformation implementation for the Nedelec basis on tetrahedra
+class ND_TetDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_TetDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+/// DoF transformation implementation for the Nedelec basis on wedge elements
+/** TODO: (Under development) */
+class ND_WedgeDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_WedgeDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+} // namespace mfem
+
+#endif // MFEM_DOFTRANSFORM

fem/eltrans.cpp

@@ -380,6 +380,7 @@ void IsoparametricTransformation::SetIdentityTransformation(
       case Geometry::TETRAHEDRON : FElem = &TetrahedronFE; break;
       case Geometry::CUBE :        FElem = &HexahedronFE; break;
       case Geometry::PRISM :       FElem = &WedgeFE; break;
+      case Geometry::PYRAMID :     FElem = &PyramidFE; break;
       default:
          MFEM_ABORT("unknown Geometry::Type!");
    }

fem/estimators.cpp

@@ -329,7 +329,7 @@ void KellyErrorEstimator::ComputeEstimates()
          error_estimates(e) = sqrt(factor * error_estimates(e));
       }
 
-      total_error = error_estimates.Sum();
+      total_error = error_estimates.Norml2();
       delete flux;
       return;
    }
@@ -452,9 +452,10 @@ void KellyErrorEstimator::ComputeEstimates()
    auto pfes = dynamic_cast<ParFiniteElementSpace*>(xfes);
    MFEM_VERIFY(pfes, "xfes is not a ParFiniteElementSpace pointer");
 
-   double process_local_error = error_estimates.Sum();
+   double process_local_error = pow(error_estimates.Norml2(),2.0);
    MPI_Allreduce(&process_local_error, &total_error, 1, MPI_DOUBLE,
                  MPI_SUM, pfes->GetComm());
+   total_error = sqrt(total_error);
 #endif // MFEM_USE_MPI
 }
 

fem/fe.hpp

@@ -1313,6 +1313,64 @@ public:
                            DenseMatrix &dshape) const;
 };
 
+/// A linear element defined on a triangular prism
+class LinearWedgeFiniteElement : public NodalFiniteElement
+{
+public:
+   /// Construct the LinearWedgeFiniteElement
+   LinearWedgeFiniteElement();
+
+   /** @brief virtual function which evaluates the values of all
+       shape functions at a given point ip and stores
+       them in the vector shape of dimension Dof (4) */
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+
+   /** @brief virtual function which evaluates the values of all
+       partial derivatives of all shape functions at a given
+       point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
+       so that each row contains the derivatives of one shape function */
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+
+   virtual void ProjectDelta(int vertex, Vector &dofs) const
+   { dofs = 0.0; dofs(vertex) = 1.0; }
+
+   /** @brief Get the dofs associated with the given @a face.
+       @a *dofs is set to an internal array of the local dofc on the
+       face, while *ndofs is set to the number of dofs on that face.
+   */
+   virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
+};
+
+/// A linear element defined on a square pyramid
+class LinearPyramidFiniteElement : public NodalFiniteElement
+{
+public:
+   /// Construct the LinearPyramidFiniteElement
+   LinearPyramidFiniteElement();
+
+   /** @brief virtual function which evaluates the values of all
+       shape functions at a given point ip and stores
+       them in the vector shape of dimension Dof (4) */
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+
+   /** @brief virtual function which evaluates the values of all
+       partial derivatives of all shape functions at a given
+       point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
+       so that each row contains the derivatives of one shape function */
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+
+   virtual void ProjectDelta(int vertex, Vector &dofs) const
+   { dofs = 0.0; dofs(vertex) = 1.0; }
+
+   /** @brief Get the dofs associated with the given @a face.
+       @a *dofs is set to an internal array of the local dofc on the
+       face, while *ndofs is set to the number of dofs on that face.
+   */
+   virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
+};
+
 /// A 2D constant element on a triangle
 class P0TriangleFiniteElement : public NodalFiniteElement
 {
@@ -1690,6 +1748,32 @@ public:
    { dofs(0) = 1.0; }
 };
 
+/// A 3D constant element on a wedge
+class P0WdgFiniteElement : public NodalFiniteElement
+{
+public:
+   /// Construct the P0WdgFiniteElement
+   P0WdgFiniteElement ();
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+   virtual void ProjectDelta(int vertex, Vector &dofs) const
+   { dofs(0) = 1.0; }
+};
+
+/// A 3D constant element on a pyramid
+class P0PyrFiniteElement : public NodalFiniteElement
+{
+public:
+   /// Construct the P0PyrFiniteElement
+   P0PyrFiniteElement ();
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+   virtual void ProjectDelta(int vertex, Vector &dofs) const
+   { dofs(0) = 1.0; }
+};
+
 /** @brief Tensor products of 1D Lagrange1DFiniteElement
     (only degree 2 is functional) */
 class LagrangeHexFiniteElement : public NodalFiniteElement
@@ -1828,6 +1912,10 @@ public:
    using FiniteElement::Project;
    virtual void Project (VectorCoefficient &vc,
                          ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectGrad(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &grad) const;
 };
 
 
@@ -1852,6 +1940,66 @@ public:
    using FiniteElement::Project;
    virtual void Project (VectorCoefficient &vc,
                          ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectGrad(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &grad) const;
+};
+
+
+/// A 3D 1st order Nedelec element on a wedge
+class Nedelec1WdgFiniteElement : public VectorFiniteElement
+{
+private:
+   static const double tk[9][3];
+
+public:
+   /// Construct the Nedelec1WdgFiniteElement
+   Nedelec1WdgFiniteElement();
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const
+   { CalcVShape_ND(Trans, shape); }
+   virtual void CalcCurlShape(const IntegrationPoint &ip,
+                              DenseMatrix &curl_shape) const;
+   virtual void GetLocalInterpolation (ElementTransformation &Trans,
+                                       DenseMatrix &I) const;
+   using FiniteElement::Project;
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectGrad(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &grad) const;
+};
+
+
+/// A 3D 1st order Nedelec element on a pyramid
+class Nedelec1PyrFiniteElement : public VectorFiniteElement
+{
+private:
+   static const double tk[8][3];
+
+public:
+   /// Construct the Nedelec1PyrFiniteElement
+   Nedelec1PyrFiniteElement();
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const
+   { CalcVShape_ND(Trans, shape); }
+   virtual void CalcCurlShape(const IntegrationPoint &ip,
+                              DenseMatrix &curl_shape) const;
+   virtual void GetLocalInterpolation (ElementTransformation &Trans,
+                                       DenseMatrix &I) const;
+   using FiniteElement::Project;
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectGrad(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &grad) const;
 };
 
 
@@ -1945,6 +2093,77 @@ public:
 };
 
 
+/// A 3D 0th order Raviert-Thomas element on a wedge
+class RT0WdgFiniteElement : public VectorFiniteElement
+{
+private:
+   static const double nk[5][3];
+
+public:
+   /// Construct the RT0WdgFiniteElement
+   RT0WdgFiniteElement();
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const
+   { CalcVShape_RT(Trans, shape); }
+
+   virtual void CalcDivShape(const IntegrationPoint &ip,
+                             Vector &divshape) const;
+
+   virtual void GetLocalInterpolation (ElementTransformation &Trans,
+                                       DenseMatrix &I) const;
+
+   using FiniteElement::Project;
+
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectCurl(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &curl) const;
+};
+
+
+/// A 3D 0th order Raviert-Thomas element on a pyramid
+class RT0PyrFiniteElement : public VectorFiniteElement
+{
+private:
+   static const double nk[5][3];
+
+   // If true match RT0TetFiniteElement rather than RT_TetrahedronElement(0)
+   bool rt0;
+
+public:
+   /// Construct the RT0PyrFiniteElement
+   RT0PyrFiniteElement(bool rt0tets = true);
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const
+   { CalcVShape_RT(Trans, shape); }
+
+   virtual void CalcDivShape(const IntegrationPoint &ip,
+                             Vector &divshape) const;
+
+   virtual void GetLocalInterpolation (ElementTransformation &Trans,
+                                       DenseMatrix &I) const;
+
+   using FiniteElement::Project;
+
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;
+
+   virtual void ProjectCurl(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &curl) const;
+};
+
+
 class RotTriLinearHexFiniteElement : public NodalFiniteElement
 {
 public:

fem/fe_coll.cpp

@@ -33,6 +33,9 @@ int FiniteElementCollection::HasFaceDofs(Geometry::Type geom, int p) const
       case Geometry::PRISM:
          return max(GetNumDof(Geometry::TRIANGLE, p),
                     GetNumDof(Geometry::SQUARE, p));
+      case Geometry::PYRAMID:
+         return max(GetNumDof(Geometry::TRIANGLE, p),
+                    GetNumDof(Geometry::SQUARE, p));
       default:
          MFEM_ABORT("unknown geometry type");
    }
@@ -574,6 +577,7 @@ LinearFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
       case Geometry::PRISM:       return &WedgeFE;
+      case Geometry::PYRAMID:     return &PyramidFE;
       default:
          mfem_error ("LinearFECollection: unknown geometry type.");
    }
@@ -591,6 +595,7 @@ int LinearFECollection::DofForGeometry(Geometry::Type GeomType) const
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 0;
       case Geometry::PRISM:       return 0;
+      case Geometry::PYRAMID:     return 0;
       default:
          mfem_error ("LinearFECollection: unknown geometry type.");
    }
@@ -1240,6 +1245,7 @@ Const3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
       case Geometry::PRISM:       return &WedgeFE;
+      case Geometry::PYRAMID:     return &PyramidFE;
       default:
          mfem_error ("Const3DFECollection: unknown geometry type.");
    }
@@ -1257,6 +1263,7 @@ int Const3DFECollection::DofForGeometry(Geometry::Type GeomType) const
       case Geometry::TETRAHEDRON: return 1;
       case Geometry::CUBE:        return 1;
       case Geometry::PRISM:       return 1;
+      case Geometry::PYRAMID:     return 1;
       default:
          mfem_error ("Const3DFECollection: unknown geometry type.");
    }
@@ -1277,6 +1284,8 @@ LinearDiscont3DFECollection::FiniteElementForGeometry(
    switch (GeomType)
    {
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
+      case Geometry::PYRAMID:     return &PyramidFE;
+      case Geometry::PRISM:       return &WedgeFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
       default:
          mfem_error ("LinearDiscont3DFECollection: unknown geometry type.");
@@ -1293,6 +1302,8 @@ int LinearDiscont3DFECollection::DofForGeometry(Geometry::Type GeomType) const
       case Geometry::TRIANGLE:    return 0;
       case Geometry::SQUARE:      return 0;
       case Geometry::TETRAHEDRON: return 4;
+      case Geometry::PYRAMID:     return 5;
+      case Geometry::PRISM:       return 6;
       case Geometry::CUBE:        return 8;
       default:
          mfem_error ("LinearDiscont3DFECollection: unknown geometry type.");
@@ -1394,6 +1405,8 @@ ND1_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
    {
       case Geometry::CUBE:        return &HexahedronFE;
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
+      case Geometry::PRISM:       return &WedgeFE;
+      case Geometry::PYRAMID:     return &PyramidFE;
       default:
          mfem_error ("ND1_3DFECollection: unknown geometry type.");
    }
@@ -1410,6 +1423,8 @@ int ND1_3DFECollection::DofForGeometry(Geometry::Type GeomType) const
       case Geometry::SQUARE:      return 0;
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 0;
+      case Geometry::PRISM:       return 0;
+      case Geometry::PYRAMID:     return 0;
       default:
          mfem_error ("ND1_3DFECollection: unknown geometry type.");
    }
@@ -1439,6 +1454,8 @@ RT0_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
       case Geometry::SQUARE:      return &QuadrilateralFE;
       case Geometry::CUBE:        return &HexahedronFE;
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
+      case Geometry::PRISM:       return &WedgeFE;
+      case Geometry::PYRAMID:     return &PyramidFE;
       default:
          mfem_error ("RT0_3DFECollection: unknown geometry type.");
    }
@@ -1455,6 +1472,8 @@ int RT0_3DFECollection::DofForGeometry(Geometry::Type GeomType) const
       case Geometry::SQUARE:      return 1;
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 0;
+      case Geometry::PRISM:       return 0;
+      case Geometry::PYRAMID:     return 0;
       default:
          mfem_error ("RT0_3DFECollection: unknown geometry type.");
    }
@@ -1730,6 +1749,7 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype)
          H1_dof[Geometry::TETRAHEDRON] = (TriDof*pm3)/3;
          H1_dof[Geometry::CUBE] = QuadDof*pm1;
          H1_dof[Geometry::PRISM] = TriDof*pm1;
+         H1_dof[Geometry::PYRAMID] = 0;
          if (b_type == BasisType::Positive)
          {
             H1_Elements[Geometry::TETRAHEDRON] = new H1Pos_TetrahedronElement(p);
@@ -1743,6 +1763,7 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype)
             H1_Elements[Geometry::CUBE] = new H1_HexahedronElement(p, btype);
             H1_Elements[Geometry::PRISM] = new H1_WedgeElement(p, btype);
          }
+         H1_Elements[Geometry::PYRAMID] = new LinearPyramidFiniteElement;
 
          const int &TetDof = H1_dof[Geometry::TETRAHEDRON];
          TetDofOrd[0] = new int[24*TetDof];
@@ -1837,6 +1858,21 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype)
    }
 }
 
+const FiniteElement *
+H1_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   if (GeomType != Geometry::PYRAMID || this->GetOrder() == 1)
+   {
+      return H1_Elements[GeomType];
+   }
+   else
+   {
+      MFEM_ABORT("H1 Pyramid basis functions are not yet supported "
+                 "for order > 1.");
+      return NULL;
+   }
+}
+
 const int *H1_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
                                                    int Or) const
 {
@@ -2076,9 +2112,12 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
          L2_Elements[Geometry::CUBE] = new L2_HexahedronElement(p, btype);
          L2_Elements[Geometry::PRISM] = new L2_WedgeElement(p, btype);
       }
+      L2_Elements[Geometry::PYRAMID] = new P0PyrFiniteElement;
+
       L2_Elements[Geometry::TETRAHEDRON]->SetMapType(map_type);
       L2_Elements[Geometry::CUBE]->SetMapType(map_type);
       L2_Elements[Geometry::PRISM]->SetMapType(map_type);
+      L2_Elements[Geometry::PYRAMID]->SetMapType(map_type);
       // Trace element use the default Gauss-Legendre nodal points for positive basis
       if (b_type == BasisType::Positive)
       {
@@ -2199,6 +2238,21 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
    }
 }
 
+const FiniteElement *
+L2_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   if (GeomType != Geometry::PYRAMID || this->GetOrder() == 0)
+   {
+      return L2_Elements[GeomType];
+   }
+   else
+   {
+      MFEM_ABORT("L2 Pyramid basis functions are not yet supported "
+                 "for order > 0.");
+      return NULL;
+   }
+}
+
 const int *L2_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
                                                    int Or) const
 {
@@ -2290,6 +2344,12 @@ RT_FECollection::RT_FECollection(const int order, const int dim,
 
       RT_Elements[Geometry::CUBE] = new RT_HexahedronElement(p, cb_type, ob_type);
       RT_dof[Geometry::CUBE] = 3*p*pp1*pp1;
+
+      RT_Elements[Geometry::PRISM] = new RT0WdgFiniteElement;
+      RT_dof[Geometry::PRISM] = 0;
+
+      RT_Elements[Geometry::PYRAMID] = new RT0PyrFiniteElement(false);
+      RT_dof[Geometry::PYRAMID] = 0;
    }
    else
    {
@@ -2433,6 +2493,22 @@ void RT_FECollection::InitFaces(const int p, const int dim,
    }
 }
 
+const FiniteElement *
+RT_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   if ((GeomType != Geometry::PRISM && GeomType != Geometry::PYRAMID) ||
+       this->GetOrder() == 1)
+   {
+      return RT_Elements[GeomType];
+   }
+   else
+   {
+      MFEM_ABORT("RT Wedge and Pyramid basis functions are not yet supported "
+                 "for order > 0.");
+      return NULL;
+   }
+}
+
 const int *RT_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
                                                    int Or) const
 {
@@ -2656,18 +2732,31 @@ ND_FECollection::ND_FECollection(const int p, const int dim,
       {
          for (int i = 0; i + j <= pm2; i++)
          {
-            int k1 = p*pm1 - (p - j)*(pm1 - j) + 2*i;
-            int k2 = p*pm1 - (p - i)*(pm1 - i) + 2*j;
-            // (0,1,2)
-            TriDofOrd[0][k1  ] = k1;
-            TriDofOrd[0][k1+1] = k1 + 1;
-            // (0,2,1)
-            TriDofOrd[5][k1  ] = k2 + 1;
-            TriDofOrd[5][k1+1] = k2;
+            int k0 = p*pm1 - (p - j)*(pm1 - j) + 2*i;
+            int k1 = 2*pm2 - 2*i + ((2*p-3)-j)*j;
+            int k2 = 2*pm2 - 2*j + ((2*p-3)-i)*i;
+            int k3 = p*pm1 - 2 - 3*j - i - (i+j)*(i+j);
+            int k4 = p*pm1 - 2 - 3*i - j - (i+j)*(i+j);
+            int k5 = p*pm1 - (p - i)*(pm1 - i) + 2*j;
 
-            // The other orientations can not be supported with the current
-            // interface. The method Mesh::ReorientTetMesh will ensure that
-            // only orientations 0 and 5 are generated.
+            // (0,1,2)
+            TriDofOrd[0][k0  ] = k0;
+            TriDofOrd[0][k0+1] = k0 + 1;
+            // (1,0,2)
+            TriDofOrd[1][k0  ] = k1;
+            TriDofOrd[1][k0+1] = k1 + 1;
+            // (2,0,1)
+            TriDofOrd[2][k0  ] = k2;
+            TriDofOrd[2][k0+1] = k2 + 1;
+            // (2,1,0)
+            TriDofOrd[3][k0  ] = k3;
+            TriDofOrd[3][k0+1] = k3 + 1;
+            // (1,2,0)
+            TriDofOrd[4][k0  ] = k4;
+            TriDofOrd[4][k0+1] = k4 + 1;
+            // (0,2,1)
+            TriDofOrd[5][k0  ] = k5;
+            TriDofOrd[5][k0+1] = k5 + 1;
          }
       }
    }
@@ -2680,6 +2769,28 @@ ND_FECollection::ND_FECollection(const int p, const int dim,
       // TODO: cb_type and ob_type for tets
       ND_Elements[Geometry::TETRAHEDRON] = new ND_TetrahedronElement(p);
       ND_dof[Geometry::TETRAHEDRON] = p*pm1*pm2/2;
+
+      ND_Elements[Geometry::PRISM] = new Nedelec1WdgFiniteElement;
+      ND_dof[Geometry::PRISM] = 0;
+
+      ND_Elements[Geometry::PYRAMID] = new Nedelec1PyrFiniteElement;
+      ND_dof[Geometry::PYRAMID] = 0;
+   }
+}
+
+const FiniteElement *
+ND_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   if ((GeomType != Geometry::PRISM && GeomType != Geometry::PYRAMID) ||
+       this->GetOrder() == 1)
+   {
+      return ND_Elements[GeomType];
+   }
+   else
+   {
+      MFEM_ABORT("ND Wedge and Pyramid basis functions are not yet supported "
+                 "for order > 1.");
+      return NULL;
    }
 }
 
@@ -2692,11 +2803,6 @@ const int *ND_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
    }
    else if (GeomType == Geometry::TRIANGLE)
    {
-      if (Or != 0 && Or != 5)
-      {
-         MFEM_ABORT("triangle face orientation " << Or << " is not supported! "
-                    "Use Mesh::ReorientTetMesh to fix it.");
-      }
       return TriDofOrd[Or%6];
    }
    else if (GeomType == Geometry::SQUARE)

fem/fe_coll.hpp

@@ -228,8 +228,7 @@ public:
                             const int btype = BasisType::GaussLobatto);
 
    virtual const FiniteElement *FiniteElementForGeometry(
-      Geometry::Type GeomType) const
-   { return H1_Elements[GeomType]; }
+      Geometry::Type GeomType) const;
    virtual int DofForGeometry(Geometry::Type GeomType) const
    { return H1_dof[GeomType]; }
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
@@ -302,10 +301,7 @@ public:
                    const int map_type = FiniteElement::VALUE);
 
    virtual const FiniteElement *FiniteElementForGeometry(
-      Geometry::Type GeomType) const
-   {
-      return L2_Elements[GeomType];
-   }
+      Geometry::Type GeomType) const;
    virtual int DofForGeometry(Geometry::Type GeomType) const
    {
       if (L2_Elements[GeomType])
@@ -371,8 +367,7 @@ public:
                    const int ob_type = BasisType::GaussLegendre);
 
    virtual const FiniteElement *FiniteElementForGeometry(
-      Geometry::Type GeomType) const
-   { return RT_Elements[GeomType]; }
+      Geometry::Type GeomType) const;
    virtual int DofForGeometry(Geometry::Type GeomType) const
    { return RT_dof[GeomType]; }
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
@@ -430,8 +425,7 @@ public:
                    const int ob_type = BasisType::GaussLegendre);
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(Geometry::Type GeomType) const
-   { return ND_Elements[GeomType]; }
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
    virtual int DofForGeometry(Geometry::Type GeomType) const
    { return ND_dof[GeomType]; }
@@ -529,9 +523,10 @@ private:
    const BiLinear2DFiniteElement QuadrilateralFE;
    const Linear3DFiniteElement TetrahedronFE;
    const TriLinear3DFiniteElement ParallelepipedFE;
-   const H1_WedgeElement WedgeFE;
+   const LinearWedgeFiniteElement WedgeFE;
+   const LinearPyramidFiniteElement PyramidFE;
 public:
-   LinearFECollection() : FiniteElementCollection(1), WedgeFE(1) { }
+   LinearFECollection() : FiniteElementCollection(1) { }
 
    virtual const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const;
@@ -936,10 +931,11 @@ class Const3DFECollection : public FiniteElementCollection
 private:
    const P0TetFiniteElement TetrahedronFE;
    const P0HexFiniteElement ParallelepipedFE;
-   const L2_WedgeElement WedgeFE;
+   const P0WdgFiniteElement WedgeFE;
+   const P0PyrFiniteElement PyramidFE;
 
 public:
-   Const3DFECollection() : FiniteElementCollection(0), WedgeFE(0) { }
+   Const3DFECollection() : FiniteElementCollection(0) { }
 
    virtual const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const;
@@ -960,6 +956,8 @@ class LinearDiscont3DFECollection : public FiniteElementCollection
 {
 private:
    const Linear3DFiniteElement TetrahedronFE;
+   const LinearPyramidFiniteElement PyramidFE;
+   const LinearWedgeFiniteElement WedgeFE;
    const TriLinear3DFiniteElement ParallelepipedFE;
 
 public:
@@ -1036,6 +1034,8 @@ class ND1_3DFECollection : public FiniteElementCollection
 private:
    const Nedelec1HexFiniteElement HexahedronFE;
    const Nedelec1TetFiniteElement TetrahedronFE;
+   const Nedelec1WdgFiniteElement WedgeFE;
+   const Nedelec1PyrFiniteElement PyramidFE;
 
 public:
    ND1_3DFECollection() : FiniteElementCollection(1) { }
@@ -1061,6 +1061,8 @@ private:
    const P0QuadFiniteElement QuadrilateralFE;
    const RT0HexFiniteElement HexahedronFE;
    const RT0TetFiniteElement TetrahedronFE;
+   const RT0WdgFiniteElement WedgeFE;
+   const RT0PyrFiniteElement PyramidFE;
 public:
    RT0_3DFECollection() : FiniteElementCollection(1) { }
 

fem/fem.hpp

@@ -16,6 +16,7 @@
 #include "geom.hpp"
 #include "fe.hpp"
 #include "fe_coll.hpp"
+#include "doftrans.hpp"
 #include "eltrans.hpp"
 #include "coefficient.hpp"
 #include "complex_fem.hpp"

fem/fespace.cpp

@@ -58,9 +58,12 @@ DofsToVDofs<Ordering::byVDIM>(int ndofs, int vdim, Array<int> &dofs)
 
 FiniteElementSpace::FiniteElementSpace()
    : mesh(NULL), fec(NULL), vdim(0), ordering(Ordering::byNODES),
-     ndofs(0), nvdofs(0), nedofs(0), nfdofs(0), nbdofs(0), bdofs(NULL),
-     elem_dof(NULL), bdr_elem_dof(NULL), face_dof(NULL),
+     ndofs(0), nvdofs(0), nedofs(0), nfdofs(0), nbdofs(0),
+     bdofs(NULL),
+     elem_dof(NULL), elem_fos(NULL), bdr_elem_dof(NULL), bdr_elem_fos(NULL),
+     face_dof(NULL),
      NURBSext(NULL), own_ext(false),
+     DoFTrans(0), VDoFTrans(vdim, ordering),
      cP(NULL), cR(NULL), cR_hp(NULL), cP_is_set(false),
      Th(Operator::ANY_TYPE),
      sequence(0), mesh_sequence(0), orders_changed(false), relaxed_hp(false)
@@ -69,6 +72,7 @@ FiniteElementSpace::FiniteElementSpace()
 FiniteElementSpace::FiniteElementSpace(const FiniteElementSpace &orig,
                                        Mesh *mesh,
                                        const FiniteElementCollection *fec)
+   : VDoFTrans(orig.vdim, orig.ordering)
 {
    mesh = mesh ? mesh : orig.mesh;
    fec = fec ? fec : orig.fec;
@@ -259,16 +263,36 @@ void FiniteElementSpace::AdjustVDofs (Array<int> &vdofs)
    }
 }
 
-void FiniteElementSpace::GetElementVDofs(int i, Array<int> &vdofs) const
+DofTransformation *
+FiniteElementSpace::GetElementVDofs(int i, Array<int> &vdofs) const
 {
-   GetElementDofs(i, vdofs);
+   DofTransformation * doftrans = GetElementDofs(i, vdofs);
    DofsToVDofs(vdofs);
+   if (vdim == 1 || doftrans == NULL)
+   {
+      return doftrans;
+   }
+   else
+   {
+      VDoFTrans.SetDofTransformation(*doftrans);
+      return &VDoFTrans;
+   }
 }
 
-void FiniteElementSpace::GetBdrElementVDofs(int i, Array<int> &vdofs) const
+DofTransformation *
+FiniteElementSpace::GetBdrElementVDofs(int i, Array<int> &vdofs) const
 {
-   GetBdrElementDofs(i, vdofs);
+   DofTransformation * doftrans = GetBdrElementDofs(i, vdofs);
    DofsToVDofs(vdofs);
+   if (vdim == 1 || doftrans == NULL)
+   {
+      return doftrans;
+   }
+   else
+   {
+      VDoFTrans.SetDofTransformation(*doftrans);
+      return &VDoFTrans;
+   }
 }
 
 void FiniteElementSpace::GetFaceVDofs(int i, Array<int> &vdofs) const
@@ -307,21 +331,39 @@ void FiniteElementSpace::BuildElementToDofTable() const
 
    // TODO: can we call GetElementDofs only once per element?
    Table *el_dof = new Table;
+   Table *el_fos = (mesh->Dimension() > 2) ? (new Table) : NULL;
    Array<int> dofs;
+   Array<int> F, Fo;
    el_dof -> MakeI (mesh -> GetNE());
+   if (el_fos) { el_fos -> MakeI (mesh -> GetNE()); }
    for (int i = 0; i < mesh -> GetNE(); i++)
    {
       GetElementDofs (i, dofs);
       el_dof -> AddColumnsInRow (i, dofs.Size());
+
+      if (el_fos)
+      {
+         mesh->GetElementFaces(i, F, Fo);
+         el_fos -> AddColumnsInRow (i, Fo.Size());
+      }
    }
    el_dof -> MakeJ();
+   if (el_fos) { el_fos -> MakeJ(); }
    for (int i = 0; i < mesh -> GetNE(); i++)
    {
       GetElementDofs (i, dofs);
       el_dof -> AddConnections (i, (int *)dofs, dofs.Size());
+
+      if (el_fos)
+      {
+         mesh->GetElementFaces(i, F, Fo);
+         el_fos -> AddConnections (i, (int *)Fo, Fo.Size());
+      }
    }
    el_dof -> ShiftUpI();
+   if (el_fos) { el_fos -> ShiftUpI(); }
    elem_dof = el_dof;
+   elem_fos = el_fos;
 }
 
 void FiniteElementSpace::BuildBdrElementToDofTable() const
@@ -375,7 +417,9 @@ void FiniteElementSpace::BuildFaceToDofTable() const
 void FiniteElementSpace::RebuildElementToDofTable()
 {
    delete elem_dof;
+   delete elem_fos;
    elem_dof = NULL;
+   elem_fos = NULL;
    BuildElementToDofTable();
 }
 
@@ -1315,8 +1359,10 @@ const FaceQuadratureInterpolator
 
 SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    const int coarse_ndofs, const Table &coarse_elem_dof,
-   const DenseTensor localP[]) const
+   const Table *coarse_elem_fos, const DenseTensor localP[]) const
 {
+   /// TODO: Implement DofTransformation support
+
    MFEM_VERIFY(mesh->GetLastOperation() == Mesh::REFINE, "");
 
    Array<int> dofs, coarse_dofs, coarse_vdofs;
@@ -1399,7 +1445,8 @@ void FiniteElementSpace::GetLocalRefinementMatrices(
 }
 
 SparseMatrix* FiniteElementSpace::RefinementMatrix(int old_ndofs,
-                                                   const Table* old_elem_dof)
+                                                   const Table* old_elem_dof,
+                                                   const Table* old_elem_fos)
 {
    MFEM_VERIFY(GetNE() >= old_elem_dof->Size(),
                "Previous mesh is not coarser.");
@@ -1412,13 +1459,16 @@ SparseMatrix* FiniteElementSpace::RefinementMatrix(int old_ndofs,
       GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
    }
 
-   return RefinementMatrix_main(old_ndofs, *old_elem_dof, localP);
+   return RefinementMatrix_main(old_ndofs, *old_elem_dof, old_elem_fos,
+                                localP);
 }
 
 FiniteElementSpace::RefinementOperator::RefinementOperator
-(const FiniteElementSpace* fespace, Table* old_elem_dof, int old_ndofs)
+(const FiniteElementSpace* fespace, Table* old_elem_dof, Table* old_elem_fos,
+ int old_ndofs)
    : fespace(fespace)
    , old_elem_dof(old_elem_dof)
+   , old_elem_fos(old_elem_fos)
 {
    MFEM_VERIFY(fespace->GetNE() >= old_elem_dof->Size(),
                "Previous mesh is not coarser.");
@@ -1432,12 +1482,14 @@ FiniteElementSpace::RefinementOperator::RefinementOperator
    {
       fespace->GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
    }
+
+   ConstructDoFTrans();
 }
 
 FiniteElementSpace::RefinementOperator::RefinementOperator(
    const FiniteElementSpace *fespace, const FiniteElementSpace *coarse_fes)
    : Operator(fespace->GetVSize(), coarse_fes->GetVSize()),
-     fespace(fespace), old_elem_dof(NULL)
+     fespace(fespace), old_elem_dof(NULL), old_elem_fos(NULL)
 {
    Mesh::GeometryList elem_geoms(*fespace->GetMesh());
 
@@ -1449,11 +1501,50 @@ FiniteElementSpace::RefinementOperator::RefinementOperator(
 
    // Make a copy of the coarse elem_dof Table.
    old_elem_dof = new Table(coarse_fes->GetElementToDofTable());
+
+   // Make a copy of the coarse elem_fos Table if it exists.
+   if (coarse_fes->GetElementToFaceOrientationTable())
+   {
+      old_elem_fos = new Table(*coarse_fes->GetElementToFaceOrientationTable());
+   }
+
+   ConstructDoFTrans();
 }
 
 FiniteElementSpace::RefinementOperator::~RefinementOperator()
 {
    delete old_elem_dof;
+   delete old_elem_fos;
+}
+
+void FiniteElementSpace::RefinementOperator
+::ConstructDoFTrans()
+{
+   old_DoFTrans.SetSize(Geometry::NUM_GEOMETRIES);
+   for (int i=0; i<old_DoFTrans.Size(); i++)
+   {
+      old_DoFTrans[i] = NULL;
+   }
+
+   const FiniteElementCollection *fec = fespace->FEColl();
+   if (dynamic_cast<const ND_FECollection*>(fec))
+   {
+      const FiniteElement * nd_tri =
+         fec->FiniteElementForGeometry(Geometry::TRIANGLE);
+      if (nd_tri)
+      {
+         old_DoFTrans[Geometry::TRIANGLE] =
+            new ND_TriDofTransformation(nd_tri->GetOrder());
+      }
+
+      const FiniteElement * nd_tet =
+         fec->FiniteElementForGeometry(Geometry::TETRAHEDRON);
+      if (nd_tet)
+      {
+         old_DoFTrans[Geometry::TETRAHEDRON] =
+            new ND_TetDofTransformation(nd_tet->GetOrder());
+      }
+   }
 }
 
 void FiniteElementSpace::RefinementOperator
@@ -1462,7 +1553,7 @@ void FiniteElementSpace::RefinementOperator
    Mesh* mesh = fespace->GetMesh();
    const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
 
-   Array<int> dofs, vdofs, old_dofs, old_vdofs;
+   Array<int> dofs, vdofs, old_dofs, old_vdofs, old_Fo;
 
    int vdim = fespace->GetVDim();
    int old_ndofs = width / vdim;
@@ -1477,18 +1568,53 @@ void FiniteElementSpace::RefinementOperator
 
       subY.SetSize(lP.Height());
 
-      fespace->GetElementDofs(k, dofs);
+      DofTransformation *doftrans = fespace->GetElementDofs(k, dofs);
       old_elem_dof->GetRow(emb.parent, old_dofs);
 
-      for (int vd = 0; vd < vdim; vd++)
+      if (!doftrans)
       {
-         dofs.Copy(vdofs);
-         fespace->DofsToVDofs(vd, vdofs);
-         old_dofs.Copy(old_vdofs);
-         fespace->DofsToVDofs(vd, old_vdofs, old_ndofs);
-         x.GetSubVector(old_vdofs, subX);
-         lP.Mult(subX, subY);
-         y.SetSubVector(vdofs, subY);
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            dofs.Copy(vdofs);
+            fespace->DofsToVDofs(vd, vdofs);
+            old_dofs.Copy(old_vdofs);
+            fespace->DofsToVDofs(vd, old_vdofs, old_ndofs);
+            x.GetSubVector(old_vdofs, subX);
+            lP.Mult(subX, subY);
+            y.SetSubVector(vdofs, subY);
+         }
+      }
+      else
+      {
+         old_elem_fos->GetRow(emb.parent, old_Fo);
+         old_DoFTrans[geom]->SetFaceOrientations(old_Fo);
+
+         DofTransformation *new_doftrans = NULL;
+         VDofTransformation *vdoftrans =
+            dynamic_cast<VDofTransformation*>(doftrans);
+         if (vdoftrans)
+         {
+            new_doftrans = doftrans;
+            doftrans = vdoftrans->GetDofTransformation();
+         }
+
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            dofs.Copy(vdofs);
+            fespace->DofsToVDofs(vd, vdofs);
+            old_dofs.Copy(old_vdofs);
+            fespace->DofsToVDofs(vd, old_vdofs, old_ndofs);
+            x.GetSubVector(old_vdofs, subX);
+            old_DoFTrans[geom]->InvTransformPrimal(subX);
+            lP.Mult(subX, subY);
+            doftrans->TransformPrimal(subY);
+            y.SetSubVector(vdofs, subY);
+         }
+
+         if (vdoftrans)
+         {
+            doftrans = new_doftrans;
+         }
       }
    }
 }
@@ -1504,12 +1630,12 @@ void FiniteElementSpace::RefinementOperator
    Array<char> processed(fespace->GetVSize());
    processed = 0;
 
-   Array<int> f_dofs, c_dofs, f_vdofs, c_vdofs;
+   Array<int> f_dofs, c_dofs, f_vdofs, c_vdofs, old_Fo;
 
    int vdim = fespace->GetVDim();
    int old_ndofs = width / vdim;
 
-   Vector subY, subX;
+   Vector subY, subX, subYt, subXt;
 
    for (int k = 0; k < mesh->GetNE(); k++)
    {
@@ -1517,30 +1643,77 @@ void FiniteElementSpace::RefinementOperator
       const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
       const DenseMatrix &lP = localP[geom](emb.matrix);
 
-      fespace->GetElementDofs(k, f_dofs);
+      DofTransformation * doftrans = fespace->GetElementDofs(k, f_dofs);
       old_elem_dof->GetRow(emb.parent, c_dofs);
 
-      subY.SetSize(lP.Width());
-
-      for (int vd = 0; vd < vdim; vd++)
+      if (!doftrans)
       {
-         f_dofs.Copy(f_vdofs);
-         fespace->DofsToVDofs(vd, f_vdofs);
-         c_dofs.Copy(c_vdofs);
-         fespace->DofsToVDofs(vd, c_vdofs, old_ndofs);
+         subY.SetSize(lP.Width());
 
-         x.GetSubVector(f_vdofs, subX);
-
-         for (int p = 0; p < f_dofs.Size(); ++p)
+         for (int vd = 0; vd < vdim; vd++)
          {
-            if (processed[DecodeDof(f_dofs[p])])
+            f_dofs.Copy(f_vdofs);
+            fespace->DofsToVDofs(vd, f_vdofs);
+            c_dofs.Copy(c_vdofs);
+            fespace->DofsToVDofs(vd, c_vdofs, old_ndofs);
+
+            x.GetSubVector(f_vdofs, subX);
+
+            for (int p = 0; p < f_dofs.Size(); ++p)
             {
-               subX[p] = 0.0;
+               if (processed[DecodeDof(f_dofs[p])])
+               {
+                  subX[p] = 0.0;
+               }
             }
+
+            lP.MultTranspose(subX, subY);
+            y.AddElementVector(c_vdofs, subY);
+         }
+      }
+      else
+      {
+         subYt.SetSize(lP.Width());
+
+         old_elem_fos->GetRow(emb.parent, old_Fo);
+         old_DoFTrans[geom]->SetFaceOrientations(old_Fo);
+
+         DofTransformation *new_doftrans = NULL;
+         VDofTransformation *vdoftrans =
+            dynamic_cast<VDofTransformation*>(doftrans);
+         if (vdoftrans)
+         {
+            new_doftrans = doftrans;
+            doftrans = vdoftrans->GetDofTransformation();
          }
 
-         lP.MultTranspose(subX, subY);
-         y.AddElementVector(c_vdofs, subY);
+         for (int vd = 0; vd < vdim; vd++)
+         {
+            f_dofs.Copy(f_vdofs);
+            fespace->DofsToVDofs(vd, f_vdofs);
+            c_dofs.Copy(c_vdofs);
+            fespace->DofsToVDofs(vd, c_vdofs, old_ndofs);
+
+            x.GetSubVector(f_vdofs, subX);
+            old_DoFTrans[geom]->InvTransformPrimal(subX);
+
+            for (int p = 0; p < f_dofs.Size(); ++p)
+            {
+               if (processed[DecodeDof(f_dofs[p])])
+               {
+                  subX[p] = 0.0;
+               }
+            }
+
+            lP.MultTranspose(subX, subY);
+            doftrans->TransformPrimal(subY);
+            y.AddElementVector(c_vdofs, subY);
+         }
+
+         if (vdoftrans)
+         {
+            doftrans = new_doftrans;
+         }
       }
 
       for (int p = 0; p < f_dofs.Size(); ++p)
@@ -1550,6 +1723,7 @@ void FiniteElementSpace::RefinementOperator
    }
 }
 
+/// TODO: Implement DofTransformation support
 FiniteElementSpace::DerefinementOperator::DerefinementOperator(
    const FiniteElementSpace *f_fes, const FiniteElementSpace *c_fes,
    BilinearFormIntegrator *mass_integ)
@@ -1707,8 +1881,11 @@ void FiniteElementSpace::GetLocalDerefinementMatrices(Geometry::Type geom,
 }
 
 SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
-                                                     const Table* old_elem_dof)
+                                                     const Table* old_elem_dof,
+                                                     const Table* old_elem_fos)
 {
+   /// TODO: Implement DofTransformation support
+
    MFEM_VERIFY(Nonconforming(), "Not implemented for conforming meshes.");
    MFEM_VERIFY(old_ndofs, "Missing previous (finer) space.");
    MFEM_VERIFY(ndofs <= old_ndofs, "Previous space is not finer.");
@@ -1814,6 +1991,7 @@ void FiniteElementSpace::Constructor(Mesh *mesh, NURBSExtension *NURBSext,
    this->ordering = (Ordering::Type) ordering;
 
    elem_dof = NULL;
+   elem_fos = NULL;
    face_dof = NULL;
 
    sequence = 0;
@@ -1841,6 +2019,8 @@ void FiniteElementSpace::Constructor(Mesh *mesh, NURBSExtension *NURBSext,
       UpdateNURBS();
       cP = cR = cR_hp = NULL;
       cP_is_set = false;
+
+      ConstructDoFTrans();
    }
    else
    {
@@ -1848,9 +2028,41 @@ void FiniteElementSpace::Constructor(Mesh *mesh, NURBSExtension *NURBSext,
       own_ext = 0;
       Construct();
    }
+
    BuildElementToDofTable();
 }
 
+void FiniteElementSpace::ConstructDoFTrans()
+{
+   DestroyDoFTrans();
+
+   VDoFTrans.SetVDim(vdim);
+   DoFTrans.SetSize(Geometry::NUM_GEOMETRIES);
+   for (int i=0; i<DoFTrans.Size(); i++)
+   {
+      DoFTrans[i] = NULL;
+   }
+   if (mesh->Dimension() < 3) { return; }
+   if (dynamic_cast<const ND_FECollection*>(fec))
+   {
+      const FiniteElement * nd_tri =
+         fec->FiniteElementForGeometry(Geometry::TRIANGLE);
+      if (nd_tri)
+      {
+         DoFTrans[Geometry::TRIANGLE] =
+            new ND_TriDofTransformation(nd_tri->GetOrder());
+      }
+
+      const FiniteElement * nd_tet =
+         fec->FiniteElementForGeometry(Geometry::TETRAHEDRON);
+      if (nd_tet)
+      {
+         DoFTrans[Geometry::TETRAHEDRON] =
+            new ND_TetDofTransformation(nd_tet->GetOrder());
+      }
+   }
+}
+
 NURBSExtension *FiniteElementSpace::StealNURBSext()
 {
    if (NURBSext && !own_ext)
@@ -1946,7 +2158,9 @@ void FiniteElementSpace::Construct()
                "Variable order space requires a nonconforming mesh.");
 
    elem_dof = NULL;
+   elem_fos = NULL;
    bdr_elem_dof = NULL;
+   bdr_elem_fos = NULL;
    face_dof = NULL;
 
    ndofs = 0;
@@ -2044,6 +2258,8 @@ void FiniteElementSpace::Construct()
 
    ndofs = nvdofs + nedofs + nfdofs + nbdofs;
 
+   ConstructDoFTrans();
+
    // record the current mesh sequence number to detect refinement etc.
    mesh_sequence = mesh->GetSequence();
 
@@ -2295,14 +2511,22 @@ int FiniteElementSpace::GetNVariants(int entity, int index) const
 static const char* msg_orders_changed =
    "Element orders changed, you need to Update() the space first.";
 
-void FiniteElementSpace::GetElementDofs(int elem, Array<int> &dofs) const
+DofTransformation *
+FiniteElementSpace::GetElementDofs(int elem, Array<int> &dofs) const
 {
    MFEM_VERIFY(!orders_changed, msg_orders_changed);
 
    if (elem_dof)
    {
       elem_dof->GetRow(elem, dofs);
-      return;
+
+      if (DoFTrans[mesh->GetElementBaseGeometry(elem)])
+      {
+         Array<int> Fo;
+         elem_fos -> GetRow (elem, Fo);
+         DoFTrans[mesh->GetElementBaseGeometry(elem)]->SetFaceOrientations(Fo);
+      }
+      return DoFTrans[mesh->GetElementBaseGeometry(elem)];
    }
 
    Array<int> V, E, Eo, F, Fo; // TODO: LocalArray
@@ -2326,6 +2550,11 @@ void FiniteElementSpace::GetElementDofs(int elem, Array<int> &dofs) const
       {
          nfd += fec->GetNumDof(mesh->GetFaceGeometry(F[i]), order);
       }
+      if (DoFTrans[mesh->GetElementBaseGeometry(elem)])
+      {
+         DoFTrans[mesh->GetElementBaseGeometry(elem)]
+         -> SetFaceOrientations(Fo);
+      }
    }
 
    dofs.SetSize(0);
@@ -2383,6 +2612,7 @@ void FiniteElementSpace::GetElementDofs(int elem, Array<int> &dofs) const
          dofs.Append(bbase + j);
       }
    }
+   return DoFTrans[mesh->GetElementBaseGeometry(elem)];
 }
 
 const FiniteElement *FiniteElementSpace::GetFE(int i) const
@@ -2415,18 +2645,27 @@ const FiniteElement *FiniteElementSpace::GetFE(int i) const
    return FE;
 }
 
-void FiniteElementSpace::GetBdrElementDofs(int bel, Array<int> &dofs) const
+DofTransformation *
+FiniteElementSpace::GetBdrElementDofs(int bel, Array<int> &dofs) const
 {
    MFEM_VERIFY(!orders_changed, msg_orders_changed);
 
    if (bdr_elem_dof)
    {
       bdr_elem_dof->GetRow(bel, dofs);
-      return;
+
+      if (DoFTrans[mesh->GetBdrElementBaseGeometry(bel)])
+      {
+         Array<int> Fo;
+         bdr_elem_fos -> GetRow (bel, Fo);
+         DoFTrans[mesh->GetBdrElementBaseGeometry(bel)]->
+         SetFaceOrientations(Fo);
+      }
+      return DoFTrans[mesh->GetBdrElementBaseGeometry(bel)];
    }
 
-   Array<int> V, E, Eo; // TODO: LocalArray
-   int F, Fo;
+   Array<int> V, E, Eo, Fo; // TODO: LocalArray
+   int F, oF;
 
    int dim = mesh->Dimension();
    auto geom = mesh->GetBdrElementGeometry(bel);
@@ -2445,7 +2684,17 @@ void FiniteElementSpace::GetBdrElementDofs(int bel, Array<int> &dofs) const
 
    if (nv) { mesh->GetBdrElementVertices(bel, V); }
    if (ne) { mesh->GetBdrElementEdges(bel, E, Eo); }
-   if (nf) { mesh->GetBdrElementFace(bel, &F, &Fo); }
+   if (nf)
+   {
+      mesh->GetBdrElementFace(bel, &F, &oF);
+
+      if (DoFTrans[mesh->GetBdrElementBaseGeometry(bel)])
+      {
+         Fo.Append(oF);
+         DoFTrans[mesh->GetBdrElementBaseGeometry(bel)]->
+         SetFaceOrientations(Fo);
+      }
+   }
 
    dofs.SetSize(0);
    dofs.Reserve(nv*V.Size() + ne*E.Size() + nf);
@@ -2478,13 +2727,15 @@ void FiniteElementSpace::GetBdrElementDofs(int bel, Array<int> &dofs) const
    if (nf) // face DOFs
    {
       int fbase = (var_face_dofs.Size() > 0) ? FindFaceDof(F, nf) : F*nf;
-      const int *ind = fec->GetDofOrdering(geom, order, Fo);
+      const int *ind = fec->GetDofOrdering(geom, order, oF);
 
       for (int j = 0; j < nf; j++)
       {
          dofs.Append(EncodeDof(nvdofs + nedofs + fbase, ind[j]));
       }
    }
+
+   return DoFTrans[mesh->GetBdrElementBaseGeometry(bel)];
 }
 
 int FiniteElementSpace::GetFaceDofs(int face, Array<int> &dofs,
@@ -2794,6 +3045,8 @@ void FiniteElementSpace::Destroy()
    }
    E2BFQ_array.SetSize(0);
 
+   DestroyDoFTrans();
+
    dof_elem_array.DeleteAll();
    dof_ldof_array.DeleteAll();
 
@@ -2806,7 +3059,9 @@ void FiniteElementSpace::Destroy()
    else
    {
       delete elem_dof;
+      delete elem_fos;
       delete bdr_elem_dof;
+      delete bdr_elem_fos;
       delete face_dof;
 
       delete [] bdofs;
@@ -2814,6 +3069,15 @@ void FiniteElementSpace::Destroy()
    ceed::RemoveBasisAndRestriction(this);
 }
 
+void FiniteElementSpace::DestroyDoFTrans()
+{
+   for (int i = 0; i < DoFTrans.Size(); i++)
+   {
+      delete DoFTrans[i];
+   }
+   DoFTrans.SetSize(0);
+}
+
 void FiniteElementSpace::GetTransferOperator(
    const FiniteElementSpace &coarse_fes, OperatorHandle &T) const
 {
@@ -2831,6 +3095,8 @@ void FiniteElementSpace::GetTransferOperator(
       }
       T.Reset(RefinementMatrix_main(coarse_fes.GetNDofs(),
                                     coarse_fes.GetElementToDofTable(),
+                                    coarse_fes.
+                                    GetElementToFaceOrientationTable(),
                                     localP));
    }
    else
@@ -2933,6 +3199,7 @@ void FiniteElementSpace::Update(bool want_transform)
    }
 
    Table* old_elem_dof = NULL;
+   Table* old_elem_fos = NULL;
    int old_ndofs;
    bool old_orders_changed = orders_changed;
 
@@ -2940,7 +3207,9 @@ void FiniteElementSpace::Update(bool want_transform)
    if (want_transform)
    {
       old_elem_dof = elem_dof;
+      old_elem_fos = elem_fos;
       elem_dof = NULL;
+      elem_fos = NULL;
       old_ndofs = ndofs;
    }
 
@@ -2966,15 +3235,18 @@ void FiniteElementSpace::Update(bool want_transform)
          {
             if (Th.Type() != Operator::MFEM_SPARSEMAT)
             {
-               Th.Reset(new RefinementOperator(this, old_elem_dof, old_ndofs));
+               Th.Reset(new RefinementOperator(this, old_elem_dof,
+                                               old_elem_fos, old_ndofs));
                // The RefinementOperator takes ownership of 'old_elem_dof', so
                // we no longer own it:
                old_elem_dof = NULL;
+               old_elem_fos = NULL;
             }
             else
             {
                // calculate fully assembled matrix
-               Th.Reset(RefinementMatrix(old_ndofs, old_elem_dof));
+               Th.Reset(RefinementMatrix(old_ndofs, old_elem_dof,
+                                         old_elem_fos));
             }
             break;
          }
@@ -2982,7 +3254,7 @@ void FiniteElementSpace::Update(bool want_transform)
          case Mesh::DEREFINE:
          {
             BuildConformingInterpolation();
-            Th.Reset(DerefinementMatrix(old_ndofs, old_elem_dof));
+            Th.Reset(DerefinementMatrix(old_ndofs, old_elem_dof, old_elem_fos));
             if (cP && cR)
             {
                Th.SetOperatorOwner(false);
@@ -2997,6 +3269,7 @@ void FiniteElementSpace::Update(bool want_transform)
       }
 
       delete old_elem_dof;
+      delete old_elem_fos;
    }
 }
 

fem/fespace.hpp

@@ -16,6 +16,7 @@
 #include "../linalg/sparsemat.hpp"
 #include "../mesh/mesh.hpp"
 #include "fe_coll.hpp"
+#include "doftrans.hpp"
 #include "restriction.hpp"
 #include <iostream>
 #include <unordered_map>
@@ -128,7 +129,9 @@ protected:
 
    // precalculated DOFs for each element, boundary element, and face
    mutable Table *elem_dof; // owned (except in NURBS FE space)
+   mutable Table *elem_fos; // face orientations by element index
    mutable Table *bdr_elem_dof; // owned (except in NURBS FE space)
+   mutable Table *bdr_elem_fos; // bdr face orientations by bdr element index
    mutable Table *face_dof; // owned; in var-order space contains variant 0 DOFs
 
    Array<int> dof_elem_array, dof_ldof_array;
@@ -137,6 +140,9 @@ protected:
    int own_ext;
    mutable Array<int> face_to_be; // NURBS FE space only
 
+   Array<DofTransformation*> DoFTrans;
+   mutable VDofTransformation VDoFTrans;
+
    /** Matrix representing the prolongation from the global conforming dofs to
        a set of intermediate partially conforming dofs, e.g. the dofs associated
        with a "cut" space on a non-conforming mesh. */
@@ -189,6 +195,9 @@ protected:
    void Construct();
    void Destroy();
 
+   void ConstructDoFTrans();
+   void DestroyDoFTrans();
+
    void BuildElementToDofTable() const;
    void BuildBdrElementToDofTable() const;
    void BuildFaceToDofTable() const;
@@ -283,12 +292,19 @@ protected:
       const FiniteElementSpace* fespace;
       DenseTensor localP[Geometry::NumGeom];
       Table* old_elem_dof; // Owned.
+      Table* old_elem_fos; // Owned.
+
+      Array<DofTransformation*> old_DoFTrans;
+      mutable VDofTransformation old_VDoFTrans;
+
+      void ConstructDoFTrans();
 
    public:
       /** Construct the operator based on the elem_dof table of the original
           (coarse) space. The class takes ownership of the table. */
       RefinementOperator(const FiniteElementSpace* fespace,
-                         Table *old_elem_dof/*takes ownership*/, int old_ndofs);
+                         Table *old_elem_dof/*takes ownership*/,
+                         Table *old_elem_fos/*takes ownership*/, int old_ndofs);
       RefinementOperator(const FiniteElementSpace *fespace,
                          const FiniteElementSpace *coarse_fes);
       virtual void Mult(const Vector &x, Vector &y) const;
@@ -302,6 +318,7 @@ protected:
       const FiniteElementSpace *fine_fes; // Not owned.
       DenseTensor localR[Geometry::NumGeom];
       Table *coarse_elem_dof; // Owned.
+      // Table *coarse_elem_fos; // Owned.
       Table coarse_to_fine;
       Array<int> coarse_to_ref_type;
       Array<Geometry::Type> ref_type_to_geom;
@@ -323,6 +340,7 @@ protected:
        the same vector dimension, vdim. */
    SparseMatrix *RefinementMatrix_main(const int coarse_ndofs,
                                        const Table &coarse_elem_dof,
+                                       const Table *coarse_elem_fos,
                                        const DenseTensor localP[]) const;
 
    void GetLocalRefinementMatrices(Geometry::Type geom,
@@ -333,10 +351,12 @@ protected:
    /** Calculate explicit GridFunction interpolation matrix (after mesh
        refinement). NOTE: consider using the RefinementOperator class instead
        of the fully assembled matrix, which can take a lot of memory. */
-   SparseMatrix* RefinementMatrix(int old_ndofs, const Table* old_elem_dof);
+   SparseMatrix* RefinementMatrix(int old_ndofs, const Table* old_elem_dof,
+                                  const Table* old_elem_fos);
 
    /// Calculate GridFunction restriction matrix after mesh derefinement.
-   SparseMatrix* DerefinementMatrix(int old_ndofs, const Table* old_elem_dof);
+   SparseMatrix* DerefinementMatrix(int old_ndofs, const Table* old_elem_dof,
+                                    const Table* old_elem_fos);
 
    /** @brief Return in @a localP the local refinement matrices that map
        between fespaces after mesh refinement. */
@@ -614,10 +634,11 @@ public:
    int GetBdrAttribute(int i) const { return mesh->GetBdrAttribute(i); }
 
    /// Returns indices of degrees of freedom of element 'elem'.
-   virtual void GetElementDofs(int elem, Array<int> &dofs) const;
+   virtual DofTransformation *GetElementDofs(int elem, Array<int> &dofs) const;
 
    /// Returns indices of degrees of freedom for boundary element 'bel'.
-   virtual void GetBdrElementDofs(int bel, Array<int> &dofs) const;
+   virtual DofTransformation *GetBdrElementDofs(int bel,
+                                                Array<int> &dofs) const;
 
    /** @brief Returns the indices of the degrees of freedom for the specified
        face, including the DOFs for the edges and the vertices of the face. */
@@ -666,10 +687,10 @@ public:
    static void AdjustVDofs(Array<int> &vdofs);
 
    /// Returns indexes of degrees of freedom in array dofs for i'th element.
-   void GetElementVDofs(int i, Array<int> &vdofs) const;
+   DofTransformation *GetElementVDofs(int i, Array<int> &vdofs) const;
 
    /// Returns indexes of degrees of freedom for i'th boundary element.
-   void GetBdrElementVDofs(int i, Array<int> &vdofs) const;
+   DofTransformation *GetBdrElementVDofs(int i, Array<int> &vdofs) const;
 
    /// Returns indexes of degrees of freedom for i'th face element (2D and 3D).
    void GetFaceVDofs(int i, Array<int> &vdofs) const;
@@ -695,6 +716,8 @@ public:
        is preserved. */
    void ReorderElementToDofTable();
 
+   const Table *GetElementToFaceOrientationTable() const { return elem_fos; }
+
    /** @brief Return a reference to the internal Table that stores the lists of
        scalar dofs, for each mesh element, as returned by GetElementDofs(). */
    const Table &GetElementToDofTable() const { return *elem_dof; }

fem/geom.cpp

@@ -11,15 +11,19 @@
 
 #include "fem.hpp"
 #include "../mesh/wedge.hpp"
+#include "../mesh/pyramid.hpp"
 
 namespace mfem
 {
 
 const char *Geometry::Name[NumGeom] =
-{ "Point", "Segment", "Triangle", "Square", "Tetrahedron", "Cube", "Prism" };
+{
+   "Point", "Segment", "Triangle", "Square", "Tetrahedron", "Cube", "Prism",
+   "Pyramid"
+};
 
 const double Geometry::Volume[NumGeom] =
-{ 1.0, 1.0, 0.5, 1.0, 1./6, 1.0, 0.5 };
+{ 1.0, 1.0, 0.5, 1.0, 1./6, 1.0, 0.5, 1./3 };
 
 Geometry::Geometry()
 {
@@ -139,6 +143,28 @@ Geometry::Geometry()
    GeomVert[6]->IntPoint(5).y = 1.0;
    GeomVert[6]->IntPoint(5).z = 1.0;
 
+   // Vertices for Geometry::PYRAMID
+   GeomVert[7] = new IntegrationRule(5);
+   GeomVert[7]->IntPoint(0).x = 0.0;
+   GeomVert[7]->IntPoint(0).y = 0.0;
+   GeomVert[7]->IntPoint(0).z = 0.0;
+
+   GeomVert[7]->IntPoint(1).x = 1.0;
+   GeomVert[7]->IntPoint(1).y = 0.0;
+   GeomVert[7]->IntPoint(1).z = 0.0;
+
+   GeomVert[7]->IntPoint(2).x = 1.0;
+   GeomVert[7]->IntPoint(2).y = 1.0;
+   GeomVert[7]->IntPoint(2).z = 0.0;
+
+   GeomVert[7]->IntPoint(3).x = 0.0;
+   GeomVert[7]->IntPoint(3).y = 1.0;
+   GeomVert[7]->IntPoint(3).z = 0.0;
+
+   GeomVert[7]->IntPoint(4).x = 0.0;
+   GeomVert[7]->IntPoint(4).y = 0.0;
+   GeomVert[7]->IntPoint(4).z = 1.0;
+
    GeomCenter[POINT].x = 0.0;
    GeomCenter[POINT].y = 0.0;
    GeomCenter[POINT].z = 0.0;
@@ -167,6 +193,10 @@ Geometry::Geometry()
    GeomCenter[PRISM].y = 1.0 / 3.0;
    GeomCenter[PRISM].z = 0.5;
 
+   GeomCenter[PYRAMID].x = 0.375;
+   GeomCenter[PYRAMID].y = 0.375;
+   GeomCenter[PYRAMID].z = 0.25;
+
    GeomToPerfGeomJac[POINT]       = NULL;
    GeomToPerfGeomJac[SEGMENT]     = new DenseMatrix(1);
    GeomToPerfGeomJac[TRIANGLE]    = new DenseMatrix(2);
@@ -174,6 +204,7 @@ Geometry::Geometry()
    GeomToPerfGeomJac[TETRAHEDRON] = new DenseMatrix(3);
    GeomToPerfGeomJac[CUBE]        = new DenseMatrix(3);
    GeomToPerfGeomJac[PRISM]       = new DenseMatrix(3);
+   GeomToPerfGeomJac[PYRAMID]     = new DenseMatrix(3);
 
    PerfGeomToGeomJac[POINT]       = NULL;
    PerfGeomToGeomJac[SEGMENT]     = NULL;
@@ -182,6 +213,7 @@ Geometry::Geometry()
    PerfGeomToGeomJac[TETRAHEDRON] = new DenseMatrix(3);
    PerfGeomToGeomJac[CUBE]        = NULL;
    PerfGeomToGeomJac[PRISM]       = new DenseMatrix(3);
+   PerfGeomToGeomJac[PYRAMID]     = new DenseMatrix(3);
 
    GeomToPerfGeomJac[SEGMENT]->Diag(1.0, 1);
    {
@@ -210,6 +242,14 @@ Geometry::Geometry()
       *GeomToPerfGeomJac[PRISM] = pri_T.Jacobian();
       CalcInverse(pri_T.Jacobian(), *PerfGeomToGeomJac[PRISM]);
    }
+   {
+      IsoparametricTransformation pyr_T;
+      pyr_T.SetFE(&PyramidFE);
+      GetPerfPointMat (PYRAMID, pyr_T.GetPointMat());
+      pyr_T.SetIntPoint(&GeomCenter[PYRAMID]);
+      *GeomToPerfGeomJac[PYRAMID] = pyr_T.Jacobian();
+      CalcInverse(pyr_T.Jacobian(), *PerfGeomToGeomJac[PYRAMID]);
+   }
 }
 
 Geometry::~Geometry()
@@ -233,6 +273,7 @@ const IntegrationRule * Geometry::GetVertices(int GeomType)
       case Geometry::TETRAHEDRON: return GeomVert[4];
       case Geometry::CUBE:        return GeomVert[5];
       case Geometry::PRISM:       return GeomVert[6];
+      case Geometry::PYRAMID:     return GeomVert[7];
       default:
          mfem_error ("Geometry::GetVertices(...)");
    }
@@ -310,6 +351,25 @@ void Geometry::GetRandomPoint(int GeomType, IntegrationPoint &ip)
             ip.y = 1.0 - ip.y;
          }
          break;
+      case Geometry::PYRAMID:
+         ip.x = double(rand()) / RAND_MAX;
+         ip.y = double(rand()) / RAND_MAX;
+         ip.z = double(rand()) / RAND_MAX;
+         if (ip.x + ip.z > 1.0 && ip.y < ip.x)
+         {
+            double x = ip.x;
+            ip.x = ip.y;
+            ip.y = 1.0 - ip.z;
+            ip.z = 1.0 - x;
+         }
+         else if (ip.y + ip.z > 1.0)
+         {
+            double z = ip.z;
+            ip.z = 1.0 - ip.y;
+            ip.y = ip.x;
+            ip.x = 1.0 - z;
+         }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -371,6 +431,10 @@ bool Geometry::CheckPoint(int GeomType, const IntegrationPoint &ip)
          if (ip.x < 0.0 || ip.y < 0.0 || ip.x+ip.y > 1.0 ||
              ip.z < 0.0 || ip.z > 1.0) { return false; }
          break;
+      case Geometry::PYRAMID:
+         if (ip.x < 0.0 || ip.y < 0.0 || ip.x+ip.z > 1.0 || ip.y+ip.z > 1.0 ||
+             ip.z < 0.0 || ip.z > 1.0) { return false; }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -441,6 +505,17 @@ bool Geometry::CheckPoint(int GeomType, const IntegrationPoint &ip, double eps)
             return false;
          }
          break;
+      case Geometry::PYRAMID:
+         if (internal::FuzzyLT(ip.x, 0.0, eps)
+             || internal::FuzzyLT(ip.y, 0.0, eps)
+             || internal::FuzzyGT(ip.x+ip.z, 1.0, eps)
+             || internal::FuzzyGT(ip.y+ip.z, 1.0, eps)
+             || internal::FuzzyLT(ip.z, 0.0, eps)
+             || internal::FuzzyGT(ip.z, 1.0, eps) )
+         {
+            return false;
+         }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -555,6 +630,16 @@ bool Geometry::ProjectPoint(int GeomType, const IntegrationPoint &beg,
          double lbeg[5] = { beg.x, beg.y, beg.z, 1.0-beg.x-beg.y, 1.0-beg.z };
          return internal::IntersectSegment<5,3>(lbeg, lend, end);
       }
+      case Geometry::PYRAMID:
+      {
+         double lend[6] = { end.x, end.y, end.z,
+                            1.0-end.x-end.z, 1.0-end.y-end.z, 1.0-end.z
+                          };
+         double lbeg[6] = { beg.x, beg.y, beg.z,
+                            1.0-beg.x-beg.z, 1.0-beg.y-beg.z, 1.0-beg.z
+                          };
+         return internal::IntersectSegment<6,3>(lbeg, lend, end);
+      }
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -652,6 +737,43 @@ bool Geometry::ProjectPoint(int GeomType, IntegrationPoint &ip)
          return in_tri && in_z;
       }
 
+      case PYRAMID:
+      {
+         if (ip.x < 0.0)
+         {
+            ip.x = 0.0;
+            internal::ProjectTriangle(ip.y, ip.z);
+            return false;
+         }
+         if (ip.y < 0.0)
+         {
+            ip.y = 0.0;
+            internal::ProjectTriangle(ip.x, ip.z);
+            return false;
+         }
+         if (ip.z < 0.0)
+         {
+            ip.z = 0.0;
+            if (ip.x > 1.0) { ip.x = 1.0; }
+            if (ip.y > 1.0) { ip.y = 1.0; }
+            return false;
+         }
+         if (ip.x >= ip.y)
+         {
+            bool in_y = true;
+            bool in_tri = internal::ProjectTriangle(ip.x, ip.z);
+            if (ip.y > ip.z) { in_y = false; ip.y = ip.z; }
+            return in_tri && in_y;
+         }
+         else
+         {
+            bool in_x = true;
+            bool in_tri = internal::ProjectTriangle(ip.y, ip.z);
+            if (ip.x > ip.z) { in_x = false; ip.x = ip.z; }
+            return in_tri && in_x;
+         }
+      }
+
       default:
          MFEM_ABORT("Reference element type is not supported!");
    }
@@ -726,6 +848,17 @@ void Geometry::GetPerfPointMat(int GeomType, DenseMatrix &pm)
       }
       break;
 
+      case Geometry::PYRAMID:
+      {
+         pm.SetSize (3, 5);
+         pm(0,0) = 0.0;  pm(1,0) = 0.0;  pm(2,0) = 0.0;
+         pm(0,1) = 1.0;  pm(1,1) = 0.0;  pm(2,1) = 0.0;
+         pm(0,2) = 1.0;  pm(1,2) = 1.0;  pm(2,2) = 0.0;
+         pm(0,3) = 0.0;  pm(1,3) = 1.0;  pm(2,3) = 0.0;
+         pm(0,4) = 0.5;  pm(1,4) = 0.5;  pm(2,4) = 0.7071067811865475;
+      }
+      break;
+
       default:
          mfem_error ("Geometry::GetPerfPointMat (...)");
    }
@@ -744,13 +877,13 @@ void Geometry::JacToPerfJac(int GeomType, const DenseMatrix &J,
    }
 }
 
-const int Geometry::NumBdrArray[NumGeom] = { 0, 2, 3, 4, 4, 6, 5 };
-const int Geometry::Dimension[NumGeom] = { 0, 1, 2, 2, 3, 3, 3 };
+const int Geometry::NumBdrArray[NumGeom] = { 0, 2, 3, 4, 4, 6, 5, 5 };
+const int Geometry::Dimension[NumGeom] = { 0, 1, 2, 2, 3, 3, 3, 3 };
 const int Geometry::DimStart[MaxDim+2] =
 { POINT, SEGMENT, TRIANGLE, TETRAHEDRON, NUM_GEOMETRIES };
-const int Geometry::NumVerts[NumGeom] = { 1, 2, 3, 4, 4, 8, 6 };
-const int Geometry::NumEdges[NumGeom] = { 0, 1, 3, 4, 6, 12, 9 };
-const int Geometry::NumFaces[NumGeom] = { 0, 0, 1, 1, 4, 6, 5 };
+const int Geometry::NumVerts[NumGeom] = { 1, 2, 3, 4, 4, 8, 6, 5 };
+const int Geometry::NumEdges[NumGeom] = { 0, 1, 3, 4, 6, 12, 9, 8 };
+const int Geometry::NumFaces[NumGeom] = { 0, 0, 1, 1, 4, 6, 5, 5 };
 
 const int Geometry::
 Constants<Geometry::POINT>::Orient[1][1] = {{0}};
@@ -897,6 +1030,30 @@ Constants<Geometry::PRISM>::VertToVert::J[9][2] =
    {5, 4}                   // 4,5:4
 };
 
+const int Geometry::
+Constants<Geometry::PYRAMID>::Edges[8][2] =
+{{0, 1}, {1, 2}, {3, 2}, {0, 3}, {0, 4}, {1, 4}, {2, 4}, {3, 4}};
+const int Geometry::
+Constants<Geometry::PYRAMID>::FaceTypes[5] =
+{
+   Geometry::SQUARE,
+   Geometry::TRIANGLE, Geometry::TRIANGLE,
+   Geometry::TRIANGLE, Geometry::TRIANGLE
+};
+const int Geometry::
+Constants<Geometry::PYRAMID>::FaceVert[5][4] =
+{{3, 2, 1, 0}, {0, 1, 4, -1}, {1, 2, 4, -1}, {2, 3, 4, -1}, {3, 0, 4, -1}};
+const int Geometry::
+Constants<Geometry::PYRAMID>::VertToVert::I[5] = {0, 3, 5, 7, 8};
+const int Geometry::
+Constants<Geometry::PYRAMID>::VertToVert::J[8][2] =
+{
+   {1, 0}, {3, 3}, {4, 4}, // 0,1:0   0,3:3  0,4:4
+   {2, 1}, {4, 5},         // 1,2:1   1,4:5
+   {3,-3}, {4, 6},         // 2,3:-3  2,4:6
+   {4, 7}                  // 3,4:7
+};
+
 
 GeometryRefiner::GeometryRefiner()
 {
@@ -1262,6 +1419,104 @@ RefinedGeometry * GeometryRefiner::Refine(Geometry::Type Geom,
          return RG;
       }
 
+      case Geometry::PYRAMID:
+      {
+         const int n = Times;
+         RG = new RefinedGeometry ((n+1)*(n+2)*(2*n+3)/6,
+                                   5*n*(2*n-1)*(2*n+1)/3, 0);
+         RG->Times = Times;
+         RG->ETimes = ETimes;
+         RG->Type = type;
+         // enumerate and define the vertices
+         m = 0;
+         for (k = 0; k <= n; k++)
+         {
+            const double *cpij =
+               poly1d.GetPoints(Times - k, BasisType::GetNodalBasis(type));
+            for (j = 0; j <= n - k; j++)
+               for (i = 0; i <= n - k; i++)
+               {
+                  IntegrationPoint &ip = RG->RefPts.IntPoint(m);
+                  if (type == 0)
+                  {
+                     ip.x = (n > k) ? (double(i) / (n - k)) : 0.0;
+                     ip.y = (n > k) ? (double(j) / (n - k)) : 0.0;
+                     ip.z = double(k) / n;
+                  }
+                  else
+                  {
+                     ip.x = cpij[i] * (1.0 - cp[k]);
+                     ip.y = cpij[j] * (1.0 - cp[k]);
+                     ip.z = cp[k];
+                  }
+                  m++;
+               }
+         }
+         if (m != (n+1)*(n+2)*(2*n+3)/6)
+         {
+            mfem_error("GeometryRefiner::Refine() for PYRAMID #1");
+         }
+         // elements
+         Array<int> &G = RG->RefGeoms;
+         m = 0;
+         for (k = 0; k < n; k++)
+         {
+            int lk = k * (k * (2 * k - 6 * n - 9) + 6 * n * (n + 3) + 13) / 6;
+            int lkp1 = (k + 1) *
+                       (k * (2 * k - 6 * n -5) + 6 * n * (n + 2) + 6) / 6;
+            for (j = 0; j < n - k; j++)
+            {
+               for (i = 0; i < n - k; i++)
+               {
+                  G[m++] = lk + j * (n - k + 1) + i;
+                  G[m++] = lk + j * (n - k + 1) + i + 1;
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i + 1;
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i;
+                  G[m++] = lkp1 + j * (n - k) + i;
+               }
+            }
+            for (j = 0; j < n - k - 1; j++)
+            {
+               for (i = 0; i < n - k - 1; i++)
+               {
+                  G[m++] = lkp1 + j * (n - k) + i;
+                  G[m++] = lkp1 + (j + 1) * (n - k) + i;
+                  G[m++] = lkp1 + (j + 1) * (n - k) + i + 1;
+                  G[m++] = lkp1 + j * (n - k) + i + 1;
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i + 1;
+               }
+            }
+            for (j = 0; j < n - k; j++)
+            {
+               for (i = 0; i < n - k - 1; i++)
+               {
+                  G[m++] = lk + j * (n - k + 1) + i + 1;
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i + 1;
+                  G[m++] = lkp1 + j * (n - k) + i;
+                  G[m++] = lkp1 + j * (n - k) + i + 1;
+                  G[m++] = -1;
+               }
+            }
+            for (j = 0; j < n - k - 1; j++)
+            {
+               for (i = 0; i < n - k; i++)
+               {
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i;
+                  G[m++] = lk + (j + 1) * (n - k + 1) + i + 1;
+                  G[m++] = lkp1 + (j + 1) * (n - k) + i;
+                  G[m++] = lkp1 + j * (n - k) + i;
+                  G[m++] = -1;
+               }
+            }
+         }
+         if (m != 5*n*(2*n-1)*(2*n+1)/3)
+         {
+            mfem_error("GeometryRefiner::Refine() for PYRAMID #2");
+         }
+         RGeom[Geometry::PYRAMID].Append(RG);
+         return RG;
+      }
+
       case Geometry::PRISM:
       {
          const int n = Times;

fem/geom.hpp

@@ -27,6 +27,7 @@ namespace mfem
     Geometry::TETRAHEDRON - w/ vert. (0,0,0),(1,0,0),(0,1,0),(0,0,1)
     Geometry::CUBE - the unit cube
     Geometry::PRISM - w/ vert. (0,0,0),(1,0,0),(0,1,0),(0,0,1),(1,0,1),(0,1,1)
+    Geometry::PYRAMID - w/ vert. (0,0,0),(1,0,0),(1,1,0),(0,1,0),(0,0,1)
 */
 class Geometry
 {
@@ -34,7 +35,7 @@ public:
    enum Type
    {
       INVALID = -1,
-      POINT = 0, SEGMENT, TRIANGLE, SQUARE, TETRAHEDRON, CUBE, PRISM,
+      POINT = 0, SEGMENT, TRIANGLE, SQUARE, TETRAHEDRON, CUBE, PRISM, PYRAMID,
       NUM_GEOMETRIES
    };
 
@@ -251,7 +252,26 @@ template <> struct Geometry::Constants<Geometry::PRISM>
    };
 };
 
-// Defined in fe.cpp to ensure construction after 'mfem::WedgeFE'.
+template <> struct Geometry::Constants<Geometry::PYRAMID>
+{
+   static const int Dimension = 3;
+   static const int NumVert = 5;
+   static const int NumEdges = 8;
+   static const int Edges[NumEdges][2];
+   static const int NumFaces = 5;
+   static const int FaceTypes[NumFaces];
+   static const int MaxFaceVert = 4;
+   static const int FaceVert[NumFaces][MaxFaceVert];
+   // Upper-triangular part of the local vertex-to-vertex graph.
+   struct VertToVert
+   {
+      static const int I[NumVert];
+      static const int J[NumEdges][2]; // {end,edge_idx}
+   };
+};
+
+// Defined in fe.cpp to ensure construction after 'mfem::TriangleFE' and
+// `mfem::TetrahedronFE`.
 extern Geometry Geometries;
 
 

fem/gridfunc.cpp

@@ -255,6 +255,8 @@ void GridFunction::SumFluxAndCount(BilinearFormIntegrator &blfi,
    GridFunction &u = *this;
 
    ElementTransformation *Transf;
+   DofTransformation *udoftrans;
+   DofTransformation *fdoftrans;
 
    FiniteElementSpace *ufes = u.FESpace();
    FiniteElementSpace *ffes = flux.FESpace();
@@ -274,15 +276,23 @@ void GridFunction::SumFluxAndCount(BilinearFormIntegrator &blfi,
          continue;
       }
 
-      ufes->GetElementVDofs(i, udofs);
-      ffes->GetElementVDofs(i, fdofs);
+      udoftrans = ufes->GetElementVDofs(i, udofs);
+      fdoftrans = ffes->GetElementVDofs(i, fdofs);
 
       u.GetSubVector(udofs, ul);
+      if (udoftrans)
+      {
+         udoftrans->InvTransformPrimal(ul);
+      }
 
       Transf = ufes->GetElementTransformation(i);
       blfi.ComputeElementFlux(*ufes->GetFE(i), *Transf, ul,
                               *ffes->GetFE(i), fl, wcoef);
 
+      if (fdoftrans)
+      {
+         fdoftrans->TransformPrimal(fl);
+      }
       flux.AddElementVector(fdofs, fl);
 
       FiniteElementSpace::AdjustVDofs(fdofs);
@@ -364,7 +374,7 @@ void GridFunction::GetNodalValues(int i, Array<double> &nval, int vdim) const
 
    int k;
 
-   fes->GetElementVDofs(i, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(i, vdofs);
    const FiniteElement *FElem = fes->GetFE(i);
    const IntegrationRule *ElemVert =
       Geometries.GetVertices(FElem->GetGeomType());
@@ -374,6 +384,10 @@ void GridFunction::GetNodalValues(int i, Array<double> &nval, int vdim) const
    vdim--;
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
 
    if (FElem->GetRangeType() == FiniteElement::SCALAR)
    {
@@ -403,7 +417,7 @@ double GridFunction::GetValue(int i, const IntegrationPoint &ip, int vdim)
 const
 {
    Array<int> dofs;
-   fes->GetElementDofs(i, dofs);
+   DofTransformation * doftrans = fes->GetElementDofs(i, dofs);
    fes->DofsToVDofs(vdim-1, dofs);
    Vector DofVal(dofs.Size()), LocVec;
    const FiniteElement *fe = fes->GetFE(i);
@@ -418,6 +432,10 @@ const
       fe->CalcPhysShape(*Tr, DofVal);
    }
    GetSubVector(dofs, LocVec);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(LocVec);
+   }
 
    return (DofVal * LocVec);
 }
@@ -428,9 +446,13 @@ void GridFunction::GetVectorValue(int i, const IntegrationPoint &ip,
    const FiniteElement *FElem = fes->GetFE(i);
    int dof = FElem->GetDof();
    Array<int> vdofs;
-   fes->GetElementVDofs(i, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(i, vdofs);
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
    if (FElem->GetRangeType() == FiniteElement::SCALAR)
    {
       Vector shape(dof);
@@ -470,30 +492,35 @@ const
    Array<int> dofs;
    int n = ir.GetNPoints();
    vals.SetSize(n);
-   fes->GetElementDofs(i, dofs);
+   DofTransformation * doftrans = fes->GetElementDofs(i, dofs);
    fes->DofsToVDofs(vdim-1, dofs);
    const FiniteElement *FElem = fes->GetFE(i);
    int dof = FElem->GetDof();
    Vector DofVal(dof), loc_data(dof);
    GetSubVector(dofs, loc_data);
-   if (FElem->GetMapType() == FiniteElement::VALUE)
+   if (doftrans)
    {
-      for (int k = 0; k < n; k++)
-      {
-         FElem->CalcShape(ir.IntPoint(k), DofVal);
-         vals(k) = DofVal * loc_data;
-      }
+      doftrans->InvTransformPrimal(loc_data);
    }
-   else
-   {
-      ElementTransformation *Tr = fes->GetElementTransformation(i);
-      for (int k = 0; k < n; k++)
+   for (int k = 0; k < n; k++)
+      if (FElem->GetMapType() == FiniteElement::VALUE)
       {
-         Tr->SetIntPoint(&ir.IntPoint(k));
-         FElem->CalcPhysShape(*Tr, DofVal);
-         vals(k) = DofVal * loc_data;
+         for (int k = 0; k < n; k++)
+         {
+            FElem->CalcShape(ir.IntPoint(k), DofVal);
+            vals(k) = DofVal * loc_data;
+         }
+      }
+      else
+      {
+         ElementTransformation *Tr = fes->GetElementTransformation(i);
+         for (int k = 0; k < n; k++)
+         {
+            Tr->SetIntPoint(&ir.IntPoint(k));
+            FElem->CalcPhysShape(*Tr, DofVal);
+            vals(k) = DofVal * loc_data;
+         }
       }
-   }
 }
 
 void GridFunction::GetValues(int i, const IntegrationRule &ir, Vector &vals,
@@ -861,11 +888,12 @@ void GridFunction::GetVectorValue(ElementTransformation &T,
 
    Array<int> vdofs;
    const FiniteElement *fe = NULL;
+   DofTransformation * doftrans = NULL;
 
    switch (T.ElementType)
    {
       case ElementTransformation::ELEMENT:
-         fes->GetElementVDofs(T.ElementNo, vdofs);
+         doftrans = fes->GetElementVDofs(T.ElementNo, vdofs);
          fe = fes->GetFE(T.ElementNo);
          break;
       case ElementTransformation::EDGE:
@@ -956,6 +984,10 @@ void GridFunction::GetVectorValue(ElementTransformation &T,
    int dof = fe->GetDof();
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
    if (fe->GetRangeType() == FiniteElement::SCALAR)
    {
       Vector shape(dof);
@@ -998,10 +1030,14 @@ void GridFunction::GetVectorValues(ElementTransformation &T,
    int dof = FElem->GetDof();
 
    Array<int> vdofs;
-   fes->GetElementVDofs(T.ElementNo, vdofs);
-
+   DofTransformation * doftrans = fes->GetElementVDofs(T.ElementNo, vdofs);
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
+
    int nip = ir.GetNPoints();
 
    if (FElem->GetRangeType() == FiniteElement::SCALAR)
@@ -1089,6 +1125,8 @@ void GridFunction::GetValuesFrom(const GridFunction &orig_func)
    // Without averaging ...
 
    const FiniteElementSpace *orig_fes = orig_func.FESpace();
+   DofTransformation * doftrans;
+   DofTransformation * orig_doftrans;
    Array<int> vdofs, orig_vdofs;
    Vector shape, loc_values, orig_loc_values;
    int i, j, d, ne, dof, odof, vdim;
@@ -1097,9 +1135,13 @@ void GridFunction::GetValuesFrom(const GridFunction &orig_func)
    vdim = fes->GetVDim();
    for (i = 0; i < ne; i++)
    {
-      fes->GetElementVDofs(i, vdofs);
-      orig_fes->GetElementVDofs(i, orig_vdofs);
+      doftrans = fes->GetElementVDofs(i, vdofs);
+      orig_doftrans = orig_fes->GetElementVDofs(i, orig_vdofs);
       orig_func.GetSubVector(orig_vdofs, orig_loc_values);
+      if (orig_doftrans)
+      {
+         orig_doftrans->InvTransformPrimal(orig_loc_values);
+      }
       const FiniteElement *fe = fes->GetFE(i);
       const FiniteElement *orig_fe = orig_fes->GetFE(i);
       dof = fe->GetDof();
@@ -1117,6 +1159,10 @@ void GridFunction::GetValuesFrom(const GridFunction &orig_func)
                shape * ((const double *)orig_loc_values + d * odof) ;
          }
       }
+      if (doftrans)
+      {
+         doftrans->TransformPrimal(loc_values);
+      }
       SetSubVector(vdofs, loc_values);
    }
 }
@@ -1126,8 +1172,10 @@ void GridFunction::GetBdrValuesFrom(const GridFunction &orig_func)
    // Without averaging ...
 
    const FiniteElementSpace *orig_fes = orig_func.FESpace();
+   // DofTransformation * doftrans;
+   // DofTransformation * orig_doftrans;
    Array<int> vdofs, orig_vdofs;
-   Vector shape, loc_values, orig_loc_values;
+   Vector shape, loc_values, loc_values_t, orig_loc_values, orig_loc_values_t;
    int i, j, d, nbe, dof, odof, vdim;
 
    nbe = fes->GetNBE();
@@ -1165,37 +1213,33 @@ void GridFunction::GetVectorFieldValues(
    Array<int> vdofs;
    ElementTransformation *transf;
 
-   int d, j, k, n, sdim, dof, ind;
+   int d, k, n, sdim, dof;
 
    n = ir.GetNPoints();
-   fes->GetElementVDofs(i, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(i, vdofs);
    const FiniteElement *fe = fes->GetFE(i);
    dof = fe->GetDof();
    sdim = fes->GetMesh()->SpaceDimension();
-   int *dofs = &vdofs[comp*dof];
+   // int *dofs = &vdofs[comp*dof];
    transf = fes->GetElementTransformation(i);
    transf->Transform(ir, tr);
    vals.SetSize(n, sdim);
    DenseMatrix vshape(dof, sdim);
-   double a;
+   Vector loc_data, val(sdim);
+   GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
    for (k = 0; k < n; k++)
    {
       const IntegrationPoint &ip = ir.IntPoint(k);
       transf->SetIntPoint(&ip);
       fe->CalcVShape(*transf, vshape);
+      vshape.MultTranspose(loc_data, val);
       for (d = 0; d < sdim; d++)
       {
-         a = 0.0;
-         for (j = 0; j < dof; j++)
-            if ( (ind=dofs[j]) >= 0 )
-            {
-               a += vshape(j, d) * data[ind];
-            }
-            else
-            {
-               a -= vshape(j, d) * data[-1-ind];
-            }
-         vals(k, d) = a;
+         vals(k,d) = val(d);
       }
    }
 }
@@ -1365,9 +1409,13 @@ void GridFunction::GetVectorGradientHat(
    const FiniteElement *FElem = fes->GetFE(elNo);
    int dim = FElem->GetDim(), dof = FElem->GetDof();
    Array<int> vdofs;
-   fes->GetElementVDofs(elNo, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(elNo, vdofs);
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
    // assuming scalar FE
    int vdim = fes->GetVDim();
    DenseMatrix dshape(dof, dim);
@@ -1406,9 +1454,13 @@ double GridFunction::GetDivergence(ElementTransformation &T) const
          {
             // Assuming RT-type space
             Array<int> dofs;
-            fes->GetElementDofs(elNo, dofs);
+            DofTransformation * doftrans = fes->GetElementDofs(elNo, dofs);
             Vector loc_data, divshape(fe->GetDof());
             GetSubVector(dofs, loc_data);
+            if (doftrans)
+            {
+               doftrans->InvTransformPrimal(loc_data);
+            }
             fe->CalcDivShape(T.GetIntPoint(), divshape);
             return (loc_data * divshape) / T.Weight();
          }
@@ -1499,9 +1551,13 @@ void GridFunction::GetCurl(ElementTransformation &T, Vector &curl) const
          {
             // Assuming ND-type space
             Array<int> dofs;
-            fes->GetElementDofs(elNo, dofs);
+            DofTransformation * doftrans = fes->GetElementDofs(elNo, dofs);
             Vector loc_data;
             GetSubVector(dofs, loc_data);
+            if (doftrans)
+            {
+               doftrans->InvTransformPrimal(loc_data);
+            }
             DenseMatrix curl_shape(fe->GetDof(), fe->GetDim() == 3 ? 3 : 1);
             fe->CalcCurlShape(T.GetIntPoint(), curl_shape);
             curl.SetSize(curl_shape.Width());
@@ -1643,8 +1699,12 @@ void GridFunction::GetGradients(ElementTransformation &tr,
    DenseMatrix dshape(fe->GetDof(), fe->GetDim());
    Vector lval, gh(fe->GetDim()), gcol;
    Array<int> dofs;
-   fes->GetElementDofs(elNo, dofs);
+   DofTransformation * doftrans = fes->GetElementDofs(elNo, dofs);
    GetSubVector(dofs, lval);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(lval);
+   }
    grad.SetSize(fe->GetDim(), ir.GetNPoints());
    for (int i = 0; i < ir.GetNPoints(); i++)
    {
@@ -1724,6 +1784,8 @@ void GridFunction::GetElementAverages(GridFunction &avgs) const
 {
    MassIntegrator Mi;
    DenseMatrix loc_mass;
+   DofTransformation * te_doftrans;
+   DofTransformation * tr_doftrans;
    Array<int> te_dofs, tr_dofs;
    Vector loc_avgs, loc_this;
    Vector int_psi(avgs.Size());
@@ -1734,11 +1796,19 @@ void GridFunction::GetElementAverages(GridFunction &avgs) const
    {
       Mi.AssembleElementMatrix2(*fes->GetFE(i), *avgs.FESpace()->GetFE(i),
                                 *fes->GetElementTransformation(i), loc_mass);
-      fes->GetElementDofs(i, tr_dofs);
-      avgs.FESpace()->GetElementDofs(i, te_dofs);
+      tr_doftrans = fes->GetElementDofs(i, tr_dofs);
+      te_doftrans = avgs.FESpace()->GetElementDofs(i, te_dofs);
       GetSubVector(tr_dofs, loc_this);
+      if (tr_doftrans)
+      {
+         tr_doftrans->InvTransformPrimal(loc_this);
+      }
       loc_avgs.SetSize(te_dofs.Size());
       loc_mass.Mult(loc_this, loc_avgs);
+      if (te_doftrans)
+      {
+         te_doftrans->TransformPrimal(loc_avgs);
+      }
       avgs.AddElementVector(te_dofs, loc_avgs);
       loc_this = 1.0; // assume the local basis for 'this' sums to 1
       loc_mass.Mult(loc_this, loc_avgs);
@@ -1753,8 +1823,12 @@ void GridFunction::GetElementAverages(GridFunction &avgs) const
 void GridFunction::GetElementDofValues(int el, Vector &dof_vals) const
 {
    Array<int> dof_idx;
-   fes->GetElementVDofs(el, dof_idx);
+   DofTransformation * doftrans = fes->GetElementVDofs(el, dof_idx);
    GetSubVector(dof_idx, dof_vals);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(dof_vals);
+   }
 }
 
 void GridFunction::ProjectGridFunction(const GridFunction &src)
@@ -1790,13 +1864,21 @@ void GridFunction::ProjectGridFunction(const GridFunction &src)
          cached_geom = geom;
       }
 
-      src.fes->GetElementVDofs(i, src_vdofs);
+      DofTransformation * src_doftrans = src.fes->GetElementVDofs(i, src_vdofs);
       src.GetSubVector(src_vdofs, src_lvec);
+      if (src_doftrans)
+      {
+         src_doftrans->InvTransformPrimal(src_lvec);
+      }
       for (int vd = 0; vd < vdim; vd++)
       {
          P.Mult(&src_lvec[vd*P.Width()], &dest_lvec[vd*P.Height()]);
       }
-      fes->GetElementVDofs(i, dest_vdofs);
+      DofTransformation * doftrans = fes->GetElementVDofs(i, dest_vdofs);
+      if (doftrans)
+      {
+         doftrans->TransformPrimal(dest_lvec);
+      }
       SetSubVector(dest_vdofs, dest_lvec);
    }
 }
@@ -1805,10 +1887,15 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
                                 const Vector &lo_, const Vector &hi_)
 {
    Array<int> vdofs;
-   fes->GetElementVDofs(i, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(i, vdofs);
    int size = vdofs.Size();
    Vector vals, new_vals(size);
+
    GetSubVector(vdofs, vals);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(vals);
+   }
 
    MFEM_ASSERT(weights.Size() == size, "Different # of weights and dofs.");
    MFEM_ASSERT(lo_.Size() == size, "Different # of lower bounds and dofs.");
@@ -1825,6 +1912,10 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
    slbqp.SetPrintLevel(0); // print messages only if not converged
    slbqp.Mult(vals, new_vals);
 
+   if (doftrans)
+   {
+      doftrans->TransformPrimal(new_vals);
+   }
    SetSubVector(vdofs, new_vals);
 }
 
@@ -1832,10 +1923,14 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
                                 double min_, double max_)
 {
    Array<int> vdofs;
-   fes->GetElementVDofs(i, vdofs);
+   DofTransformation * doftrans = fes->GetElementVDofs(i, vdofs);
    int size = vdofs.Size();
    Vector vals, new_vals(size);
    GetSubVector(vdofs, vals);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(vals);
+   }
 
    double max_val = vals.Max();
    double min_val = vals.Min();
@@ -1843,6 +1938,10 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
    if (max_val <= min_)
    {
       new_vals = min_;
+      if (doftrans)
+      {
+         doftrans->TransformPrimal(new_vals);
+      }
       SetSubVector(vdofs, new_vals);
       return;
    }
@@ -2278,6 +2377,7 @@ void GridFunction::ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
 void GridFunction::ProjectCoefficient(Coefficient &coeff)
 {
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
+   DofTransformation * doftrans = NULL;
 
    if (delta_c == NULL)
    {
@@ -2286,9 +2386,13 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff)
 
       for (int i = 0; i < fes->GetNE(); i++)
       {
-         fes->GetElementVDofs(i, vdofs);
+         doftrans = fes->GetElementVDofs(i, vdofs);
          vals.SetSize(vdofs.Size());
          fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+         if (doftrans)
+         {
+            doftrans->TransformPrimal(vals);
+         }
          SetSubVector(vdofs, vals);
       }
    }
@@ -2334,11 +2438,17 @@ void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
    Array<int> vdofs;
    Vector vals;
 
+   DofTransformation * doftrans = NULL;
+
    for (i = 0; i < fes->GetNE(); i++)
    {
-      fes->GetElementVDofs(i, vdofs);
+      doftrans = fes->GetElementVDofs(i, vdofs);
       vals.SetSize(vdofs.Size());
       fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+      if (doftrans)
+      {
+         doftrans->TransformPrimal(vals);
+      }
       SetSubVector(vdofs, vals);
    }
 }
@@ -2401,6 +2511,7 @@ void GridFunction::ProjectCoefficient(Coefficient *coeff[])
    double val;
    const FiniteElement *fe;
    ElementTransformation *transf;
+   // DofTransformation * doftrans;
    Array<int> vdofs;
 
    vdim = fes->GetVDim();
@@ -2410,6 +2521,7 @@ void GridFunction::ProjectCoefficient(Coefficient *coeff[])
       fdof = fe->GetDof();
       transf = fes->GetElementTransformation(i);
       const IntegrationRule &ir = fe->GetNodes();
+      // doftrans = fes->GetElementVDofs(i, vdofs);
       fes->GetElementVDofs(i, vdofs);
       for (j = 0; j < fdof; j++)
       {

fem/intrules.cpp

@@ -910,6 +910,9 @@ IntegrationRules::IntegrationRules(int Ref, int type_):
    TetrahedronIntRules.SetSize(32, h_mt);
    TetrahedronIntRules = NULL;
 
+   PyramidIntRules.SetSize(32, h_mt);
+   PyramidIntRules = NULL;
+
    PrismIntRules.SetSize(32, h_mt);
    PrismIntRules = NULL;
 
@@ -930,6 +933,7 @@ const IntegrationRule &IntegrationRules::Get(int GeomType, int Order)
       case Geometry::TETRAHEDRON: ir_array = &TetrahedronIntRules; break;
       case Geometry::CUBE:        ir_array = &CubeIntRules; break;
       case Geometry::PRISM:       ir_array = &PrismIntRules; break;
+      case Geometry::PYRAMID:     ir_array = &PyramidIntRules; break;
       default:
          mfem_error("IntegrationRules::Get(...) : Unknown geometry type!");
          ir_array = NULL;
@@ -976,6 +980,7 @@ void IntegrationRules::Set(int GeomType, int Order, IntegrationRule &IntRule)
       case Geometry::TETRAHEDRON: ir_array = &TetrahedronIntRules; break;
       case Geometry::CUBE:        ir_array = &CubeIntRules; break;
       case Geometry::PRISM:       ir_array = &PrismIntRules; break;
+      case Geometry::PYRAMID:     ir_array = &PyramidIntRules; break;
       default:
          mfem_error("IntegrationRules::Set(...) : Unknown geometry type!");
          ir_array = NULL;
@@ -1019,6 +1024,7 @@ IntegrationRules::~IntegrationRules()
    DeleteIntRuleArray(TetrahedronIntRules);
    DeleteIntRuleArray(CubeIntRules);
    DeleteIntRuleArray(PrismIntRules);
+   DeleteIntRuleArray(PyramidIntRules);
 }
 
 
@@ -1041,6 +1047,8 @@ IntegrationRule *IntegrationRules::GenerateIntegrationRule(int GeomType,
          return CubeIntegrationRule(Order);
       case Geometry::PRISM:
          return PrismIntegrationRule(Order);
+      case Geometry::PYRAMID:
+         return PyramidIntegrationRule(Order);
       default:
          mfem_error("IntegrationRules::Set(...) : Unknown geometry type!");
          return NULL;
@@ -1648,6 +1656,30 @@ IntegrationRule *IntegrationRules::TetrahedronIntegrationRule(int Order)
    }
 }
 
+// Integration rules for reference pyramid
+IntegrationRule *IntegrationRules::PyramidIntegrationRule(int Order)
+{
+   // This is a simple integration rule adapted from an integration
+   // rule for a cube which seems to be adequate for now. When we
+   // implement high order finite elements for pyramids we should
+   // revisit this and see if we can improve upon it.
+   const IntegrationRule &irc = Get(Geometry::CUBE, Order);
+   int npts = irc.GetNPoints();
+   AllocIntRule(PyramidIntRules, Order);
+   PyramidIntRules[Order] = new IntegrationRule(npts);
+
+   for (int k=0; k<npts; k++)
+   {
+      const IntegrationPoint & ipc = irc.IntPoint(k);
+      IntegrationPoint & ipp = PyramidIntRules[Order]->IntPoint(k);
+      ipp.x = ipc.x * (1.0 - ipc.z);
+      ipp.y = ipc.y * (1.0 - ipc.z);
+      ipp.z = ipc.z;
+      ipp.weight = ipc.weight / 3.0;
+   }
+   return PyramidIntRules[Order];
+}
+
 // Integration rules for reference prism
 IntegrationRule *IntegrationRules::PrismIntegrationRule(int Order)
 {

fem/intrules.hpp

@@ -323,6 +323,7 @@ private:
    Array<IntegrationRule *> TriangleIntRules;
    Array<IntegrationRule *> SquareIntRules;
    Array<IntegrationRule *> TetrahedronIntRules;
+   Array<IntegrationRule *> PyramidIntRules;
    Array<IntegrationRule *> PrismIntRules;
    Array<IntegrationRule *> CubeIntRules;
 
@@ -351,6 +352,7 @@ private:
    IntegrationRule *TriangleIntegrationRule(int Order);
    IntegrationRule *SquareIntegrationRule(int Order);
    IntegrationRule *TetrahedronIntegrationRule(int Order);
+   IntegrationRule *PyramidIntegrationRule(int Order);
    IntegrationRule *PrismIntegrationRule(int Order);
    IntegrationRule *CubeIntegrationRule(int Order);
 

fem/linearform.cpp

@@ -103,6 +103,7 @@ void LinearForm::Assemble()
 {
    Array<int> vdofs;
    ElementTransformation *eltrans;
+   DofTransformation *doftrans;
    Vector elemvect;
 
    int i;
@@ -134,10 +135,14 @@ void LinearForm::Assemble()
             if ( domain_integs_marker[k] == NULL ||
                  (*(domain_integs_marker[k]))[elem_attr-1] == 1 )
             {
-               fes -> GetElementVDofs (i, vdofs);
+               doftrans = fes -> GetElementVDofs (i, vdofs);
                eltrans = fes -> GetElementTransformation (i);
                domain_integs[k]->AssembleRHSElementVect(*fes->GetFE(i),
                                                         *eltrans, elemvect);
+               if (doftrans)
+               {
+                  doftrans->TransformDual(elemvect);
+               }
                AddElementVector (vdofs, elemvect);
             }
          }
@@ -174,7 +179,7 @@ void LinearForm::Assemble()
       {
          const int bdr_attr = mesh->GetBdrAttribute(i);
          if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
-         fes -> GetBdrElementVDofs (i, vdofs);
+         doftrans = fes -> GetBdrElementVDofs (i, vdofs);
          eltrans = fes -> GetBdrElementTransformation (i);
          for (int k=0; k < boundary_integs.Size(); k++)
          {
@@ -184,6 +189,10 @@ void LinearForm::Assemble()
             boundary_integs[k]->AssembleRHSElementVect(*fes->GetBE(i),
                                                        *eltrans, elemvect);
 
+            if (doftrans)
+            {
+               doftrans->TransformDual(elemvect);
+            }
             AddElementVector (vdofs, elemvect);
          }
       }

fem/nonlininteg_vectorconvection.cpp

@@ -116,15 +116,15 @@ void VectorConvectionNLFIntegrator::AssemblePA(const FiniteElementSpace &fes)
 
 // PA Convection NL 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAConvectionNLApply2D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Array<double> &bt,
-                                  const Vector &q_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PAConvectionNLApply2D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Array<double> &bt,
+                           const Vector &q_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -252,15 +252,15 @@ static void PAConvectionNLApply2D(const int NE,
 
 // PA Convection NL 3D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAConvectionNLApply3D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Array<double> &bt,
-                                  const Vector &q_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PAConvectionNLApply3D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Array<double> &bt,
+                           const Vector &q_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
    constexpr int VDIM = 3;
    const int D1D = T_D1D ? T_D1D : d1d;
@@ -558,14 +558,14 @@ static void PAConvectionNLApply3D(const int NE,
 }
 
 template<int T_D1D = 0, int T_Q1D = 0, int T_MAX_D1D =0, int T_MAX_Q1D =0>
-static void SmemPAConvectionNLApply3D(const int NE,
-                                      const Array<double> &b_,
-                                      const Array<double> &g_,
-                                      const Vector &d_,
-                                      const Vector &x_,
-                                      Vector &y_,
-                                      const int d1d = 0,
-                                      const int q1d = 0)
+void SmemPAConvectionNLApply3D(const int NE,
+                               const Array<double> &b_,
+                               const Array<double> &g_,
+                               const Vector &d_,
+                               const Vector &x_,
+                               Vector &y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
 {
    constexpr int VDIM = 3;
    const int D1D = T_D1D ? T_D1D : d1d;

fem/pbilinearform.cpp

@@ -321,6 +321,7 @@ const
    {
       X.SetSpace(pfes);
       Y.SetSpace(pfes);
+      Ytmp.SetSize(pfes->GetTrueVSize());
    }
 
    X.Distribute(&x);
@@ -335,7 +336,8 @@ const
                   " implemented");
       mat->Mult(X, Y);
    }
-   pfes->Dof_TrueDof_Matrix()->MultTranspose(a, Y, 1.0, y);
+   pfes->GetProlongationMatrix()->MultTranspose(Y, Ytmp);
+   y.Add(a,Ytmp);
 }
 
 void ParBilinearForm::FormLinearSystem(

fem/pbilinearform.hpp

@@ -33,6 +33,7 @@ protected:
 
    /// Auxiliary objects used in TrueAddMult().
    mutable ParGridFunction X, Y;
+   mutable Vector Ytmp;
 
    OperatorHandle p_mat, p_mat_e;
 

fem/pfespace.cpp

@@ -128,6 +128,9 @@ void ParFiniteElementSpace::ParInit(ParMesh *pm)
    {
       ApplyLDofSigns(*elem_dof);
    }
+
+   // Check for shared trianglular faces with interior Nedelec DoFs
+   CheckNDSTriaDofs();
 }
 
 void ParFiniteElementSpace::Construct()
@@ -464,32 +467,53 @@ void ParFiniteElementSpace::ApplyLDofSigns(Table &el_dof) const
    ApplyLDofSigns(all_dofs);
 }
 
-void ParFiniteElementSpace::GetElementDofs(int i, Array<int> &dofs) const
+DofTransformation *
+ParFiniteElementSpace::GetElementDofs(int i, Array<int> &dofs) const
 {
    if (elem_dof)
    {
       elem_dof->GetRow(i, dofs);
-      return;
+
+      if (DoFTrans[mesh->GetElementBaseGeometry(i)])
+      {
+         Array<int> Fo;
+         elem_fos->GetRow(i, Fo);
+         DoFTrans[mesh->GetElementBaseGeometry(i)]->SetFaceOrientations(Fo);
+         return DoFTrans[mesh->GetElementBaseGeometry(i)];
+      }
+      return NULL;
    }
-   FiniteElementSpace::GetElementDofs(i, dofs);
+   DofTransformation * doftrans = FiniteElementSpace::GetElementDofs(i, dofs);
    if (Conforming())
    {
       ApplyLDofSigns(dofs);
    }
+   return doftrans;
 }
 
-void ParFiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
+DofTransformation *
+ParFiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
 {
    if (bdr_elem_dof)
    {
       bdr_elem_dof->GetRow(i, dofs);
-      return;
+
+      if (DoFTrans[mesh->GetBdrElementBaseGeometry(i)])
+      {
+         Array<int> Fo;
+         bdr_elem_fos -> GetRow (i, Fo);
+         DoFTrans[mesh->GetBdrElementBaseGeometry(i)]->SetFaceOrientations(Fo);
+         return DoFTrans[mesh->GetBdrElementBaseGeometry(i)];
+      }
+      return NULL;
    }
-   FiniteElementSpace::GetBdrElementDofs(i, dofs);
+   DofTransformation * doftrans =
+      FiniteElementSpace::GetBdrElementDofs(i, dofs);
    if (Conforming())
    {
       ApplyLDofSigns(dofs);
    }
+   return doftrans;
 }
 
 int ParFiniteElementSpace::GetFaceDofs(int i, Array<int> &dofs,
@@ -657,59 +681,266 @@ void ParFiniteElementSpace::GenerateGlobalOffsets() const
    }
 }
 
+void ParFiniteElementSpace::CheckNDSTriaDofs()
+{
+   // Check for Nedelec basis
+   bool nd_basis = dynamic_cast<const ND_FECollection*>(fec);
+   if (!nd_basis)
+   {
+      nd_strias = false;
+      return;
+   }
+
+   // Check for interior face dofs on triangles (the use of TETRAHEDRON
+   // is not an error)
+   bool nd_fdof  = fec->HasFaceDofs(Geometry::TETRAHEDRON,
+                                    GetMaxElementOrder());
+   if (!nd_fdof)
+   {
+      nd_strias = false;
+      return;
+   }
+
+   // Check for shared triangle faces
+   bool strias   = false;
+   {
+      int ngrps = pmesh->GetNGroups();
+      for (int g = 1; g < ngrps; g++)
+      {
+         strias |= pmesh->GroupNTriangles(g);
+      }
+   }
+
+   // Combine results
+   int loc_nd_strias = strias ? 1 : 0;
+   int glb_nd_strias = 0;
+   MPI_Allreduce(&loc_nd_strias, &glb_nd_strias, 1,
+                 MPI_INTEGER, MPI_SUM, MyComm);
+   nd_strias = glb_nd_strias > 0;
+}
+
 void ParFiniteElementSpace::Build_Dof_TrueDof_Matrix() const // matrix P
 {
    MFEM_ASSERT(Conforming(), "wrong code path");
 
    if (P) { return; }
 
-   int ldof  = GetVSize();
-   int ltdof = TrueVSize();
-
-   HYPRE_Int *i_diag = Memory<HYPRE_Int>(ldof+1);
-   HYPRE_Int *j_diag = Memory<HYPRE_Int>(ltdof);
-   int diag_counter;
-
-   HYPRE_Int *i_offd = Memory<HYPRE_Int>(ldof+1);
-   HYPRE_Int *j_offd = Memory<HYPRE_Int>(ldof-ltdof);
-   int offd_counter;
-
-   HYPRE_BigInt *cmap = Memory<HYPRE_BigInt>(ldof-ltdof);
-
-   HYPRE_BigInt *col_starts = GetTrueDofOffsets();
-   HYPRE_BigInt *row_starts = GetDofOffsets();
-
-   Array<Pair<HYPRE_BigInt, int> > cmap_j_offd(ldof-ltdof);
-
-   i_diag[0] = i_offd[0] = 0;
-   diag_counter = offd_counter = 0;
-   for (int i = 0; i < ldof; i++)
+   if (!nd_strias)
    {
-      int ltdof = GetLocalTDofNumber(i);
-      if (ltdof >= 0)
+      // Safe to assume 1-1 correspondence between shared dofs
+      int ldof  = GetVSize();
+      int ltdof = TrueVSize();
+
+      HYPRE_Int *i_diag = Memory<HYPRE_Int>(ldof+1);
+      HYPRE_Int *j_diag = Memory<HYPRE_Int>(ltdof);
+      int diag_counter;
+
+      HYPRE_Int *i_offd = Memory<HYPRE_Int>(ldof+1);
+      HYPRE_Int *j_offd = Memory<HYPRE_Int>(ldof-ltdof);
+      int offd_counter;
+
+      HYPRE_BigInt *cmap   = Memory<HYPRE_BigInt>(ldof-ltdof);
+
+      HYPRE_BigInt *col_starts = GetTrueDofOffsets();
+      HYPRE_BigInt *row_starts = GetDofOffsets();
+
+      Array<Pair<HYPRE_BigInt, int> > cmap_j_offd(ldof-ltdof);
+
+      i_diag[0] = i_offd[0] = 0;
+      diag_counter = offd_counter = 0;
+      for (int i = 0; i < ldof; i++)
       {
-         j_diag[diag_counter++] = ltdof;
+         int ltdof = GetLocalTDofNumber(i);
+         if (ltdof >= 0)
+         {
+            j_diag[diag_counter++] = ltdof;
+         }
+         else
+         {
+            cmap_j_offd[offd_counter].one = GetGlobalTDofNumber(i);
+            cmap_j_offd[offd_counter].two = offd_counter;
+            offd_counter++;
+         }
+         i_diag[i+1] = diag_counter;
+         i_offd[i+1] = offd_counter;
       }
-      else
+
+      SortPairs<HYPRE_BigInt, int>(cmap_j_offd, offd_counter);
+
+      for (int i = 0; i < offd_counter; i++)
       {
-         cmap_j_offd[offd_counter].one = GetGlobalTDofNumber(i);
-         cmap_j_offd[offd_counter].two = offd_counter;
-         offd_counter++;
+         cmap[i] = cmap_j_offd[i].one;
+         j_offd[cmap_j_offd[i].two] = i;
       }
-      i_diag[i+1] = diag_counter;
-      i_offd[i+1] = offd_counter;
+
+      P = new HypreParMatrix(MyComm, MyRank, NRanks, row_starts, col_starts,
+                             i_diag, j_diag, i_offd, j_offd,
+                             cmap, offd_counter);
    }
-
-   SortPairs<HYPRE_BigInt, int>(cmap_j_offd, offd_counter);
-
-   for (int i = 0; i < offd_counter; i++)
+   else
    {
-      cmap[i] = cmap_j_offd[i].one;
-      j_offd[cmap_j_offd[i].two] = i;
-   }
+      // Some shared dofs will be linear combinations of others
+      int ldof  = GetVSize();
+      int ltdof = TrueVSize();
 
-   P = new HypreParMatrix(MyComm, MyRank, NRanks, row_starts, col_starts,
-                          i_diag, j_diag, i_offd, j_offd, cmap, offd_counter);
+      HYPRE_Int gdof  = -1;
+      HYPRE_Int gtdof = -1;
+
+      MPI_Allreduce(&ldof, &gdof, 1, HYPRE_MPI_INT, MPI_SUM, MyComm);
+      MPI_Allreduce(&ltdof, &gtdof, 1, HYPRE_MPI_INT, MPI_SUM, MyComm);
+
+      // Ensure face orientations have been communicated
+      pmesh->ExchangeFaceNbrData();
+
+      // Locate and count non-zeros in off-diagonal portion of P
+      int nnz_offd = 0;
+      Array<int> ldsize(ldof); ldsize = 0;
+      Array<int> ltori(ldof);  ltori = 0; // Local triangle orientations
+      {
+         int ngrps = pmesh->GetNGroups();
+         int nedofs = fec->DofForGeometry(Geometry::SEGMENT);
+         Array<int> sdofs;
+         for (int g = 1; g < ngrps; g++)
+         {
+            if (pmesh->gtopo.IAmMaster(g))
+            {
+               continue;
+            }
+            for (int ei=0; ei<pmesh->GroupNEdges(g); ei++)
+            {
+               this->GetSharedEdgeDofs(g, ei, sdofs);
+               for (int i=0; i<sdofs.Size(); i++)
+               {
+                  int ind = (sdofs[i]>=0) ? sdofs[i] : (-sdofs[i]-1);
+                  if (ldsize[ind] == 0) { nnz_offd++; }
+                  ldsize[ind] = 1;
+               }
+            }
+            for (int fi=0; fi<pmesh->GroupNTriangles(g); fi++)
+            {
+               int face, ori, info1, info2;
+               pmesh->GroupTriangle(g, fi, face, ori);
+               pmesh->GetFaceInfos(face, &info1, &info2);
+               this->GetSharedTriangleDofs(g, fi, sdofs);
+               for (int i=0; i<3*nedofs; i++)
+               {
+                  int ind = (sdofs[i]>=0) ? sdofs[i] : (-sdofs[i]-1);
+                  if (ldsize[ind] == 0) { nnz_offd++; }
+                  ldsize[ind] = 1;
+               }
+               for (int i=3*nedofs; i<sdofs.Size(); i++)
+               {
+                  if (ldsize[sdofs[i]] == 0) { nnz_offd += 2; }
+                  ldsize[sdofs[i]] = 2;
+                  ltori[sdofs[i]]  = info2 % 64;
+               }
+            }
+            for (int fi=0; fi<pmesh->GroupNQuadrilaterals(g); fi++)
+            {
+               this->GetSharedQuadrilateralDofs(g, fi, sdofs);
+               for (int i=0; i<sdofs.Size(); i++)
+               {
+                  int ind = (sdofs[i]>=0) ? sdofs[i] : (-sdofs[i]-1);
+                  if (ldsize[ind] == 0) { nnz_offd++; }
+                  ldsize[ind] = 1;
+               }
+            }
+         }
+      }
+
+      HYPRE_Int *i_diag = new HYPRE_Int[ldof+1];
+      HYPRE_Int *j_diag = new HYPRE_Int[ltdof];
+      double    *d_diag = new double[ltdof];
+      int diag_counter;
+
+      HYPRE_Int *i_offd = new HYPRE_Int[ldof+1];
+      HYPRE_Int *j_offd = new HYPRE_Int[nnz_offd];
+      double    *d_offd = new double[nnz_offd];
+      int offd_counter;
+
+      HYPRE_BigInt *cmap   = new HYPRE_BigInt[ldof-ltdof];
+
+      HYPRE_BigInt *col_starts = GetTrueDofOffsets();
+      HYPRE_BigInt *row_starts = GetDofOffsets();
+
+      Array<Pair<HYPRE_BigInt, int> > cmap_j_offd(ldof-ltdof);
+
+      i_diag[0] = i_offd[0] = 0;
+      diag_counter = offd_counter = 0;
+      int offd_col_counter = 0;
+      for (int i = 0; i < ldof; i++)
+      {
+         int ltdof = GetLocalTDofNumber(i);
+         if (ltdof >= 0)
+         {
+            j_diag[diag_counter]   = ltdof;
+            d_diag[diag_counter++] = 1.0;
+         }
+         else
+         {
+            if (ldsize[i] == 1)
+            {
+               cmap_j_offd[offd_col_counter].one = GetGlobalTDofNumber(i);
+               cmap_j_offd[offd_col_counter].two = offd_counter;
+               offd_counter++;
+               offd_col_counter++;
+            }
+            else
+            {
+               cmap_j_offd[offd_col_counter].one = GetGlobalTDofNumber(i);
+               cmap_j_offd[offd_col_counter].two = offd_counter;
+               offd_counter += 2;
+               offd_col_counter++;
+               i_diag[i+1] = diag_counter;
+               i_offd[i+1] = offd_counter;
+               i++;
+               cmap_j_offd[offd_col_counter].one = GetGlobalTDofNumber(i);
+               cmap_j_offd[offd_col_counter].two = offd_counter;
+               offd_counter += 2;
+               offd_col_counter++;
+            }
+         }
+         i_diag[i+1] = diag_counter;
+         i_offd[i+1] = offd_counter;
+      }
+
+      SortPairs<HYPRE_BigInt, int>(cmap_j_offd, offd_col_counter);
+
+      for (int i = 0; i < nnz_offd; i++)
+      {
+         j_offd[i] = -1;
+         d_offd[i] = 0.0;
+      }
+
+      for (int i = 0; i < offd_col_counter; i++)
+      {
+         cmap[i] = cmap_j_offd[i].one;
+         j_offd[cmap_j_offd[i].two] = i;
+      }
+
+      for (int i = 0; i < ldof; i++)
+      {
+         if (i_offd[i+1] == i_offd[i] + 1)
+         {
+            d_offd[i_offd[i]] = 1.0;
+         }
+         else if (i_offd[i+1] == i_offd[i] + 2)
+         {
+            const double * T = ND_DofTransformation
+                               ::GetFaceTransform(ltori[i]).GetData();
+            j_offd[i_offd[i] + 1] = j_offd[i_offd[i]] + 1;
+            d_offd[i_offd[i]] = T[0]; d_offd[i_offd[i] + 1] = T[2];
+            i++;
+            j_offd[i_offd[i] + 1] = j_offd[i_offd[i]];
+            j_offd[i_offd[i]] = j_offd[i_offd[i] + 1] - 1;
+            d_offd[i_offd[i]] = T[1]; d_offd[i_offd[i] + 1] = T[3];
+         }
+      }
+
+      P = new HypreParMatrix(MyComm, gdof, gtdof, row_starts, col_starts,
+                             i_diag, j_diag, d_diag, i_offd, j_offd, d_offd,
+                             offd_col_counter, cmap);
+   }
 
    SparseMatrix Pdiag;
    P->GetDiag(Pdiag);
@@ -913,6 +1144,8 @@ const Operator *ParFiniteElementSpace::GetProlongationMatrix() const
    {
       if (Pconf) { return Pconf; }
 
+      if (nd_strias) { return Dof_TrueDof_Matrix(); }
+
       if (NRanks == 1)
       {
          Pconf = new IdentityOperator(GetTrueVSize());
@@ -1216,10 +1449,29 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
    delete [] requests;
 }
 
-void ParFiniteElementSpace::GetFaceNbrElementVDofs(
+DofTransformation *ParFiniteElementSpace::GetFaceNbrElementVDofs(
    int i, Array<int> &vdofs) const
 {
    face_nbr_element_dof.GetRow(i, vdofs);
+
+   DofTransformation *doftrans = NULL;
+   Geometry::Type geom = GetFaceNbrFE(i)->GetGeomType();
+   if (DoFTrans[geom])
+   {
+      Array<int> F, Fo;
+      pmesh->GetFaceNbrElementFaces(pmesh->GetNE() + i, F, Fo);
+      doftrans = DoFTrans[geom];
+      doftrans->SetFaceOrientations(Fo);
+   }
+   if (vdim == 1 || doftrans == NULL)
+   {
+      return doftrans;
+   }
+   else
+   {
+      VDoFTrans.SetDofTransformation(*doftrans);
+      return &VDoFTrans;
+   }
 }
 
 void ParFiniteElementSpace::GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const
@@ -1278,12 +1530,17 @@ const FiniteElement *ParFiniteElementSpace::GetFaceNbrFaceFE(int i) const
 
 void ParFiniteElementSpace::Lose_Dof_TrueDof_Matrix()
 {
+   P -> StealData();
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrix *csrP = (hypre_ParCSRMatrix*)(*P);
    hypre_ParCSRMatrixOwnsRowStarts(csrP) = 1;
    hypre_ParCSRMatrixOwnsColStarts(csrP) = 1;
-   P -> StealData();
    dof_offsets.LoseData();
    tdof_offsets.LoseData();
+#else
+   dof_offsets.DeleteAll();
+   tdof_offsets.DeleteAll();
+#endif
 }
 
 void ParFiniteElementSpace::ConstructTrueDofs()
@@ -2526,7 +2783,8 @@ static int_type* make_j_array(int_type* I, int nrows)
 
 HypreParMatrix*
 ParFiniteElementSpace::RebalanceMatrix(int old_ndofs,
-                                       const Table* old_elem_dof)
+                                       const Table* old_elem_dof,
+                                       const Table* old_elem_fos)
 {
    MFEM_VERIFY(Nonconforming(), "Only supported for nonconforming meshes.");
    MFEM_VERIFY(old_dof_offsets.Size(), "ParFiniteElementSpace::Update needs to "
@@ -2651,7 +2909,8 @@ struct DerefDofMessage
 
 HypreParMatrix*
 ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
-                                                  const Table* old_elem_dof)
+                                                  const Table* old_elem_dof,
+                                                  const Table *old_elem_fos)
 {
    int nrk = HYPRE_AssumedPartitionCheck() ? 2 : NRanks;
 
@@ -3007,13 +3266,16 @@ void ParFiniteElementSpace::Update(bool want_transform)
    }
 
    Table* old_elem_dof = NULL;
+   Table* old_elem_fos = NULL;
    int old_ndofs;
 
    // save old DOF table
    if (want_transform)
    {
       old_elem_dof = elem_dof;
+      old_elem_fos = elem_fos;
       elem_dof = NULL;
+      elem_fos = NULL;
       old_ndofs = ndofs;
       Swap(dof_offsets, old_dof_offsets);
    }
@@ -3035,22 +3297,25 @@ void ParFiniteElementSpace::Update(bool want_transform)
          {
             if (Th.Type() != Operator::MFEM_SPARSEMAT)
             {
-               Th.Reset(new RefinementOperator(this, old_elem_dof, old_ndofs));
+               Th.Reset(new RefinementOperator(this, old_elem_dof,
+                                               old_elem_fos, old_ndofs));
                // The RefinementOperator takes ownership of 'old_elem_dofs', so
                // we no longer own it:
                old_elem_dof = NULL;
+               old_elem_fos = NULL;
             }
             else
             {
                // calculate fully assembled matrix
-               Th.Reset(RefinementMatrix(old_ndofs, old_elem_dof));
+               Th.Reset(RefinementMatrix(old_ndofs, old_elem_dof, old_elem_fos));
             }
             break;
          }
 
          case Mesh::DEREFINE:
          {
-            Th.Reset(ParallelDerefinementMatrix(old_ndofs, old_elem_dof));
+            Th.Reset(ParallelDerefinementMatrix(old_ndofs, old_elem_dof,
+                                                old_elem_fos));
             if (Nonconforming())
             {
                Th.SetOperatorOwner(false);
@@ -3062,7 +3327,7 @@ void ParFiniteElementSpace::Update(bool want_transform)
 
          case Mesh::REBALANCE:
          {
-            Th.Reset(RebalanceMatrix(old_ndofs, old_elem_dof));
+            Th.Reset(RebalanceMatrix(old_ndofs, old_elem_dof, old_elem_fos));
             break;
          }
 
@@ -3071,6 +3336,7 @@ void ParFiniteElementSpace::Update(bool want_transform)
       }
 
       delete old_elem_dof;
+      delete old_elem_fos;
    }
 }
 

fem/pfespace.hpp

@@ -87,6 +87,12 @@ private:
        this is a TransposeOperator wrapping R. */
    mutable Operator *R_transpose;
 
+   /// Flag indicating the existence of shared triangles with interior ND dofs
+   bool nd_strias;
+
+   /// Resets nd_strias flag at constuction or after rebalancing
+   void CheckNDSTriaDofs();
+
    ParNURBSExtension *pNURBSext() const
    { return dynamic_cast<ParNURBSExtension *>(NURBSext); }
 
@@ -174,14 +180,16 @@ private:
        The result is a parallel permutation matrix that can be used to update
        all grid functions defined on this space. */
    HypreParMatrix* RebalanceMatrix(int old_ndofs,
-                                   const Table* old_elem_dof);
+                                   const Table* old_elem_dof,
+                                   const Table* old_elem_fos);
 
    /** Calculate a GridFunction restriction matrix after mesh derefinement.
        The matrix is constructed so that the new grid function interpolates
        the original function, i.e., the original function is evaluated at the
        nodes of the coarse function. */
    HypreParMatrix* ParallelDerefinementMatrix(int old_ndofs,
-                                              const Table *old_elem_dof);
+                                              const Table *old_elem_dof,
+                                              const Table *old_elem_fos);
 
    /// Updates the internal mesh pointer. @warning @a new_mesh must be
    /// <b>topologically identical</b> to the existing mesh. Used if the address
@@ -202,6 +210,8 @@ public:
    int num_face_nbr_dofs;
    // Face-neighbor-element to face-neighbor dof
    Table face_nbr_element_dof;
+   // Face-neighbor-element face orientations
+   Table face_nbr_element_fos;
    // Face-neighbor to ldof in the face-neighbor numbering
    Table face_nbr_ldof;
    // The global ldof indices of the face-neighbor dofs
@@ -279,10 +289,10 @@ public:
    virtual int GetTrueVSize() const { return ltdof_size; }
 
    /// Returns indexes of degrees of freedom in array dofs for i'th element.
-   virtual void GetElementDofs(int i, Array<int> &dofs) const;
+   virtual DofTransformation *GetElementDofs(int i, Array<int> &dofs) const;
 
    /// Returns indexes of degrees of freedom for i'th boundary element.
-   virtual void GetBdrElementDofs(int i, Array<int> &dofs) const;
+   virtual DofTransformation *GetBdrElementDofs(int i, Array<int> &dofs) const;
 
    /** Returns the indexes of the degrees of freedom for i'th face
        including the dofs for the edges and the vertices of the face. */
@@ -382,7 +392,7 @@ public:
    // Face-neighbor functions
    void ExchangeFaceNbrData();
    int GetFaceNbrVSize() const { return num_face_nbr_dofs; }
-   void GetFaceNbrElementVDofs(int i, Array<int> &vdofs) const;
+   DofTransformation *GetFaceNbrElementVDofs(int i, Array<int> &vdofs) const;
    void GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const;
    const FiniteElement *GetFaceNbrFE(int i) const;
    const FiniteElement *GetFaceNbrFaceFE(int i) const;
@@ -397,6 +407,8 @@ public:
    bool Conforming() const { return pmesh->pncmesh == NULL && !nonconf_P; }
    bool Nonconforming() const { return pmesh->pncmesh != NULL || nonconf_P; }
 
+   bool SharedNDTriangleDofs() const { return nd_strias; }
+
    // Transfer parallel true-dof data from coarse_fes, defined on a coarse mesh,
    // to this FE space, defined on a refined mesh. See full documentation in the
    // base class, FiniteElementSpace::GetTrueTransferOperator.

fem/pgridfunc.cpp

@@ -325,9 +325,14 @@ void ParGridFunction::GetVectorValue(int i, const IntegrationPoint &ip,
    if (nbr_el_no >= 0)
    {
       Array<int> dofs;
-      pfes->GetFaceNbrElementVDofs(nbr_el_no, dofs);
+      DofTransformation * doftrans = pfes->GetFaceNbrElementVDofs(nbr_el_no,
+                                                                  dofs);
       Vector loc_data;
       face_nbr_data.GetSubVector(dofs, loc_data);
+      if (doftrans)
+      {
+         doftrans->InvTransformPrimal(loc_data);
+      }
       const FiniteElement *FElem = pfes->GetFaceNbrFE(nbr_el_no);
       int dof = FElem->GetDof();
       if (FElem->GetRangeType() == FiniteElement::SCALAR)
@@ -437,12 +442,17 @@ void ParGridFunction::GetVectorValue(ElementTransformation &T,
    }
 
    Array<int> vdofs;
-   pfes->GetFaceNbrElementVDofs(nbr_el_no, vdofs);
+   DofTransformation * doftrans = pfes->GetFaceNbrElementVDofs(nbr_el_no,
+                                                               vdofs);
    const FiniteElement *fe = pfes->GetFaceNbrFE(nbr_el_no);
 
    int dof = fe->GetDof();
    Vector loc_data;
    face_nbr_data.GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
    if (fe->GetRangeType() == FiniteElement::SCALAR)
    {
       Vector shape(dof);

fem/qinterp/det.cpp

@@ -27,14 +27,14 @@ namespace quadrature_interpolator
 {
 
 template<int T_D1D = 0, int T_Q1D = 0, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Det2D(const int NE,
-                  const double *b,
-                  const double *g,
-                  const double *x,
-                  double *y,
-                  const int vdim = 1,
-                  const int d1d = 0,
-                  const int q1d = 0)
+void Det2D(const int NE,
+           const double *b,
+           const double *g,
+           const double *x,
+           double *y,
+           const int vdim = 1,
+           const int d1d = 0,
+           const int q1d = 0)
 {
    constexpr int DIM = 2;
    static constexpr int NBZ = 1;
@@ -79,15 +79,15 @@ static void Det2D(const int NE,
 
 template<int T_D1D = 0, int T_Q1D = 0, int MAX_D1D = 0, int MAX_Q1D = 0,
          bool SMEM = true>
-static void Det3D(const int NE,
-                  const double *b,
-                  const double *g,
-                  const double *x,
-                  double *y,
-                  const int vdim = 1,
-                  const int d1d = 0,
-                  const int q1d = 0,
-                  Vector *d_buff = nullptr) // used only with SMEM = false
+void Det3D(const int NE,
+           const double *b,
+           const double *g,
+           const double *x,
+           double *y,
+           const int vdim = 1,
+           const int d1d = 0,
+           const int q1d = 0,
+           Vector *d_buff = nullptr) // used only with SMEM = false
 {
    constexpr int DIM = 3;
    static constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;

fem/qinterp/eval.hpp

@@ -31,13 +31,13 @@ namespace quadrature_interpolator
 template<QVectorLayout Q_LAYOUT,
          int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
          int T_NBZ = 1, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Values2D(const int NE,
-                     const double *b_,
-                     const double *x_,
-                     double *y_,
-                     const int vdim = 0,
-                     const int d1d = 0,
-                     const int q1d = 0)
+void Values2D(const int NE,
+              const double *b_,
+              const double *x_,
+              double *y_,
+              const int vdim = 0,
+              const int d1d = 0,
+              const int q1d = 0)
 {
    static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
 
@@ -95,13 +95,13 @@ static void Values2D(const int NE,
 template<QVectorLayout Q_LAYOUT,
          int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
          int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Values3D(const int NE,
-                     const double *b_,
-                     const double *x_,
-                     double *y_,
-                     const int vdim = 0,
-                     const int d1d = 0,
-                     const int q1d = 0)
+void Values3D(const int NE,
+              const double *b_,
+              const double *x_,
+              double *y_,
+              const int vdim = 0,
+              const int d1d = 0,
+              const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/qinterp/grad.hpp

@@ -31,15 +31,15 @@ namespace quadrature_interpolator
 template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS,
          int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
          int T_NBZ = 1, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Derivatives2D(const int NE,
-                          const double *b_,
-                          const double *g_,
-                          const double *j_,
-                          const double *x_,
-                          double *y_,
-                          const int vdim = 0,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void Derivatives2D(const int NE,
+                   const double *b_,
+                   const double *g_,
+                   const double *j_,
+                   const double *x_,
+                   double *y_,
+                   const int vdim = 0,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -139,15 +139,15 @@ static void Derivatives2D(const int NE,
 template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS,
          int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
          int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Derivatives3D(const int NE,
-                          const double *b_,
-                          const double *g_,
-                          const double *j_,
-                          const double *x_,
-                          double *y_,
-                          const int vdim = 0,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void Derivatives3D(const int NE,
+                   const double *b_,
+                   const double *g_,
+                   const double *j_,
+                   const double *x_,
+                   double *y_,
+                   const int vdim = 0,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;

fem/quadinterpolator.cpp

@@ -61,16 +61,16 @@ namespace quadrature_interpolator
 // * assumes 'e_vec' is using ElementDofOrdering::NATIVE,
 // * assumes 'maps.mode == FULL'.
 template<const int T_VDIM, const int T_ND, const int T_NQ>
-static void Eval2D(const int NE,
-                   const int vdim,
-                   const QVectorLayout q_layout,
-                   const GeometricFactors *geom,
-                   const DofToQuad &maps,
-                   const Vector &e_vec,
-                   Vector &q_val,
-                   Vector &q_der,
-                   Vector &q_det,
-                   const int eval_flags)
+void Eval2D(const int NE,
+            const int vdim,
+            const QVectorLayout q_layout,
+            const GeometricFactors *geom,
+            const DofToQuad &maps,
+            const Vector &e_vec,
+            Vector &q_val,
+            Vector &q_der,
+            Vector &q_det,
+            const int eval_flags)
 {
    using QI = QuadratureInterpolator;
 
@@ -209,16 +209,16 @@ static void Eval2D(const int NE,
 // * assumes 'e_vec' is using ElementDofOrdering::NATIVE,
 // * assumes 'maps.mode == FULL'.
 template<const int T_VDIM, const int T_ND, const int T_NQ>
-static void Eval3D(const int NE,
-                   const int vdim,
-                   const QVectorLayout q_layout,
-                   const GeometricFactors *geom,
-                   const DofToQuad &maps,
-                   const Vector &e_vec,
-                   Vector &q_val,
-                   Vector &q_der,
-                   Vector &q_det,
-                   const int eval_flags)
+void Eval3D(const int NE,
+            const int vdim,
+            const QVectorLayout q_layout,
+            const GeometricFactors *geom,
+            const DofToQuad &maps,
+            const Vector &e_vec,
+            Vector &q_val,
+            Vector &q_der,
+            Vector &q_det,
+            const int eval_flags)
 {
    using QI = QuadratureInterpolator;
 

fem/tmop.cpp

@@ -1306,7 +1306,7 @@ namespace internal
 // MFEM_FORALL-based copy kernel -- used by protected methods below.
 // Needed as a workaround for the nvcc restriction that methods with MFEM_FORALL
 // in them must to be public.
-static inline void device_copy(double *d_dest, const double *d_src, int size)
+inline void device_copy(double *d_dest, const double *d_src, int size)
 {
    MFEM_FORALL(i, size, d_dest[i] = d_src[i];);
 }

fem/tmop_amr.cpp

@@ -234,7 +234,7 @@ void TMOPRefinerEstimator::SetTriIntRules()
 
    // Reftype = 0 // original element
    const int Nvert = 3, NEsplit = 1;
-   Mesh meshsplit(2, Nvert, NEsplit, 0 ,2);
+   Mesh meshsplit(2, Nvert, NEsplit, 0,2);
    const double tri_v[3][2] =
    {
       {0, 0}, {1, 0}, {0, 1}

fem/transfer.cpp

@@ -175,7 +175,8 @@ const Operator &InterpolationGridTransfer::ForwardOperator()
                                             localP[elem_geoms[i]]);
       }
       F.Reset(ran_fes.RefinementMatrix_main(
-                 dom_fes.GetNDofs(), dom_fes.GetElementToDofTable(), localP));
+                 dom_fes.GetNDofs(), dom_fes.GetElementToDofTable(),
+                 dom_fes.GetElementToFaceOrientationTable(), localP));
    }
    else
    {

general/annotation.hpp

@@ -21,12 +21,16 @@
 #define MFEM_PERF_FUNCTION CALI_CXX_MARK_FUNCTION
 #define MFEM_PERF_BEGIN(s) CALI_MARK_BEGIN(s)
 #define MFEM_PERF_END(s) CALI_MARK_END(s)
+#define MFEM_PERF_SCOPE(name) \
+  cali::Annotation::Guard cali_autogenerated_guard_name(cali::Annotation("function").begin(std::string(name).c_str()))
+
 
 #else
 
 #define MFEM_PERF_FUNCTION
 #define MFEM_PERF_BEGIN(s)
 #define MFEM_PERF_END(s)
+#define MFEM_PERF_SCOPE(name)
 
 #endif
 

general/error.hpp

@@ -164,7 +164,13 @@ __device__ void abort_msg(T & msg)
 #endif
 
 // Abort inside a device kernel
-#if defined(__CUDA_ARCH__)
+#if defined(__CUDA_ARCH__) && defined(_WIN32)
+#define MFEM_ABORT_KERNEL(msg) \
+   {                           \
+      printf(msg);             \
+      __debugbreak();          \
+   }
+#elif defined(__CUDA_ARCH__)
 #define MFEM_ABORT_KERNEL(msg) \
    {                           \
       printf(msg);             \

general/forall.hpp

@@ -13,6 +13,7 @@
 #define MFEM_FORALL_HPP
 
 #include "../config/config.hpp"
+#include "annotation.hpp"
 #include "error.hpp"
 #include "backends.hpp"
 #include "device.hpp"

general/isockstream.cpp

@@ -79,7 +79,13 @@ int isockstream::establish()
    int on=1;
    setsockopt(port, SOL_SOCKET, SO_REUSEADDR, (char *)(&on), sizeof(on));
 
-   if (bind(port,(const sockaddr*)&sa,(socklen_t)sizeof(struct sockaddr_in)) < 0)
+   if (bind(
+#ifdef _WIN32
+          (SOCKET)port
+#else
+          port
+#endif
+          ,(const sockaddr*)&sa,(socklen_t)sizeof(struct sockaddr_in)) < 0)
    {
       mfem::err << "isockstream::establish(): bind() failed!" << endl;
       close(port);

general/stable3d.cpp

@@ -118,6 +118,11 @@ int STable3D::Index (int r, int c, int f) const
 {
    STable3DNode *node;
 
+   if (r >= Size)
+   {
+      return -1;
+   }
+
    Sort3 (r, c, f);
 
    for (node = Rows[r]; node != NULL; node = node->Prev)

linalg/complex_operator.cpp

@@ -787,10 +787,16 @@ HypreParMatrix * ComplexHypreParMatrix::GetSystemMatrix() const
                                            2 * num_cols_offd, cmap,
                                            true);
 
+#if MFEM_HYPRE_VERSION <= 22200
    // Give the new matrix ownership of row_starts and col_starts
    hypre_ParCSRMatrix *hA = (hypre_ParCSRMatrix*)(*A);
+
    hypre_ParCSRMatrixSetRowStartsOwner(hA,1);
    hypre_ParCSRMatrixSetColStartsOwner(hA,1);
+#else
+   mfem_hypre_TFree_host(row_starts);
+   mfem_hypre_TFree_host(col_starts);
+#endif
 
    return A;
 }

linalg/densemat.hpp

@@ -763,6 +763,13 @@ public:
       tdata.New(i*j*k);
    }
 
+   DenseTensor(double *d, int i, int j, int k)
+      : Mk(NULL, i, j)
+   {
+      nk = k;
+      tdata.Wrap(d, i*j*k, false);
+   }
+
    DenseTensor(int i, int j, int k, MemoryType mt)
       : Mk(NULL, i, j)
    {

linalg/hypre.cpp

@@ -88,7 +88,9 @@ HypreParVector::HypreParVector(MPI_Comm comm, HYPRE_BigInt glob_size,
 {
    x = hypre_ParVectorCreate(comm,glob_size,col);
    hypre_ParVectorInitialize(x);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParVectorSetPartitioningOwner(x,0);
+#endif
    // The data will be destroyed by hypre (this is the default)
    hypre_ParVectorSetDataOwner(x,1);
    hypre_SeqVectorSetDataOwner(hypre_ParVectorLocalVector(x),1);
@@ -105,7 +107,9 @@ HypreParVector::HypreParVector(MPI_Comm comm, HYPRE_BigInt glob_size,
    hypre_ParVectorSetDataOwner(x,1); // owns the seq vector
    hypre_Vector *x_loc = hypre_ParVectorLocalVector(x);
    hypre_SeqVectorSetDataOwner(x_loc,0);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParVectorSetPartitioningOwner(x,0);
+#endif
    double tmp = 0.0;
    hypre_VectorData(x_loc) = &tmp;
 #ifdef HYPRE_USING_CUDA
@@ -128,7 +132,9 @@ HypreParVector::HypreParVector(const HypreParVector &y) : Vector()
    x = hypre_ParVectorCreate(y.x -> comm, y.x -> global_size,
                              y.x -> partitioning);
    hypre_ParVectorInitialize(x);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParVectorSetPartitioningOwner(x,0);
+#endif
    hypre_ParVectorSetDataOwner(x,1);
    hypre_SeqVectorSetDataOwner(hypre_ParVectorLocalVector(x),1);
    _SetDataAndSize_();
@@ -162,7 +168,9 @@ HypreParVector::HypreParVector(ParFiniteElementSpace *pfes)
    x = hypre_ParVectorCreate(pfes->GetComm(), pfes->GlobalTrueVSize(),
                              pfes->GetTrueDofOffsets());
    hypre_ParVectorInitialize(x);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParVectorSetPartitioningOwner(x,0);
+#endif
    // The data will be destroyed by hypre (this is the default)
    hypre_ParVectorSetDataOwner(x,1);
    hypre_SeqVectorSetDataOwner(hypre_ParVectorLocalVector(x),1);
@@ -683,8 +691,10 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm, HYPRE_BigInt glob_size,
    A = hypre_ParCSRMatrixCreate(comm, glob_size, glob_size, row_starts,
                                 row_starts, 0, diag->NumNonZeroElems(), 0);
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    hypre_CSRMatrixSetDataOwner(A->diag,0);
    diagOwner = CopyCSR(diag, mem_diag, A->diag, false);
@@ -726,8 +736,10 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm,
                                 row_starts, col_starts,
                                 0, diag->NumNonZeroElems(), 0);
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    hypre_CSRMatrixSetDataOwner(A->diag,0);
    diagOwner = CopyCSR(diag, mem_diag, A->diag, false);
@@ -770,8 +782,10 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm,
                                 offd->Width(), diag->NumNonZeroElems(),
                                 offd->NumNonZeroElems());
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    hypre_CSRMatrixSetDataOwner(A->diag,0);
    diagOwner = CopyCSR(diag, mem_diag, A->diag, own_diag_offd);
@@ -817,8 +831,10 @@ HypreParMatrix::HypreParMatrix(
    A = hypre_ParCSRMatrixCreate(comm, global_num_rows, global_num_cols,
                                 row_starts, col_starts, offd_num_cols, 0, 0);
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    HYPRE_Int local_num_rows = hypre_CSRMatrixNumRows(A->diag);
 
@@ -931,8 +947,10 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm,
    A = hypre_ParCSRMatrixCreate(comm, global_num_rows, global_num_cols,
                                 row_starts, col_starts, 0, nnz, 0);
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    hypre_CSRMatrixSetDataOwner(A->diag,0);
    diagOwner = CopyBoolCSR(diag, mem_diag, A->diag);
@@ -989,8 +1007,10 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm, int id, int np,
    }
 
    hypre_ParCSRMatrixSetDataOwner(A,1);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(A,0);
    hypre_ParCSRMatrixSetColStartsOwner(A,0);
+#endif
 
    mem_diag.data.New(diag_nnz);
    for (HYPRE_Int i = 0; i < diag_nnz; i++)
@@ -1177,6 +1197,13 @@ HypreParMatrix::HypreParMatrix(MPI_Comm comm, int nrows,
    {
       hypre_CSRMatrixReorder(hypre_ParCSRMatrixDiag(A));
    }
+#if MFEM_HYPRE_VERSION > 22200
+   mfem_hypre_TFree_host(row_starts);
+   if (rows != cols)
+   {
+      mfem_hypre_TFree_host(col_starts);
+   }
+#endif
    hypre_MatvecCommPkgCreate(A);
 
    height = GetNumRows();
@@ -1263,6 +1290,7 @@ void HypreParMatrix::SetOwnerFlags(signed char diag, signed char offd,
 
 void HypreParMatrix::CopyRowStarts()
 {
+#if MFEM_HYPRE_VERSION <= 22200
    if (!A || hypre_ParCSRMatrixOwnsRowStarts(A) ||
        (hypre_ParCSRMatrixRowStarts(A) == hypre_ParCSRMatrixColStarts(A) &&
         hypre_ParCSRMatrixOwnsColStarts(A)))
@@ -1297,10 +1325,12 @@ void HypreParMatrix::CopyRowStarts()
       hypre_ParCSRMatrixColStarts(A) = new_row_starts;
       hypre_ParCSRMatrixOwnsColStarts(A) = 0;
    }
+#endif
 }
 
 void HypreParMatrix::CopyColStarts()
 {
+#if MFEM_HYPRE_VERSION <= 22200
    if (!A || hypre_ParCSRMatrixOwnsColStarts(A) ||
        (hypre_ParCSRMatrixRowStarts(A) == hypre_ParCSRMatrixColStarts(A) &&
         hypre_ParCSRMatrixOwnsRowStarts(A)))
@@ -1339,6 +1369,7 @@ void HypreParMatrix::CopyColStarts()
    {
       hypre_ParCSRMatrixOwnsColStarts(A) = 1;
    }
+#endif
 }
 
 void HypreParMatrix::GetDiag(Vector &diag) const
@@ -1791,9 +1822,14 @@ HypreParMatrix* HypreParMatrix::LeftDiagMult(const SparseMatrix &D,
                          DA_diag, DA_offd, new_col_map_offd,
                          own_diag_offd);
 
+#if MFEM_HYPRE_VERSION <= 22200
    // Give ownership of row_starts, col_starts, and col_map_offd to DA
    hypre_ParCSRMatrixSetRowStartsOwner(DA->A, 1);
    hypre_ParCSRMatrixSetColStartsOwner(DA->A, 1);
+#else
+   mfem_hypre_TFree_host(new_row_starts);
+   mfem_hypre_TFree_host(new_col_starts);
+#endif
    DA->colMapOwner = 1;
 
    return DA;
@@ -1948,18 +1984,22 @@ void HypreParMatrix::Threshold(double threshold)
    row_starts = hypre_ParCSRMatrixRowStarts(A);
    col_starts = hypre_ParCSRMatrixColStarts(A);
 
+#if MFEM_HYPRE_VERSION <= 22200
    bool old_owns_row = hypre_ParCSRMatrixOwnsRowStarts(A);
    bool old_owns_col = hypre_ParCSRMatrixOwnsColStarts(A);
+#endif
    HYPRE_BigInt global_num_rows = hypre_ParCSRMatrixGlobalNumRows(A);
    HYPRE_BigInt global_num_cols = hypre_ParCSRMatrixGlobalNumCols(A);
    parcsr_A_ptr = hypre_ParCSRMatrixCreate(comm, global_num_rows,
                                            global_num_cols,
                                            row_starts, col_starts,
                                            0, 0, 0);
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixOwnsRowStarts(parcsr_A_ptr) = old_owns_row;
    hypre_ParCSRMatrixOwnsColStarts(parcsr_A_ptr) = old_owns_col;
    hypre_ParCSRMatrixOwnsRowStarts(A) = 0;
    hypre_ParCSRMatrixOwnsColStarts(A) = 0;
+#endif
 
    csr_A = hypre_MergeDiagAndOffd(A);
 
@@ -1994,7 +2034,12 @@ void HypreParMatrix::Threshold(double threshold)
 
    hypre_ParCSRMatrixSetNumNonzeros(A);
    /* Make sure that the first entry in each row is the diagonal one. */
+#if MFEM_HYPRE_VERSION <= 22200
    if (row_starts == col_starts)
+#else
+   if ((row_starts[0] == col_starts[0]) &&
+       (row_starts[1] == col_starts[1]))
+#endif
    {
       hypre_CSRMatrixReorder(hypre_ParCSRMatrixDiag(A));
    }
@@ -2503,11 +2548,14 @@ HypreParMatrix * RAP(const HypreParMatrix *A, const HypreParMatrix *P)
       // hypre_ParCSRMatrixRAPKT
    }
 #else
+#if MFEM_HYPRE_VERSION <= 22200
    HYPRE_Int P_owns_its_col_starts =
       hypre_ParCSRMatrixOwnsColStarts((hypre_ParCSRMatrix*)(*P));
+#endif
 
    hypre_BoomerAMGBuildCoarseOperator(*P,*A,*P,&rap);
 
+#if MFEM_HYPRE_VERSION <= 22200
    /* Warning: hypre_BoomerAMGBuildCoarseOperator steals the col_starts
       from P (even if it does not own them)! */
    hypre_ParCSRMatrixSetRowStartsOwner(rap,0);
@@ -2516,6 +2564,7 @@ HypreParMatrix * RAP(const HypreParMatrix *A, const HypreParMatrix *P)
    {
       hypre_ParCSRMatrixSetColStartsOwner(*P, 1);
    }
+#endif
 #endif
 
    hypre_ParCSRMatrixSetNumNonzeros(rap);
@@ -2536,13 +2585,16 @@ HypreParMatrix * RAP(const HypreParMatrix * Rt, const HypreParMatrix *A,
       hypre_ParCSRMatrixDestroy(Q);
    }
 #else
+#if MFEM_HYPRE_VERSION <= 22200
    HYPRE_Int P_owns_its_col_starts =
       hypre_ParCSRMatrixOwnsColStarts((hypre_ParCSRMatrix*)(*P));
    HYPRE_Int Rt_owns_its_col_starts =
       hypre_ParCSRMatrixOwnsColStarts((hypre_ParCSRMatrix*)(*Rt));
+#endif
 
    hypre_BoomerAMGBuildCoarseOperator(*Rt,*A,*P,&rap);
 
+#if MFEM_HYPRE_VERSION <= 22200
    /* Warning: hypre_BoomerAMGBuildCoarseOperator steals the col_starts
       from Rt and P (even if they do not own them)! */
    hypre_ParCSRMatrixSetRowStartsOwner(rap,0);
@@ -2555,6 +2607,7 @@ HypreParMatrix * RAP(const HypreParMatrix * Rt, const HypreParMatrix *A,
    {
       hypre_ParCSRMatrixSetColStartsOwner(*Rt, 1);
    }
+#endif
 #endif
 
    hypre_ParCSRMatrixSetNumNonzeros(rap);
@@ -3144,8 +3197,12 @@ void HypreSmoother::SetOperator(const Operator &op)
       }
       else
       {
+#if MFEM_HYPRE_VERSION <= 22200
          min_eig_est = 0;
          hypre_ParCSRMaxEigEstimate(*A, poly_scale, &max_eig_est);
+#else
+         hypre_ParCSRMaxEigEstimate(*A, poly_scale, &max_eig_est, &min_eig_est);
+#endif
       }
       Z = new HypreParVector(*A);
    }
@@ -3159,8 +3216,12 @@ void HypreSmoother::SetOperator(const Operator &op)
       }
       else
       {
+#if MFEM_HYPRE_VERSION <= 22200
          min_eig_est = 0;
          hypre_ParCSRMaxEigEstimate(*A, poly_scale, &max_eig_est);
+#else
+         hypre_ParCSRMaxEigEstimate(*A, poly_scale, &max_eig_est, &min_eig_est);
+#endif
       }
 
       // The Taubin and FIR polynomials are defined on [0, 2]
@@ -4997,11 +5058,11 @@ HypreADS::HypreADS(const HypreParMatrix &A, ParFiniteElementSpace *face_fespace)
 void HypreADS::Init(ParFiniteElementSpace *face_fespace)
 {
    int cycle_type       = 11;
-   int rlx_type         = 2;
    int rlx_sweeps       = 1;
    double rlx_weight    = 1.0;
    double rlx_omega     = 1.0;
 #ifndef HYPRE_USING_CUDA
+   int rlx_type         = 2;
    int amg_coarsen_type = 10;
    int amg_agg_levels   = 1;
    int amg_rlx_type     = 8;
@@ -5009,6 +5070,7 @@ void HypreADS::Init(ParFiniteElementSpace *face_fespace)
    int amg_interp_type  = 6;
    int amg_Pmax         = 4;
 #else
+   int rlx_type         = 1;
    int amg_coarsen_type = 8;
    int amg_agg_levels   = 0;
    int amg_rlx_type     = 18;

linalg/hypre_parcsr.cpp

@@ -508,8 +508,10 @@ void hypre_ParCSRMatrixEliminateAAe(hypre_ParCSRMatrix *A,
                                   hypre_ParCSRMatrixColStarts(A),
                                   0, 0, 0);
 
+#if MFEM_HYPRE_VERSION <= 22200
    hypre_ParCSRMatrixSetRowStartsOwner(*Ae, 0);
    hypre_ParCSRMatrixSetColStartsOwner(*Ae, 0);
+#endif
 
    hypre_CSRMatrix *Ae_diag = hypre_ParCSRMatrixDiag(*Ae);
    hypre_CSRMatrix *Ae_offd = hypre_ParCSRMatrixOffd(*Ae);
@@ -1002,10 +1004,17 @@ void hypre_ParCSRMatrixSplit(hypre_ParCSRMatrix *A,
 
       hypre_ParCSRMatrixOwnsData(blocks[i]) = 1;
 
+#if MFEM_HYPRE_VERSION <= 22200
       /* only the first block will own the row/col_starts */
       hypre_ParCSRMatrixOwnsRowStarts(blocks[i]) = !i;
       hypre_ParCSRMatrixOwnsColStarts(blocks[i]) = !i;
+#endif
    }
+
+#if MFEM_HYPRE_VERSION > 22200
+   mfem_hypre_TFree_host(row_starts);
+   mfem_hypre_TFree_host(col_starts);
+#endif
 }
 
 /* Based on hypre_CSRMatrixMatvec in hypre's csr_matvec.c */
@@ -1916,9 +1925,12 @@ hypre_ParCSRMatrixAdd(hypre_ParCSRMatrix *A,
 
    /* C owns diag, offd, and cmap. */
    hypre_ParCSRMatrixSetDataOwner(C, 1);
+
+#if MFEM_HYPRE_VERSION <= 22200
    /* C does not own row and column starts. */
    hypre_ParCSRMatrixSetRowStartsOwner(C, 0);
    hypre_ParCSRMatrixSetColStartsOwner(C, 0);
+#endif
 
    return C;
 }

linalg/kernels.hpp

@@ -378,7 +378,7 @@ void Swap(T &a, T &b)
    b = tmp;
 }
 
-const double Epsilon = std::numeric_limits<double>::epsilon();
+constexpr double Epsilon = std::numeric_limits<double>::epsilon();
 
 /// Utility function used in CalcSingularvalue<3>.
 MFEM_HOST_DEVICE static inline

linalg/sundials.cpp

@@ -1677,7 +1677,7 @@ int KINSolver::GradientMult(N_Vector v, N_Vector Jv, N_Vector u,
 
 // Wrapper for evaluating linear systems J u = b
 int KINSolver::LinSysSetup(N_Vector u, N_Vector, SUNMatrix J,
-                           void *, N_Vector , N_Vector )
+                           void *, N_Vector, N_Vector )
 {
    const SundialsNVector mfem_u(u);
    KINSolver *self = static_cast<KINSolver*>(GET_CONTENT(J));

makefile

@@ -119,7 +119,7 @@ $(if $(word 2,$(SRC)),$(error Spaces in SRC = "$(SRC)" are not supported))
 MFEM_GIT_STRING = $(shell [ -d $(MFEM_DIR)/.git ] && git -C $(MFEM_DIR) \
    describe --all --long --abbrev=40 --dirty --always 2> /dev/null)
 
-EXAMPLE_SUBDIRS = amgx ginkgo hiop petsc pumi sundials superlu
+EXAMPLE_SUBDIRS = amgx caliper ginkgo hiop petsc pumi sundials superlu
 EXAMPLE_DIRS := examples $(addprefix examples/,$(EXAMPLE_SUBDIRS))
 EXAMPLE_TEST_DIRS := examples
 

mesh/CMakeLists.txt

@@ -19,6 +19,7 @@ set(SRCS
   ncmesh.cpp
   nurbs.cpp
   point.cpp
+  pyramid.cpp
   quadrilateral.cpp
   segment.cpp
   tetrahedron.cpp
@@ -38,6 +39,7 @@ set(HDRS
   ncmesh.hpp
   nurbs.hpp
   point.hpp
+  pyramid.hpp
   quadrilateral.hpp
   segment.hpp
   tetrahedron.hpp

mesh/element.hpp

@@ -39,7 +39,7 @@ public:
 
    /// Constants for the classes derived from Element.
    enum Type { POINT, SEGMENT, TRIANGLE, QUADRILATERAL,
-               TETRAHEDRON, HEXAHEDRON, WEDGE
+               TETRAHEDRON, HEXAHEDRON, WEDGE, PYRAMID
              };
 
    /// Default element constructor.

mesh/mesh.cpp

@@ -335,6 +335,7 @@ FiniteElement *Mesh::GetTransformationFEforElementType(Element::Type ElemType)
       case Element::TETRAHEDRON :    return &TetrahedronFE;
       case Element::HEXAHEDRON :     return &HexahedronFE;
       case Element::WEDGE :          return &WedgeFE;
+      case Element::PYRAMID :        return &PyramidFE;
       default:
          MFEM_ABORT("Unknown element type \"" << ElemType << "\"");
          break;
@@ -735,6 +736,31 @@ void Mesh::GetLocalTriToWdgTransformation(
    }
 }
 
+void Mesh::GetLocalTriToPyrTransformation(
+   IsoparametricTransformation &Transf, int i)
+{
+   DenseMatrix &locpm = Transf.GetPointMat();
+
+   Transf.SetFE(&TriangleFE);
+   //  (i/64) is the local face no. in the pyr
+   MFEM_VERIFY(i >= 64, "Local face index " << i/64
+               << " is not a triangular face of a pyramid.");
+   const int *pv = pyr_t::FaceVert[i/64];
+   //  (i%64) is the orientation of the pyramid face
+   //         w.r.t. the face element
+   const int *to = tri_t::Orient[i%64];
+   const IntegrationRule *PyrVert =
+      Geometries.GetVertices(Geometry::PYRAMID);
+   locpm.SetSize(3, 3);
+   for (int j = 0; j < 3; j++)
+   {
+      const IntegrationPoint &vert = PyrVert->IntPoint(pv[to[j]]);
+      locpm(0, j) = vert.x;
+      locpm(1, j) = vert.y;
+      locpm(2, j) = vert.z;
+   }
+}
+
 void Mesh::GetLocalQuadToHexTransformation(
    IsoparametricTransformation &Transf, int i)
 {
@@ -781,6 +807,29 @@ void Mesh::GetLocalQuadToWdgTransformation(
    }
 }
 
+void Mesh::GetLocalQuadToPyrTransformation(
+   IsoparametricTransformation &Transf, int i)
+{
+   DenseMatrix &locpm = Transf.GetPointMat();
+
+   Transf.SetFE(&QuadrilateralFE);
+   //  (i/64) is the local face no. in the pyr
+   MFEM_VERIFY(i < 64, "Local face index " << i/64
+               << " is not a quadrilateral face of a pyramid.");
+   const int *pv = pyr_t::FaceVert[i/64];
+   //  (i%64) is the orientation of the quad
+   const int *qo = quad_t::Orient[i%64];
+   const IntegrationRule *PyrVert = Geometries.GetVertices(Geometry::PYRAMID);
+   locpm.SetSize(3, 4);
+   for (int j = 0; j < 4; j++)
+   {
+      const IntegrationPoint &vert = PyrVert->IntPoint(pv[qo[j]]);
+      locpm(0, j) = vert.x;
+      locpm(1, j) = vert.y;
+      locpm(2, j) = vert.z;
+   }
+}
+
 const GeometricFactors* Mesh::GetGeometricFactors(const IntegrationRule& ir,
                                                   const int flags,
                                                   MemoryType d_mt)
@@ -862,10 +911,19 @@ void Mesh::GetLocalFaceTransformation(
          {
             GetLocalTriToTetTransformation(Transf, info);
          }
+         else if (elem_type == Element::WEDGE)
+         {
+            GetLocalTriToWdgTransformation(Transf, info);
+         }
+         else if (elem_type == Element::PYRAMID)
+         {
+            GetLocalTriToPyrTransformation(Transf, info);
+         }
          else
          {
-            MFEM_ASSERT(elem_type == Element::WEDGE, "");
-            GetLocalTriToWdgTransformation(Transf, info);
+            MFEM_ABORT("Mesh::GetLocalFaceTransformation not defined for "
+                       "face type " << face_type
+                       << " and element type " << elem_type << "\n");
          }
          break;
 
@@ -874,10 +932,19 @@ void Mesh::GetLocalFaceTransformation(
          {
             GetLocalQuadToHexTransformation(Transf, info);
          }
+         else if (elem_type == Element::WEDGE)
+         {
+            GetLocalQuadToWdgTransformation(Transf, info);
+         }
+         else if (elem_type == Element::PYRAMID)
+         {
+            GetLocalQuadToPyrTransformation(Transf, info);
+         }
          else
          {
-            MFEM_ASSERT(elem_type == Element::WEDGE, "");
-            GetLocalQuadToWdgTransformation(Transf, info);
+            MFEM_ABORT("Mesh::GetLocalFaceTransformation not defined for "
+                       "face type " << face_type
+                       << " and element type " << elem_type << "\n");
          }
          break;
    }
@@ -1370,6 +1437,20 @@ int Mesh::AddWedge(const int *vi, int attr)
    return NumOfElements++;
 }
 
+int Mesh::AddPyramid(int v1, int v2, int v3, int v4, int v5, int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Pyramid(v1, v2, v3, v4, v5, attr);
+   return NumOfElements++;
+}
+
+int Mesh::AddPyramid(const int *vi, int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Pyramid(vi, attr);
+   return NumOfElements++;
+}
+
 int Mesh::AddHex(int v1, int v2, int v3, int v4, int v5, int v6, int v7, int v8,
                  int attr)
 {
@@ -1423,6 +1504,25 @@ void Mesh::AddHexAsWedges(const int *vi, int attr)
    }
 }
 
+void Mesh::AddHexAsPyramids(const int *vi, int attr)
+{
+   static const int hex_to_pyr[6][5] =
+   {
+      { 0, 1, 2, 3, 8 }, { 0, 4, 5, 1, 8 }, { 1, 5, 6, 2, 8 },
+      { 2, 6, 7, 3, 8 }, { 3, 7, 4, 0, 8 }, { 7, 6, 5, 4, 8 }
+   };
+   int ti[5];
+
+   for (int i = 0; i < 6; i++)
+   {
+      for (int j = 0; j < 5; j++)
+      {
+         ti[j] = vi[hex_to_pyr[i][j]];
+      }
+      AddPyramid(ti, attr);
+   }
+}
+
 int Mesh::AddElement(Element *elem)
 {
    CheckEnlarge(elements, NumOfElements);
@@ -2692,11 +2792,16 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
       NElem *= 2;
       NBdrElem += 2*nx*ny;
    }
+   else if (type == Element::PYRAMID)
+   {
+      NElem *= 6;
+      NVert += nx * ny * nz;
+   }
 
    InitMesh(3, 3, NVert, NElem, NBdrElem);
 
    double coord[3];
-   int ind[8];
+   int ind[9];
 
    // Sets vertices and the corresponding coordinates
    for (z = 0; z <= nz; z++)
@@ -2712,8 +2817,25 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
          }
       }
    }
+   if (type == Element::PYRAMID)
+   {
+      for (z = 0; z < nz; z++)
+      {
+         coord[2] = (((double) z + 0.5) / nz) * sz;
+         for (y = 0; y < ny; y++)
+         {
+            coord[1] = (((double) y + 0.5 ) / ny) * sy;
+            for (x = 0; x < nx; x++)
+            {
+               coord[0] = (((double) x + 0.5 ) / nx) * sx;
+               AddVertex(coord);
+            }
+         }
+      }
+   }
 
 #define VTX(XC, YC, ZC) ((XC)+((YC)+(ZC)*(ny+1))*(nx+1))
+#define VTXP(XC, YC, ZC) ((nx+1)*(ny+1)*(nz+1)+(XC)+((YC)+(ZC)*ny)*nx)
 
    // Sets elements and the corresponding indices of vertices
    if (sfc_ordering && type == Element::HEXAHEDRON)
@@ -2728,14 +2850,14 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
          y = sfc[3*k + 1];
          z = sfc[3*k + 2];
 
-         ind[0] = VTX(x  , y  , z  );
-         ind[1] = VTX(x+1, y  , z  );
+         ind[0] = VTX(x, y, z  );
+         ind[1] = VTX(x+1, y, z  );
          ind[2] = VTX(x+1, y+1, z  );
-         ind[3] = VTX(x  , y+1, z  );
-         ind[4] = VTX(x  , y  , z+1);
-         ind[5] = VTX(x+1, y  , z+1);
+         ind[3] = VTX(x, y+1, z  );
+         ind[4] = VTX(x, y, z+1);
+         ind[5] = VTX(x+1, y, z+1);
          ind[6] = VTX(x+1, y+1, z+1);
-         ind[7] = VTX(x  , y+1, z+1);
+         ind[7] = VTX(x, y+1, z+1);
 
          AddHex(ind, 1);
       }
@@ -2748,12 +2870,12 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
          {
             for (x = 0; x < nx; x++)
             {
-               ind[0] = VTX(x  , y  , z  );
-               ind[1] = VTX(x+1, y  , z  );
+               ind[0] = VTX(x, y, z  );
+               ind[1] = VTX(x+1, y, z  );
                ind[2] = VTX(x+1, y+1, z  );
-               ind[3] = VTX(x  , y+1, z  );
-               ind[4] = VTX(x  , y  , z+1);
-               ind[5] = VTX(x+1, y  , z+1);
+               ind[3] = VTX(x, y+1, z  );
+               ind[4] = VTX(x, y, z+1);
+               ind[5] = VTX(x+1, y, z+1);
                ind[6] = VTX(x+1, y+1, z+1);
                ind[7] = VTX(  x, y+1, z+1);
                if (type == Element::TETRAHEDRON)
@@ -2764,6 +2886,11 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
                {
                   AddHexAsWedges(ind, 1);
                }
+               else if (type == Element::PYRAMID)
+               {
+                  ind[8] = VTXP(  x, y, z);
+                  AddHexAsPyramids(ind, 1);
+               }
                else
                {
                   AddHex(ind, 1);
@@ -2779,10 +2906,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (x = 0; x < nx; x++)
       {
-         ind[0] = VTX(x  , y  , 0);
-         ind[1] = VTX(x  , y+1, 0);
+         ind[0] = VTX(x, y, 0);
+         ind[1] = VTX(x, y+1, 0);
          ind[2] = VTX(x+1, y+1, 0);
-         ind[3] = VTX(x+1, y  , 0);
+         ind[3] = VTX(x+1, y, 0);
          if (type == Element::TETRAHEDRON)
          {
             AddBdrQuadAsTriangles(ind, 1);
@@ -2802,10 +2929,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (x = 0; x < nx; x++)
       {
-         ind[0] = VTX(x  , y  , nz);
-         ind[1] = VTX(x+1, y  , nz);
+         ind[0] = VTX(x, y, nz);
+         ind[1] = VTX(x+1, y, nz);
          ind[2] = VTX(x+1, y+1, nz);
-         ind[3] = VTX(x  , y+1, nz);
+         ind[3] = VTX(x, y+1, nz);
          if (type == Element::TETRAHEDRON)
          {
             AddBdrQuadAsTriangles(ind, 6);
@@ -2825,10 +2952,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (y = 0; y < ny; y++)
       {
-         ind[0] = VTX(0  , y  , z  );
-         ind[1] = VTX(0  , y  , z+1);
-         ind[2] = VTX(0  , y+1, z+1);
-         ind[3] = VTX(0  , y+1, z  );
+         ind[0] = VTX(0, y, z  );
+         ind[1] = VTX(0, y, z+1);
+         ind[2] = VTX(0, y+1, z+1);
+         ind[3] = VTX(0, y+1, z  );
          if (type == Element::TETRAHEDRON)
          {
             AddBdrQuadAsTriangles(ind, 5);
@@ -2844,10 +2971,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (y = 0; y < ny; y++)
       {
-         ind[0] = VTX(nx, y  , z  );
+         ind[0] = VTX(nx, y, z  );
          ind[1] = VTX(nx, y+1, z  );
          ind[2] = VTX(nx, y+1, z+1);
-         ind[3] = VTX(nx, y  , z+1);
+         ind[3] = VTX(nx, y, z+1);
          if (type == Element::TETRAHEDRON)
          {
             AddBdrQuadAsTriangles(ind, 3);
@@ -2863,10 +2990,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (z = 0; z < nz; z++)
       {
-         ind[0] = VTX(x  , 0, z  );
+         ind[0] = VTX(x, 0, z  );
          ind[1] = VTX(x+1, 0, z  );
          ind[2] = VTX(x+1, 0, z+1);
-         ind[3] = VTX(x  , 0, z+1);
+         ind[3] = VTX(x, 0, z+1);
          if (type == Element::TETRAHEDRON)
          {
             AddBdrQuadAsTriangles(ind, 2);
@@ -2882,8 +3009,8 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    {
       for (z = 0; z < nz; z++)
       {
-         ind[0] = VTX(x  , ny, z  );
-         ind[1] = VTX(x  , ny, z+1);
+         ind[0] = VTX(x, ny, z  );
+         ind[1] = VTX(x, ny, z+1);
          ind[2] = VTX(x+1, ny, z+1);
          ind[3] = VTX(x+1, ny, z  );
          if (type == Element::TETRAHEDRON)
@@ -3428,6 +3555,7 @@ Element *Mesh::NewElement(int geom)
 #endif
       case Geometry::CUBE:      return (new Hexahedron);
       case Geometry::PRISM:     return (new Wedge);
+      case Geometry::PYRAMID:   return (new Pyramid);
       default:
          MFEM_ABORT("invalid Geometry::Type, geom = " << geom);
    }
@@ -3520,6 +3648,15 @@ void Mesh::SetMeshGen()
             meshgen |= 4;
             break;
 
+         case Element::PYRAMID:
+            mesh_geoms |= (1 << Geometry::PYRAMID);
+            mesh_geoms |= (1 << Geometry::SQUARE);
+            mesh_geoms |= (1 << Geometry::TRIANGLE);
+            mesh_geoms |= (1 << Geometry::SEGMENT);
+            mesh_geoms |= (1 << Geometry::POINT);
+            meshgen |= 8;
+            break;
+
          default:
             MFEM_ABORT("invalid element type: " << type);
             break;
@@ -3974,6 +4111,12 @@ void Mesh::MakeRefined_(Mesh &orig_mesh, const Array<int> ref_factors,
       }
    }
 
+   if (Dim > 2)
+   {
+      GetElementToFaceTable(false);
+      GenerateFaces();
+   }
+
    // Add refined boundary elements
    for (int el = 0; el < orig_mesh.GetNBE(); el++)
    {
@@ -5054,6 +5197,19 @@ int Mesh::CheckElementOrientation(bool fix_it)
                }
                break;
 
+            case Element::PYRAMID:
+               // only check the Jacobian at the center of the element
+               GetElementJacobian(i, J);
+               if (J.Det() < 0.0)
+               {
+                  wo++;
+                  if (fix_it)
+                  {
+                     // how?
+                  }
+               }
+               break;
+
             case Element::HEXAHEDRON:
                // only check the Jacobian at the center of the element
                GetElementJacobian(i, J);
@@ -6136,6 +6292,22 @@ void Mesh::GenerateFaces()
                }
                break;
             }
+            case Element::PYRAMID:
+            {
+               for (int j = 0; j < 1; j++)
+               {
+                  const int *fv = pyr_t::FaceVert[j];
+                  AddQuadFaceElement(j, ef[j], i,
+                                     v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+               }
+               for (int j = 1; j < 5; j++)
+               {
+                  const int *fv = pyr_t::FaceVert[j];
+                  AddTriangleFaceElement(j, ef[j], i,
+                                         v[fv[0]], v[fv[1]], v[fv[2]]);
+               }
+               break;
+            }
             case Element::HEXAHEDRON:
             {
                for (int j = 0; j < 6; j++)
@@ -6228,6 +6400,20 @@ STable3D *Mesh::GetFacesTable()
             }
             break;
          }
+         case Element::PYRAMID:
+         {
+            for (int j = 0; j < 1; j++)
+            {
+               const int *fv = pyr_t::FaceVert[j];
+               faces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+            }
+            for (int j = 1; j < 5; j++)
+            {
+               const int *fv = pyr_t::FaceVert[j];
+               faces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]);
+            }
+            break;
+         }
          case Element::WEDGE:
          {
             for (int j = 0; j < 2; j++)
@@ -6302,6 +6488,22 @@ STable3D *Mesh::GetElementToFaceTable(int ret_ftbl)
             }
             break;
          }
+         case Element::PYRAMID:
+         {
+            for (int j = 0; j < 1; j++)
+            {
+               const int *fv = pyr_t::FaceVert[j];
+               el_to_face->Push(
+                  i, faces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]));
+            }
+            for (int j = 1; j < 5; j++)
+            {
+               const int *fv = pyr_t::FaceVert[j];
+               el_to_face->Push(
+                  i, faces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]));
+            }
+            break;
+         }
          case Element::HEXAHEDRON:
          {
             // find the face by the vertices with the smallest 3 numbers
@@ -7638,8 +7840,22 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
       }
    }
 
+   int pyr_counter = 0;
+   if (HasGeometry(Geometry::PYRAMID))
+   {
+      for (int i = 0; i < elements.Size(); i++)
+      {
+         if (elements[i]->GetType() == Element::PYRAMID)
+         {
+            pyr_counter++;
+         }
+      }
+   }
+
    // Map from edge-index to vertex-index, needed for ReorientTetMesh() for
    // parallel meshes.
+   // Note: with the removal of ReorientTetMesh() this may no longer
+   // be needed.  Unfortunately, it's hard to be sure.
    Array<int> e2v;
    if (HasGeometry(Geometry::TETRAHEDRON))
    {
@@ -7695,7 +7911,7 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
    Array<Element*> new_boundary;
 
    vertices.SetSize(oelem + hex_counter);
-   new_elements.SetSize(8 * NumOfElements);
+   new_elements.SetSize(8 * NumOfElements + 2 * pyr_counter);
    CoarseFineTr.embeddings.SetSize(new_elements.Size());
 
    hex_counter = 0;
@@ -7961,6 +8177,73 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
          }
          break;
 
+         case Element::PYRAMID:
+         {
+            const int *f = el_to_face->GetRow(i);
+            // pyr_counter++;
+
+            for (int fi = 0; fi < 1; fi++)
+            {
+               for (int k = 0; k < 4; k++)
+               {
+                  vv[k] = v[pyr_t::FaceVert[fi][k]];
+               }
+               AverageVertices(vv, 4, oface + f2qf[f[fi]]);
+            }
+
+            for (int ei = 0; ei < 8; ei++)
+            {
+               for (int k = 0; k < 2; k++)
+               {
+                  vv[k] = v[pyr_t::Edges[ei][k]];
+               }
+               AverageVertices(vv, 2, oedge+e[ei]);
+            }
+
+            const int qf0 = f2qf[f[0]];
+
+            new_elements[j++] =
+               new Pyramid(v[0], oedge+e[0], oface+qf0,
+                           oedge+e[3], oedge+e[4], attr);
+
+            new_elements[j++] =
+               new Pyramid(oedge+e[0], v[1], oedge+e[1],
+                           oface+qf0, oedge+e[5], attr);
+
+            new_elements[j++] =
+               new Pyramid(oface+qf0, oedge+e[1], v[2],
+                           oedge+e[2], oedge+e[6], attr);
+
+            new_elements[j++] =
+               new Pyramid(oedge+e[3], oface+qf0, oedge+e[2],
+                           v[3], oedge+e[7], attr);
+
+            new_elements[j++] =
+               new Pyramid(oedge+e[4], oedge+e[5], oedge+e[6],
+                           oedge+e[7], v[4], attr);
+
+            new_elements[j++] =
+               new Pyramid(oedge+e[7], oedge+e[6], oedge+e[5],
+                           oedge+e[4], oface+qf0, attr);
+
+            new_elements[j++] =
+               new Tetrahedron(oedge+e[0], oedge+e[4], oedge+e[5],
+                               oface+qf0, attr);
+
+            new_elements[j++] =
+               new Tetrahedron(oedge+e[1], oedge+e[5], oedge+e[6],
+                               oface+qf0, attr);
+
+            new_elements[j++] =
+               new Tetrahedron(oedge+e[2], oedge+e[6], oedge+e[7],
+                               oface+qf0, attr);
+
+            new_elements[j++] =
+               new Tetrahedron(oedge+e[3], oedge+e[7], oedge+e[4],
+                               oface+qf0, attr);
+         }
+         break;
+
          case Element::HEXAHEDRON:
          {
             const int *f = el_to_face->GetRow(i);
@@ -8092,7 +8375,7 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
    }
    mfem::Swap(boundary, new_boundary);
 
-   static const double A = 0.0, B = 0.5, C = 1.0;
+   static const double A = 0.0, B = 0.5, C = 1.0, D = -1.0;
    static double tet_children[3*4*16] =
    {
       A,A,A, B,A,A, A,B,A, A,A,B,
@@ -8118,6 +8401,19 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
       A,A,B, A,B,B, B,A,B, B,B,A,
       A,A,B, B,A,B, B,A,A, B,B,A
    };
+   static double pyr_children[3*5*10] =
+   {
+      A,A,A, B,A,A, B,B,A, A,B,A, A,A,B,
+      B,A,A, C,A,A, C,B,A, B,B,A, B,A,B,
+      B,B,A, C,B,A, C,C,A, B,C,A, B,B,B,
+      A,B,A, B,B,A, B,C,A, A,C,A, A,B,B,
+      A,A,B, B,A,B, B,B,B, A,B,B, A,A,C,
+      A,B,B, B,B,B, B,A,B, A,A,B, B,B,A,
+      B,A,A, A,A,B, B,A,B, B,B,A, D,D,D,
+      C,B,A, B,A,B, B,B,B, B,B,A, D,D,D,
+      B,C,A, B,B,B, A,B,B, B,B,A, D,D,D,
+      A,B,A, A,B,B, A,A,B, B,B,A, D,D,D
+   };
    static double pri_children[3*6*8] =
    {
       A,A,A, B,A,A, A,B,A, A,A,B, B,A,B, A,B,B,
@@ -8143,6 +8439,8 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
 
    CoarseFineTr.point_matrices[Geometry::TETRAHEDRON]
    .UseExternalData(tet_children, 3, 4, 16);
+   CoarseFineTr.point_matrices[Geometry::PYRAMID]
+   .UseExternalData(pyr_children, 3, 5, 10);
    CoarseFineTr.point_matrices[Geometry::PRISM]
    .UseExternalData(pri_children, 3, 6, 8);
    CoarseFineTr.point_matrices[Geometry::CUBE]
@@ -8159,7 +8457,7 @@ void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p,
    }
 
    NumOfVertices    = vertices.Size();
-   NumOfElements    = 8 * NumOfElements;
+   NumOfElements    = 8 * NumOfElements + 2 * pyr_counter;
    NumOfBdrElements = 4 * NumOfBdrElements;
 
    GetElementToFaceTable();
@@ -8743,7 +9041,7 @@ void Mesh::GeneralRefinement(const Array<Refinement> &refinements,
    else if (nonconforming < 0)
    {
       // determine if nonconforming refinement is suitable
-      if ((meshgen & 2) || (meshgen & 4))
+      if ((meshgen & 2) || (meshgen & 4) || (meshgen & 8))
       {
          nonconforming = 1; // tensor product elements and wedges
       }
@@ -9527,6 +9825,7 @@ void Mesh::Printer(std::ostream &out, std::string section_delimiter) const
        "# TETRAHEDRON = 4\n"
        "# CUBE        = 5\n"
        "# PRISM       = 6\n"
+       "# PYRAMID     = 7\n"
        "#\n";
 
    out << "\ndimension\n" << Dim;

mesh/mesh.hpp

@@ -177,6 +177,7 @@ protected:
    int own_nodes;
 
    static const int vtk_quadratic_tet[10];
+   static const int vtk_quadratic_pyramid[13];
    static const int vtk_quadratic_wedge[18];
    static const int vtk_quadratic_hex[27];
 
@@ -195,6 +196,7 @@ public:
    typedef Geometry::Constants<Geometry::TETRAHEDRON> tet_t;
    typedef Geometry::Constants<Geometry::CUBE>        hex_t;
    typedef Geometry::Constants<Geometry::PRISM>       pri_t;
+   typedef Geometry::Constants<Geometry::PYRAMID>     pyr_t;
 
    enum Operation { NONE, REFINE, DEREFINE, REBALANCE };
 
@@ -373,11 +375,17 @@ protected:
    void GetLocalTriToWdgTransformation (IsoparametricTransformation &loc,
                                         int i);
    /// Used in GetFaceElementTransformations (...)
+   void GetLocalTriToPyrTransformation (IsoparametricTransformation &loc,
+                                        int i);
+   /// Used in GetFaceElementTransformations (...)
    void GetLocalQuadToHexTransformation (IsoparametricTransformation &loc,
                                          int i);
    /// Used in GetFaceElementTransformations (...)
    void GetLocalQuadToWdgTransformation (IsoparametricTransformation &loc,
                                          int i);
+   /// Used in GetFaceElementTransformations (...)
+   void GetLocalQuadToPyrTransformation (IsoparametricTransformation &loc,
+                                         int i);
 
    /** Used in GetFaceElementTransformations to account for the fact that a
        slave face occupies only a portion of its master face. */
@@ -657,11 +665,15 @@ public:
    int AddWedge(int v1, int v2, int v3, int v4, int v5, int v6, int attr = 1);
    int AddWedge(const int *vi, int attr = 1);
 
+   int AddPyramid(int v1, int v2, int v3, int v4, int v5, int attr = 1);
+   int AddPyramid(const int *vi, int attr = 1);
+
    int AddHex(int v1, int v2, int v3, int v4, int v5, int v6, int v7, int v8,
               int attr = 1);
    int AddHex(const int *vi, int attr = 1);
    void AddHexAsTets(const int *vi, int attr = 1);
    void AddHexAsWedges(const int *vi, int attr = 1);
+   void AddHexAsPyramids(const int *vi, int attr = 1);
 
    /// The parameter @a elem should be allocated using the NewElement() method
    int AddElement(Element *elem);
@@ -829,10 +841,16 @@ public:
 
    /** @brief Get the mesh generator/type.
 
+       The purpose of this is to be able to quickly tell what type of elements
+       one has in the mesh. Examination of this bitmask along with knowledge
+       of the mesh dimension can be used to identify which element types are
+       present.
+
        @return A bitmask:
        - bit 0 - simplices are present in the mesh (triangles, tets),
        - bit 1 - tensor product elements are present in the mesh (quads, hexes),
        - bit 2 - the mesh has wedge elements.
+       - bit 3 - the mesh has pyramid elements.
 
        In parallel, the result takes into account elements on all processors.
    */
@@ -1227,7 +1245,7 @@ public:
        satisfy: v0 < min(v1, v2).
 
        @note Refinement does not work after a call to this method! */
-   virtual void ReorientTetMesh();
+   MFEM_DEPRECATED virtual void ReorientTetMesh();
 
    int *CartesianPartitioning(int nxyz[]);
    int *GeneratePartitioning(int nparts, int part_method = 1);

mesh/mesh_headers.hpp

@@ -27,6 +27,7 @@
 #include "mesh_operators.hpp"
 #include "nurbs.hpp"
 #include "wedge.hpp"
+#include "pyramid.hpp"
 
 #ifdef MFEM_USE_MESQUITE
 #include "mesquite.hpp"

mesh/mesh_readers.cpp

@@ -352,6 +352,11 @@ void Mesh::ReadTrueGridMesh(std::istream &input)
 const int Mesh::vtk_quadratic_tet[10] =
 { 0, 1, 2, 3, 4, 7, 5, 6, 8, 9 };
 
+// see Pyramid::edges & Mesh::GenerateFaces
+// https://www.vtk.org/doc/nightly/html/classvtkBiQuadraticQuadraticWedge.html
+const int Mesh::vtk_quadratic_pyramid[13] =
+{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
+
 // see Wedge::edges & Mesh::GenerateFaces
 // https://www.vtk.org/doc/nightly/html/classvtkBiQuadraticQuadraticWedge.html
 const int Mesh::vtk_quadratic_wedge[18] =
@@ -514,8 +519,7 @@ void Mesh::CreateVTKMesh(const Vector &points, const Array<int> &cell_data,
             }
          }
       }
-      // Generate faces and edges so that we can define
-      // FE space on the mesh
+      // Generate faces and edges so that we can define FE space on the mesh
       FinalizeTopology();
 
       FiniteElementCollection *fec;
@@ -546,6 +550,8 @@ void Mesh::CreateVTKMesh(const Vector &points, const Array<int> &cell_data,
                   vtk_mfem = vtk_quadratic_hex; break;
                case Geometry::PRISM:
                   vtk_mfem = vtk_quadratic_wedge; break;
+               case Geometry::PYRAMID:
+                  vtk_mfem = vtk_quadratic_pyramid; break;
                default:
                   vtk_mfem = NULL; // suppress a warning
                   break;
@@ -1394,6 +1400,10 @@ void Mesh::ReadInlineMesh(std::istream &input, bool generate_edges)
          {
             type = Element::WEDGE;
          }
+         else if (eltype == "pyramid")
+         {
+            type = Element::PYRAMID;
+         }
          else if (eltype == "tet")
          {
             type = Element::TETRAHEDRON;
@@ -1448,7 +1458,7 @@ void Mesh::ReadInlineMesh(std::istream &input, bool generate_edges)
       Make2D(nx, ny, type, sx, sy, generate_edges, true);
    }
    else if (type == Element::TETRAHEDRON || type == Element::WEDGE ||
-            type == Element::HEXAHEDRON)
+            type == Element::HEXAHEDRON  || type == Element::PYRAMID)
    {
       MFEM_VERIFY(nx > 0 && ny > 0 && nz > 0 &&
                   sx > 0.0 && sy > 0.0 && sz > 0.0,
@@ -2445,6 +2455,10 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
             // initialize mesh_geoms so we can create Nodes FE space below
             this->SetMeshGen();
 
+            // Generate faces and edges so that we can define
+            // FE space on the mesh
+            this->FinalizeTopology();
+
             // Construct GridFunction for uniformly spaced high order coords
             FiniteElementCollection* nfec;
             FiniteElementSpace* nfes;
@@ -2666,6 +2680,7 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
          // Convert nodes to discontinuous GridFunction (if they aren't already)
          if (mesh_order == 1)
          {
+            this->FinalizeTopology();
             this->SetMeshGen();
             this->SetCurvature(1, true, spaceDim, Ordering::byVDIM);
          }

mesh/ncmesh.cpp

@@ -612,7 +612,7 @@ int NCMesh::NewSegment(int n0, int n1, int attr, int vattr1, int vattr2)
    // get (degenerate) faces and assign face attributes
    int v0 = el.node[0], v1 = el.node[1];
    faces.Get(v0, v0, v0, v0)->attribute = vattr1;
-   faces.Get(v1, v1, v1 ,v1)->attribute = vattr2;
+   faces.Get(v1, v1, v1,v1)->attribute = vattr2;
 
    return new_id;
 }

mesh/pmesh.cpp

@@ -34,6 +34,7 @@ ParMesh::ParMesh(const ParMesh &pmesh, bool copy_nodes)
      group_sedge(pmesh.group_sedge),
      group_stria(pmesh.group_stria),
      group_squad(pmesh.group_squad),
+     face_nbr_el_to_face(NULL),
      glob_elem_offset(-1),
      glob_offset_sequence(-1),
      gtopo(pmesh.gtopo)
@@ -105,7 +106,8 @@ ParMesh& ParMesh::operator=(ParMesh &&mesh)
 
 ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
                  int part_method)
-   : glob_elem_offset(-1)
+   : face_nbr_el_to_face(NULL)
+   , glob_elem_offset(-1)
    , glob_offset_sequence(-1)
    , gtopo(comm)
 {
@@ -852,6 +854,7 @@ ParMesh::ParMesh(const ParNCMesh &pncmesh)
    : MyComm(pncmesh.MyComm)
    , NRanks(pncmesh.NRanks)
    , MyRank(pncmesh.MyRank)
+   , face_nbr_el_to_face(NULL)
    , glob_elem_offset(-1)
    , glob_offset_sequence(-1)
    , gtopo(MyComm)
@@ -918,7 +921,8 @@ void ParMesh::FinalizeParTopo()
 }
 
 ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
-   : glob_elem_offset(-1)
+   : face_nbr_el_to_face(NULL)
+   , glob_elem_offset(-1)
    , glob_offset_sequence(-1)
    , gtopo(comm)
 {
@@ -1129,6 +1133,7 @@ void ParMesh::MakeRefined_(ParMesh &orig_mesh, int ref_factor, int ref_type)
    MyComm = orig_mesh.GetComm();
    NRanks = orig_mesh.GetNRanks();
    MyRank = orig_mesh.GetMyRank();
+   face_nbr_el_to_face = NULL;
    glob_elem_offset = -1;
    glob_offset_sequence = -1;
    gtopo = orig_mesh.gtopo;
@@ -2073,6 +2078,11 @@ void ParMesh::ExchangeFaceNbrData()
 
    ExchangeFaceNbrData(gr_sface, s2l_face);
 
+   if (Dim == 3)
+   {
+      GetFaceNbrElementToFaceTable();
+   }
+
    if (del_tables) { delete gr_sface; }
 
    if ( have_face_nbr_data ) { return; }
@@ -2141,6 +2151,8 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
    el_marker = -1;
    vertex_marker = -1;
 
+   Array<int> fcs, cor;
+
    Table send_face_nbr_elemdata, send_face_nbr_facedata;
 
    send_face_nbr_elements.MakeI(num_face_nbrs);
@@ -2170,7 +2182,9 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
                   send_face_nbr_vertices.AddAColumnInRow(fn);
                }
 
-            send_face_nbr_elemdata.AddColumnsInRow(fn, nv + 2);
+            const int nf = elements[el]->GetNFaces();
+
+            send_face_nbr_elemdata.AddColumnsInRow(fn, nv + nf + 2);
          }
       }
       send_face_nbr_facedata.AddColumnsInRow(fn, 2*num_sfaces);
@@ -2222,6 +2236,13 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
             send_face_nbr_elemdata.AddConnection(
                fn, GetElementBaseGeometry(el));
             send_face_nbr_elemdata.AddConnections(fn, v, nv);
+
+            if (Dim == 3)
+            {
+               const int nf = elements[el]->GetNFaces();
+               GetElementFaces(el, fcs, cor);
+               send_face_nbr_elemdata.AddConnections(fn, cor, nf);
+            }
          }
          send_face_nbr_facedata.AddConnection(fn, el);
          int info = faces_info[lface].Elem1Inf;
@@ -2267,12 +2288,13 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
       for (int el = 0; el < num_elems; el++)
       {
          const int nv = elements[elems[el]]->GetNVertices();
+         const int nf = (Dim == 3) ? elements[elems[el]]->GetNFaces() : 0;
          elemdata += 2; // skip the attribute and the geometry type
          for (int j = 0; j < nv; j++)
          {
             elemdata[j] = vertex_marker[elemdata[j]];
          }
-         elemdata += nv;
+         elemdata += nv + nf;
 
          el_marker[elems[el]] = el;
       }
@@ -2323,6 +2345,8 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
 
    // convert the element data into face_nbr_elements
    face_nbr_elements.SetSize(face_nbr_elements_offset[num_face_nbrs]);
+   face_nbr_el_ori.Clear();
+   face_nbr_el_ori.SetSize(face_nbr_elements_offset[num_face_nbrs], 6);
    while (true)
    {
       int fn;
@@ -2350,9 +2374,20 @@ void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
          }
          el->SetVertices(recv_elemdata);
          recv_elemdata += nv;
+         if (Dim == 3)
+         {
+            int nf = el->GetNFaces();
+            int * fn_ori = face_nbr_el_ori.GetRow(elem_off);
+            for (int j = 0; j < nf; j++)
+            {
+               fn_ori[j] = recv_elemdata[j];
+            }
+            recv_elemdata += nf;
+         }
          face_nbr_elements[elem_off++] = el;
       }
    }
+   face_nbr_el_ori.Finalize();
 
    MPI_Waitall(num_face_nbrs, send_requests, statuses);
 
@@ -2511,6 +2546,179 @@ void ParMesh::ExchangeFaceNbrNodes()
    }
 }
 
+STable3D *ParMesh::GetSharedFacesTable()
+{
+   STable3D *sfaces_tbl = new STable3D(face_nbr_vertices.Size());
+   for (int i = 0; i < face_nbr_elements.Size(); i++)
+   {
+      const int *v = face_nbr_elements[i]->GetVertices();
+      switch (face_nbr_elements[i]->GetType())
+      {
+         case Element::TETRAHEDRON:
+         {
+            for (int j = 0; j < 4; j++)
+            {
+               const int *fv = tet_t::FaceVert[j];
+               sfaces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]);
+            }
+            break;
+         }
+         case Element::WEDGE:
+         {
+            for (int j = 0; j < 2; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               sfaces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]);
+            }
+            for (int j = 2; j < 5; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               sfaces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+            }
+            break;
+         }
+         case Element::HEXAHEDRON:
+         {
+            // find the face by the vertices with the smallest 3 numbers
+            // z = 0, y = 0, x = 1, y = 1, x = 0, z = 1
+            for (int j = 0; j < 6; j++)
+            {
+               const int *fv = hex_t::FaceVert[j];
+               sfaces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+            }
+            break;
+         }
+         default:
+            MFEM_ABORT("Unexpected type of Element.");
+      }
+   }
+   return sfaces_tbl;
+}
+
+STable3D *ParMesh::GetFaceNbrElementToFaceTable(int ret_ftbl)
+{
+   int i, *v;
+   STable3D * faces_tbl = GetFacesTable();
+   STable3D * sfaces_tbl = GetSharedFacesTable();
+
+   if (face_nbr_el_to_face != NULL)
+   {
+      delete face_nbr_el_to_face;
+   }
+   face_nbr_el_to_face = new Table(face_nbr_elements.Size(), 6);
+   for (i = 0; i < face_nbr_elements.Size(); i++)
+   {
+      v = face_nbr_elements[i]->GetVertices();
+      switch (face_nbr_elements[i]->GetType())
+      {
+         case Element::TETRAHEDRON:
+         {
+            for (int j = 0; j < 4; j++)
+            {
+               const int *fv = tet_t::FaceVert[j];
+               int lf = faces_tbl->Index(v[fv[0]], v[fv[1]], v[fv[2]]);
+               if (lf < 0)
+               {
+                  lf = sfaces_tbl->Index(v[fv[0]], v[fv[1]], v[fv[2]]);
+                  if (lf >= 0)
+                  {
+                     lf += NumOfFaces;
+                  }
+               }
+               face_nbr_el_to_face->Push(i, lf);
+            }
+            break;
+         }
+         case Element::WEDGE:
+         {
+            for (int j = 0; j < 2; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               face_nbr_el_to_face->Push(
+                  i, faces_tbl->Index(v[fv[0]], v[fv[1]], v[fv[2]]));
+            }
+            for (int j = 2; j < 5; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               int k = 0;
+               int max = v[fv[0]];
+
+               if (max < v[fv[1]]) { max = v[fv[1]], k = 1; }
+               if (max < v[fv[2]]) { max = v[fv[2]], k = 2; }
+               if (max < v[fv[3]]) { k = 3; }
+
+               switch (k)
+               {
+                  case 0:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[1]],v[fv[2]],v[fv[3]]));
+                     break;
+                  case 1:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[2]],v[fv[3]]));
+                     break;
+                  case 2:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[1]],v[fv[3]]));
+                     break;
+                  case 3:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[1]],v[fv[2]]));
+                     break;
+               }
+            }
+            break;
+         }
+         case Element::HEXAHEDRON:
+         {
+            // find the face by the vertices with the smallest 3 numbers
+            // z = 0, y = 0, x = 1, y = 1, x = 0, z = 1
+            for (int j = 0; j < 6; j++)
+            {
+               const int *fv = hex_t::FaceVert[j];
+               int k = 0;
+               int max = v[fv[0]];
+
+               if (max < v[fv[1]]) { max = v[fv[1]], k = 1; }
+               if (max < v[fv[2]]) { max = v[fv[2]], k = 2; }
+               if (max < v[fv[3]]) { k = 3; }
+
+               switch (k)
+               {
+                  case 0:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[1]],v[fv[2]],v[fv[3]]));
+                     break;
+                  case 1:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[2]],v[fv[3]]));
+                     break;
+                  case 2:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[1]],v[fv[3]]));
+                     break;
+                  case 3:
+                     face_nbr_el_to_face->Push(
+                        i, faces_tbl->Index(v[fv[0]],v[fv[1]],v[fv[2]]));
+                     break;
+               }
+            }
+            break;
+         }
+         default:
+            MFEM_ABORT("Unexpected type of Element.");
+      }
+   }
+   face_nbr_el_to_face->Finalize();
+
+   if (ret_ftbl)
+   {
+      return faces_tbl;
+   }
+   delete faces_tbl;
+   return NULL;
+}
+
 int ParMesh::GetFaceNbrRank(int fn) const
 {
    if (Conforming())
@@ -2528,6 +2736,37 @@ int ParMesh::GetFaceNbrRank(int fn) const
    }
 }
 
+void
+ParMesh::GetFaceNbrElementFaces(int i, Array<int> &fcs, Array<int> &cor) const
+{
+   int n, j;
+   int el_nbr = i - GetNE();
+   if (face_nbr_el_to_face)
+   {
+      face_nbr_el_to_face->GetRow(el_nbr, fcs);
+   }
+   else
+   {
+      MFEM_ABORT("ParMesh::GetFaceNbrElementFaces(...) : "
+                 "face_nbr_el_to_face not generated.");
+   }
+   if (el_nbr < face_nbr_el_ori.Size())
+   {
+      const int * row = face_nbr_el_ori.GetRow(el_nbr);
+      n = fcs.Size();
+      cor.SetSize(n);
+      for (j=0; j<n; j++)
+      {
+         cor[j] = row[j];
+      }
+   }
+   else
+   {
+      MFEM_ABORT("ParMesh::GetFaceNbrElementFaces(...) : "
+                 "face_nbr_el_to_face not generated.");
+   }
+}
+
 Table *ParMesh::GetFaceToAllElementTable() const
 {
    const Array<int> *s2l_face;

mesh/pmesh.hpp

@@ -75,6 +75,9 @@ protected:
    // sface ids: all triangles first, then all quads
    Array<int> sface_lface;
 
+   Table *face_nbr_el_to_face;
+   Table  face_nbr_el_ori; // orientations for each face (from nbr processor)
+
    IsoparametricTransformation FaceNbrTransformation;
 
    // glob_elem_offset + local element number defines a global element numbering
@@ -103,6 +106,8 @@ protected:
    bool DecodeFaceSplittings(HashTable<Hashed2> &v_to_v, const int *v,
                              const Array<unsigned> &codes, int &pos);
 
+   STable3D *GetFaceNbrElementToFaceTable(int ret_ftbl = 0);
+
    void GetFaceNbrElementTransformation(
       int i, IsoparametricTransformation *ElTr);
 
@@ -196,6 +201,9 @@ protected:
    void BuildSharedVertMapping(int nvert, const Table* vert_element,
                                const Array<int> &vert_global_local);
 
+   // Similar to Mesh::GetFacesTable()
+   STable3D *GetSharedFacesTable();
+
    /// Ensure that bdr_attributes and attributes agree across processors
    void DistributeAttributes(Array<int> &attr);
 
@@ -216,8 +224,9 @@ protected:
 
 public:
    /// Default constructor. Create an empty @a ParMesh.
-   ParMesh() : MyComm(0), NRanks(0), MyRank(-1), glob_elem_offset(-1),
-      glob_offset_sequence(-1), have_face_nbr_data(false), pncmesh(NULL) { }
+   ParMesh() : MyComm(0), NRanks(0), MyRank(-1), face_nbr_el_to_face(NULL),
+      glob_elem_offset(-1), glob_offset_sequence(-1),
+      have_face_nbr_data(false), pncmesh(NULL) { }
 
    /// Create a parallel mesh by partitioning a serial Mesh.
    /** The mesh is partitioned automatically or using external partitioning
@@ -341,6 +350,9 @@ public:
    int GetFaceNbrGroup(int fn) const { return face_nbr_group[fn]; }
    int GetFaceNbrRank(int fn) const;
 
+   /** Similar to Mesh::GetElementFaces */
+   void GetFaceNbrElementFaces(int i, Array<int> &fcs, Array<int> &cor) const;
+
    /** Similar to Mesh::GetFaceToElementTable with added face-neighbor elements
        with indices offset by the local number of elements. */
    Table *GetFaceToAllElementTable() const;
@@ -370,7 +382,7 @@ public:
    int GetSharedFace(int sface) const;
 
    /// See the remarks for the serial version in mesh.hpp
-   virtual void ReorientTetMesh();
+   MFEM_DEPRECATED virtual void ReorientTetMesh();
 
    /// Utility function: sum integers from all processors (Allreduce).
    virtual long ReduceInt(int value) const;

mesh/pumi.hpp

@@ -84,8 +84,7 @@ public:
        the PUMI and MFEM meshes. E.g.,
        PUMI_tet{v0,v1,v2,v3}  --->  MFEM_tet{v1,v0,v3,v2}
        * Note that change in the orientation can be caused by
-         a) fixing wrong boundary element orientations
-         b) a call to ReorientTetMesh() which is required for Nedelec */
+         fixing wrong boundary element orientations */
    int RotationPUMItoMFEM(apf::Mesh2* apf_mesh,
                           apf::MeshEntity* tet,
                           int elemId);

mesh/pyramid.cpp

@@ -0,0 +1,64 @@
+// Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+// Implementation of class Pyramid
+
+#include "mesh_headers.hpp"
+
+namespace mfem
+{
+
+Pyramid::Pyramid(const int *ind, int attr)
+   : Element(Geometry::PYRAMID)
+{
+   attribute = attr;
+   for (int i = 0; i < 5; i++)
+   {
+      indices[i] = ind[i];
+   }
+}
+
+Pyramid::Pyramid(int ind1, int ind2, int ind3, int ind4, int ind5, int attr)
+   : Element(Geometry::PYRAMID)
+{
+   attribute  = attr;
+   indices[0] = ind1;
+   indices[1] = ind2;
+   indices[2] = ind3;
+   indices[3] = ind4;
+   indices[4] = ind5;
+}
+
+void Pyramid::SetVertices(const int *ind)
+{
+   for (int i = 0; i < 5; i++)
+   {
+      indices[i] = ind[i];
+   }
+}
+
+void Pyramid::GetVertices(Array<int> &v) const
+{
+   v.SetSize(5);
+   for (int i = 0; i < 5; i++)
+   {
+      v[i] = indices[i];
+   }
+}
+
+int Pyramid::GetNFaces(int &nFaceVertices) const
+{
+   MFEM_ABORT("this method is not valid for Pyramid elements");
+   nFaceVertices = 4;
+   return 5;
+}
+
+}

mesh/pyramid.hpp

@@ -0,0 +1,78 @@
+// Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_PYRAMID
+#define MFEM_PYRAMID
+
+#include "../config/config.hpp"
+#include "element.hpp"
+
+namespace mfem
+{
+
+/// Data type Pyramid element
+class Pyramid : public Element
+{
+protected:
+   int indices[5];
+
+public:
+   typedef Geometry::Constants<Geometry::PYRAMID> geom_t;
+
+   Pyramid() : Element(Geometry::PYRAMID) { }
+
+   /// Constructs pyramid by specifying the indices and the attribute.
+   Pyramid(const int *ind, int attr = 1);
+
+   /// Constructs pyramid by specifying the indices and the attribute.
+   Pyramid(int ind1, int ind2, int ind3, int ind4, int ind5,
+           int attr = 1);
+
+   /// Return element's type.
+   virtual Type GetType() const { return Element::PYRAMID; }
+
+   /// Set the vertices according to the given input.
+   virtual void SetVertices(const int *ind);
+
+   /// Returns the indices of the element's  vertices.
+   virtual void GetVertices(Array<int> &v) const;
+
+   virtual int *GetVertices() { return indices; }
+
+   virtual int GetNVertices() const { return 5; }
+
+   virtual int GetNEdges() const { return 8; }
+
+   virtual const int *GetEdgeVertices(int ei) const
+   { return geom_t::Edges[ei]; }
+
+   /// @deprecated Use GetNFaces(void) and GetNFaceVertices(int) instead.
+   MFEM_DEPRECATED virtual int GetNFaces(int &nFaceVertices) const;
+
+   virtual int GetNFaces() const { return 5; }
+
+   virtual int GetNFaceVertices(int fi) const
+   { return ( ( fi < 1 ) ? 4 : 3); }
+
+   virtual const int *GetFaceVertices(int fi) const
+   { return geom_t::FaceVert[fi]; }
+
+   virtual Element *Duplicate(Mesh *m) const
+   { return new Pyramid(indices, attribute); }
+
+   virtual ~Pyramid() { }
+};
+
+extern class LinearPyramidFiniteElement PyramidFE;
+
+}
+
+#endif

mesh/wedge.hpp

@@ -71,8 +71,7 @@ public:
    virtual ~Wedge() { }
 };
 
-// Defined in fe.cpp to ensure construction after 'mfem::poly1d'.
-extern class H1_WedgeElement WedgeFE;
+extern class LinearWedgeFiniteElement WedgeFE;
 
 }