Move face map logic from restriction.cpp into FiniteElement derived classes

Use inheritance instead of switch statement to dispatch
Make SupportsDevice const
2023-01-09 20:46:51 -08:00 · 2023-01-09 19:40:21 -08:00 · 2023-01-09 19:35:51 -08:00 · 2023-01-09 19:17:26 -08:00 · 2023-01-08 17:14:57 -08:00 · 2023-01-05 08:55:45 -08:00
145 changed files with 1899 additions and 9196 deletions
@@ -141,7 +141,7 @@ jobs:

    - name: get MPI (Windows)
      if: matrix.mpi == 'par' && matrix.os == 'windows-latest'
-      uses: mpi4py/setup-mpi@v1.1.4
+      uses: mpi4py/setup-mpi@v1.1.2

    # Get Hypre through cache, or build it.
    # Install will only run on cache miss.
@@ -131,12 +131,6 @@ examples/hiop/ex9-mesh.*
 examples/hiop/ex9-init.*
 examples/hiop/ex9-final.*

-examples/ipopt/exContactBlockTL
-examples/ipopt/exContactBlockTL.mesh
-examples/ipopt/exContactBlockTL-mesh.*
-examples/ipopt/exContactBlockTL-init.*
-examples/ipopt/exContactBlockTL-final.*
-
 examples/petsc/ex[1-69]p
 examples/petsc/ex1[0-1]p
 examples/petsc/mesh.*
@@ -209,7 +203,6 @@ miniapps/meshing/mesh-explorer
 miniapps/meshing/shaper
 miniapps/meshing/extruder
 miniapps/meshing/trimmer
-miniapps/meshing/reflector
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
 miniapps/meshing/minimal-surface
@@ -221,12 +214,9 @@ miniapps/meshing/toroid-*.mesh
 miniapps/meshing/twist-*.mesh
 miniapps/meshing/mesh-explorer.mesh
 miniapps/meshing/partitioning.txt
-miniapps/meshing/mesh-explorer-visit*
-miniapps/meshing/mesh-explorer-paraview/
 miniapps/meshing/shaper.mesh
 miniapps/meshing/extruder.mesh
 miniapps/meshing/trimmer.mesh
-miniapps/meshing/reflected.mesh
 miniapps/meshing/optimized*
 miniapps/meshing/perturbed*
 miniapps/meshing/polar-nc.mesh
@@ -286,7 +276,6 @@ miniapps/tools/convert-dc
 miniapps/tools/lor-transfer
 miniapps/tools/get-values
 miniapps/tools/check-tmop-metric
-miniapps/tools/tmop-metric-magnitude

 miniapps/toys/automata
 miniapps/toys/life
@@ -93,7 +93,7 @@ report_baseline:
          git pull && \
          git add ${rundir} && \
          git commit -m "${msg}" && \
-          ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
+          git push origin master
        else
          for file in ${rundir}/*; do
            echo "------------------------------"
@@ -1,41 +0,0 @@
-#!/bin/bash
-
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
-
-# Try to push to the remote 5 times. If the push fails, and the local and remote
-# have diverged, then pull from the remote to merge changes, and try pushing
-# again. If some other failure happens
-for i in {1..5}; do
-   git push origin master && exit 0
-   # Wait for 20 seconds in case someone else is pushing to the remote
-   # concurrently
-   sleep 20
-   # Fetch any updates from the remote
-   git remote update
-   # Get the latest commit on the local branch
-   LOCAL=$(git rev-parse @)
-   # Get the latest commit on the remote
-   REMOTE=$(git rev-parse @{u})
-   # Get the common ancestor
-   BASE=$(git merge-base @ @{u})
-   # Have the local and remote diverged?
-   if [[ $LOCAL != $REMOTE && $LOCAL != $BASE && $REMOTE != $BASE ]]; then
-      git pull
-      if [[ $? == 0 ]]; then
-         continue
-      else
-         exit 1 # Something else went wrong trying to pull
-      fi
-   fi
-done
-
-exit 1 # Did not succeed in 5 attempts
@@ -32,7 +32,7 @@ if [[ "$AUTOTEST_COMMIT" != "NO" ]]; then
  git pull && \
  git add ${rundir} && \
  git commit -m "${msg}" && \
-  ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
+  git push origin master
 else
  for file in ${rundir}/*; do
    echo "------------------------------"
@@ -29,7 +29,7 @@ if [[ "$AUTOTEST_COMMIT" != "NO" ]]; then
  git pull && \
  git add ${rundir} && \
  git commit -m "${msg}" && \
-  ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
+  git push origin master
 else
  for file in ${rundir}/*; do
    echo "------------------------------"
@@ -10,26 +10,18 @@

 Version 4.5.1 (development)
 ===========================
- When using discontinuous (L2) spaces, use local (element-wise) L2 projection
-  as the coarsening operator for non-conforming AMR meshes.

 Meshing improvements
 --------------------
 - Added support for pyramids in non-conforming meshes. Currently only isotropic
  refinement is supported in this case.

- Updated logic in FindPointsGSLIB to ignore points found near (but outside) the
-  domain boundary.
-
- Added support for pyramids in Gmsh meshes.
-
- Fixed a bug in TMOP metric 301.
-
- Added an option to auto-balance compound TMOP metrics.
-
 Discretization improvements
 ---------------------------
- TBD
+- Face restriction operators for Nedelec and Raviart-Thomas finite element
+  spaces are now supported through the H1_ND_RT_FaceRestriction class.
+
+- VectorFEBoundaryFluxLFIntegrator is now supported on device/GPU.

 Linear and nonlinear solvers
 ----------------------------
@@ -38,12 +30,7 @@ Linear and nonlinear solvers

 New and updated examples and miniapps
 -------------------------------------
- Added a new meshing miniapp, reflector, which reflects a high-order or NURBS
-  hexahedral mesh about a plane.
-
- The mesh-explorer miniapp can now save mesh files in the VisIt or ParaView
-  formats using the corresponding DataCollection objects. See option 'D' in the
-  main menu.
+- TBD

 Integrations, testing and documentation
 ---------------------------------------
@@ -69,9 +56,6 @@ API changes
  have been deprecated and generate deprecation warnings if used. They will be
  removed in a future release.

- The methods Mesh::GetFaceBaseGeometry and Mesh::GetFaceGeometryType have been
-  deprecated, and Mesh::GetFaceGeometry (which provides identical functionality)
-  should be used instead.

 Version 4.5, released on October 22, 2022
 =========================================
@@ -116,9 +100,6 @@ Discretization improvements
 - Added a class CoefficientVector for efficient access of variable coefficient
  values at quadrature points (in particular for GPU/device kernels).

- Added support for GridFunction::GetGradients() and
-  GriFunction::GetVectorGradient() on face-neighbor elements.
-
 - Added WhiteGaussianNoiseDomainLFIntegrator: a LinearFormIntegrator class for
  spatial Gaussian white noise.

@@ -134,7 +134,8 @@ if (MFEM_USE_CUDA)
      set(CUDA_FLAGS "-ccbin=${CMAKE_CXX_COMPILER} ${CUDA_FLAGS}")
      set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CMAKE_CXX_COMPILER})
   endif()
-   set(CMAKE_CUDA_FLAGS ${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS})
+   set(CMAKE_CUDA_FLAGS "${CUDA_FLAGS}" CACHE STRING
+       "CUDA flags set for MFEM" FORCE)
   set(CUSPARSE_FOUND TRUE)
   set(CUSPARSE_LIBRARIES "cusparse")
   set(CUBLAS_FOUND TRUE)
@@ -404,15 +405,6 @@ if (MFEM_USE_HIOP)
  # find_package updates HIOP_FOUND, HIOP_INCLUDE_DIRS, HIOP_LIBRARIES
 endif()

-# IpOpt optimizer
-if (MFEM_USE_IPOPT)
-  find_package(IPOPT REQUIRED)
-  message(
-      STATUS
-      "IPOPT_INCLUDE_DIRS=${IPOPT_INCLUDE_DIRS}, IPOPT_LIBRARIES=${IPOPT_LIBRARIES}, IPOPT_DIR=${IPOPT_DIR}")
-  # find_package updates IPOPT_FOUND, IPOPT_INCLUDE_DIRS, IPOPT_LIBRARIES
-endif()
-
 # CoDiPack package
 if (MFEM_USE_CODIPACK)
  find_package(CODIPACK REQUIRED)
@@ -508,7 +500,7 @@ find_package(Threads REQUIRED)
 #    be before SuiteSparse.
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
-    NETCDF MPFR PUMI HIOP IPOPT POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
+    NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
    ADIOS2 CUBLAS CUSPARSE MKL_CPARDISO AMGX CALIPER CODIPACK BENCHMARK PARELAG
    MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)

@@ -706,8 +698,6 @@ add_subdirectory(doc)
 message(STATUS "CMAKE_INSTALL_PREFIX = ${CMAKE_INSTALL_PREFIX}")
 set(INSTALL_INCLUDE_DIR include
  CACHE PATH "Relative path for installing header files.")
-set(INSTALL_BIN_DIR bin
-  CACHE PATH "Relative path for installing the binaries.")
 set(INSTALL_LIB_DIR lib
  CACHE PATH "Relative path for installing the library.")
 # other options: "share/mfem/cmake", "lib/mfem/cmake"
@@ -726,9 +716,7 @@ set(CMAKE_INSTALL_DEFAULT_COMPONENT_NAME Development)
 # Install the library
 install(TARGETS ${PROJECT_NAME}
  EXPORT ${PROJECT_NAME_UC}Targets
-  RUNTIME DESTINATION ${INSTALL_BIN_DIR}
-  LIBRARY DESTINATION ${INSTALL_LIB_DIR}
-  ARCHIVE DESTINATION ${INSTALL_LIB_DIR})
+  DESTINATION ${INSTALL_LIB_DIR})

 # Install the master headers
 foreach(Header mfem.hpp mfem-performance.hpp)
@@ -112,7 +112,6 @@ The MFEM source code has the following structure:
  │   ├── caliper
  │   ├── ginkgo
  │   ├── hiop
-  │   ├── ipopt
  │   ├── jupyter
  │   ├── moonolith
  │   ├── petsc
@@ -471,9 +471,6 @@ MFEM_USE_HIOP = YES/NO
   Enable the usage of HiOp (https://github.com/LLNL/hiop) in MFEM. HiOp is an
   HPC solver for nonlinear optimization problems.

-MFEM_USE_IPOPT = YES/NO
-   Enable the usage of Ipopt in MFEM.
-
 MFEM_USE_CODIPACK = YES/NO
  Enable automatic differentiation using the CoDiPack library.
  www.scicomp.uni-kl.de/codi/
@@ -741,11 +738,6 @@ The specific libraries and their options are:
  Options: HIOP_OPT, HIOP_LIB.
  Versions: HIOP >= 0.4.6.

- Ipopt (optional), used when MFEM_USE_IPOPT = YES.
-  URL: https://github.com/coin-or/Ipopt
-  Options: IPOPT_OPT, IPOPT_LIB.
-  Versions: IPOPT >= 3.14
-
 - CoDiPack (optional), used with MFEM_USE_CODIPACK = YES
  URL: https://www.scicomp.uni-kl.de/codi/
  Options: CODIPACK_OPT
@@ -980,7 +972,6 @@ MFEM_USE_MPFR
 MFEM_USE_ZLIB
 MFEM_USE_PUMI
 MFEM_USE_HIOP
-MFEM_USE_IPOPT
 MFEM_USE_CODIPACK
 MFEM_USE_ADFORWARD
 MFEM_USE_CUDA
@@ -1044,7 +1035,6 @@ The CMake build system adds auto-detection for the following packages/libraries:
 - POSIXCLOCKS
 - PUMI
 - HIOP
- - IPOPT
 - CoDiPack
 - OCCA
 - RAJA
@@ -36,7 +36,6 @@ set(MFEM_USE_STRUMPACK @MFEM_USE_STRUMPACK@)
 set(MFEM_USE_GINKGO @MFEM_USE_GINKGO@)
 set(MFEM_USE_AMGX @MFEM_USE_AMGX@)
 set(MFEM_USE_HIOP @MFEM_USE_HIOP@)
-set(MFEM_USE_IPOPT @MFEM_USE_IPOPT@)
 set(MFEM_USE_GNUTLS @MFEM_USE_GNUTLS@)
 set(MFEM_USE_GSLIB @MFEM_USE_GSLIB@)
 set(MFEM_USE_NETCDF @MFEM_USE_NETCDF@)
@@ -131,9 +131,6 @@
 // Enable MFEM functionality based on the HiOp library
 #cmakedefine MFEM_USE_HIOP

-// Enable MFEM functionality based on the Ipopt library
-#cmakedefine MFEM_USE_IPOPT
-
 // Build the GPU/CUDA-enabled version of the MFEM library.
 // Requires a CUDA compiler (nvcc).
 #cmakedefine MFEM_USE_CUDA
@@ -16,7 +16,7 @@

 include(MfemCmakeUtilities)
 mfem_find_package(Algoim ALGOIM ALGOIM_DIR
-        "include;src" "algoim_quad.hpp"
+       	"include" "algoim_quad.hpp"
       	"" ""
-        "Paths to headers required by Algoim."
-        "Libraries required by Algoim.")
+	"Paths to headers required by Algoim."
+	"Libraries required by Algoim.")
@@ -1,23 +0,0 @@
-# Copyright (c) 2010-2022, 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.
-
-# Sets the following variables:
-#   - IPOPT_FOUND
-#   - IPOPT_INCLUDE_DIRS
-#   - IPOPT_LIBRARIES
-
-include(MfemCmakeUtilities)
-mfem_find_package(IPOPT IPOPT IPOPT_DIR
-  "include" "IpTNLP.hpp"
-  "lib" "ipopt"
-  "Paths to headers required by IPOPT."
-  "Libraries required by IPOPT.")
-
@@ -869,7 +869,7 @@ function(mfem_export_mk_files)
      MFEM_USE_SUPERLU MFEM_USE_SUPERLU5 MFEM_USE_MUMPS MFEM_USE_STRUMPACK
      MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_GNUTLS MFEM_USE_NETCDF
      MFEM_USE_PETSC MFEM_USE_SLEPC MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_FMS
-      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_IPOPT MFEM_USE_GSLIB MFEM_USE_CUDA
+      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_GSLIB MFEM_USE_CUDA
      MFEM_USE_HIP MFEM_USE_RAJA MFEM_USE_OCCA MFEM_USE_CEED MFEM_USE_CALIPER
      MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2 MFEM_USE_MKL_CPARDISO
      MFEM_USE_ADFORWARD MFEM_USE_CODIPACK MFEM_USE_BENCHMARK MFEM_USE_PARELAG
@@ -141,9 +141,6 @@
 // Enable MFEM functionality based on the HIOP library.
 // #define MFEM_USE_HIOP

-// Enable MFEM functionality based on the IPOPT library.
-// #define MFEM_USE_IPOPT
-
 // Enable MFEM functionality based on the GSLIB library
 // #define MFEM_USE_GSLIB

@@ -46,7 +46,6 @@ MFEM_USE_FMS           = @MFEM_USE_FMS@
 MFEM_USE_CONDUIT       = @MFEM_USE_CONDUIT@
 MFEM_USE_PUMI          = @MFEM_USE_PUMI@
 MFEM_USE_HIOP          = @MFEM_USE_HIOP@
-MFEM_USE_IPOPT          = @MFEM_USE_IPOPT@
 MFEM_USE_GSLIB         = @MFEM_USE_GSLIB@
 MFEM_USE_CUDA          = @MFEM_USE_CUDA@
 MFEM_USE_HIP           = @MFEM_USE_HIP@
@@ -48,7 +48,6 @@ option(MFEM_USE_FMS "Enable FMS usage" OFF)
 option(MFEM_USE_CONDUIT "Enable Conduit usage" OFF)
 option(MFEM_USE_PUMI "Enable PUMI" OFF)
 option(MFEM_USE_HIOP "Enable HiOp" OFF)
-option(MFEM_USE_IPOPT "Enable Ipopt" OFF)
 option(MFEM_USE_CUDA "Enable CUDA" OFF)
 option(MFEM_USE_HIP "Enable HIP" OFF)
 option(MFEM_USE_OCCA "Enable OCCA" OFF)
@@ -221,10 +220,6 @@ set(HIOP_DIR "${MFEM_DIR}/../hiop/install" CACHE STRING
    "Directory where HiOp is installed")
 set(HIOP_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
    "Packages that HiOp depends on.")
-set(IPOPT_DIR "${MFEM_DIR}/../ipopt/install" CACHE STRING
-    "Directory where IpOpt is installed")
-set(IPOPT_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
-    "Packages that IpOpt depends on.")

 set(MKL_CPARDISO_DIR "" CACHE STRING "MKL installation path.")
 set(MKL_MPI_WRAPPER_LIB "mkl_blacs_mpich_lp64" CACHE STRING "MKL MPI wrapper library")
@@ -237,7 +232,7 @@ set(UMPIRE_DIR "${MFEM_DIR}/../umpire" CACHE PATH "Path to Umpire")
 set(CALIPER_DIR "${MFEM_DIR}/../caliper" CACHE PATH "Path to Caliper")
 set(BLITZ_DIR "${MFEM_DIR}/../blitz" CACHE PATH "Path to Blitz")
 set(ALGOIM_DIR "${MFEM_DIR}/../algoim" CACHE PATH "Path to Algoim")
-set(Algoim_REQUIRED_PACKAGES "Blitz" CACHE STRING
+set(ALGOIM_REQUIRED_PACKAGES "BLITZ" CACHE STRING
    "Packages that ALGOIM depends on.")

 set(BENCHMARK_DIR "${MFEM_DIR}/../google-benchmark" CACHE PATH
@@ -148,7 +148,6 @@ MFEM_USE_FMS           = NO
 MFEM_USE_CONDUIT       = NO
 MFEM_USE_PUMI          = NO
 MFEM_USE_HIOP          = NO
-MFEM_USE_IPOPT         = NO
 MFEM_USE_GSLIB         = NO
 MFEM_USE_CUDA          = NO
 MFEM_USE_HIP           = NO
@@ -448,11 +447,6 @@ HIOP_DIR = @MFEM_DIR@/../hiop/install
 HIOP_OPT = -I$(HIOP_DIR)/include
 HIOP_LIB = -L$(HIOP_DIR)/lib -lhiop $(LAPACK_LIB)

-# IPOPT
-IPOPT_DIR = @MFEM_DIR@/../ipopt/install
-IPOPT_OPT = -I$(IPOPT_DIR)/include
-IPOPT_LIB = -L$(IPOPT_DIR)/lib -lipopt $(LAPACK_LIB)
-
 # CoDiPack
 CODIPACK_DIR = @MFEM_DIR@/../CoDiPack
 CODIPACK_OPT = -I$(CODIPACK_DIR)
@@ -58,10 +58,6 @@ groups_serial=(
   "HiOp examples:"
   "examples/hiop"
   "ex9.cpp"'
-'"ipopt"
-   "IpOpt examples:"
-   "examples/ipopt"
-   "ex10.cpp"'
 '"pumi"
   "PUMI examples:"
   "examples/pumi"
@@ -219,10 +215,6 @@ groups_all=(
   "HiOp examples:"
   "examples/hiop"
   "ex9.cpp ex9p.cpp"'
-'"ipopt"
-   "IpOpt examples:"
-   "examples/ipopt"
-   "ex10.cpp"'
 '"pumi"
   "PUMI examples:"
   "examples/pumi"
@@ -785,7 +785,6 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/examples/caliper \
                         @MFEM_SOURCE_DIR@/examples/ginkgo \
                         @MFEM_SOURCE_DIR@/examples/hiop \
-                         @MFEM_SOURCE_DIR@/examples/ipopt \
                         @MFEM_SOURCE_DIR@/examples/moonolith \
                         @MFEM_SOURCE_DIR@/examples/petsc \
                         @MFEM_SOURCE_DIR@/examples/pumi \
@@ -178,11 +178,6 @@ if (MFEM_USE_HIOP)
  add_subdirectory(hiop)
 endif()

-# Include the examples/ipopt directory if IpOpt is enabled
-if (MFEM_USE_IPOPT)
-  add_subdirectory(ipopt)
-endif()
-
 # Include the examples/petsc directory if PETSc is enabled.
 if (MFEM_USE_PETSC)
  add_subdirectory(petsc)
@@ -1,810 +0,0 @@
-//                                Contact example
-//
-// Compile with: make contact
-//
-// Sample runs:  ./contact -m1 block1.mesh -m2 block2.mesh -at "5 6 7 8"
-// Sample runs:  ./contact -m1 block1_d.mesh -m2 block2_d.mesh -at "5 6 7 8"
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-#include "nodepair.hpp"
-
-using namespace std;
-using namespace mfem;
-
-bool ifequalarray(const Array<int> a1, const Array<int> a2)
-{
-   if (a1.Size()!=a2.Size())
-   {
-      return false;
-   }
-   for (int i=0; i<a1.Size(); i++)
-   {
-      if (a1[i] != a2[i])
-      {
-         return false;
-      }
-   }
-   return true;
-}
-
-void FindSurfaceToProject(Mesh& mesh, const int elem, int& cbdrface)
-{
-   Array<int> attr;
-   attr.Append(2);
-   Array<int> faces;
-   Array<int> ori;
-   std::vector<Array<int> > facesVertices;
-   std::vector<int > faceid;
-   mesh.GetElementFaces(elem, faces, ori);
-   int face = -1;
-   for (int i=0; i<faces.Size(); i++)
-   {
-      face = faces[i];
-      Array<int> faceVert;
-      if (!mesh.FaceIsInterior(face)) // if on the boundary
-      {
-         mesh.GetFaceVertices(face, faceVert);
-         faceVert.Sort();
-         facesVertices.push_back(faceVert);
-         faceid.push_back(face);
-      }
-   }
-   int bdrface = facesVertices.size();
-
-   Array<int> bdryFaces;
-   // This shoulnd't need to be rebuilt
-   std::vector<Array<int> > bdryVerts;
-   for (int b=0; b<mesh.GetNBE(); ++b)
-   {
-      if (attr.FindSorted(mesh.GetBdrAttribute(b)) >= 0)  // found the contact surface
-      {
-         bdryFaces.Append(b);
-         Array<int> vert;
-         mesh.GetBdrElementVertices(b, vert);
-         vert.Sort();
-         bdryVerts.push_back(vert);
-      }
-   }
-
-   int bdrvert = bdryVerts.size();
-   cbdrface = -1;  // the face number of the contact surface element
-   int count_cbdrface = 0;  // the number of matching surfaces, used for checks
-
-   for (int i=0; i<bdrface; i++)
-   {
-      for (int j=0; j<bdrvert; j++)
-      {
-         if (ifequalarray(facesVertices[i], bdryVerts[j]))
-         {
-            cbdrface = faceid[i];
-            count_cbdrface += 1;
-         }
-      }
-   }
-   MFEM_VERIFY(count_cbdrface == 1,"projection surface not found");
-
-};
-
-Vector GetNormalVector(Mesh & mesh, const int elem, const double *ref,
-                       int & refFace, int & refNormal, bool & interior)
-{
-   ElementTransformation *trans = mesh.GetElementTransformation(elem);
-   const int dim = mesh.Dimension();
-   const int spaceDim = trans->GetSpaceDim();
-
-   MFEM_VERIFY(spaceDim == 3, "");
-
-   Vector n(spaceDim);
-
-   IntegrationPoint ip;
-   ip.Set(ref, dim);
-
-   trans->SetIntPoint(&ip);
-   //CalcOrtho(trans->Jacobian(), n);  // Works only for face transformations
-   const DenseMatrix jac = trans->Jacobian();
-
-   int dimNormal = -1;
-   int normalSide = -1;
-
-   const double tol = 1.0e-8;
-   for (int i=0; i<dim; ++i)
-   {
-      const double d0 = std::abs(ref[i]);
-      const double d1 = std::abs(ref[i] - 1.0);
-
-      const double d = std::min(d0, d1);
-      // TODO: this works only for hexahedral meshes!
-
-      if (d < tol)
-      {
-         MFEM_VERIFY(dimNormal == -1, "");
-         dimNormal = i;
-
-         if (d0 < tol)
-         {
-            normalSide = 0;
-         }
-         else
-         {
-            normalSide = 1;
-         }
-      }
-   }
-   // closest point on the boundary
-   if (dimNormal < 0 || normalSide < 0) // node is inside the element
-   {
-      interior = 1;
-      Vector n(3);
-      n = 0.0;
-      return n;
-   }
-
-   MFEM_VERIFY(dimNormal >= 0 && normalSide >= 0, "");
-   refNormal = dimNormal;
-
-   MFEM_VERIFY(dim == 3, "");
-
-   {
-      // Find the reference face
-      if (dimNormal == 0)
-      {
-         refFace = (normalSide == 1) ? 2 : 4;
-      }
-      else if (dimNormal == 1)
-      {
-         refFace = (normalSide == 1) ? 3 : 1;
-      }
-      else
-      {
-         refFace = (normalSide == 1) ? 5 : 0;
-      }
-   }
-
-   std::vector<Vector> tang(2);
-
-   int tangDir[2] = {-1, -1};
-   {
-      int t = 0;
-      for (int i=0; i<dim; ++i)
-      {
-         if (i != dimNormal)
-         {
-            tangDir[t] = i;
-            t++;
-         }
-      }
-
-      MFEM_VERIFY(t == 2, "");
-   }
-
-   for (int i=0; i<2; ++i)
-   {
-      tang[i].SetSize(3);
-
-      Vector tangRef(3);
-      tangRef = 0.0;
-      tangRef[tangDir[i]] = 1.0;
-
-      jac.Mult(tangRef, tang[i]);
-   }
-
-   Vector c(3);  // Cross product
-
-   c[0] = (tang[0][1] * tang[1][2]) - (tang[0][2] * tang[1][1]);
-   c[1] = (tang[0][2] * tang[1][0]) - (tang[0][0] * tang[1][2]);
-   c[2] = (tang[0][0] * tang[1][1]) - (tang[0][1] * tang[1][0]);
-
-   c /= c.Norml2();
-
-   Vector nref(3);
-   nref = 0.0;
-   nref[dimNormal] = 1.0;
-
-   Vector ndir(3);
-   jac.Mult(nref, ndir);
-
-   ndir /= ndir.Norml2();
-
-   const double dp = ndir * c;
-
-   // TODO: eliminate c?
-   n = c;
-   if (dp < 0.0)
-   {
-      n *= -1.0;
-   }
-   interior = 0;
-   return n;
-}
-
-// WARNING: global variable, just for this little example.
-std::array<std::array<int, 3>, 8> HEX_VERT =
-{
-   {  {0,0,0},
-      {1,0,0},
-      {1,1,0},
-      {0,1,0},
-      {0,0,1},
-      {1,0,1},
-      {1,1,1},
-      {0,1,1}
-   }
-};
-
-int GetHexVertex(int cdim, int c, int fa, int fb, Vector & refCrd)
-{
-   int ref[3];
-   ref[cdim] = c;
-   ref[cdim == 0 ? 1 : 0] = fa;
-   ref[cdim == 2 ? 1 : 2] = fb;
-
-   for (int i=0; i<3; ++i) { refCrd[i] = ref[i]; }
-
-   int refv = -1;
-
-   for (int i=0; i<8; ++i)
-   {
-      bool match = true;
-      for (int j=0; j<3; ++j)
-      {
-         if (ref[j] != HEX_VERT[i][j]) { match = false; }
-      }
-
-      if (match) { refv = i; }
-   }
-
-   MFEM_VERIFY(refv >= 0, "");
-
-   return refv;
-}
-
-// Coordinates in xyz are assumed to be ordered as [X, Y, Z]
-// where X is the list of x-coordinates for all points and so on.
-// conn: connectivity of the target surface elements
-// xi: surface reference cooridnates for the cloest point, involves a linear transformation from [0,1] to [-1,1]
-void FindPointsInMesh(Mesh & mesh, Vector const& xyz, Array<int>& conn,
-                      Vector& xi)
-{
-   const int dim = mesh.Dimension();
-   const int np = xyz.Size() / dim;
-
-   MFEM_VERIFY(np * dim == xyz.Size(), "");
-
-   mesh.EnsureNodes();
-
-   //FindPointsGSLIB finder(MPI_COMM_WORLD);
-   FindPointsGSLIB finder;
-
-   finder.SetDistanceToleranceForPointsFoundOnBoundary(0.5);
-
-   const double bb_t = 0.5;
-   finder.Setup(mesh, bb_t);
-
-   finder.FindPoints(xyz);
-
-   /// Return code for each point searched by FindPoints: inside element (0), on
-   /// element boundary (1), or not found (2).
-   Array<unsigned int> codes = finder.GetCode();
-
-   /// Return element number for each point found by FindPoints.
-   Array<unsigned int> elems = finder.GetElem();
-
-   /// Return reference coordinates for each point found by FindPoints.
-   Vector refcrd = finder.GetReferencePosition();
-
-   /// Return distance between the sought and the found point in physical space,
-   /// for each point found by FindPoints.
-   Vector dist = finder.GetDist();
-
-   MFEM_VERIFY(dist.Size() == np, "");
-   MFEM_VERIFY(refcrd.Size() == np * dim, "");
-   MFEM_VERIFY(elems.Size() == np, "");
-   MFEM_VERIFY(codes.Size() == np, "");
-
-   bool allfound = true;
-   for (auto code : codes)
-      if (code == 2) { allfound = false; }
-
-   MFEM_VERIFY(allfound, "A point was not found");
-
-   cout << "Maximum distance of projected points: " << dist.Max() << endl;
-
-   // extract information
-   for (int i=0; i<np; ++i)
-   {
-      /*cout << "Point " << i << ": (";
-      for (int j=0; j<dim; ++j)
-      {
-         cout << xyz[i + (j*np)];
-         if (j == dim-1) {cout << ")" << endl;}
-         else{cout << ", ";}
-      }*/
-      //cout << "  element: " << elems[i] << endl;
-      //cout << "  element " << elems[i] << " vertices:" << endl;
-      //Array<int> vert;
-      //mesh.GetElementVertices(elems[i], vert);
-      //for (auto v : vert)
-      //{
-      //   cout << "    " << v << endl;
-      //}
-
-      /*cout << "  reference coordinates: (";
-      for (int j=0; j<dim; ++j)
-      {
-         cout << refcrd[(i*dim) + j];
-         if (j == dim-1)
-         {
-            cout << ")" << endl;
-         }
-         else
-         {
-            cout << ", ";
-         }
-      }*/
-
-      int refFace, refNormal, refNormalSide;
-      bool is_interior = -1;
-      Vector normal = GetNormalVector(mesh, elems[i], refcrd.GetData() + (i*dim),
-                                      refFace, refNormal, is_interior);
-      int phyFace;
-      if (is_interior)
-      {
-         phyFace = -1; // the id of the face that has the closest point
-         FindSurfaceToProject(mesh, elems[i], phyFace);
-
-         Array<int> cbdrVert;
-         mesh.GetFaceVertices(phyFace, cbdrVert);
-         Vector xs(dim);
-         xs[0] = xyz[i + 0*np];
-         xs[1] = xyz[i + 1*np];
-         xs[2] = xyz[i + 2*np];
-         Vector xi_tmp(dim-1);
-         // get nodes!
-
-         GridFunction *nodes = mesh.GetNodes();
-         DenseMatrix coords(4,3);
-         for (int i=0; i<4; i++)
-         {
-            for (int j=0; j<3; j++)
-            {
-               coords(i,j) = (*nodes)[cbdrVert[i]*3+j];
-            }
-         }
-         SlaveToMaster(coords, xs, xi_tmp);
-
-         for (int j=0; j<dim-1; ++j)
-         {
-            xi[i*(dim-1)+j] = xi_tmp[j];
-         }
-         // now get get the projection to the surface
-      }
-      else
-      {
-         Vector faceRefCrd(dim-1);
-         {
-            int fd = 0;
-            for (int j=0; j<dim; ++j)
-            {
-               if (j == refNormal)
-               {
-                  refNormalSide = (refcrd[(i*dim) + j] > 0.5);
-               }
-               else
-               {
-                  faceRefCrd[fd] = refcrd[(i*dim) + j];
-                  fd++;
-               }
-            }
-
-            MFEM_VERIFY(fd == dim-1, "");
-         }
-
-         for (int j=0; j<dim-1; ++j)
-         {
-            xi[i*(dim-1)+j] = faceRefCrd[j]*2.0 - 1.0;
-         }
-         //cout << "  face reference coordinates: (";
-         /*for (int j=0; j<dim-1; ++j)
-         {
-            cout << faceRefCrd[j];
-            if (j == dim-2){cout << ")" << endl;}
-            else{cout << ", ";}
-         }*/
-      }
-      //cout << "  normal vector: ";
-      //normal.Print();
-
-      // ask, does this do anything?
-      /*
-      IntegrationPoint ip;
-      ip.Set(refcrd.GetData() + (i*dim), dim);
-      ElementTransformation *trans = mesh.GetElementTransformation(elems[i]);
-      Vector phys(trans->GetSpaceDim());
-      trans->Transform(ip, phys);
-      cout << "  physical coordinates: ";
-      phys.Print();
-      */
-
-      // Get the element face
-      Array<int> faces;
-      Array<int> ori;
-      int face;
-
-      if (is_interior)
-      {
-         face = phyFace;
-      }
-      else
-      {
-         mesh.GetElementFaces(elems[i], faces, ori);
-         face = faces[refFace];
-      }
-
-      Array<int> faceVert;
-      mesh.GetFaceVertices(face, faceVert);
-
-      //cout << "  face " << face << " vertices:" << endl;
-      //for (auto v : faceVert){ cout << "    " << v << endl;}
-
-      for (int p=0; p<4; p++)
-      {
-         conn[4*i+p] = faceVert[p];
-      }
-      /*
-      Vector ref(dim);
-
-      for (int p=0; p<2; ++p)
-         for (int q=0; q<2; ++q)
-         {
-            const int refv = GetHexVertex(refNormal, refNormalSide, p, q, ref);
-            cout << "  face reference vertex (" << p << "," << q
-                 << ") is global vertex " << vert[refv] << endl;
-
-            {
-               // Sanity check
-               ip.Set(ref.GetData(), dim);
-               trans->Transform(ip, phys);
-               for (int j=0; j<dim; ++j)
-               {
-                  phys[j] -= mesh.GetVertex(vert[refv])[j];
-               }
-          phys.Print();
-          cout<<vert[refv]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[0]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[1]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[2]<<endl;
-               MFEM_VERIFY(phys.Norml2() < 1.0e-12, "Sanity check failed");
-            }
-         }*/
-   }
-}
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   const char *mesh_file1 = "block1.mesh";
-   const char *mesh_file2 = "block2.mesh";
-
-   Array<int> attr;
-   Array<int> m_attr;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file1, "-m1", "--mesh1",
-                  "First mesh file to use.");
-   args.AddOption(&mesh_file2, "-m2", "--mesh2",
-                  "Second mesh file to use.");
-   args.AddOption(&attr, "-at", "--attributes-surf",
-                  "Attributes of boundary faces on contact surface for mesh 2.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   args.PrintOptions(cout);
-
-   Mesh mesh1(mesh_file1, 1, 1);
-   Mesh mesh2(mesh_file2, 1, 1);
-
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream mesh1a_sock(vishost, visport);
-      mesh1a_sock.precision(8);
-      mesh1a_sock << "mesh\n" << mesh1 << flush;
-      socketstream mesh2a_sock(vishost, visport);
-      mesh2a_sock.precision(8);
-      mesh2a_sock << "mesh\n" << mesh2 << flush;
-   }
-
-   const int dim = mesh1.Dimension();
-   MFEM_VERIFY(dim == mesh2.Dimension(), "");
-
-   // boundary attribute 2 is the potential contact surface of nodes
-   attr.Append(2);
-   // boundary attribute 2 is the potential contact surface for master surface
-   m_attr.Append(2);
-
-   //  Define a finite element space on the mesh. Here we use vector finite
-   //  elements, i.e. dim copies of a scalar finite element space. The vector
-   //  dimension is specified by the last argument of the FiniteElementSpace
-   //  constructor.
-   FiniteElementCollection *fec1;
-   FiniteElementSpace *fespace1;
-   fec1 = new H1_FECollection(1, dim);
-   fespace1 = new FiniteElementSpace(&mesh1, fec1, dim, Ordering::byVDIM);
-   cout << "Number of finite element unknowns for mesh1: "
-        << fespace1->GetTrueVSize() << endl;
-   mesh1.SetNodalFESpace(fespace1);
-   GridFunction nodes0 = *mesh1.GetNodes(); // undeformed mesh1 nodal grid function
-   GridFunction *nodes1 = mesh1.GetNodes();
-
-   FiniteElementCollection *fec2 = new H1_FECollection(1, dim);
-   FiniteElementSpace *fespace2 = new FiniteElementSpace(&mesh2, fec2, dim,
-                                                         Ordering::byVDIM);
-   cout << "Number of finite element unknowns for mesh2: "
-        << fespace2->GetTrueVSize() << endl;
-
-   // degrees of freedom of both meshes
-   int ndof_1 = fespace1->GetTrueVSize();
-   int ndof_2 = fespace2->GetTrueVSize();
-   int ndofs = ndof_1 + ndof_2;
-   // number of nodes for each mesh
-   int nnd_1 = mesh1.GetNV();
-   int nnd_2 = mesh2.GetNV();
-   int nnd = nnd_1 + nnd_2;
-   // Determine the list of true (i.e. conforming) essential boundary dofs.
-   // In this example, the boundary conditions are defined by marking only
-   // boundary attribute 1 from the mesh as essential and converting it to a
-   // list of true dofs.
-   Array<int> ess_tdof_list1, ess_bdr1(mesh1.bdr_attributes.Max());
-   ess_bdr1 = 0;
-   //ess_bdr1[0] = 1;
-   // Not ready to be passed on yet
-   // fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-
-   Array<int> ess_tdof_list2, ess_bdr2(mesh2.bdr_attributes.Max());
-   ess_bdr2 = 0;
-   //ess_bdr2[0] = 1;
-
-   // Define the displacement vector x as a finite element grid function
-   // corresponding to fespace. GridFunction is a derived class of Vector.
-   GridFunction x1(fespace1);
-   x1 = 0.0;
-   GridFunction x2(fespace2);
-   x2 = 0.0;
-
-   // Generate force
-   LinearForm *b1 = new LinearForm(fespace1);
-   b1->Assemble();
-
-   LinearForm *b2 = new LinearForm(fespace2);
-   b2->Assemble();
-
-   // Set up the bilinear form a(.,.) on the finite element space
-   //  corresponding to the linear elasticity integrator with piece-wise
-   //  constants coefficient lambda and mu.
-   Vector lambda1(mesh1.attributes.Max());
-   lambda1 = 57.6923076923;
-   PWConstCoefficient lambda1_func(lambda1);
-   Vector mu1(mesh1.attributes.Max());
-   mu1 = 38.4615384615;
-   PWConstCoefficient mu1_func(mu1);
-
-   BilinearForm *a1 = new BilinearForm(fespace1);
-   a1->AddDomainIntegrator(new ElasticityIntegrator(lambda1_func,mu1_func));
-
-   Vector lambda2(mesh2.attributes.Max());
-   lambda2 = 57.6923076923;
-   PWConstCoefficient lambda2_func(lambda2);
-   Vector mu2(mesh2.attributes.Max());
-   mu2 = 38.4615384615;
-   PWConstCoefficient mu2_func(mu2);
-
-   BilinearForm *a2 = new BilinearForm(fespace2);
-   a2->AddDomainIntegrator(new ElasticityIntegrator(lambda2_func,mu2_func));
-
-   a1->Assemble();
-   SparseMatrix A1;
-   Vector B1, X1;
-   a1->FormLinearSystem(ess_tdof_list1, x1, *b1, A1, X1, B1);
-
-   a2->Assemble();
-   SparseMatrix A2;
-   Vector B2, X2;
-   a2->FormLinearSystem(ess_tdof_list2, x2, *b2, A2, X2, B2);
-
-   // Combine elasticity operator for two meshes into one.
-   // Block Matrix
-   SparseMatrix K(ndofs,ndofs);
-   for (int i=0; i<A1.Height(); i++)
-   {
-      Array<int> col_tmp;
-      Vector v_tmp;
-      col_tmp = 0;
-      v_tmp = 0.0;
-      A1.GetRow(i, col_tmp, v_tmp);
-      K.SetRow(i, col_tmp, v_tmp);
-   }
-   for (int i=0; i<A2.Height(); i++)
-   {
-      Array<int> col_tmp;
-      Vector v_tmp;
-      col_tmp = 0;
-      v_tmp = 0.0;
-      A2.GetRow(i, col_tmp, v_tmp);
-      for (int j=0; j<col_tmp.Size(); j++)
-      {
-         col_tmp[j] += ndof_1;
-      }
-      K.SetRow(i+ndof_1, col_tmp, v_tmp);  // mesh1 top left corner
-   }
-
-   // Construct node to segment contact constraint.
-
-   attr.Sort();
-   cout << "Boundary attributes for contact surface faces in mesh 2" << endl;
-   for (auto a : attr) { cout << a << endl; }
-
-   Array<int> bdryFaces2;  // TODO: remove this?
-
-   std::set<int> bdryVerts2;
-   for (int b=0; b<mesh2.GetNBE(); ++b)
-   {
-      if (attr.FindSorted(mesh2.GetBdrAttribute(b)) >= 0)
-      {
-         bdryFaces2.Append(b);
-         Array<int> vert;
-         mesh2.GetBdrElementVertices(b, vert);
-         for (auto v : vert)
-         {
-            bdryVerts2.insert(v);
-         }
-      }
-   }
-
-   int npoints = bdryVerts2.size();
-   Array<int> s_conn(npoints); // connectivity of the second/slave mesh
-   Vector xyz(dim * npoints);
-   xyz = 0.0;
-
-   cout << "Boundary vertices for contact surface vertices in mesh 2" << endl;
-
-   // construct the nodal coordinates on mesh2 to be projected, including displacement
-   int count = 0;
-   for (auto v : bdryVerts2)
-   {
-      cout << v << ": " << mesh2.GetVertex(v)[0] << ", "
-           << mesh2.GetVertex(v)[1] << ", "
-           << mesh2.GetVertex(v)[2] << endl;
-
-      for (int i=0; i<dim; ++i)
-      {
-         xyz[count + (i * npoints)] = mesh2.GetVertex(v)[i] + x2[v*dim+i];
-      }
-
-      s_conn[count] = v + nnd_1; // dof1 is the master
-      count++;
-   }
-
-   MFEM_VERIFY(count == npoints, "");
-
-   // gap function
-   Vector g(npoints*dim);
-   g = -1.0;
-   // segment reference coordinates of the closest point
-   Vector m_xi(npoints*(dim-1));
-   m_xi = -1.0;
-   Vector xs(dim*npoints);
-   xs = 0.0;
-   for (int i=0; i<npoints; i++)
-   {
-      for (int j=0; j<dim; j++)
-      {
-         xs[i*dim+j] = xyz[i + (j*npoints)];
-      }
-   }
-
-   Array<int> m_conn(
-      npoints*4); // only works for linear elements that have 4 vertices!
-   DenseMatrix coordsm(npoints*4, dim);
-
-   // adding displacement to mesh1 using a fixed grid function from mesh1
-   x1 = 1e-4; // x1 order: [xyz xyz... xyz]
-   add(nodes0, x1, *nodes1);
-
-   FindPointsInMesh(mesh1, xyz, m_conn, m_xi);
-
-   for (int i=0; i<npoints; i++)
-   {
-      for (int j=0; j<4; j++)
-      {
-         for (int k=0; k<dim; k++)
-         {
-            coordsm(i*4+j,k) = mesh1.GetVertex(m_conn[i*4+j])[k]+x1[dim*m_conn[i*4+j]+k];
-         }
-      }
-   }
-   //coordsm.Print();
-   SparseMatrix M(nnd,ndofs);
-   std::vector<SparseMatrix> dM(nnd, SparseMatrix(ndofs,ndofs));
-
-   Assemble_Contact(nnd, npoints, ndofs, xs, m_xi, coordsm,
-                    s_conn, m_conn, g, M, dM);
-
-   std::set<int> dirbdryv2;
-   for (int b=0; b<mesh2.GetNBE(); ++b)
-   {
-      if (mesh2.GetBdrAttribute(b) == 1)
-      {
-         Array<int> vert;
-         mesh2.GetBdrElementVertices(b, vert);
-         for (auto v : vert)
-         {
-            dirbdryv2.insert(v);
-         }
-      }
-   }
-   std::set<int> dirbdryv1;
-   for (int b=0; b<mesh1.GetNBE(); ++b)
-   {
-      if (mesh1.GetBdrAttribute(b) == 1)
-      {
-         Array<int> vert;
-         mesh1.GetBdrElementVertices(b, vert);
-         for (auto v : vert)
-         {
-            dirbdryv1.insert(v);
-         }
-      }
-   }
-
-   Array<int> Dirichlet_dof;
-   Array<double> Dirichlet_val;
-
-   for (auto v : dirbdryv2)
-   {
-      for (int i=0; i<dim; ++i)
-      {
-         Dirichlet_dof.Append(v*dim + i + ndof_1);
-         Dirichlet_val.Append(0.);
-      }
-   }
-   double delta = 0.1;
-   for (auto v : dirbdryv1)
-   {
-      Dirichlet_dof.Append(v*dim + 0);
-      Dirichlet_val.Append(delta);
-      Dirichlet_dof.Append(v*dim + 1);
-      Dirichlet_val.Append(0.);
-      Dirichlet_dof.Append(v*dim + 2);
-      Dirichlet_val.Append(0.);
-   }
-
-
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream mesh1_sock(vishost, visport);
-      mesh1_sock.precision(8);
-      mesh1_sock << "mesh\n" << mesh1 << flush;
-      socketstream mesh2_sock(vishost, visport);
-      mesh2_sock.precision(8);
-      mesh2_sock << "mesh\n" << mesh2 << flush;
-   }
-
-   //M.Print();
-   /*Vector eps(ndofs);
-   Vector sol(ndofs); sol = 0.;
-   for(int i=0;i<ndofs;i++) eps[i] = 1e-5 * i ;
-   for(int i=0;i<9;i++)
-   {
-     cout<<i<<endl;
-     dM[s_conn[i]].Mult(eps,sol);
-     sol.Print();
-   }
-   */
-   return 0;
-}
@@ -1,60 +0,0 @@
-# Copyright (c) 2010-2022, 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.
-
-set(IPOPT_EXAMPLES_SRCS)
-list(APPEND IPOPT_EXAMPLES_SRCS exContactBlockTL.cpp)
-
-# Include the source directory where mfem.hpp and mfem-performance.hpp are.
-include_directories(BEFORE ${PROJECT_BINARY_DIR})
-
-# Add "test_ipopt" target, see below.
-add_custom_target(test_ipopt
-  ${CMAKE_CTEST_COMMAND} -R ipopt USES_TERMINAL)
-
-# Add one executable per cpp file, adding "ipopt_" as prefix. Sets
-# "test_ipopt" as a target that depends on the given examples.
-set(PFX ipopt_)
-add_mfem_examples(IPOPT_EXAMPLES_SRCS ${PFX} "" test_ipopt)
-
-# Testing.
-# The IPOPT tests can be run separately using the target "test_ipopt"
-# which builds the examples and runs:
-#   ctest -R ipopt
-
-if (MFEM_ENABLE_TESTING)
-  # Command line options for the tests.
-  # Example 9:
-  set(EXCONTACTBTL_COMMON_OPTS -m ../../data/periodic-segment.mesh -p 0 -dt 0.005)
-  set(EXCONTACTBTL_TEST_OPTS ${EXCONTACTBTL_COMMON_OPTS}  -r  2 )
-
-  # Add the tests: one test per source file.
-  foreach(SRC_FILE ${IPOPT_EXAMPLES_SRCS})
-    get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
-    string(REPLACE ".cpp" "" TEST_NAME ${SRC_FILENAME})
-    string(TOUPPER ${TEST_NAME} UP_TEST_NAME)
-    set(TEST_NAME ${PFX}${TEST_NAME})
-
-    set(THIS_TEST_OPTIONS "-no-vis")
-    list(APPEND THIS_TEST_OPTIONS ${${UP_TEST_NAME}_TEST_OPTS})
-    # message(STATUS "Test ${TEST_NAME} options: ${THIS_TEST_OPTIONS}")
-
-    if (NOT (${TEST_NAME} MATCHES ".*p$"))
-      add_test(NAME ${TEST_NAME}_ser
-        COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
-    else()
-      add_test(NAME ${TEST_NAME}_np=4
-        COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
-        ${MPIEXEC_PREFLAGS}
-        $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS}
-        ${MPIEXEC_POSTFLAGS})
-    endif()
-  endforeach()
-endif()
@@ -1,19 +0,0 @@
-                    Finite Element Discretization Library
-                                   __
-                       _ __ ___   / _|  ___  _ __ ___
-                      | '_ ` _ \ | |_  / _ \| '_ ` _ \
-                      | | | | | ||  _||  __/| | | | | |
-                      |_| |_| |_||_|   \___||_| |_| |_|
-
-                               https://mfem.org
-
-This directory contains modifications of the example codes that illustrate the
-use of MFEM for solving nonlinear constrained optimization problems, including
-features based on the IpOpt, a lightweight HPC solver for nonlinear optimization
-problems.
-
-To use the Ipopt features, make sure that MFEM is configured with the option
-"MFEM_USE_IPOPT = YES", see the top-level INSTALL file for details.
-
-We recommend comparing the original example codes with the corresponding files
-in the current directory.
@@ -1,103 +0,0 @@
-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
-#
-
-dimension
-3
-
-elements
-9
-1   5     0      1     3     2     8    9     11    10
-1   5     2      3     5     4    10    11    13    12
-1   5     4      5     7     6    12    13    15    14
-1   5     8      9    11    10    16    17    19    18
-1   5     10    11    13    12    18    19    21    20
-1   5     12    13    15    14    20    21    23    22
-1   5     16    17    19    18    24    25    27    26
-1   5     18    19    21    20    26    27    29    28
-1   5     20    21    23    22    28    29    31    30
-
-
-
-# 0 nothing
-# 1 dirichlet bc
-# 2 contact
-boundary
-30
-0   3    1     0     2     3
-0   3    3     2     4     5
-0   3    5     4     6     7
-0   3    24    25    27    26
-0   3    26    27    29    28
-0   3    28    29    31    30
-1   3    2     0     8    10
-1   3    4     2    10    12
-1   3    6     4    12    14
-1  3    10    8    16    18
-1  3    12    10    18    20
-1  3    14    12    20    22
-1  3    18    16    24    26
-1  3    20    18    26    28
-1  3    22    20    28    30
-2  3    1     3    11    9
-2  3     3     5    13    11
-2  3     5     7    15    13
-2  3    9    11    19    17
-2  3    11    13    21    19
-2  3    13    15    23    21
-2  3    17    19    27    25
-2  3    19    21    29    27
-2  3    21    23    31    29
-0  3     8     0     1    9
-0  3    16     8    9    17
-0  3    24    16    17    25
-0  3     6    14    15     7
-0  3    14    22    23    15
-0  3    22    30    31    23
-
-
-vertices
-32
-3
-   -1.0000         0         0
-         0         0         0
-   -1.0000    0.3333         0
-         0    0.3333         0
-   -1.0000    0.6667         0
-         0    0.6667         0
-   -1.0000    1.0000         0
-         0    1.0000         0
-   -1.0000         0    0.3333
-         0         0    0.3333
-   -1.0000    0.3333    0.3333
-         0    0.3333    0.3333
-   -1.0000    0.6667    0.3333
-         0    0.6667    0.3333
-   -1.0000    1.0000    0.3333
-         0    1.0000    0.3333
-   -1.0000         0    0.6667
-         0         0    0.6667
-   -1.0000    0.3333    0.6667
-         0    0.3333    0.6667
-   -1.0000    0.6667    0.6667
-         0    0.6667    0.6667
-   -1.0000    1.0000    0.6667
-         0    1.0000    0.6667
-   -1.0000         0    1.0000
-         0         0    1.0000
-   -1.0000    0.3333    1.0000
-         0    0.3333    1.0000
-   -1.0000    0.6667    1.0000
-         0    0.6667    1.0000
-   -1.0000    1.0000    1.0000
-         0    1.0000    1.0000
@@ -1,68 +0,0 @@
-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
-#
-
-dimension
-3
-
-# 1 nothing
-elements
-4
-1   5     0     1     3     2     6     7    9     8
-1   5     2     3     5     4     8     9    11    10
-1   5     6     7     9     8    12    13    15    14
-1   5     8     9    11    10    14    15    17    16
-
-# 0 nothing
-# 1 dirichlet bc
-# 2 contact
-boundary
-16
-0   3     1     0     2     3
-0   3     3     2     4     5
-0   3    12    13    15    14
-0   3    14    15    17    16
-2   3     2     0     6     8
-2   3     4     2     8    10
-2   3     8     6    12    14
-2   3    10     8    14    16
-1   3     1     3     9     7
-1   3     3     5    11    9
-1   3     7    9    15    13
-1   3     9    11    17    15
-0   3     6     0     1     7
-0   3    12     6     7    13
-0   3     4    10    11     5
-0   3    10    16    17    11
-
-vertices
-18
-3
-         0    0.2464    0.2464
-    0.5071    0.2464    0.2464
-         0    0.5000    0.2464
-    0.5071    0.5000    0.2464
-         0    0.7536    0.2464
-    0.5071    0.7536    0.2464
-         0    0.2464    0.5000
-    0.5071    0.2464    0.5000
-         0    0.5000    0.5000
-    0.5071    0.5000    0.5000
-         0    0.7536    0.5000
-    0.5071    0.7536    0.5000
-         0    0.2464    0.7536
-    0.5071    0.2464    0.7536
-         0    0.5000    0.7536
-    0.5071    0.5000    0.7536
-         0    0.7536    0.7536
-    0.5071    0.7536    0.7536
@@ -1,742 +0,0 @@
-//                                Contact example
-//
-// Compile with: make contact
-//
-// Sample runs:  ./contact -m1 block1.mesh -m2 block2.mesh -at "5 6 7 8"
-// Sample runs:  ./contact -m1 block1_d.mesh -m2 block2_d.mesh -at "5 6 7 8"
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-#include "nodepair.hpp"
-
-using namespace std;
-using namespace mfem;
-
-bool ifequalarray(const Array<int> a1, const Array<int> a2)
-{
-   if (a1.Size()!=a2.Size())
-   {
-      return false;
-   }
-   for (int i=0; i<a1.Size(); i++)
-   {
-      if (a1[i] != a2[i])
-      {
-         return false;
-      }
-   }
-   return true;
-}
-
-void FindSurfaceToProject(Mesh& mesh, const int elem, int& cbdrface)
-{
-   Array<int> attr;
-   attr.Append(2);
-   Array<int> faces;
-   Array<int> ori;
-   std::vector<Array<int> > facesVertices;
-   std::vector<int > faceid;
-   mesh.GetElementFaces(elem, faces, ori);
-   int face = -1;
-   for (int i=0; i<faces.Size(); i++)
-   {
-      face = faces[i];
-      Array<int> faceVert;
-      if (!mesh.FaceIsInterior(face)) // if on the boundary
-      {
-         mesh.GetFaceVertices(face, faceVert);
-         faceVert.Sort();
-         facesVertices.push_back(faceVert);
-         faceid.push_back(face);
-      }
-   }
-   int bdrface = facesVertices.size();
-
-   Array<int> bdryFaces;
-   // This shoulnd't need to be rebuilt
-   std::vector<Array<int> > bdryVerts;
-   for (int b=0; b<mesh.GetNBE(); ++b)
-   {
-      if (attr.FindSorted(mesh.GetBdrAttribute(b)) >= 0)  // found the contact surface
-      {
-         bdryFaces.Append(b);
-         Array<int> vert;
-         mesh.GetBdrElementVertices(b, vert);
-         vert.Sort();
-         bdryVerts.push_back(vert);
-      }
-   }
-
-   int bdrvert = bdryVerts.size();
-   cbdrface = -1;  // the face number of the contact surface element
-   int count_cbdrface = 0;  // the number of matching surfaces, used for checks
-
-   for (int i=0; i<bdrface; i++)
-   {
-      for (int j=0; j<bdrvert; j++)
-      {
-         if (ifequalarray(facesVertices[i], bdryVerts[j]))
-         {
-            cbdrface = faceid[i];
-            count_cbdrface += 1;
-         }
-      }
-   }
-   MFEM_VERIFY(count_cbdrface == 1,"projection surface not found");
-
-};
-
-Vector GetNormalVector(Mesh & mesh, const int elem, const double *ref,
-                       int & refFace, int & refNormal, bool & interior)
-{
-   ElementTransformation *trans = mesh.GetElementTransformation(elem);
-   const int dim = mesh.Dimension();
-   const int spaceDim = trans->GetSpaceDim();
-
-   MFEM_VERIFY(spaceDim == 3, "");
-
-   Vector n(spaceDim);
-
-   IntegrationPoint ip;
-   ip.Set(ref, dim);
-
-   trans->SetIntPoint(&ip);
-   //CalcOrtho(trans->Jacobian(), n);  // Works only for face transformations
-   const DenseMatrix jac = trans->Jacobian();
-
-   int dimNormal = -1;
-   int normalSide = -1;
-
-   const double tol = 1.0e-8;
-   for (int i=0; i<dim; ++i)
-   {
-      const double d0 = std::abs(ref[i]);
-      const double d1 = std::abs(ref[i] - 1.0);
-
-      const double d = std::min(d0, d1);
-      // TODO: this works only for hexahedral meshes!
-
-      if (d < tol)
-      {
-         MFEM_VERIFY(dimNormal == -1, "");
-         dimNormal = i;
-
-         if (d0 < tol)
-         {
-            normalSide = 0;
-         }
-         else
-         {
-            normalSide = 1;
-         }
-      }
-   }
-   // closest point on the boundary
-   if (dimNormal < 0 || normalSide < 0) // node is inside the element
-   {
-      interior = 1;
-      Vector n(3);
-      n = 0.0;
-      return n;
-   }
-
-   MFEM_VERIFY(dimNormal >= 0 && normalSide >= 0, "");
-   refNormal = dimNormal;
-
-   MFEM_VERIFY(dim == 3, "");
-
-   {
-      // Find the reference face
-      if (dimNormal == 0)
-      {
-         refFace = (normalSide == 1) ? 2 : 4;
-      }
-      else if (dimNormal == 1)
-      {
-         refFace = (normalSide == 1) ? 3 : 1;
-      }
-      else
-      {
-         refFace = (normalSide == 1) ? 5 : 0;
-      }
-   }
-
-   std::vector<Vector> tang(2);
-
-   int tangDir[2] = {-1, -1};
-   {
-      int t = 0;
-      for (int i=0; i<dim; ++i)
-      {
-         if (i != dimNormal)
-         {
-            tangDir[t] = i;
-            t++;
-         }
-      }
-
-      MFEM_VERIFY(t == 2, "");
-   }
-
-   for (int i=0; i<2; ++i)
-   {
-      tang[i].SetSize(3);
-
-      Vector tangRef(3);
-      tangRef = 0.0;
-      tangRef[tangDir[i]] = 1.0;
-
-      jac.Mult(tangRef, tang[i]);
-   }
-
-   Vector c(3);  // Cross product
-
-   c[0] = (tang[0][1] * tang[1][2]) - (tang[0][2] * tang[1][1]);
-   c[1] = (tang[0][2] * tang[1][0]) - (tang[0][0] * tang[1][2]);
-   c[2] = (tang[0][0] * tang[1][1]) - (tang[0][1] * tang[1][0]);
-
-   c /= c.Norml2();
-
-   Vector nref(3);
-   nref = 0.0;
-   nref[dimNormal] = 1.0;
-
-   Vector ndir(3);
-   jac.Mult(nref, ndir);
-
-   ndir /= ndir.Norml2();
-
-   const double dp = ndir * c;
-
-   // TODO: eliminate c?
-   n = c;
-   if (dp < 0.0)
-   {
-      n *= -1.0;
-   }
-   interior = 0;
-   return n;
-}
-
-// WARNING: global variable, just for this little example.
-std::array<std::array<int, 3>, 8> HEX_VERT =
-{
-   {  {0,0,0},
-      {1,0,0},
-      {1,1,0},
-      {0,1,0},
-      {0,0,1},
-      {1,0,1},
-      {1,1,1},
-      {0,1,1}
-   }
-};
-
-int GetHexVertex(int cdim, int c, int fa, int fb, Vector & refCrd)
-{
-   int ref[3];
-   ref[cdim] = c;
-   ref[cdim == 0 ? 1 : 0] = fa;
-   ref[cdim == 2 ? 1 : 2] = fb;
-
-   for (int i=0; i<3; ++i) { refCrd[i] = ref[i]; }
-
-   int refv = -1;
-
-   for (int i=0; i<8; ++i)
-   {
-      bool match = true;
-      for (int j=0; j<3; ++j)
-      {
-         if (ref[j] != HEX_VERT[i][j]) { match = false; }
-      }
-
-      if (match) { refv = i; }
-   }
-
-   MFEM_VERIFY(refv >= 0, "");
-
-   return refv;
-}
-
-// Coordinates in xyz are assumed to be ordered as [X, Y, Z]
-// where X is the list of x-coordinates for all points and so on.
-// conn: connectivity of the target surface elements
-// xi: surface reference cooridnates for the cloest point, involves a linear transformation from [0,1] to [-1,1]
-void FindPointsInMesh(Mesh & mesh, Vector const& xyz, Array<int>& conn,
-                      Vector& xi)
-{
-   const int dim = mesh.Dimension();
-   const int np = xyz.Size() / dim;
-
-   MFEM_VERIFY(np * dim == xyz.Size(), "");
-
-   mesh.EnsureNodes();
-
-   //FindPointsGSLIB finder(MPI_COMM_WORLD);
-   FindPointsGSLIB finder;
-
-   finder.SetDistanceToleranceForPointsFoundOnBoundary(0.5);
-
-   const double bb_t = 0.5;
-   finder.Setup(mesh, bb_t);
-
-   finder.FindPoints(xyz);
-
-   /// Return code for each point searched by FindPoints: inside element (0), on
-   /// element boundary (1), or not found (2).
-   Array<unsigned int> codes = finder.GetCode();
-
-   /// Return element number for each point found by FindPoints.
-   Array<unsigned int> elems = finder.GetElem();
-
-   /// Return reference coordinates for each point found by FindPoints.
-   Vector refcrd = finder.GetReferencePosition();
-
-   /// Return distance between the sought and the found point in physical space,
-   /// for each point found by FindPoints.
-   Vector dist = finder.GetDist();
-
-   MFEM_VERIFY(dist.Size() == np, "");
-   MFEM_VERIFY(refcrd.Size() == np * dim, "");
-   MFEM_VERIFY(elems.Size() == np, "");
-   MFEM_VERIFY(codes.Size() == np, "");
-
-   bool allfound = true;
-   for (auto code : codes)
-      if (code == 2) { allfound = false; }
-
-   MFEM_VERIFY(allfound, "A point was not found");
-
-   cout << "Maximum distance of projected points: " << dist.Max() << endl;
-
-   // extract information
-   for (int i=0; i<np; ++i)
-   {
-      cout << "Point " << i << ": (";
-      for (int j=0; j<dim; ++j)
-      {
-         cout << xyz[i + (j*np)];
-         if (j == dim-1) {cout << ")" << endl;}
-         else {cout << ", ";}
-      }
-      //cout << "  element: " << elems[i] << endl;
-      //cout << "  element " << elems[i] << " vertices:" << endl;
-      //Array<int> vert;
-      //mesh.GetElementVertices(elems[i], vert);
-      //for (auto v : vert)
-      //{
-      //   cout << "    " << v << endl;
-      //}
-
-      /*cout << "  reference coordinates: (";
-      for (int j=0; j<dim; ++j)
-      {
-         cout << refcrd[(i*dim) + j];
-         if (j == dim-1)
-         {
-            cout << ")" << endl;
-         }
-         else
-         {
-            cout << ", ";
-         }
-      }*/
-
-      int refFace, refNormal, refNormalSide;
-      bool is_interior = -1;
-      Vector normal = GetNormalVector(mesh, elems[i], refcrd.GetData() + (i*dim),
-                                      refFace, refNormal, is_interior);
-      int phyFace;
-      if (is_interior)
-      {
-         phyFace = -1; // the id of the face that has the closest point
-         FindSurfaceToProject(mesh, elems[i], phyFace);
-
-         Array<int> cbdrVert;
-         mesh.GetFaceVertices(phyFace, cbdrVert);
-         Vector xs(dim);
-         xs[0] = xyz[i + 0*np];
-         xs[1] = xyz[i + 1*np];
-         xs[2] = xyz[i + 2*np];
-         Vector xi_tmp(dim-1);
-         // get nodes!
-
-         GridFunction *nodes = mesh.GetNodes();
-         DenseMatrix coords(4,3);
-         for (int i=0; i<4; i++)
-         {
-            for (int j=0; j<3; j++)
-            {
-               coords(i,j) = (*nodes)[cbdrVert[i]*3+j];
-            }
-         }
-         SlaveToMaster(coords, xs, xi_tmp);
-
-         for (int j=0; j<dim-1; ++j)
-         {
-            xi[i*(dim-1)+j] = xi_tmp[j];
-         }
-         // now get get the projection to the surface
-      }
-      else
-      {
-         Vector faceRefCrd(dim-1);
-         {
-            int fd = 0;
-            for (int j=0; j<dim; ++j)
-            {
-               if (j == refNormal)
-               {
-                  refNormalSide = (refcrd[(i*dim) + j] > 0.5);
-               }
-               else
-               {
-                  faceRefCrd[fd] = refcrd[(i*dim) + j];
-                  fd++;
-               }
-            }
-
-            MFEM_VERIFY(fd == dim-1, "");
-         }
-
-         for (int j=0; j<dim-1; ++j)
-         {
-            xi[i*(dim-1)+j] = faceRefCrd[j]*2.0 - 1.0;
-         }
-         //cout << "  face reference coordinates: (";
-         for (int j=0; j<dim-1; ++j)
-         {
-            cout << faceRefCrd[j];
-            if (j == dim-2) {cout << ")" << endl;}
-            else {cout << ", ";}
-         }
-      }
-      //cout << "  normal vector: ";
-      //normal.Print();
-
-      // ask, does this do anything?
-      /*
-      IntegrationPoint ip;
-      ip.Set(refcrd.GetData() + (i*dim), dim);
-      ElementTransformation *trans = mesh.GetElementTransformation(elems[i]);
-      Vector phys(trans->GetSpaceDim());
-      trans->Transform(ip, phys);
-      cout << "  physical coordinates: ";
-      phys.Print();
-      */
-
-      // Get the element face
-      Array<int> faces;
-      Array<int> ori;
-      int face;
-
-      if (is_interior)
-      {
-         face = phyFace;
-      }
-      else
-      {
-         mesh.GetElementFaces(elems[i], faces, ori);
-         face = faces[refFace];
-      }
-
-      Array<int> faceVert;
-      mesh.GetFaceVertices(face, faceVert);
-
-      //cout << "  face " << face << " vertices:" << endl;
-      //for (auto v : faceVert){ cout << "    " << v << endl;}
-
-      for (int p=0; p<4; p++)
-      {
-         conn[4*i+p] = faceVert[p];
-      }
-      /*
-      Vector ref(dim);
-
-      for (int p=0; p<2; ++p)
-         for (int q=0; q<2; ++q)
-         {
-            const int refv = GetHexVertex(refNormal, refNormalSide, p, q, ref);
-            cout << "  face reference vertex (" << p << "," << q
-                 << ") is global vertex " << vert[refv] << endl;
-
-            {
-               // Sanity check
-               ip.Set(ref.GetData(), dim);
-               trans->Transform(ip, phys);
-               for (int j=0; j<dim; ++j)
-               {
-                  phys[j] -= mesh.GetVertex(vert[refv])[j];
-               }
-          phys.Print();
-          cout<<vert[refv]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[0]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[1]<<endl;
-               cout<<mesh.GetVertex(vert[refv])[2]<<endl;
-               MFEM_VERIFY(phys.Norml2() < 1.0e-12, "Sanity check failed");
-            }
-         }*/
-   }
-}
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   const char *mesh_file1 = "block1.mesh";
-   const char *mesh_file2 = "block2.mesh";
-
-   Array<int> attr;
-   Array<int> m_attr;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file1, "-m1", "--mesh1",
-                  "First mesh file to use.");
-   args.AddOption(&mesh_file2, "-m2", "--mesh2",
-                  "Second mesh file to use.");
-   args.AddOption(&attr, "-at", "--attributes-surf",
-                  "Attributes of boundary faces on contact surface for mesh 2.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   args.PrintOptions(cout);
-
-   Mesh mesh1(mesh_file1, 1, 1);
-   Mesh mesh2(mesh_file2, 1, 1);
-
-   const int dim = mesh1.Dimension();
-   MFEM_VERIFY(dim == mesh2.Dimension(), "");
-
-   // boundary attribute 2 is the potential contact surface of nodes
-   attr.Append(2);
-   // boundary attribute 2 is the potential contact surface for master surface
-   m_attr.Append(2);
-
-   //  Define a finite element space on the mesh. Here we use vector finite
-   //  elements, i.e. dim copies of a scalar finite element space. The vector
-   //  dimension is specified by the last argument of the FiniteElementSpace
-   //  constructor.
-   FiniteElementCollection *fec1;
-   FiniteElementSpace *fespace1;
-   fec1 = new H1_FECollection(1, dim);
-   fespace1 = new FiniteElementSpace(&mesh1, fec1, dim, Ordering::byVDIM);
-   cout << "Number of finite element unknowns for mesh1: "
-        << fespace1->GetTrueVSize() << endl;
-   mesh1.SetNodalFESpace(fespace1);
-   GridFunction nodes0 = *mesh1.GetNodes(); // undeformed mesh1 nodal grid function
-   GridFunction *nodes1 = mesh1.GetNodes();
-
-   FiniteElementCollection *fec2 = new H1_FECollection(1, dim);
-   FiniteElementSpace *fespace2 = new FiniteElementSpace(&mesh2, fec2, dim,
-                                                         Ordering::byVDIM);
-   cout << "Number of finite element unknowns for mesh2: "
-        << fespace2->GetTrueVSize() << endl;
-
-   // degrees of freedom of both meshes
-   int ndof_1 = fespace1->GetTrueVSize();
-   int ndof_2 = fespace2->GetTrueVSize();
-   int ndofs = ndof_1 + ndof_2;
-   // number of nodes for each mesh
-   int nnd_1 = mesh1.GetNV();
-   int nnd_2 = mesh2.GetNV();
-   int nnd = nnd_1 + nnd_2;
-   // Determine the list of true (i.e. conforming) essential boundary dofs.
-   // In this example, the boundary conditions are defined by marking only
-   // boundary attribute 1 from the mesh as essential and converting it to a
-   // list of true dofs.
-   Array<int> ess_tdof_list1, ess_bdr1(mesh1.bdr_attributes.Max());
-   cout<<mesh1.bdr_attributes.Max()<<endl;
-   ess_bdr1 = 0;
-   //ess_bdr1[0] = 1;
-   // Not ready to be passed on yet
-   // fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-
-   Array<int> ess_tdof_list2, ess_bdr2(mesh2.bdr_attributes.Max());
-   ess_bdr2 = 0;
-   //ess_bdr2[0] = 1;
-
-   // Define the displacement vector x as a finite element grid function
-   // corresponding to fespace. GridFunction is a derived class of Vector.
-   GridFunction x1(fespace1);
-   x1 = 0.0;
-   GridFunction x2(fespace2);
-   x2 = 0.0;
-
-   // Generate force
-   LinearForm *b1 = new LinearForm(fespace1);
-   b1->Assemble();
-
-   LinearForm *b2 = new LinearForm(fespace2);
-   b2->Assemble();
-
-   // Set up the bilinear form a(.,.) on the finite element space
-   //  corresponding to the linear elasticity integrator with piece-wise
-   //  constants coefficient lambda and mu.
-   Vector lambda1(mesh1.attributes.Max());
-   lambda1 = 57.6923076923;
-   PWConstCoefficient lambda1_func(lambda1);
-   Vector mu1(mesh1.attributes.Max());
-   mu1 = 38.4615384615;
-   PWConstCoefficient mu1_func(mu1);
-
-   BilinearForm *a1 = new BilinearForm(fespace1);
-   a1->AddDomainIntegrator(new ElasticityIntegrator(lambda1_func,mu1_func));
-
-   Vector lambda2(mesh2.attributes.Max());
-   lambda2 = 57.6923076923;
-   PWConstCoefficient lambda2_func(lambda2);
-   Vector mu2(mesh2.attributes.Max());
-   mu2 = 38.4615384615;
-   PWConstCoefficient mu2_func(mu2);
-
-   BilinearForm *a2 = new BilinearForm(fespace2);
-   a2->AddDomainIntegrator(new ElasticityIntegrator(lambda2_func,mu2_func));
-
-   a1->Assemble();
-   SparseMatrix A1;
-   Vector B1, X1;
-   a1->FormLinearSystem(ess_tdof_list1, x1, *b1, A1, X1, B1);
-
-   a2->Assemble();
-   SparseMatrix A2;
-   Vector B2, X2;
-   a2->FormLinearSystem(ess_tdof_list2, x2, *b2, A2, X2, B2);
-
-   // Combine elasticity operator for two meshes into one.
-   // Block Matrix
-   SparseMatrix K(ndofs,ndofs);
-   for (int i=0; i<A1.Height(); i++)
-   {
-      Array<int> col_tmp;
-      Vector v_tmp;
-      col_tmp = 0;
-      v_tmp = 0.0;
-      A1.GetRow(i, col_tmp, v_tmp);
-      K.SetRow(i, col_tmp, v_tmp);
-   }
-   for (int i=0; i<A2.Height(); i++)
-   {
-      Array<int> col_tmp;
-      Vector v_tmp;
-      col_tmp = 0;
-      v_tmp = 0.0;
-      A2.GetRow(i, col_tmp, v_tmp);
-      for (int j=0; j<col_tmp.Size(); j++)
-      {
-         col_tmp[j] += ndof_1;
-      }
-      K.SetRow(i+ndof_1, col_tmp, v_tmp);  // mesh1 top left corner
-   }
-
-   // Construct node to segment contact constraint.
-
-   attr.Sort();
-   cout << "Boundary attributes for contact surface faces in mesh 2" << endl;
-   for (auto a : attr)
-   {
-      cout << a << endl;
-   }
-
-   Array<int> bdryFaces2;  // TODO: remove this?
-
-   std::set<int> bdryVerts2;
-   for (int b=0; b<mesh2.GetNBE(); ++b)
-   {
-      if (attr.FindSorted(mesh2.GetBdrAttribute(b)) >= 0)
-      {
-         bdryFaces2.Append(b);
-         Array<int> vert;
-         mesh2.GetBdrElementVertices(b, vert);
-         for (auto v : vert)
-         {
-            bdryVerts2.insert(v);
-         }
-      }
-   }
-
-   int npoints = bdryVerts2.size();
-   Array<int> s_conn(npoints); // connectivity of the second/slave mesh
-   Vector xyz(dim * npoints);
-   xyz = 0.0;
-
-   cout << "Boundary vertices for contact surface vertices in mesh 2" << endl;
-
-   // construct the nodal coordinates on mesh2 to be projected, including displacement
-   int count = 0;
-   for (auto v : bdryVerts2)
-   {
-      cout << v << ": " << mesh2.GetVertex(v)[0] << ", "
-           << mesh2.GetVertex(v)[1] << ", "
-           << mesh2.GetVertex(v)[2] << endl;
-
-      for (int i=0; i<dim; ++i)
-      {
-         xyz[count + (i * npoints)] = mesh2.GetVertex(v)[i] + x2[v*dim+i];
-      }
-
-      s_conn[count] = v + nnd_1; // dof1 is the master
-      count++;
-   }
-
-   MFEM_VERIFY(count == npoints, "");
-
-   // gap function
-   Vector g(npoints*dim);
-   g = -1.0;
-   // segment reference coordinates of the closest point
-   Vector m_xi(npoints*(dim-1));
-   m_xi = -1.0;
-   Vector xs(dim*npoints);
-   xs = 0.0;
-   for (int i=0; i<npoints; i++)
-   {
-      for (int j=0; j<dim; j++)
-      {
-         xs[i*dim+j] = xyz[i + (j*npoints)];
-      }
-   }
-
-   Array<int> m_conn(
-      npoints*4); // only works for linear elements that have 4 vertices!
-   DenseMatrix coordsm(npoints*4, dim);
-
-   // adding displacement to mesh1 using a fixed grid function from mesh1
-   x1 = 1e-4; // x1 order: [xyz xyz... xyz]
-   add(nodes0, x1, *nodes1);
-
-   FindPointsInMesh(mesh1, xyz, m_conn, m_xi);
-
-   for (int i=0; i<npoints; i++)
-   {
-      for (int j=0; j<4; j++)
-      {
-         for (int k=0; k<dim; k++)
-         {
-            coordsm(i*4+j,k) = mesh1.GetVertex(m_conn[i*4+j])[k]+x1[dim*m_conn[i*4+j]+k];
-         }
-      }
-   }
-   //coordsm.Print();
-   SparseMatrix M(nnd,ndofs);
-   std::vector<SparseMatrix> dM(nnd, SparseMatrix(ndofs,ndofs));
-
-   Assemble_Contact(nnd, npoints, ndofs, xs, m_xi, coordsm,
-                    s_conn, m_conn, g, M, dM);
-
-   //M.Print();
-   /*Vector eps(ndofs);
-   Vector sol(ndofs); sol = 0.;
-   for(int i=0;i<ndofs;i++) eps[i] = 1e-5 * i ;
-   for(int i=0;i<9;i++)
-   {
-     cout<<i<<endl;
-     dM[s_conn[i]].Mult(eps,sol);
-     sol.Print();
-   }
-   */
-   return 0;
-}
@@ -1,230 +0,0 @@
-//                                Contact example
-//
-// Compile with: make exContactBlockTL
-//
-// Sample runs:  ./exContactBlockTL -m1 block1.mesh -m2 block2.mesh -at "5 6 7 8"
-// Sample runs:  ./exContactBlockTL -m1 block1_d.mesh -m2 block2_d.mesh -at "5 6 7 8"
-
-#ifndef EXCONTACTBLOCKTL_HPP
-#define EXCONTACTBLOCKTL_HPP
-
-#include "mfem.hpp"
-#include "IpTNLP.hpp"
-
-using namespace std;
-using namespace mfem;
-using namespace Ipopt;
-
-
-class ExContactBlockTL: public TNLP
-{
-public:
-   /** default constructor */
-   ExContactBlockTL(int argc, char *argv[]);
-
-   /** default destructor */
-   virtual ~ExContactBlockTL();
-
-   /**@name Overloaded from TNLP */
-   /** Method to return some info about the nlp */
-   virtual bool get_nlp_info(
-      Index&          n,
-      Index&          m,
-      Index&          nnz_jac_g,
-      Index&          nnz_h_lag,
-      IndexStyleEnum& index_style
-   );
-
-   /** Method to return the bounds for my problem */
-   virtual bool get_bounds_info(
-      Index   n,
-      Number* x_l,
-      Number* x_u,
-      Index   m,
-      Number* g_l,
-      Number* g_u
-   );
-
-   /** Method to return the starting point for the algorithm */
-   virtual bool get_starting_point(
-      Index   n,
-      bool    init_x,
-      Number* x,
-      bool    init_z,
-      Number* z_L,
-      Number* z_U,
-      Index   m,
-      bool    init_lambda,
-      Number* lambda
-   );
-
-   /** Method to return the objective value */
-   virtual bool eval_f(
-      Index         n,
-      const Number* x,
-      bool          new_x,
-      Number&       obj_value
-   );
-
-   /** Method to return the gradient of the objective */
-   virtual bool eval_grad_f(
-      Index         n,
-      const Number* x,
-      bool          new_x,
-      Number*       grad_f
-   );
-
-   /** Method to return the constraint residuals */
-   virtual bool eval_g(
-      Index         n,
-      const Number* x,
-      bool          new_x,
-      Index         m,
-      Number*       cons
-   );
-
-   /** Method to return:
-    *   1) The structure of the Jacobian (if "values" is NULL)
-    *   2) The values of the Jacobian (if "values" is not NULL)
-    */
-   virtual bool eval_jac_g(
-      Index         n,
-      const Number* x,
-      bool          new_x,
-      Index         m,
-      Index         nele_jac,
-      Index*        iRow,
-      Index*        jCol,
-      Number*       values
-   );
-
-   /** Method to return:
-    *   1) The structure of the Hessian of the Lagrangian (if "values" is NULL)
-    *   2) The values of the Hessian of the Lagrangian (if "values" is not NULL)
-    */
-   virtual bool eval_h(
-      Index         n,
-      const Number* x,
-      bool          new_x,
-      Number        obj_factor,
-      Index         m,
-      const Number* lambda,
-      bool          new_lambda,
-      Index         nele_hess,
-      Index*        iRow,
-      Index*        jCol,
-      Number*       values
-   );
-
-   /** This method is called when the algorithm is complete so the TNLP can store/write the solution */
-   virtual void finalize_solution(
-      SolverReturn               status,
-      Index                      n,
-      const Number*              x,
-      const Number*              z_L,
-      const Number*              z_U,
-      Index                      m,
-      const Number*              g,
-      const Number*              lambda,
-      Number                     obj_value,
-      const IpoptData*           ip_data,
-      IpoptCalculatedQuantities* ip_cq
-   );
-
-private:
-   void update_g();
-   void update_jac();
-   void update_hess();
-
-private:
-   /**@name Methods to block default compiler methods.
-    *
-    * The compiler automatically generates the following three methods.
-    *  Since the default compiler implementation is generally not what
-    *  you want (for all but the most simple classes), we usually
-    *  put the declarations of these methods in the private section
-    *  and never implement them. This prevents the compiler from
-    *  implementing an incorrect "default" behavior without us
-    *  knowing. (See Scott Meyers book, "Effective C++")
-    */
-   ExContactBlockTL(
-      const ExContactBlockTL&
-   );
-
-   ExContactBlockTL& operator=(
-      const ExContactBlockTL&
-   );
-
-   Array<int> attr;
-   Array<int> m_attr;
-   Array<int> s_conn; // connectivity of the second/slave mesh
-   std::string mesh_file1;
-   std::string mesh_file2;
-   Mesh* mesh1;
-   Mesh* mesh2;
-   FiniteElementCollection* fec1;
-   FiniteElementCollection* fec2;
-   FiniteElementSpace* fespace1;
-   FiniteElementSpace* fespace2;
-   Array<int> ess_tdof_list1;
-   Array<int> ess_tdof_list2;
-   GridFunction nodes0;
-   GridFunction* nodes1;
-   GridFunction* nodes2;
-   GridFunction* x1;
-   GridFunction* x2;
-   LinearForm* b1;
-   LinearForm* b2;
-   PWConstCoefficient* lambda1_func;
-   PWConstCoefficient* lambda2_func;
-   PWConstCoefficient* mu1_func;
-   PWConstCoefficient* mu2_func;
-   BilinearForm* a1;
-   BilinearForm* a2;
-
-   mfem::Vector lambda1;
-   mfem::Vector lambda2;
-   mfem::Vector mu1;
-   mfem::Vector mu2;
-   mfem::Vector xyz;
-
-   std::set<int> bdryVerts2;
-
-   int dim;
-   // degrees of freedom of both meshes
-   int ndof_1;
-   int ndof_2;
-   int ndofs;
-   // number of nodes for each mesh
-   int nnd_1;
-   int nnd_2;
-   int nnd;
-
-   int npoints;
-
-   SparseMatrix A1;
-   mfem::Vector B1, X1;
-   SparseMatrix A2;
-   mfem::Vector B2, X2;
-
-   SparseMatrix* K;
-   mfem::Vector g;
-   mfem::Vector m_xi;
-   mfem::Vector xs;
-
-   Array<int> m_conn; // only works for linear elements that have 4 vertices!
-   DenseMatrix* coordsm;
-   SparseMatrix* M;
-
-   std::vector<SparseMatrix>* dM;
-
-   Array<int> Dirichlet_dof;
-   Array<double> Dirichlet_val;
-
-public: 
-   Mesh * GetMesh1() {return mesh1;}
-   Mesh * GetMesh2() {return mesh2;}
-
-};
-
-#endif
@@ -1,68 +0,0 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
-
-# Use the MFEM build directory
-MFEM_DIR ?= ../..
-MFEM_BUILD_DIR ?= ../..
-SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ipopt/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
-
-MFEM_LIB_FILE = mfem_is_not_built
-include $(CONFIG_MK)
-
-SEQ_EXAMPLES = exContactBlockTL
-EXAMPLES = $(SEQ_EXAMPLES)
-
-.SUFFIXES:
-.SUFFIXES: .o .cpp .mk
-.PHONY: all clean clean-build clean-exec
-
-# Remove built-in rule
-%: %.cpp
-
-# Replace the default implicit rule for *.cpp files
-%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
-
-all: $(EXAMPLES)
-
-ifeq ($(MFEM_USE_IPOPT),NO)
-$(EXAMPLES):
-	$(error MFEM is not configured with IPOPT)
-endif
-
-MFEM_TESTS = EXAMPLES
-include $(MFEM_TEST_MK)
-
-# Testing: Parallel vs. serial runs
-RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
-%-test-par: %
-	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
-%-test-seq: %
-	@$(call mfem-test,$<,, Serial example)
-
-# Testing: "test" target and mfem-test* variables are defined in config/test.mk
-
-# Generate an error message if the MFEM library is not built and exit
-$(MFEM_LIB_FILE):
-	$(error The MFEM library is not built)
-
-clean: clean-build clean-exec
-
-clean-build:
-	rm -f *.o *~ $(SEQ_EXAMPLES)
-	rm -rf *.dSYM *.TVD.*breakpoints
-
-clean-exec:
-	@rm -f exContactBlockTL.mesh exContactBlockTL-mesh.* exContactBlockTL-init.* exContactBlockTL-final.* ExampleContactBlockTL*
@@ -1,888 +0,0 @@
-
-using namespace std;
-using namespace mfem;
-
-void BasisEval(const Vector xi, Vector &N, DenseMatrix &dNdxi) // dNdxi is 2*4
-{
-   N[0] = 0.25*(1-xi[0])*(1-xi[1]);
-   N[1] = 0.25*(1+xi[0])*(1-xi[1]);
-   N[2] = 0.25*(1+xi[0])*(1+xi[1]);
-   N[3] = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi(0,0) = 0.25*(-1+xi[1]);
-   dNdxi(0,1) = 0.25*(1-xi[1]);
-   dNdxi(0,2) = 0.25*(1+xi[1]);
-   dNdxi(0,3) = 0.25*(-1-xi[1]);
-   dNdxi(1,0) = 0.25*(-1+xi[0]);
-   dNdxi(1,1) = 0.25*(-1-xi[0]);
-   dNdxi(1,2) = 0.25*(1+xi[0]);
-   dNdxi(1,3) = 0.25*(1-xi[0]);
-}
-
-
-void BasisEvalDerivs(const Vector xi, Vector& N, DenseMatrix& dNdxi,
-                     DenseMatrix& dN2dxi)
-{
-   N[0] = 0.25*(1-xi[0])*(1-xi[1]);
-   N[1] = 0.25*(1+xi[0])*(1-xi[1]);
-   N[2] = 0.25*(1+xi[0])*(1+xi[1]);
-   N[3] = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi.SetSize(2,4); dNdxi = 0.0;
-   dN2dxi.SetSize(3,4);
-   dN2dxi = 0.0;  // first row dxi2, second detadxi, third deta2
-
-   dNdxi(0,0) = 0.25*(-1+xi[1]); dNdxi(0,1) = 0.25*(1-xi[1]);
-   dNdxi(0,2) = 0.25*(1+xi[1]);  dNdxi(0,3) = 0.25*(-1-xi[1]);
-   dNdxi(1,0) = 0.25*(-1+xi[0]); dNdxi(1,1) = 0.25*(-1-xi[0]);
-   dNdxi(1,2) = 0.25*(1+xi[0]);  dNdxi(1,3) = 0.25*(1-xi[0]);
-
-   dN2dxi(1,0) = 0.25; dN2dxi(1,1) = -0.25; dN2dxi(1,2) = 0.25;
-   dN2dxi(1,3) = -0.25;
-}
-
-// returns the vector and matrix form of the shape functions and its derivative
-void BasisVectorDerivs(const Vector xi, DenseMatrix& N, DenseMatrix& dNdxi,
-                       DenseMatrix& ddNdxi)
-{
-   N.SetSize(3,12); N = 0.0;
-   N(0,0) = 0.25*(1-xi[0])*(1-xi[1]); N(0,3) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(0,6) = 0.25*(1+xi[0])*(1+xi[1]); N(0,9) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   N(1,1) = 0.25*(1-xi[0])*(1-xi[1]); N(1,4) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(1,7) = 0.25*(1+xi[0])*(1+xi[1]); N(1,10) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   N(2,2) = 0.25*(1-xi[0])*(1-xi[1]); N(2,5) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(2,8) = 0.25*(1+xi[0])*(1+xi[1]); N(2,11) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi.SetSize(3*2, 3*4);  dNdxi = 0.0;
-   dNdxi(0,0) = 0.25*(-1+xi[1]);  dNdxi(0,3) = 0.25*(1-xi[1]);
-   dNdxi(0,6) = 0.25*(1+xi[1]);  dNdxi(0,9) = 0.25*(-1-xi[1]);
-   dNdxi(1,1) = 0.25*(-1+xi[1]);  dNdxi(1,4) = 0.25*(1-xi[1]);
-   dNdxi(1,7) = 0.25*(1+xi[1]);  dNdxi(1,10) = 0.25*(-1-xi[1]);
-   dNdxi(2,2) = 0.25*(-1+xi[1]);  dNdxi(2,5) = 0.25*(1-xi[1]);
-   dNdxi(2,8) = 0.25*(1+xi[1]);  dNdxi(2,11) = 0.25*(-1-xi[1]);
-
-   dNdxi(3,0) = 0.25*(-1+xi[0]);  dNdxi(3,3) = 0.25*(-1-xi[0]);
-   dNdxi(3,6) = 0.25*(1+xi[0]);  dNdxi(3,9) = 0.25*(1-xi[0]);
-   dNdxi(4,1) = 0.25*(-1+xi[0]);  dNdxi(4,4) = 0.25*(-1-xi[0]);
-   dNdxi(4,7) = 0.25*(1+xi[0]);  dNdxi(4,10) = 0.25*(1-xi[0]);
-   dNdxi(5,2) = 0.25*(-1+xi[0]);  dNdxi(5,5) = 0.25*(-1-xi[0]);
-   dNdxi(5,8) = 0.25*(1+xi[0]);  dNdxi(5,11) = 0.25*(1-xi[0]);
-
-   ddNdxi.SetSize(3*4, 3*4); ddNdxi = 0.0;
-   ddNdxi(3,0) = 0.25; ddNdxi(3,3) = -0.25;
-   ddNdxi(3,6) = 0.25; ddNdxi(3,9) = -0.25;
-   ddNdxi(4,1) = 0.25; ddNdxi(4,4) = -0.25;
-   ddNdxi(4,7) = 0.25; ddNdxi(4,10) = -0.25;
-   ddNdxi(5,2) = 0.25; ddNdxi(5,5) = -0.25;
-   ddNdxi(5,8) = 0.25; ddNdxi(5,11) = -0.25;
-
-   ddNdxi(6,0) = 0.25; ddNdxi(6,3) = -0.25;
-   ddNdxi(6,6) = 0.25; ddNdxi(6,9) = -0.25;
-   ddNdxi(7,1) = 0.25; ddNdxi(7,4) = -0.25;
-   ddNdxi(7,7) = 0.25; ddNdxi(7,10) = -0.25;
-   ddNdxi(8,2) = 0.25; ddNdxi(8,5) = -0.25;
-   ddNdxi(8,8) = 0.25; ddNdxi(8,11) = -0.25;
-}
-
-
-void cross(const Vector a, const Vector b, Vector& c)
-{
-   assert(a.Size()==3);
-   c.SetSize(3);
-   c[0] = a[1]*b[2] - a[2]*b[1];
-   c[1] = -a[0]*b[2] + b[0]*a[2];
-   c[2] = a[0]*b[1] - a[1]*b[0];
-
-}
-// a outer b
-void outer(const Vector a, const Vector b, DenseMatrix& c)
-{
-   int m = a.Size();
-   int n = b.Size();
-   assert(c.Height()==m);
-   assert(c.Width() ==n);
-   for (int i=0; i<m; i++)
-   {
-      for (int j=0; j<n; j++)
-      {
-         c(i,j) = a[i]*b[j];
-      }
-   }
-}
-// dphidxi 2*4
-// coords 4*3
-void ComputeNormal(const DenseMatrix& dphidxi, const DenseMatrix& coords,
-                   Vector& normal, double& nnorm)
-{
-
-   DenseMatrix dxdxi(2,3);
-   Mult(dphidxi, coords, dxdxi);
-   Vector dxdxi1(3);
-   Vector dxdxi2(3);
-
-   dxdxi.GetRow(0,dxdxi1);
-   dxdxi.GetRow(1,dxdxi2);
-
-   cross(dxdxi1, dxdxi2, normal);  // is there a cross product?  no
-   // VectorCrossProductCoefficient::Eval has hard-coded cross product
-   nnorm = normal.Norml2( );
-   normal /=  nnorm;
-}
-
-void SlaveToMaster(const DenseMatrix& m_coords, const Vector& s_x, Vector& xi)
-{
-   bool converged = false;
-   bool pt_on_elem = false;
-   int dim = 3;
-   xi.SetSize(dim-1);
-   xi = 0.0;
-   double r = 1e10;
-   int max_iter = 15;
-   double off_el_xi = 1e-2;
-   double proj_newton_tol = 1e-13;
-   double proj_max_gap = 0.5;
-   Vector gap_v(dim);
-   // warm start from linear solution
-
-   for (int it=0; it<max_iter; it++)
-   {
-      //cout<<it<<endl;
-      Vector m_N(4);
-      m_N = 0.;
-      DenseMatrix m_dN(2,4);
-      m_dN = 0.;
-      DenseMatrix m_dN2(3,4);
-      m_dN2 = 0.;
-      BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-      Vector x_c(dim);
-      m_coords.MultTranspose(m_N, x_c);
-
-      gap_v = s_x;
-      gap_v -= x_c;
-
-      DenseMatrix m_dx(2,3);
-      m_dx = 0.;
-      Mult(m_dN, m_coords, m_dx);
-
-      Vector r(dim-1);
-      r = 0.0;
-      m_dx.Mult(gap_v, r);
-
-      if (r.Normlinf() < proj_newton_tol)
-      {
-         converged = true;
-         break;
-      }
-
-      DenseMatrix drdxi(dim-1,dim-1);
-      drdxi = 0.;
-      MultABt(m_dx, m_dx, drdxi); // m_dx * m_dx.T
-      drdxi *= -1.0;
-
-      DenseMatrix m_dx2(3,3); m_dx2 = 0.0;
-      Mult(m_dN2,m_coords, m_dx2);
-
-      //m_d2x = m_dN(:,:,2) * m_elem_coords(1:4,:);  //m_dN(:,:,2) is 3*4
-      for (int d=0; d<3; d++)
-      {
-         DenseMatrix Mtemp(2,2); Mtemp = 0.0;
-         Mtemp(0,0) = m_dx2(0,d); Mtemp(0,1) = m_dx2(1,d);
-         Mtemp(1,0) = m_dx2(1,d); Mtemp(1,1) = m_dx2(2,d);
-
-         drdxi.Add(gap_v[d], Mtemp);
-      }
-
-      //cond_num = rcond(drdxi);  condition number?
-      //drdxi.TestInversion();
-      DenseMatrixInverse drdxi_inv(drdxi);
-      Vector xi_tmp(dim-1);
-
-      drdxi_inv.Mult(r,xi_tmp);
-      xi -= xi_tmp;
-   }
-   if (!converged)
-   {
-      xi = 0.0;
-   }
-   off_el_xi += 1 ; // tolerance of offset of xi outside [-1,1]
-
-   //cout<<gap_v.Norml2()<<" " <<xi.Normlinf()<<endl;
-   if (gap_v.Norml2() < proj_max_gap && xi.Normlinf() <= off_el_xi)
-   {
-      pt_on_elem = true;
-   }
-
-   MFEM_VERIFY(pt_on_elem == true, "xi went out of bounds");
-   MFEM_VERIFY(converged == true, "projection didn't converge");
-}
-
-
-
-// m_coords is expected to be 4 * 3
-void  ComputeGapJacobian(const Vector x_s, const Vector xi,
-                         const DenseMatrix m_coords,
-                         double& gap, Vector& normal, Vector& dgdxm, Vector& dgdxs)
-{
-   Vector m_N(4);
-   DenseMatrix m_dN(2,4);
-   DenseMatrix m_dN2(3,4);
-   BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-   Vector x_c(3);
-   m_coords.MultTranspose(m_N, x_c);
-
-   Vector gap_v(3); gap_v = 0.0;
-   gap_v  = x_s;
-   gap_v -= x_c;
-
-   DenseMatrix m_dx(2,3);
-   Mult(m_dN, m_coords, m_dx);
-
-   double nnorm = 0;
-   ComputeNormal(m_dN, m_coords, normal, nnorm);
-
-   gap = gap_v * normal; // gap function value, dot product between vectors
-
-   //dr_dx = zeros(2,4,3); % nsegment, nodes in quad, ndim
-
-   DenseMatrix dr_dx_res1(4,3); dr_dx_res1 = 0.;
-   DenseMatrix dr_dx_res2(4,3); dr_dx_res2 = 0.;
-
-   Vector m_dxrow1(3);
-   m_dx.GetRow(0, m_dxrow1);
-   outer(m_N, m_dxrow1, dr_dx_res1);// 4*1 times 1*3
-   dr_dx_res1 *= -1.0;
-
-   Vector m_dxrow2(3);
-   m_dx.GetRow(1, m_dxrow2);
-   outer(m_N, m_dxrow2, dr_dx_res2);// 4*1 times 1*3
-   dr_dx_res2 *= -1.0;
-
-   Vector m_dNrow1(4); m_dN.GetRow(0, m_dNrow1);
-   Vector m_dNrow2(4); m_dN.GetRow(1, m_dNrow2);
-
-   DenseMatrix dr_dx_res1_tmp(4,3); dr_dx_res1_tmp = 0.;
-   DenseMatrix dr_dx_res2_tmp(4,3); dr_dx_res2_tmp = 0.;
-   outer(m_dNrow1, gap_v, dr_dx_res1_tmp);// 4*1 times 1*3
-   outer(m_dNrow2, gap_v, dr_dx_res2_tmp);// 4*1 times 1*3
-
-   dr_dx_res1 += dr_dx_res1_tmp; // outer product in vector?
-   dr_dx_res2 += dr_dx_res2_tmp;
-
-
-   DenseMatrix K_dxidx1(2,2); // 2*2
-   K_dxidx1 = 0.;
-   MultABt(m_dx, m_dx, K_dxidx1); // m_dx * m_dx.T
-
-   Vector v_dxidx2(4);
-   m_coords.Mult(gap_v, v_dxidx2); // m_coords * gap_v;  // 4*3 * 3 = 4
-
-   DenseMatrix K_dxidx2(2,2); K_dxidx2 = 0.0;
-
-   Vector m_dN2row1(4); m_dN2.GetRow(0, m_dN2row1);
-   Vector m_dN2row2(4); m_dN2.GetRow(1, m_dN2row2);
-   Vector m_dN2row3(4); m_dN2.GetRow(2, m_dN2row3);
-   // how to get 2nd order? multidimensional matrix?
-   K_dxidx2(0,0) = m_dN2row1 * v_dxidx2; // how would 4*1 * 1*4 be computed?
-   K_dxidx2(0,1) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,0) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,1) = m_dN2row3 * v_dxidx2;
-
-   DenseMatrix K_dxidx(2,2);
-   K_dxidx -= K_dxidx1;
-   K_dxidx += K_dxidx2;
-
-   // resize the vectors and matrices
-   Vector dxidx(24); dxidx = 0.0;
-   Vector drdx_r(24); drdx_r = 0.0;
-
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         drdx_r[4*j+i] = dr_dx_res1(i,j);
-         drdx_r[4*j+i+12] = dr_dx_res2(i,j);
-
-      }
-   }
-   //drdx_r(1:4*3,1) = reshape(dr_dx_res(:,:,1),4*3,1);
-   //drdx_r(4*3+1:2*4*3,1) = reshape(dr_dx_res(:,:,2),4*3,1);
-   DenseMatrix drdx_K(24,24); drdx_K = 0.;
-   for (int i =0; i<12; i++)
-   {
-      drdx_K(i,i) = K_dxidx(0,0);
-      drdx_K(i,12+i) = K_dxidx(0,1);
-      drdx_K(12+i,i) = K_dxidx(1,0);
-      drdx_K(12+i,12+i) = K_dxidx(1,1);
-   }
-
-   DenseMatrixInverse drdxK_inv(drdx_K);
-   drdxK_inv.Mult(drdx_r,dxidx);
-   // LinearSolve (drdx_K,drdx_r, dxidx) ; //???
-   dxidx *= -1.0;
-
-
-
-   Vector drdxs_r(6);
-   drdxs_r[0] = m_dx(0,0); drdxs_r[1] = m_dx(0,1); drdxs_r[2] = m_dx(0,2);
-   drdxs_r[3] = m_dx(1,0); drdxs_r[4] = m_dx(1,1); drdxs_r[5] = m_dx(1,2);
-
-   DenseMatrix drdxs_K(6,6); drdxs_K = 0.;
-   for (int i=0; i<3; i++)
-   {
-      drdxs_K(i,i) = K_dxidx(0,0);
-      drdxs_K(i,3+i) = K_dxidx(0,1);
-      drdxs_K(i+3,i) = K_dxidx(1,0);
-      drdxs_K(i+3,i+3) = K_dxidx(1,1);
-   }
-
-   Vector dxidxs(6); dxidxs = 0.0;
-   DenseMatrixInverse drdxsK_inv(drdxs_K);
-   drdxsK_inv.Mult(drdxs_r,dxidxs);
-   dxidxs *= -1.0;
-   //dxidxs = -drdxs_K\drdxs_r;
-
-   //dxidx = reshape(dxidx, 4,3,2); dxidxs = reshape(dxidxs, 1,3,2);
-
-   dgdxm.SetSize(12); dgdxm = 0.;
-   DenseMatrix dgdxm_tmp(4,3);
-   outer(m_N, normal,dgdxm_tmp);
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         dgdxm[3*i+j] = -dgdxm_tmp(i,j);
-      }
-   }
-   //dxidx_M = -m_dN(1:2,:,1) * (m_coords(1:4,:)*normal'); % this turns out to be 0
-
-   dgdxs.SetSize(3);
-   dgdxs += normal;
-   //dgdxs = dgdxs + dxidx_M(1) * dxidxs(:,:,1) + dxidx_M(2) * dxidxs(:,:,2);
-};
-
-void ComputeGapHessian(const Vector x_s, const Vector xi,
-                       const DenseMatrix m_coords,
-                       DenseMatrix& dg2dx)
-{
-   Vector m_N(4);
-   DenseMatrix m_dN(2,4);
-   DenseMatrix m_dN2(3,4);
-   BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-   int dim = 3;
-   int num_dofs1 = dim;
-   int num_dofs2 = 4*dim;
-   int num_dofs = num_dofs1 + num_dofs2;
-   dg2dx.SetSize(num_dofs,num_dofs); dg2dx = 0.0;
-
-   Vector x_c(3);
-   m_coords.MultTranspose(m_N,x_c);
-
-   Vector gap_v(3); gap_v = 0.0;
-   gap_v  = x_s;
-   gap_v -= x_c;
-
-   DenseMatrix m_dx(2,3);
-   Mult(m_dN, m_coords, m_dx);
-
-   DenseMatrix m_dx2(3,3); m_dx2 = 0.0;
-   Mult(m_dN2,m_coords, m_dx2);
-   double nnorm = 0.0;
-   Vector normal(3); normal = 0.0;
-   ComputeNormal(m_dN, m_coords, normal, nnorm);
-
-   double gap = gap_v * normal; // gap function value, dot product between vectors
-
-   DenseMatrix M(2,2); M = 0.0;
-   MultABt(m_dx, m_dx, M);
-
-   DenseMatrix f(2, num_dofs2); f = 0.0;
-
-   for (int d=0; d<3; d++)
-   {
-      DenseMatrix Mtemp(2,2); Mtemp = 0.0;
-      Mtemp(0,0) = m_dx2(0,d); Mtemp(0,1) = m_dx2(1,d);
-      Mtemp(1,0) = m_dx2(1,d); Mtemp(1,1) = m_dx2(2,d);
-
-      M.Add(-gap_v[d], Mtemp);
-
-      Vector m_dxcol(2); m_dx.GetColumn(d, m_dxcol);
-      DenseMatrix ftmp(2,4);
-      outer(m_dxcol, m_N, ftmp);
-      ftmp *= -1;
-      ftmp.Add( gap_v[d], m_dN);   // 2*4
-
-      for (int j=0; j<4; j++)
-      {
-         assert(d+3*j<num_dofs2);
-         f(0,d+j*3) = ftmp(0,j);
-         f(1,d+j*3) = ftmp(1,j);
-      }
-   }
-   //fprintf('hess dxidxm\n');
-   DenseMatrixInverse Minv(M);
-   DenseMatrix dxidxm(2,num_dofs2); dxidxm = 0.0;
-   Minv.Mult(f, dxidxm);
-   //LinearSolve??
-   //dxidxm = M\f;
-
-   DenseMatrix nde2(2,2); nde2 = 0.0;
-   DenseMatrix Nndx2(2,num_dofs2); Nndx2 = 0.0;
-
-   for (int d=0; d<3; d++)
-   {
-      DenseMatrix ndetmp(2,2); ndetmp = 0.0;
-      ndetmp(0,0) = normal(d)*m_dx2(0,d); ndetmp(0,1) = normal(d)*m_dx2(1,d);
-      ndetmp(1,0) = normal(d)*m_dx2(1,d); ndetmp(1,1) = normal(d)*m_dx2(2,d);
-
-      nde2 += ndetmp;
-
-      for (int j=0; j<4; j++)
-      {
-         assert(d+3*j<num_dofs2);
-         Nndx2(0,d+j*3) = normal[d]*m_dN(0,j);
-         Nndx2(1,d+j*3) = normal[d]*m_dN(1,j);
-      }
-
-   }
-
-   DenseMatrix Ndn(2,num_dofs2); Ndn = 0.0;
-   Ndn += Nndx2;
-   AddMult(nde2, dxidxm, Ndn);
-
-
-   DenseMatrix M2(2,2); M2 = 0.0;
-   MultABt(m_dx, m_dx, M2);
-   DenseMatrixInverse M2inv(M2);
-   DenseMatrix diag2(2,2); diag2(0,0) = 1.0; diag2(1,1) = 1.0;
-   DenseMatrix m_con(2,2); m_con = 0.0;
-
-   M2inv.Mult(diag2, m_con);
-
-   DenseMatrix dg2dxm(num_dofs2, num_dofs2); dg2dxm = 0.0;
-
-   DenseMatrix dg2dxm_tmp(num_dofs2,2); dg2dxm_tmp = 0.0;
-   MultAtB(Ndn, m_con, dg2dxm_tmp);
-   Mult(dg2dxm_tmp, Ndn, dg2dxm);
-   dg2dxm *= gap;
-
-   DenseMatrix dg2dxm_tmp2(num_dofs2,num_dofs2); dg2dxm_tmp2 = 0.0;
-   MultAtB(Nndx2, dxidxm, dg2dxm_tmp2);
-   dg2dxm.Add(-1.0, dg2dxm_tmp2);
-
-   dg2dxm_tmp = 0.0;
-   MultAtB(dxidxm, nde2, dg2dxm_tmp);
-
-   AddMult_a(-1.0, dg2dxm_tmp, dxidxm, dg2dxm);
-
-   dg2dxm_tmp2 = 0.0;
-   MultAtB(dxidxm, Nndx2, dg2dxm_tmp2);
-   dg2dxm.Add(-1.0, dg2dxm_tmp2);
-
-   Vector v_dxidx2(4);
-   m_coords.Mult(gap_v, v_dxidx2); // m_coords * gap_v;  // 4*3 * 3 = 4
-
-   DenseMatrix K_dxidx2(2,2); K_dxidx2 = 0.0;
-
-   Vector m_dN2row1(4); m_dN2.GetRow(0, m_dN2row1);
-   Vector m_dN2row2(4); m_dN2.GetRow(1, m_dN2row2);
-   Vector m_dN2row3(4); m_dN2.GetRow(2, m_dN2row3);
-   K_dxidx2(0,0) = m_dN2row1 * v_dxidx2; // how would 4*1 * 1*4 be computed?
-   K_dxidx2(0,1) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,0) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,1) = m_dN2row3 * v_dxidx2;
-
-   DenseMatrix K_dxidx(2,2);
-   K_dxidx -= M2;
-   K_dxidx += K_dxidx2;
-
-   Vector drdxs_r(6);
-   drdxs_r[0] = m_dx(0,0); drdxs_r[1] = m_dx(0,1); drdxs_r[2] = m_dx(0,2);
-   drdxs_r[3] = m_dx(1,0); drdxs_r[4] = m_dx(1,1); drdxs_r[5] = m_dx(1,2);
-
-   DenseMatrix drdxs_K(6,6); drdxs_K = 0.;
-   for (int i=0; i<3; i++)
-   {
-      drdxs_K(i,i) = K_dxidx(0,0);
-      drdxs_K(i,3+i) = K_dxidx(0,1);
-      drdxs_K(i+3,i) = K_dxidx(1,0);
-      drdxs_K(i+3,i+3) = K_dxidx(1,1);
-   }
-   Vector dxidxs(6);
-
-   DenseMatrixInverse drdxsK_inv(drdxs_K);
-   drdxsK_inv.Mult(drdxs_r,dxidxs);
-   dxidxs *= -1.0;
-   //dxidxs = -drdxs_K\drdxs_r;
-
-   DenseMatrix dxidxs_m(2,3); dxidxs_m = 0.0;
-   dxidxs_m(0,0) = dxidxs[0]; dxidxs_m(0,1) = dxidxs[1]; dxidxs_m(0,2) = dxidxs[2];
-   dxidxs_m(1,0) = dxidxs[3]; dxidxs_m(1,1) = dxidxs[4]; dxidxs_m(1,2) = dxidxs[5];
-
-   DenseMatrix dtao1dxs(3,3); dtao1dxs = 0.0;
-   DenseMatrix dtao2dxs(3,3); dtao2dxs = 0.0;
-
-   Vector dxidxs_row1(3); dxidxs_row1 = 0.0; Vector dxidxs_row2(3);
-   dxidxs_row2 = 0.0;
-   Vector mdx2_row1(3); mdx2_row1 = 0.0; Vector mdx2_row2(3); mdx2_row2 = 0.0;
-   Vector mdx2_row3(3); mdx2_row3 = 0.0;
-   dxidxs_m.GetRow(0,dxidxs_row1);
-   dxidxs_m.GetRow(1,dxidxs_row2);
-   m_dx2.GetRow(0,mdx2_row1);
-   m_dx2.GetRow(1,mdx2_row2);
-   m_dx2.GetRow(2,mdx2_row3);
-
-   DenseMatrix dtaotmp(3,3); dtaotmp = 0.0;
-   outer(mdx2_row1, dxidxs_row1,dtaotmp);
-   dtao1dxs += dtaotmp; dtaotmp = 0.0;
-   outer(mdx2_row2, dxidxs_row1,dtaotmp);
-   dtao1dxs += dtaotmp; dtaotmp = 0.0;
-
-   outer(mdx2_row2, dxidxs_row2, dtaotmp);
-   dtao2dxs += dtaotmp; dtaotmp = 0.0;
-   outer(mdx2_row3, dxidxs_row2, dtaotmp);
-   dtao2dxs += dtaotmp; dtaotmp = 0.0;
-
-   DenseMatrix dtaodxs(3,3); dtaodxs = 0.0; //tao = tao1 cross tao2
-
-   for (int d=0; d<3; d++)
-   {
-      Vector dtao1dxs_tmp(3); dtao1dxs_tmp = 0.0;
-      dtao1dxs.GetColumn(d,dtao1dxs_tmp);
-      Vector m_dxrow(3); m_dx.GetRow(1, m_dxrow);
-
-      Vector dtaodxs_tmp(3); dtaodxs_tmp = 0.0;
-      cross(dtao1dxs_tmp, m_dxrow, dtaodxs_tmp);
-
-      Vector dtaodxs_tmp2(3); dtaodxs_tmp2 = 0.0;
-      m_dx.GetRow(0, m_dxrow);
-      dtao1dxs_tmp = 0.0;  // reuse the same vector for dtao2
-      dtao2dxs.GetColumn(d,dtao1dxs_tmp);
-      cross(m_dxrow, dtao1dxs_tmp, dtaodxs_tmp2);
-
-      dtaodxs_tmp2 += dtaodxs_tmp;
-      dtaodxs.SetCol(d, dtaodxs_tmp2);
-   }
-
-   DenseMatrix dndxs(3,3); dndxs = 0.0; dndxs += dtaodxs; dndxs *= 1.0/nnorm;
-   DenseMatrix dndxs_tmp(3,3); dndxs_tmp = 0.0;
-   outer(normal, normal, dndxs_tmp);
-   AddMult_a(-1/nnorm, dndxs_tmp, dtaodxs, dndxs);
-
-   DenseMatrix dgvdxs(3,3); dgvdxs = 0.0;
-   MultAtB(m_dx, dxidxs_m, dgvdxs);
-   dgvdxs *= -1;
-   for (int d=0; d<3; d++)
-   {
-      dgvdxs(d,d) += 1.0;
-   }
-   //dxidxs: 2*3
-
-   DenseMatrix dg2dxs(3,3); dg2dxs = 0.0;
-   DenseMatrix dg2dxs_tmp(3,2); dg2dxs_tmp = 0.0;
-   MultAtB(dxidxs_m, nde2, dg2dxs_tmp);
-   AddMult_a(-1.0, dg2dxs_tmp, dxidxs_m, dg2dxs);
-   DenseMatrix dg2dxs_tmp2(3,3); dg2dxs_tmp2 = 0.0;
-   MultAtB(dgvdxs, dndxs, dg2dxs_tmp2);
-   dg2dxs += dg2dxs_tmp2;
-   dg2dxs_tmp2 = 0.0;
-   MultAtB(dndxs, dndxs_tmp, dg2dxs_tmp2);
-   AddMult(dg2dxs_tmp2, dgvdxs, dg2dxs);
-
-   DenseMatrix Ne(3,12), Be(6,12), dBe(12,12);
-   BasisVectorDerivs(xi, Ne, Be, dBe);
-
-   DenseMatrix dtao1dxm(3,12); dtao1dxm.CopyRows(Be, 0, 2);
-   DenseMatrix dtao2dxm(3,12); dtao2dxm.CopyRows(Be, 3, 5);
-
-   Vector m_coords_v(12);
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         m_coords_v[i*3+j] = m_coords(i,j);
-      }
-   }
-
-   for (int i=0; i<2; i++)
-   {
-      Vector dxidxm_tmp(num_dofs2); dxidxm_tmp = 0.0;
-      dxidxm.GetRow(i,dxidxm_tmp);
-
-      DenseMatrix dBe_tmp(3,12);
-      dBe_tmp.CopyRows(dBe,i*3,(i+1)*3-1);
-
-      DenseMatrix dtaodxm_tmp(12,12); dtaodxm_tmp = 0.0;
-      outer(m_coords_v, dxidxm_tmp, dtaodxm_tmp);
-      AddMult(dBe_tmp, dtaodxm_tmp, dtao1dxm);
-
-      //dtao1dxm += dBe(:,:,i)*reshape(m_coords(1:4,:)',12,1)*reshape(dxidxm(i,:),1,12); % 3*12
-      dBe_tmp = 0.0;
-      dBe_tmp.CopyRows(dBe,(i+2)*3,(i+3)*3-1);
-      AddMult(dBe_tmp, dtaodxm_tmp, dtao2dxm);
-
-   }
-
-   DenseMatrix dtaodxm(3,12); dtaodxm = 0.0;//tao = tao1 cross tao2
-
-   for (int d=0; d<12; d++)
-   {
-      Vector dtaodxm_tmp(3); dtaodxm_tmp = 0.0;
-      Vector dtaodxm_tmp2(3); dtaodxm_tmp2 = 0.0;
-      Vector tmp1(3); tmp1 = 0.0;  dtao1dxm.GetColumn(d,tmp1);
-      Vector m_dxrow2(3); m_dx.GetRow(1, m_dxrow2);
-      Vector m_dxrow1(3); m_dx.GetRow(0, m_dxrow1);
-      Vector tmp2(3); tmp2 = 0.0;  dtao2dxm.GetColumn(d,tmp2);
-
-      cross(tmp1, m_dxrow2, dtaodxm_tmp);
-      cross(m_dxrow1,tmp2, dtaodxm_tmp2);
-      dtaodxm_tmp += dtaodxm_tmp2;
-
-      dtaodxm.SetCol(d, dtaodxm_tmp);
-   }
-
-   DenseMatrix dndxm(3,12); dndxm = 0.0;
-   dndxm += dtaodxm;
-   dndxm *= 1.0/nnorm;
-   AddMult_a(-1/nnorm, dndxs_tmp, dtaodxm, dndxm); //dndxs_tmp = normal'*normal
-
-   DenseMatrix dgvdxm(3,12); dgvdxm = 0.0;
-   dgvdxm -= Ne;
-
-   for (int i=0; i<2; i++)
-   {
-      Vector dxidxm_tmp(num_dofs2); dxidxm_tmp = 0.0;
-      dxidxm.GetRow(i,dxidxm_tmp);
-
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-
-      DenseMatrix dgvdxm_tmp(12,12); dgvdxm_tmp = 0.0;
-      outer(m_coords_v, dxidxm_tmp, dgvdxm_tmp);
-      AddMult_a(-1.0, Be_tmp, dgvdxm_tmp, dgvdxm);
-
-   }
-
-   DenseMatrix dg2dxsxm(3,12); dg2dxsxm = 0.0;
-   DenseMatrix dg2dxsxm_tmp(3,3); dg2dxsxm_tmp = 0.0;
-   MultAtB(dgvdxs, dndxm, dg2dxsxm);
-
-   MultAtB(dndxs, dndxs_tmp, dg2dxsxm_tmp);
-   AddMult(dg2dxsxm_tmp, dgvdxm, dg2dxsxm); // += dndxs'*normal'*normal*dgvdxm;
-
-   DenseMatrix dgvdxsxmn(3,12); dgvdxsxmn = 0.0;
-   DenseMatrix dgvdxsxmn_tmp(3,2); dgvdxsxmn_tmp = 0.0;
-   MultAtB(dxidxs_m, nde2, dgvdxsxmn_tmp);   //dxidxs_m: 2*3
-
-   AddMult_a(-1.0, dgvdxsxmn_tmp, dxidxm, dgvdxsxmn);
-
-
-   for (int i =0; i<2; i++)
-   {
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-
-      Vector dxidxs_row(3); dxidxs_row = 0.0; dxidxs_m.GetRow(i,dxidxs_row);
-      DenseMatrix dgvdxsxmn_tmp2(3,3); dgvdxsxmn_tmp2 = 0.0;
-      outer(dxidxs_row, normal, dgvdxsxmn_tmp2);
-      AddMult_a(-1.0, dgvdxsxmn_tmp2, Be_tmp, dgvdxsxmn);
-   }
-
-   dg2dxsxm += dgvdxsxmn;
-
-   DenseMatrix dg2dxmxs(12,3); dg2dxmxs = 0.0;
-   DenseMatrix dg2dxmxs_tmp(12,3); dg2dxmxs_tmp = 0.0;
-   MultAtB(dgvdxm, dndxs, dg2dxmxs);
-   MultAtB(dndxm, dndxs_tmp, dg2dxmxs_tmp);
-   AddMult(dg2dxmxs_tmp, dgvdxs, dg2dxmxs);
-
-   DenseMatrix dgvdxmxsn(12,3); dgvdxmxsn = 0.0;
-   DenseMatrix dgvdxmxsn_tmp(12,2); dgvdxmxsn_tmp = 0.0;
-
-   MultAtB(dxidxm, nde2, dgvdxmxsn_tmp);
-   dgvdxmxsn_tmp *= -1.0;
-   AddMult(dgvdxmxsn_tmp, dxidxs_m, dgvdxmxsn);
-
-   for (int i =0; i<2; i++)
-   {
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-      Be_tmp.Transpose(); // Be is now 12*3
-
-      Vector dxidxs_row(3); dxidxs_row = 0.0; dxidxs_m.GetRow(i,dxidxs_row);
-      DenseMatrix dgvdxmxsn_tmp2(3,3); dgvdxmxsn_tmp2 = 0.0;
-      outer(normal, dxidxs_row, dgvdxmxsn_tmp2);
-      AddMult_a(-1.0, Be_tmp, dgvdxmxsn_tmp2, dgvdxmxsn);
-
-   }
-
-   dg2dxmxs += dgvdxmxsn;
-
-   dg2dx.CopyMN(dg2dxs, 0, 0);
-   dg2dx.CopyMN(dg2dxm, 3, 3);
-   dg2dx.CopyMN(dg2dxsxm, 0, 3);
-   dg2dx.CopyMN(dg2dxmxs, 3, 0);
-
-};
-
-
-
-void NodeSegConPairs(const Vector x1, const Vector xi2,
-                     const DenseMatrix coords2,
-                     double& node_g, Vector& node_dg, DenseMatrix& node_dg2)
-{
-   double gap = 0.0;
-   Vector normal(3); normal = 0.0;
-   Vector dgdxm(12); dgdxm = 0.0;
-   Vector dgdxs(3); dgdxs = 0.0;
-
-   ComputeGapJacobian(x1, xi2, coords2, gap, normal, dgdxm, dgdxs);
-   node_g = gap;
-
-   node_dg.SetSize(12+3);
-   for (int i=0; i<3; i++) { node_dg[i] = dgdxs[i]; }
-   for (int i=0; i<12; i++) { node_dg[i+3] = dgdxm[i]; }
-
-   DenseMatrix dg2dx(15,15); dg2dx = 0.0;
-   DenseMatrix dgvdxmxsn(12,3); dgvdxmxsn = 0.0;
-   ComputeGapHessian(x1, xi2, coords2, dg2dx);
-
-   node_dg2.SetSize(15,15);
-   node_dg2 = dg2dx;
-
-   /*
-   if(obj.space1.conns{e1}(i)==150)  % for debugging purpose
-
-   v1 = 1:3;
-   v2 = 1:12;
-   %v1 = ones(1,3)
-   %v2 = ones(1,12)
-   v2 = reshape(v2,4,3);
-   x1n1 = x1 + 0.01*v1;
-   coords2n1 = coords2 + 0.001*v2;
-      [xi2n1, gapv1, ~, ~] = SlaveToMaster(obj, coords2n1, x1n1);
-      [gapn1, n1,dgdxmn1, dgdxsn1] = ComputeGapJacobian(obj, x1n1, xi2n1, coords2n1);
-   x1n2 = x1 - 0.01*v1;
-   coords2n2 = coords2 - 0.001*v2;
-      [xi2n2, gapv2, ~, ~] = SlaveToMaster(obj, coords2n2, x1n2);
-      [gapn2, n2,dgdxmn2, dgdxsn2] = ComputeGapJacobian(obj, x1n2, xi2n2, coords2n2);
-   fprintf('fd\n');
-      %gapv1-gapv2
-   [dgdxsn1(:)',dgdxmn1(:)'] - [dgdxsn2(:)',dgdxmn2(:)']
-
-   %dgdxsn1-dgdxsn2
-   fprintf('code\n');
-   v2n = v2';
-   %dg2dx(1:3,1:3)*0.04*ones(3,1)
-   temp = zeros(12,3);
-   for i = 1:4
-   temp1 = dg2dx(3+(i-1)*3+1:3+i*3,1:3);
-   temp((i-1)*3+1:i*3,:) = temp1';
-   end
-   temp2 = zeros(3,12);
-   for i = 1:4
-   temp3 = dg2dx(1:3,3+(i-1)*3+1:3+i*3);
-   temp2(:,(i-1)*3+1:i*3) = temp3';
-   end
-   %dg2dx
-   %dg2dx(4:end,1:3) = temp;
-   %dg2dx(1:3,4:end) = temp2;
-   %dgvdxm * 0.002*v2n(:)
-   (dg2dx*[0.02*v1(:)',0.002*v2n(:)']')'
-   %dg2dx(4:end,1:3)
-   end*/
-
-};
-
-
-// coordsm : (npoints*4, 3) use what class?
-// m_conn: (npoints*4)
-void Assemble_Contact(const int m, const int npoints, const int ndofs,
-                      const Vector x_s,
-                      const Vector xi, const DenseMatrix coordsm, const Array<int> s_conn,
-                      const Array<int> m_conn, Vector& g, SparseMatrix& M,
-                      std::vector<SparseMatrix>& dM)
-{
-   int n = ndofs;
-   int ndim = 3;
-
-   g.SetSize(m);
-   g = 0.0;
-
-   //SparseMatrix M(m, n);  // M needs to be the correct size
-
-   //dM.resize(m); // needs to clear?
-
-   double g_tmp = 0.;
-   Vector dg(4*ndim+ndim);
-   dg = 0.;
-   DenseMatrix dg2(4*ndim+ndim,4*ndim+ndim);
-   dg2 = 0.;
-
-   for (int i=0; i<npoints; i++)
-   {
-      Vector x1(ndim);
-      x1[0] = x_s[i*ndim];
-      x1[1] = x_s[i*ndim+1];
-      x1[2] = x_s[i*ndim+2];
-
-      Vector xi2(ndim-1);
-      xi2[0] = xi[i*(ndim-1)];
-      xi2[1] = xi[i*(ndim-1)+1];
-
-      DenseMatrix coords2(4,3);
-      coords2.CopyRows(coordsm, i*4,(i+1)*4-1);
-
-      //how to get coords2?
-      dg = 0.0;
-      dg2 = 0.;
-      NodeSegConPairs(x1, xi2, coords2, g_tmp, dg, dg2);
-      //x1.Print();
-      //xi2.Print();
-      //coords2.Print();
-      g[s_conn[i]] = g_tmp; // should be unique
-      Array<int> m_conn_i(4);
-      m_conn.GetSubArray(4*i, 4, m_conn_i);
-
-      Array<int> node_conn(5);
-      node_conn[0] = s_conn[i];
-      for (int j=0; j<4; j++)
-      {
-         node_conn[j+1] = m_conn_i[j];
-      }
-
-      Array<int>  M_i_tmp(1);
-      M_i_tmp[0] = s_conn[i];
-
-      //j_idx = (node_conn-1)*obj.disp_field.num_components +repmat((1:obj.disp_field.num_components)', 1, length(node_conn{i}));
-      Array<int> j_idx(5*ndim); j_idx = 0;
-      for (int j=0; j< 5; j++)
-      {
-         for (int k=0; k<ndim; k++)
-         {
-            j_idx[j*ndim+k] = node_conn[j]*ndim+k;
-         }
-      }
-      DenseMatrix M_v_tmp(1, ndim*(4+1));   // SetData now?
-      M_v_tmp.SetRow(0, dg);
-
-      M.AddSubMatrix(M_i_tmp, j_idx, M_v_tmp);
-
-      Array<int> dM_i(ndim*(4+1));
-      Array<int> dM_j(ndim*(4+1));
-
-      for (int j=0; j< ndim*(4+1); j++)
-      {
-         dM_i[j] = j_idx[j];
-         dM_j[j] = j_idx[j];
-      }
-      //dg2.Print();
-      //dM[s_conn[i]].Print();
-      dM[s_conn[i]].AddSubMatrix(dM_i,dM_j, dg2);
-   }
-};
-
@@ -46,9 +46,6 @@ endif
 ifeq ($(MFEM_USE_HIOP),YES)
   SUBDIRS += hiop
 endif
-ifeq ($(MFEM_USE_IPOPT),YES)
-   SUBDIRS += ipopt
-endif
 ifeq ($(MFEM_USE_PETSC),YES)
   SUBDIRS += petsc
 endif
@@ -1,888 +0,0 @@
-
-using namespace std;
-using namespace mfem;
-
-void BasisEval(const Vector xi, Vector &N, DenseMatrix &dNdxi) // dNdxi is 2*4
-{
-   N[0] = 0.25*(1-xi[0])*(1-xi[1]);
-   N[1] = 0.25*(1+xi[0])*(1-xi[1]);
-   N[2] = 0.25*(1+xi[0])*(1+xi[1]);
-   N[3] = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi(0,0) = 0.25*(-1+xi[1]);
-   dNdxi(0,1) = 0.25*(1-xi[1]);
-   dNdxi(0,2) = 0.25*(1+xi[1]);
-   dNdxi(0,3) = 0.25*(-1-xi[1]);
-   dNdxi(1,0) = 0.25*(-1+xi[0]);
-   dNdxi(1,1) = 0.25*(-1-xi[0]);
-   dNdxi(1,2) = 0.25*(1+xi[0]);
-   dNdxi(1,3) = 0.25*(1-xi[0]);
-}
-
-
-void BasisEvalDerivs(const Vector xi, Vector& N, DenseMatrix& dNdxi,
-                     DenseMatrix& dN2dxi)
-{
-   N[0] = 0.25*(1-xi[0])*(1-xi[1]);
-   N[1] = 0.25*(1+xi[0])*(1-xi[1]);
-   N[2] = 0.25*(1+xi[0])*(1+xi[1]);
-   N[3] = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi.SetSize(2,4); dNdxi = 0.0;
-   dN2dxi.SetSize(3,4);
-   dN2dxi = 0.0;  // first row dxi2, second detadxi, third deta2
-
-   dNdxi(0,0) = 0.25*(-1+xi[1]); dNdxi(0,1) = 0.25*(1-xi[1]);
-   dNdxi(0,2) = 0.25*(1+xi[1]);  dNdxi(0,3) = 0.25*(-1-xi[1]);
-   dNdxi(1,0) = 0.25*(-1+xi[0]); dNdxi(1,1) = 0.25*(-1-xi[0]);
-   dNdxi(1,2) = 0.25*(1+xi[0]);  dNdxi(1,3) = 0.25*(1-xi[0]);
-
-   dN2dxi(1,0) = 0.25; dN2dxi(1,1) = -0.25; dN2dxi(1,2) = 0.25;
-   dN2dxi(1,3) = -0.25;
-}
-
-// returns the vector and matrix form of the shape functions and its derivative
-void BasisVectorDerivs(const Vector xi, DenseMatrix& N, DenseMatrix& dNdxi,
-                       DenseMatrix& ddNdxi)
-{
-   N.SetSize(3,12); N = 0.0;
-   N(0,0) = 0.25*(1-xi[0])*(1-xi[1]); N(0,3) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(0,6) = 0.25*(1+xi[0])*(1+xi[1]); N(0,9) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   N(1,1) = 0.25*(1-xi[0])*(1-xi[1]); N(1,4) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(1,7) = 0.25*(1+xi[0])*(1+xi[1]); N(1,10) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   N(2,2) = 0.25*(1-xi[0])*(1-xi[1]); N(2,5) = 0.25*(1+xi[0])*(1-xi[1]);
-   N(2,8) = 0.25*(1+xi[0])*(1+xi[1]); N(2,11) = 0.25*(1-xi[0])*(1+xi[1]);
-
-   dNdxi.SetSize(3*2, 3*4);  dNdxi = 0.0;
-   dNdxi(0,0) = 0.25*(-1+xi[1]);  dNdxi(0,3) = 0.25*(1-xi[1]);
-   dNdxi(0,6) = 0.25*(1+xi[1]);  dNdxi(0,9) = 0.25*(-1-xi[1]);
-   dNdxi(1,1) = 0.25*(-1+xi[1]);  dNdxi(1,4) = 0.25*(1-xi[1]);
-   dNdxi(1,7) = 0.25*(1+xi[1]);  dNdxi(1,10) = 0.25*(-1-xi[1]);
-   dNdxi(2,2) = 0.25*(-1+xi[1]);  dNdxi(2,5) = 0.25*(1-xi[1]);
-   dNdxi(2,8) = 0.25*(1+xi[1]);  dNdxi(2,11) = 0.25*(-1-xi[1]);
-
-   dNdxi(3,0) = 0.25*(-1+xi[0]);  dNdxi(3,3) = 0.25*(-1-xi[0]);
-   dNdxi(3,6) = 0.25*(1+xi[0]);  dNdxi(3,9) = 0.25*(1-xi[0]);
-   dNdxi(4,1) = 0.25*(-1+xi[0]);  dNdxi(4,4) = 0.25*(-1-xi[0]);
-   dNdxi(4,7) = 0.25*(1+xi[0]);  dNdxi(4,10) = 0.25*(1-xi[0]);
-   dNdxi(5,2) = 0.25*(-1+xi[0]);  dNdxi(5,5) = 0.25*(-1-xi[0]);
-   dNdxi(5,8) = 0.25*(1+xi[0]);  dNdxi(5,11) = 0.25*(1-xi[0]);
-
-   ddNdxi.SetSize(3*4, 3*4); ddNdxi = 0.0;
-   ddNdxi(3,0) = 0.25; ddNdxi(3,3) = -0.25;
-   ddNdxi(3,6) = 0.25; ddNdxi(3,9) = -0.25;
-   ddNdxi(4,1) = 0.25; ddNdxi(4,4) = -0.25;
-   ddNdxi(4,7) = 0.25; ddNdxi(4,10) = -0.25;
-   ddNdxi(5,2) = 0.25; ddNdxi(5,5) = -0.25;
-   ddNdxi(5,8) = 0.25; ddNdxi(5,11) = -0.25;
-
-   ddNdxi(6,0) = 0.25; ddNdxi(6,3) = -0.25;
-   ddNdxi(6,6) = 0.25; ddNdxi(6,9) = -0.25;
-   ddNdxi(7,1) = 0.25; ddNdxi(7,4) = -0.25;
-   ddNdxi(7,7) = 0.25; ddNdxi(7,10) = -0.25;
-   ddNdxi(8,2) = 0.25; ddNdxi(8,5) = -0.25;
-   ddNdxi(8,8) = 0.25; ddNdxi(8,11) = -0.25;
-}
-
-
-void cross(const Vector a, const Vector b, Vector& c)
-{
-   assert(a.Size()==3);
-   c.SetSize(3);
-   c[0] = a[1]*b[2] - a[2]*b[1];
-   c[1] = -a[0]*b[2] + b[0]*a[2];
-   c[2] = a[0]*b[1] - a[1]*b[0];
-
-}
-// a outer b
-void outer(const Vector a, const Vector b, DenseMatrix& c)
-{
-   int m = a.Size();
-   int n = b.Size();
-   assert(c.Height()==m);
-   assert(c.Width() ==n);
-   for (int i=0; i<m; i++)
-   {
-      for (int j=0; j<n; j++)
-      {
-         c(i,j) = a[i]*b[j];
-      }
-   }
-}
-// dphidxi 2*4
-// coords 4*3
-void ComputeNormal(const DenseMatrix& dphidxi, const DenseMatrix& coords,
-                   Vector& normal, double& nnorm)
-{
-
-   DenseMatrix dxdxi(2,3);
-   Mult(dphidxi, coords, dxdxi);
-   Vector dxdxi1(3);
-   Vector dxdxi2(3);
-
-   dxdxi.GetRow(0,dxdxi1);
-   dxdxi.GetRow(1,dxdxi2);
-
-   cross(dxdxi1, dxdxi2, normal);  // is there a cross product?  no
-   // VectorCrossProductCoefficient::Eval has hard-coded cross product
-   nnorm = normal.Norml2( );
-   normal /=  nnorm;
-}
-
-void SlaveToMaster(const DenseMatrix& m_coords, const Vector& s_x, Vector& xi)
-{
-   bool converged = false;
-   bool pt_on_elem = false;
-   int dim = 3;
-   xi.SetSize(dim-1);
-   xi = 0.0;
-   double r = 1e10;
-   int max_iter = 15;
-   double off_el_xi = 1e-2;
-   double proj_newton_tol = 1e-13;
-   double proj_max_gap = 0.5;
-   Vector gap_v(dim);
-   // warm start from linear solution
-
-   for (int it=0; it<max_iter; it++)
-   {
-      //cout<<it<<endl;
-      Vector m_N(4);
-      m_N = 0.;
-      DenseMatrix m_dN(2,4);
-      m_dN = 0.;
-      DenseMatrix m_dN2(3,4);
-      m_dN2 = 0.;
-      BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-      Vector x_c(dim);
-      m_coords.MultTranspose(m_N, x_c);
-
-      gap_v = s_x;
-      gap_v -= x_c;
-
-      DenseMatrix m_dx(2,3);
-      m_dx = 0.;
-      Mult(m_dN, m_coords, m_dx);
-
-      Vector r(dim-1);
-      r = 0.0;
-      m_dx.Mult(gap_v, r);
-
-      if (r.Normlinf() < proj_newton_tol)
-      {
-         converged = true;
-         break;
-      }
-
-      DenseMatrix drdxi(dim-1,dim-1);
-      drdxi = 0.;
-      MultABt(m_dx, m_dx, drdxi); // m_dx * m_dx.T
-      drdxi *= -1.0;
-
-      DenseMatrix m_dx2(3,3); m_dx2 = 0.0;
-      Mult(m_dN2,m_coords, m_dx2);
-
-      //m_d2x = m_dN(:,:,2) * m_elem_coords(1:4,:);  //m_dN(:,:,2) is 3*4
-      for (int d=0; d<3; d++)
-      {
-         DenseMatrix Mtemp(2,2); Mtemp = 0.0;
-         Mtemp(0,0) = m_dx2(0,d); Mtemp(0,1) = m_dx2(1,d);
-         Mtemp(1,0) = m_dx2(1,d); Mtemp(1,1) = m_dx2(2,d);
-
-         drdxi.Add(gap_v[d], Mtemp);
-      }
-
-      //cond_num = rcond(drdxi);  condition number?
-      //drdxi.TestInversion();
-      DenseMatrixInverse drdxi_inv(drdxi);
-      Vector xi_tmp(dim-1);
-
-      drdxi_inv.Mult(r,xi_tmp);
-      xi -= xi_tmp;
-   }
-   if (!converged)
-   {
-      xi = 0.0;
-   }
-   off_el_xi += 1 ; // tolerance of offset of xi outside [-1,1]
-
-   //cout<<gap_v.Norml2()<<" " <<xi.Normlinf()<<endl;
-   if (gap_v.Norml2() < proj_max_gap && xi.Normlinf() <= off_el_xi)
-   {
-      pt_on_elem = true;
-   }
-
-   MFEM_VERIFY(pt_on_elem == true, "xi went out of bounds");
-   MFEM_VERIFY(converged == true, "projection didn't converge");
-}
-
-
-
-// m_coords is expected to be 4 * 3
-void  ComputeGapJacobian(const Vector x_s, const Vector xi,
-                         const DenseMatrix m_coords,
-                         double& gap, Vector& normal, Vector& dgdxm, Vector& dgdxs)
-{
-   Vector m_N(4);
-   DenseMatrix m_dN(2,4);
-   DenseMatrix m_dN2(3,4);
-   BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-   Vector x_c(3);
-   m_coords.MultTranspose(m_N, x_c);
-
-   Vector gap_v(3); gap_v = 0.0;
-   gap_v  = x_s;
-   gap_v -= x_c;
-
-   DenseMatrix m_dx(2,3);
-   Mult(m_dN, m_coords, m_dx);
-
-   double nnorm = 0;
-   ComputeNormal(m_dN, m_coords, normal, nnorm);
-
-   gap = gap_v * normal; // gap function value, dot product between vectors
-
-   //dr_dx = zeros(2,4,3); % nsegment, nodes in quad, ndim
-
-   DenseMatrix dr_dx_res1(4,3); dr_dx_res1 = 0.;
-   DenseMatrix dr_dx_res2(4,3); dr_dx_res2 = 0.;
-
-   Vector m_dxrow1(3);
-   m_dx.GetRow(0, m_dxrow1);
-   outer(m_N, m_dxrow1, dr_dx_res1);// 4*1 times 1*3
-   dr_dx_res1 *= -1.0;
-
-   Vector m_dxrow2(3);
-   m_dx.GetRow(1, m_dxrow2);
-   outer(m_N, m_dxrow2, dr_dx_res2);// 4*1 times 1*3
-   dr_dx_res2 *= -1.0;
-
-   Vector m_dNrow1(4); m_dN.GetRow(0, m_dNrow1);
-   Vector m_dNrow2(4); m_dN.GetRow(1, m_dNrow2);
-
-   DenseMatrix dr_dx_res1_tmp(4,3); dr_dx_res1_tmp = 0.;
-   DenseMatrix dr_dx_res2_tmp(4,3); dr_dx_res2_tmp = 0.;
-   outer(m_dNrow1, gap_v, dr_dx_res1_tmp);// 4*1 times 1*3
-   outer(m_dNrow2, gap_v, dr_dx_res2_tmp);// 4*1 times 1*3
-
-   dr_dx_res1 += dr_dx_res1_tmp; // outer product in vector?
-   dr_dx_res2 += dr_dx_res2_tmp;
-
-
-   DenseMatrix K_dxidx1(2,2); // 2*2
-   K_dxidx1 = 0.;
-   MultABt(m_dx, m_dx, K_dxidx1); // m_dx * m_dx.T
-
-   Vector v_dxidx2(4);
-   m_coords.Mult(gap_v, v_dxidx2); // m_coords * gap_v;  // 4*3 * 3 = 4
-
-   DenseMatrix K_dxidx2(2,2); K_dxidx2 = 0.0;
-
-   Vector m_dN2row1(4); m_dN2.GetRow(0, m_dN2row1);
-   Vector m_dN2row2(4); m_dN2.GetRow(1, m_dN2row2);
-   Vector m_dN2row3(4); m_dN2.GetRow(2, m_dN2row3);
-   // how to get 2nd order? multidimensional matrix?
-   K_dxidx2(0,0) = m_dN2row1 * v_dxidx2; // how would 4*1 * 1*4 be computed?
-   K_dxidx2(0,1) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,0) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,1) = m_dN2row3 * v_dxidx2;
-
-   DenseMatrix K_dxidx(2,2);
-   K_dxidx -= K_dxidx1;
-   K_dxidx += K_dxidx2;
-
-   // resize the vectors and matrices
-   Vector dxidx(24); dxidx = 0.0;
-   Vector drdx_r(24); drdx_r = 0.0;
-
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         drdx_r[4*j+i] = dr_dx_res1(i,j);
-         drdx_r[4*j+i+12] = dr_dx_res2(i,j);
-
-      }
-   }
-   //drdx_r(1:4*3,1) = reshape(dr_dx_res(:,:,1),4*3,1);
-   //drdx_r(4*3+1:2*4*3,1) = reshape(dr_dx_res(:,:,2),4*3,1);
-   DenseMatrix drdx_K(24,24); drdx_K = 0.;
-   for (int i =0; i<12; i++)
-   {
-      drdx_K(i,i) = K_dxidx(0,0);
-      drdx_K(i,12+i) = K_dxidx(0,1);
-      drdx_K(12+i,i) = K_dxidx(1,0);
-      drdx_K(12+i,12+i) = K_dxidx(1,1);
-   }
-
-   DenseMatrixInverse drdxK_inv(drdx_K);
-   drdxK_inv.Mult(drdx_r,dxidx);
-   // LinearSolve (drdx_K,drdx_r, dxidx) ; //???
-   dxidx *= -1.0;
-
-
-
-   Vector drdxs_r(6);
-   drdxs_r[0] = m_dx(0,0); drdxs_r[1] = m_dx(0,1); drdxs_r[2] = m_dx(0,2);
-   drdxs_r[3] = m_dx(1,0); drdxs_r[4] = m_dx(1,1); drdxs_r[5] = m_dx(1,2);
-
-   DenseMatrix drdxs_K(6,6); drdxs_K = 0.;
-   for (int i=0; i<3; i++)
-   {
-      drdxs_K(i,i) = K_dxidx(0,0);
-      drdxs_K(i,3+i) = K_dxidx(0,1);
-      drdxs_K(i+3,i) = K_dxidx(1,0);
-      drdxs_K(i+3,i+3) = K_dxidx(1,1);
-   }
-
-   Vector dxidxs(6); dxidxs = 0.0;
-   DenseMatrixInverse drdxsK_inv(drdxs_K);
-   drdxsK_inv.Mult(drdxs_r,dxidxs);
-   dxidxs *= -1.0;
-   //dxidxs = -drdxs_K\drdxs_r;
-
-   //dxidx = reshape(dxidx, 4,3,2); dxidxs = reshape(dxidxs, 1,3,2);
-
-   dgdxm.SetSize(12); dgdxm = 0.;
-   DenseMatrix dgdxm_tmp(4,3);
-   outer(m_N, normal,dgdxm_tmp);
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         dgdxm[3*i+j] = -dgdxm_tmp(i,j);
-      }
-   }
-   //dxidx_M = -m_dN(1:2,:,1) * (m_coords(1:4,:)*normal'); % this turns out to be 0
-
-   dgdxs.SetSize(3);
-   dgdxs += normal;
-   //dgdxs = dgdxs + dxidx_M(1) * dxidxs(:,:,1) + dxidx_M(2) * dxidxs(:,:,2);
-};
-
-void ComputeGapHessian(const Vector x_s, const Vector xi,
-                       const DenseMatrix m_coords,
-                       DenseMatrix& dg2dx)
-{
-   Vector m_N(4);
-   DenseMatrix m_dN(2,4);
-   DenseMatrix m_dN2(3,4);
-   BasisEvalDerivs(xi, m_N, m_dN, m_dN2);
-
-   int dim = 3;
-   int num_dofs1 = dim;
-   int num_dofs2 = 4*dim;
-   int num_dofs = num_dofs1 + num_dofs2;
-   dg2dx.SetSize(num_dofs,num_dofs); dg2dx = 0.0;
-
-   Vector x_c(3);
-   m_coords.MultTranspose(m_N,x_c);
-
-   Vector gap_v(3); gap_v = 0.0;
-   gap_v  = x_s;
-   gap_v -= x_c;
-
-   DenseMatrix m_dx(2,3);
-   Mult(m_dN, m_coords, m_dx);
-
-   DenseMatrix m_dx2(3,3); m_dx2 = 0.0;
-   Mult(m_dN2,m_coords, m_dx2);
-   double nnorm = 0.0;
-   Vector normal(3); normal = 0.0;
-   ComputeNormal(m_dN, m_coords, normal, nnorm);
-
-   double gap = gap_v * normal; // gap function value, dot product between vectors
-
-   DenseMatrix M(2,2); M = 0.0;
-   MultABt(m_dx, m_dx, M);
-
-   DenseMatrix f(2, num_dofs2); f = 0.0;
-
-   for (int d=0; d<3; d++)
-   {
-      DenseMatrix Mtemp(2,2); Mtemp = 0.0;
-      Mtemp(0,0) = m_dx2(0,d); Mtemp(0,1) = m_dx2(1,d);
-      Mtemp(1,0) = m_dx2(1,d); Mtemp(1,1) = m_dx2(2,d);
-
-      M.Add(-gap_v[d], Mtemp);
-
-      Vector m_dxcol(2); m_dx.GetColumn(d, m_dxcol);
-      DenseMatrix ftmp(2,4);
-      outer(m_dxcol, m_N, ftmp);
-      ftmp *= -1;
-      ftmp.Add( gap_v[d], m_dN);   // 2*4
-
-      for (int j=0; j<4; j++)
-      {
-         assert(d+3*j<num_dofs2);
-         f(0,d+j*3) = ftmp(0,j);
-         f(1,d+j*3) = ftmp(1,j);
-      }
-   }
-   //fprintf('hess dxidxm\n');
-   DenseMatrixInverse Minv(M);
-   DenseMatrix dxidxm(2,num_dofs2); dxidxm = 0.0;
-   Minv.Mult(f, dxidxm);
-   //LinearSolve??
-   //dxidxm = M\f;
-
-   DenseMatrix nde2(2,2); nde2 = 0.0;
-   DenseMatrix Nndx2(2,num_dofs2); Nndx2 = 0.0;
-
-   for (int d=0; d<3; d++)
-   {
-      DenseMatrix ndetmp(2,2); ndetmp = 0.0;
-      ndetmp(0,0) = normal(d)*m_dx2(0,d); ndetmp(0,1) = normal(d)*m_dx2(1,d);
-      ndetmp(1,0) = normal(d)*m_dx2(1,d); ndetmp(1,1) = normal(d)*m_dx2(2,d);
-
-      nde2 += ndetmp;
-
-      for (int j=0; j<4; j++)
-      {
-         assert(d+3*j<num_dofs2);
-         Nndx2(0,d+j*3) = normal[d]*m_dN(0,j);
-         Nndx2(1,d+j*3) = normal[d]*m_dN(1,j);
-      }
-
-   }
-
-   DenseMatrix Ndn(2,num_dofs2); Ndn = 0.0;
-   Ndn += Nndx2;
-   AddMult(nde2, dxidxm, Ndn);
-
-
-   DenseMatrix M2(2,2); M2 = 0.0;
-   MultABt(m_dx, m_dx, M2);
-   DenseMatrixInverse M2inv(M2);
-   DenseMatrix diag2(2,2); diag2(0,0) = 1.0; diag2(1,1) = 1.0;
-   DenseMatrix m_con(2,2); m_con = 0.0;
-
-   M2inv.Mult(diag2, m_con);
-
-   DenseMatrix dg2dxm(num_dofs2, num_dofs2); dg2dxm = 0.0;
-
-   DenseMatrix dg2dxm_tmp(num_dofs2,2); dg2dxm_tmp = 0.0;
-   MultAtB(Ndn, m_con, dg2dxm_tmp);
-   Mult(dg2dxm_tmp, Ndn, dg2dxm);
-   dg2dxm *= gap;
-
-   DenseMatrix dg2dxm_tmp2(num_dofs2,num_dofs2); dg2dxm_tmp2 = 0.0;
-   MultAtB(Nndx2, dxidxm, dg2dxm_tmp2);
-   dg2dxm.Add(-1.0, dg2dxm_tmp2);
-
-   dg2dxm_tmp = 0.0;
-   MultAtB(dxidxm, nde2, dg2dxm_tmp);
-
-   AddMult_a(-1.0, dg2dxm_tmp, dxidxm, dg2dxm);
-
-   dg2dxm_tmp2 = 0.0;
-   MultAtB(dxidxm, Nndx2, dg2dxm_tmp2);
-   dg2dxm.Add(-1.0, dg2dxm_tmp2);
-
-   Vector v_dxidx2(4);
-   m_coords.Mult(gap_v, v_dxidx2); // m_coords * gap_v;  // 4*3 * 3 = 4
-
-   DenseMatrix K_dxidx2(2,2); K_dxidx2 = 0.0;
-
-   Vector m_dN2row1(4); m_dN2.GetRow(0, m_dN2row1);
-   Vector m_dN2row2(4); m_dN2.GetRow(1, m_dN2row2);
-   Vector m_dN2row3(4); m_dN2.GetRow(2, m_dN2row3);
-   K_dxidx2(0,0) = m_dN2row1 * v_dxidx2; // how would 4*1 * 1*4 be computed?
-   K_dxidx2(0,1) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,0) = m_dN2row2 * v_dxidx2;
-   K_dxidx2(1,1) = m_dN2row3 * v_dxidx2;
-
-   DenseMatrix K_dxidx(2,2);
-   K_dxidx -= M2;
-   K_dxidx += K_dxidx2;
-
-   Vector drdxs_r(6);
-   drdxs_r[0] = m_dx(0,0); drdxs_r[1] = m_dx(0,1); drdxs_r[2] = m_dx(0,2);
-   drdxs_r[3] = m_dx(1,0); drdxs_r[4] = m_dx(1,1); drdxs_r[5] = m_dx(1,2);
-
-   DenseMatrix drdxs_K(6,6); drdxs_K = 0.;
-   for (int i=0; i<3; i++)
-   {
-      drdxs_K(i,i) = K_dxidx(0,0);
-      drdxs_K(i,3+i) = K_dxidx(0,1);
-      drdxs_K(i+3,i) = K_dxidx(1,0);
-      drdxs_K(i+3,i+3) = K_dxidx(1,1);
-   }
-   Vector dxidxs(6);
-
-   DenseMatrixInverse drdxsK_inv(drdxs_K);
-   drdxsK_inv.Mult(drdxs_r,dxidxs);
-   dxidxs *= -1.0;
-   //dxidxs = -drdxs_K\drdxs_r;
-
-   DenseMatrix dxidxs_m(2,3); dxidxs_m = 0.0;
-   dxidxs_m(0,0) = dxidxs[0]; dxidxs_m(0,1) = dxidxs[1]; dxidxs_m(0,2) = dxidxs[2];
-   dxidxs_m(1,0) = dxidxs[3]; dxidxs_m(1,1) = dxidxs[4]; dxidxs_m(1,2) = dxidxs[5];
-
-   DenseMatrix dtao1dxs(3,3); dtao1dxs = 0.0;
-   DenseMatrix dtao2dxs(3,3); dtao2dxs = 0.0;
-
-   Vector dxidxs_row1(3); dxidxs_row1 = 0.0; Vector dxidxs_row2(3);
-   dxidxs_row2 = 0.0;
-   Vector mdx2_row1(3); mdx2_row1 = 0.0; Vector mdx2_row2(3); mdx2_row2 = 0.0;
-   Vector mdx2_row3(3); mdx2_row3 = 0.0;
-   dxidxs_m.GetRow(0,dxidxs_row1);
-   dxidxs_m.GetRow(1,dxidxs_row2);
-   m_dx2.GetRow(0,mdx2_row1);
-   m_dx2.GetRow(1,mdx2_row2);
-   m_dx2.GetRow(2,mdx2_row3);
-
-   DenseMatrix dtaotmp(3,3); dtaotmp = 0.0;
-   outer(mdx2_row1, dxidxs_row1,dtaotmp);
-   dtao1dxs += dtaotmp; dtaotmp = 0.0;
-   outer(mdx2_row2, dxidxs_row1,dtaotmp);
-   dtao1dxs += dtaotmp; dtaotmp = 0.0;
-
-   outer(mdx2_row2, dxidxs_row2, dtaotmp);
-   dtao2dxs += dtaotmp; dtaotmp = 0.0;
-   outer(mdx2_row3, dxidxs_row2, dtaotmp);
-   dtao2dxs += dtaotmp; dtaotmp = 0.0;
-
-   DenseMatrix dtaodxs(3,3); dtaodxs = 0.0; //tao = tao1 cross tao2
-
-   for (int d=0; d<3; d++)
-   {
-      Vector dtao1dxs_tmp(3); dtao1dxs_tmp = 0.0;
-      dtao1dxs.GetColumn(d,dtao1dxs_tmp);
-      Vector m_dxrow(3); m_dx.GetRow(1, m_dxrow);
-
-      Vector dtaodxs_tmp(3); dtaodxs_tmp = 0.0;
-      cross(dtao1dxs_tmp, m_dxrow, dtaodxs_tmp);
-
-      Vector dtaodxs_tmp2(3); dtaodxs_tmp2 = 0.0;
-      m_dx.GetRow(0, m_dxrow);
-      dtao1dxs_tmp = 0.0;  // reuse the same vector for dtao2
-      dtao2dxs.GetColumn(d,dtao1dxs_tmp);
-      cross(m_dxrow, dtao1dxs_tmp, dtaodxs_tmp2);
-
-      dtaodxs_tmp2 += dtaodxs_tmp;
-      dtaodxs.SetCol(d, dtaodxs_tmp2);
-   }
-
-   DenseMatrix dndxs(3,3); dndxs = 0.0; dndxs += dtaodxs; dndxs *= 1.0/nnorm;
-   DenseMatrix dndxs_tmp(3,3); dndxs_tmp = 0.0;
-   outer(normal, normal, dndxs_tmp);
-   AddMult_a(-1/nnorm, dndxs_tmp, dtaodxs, dndxs);
-
-   DenseMatrix dgvdxs(3,3); dgvdxs = 0.0;
-   MultAtB(m_dx, dxidxs_m, dgvdxs);
-   dgvdxs *= -1;
-   for (int d=0; d<3; d++)
-   {
-      dgvdxs(d,d) += 1.0;
-   }
-   //dxidxs: 2*3
-
-   DenseMatrix dg2dxs(3,3); dg2dxs = 0.0;
-   DenseMatrix dg2dxs_tmp(3,2); dg2dxs_tmp = 0.0;
-   MultAtB(dxidxs_m, nde2, dg2dxs_tmp);
-   AddMult_a(-1.0, dg2dxs_tmp, dxidxs_m, dg2dxs);
-   DenseMatrix dg2dxs_tmp2(3,3); dg2dxs_tmp2 = 0.0;
-   MultAtB(dgvdxs, dndxs, dg2dxs_tmp2);
-   dg2dxs += dg2dxs_tmp2;
-   dg2dxs_tmp2 = 0.0;
-   MultAtB(dndxs, dndxs_tmp, dg2dxs_tmp2);
-   AddMult(dg2dxs_tmp2, dgvdxs, dg2dxs);
-
-   DenseMatrix Ne(3,12), Be(6,12), dBe(12,12);
-   BasisVectorDerivs(xi, Ne, Be, dBe);
-
-   DenseMatrix dtao1dxm(3,12); dtao1dxm.CopyRows(Be, 0, 2);
-   DenseMatrix dtao2dxm(3,12); dtao2dxm.CopyRows(Be, 3, 5);
-
-   Vector m_coords_v(12);
-   for (int i=0; i<4; i++)
-   {
-      for (int j=0; j<3; j++)
-      {
-         m_coords_v[i*3+j] = m_coords(i,j);
-      }
-   }
-
-   for (int i=0; i<2; i++)
-   {
-      Vector dxidxm_tmp(num_dofs2); dxidxm_tmp = 0.0;
-      dxidxm.GetRow(i,dxidxm_tmp);
-
-      DenseMatrix dBe_tmp(3,12);
-      dBe_tmp.CopyRows(dBe,i*3,(i+1)*3-1);
-
-      DenseMatrix dtaodxm_tmp(12,12); dtaodxm_tmp = 0.0;
-      outer(m_coords_v, dxidxm_tmp, dtaodxm_tmp);
-      AddMult(dBe_tmp, dtaodxm_tmp, dtao1dxm);
-
-      //dtao1dxm += dBe(:,:,i)*reshape(m_coords(1:4,:)',12,1)*reshape(dxidxm(i,:),1,12); % 3*12
-      dBe_tmp = 0.0;
-      dBe_tmp.CopyRows(dBe,(i+2)*3,(i+3)*3-1);
-      AddMult(dBe_tmp, dtaodxm_tmp, dtao2dxm);
-
-   }
-
-   DenseMatrix dtaodxm(3,12); dtaodxm = 0.0;//tao = tao1 cross tao2
-
-   for (int d=0; d<12; d++)
-   {
-      Vector dtaodxm_tmp(3); dtaodxm_tmp = 0.0;
-      Vector dtaodxm_tmp2(3); dtaodxm_tmp2 = 0.0;
-      Vector tmp1(3); tmp1 = 0.0;  dtao1dxm.GetColumn(d,tmp1);
-      Vector m_dxrow2(3); m_dx.GetRow(1, m_dxrow2);
-      Vector m_dxrow1(3); m_dx.GetRow(0, m_dxrow1);
-      Vector tmp2(3); tmp2 = 0.0;  dtao2dxm.GetColumn(d,tmp2);
-
-      cross(tmp1, m_dxrow2, dtaodxm_tmp);
-      cross(m_dxrow1,tmp2, dtaodxm_tmp2);
-      dtaodxm_tmp += dtaodxm_tmp2;
-
-      dtaodxm.SetCol(d, dtaodxm_tmp);
-   }
-
-   DenseMatrix dndxm(3,12); dndxm = 0.0;
-   dndxm += dtaodxm;
-   dndxm *= 1.0/nnorm;
-   AddMult_a(-1/nnorm, dndxs_tmp, dtaodxm, dndxm); //dndxs_tmp = normal'*normal
-
-   DenseMatrix dgvdxm(3,12); dgvdxm = 0.0;
-   dgvdxm -= Ne;
-
-   for (int i=0; i<2; i++)
-   {
-      Vector dxidxm_tmp(num_dofs2); dxidxm_tmp = 0.0;
-      dxidxm.GetRow(i,dxidxm_tmp);
-
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-
-      DenseMatrix dgvdxm_tmp(12,12); dgvdxm_tmp = 0.0;
-      outer(m_coords_v, dxidxm_tmp, dgvdxm_tmp);
-      AddMult_a(-1.0, Be_tmp, dgvdxm_tmp, dgvdxm);
-
-   }
-
-   DenseMatrix dg2dxsxm(3,12); dg2dxsxm = 0.0;
-   DenseMatrix dg2dxsxm_tmp(3,3); dg2dxsxm_tmp = 0.0;
-   MultAtB(dgvdxs, dndxm, dg2dxsxm);
-
-   MultAtB(dndxs, dndxs_tmp, dg2dxsxm_tmp);
-   AddMult(dg2dxsxm_tmp, dgvdxm, dg2dxsxm); // += dndxs'*normal'*normal*dgvdxm;
-
-   DenseMatrix dgvdxsxmn(3,12); dgvdxsxmn = 0.0;
-   DenseMatrix dgvdxsxmn_tmp(3,2); dgvdxsxmn_tmp = 0.0;
-   MultAtB(dxidxs_m, nde2, dgvdxsxmn_tmp);   //dxidxs_m: 2*3
-
-   AddMult_a(-1.0, dgvdxsxmn_tmp, dxidxm, dgvdxsxmn);
-
-
-   for (int i =0; i<2; i++)
-   {
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-
-      Vector dxidxs_row(3); dxidxs_row = 0.0; dxidxs_m.GetRow(i,dxidxs_row);
-      DenseMatrix dgvdxsxmn_tmp2(3,3); dgvdxsxmn_tmp2 = 0.0;
-      outer(dxidxs_row, normal, dgvdxsxmn_tmp2);
-      AddMult_a(-1.0, dgvdxsxmn_tmp2, Be_tmp, dgvdxsxmn);
-   }
-
-   dg2dxsxm += dgvdxsxmn;
-
-   DenseMatrix dg2dxmxs(12,3); dg2dxmxs = 0.0;
-   DenseMatrix dg2dxmxs_tmp(12,3); dg2dxmxs_tmp = 0.0;
-   MultAtB(dgvdxm, dndxs, dg2dxmxs);
-   MultAtB(dndxm, dndxs_tmp, dg2dxmxs_tmp);
-   AddMult(dg2dxmxs_tmp, dgvdxs, dg2dxmxs);
-
-   DenseMatrix dgvdxmxsn(12,3); dgvdxmxsn = 0.0;
-   DenseMatrix dgvdxmxsn_tmp(12,2); dgvdxmxsn_tmp = 0.0;
-
-   MultAtB(dxidxm, nde2, dgvdxmxsn_tmp);
-   dgvdxmxsn_tmp *= -1.0;
-   AddMult(dgvdxmxsn_tmp, dxidxs_m, dgvdxmxsn);
-
-   for (int i =0; i<2; i++)
-   {
-      DenseMatrix Be_tmp(3,12);
-      Be_tmp.CopyRows(Be,i*3,(i+1)*3-1);
-      Be_tmp.Transpose(); // Be is now 12*3
-
-      Vector dxidxs_row(3); dxidxs_row = 0.0; dxidxs_m.GetRow(i,dxidxs_row);
-      DenseMatrix dgvdxmxsn_tmp2(3,3); dgvdxmxsn_tmp2 = 0.0;
-      outer(normal, dxidxs_row, dgvdxmxsn_tmp2);
-      AddMult_a(-1.0, Be_tmp, dgvdxmxsn_tmp2, dgvdxmxsn);
-
-   }
-
-   dg2dxmxs += dgvdxmxsn;
-
-   dg2dx.CopyMN(dg2dxs, 0, 0);
-   dg2dx.CopyMN(dg2dxm, 3, 3);
-   dg2dx.CopyMN(dg2dxsxm, 0, 3);
-   dg2dx.CopyMN(dg2dxmxs, 3, 0);
-
-};
-
-
-
-void NodeSegConPairs(const Vector x1, const Vector xi2,
-                     const DenseMatrix coords2,
-                     double& node_g, Vector& node_dg, DenseMatrix& node_dg2)
-{
-   double gap = 0.0;
-   Vector normal(3); normal = 0.0;
-   Vector dgdxm(12); dgdxm = 0.0;
-   Vector dgdxs(3); dgdxs = 0.0;
-
-   ComputeGapJacobian(x1, xi2, coords2, gap, normal, dgdxm, dgdxs);
-   node_g = gap;
-
-   node_dg.SetSize(12+3);
-   for (int i=0; i<3; i++) { node_dg[i] = dgdxs[i]; }
-   for (int i=0; i<12; i++) { node_dg[i+3] = dgdxm[i]; }
-
-   DenseMatrix dg2dx(15,15); dg2dx = 0.0;
-   DenseMatrix dgvdxmxsn(12,3); dgvdxmxsn = 0.0;
-   ComputeGapHessian(x1, xi2, coords2, dg2dx);
-
-   node_dg2.SetSize(15,15);
-   node_dg2 = dg2dx;
-
-   /*
-   if(obj.space1.conns{e1}(i)==150)  % for debugging purpose
-
-   v1 = 1:3;
-   v2 = 1:12;
-   %v1 = ones(1,3)
-   %v2 = ones(1,12)
-   v2 = reshape(v2,4,3);
-   x1n1 = x1 + 0.01*v1;
-   coords2n1 = coords2 + 0.001*v2;
-      [xi2n1, gapv1, ~, ~] = SlaveToMaster(obj, coords2n1, x1n1);
-      [gapn1, n1,dgdxmn1, dgdxsn1] = ComputeGapJacobian(obj, x1n1, xi2n1, coords2n1);
-   x1n2 = x1 - 0.01*v1;
-   coords2n2 = coords2 - 0.001*v2;
-      [xi2n2, gapv2, ~, ~] = SlaveToMaster(obj, coords2n2, x1n2);
-      [gapn2, n2,dgdxmn2, dgdxsn2] = ComputeGapJacobian(obj, x1n2, xi2n2, coords2n2);
-   fprintf('fd\n');
-      %gapv1-gapv2
-   [dgdxsn1(:)',dgdxmn1(:)'] - [dgdxsn2(:)',dgdxmn2(:)']
-
-   %dgdxsn1-dgdxsn2
-   fprintf('code\n');
-   v2n = v2';
-   %dg2dx(1:3,1:3)*0.04*ones(3,1)
-   temp = zeros(12,3);
-   for i = 1:4
-   temp1 = dg2dx(3+(i-1)*3+1:3+i*3,1:3);
-   temp((i-1)*3+1:i*3,:) = temp1';
-   end
-   temp2 = zeros(3,12);
-   for i = 1:4
-   temp3 = dg2dx(1:3,3+(i-1)*3+1:3+i*3);
-   temp2(:,(i-1)*3+1:i*3) = temp3';
-   end
-   %dg2dx
-   %dg2dx(4:end,1:3) = temp;
-   %dg2dx(1:3,4:end) = temp2;
-   %dgvdxm * 0.002*v2n(:)
-   (dg2dx*[0.02*v1(:)',0.002*v2n(:)']')'
-   %dg2dx(4:end,1:3)
-   end*/
-
-};
-
-
-// coordsm : (npoints*4, 3) use what class?
-// m_conn: (npoints*4)
-void Assemble_Contact(const int m, const int npoints, const int ndofs,
-                      const Vector x_s,
-                      const Vector xi, const DenseMatrix coordsm, const Array<int> s_conn,
-                      const Array<int> m_conn, Vector& g, SparseMatrix& M,
-                      std::vector<SparseMatrix>& dM)
-{
-   int n = ndofs;
-   int ndim = 3;
-
-   g.SetSize(m);
-   g = 0.0;
-
-   //SparseMatrix M(m, n);  // M needs to be the correct size
-
-   //dM.resize(m); // needs to clear?
-
-   double g_tmp = 0.;
-   Vector dg(4*ndim+ndim);
-   dg = 0.;
-   DenseMatrix dg2(4*ndim+ndim,4*ndim+ndim);
-   dg2 = 0.;
-
-   for (int i=0; i<npoints; i++)
-   {
-      Vector x1(ndim);
-      x1[0] = x_s[i*ndim];
-      x1[1] = x_s[i*ndim+1];
-      x1[2] = x_s[i*ndim+2];
-
-      Vector xi2(ndim-1);
-      xi2[0] = xi[i*(ndim-1)];
-      xi2[1] = xi[i*(ndim-1)+1];
-
-      DenseMatrix coords2(4,3);
-      coords2.CopyRows(coordsm, i*4,(i+1)*4-1);
-
-      //how to get coords2?
-      dg = 0.0;
-      dg2 = 0.;
-      NodeSegConPairs(x1, xi2, coords2, g_tmp, dg, dg2);
-      //x1.Print();
-      //xi2.Print();
-      //coords2.Print();
-      g[s_conn[i]] = g_tmp; // should be unique
-      Array<int> m_conn_i(4);
-      m_conn.GetSubArray(4*i, 4, m_conn_i);
-
-      Array<int> node_conn(5);
-      node_conn[0] = s_conn[i];
-      for (int j=0; j<4; j++)
-      {
-         node_conn[j+1] = m_conn_i[j];
-      }
-
-      Array<int>  M_i_tmp(1);
-      M_i_tmp[0] = s_conn[i];
-
-      //j_idx = (node_conn-1)*obj.disp_field.num_components +repmat((1:obj.disp_field.num_components)', 1, length(node_conn{i}));
-      Array<int> j_idx(5*ndim); j_idx = 0;
-      for (int j=0; j< 5; j++)
-      {
-         for (int k=0; k<ndim; k++)
-         {
-            j_idx[j*ndim+k] = node_conn[j]*ndim+k;
-         }
-      }
-      DenseMatrix M_v_tmp(1, ndim*(4+1));   // SetData now?
-      M_v_tmp.SetRow(0, dg);
-
-      M.AddSubMatrix(M_i_tmp, j_idx, M_v_tmp);
-
-      Array<int> dM_i(ndim*(4+1));
-      Array<int> dM_j(ndim*(4+1));
-
-      for (int j=0; j< ndim*(4+1); j++)
-      {
-         dM_i[j] = j_idx[j];
-         dM_j[j] = j_idx[j];
-      }
-      //dg2.Print();
-      //dM[s_conn[i]].Print();
-      dM[s_conn[i]].AddSubMatrix(dM_i,dM_j, dg2);
-   }
-};
-
@@ -44,6 +44,7 @@ set(SRCS
  eltrans.cpp
  estimators.cpp
  fe.cpp
+  fe/face_map_utils.cpp
  fe/fe_base.cpp
  fe/fe_fixed_order.cpp
  fe/fe_h1.cpp
@@ -74,6 +75,7 @@ set(SRCS
  linearform_ext.cpp
  lininteg.cpp
  lininteg_boundary.cpp
+  lininteg_boundary_flux.cpp
  lininteg_domain.cpp
  lininteg_domain_grad.cpp
  lor/lor.cpp
@@ -151,6 +153,7 @@ set(HDRS
  eltrans.hpp
  estimators.hpp
  fe.hpp
+  fe/face_map_utils.hpp
  fe/fe_base.hpp
  fe/fe_fixed_order.hpp
  fe/fe_h1.hpp
@@ -529,7 +529,7 @@ void EABilinearFormExtension::Assemble()
   }

   faceDofs = trial_fes ->
-              GetTraceElement(0, trial_fes->GetMesh()->GetFaceGeometry(0)) ->
+              GetTraceElement(0, trial_fes->GetMesh()->GetFaceBaseGeometry(0)) ->
              GetDof();

   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
@@ -208,6 +208,10 @@ public:
                                            Vector &x, Vector &b,
                                            OperatorHandle &A, Vector &X, Vector &B) = 0;

+   virtual void AddMult(const Vector &x, Vector &y, const double c=1.0) const = 0;
+   virtual void AddMultTranspose(const Vector &x, Vector &y,
+                                 const double c=1.0) const = 0;
+
   virtual void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const = 0;

   virtual void Update() = 0;
@@ -283,7 +287,7 @@ public:
   /// Partial assembly of all internal integrators
   void Assemble();

-   void AddMult(const Vector &x, Vector &y, const double c=1.0) const;
+   void AddMult(const Vector &x, Vector &y, const double c) const;

   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;

@@ -145,7 +145,7 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
   // Assumes tensor-product elements
   Mesh *mesh = fes.GetMesh();
   const FiniteElement &el =
-      *fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0));
+      *fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0));
   FaceElementTransformations &T0 =
      *fes.GetMesh()->GetFaceElementTransformations(0);
   const IntegrationRule *ir = IntRule?
@@ -56,7 +56,8 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dim = mesh->Dimension();
   ne = fes.GetMesh()->GetNE();
   nq = ir->GetNPoints();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::DETERMINANTS, mt);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
+                                    GeometricFactors::JACOBIANS, mt);
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
@@ -73,7 +74,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
      const bool const_c = coeff.Size() == 1;
      const bool by_val = map_type == FiniteElement::VALUE;
      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
-      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,NE);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
                     Reshape(coeff.Read(), Q1D,Q1D,NE);
      auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
@@ -83,7 +84,11 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
         {
            MFEM_FOREACH_THREAD(qy,y,Q1D)
            {
-               const double detJ = J(qx,qy,e);
+               const double J11 = J(qx,qy,0,0,e);
+               const double J12 = J(qx,qy,1,0,e);
+               const double J21 = J(qx,qy,0,1,e);
+               const double J22 = J(qx,qy,1,1,e);
+               const double detJ = (J11*J22)-(J21*J12);
               const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
               v(qx,qy,e) =  W(qx,qy) * coeff * (by_val ? detJ : 1.0/detJ);
            }
@@ -97,7 +102,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
      const bool const_c = coeff.Size() == 1;
      const bool by_val = map_type == FiniteElement::VALUE;
      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
-      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,Q1D,NE);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
                     Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
      auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
@@ -109,7 +114,18 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
            {
               MFEM_FOREACH_THREAD(qz,z,Q1D)
               {
-                  const double detJ = J(qx,qy,qz,e);
+                  const double J11 = J(qx,qy,qz,0,0,e);
+                  const double J21 = J(qx,qy,qz,1,0,e);
+                  const double J31 = J(qx,qy,qz,2,0,e);
+                  const double J12 = J(qx,qy,qz,0,1,e);
+                  const double J22 = J(qx,qy,qz,1,1,e);
+                  const double J32 = J(qx,qy,qz,2,1,e);
+                  const double J13 = J(qx,qy,qz,0,2,e);
+                  const double J23 = J(qx,qy,qz,1,2,e);
+                  const double J33 = J(qx,qy,qz,2,2,e);
+                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
+                  /* */               J21 * (J12 * J33 - J32 * J13) +
+                  /* */               J31 * (J12 * J23 - J22 * J13);
                  const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * (by_val ? detJ : 1.0/detJ);
               }
@@ -75,7 +75,7 @@ void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
      Vector ea_data_ext_tmp(ea_data_ext.Size());
      bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
      auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
      auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
      auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
@@ -102,7 +102,7 @@ void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
   {
      bfi->AssembleEAInteriorFaces(fes, ea_data_int, ea_data_ext, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
      auto A_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
      auto A_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
      MFEM_FORALL(f, nf,
@@ -146,7 +146,7 @@ void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
      Vector ea_data_bdr_tmp(ea_data_bdr.Size());
      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
      auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
      auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
      MFEM_FORALL(f, nf,
@@ -165,7 +165,7 @@ void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
   {
      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
      auto A_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
      MFEM_FORALL(f, nf,
      {
@@ -69,11 +69,9 @@ void Operator::Mult(const mfem::Vector &x, mfem::Vector &y) const
 #endif
 }

-void Operator::AddMult(const mfem::Vector &x, mfem::Vector &y,
-                       const double a) const
+void Operator::AddMult(const mfem::Vector &x, mfem::Vector &y) const
 {
 #ifdef MFEM_USE_CEED
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   const CeedScalar *x_ptr;
   CeedScalar *y_ptr;
   CeedMemType mem;
@@ -38,8 +38,7 @@ public:
   Operator(CeedOperator op);
 #endif
   void Mult(const mfem::Vector &x, mfem::Vector &y) const override;
-   void AddMult(const mfem::Vector &x, mfem::Vector &y,
-                const double a = 1.0) const override;
+   void AddMult(const mfem::Vector &x, mfem::Vector &y) const;
   void GetDiagonal(mfem::Vector &diag) const;
   using mfem::Operator::SetupRAP;
   virtual ~Operator()
@@ -1319,6 +1319,7 @@ public:
   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip) = 0;

+   using MatrixCoefficient::Eval;
   /** @brief Evaluate the matrix coefficient in the element described by @a T
       at the point @a ip, storing the result as a dense matrix @a K. */
   /** This function allows the use of SymmetricMatrixCoefficient in situations
@@ -1347,6 +1348,7 @@ public:
   ///Construct using matrix @a m for the constant.
   SymmetricMatrixConstantCoefficient(const DenseSymmetricMatrix &m)
      : SymmetricMatrixCoefficient(m.Height()), mat(m) { }
+   using MatrixCoefficient::Eval;
   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
@@ -1398,6 +1400,7 @@ public:
   /// Set the time for internally stored coefficients
   void SetTime(double t);

+   using MatrixCoefficient::Eval;
   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
@@ -110,8 +110,8 @@ DataCollection::DataCollection(const std::string& collection_name, Mesh *mesh_)
   precision = precision_default;
   pad_digits_cycle = pad_digits_rank = pad_digits_default;
   format = SERIAL_FORMAT; // use serial mesh format
-   compression = 0;
-   error = No_Error;
+   compression = false;
+   error = NO_ERROR;
 }

 void DataCollection::SetMesh(Mesh *new_mesh)
@@ -494,7 +494,7 @@ void VisItDataCollection::Load(int cycle_)
 {
   DeleteAll();
   time_step = 0.0;
-   error = No_Error;
+   error = NO_ERROR;
   cycle = cycle_;
   std::string root_name = prefix_path + name + "_" +
                           to_padded_string(cycle, pad_digits_cycle) +
@@ -767,13 +767,10 @@ ParaViewDataCollection::ParaViewDataCollection(const std::string&
     high_order_output(false),
     restart_mode(false)
 {
-   cycle = 0; // always include a valid cycle index in file names
-
-   compression_level = -1;  // default zlib compression level, equivalent to 6
 #ifdef MFEM_USE_ZLIB
-   compression = true; // if we have zlib, enable compression
+   compression = -1; // default zlib compression level, equivalent to 6
 #else
-   compression = false; // otherwise, disable compression
+   compression = 0;
 #endif
 }

@@ -922,7 +919,7 @@ void ParaViewDataCollection::Save()
   {
      const std::string &field_name = qfield.first;
      std::ofstream os(vtu_prefix + GenerateVTUFileName(field_name, myid));
-      qfield.second->SaveVTU(os, pv_data_format, GetCompressionLevel());
+      qfield.second->SaveVTU(os, pv_data_format, compression);
   }

   // MPI rank 0 also creates a "PVTU" file that points to all of the separately
@@ -1036,13 +1033,13 @@ void ParaViewDataCollection::WritePVTUFooter(std::ostream &os,
 void ParaViewDataCollection::SaveDataVTU(std::ostream &os, int ref)
 {
   os << "<VTKFile type=\"UnstructuredGrid\"";
-   if (GetCompressionLevel() != 0)
+   if (compression != 0)
   {
      os << " compressor=\"vtkZLibDataCompressor\"";
   }
   os << " version=\"0.1\" byte_order=\"" << VTKByteOrder() << "\">\n";
   os << "<UnstructuredGrid>\n";
-   mesh->PrintVTU(os,ref,pv_data_format,high_order_output,GetCompressionLevel());
+   mesh->PrintVTU(os,ref,pv_data_format,high_order_output,compression);

   // dump out the grid functions as point data
   os << "<PointData >\n";
@@ -1106,7 +1103,7 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,

   if (IsBinaryFormat())
   {
-      WriteVTKEncodedCompressed(os,buf.data(),buf.size(),GetCompressionLevel());
+      WriteVTKEncodedCompressed(os,buf.data(),buf.size(),compression);
      os << '\n';
   }
   os << "</DataArray>" << std::endl;
@@ -1131,13 +1128,18 @@ void ParaViewDataCollection::SetCompressionLevel(int compression_level_)
 {
   MFEM_ASSERT(compression_level_ >= -1 && compression_level_ <= 9,
               "Compression level must be between -1 and 9 (inclusive).");
-   compression_level = compression_level_;
-   compression = compression_level_ != 0;
+   compression = compression_level_;
 }

 void ParaViewDataCollection::SetCompression(bool compression_)
 {
-   compression = compression_;
+   // If we are enabling compression, and it was disabled previously, use the
+   // default compression level. Otherwise, leave the compression level
+   // unchanged.
+   if (compression_ && compression == 0)
+   {
+      SetCompressionLevel(-1);
+   }
 }

 void ParaViewDataCollection::UseRestartMode(bool restart_mode_)
@@ -1169,9 +1171,4 @@ const char *ParaViewDataCollection::GetDataTypeString() const
   }
 }

-int ParaViewDataCollection::GetCompressionLevel() const
-{
-   return compression ? compression_level : 0;
-}
-
 }  // end namespace MFEM
@@ -378,24 +378,12 @@ public:
   virtual ~DataCollection();

   /// Errors returned by Error()
-   enum
-   {
-      // Workaround for use with headers that define NO_ERROR as a macro,
-      // e.g. winerror.h (which is included by Windows.h):
-#ifndef NO_ERROR
-      NO_ERROR = 0,
-#endif
-      // Use the following identifier if NO_ERROR is defined as a macro,
-      // e.g. winerror.h (which is included by Windows.h):
-      No_Error    = 0,
-      READ_ERROR  = 1,
-      WRITE_ERROR = 2
-   };
+   enum { NO_ERROR = 0, READ_ERROR = 1, WRITE_ERROR = 2 };

   /// Get the current error state
   int Error() const { return error; }
   /// Reset the error state
-   void ResetError(int err_state = No_Error) { error = err_state; }
+   void ResetError(int err_state = NO_ERROR) { error = err_state; }

 #ifdef MFEM_USE_MPI
   friend class ParMesh;
@@ -507,7 +495,6 @@ class ParaViewDataCollection : public DataCollection
 {
 private:
   int levels_of_detail;
-   int compression_level;
   std::fstream pvd_stream;
   VTKFormat pv_data_format;
   bool high_order_output;
@@ -520,9 +507,6 @@ protected:
   void SaveGFieldVTU(std::ostream& out, int ref_, const FieldMapIterator& it);
   const char *GetDataFormatString() const;
   const char *GetDataTypeString() const;
-   /// @brief If compression is enabled, return the compression level, otherwise
-   /// return 0.
-   int GetCompressionLevel() const;

   std::string GenerateCollectionPath();
   std::string GenerateVTUFileName(const std::string &prefix, int rank);
@@ -541,7 +525,7 @@ public:
                          mfem::Mesh *mesh_ = NULL);

   /// Set refinement levels - every element is uniformly split based on
-   /// levels_of_detail_. The initial value is 1.
+   /// levels_of_detail_
   void SetLevelsOfDetail(int levels_of_detail_);

   /// Save the collection - the directory name is constructed based on the
@@ -552,27 +536,18 @@ public:
   /// VTKFormat::ASCII, VTKFormat::BINARY, and VTKFormat::BINARY32.
   /// The ASCII and BINARY options output double precision data, whereas the
   /// BINARY32 option outputs single precision data.
-   ///
-   /// The initial format is VTKFormat::BINARY.
   void SetDataFormat(VTKFormat fmt);

-   /// @brief Set the zlib compression level.
-   ///
-   /// 0 indicates no compression, -1 indicates the default compression level.
-   /// Otherwise, specify a number between 1 and 9, 1 being the fastest, and 9
-   /// being the best compression. Compression only takes effect if the output
-   /// format is BINARY or BINARY32. MFEM must be compiled with MFEM_USE_ZLIB =
-   /// YES.
-   ///
-   /// The initial compression level is 0 if MFEM is compiled with MFEM_USE_ZLIB
-   /// turned off, and -1 otherwise.
-   ///
-   /// Any nonzero compression level will enable compression.
+   /// Set the zlib compression level. 0 indicates no compression, -1 indicates
+   /// the default compression level. Otherwise, specify a number between 1 and
+   /// 9, 1 being the fastest, and 9 being the best compression. Compression
+   /// only takes effect if the output format is BINARY or BINARY32. MFEM must
+   /// be compiled with MFEM_USE_ZLIB = YES.
   void SetCompressionLevel(int compression_level_);

   /// Enable or disable zlib compression. If the input is true, use the default
   /// zlib compression level (unless the compression level has previously been
-   /// set by calling SetCompressionLevel()).
+   /// set by calling SetCompressionLevel).
   void SetCompression(bool compression_) override;

   /// Returns true if the output format is BINARY or BINARY32, false if ASCII.
@@ -585,8 +560,6 @@ public:
   /// Enable or disable restart mode. If restart is enabled, new writes will
   /// preserve timestep metadata for any solutions prior to the currently
   /// defined time.
-   ///
-   /// Initially, restart mode is disabled.
   void UseRestartMode(bool restart_mode_);

   /// Load the collection - not implemented in the ParaView writer
@@ -0,0 +1,60 @@
+// Copyright (c) 2010-2022, 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.
+
+// Finite Element Base classes
+
+#include "face_map_utils.hpp"
+
+namespace mfem
+{
+
+std::pair<int,int> GetFaceNormal3D(const int face_id)
+{
+   switch (face_id)
+   {
+      case 0: return std::make_pair(2, 0); // z = 0
+      case 1: return std::make_pair(1, 0); // y = 0
+      case 2: return std::make_pair(0, 1); // x = 1
+      case 3: return std::make_pair(1, 1); // y = 1
+      case 4: return std::make_pair(0, 0); // x = 0
+      case 5: return std::make_pair(2, 1); // z = 1
+      default: MFEM_ABORT("Invalid face ID.")
+   }
+   return std::make_pair(-1, -1); // invalid
+}
+
+void FillFaceMap(const int n_face_dofs_per_component,
+                 const std::vector<int> offsets,
+                 const std::vector<int> &strides,
+                 const std::vector<int> &n_dofs_per_dim,
+                 Array<int> &face_map)
+{
+   const int n_components = offsets.size();
+   const int face_dim = strides.size() / n_components;
+   for (int comp = 0; comp < n_components; ++comp)
+   {
+      const int offset = offsets[comp];
+      for (int i = 0; i < n_face_dofs_per_component; ++i)
+      {
+         int idx = offset;
+         int j = i;
+         for (int d = 0; d < face_dim; ++d)
+         {
+            const int dof1d = n_dofs_per_dim[comp*(face_dim) + d];
+            idx += strides[comp*(face_dim) + d]*(j % dof1d);
+            j /= dof1d;
+         }
+         face_map[comp*n_face_dofs_per_component + i] = idx;
+      }
+   }
+}
+
+}
@@ -0,0 +1,49 @@
+// Copyright (c) 2010-2022, 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_FACE_MAP_UTILS_HPP
+#define MFEM_FACE_MAP_UTILS_HPP
+
+#include "../../general/array.hpp"
+#include <utility> // std::pair
+#include <vector>
+
+namespace mfem
+{
+
+/// Each face of a hexahedron is given by a level set x_i = l, where x_i is one
+/// of x, y, or z (corresponding to i = 0, i=1, i = 3), and l is either 0 or 1.
+/// Returns i and level.
+std::pair<int,int> GetFaceNormal3D(const int face_id);
+
+/// @brief Fills in the entries of the lexicographic face_map.
+///
+/// For use in FiniteElement::GetFaceMap.
+///
+/// n_face_dofs_per_component is the number of DOFs for each vector component
+/// on the face (there is only one vector component in all cases except for 3D
+/// Nedelec elements, where the face DOFs have two components to span the
+/// tangent space).
+///
+/// The DOFs for the i-th vector component begin at offsets[i] (i.e. the number
+/// of vector components is given by offsets.size()).
+///
+/// The DOFs for each vector component are arranged in a Cartesian grid defined
+/// by strides and n_dofs_per_dim.
+void FillFaceMap(const int n_face_dofs_per_component,
+                 const std::vector<int> offsets,
+                 const std::vector<int> &strides,
+                 const std::vector<int> &n_dofs_per_dim,
+                 Array<int> &face_map);
+
+} // namespace mfem
+
+#endif
@@ -12,6 +12,7 @@
 // Finite Element Base classes

 #include "fe_base.hpp"
+#include "face_map_utils.hpp"
 #include "../coefficient.hpp"

 namespace mfem
@@ -36,19 +37,19 @@ FiniteElement::FiniteElement(int D, Geometry::Type G,
 #endif
 }

-void FiniteElement::CalcVShape(
+void FiniteElement::CalcVShape (
   const IntegrationPoint &ip, DenseMatrix &shape) const
 {
   MFEM_ABORT("method is not implemented for this class");
 }

-void FiniteElement::CalcVShape(
+void FiniteElement::CalcVShape (
   ElementTransformation &Trans, DenseMatrix &shape) const
 {
   MFEM_ABORT("method is not implemented for this class");
 }

-void FiniteElement::CalcDivShape(
+void FiniteElement::CalcDivShape (
   const IntegrationPoint &ip, Vector &divshape) const
 {
   MFEM_ABORT("method is not implemented for this class");
@@ -97,14 +98,14 @@ void FiniteElement::GetFaceDofs(int face, int **dofs, int *ndofs) const
   MFEM_ABORT("method is not overloaded");
 }

-void FiniteElement::CalcHessian(const IntegrationPoint &ip,
-                                DenseMatrix &h) const
+void FiniteElement::CalcHessian (const IntegrationPoint &ip,
+                                 DenseMatrix &h) const
 {
   MFEM_ABORT("method is not overloaded");
 }

-void FiniteElement::GetLocalInterpolation(ElementTransformation &Trans,
-                                          DenseMatrix &I) const
+void FiniteElement::GetLocalInterpolation (ElementTransformation &Trans,
+                                           DenseMatrix &I) const
 {
   MFEM_ABORT("method is not overloaded");
 }
@@ -122,13 +123,13 @@ void FiniteElement::GetTransferMatrix(const FiniteElement &fe,
   MFEM_ABORT("method is not overloaded");
 }

-void FiniteElement::Project(
+void FiniteElement::Project (
   Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 {
   MFEM_ABORT("method is not overloaded");
 }

-void FiniteElement::Project(
+void FiniteElement::Project (
   VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 {
   MFEM_ABORT("method is not overloaded");
@@ -137,7 +138,7 @@ void FiniteElement::Project(
 void FiniteElement::ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
                                     Vector &dofs) const
 {
-   mfem_error("FiniteElement::ProjectFromNodes() (vector) is not overloaded!");
+   mfem_error ("FiniteElement::ProjectFromNodes() (vector) is not overloaded!");
 }

 void FiniteElement::ProjectMatrixCoefficient(
@@ -239,6 +240,7 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
   }
 }

+
 // Assume a linear mapping
 void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
                                         Vector &Laplacian) const
@@ -249,7 +251,7 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
   DenseMatrix Gij(dim,dim);
   Vector scale(size);

-   CalcHessian(Trans.GetIntPoint(), hess);
+   CalcHessian (Trans.GetIntPoint(), hess);
   MultAAt(Trans.InverseJacobian(), Gij);

   if (dim == 3)
@@ -282,6 +284,7 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
         Laplacian[nd] += hess(nd,ii)*scale[ii];
      }
   }
+
 }

 void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
@@ -361,128 +364,17 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
   Mult( hess, lhm, Hessian);
 }

-const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &ir,
-                                             DofToQuad::Mode mode) const
+const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &,
+                                             DofToQuad::Mode) const
 {
-   MFEM_VERIFY(mode == DofToQuad::FULL, "invalid mode requested");
+   MFEM_ABORT("method is not implemented for this element");
+   return *dof2quad_array[0]; // suppress a warning
+}

-   for (int i = 0; i < dof2quad_array.Size(); i++)
-   {
-      const DofToQuad &d2q = *dof2quad_array[i];
-      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
-   }
-
-#ifdef MFEM_THREAD_SAFE
-   DenseMatrix vshape(dof, dim);
-#endif
-
-   DofToQuad *d2q = new DofToQuad;
-   const int nqpt = ir.GetNPoints();
-   d2q->FE = this;
-   d2q->IntRule = &ir;
-   d2q->mode = mode;
-   d2q->ndof = dof;
-   d2q->nqpt = nqpt;
-   if (range_type == SCALAR)
-   {
-      d2q->B.SetSize(nqpt*dof);
-      d2q->Bt.SetSize(dof*nqpt);
-
-      Vector shape;
-      vshape.GetColumnReference(0, shape);
-      for (int i = 0; i < nqpt; i++)
-      {
-         const IntegrationPoint &ip = ir.IntPoint(i);
-         CalcShape(ip, shape);
-         for (int j = 0; j < dof; j++)
-         {
-            d2q->B[i+nqpt*j] = d2q->Bt[j+dof*i] = shape(j);
-         }
-      }
-   }
-   else
-   {
-      d2q->B.SetSize(nqpt*dim*dof);
-      d2q->Bt.SetSize(dof*nqpt*dim);
-
-      for (int i = 0; i < nqpt; i++)
-      {
-         const IntegrationPoint &ip = ir.IntPoint(i);
-         CalcVShape(ip, vshape);
-         for (int d = 0; d < dim; d++)
-         {
-            for (int j = 0; j < dof; j++)
-            {
-               d2q->B[i+nqpt*(d+dim*j)] = d2q->Bt[j+dof*(i+nqpt*d)] = vshape(j, d);
-            }
-         }
-      }
-   }
-   switch (deriv_type)
-   {
-      case GRAD:
-      {
-         d2q->G.SetSize(nqpt*dim*dof);
-         d2q->Gt.SetSize(dof*nqpt*dim);
-
-         for (int i = 0; i < nqpt; i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-            CalcDShape(ip, vshape);
-            for (int d = 0; d < dim; d++)
-            {
-               for (int j = 0; j < dof; j++)
-               {
-                  d2q->G[i+nqpt*(d+dim*j)] = d2q->Gt[j+dof*(i+nqpt*d)] = vshape(j, d);
-               }
-            }
-         }
-         break;
-      }
-      case DIV:
-      {
-         d2q->G.SetSize(nqpt*dof);
-         d2q->Gt.SetSize(dof*nqpt);
-
-         Vector divshape;
-         vshape.GetColumnReference(0, divshape);
-         for (int i = 0; i < nqpt; i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-            CalcDivShape(ip, divshape);
-            for (int j = 0; j < dof; j++)
-            {
-               d2q->G[i+nqpt*j] = d2q->Gt[j+dof*i] = divshape(j);
-            }
-         }
-         break;
-      }
-      case CURL:
-      {
-         d2q->G.SetSize(nqpt*cdim*dof);
-         d2q->Gt.SetSize(dof*nqpt*cdim);
-
-         DenseMatrix curlshape(vshape.GetData(), dof, cdim);  // cdim <= dim
-         for (int i = 0; i < nqpt; i++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
-            CalcCurlShape(ip, curlshape);
-            for (int d = 0; d < cdim; d++)
-            {
-               for (int j = 0; j < dof; j++)
-               {
-                  d2q->G[i+nqpt*(d+dim*j)] = d2q->Gt[j+dof*(i+nqpt*d)] = curlshape(j, d);
-               }
-            }
-         }
-         break;
-      }
-      case NONE:
-      default:
-         MFEM_ABORT("invalid finite element derivative type");
-   }
-   dof2quad_array.Append(d2q);
-   return *d2q;
+void FiniteElement::GetFaceMap(const int face_id,
+                               Array<int> &face_map) const
+{
+   MFEM_ABORT("method is not implemented for this element");
 }

 FiniteElement::~FiniteElement()
@@ -494,19 +386,16 @@ FiniteElement::~FiniteElement()
 }


-void ScalarFiniteElement::NodalLocalInterpolation(
+void ScalarFiniteElement::NodalLocalInterpolation (
   ElementTransformation &Trans, DenseMatrix &I,
   const ScalarFiniteElement &fine_fe) const
 {
   double v[Geometry::MaxDim];
-   Vector vv(v, dim);
+   Vector vv (v, dim);
   IntegrationPoint f_ip;

 #ifdef MFEM_THREAD_SAFE
-   Vector shape(dof);
-#else
-   Vector shape;
-   vshape.GetColumnReference(0, shape);
+   Vector c_shape(dof);
 #endif

   MFEM_ASSERT(map_type == fine_fe.GetMapType(), "");
@@ -516,10 +405,10 @@ void ScalarFiniteElement::NodalLocalInterpolation(
   {
      Trans.Transform(fine_fe.Nodes.IntPoint(i), vv);
      f_ip.Set(v, dim);
-      CalcShape(f_ip, shape);
+      CalcShape(f_ip, c_shape);
      for (int j = 0; j < dof; j++)
      {
-         if (fabs(I(i,j) = shape(j)) < 1.0e-12)
+         if (fabs(I(i,j) = c_shape(j)) < 1.0e-12)
         {
            I(i,j) = 0.0;
         }
@@ -540,7 +429,7 @@ void ScalarFiniteElement::ScalarLocalInterpolation(
   // General "interpolation", defined by L2 projection

   double v[Geometry::MaxDim];
-   Vector vv(v, dim);
+   Vector vv (v, dim);
   IntegrationPoint f_ip;

   const int fs = fine_fe.GetDof(), cs = this->GetDof();
@@ -574,13 +463,14 @@ void ScalarFiniteElement::ScalarLocalInterpolation(
   }
 }

-void ScalarFiniteElement::ScalarLocalL2Restriction(
+void ScalarFiniteElement::ScalarLocalRestriction(
   ElementTransformation &Trans, DenseMatrix &R,
   const ScalarFiniteElement &coarse_fe) const
 {
   // General "restriction", defined by L2 projection
   double v[Geometry::MaxDim];
-   Vector vv(v, dim);
+   Vector vv (v, dim);
+   IntegrationPoint f_ip;

   const int cs = coarse_fe.GetDof(), fs = this->GetDof();
   R.SetSize(cs, fs);
@@ -589,27 +479,16 @@ void ScalarFiniteElement::ScalarLocalL2Restriction(
   const int ir_order = GetOrder() + coarse_fe.GetOrder();
   const IntegrationRule &ir = IntRules.Get(coarse_fe.GetGeomType(), ir_order);

-   // integrate coarse_mass in the coarse space
   for (int i = 0; i < ir.GetNPoints(); i++)
   {
-      const IntegrationPoint &c_ip = ir.IntPoint(i);
-      coarse_fe.CalcShape(c_ip, coarse_shape);
-      AddMult_a_VVt(c_ip.weight, coarse_shape, coarse_mass);
-   }
+      const IntegrationPoint &ip = ir.IntPoint(i);
+      this->CalcShape(ip, fine_shape);
+      Trans.Transform(ip, vv);
+      f_ip.Set(v, dim);
+      coarse_fe.CalcShape(f_ip, coarse_shape);

-   // integrate coarse_fine_mass in the fine space
-   Trans.SetIntPoint(&Geometries.GetCenter(geom_type));
-   for (int i = 0; i < ir.GetNPoints(); i++)
-   {
-      const IntegrationPoint &f_ip = ir.IntPoint(i);
-      this->CalcShape(f_ip, fine_shape);
-      Trans.Transform(f_ip, vv);
-
-      IntegrationPoint c_ip;
-      c_ip.Set(v, dim);
-      coarse_fe.CalcShape(c_ip, coarse_shape);
-      AddMult_a_VWt(f_ip.weight*Trans.Weight(), coarse_shape, fine_shape,
-                    coarse_fine_mass);
+      AddMult_a_VVt(ip.weight, coarse_shape, coarse_mass);
+      AddMult_a_VWt(ip.weight, coarse_shape, fine_shape, coarse_fine_mass);
   }

   DenseMatrixInverse coarse_mass_inv(coarse_mass);
@@ -622,6 +501,95 @@ void ScalarFiniteElement::ScalarLocalL2Restriction(
      R *= 1.0 / Trans.Weight();
   }
 }
+const DofToQuad &ScalarFiniteElement::GetDofToQuad(const IntegrationRule &ir,
+                                                   DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::FULL, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const int nqpt = ir.GetNPoints();
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = dof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*dof);
+   d2q->Bt.SetSize(dof*nqpt);
+   d2q->G.SetSize(nqpt*dim*dof);
+   d2q->Gt.SetSize(dof*nqpt*dim);
+#ifdef MFEM_THREAD_SAFE
+   Vector c_shape(dof);
+   DenseMatrix vshape(dof, dim);
+#endif
+   for (int i = 0; i < nqpt; i++)
+   {
+      const IntegrationPoint &ip = ir.IntPoint(i);
+      CalcShape(ip, c_shape);
+      for (int j = 0; j < dof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+dof*i] = c_shape(j);
+      }
+      CalcDShape(ip, vshape);
+      for (int d = 0; d < dim; d++)
+      {
+         for (int j = 0; j < dof; j++)
+         {
+            d2q->G[i+nqpt*(d+dim*j)] = d2q->Gt[j+dof*(i+nqpt*d)] = vshape(j,d);
+         }
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+
+// protected method
+const DofToQuad &ScalarFiniteElement::GetTensorDofToQuad(
+   const TensorBasisElement &tb,
+   const IntegrationRule &ir, DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::TENSOR, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const Poly_1D::Basis &basis_1d = tb.GetBasis1D();
+   const int ndof = order + 1;
+   const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5);
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = ndof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*ndof);
+   d2q->Bt.SetSize(ndof*nqpt);
+   d2q->G.SetSize(nqpt*ndof);
+   d2q->Gt.SetSize(ndof*nqpt);
+   Vector val(ndof), grad(ndof);
+   for (int i = 0; i < nqpt; i++)
+   {
+      // The first 'nqpt' points in 'ir' have the same x-coordinates as those
+      // of the 1D rule.
+      basis_1d.Eval(ir.IntPoint(i).x, val, grad);
+      for (int j = 0; j < ndof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+ndof*i] = val(j);
+         d2q->G[i+nqpt*j] = d2q->Gt[j+ndof*i] = grad(j);
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+

 void NodalFiniteElement::ProjectCurl_2D(
   const FiniteElement &fe, ElementTransformation &Trans,
@@ -670,10 +638,7 @@ void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
   Vector pt(&ipt.x, dim);

 #ifdef MFEM_THREAD_SAFE
-   Vector shape(dof);
-#else
-   Vector shape;
-   vshape.GetColumnReference(0, shape);
+   Vector c_shape(dof);
 #endif

   Trans.SetIntPoint(&Nodes[0]);
@@ -683,8 +648,8 @@ void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
      InvertLinearTrans(Trans, Nodes[j], pt);
      if (Geometries.CheckPoint(geom_type, ipt)) // do we need an epsilon here?
      {
-         CalcShape(ipt, shape);
-         R.SetRow(j, shape);
+         CalcShape(ipt, c_shape);
+         R.SetRow(j, c_shape);
      }
      else
      {
@@ -695,7 +660,7 @@ void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
   R.Threshold(1e-12);
 }

-void NodalFiniteElement::Project(
+void NodalFiniteElement::Project (
   Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 {
   for (int i = 0; i < dof; i++)
@@ -704,7 +669,7 @@ void NodalFiniteElement::Project(
      // some coefficients expect that Trans.IntPoint is the same
      // as the second argument of Eval
      Trans.SetIntPoint(&ip);
-      dofs(i) = coeff.Eval(Trans, ip);
+      dofs(i) = coeff.Eval (Trans, ip);
      if (map_type == INTEGRAL)
      {
         dofs(i) *= Trans.Weight();
@@ -712,7 +677,7 @@ void NodalFiniteElement::Project(
   }
 }

-void NodalFiniteElement::Project(
+void NodalFiniteElement::Project (
   VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 {
   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
@@ -891,18 +856,18 @@ VectorFiniteElement::VectorFiniteElement(int D, Geometry::Type G,
   }
 }

-void VectorFiniteElement::CalcShape(
+void VectorFiniteElement::CalcShape (
   const IntegrationPoint &ip, Vector &shape ) const
 {
-   mfem_error("Error: Cannot use scalar CalcShape(...) function with\n"
-              "   VectorFiniteElements!");
+   mfem_error ("Error: Cannot use scalar CalcShape(...) function with\n"
+               "   VectorFiniteElements!");
 }

-void VectorFiniteElement::CalcDShape(
+void VectorFiniteElement::CalcDShape (
   const IntegrationPoint &ip, DenseMatrix &dshape ) const
 {
-   mfem_error("Error: Cannot use scalar CalcDShape(...) function with\n"
-              "   VectorFiniteElements!");
+   mfem_error ("Error: Cannot use scalar CalcDShape(...) function with\n"
+               "   VectorFiniteElements!");
 }

 void VectorFiniteElement::SetDerivMembers()
@@ -942,7 +907,7 @@ void VectorFiniteElement::SetDerivMembers()
   }
 }

-void VectorFiniteElement::CalcVShape_RT(
+void VectorFiniteElement::CalcVShape_RT (
   ElementTransformation &Trans, DenseMatrix &shape) const
 {
   MFEM_ASSERT(map_type == H_DIV, "");
@@ -954,7 +919,7 @@ void VectorFiniteElement::CalcVShape_RT(
   shape *= (1.0 / Trans.Weight());
 }

-void VectorFiniteElement::CalcVShape_ND(
+void VectorFiniteElement::CalcVShape_ND (
   ElementTransformation &Trans, DenseMatrix &shape) const
 {
   MFEM_ASSERT(map_type == H_CURL, "");
@@ -2444,46 +2409,6 @@ TensorBasisElement::TensorBasisElement(const int dims, const int p,
   }
 }

-const DofToQuad &TensorBasisElement::GetTensorDofToQuad(
-   const FiniteElement &fe, const IntegrationRule &ir,
-   DofToQuad::Mode mode, const Poly_1D::Basis &basis, bool closed,
-   Array<DofToQuad*> &dof2quad_array)
-{
-   MFEM_VERIFY(mode == DofToQuad::TENSOR, "invalid mode requested");
-
-   for (int i = 0; i < dof2quad_array.Size(); i++)
-   {
-      const DofToQuad &d2q = *dof2quad_array[i];
-      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
-   }
-
-   DofToQuad *d2q = new DofToQuad;
-   const int ndof = closed ? fe.GetOrder() + 1 : fe.GetOrder();
-   const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/fe.GetDim()) + 0.5);
-   d2q->FE = &fe;
-   d2q->IntRule = &ir;
-   d2q->mode = mode;
-   d2q->ndof = ndof;
-   d2q->nqpt = nqpt;
-   d2q->B.SetSize(nqpt*ndof);
-   d2q->Bt.SetSize(ndof*nqpt);
-   d2q->G.SetSize(nqpt*ndof);
-   d2q->Gt.SetSize(ndof*nqpt);
-   Vector val(ndof), grad(ndof);
-   for (int i = 0; i < nqpt; i++)
-   {
-      // The first 'nqpt' points in 'ir' have the same x-coordinates as those
-      // of the 1D rule.
-      basis.Eval(ir.IntPoint(i).x, val, grad);
-      for (int j = 0; j < ndof; j++)
-      {
-         d2q->B[i+nqpt*j] = d2q->Bt[j+ndof*i] = val(j);
-         d2q->G[i+nqpt*j] = d2q->Gt[j+ndof*i] = grad(j);
-      }
-   }
-   dof2quad_array.Append(d2q);
-   return *d2q;
-}

 NodalTensorFiniteElement::NodalTensorFiniteElement(const int dims,
                                                   const int p,
@@ -2509,6 +2434,55 @@ void NodalTensorFiniteElement::SetMapType(const int map_type)
   }
 }

+void NodalTensorFiniteElement::GetFaceMap(const int face_id,
+                                          Array<int> &face_map) const
+{
+   const int dof1d = order + 1;
+   int n_face_dofs = pow(dof1d, dim - 1);
+   std::vector<int> offsets, strides;
+   switch (dim)
+   {
+      case 1:
+         offsets = {(face_id == 0) ? 0 : dof1d - 1};
+         break;
+      case 2:
+         strides = {(face_id == 0 || face_id == 2) ? 1 : dof1d};
+         switch (face_id)
+         {
+            case 0: offsets = {0}; break; // y = 0
+            case 1: offsets = {dof1d - 1}; break; // x = 1
+            case 2: offsets = {(dof1d-1)*dof1d}; break; // y = 1
+            case 3: offsets = {0}; break; // x = 0
+         }
+         break;
+      case 3:
+      {
+         const auto f = GetFaceNormal3D(face_id);
+         const int face_normal = f.first, level = f.second;
+         if (face_normal == 0) // x-normal
+         {
+            offsets = {level ? dof1d-1 : 0};
+            strides = {dof1d, dof1d*dof1d};
+         }
+         else if (face_normal == 1) // y-normal
+         {
+            offsets = {level ? (dof1d-1)*dof1d : 0};
+            strides = {1, dof1d*dof1d};
+         }
+         else if (face_normal == 2) // z-normal
+         {
+            offsets = {level ? (dof1d-1)*dof1d*dof1d : 0};
+            strides = {1, dof1d};
+         }
+         break;
+      }
+   }
+
+   // same number of DOFs in each dimension, repeat dof1d (dim - 1) times
+   std::vector<int> n_dofs(dim - 1, dof1d);
+   FillFaceMap(n_face_dofs, offsets, strides, n_dofs, face_map);
+}
+
 VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                                                     const int d,
                                                     const int p,
@@ -2518,7 +2492,8 @@ VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                                                     const DofMapType dmtype)
   : VectorFiniteElement(dims, GetTensorProductGeometry(dims), d,
                         p, M, FunctionSpace::Qk),
-     TensorBasisElement(dims, p, VerifyNodal(VerifyClosed(cbtype)), dmtype),
+     TensorBasisElement(dims, p, VerifyNodal(cbtype), dmtype),
+     cbasis1d(poly1d.GetBasis(p, VerifyClosed(cbtype))),
     obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(obtype)))
 {
   MFEM_VERIFY(dims > 1, "Constructor for VectorTensorFiniteElement with both "
@@ -2533,13 +2508,93 @@ VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                                                     const DofMapType dmtype)
   : VectorFiniteElement(dims, GetTensorProductGeometry(dims), d,
                         p, M, FunctionSpace::Pk),
-     TensorBasisElement(dims, p, VerifyOpen(obtype), dmtype),
+     TensorBasisElement(dims, p, obtype, dmtype),
+     cbasis1d(poly1d.GetBasis(p, VerifyOpen(obtype))),
     obasis1d(poly1d.GetBasis(p, VerifyOpen(obtype)))
 {
   MFEM_VERIFY(dims == 1, "Constructor for VectorTensorFiniteElement without "
               "closed basis is only valid for 1D elements.");
 }

+const DofToQuad &VectorTensorFiniteElement::GetDofToQuad(
+   const IntegrationRule &ir,
+   DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
+
+   return GetTensorDofToQuad(ir, mode, true);
+}
+
+const DofToQuad &VectorTensorFiniteElement::GetDofToQuadOpen(
+   const IntegrationRule &ir,
+   DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
+
+   return GetTensorDofToQuad(ir, mode, false);
+}
+
+const DofToQuad &VectorTensorFiniteElement::GetTensorDofToQuad(
+   const IntegrationRule &ir,
+   DofToQuad::Mode mode,
+   const bool closed) const
+{
+   MFEM_VERIFY(mode == DofToQuad::TENSOR, "invalid mode requested");
+
+   for (int i = 0;
+        i < (closed ? dof2quad_array.Size() : dof2quad_array_open.Size());
+        i++)
+   {
+      const DofToQuad &d2q = closed ? *dof2quad_array[i] : *dof2quad_array_open[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const int ndof = closed ? order + 1 : order;
+   const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/dim) + 0.5);
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = ndof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*ndof);
+   d2q->Bt.SetSize(ndof*nqpt);
+   d2q->G.SetSize(nqpt*ndof);
+   d2q->Gt.SetSize(ndof*nqpt);
+   Vector val(ndof), grad(ndof);
+   for (int i = 0; i < nqpt; i++)
+   {
+      // The first 'nqpt' points in 'ir' have the same x-coordinates as those
+      // of the 1D rule.
+
+      if (closed)
+      {
+         cbasis1d.Eval(ir.IntPoint(i).x, val, grad);
+      }
+      else
+      {
+         obasis1d.Eval(ir.IntPoint(i).x, val, grad);
+      }
+
+      for (int j = 0; j < ndof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+ndof*i] = val(j);
+         d2q->G[i+nqpt*j] = d2q->Gt[j+ndof*i] = grad(j);
+      }
+   }
+
+   if (closed)
+   {
+      dof2quad_array.Append(d2q);
+   }
+   else
+   {
+      dof2quad_array_open.Append(d2q);
+   }
+
+   return *d2q;
+}
+
 VectorTensorFiniteElement::~VectorTensorFiniteElement()
 {
   for (int i = 0; i < dof2quad_array_open.Size(); i++)
@@ -127,6 +127,7 @@ public:
   }
 };

+
 /** @brief Structure representing the matrices/tensors needed to evaluate (in
    reference space) the values, gradients, divergences, or curls of a
    FiniteElement at a the quadrature points of a given IntegrationRule. */
@@ -156,7 +157,8 @@ public:
          dimensions using 1D number of quadrature points and degrees of
          freedom. */
      /** When representing a vector-valued FiniteElement, two DofToQuad objects
-          are used to describe the "closed" and "open" 1D basis functions. */
+          are used to describe the "closed" and "open" 1D basis functions
+          (TODO). */
      TENSOR
   };

@@ -174,7 +176,7 @@ public:
   /// Basis functions evaluated at quadrature points.
   /** The storage layout is column-major with dimensions:
       - #nqpt x #ndof, for scalar elements, or
-       - #nqpt x dim x #ndof, for vector elements,
+       - #nqpt x dim x #ndof, for vector elements, (TODO)

       where

@@ -185,15 +187,15 @@ public:
   /// Transpose of #B.
   /** The storage layout is column-major with dimensions:
       - #ndof x #nqpt, for scalar elements, or
-       - #ndof x #nqpt x dim, for vector elements. */
+       - #ndof x #nqpt x dim, for vector elements (TODO). */
   Array<double> Bt;

   /** @brief Gradients/divergences/curls of basis functions evaluated at
       quadrature points. */
   /** The storage layout is column-major with dimensions:
       - #nqpt x dim x #ndof, for scalar elements, or
-       - #nqpt x #ndof, for H(div) vector elements, or
-       - #nqpt x cdim x #ndof, for H(curl) vector elements,
+       - #nqpt x #ndof, for H(div) vector elements (TODO), or
+       - #nqpt x cdim x #ndof, for H(curl) vector elements (TODO),

       where

@@ -206,11 +208,12 @@ public:
   /// Transpose of #G.
   /** The storage layout is column-major with dimensions:
       - #ndof x #nqpt x dim, for scalar elements, or
-       - #ndof x #nqpt, for H(div) vector elements, or
-       - #ndof x #nqpt x cdim, for H(curl) vector elements. */
+       - #ndof x #nqpt, for H(div) vector elements (TODO), or
+       - #ndof x #nqpt x cdim, for H(curl) vector elements (TODO). */
   Array<double> Gt;
 };

+
 /// Describes the function space on each element
 class FunctionSpace
 {
@@ -244,7 +247,7 @@ protected:
   mutable int orders[Geometry::MaxDim]; ///< Anisotropic orders
   IntegrationRule Nodes;
 #ifndef MFEM_THREAD_SAFE
-   mutable DenseMatrix vshape; // Dof x Dim
+   mutable DenseMatrix vshape; // Dof x VDim
 #endif
   /// Container for all DofToQuad objects created by the FiniteElement.
   /** Multiple DofToQuad objects may be needed when different quadrature rules
@@ -347,6 +350,7 @@ public:
       H_DIV, H_CURL}. */
   int GetMapType() const { return map_type; }

+
   /** @brief Returns the FiniteElement::DerivType of the element describing the
       spatial derivative method implemented, one of {NONE, GRAD,
       DIV, CURL}. */
@@ -453,8 +457,8 @@ public:
       part of the Hessian of one shape function.
       The order in 2D is {u_xx, u_xy, u_yy}.
       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
+   virtual void CalcHessian (const IntegrationPoint &ip,
+                             DenseMatrix &Hessian) const;

   /** @brief Evaluate the Hessian of all shape functions of a scalar finite
       element in reference space at the given point @a ip. */
@@ -576,6 +580,9 @@ public:
   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
                                         DofToQuad::Mode mode) const;

+   virtual void GetFaceMap(const int face_id,
+                           Array<int> &face_map) const;
+
   /// Deconstruct the FiniteElement
   virtual ~FiniteElement();

@@ -622,11 +629,16 @@ public:
   }
 };

+
 /** @brief Class for finite elements with basis functions
    that return scalar values. */
 class ScalarFiniteElement : public FiniteElement
 {
 protected:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector c_shape;
+#endif
+
   static const ScalarFiniteElement &CheckScalarFE(const FiniteElement &fe)
   {
      MFEM_VERIFY(fe.GetRangeType() == SCALAR,
@@ -634,6 +646,10 @@ protected:
      return static_cast<const ScalarFiniteElement &>(fe);
   }

+   const DofToQuad &GetTensorDofToQuad(const class TensorBasisElement &tb,
+                                       const IntegrationRule &ir,
+                                       DofToQuad::Mode mode) const;
+
 public:
   /** @brief Construct ScalarFiniteElement with given
       @param D    Reference space dimension
@@ -644,8 +660,13 @@ public:
    */
   ScalarFiniteElement(int D, Geometry::Type G, int Do, int O,
                       int F = FunctionSpace::Pk)
+#ifdef MFEM_THREAD_SAFE
      : FiniteElement(D, G, Do, O, F)
   { deriv_type = GRAD; deriv_range_type = VECTOR; deriv_map_type = H_CURL; }
+#else
+      : FiniteElement(D, G, Do, O, F), c_shape(dof)
+   { deriv_type = GRAD; deriv_range_type = VECTOR; deriv_map_type = H_CURL; }
+#endif

   /** @brief Set the FiniteElement::MapType of the element to either VALUE or
       INTEGRAL. Also sets the FiniteElement::DerivType to GRAD if the
@@ -657,6 +678,7 @@ public:
      deriv_type = (M == VALUE) ? GRAD : NONE;
   }

+
   /** @brief Get the matrix @a I that defines nodal interpolation
       @a between this element and the refined element @a fine_fe. */
   void NodalLocalInterpolation(ElementTransformation &Trans,
@@ -677,11 +699,15 @@ public:
   /** If the "fine" elements cannot represent all basis functions of the
       "coarse" element, then boundary values from different sub-elements are
       generally different. */
-   void ScalarLocalL2Restriction(ElementTransformation &Trans,
-                                 DenseMatrix &R,
-                                 const ScalarFiniteElement &coarse_fe) const;
+   void ScalarLocalRestriction(ElementTransformation &Trans,
+                               DenseMatrix &R,
+                               const ScalarFiniteElement &coarse_fe) const;
+
+   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                         DofToQuad::Mode mode) const;
 };

+
 /// Class for standard nodal finite elements.
 class NodalFiniteElement : public ScalarFiniteElement
 {
@@ -703,38 +729,38 @@ public:
                      int F = FunctionSpace::Pk)
      : ScalarFiniteElement(D, G, Do, O, F) { }

-   void GetLocalInterpolation(ElementTransformation &Trans,
-                              DenseMatrix &I) const override
+   virtual void GetLocalInterpolation(ElementTransformation &Trans,
+                                      DenseMatrix &I) const
   { NodalLocalInterpolation(Trans, I, *this); }

-   void GetLocalRestriction(ElementTransformation &Trans,
-                            DenseMatrix &R) const override;
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const;

-   void GetTransferMatrix(const FiniteElement &fe,
-                          ElementTransformation &Trans,
-                          DenseMatrix &I) const override
+   virtual void GetTransferMatrix(const FiniteElement &fe,
+                                  ElementTransformation &Trans,
+                                  DenseMatrix &I) const
   { CheckScalarFE(fe).NodalLocalInterpolation(Trans, I, *this); }

-   void Project(Coefficient &coeff,
-                ElementTransformation &Trans, Vector &dofs) const override;
+   virtual void Project (Coefficient &coeff,
+                         ElementTransformation &Trans, Vector &dofs) const;

-   void Project(VectorCoefficient &vc,
-                ElementTransformation &Trans, Vector &dofs) const override;
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;

   // (mc.height x mc.width) @ DOFs -> (Dof x mc.width x mc.height) in dofs
-   void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override;
+   virtual void ProjectMatrixCoefficient(
+      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;

-   void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                DenseMatrix &I) const override;
+   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                        DenseMatrix &I) const;

-   void ProjectGrad(const FiniteElement &fe,
-                    ElementTransformation &Trans,
-                    DenseMatrix &grad) const override;
+   virtual void ProjectGrad(const FiniteElement &fe,
+                            ElementTransformation &Trans,
+                            DenseMatrix &grad) const;

-   void ProjectDiv(const FiniteElement &fe,
-                   ElementTransformation &Trans,
-                   DenseMatrix &div) const override;
+   virtual void ProjectDiv(const FiniteElement &fe,
+                           ElementTransformation &Trans,
+                           DenseMatrix &div) const;

   /** @brief Get an Array<int> that maps lexicographically ordered indices to
       the indices of the respective nodes/dofs/basis functions.
@@ -768,12 +794,12 @@ class VectorFiniteElement : public FiniteElement
   // Hide the scalar functions CalcShape and CalcDShape.
 private:
   /// Overrides the scalar CalcShape function to print an error.
-   void CalcShape(const IntegrationPoint &ip,
-                  Vector &shape) const override;
+   virtual void CalcShape(const IntegrationPoint &ip,
+                          Vector &shape) const;

   /// Overrides the scalar CalcDShape function to print an error.
-   void CalcDShape(const IntegrationPoint &ip,
-                   DenseMatrix &dshape) const override;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;

 protected:
   bool is_nodal;
@@ -932,10 +958,11 @@ protected:
   }

 public:
-   VectorFiniteElement(int D, Geometry::Type G, int Do, int O, int M,
-                       int F = FunctionSpace::Pk);
+   VectorFiniteElement (int D, Geometry::Type G, int Do, int O, int M,
+                        int F = FunctionSpace::Pk);
 };

+
 /// @brief Class for computing 1D special polynomials and their associated basis
 /// functions
 class Poly_1D
@@ -1156,6 +1183,7 @@ public:

 extern Poly_1D poly1d;

+
 /// An element defined as an ND tensor product of 1D elements on a segment,
 /// square, or cube
 class TensorBasisElement
@@ -1179,7 +1207,7 @@ public:

   int GetBasisType() const { return b_type; }

-   const Poly_1D::Basis &GetBasis1D() const { return basis1d; }
+   const Poly_1D::Basis& GetBasis1D() const { return basis1d; }

   /** @brief Get an Array<int> that maps lexicographically ordered indices to
       the indices of the respective nodes/dofs/basis functions. If the dofs are
@@ -1211,11 +1239,6 @@ public:
         default: MFEM_ABORT("invalid dimension: " << dim); return -1;
      }
   }
-
-   static const DofToQuad &GetTensorDofToQuad(
-      const FiniteElement &fe, const IntegrationRule &ir,
-      DofToQuad::Mode mode, const Poly_1D::Basis &basis, bool closed,
-      Array<DofToQuad*> &dof2quad_array);
 };

 class NodalTensorFiniteElement : public NodalFiniteElement,
@@ -1226,18 +1249,18 @@ public:
                            const DofMapType dmtype);

   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
-                                 DofToQuad::Mode mode) const override
+                                 DofToQuad::Mode mode) const
   {
      return (mode == DofToQuad::FULL) ?
-             FiniteElement::GetDofToQuad(ir, mode) :
-             GetTensorDofToQuad(*this, ir, mode, basis1d, true, dof2quad_array);
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
   }

-   void SetMapType(const int map_type_) override;
+   virtual void SetMapType(const int map_type_);

-   void GetTransferMatrix(const FiniteElement &fe,
-                          ElementTransformation &Trans,
-                          DenseMatrix &I) const override
+   virtual void GetTransferMatrix(const FiniteElement &fe,
+                                  ElementTransformation &Trans,
+                                  DenseMatrix &I) const
   {
      if (basis1d.IsIntegratedType())
      {
@@ -1248,6 +1271,8 @@ public:
         NodalFiniteElement::GetTransferMatrix(fe, Trans, I);
      }
   }
+
+   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
 };

 class VectorTensorFiniteElement : public VectorFiniteElement,
@@ -1257,7 +1282,7 @@ private:
   mutable Array<DofToQuad*> dof2quad_array_open;

 protected:
-   Poly_1D::Basis &obasis1d;
+   Poly_1D::Basis &cbasis1d, &obasis1d;

 public:
   VectorTensorFiniteElement(const int dims, const int d, const int p,
@@ -1270,22 +1295,16 @@ public:
                             const DofMapType dmtype);

   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
-                                 DofToQuad::Mode mode) const override
-   {
-      MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
-      return GetTensorDofToQuad(*this, ir, mode, basis1d, true,
-                                dof2quad_array);
-   }
+                                 DofToQuad::Mode mode) const;

   const DofToQuad &GetDofToQuadOpen(const IntegrationRule &ir,
-                                     DofToQuad::Mode mode) const
-   {
-      MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
-      return GetTensorDofToQuad(*this, ir, mode, obasis1d, false,
-                                dof2quad_array_open);
-   }
+                                     DofToQuad::Mode mode) const;

-   virtual ~VectorTensorFiniteElement();
+   const DofToQuad &GetTensorDofToQuad(const IntegrationRule &ir,
+                                       DofToQuad::Mode mode,
+                                       const bool closed) const;
+
+   ~VectorTensorFiniteElement();
 };

 void InvertLinearTrans(ElementTransformation &trans,
@@ -32,11 +32,6 @@ public:
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
-
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
-
 };


@@ -60,11 +55,6 @@ public:
                            ElementTransformation &Trans,
                            DenseMatrix &curl) const
   { ProjectCurl_2D(fe, Trans, curl); }
-
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
-
   using FiniteElement::Project;
   virtual void ProjectDiv(const FiniteElement &fe,
                           ElementTransformation &Trans,
@@ -90,11 +80,6 @@ public:
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
-
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
-
   using FiniteElement::Project;
   virtual void ProjectDiv(const FiniteElement &fe,
                           ElementTransformation &Trans,
@@ -126,11 +111,6 @@ public:
                            ElementTransformation &Trans,
                            DenseMatrix &curl) const
   { ProjectCurl_2D(fe, Trans, curl); }
-
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
-
 };


@@ -153,11 +133,6 @@ public:
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
-
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
-
 };


@@ -12,6 +12,7 @@
 // Nedelec Finite Element classes

 #include "fe_nd.hpp"
+#include "face_map_utils.hpp"
 #include "../coefficient.hpp"

 namespace mfem
@@ -321,9 +322,9 @@ void ND_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
      Vector dshape_cx(p + 1), dshape_cy(p + 1), dshape_cz(p + 1);
 #endif
-      basis1d.Eval(ip.x, shape_cx, dshape_cx);
-      basis1d.Eval(ip.y, shape_cy, dshape_cy);
-      basis1d.Eval(ip.z, shape_cz, dshape_cz);
+      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
      obasis1d.ScaleIntegrated(false);
      obasis1d.EvalIntegrated(dshape_cx, shape_ox);
      obasis1d.EvalIntegrated(dshape_cy, shape_oy);
@@ -331,9 +332,9 @@ void ND_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
   }
   else
   {
-      basis1d.Eval(ip.x, shape_cx);
-      basis1d.Eval(ip.y, shape_cy);
-      basis1d.Eval(ip.z, shape_cz);
+      cbasis1d.Eval(ip.x, shape_cx);
+      cbasis1d.Eval(ip.y, shape_cy);
+      cbasis1d.Eval(ip.z, shape_cz);
      obasis1d.Eval(ip.x, shape_ox);
      obasis1d.Eval(ip.y, shape_oy);
      obasis1d.Eval(ip.z, shape_oz);
@@ -407,9 +408,9 @@ void ND_HexahedronElement::CalcCurlShape(const IntegrationPoint &ip,
   Vector dshape_cx(p + 1), dshape_cy(p + 1), dshape_cz(p + 1);
 #endif

-   basis1d.Eval(ip.x, shape_cx, dshape_cx);
-   basis1d.Eval(ip.y, shape_cy, dshape_cy);
-   basis1d.Eval(ip.z, shape_cz, dshape_cz);
+   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+   cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
   if (obasis1d.IsIntegratedType())
   {
      obasis1d.ScaleIntegrated(false);
@@ -481,6 +482,50 @@ void ND_HexahedronElement::CalcCurlShape(const IntegrationPoint &ip,
         }
 }

+void ND_HexahedronElement::GetFaceMap(const int face_id,
+                                      Array<int> &face_map) const
+{
+   const int p = order;
+   const int pp1 = p + 1;
+   const int n_face_dofs_per_component = p*pp1;
+   const int n_dof_per_dim = p*pp1*pp1;
+
+   std::vector<int> n_dofs = {p, pp1, pp1, p};
+   std::vector<int> offsets, strides;
+
+   const auto f = GetFaceNormal3D(face_id);
+   const int face_normal = f.first, level = f.second;
+   if (face_normal == 0) // x-normal
+   {
+      offsets =
+      {
+         n_dof_per_dim + (level ? pp1 - 1 : 0),
+         2*n_dof_per_dim + (level ? pp1 - 1 : 0)
+      };
+      strides = {pp1, p*pp1, pp1, pp1*pp1};
+   }
+   else if (face_normal == 1) // y-normal
+   {
+      offsets =
+      {
+         level ? p*(pp1 - 1) : 0,
+         2*n_dof_per_dim + (level ? pp1*(pp1 - 1) : 0)
+      };
+      strides = {1, p*pp1, 1, pp1*pp1};
+   }
+   else if (face_normal == 2) // z-normal
+   {
+      offsets =
+      {
+         level ? p*pp1*(pp1 - 1) : 0,
+         n_dof_per_dim + (level ? p*pp1*(pp1 - 1) : 0)
+      };
+      strides = {1, p, 1, pp1};
+   }
+
+   FillFaceMap(n_face_dofs_per_component, offsets, strides, n_dofs, face_map);
+}
+
 const double ND_QuadrilateralElement::tk[8] =
 { 1.,0.,  0.,1., -1.,0., 0.,-1. };

@@ -665,16 +710,16 @@ void ND_QuadrilateralElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
      Vector dshape_cx(p + 1), dshape_cy(p + 1);
 #endif
-      basis1d.Eval(ip.x, shape_cx, dshape_cx);
-      basis1d.Eval(ip.y, shape_cy, dshape_cy);
+      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      obasis1d.ScaleIntegrated(false);
      obasis1d.EvalIntegrated(dshape_cx, shape_ox);
      obasis1d.EvalIntegrated(dshape_cy, shape_oy);
   }
   else
   {
-      basis1d.Eval(ip.x, shape_cx);
-      basis1d.Eval(ip.y, shape_cy);
+      cbasis1d.Eval(ip.x, shape_cx);
+      cbasis1d.Eval(ip.y, shape_cy);
      obasis1d.Eval(ip.x, shape_ox);
      obasis1d.Eval(ip.y, shape_oy);
   }
@@ -724,8 +769,8 @@ void ND_QuadrilateralElement::CalcCurlShape(const IntegrationPoint &ip,
   Vector dshape_cx(p + 1), dshape_cy(p + 1);
 #endif

-   basis1d.Eval(ip.x, shape_cx, dshape_cx);
-   basis1d.Eval(ip.y, shape_cy, dshape_cy);
+   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
   if (obasis1d.IsIntegratedType())
   {
      obasis1d.ScaleIntegrated(false);
@@ -771,6 +816,25 @@ void ND_QuadrilateralElement::CalcCurlShape(const IntegrationPoint &ip,
      }
 }

+void ND_QuadrilateralElement::GetFaceMap(const int face_id,
+                                         Array<int> &face_map) const
+{
+   const int p = order;
+   const int pp1 = order + 1;
+   const int n_face_dofs_per_component = p;
+   std::vector<int> strides = {(face_id == 0 || face_id == 2) ? 1 : pp1};
+   std::vector<int> n_dofs = {p};
+   std::vector<int> offsets;
+   switch (face_id)
+   {
+      case 0: offsets = {0}; break; // y = 0
+      case 1: offsets = {p*pp1 + pp1 - 1}; break; // x = 1
+      case 2: offsets = {p*(pp1 - 1)}; break; // y = 1
+      case 3: offsets = {p*pp1}; break; // x = 0
+   }
+   FillFaceMap(n_face_dofs_per_component, offsets, strides, n_dofs, face_map);
+}
+

 const double ND_TetrahedronElement::tk[18] =
 { 1.,0.,0.,  0.,1.,0.,  0.,0.,1.,  -1.,1.,0.,  -1.,0.,1.,  0.,-1.,1. };
@@ -91,6 +91,8 @@ public:
                            DenseMatrix &curl) const
   { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }

+   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+
 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
                          ElementTransformation &Trans,
@@ -155,6 +157,8 @@ public:
                            DenseMatrix &grad) const
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

+   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+
 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
                          ElementTransformation &Trans,
@@ -13,7 +13,6 @@

 #include "fe_pos.hpp"
 #include "../bilininteg.hpp"
-#include "../lininteg.hpp"
 #include "../coefficient.hpp"

 namespace mfem
@@ -40,7 +40,7 @@ public:

   virtual void GetLocalRestriction(ElementTransformation &Trans,
                                    DenseMatrix &R) const
-   { ScalarLocalL2Restriction(Trans, R, *this); }
+   { ScalarLocalRestriction(Trans, R, *this); }

   virtual void GetTransferMatrix(const FiniteElement &fe,
                                  ElementTransformation &Trans,
@@ -73,8 +73,8 @@ public:
                                 DofToQuad::Mode mode) const
   {
      return (mode == DofToQuad::FULL) ?
-             FiniteElement::GetDofToQuad(ir, mode) :
-             GetTensorDofToQuad(*this, ir, mode, basis1d, true, dof2quad_array);
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
   }
 };

@@ -12,6 +12,7 @@
 // Raviart-Thomas Finite Element classes

 #include "fe_rt.hpp"
+#include "face_map_utils.hpp"
 #include "../coefficient.hpp"

 namespace mfem
@@ -152,16 +153,16 @@ void RT_QuadrilateralElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
      Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1);
 #endif
-      basis1d.Eval(ip.x, shape_cx, dshape_cx);
-      basis1d.Eval(ip.y, shape_cy, dshape_cy);
+      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      obasis1d.ScaleIntegrated(false);
      obasis1d.EvalIntegrated(dshape_cx, shape_ox);
      obasis1d.EvalIntegrated(dshape_cy, shape_oy);
   }
   else
   {
-      basis1d.Eval(ip.x, shape_cx);
-      basis1d.Eval(ip.y, shape_cy);
+      cbasis1d.Eval(ip.x, shape_cx);
+      cbasis1d.Eval(ip.y, shape_cy);
      obasis1d.Eval(ip.x, shape_ox);
      obasis1d.Eval(ip.y, shape_oy);
   }
@@ -209,8 +210,8 @@ void RT_QuadrilateralElement::CalcDivShape(const IntegrationPoint &ip,
   Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1);
 #endif

-   basis1d.Eval(ip.x, shape_cx, dshape_cx);
-   basis1d.Eval(ip.y, shape_cy, dshape_cy);
+   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
   if (obasis1d.IsIntegratedType())
   {
      obasis1d.ScaleIntegrated(false);
@@ -297,6 +298,27 @@ void RT_QuadrilateralElement::ProjectIntegrated(VectorCoefficient &vc,
   }
 }

+void RT_QuadrilateralElement::GetFaceMap(const int face_id,
+                                         Array<int> &face_map) const
+{
+   const int p = order;
+   const int pp1 = p + 1;
+   const int n_face_dofs = p;
+
+   std::vector<int> offsets;
+   std::vector<int> strides = {(face_id == 0 || face_id == 2) ? 1 : pp1};
+   switch (face_id)
+   {
+      case 0: offsets = {p*pp1}; break; // y = 0
+      case 1: offsets = {pp1 - 1}; break; // x = 1
+      case 2: offsets = {p*pp1 + p*(pp1 - 1)}; break; // y = 1
+      case 3: offsets = {0}; break; // x = 0
+   }
+
+   std::vector<int> n_dofs(dim - 1, p);
+   FillFaceMap(n_face_dofs, offsets, strides, n_dofs, face_map);
+}
+

 const double RT_HexahedronElement::nk[18] =
 { 0.,0.,-1.,  0.,-1.,0.,  1.,0.,0.,  0.,1.,0.,  -1.,0.,0.,  0.,0.,1. };
@@ -482,9 +504,9 @@ void RT_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
      Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1), dshape_cz(pp1 + 1);
 #endif
-      basis1d.Eval(ip.x, shape_cx, dshape_cx);
-      basis1d.Eval(ip.y, shape_cy, dshape_cy);
-      basis1d.Eval(ip.z, shape_cz, dshape_cz);
+      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
      obasis1d.ScaleIntegrated(false);
      obasis1d.EvalIntegrated(dshape_cx, shape_ox);
      obasis1d.EvalIntegrated(dshape_cy, shape_oy);
@@ -492,9 +514,9 @@ void RT_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
   }
   else
   {
-      basis1d.Eval(ip.x, shape_cx);
-      basis1d.Eval(ip.y, shape_cy);
-      basis1d.Eval(ip.z, shape_cz);
+      cbasis1d.Eval(ip.x, shape_cx);
+      cbasis1d.Eval(ip.y, shape_cy);
+      cbasis1d.Eval(ip.z, shape_cz);
      obasis1d.Eval(ip.x, shape_ox);
      obasis1d.Eval(ip.y, shape_oy);
      obasis1d.Eval(ip.z, shape_oz);
@@ -568,9 +590,9 @@ void RT_HexahedronElement::CalcDivShape(const IntegrationPoint &ip,
   Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1), dshape_cz(pp1 + 1);
 #endif

-   basis1d.Eval(ip.x, shape_cx, dshape_cx);
-   basis1d.Eval(ip.y, shape_cy, dshape_cy);
-   basis1d.Eval(ip.z, shape_cz, dshape_cz);
+   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
+   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+   cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
   if (obasis1d.IsIntegratedType())
   {
      obasis1d.ScaleIntegrated(false);
@@ -686,6 +708,35 @@ void RT_HexahedronElement::ProjectIntegrated(VectorCoefficient &vc,
   }
 }

+void RT_HexahedronElement::GetFaceMap(const int face_id,
+                                      Array<int> &face_map) const
+{
+   const int p = order;
+   const int pp1 = p + 1;
+   int n_face_dofs = p*p;
+   std::vector<int> strides, offsets;
+   const int n_dof_per_dim = p*p*pp1;
+   const auto f = GetFaceNormal3D(face_id);
+   const int face_normal = f.first, level = f.second;
+   if (face_normal == 0) // x-normal
+   {
+      offsets = {level ? pp1 - 1 : 0};
+      strides = {pp1, p*pp1};
+   }
+   else if (face_normal == 1) // y-normal
+   {
+      offsets = {n_dof_per_dim + (level ? p*(pp1 - 1) : 0)};
+      strides = {1, p*pp1};
+   }
+   else if (face_normal == 2) // z-normal
+   {
+      offsets = {2*n_dof_per_dim + (level ? p*p*(pp1 - 1) : 0)};
+      strides = {1, p};
+   }
+   std::vector<int> n_dofs = {p, p};
+   FillFaceMap(n_face_dofs, offsets, strides, n_dofs, face_map);
+}
+

 const double RT_TriangleElement::nk[6] =
 { 0., -1., 1., 1., -1., 0. };
@@ -82,6 +82,8 @@ public:
                            DenseMatrix &curl) const
   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }

+   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+
 protected:
   void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans,
                          Vector &dofs) const;
@@ -145,6 +147,10 @@ public:
                            DenseMatrix &curl) const
   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }

+   /// @brief Return the mapping from lexicographically ordered DOFs to face
+   /// DOFs corresponding to local face @a face_id.
+   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+
 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
                          ElementTransformation &Trans,
@@ -25,16 +25,15 @@ using namespace std;
 const FiniteElement *
 FiniteElementCollection::FiniteElementForDim(int dim) const
 {
-   ErrorMode save_error_mode = error_mode;
-   error_mode = RETURN_NULL;
-   const FiniteElement *fe = nullptr;
   for (int g = Geometry::DimStart[dim]; g < Geometry::DimStart[dim+1]; g++)
   {
-      fe = FiniteElementForGeometry((Geometry::Type)g);
-      if (fe != nullptr) { break; }
+      const FiniteElement *fe = FiniteElementForGeometry((Geometry::Type)g);
+      if (fe != NULL)
+      {
+         return fe;
+      }
   }
-   error_mode = save_error_mode;
-   return fe;
+   return NULL;
 }

 int FiniteElementCollection::GetRangeType(int dim) const
@@ -644,7 +643,6 @@ LinearFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::PRISM:       return &WedgeFE;
      case Geometry::PYRAMID:     return &PyramidFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("LinearFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -688,7 +686,6 @@ QuadraticFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::CUBE:        return &ParallelepipedFE;
      case Geometry::PRISM:       return &WedgeFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("QuadraticFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -729,7 +726,6 @@ QuadraticPosFECollection::FiniteElementForGeometry(
      case Geometry::SEGMENT:     return &SegmentFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("QuadraticPosFECollection: unknown geometry type.");
   }
   return NULL; // Make some compilers happy
@@ -770,7 +766,6 @@ CubicFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::CUBE:        return &ParallelepipedFE;
      case Geometry::PRISM:       return &WedgeFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("CubicFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -837,7 +832,6 @@ CrouzeixRaviartFECollection::FiniteElementForGeometry(
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("CrouzeixRaviartFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -875,7 +869,6 @@ RT0_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RT0_2DFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -918,7 +911,6 @@ RT1_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RT1_2DFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -960,7 +952,6 @@ RT2_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RT2_2DFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -1002,7 +993,6 @@ Const2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("Const2DFECollection: unknown geometry type.");
   }
   return &TriangleFE; // Make some compilers happy
@@ -1038,7 +1028,6 @@ LinearDiscont2DFECollection::FiniteElementForGeometry(
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("LinearDiscont2DFECollection: unknown geometry type.");
   }
   return &TriangleFE; // Make some compilers happy
@@ -1074,7 +1063,6 @@ GaussLinearDiscont2DFECollection::FiniteElementForGeometry(
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("GaussLinearDiscont2DFECollection:"
                     " unknown geometry type.");
   }
@@ -1109,7 +1097,6 @@ P1OnQuadFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
   if (GeomType != Geometry::SQUARE)
   {
-      if (error_mode == RETURN_NULL) { return nullptr; }
      mfem_error ("P1OnQuadFECollection: unknown geometry type.");
   }
   return &QuadrilateralFE;
@@ -1144,7 +1131,6 @@ QuadraticDiscont2DFECollection::FiniteElementForGeometry(
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("QuadraticDiscont2DFECollection: unknown geometry type.");
   }
   return &TriangleFE; // Make some compilers happy
@@ -1180,7 +1166,6 @@ QuadraticPosDiscont2DFECollection::FiniteElementForGeometry(
   {
      case Geometry::SQUARE:  return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("QuadraticPosDiscont2DFECollection: unknown geometry type.");
   }
   return NULL; // Make some compilers happy
@@ -1211,7 +1196,6 @@ const
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("GaussQuadraticDiscont2DFECollection:"
                     " unknown geometry type.");
   }
@@ -1250,7 +1234,6 @@ CubicDiscont2DFECollection::FiniteElementForGeometry(
      case Geometry::TRIANGLE:    return &TriangleFE;
      case Geometry::SQUARE:      return &QuadrilateralFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("CubicDiscont2DFECollection: unknown geometry type.");
   }
   return &TriangleFE; // Make some compilers happy
@@ -1288,7 +1271,6 @@ LinearNonConf3DFECollection::FiniteElementForGeometry(
      case Geometry::TETRAHEDRON: return &TetrahedronFE;
      case Geometry::CUBE:        return &ParallelepipedFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("LinearNonConf3DFECollection: unknown geometry type.");
   }
   return &TriangleFE; // Make some compilers happy
@@ -1329,7 +1311,6 @@ Const3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::PRISM:       return &WedgeFE;
      case Geometry::PYRAMID:     return &PyramidFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("Const3DFECollection: unknown geometry type.");
   }
   return &TetrahedronFE; // Make some compilers happy
@@ -1371,7 +1352,6 @@ LinearDiscont3DFECollection::FiniteElementForGeometry(
      case Geometry::PRISM:       return &WedgeFE;
      case Geometry::CUBE:        return &ParallelepipedFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("LinearDiscont3DFECollection: unknown geometry type.");
   }
   return &TetrahedronFE; // Make some compilers happy
@@ -1411,7 +1391,6 @@ QuadraticDiscont3DFECollection::FiniteElementForGeometry(
      case Geometry::TETRAHEDRON: return &TetrahedronFE;
      case Geometry::CUBE:        return &ParallelepipedFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("QuadraticDiscont3DFECollection: unknown geometry type.");
   }
   return &TetrahedronFE; // Make some compilers happy
@@ -1453,7 +1432,6 @@ RefinedLinearFECollection::FiniteElementForGeometry(
      case Geometry::TETRAHEDRON: return &TetrahedronFE;
      case Geometry::CUBE:        return &ParallelepipedFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RefinedLinearFECollection: unknown geometry type.");
   }
   return &SegmentFE; // Make some compilers happy
@@ -1494,7 +1472,6 @@ ND1_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::PRISM:       return &WedgeFE;
      case Geometry::PYRAMID:     return &PyramidFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("ND1_3DFECollection: unknown geometry type.");
   }
   return &HexahedronFE; // Make some compilers happy
@@ -1544,7 +1521,6 @@ RT0_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::PRISM:       return &WedgeFE;
      case Geometry::PYRAMID:     return &PyramidFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RT0_3DFECollection: unknown geometry type.");
   }
   return &HexahedronFE; // Make some compilers happy
@@ -1594,7 +1570,6 @@ RT1_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::SQUARE:      return &QuadrilateralFE;
      case Geometry::CUBE:        return &HexahedronFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("RT1_3DFECollection: unknown geometry type.");
   }
   return &HexahedronFE; // Make some compilers happy
@@ -1956,7 +1931,6 @@ H1_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
   }
   else
   {
-      if (error_mode == RETURN_NULL) { return nullptr; }
      MFEM_ABORT("H1 Pyramid basis functions are not yet supported "
                 "for order > 1.");
      return NULL;
@@ -2337,7 +2311,6 @@ L2_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
   }
   else
   {
-      if (error_mode == RETURN_NULL) { return nullptr; }
      MFEM_ABORT("L2 Pyramid basis functions are not yet supported "
                 "for order > 0.");
      return NULL;
@@ -2593,7 +2566,6 @@ RT_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
   }
   else
   {
-      if (error_mode == RETURN_NULL) { return nullptr; }
      MFEM_ABORT("RT Pyramid basis functions are not yet supported "
                 "for order > 0.");
      return NULL;
@@ -2879,7 +2851,6 @@ ND_FECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
   }
   else
   {
-      if (error_mode == RETURN_NULL) { return nullptr; }
      MFEM_ABORT("ND Pyramid basis functions are not yet supported "
                 "for order > 1.");
      return NULL;
@@ -3482,7 +3453,6 @@ NURBSFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
      case Geometry::SQUARE:      return QuadrilateralFE;
      case Geometry::CUBE:        return ParallelepipedFE;
      default:
-         if (error_mode == RETURN_NULL) { return nullptr; }
         mfem_error ("NURBSFECollection: unknown geometry type.");
   }
   return SegmentFE; // Make some compilers happy
@@ -233,19 +233,6 @@ protected:
   void InitVarOrder(int p) const;

   mutable Array<FiniteElementCollection*> var_orders;
-
-   /// How to treat errors in FiniteElementForGeometry() calls.
-   enum ErrorMode
-   {
-      RETURN_NULL,      ///< Return NULL on errors
-      RAISE_MFEM_ERROR  /**< Raise an MFEM error (default in base class).
-                             Sub-classes can ignore this and return NULL. */
-   };
-
-   /// How to treat errors in FiniteElementForGeometry() calls.
-   /** The typical error in derived classes is that no FiniteElement is defined
-       for the given Geometry, or the input is not a valid Geometry. */
-   mutable ErrorMode error_mode = RAISE_MFEM_ERROR;
 };

 /// Arbitrary order H1-conforming (continuous) finite elements.
@@ -1317,7 +1317,7 @@ const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
      }
      else
      {
-         res = new H1FaceRestriction(*this, e_ordering, type);
+         res = new H1_ND_RT_FaceRestriction(*this, e_ordering, type);
      }
      L2F[key] = res;
      return res;
@@ -1958,7 +1958,7 @@ FiniteElementSpace::DerefinementOperator::DerefinementOperator(
         DenseMatrix &lM = localM[g](mi[s]);
         DenseMatrix &lR = localR[g](lR_offset+s);
         MultAtB(lP, lM, lR); // lR = lP^T lM
-         mfem::AddMult(lR, lP, lPtMP); // lPtMP += lP^T lM lP
+         AddMult(lR, lP, lPtMP); // lPtMP += lP^T lM lP
      }
      DenseMatrixInverse lPtMP_inv(lPtMP);
      for (int s = 0; s < nm; s++)
@@ -2005,7 +2005,7 @@ void FiniteElementSpace::DerefinementOperator
         x.GetSubVector(f_vdofs, loc_x);
         loc_x_mat.UseExternalData(loc_x.GetData(), f_vdofs.Size()/fine_vdim,
                                   fine_vdim);
-         mfem::AddMult(lR, loc_x_mat, loc_y_mat);
+         AddMult(lR, loc_x_mat, loc_y_mat);
      }
      y.SetSubVector(c_vdofs, loc_y);
   }
@@ -2056,7 +2056,10 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
      GetLocalDerefinementMatrices(elem_geoms[i], localR[elem_geoms[i]]);
   }

-   SparseMatrix *R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim);
+   SparseMatrix *R = (elem_geoms.Size() != 1)
+                     ? new SparseMatrix(ndofs*vdim, old_ndofs*vdim) // variable row size
+                     : new SparseMatrix(ndofs*vdim, old_ndofs*vdim,
+                                        localR[elem_geoms[0]].SizeI());

   Array<int> mark(R->Height());
   mark = 0;
@@ -2066,7 +2069,6 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,

   MFEM_ASSERT(dtrans.embeddings.Size() == old_elem_dof->Size(), "");

-   bool is_dg = FEColl()->GetContType() == FiniteElementCollection::DISCONTINUOUS;
   int num_marked = 0;
   for (int k = 0; k < dtrans.embeddings.Size(); k++)
   {
@@ -2089,11 +2091,10 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
            int r = DofToVDof(dofs[i], vd);
            int m = (r >= 0) ? r : (-1 - r);

-            if (is_dg || !mark[m])
+            if (!mark[m])
            {
               lR.GetRow(i, row);
               R->SetRow(r, old_vdofs, row);
-
               mark[m] = 1;
               num_marked++;
            }
@@ -2101,11 +2102,8 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
      }
   }

-   if (!is_dg)
-   {
-      MFEM_VERIFY(num_marked == R->Height(),
-                  "internal error: not all rows of R were set.");
-   }
+   MFEM_VERIFY(num_marked == R->Height(),
+               "internal error: not all rows of R were set.");

   R->Finalize(); // no-op if fixed width
   return R;
@@ -3147,7 +3145,7 @@ const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
         break;
      case 3:
      default:
-         fe = fec->FiniteElementForGeometry(mesh->GetFaceGeometry(i));
+         fe = fec->FiniteElementForGeometry(mesh->GetFaceBaseGeometry(i));
   }

   if (NURBSext)
@@ -38,7 +38,7 @@ public:
   /// Construct an empty finite element space hierarchy. This is useful if the
   /// hierarchy is constructed by coarsening a fine space, rather than refining
   /// a coarse space.
-   FiniteElementSpaceHierarchy() = default;
+   FiniteElementSpaceHierarchy() { }

   /// @brief Constructs a space hierarchy with the given mesh and space on the
   /// coarsest level.
@@ -91,7 +91,6 @@ public:
 class ParFiniteElementSpaceHierarchy : public FiniteElementSpaceHierarchy
 {
 public:
-   ParFiniteElementSpaceHierarchy() = default;
   /// @brief Constructs a parallel space hierarchy with the given mesh and spaces
   /// on level zero.
   /** The ownership of the mesh and space may be transferred to the
@@ -1441,13 +1441,21 @@ void GridFunction::GetDerivative(int comp, int der_comp, GridFunction &der)
   }
 }

+
 void GridFunction::GetVectorGradientHat(
   ElementTransformation &T, DenseMatrix &gh) const
 {
-   const FiniteElement *FElem = fes->GetFE(T.ElementNo);
+   int elNo = T.ElementNo;
+   const FiniteElement *FElem = fes->GetFE(elNo);
   int dim = FElem->GetDim(), dof = FElem->GetDof();
+   Array<int> vdofs;
+   DofTransformation * doftrans = fes->GetElementVDofs(elNo, vdofs);
   Vector loc_data;
-   GetElementDofValues(T.ElementNo, loc_data);
+   GetSubVector(vdofs, loc_data);
+   if (doftrans)
+   {
+      doftrans->InvTransformPrimal(loc_data);
+   }
   // assuming scalar FE
   int vdim = fes->GetVDim();
   DenseMatrix dshape(dof, dim);
@@ -1652,7 +1660,6 @@ void GridFunction::GetGradient(ElementTransformation &T, Vector &grad) const
         const FiniteElement *fe = fes->GetFE(T.ElementNo);
         MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE,
                     "invalid FE map type");
-         MFEM_ASSERT(fes->GetVDim() == 1, "Defined for scalar functions.");
         int spaceDim = fes->GetMesh()->SpaceDimension();
         int dim = fe->GetDim(), dof = fe->GetDof();
         DenseMatrix dshape(dof, dim);
@@ -1721,8 +1728,13 @@ void GridFunction::GetGradients(ElementTransformation &tr,
   MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
   DenseMatrix dshape(fe->GetDof(), fe->GetDim());
   Vector lval, gh(fe->GetDim()), gcol;
-
-   GetElementDofValues(tr.ElementNo, lval);
+   Array<int> 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++)
   {
@@ -48,6 +48,8 @@ protected:

   void SaveSTLTri(std::ostream &out, double p1[], double p2[], double p3[]);

+   void GetVectorGradientHat(ElementTransformation &T, DenseMatrix &gh) const;
+
   // Project the delta coefficient without scaling and return the (local)
   // integral of the projection.
   void ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
@@ -327,34 +329,17 @@ public:

   void GetCurl(ElementTransformation &tr, Vector &curl) const;

-   /** @brief Gradient of a scalar function at a quadrature point.
-
-       @note It is assumed that the IntegrationPoint of interest has been
-       specified by ElementTransformation::SetIntPoint() before calling
-       GetGradient().
-
-       @note Can be used from a ParGridFunction when @a tr is an
-       ElementTransformation of a face-neighbor element and face-neighbor data
-       has been exchanged. */
   void GetGradient(ElementTransformation &tr, Vector &grad) const;

-   /// Extension of GetGradient(...) for a collection of IntegrationPoints.
   void GetGradients(ElementTransformation &tr, const IntegrationRule &ir,
                     DenseMatrix &grad) const;

-   /// Extension of GetGradient(...) for a collection of IntegrationPoints.
   void GetGradients(const int elem, const IntegrationRule &ir,
                     DenseMatrix &grad) const
   { GetGradients(*fes->GetElementTransformation(elem), ir, grad); }

-   /** @brief Compute the vector gradient with respect to the physical element
-       variable. */
   void GetVectorGradient(ElementTransformation &tr, DenseMatrix &grad) const;

-   /** @brief Compute the vector gradient with respect to the reference element
-       variable. */
-   void GetVectorGradientHat(ElementTransformation &T, DenseMatrix &gh) const;
-
   /** Compute \f$ (\int_{\Omega} (*this) \psi_i)/(\int_{\Omega} \psi_i) \f$,
       where \f$ \psi_i \f$ are the basis functions for the FE space of avgs.
       Both FE spaces should be scalar and on the same mesh. */
@@ -37,7 +37,7 @@ FindPointsGSLIB::FindPointsGSLIB()
     fec_map_lin(NULL),
     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
-     avgtype(AvgType::ARITHMETIC), bdr_tol(1e-8)
+     avgtype(AvgType::ARITHMETIC)
 {
   mesh_split.SetSize(4);
   ir_split.SetSize(4);
@@ -84,7 +84,7 @@ FindPointsGSLIB::FindPointsGSLIB(MPI_Comm comm_)
     fec_map_lin(NULL),
     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
-     avgtype(AvgType::ARITHMETIC), bdr_tol(1e-8)
+     avgtype(AvgType::ARITHMETIC)
 {
   mesh_split.SetSize(4);
   ir_split.SetSize(4);
@@ -223,12 +223,10 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
   // Set the element number and reference position to 0 for points not found
   for (int i = 0; i < points_cnt; i++)
   {
-      if (gsl_code[i] == 2 ||
-          (gsl_code[i] == 1 && gsl_dist(i) > bdr_tol))
+      if (gsl_code[i] == 2)
      {
         gsl_elem[i] = 0;
         for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
-         gsl_code[i] = 2;
      }
   }

@@ -573,7 +571,7 @@ void FindPointsGSLIB::GetNodalValues(const GridFunction *gf_in,
   const int pts_el = std::pow(dof_1D, dim);
   const int pts_cnt = NE_split_total * pts_el;
   node_vals.SetSize(vdim * pts_cnt);
-   node_vals = 0.0;
+   node_vals *= 0;

   int gsl_mesh_pt_index = 0;

@@ -1155,7 +1153,7 @@ void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
   distfint.SetSize(pts_cnt);
   if (!gfmax)
   {
-      distfint = 0.0;
+      distfint = 0.;
   }
   else
   {
@@ -1250,12 +1248,10 @@ void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
   // Set the element number and reference position to 0 for points not found
   for (int i = 0; i < points_cnt; i++)
   {
-      if (gsl_code[i] == 2 ||
-          (gsl_code[i] == 1 && gsl_dist(i) > bdr_tol))
+      if (gsl_code[i] == 2)
      {
         gsl_elem[i] = 0;
         for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
-         gsl_code[i] = 2;
      }
   }

@@ -38,11 +38,6 @@ namespace mfem
 *     coordinates inside the element that each point is located in. gslib also
 *     returns a code that indicates whether the point was found inside an
 *     element, on element border, or not found in the domain.
- *     For points returned as found on `element border`, the point is either
- *     on an element edge/face or near the domain boundary, and gslib also
- *     returns a distance to the border. Points near (but outside) the domain
- *     boundary must then be marked as not found using the distance returned
- *     by gslib.
 *
 *  3. Interpolate - Interpolates any grid function at the points found using 2.
 *
@@ -75,8 +70,6 @@ protected:
   Array<int> split_element_map;
   Array<int> split_element_index;
   int        NE_split_total;
-   // Tolerance to ignore points just outside elements at the boundary.
-   double     bdr_tol;

   /// Use GSLIB for communication and interpolation
   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out);
@@ -188,14 +181,6 @@ public:
      default_interp_value = interp_value_;
   }

-   /// Set the tolerance for detecting points outside the 'curvilinear' boundary
-   /// that gslib may return as found on the boundary. Points found on boundary
-   /// with distance greater than @ bdr_tol are marked as not found.
-   virtual void SetDistanceToleranceForPointsFoundOnBoundary(double bdr_tol_)
-   {
-      bdr_tol = bdr_tol_;
-   }
-
   /** Cleans up memory allocated internally by gslib.
       Note that in parallel, this must be called before MPI_Finalize(), as it
       calls MPI_Comm_free() for internal gslib communicators. */
@@ -101,7 +101,7 @@ void LinearForm::AddInteriorFaceIntegrator(LinearFormIntegrator *lfi)
   interior_face_integs.Append(lfi);
 }

-bool LinearForm::SupportsDevice()
+bool LinearForm::SupportsDevice() const
 {
   // return false for NURBS meshes, so we don’t convert it to non-NURBS
   // through Assemble, AssembleDevice, GetGeometricFactors and EnsureNodes
@@ -203,7 +203,7 @@ public:
   void Assemble();

   /// Return true if assembly on device is supported, false otherwise.
-   virtual bool SupportsDevice();
+   virtual bool SupportsDevice() const;

   /// Assembles delta functions of the linear form
   void AssembleDelta();
@@ -31,7 +31,7 @@ protected:
 public:

   /// Method probing for assembly on device
-   virtual bool SupportsDevice() { return false; }
+   virtual bool SupportsDevice() const { return false; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -121,7 +121,7 @@ public:
   DomainLFIntegrator(Coefficient &QF, const IntegrationRule *ir)
      : DeltaLFIntegrator(QF, ir), Q(QF), oa(1), ob(1) { }

-   virtual bool SupportsDevice() { return true; }
+   virtual bool SupportsDevice() const { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -154,7 +154,7 @@ public:
   DomainLFGradIntegrator(VectorCoefficient &QF)
      : DeltaLFIntegrator(QF), Q(QF) { }

-   virtual bool SupportsDevice() { return true; }
+   virtual bool SupportsDevice() const { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -187,7 +187,7 @@ public:
   BoundaryLFIntegrator(Coefficient &QG, int a = 1, int b = 1)
      : Q(QG), oa(a), ob(b) { }

-   virtual bool SupportsDevice() { return true; }
+   virtual bool SupportsDevice() const { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -217,7 +217,7 @@ public:
   BoundaryNormalLFIntegrator(VectorCoefficient &QG, int a = 1, int b = 1)
      : Q(QG), oa(a), ob(b) { }

-   virtual bool SupportsDevice() { return true; }
+   virtual bool SupportsDevice() const { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -262,7 +262,7 @@ public:
   VectorDomainLFIntegrator(VectorCoefficient &QF)
      : DeltaLFIntegrator(QF), Q(QF) { }

-   virtual bool SupportsDevice() { return true; }
+   virtual bool SupportsDevice() const { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -296,7 +296,7 @@ public:
   VectorDomainLFGradIntegrator(VectorCoefficient &QF)
      : DeltaLFIntegrator(QF), Q(QF) { }

-   virtual bool SupportsDevice() override { return true; }
+   virtual bool SupportsDevice() const override { return true; }

   /// Method defining assembly on device
   virtual void AssembleDevice(const FiniteElementSpace &fes,
@@ -456,6 +456,12 @@ public:
                                       Vector &elvect);

   using LinearFormIntegrator::AssembleRHSElementVect;
+
+   virtual bool SupportsDevice() const { return true; }
+
+   virtual void AssembleDevice(const FiniteElementSpace &fes,
+                               const Array<int> &markers,
+                               Vector &b);
 };

 /// Class for boundary integration \f$ L(v) = (n \times f, v) \f$
@@ -0,0 +1,180 @@
+// Copyright (c) 2010-2022, 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"
+#include "../fem/kernels.hpp"
+#include "../general/forall.hpp"
+
+namespace mfem
+{
+
+template<int T_D1D = 0, int T_Q1D = 0> static
+void BFLFEvalAssemble2D(const int nbe, const int d, const int q,
+                        const int *markers, const double *b,
+                        const double *weights, const Vector &coeff, double *y)
+{
+   const auto F = coeff.Read();
+   const auto M = Reshape(markers, nbe);
+   const auto B = Reshape(b, q, d);
+   const auto W = Reshape(weights, q);
+   const bool const_coeff = coeff.Size() == 1;
+   const auto C = const_coeff ? Reshape(F,1,1) : Reshape(F,q,nbe);
+   auto Y = Reshape(y, d, nbe);
+
+   MFEM_FORALL(e, nbe,
+   {
+      if (M(e) == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : MAX_Q1D;
+      double QQ[Q];
+
+      for (int qx = 0; qx < q; ++qx)
+      {
+         const double coeff_val = const_coeff ? C(0,0) : C(qx,e);
+         QQ[qx] = W(qx) * coeff_val;
+      }
+      for (int dx = 0; dx < d; ++dx)
+      {
+         double u = 0;
+         for (int qx = 0; qx < q; ++qx) { u += QQ[qx] * B(qx,dx); }
+         Y(dx,e) += u;
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0> static
+void BFLFEvalAssemble3D(const int nbe, const int d, const int q,
+                        const int *markers, const double *b,
+                        const double *weights, const Vector &coeff, double *y)
+{
+   const auto F = coeff.Read();
+   const auto M = Reshape(markers, nbe);
+   const auto B = Reshape(b, q, d);
+   const auto W = Reshape(weights, q, q);
+   const bool const_coeff = coeff.Size() == 1;
+   const auto C = const_coeff ? Reshape(F,1,1,1) : Reshape(F,q,q,nbe);
+   auto Y = Reshape(y, d, d, nbe);
+
+   MFEM_FORALL_2D(e, nbe, q, q, 1,
+   {
+      if (M(e) == 0) { return; } // ignore
+
+      constexpr int Q = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int D = T_D1D ? T_D1D : MAX_D1D;
+
+      MFEM_SHARED double sBt[Q*D];
+      MFEM_SHARED double sQQ[Q*Q];
+      MFEM_SHARED double sQD[Q*D];
+
+      const DeviceMatrix Bt(sBt, d, q);
+      kernels::internal::LoadB<D,Q>(d, q, B, sBt);
+
+      const DeviceMatrix QQ(sQQ, q, q);
+      const DeviceMatrix QD(sQD, q, d);
+
+      MFEM_FOREACH_THREAD(x,x,q)
+      {
+         MFEM_FOREACH_THREAD(y,y,q)
+         {
+            const double coeff_val = const_coeff ? C(0,0,0) : C(x,y,e);
+            QQ(y,x) = W(x,y) * coeff_val;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,q)
+      {
+         MFEM_FOREACH_THREAD(dx,x,d)
+         {
+            double u = 0.0;
+            for (int qx = 0; qx < q; ++qx) { u += QQ(qy,qx) * Bt(dx,qx); }
+            QD(qy,dx) = u;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,d)
+      {
+         MFEM_FOREACH_THREAD(dx,x,d)
+         {
+            double u = 0.0;
+            for (int qy = 0; qy < q; ++qy) { u += QD(qy,dx) * Bt(dy,qy); }
+            Y(dx,dy,e) += u;
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+static void BFLFEvalAssemble(const FiniteElementSpace &fes,
+                             const IntegrationRule &ir,
+                             const Array<int> &markers,
+                             const Vector &coeff,
+                             Vector &y)
+{
+   Mesh &mesh = *fes.GetMesh();
+   const int dim = mesh.Dimension();
+   const FiniteElement &el = *fes.GetBE(0);
+   const DofToQuad &maps = el.GetDofToQuad(ir, DofToQuad::TENSOR);
+   const int d = maps.ndof, q = maps.nqpt;
+   auto ker = (dim == 2) ? BFLFEvalAssemble2D<> : BFLFEvalAssemble3D<>;
+
+   if (dim==2)
+   {
+      if (d==1 && q==1) { ker=BFLFEvalAssemble2D<1,1>; }
+      if (d==2 && q==2) { ker=BFLFEvalAssemble2D<2,2>; }
+      if (d==3 && q==3) { ker=BFLFEvalAssemble2D<3,3>; }
+      if (d==4 && q==4) { ker=BFLFEvalAssemble2D<4,4>; }
+      if (d==5 && q==5) { ker=BFLFEvalAssemble2D<5,5>; }
+      if (d==2 && q==3) { ker=BFLFEvalAssemble2D<2,3>; }
+      if (d==3 && q==4) { ker=BFLFEvalAssemble2D<3,4>; }
+      if (d==4 && q==5) { ker=BFLFEvalAssemble2D<4,5>; }
+      if (d==5 && q==6) { ker=BFLFEvalAssemble2D<5,6>; }
+   }
+
+   if (dim==3)
+   {
+      if (d==1 && q==1) { ker=BFLFEvalAssemble3D<1,1>; }
+      if (d==2 && q==2) { ker=BFLFEvalAssemble3D<2,2>; }
+      if (d==3 && q==3) { ker=BFLFEvalAssemble3D<3,3>; }
+      if (d==4 && q==4) { ker=BFLFEvalAssemble3D<4,4>; }
+      if (d==5 && q==5) { ker=BFLFEvalAssemble3D<5,5>; }
+      if (d==2 && q==3) { ker=BFLFEvalAssemble3D<2,3>; }
+      if (d==3 && q==4) { ker=BFLFEvalAssemble3D<3,4>; }
+      if (d==4 && q==5) { ker=BFLFEvalAssemble3D<4,5>; }
+      if (d==5 && q==6) { ker=BFLFEvalAssemble3D<5,6>; }
+   }
+
+   MFEM_VERIFY(ker, "No kernel ndof " << d << " nqpt " << q);
+
+   const int nbe = fes.GetMesh()->GetNFbyType(FaceType::Boundary);
+   const int *M = markers.Read();
+   const double *B = maps.B.Read();
+   const double *W = ir.GetWeights().Read();
+   double *Y = y.ReadWrite();
+   ker(nbe, d, q, M, B, W, coeff, Y);
+}
+
+void VectorFEBoundaryFluxLFIntegrator::AssembleDevice(
+   const FiniteElementSpace &fes,
+   const Array<int> &markers,
+   Vector &b)
+{
+   const FiniteElement &fe = *fes.GetBE(0);
+   const int qorder = oa * fe.GetOrder() + ob;
+   const Geometry::Type gtype = fe.GetGeomType();
+   const IntegrationRule &ir = IntRule ? *IntRule : IntRules.Get(gtype, qorder);
+   Mesh &mesh = *fes.GetMesh();
+
+   FaceQuadratureSpace qs(mesh, ir, FaceType::Boundary);
+   CoefficientVector coeff(F, qs, CoefficientStorage::COMPRESSED);
+   BFLFEvalAssemble(fes, ir, markers, coeff, b);
+}
+
+} // namespace mfem
@@ -14,26 +14,41 @@
 namespace mfem
 {

-MultigridBase::MultigridBase()
-   : cycleType(CycleType::VCYCLE), preSmoothingSteps(1), postSmoothingSteps(1),
-     nrhs(0)
+Multigrid::Multigrid()
+   : cycleType(CycleType::VCYCLE), preSmoothingSteps(1), postSmoothingSteps(1)
 {}

-MultigridBase::MultigridBase(const Array<Operator*>& operators_,
-                             const Array<Solver*>& smoothers_,
-                             const Array<bool>& ownedOperators_,
-                             const Array<bool>& ownedSmoothers_)
-   : Solver(operators_.Last()->Height(), operators_.Last()->Width()),
-     cycleType(CycleType::VCYCLE), preSmoothingSteps(1), postSmoothingSteps(1),
-     nrhs(0)
+Multigrid::Multigrid(const Array<Operator*>& operators_,
+                     const Array<Solver*>& smoothers_,
+                     const Array<Operator*>& prolongations_,
+                     const Array<bool>& ownedOperators_,
+                     const Array<bool>& ownedSmoothers_,
+                     const Array<bool>& ownedProlongations_)
+   : Solver(operators_.Last()->NumRows()), cycleType(CycleType::VCYCLE),
+     preSmoothingSteps(1), postSmoothingSteps(1),
+     X(operators_.Size()), Y(X.Size()), R(X.Size()), Z(X.Size())
 {
   operators_.Copy(operators);
   smoothers_.Copy(smoothers);
+   prolongations_.Copy(prolongations);
   ownedOperators_.Copy(ownedOperators);
   ownedSmoothers_.Copy(ownedSmoothers);
+   ownedProlongations_.Copy(ownedProlongations);
+
+   for (int level = 0; level < operators.Size(); ++level)
+   {
+      X[level] = new Vector(operators[level]->NumRows());
+      *X[level] = 0.0;
+      Y[level] = new Vector(operators[level]->NumRows());
+      *Y[level] = 0.0;
+      R[level] = new Vector(operators[level]->NumRows());
+      *R[level] = 0.0;
+      Z[level] = new Vector(operators[level]->NumRows());
+      *Z[level] = 0.0;
+   }
 }

-MultigridBase::~MultigridBase()
+Multigrid::~Multigrid()
 {
   for (int i = 0; i < operators.Size(); ++i)
   {
@@ -45,210 +60,12 @@ MultigridBase::~MultigridBase()
      {
         delete smoothers[i];
      }
-   }
-   EraseVectors();
-}
-
-void MultigridBase::InitVectors() const
-{
-   if (X.NumRows() > 0 && X.NumCols() > 0) { EraseVectors(); }
-   const int M = NumLevels();
-   X.SetSize(M, nrhs);
-   Y.SetSize(M, nrhs);
-   R.SetSize(M, nrhs);
-   Z.SetSize(M, nrhs);
-   for (int i = 0; i < X.NumRows(); ++i)
-   {
-      const int n = operators[i]->Height();
-      for (int j = 0; j < X.NumCols(); ++j)
-      {
-         X(i, j) = new Vector(n);
-         Y(i, j) = new Vector(n);
-         R(i, j) = new Vector(n);
-         Z(i, j) = new Vector(n);
-      }
-   }
-}
-
-void MultigridBase::EraseVectors() const
-{
-   for (int i = 0; i < X.NumRows(); ++i)
-   {
-      for (int j = 0; j < X.NumCols(); ++j)
-      {
-         delete X(i, j);
-         delete Y(i, j);
-         delete R(i, j);
-         delete Z(i, j);
-      }
-   }
-}
-
-void MultigridBase::AddLevel(Operator* op, Solver* smoother,
-                             bool ownOperator, bool ownSmoother)
-{
-   height = op->Height();
-   width = op->Width();
-   operators.Append(op);
-   smoothers.Append(smoother);
-   ownedOperators.Append(ownOperator);
-   ownedSmoothers.Append(ownSmoother);
-}
-
-void MultigridBase::SetCycleType(CycleType cycleType_, int preSmoothingSteps_,
-                                 int postSmoothingSteps_)
-{
-   cycleType = cycleType_;
-   preSmoothingSteps = preSmoothingSteps_;
-   postSmoothingSteps = postSmoothingSteps_;
-}
-
-void MultigridBase::Mult(const Vector& x, Vector& y) const
-{
-   Array<const Vector*> X_(1);
-   Array<Vector*> Y_(1);
-   X_[0] = &x;
-   Y_[0] = &y;
-   ArrayMult(X_, Y_);
-}
-
-void MultigridBase::ArrayMult(const Array<const Vector*>& X_,
-                              Array<Vector*>& Y_) const
-{
-   MFEM_ASSERT(operators.Size() > 0,
-               "Multigrid solver does not have operators set!");
-   MFEM_ASSERT(X_.Size() == Y_.Size(),
-               "Number of columns mismatch in MultigridBase::Mult!");
-   if (iterative_mode)
-   {
-      MFEM_WARNING("Multigrid solver does not use iterative_mode and ignores "
-                   "the initial guess!");
+      delete X[i];
+      delete Y[i];
+      delete R[i];
+      delete Z[i];
   }

-   // Add capacity as necessary
-   nrhs = X_.Size();
-   if (X.NumCols() < nrhs) { InitVectors(); }
-
-   // Perform a single cycle
-   const int M = NumLevels();
-   for (int j = 0; j < nrhs; ++j)
-   {
-      MFEM_ASSERT(X_[j] && Y_[j], "Missing Vector in MultigridBase::Mult!");
-      *X(M - 1, j) = *X_[j];
-      *Y(M - 1, j) = 0.0;
-   }
-   Cycle(M - 1);
-   for (int j = 0; j < nrhs; ++j)
-   {
-      *Y_[j] = *Y(M - 1, j);
-   }
-}
-
-void MultigridBase::SmoothingStep(int level, bool zero, bool transpose) const
-{
-   // y = y + S (x - A y) or y = y + S^T (x - A y)
-   if (zero)
-   {
-      Array<Vector *> X_(X[level], nrhs), Y_(Y[level], nrhs);
-      GetSmootherAtLevel(level)->ArrayMult(X_, Y_);
-   }
-   else
-   {
-      Array<Vector *> Y_(Y[level], nrhs), R_(R[level], nrhs),
-            Z_(Z[level], nrhs);
-      for (int j = 0; j < nrhs; ++j)
-      {
-         *R_[j] = *X(level, j);
-      }
-      GetOperatorAtLevel(level)->ArrayAddMult(Y_, R_, -1.0);
-      if (transpose)
-      {
-         GetSmootherAtLevel(level)->ArrayMultTranspose(R_, Z_);
-      }
-      else
-      {
-         GetSmootherAtLevel(level)->ArrayMult(R_, Z_);
-      }
-      for (int j = 0; j < nrhs; ++j)
-      {
-         *Y_[j] += *Z_[j];
-      }
-   }
-}
-
-void MultigridBase::Cycle(int level) const
-{
-   // Coarse solve
-   if (level == 0)
-   {
-      SmoothingStep(0, true, false);
-      return;
-   }
-
-   // Pre-smooth
-   for (int i = 0; i < preSmoothingSteps; ++i)
-   {
-      SmoothingStep(level, (cycleType == CycleType::VCYCLE && i == 0), false);
-   }
-
-   // Compute residual and restrict
-   {
-      Array<Vector *> Y_(Y[level], nrhs), R_(R[level], nrhs),
-            X_(X[level - 1], nrhs);
-      for (int j = 0; j < nrhs; ++j)
-      {
-         *R_[j] = *X(level, j);
-      }
-      GetOperatorAtLevel(level)->ArrayAddMult(Y_, R_, -1.0);
-      GetProlongationAtLevel(level - 1)->ArrayMultTranspose(R_, X_);
-      for (int j = 0; j < nrhs; ++j)
-      {
-         *Y(level - 1, j) = 0.0;
-      }
-   }
-
-   // Corrections
-   Cycle(level - 1);
-   if (cycleType == CycleType::WCYCLE)
-   {
-      Cycle(level - 1);
-   }
-
-   // Prolongate and add
-   {
-      Array<Vector *> Y_(Y[level - 1], nrhs), Z_(Z[level], nrhs);
-      GetProlongationAtLevel(level - 1)->ArrayMult(Y_, Z_);
-      for (int j = 0; j < nrhs; ++j)
-      {
-         *Y(level, j) += *Z_[j];
-      }
-   }
-
-   // Post-smooth
-   for (int i = 0; i < postSmoothingSteps; ++i)
-   {
-      SmoothingStep(level, false, true);
-   }
-}
-
-Multigrid::Multigrid()
-   : MultigridBase()
-{}
-
-Multigrid::Multigrid(const Array<Operator*>& operators_,
-                     const Array<Solver*>& smoothers_,
-                     const Array<Operator*>& prolongations_,
-                     const Array<bool>& ownedOperators_,
-                     const Array<bool>& ownedSmoothers_,
-                     const Array<bool>& ownedProlongations_)
-   : MultigridBase(operators_, smoothers_, ownedOperators_, ownedSmoothers_)
-{
-   prolongations_.Copy(prolongations);
-   ownedProlongations_.Copy(ownedProlongations);
-}
-
-Multigrid::~Multigrid()
-{
   for (int i = 0; i < prolongations.Size(); ++i)
   {
      if (ownedProlongations[i])
@@ -256,12 +73,158 @@ Multigrid::~Multigrid()
         delete prolongations[i];
      }
   }
+
+   operators.DeleteAll();
+   smoothers.DeleteAll();
+   prolongations.DeleteAll();
+   X.DeleteAll();
+   Y.DeleteAll();
+   R.DeleteAll();
+   Z.DeleteAll();
 }

-GeometricMultigrid::
-GeometricMultigrid(const FiniteElementSpaceHierarchy& fespaces_)
-   : MultigridBase(), fespaces(fespaces_)
-{}
+void Multigrid::AddLevel(Operator* opr, Solver* smoother, bool ownOperator,
+                         bool ownSmoother)
+{
+   operators.Append(opr);
+   smoothers.Append(smoother);
+   ownedOperators.Append(ownOperator);
+   ownedSmoothers.Append(ownSmoother);
+   width = opr->Width();
+   height = opr->Height();
+
+   X.Append(new Vector(height));
+   *X.Last() = 0.0;
+   Y.Append(new Vector(height));
+   *Y.Last() = 0.0;
+   R.Append(new Vector(height));
+   *R.Last() = 0.0;
+   Z.Append(new Vector(height));
+   *Z.Last() = 0.0;
+}
+
+int Multigrid::NumLevels() const { return operators.Size(); }
+
+int Multigrid::GetFinestLevelIndex() const { return NumLevels() - 1; }
+
+const Operator* Multigrid::GetOperatorAtLevel(int level) const
+{
+   return operators[level];
+}
+
+Operator* Multigrid::GetOperatorAtLevel(int level)
+{
+   return operators[level];
+}
+
+const Operator* Multigrid::GetOperatorAtFinestLevel() const
+{
+   return GetOperatorAtLevel(operators.Size() - 1);
+}
+
+Operator* Multigrid::GetOperatorAtFinestLevel()
+{
+   return GetOperatorAtLevel(operators.Size() - 1);
+}
+
+Solver* Multigrid::GetSmootherAtLevel(int level) const
+{
+   return smoothers[level];
+}
+
+Solver* Multigrid::GetSmootherAtLevel(int level)
+{
+   return smoothers[level];
+}
+
+void Multigrid::SetCycleType(CycleType cycleType_, int preSmoothingSteps_,
+                             int postSmoothingSteps_)
+{
+   cycleType = cycleType_;
+   preSmoothingSteps = preSmoothingSteps_;
+   postSmoothingSteps = postSmoothingSteps_;
+}
+
+void Multigrid::Mult(const Vector& x, Vector& y) const
+{
+   MFEM_ASSERT(NumLevels() > 0, "");
+   *X.Last() = x;
+   *Y.Last() = 0.0;
+   Cycle(GetFinestLevelIndex());
+   y = *Y.Last();
+}
+
+void Multigrid::SetOperator(const Operator& op)
+{
+   MFEM_ABORT("SetOperator not supported in Multigrid");
+}
+
+void Multigrid::SmoothingStep(int level, bool transpose) const
+{
+   GetOperatorAtLevel(level)->Mult(*Y[level], *R[level]); // r = A x
+   subtract(*X[level], *R[level], *R[level]);             // r = b - A x
+   if (transpose)
+   {
+      GetSmootherAtLevel(level)->MultTranspose(*R[level], *Z[level]); // z = S r
+   }
+   else
+   {
+      GetSmootherAtLevel(level)->Mult(*R[level], *Z[level]); // z = S r
+   }
+   add(*Y[level], 1.0, *Z[level], *Y[level]);             // x = x + S (b - A x)
+}
+
+void Multigrid::Cycle(int level) const
+{
+   if (level == 0)
+   {
+      GetSmootherAtLevel(level)->Mult(*X[level], *Y[level]);
+      return;
+   }
+
+   for (int i = 0; i < preSmoothingSteps; i++)
+   {
+      SmoothingStep(level, false);
+   }
+
+   // Compute residual
+   GetOperatorAtLevel(level)->Mult(*Y[level], *R[level]);
+   subtract(*X[level], *R[level], *R[level]);
+
+   // Restrict residual
+   GetProlongationAtLevel(level - 1)->MultTranspose(*R[level], *X[level - 1]);
+
+   // Init zeros
+   *Y[level - 1] = 0.0;
+
+   // Corrections
+   int corrections = 1;
+   if (cycleType == CycleType::WCYCLE)
+   {
+      corrections = 2;
+   }
+   for (int correction = 0; correction < corrections; ++correction)
+   {
+      Cycle(level - 1);
+   }
+
+   // Prolongate
+   GetProlongationAtLevel(level - 1)->Mult(*Y[level - 1], *R[level]);
+
+   // Add update
+   *Y[level] += *R[level];
+
+   // Post-smooth
+   for (int i = 0; i < postSmoothingSteps; i++)
+   {
+      SmoothingStep(level, true);
+   }
+}
+
+const Operator* Multigrid::GetProlongationAtLevel(int level) const
+{
+   return prolongations[level];
+}

 GeometricMultigrid::~GeometricMultigrid()
 {
@@ -269,10 +232,15 @@ GeometricMultigrid::~GeometricMultigrid()
   {
      delete bfs[i];
   }
+
+   bfs.DeleteAll();
+
   for (int i = 0; i < essentialTrueDofs.Size(); ++i)
   {
      delete essentialTrueDofs[i];
   }
+
+   essentialTrueDofs.DeleteAll();
 }

 void GeometricMultigrid::FormFineLinearSystem(Vector& x, Vector& b,
@@ -288,4 +256,9 @@ void GeometricMultigrid::RecoverFineFEMSolution(const Vector& X,
   bfs.Last()->RecoverFEMSolution(X, b, x);
 }

+const Operator* GeometricMultigrid::GetProlongationAtLevel(int level) const
+{
+   return fespaces.GetProlongationAtLevel(level);
+}
+
 } // namespace mfem
@@ -21,8 +21,8 @@
 namespace mfem
 {

-/// Abstract base class for Multigrid solvers
-class MultigridBase : public Solver
+/// Multigrid solver class
+class Multigrid : public Solver
 {
 public:
   enum class CycleType
@@ -34,118 +34,29 @@ public:
 protected:
   Array<Operator*> operators;
   Array<Solver*> smoothers;
+   Array<Operator*> prolongations;
+
   Array<bool> ownedOperators;
   Array<bool> ownedSmoothers;
+   Array<bool> ownedProlongations;

   CycleType cycleType;
   int preSmoothingSteps;
   int postSmoothingSteps;

-   mutable Array2D<Vector*> X, Y, R, Z;
-   mutable int nrhs;
+   mutable Array<Vector*> X;
+   mutable Array<Vector*> Y;
+   mutable Array<Vector*> R;
+   mutable Array<Vector*> Z;

 public:
-   /// Constructs an empty multigrid hierarchy
-   MultigridBase();
-
-   /// Constructs a multigrid hierarchy from the given inputs
-   /** Inputs include operators and smoothers on all levels, and ownership of
-       the given operators and smoothers */
-   MultigridBase(const Array<Operator*>& operators_,
-                 const Array<Solver*>& smoothers_,
-                 const Array<bool>& ownedOperators_,
-                 const Array<bool>& ownedSmoothers_);
-
-   /// Destructor
-   virtual ~MultigridBase();
-
-   /// Adds a level to the multigrid operator hierarchy
-   /** The ownership of the operators and solvers/smoothers may be transferred
-       to the Multigrid by setting the according boolean variables */
-   void AddLevel(Operator* op, Solver* smoother, bool ownOperator,
-                 bool ownSmoother);
-
-   /// Returns the number of levels
-   int NumLevels() const { return operators.Size(); }
-
-   /// Returns the index of the finest level
-   int GetFinestLevelIndex() const { return NumLevels() - 1; }
-
-   /// Returns operator at given level
-   const Operator* GetOperatorAtLevel(int level) const
-   {
-      return operators[level];
-   }
-   Operator* GetOperatorAtLevel(int level)
-   {
-      return operators[level];
-   }
-
-   /// Returns operator at finest level
-   const Operator* GetOperatorAtFinestLevel() const
-   {
-      return GetOperatorAtLevel(GetFinestLevelIndex());
-   }
-   Operator* GetOperatorAtFinestLevel()
-   {
-      return GetOperatorAtLevel(GetFinestLevelIndex());
-   }
-
-   /// Returns smoother at given level
-   const Solver* GetSmootherAtLevel(int level) const
-   {
-      return smoothers[level];
-   }
-   Solver* GetSmootherAtLevel(int level)
-   {
-      return smoothers[level];
-   }
-
-   /// Set cycle type and number of pre- and post-smoothing steps used by Mult
-   void SetCycleType(CycleType cycleType_, int preSmoothingSteps_,
-                     int postSmoothingSteps_);
-
-   /// Application of the multigrid as a preconditioner
-   virtual void Mult(const Vector& x, Vector& y) const override;
-   virtual void ArrayMult(const Array<const Vector*>& X_,
-                          Array<Vector*>& Y_) const override;
-
-   /// Not supported for multigrid
-   virtual void SetOperator(const Operator& op) override
-   {
-      MFEM_ABORT("SetOperator is not supported in Multigrid!");
-   }
-
-private:
-   /// Application of a multigrid cycle at particular level
-   void Cycle(int level) const;
-
-   /// Application of a pre-/post-smoothing step at particular level
-   void SmoothingStep(int level, bool zero, bool transpose) const;
-
-   /// Allocate or destroy temporary storage
-   void InitVectors() const;
-   void EraseVectors() const;
-
-   /// Returns prolongation operator at given level
-   virtual const Operator* GetProlongationAtLevel(int level) const = 0;
-};
-
-/// Multigrid solver class
-class Multigrid : public MultigridBase
-{
-protected:
-   Array<Operator*> prolongations;
-   Array<bool> ownedProlongations;
-
-public:
-   /// Constructs an empty multigrid hierarchy
+   /// Constructs an empty multigrid hierarchy.
   Multigrid();

-   /// Constructs a multigrid hierarchy from the given inputs
+   /// Constructs a multigrid hierarchy from the given inputs.
   /** Inputs include operators and smoothers on all levels, prolongation
       operators that go from coarser to finer levels, and ownership of the
-       given operators, smoothers, and prolongations */
+       given operators, smoothers, and prolongations. */
   Multigrid(const Array<Operator*>& operators_, const Array<Solver*>& smoothers_,
             const Array<Operator*>& prolongations_, const Array<bool>& ownedOperators_,
             const Array<bool>& ownedSmoothers_, const Array<bool>& ownedProlongations_);
@@ -153,16 +64,59 @@ public:
   /// Destructor
   virtual ~Multigrid();

+   /// Adds a level to the multigrid operator hierarchy.
+   /** The ownership of the operators and solvers/smoothers may be transferred
+       to the Multigrid by setting the according boolean variables. */
+   void AddLevel(Operator* opr, Solver* smoother, bool ownOperator,
+                 bool ownSmoother);
+
+   /// Returns the number of levels
+   int NumLevels() const;
+
+   /// Returns the index of the finest level
+   int GetFinestLevelIndex() const;
+
+   /// Returns operator at given level
+   const Operator* GetOperatorAtLevel(int level) const;
+
+   /// Returns operator at given level
+   Operator* GetOperatorAtLevel(int level);
+
+   /// Returns operator at finest level
+   const Operator* GetOperatorAtFinestLevel() const;
+
+   /// Returns operator at finest level
+   Operator* GetOperatorAtFinestLevel();
+
+   /// Returns smoother at given level
+   Solver* GetSmootherAtLevel(int level) const;
+
+   /// Returns smoother at given level
+   Solver* GetSmootherAtLevel(int level);
+
+   /// Set cycle type and number of pre- and post-smoothing steps used by Mult
+   void SetCycleType(CycleType cycleType_, int preSmoothingSteps_,
+                     int postSmoothingSteps_);
+
+   /// Application of the multigrid as a preconditioner
+   virtual void Mult(const Vector& x, Vector& y) const override;
+
+   /// Not supported for multigrid
+   virtual void SetOperator(const Operator& op) override;
+
 private:
+   /// Application of a smoothing step at particular level
+   void SmoothingStep(int level, bool transpose) const;
+
+   /// Application of a multigrid cycle at particular level
+   void Cycle(int level) const;
+
   /// Returns prolongation operator at given level
-   virtual const Operator* GetProlongationAtLevel(int level) const override
-   {
-      return prolongations[level];
-   }
+   virtual const Operator* GetProlongationAtLevel(int level) const;
 };

 /// Geometric multigrid associated with a hierarchy of finite element spaces
-class GeometricMultigrid : public MultigridBase
+class GeometricMultigrid : public Multigrid
 {
 protected:
   const FiniteElementSpaceHierarchy& fespaces;
@@ -172,7 +126,8 @@ protected:
 public:
   /** Construct an empty multigrid object for the given finite element space
       hierarchy @a fespaces_ */
-   GeometricMultigrid(const FiniteElementSpaceHierarchy& fespaces_);
+   GeometricMultigrid(const FiniteElementSpaceHierarchy& fespaces_)
+      : Multigrid(), fespaces(fespaces_) { }

   /// Destructor
   virtual ~GeometricMultigrid();
@@ -187,10 +142,7 @@ public:

 private:
   /// Returns prolongation operator at given level
-   virtual const Operator* GetProlongationAtLevel(int level) const override
-   {
-      return fespaces.GetProlongationAtLevel(level);
-   }
+   virtual const Operator* GetProlongationAtLevel(int level) const override;
 };

 } // namespace mfem
@@ -347,12 +347,14 @@ ParallelEliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
 void ParBilinearForm::TrueAddMult(const Vector &x, Vector &y, const double a)
 const
 {
-   const Operator *P = pfes->GetProlongationMatrix();
-   Xaux.SetSize(P->Height());
-   Yaux.SetSize(P->Height());
-   Ytmp.SetSize(P->Width());
+   if (Xaux.ParFESpace() != pfes)
+   {
+      Xaux.SetSpace(pfes);
+      Yaux.SetSpace(pfes);
+      Ytmp.SetSize(pfes->GetTrueVSize());
+   }

-   P->Mult(x, Xaux);
+   Xaux.Distribute(&x);
   if (ext)
   {
      ext->Mult(Xaux, Yaux);
@@ -364,8 +366,8 @@ const
                  " implemented");
      mat->Mult(Xaux, Yaux);
   }
-   P->MultTranspose(Yaux, Ytmp);
-   y.Add(a, Ytmp);
+   pfes->GetProlongationMatrix()->MultTranspose(Yaux, Ytmp);
+   y.Add(a,Ytmp);
 }

 void ParBilinearForm::FormLinearSystem(
@@ -31,8 +31,9 @@ class ParBilinearForm : public BilinearForm
 protected:
   ParFiniteElementSpace *pfes; ///< Points to the same object as #fes

-   /// Auxiliary vectors used in TrueAddMult(): L-, L-, and T-vector, resp.
-   mutable Vector Xaux, Yaux, Ytmp;
+   /// Auxiliary objects used in TrueAddMult().
+   mutable ParGridFunction Xaux, Yaux;
+   mutable Vector Ytmp;

   OperatorHandle p_mat, p_mat_e;

@@ -569,7 +569,7 @@ const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
      {
         if (Conforming())
         {
-            res = new H1FaceRestriction(*this, e_ordering, type);
+            res = new H1_ND_RT_FaceRestriction(*this, e_ordering, type);
         }
         else
         {
@@ -1536,7 +1536,7 @@ const FiniteElement *ParFiniteElementSpace::GetFaceNbrFaceFE(int i) const
   // Works in tandem with GetFaceNbrFaceVDofs() defined above.

   MFEM_ASSERT(Nonconforming() && !NURBSext, "");
-   Geometry::Type face_geom = pmesh->GetFaceGeometry(i);
+   Geometry::Type face_geom = pmesh->GetFaceGeometryType(i);
   return fec->FiniteElementForGeometry(face_geom);
 }

@@ -3025,8 +3025,6 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
   Array<char> mark(diag->Height());
   mark = 0;

-   bool is_dg = FEColl()->GetContType() == FiniteElementCollection::DISCONTINUOUS;
-
   for (int k = 0; k < dtrans.embeddings.Size(); k++)
   {
      const Embedding &emb = dtrans.embeddings[k];
@@ -3055,7 +3053,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
               int r = DofToVDof(dofs[i], vd);
               int m = (r >= 0) ? r : (-1 - r);

-               if (is_dg || !mark[m])
+               if (!mark[m])
               {
                  lR.GetRow(i, row);
                  diag->SetRow(r, old_vdofs, row);
@@ -3107,7 +3105,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
               int r = DofToVDof(dofs[i], vd);
               int m = (r >= 0) ? r : (-1 - r);

-               if (is_dg || !mark[m])
+               if (!mark[m])
               {
                  lR.GetRow(i, row);
                  MFEM_ASSERT(ldof[geom] == row.Size(), "");
@@ -3124,7 +3122,6 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
         }
      }
   }
-
   messages.clear();
   offd->Finalize(0);
   offd->SetWidth(col_map.size());
@@ -54,7 +54,7 @@ void ParLinearForm::Assemble()
   }
 }

-bool ParLinearForm::SupportsDevice()
+bool ParLinearForm::SupportsDevice() const
 {
   bool parallel;
   bool local = LinearForm::SupportsDevice();
@@ -120,7 +120,7 @@ public:
   void Assemble();

   /// Return true if assembly on device is supported, false otherwise.
-   virtual bool SupportsDevice();
+   virtual bool SupportsDevice() const;

   void AssembleSharedFaces();

@@ -91,10 +91,8 @@ void ParNCH1FaceRestriction::NonconformingInterpolation(Vector& y) const
   });
 }

-void ParNCH1FaceRestriction::AddMultTranspose(const Vector &x, Vector &y,
-                                              const double a) const
+void ParNCH1FaceRestriction::AddMultTranspose(const Vector &x, Vector &y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   if (nf==0) { return; }
   NonconformingTransposeInterpolation(x);
   H1FaceRestriction::AddMultTranspose(x_interp, y);
@@ -776,10 +774,8 @@ void ParNCL2FaceRestriction::Mult(const Vector& x, Vector& y) const
   }
 }

-void ParNCL2FaceRestriction::AddMultTranspose(const Vector &x, Vector &y,
-                                              const double a) const
+void ParNCL2FaceRestriction::AddMultTranspose(const Vector &x, Vector &y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   if (nf==0) { return; }
   if (type==FaceType::Interior)
   {
@@ -65,10 +65,8 @@ public:
                     requested by @a type in the constructor.
                     The face_dofs should be ordered according to the given
                     ElementDofOrdering.
-       @param[in,out] y The L-vector degrees of freedom.
-       @param[in]  a Scalar coefficient for addition. */
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+       @param[in,out] y The L-vector degrees of freedom. */
+   void AddMultTranspose(const Vector &x, Vector &y) const override;

   /** @brief Gather the degrees of freedom, i.e. goes from face E-Vector to
       L-Vector.
@@ -304,10 +302,8 @@ public:
                     requested by @a type in the constructor.
                     The face_dofs should be ordered according to the given
                     ElementDofOrdering
-       @param[in,out] y The L-vector degrees of freedom.
-       @param[in]  a Scalar coefficient for addition. */
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+       @param[in,out] y The L-vector degrees of freedom. */
+   void AddMultTranspose(const Vector &x, Vector &y) const override;

   /** @brief Gather the degrees of freedom, i.e. goes from face E-Vector to
       L-Vector.
@@ -588,7 +588,7 @@ void FaceQuadratureInterpolator::Mult(
   const int vdim = fespace->GetVDim();
   const int dim = fespace->GetMesh()->Dimension();
   const FiniteElement *fe =
-      fespace->GetTraceElement(0, fespace->GetMesh()->GetFaceGeometry(0));
+      fespace->GetTraceElement(0, fespace->GetMesh()->GetFaceBaseGeometry(0));
   const IntegrationRule *ir = IntRule;
   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
   const int nd1d = maps.ndof;
@@ -148,7 +148,7 @@ void ElementRestriction::MultUnsigned(const Vector& x, Vector& y) const
 }

 template <bool ADD>
-void ElementRestriction::TAddMultTranspose(const Vector& x, Vector& y) const
+void ElementRestriction::AddMultTranspose(const Vector& x, Vector& y) const
 {
   // Assumes all elements have the same number of dofs
   const int nd = dof;
@@ -180,15 +180,13 @@ void ElementRestriction::TAddMultTranspose(const Vector& x, Vector& y) const
 void ElementRestriction::MultTranspose(const Vector& x, Vector& y) const
 {
   constexpr bool ADD = false;
-   TAddMultTranspose<ADD>(x, y);
+   AddMultTranspose<ADD>(x, y);
 }

-void ElementRestriction::AddMultTranspose(const Vector& x, Vector& y,
-                                          const double a) const
+void ElementRestriction::AddMultTranspose(const Vector& x, Vector& y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   constexpr bool ADD = true;
-   TAddMultTranspose<ADD>(x, y);
+   AddMultTranspose<ADD>(x, y);
 }

 void ElementRestriction::MultTransposeUnsigned(const Vector& x, Vector& y) const
@@ -523,7 +521,7 @@ void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
 }

 template <bool ADD>
-void L2ElementRestriction::TAddMultTranspose(const Vector &x, Vector &y) const
+void L2ElementRestriction::AddMultTranspose(const Vector &x, Vector &y) const
 {
   const int nd = ndof;
   const int vd = vdim;
@@ -546,15 +544,13 @@ void L2ElementRestriction::TAddMultTranspose(const Vector &x, Vector &y) const
 void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
 {
   constexpr bool ADD = false;
-   TAddMultTranspose<ADD>(x, y);
+   AddMultTranspose<ADD>(x, y);
 }

-void L2ElementRestriction::AddMultTranspose(const Vector &x, Vector &y,
-                                            const double a) const
+void L2ElementRestriction::AddMultTranspose(const Vector &x, Vector &y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   constexpr bool ADD = true;
-   TAddMultTranspose<ADD>(x, y);
+   AddMultTranspose<ADD>(x, y);
 }

 void L2ElementRestriction::FillI(SparseMatrix &mat) const
@@ -598,119 +594,11 @@ void L2ElementRestriction::FillJAndData(const Vector &ea_data,
   });
 }

-/** Return the face degrees of freedom returned in Lexicographic order.
-    Note: Only for quad and hex */
-void GetFaceDofs(const int dim, const int face_id,
-                 const int dof1d, Array<int> &face_map)
-{
-   switch (dim)
-   {
-      case 1:
-         switch (face_id)
-         {
-            case 0: // WEST
-               face_map[0] = 0;
-               break;
-            case 1: // EAST
-               face_map[0] = dof1d-1;
-               break;
-         }
-         break;
-      case 2:
-         switch (face_id)
-         {
-            case 0: // SOUTH
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  face_map[i] = i;
-               }
-               break;
-            case 1: // EAST
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  face_map[i] = dof1d-1 + i*dof1d;
-               }
-               break;
-            case 2: // NORTH
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  face_map[i] = (dof1d-1)*dof1d + i;
-               }
-               break;
-            case 3: // WEST
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  face_map[i] = i*dof1d;
-               }
-               break;
-         }
-         break;
-      case 3:
-         switch (face_id)
-         {
-            case 0: // BOTTOM
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = i + j*dof1d;
-                  }
-               }
-               break;
-            case 1: // SOUTH
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = i + j*dof1d*dof1d;
-                  }
-               }
-               break;
-            case 2: // EAST
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = dof1d-1 + i*dof1d + j*dof1d*dof1d;
-                  }
-               }
-               break;
-            case 3: // NORTH
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = (dof1d-1)*dof1d + i + j*dof1d*dof1d;
-                  }
-               }
-               break;
-            case 4: // WEST
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = i*dof1d + j*dof1d*dof1d;
-                  }
-               }
-               break;
-            case 5: // TOP
-               for (int i = 0; i < dof1d; ++i)
-               {
-                  for (int j = 0; j < dof1d; ++j)
-                  {
-                     face_map[i+j*dof1d] = (dof1d-1)*dof1d*dof1d + i + j*dof1d;
-                  }
-               }
-               break;
-         }
-         break;
-   }
-}
-
-H1FaceRestriction::H1FaceRestriction(const FiniteElementSpace &fes,
-                                     const ElementDofOrdering e_ordering,
-                                     const FaceType type,
-                                     bool build)
+H1_ND_RT_FaceRestriction::H1_ND_RT_FaceRestriction(
+   const FiniteElementSpace &fes,
+   const ElementDofOrdering e_ordering,
+   const FaceType type,
+   bool build)
   : fes(fes),
     nf(fes.GetNFbyType(type)),
     vdim(fes.GetVDim()),
@@ -731,18 +619,36 @@ H1FaceRestriction::H1FaceRestriction(const FiniteElementSpace &fes,

   CheckFESpace(e_ordering);

-   ComputeScatterIndicesAndOffsets(e_ordering, type);
+   // Get the mapping from native DOF ordering to lexicographic ordering.
+   const FiniteElement *fe = fes.GetFE(0);
+   const TensorBasisElement* el =
+      dynamic_cast<const TensorBasisElement*>(fe);
+   const Array<int> &dof_map_ = el->GetDofMap();
+   if (dof_map_.Size() > 0)
+   {
+      dof_map.MakeRef(dof_map_);
+   }
+   else
+   {
+      // For certain types of elements dof_map_ is empty, in this case that
+      // means the element is already ordered lexicographically, so the
+      // permutation is the identity.
+      dof_map.SetSize(elem_dofs);
+      for (int i = 0; i < elem_dofs; ++i) { dof_map[i] = i; }
+   }

+   ComputeScatterIndicesAndOffsets(e_ordering, type);
   ComputeGatherIndices(e_ordering,type);
 }

-H1FaceRestriction::H1FaceRestriction(const FiniteElementSpace &fes,
-                                     const ElementDofOrdering e_ordering,
-                                     const FaceType type)
-   : H1FaceRestriction(fes, e_ordering, type, true)
+H1_ND_RT_FaceRestriction::H1_ND_RT_FaceRestriction(
+   const FiniteElementSpace &fes,
+   const ElementDofOrdering e_ordering,
+   const FaceType type)
+   : H1_ND_RT_FaceRestriction(fes, e_ordering, type, true)
 { }

-void H1FaceRestriction::Mult(const Vector& x, Vector& y) const
+void H1_ND_RT_FaceRestriction::Mult(const Vector& x, Vector& y) const
 {
   if (nf==0) { return; }
   // Assumes all elements have the same number of dofs
@@ -754,20 +660,21 @@ void H1FaceRestriction::Mult(const Vector& x, Vector& y) const
   auto d_y = Reshape(y.Write(), nface_dofs, vd, nf);
   MFEM_FORALL(i, nfdofs,
   {
-      const int idx = d_indices[i];
+      const int s_idx = d_indices[i];
+      const int sgn = (s_idx >= 0) ? 1 : -1;
+      const int idx = (s_idx >= 0) ? s_idx : -1 - s_idx;
      const int dof = i % nface_dofs;
      const int face = i / nface_dofs;
      for (int c = 0; c < vd; ++c)
      {
-         d_y(dof, c, face) = d_x(t?c:idx, t?idx:c);
+         d_y(dof, c, face) = sgn*d_x(t?c:idx, t?idx:c);
      }
   });
 }

-void H1FaceRestriction::AddMultTranspose(const Vector& x, Vector& y,
-                                         const double a) const
+void H1_ND_RT_FaceRestriction::AddMultTranspose(
+   const Vector& x, Vector& y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   if (nf==0) { return; }
   // Assumes all elements have the same number of dofs
   const int nface_dofs = face_dofs;
@@ -786,15 +693,17 @@ void H1FaceRestriction::AddMultTranspose(const Vector& x, Vector& y,
         double dof_value = 0;
         for (int j = offset; j < next_offset; ++j)
         {
-            const int idx_j = d_indices[j];
-            dof_value +=  d_x(idx_j % nface_dofs, c, idx_j / nface_dofs);
+            const int s_idx_j = d_indices[j];
+            const int sgn = (s_idx_j >= 0) ? 1 : -1;
+            const int idx_j = (s_idx_j >= 0) ? s_idx_j : -1 - s_idx_j;
+            dof_value += sgn*d_x(idx_j % nface_dofs, c, idx_j / nface_dofs);
         }
         d_y(t?c:i,t?i:c) += dof_value;
      }
   });
 }

-void H1FaceRestriction::CheckFESpace(const ElementDofOrdering e_ordering)
+void H1_ND_RT_FaceRestriction::CheckFESpace(const ElementDofOrdering e_ordering)
 {
 #ifdef MFEM_USE_MPI

@@ -816,7 +725,7 @@ void H1FaceRestriction::CheckFESpace(const ElementDofOrdering e_ordering)
               (tfe->GetBasisType()==BasisType::GaussLobatto ||
                tfe->GetBasisType()==BasisType::Positive),
               "Only Gauss-Lobatto and Bernstein basis are supported in "
-               "H1FaceRestriction.");
+               "H1_ND_RT_FaceRestriction.");

   // Assuming all finite elements are using Gauss-Lobatto.
   const bool dof_reorder = (e_ordering == ElementDofOrdering::LEXICOGRAPHIC);
@@ -830,16 +739,11 @@ void H1FaceRestriction::CheckFESpace(const ElementDofOrdering e_ordering)
         if (el) { continue; }
         MFEM_ABORT("Finite element not suitable for lexicographic ordering");
      }
-      const FiniteElement *fe = fes.GetFaceElement(0);
-      const TensorBasisElement* el =
-         dynamic_cast<const TensorBasisElement*>(fe);
-      const Array<int> &fe_dof_map = el->GetDofMap();
-      MFEM_VERIFY(fe_dof_map.Size() > 0, "invalid dof map");
   }
 #endif
 }

-void H1FaceRestriction::ComputeScatterIndicesAndOffsets(
+void H1_ND_RT_FaceRestriction::ComputeScatterIndicesAndOffsets(
   const ElementDofOrdering ordering,
   const FaceType type)
 {
@@ -877,7 +781,7 @@ void H1FaceRestriction::ComputeScatterIndicesAndOffsets(
   }
 }

-void H1FaceRestriction::ComputeGatherIndices(
+void H1_ND_RT_FaceRestriction::ComputeGatherIndices(
   const ElementDofOrdering ordering,
   const FaceType type)
 {
@@ -910,7 +814,9 @@ void H1FaceRestriction::ComputeGatherIndices(
   gather_offsets[0] = 0;
 }

-void H1FaceRestriction::SetFaceDofsScatterIndices(
+static inline int absdof(int i) { return i < 0 ? -1-i : i; }
+
+void H1_ND_RT_FaceRestriction::SetFaceDofsScatterIndices(
   const Mesh::FaceInformation &face,
   const int face_index,
   const ElementDofOrdering ordering)
@@ -920,32 +826,29 @@ void H1FaceRestriction::SetFaceDofsScatterIndices(
   MFEM_ASSERT(face.element[0].orientation==0,
               "FaceRestriction used on degenerated mesh.");

-   const TensorBasisElement* el =
-      dynamic_cast<const TensorBasisElement*>(fes.GetFE(0));
-   const int *dof_map = el->GetDofMap().GetData();
+   fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
+
   const Table& e2dTable = fes.GetElementToDofTable();
   const int* elem_map = e2dTable.GetJ();
-   const int face_id = face.element[0].local_face_id;
-   const int dim = fes.GetMesh()->Dimension();
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
   const int elem_index = face.element[0].index;
   const bool dof_reorder = (ordering == ElementDofOrdering::LEXICOGRAPHIC);
-   GetFaceDofs(dim, face_id, dof1d, face_map); // Only for quad and hex

   for (int face_dof = 0; face_dof < face_dofs; ++face_dof)
   {
      const int nat_volume_dof = face_map[face_dof];
-      const int volume_dof = (!dof_reorder)?
-                             nat_volume_dof:
-                             dof_map[nat_volume_dof];
-      const int global_dof = elem_map[elem_index*elem_dofs + volume_dof];
+      const int s_volume_dof = (!dof_reorder) ?
+                               nat_volume_dof :
+                               dof_map[nat_volume_dof]; // signed
+      const int volume_dof = absdof(s_volume_dof);
+      const int s_global_dof = elem_map[elem_index*elem_dofs + volume_dof];
+      const int global_dof = absdof(s_global_dof);
      const int restriction_dof = face_dofs*face_index + face_dof;
-      scatter_indices[restriction_dof] = global_dof;
+      scatter_indices[restriction_dof] = s_global_dof;
      ++gather_offsets[global_dof + 1];
   }
 }

-void H1FaceRestriction::SetFaceDofsGatherIndices(
+void H1_ND_RT_FaceRestriction::SetFaceDofsGatherIndices(
   const Mesh::FaceInformation &face,
   const int face_index,
   const ElementDofOrdering ordering)
@@ -953,25 +856,25 @@ void H1FaceRestriction::SetFaceDofsGatherIndices(
   MFEM_ASSERT(!(face.IsNonconformingCoarse()),
               "This method should not be used on nonconforming coarse faces.");

-   const TensorBasisElement* el =
-      dynamic_cast<const TensorBasisElement*>(fes.GetFE(0));
-   const int *dof_map = el->GetDofMap().GetData();
+   fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
+
   const Table& e2dTable = fes.GetElementToDofTable();
   const int* elem_map = e2dTable.GetJ();
-   const int face_id = face.element[0].local_face_id;
-   const int dim = fes.GetMesh()->Dimension();
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
   const int elem_index = face.element[0].index;
   const bool dof_reorder = (ordering == ElementDofOrdering::LEXICOGRAPHIC);
-   GetFaceDofs(dim, face_id, dof1d, face_map); // Only for quad and hex

   for (int face_dof = 0; face_dof < face_dofs; ++face_dof)
   {
      const int nat_volume_dof = face_map[face_dof];
-      const int volume_dof = (!dof_reorder)?nat_volume_dof:dof_map[nat_volume_dof];
-      const int global_dof = elem_map[elem_index*elem_dofs + volume_dof];
+      const int s_volume_dof = (!dof_reorder)?nat_volume_dof:dof_map[nat_volume_dof];
+      const int volume_dof = absdof(s_volume_dof);
+      const int s_global_dof = elem_map[elem_index*elem_dofs + volume_dof];
+      const int sgn = (s_global_dof >= 0) ? 1 : -1;
+      const int global_dof = absdof(s_global_dof);
      const int restriction_dof = face_dofs*face_index + face_dof;
-      gather_indices[gather_offsets[global_dof]++] = restriction_dof;
+      const int s_restriction_dof = (sgn >= 0) ? restriction_dof : -1 -
+                                    restriction_dof;
+      gather_indices[gather_offsets[global_dof]++] = s_restriction_dof;
   }
 }

@@ -1111,7 +1014,7 @@ L2FaceRestriction::L2FaceRestriction(const FiniteElementSpace &fes,
     vdim(fes.GetVDim()),
     byvdim(fes.GetOrdering() == Ordering::byVDIM),
     face_dofs(nf > 0 ?
-               fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0))->GetDof()
+               fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof()
               : 0),
     elem_dofs(fes.GetFE(0)->GetDof()),
     nfdofs(nf*face_dofs),
@@ -1272,10 +1175,8 @@ void L2FaceRestriction::DoubleValuedConformingAddMultTranspose(
   });
 }

-void L2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y,
-                                         const double a) const
+void L2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   if (nf==0) { return; }
   if (m == L2FaceValues::DoubleValued)
   {
@@ -1428,7 +1329,7 @@ void L2FaceRestriction::CheckFESpace(const ElementDofOrdering e_ordering)
      for (int f = 0; f < fes.GetNF(); ++f)
      {
         const FiniteElement *fe =
-            fes.GetTraceElement(f, fes.GetMesh()->GetFaceGeometry(f));
+            fes.GetTraceElement(f, fes.GetMesh()->GetFaceBaseGeometry(f));
         const TensorBasisElement* el =
            dynamic_cast<const TensorBasisElement*>(fe);
         if (el) { continue; }
@@ -1525,10 +1426,8 @@ void L2FaceRestriction::SetFaceDofsScatterIndices1(
   const Table& e2dTable = fes.GetElementToDofTable();
   const int* elem_map = e2dTable.GetJ();
   const int face_id1 = face.element[0].local_face_id;
-   const int dim = fes.GetMesh()->Dimension();
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
   const int elem_index = face.element[0].index;
-   GetFaceDofs(dim, face_id1, dof1d, face_map); // Only for quad and hex
+   fes.GetFE(0)->GetFaceMap(face_id1, face_map);

   for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
   {
@@ -1554,7 +1453,7 @@ void L2FaceRestriction::PermuteAndSetFaceDofsScatterIndices2(
   const int orientation = face.element[1].orientation;
   const int dim = fes.GetMesh()->Dimension();
   const int dof1d = fes.GetFE(0)->GetOrder()+1;
-   GetFaceDofs(dim, face_id2, dof1d, face_map); // Only for quad and hex
+   fes.GetFE(0)->GetFaceMap(face_id2, face_map);

   for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
   {
@@ -1582,7 +1481,7 @@ void L2FaceRestriction::PermuteAndSetSharedFaceDofsScatterIndices2(
   const int orientation = face.element[1].orientation;
   const int dim = fes.GetMesh()->Dimension();
   const int dof1d = fes.GetFE(0)->GetOrder()+1;
-   GetFaceDofs(dim, face_id2, dof1d, face_map); // Only for quad and hex
+   fes.GetFE(0)->GetFaceMap(face_id2, face_map);
   Array<int> face_nbr_dofs;
   const ParFiniteElementSpace &pfes =
      static_cast<const ParFiniteElementSpace&>(this->fes);
@@ -1624,10 +1523,8 @@ void L2FaceRestriction::SetFaceDofsGatherIndices1(
   const Table& e2dTable = fes.GetElementToDofTable();
   const int* elem_map = e2dTable.GetJ();
   const int face_id1 = face.element[0].local_face_id;
-   const int dim = fes.GetMesh()->Dimension();
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
   const int elem_index = face.element[0].index;
-   GetFaceDofs(dim, face_id1, dof1d, face_map); // Only for quad and hex
+   fes.GetFE(0)->GetFaceMap(face_id1, face_map);

   for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
   {
@@ -1653,7 +1550,7 @@ void L2FaceRestriction::PermuteAndSetFaceDofsGatherIndices2(
   const int orientation = face.element[1].orientation;
   const int dim = fes.GetMesh()->Dimension();
   const int dof1d = fes.GetFE(0)->GetOrder()+1;
-   GetFaceDofs(dim, face_id2, dof1d, face_map); // Only for quad and hex
+   fes.GetFE(0)->GetFaceMap(face_id2, face_map);

   for (int face_dof_elem1 = 0; face_dof_elem1 < face_dofs; ++face_dof_elem1)
   {
@@ -1788,7 +1685,7 @@ void InterpolationManager::LinearizeInterpolatorMapIntoVector()
 {
   // Assumes all trace elements are the same.
   const FiniteElement *trace_fe =
-      fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0));
+      fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0));
   const int face_dofs = trace_fe->GetDof();
   const int nc_size = interp_map.size();
   MFEM_VERIFY(nc_cpt==nc_size, "Unexpected number of interpolators.");
@@ -2058,10 +1955,8 @@ void NCL2FaceRestriction::DoubleValuedNonconformingTransposeInterpolationInPlace
   });
 }

-void NCL2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y,
-                                           const double a) const
+void NCL2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
 {
-   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   if (nf==0) { return; }
   if (type==FaceType::Interior)
   {
@@ -27,8 +27,7 @@ class ElementRestrictionOperator : public Operator
 public:
   /// @brief Add the E-vector degrees of freedom @a x to the L-vector degrees
   /// of freedom @a y.
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override = 0;
+   virtual void AddMultTranspose(const Vector &x, Vector &y) const = 0;
 };

 /// Operator that converts FiniteElementSpace L-vectors to E-vectors.
@@ -66,10 +65,9 @@ protected:

 public:
   ElementRestriction(const FiniteElementSpace&, ElementDofOrdering);
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+   void AddMultTranspose(const Vector &x, Vector &y) const;

   /// Compute Mult without applying signs based on DOF orientations.
   void MultUnsigned(const Vector &x, Vector &y) const;
@@ -101,7 +99,7 @@ public:
   ///
   /// Performs either MultTranspose or AddMultTranspose depending on the
   /// boolean template parameter @a ADD.
-   template <bool ADD> void TAddMultTranspose(const Vector &x, Vector &y) const;
+   template <bool ADD> void AddMultTranspose(const Vector &x, Vector &y) const;
 };

 /// Operator that converts L2 FiniteElementSpace L-vectors to E-vectors.
@@ -118,10 +116,9 @@ class L2ElementRestriction : public ElementRestrictionOperator
   const int ndofs;
 public:
   L2ElementRestriction(const FiniteElementSpace&);
-   void Mult(const Vector &x, Vector &y) const override;
-   void MultTranspose(const Vector &x, Vector &y) const override;
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+   void AddMultTranspose(const Vector &x, Vector &y) const;
   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
       given by this ElementRestriction. */
   void FillI(SparseMatrix &mat) const;
@@ -132,7 +129,7 @@ public:
   ///
   /// Performs either MultTranspose or AddMultTranspose depending on the
   /// boolean template parameter @a ADD.
-   template <bool ADD> void TAddMultTranspose(const Vector &x, Vector &y) const;
+   template <bool ADD> void AddMultTranspose(const Vector &x, Vector &y) const;
 };

 /** An enum type to specify if only e1 value is requested (SingleValued) or both
@@ -183,10 +180,8 @@ public:
       @param[in]     x The face degrees of freedom on the face.
       @param[in,out] y The L-vector of degrees of freedom to which we add the
                        face degrees of freedom.
-       @param[in]     a Scalar coefficient for addition.
   */
-   virtual void AddMultTranspose(const Vector &x, Vector &y,
-                                 const double a = 1.0) const override = 0;
+   virtual void AddMultTranspose(const Vector &x, Vector &y) const = 0;

   /** @brief Add the face degrees of freedom @a x to the element degrees of
       freedom @a y. Perform the same computation as AddMultTranspose, but
@@ -221,7 +216,7 @@ public:
 /// Operator that extracts Face degrees of freedom for H1 FiniteElementSpaces.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetFaceRestriction(). */
-class H1FaceRestriction : public FaceRestriction
+class H1_ND_RT_FaceRestriction : public FaceRestriction
 {
 protected:
   const FiniteElementSpace &fes;
@@ -235,29 +230,30 @@ protected:
   Array<int> scatter_indices; // Scattering indices for element 1 on each face
   Array<int> gather_offsets; // offsets for the gathering indices of each dof
   Array<int> gather_indices; // gathering indices for each dof
+   Array<int> dof_map; // mapping to lexicographic ordering

-   /** @brief Construct an H1FaceRestriction.
+   /** @brief Construct an H1_ND_RT_FaceRestriction.

       @param[in] fes      The FiniteElementSpace on which this operates
       @param[in] ordering Request a specific element ordering
       @param[in] type     Request internal or boundary faces dofs
       @param[in] build    Request the NCL2FaceRestriction to compute the
                           scatter/gather indices. False should only be used
-                           when inheriting from H1FaceRestriction.
+                           when inheriting from H1_ND_RT_FaceRestriction.
   */
-   H1FaceRestriction(const FiniteElementSpace& fes,
-                     const ElementDofOrdering ordering,
-                     const FaceType type,
-                     bool build);
+   H1_ND_RT_FaceRestriction(const FiniteElementSpace& fes,
+                            const ElementDofOrdering ordering,
+                            const FaceType type,
+                            bool build);
 public:
-   /** @brief Construct an H1FaceRestriction.
+   /** @brief Construct an H1_ND_RT_FaceRestriction.

       @param[in] fes      The FiniteElementSpace on which this operates
       @param[in] ordering Request a specific element ordering
       @param[in] type     Request internal or boundary faces dofs */
-   H1FaceRestriction(const FiniteElementSpace& fes,
-                     const ElementDofOrdering ordering,
-                     const FaceType type);
+   H1_ND_RT_FaceRestriction(const FiniteElementSpace& fes,
+                            const ElementDofOrdering ordering,
+                            const FaceType type);

   /** @brief Scatter the degrees of freedom, i.e. goes from L-Vector to
       face E-Vector.
@@ -282,10 +278,8 @@ public:
                     requested by @a type in the constructor.
                     The face_dofs should be ordered according to the given
                     ElementDofOrdering
-       @param[in,out] y The L-vector degrees of freedom.
-       @param[in]  a Scalar coefficient for addition. */
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+       @param[in,out] y The L-vector degrees of freedom. */
+   void AddMultTranspose(const Vector &x, Vector &y) const override;

 private:
   /** @brief Compute the scatter indices: L-vector to E-vector, and the offsets
@@ -310,7 +304,7 @@ private:
 protected:
   mutable Array<int> face_map; // Used in the computation of GetFaceDofs

-   /** @brief Verify that H1FaceRestriction is build from an H1 FESpace.
+   /** @brief Verify that H1_ND_RT_FaceRestriction is build from an H1 FESpace.

       @param[in] ordering The FESpace element ordering.
   */
@@ -339,6 +333,10 @@ protected:
                                 const ElementDofOrdering ordering);
 };

+/// @brief Alias for H1_ND_RT_FaceRestriction, for backwards compatibility and
+/// as base class for ParNCH1FaceRestriction.
+using H1FaceRestriction = H1_ND_RT_FaceRestriction;
+
 /// Operator that extracts Face degrees of freedom for L2 spaces.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetFaceRestriction(). */
@@ -416,10 +414,8 @@ public:
                     requested by @a type in the constructor.
                     The face_dofs should be ordered according to the given
                     ElementDofOrdering
-       @param[in,out] y The L-vector degrees of freedom.
-       @param[in]  a Scalar coefficient for addition. */
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+       @param[in,out] y The L-vector degrees of freedom. */
+   void AddMultTranspose(const Vector &x, Vector &y) const override;

   /** @brief Fill the I array of SparseMatrix corresponding to the sparsity
       pattern given by this L2FaceRestriction.
@@ -840,10 +836,8 @@ public:
                     requested by @a type in the constructor.
                     The face_dofs should be ordered according to the given
                     ElementDofOrdering
-       @param[in,out] y The L-vector degrees of freedom.
-       @param[in]  a Scalar coefficient for addition. */
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override;
+       @param[in,out] y The L-vector degrees of freedom. */
+   void AddMultTranspose(const Vector &x, Vector &y) const override;

   /** @brief Gather the degrees of freedom, i.e. goes from face E-Vector to
       L-Vector.
@@ -615,7 +615,6 @@ public:
         solFES.VectorAssemble(y_dof.layout, y_dof, solVecLayoutLoc, y);
      }
   }
-   using Operator::AddMult;
 };

 } // namespace mfem
@@ -48,7 +48,8 @@ void TMOP_Combo_QualityMetric::EvalP(const DenseMatrix &Jpt,
   for (int i = 0; i < tmop_q_arr.Size(); i++)
   {
      tmop_q_arr[i]->EvalP(Jpt, Pt);
-      P.Add(wt_arr[i], Pt);
+      Pt *= wt_arr[i];
+      P += Pt;
   }
 }

@@ -61,109 +62,12 @@ void TMOP_Combo_QualityMetric::AssembleH(const DenseMatrix &Jpt,
   for (int i = 0; i < tmop_q_arr.Size(); i++)
   {
      At = 0.0;
-      tmop_q_arr[i]->AssembleH(Jpt, DS, weight * wt_arr[i], At);
+      tmop_q_arr[i]->AssembleH(Jpt, DS, weight, At);
+      At *= wt_arr[i];
      A += At;
   }
 }

-void TMOP_Combo_QualityMetric::
-ComputeBalancedWeights(const GridFunction &nodes,
-                       const TargetConstructor &tc, Vector &weights) const
-{
-   const int m_cnt = tmop_q_arr.Size();
-   Vector averages;
-   ComputeAvgMetrics(nodes, tc, averages);
-   weights.SetSize(m_cnt);
-
-   // For [ combo_A_B_C = a m_A + b m_B + c m_C ] we would have:
-   // a = BC / (AB + AC + BC), b = AC / (AB + AC + BC), c = AB / (AB + AC + BC),
-   // where A = avg_m_A, B = avg_m_B, C = avg_m_C.
-   // Nested loop to avoid division, as some avg may be 0.
-   Vector products_no_m(m_cnt); products_no_m = 1.0;
-   for (int m_p = 0; m_p < m_cnt; m_p++)
-   {
-      for (int m_a = 0; m_a < m_cnt; m_a++)
-      {
-         if (m_p != m_a) { products_no_m(m_p) *= averages(m_a); }
-      }
-   }
-   const double pnm_sum = products_no_m.Sum();
-
-   if (pnm_sum == 0.0) { weights = 1.0 / m_cnt; return; }
-   for (int m = 0; m < m_cnt; m++) { weights(m) = products_no_m(m) / pnm_sum; }
-
-   MFEM_ASSERT(fabs(weights.Sum() - 1.0) < 1e-14,
-               "Error: sum should be 1 always: " << weights.Sum());
-}
-
-void TMOP_Combo_QualityMetric::ComputeAvgMetrics(const GridFunction &nodes,
-                                                 const TargetConstructor &tc,
-                                                 Vector &averages) const
-{
-   const int m_cnt = tmop_q_arr.Size(),
-             NE    = nodes.FESpace()->GetNE(),
-             dim   = nodes.FESpace()->GetMesh()->Dimension();
-
-   averages.SetSize(m_cnt);
-
-   // Integrals of all metrics.
-   Array<int> pos_dofs;
-   averages = 0.0;
-   double volume = 0.0;
-   for (int e = 0; e < NE; e++)
-   {
-      const FiniteElement &fe_pos = *nodes.FESpace()->GetFE(e);
-      const IntegrationRule &ir = IntRules.Get(fe_pos.GetGeomType(),
-                                               2 * fe_pos.GetOrder());
-      const int nsp = ir.GetNPoints(), dof = fe_pos.GetDof();
-
-      DenseMatrix dshape(dof, dim);
-      DenseMatrix pos(dof, dim);
-      pos.SetSize(dof, dim);
-      Vector posV(pos.Data(), dof * dim);
-
-      nodes.FESpace()->GetElementVDofs(e, pos_dofs);
-      nodes.GetSubVector(pos_dofs, posV);
-
-      DenseTensor W(dim, dim, nsp);
-      DenseMatrix Winv(dim), T(dim), A(dim);
-      tc.ComputeElementTargets(e, fe_pos, ir, posV, W);
-
-      for (int q = 0; q < nsp; q++)
-      {
-         const DenseMatrix &Wj = W(q);
-         CalcInverse(Wj, Winv);
-
-         const IntegrationPoint &ip = ir.IntPoint(q);
-         fe_pos.CalcDShape(ip, dshape);
-         MultAtB(pos, dshape, A);
-         Mult(A, Winv, T);
-
-         const double w_detA = ip.weight * A.Det();
-         for (int m = 0; m < m_cnt; m++)
-         {
-            tmop_q_arr[m]->SetTargetJacobian(Wj);
-            averages(m) += tmop_q_arr[m]->EvalW(T) * w_detA;
-         }
-         volume += w_detA;
-      }
-   }
-
-   // Parallel case.
-#ifdef MFEM_USE_MPI
-   auto par_nodes = dynamic_cast<const ParGridFunction *>(&nodes);
-   if (par_nodes)
-   {
-      MPI_Allreduce(MPI_IN_PLACE, averages.GetData(), m_cnt,
-                    MPI_DOUBLE, MPI_SUM, par_nodes->ParFESpace()->GetComm());
-      MPI_Allreduce(MPI_IN_PLACE, &volume, 1, MPI_DOUBLE, MPI_SUM,
-                    par_nodes->ParFESpace()->GetComm());
-   }
-#endif
-
-   averages /= volume;
-}
-
 double TMOP_WorstCaseUntangleOptimizer_Metric::EvalW(const DenseMatrix &Jpt)
 const
 {
@@ -824,30 +728,30 @@ void TMOP_Metric_301::AssembleH(const DenseMatrix &Jpt,
   //  dW = (1/6)*[z2*dI1b + z1*dI2b], z1 = sqrt(I1b/I2b), z2 = sqrt(I2b/I1b)
   // ddW = (1/6)*[dI1b x dz2 + z2*ddI1b + dI2b x dz1 + z1*ddI2b]
   //
-   // dz1 = (1/2)*sqrt(I2b/I1b) [ (1/I2b)*dI1b - (I1b/(I2b*I2b))*dI2b ]
-   //     = (1/2)/sqrt(I1b*I2b) [ dI1b - (I1b/I2b)*dI2b ]
-   // dz2 = (1/2)/sqrt(I1b*I2b) [ dI2b - (I2b/I1b)*dI1b ]
+   // dz1 = (1/2)*sqrt(I2b/I1b) [ (1/I2b)*dI1b + (I1b/(I2b*I2b))*dI2b ]
+   //     = (1/2)/sqrt(I1b*I2b) [ dI1b + (I1b/I2b)*dI2b ]
+   // dz2 = (1/2)/sqrt(I1b*I2b) [ (I2b/I1b)*dI1b + dI2b ]
   //
   // dI1b x dz2 + dI2b x dz1 =
-   //    (1/2)/sqrt(I1b*I2b) dI1b x [ dI2b - (I2b/I1b)*dI1b ] +
-   //    (1/2)/sqrt(I1b*I2b) dI2b x [ dI1b - (I1b/I2b)*dI2b ] =
-   //    (1/2)/sqrt(I1b*I2b) [sqrt(I1b/I2b)*dI2b - sqrt(I2b/I1b)*dI1b] x
-   //                        [sqrt(I2b/I1b)*dI1b - sqrt(I1b/I2b)*dI2b] =
-   //    (1/2)*(I1b*I2b)^{-3/2} (I1b*dI2b - I2b*dI1b) x (I2b*dI1b - I1b*dI2b)
-   //      and the last two parentheses are the same up to a sign.
+   //    (1/2)/sqrt(I1b*I2b) dI1b x [ (I2b/I1b)*dI1b + dI2b ] +
+   //    (1/2)/sqrt(I1b*I2b) dI2b x [ dI1b + (I1b/I2b)*dI2b ] =
+   //    (1/2)/sqrt(I1b*I2b) [sqrt(I2b/I1b)*dI1b + sqrt(I1b/I2b)*dI2b] x
+   //                        [sqrt(I2b/I1b)*dI1b + sqrt(I1b/I2b)*dI2b] =
+   //    (1/2)/sqrt(I1b*I2b) [ 6*dW x 6*dW ] =
+   //    (1/2)*(I1b*I2b)^{-3/2} (I2b*dI1b + I1b*dI2b) x (I2b*dI1b + I1b*dI2b)
   //
   // z1 = I1b/sqrt(I1b*I2b), z2 = I2b/sqrt(I1b*I2b)

   ie.SetJacobian(Jpt.GetData());
   ie.SetDerivativeMatrix(DS.Height(), DS.GetData());
-   double X_data[9];
-   DenseMatrix X(X_data, 3, 3);
-   Add(- ie.Get_I2b(), ie.Get_dI1b(), ie.Get_I1b(), ie.Get_dI2b(), X);
+   double d_I1b_I2b_data[9];
+   DenseMatrix d_I1b_I2b(d_I1b_I2b_data, 3, 3);
+   Add(ie.Get_I2b(), ie.Get_dI1b(), ie.Get_I1b(), ie.Get_dI2b(), d_I1b_I2b);
   const double I1b_I2b = ie.Get_I1b()*ie.Get_I2b();
   const double a = weight/(6*std::sqrt(I1b_I2b));
   ie.Assemble_ddI1b(a*ie.Get_I2b(), A.GetData());
   ie.Assemble_ddI2b(a*ie.Get_I1b(), A.GetData());
-   ie.Assemble_TProd(-a/(2*I1b_I2b), X_data, A.GetData());
+   ie.Assemble_TProd(a/(2*I1b_I2b), d_I1b_I2b_data, A.GetData());
 }

 double TMOP_Metric_302::EvalWMatrixForm(const DenseMatrix &Jpt) const
@@ -2894,6 +2798,8 @@ void TMOP_Integrator::GetSurfaceFittingErrors(double &err_avg, double &err_max)
         loc_sum += std::abs((*surf_fit_gf)(i));
      }
   }
+   err_avg = loc_sum / loc_cnt;
+   err_max = loc_max;

 #ifdef MFEM_USE_MPI
   if (targetC->Parallel() == false) { return; }
@@ -2903,9 +2809,6 @@ void TMOP_Integrator::GetSurfaceFittingErrors(double &err_avg, double &err_max)
   MPI_Allreduce(&loc_cnt, &glob_cnt, 1, MPI_INT, MPI_SUM, comm);
   MPI_Allreduce(&loc_sum, &err_avg, 1, MPI_DOUBLE, MPI_SUM, comm);
   err_avg = err_avg / glob_cnt;
-#else
-   err_avg = loc_sum / loc_cnt;
-   err_max = loc_max;
 #endif
 }

@@ -4094,14 +3997,6 @@ void TMOP_Integrator::EnableFiniteDifferences(const GridFunction &x)
   ComputeFDh(x,*fes);
   if (discr_tc)
   {
-#ifdef MFEM_USE_GSLIB
-      const AdaptivityEvaluator *ae = discr_tc->GetAdaptivityEvaluator();
-      if (dynamic_cast<const InterpolatorFP *>(ae))
-      {
-         MFEM_ABORT("Using GSLIB-based interpolation with finite differences"
-                    "requires careful consideration. Contact TMOP team.");
-      }
-#endif
      discr_tc->UpdateTargetSpecification(x, false, fes->GetOrdering());
      discr_tc->UpdateGradientTargetSpecification(x, dx, false, fes->GetOrdering());
      discr_tc->UpdateHessianTargetSpecification(x, dx, false, fes->GetOrdering());
@@ -4116,14 +4011,6 @@ void TMOP_Integrator::EnableFiniteDifferences(const ParGridFunction &x)
   ComputeFDh(x,*pfes);
   if (discr_tc)
   {
-#ifdef MFEM_USE_GSLIB
-      const AdaptivityEvaluator *ae = discr_tc->GetAdaptivityEvaluator();
-      if (dynamic_cast<const InterpolatorFP *>(ae))
-      {
-         MFEM_ABORT("Using GSLIB-based interpolation with finite differences"
-                    "requires careful consideration. Contact TMOP team.");
-      }
-#endif
      discr_tc->UpdateTargetSpecification(x, false, pfes->GetOrdering());
      discr_tc->UpdateGradientTargetSpecification(x, dx, false, pfes->GetOrdering());
      discr_tc->UpdateHessianTargetSpecification(x, dx, false, pfes->GetOrdering());
@@ -78,14 +78,11 @@ public:
   virtual int Id() const { return 0; }
 };

-class TargetConstructor;
-
-/// Abstract class used to define explicit combination of metrics with constant
-/// coefficients.
+/// Abstract class used to define combination of metrics with constant coefficients.
 class TMOP_Combo_QualityMetric : public TMOP_QualityMetric
 {
 protected:
-   Array<TMOP_QualityMetric *> tmop_q_arr; //the metrics are not owned
+   Array<TMOP_QualityMetric *> tmop_q_arr; //not owned
   Array<double> wt_arr;

 public:
@@ -111,25 +108,6 @@ public:

   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
                          const double weight, DenseMatrix &A) const;
-
-   /// Computes the averages of all metrics (integral of metric / volume).
-   /// Works in parallel when called with a ParGridFunction.
-   void ComputeAvgMetrics(const GridFunction &nodes,
-                          const TargetConstructor &tc,
-                          Vector &averages) const;
-
-   /// Computes weights so that the averages of all metrics are equal, and the
-   /// weights sum to one. Works in parallel when called with a ParGridFunction.
-   void ComputeBalancedWeights(const GridFunction &nodes,
-                               const TargetConstructor &tc,
-                               Vector &weights) const;
-
-   /// Changes the weights of the metrics in the combination.
-   void SetWeights(const Vector &weights)
-   {
-      MFEM_VERIFY(tmop_q_arr.Size() == weights.Size(), "Incorrect #weights");
-      for (int i = 0; i < tmop_q_arr.Size(); i++) { wt_arr[i] = weights(i); }
-   }
 };

 /// Simultaneous Untangler + Worst Case Improvement Metric
@@ -294,7 +272,6 @@ public:
 };

 /// 2D barrier shape (S) metric (polyconvex).
-/// Grade - A.
 class TMOP_Metric_002 : public TMOP_QualityMetric
 {
 protected:
@@ -316,7 +293,6 @@ public:
 };

 /// 2D non-barrier shape (S) metric.
-/// Grade - F.
 class TMOP_Metric_004 : public TMOP_QualityMetric
 {
 protected:
@@ -402,8 +378,7 @@ public:
                          const double weight, DenseMatrix &A) const;
 };

-/// 2D barrier shape metric (polyconvex).
-/// Grade - A.
+/// 2D barrier (not a shape) metric (polyconvex).
 class TMOP_Metric_050 : public TMOP_QualityMetric
 {
 protected:
@@ -420,7 +395,6 @@ public:
 };

 /// 2D non-barrier size (V) metric (not polyconvex).
-/// Grade - F.
 class TMOP_Metric_055 : public TMOP_QualityMetric
 {
 protected:
@@ -438,7 +412,6 @@ public:
 };

 /// 2D barrier size (V) metric (polyconvex).
-/// Grade - C.
 class TMOP_Metric_056 : public TMOP_QualityMetric
 {
 protected:
@@ -476,29 +449,29 @@ public:
 };

 /// 2D non-barrier Shape+Size (VS) metric.
-/// Grade - F.
 class TMOP_Metric_066 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_066(double gamma)
-      : sh_metric(new TMOP_Metric_004), sz_metric(new TMOP_Metric_055)
+   TMOP_Metric_066(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_004),
+      sz_metric(new TMOP_Metric_055)
   {
      // (1-gamma) mu_4 + gamma mu_55
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }
   virtual int Id() const { return 66; }
-   double GetGamma() const { return wt_arr[1]; }
+   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_066() { delete sh_metric; delete sz_metric; }
 };

 /// 2D barrier size (V) metric (polyconvex).
-/// Grade - C.
 class TMOP_Metric_077 : public TMOP_QualityMetric
 {
 protected:
@@ -517,24 +490,24 @@ public:
 };

 /// 2D barrier Shape+Size (VS) metric (polyconvex).
-/// Grade - A.
 class TMOP_Metric_080 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_080(double gamma)
-      : sh_metric(new TMOP_Metric_002), sz_metric(new TMOP_Metric_077)
+   TMOP_Metric_080(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_002),
+      sz_metric(new TMOP_Metric_077)
   {
      // (1-gamma) mu_2 + gamma mu_77
-      AddQualityMetric(sh_metric, 1.0 - gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }
-
   virtual int Id() const { return 80; }
-   double GetGamma() const { return wt_arr[1]; }
+   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_080() { delete sh_metric; delete sz_metric; }
 };
@@ -835,15 +808,17 @@ class TMOP_Metric_328 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_328(double gamma)
-      : sh_metric(new TMOP_Metric_301), sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_328(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_301),
+      sz_metric(new TMOP_Metric_316)
   {
      // (1-gamma) mu_301 + gamma mu_316
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual ~TMOP_Metric_328() { delete sh_metric; delete sz_metric; }
@@ -853,19 +828,21 @@ public:
 class TMOP_Metric_332 : public TMOP_Combo_QualityMetric
 {
 protected:
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_332(double gamma)
-      : sh_metric(new TMOP_Metric_302), sz_metric(new TMOP_Metric_315)
+   TMOP_Metric_332(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_302),
+      sz_metric(new TMOP_Metric_315)
   {
      // (1-gamma) mu_302 + gamma mu_315
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual int Id() const { return 332; }
-   double GetGamma() const { return wt_arr[1]; }
+   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_332() { delete sh_metric; delete sz_metric; }
 };
@@ -875,15 +852,17 @@ class TMOP_Metric_333 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_333(double gamma)
-      : sh_metric(new TMOP_Metric_302), sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_333(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_302),
+      sz_metric(new TMOP_Metric_316)
   {
      // (1-gamma) mu_302 + gamma mu_316
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual ~TMOP_Metric_333() { delete sh_metric; delete sz_metric; }
@@ -894,19 +873,21 @@ class TMOP_Metric_334 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_334(double gamma)
-      : sh_metric(new TMOP_Metric_303), sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_334(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_303),
+      sz_metric(new TMOP_Metric_316)
   {
      // (1-gamma) mu_303 + gamma mu_316
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual int Id() const { return 334; }
-   double GetGamma() const { return wt_arr[1]; }
+   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_334() { delete sh_metric; delete sz_metric; }
 };
@@ -916,19 +897,21 @@ class TMOP_Metric_347 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_Metric_347(double gamma)
-      : sh_metric(new TMOP_Metric_304), sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_347(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_304),
+      sz_metric(new TMOP_Metric_316)
   {
      // (1-gamma) mu_304 + gamma mu_316
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual int Id() const { return 347; }
-   double GetGamma() const { return wt_arr[1]; }
+   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_347() { delete sh_metric; delete sz_metric; }
 };
@@ -1051,15 +1034,17 @@ class TMOP_AMetric_126 : public TMOP_Combo_QualityMetric
 {
 protected:
   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
   TMOP_QualityMetric *sh_metric, *sz_metric;

 public:
-   TMOP_AMetric_126(double gamma)
-      : sh_metric(new TMOP_AMetric_011), sz_metric(new TMOP_AMetric_014a)
+   TMOP_AMetric_126(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_AMetric_011),
+      sz_metric(new TMOP_AMetric_014a)
   {
      // (1-gamma) nu_11 + gamma nu_14
-      AddQualityMetric(sh_metric, 1.-gamma);
-      AddQualityMetric(sz_metric, gamma);
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
   }

   virtual ~TMOP_AMetric_126() { delete sh_metric; delete sz_metric; }
@@ -1566,11 +1551,6 @@ public:
      adapt_eval = ae;
   }

-   const AdaptivityEvaluator *GetAdaptivityEvaluator() const
-   {
-      return adapt_eval;
-   }
-
   const Vector &GetTspecPert1H()   { return tspec_pert1h; }
   const Vector &GetTspecPert2H()   { return tspec_pert2h; }
   const Vector &GetTspecPertMixH() { return tspec_pertmix; }
@@ -68,11 +68,6 @@ public:
                                     Vector &new_field,
                                     int new_nodes_ordering = Ordering::byNODES);

-   const FindPointsGSLIB *GetFindPointsGSLIB() const
-   {
-      return finder;
-   }
-
   ~InterpolatorFP()
   {
      finder->FreeData();
@@ -291,10 +291,6 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space(
   int nel_ho = mesh_ho->GetNE();
   int nel_lor = mesh_lor->GetNE();

-   // The prolongation operation is only well-defined when the LOR space has at
-   // least as many DOFs as the high-order space.
-   const bool build_P = fes_lor.GetTrueVSize() >= fes_ho.GetTrueVSize();
-
   // If the local mesh is empty, skip all computations
   if (nel_ho == 0) { return; }

@@ -323,11 +319,8 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space(
   // R will contain the restriction (L^2 projection operator) defined on each
   // coarse HO element (and corresponding patch of LOR elements)
   R.SetSize(offsets[nel_ho]);
-   if (build_P)
-   {
-      // P will contain the corresponding prolongation operator
-      P.SetSize(offsets[nel_ho]);
-   }
+   // P will contain the corresponding prolongation operator
+   P.SetSize(offsets[nel_ho]);

   IntegrationPointTransformation ip_tr;
   IsoparametricTransformation &emb_tr = ip_tr.Transf;
@@ -348,6 +341,7 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space(
      const DenseTensor &pmats = cf_tr.point_matrices[geom];

      DenseMatrix R_iho(&R[offsets[iho]], ndof_lor*nref, ndof_ho);
+      DenseMatrix P_iho(&P[offsets[iho]], ndof_ho, ndof_lor*nref);

      DenseMatrix Minv_lor(ndof_lor*nref, ndof_lor*nref);
      DenseMatrix M_mixed(ndof_lor*nref, ndof_ho);
@@ -391,15 +385,10 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space(
      }
      mfem::Mult(Minv_lor, M_mixed, R_iho);

-      if (build_P)
-      {
-         DenseMatrix P_iho(&P[offsets[iho]], ndof_ho, ndof_lor*nref);
-
-         mfem::MultAtB(R_iho, M_lor, RtMlor);
-         mfem::Mult(RtMlor, R_iho, RtMlorR);
-         RtMlorR_inv.Factor();
-         RtMlorR_inv.Mult(RtMlor, P_iho);
-      }
+      mfem::MultAtB(R_iho, M_lor, RtMlor);
+      mfem::Mult(RtMlor, R_iho, RtMlorR);
+      RtMlorR_inv.Factor();
+      RtMlorR_inv.Mult(RtMlor, P_iho);
   }
 }

@@ -473,8 +462,6 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::MultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::Prolongate(
   const Vector &x, Vector &y) const
 {
-   if (fes_ho.GetNE() == 0) { return; }
-   MFEM_VERIFY(P.Size() > 0, "Prolongation not supported for these spaces.")
   int vdim = fes_ho.GetVDim();
   Array<int> vdofs;
   DenseMatrix xel_mat,yel_mat;
@@ -510,8 +497,6 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::Prolongate(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::ProlongateTranspose(
   const Vector &x, Vector &y) const
 {
-   if (fes_ho.GetNE() == 0) { return; }
-   MFEM_VERIFY(P.Size() > 0, "Prolongation not supported for these spaces.")
   int vdim = fes_ho.GetVDim();
   Array<int> vdofs;
   DenseMatrix xel_mat,yel_mat;
@@ -913,11 +898,6 @@ void L2ProjectionGridTransfer::BuildF()
   }
 }

-bool L2ProjectionGridTransfer::SupportsBackwardsOperator() const
-{
-   return ran_fes.GetTrueVSize() >= dom_fes.GetTrueVSize();
-}
-

 TransferOperator::TransferOperator(const FiniteElementSpace& lFESpace_,
                                   const FiniteElementSpace& hFESpace_)
@@ -98,8 +98,6 @@ public:
   {
      return MakeTrueOperator(ran_fes, dom_fes, BackwardOperator(), bw_t_oper);
   }
-
-   virtual bool SupportsBackwardsOperator() const { return true; }
 };


@@ -348,8 +346,6 @@ public:
   virtual const Operator &ForwardOperator();

   virtual const Operator &BackwardOperator();
-
-   virtual bool SupportsBackwardsOperator() const;
 private:
   void BuildF();
 };
@@ -92,9 +92,6 @@ public:
   template <typename CT, int N>
   explicit inline Array(const CT (&values)[N]);

-   /// Move constructor ("steals" data from 'src')
-   inline Array(Array<T> &&src) { Swap(src, *this); }
-
   /// Destructor
   inline ~Array() { TypeAssert(); data.Delete(); }

@@ -65,7 +65,7 @@

 // 'double' atomicAdd implementation for previous versions of CUDA
 #if defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ < 600
-MFEM_DEVICE inline double atomicAdd(double *add, double val)
+MFEM_DEVICE double atomicAdd(double *add, double val)
 {
   unsigned long long int *ptr = (unsigned long long int *) add;
   unsigned long long int old = *ptr, reg;
@@ -786,7 +786,7 @@ void *MemoryManager::New_(void *h_tmp, size_t bytes, MemoryType h_mt,
   void *h_ptr;
   if (h_tmp == nullptr) { ctrl->Host(h_mt)->Alloc(&h_ptr, bytes); }
   else { h_ptr = h_tmp; }
-   flags = Mem::Registered | Mem::OWNS_INTERNAL | Mem::OWNS_HOST |
+   flags = Mem::REGISTERED | Mem::OWNS_INTERNAL | Mem::OWNS_HOST |
           Mem::OWNS_DEVICE | valid_flags;
   // The other New_() method relies on this lazy allocation behavior.
   mm.Insert(h_ptr, bytes, h_mt, d_mt); // lazy dev alloc
@@ -820,7 +820,7 @@ void *MemoryManager::Register_(void *ptr, void *h_tmp, size_t bytes,
      return nullptr;
   }

-   flags |= Mem::Registered | Mem::OWNS_INTERNAL;
+   flags |= Mem::REGISTERED | Mem::OWNS_INTERNAL;
   void *h_ptr;

   if (is_host_mem) // HOST TYPES + MANAGED
@@ -859,7 +859,7 @@ void MemoryManager::Register2_(void *h_ptr, void *d_ptr, size_t bytes,
      return;
   }

-   flags |= Mem::Registered | Mem::OWNS_INTERNAL;
+   flags |= Mem::REGISTERED | Mem::OWNS_INTERNAL;

   MFEM_VERIFY(d_ptr || bytes == 0,
               "cannot register NULL device pointer with bytes = " << bytes);
@@ -911,7 +911,7 @@ void MemoryManager::SetDeviceMemoryType_(void *h_ptr, unsigned flags,
 void MemoryManager::Delete_(void *h_ptr, MemoryType h_mt, unsigned flags)
 {
   const bool alias = flags & Mem::ALIAS;
-   const bool registered = flags & Mem::Registered;
+   const bool registered = flags & Mem::REGISTERED;
   const bool owns_host = flags & Mem::OWNS_HOST;
   const bool owns_device = flags & Mem::OWNS_DEVICE;
   const bool owns_internal = flags & Mem::OWNS_INTERNAL;
@@ -1018,7 +1018,7 @@ void *MemoryManager::ReadWrite_(void *h_ptr, MemoryType h_mt, MemoryClass mc,
                                size_t bytes, unsigned &flags)
 {
   if (h_ptr) { CheckHostMemoryType_(h_mt, h_ptr, flags & Mem::ALIAS); }
-   if (bytes > 0) { MFEM_VERIFY(flags & Mem::Registered,""); }
+   if (bytes > 0) { MFEM_VERIFY(flags & Mem::REGISTERED,""); }
   MFEM_ASSERT(MemoryClassCheck_(mc, h_ptr, h_mt, bytes, flags),"");
   if (IsHostMemory(GetMemoryType(mc)) && mc < MemoryClass::DEVICE)
   {
@@ -1042,7 +1042,7 @@ const void *MemoryManager::Read_(void *h_ptr, MemoryType h_mt, MemoryClass mc,
                                 size_t bytes, unsigned &flags)
 {
   if (h_ptr) { CheckHostMemoryType_(h_mt, h_ptr, flags & Mem::ALIAS); }
-   if (bytes > 0) { MFEM_VERIFY(flags & Mem::Registered,""); }
+   if (bytes > 0) { MFEM_VERIFY(flags & Mem::REGISTERED,""); }
   MFEM_ASSERT(MemoryClassCheck_(mc, h_ptr, h_mt, bytes, flags),"");
   if (IsHostMemory(GetMemoryType(mc)) && mc < MemoryClass::DEVICE)
   {
@@ -1066,7 +1066,7 @@ void *MemoryManager::Write_(void *h_ptr, MemoryType h_mt, MemoryClass mc,
                            size_t bytes, unsigned &flags)
 {
   if (h_ptr) { CheckHostMemoryType_(h_mt, h_ptr, flags & Mem::ALIAS); }
-   if (bytes > 0) { MFEM_VERIFY(flags & Mem::Registered,""); }
+   if (bytes > 0) { MFEM_VERIFY(flags & Mem::REGISTERED,""); }
   MFEM_ASSERT(MemoryClassCheck_(mc, h_ptr, h_mt, bytes, flags),"");
   if (IsHostMemory(GetMemoryType(mc)) && mc < MemoryClass::DEVICE)
   {
@@ -1088,8 +1088,8 @@ void MemoryManager::SyncAlias_(const void *base_h_ptr, void *alias_h_ptr,
                               size_t alias_bytes, unsigned base_flags,
                               unsigned &alias_flags)
 {
-   // This is called only when (base_flags & Mem::Registered) is true.
-   // Note that (alias_flags & Registered) may not be true.
+   // This is called only when (base_flags & Mem::REGISTERED) is true.
+   // Note that (alias_flags & REGISTERED) may not be true.
   MFEM_ASSERT(alias_flags & Mem::ALIAS, "not an alias");
   if ((base_flags & Mem::VALID_HOST) && !(alias_flags & Mem::VALID_HOST))
   {
@@ -1097,10 +1097,10 @@ void MemoryManager::SyncAlias_(const void *base_h_ptr, void *alias_h_ptr,
   }
   if ((base_flags & Mem::VALID_DEVICE) && !(alias_flags & Mem::VALID_DEVICE))
   {
-      if (!(alias_flags & Mem::Registered))
+      if (!(alias_flags & Mem::REGISTERED))
      {
         mm.InsertAlias(base_h_ptr, alias_h_ptr, alias_bytes, base_flags & Mem::ALIAS);
-         alias_flags = (alias_flags | Mem::Registered | Mem::OWNS_INTERNAL) &
+         alias_flags = (alias_flags | Mem::REGISTERED | Mem::OWNS_INTERNAL) &
                       ~(Mem::OWNS_HOST | Mem::OWNS_DEVICE);
      }
      mm.GetAliasDevicePtr(alias_h_ptr, alias_bytes, true);
@@ -1671,7 +1671,7 @@ void MemoryPrintFlags(unsigned flags)
 {
   typedef Memory<int> Mem;
   mfem::out
-         << "\n   registered    = " << bool(flags & Mem::Registered)
+         << "\n   registered    = " << bool(flags & Mem::REGISTERED)
         << "\n   owns host     = " << bool(flags & Mem::OWNS_HOST)
         << "\n   owns device   = " << bool(flags & Mem::OWNS_DEVICE)
         << "\n   owns internal = " << bool(flags & Mem::OWNS_INTERNAL)
@@ -165,16 +165,8 @@ protected:

   enum FlagMask: unsigned
   {
-      // Workaround for use with headers that define REGISTERED as a macro,
-      // e.g. nb30.h (which is included by Windows.h):
-#ifndef REGISTERED
      REGISTERED    = 1 << 0, /**< The host pointer is registered with the
                                   MemoryManager */
-#endif
-      // Use the following identifier if REGISTERED is defined as a macro,
-      // e.g. nb30.h (which is included by Windows.h):
-      Registered    = 1 << 0, /**< The host pointer is registered with the
-                                   MemoryManager */
      OWNS_HOST     = 1 << 1, ///< The host pointer will be deleted by Delete()
      OWNS_DEVICE   = 1 << 2, /**< The device pointer will be deleted by
                                   Delete() */
@@ -219,8 +211,6 @@ public:
       validity flags of @a *this to those of @a other. Resets @a other. */
   Memory &operator=(Memory &&orig)
   {
-      // Guard self-assignment:
-      if (this == &orig) { return *this; }
      *this = orig;
      orig.Reset();
      return *this;
@@ -982,7 +972,7 @@ inline void Memory<T>::MakeAlias(const Memory &base, int offset, int size)
   capacity = size;
   h_mt = base.h_mt;
   h_ptr = base.h_ptr + offset;
-   if (!(base.flags & Registered))
+   if (!(base.flags & REGISTERED))
   {
      if (
 #if !defined(HYPRE_USING_GPU)
@@ -1018,7 +1008,7 @@ template <typename T>
 inline void Memory<T>::SetDeviceMemoryType(MemoryType d_mt)
 {
   if (!IsDeviceMemory(d_mt)) { return; }
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      MemoryManager::Register_(h_ptr, nullptr, capacity*sizeof(T), h_mt,
                               flags & OWNS_HOST, flags & ALIAS, flags);
@@ -1029,7 +1019,7 @@ inline void Memory<T>::SetDeviceMemoryType(MemoryType d_mt)
 template <typename T>
 inline void Memory<T>::Delete()
 {
-   const bool registered = flags & Registered;
+   const bool registered = flags & REGISTERED;
   const bool mt_host = h_mt == MemoryType::HOST;
   const bool std_delete = !registered && mt_host;

@@ -1048,7 +1038,7 @@ inline void Memory<T>::Delete()
 template <typename T>
 inline void Memory<T>::DeleteDevice(bool copy_to_host)
 {
-   if (flags & Registered)
+   if (flags & REGISTERED)
   {
      if (copy_to_host) { Read(MemoryClass::HOST, capacity); }
      MemoryManager::DeleteDevice_((void*)h_ptr, flags);
@@ -1108,7 +1098,7 @@ template <typename T>
 inline T *Memory<T>::ReadWrite(MemoryClass mc, int size)
 {
   const size_t bytes = size * sizeof(T);
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      if (mc == MemoryClass::HOST) { return h_ptr; }
      MemoryManager::Register_(h_ptr, nullptr, capacity*sizeof(T), h_mt,
@@ -1121,7 +1111,7 @@ template <typename T>
 inline const T *Memory<T>::Read(MemoryClass mc, int size) const
 {
   const size_t bytes = size * sizeof(T);
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      if (mc == MemoryClass::HOST) { return h_ptr; }
      MemoryManager::Register_(h_ptr, nullptr, capacity*sizeof(T), h_mt,
@@ -1134,7 +1124,7 @@ template <typename T>
 inline T *Memory<T>::Write(MemoryClass mc, int size)
 {
   const size_t bytes = size * sizeof(T);
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      if (mc == MemoryClass::HOST) { return h_ptr; }
      MemoryManager::Register_(h_ptr, nullptr, capacity*sizeof(T), h_mt,
@@ -1146,12 +1136,12 @@ inline T *Memory<T>::Write(MemoryClass mc, int size)
 template <typename T>
 inline void Memory<T>::Sync(const Memory &other) const
 {
-   if (!(flags & Registered) && (other.flags & Registered))
+   if (!(flags & REGISTERED) && (other.flags & REGISTERED))
   {
      MFEM_ASSERT(h_ptr == other.h_ptr &&
                  (flags & ALIAS) == (other.flags & ALIAS),
                  "invalid input");
-      flags = (flags | Registered) & ~(OWNS_DEVICE | OWNS_INTERNAL);
+      flags = (flags | REGISTERED) & ~(OWNS_DEVICE | OWNS_INTERNAL);
   }
   flags = (flags & ~(VALID_HOST | VALID_DEVICE)) |
           (other.flags & (VALID_HOST | VALID_DEVICE));
@@ -1161,9 +1151,9 @@ template <typename T>
 inline void Memory<T>::SyncAlias(const Memory &base, int alias_size) const
 {
   // Assuming that if *this is registered then base is also registered.
-   MFEM_ASSERT(!(flags & Registered) || (base.flags & Registered),
+   MFEM_ASSERT(!(flags & REGISTERED) || (base.flags & REGISTERED),
               "invalid base state");
-   if (!(base.flags & Registered)) { return; }
+   if (!(base.flags & REGISTERED)) { return; }
   MemoryManager::SyncAlias_(base.h_ptr, h_ptr, alias_size*sizeof(T),
                             base.flags, flags);
 }
@@ -1178,7 +1168,7 @@ inline MemoryType Memory<T>::GetMemoryType() const
 template <typename T>
 inline MemoryType Memory<T>::GetDeviceMemoryType() const
 {
-   if (!(flags & Registered)) { return MemoryType::DEFAULT; }
+   if (!(flags & REGISTERED)) { return MemoryType::DEFAULT; }
   return MemoryManager::GetDeviceMemoryType_(h_ptr, flags & ALIAS);
 }

@@ -1198,7 +1188,7 @@ template <typename T>
 inline void Memory<T>::CopyFrom(const Memory &src, int size)
 {
   MFEM_VERIFY(src.capacity>=size && capacity>=size, "Incorrect size");
-   if (!(flags & Registered) && !(src.flags & Registered))
+   if (!(flags & REGISTERED) && !(src.flags & REGISTERED))
   {
      if (h_ptr != src.h_ptr && size != 0)
      {
@@ -1218,7 +1208,7 @@ template <typename T>
 inline void Memory<T>::CopyFromHost(const T *src, int size)
 {
   MFEM_VERIFY(capacity>=size, "Incorrect size");
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      if (h_ptr != src && size != 0)
      {
@@ -1245,7 +1235,7 @@ template <typename T>
 inline void Memory<T>::CopyToHost(T *dest, int size) const
 {
   MFEM_VERIFY(capacity>=size, "Incorrect size");
-   if (!(flags & Registered))
+   if (!(flags & REGISTERED))
   {
      if (h_ptr != dest && size != 0)
      {
@@ -97,9 +97,6 @@ const char *GetConfigStr()
 #ifdef MFEM_USE_HIOP
      "MFEM_USE_HIOP\n"
 #endif
-#ifdef MFEM_USE_IPOPT
-      "MFEM_USE_IPOPT\n"
-#endif
 #ifdef MFEM_USE_HIP
      "MFEM_USE_HIP\n"
 #endif
@@ -35,8 +35,6 @@
 #ifndef __ZSTR_HPP
 #define __ZSTR_HPP

-#include "../config/config.hpp"
-
 #include <cassert>
 #include <fstream>
 #include <sstream>
@@ -111,9 +111,6 @@ public:
   virtual void Mult(const Vector &x, Vector &y) const;
   virtual void MultTranspose(const Vector &x, Vector &y) const;

-   using Operator::Mult;
-   using Operator::MultTranspose;
-
   virtual Type GetType() const { return Complex_Operator; }

   Convention GetConvention() const { return convention_; }
@@ -352,7 +352,6 @@ void EliminationSolver::Mult(const Vector& rhs, Vector& sol) const
   reducedsol = 0.0;
   krylov->Mult(reducedrhs, reducedsol);
   final_iter = krylov->GetNumIterations();
-   initial_norm = krylov->GetInitialNorm();
   final_norm = krylov->GetFinalNorm();
   converged = krylov->GetConverged();

@@ -486,7 +485,6 @@ void PenaltyConstrainedSolver::Mult(const Vector& b, Vector& x) const
   krylov->SetPrintLevel(print_options);
   krylov->Mult(penalized_rhs, x);
   final_iter = krylov->GetNumIterations();
-   initial_norm = krylov->GetInitialNorm();
   final_norm = krylov->GetFinalNorm();
   converged = krylov->GetConverged();

@@ -618,7 +616,6 @@ void SchurConstrainedSolver::LagrangeSystemMult(const Vector& x,
   gmres->Mult(x, y);
   final_iter = gmres->GetNumIterations();
   converged = gmres->GetConverged();
-   initial_norm = gmres->GetInitialNorm();
   final_norm = gmres->GetFinalNorm();
   delete gmres;
 }
@@ -249,13 +249,8 @@ void DenseMatrix::MultTranspose(const Vector &x, Vector &y) const
   MultTranspose(x.GetData(), y.GetData());
 }

-void DenseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
+void DenseMatrix::AddMult(const Vector &x, Vector &y) const
 {
-   if (a != 1.0)
-   {
-      AddMult_a(a, x, y);
-      return;
-   }
   MFEM_ASSERT(height == y.Size() && width == x.Size(),
               "incompatible dimensions");

@@ -272,14 +267,8 @@ void DenseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
   }
 }

-void DenseMatrix::AddMultTranspose(const Vector &x, Vector &y,
-                                   const double a) const
+void DenseMatrix::AddMultTranspose(const Vector &x, Vector &y) const
 {
-   if (a != 1.0)
-   {
-      AddMultTranspose_a(a, x, y);
-      return;
-   }
   MFEM_ASSERT(height == x.Size() && width == y.Size(),
               "incompatible dimensions");

@@ -162,15 +162,11 @@ public:
   /// Multiply a vector with the transpose matrix.
   virtual void MultTranspose(const Vector &x, Vector &y) const;

-   using Operator::Mult;
-   using Operator::MultTranspose;
+   /// y += A.x
+   void AddMult(const Vector &x, Vector &y) const;

-   /// y += a * A.x
-   virtual void AddMult(const Vector &x, Vector &y, const double a = 1.0) const;
-
-   /// y += a * A^t x
-   virtual void AddMultTranspose(const Vector &x, Vector &y,
-                                 const double a = 1.0) const;
+   /// y += A^t x
+   void AddMultTranspose(const Vector &x, Vector &y) const;

   /// y += a * A.x
   void AddMult_a(double a, const Vector &x, Vector &y) const;
@@ -862,8 +858,6 @@ public:
   /// Multiply the inverse matrix by another matrix: X <- A^{-1} X.
   void Mult(DenseMatrix &X) const {factors->Solve(width, X.Width(), X.Data());}

-   using Operator::Mult;
-
   /// Compute and return the inverse matrix in Ainv.
   void GetInverseMatrix(DenseMatrix &Ainv) const;

@@ -292,14 +292,13 @@ HypreParVector& HypreParVector::operator=(const HypreParVector &y)

 HypreParVector& HypreParVector::operator=(HypreParVector &&y)
 {
-   Vector::operator=(std::move(y));
-   // Self-assignment-safe way to move for 'own_ParVector' and 'x':
-   const auto own_tmp = y.own_ParVector;
+   // If the argument vector owns its data, then the calling vector will as well
+   WrapHypreParVector(static_cast<hypre_ParVector*>(y), y.own_ParVector);
+   // Either way the argument vector will no longer own its data
   y.own_ParVector = 0;
-   own_ParVector = own_tmp;
-   const auto x_tmp = y.x;
   y.x = nullptr;
-   x = x_tmp;
+   y.data.Reset();
+   y.size = 0;
   return *this;
 }

@@ -599,7 +599,7 @@ public:
   void MergeDiagAndOffd(SparseMatrix &merged);

   /// Return the diagonal of the matrix (Operator interface).
-   void AssembleDiagonal(Vector &diag) const override { GetDiag(diag); }
+   virtual void AssembleDiagonal(Vector &diag) const { GetDiag(diag); }

   /** Split the matrix into M x N equally sized blocks of parallel matrices.
       The size of 'blocks' must already be set to M x N. */
@@ -649,7 +649,7 @@ public:
       partitioning array. */
   HYPRE_BigInt *GetColStarts() const { return hypre_ParCSRMatrixColStarts(A); }

-   MemoryClass GetMemoryClass() const override { return GetHypreMemoryClass(); }
+   virtual MemoryClass GetMemoryClass() const { return GetHypreMemoryClass(); }

   /// Ensure the action of the transpose is performed fast.
   /** When HYPRE is built for GPUs, this method will construct and store the
@@ -691,25 +691,16 @@ public:
       transpose. */
   void MultTranspose(double a, const Vector &x, double b, Vector &y) const;

-   void Mult(const Vector &x, Vector &y) const override
+   virtual void Mult(const Vector &x, Vector &y) const
   { Mult(1.0, x, 0.0, y); }

   /// Computes y = A^t * x
   /** If the matrix is modified, call ResetTranspose() and optionally
       EnsureMultTranspose() to make sure this method uses the correct updated
       transpose. */
-   void MultTranspose(const Vector &x, Vector &y) const override
+   virtual void MultTranspose(const Vector &x, Vector &y) const
   { MultTranspose(1.0, x, 0.0, y); }

-   void AddMult(const Vector &x, Vector &y, const double a = 1.0) const override
-   { Mult(a, x, 1.0, y); }
-   void AddMultTranspose(const Vector &x, Vector &y,
-                         const double a = 1.0) const override
-   { MultTranspose(a, x, 1.0, y); }
-
-   using Operator::Mult;
-   using Operator::MultTranspose;
-
   /** @brief Computes y = a * |A| * x + b * y, using entry-wise absolute values
       of the matrix A. */
   void AbsMult(double a, const Vector &x, double b, Vector &y) const;
@@ -1089,7 +1080,6 @@ public:
   /// Relax the linear system Ax=b
   virtual void Mult(const HypreParVector &b, HypreParVector &x) const;
   virtual void Mult(const Vector &b, Vector &x) const;
-   using Operator::Mult;

   /// Apply transpose of the smoother to relax the linear system Ax=b
   virtual void MultTranspose(const Vector &b, Vector &x) const;
@@ -1166,7 +1156,6 @@ public:
   virtual void Mult(const HypreParVector &b, HypreParVector &x) const;
   /// Solve the linear system Ax=b
   virtual void Mult(const Vector &b, Vector &x) const;
-   using Operator::Mult;

   ///@}

@@ -48,69 +48,6 @@ void Operator::InitTVectors(const Operator *Po, const Operator *Ri,
   }
 }

-void Operator::AddMult(const Vector &x, Vector &y, const double a) const
-{
-   mfem::Vector z(y.Size());
-   Mult(x, z);
-   y.Add(a, z);
-}
-
-void Operator::AddMultTranspose(const Vector &x, Vector &y,
-                                const double a) const
-{
-   mfem::Vector z(y.Size());
-   MultTranspose(x, z);
-   y.Add(a, z);
-}
-
-void Operator::ArrayMult(const Array<const Vector *> &X,
-                         Array<Vector *> &Y) const
-{
-   MFEM_ASSERT(X.Size() == Y.Size(),
-               "Number of columns mismatch in Operator::Mult!");
-   for (int i = 0; i < X.Size(); i++)
-   {
-      MFEM_ASSERT(X[i] && Y[i], "Missing Vector in Operator::Mult!");
-      Mult(*X[i], *Y[i]);
-   }
-}
-
-void Operator::ArrayMultTranspose(const Array<const Vector *> &X,
-                                  Array<Vector *> &Y) const
-{
-   MFEM_ASSERT(X.Size() == Y.Size(),
-               "Number of columns mismatch in Operator::MultTranspose!");
-   for (int i = 0; i < X.Size(); i++)
-   {
-      MFEM_ASSERT(X[i] && Y[i], "Missing Vector in Operator::MultTranspose!");
-      MultTranspose(*X[i], *Y[i]);
-   }
-}
-
-void Operator::ArrayAddMult(const Array<const Vector *> &X, Array<Vector *> &Y,
-                            const double a) const
-{
-   MFEM_ASSERT(X.Size() == Y.Size(),
-               "Number of columns mismatch in Operator::AddMult!");
-   for (int i = 0; i < X.Size(); i++)
-   {
-      MFEM_ASSERT(X[i] && Y[i], "Missing Vector in Operator::AddMult!");
-      AddMult(*X[i], *Y[i], a);
-   }
-}
-
-void Operator::ArrayAddMultTranspose(const Array<const Vector *> &X,
-                                     Array<Vector *> &Y, const double a) const
-{
-   MFEM_ASSERT(X.Size() == Y.Size(),
-               "Number of columns mismatch in Operator::AddMultTranspose!");
-   for (int i = 0; i < X.Size(); i++)
-   {
-      MFEM_ASSERT(X[i] && Y[i], "Missing Vector in Operator::AddMultTranspose!");
-      AddMultTranspose(*X[i], *Y[i], a);
-   }
-}
-
 void Operator::FormLinearSystem(const Array<int> &ess_tdof_list,
                                Vector &x, Vector &b,
                                Operator* &Aout, Vector &X, Vector &B,
@@ -53,7 +53,8 @@ public:

   /// Initializes memory for true vectors of linear system
   void InitTVectors(const Operator *Po, const Operator *Ri, const Operator *Pi,
-                     Vector &x, Vector &b, Vector &X, Vector &B) const;
+                     Vector &x, Vector &b,
+                     Vector &X, Vector &B) const;

   /// Construct a square Operator with given size s (default 0).
   explicit Operator(int s = 0) { height = width = s; }
@@ -91,37 +92,13 @@ public:
   /** @brief Action of the transpose operator: `y=A^t(x)`. The default behavior
       in class Operator is to generate an error. */
   virtual void MultTranspose(const Vector &x, Vector &y) const
-   { mfem_error("Operator::MultTranspose() is not overridden!"); }
-
-   /// Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.
-   virtual void AddMult(const Vector &x, Vector &y, const double a = 1.0) const;
-
-   /// Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.
-   virtual void AddMultTranspose(const Vector &x, Vector &y,
-                                 const double a = 1.0) const;
-
-   /// Operator application on a matrix: `Y=A(X)`.
-   virtual void ArrayMult(const Array<const Vector *> &X,
-                          Array<Vector *> &Y) const;
-
-   /// Action of the transpose operator on a matrix: `Y=A^t(X)`.
-   virtual void ArrayMultTranspose(const Array<const Vector *> &X,
-                                   Array<Vector *> &Y) const;
-
-   /// Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.
-   virtual void ArrayAddMult(const Array<const Vector *> &X, Array<Vector *> &Y,
-                             const double a = 1.0) const;
-
-   /** @brief Operator transpose application on a matrix: `Y+=A^t(X)` (default)
-       or `Y+=a*A^t(X)`. */
-   virtual void ArrayAddMultTranspose(const Array<const Vector *> &X,
-                                      Array<Vector *> &Y, const double a = 1.0) const;
+   { mfem_error("Operator::MultTranspose() is not overloaded!"); }

   /** @brief Evaluate the gradient operator at the point @a x. The default
       behavior in class Operator is to generate an error. */
   virtual Operator &GetGradient(const Vector &x) const
   {
-      mfem_error("Operator::GetGradient() is not overridden!");
+      mfem_error("Operator::GetGradient() is not overloaded!");
      return const_cast<Operator &>(*this);
   }

@@ -137,24 +114,20 @@ public:
   /** @brief Prolongation operator from linear algebra (linear system) vectors,
       to input vectors for the operator. `NULL` means identity. */
   virtual const Operator *GetProlongation() const { return NULL; }
-
   /** @brief Restriction operator from input vectors for the operator to linear
       algebra (linear system) vectors. `NULL` means identity. */
   virtual const Operator *GetRestriction() const  { return NULL; }
-
   /** @brief Prolongation operator from linear algebra (linear system) vectors,
       to output vectors for the operator. `NULL` means identity. */
   virtual const Operator *GetOutputProlongation() const
   {
      return GetProlongation(); // Assume square unless specialized
   }
-
   /** @brief Transpose of GetOutputRestriction, directly available in this
       form to facilitate matrix-free RAP-type operators.

       `NULL` means identity. */
   virtual const Operator *GetOutputRestrictionTranspose() const { return NULL; }
-
   /** @brief Restriction operator from output vectors for the operator to linear
       algebra (linear system) vectors. `NULL` means identity. */
   virtual const Operator *GetOutputRestriction() const
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Will Pazner	35cea24e21	Move face map logic from restriction.cpp into FiniteElement derived classes Use inheritance instead of switch statement to dispatch	2023-01-09 20:46:51 -08:00
Will Pazner	9732e4dc6f	Make SupportsDevice const In both LinearFormIntegrator and LinearForm classes	2023-01-09 19:40:21 -08:00
Will Pazner	035301c212	Comment	2023-01-09 19:35:51 -08:00
Will Pazner	f6efd6e56b	Fix comment	2023-01-09 19:17:26 -08:00
Will Pazner	896922fbe4	Update CHANGELOG	2023-01-08 17:14:57 -08:00
Will Pazner	f726606b96	Add GetFaceNormal3D to help manage 3D hexahedron face cases	2023-01-05 08:55:45 -08:00
Will Pazner	02fa406807	Refactor FillFaceMap and add explanatory comment	2023-01-05 08:55:20 -08:00
Will Pazner	1e34a98337	ND face restriction	2023-01-05 08:55:19 -08:00
Will Pazner	bbd28f5f45	VectorFEBoundaryFluxLFIntegrator kernel in 3D	2023-01-04 18:49:04 -08:00
Will Pazner	f413481bff	RT face restriction in 3D	2023-01-04 18:49:04 -08:00
Will Pazner	61a922a812	Fix Mesh::FaceInformation output with operator<< Newline was missing after face topology. Also use '\n' instead of std::endl for all but last newline since there is no reason to flush the buffer before then.	2023-01-04 18:48:46 -08:00
Will Pazner	25ba954475	Test device kernel for VectorFEBoundaryFluxLFIntegrator in 2D	2023-01-04 18:48:46 -08:00
Will Pazner	a9829da2cb	Add device kernel for VectorFEBoundaryFluxLFIntegrator	2023-01-04 18:48:46 -08:00
Will Pazner	1b2ab9253b	Add test case for 2D RT face restriction	2023-01-04 18:48:44 -08:00
Will Pazner	067f571dc4	Support 2D RT elements in H1_ND_RT_FaceRestriction	2023-01-04 14:18:27 -08:00
Will Pazner	452cf127c6	Rename H1FaceRestriction to H1_ND_RT_FaceRestriction The same class should be able to be used for H1, ND, and RT spaces	2023-01-04 14:18:27 -08:00
Will Pazner	328df07f5d	Refactor GetFaceDofs to use offset and strides	2023-01-04 14:18:27 -08:00