RZ example with Robin conditions

Add check using IsIdentityProlongation
Fix issue in grad-div mode with map type VALUE
2023-10-09 14:57:28 -07:00 · 2023-04-03 15:24:08 -07:00 · 2023-04-03 15:21:47 -07:00 · 2023-03-15 13:00:13 -07:00 · 2023-03-14 15:18:36 -07:00 · 2023-03-14 15:18:20 -07:00
110 changed files with 3077 additions and 8296 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
@@ -226,7 +219,6 @@ 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 +278,6 @@ 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
@@ -316,6 +307,12 @@ miniapps/solvers/ParaView
 miniapps/solvers/mesh.*
 miniapps/solvers/sol.*

+miniapps/hdiv-linear-solver/darcy
+miniapps/hdiv-linear-solver/grad_div
+miniapps/hdiv-linear-solver/residual
+miniapps/hdiv-linear-solver/rz
+miniapps/hdiv-linear-solver/ParaView
+
 miniapps/parelag/MultilevelHcurlHdivSolver
 miniapps/parelag/*.mesh

@@ -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 "------------------------------"
@@ -10,23 +10,12 @@

 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
@@ -38,9 +27,6 @@ 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.
@@ -116,9 +102,6 @@ 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)

@@ -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
@@ -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")
@@ -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
@@ -1,888 +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);
-   }
-};
-
@@ -111,7 +111,7 @@ DataCollection::DataCollection(const std::string& collection_name, Mesh *mesh_)
   pad_digits_cycle = pad_digits_rank = pad_digits_default;
   format = SERIAL_FORMAT; // use serial mesh format
   compression = 0;
-   error = No_Error;
+   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) +
@@ -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;
@@ -87,6 +87,8 @@ public:
   ///
   /// If @ref iterative_mode is @a true, @a u is used as an initial guess.
   void Mult(const Vector &b, Vector &u) const;
+   /// Same as Mult() since the mass matrix is symmetric.
+   void MultTranspose(const Vector &b, Vector &u) const { Mult(b, u); }
   /// Not implemented. Aborts.
   void SetOperator(const Operator &op);
   /// Set the relative tolerance.
@@ -36,19 +36,19 @@ 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 +97,14 @@ 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 +122,13 @@ 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 +137,7 @@ 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 +239,7 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
   }
 }

+
 // Assume a linear mapping
 void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
                                         Vector &Laplacian) const
@@ -249,7 +250,7 @@ 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 +283,7 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
         Laplacian[nd] += hess(nd,ii)*scale[ii];
      }
   }
+
 }

 void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
@@ -361,128 +363,11 @@ 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");
-
-   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;
+   MFEM_ABORT("method is not implemented for this element");
+   return *dof2quad_array[0]; // suppress a warning
 }

 FiniteElement::~FiniteElement()
@@ -494,19 +379,16 @@ 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 +398,10 @@ 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 +422,7 @@ 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 +456,14 @@ 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 +472,16 @@ 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 +494,95 @@ 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 +631,7 @@ 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 +641,8 @@ 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 +653,7 @@ 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 +662,7 @@ 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 +670,7 @@ 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 +849,18 @@ 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 +900,7 @@ void VectorFiniteElement::SetDerivMembers()
   }
 }

-void VectorFiniteElement::CalcVShape_RT(
+void VectorFiniteElement::CalcVShape_RT (
   ElementTransformation &Trans, DenseMatrix &shape) const
 {
   MFEM_ASSERT(map_type == H_DIV, "");
@@ -954,7 +912,7 @@ 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 +2402,6 @@ 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,
@@ -2518,7 +2436,8 @@ 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 +2452,93 @@ 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. */
@@ -575,7 +579,6 @@ public:
   /** See the documentation for DofToQuad for more details. */
   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
                                         DofToQuad::Mode mode) const;
-
   /// Deconstruct the FiniteElement
   virtual ~FiniteElement();

@@ -622,11 +625,16 @@ 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 +642,10 @@ 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 +656,13 @@ 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 +674,7 @@ 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 +695,15 @@ 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 +725,38 @@ 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 +790,12 @@ 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 +954,11 @@ 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 +1179,7 @@ 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 +1203,7 @@ 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 +1235,6 @@ 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 +1245,18 @@ 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())
      {
@@ -1257,7 +1276,7 @@ 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 +1289,16 @@ 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); }
-
 };


@@ -321,9 +321,9 @@ 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 +331,9 @@ 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 +407,9 @@ 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);
@@ -665,16 +665,16 @@ 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 +724,8 @@ 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);
@@ -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);
   }
 };

@@ -152,16 +152,16 @@ 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 +209,8 @@ 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);
@@ -482,9 +482,9 @@ 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 +492,9 @@ 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 +568,9 @@ 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);
@@ -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.
@@ -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;
@@ -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. */
@@ -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;

@@ -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());
@@ -53,17 +53,6 @@ protected:
   Array<int> indices;
   Array<int> gather_map;

-   friend class BatchedLORAssembly;
-   friend class BatchedLOR_ADS;
-   friend class BatchedLOR_AMS;
-
-   /// @name Low-level access to the underlying element-dof mappings
-   ///@{
-   const Array<int> &GatherMap() const { return gather_map; }
-   const Array<int> &Indices() const { return indices; }
-   const Array<int> &Offsets() const { return offsets; }
-   ///@}
-
 public:
   ElementRestriction(const FiniteElementSpace&, ElementDofOrdering);
   void Mult(const Vector &x, Vector &y) const override;
@@ -102,6 +91,13 @@ 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;
+
+   /// @name Low-level access to the underlying element-dof mappings
+   ///@{
+   const Array<int> &GatherMap() const { return gather_map; }
+   const Array<int> &Indices() const { return indices; }
+   const Array<int> &Offsets() const { return offsets; }
+   ///@}
 };

 /// Operator that converts L2 FiniteElementSpace L-vectors to E-vectors.
@@ -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();
 };
@@ -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
@@ -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;
 }
@@ -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;
 }

@@ -583,7 +583,6 @@ void SLISolver::Mult(const Vector &b, Vector &x) const
   {
      nom0 = nom = sqrt(Dot(r, r));
   }
-   initial_norm = nom0;

   if (print_options.iterations | print_options.first_and_last)
   {
@@ -736,7 +735,6 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
      d = r;
   }
   nom0 = nom = Dot(d, r);
-   if (nom0 >= 0.0) { initial_norm = sqrt(nom0); }
   MFEM_ASSERT(IsFinite(nom), "nom = " << nom);
   if (print_options.iterations || print_options.first_and_last)
   {
@@ -754,7 +752,6 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
      }
      converged = false;
      final_iter = 0;
-      initial_norm = nom;
      final_norm = nom;
      return;
   }
@@ -1018,7 +1015,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
         r = b;
      }
   }
-   double beta = initial_norm = Norm(r);  // beta = ||r||
+   double beta = Norm(r);  // beta = ||r||
   MFEM_ASSERT(IsFinite(beta), "beta = " << beta);

   final_norm = std::max(rel_tol*beta, abs_tol);
@@ -1178,7 +1175,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
      x = 0.;
      r = b;
   }
-   double beta = initial_norm = Norm(r);  // beta = ||r||
+   double beta = Norm(r);  // beta = ||r||
   // We need to preallocate this to report the correct result in the case of
   // no convergence.
   double resid;
@@ -1394,7 +1391,7 @@ void BiCGSTABSolver::Mult(const Vector &b, Vector &x) const
   }
   rtilde = r;

-   resid = initial_norm = Norm(r);
+   resid = Norm(r);
   MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
   if (print_options.iterations || print_options.first_and_last)
   {
@@ -1641,7 +1638,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
   {
      prec->Mult(v1, u1);
   }
-   eta = beta = initial_norm = sqrt(Dot(*z, v1));
+   eta = beta = sqrt(Dot(*z, v1));
   MFEM_ASSERT(IsFinite(eta), "eta = " << eta);
   gamma0 = gamma1 = 1.;
   sigma0 = sigma1 = 0.;
@@ -1836,7 +1833,7 @@ void NewtonSolver::Mult(const Vector &b, Vector &x) const
      r -= b;
   }

-   norm0 = norm = initial_norm = Norm(r);
+   norm0 = norm = Norm(r);
   if (print_options.first_and_last && !print_options.iterations)
   {
      mfem::out << "Newton iteration " << setw(2) << 0
@@ -2034,7 +2031,7 @@ void LBFGSSolver::Mult(const Vector &b, Vector &x) const

   c = r;           // initial descent direction

-   norm0 = norm = initial_norm = Norm(r);
+   norm0 = norm = Norm(r);
   if (print_options.first_and_last && !print_options.iterations)
   {
      mfem::out << "LBFGS iteration " << setw(2) << 0
@@ -2407,7 +2404,7 @@ void SLBQPOptimizer::Mult(const Vector& xt, Vector& x) const
   }

   // Solve QP with fixed Lagrange multiplier
-   r = initial_norm = solve(l,xt,x,nclip);
+   r = solve(l,xt,x,nclip);
   print_iteration(nclip, r, l);


@@ -159,12 +159,11 @@ protected:
   ///@}

   /// @name Solver statistics (protected attributes)
-   /// Every IterativeSolver is expected to define these in its Mult() call.
   ///@{

-   mutable int final_iter = -1;
-   mutable bool converged = false;
-   mutable double initial_norm = -1.0, final_norm = -1.0;
+   mutable int final_iter;
+   mutable bool converged;
+   mutable double final_norm;

   ///@}

@@ -242,38 +241,11 @@ public:
   virtual void SetPrintLevel(PrintLevel);
   ///@}

-   /// @name Solver statistics.
-   /// These are valid after the call to Mult().
+   /// @name Solver statistics
   ///@{
-
-   /// Returns the number of iterations taken during the last call to Mult()
   int GetNumIterations() const { return final_iter; }
-   /// Returns true if the last call to Mult() converged successfully.
   bool GetConverged() const { return converged; }
-   /// @brief Returns the initial residual norm from the last call to Mult().
-   ///
-   /// This function returns the norm of the residual (or preconditioned
-   /// residual, depending on the solver), computed before the start of the
-   /// iteration.
-   double GetInitialNorm() const { return initial_norm; }
-   /// @brief Returns the final residual norm after termination of the solver
-   /// during the last call to Mult().
-   ///
-   /// This function returns the norm of the residual (or preconditioned
-   /// residual, depending on the solver), corresponding to the returned
-   /// solution.
   double GetFinalNorm() const { return final_norm; }
-   /// @brief Returns the final residual norm after termination of the solver
-   /// during the last call to Mult(), divided by the initial residual norm.
-   /// Returns -1 if one of these norms is left undefined by the solver.
-   ///
-   /// @sa GetFinalNorm(), GetInitialNorm()
-   double GetFinalRelNorm() const
-   {
-      if (final_norm < 0.0 || initial_norm < 0.0) { return -1.0; }
-      return final_norm / initial_norm;
-   }
-
   ///@}

   /// This should be called before SetOperator
@@ -149,10 +149,9 @@ Vector &Vector::operator=(const Vector &v)
 Vector &Vector::operator=(Vector &&v)
 {
   data = std::move(v.data);
-   // Self-assignment-safe way to move v.size to size:
-   const auto size_tmp = v.size;
+   size = v.size;
+   v.data.Reset();
   v.size = 0;
-   size = size_tmp;
   return *this;
 }

@@ -594,7 +593,7 @@ void Vector::SetSubVector(const Array<int> &dofs, const double value)

 void Vector::SetSubVector(const Array<int> &dofs, const Vector &elemvect)
 {
-   MFEM_ASSERT(dofs.Size() <= elemvect.Size(),
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(),
               "Size mismatch: length of dofs is " << dofs.Size()
               << ", length of elemvect is " << elemvect.Size());

@@ -639,7 +638,7 @@ void Vector::SetSubVector(const Array<int> &dofs, double *elem_data)

 void Vector::AddElementVector(const Array<int> &dofs, const Vector &elemvect)
 {
-   MFEM_ASSERT(dofs.Size() <= elemvect.Size(), "Size mismatch: "
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(), "Size mismatch: "
               "length of dofs is " << dofs.Size() <<
               ", length of elemvect is " << elemvect.Size());

@@ -683,7 +682,7 @@ void Vector::AddElementVector(const Array<int> &dofs, double *elem_data)
 void Vector::AddElementVector(const Array<int> &dofs, const double a,
                              const Vector &elemvect)
 {
-   MFEM_ASSERT(dofs.Size() <= elemvect.Size(), "Size mismatch: "
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(), "Size mismatch: "
               "length of dofs is " << dofs.Size() <<
               ", length of elemvect is " << elemvect.Size());

@@ -119,7 +119,7 @@ $(if $(word 2,$(SRC)),$(error Spaces in SRC = "$(SRC)" are not supported))
 MFEM_GIT_STRING = $(shell [ -d $(MFEM_DIR)/.git ] && git -C $(MFEM_DIR) \
   describe --all --long --abbrev=40 --dirty --always 2> /dev/null)

-EXAMPLE_SUBDIRS = amgx caliper ginkgo hiop ipopt petsc pumi sundials superlu moonolith
+EXAMPLE_SUBDIRS = amgx caliper ginkgo hiop petsc pumi sundials superlu moonolith
 EXAMPLE_DIRS := examples $(addprefix examples/,$(EXAMPLE_SUBDIRS))
 EXAMPLE_TEST_DIRS := examples

@@ -275,7 +275,7 @@ endif

 # List of MFEM dependencies, that require the *_LIB variable to be non-empty
 MFEM_REQ_LIB_DEPS = ENZYME SUPERLU MUMPS METIS FMS CONDUIT SIDRE LAPACK SUNDIALS\
- SUITESPARSE STRUMPACK GINKGO GNUTLS NETCDF PETSC SLEPC MPFR PUMI HIOP IPOPT\
+ SUITESPARSE STRUMPACK GINKGO GNUTLS NETCDF PETSC SLEPC MPFR PUMI HIOP\
 GSLIB OCCA CEED RAJA UMPIRE MKL_CPARDISO AMGX CALIPER PARELAG BENCHMARK\
 MOONOLITH ALGOIM

@@ -341,7 +341,7 @@ MFEM_DEFINES = MFEM_VERSION MFEM_VERSION_STRING MFEM_GIT_STRING MFEM_USE_MPI\
 MFEM_USE_SUITESPARSE MFEM_USE_GINKGO MFEM_USE_SUPERLU MFEM_USE_SUPERLU5\
 MFEM_USE_STRUMPACK 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_HIP\
+ MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_GSLIB MFEM_USE_CUDA MFEM_USE_HIP\
 MFEM_USE_OCCA MFEM_USE_MOONOLITH MFEM_USE_CEED MFEM_USE_RAJA MFEM_USE_UMPIRE\
 MFEM_USE_SIMD MFEM_USE_ADIOS2 MFEM_USE_MKL_CPARDISO MFEM_USE_AMGX\
 MFEM_USE_MUMPS MFEM_USE_ADFORWARD MFEM_USE_CODIPACK MFEM_USE_CALIPER\
@@ -690,7 +690,6 @@ status info:
 	$(info MFEM_USE_CONDUIT       = $(MFEM_USE_CONDUIT))
 	$(info MFEM_USE_PUMI          = $(MFEM_USE_PUMI))
 	$(info MFEM_USE_HIOP          = $(MFEM_USE_HIOP))
-	$(info MFEM_USE_IPOPT          = $(MFEM_USE_IPOPT))
 	$(info MFEM_USE_GSLIB         = $(MFEM_USE_GSLIB))
 	$(info MFEM_USE_CUDA          = $(MFEM_USE_CUDA))
 	$(info MFEM_USE_HIP           = $(MFEM_USE_HIP))
@@ -1467,7 +1467,6 @@ void Mesh::InitTables()
 {
   el_to_edge =
      el_to_face = el_to_el = bel_to_edge = face_edge = edge_vertex = NULL;
-   face_to_elem = NULL;
 }

 void Mesh::SetEmpty()
@@ -1490,9 +1489,6 @@ void Mesh::DestroyTables()

   delete face_edge;
   delete edge_vertex;
-
-   delete face_to_elem;
-   face_to_elem = NULL;
 }

 void Mesh::DestroyPointers()
@@ -1554,7 +1550,6 @@ void Mesh::ResetLazyData()
 {
   delete el_to_el;     el_to_el = NULL;
   delete face_edge;    face_edge = NULL;
-   delete face_to_elem;    face_to_elem = NULL;
   delete edge_vertex;  edge_vertex = NULL;
   DeleteGeometricFactors();
   nbInteriorFaces = -1;
@@ -3637,7 +3632,6 @@ Mesh::Mesh(const Mesh &mesh, bool copy_nodes)

   // Do NOT copy the face-to-edge Table, face_edge
   face_edge = NULL;
-   face_to_elem = NULL;

   // Copy the edge-to-vertex Table, edge_vertex
   edge_vertex = (mesh.edge_vertex) ? new Table(*mesh.edge_vertex) : NULL;
@@ -6181,34 +6175,6 @@ void Mesh::GetElementFaces(int i, Array<int> &el_faces, Array<int> &ori) const
   }
 }

-Array<int> Mesh::FindFaceNeighbors(const int elem) const
-{
-   if (face_to_elem == NULL)
-   {
-      face_to_elem = GetFaceToElementTable();
-   }
-
-   Array<int> elem_faces;
-   Array<int> ori;
-   GetElementFaces(elem, elem_faces, ori);
-
-   Array<int> nghb;
-   for (auto f : elem_faces)
-   {
-      Array<int> row;
-      face_to_elem->GetRow(f, row);
-      for (auto r : row)
-      {
-         nghb.Append(r);
-      }
-   }
-
-   nghb.Sort();
-   nghb.Unique();
-
-   return nghb;
-}
-
 void Mesh::GetBdrElementFace(int i, int *f, int *o) const
 {
   const int *bv, *fv;
@@ -9186,9 +9152,8 @@ void Mesh::NonconformingRefinement(const Array<Refinement> &refinements,
 double Mesh::AggregateError(const Array<double> &elem_error,
                            const int *fine, int nfine, int op)
 {
-   double error = elem_error[fine[0]];
-
-   for (int i = 1; i < nfine; i++)
+   double error = 0.0;
+   for (int i = 0; i < nfine; i++)
   {
      MFEM_VERIFY(fine[i] < elem_error.Size(), "");

@@ -9352,7 +9317,6 @@ void Mesh::Swap(Mesh& other, bool non_geometry)
   mfem::Swap(bel_to_edge, other.bel_to_edge);
   mfem::Swap(be_to_face, other.be_to_face);
   mfem::Swap(face_edge, other.face_edge);
-   mfem::Swap(face_to_elem, other.face_to_elem);
   mfem::Swap(edge_vertex, other.edge_vertex);

   mfem::Swap(attributes, other.attributes);
@@ -223,13 +223,8 @@ protected:
   Array<int> be_to_edge;  // for 2D
   Table *bel_to_edge;     // for 3D
   Array<int> be_to_face;
-
-   // Note that the following tables are owned by this class and should not be
-   // deleted by the caller. Of these three tables, only face_edge and
-   // edge_vertex are returned by access functions.
-   mutable Table *face_to_elem;  // Used by FindFaceNeighbors, not returned.
-   mutable Table *face_edge;     // Returned by GetFaceEdgeTable().
-   mutable Table *edge_vertex;   // Returned by GetEdgeVertexTable().
+   mutable Table *face_edge;
+   mutable Table *edge_vertex;

   IsoparametricTransformation Transformation, Transformation2;
   IsoparametricTransformation BdrTransformation;
@@ -1187,10 +1182,6 @@ public:
   /// Return the indices and the orientations of all faces of element i.
   void GetElementFaces(int i, Array<int> &faces, Array<int> &ori) const;

-   /** @brief Returns the sorted, unique indices of elements sharing a face with
-       element @a elem, including @a elem. */
-   Array<int> FindFaceNeighbors(const int elem) const;
-
   /// Return the index and the orientation of the face of bdr element i. (3D)
   void GetBdrElementFace(int i, int *f, int *o) const;

@@ -1235,32 +1226,24 @@ public:

   static FiniteElement *GetTransformationFEforElementType(Element::Type);

-   /// Builds the transformation defining the i-th element in @a ElTr.
-   /// @a ElTr must be allocated in advance and will be owned by the caller.
+   /** Builds the transformation defining the i-th element in the user-defined
+       variable. */
   void GetElementTransformation(int i, IsoparametricTransformation *ElTr);

-   /// Returns a pointer to the transformation defining the i-th element.
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
+   /// Returns the transformation defining the i-th element
   ElementTransformation *GetElementTransformation(int i);

-   /// Builds the transformation defining the i-th element in @a ElTr
-   /// assuming position of the vertices/nodes are given by @a nodes.
-   /// @a ElTr must be allocated in advance and will be owned by the caller.
+   /** Return the transformation defining the i-th element assuming
+       the position of the vertices/nodes are given by 'nodes'. */
   void GetElementTransformation(int i, const Vector &nodes,
                                 IsoparametricTransformation *ElTr);

-   /// Returns a pointer to the transformation defining the i-th boundary
-   /// element. Note that the pointer is owned by the class and is shared, i.e.,
-   /// calling this function resets pointers obtained from previous calls.
-   ElementTransformation *GetBdrElementTransformation(int i);
-
-   /// Builds the transformation defining the i-th boundary element in @a ElTr.
-   /// @a ElTr must be allocated in advance and will be owned by the caller.
+   /// Returns the transformation defining the i-th boundary element
+   ElementTransformation * GetBdrElementTransformation(int i);
   void GetBdrElementTransformation(int i, IsoparametricTransformation *ElTr);

-   /// Builds the transformation defining the i-th face element in @a FTr.
-   /// @a FTr must be allocated in advance and will be owned by the caller.
+   /** @brief Returns the transformation defining the given face element in a
+       user-defined variable. */
   void GetFaceTransformation(int i, IsoparametricTransformation *FTr);

   /** @brief A helper method that constructs a transformation from the
@@ -1272,18 +1255,14 @@ public:
                                   IsoparametricTransformation &Transf,
                                   int info);

-   /// Returns a pointer to the transformation defining the given face element.
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
+   /// Returns the transformation defining the given face element
   ElementTransformation *GetFaceTransformation(int FaceNo);

-   /// Builds the transformation defining the i-th edge element in @a EdTr.
-   /// @a EdTr must be allocated in advance and will be owned by the caller.
+   /** Returns the transformation defining the given edge element.
+       The transformation is stored in a user-defined variable. */
   void GetEdgeTransformation(int i, IsoparametricTransformation *EdTr);

-   /// Returns a pointer to the transformation defining the given edge element.
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
+   /// Returns the transformation defining the given face element
   ElementTransformation *GetEdgeTransformation(int EdgeNo);

   /// Returns (a pointer to an object containing) the following data:
@@ -1316,22 +1295,16 @@ public:
   ///    mask & 4 - Loc1, mask & 8 - Loc2, mask & 16 - Face.
   /// These mask values are defined in the ConfigMasks enum type as part of the
   /// FaceElementTransformations class in fem/eltrans.hpp.
-   ///
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
   virtual FaceElementTransformations *GetFaceElementTransformations(
      int FaceNo,
      int mask = 31);

-   /// See GetFaceElementTransformations().
   FaceElementTransformations *GetInteriorFaceTransformations (int FaceNo)
   {
      if (faces_info[FaceNo].Elem2No < 0) { return NULL; }
      return GetFaceElementTransformations (FaceNo);
   }

-   /// Builds the transformation defining the given boundary face.
-   /// The returned pointer is owned by the caller.
   FaceElementTransformations *GetBdrFaceTransformations (int BdrElemNo);

   /// Return the local face index for the given boundary face.
@@ -1603,10 +1576,6 @@ public:
   void SetNodes(const Vector &node_coord);

   /// Return a pointer to the internal node GridFunction (may be NULL).
-   /** If the mesh is straight-sided (low-order), it may not have a GridFunction
-       for the nodes, in which case this function returns NULL. To ensure that
-       the nodal GridFunction exists, call EnsureNodes().
-       @sa SetCurvature(). */
   GridFunction *GetNodes() { return Nodes; }
   const GridFunction *GetNodes() const { return Nodes; }
   /// Return the mesh nodes ownership flag.
@@ -1634,22 +1603,15 @@ public:
   /** Return the FiniteElementSpace on which the current mesh nodes are
       defined or NULL if the mesh does not have nodes. */
   const FiniteElementSpace *GetNodalFESpace() const;
-   /** @brief Make sure that the mesh has valid nodes, i.e. its geometry is
-       described by a vector finite element grid function (even if it is a
-       low-order mesh with straight edges).
-
-       @sa GetNodes(). */
+   /** Make sure that the mesh has valid nodes, i.e. its geometry is described
+       by a vector finite element grid function (even if it is a low-order mesh
+       with straight edges). */
   void EnsureNodes();

-   /// Set the curvature of the mesh nodes using the given polynomial degree.
-   /** Creates a nodal GridFunction if one doesn't already exist.
-
-       @param[in]  order       Polynomial degree of the nodal FE space.
-       @param[in]  discont     Whether to use a discontinuous or continuous
-                               finite element space (continuous is default).
-       @param[in]  space_dim   The space dimension (optional).
-       @param[in]  ordering    The Ordering of the finite element space
-                               (Ordering::byVDIM is the default). */
+   /** Set the curvature of the mesh nodes using the given polynomial degree,
+       'order', and optionally: discontinuous or continuous FE space, 'discont',
+       new space dimension, 'space_dim' (if != -1), and 'ordering' (byVDim by
+       default). */
   virtual void SetCurvature(int order, bool discont = false, int space_dim = -1,
                             int ordering = 1);

@@ -2107,6 +2107,8 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                           }
                           break;
                        }
+                     /*
+                     // MFEM does not support pyramids yet
                     case   7: el_order--; //   5-node pyramid
                     case  14: el_order--; //  14-node pyramid (2nd order)
                     case 118: el_order--; //  30-node pyramid (3rd order)
@@ -2119,7 +2121,7 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                        {
                           el_order--; // Gmsh does not define an order 10 pyr
                           elements_3D.push_back(
-                              new Pyramid(&vert_indices[0], phys_domain));
+                               new Pyramid(&vert_indices[0], phys_domain));
                           if (el_order > 1)
                           {
                              Array<int> * hov = new Array<int>;
@@ -2129,6 +2131,7 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                           }
                           break;
                        }
+                     */
                     case 15: // 1-node point
                     {
                        elements_0D.push_back(
@@ -2333,6 +2336,8 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                        }
                        break;
                     }
+                  /*
+                  // MFEM does not support pyramids yet
                  case   7: el_order--; //   5-node pyramid
                  case  14: el_order--; //  14-node pyramid (2nd order)
                  case 118: el_order--; //  30-node pyramid (3rd order)
@@ -2345,7 +2350,7 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                     {
                        el_order--;
                        elements_3D.push_back(
-                           new Pyramid(&vert_indices[0], phys_domain));
+                            new Pyramid(&vert_indices[0], phys_domain));
                        if (el_order > 1)
                        {
                           Array<int> * hov = new Array<int>;
@@ -2355,6 +2360,7 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                        }
                        break;
                     }
+                  */
                  case 15: // 1-node point
                  {
                     elements_0D.push_back(
@@ -2557,16 +2563,16 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                     }
                     vm = ho_wdg[el_order];
                     break;
-                  case Element::PYRAMID:
-                     ho_verts = ho_verts_3D[el];
-                     el_order = ho_el_order_3D[el];
-                     if (!ho_pyr[el_order])
-                     {
-                        ho_pyr[el_order] = new int[ho_verts->Size()];
-                        GmshHOPyramidMapping(el_order, ho_pyr[el_order]);
-                     }
-                     vm = ho_pyr[el_order];
-                     break;
+                  // case Element::PYRAMID:
+                  //    ho_verts = ho_verts_3D[el];
+                  //    el_order = ho_el_order_3D[el];
+                  //    if (ho_pyr[el_order])
+                  //    {
+                  //      ho_pyr[el_order] = new int[ho_verts->Size()];
+                  //      GmshHOPyramidMapping(el_order, ho_pyr[el_order]);
+                  //    }
+                  //    vm = ho_pyr[el_order];
+                  //    break;
                  default: // Any other element type
                     MFEM_WARNING("Unsupported Gmsh element type.");
                     break;
@@ -3706,28 +3706,20 @@ void NCMesh::FindSetNeighbors(const Array<char> &elem_set,

 static bool sorted_lists_intersect(const int* a, const int* b, int na, int nb)
 {
-   // pointers to "end" sentinel, not last entry. Not for dereferencing.
-   const int * const a_end = a + na;
-   const int * const b_end = b + nb;
-   while (a != a_end && b != b_end)
-   {
-      if (*a < *b)
-      {
-         ++a;
-      }
-      else if (*b < *a)
-      {
-         ++b;
-      }
-      else
-      {
-         return true; // neither *a < *b nor *b < *a thus a == b
-      }
-   }
-   return false; // no common element found
+   if (!na || !nb) { return false; }
+   int a_last = a[na-1], b_last = b[nb-1];
+   if (*b < *a) { goto l2; }  // woo-hoo! I always wanted to use a goto! :)
+l1:
+   if (a_last < *b) { return false; }
+   while (*a < *b) { a++; }
+   if (*a == *b) { return true; }
+l2:
+   if (b_last < *a) { return false; }
+   while (*b < *a) { b++; }
+   if (*a == *b) { return true; }
+   goto l1;
 }

-
 void NCMesh::FindNeighbors(int elem, Array<int> &neighbors,
                           const Array<int> *search_set)
 {
@@ -4488,19 +4480,6 @@ void NCMesh::GetPointMatrix(Geometry::Type geom, const char* ref_path,
            pm = PointMatrix(mid12, mid20, mid01);
         }
      }
-      else if (geom == Geometry::SEGMENT)
-      {
-         Point mid01(pm(0), pm(1));
-
-         if (child == 0)
-         {
-            pm = PointMatrix(pm(0), mid01);
-         }
-         else if (child == 1)
-         {
-            pm = PointMatrix(mid01, pm(1));
-         }
-      }
   }

   // write the points to the matrix
@@ -2689,20 +2689,6 @@ STable3D *ParMesh::GetSharedFacesTable()
            }
            break;
         }
-         case Element::PYRAMID:
-         {
-            for (int j = 0; j < 1; j++)
-            {
-               const int *fv = pyr_t::FaceVert[j];
-               sfaces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
-            }
-            for (int j = 1; j < 5; j++)
-            {
-               const int *fv = pyr_t::FaceVert[j];
-               sfaces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]);
-            }
-            break;
-         }
         case Element::HEXAHEDRON:
         {
            // find the face by the vertices with the smallest 3 numbers
@@ -2810,61 +2796,6 @@ STable3D *ParMesh::GetFaceNbrElementToFaceTable(int ret_ftbl)
            }
            break;
         }
-         case Element::PYRAMID:
-         {
-            for (int j = 0; j < 1; j++)
-            {
-               const int *fv = pyr_t::FaceVert[j];
-               int k = 0;
-               int max = v[fv[0]];
-
-               if (max < v[fv[1]]) { max = v[fv[1]], k = 1; }
-               if (max < v[fv[2]]) { max = v[fv[2]], k = 2; }
-               if (max < v[fv[3]]) { k = 3; }
-
-               int v0 = -1, v1 = -1, v2 = -1;
-               switch (k)
-               {
-                  case 0:
-                     v0 = v[fv[1]]; v1 = v[fv[2]]; v2 = v[fv[3]];
-                     break;
-                  case 1:
-                     v0 = v[fv[0]]; v1 = v[fv[2]]; v2 = v[fv[3]];
-                     break;
-                  case 2:
-                     v0 = v[fv[0]]; v1 = v[fv[1]]; v2 = v[fv[3]];
-                     break;
-                  case 3:
-                     v0 = v[fv[0]]; v1 = v[fv[1]]; v2 = v[fv[2]];
-                     break;
-               }
-               int lf = faces_tbl->Index(v0, v1, v2);
-               if (lf < 0)
-               {
-                  lf = sfaces_tbl->Index(v0, v1, v2);
-                  if (lf >= 0)
-                  {
-                     lf += NumOfFaces;
-                  }
-               }
-               face_nbr_el_to_face->Push(i, lf);
-            }
-            for (int j = 1; j < 5; j++)
-            {
-               const int *fv = pyr_t::FaceVert[j];
-               int lf = faces_tbl->Index(v[fv[0]], v[fv[1]], v[fv[2]]);
-               if (lf < 0)
-               {
-                  lf = sfaces_tbl->Index(v[fv[0]], v[fv[1]], v[fv[2]]);
-                  if (lf >= 0)
-                  {
-                     lf += NumOfFaces;
-                  }
-               }
-               face_nbr_el_to_face->Push(i, lf);
-            }
-            break;
-         }
         case Element::HEXAHEDRON:
         {
            // find the face by the vertices with the smallest 3 numbers
@@ -501,9 +501,6 @@ public:
   ///    mask & 4 - Loc1, mask & 8 - Loc2, mask & 16 - Face.
   /// These mask values are defined in the ConfigMasks enum type as part of the
   /// FaceElementTransformations class in fem/eltrans.hpp.
-   ///
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
   FaceElementTransformations *GetFaceElementTransformations(
      int FaceNo,
      int mask = 31) override;
@@ -512,9 +509,7 @@ public:
       using the shared face index @a sf. @a fill2 specify if the information
       for elem2 of the face should be computed or not.
       In the returned object, 1 and 2 refer to the local and the neighbor
-       elements, respectively.
-       Note that the pointer is owned by the class and is shared, i.e., calling
-       this function resets pointers obtained from previous calls. */
+       elements, respectively. */
   FaceElementTransformations *
   GetSharedFaceTransformations(int sf, bool fill2 = true);

@@ -522,16 +517,12 @@ public:
       using the face index @a FaceNo. @a fill2 specify if the information
       for elem2 of the face should be computed or not.
       In the returned object, 1 and 2 refer to the local and the neighbor
-       elements, respectively.
-       Note that the pointer is owned by the class and is shared, i.e., calling
-       this function resets pointers obtained from previous calls. */
+       elements, respectively. */
   FaceElementTransformations *
   GetSharedFaceTransformationsByLocalIndex(int FaceNo, bool fill2 = true);

-   /// Returns a pointer to the transformation defining the i-th face neighbor.
-   /// Note that the pointer is owned by the class and is shared, i.e., calling
-   /// this function resets pointers obtained from previous calls.
-   ElementTransformation *GetFaceNbrElementTransformation(int i)
+   ElementTransformation *
+   GetFaceNbrElementTransformation(int i)
   {
      GetFaceNbrElementTransformation(i, &FaceNbrTransformation);

@@ -0,0 +1,359 @@
+// 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 "change_basis.hpp"
+#include "fem/qinterp/dispatch.hpp"
+#include "general/forall.hpp"
+#include "linalg/dtensor.hpp"
+
+namespace mfem
+{
+
+/// @brief Compute the inverse of the matrix A and store the result in Ainv.
+///
+/// The input A is an array of size n*n, interpreted as a matrix with column
+/// major ordering.
+void ComputeInverse(const Array<double> &A, Array<double> &Ainv)
+{
+   Array<double> A2 = A;
+   const int n2 = A.Size();
+   const int n = sqrt(n2);
+   Array<int> ipiv(n);
+   LUFactors lu(A2.GetData(), ipiv.GetData());
+   lu.Factor(n);
+   Ainv.SetSize(n2);
+   lu.GetInverseMatrix(n, Ainv.GetData());
+}
+
+void SubcellIntegrals(int n, const Poly_1D::Basis &basis, Array<double> &B)
+{
+   const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, n);
+   const double *gll_pts = poly1d.GetPoints(n, BasisType::GaussLobatto);
+   Vector u(n);
+   B.SetSize(n*n);
+   B = 0.0;
+
+   for (int i = 0; i < n; ++i)
+   {
+      const double h = gll_pts[i+1] - gll_pts[i];
+      // Loop over subcell quadrature points
+      for (int iq = 0; iq < ir.Size(); ++iq)
+      {
+         const IntegrationPoint &ip = ir[iq];
+         const double x = gll_pts[i] + h*ip.x;
+         const double w = h*ip.weight;
+         basis.Eval(x, u);
+         for (int j = 0; j < n; ++j)
+         {
+            B[i + j*n] += w*u[j];
+         }
+      }
+   }
+}
+
+void Transpose(const Array<double> &B, Array<double> &Bt)
+{
+   const int n = sqrt(B.Size());
+   Bt.SetSize(n*n);
+   for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) { Bt[i+j*n] = B[j+i*n]; }
+}
+
+ChangeOfBasis_L2::ChangeOfBasis_L2(FiniteElementSpace &fes)
+   : Operator(fes.GetTrueVSize()),
+     ne(fes.GetNE())
+{
+   auto *fec1 = dynamic_cast<const L2_FECollection*>(fes.FEColl());
+   MFEM_VERIFY(fec1, "Must be L2 finite element space");
+
+   const int btype = fec1->GetBasisType();
+
+   // If the basis types are the same, don't need to perform change of basis.
+   no_op = (btype == BasisType::IntegratedGLL);
+   if (no_op) { return; }
+
+   // Convert from the given basis to the "integrated GLL basis".
+   // The degrees of freedom are integrals over subcells.
+   const FiniteElement *fe = fes.GetFE(0);
+   auto *tbe = dynamic_cast<const TensorBasisElement*>(fe);
+   MFEM_VERIFY(tbe != nullptr, "Must be a tensor element.");
+   const Poly_1D::Basis &basis = tbe->GetBasis1D();
+
+   const int p = fes.GetMaxElementOrder();
+   const int pp1 = p + 1;
+
+   Array<double> B_inv;
+   SubcellIntegrals(pp1, basis, B_inv);
+
+   ComputeInverse(B_inv, B_1d);
+   Transpose(B_1d, Bt_1d);
+
+   // Set up the DofToQuad object, used in TensorValues
+   dof2quad.FE = fe;
+   dof2quad.mode = DofToQuad::TENSOR;
+   dof2quad.ndof = pp1;
+   dof2quad.nqpt = pp1;
+}
+
+void ChangeOfBasis_L2::Mult(const Vector &x, Vector &y) const
+{
+   if (no_op) { y = x; return; }
+   using namespace internal::quadrature_interpolator;
+   dof2quad.B.MakeRef(B_1d);
+   TensorValues<QVectorLayout::byVDIM>(ne, 1, dof2quad, x, y);
+}
+
+void ChangeOfBasis_L2::MultTranspose(const Vector &x, Vector &y) const
+{
+   if (no_op) { y = x; return; }
+   using namespace internal::quadrature_interpolator;
+   dof2quad.B.MakeRef(Bt_1d);
+   TensorValues<QVectorLayout::byVDIM>(ne, 1, dof2quad, x, y);
+}
+
+ChangeOfBasis_RT::ChangeOfBasis_RT(FiniteElementSpace &fes)
+   : Operator(fes.GetTrueVSize()),
+     fes(fes),
+     dim(fes.GetMesh()->Dimension()),
+     ne(fes.GetNE()),
+     p(fes.GetMaxElementOrder())
+{
+   auto op = fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC);
+   elem_restr = dynamic_cast<const ElementRestriction*>(op);
+   MFEM_VERIFY(elem_restr != NULL, "Missing element restriciton.");
+
+   const auto *rt_fec = dynamic_cast<const RT_FECollection*>(fes.FEColl());
+   MFEM_VERIFY(rt_fec, "Must be RT finite element space.");
+
+   const int cb_type = rt_fec->GetClosedBasisType();
+   const int ob_type = rt_fec->GetOpenBasisType();
+
+   no_op = (cb_type == BasisType::GaussLobatto &&
+            ob_type == BasisType::IntegratedGLL);
+   if (no_op) { return; }
+
+   const int pp1 = p + 1;
+
+   Poly_1D::Basis &cbasis = poly1d.GetBasis(p, cb_type);
+   Poly_1D::Basis &obasis = poly1d.GetBasis(p-1, ob_type);
+
+   const double *cpts2 = poly1d.GetPoints(p, BasisType::GaussLobatto);
+
+   Bci_1d.SetSize(pp1*pp1);
+   Vector b(pp1);
+   for (int i = 0; i < pp1; ++i)
+   {
+      cbasis.Eval(cpts2[i], b);
+      for (int j = 0; j < pp1; ++j)
+      {
+         Bci_1d[i + j*pp1] = b[j];
+      }
+   }
+   SubcellIntegrals(p, obasis, Boi_1d);
+
+   ComputeInverse(Boi_1d, Bo_1d);
+   Transpose(Bo_1d, Bot_1d);
+   ComputeInverse(Bci_1d, Bc_1d);
+   Transpose(Bc_1d, Bct_1d);
+}
+
+const double *ChangeOfBasis_RT::GetOpenMap(Mode mode) const
+{
+   switch (mode)
+   {
+      case NORMAL: return Bo_1d.Read();
+      case TRANSPOSE: return Bot_1d.Read();
+      case INVERSE: return Boi_1d.Read();
+   }
+   return nullptr;
+}
+
+const double *ChangeOfBasis_RT::GetClosedMap(Mode mode) const
+{
+   switch (mode)
+   {
+      case NORMAL: return Bc_1d.Read();
+      case TRANSPOSE: return Bct_1d.Read();
+      case INVERSE: return Bci_1d.Read();
+   }
+   return nullptr;
+}
+
+void ChangeOfBasis_RT::MultRT_2D(const Vector &x, Vector &y, Mode mode) const
+{
+   const int DIM = dim;
+   const int NE = ne;
+   const int D1D = p + 1;
+   const int ND = (p+1)*p;
+   const double *BC = GetClosedMap(mode);
+   const double *BO = GetOpenMap(mode);
+   const auto X = Reshape(x.Read(), DIM*ND, ne);
+   auto Y = Reshape(y.Write(), DIM*ND, ne);
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int c = 0; c < DIM; ++c)
+      {
+         const int nx = (c == 0) ? D1D : D1D-1;
+         const int ny = (c == 1) ? D1D : D1D-1;
+         const double *Bx = (c == 0) ? BC : BO;
+         const double *By = (c == 1) ? BC : BO;
+
+         for (int i = 0; i < ND; ++i)
+         {
+            Y(i + c*ND, e) = 0.0;
+         }
+         for (int iy = 0; iy < ny; ++ iy)
+         {
+            double xx[MAX_D1D];
+            for (int ix = 0; ix < nx; ++ix) { xx[ix] = 0.0; }
+            for (int jx = 0; jx < nx; ++jx)
+            {
+               const double val = X(jx + iy*nx + c*nx*ny, e);
+               for (int ix = 0; ix < nx; ++ix)
+               {
+                  xx[ix] += val*Bx[ix + jx*nx];
+               }
+            }
+            for (int jy = 0; jy < ny; ++jy)
+            {
+               const double b = By[jy + iy*ny];
+               for (int ix = 0; ix < nx; ++ix)
+               {
+                  Y(ix + jy*nx + c*nx*ny, e) += xx[ix]*b;
+               }
+            }
+         }
+      }
+   });
+}
+
+void ChangeOfBasis_RT::MultRT_3D(const Vector &x, Vector &y, Mode mode) const
+{
+   const int DIM = dim;
+   const int NE = ne;
+   const int D1D = p + 1;
+   const int ND = (p+1)*p*p;
+   const double *BC = GetClosedMap(mode);
+   const double *BO = GetOpenMap(mode);
+   const auto X = Reshape(x.Read(), DIM*ND, ne);
+   auto Y = Reshape(y.Write(), DIM*ND, ne);
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int c = 0; c < DIM; ++c)
+      {
+         const int nx = (c == 0) ? D1D : D1D-1;
+         const int ny = (c == 1) ? D1D : D1D-1;
+         const int nz = (c == 2) ? D1D : D1D-1;
+         const double *Bx = (c == 0) ? BC : BO;
+         const double *By = (c == 1) ? BC : BO;
+         const double *Bz = (c == 2) ? BC : BO;
+
+         for (int i = 0; i < ND; ++i)
+         {
+            Y(i + c*ND, e) = 0.0;
+         }
+         for (int iz = 0; iz < nz; ++ iz)
+         {
+            double xy[MAX_D1D][MAX_D1D];
+            for (int iy = 0; iy < ny; ++iy)
+            {
+               for (int ix = 0; ix < nx; ++ix)
+               {
+                  xy[iy][ix] = 0.0;
+               }
+            }
+            for (int iy = 0; iy < ny; ++iy)
+            {
+               double xx[MAX_D1D];
+               for (int ix = 0; ix < nx; ++ix) { xx[ix] = 0.0; }
+               for (int ix = 0; ix < nx; ++ix)
+               {
+                  const double val = X(ix + iy*nx + iz*nx*ny + c*ND, e);
+                  for (int jx = 0; jx < nx; ++jx)
+                  {
+                     xx[jx] += val*Bx[jx + ix*nx];
+                  }
+               }
+               for (int jy = 0; jy < ny; ++jy)
+               {
+                  const double b = By[jy + iy*ny];
+                  for (int jx = 0; jx < nx; ++jx)
+                  {
+                     xy[jy][jx] += xx[jx] * b;
+                  }
+               }
+            }
+            for (int jz = 0; jz < nz; ++jz)
+            {
+               const double b = Bz[jz + iz*nz];
+               for (int jy = 0; jy < ny; ++jy)
+               {
+                  for (int jx = 0; jx < nx; ++jx)
+                  {
+                     Y(jx + jy*nx + jz*nx*ny + c*ND, e) += xy[jy][jx] * b;
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
+void ChangeOfBasis_RT::Mult(const Vector &x, Vector &y, Mode mode) const
+{
+   if (no_op) { y = x; return; }
+
+   const Operator *P = fes.GetProlongationMatrix();
+
+   if (IsIdentityProlongation(P))
+   {
+      x_l.MakeRef(const_cast<Vector&>(x), 0, fes.GetVSize());
+      y_l.MakeRef(y, 0, fes.GetVSize());
+   }
+   else
+   {
+      x_l.SetSize(fes.GetVSize());
+      y_l.SetSize(fes.GetVSize());
+      P->Mult(x, x_l);
+   }
+
+   x_e.SetSize(elem_restr->Height());
+   y_e.SetSize(elem_restr->Height());
+
+   elem_restr->Mult(x_l, x_e);
+
+   if (dim == 2) { MultRT_2D(x_e, y_e, mode); }
+   else { MultRT_3D(x_e, y_e, mode); }
+
+   elem_restr->MultLeftInverse(y_e, y_l);
+
+   const Operator *R = fes.GetRestrictionOperator();
+   if (R) { R->Mult(y_l, y); }
+   else { MFEM_VERIFY(P == NULL, "Invalid state."); }
+}
+
+void ChangeOfBasis_RT::Mult(const Vector &x, Vector &y) const
+{
+   Mult(x, y, NORMAL);
+}
+
+void ChangeOfBasis_RT::MultTranspose(const Vector &x, Vector &y) const
+{
+   Mult(x, y, TRANSPOSE);
+}
+
+void ChangeOfBasis_RT::MultInverse(const Vector &x, Vector &y) const
+{
+   Mult(x, y, INVERSE);
+}
+
+} // namespace mfem
@@ -0,0 +1,87 @@
+// 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 CHANGE_BASIS_HPP
+#define CHANGE_BASIS_HPP
+
+#include "mfem.hpp"
+
+namespace mfem
+{
+
+/// @brief Change of basis operator between L2 spaces.
+///
+/// This represents the change-of-basis operator from the given L2 space to a
+/// space using the IntegratedGLL basis.
+class ChangeOfBasis_L2 : public Operator
+{
+private:
+   const int ne; ///< Number of elements in the mesh.
+   mutable DofToQuad dof2quad; ///< 1D basis transformation.
+   Array<double> B_1d; ///< 1D basis transformation matrix.
+   Array<double> Bt_1d; ///< 1D basis transformation matrix traspose.
+   bool no_op; ///< If the basis types are the same, the operation is a no-op.
+public:
+   ChangeOfBasis_L2(FiniteElementSpace &fes);
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;
+};
+
+/// Change of basis operator between RT spaces.
+///
+/// This represents the change-of-basis operator from the given RT space to a
+/// space using Gauss-Lobatto as the "open" basis and IntegratedGLL as the
+/// "closed" basis.
+class ChangeOfBasis_RT : public Operator
+{
+public:
+   // Should be private, nvcc limitation...
+   enum Mode
+   {
+      NORMAL,
+      TRANSPOSE,
+      INVERSE
+   };
+private:
+   FiniteElementSpace &fes; ///< The finite element space.
+   const int dim; ///< Dimension of the mesh.
+   const int ne; ///< Number of elements.
+   const int p; ///< Polynomial degree.
+   const ElementRestriction *elem_restr; ///< Element restriction operator.
+   Array<double> Bc_1d; ///< 1D closed basis transformation matrix.
+   Array<double> Bci_1d; ///< 1D closed basis transformation matrix inverse.
+   Array<double> Bct_1d; ///< 1D closed basis transformation matrix transpose.
+   Array<double> Bo_1d; ///< 1D open basis transformation matrix.
+   Array<double> Boi_1d; ///< 1D open basis transformation matrix inverse.
+   Array<double> Bot_1d; ///< 1D open basis transformation matrix transpose.
+
+   mutable Vector x_l, y_l; ///< L-vector layout
+   mutable Vector x_e, y_e; ///< E-vector layout
+
+   bool no_op; ///< If the spaces are the same, the operation is a no-op.
+
+   void Mult(const Vector &x, Vector &y, Mode mode) const;
+   const double *GetOpenMap(Mode mode) const;
+   const double *GetClosedMap(Mode mode) const;
+public:
+   ChangeOfBasis_RT(FiniteElementSpace &fes);
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;
+   void MultInverse(const Vector &x, Vector &y) const;
+   // The following should be considered private, public because of compiler
+   // limitations
+   void MultRT_2D(const Vector &x, Vector &y, Mode mode) const;
+   void MultRT_3D(const Vector &x, Vector &y, Mode mode) const;
+};
+
+} // namespace mfem
+
+#endif
@@ -0,0 +1,212 @@
+// 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.
+//
+//                     ---------------------------------
+//                     Poisson/Darcy Mixed Method Solver
+//                     ---------------------------------
+//
+// Solves a Poisson problem -Delta p = f using a mixed finite element
+// formulation). The right-hand side of the Poisson problem is the same as that
+// used in the LOR Solvers miniapp (see miniapps/solvers). Dirichlet boundary
+// conditions are enforced on all domain boundaries.
+//
+// Optionally, the equation alpha*p - Delta p = f can be solved by setting the
+// alpha parameter to a nonzero value.
+
+// This can be written in the form of a Darcy problem
+//
+//                           -u - grad(p) = 0
+//                       alpha*p + div(u) = f
+//
+// where natural boundary conditions are enforced on the flux u, and the
+// Dirichlet condition on p is enforced by modifying the right-hand side.
+//
+// The resulting saddle-point system is solved using MINRES with a matrix-free
+// block-diagonal preconditioner.
+//
+// See also example 5 and its parallel version.
+//
+// Sample runs:
+//
+//    darcy
+//    mpirun -np 4 darcy -m ../../data/fichera-q2.mesh
+
+#include "mfem.hpp"
+#include <iostream>
+#include <memory>
+
+#include "discrete_divergence.hpp"
+#include "hdiv_linear_solver.hpp"
+
+#include "../solvers/lor_mms.hpp"
+
+using namespace std;
+using namespace mfem;
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref = 0, int par_ref = 0);
+
+class RobinCoefficient : public Coefficient
+{
+   double Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   {
+      double xdata[3];
+      Vector xvec(xdata, 3);
+      T.Transform(ip, xvec);
+      const int dim = xvec.Size();
+
+      Vector n(dim);
+      CalcOrtho(T.Jacobian(), n);
+      n /= n.Norml2();
+
+      const double p_val = u(xvec);
+      const double x = pi*xvec[0];
+      const double y = pi*xvec[1];
+
+      if (dim == 2)
+      {
+         const double u_val = -pi*(n[0]*cos(x)*sin(y) + n[1]*sin(x)*cos(y));
+         return p_val - u_val;
+      }
+      else
+      {
+         MFEM_ABORT("Not implemented");
+      }
+      return 0.0;
+   }
+};
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init(argc, argv);
+   Hypre::Init();
+
+   const char *mesh_file = "../../data/star.mesh";
+   const char *device_config = "cpu";
+   int ser_ref = 1;
+   int par_ref = 1;
+   int order = 3;
+   double alpha = 0.0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&ser_ref, "-rs", "--serial-refine",
+                  "Number of times to refine the mesh in serial.");
+   args.AddOption(&par_ref, "-rp", "--parallel-refine",
+                  "Number of times to refine the mesh in parallel.");
+   args.AddOption(&order, "-o", "--order", "Polynomial degree.");
+   args.AddOption(&alpha, "-a", "--alpha", "Value of alpha coefficient.");
+   args.ParseCheck();
+
+   Device device(device_config);
+   if (Mpi::Root()) { device.Print(); }
+
+   ParMesh mesh = LoadParMesh(mesh_file, ser_ref, par_ref);
+   const int dim = mesh.Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "Spatial dimension must be 2 or 3.");
+
+   const int b1 = BasisType::GaussLobatto, b2 = BasisType::GaussLegendre;
+   const int mt = FiniteElement::VALUE;
+   RT_FECollection fec_rt(order-1, dim, b1, b2);
+   L2_FECollection fec_l2(order-1, dim, b2, mt);
+   ParFiniteElementSpace fes_rt(&mesh, &fec_rt);
+   ParFiniteElementSpace fes_l2(&mesh, &fec_l2);
+
+   HYPRE_BigInt ndofs_rt = fes_rt.GlobalTrueVSize();
+   HYPRE_BigInt ndofs_l2 = fes_l2.GlobalTrueVSize();
+
+   if (Mpi::Root())
+   {
+      cout << "\nRT DOFs: " << ndofs_rt << "\nL2 DOFs: " << ndofs_l2 << endl;
+   }
+
+   Array<int> ess_rt_dofs; // empty
+
+   // f is the RHS, u is the exact solution
+   FunctionCoefficient f_coeff(f(alpha)), u_coeff(u);
+   // Coefficient to enforce Robin boundary condition
+   RobinCoefficient bc_coeff;
+
+   // Assemble the right-hand side for the scalar (L2) unknown.
+   ParLinearForm b_l2(&fes_l2);
+   b_l2.AddDomainIntegrator(new DomainLFIntegrator(f_coeff));
+   b_l2.UseFastAssembly(true);
+   b_l2.Assemble();
+
+   // Enforce Dirichlet boundary conditions on the scalar unknown by adding
+   // the boundary term to the flux equation.
+   ParLinearForm b_rt(&fes_rt);
+   b_rt.AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(bc_coeff));
+   b_rt.UseFastAssembly(true);
+   b_rt.Assemble();
+
+   if (Mpi::Root()) { cout << "\nSaddle point solver... " << flush; }
+   tic_toc.Clear(); tic_toc.Start();
+
+   // Set up the block system of the form
+   //
+   // [  W     D ][ u ] = [  f  ]
+   // [ D^T   -M ][ q ] = [ g_D ]
+   //
+   // where W is the L2 mass matrix, D is the discrete divergence, and M is
+   // the RT mass matrix.
+   //
+   // If the coefficient alpha is set to zero, the system takes the form
+   //
+   // [  0     D ][ u ] = [  f  ]
+   // [ D^T   -M ][ q ] = [ g_D ]
+   //
+   // u is the scalar unknown, and q is the flux. f is the right-hand side from
+   // the Poisson problem, and g_D is the contribution to the right-hand side
+   // from the Dirichlet boundary condition.
+
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient alpha_coeff(alpha);
+   const auto solver_mode = HdivSaddlePointSolver::Mode::DARCY;
+   HdivSaddlePointSolver saddle_point_solver(
+      mesh, fes_rt, fes_l2, alpha_coeff, one, one, ess_rt_dofs, solver_mode);
+
+   const Array<int> &offsets = saddle_point_solver.GetOffsets();
+   BlockVector X_block(offsets), B_block(offsets);
+
+   b_l2.ParallelAssemble(B_block.GetBlock(0));
+   b_rt.ParallelAssemble(B_block.GetBlock(1));
+   B_block.SyncFromBlocks();
+
+   X_block = 0.0;
+   saddle_point_solver.Mult(B_block, X_block);
+   X_block.SyncToBlocks();
+
+   if (Mpi::Root())
+   {
+      cout << "Done.\nIterations: "
+           << saddle_point_solver.GetNumIterations()
+           << "\nElapsed: " << tic_toc.RealTime() << endl;
+   }
+
+   ParGridFunction x(&fes_l2);
+   x.SetFromTrueDofs(X_block.GetBlock(0));
+   const double error = x.ComputeL2Error(u_coeff);
+   if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+
+   return 0;
+}
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref, int par_ref)
+{
+   Mesh serial_mesh = Mesh::LoadFromFile(mesh_file);
+   for (int i = 0; i < ser_ref; ++i) { serial_mesh.UniformRefinement(); }
+   ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
+   serial_mesh.Clear();
+   for (int i = 0; i < par_ref; ++i) { mesh.UniformRefinement(); }
+   return mesh;
+}
@@ -0,0 +1,276 @@
+// 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 "mfem.hpp"
+#include "general/forall.hpp"
+#include "discrete_divergence.hpp"
+
+namespace mfem
+{
+
+/// @brief Eliminates columns in the given HypreParMatrix.
+///
+/// This is similar to HypreParMatrix::EliminateBC, except that only the columns
+/// are eliminated.
+void EliminateColumns(HypreParMatrix &D, const Array<int> &ess_dofs)
+{
+
+   hypre_ParCSRMatrix *A_hypre = D;
+   D.HypreReadWrite();
+
+   hypre_CSRMatrix *diag = hypre_ParCSRMatrixDiag(A_hypre);
+   hypre_CSRMatrix *offd = hypre_ParCSRMatrixOffd(A_hypre);
+
+   HYPRE_Int diag_ncols = hypre_CSRMatrixNumCols(diag);
+   HYPRE_Int offd_ncols = hypre_CSRMatrixNumCols(offd);
+
+   const int n_ess_dofs = ess_dofs.Size();
+
+   // Start communication to figure out which columns need to be eliminated in
+   // the off-diagonal block
+   hypre_ParCSRCommHandle *comm_handle;
+   HYPRE_Int *int_buf_data, *eliminate_col_diag, *eliminate_col_offd;
+   {
+      eliminate_col_diag = mfem_hypre_CTAlloc_host(HYPRE_Int, diag_ncols);
+      eliminate_col_offd = mfem_hypre_CTAlloc_host(HYPRE_Int, offd_ncols);
+
+      // Make sure A has a communication package
+      hypre_ParCSRCommPkg *comm_pkg = hypre_ParCSRMatrixCommPkg(A_hypre);
+      if (!comm_pkg)
+      {
+         hypre_MatvecCommPkgCreate(A_hypre);
+         comm_pkg = hypre_ParCSRMatrixCommPkg(A_hypre);
+      }
+
+      // Which of the local columns are to be eliminated?
+      for (int i = 0; i < diag_ncols; i++)
+      {
+         eliminate_col_diag[i] = 0;
+      }
+
+      ess_dofs.HostRead();
+      for (int i = 0; i < n_ess_dofs; i++)
+      {
+         eliminate_col_diag[ess_dofs[i]] = 1;
+      }
+
+      // Use a matvec communication pattern to find (in eliminate_col_offd)
+      // which of the local offd columns are to be eliminated
+      HYPRE_Int num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
+      HYPRE_Int int_buf_sz = hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends);
+      int_buf_data = mfem_hypre_CTAlloc_host(HYPRE_Int, int_buf_sz);
+      HYPRE_Int *send_map_elmts = hypre_ParCSRCommPkgSendMapElmts(comm_pkg);
+      for (int i = 0; i < int_buf_sz; ++i)
+      {
+         const int k = send_map_elmts[i];
+         int_buf_data[i] = eliminate_col_diag[k];
+      }
+      comm_handle = hypre_ParCSRCommHandleCreate(
+                       11, comm_pkg, int_buf_data, eliminate_col_offd);
+   }
+
+   // Eliminate columns in the diagonal block
+   {
+      Memory<HYPRE_Int> col_mem(eliminate_col_diag, diag_ncols, false);
+      const auto cols = col_mem.Read(GetHypreMemoryClass(), diag_ncols);
+      const int nrows_diag = hypre_CSRMatrixNumRows(diag);
+      const auto I = diag->i;
+      const auto J = diag->j;
+      auto data = diag->data;
+      MFEM_HYPRE_FORALL(i, nrows_diag,
+      {
+         for (int jj=I[i]; jj<I[i+1]; ++jj)
+         {
+            const int j = J[jj];
+            data[jj] *= 1 - cols[j];
+         }
+      });
+      col_mem.Delete();
+   }
+
+   // Wait for MPI communication to finish
+   hypre_ParCSRCommHandleDestroy(comm_handle);
+   mfem_hypre_TFree_host(int_buf_data);
+   mfem_hypre_TFree_host(eliminate_col_diag);
+
+   // Eliminate columns in the off-diagonal block
+   {
+      Memory<HYPRE_Int> col_mem(eliminate_col_offd, offd_ncols, false);
+      const auto cols = col_mem.Read(GetHypreMemoryClass(), offd_ncols);
+      const int nrows_offd = hypre_CSRMatrixNumRows(offd);
+      const auto I = offd->i;
+      const auto J = offd->j;
+      auto data = offd->data;
+      MFEM_HYPRE_FORALL(i, nrows_offd,
+      {
+         for (int jj=I[i]; jj<I[i+1]; ++jj)
+         {
+            const int j = J[jj];
+            data[jj] *= 1 - cols[j];
+         }
+      });
+      col_mem.Delete();
+   }
+
+   mfem_hypre_TFree_host(eliminate_col_offd);
+}
+
+void FormElementToFace2D(int order, Array<int> &element2face)
+{
+   const int o = order;
+   const int op1 = order + 1;
+
+   for (int iy = 0; iy < o; ++iy)
+   {
+      for (int ix = 0; ix < o; ++ix)
+      {
+         const int ivol = ix + iy*o;
+         element2face[0 + 4*ivol] = -1 - (ix + iy*op1); // left, x = 0
+         element2face[1 + 4*ivol] = ix+1 + iy*op1; // right, x = 1
+         element2face[2 + 4*ivol] = -1 - (ix + iy*o + o*op1); // bottom, y = 0
+         element2face[3 + 4*ivol] = ix + (iy+1)*o + o*op1; // top, y = 1
+      }
+   }
+}
+
+void FormElementToFace3D(int order, Array<int> &element2face)
+{
+   const int o = order;
+   const int op1 = order + 1;
+
+   const int n = o*o*op1; // number of faces per dimension
+
+   for (int iz = 0; iz < o; ++iz)
+   {
+      for (int iy = 0; iy < o; ++iy)
+      {
+         for (int ix = 0; ix < o; ++ix)
+         {
+            const int ivol = ix + iy*o + iz*o*o;
+            element2face[0 + 6*ivol] = -1 - (ix + iy*op1 + iz*o*op1); // x = 0
+            element2face[1 + 6*ivol] = ix+1 + iy*op1 + iz*o*op1; // x = 1
+            element2face[2 + 6*ivol] = -1 - (ix + iy*o + iz*o*op1 + n); // y = 0
+            element2face[3 + 6*ivol] = ix + (iy+1)*o + iz*o*op1 + n; // y = 1
+            element2face[4 + 6*ivol] = -1 - (ix + iy*o + iz*o*o + 2*n); // z = 0
+            element2face[5 + 6*ivol] = ix + iy*o + (iz+1)*o*o + 2*n; // z = 1
+         }
+      }
+   }
+}
+
+HypreParMatrix *FormDiscreteDivergenceMatrix(ParFiniteElementSpace &fes_rt,
+                                             ParFiniteElementSpace &fes_l2,
+                                             const Array<int> &ess_dofs)
+{
+   const Mesh &mesh = *fes_rt.GetMesh();
+   const int dim = mesh.Dimension();
+   const int order = fes_rt.GetMaxElementOrder();
+
+   const int n_rt = fes_rt.GetNDofs();
+   const int n_l2 = fes_l2.GetNDofs();
+
+   SparseMatrix D_local;
+   D_local.OverrideSize(n_l2, n_rt);
+
+   D_local.GetMemoryI().New(n_l2 + 1);
+   // Each row always has 2*dim nonzeros (one for each face of the element)
+   const int nnz = n_l2*2*dim;
+   auto I = D_local.WriteI();
+   MFEM_FORALL(i, n_l2+1, I[i] = 2*dim*i; );
+
+   const int nel_ho = mesh.GetNE();
+   const int nface_per_el = dim*pow(order, dim-1)*(order+1);
+   const int nvol_per_el = pow(order, dim);
+
+   // element2face is a mapping of size (2*dim, nvol_per_el) such that with a
+   // macro element, subelement i (in lexicographic ordering) has faces (also
+   // in lexicographic order) given by the entries (j, i).
+   Array<int> element2face;
+   element2face.SetSize(2*dim*nvol_per_el);
+
+   if (dim == 2) { FormElementToFace2D(order, element2face); }
+   else if (dim == 3) { FormElementToFace3D(order, element2face); }
+   else { MFEM_ABORT("Unsupported dimension.") }
+
+   const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
+   const auto *R_rt = dynamic_cast<const ElementRestriction*>(
+                         fes_rt.GetElementRestriction(ordering));
+   const auto gather_rt = Reshape(R_rt->GatherMap().Read(), nface_per_el, nel_ho);
+   const auto e2f = Reshape(element2face.Read(), 2*dim, nvol_per_el);
+
+   // Fill J and data
+   D_local.GetMemoryJ().New(nnz);
+   D_local.GetMemoryData().New(nnz);
+
+   auto J = D_local.WriteJ();
+   auto V = D_local.WriteData();
+
+   // Loop over L2 DOFs
+   MFEM_FORALL(i, n_l2,
+   {
+      const int i_loc = i%nvol_per_el;
+      const int i_el = i/nvol_per_el;
+
+      for (int k = 0; k < 2*dim; ++k)
+      {
+         const int sjv_loc = e2f(k, i_loc);
+         const int jv_loc = (sjv_loc >= 0) ? sjv_loc : -1 - sjv_loc;
+         const int sgn1 = (sjv_loc >= 0) ? 1 : -1;
+         const int sj = gather_rt(jv_loc, i_el);
+         const int j = (sj >= 0) ? sj : -1 - sj;
+         const int sgn2 = (sj >= 0) ? 1 : -1;
+
+         J[k + 2*dim*i] = j;
+         V[k + 2*dim*i] = sgn1*sgn2;
+      }
+   });
+
+   // Create a block diagonal parallel matrix
+   OperatorHandle D_diag(Operator::Hypre_ParCSR);
+   D_diag.MakeRectangularBlockDiag(fes_rt.GetComm(),
+                                   fes_l2.GlobalVSize(),
+                                   fes_rt.GlobalVSize(),
+                                   fes_l2.GetDofOffsets(),
+                                   fes_rt.GetDofOffsets(),
+                                   &D_local);
+
+   HypreParMatrix *D;
+   // Assemble the parallel gradient matrix, must be deleted by the caller
+   if (IsIdentityProlongation(fes_rt.GetProlongationMatrix()))
+   {
+      D = D_diag.As<HypreParMatrix>();
+      D_diag.SetOperatorOwner(false);
+      HypreStealOwnership(*D, D_local);
+   }
+   else
+   {
+      OperatorHandle Rt(Transpose(*fes_l2.GetRestrictionMatrix()));
+      OperatorHandle Rt_diag(Operator::Hypre_ParCSR);
+      Rt_diag.MakeRectangularBlockDiag(fes_l2.GetComm(),
+                                       fes_l2.GlobalVSize(),
+                                       fes_l2.GlobalTrueVSize(),
+                                       fes_l2.GetDofOffsets(),
+                                       fes_l2.GetTrueDofOffsets(),
+                                       Rt.As<SparseMatrix>());
+      D = RAP(Rt_diag.As<HypreParMatrix>(),
+              D_diag.As<HypreParMatrix>(),
+              fes_rt.Dof_TrueDof_Matrix());
+   }
+   D->CopyRowStarts();
+   D->CopyColStarts();
+
+   // Eliminate the boundary conditions
+   EliminateColumns(*D, ess_dofs);
+
+   return D;
+}
+
+} // namespace mfem
@@ -0,0 +1,32 @@
+// 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_DISCRETE_DIVERGENCE_HPP
+#define MFEM_DISCRETE_DIVERGENCE_HPP
+
+#include "mfem.hpp"
+
+namespace mfem
+{
+
+/// @brief Eliminates columns in the given HypreParMatrix.
+///
+/// This is similar to HypreParMatrix::EliminateBC, except that only the columns
+/// are eliminated.
+void EliminateColumns(HypreParMatrix &D, const Array<int> &ess_dofs);
+
+HypreParMatrix *FormDiscreteDivergenceMatrix(ParFiniteElementSpace &fes_rt,
+                                             ParFiniteElementSpace &fes_l2,
+                                             const Array<int> &ess_dofs);
+
+} // namespace mfem
+
+#endif
@@ -0,0 +1,280 @@
+// 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.
+//
+//                     ---------------------------------
+//                     H(div) saddle-point system solver
+//                     ---------------------------------
+//
+// Solves the grad-div problem u - grad(div(u)) = f using a variety of solver
+// techniques. This miniapp supports solving this problem using a variety of
+// matrix-free and matrix-based preconditioning methods, inclding:
+//
+// * Matrix-free block-diagonal preconditioning for the saddle-point system.
+// * ADS-AMG preconditioning.
+// * Low-order-refined ADS-AMG preconditioning (matrix-free).
+// * Hybridization with AMG preconditioning.
+//
+// The problem setup is the same as in the LOR solvers miniapps (in the
+// miniapps/solvers directory). Dirichlet conditions are enforced on the normal
+// component of u.
+//
+// Sample runs:
+//
+//    grad_div -sp -ams -lor -hb
+//    mpirun -np 4 grad_div -sp -ams -lor -hb -m ../../data/fichera-q2.mesh -rp 0
+
+#include "mfem.hpp"
+#include <iostream>
+#include <memory>
+#include "hdiv_linear_solver.hpp"
+#include "../solvers/lor_mms.hpp"
+
+using namespace std;
+using namespace mfem;
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref = 0, int par_ref = 0);
+void SolveCG(Operator &A, Solver &P, const Vector &B, Vector &X);
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init(argc, argv);
+   Hypre::Init();
+
+   const char *mesh_file = "../../data/star.mesh";
+   const char *device_config = "cpu";
+   int ser_ref = 1;
+   int par_ref = 1;
+   int order = 3;
+   bool use_saddle_point = false;
+   bool use_ams = false;
+   bool use_lor_ams = false;
+   bool use_hybridization = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&ser_ref, "-rs", "--serial-refine",
+                  "Number of times to refine the mesh in serial.");
+   args.AddOption(&par_ref, "-rp", "--parallel-refine",
+                  "Number of times to refine the mesh in parallel.");
+   args.AddOption(&order, "-o", "--order", "Polynomial degree.");
+   args.AddOption(&use_saddle_point,
+                  "-sp", "--saddle-point", "-no-sp", "--no-saddle-point",
+                  "Enable or disable saddle-point solver.");
+   args.AddOption(&use_ams, "-ams", "--ams", "-no-ams", "--no-ams",
+                  "Enable or disable AMS solver.");
+   args.AddOption(&use_lor_ams, "-lor", "--lor-ams", "-no-lor", "--no-lor-ams",
+                  "Enable or disable LOR-AMS solver.");
+   args.AddOption(&use_hybridization,
+                  "-hb", "--hybridization", "-no-hb", "--no-hybridization",
+                  "Enable or disable hybridization solver.");
+   args.ParseCheck();
+
+   if (!use_saddle_point && !use_ams && !use_lor_ams && !use_hybridization)
+   {
+      if (Mpi::Root()) { cout << "No solver enabled. Exiting.\n"; }
+      return 0;
+   }
+
+   Device device(device_config);
+   if (Mpi::Root()) { device.Print(); }
+
+   ParMesh mesh = LoadParMesh(mesh_file, ser_ref, par_ref);
+   const int dim = mesh.Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "Spatial dimension must be 2 or 3.");
+
+   const int b1 = BasisType::GaussLobatto, b2 = BasisType::GaussLegendre;
+   RT_FECollection fec_rt(order-1, dim, b1, b2);
+   ParFiniteElementSpace fes_rt(&mesh, &fec_rt);
+
+   Array<int> ess_rt_dofs;
+   fes_rt.GetBoundaryTrueDofs(ess_rt_dofs);
+
+   VectorFunctionCoefficient f_vec_coeff(dim, f_vec(true)), u_vec_coeff(dim, u_vec);
+
+   ParLinearForm b(&fes_rt);
+   b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(f_vec_coeff));
+   b.UseFastAssembly(true);
+   b.Assemble();
+
+   ConstantCoefficient alpha_coeff(1.0);
+   ConstantCoefficient beta_coeff(1.0);
+
+   ParGridFunction x(&fes_rt);
+   x.ProjectCoefficient(u_vec_coeff);
+
+   cout.precision(4);
+   cout << scientific;
+
+   if (use_saddle_point)
+   {
+      if (Mpi::Root()) { cout << "\nSaddle point solver... " << flush; }
+      tic_toc.Clear(); tic_toc.Start();
+
+      const int mt = FiniteElement::INTEGRAL;
+      L2_FECollection fec_l2(order-1, dim, b2, mt);
+      ParFiniteElementSpace fes_l2(&mesh, &fec_l2);
+
+      HdivSaddlePointSolver saddle_point_solver(
+         mesh, fes_rt, fes_l2, alpha_coeff, beta_coeff, ess_rt_dofs,
+         HdivSaddlePointSolver::Mode::GRAD_DIV);
+
+      const Array<int> &offsets = saddle_point_solver.GetOffsets();
+
+      BlockVector X_block(offsets), B_block(offsets);
+      B_block.GetBlock(0) = 0.0;
+      b.ParallelAssemble(B_block.GetBlock(1));
+      B_block.GetBlock(1) *= -1.0;
+      B_block.SyncFromBlocks();
+
+      x.ParallelProject(X_block.GetBlock(1));
+      saddle_point_solver.SetBC(X_block.GetBlock(1));
+
+      X_block = 0.0;
+      saddle_point_solver.Mult(B_block, X_block);
+
+      if (Mpi::Root())
+      {
+         cout << "Done.\nIterations: "
+              << saddle_point_solver.GetNumIterations()
+              << "\nElapsed: " << tic_toc.RealTime() << endl;
+      }
+
+      X_block.SyncToBlocks();
+      x.SetFromTrueDofs(X_block.GetBlock(1));
+      const double error = x.ComputeL2Error(u_vec_coeff);
+      if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+   }
+
+   if (use_ams)
+   {
+      if (Mpi::Root()) { cout << "\nAMS solver... " << flush; }
+      tic_toc.Clear(); tic_toc.Start();
+
+      ParBilinearForm a(&fes_rt);
+      a.AddDomainIntegrator(new DivDivIntegrator(alpha_coeff));
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(beta_coeff));
+      a.Assemble();
+
+      OperatorHandle A;
+      Vector B, X;
+      b.Assemble();
+      x.ProjectCoefficient(u_vec_coeff);
+      a.FormLinearSystem(ess_rt_dofs, x, b, A, X, B);
+      HypreParMatrix &Ah = *A.As<HypreParMatrix>();
+
+      std::unique_ptr<Solver> prec;
+      if (dim == 2) { prec.reset(new HypreAMS(Ah, &fes_rt)); }
+      else  { prec.reset(new HypreADS(Ah, &fes_rt)); }
+
+      SolveCG(Ah, *prec, B, X);
+      x.SetFromTrueDofs(X);
+      const double error = x.ComputeL2Error(u_vec_coeff);
+      if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+   }
+
+   if (use_lor_ams)
+   {
+      const int b2_lor = BasisType::IntegratedGLL;
+      RT_FECollection fec_rt_lor(order-1, dim, b1, b2_lor);
+      ParFiniteElementSpace fes_rt_lor(&mesh, &fec_rt_lor);
+
+      ParLinearForm b_lor(&fes_rt_lor);
+      b_lor.AddDomainIntegrator(new VectorFEDomainLFIntegrator(f_vec_coeff));
+      b_lor.UseFastAssembly(true);
+      b_lor.Assemble();
+
+      if (Mpi::Root()) { cout << "\nLOR-AMS solver... " << flush; }
+      tic_toc.Clear(); tic_toc.Start();
+
+      ParBilinearForm a(&fes_rt_lor);
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a.AddDomainIntegrator(new DivDivIntegrator(alpha_coeff));
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(beta_coeff));
+      a.Assemble();
+
+      ParGridFunction x_lor(&fes_rt_lor);
+      x_lor.ProjectCoefficient(u_vec_coeff);
+
+      OperatorHandle A;
+      Vector B, X;
+      a.FormLinearSystem(ess_rt_dofs, x_lor, b_lor, A, X, B);
+
+      std::unique_ptr<Solver> prec;
+      if (dim == 2) { prec.reset(new LORSolver<HypreAMS>(a, ess_rt_dofs)); }
+      else { prec.reset(new LORSolver<HypreADS>(a, ess_rt_dofs)); }
+
+      SolveCG(*A, *prec, B, X);
+      a.RecoverFEMSolution(X, b_lor, x_lor);
+      const double error = x_lor.ComputeL2Error(u_vec_coeff);
+      if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+   }
+
+   if (use_hybridization)
+   {
+      if (Mpi::Root()) { cout << "\nHybridization solver... " << flush; }
+      tic_toc.Clear(); tic_toc.Start();
+
+      DG_Interface_FECollection fec_hb(order-1, dim);
+      ParFiniteElementSpace fes_hb(&mesh, &fec_hb);
+
+      ParBilinearForm a(&fes_rt);
+      a.AddDomainIntegrator(new DivDivIntegrator(alpha_coeff));
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(beta_coeff));
+      a.EnableHybridization(&fes_hb, new NormalTraceJumpIntegrator, ess_rt_dofs);
+      a.Assemble();
+
+      OperatorHandle A;
+      Vector B, X;
+      b.Assemble();
+      x.ProjectCoefficient(u_vec_coeff);
+      a.FormLinearSystem(ess_rt_dofs, x, b, A, X, B);
+
+      HypreBoomerAMG amg_hb(*A.As<HypreParMatrix>());
+      amg_hb.SetPrintLevel(0);
+
+      SolveCG(*A, amg_hb, B, X);
+      a.RecoverFEMSolution(X, b, x);
+      const double error = x.ComputeL2Error(u_vec_coeff);
+      if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+   }
+
+   return 0;
+}
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref, int par_ref)
+{
+   Mesh serial_mesh = Mesh::LoadFromFile(mesh_file);
+   for (int i = 0; i < ser_ref; ++i) { serial_mesh.UniformRefinement(); }
+   ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
+   serial_mesh.Clear();
+   for (int i = 0; i < par_ref; ++i) { mesh.UniformRefinement(); }
+   return mesh;
+}
+
+void SolveCG(Operator &A, Solver &P, const Vector &B, Vector &X)
+{
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetAbsTol(0.0);
+   cg.SetRelTol(1e-12);
+   cg.SetMaxIter(500);
+   cg.SetPrintLevel(0);
+   cg.SetOperator(A);
+   cg.SetPreconditioner(P);
+   X = 0.0;
+   cg.Mult(B, X);
+   if (Mpi::Root())
+   {
+      cout << "Done.\nIterations: " << cg.GetNumIterations()
+            << "\nElapsed: " << tic_toc.RealTime() << endl;
+   }
+};
@@ -0,0 +1,387 @@
+// 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 "general/forall.hpp"
+#include "hdiv_linear_solver.hpp"
+#include "discrete_divergence.hpp"
+
+namespace mfem
+{
+
+/// Replace x[i] with 1.0/x[i] for all i.
+void Reciprocal(Vector &x)
+{
+   const int n = x.Size();
+   double *d_x = x.ReadWrite();
+   MFEM_FORALL(i, n, d_x[i] = 1.0/d_x[i]; );
+}
+
+/// Return a new HypreParMatrix with given diagonal entries
+HypreParMatrix *MakeDiagonalMatrix(Vector &diag,
+                                   const ParFiniteElementSpace &fes)
+{
+   const int n = diag.Size();
+
+   SparseMatrix diag_spmat;
+   diag_spmat.OverrideSize(n, n);
+   diag_spmat.GetMemoryI().New(n+1, Device::GetDeviceMemoryType());
+   diag_spmat.GetMemoryJ().New(n, Device::GetDeviceMemoryType());
+   diag_spmat.GetMemoryData().New(n, Device::GetDeviceMemoryType());
+
+   {
+      int *I = diag_spmat.WriteI();
+      int *J = diag_spmat.WriteJ();
+      double *A = diag_spmat.WriteData();
+      const double *d_diag = diag.Read();
+      MFEM_FORALL(i, n+1, I[i] = i;);
+      MFEM_FORALL(i, n,
+      {
+         J[i] = i;
+         A[i] = d_diag[i];
+      });
+   }
+
+   HYPRE_BigInt global_size = fes.GlobalTrueVSize();
+   HYPRE_BigInt *row_starts = fes.GetTrueDofOffsets();
+   HypreParMatrix D(MPI_COMM_WORLD, global_size, row_starts, &diag_spmat);
+   return new HypreParMatrix(D); // make a deep copy
+}
+
+const IntegrationRule &GetMassIntRule(FiniteElementSpace &fes_l2)
+{
+   Mesh *mesh = fes_l2.GetMesh();
+   const FiniteElement *fe = fes_l2.GetFE(0);
+   return MassIntegrator::GetRule(*fe, *fe, *mesh->GetElementTransformation(0));
+}
+
+HdivSaddlePointSolver::HdivSaddlePointSolver(
+   ParMesh &mesh, ParFiniteElementSpace &fes_rt_, ParFiniteElementSpace &fes_l2_,
+   Coefficient &L_coeff_, Coefficient &R_coeff_, Coefficient &B_coeff_,
+   const Array<int> &ess_rt_dofs_, Mode mode_)
+   : minres(mesh.GetComm()),
+     order(fes_rt_.GetMaxElementOrder()),
+     fec_l2(order - 1, mesh.Dimension(), b2, mt),
+     fes_l2(&mesh, &fec_l2),
+     fec_rt(order - 1, mesh.Dimension(), b1, b2),
+     fes_rt(&mesh, &fec_rt),
+     ess_rt_dofs(ess_rt_dofs_),
+     basis_l2(fes_l2_),
+     basis_rt(fes_rt_),
+     convert_map_type(fes_l2_.GetFE(0)->GetMapType() == FiniteElement::VALUE),
+     mass_l2(&fes_l2),
+     mass_rt(&fes_rt),
+     L_coeff(L_coeff_),
+     R_coeff(R_coeff_),
+     B_coeff(B_coeff_),
+     mode(mode_),
+     qs(mesh, GetMassIntRule(fes_l2)),
+     W_coeff_qf(qs),
+     W_mix_coeff_qf(qs),
+     W_coeff(W_coeff_qf),
+     W_mix_coeff(W_mix_coeff_qf)
+{
+   // If the user gives zero L coefficient, switch mode to DARCY_ZERO
+   auto *L_const_coeff = dynamic_cast<ConstantCoefficient*>(&L_coeff);
+   zero_l2_block = (L_const_coeff && L_const_coeff->constant == 0.0);
+
+   if (mode == Mode::GRAD_DIV)
+   {
+      MFEM_VERIFY(!zero_l2_block,
+                  "Mode::GRAD_DIV incompatible with zero coefficient.");
+   }
+
+   mass_l2.AddDomainIntegrator(new MassIntegrator(W_coeff));
+   mass_l2.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+
+   mass_rt.AddDomainIntegrator(new VectorFEMassIntegrator(&R_coeff));
+   mass_rt.AddBoundaryIntegrator(new MassIntegrator(B_coeff));
+   // mass_rt.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+
+   D.reset(FormDiscreteDivergenceMatrix(fes_rt, fes_l2, ess_rt_dofs));
+   Dt.reset(D->Transpose());
+
+   // Versions without BCs needed for elimination
+   D_e.reset(FormDiscreteDivergenceMatrix(fes_rt, fes_l2, empty));
+   mass_rt.FormSystemMatrix(empty, R_e);
+
+   offsets.SetSize(3);
+   offsets[0] = 0;
+   offsets[1] = fes_l2.GetTrueVSize();
+   offsets[2] = offsets[1] + fes_rt.GetTrueVSize();
+
+   minres.SetAbsTol(0.0);
+   minres.SetRelTol(1e-12);
+   minres.SetMaxIter(500);
+   minres.SetPrintLevel(IterativeSolver::PrintLevel().None());
+   minres.iterative_mode = false;
+
+   R_diag.SetSize(fes_rt.GetTrueVSize());
+   L_diag.SetSize(fes_l2.GetTrueVSize());
+
+   S_inv.SetPrintLevel(0);
+
+   if (mode == Mode::DARCY && !zero_l2_block)
+   {
+      ParBilinearForm mass_l2_unweighted(&fes_l2);
+      QuadratureFunction det_J_qf(qs);
+      QuadratureFunctionCoefficient det_J_coeff(det_J_qf);
+      if (convert_map_type)
+      {
+         const auto flags = GeometricFactors::DETERMINANTS;
+         auto *geom = fes_l2.GetMesh()->GetGeometricFactors(qs.GetIntRule(0), flags);
+         det_J_qf = geom->detJ;
+         mass_l2_unweighted.AddDomainIntegrator(new MassIntegrator(det_J_coeff));
+      }
+      else
+      {
+         mass_l2_unweighted.AddDomainIntegrator(new MassIntegrator);
+      }
+      mass_l2_unweighted.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      mass_l2_unweighted.Assemble();
+      const int n_l2 = fes_l2.GetTrueVSize();
+      L_diag_unweighted.SetSize(n_l2);
+      mass_l2_unweighted.AssembleDiagonal(L_diag_unweighted);
+   }
+
+   Setup();
+}
+
+HdivSaddlePointSolver::HdivSaddlePointSolver(
+   ParMesh &mesh_, ParFiniteElementSpace &fes_rt_,
+   ParFiniteElementSpace &fes_l2_, Coefficient &L_coeff_, Coefficient &R_coeff_,
+   const Array<int> &ess_rt_dofs_, Mode mode_)
+   : HdivSaddlePointSolver(mesh_, fes_rt_, fes_l2_, L_coeff_, R_coeff_, zero,
+                           ess_rt_dofs_, mode_)
+{ }
+
+HdivSaddlePointSolver::HdivSaddlePointSolver(
+   ParMesh &mesh, ParFiniteElementSpace &fes_rt_, ParFiniteElementSpace &fes_l2_,
+   Coefficient &R_coeff_, const Array<int> &ess_rt_dofs_)
+   : HdivSaddlePointSolver(mesh, fes_rt_, fes_l2_, zero, R_coeff_, zero,
+                           ess_rt_dofs_, Mode::DARCY)
+{ }
+
+void HdivSaddlePointSolver::Setup()
+{
+   const auto flags = GeometricFactors::DETERMINANTS;
+   auto *geom = fes_l2.GetMesh()->GetGeometricFactors(qs.GetIntRule(0), flags);
+
+   if (!zero_l2_block) { L_coeff.Project(W_coeff_qf); }
+   // In "grad-div mode", the transformation matrix is scaled by the coefficient
+   // of the mass and divergence matrices.
+   // In "Darcy mode", the transformation matrix is unweighted.
+   if (mode == Mode::GRAD_DIV) { W_mix_coeff_qf = W_coeff_qf; }
+   else { W_mix_coeff_qf = 1.0; }
+
+   // The transformation matrix has to be "mixed" value and integral map type,
+   // which means that the coefficient has to be scaled like the Jacobian
+   // determinant.
+   if (convert_map_type)
+   {
+      const int n = W_mix_coeff_qf.Size();
+      const double *d_detJ = geom->detJ.Read();
+      double *d_w_mix = W_mix_coeff_qf.ReadWrite();
+      double *d_w = W_coeff_qf.ReadWrite();
+      const bool zero_l2 = zero_l2_block;
+      MFEM_FORALL(i, n,
+      {
+         const double detJ = d_detJ[i];
+         if (!zero_l2) { d_w[i] *= detJ*detJ; }
+         d_w_mix[i] *= detJ;
+      });
+   }
+
+   L_inv.reset(new DGMassInverse(fes_l2, W_mix_coeff));
+
+   if (zero_l2_block)
+   {
+      A_11.reset();
+   }
+   else
+   {
+      mass_l2.Assemble();
+      mass_l2.AssembleDiagonal(L_diag);
+      mass_l2.FormSystemMatrix(empty, L);
+
+      A_11.reset(new RAPOperator(*L_inv, *L, *L_inv));
+
+      if (mode == GRAD_DIV)
+      {
+         L_diag_unweighted.SetSize(L_diag.Size());
+
+         BilinearForm mass_l2_mix(&fes_l2);
+         mass_l2_mix.AddDomainIntegrator(new MassIntegrator(W_mix_coeff));
+         mass_l2_mix.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+         mass_l2_mix.Assemble();
+         mass_l2_mix.AssembleDiagonal(L_diag_unweighted);
+      }
+
+      const double *d_L_diag_unweighted = L_diag_unweighted.Read();
+      double *d_L_diag = L_diag.ReadWrite();
+      MFEM_FORALL(i, L_diag.Size(),
+      {
+         const double d = d_L_diag_unweighted[i];
+         d_L_diag[i] /= d*d;
+      });
+   }
+
+   // Reassmble the RT mass operator with the new coefficient
+   mass_rt.Update();
+   mass_rt.Assemble();
+   mass_rt.FormSystemMatrix(ess_rt_dofs, R);
+
+   // Form the updated approximate Schur complement
+   mass_rt.AssembleDiagonal(R_diag);
+
+   // Update the mass RT diagonal for essential DOFs
+   {
+      const int *d_I = ess_rt_dofs.Read();
+      double *d_R_diag = R_diag.ReadWrite();
+      MFEM_FORALL(i, ess_rt_dofs.Size(), d_R_diag[d_I[i]] = 1.0;);
+   }
+
+   // Form the approximate Schur complement
+   {
+      Reciprocal(R_diag);
+      std::unique_ptr<HypreParMatrix> R_diag_inv(MakeDiagonalMatrix(R_diag, fes_rt));
+      if (zero_l2_block)
+      {
+         S.reset(RAP(R_diag_inv.get(), Dt.get()));
+      }
+      else
+      {
+         std::unique_ptr<HypreParMatrix> D_Minv_Dt(RAP(R_diag_inv.get(), Dt.get()));
+         std::unique_ptr<HypreParMatrix> L_diag_inv(MakeDiagonalMatrix(L_diag, fes_l2));
+         S.reset(ParAdd(D_Minv_Dt.get(), L_diag_inv.get()));
+      }
+   }
+
+   // Reassemble the preconditioners
+   R_inv.reset(new OperatorJacobiSmoother(mass_rt, ess_rt_dofs));
+   S_inv.SetOperator(*S);
+
+   // Set up the block operators
+   A_block.reset(new BlockOperator(offsets));
+   // Omit the (1,1)-block when the L coefficient is identically zero.
+   if (A_11) { A_block->SetBlock(0, 0, A_11.get()); }
+   A_block->SetBlock(0, 1, D.get());
+   A_block->SetBlock(1, 0, Dt.get());
+   A_block->SetBlock(1, 1, R.Ptr(), -1.0);
+
+   D_prec.reset(new BlockDiagonalPreconditioner(offsets));
+   D_prec->SetDiagonalBlock(0, &S_inv);
+   D_prec->SetDiagonalBlock(1, R_inv.get());
+
+   minres.SetPreconditioner(*D_prec);
+   minres.SetOperator(*A_block);
+}
+
+void HdivSaddlePointSolver::EliminateBC(Vector &b) const
+{
+   const int n_ess_dofs = ess_rt_dofs.Size();
+   if (fes_l2.GetParMesh()->ReduceInt(n_ess_dofs) == 0) { return; }
+
+   const int n_l2 = offsets[1];
+   const int n_rt = offsets[2]-offsets[1];
+   Vector bE(b, 0, n_l2);
+   Vector bF(b, n_l2, n_rt);
+
+   // SetBC must be called first
+   MFEM_VERIFY(x_bc.Size() == n_rt || n_ess_dofs == 0, "BCs not set");
+
+   // Create a vector z that has the BC values at essential DOFs, zero elsewhere
+   z.SetSize(n_rt);
+   z.UseDevice(true);
+   z = 0.0;
+   const int *d_I = ess_rt_dofs.Read();
+   const double *d_x_bc = x_bc.Read();
+   double *d_z = z.ReadWrite();
+   MFEM_FORALL(i, n_ess_dofs,
+   {
+      const int j = d_I[i];
+      d_z[j] = d_x_bc[j];
+   });
+
+   // Convert to the IntegratedGLL basis used internally
+   w.SetSize(n_rt);
+   basis_rt.MultInverse(z, w);
+
+   // Eliminate the BCs in the L2 RHS
+   D_e->Mult(-1.0, w, 1.0, bE);
+
+   // Eliminate the BCs in the RT RHS
+   // Flip the sign because the R block appears with multiplier -1
+   z.SetSize(n_rt);
+   R_e->Mult(w, z);
+   bF += z;
+
+   // Insert the RT BCs into the RHS at the essential DOFs.
+   const double *d_w = w.Read();
+   double *d_bF = bF.ReadWrite(); // Need read-write access to set subvector
+   MFEM_FORALL(i, n_ess_dofs,
+   {
+      const int j = d_I[i];
+      d_bF[j] = -d_w[j];
+   });
+
+   // Make sure the monolithic RHS is updated
+   bE.SyncAliasMemory(b);
+   bF.SyncAliasMemory(b);
+}
+
+void HdivSaddlePointSolver::Mult(const Vector &b, Vector &x) const
+{
+   w.SetSize(fes_l2.GetTrueVSize());
+   b_prime.SetSize(b.Size());
+   x_prime.SetSize(x.Size());
+
+   // Transform RHS to the IntegratedGLL basis
+   Vector bE_prime(b_prime, offsets[0], offsets[1]-offsets[0]);
+   Vector bF_prime(b_prime, offsets[1], offsets[2]-offsets[1]);
+
+   const Vector bE(const_cast<Vector&>(b), offsets[0], offsets[1]-offsets[0]);
+   const Vector bF(const_cast<Vector&>(b), offsets[1], offsets[2]-offsets[1]);
+
+   z.SetSize(bE.Size());
+   basis_l2.MultTranspose(bE, z);
+   basis_rt.MultTranspose(bF, bF_prime);
+   // Transform by the inverse of the L2 mass matrix
+   L_inv->Mult(z, bE_prime);
+
+   // Update the monolithic transformed RHS
+   bE_prime.SyncAliasMemory(b_prime);
+   bF_prime.SyncAliasMemory(b_prime);
+
+   // Eliminate the RT essential BCs
+   EliminateBC(b_prime);
+
+   // Solve the transformed system
+   minres.Mult(b_prime, x_prime);
+
+   // Transform the solution back to the user's basis
+   Vector xE_prime(x_prime, offsets[0], offsets[1]-offsets[0]);
+   Vector xF_prime(x_prime, offsets[1], offsets[2]-offsets[1]);
+
+   Vector xE(x, offsets[0], offsets[1]-offsets[0]);
+   Vector xF(x, offsets[1], offsets[2]-offsets[1]);
+
+   z.SetSize(bE.Size()); // Size of z may have changed in EliminateBC
+   L_inv->Mult(xE_prime, z);
+
+   basis_l2.Mult(z, xE);
+   basis_rt.Mult(xF_prime, xF);
+
+   // Update the monolithic solution vector
+   xE.SyncAliasMemory(x);
+   xF.SyncAliasMemory(x);
+}
+
+} // namespace mfem
@@ -0,0 +1,190 @@
+// 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 HDIV_LINEAR_SOLVER_HPP
+#define HDIV_LINEAR_SOLVER_HPP
+
+#include "mfem.hpp"
+#include "change_basis.hpp"
+#include <memory>
+
+namespace mfem
+{
+
+/// @brief Solve the H(div) saddle-point system using MINRES with matrix-free
+/// block-diagonal preconditioning.
+///
+/// See HdivSaddlePointSolver::HdivSaddlePointSolver for the problem
+/// description.
+class HdivSaddlePointSolver : public Solver
+{
+public:
+   /// Which type of saddle-point problem is being solved?
+   enum Mode
+   {
+      GRAD_DIV, ///< Grad-div problem.
+      DARCY     ///< Darcy/mixed Poisson problem.
+   };
+private:
+   MINRESSolver minres;
+
+   static constexpr int b1 = BasisType::GaussLobatto;
+   static constexpr int b2 = BasisType::IntegratedGLL;
+   static constexpr int mt = FiniteElement::INTEGRAL;
+
+   const int order;
+
+   // L2 and RT spaces, using the interpolation-histopolation bases
+   L2_FECollection fec_l2;
+   ParFiniteElementSpace fes_l2;
+
+   RT_FECollection fec_rt;
+   ParFiniteElementSpace fes_rt;
+
+   const Array<int> &ess_rt_dofs; ///< Essential BCs (in the RT space only).
+
+   // Change of basis operators
+   ChangeOfBasis_L2 basis_l2;
+   ChangeOfBasis_RT basis_rt;
+
+   /// Whether conversion from map type VALUE to INTEGRAL is required.
+   const bool convert_map_type;
+
+   ParBilinearForm mass_l2, mass_rt;
+
+   // Components needed for the block operator
+   OperatorHandle L, R, R_e; ///< Mass matrices.
+   std::unique_ptr<HypreParMatrix> D, Dt, D_e; ///< Divergence matrices.
+   std::shared_ptr<DGMassInverse> L_inv; ///< Inverse of the DG mass matrix.
+   std::shared_ptr<Operator> A_11; ///< (1,1)-block of the matrix
+
+   /// Diagonals of the mass matrices
+   Vector L_diag, R_diag, L_diag_unweighted;
+
+   // Components needed for the preconditioner
+
+   /// Jacobi preconditioner for the RT mass matrix.
+   std::unique_ptr<OperatorJacobiSmoother> R_inv;
+   std::unique_ptr<HypreParMatrix> S; ///< Approximate Schur complement.
+   HypreBoomerAMG S_inv; ///< AMG preconditioner for #S.
+
+   Array<int> offsets, empty;
+   /// The 2x2 block operator.
+   std::unique_ptr<BlockOperator> A_block;
+   /// The block-diagonal preconditioner.
+   std::unique_ptr<BlockDiagonalPreconditioner> D_prec;
+
+   Coefficient &L_coeff, &R_coeff, &B_coeff;
+
+   const Mode mode;
+   bool zero_l2_block = false;
+   QuadratureSpace qs;
+   QuadratureFunction W_coeff_qf, W_mix_coeff_qf;
+   QuadratureFunctionCoefficient W_coeff, W_mix_coeff;
+
+   ConstantCoefficient zero = ConstantCoefficient(0.0);
+
+   // Work vectors
+   mutable Vector b_prime, x_prime, x_bc, w, z;
+public:
+   /// @brief Creates a solver for the H(div) saddle-point system.
+   ///
+   /// The associated matrix is given by
+   ///
+   ///     [  L    B ]
+   ///     [ B^T  -R ]
+   ///
+   /// where L is the L2 mass matrix, R is the RT mass matrix, and B is the
+   /// divergence form (VectorFEDivergenceIntegrator).
+   ///
+   /// Essential boundary conditions in the RT space are given by @a
+   /// ess_rt_dofs_. (Rows and columns are eliminated from R and columns are
+   /// eliminated from B).
+   ///
+   /// The L block has coefficient @a L_coeff_ and the R block has coefficient
+   /// @a R_coeff_.
+   ///
+   /// The parameter @a mode_ determines whether the block system corresponds to
+   /// a grad-div problem or a Darcy problem. Specifically, if @a mode_ is
+   /// Mode::GRAD_DIV, then the B and B^T blocks are also scaled by @a L_coeff_,
+   /// and if @a mode_ is Mode::DARCY, then the B and B^T blocks are unweighted.
+   ///
+   /// Mode::GRAD_DIV corresponds to the grad-div problem
+   ///
+   ///     alpha u - grad ( beta div ( u )) = f,
+   ///
+   /// where alpha is @a R_coeff_ and beta is @a L_coeff_.
+   ///
+   /// Mode::DARCY corresponds to the Darcy-type problem
+   ///
+   ///     alpha p - div ( beta grad ( p )) = f,
+   ///
+   /// where alpha is @a L_coeff and beta is @a R_coeff_. In this case, the
+   /// coefficient alpha is allowed to be zero (see also @link
+   /// HdivSaddlePointSolver(ParMesh&, ParFiniteElementSpace&,
+   /// ParFiniteElementSpace&, Coefficient&, const Array<int>&) the zero-block
+   /// HdivSaddlePointSolver constructor@endlink).
+   HdivSaddlePointSolver(ParMesh &mesh_,
+                         ParFiniteElementSpace &fes_rt_,
+                         ParFiniteElementSpace &fes_l2_,
+                         Coefficient &L_coeff_,
+                         Coefficient &R_coeff_,
+                         Coefficient &B_coeff_,
+                         const Array<int> &ess_rt_dofs_,
+                         Mode mode_);
+
+   /// Same as the main constructor, but with B_coeff set to zero.
+   HdivSaddlePointSolver(ParMesh &mesh_,
+                         ParFiniteElementSpace &fes_rt_,
+                         ParFiniteElementSpace &fes_l2_,
+                         Coefficient &L_coeff_,
+                         Coefficient &R_coeff_,
+                         const Array<int> &ess_rt_dofs_,
+                         Mode mode_);
+
+   /// @brief Creates a linear solver for the case when the L2 diagonal block is
+   /// zero (for Darcy problems).
+   ///
+   /// Equivalent to passing ConstantCoefficient(0.0) as @a L_coeff_ and
+   /// Mode::DARCY as @a mode_ to the @link HdivSaddlePointSolver(ParMesh&,
+   /// ParFiniteElementSpace&, ParFiniteElementSpace&, Coefficient &,
+   /// Coefficient&, const Array<int>&, Mode) the primary constructor@endlink.
+   HdivSaddlePointSolver(ParMesh &mesh_,
+                         ParFiniteElementSpace &fes_rt_,
+                         ParFiniteElementSpace &fes_l2_,
+                         Coefficient &R_coeff_,
+                         const Array<int> &ess_rt_dofs_);
+
+   /// @brief Build the linear operator and solver. Must be called when the
+   /// coefficients change.
+   void Setup();
+   /// Sets the Dirichlet boundary conditions at the RT essential DOFs.
+   void SetBC(const Vector &x_rt) { x_bc = x_rt; }
+   /// @brief Solve the linear system for L2 (scalar) and RT (flux) unknowns.
+   ///
+   /// If the problem has essential boundary conditions (i.e. if @a ess_rt_dofs
+   /// is not empty), then SetBC() must be called before Mult().
+   void Mult(const Vector &b, Vector &x) const override;
+   /// No-op.
+   void SetOperator(const Operator &op) override { }
+   /// Get the number of MINRES iterations.
+   int GetNumIterations() const { return minres.GetNumIterations(); }
+   /// Eliminates the BCs (called internally, not public interface).
+   void EliminateBC(Vector &) const;
+   /// Return the offsets of the block system.
+   const Array<int> &GetOffsets() const { return offsets; }
+   /// Returns the internal MINRES solver.
+   MINRESSolver &GetMINRES() { return minres; }
+};
+
+} // namespace mfem
+
+#endif
@@ -12,7 +12,7 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
-SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ipopt/,)
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/hdiv-linear-solver/,)
 CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
 # Use the MFEM install directory
 # MFEM_INSTALL_DIR = ../../mfem
@@ -21,38 +21,29 @@ CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

-SEQ_EXAMPLES = exContactBlockTL
-EXAMPLES = $(SEQ_EXAMPLES)
+HDIV_HEADERS = hdiv_linear_solver.hpp discrete_divergence.hpp change_basis.hpp \
+					../solvers/lor_mms.hpp
+HDIV_SRC = hdiv_linear_solver.cpp change_basis.cpp discrete_divergence.cpp
+HDIV_OBJ = $(HDIV_SRC:.cpp=.o)
+
+MINIAPPS = grad_div darcy residual rz

 .SUFFIXES:
 .SUFFIXES: .o .cpp .mk
 .PHONY: all clean clean-build clean-exec
+.PRECIOUS: %.o

-# Remove built-in rule
+all: $(MINIAPPS)
+
+# Remove built-in rules
 %: %.cpp
+%.o: %.cpp

-# Replace the default implicit rule for *.cpp files
-%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+$(MINIAPPS):%: %.o $(HDIV_OBJ)
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) $(HDIV_OBJ) -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
+%.o: $(SRC)%.cpp $(HDIV_HEADERS) $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $< -o $@

 # Generate an error message if the MFEM library is not built and exit
 $(MFEM_LIB_FILE):
@@ -61,8 +52,8 @@ $(MFEM_LIB_FILE):
 clean: clean-build clean-exec

 clean-build:
-	rm -f *.o *~ $(SEQ_EXAMPLES)
+	rm -f *.o *~ $(MINIAPPS)
 	rm -rf *.dSYM *.TVD.*breakpoints

 clean-exec:
-	@rm -f exContactBlockTL.mesh exContactBlockTL-mesh.* exContactBlockTL-init.* exContactBlockTL-final.* ExampleContactBlockTL*
+	@rm -rf mesh.* sol.* ParaView
@@ -0,0 +1,205 @@
+#include "mfem.hpp"
+#include <iostream>
+
+#include "hdiv_linear_solver.hpp"
+#include "discrete_divergence.hpp"
+
+using namespace std;
+using namespace mfem;
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref = 0, int par_ref = 0);
+
+double f(const Vector &xvec);
+double g(const Vector &xvec);
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init(argc, argv);
+   Hypre::Init();
+
+   const char *mesh_file = "../../data/star.mesh";
+   const char *device_config = "cpu";
+   int ser_ref = 1;
+   int par_ref = 1;
+   int order = 3;
+   bool mt_value = true;
+   bool darcy = true;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&ser_ref, "-rs", "--serial-refine",
+                  "Number of times to refine the mesh in serial.");
+   args.AddOption(&par_ref, "-rp", "--parallel-refine",
+                  "Number of times to refine the mesh in parallel.");
+   args.AddOption(&order, "-o", "--order", "Polynomial degree.");
+   args.AddOption(&mt_value, "-val", "--value", "-int", "--integral",
+                  "Map type integral or value.");
+   args.AddOption(&darcy, "-da", "--darcy", "-g", "--grad-div",
+                  "Grad-div or Darcy problem");
+   args.ParseCheck();
+
+   Device device(device_config);
+   if (Mpi::Root()) { device.Print(); }
+
+   ParMesh mesh = LoadParMesh(mesh_file, ser_ref, par_ref);
+   const int dim = mesh.Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "Spatial dimension must be 2 or 3.");
+
+   const int b1 = BasisType::GaussLobatto, b2 = BasisType::GaussLegendre;
+   const int mt = mt_value ? FiniteElement::VALUE : FiniteElement::INTEGRAL;
+   RT_FECollection fec_rt(order-1, dim, b1, b2);
+   L2_FECollection fec_l2(order-1, dim, b2, mt);
+   ParFiniteElementSpace fes_rt(&mesh, &fec_rt);
+   ParFiniteElementSpace fes_l2(&mesh, &fec_l2);
+
+   HYPRE_BigInt ndofs_rt = fes_rt.GlobalTrueVSize();
+   HYPRE_BigInt ndofs_l2 = fes_l2.GlobalTrueVSize();
+
+   if (Mpi::Root())
+   {
+      cout << "\nRT DOFs: " << ndofs_rt << "\nL2 DOFs: " << ndofs_l2 << endl;
+   }
+
+   Array<int> ess_rt_dofs;
+
+   FunctionCoefficient a_coeff(f);
+   FunctionCoefficient b_coeff(g);
+   ConstantCoefficient one(1.0);
+
+   Coefficient &div_coeff = darcy ? (Coefficient&)one : (Coefficient&)a_coeff;
+
+   // Solve the system with the saddle-point solver
+   const auto solver_mode = darcy ? HdivSaddlePointSolver::Mode::DARCY
+                            : HdivSaddlePointSolver::Mode::GRAD_DIV;
+   HdivSaddlePointSolver saddle_point_solver(
+      mesh, fes_rt, fes_l2, a_coeff, b_coeff, ess_rt_dofs, solver_mode);
+
+   const Array<int> &offsets = saddle_point_solver.GetOffsets();
+   BlockVector X_block(offsets), B_block(offsets);
+
+   saddle_point_solver.GetMINRES().SetAbsTol(1e-18);
+   saddle_point_solver.GetMINRES().SetRelTol(1e-20);
+   saddle_point_solver.GetMINRES().SetPrintLevel(
+      IterativeSolver::PrintLevel().FirstAndLast());
+   X_block = 0.0;
+   B_block.Randomize(1);
+   B_block.GetBlock(0) = 0.0;
+   if (Mpi::Root()) { std::cout << "Saddle point solver... " << std::endl; }
+   saddle_point_solver.Mult(B_block, X_block);
+
+   // Form the matrix-based system
+   ParBilinearForm w(&fes_l2);
+   w.AddDomainIntegrator(new MassIntegrator(a_coeff));
+   w.Assemble();
+   w.Finalize();
+   std::unique_ptr<HypreParMatrix> W(w.ParallelAssemble());
+
+   ParMixedBilinearForm b(&fes_rt, &fes_l2);
+   b.AddDomainIntegrator(new VectorFEDivergenceIntegrator(div_coeff));
+   b.Assemble();
+   b.Finalize();
+   std::unique_ptr<HypreParMatrix> B(b.ParallelAssemble());
+   std::unique_ptr<HypreParMatrix> Bt(B->Transpose());
+
+   ParBilinearForm m(&fes_rt);
+   m.AddDomainIntegrator(new VectorFEMassIntegrator(b_coeff));
+   m.Assemble();
+   m.Finalize();
+   std::unique_ptr<HypreParMatrix> M(m.ParallelAssemble());
+
+   BlockOperator A(offsets);
+   A.SetBlock(0, 0, W.get());
+   A.SetBlock(0, 1, B.get());
+   A.SetBlock(1, 0, Bt.get());
+   A.SetBlock(1, 1, M.get(), -1.0);
+
+   // Compute the residual
+   BlockVector Y_block(offsets);
+   A.Mult(X_block, Y_block);
+   Y_block -= B_block;
+
+   auto nrm2 = [](const Vector &x)
+   {
+      return sqrt(InnerProduct(MPI_COMM_WORLD, x, x));
+   };
+
+   const double resnorm1 = nrm2(Y_block)/nrm2(B_block);
+   if (Mpi::Root()) { std::cout << "Linear residual norm: " << resnorm1 << "\n\n"; }
+
+   // Solve the system with a matrix-based solver (see ex5p)
+   HypreParVector Md(MPI_COMM_WORLD, M->GetGlobalNumRows(),
+                     M->GetRowStarts());
+   M->GetDiag(Md);
+   std::unique_ptr<HypreParMatrix> MinvBt(B->Transpose());
+   MinvBt->InvScaleRows(Md);
+   std::unique_ptr<HypreParMatrix> S(ParMult(B.get(), MinvBt.get()));
+
+   HypreDiagScale M_inv(*M);
+   HypreBoomerAMG S_inv(*S);
+   S_inv.SetPrintLevel(0);
+
+   BlockDiagonalPreconditioner D(offsets);
+   D.SetDiagonalBlock(0, &S_inv);
+   D.SetDiagonalBlock(1, &M_inv);
+
+   X_block = 0.0;
+   MINRESSolver minres(MPI_COMM_WORLD);
+   minres.SetAbsTol(1e-18);
+   minres.SetRelTol(1e-20);
+   minres.SetMaxIter(500);
+   minres.SetOperator(A);
+   minres.SetPreconditioner(D);
+   minres.SetPrintLevel(IterativeSolver::PrintLevel().FirstAndLast());
+   if (Mpi::Root()) { std::cout << "Matrix-based solver... " << std::endl; }
+   minres.Mult(B_block, X_block);
+
+   A.Mult(X_block, Y_block);
+   Y_block -= B_block;
+
+   const double resnorm2 = nrm2(Y_block)/nrm2(B_block);
+   if (Mpi::Root()) { std::cout << "Linear residual norm: " << resnorm2 << "\n\n"; }
+
+   return 0;
+}
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref, int par_ref)
+{
+   Mesh serial_mesh = Mesh::LoadFromFile(mesh_file);
+   for (int i = 0; i < ser_ref; ++i) { serial_mesh.UniformRefinement(); }
+   ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
+   serial_mesh.Clear();
+   for (int i = 0; i < par_ref; ++i) { mesh.UniformRefinement(); }
+   return mesh;
+}
+
+double f(const Vector &xvec)
+{
+   const int dim = xvec.Size();
+   const double x = xvec[0], y = xvec[1];
+   if (dim == 2)
+   {
+      return 2*(2.0 + sin(x)*sin(y));
+   }
+   else // dim == 3
+   {
+      const double z = xvec[2];
+      return 3*(2.0 + sin(x)*sin(y)*sin(z));
+   }
+}
+
+double g(const Vector &xvec)
+{
+   const int dim = xvec.Size();
+   const double x = xvec[0], y = xvec[1];
+   if (dim == 2)
+   {
+      return 2*(2.0 + cos(x)*cos(y));
+   }
+   else // dim == 3
+   {
+      const double z = xvec[2];
+      return 3*(2.0 + cos(x)*cos(y)*cos(z));
+   }
+}
@@ -0,0 +1,207 @@
+#include "mfem.hpp"
+#include <iostream>
+#include <memory>
+
+#include "discrete_divergence.hpp"
+#include "hdiv_linear_solver.hpp"
+
+#include "../solvers/lor_mms.hpp"
+
+using namespace std;
+using namespace mfem;
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref = 0, int par_ref = 0);
+
+double one_over_r(const Vector &xvec)
+{
+   // xvec = [z, r]
+   const double r = xvec[1];
+   return r == 0.0 ? 0.0 : 1.0/r;
+}
+
+double f_rz(const Vector &xvec)
+{
+   const double z = xvec[0];
+   const double r = xvec[1];
+
+   // alpha is the coefficient in the equation -Delta(u) + alpha*u = f
+   const double alpha = 1.0;
+   const double f = -cos(z)*(4*sin(r) + 5*r*cos(r) - (2 + alpha)*r*r*sin(r));
+
+   // scale integral by r because of coordinate transformation
+   return r*f;
+}
+
+double u_rz(const Vector &xvec)
+{
+   const double z = xvec[0];
+   const double r = xvec[1];
+
+   return r*r*sin(r)*cos(z);
+}
+
+class RobinCoefficient : public Coefficient
+{
+   double Eval(ElementTransformation &T, const IntegrationPoint &ip) override
+   {
+      double xdata[3];
+      Vector xvec(xdata, 3);
+      T.Transform(ip, xvec);
+      const int dim = xvec.Size();
+
+      Vector n(dim);
+      CalcOrtho(T.Jacobian(), n);
+      n /= n.Norml2();
+
+      const double p_val = u_rz(xvec);
+      const double z = xvec[0];
+      const double r = xvec[1];
+
+      if (dim == 2)
+      {
+         const double dpdz = -r*r*sin(r)*sin(z);
+         const double dpdr = r*cos(z)*(r*cos(r) + 2*sin(r));
+         const double u_val = n[0]*dpdz + n[1]*dpdr;
+         return p_val + u_val;
+      }
+      else
+      {
+         MFEM_ABORT("Not implemented");
+      }
+      return 0.0;
+   }
+};
+
+int main(int argc, char *argv[])
+{
+   Mpi::Init(argc, argv);
+   Hypre::Init();
+
+   const char *mesh_file = "rz.mesh";
+   const char *device_config = "cpu";
+   int ser_ref = 1;
+   int par_ref = 1;
+   int order = 3;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
+   args.AddOption(&ser_ref, "-rs", "--serial-refine",
+                  "Number of times to refine the mesh in serial.");
+   args.AddOption(&par_ref, "-rp", "--parallel-refine",
+                  "Number of times to refine the mesh in parallel.");
+   args.AddOption(&order, "-o", "--order", "Polynomial degree.");
+   args.ParseCheck();
+
+   Device device(device_config);
+   if (Mpi::Root()) { device.Print(); }
+
+   ParMesh mesh = LoadParMesh(mesh_file, ser_ref, par_ref);
+   const int dim = mesh.Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "Spatial dimension must be 2 or 3.");
+
+   const int b1 = BasisType::GaussLobatto, b2 = BasisType::GaussLegendre;
+   const int mt = FiniteElement::VALUE;
+   RT_FECollection fec_rt(order-1, dim, b1, b2);
+   L2_FECollection fec_l2(order-1, dim, b2, mt);
+   ParFiniteElementSpace fes_rt(&mesh, &fec_rt);
+   ParFiniteElementSpace fes_l2(&mesh, &fec_l2);
+
+   HYPRE_BigInt ndofs_rt = fes_rt.GlobalTrueVSize();
+   HYPRE_BigInt ndofs_l2 = fes_l2.GlobalTrueVSize();
+
+   if (Mpi::Root())
+   {
+      cout << "\nRT DOFs: " << ndofs_rt << "\nL2 DOFs: " << ndofs_l2 << endl;
+   }
+
+   Array<int> ess_rt_dofs; // empty
+
+   // f is the RHS, u is the exact solution
+   FunctionCoefficient f_coeff(f_rz), u_coeff(u_rz);
+
+   // Assemble the right-hand side for the scalar (L2) unknown.
+   ParLinearForm b_l2(&fes_l2);
+   // f_coeff has to include the r scaling for the coordinate transformation
+   b_l2.AddDomainIntegrator(new DomainLFIntegrator(f_coeff));
+   b_l2.UseFastAssembly(true);
+   b_l2.Assemble();
+
+   // Coefficient to enforce Robin boundary condition
+   RobinCoefficient bc_coeff;
+
+   // Enforce Robin boundary conditions by adding the boundary term to the flux
+   // equation.
+   ParLinearForm b_rt(&fes_rt);
+   b_rt.AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(bc_coeff));
+   b_rt.UseFastAssembly(true);
+   b_rt.Assemble();
+
+   if (Mpi::Root()) { cout << "\nSaddle point solver... " << flush; }
+   tic_toc.Clear(); tic_toc.Start();
+
+   // Have to scale the RT mass matrix by (1/r)
+   FunctionCoefficient r_recip_coeff(one_over_r);
+   // Have to scale the L2 mass matrix by r
+   FunctionCoefficient r_coeff([](const Vector &xvec) { return xvec[1]; });
+
+   const auto solver_mode = HdivSaddlePointSolver::Mode::DARCY;
+   HdivSaddlePointSolver saddle_point_solver(
+      mesh, fes_rt, fes_l2, r_coeff, r_recip_coeff, r_recip_coeff, ess_rt_dofs, solver_mode);
+
+   const Array<int> &offsets = saddle_point_solver.GetOffsets();
+   BlockVector X_block(offsets), B_block(offsets);
+
+   b_l2.ParallelAssemble(B_block.GetBlock(0));
+   b_rt.ParallelAssemble(B_block.GetBlock(1));
+   B_block.SyncFromBlocks();
+
+   X_block = 0.0;
+   saddle_point_solver.Mult(B_block, X_block);
+   X_block.SyncToBlocks();
+
+   if (Mpi::Root())
+   {
+      cout << "Done.\nIterations: "
+           << saddle_point_solver.GetNumIterations()
+           << "\nElapsed: " << tic_toc.RealTime() << endl;
+   }
+
+   ParGridFunction x(&fes_l2);
+   x.SetFromTrueDofs(X_block.GetBlock(0));
+   ParGridFunction flux(&fes_rt);
+   flux.SetFromTrueDofs(X_block.GetBlock(1));
+
+   const double error = x.ComputeL2Error(u_coeff);
+   if (Mpi::Root()) { cout << "L2 error: " << error << endl; }
+
+   ParGridFunction u_ex(&fes_l2), er(&fes_l2);
+   u_ex.ProjectCoefficient(u_coeff);
+   er = x;
+   er -= u_ex;
+
+   ParaViewDataCollection pv("RZ", &mesh);
+   pv.SetPrefixPath("ParaView");
+   pv.SetHighOrderOutput(true);
+   pv.SetLevelsOfDetail(order + 1);
+   pv.RegisterField("u", &x);
+   pv.RegisterField("flux", &flux);
+   pv.RegisterField("exact", &u_ex);
+   pv.RegisterField("error", &er);
+   pv.SetCycle(0);
+   pv.SetTime(0);
+   pv.Save();
+
+   return 0;
+}
+
+ParMesh LoadParMesh(const char *mesh_file, int ser_ref, int par_ref)
+{
+   Mesh serial_mesh = Mesh::LoadFromFile(mesh_file);
+   for (int i = 0; i < ser_ref; ++i) { serial_mesh.UniformRefinement(); }
+   ParMesh mesh(MPI_COMM_WORLD, serial_mesh);
+   serial_mesh.Clear();
+   for (int i = 0; i < par_ref; ++i) { mesh.UniformRefinement(); }
+   return mesh;
+}
@@ -0,0 +1,35 @@
+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
+2
+
+elements
+1
+1 3 0 1 2 3
+
+boundary
+4
+1 1 0 1
+2 1 1 2
+3 1 2 3
+4 1 3 0
+
+vertices
+4
+2
+0 0
+12 0
+12 7.5
+0 7.5
@@ -62,10 +62,6 @@ add_mfem_miniapp(minimal-surface
  MAIN minimal-surface.cpp
  LIBRARIES mfem)

-add_mfem_miniapp(reflector
-  MAIN reflector.cpp
-  LIBRARIES mfem)
-
 add_mfem_miniapp(toroid
  MAIN toroid.cpp
  LIBRARIES mfem)
@@ -26,7 +26,7 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

 SEQ_MINIAPPS = mobius-strip klein-bottle toroid trimmer twist mesh-explorer\
-	shaper extruder mesh-optimizer minimal-surface polar-nc reflector
+	shaper extruder mesh-optimizer minimal-surface polar-nc
 PAR_MINIAPPS = pmesh-optimizer pminimal-surface
 ifeq ($(MFEM_USE_MPI),NO)
   MINIAPPS = $(SEQ_MINIAPPS)
@@ -91,8 +91,6 @@ minimal-surface-test-seq: minimal-surface
 	@$(call mfem-test,$<,, Meshing miniapp)
 pminimal-surface-test-par: pminimal-surface
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel meshing miniapp)
-reflector-test-seq: reflector
-	@$(call mfem-test-file,$<,, Meshing miniapp,reflected.mesh)

 # Testing: Specific execution options
 mesh-explorer-test-seq:
@@ -110,14 +108,14 @@ clean: clean-build clean-exec

 clean-build:
 	rm -f *.o *~ mobius-strip klein-bottle toroid twist
-	rm -f mesh-explorer shaper extruder trimmer reflector
+	rm -f mesh-explorer shaper extruder trimmer
 	rm -f mesh-optimizer pmesh-optimizer polar-nc
 	rm -f minimal-surface pminimal-surface
 	rm -rf *.dSYM *.TVD.*breakpoints

 clean-exec:
 	@rm -f mobius-strip.mesh klein-bottle.mesh mesh-explorer.mesh
-	@rm -f toroid-*.mesh twist-*.mesh trimmer.mesh reflected.mesh
+	@rm -f toroid-*.mesh twist-*.mesh trimmer.mesh
 	@rm -f partitioning.txt shaper.mesh extruder.mesh
 	@rm -f optimized* perturbed* polar-nc.mesh
 	@rm -rf mesh-explorer-{visit,paraview}*
@@ -57,8 +57,10 @@
 //   Adapted discrete size+aspect_ratio:
 //     mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100
 //     mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100 -qo 6 -ex -st 1 -nor
-//   Adapted discrete size+orientation:
-//      mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -nor
+//   Adapted discrete size+orientation (requires GSLIB):
+//   * mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -ae 1 -nor
+//   Adapted discrete aspect-ratio+orientation (requires GSLIB):
+//   * mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 85 -tid 8 -ni 10 -bnd -qt 1 -qo 8 -fd -ae 1
 //   Adapted discrete aspect ratio (3D):
 //     mesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 302 -tid 7 -ni 20 -bnd -qt 1 -qo 8
 //
@@ -84,7 +86,7 @@
 //   Blade limited shape:
 //     mesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -bnd -qt 1 -qo 8 -lc 5000
 //   ICF shape and equal size:
-//     mesh-optimizer -o 3 -mid 80 -bec -tid 2 -ni 25 -ls 3 -art 2 -qo 5
+//     mesh-optimizer -o 3 -mid 9 -tid 2 -ni 25 -ls 3 -art 2 -qo 5
 //   ICF shape and initial size:
 //     mesh-optimizer -o 3 -mid 9 -tid 3 -ni 30 -ls 3 -bnd -qt 1 -qo 8
 //   ICF shape:
@@ -138,7 +140,6 @@ int main(int argc, char *argv[])
   int max_lin_iter      = 100;
   bool move_bnd         = true;
   int combomet          = 0;
-   bool bal_expl_combo   = false;
   bool hradaptivity     = false;
   int h_metric_id       = -1;
   bool normalization    = false;
@@ -257,9 +258,6 @@ int main(int argc, char *argv[])
                  "0: Use single metric\n\t"
                  "1: Shape + space-dependent size given analytically\n\t"
                  "2: Shape + adapted size given discretely; shared target");
-   args.AddOption(&bal_expl_combo, "-bec", "--balance-explicit-combo",
-                  "-no-bec", "--balance-explicit-combo",
-                  "Automatic balancing of explicit combo metrics.");
   args.AddOption(&hradaptivity, "-hr", "--hr-adaptivity", "-no-hr",
                  "--no-hr-adaptivity",
                  "Enable hr-adaptivity.");
@@ -742,9 +740,20 @@ int main(int argc, char *argv[])
 #endif
         }

-         ConstantCoefficient size_coeff(0.1*0.1);
-         size.ProjectCoefficient(size_coeff);
-         tc->SetSerialDiscreteTargetSize(size);
+         if (metric_id == 14 || metric_id == 36)
+         {
+            ConstantCoefficient size_coeff(0.1*0.1);
+            size.ProjectCoefficient(size_coeff);
+            tc->SetSerialDiscreteTargetSize(size);
+         }
+
+         if (metric_id == 85)
+         {
+            FunctionCoefficient aspr_coeff(discrete_aspr_2d);
+            aspr.ProjectCoefficient(aspr_coeff);
+            DiffuseField(aspr,2);
+            tc->SetSerialDiscreteTargetAspectRatio(aspr);
+         }

         FunctionCoefficient ori_coeff(discrete_ori_2d);
         ori.ProjectCoefficient(ori_coeff);
@@ -771,16 +780,6 @@ int main(int argc, char *argv[])
      target_c = new TargetConstructor(target_t);
   }
   target_c->SetNodes(x0);
-
-   // Automatically balanced gamma in composite metrics.
-   auto metric_combo = dynamic_cast<TMOP_Combo_QualityMetric *>(metric);
-   if (metric_combo && bal_expl_combo)
-   {
-      Vector bal_weights;
-      metric_combo->ComputeBalancedWeights(x, *target_c, bal_weights);
-      metric_combo->SetWeights(bal_weights);
-   }
-
   TMOP_QualityMetric *metric_to_use = barrier_type > 0 || worst_case_type > 0
                                       ? untangler_metric
                                       : metric;
@@ -791,6 +790,7 @@ int main(int argc, char *argv[])
      tmop_integ->ComputeUntangleMetricQuantiles(x, *fespace);
   }

+
   // Finite differences for computations of derivatives.
   if (fdscheme)
   {
@@ -1208,7 +1208,6 @@ int main(int argc, char *argv[])
      mesh->Print(mesh_ofs);
   }

-   // Report the final energy of the functional.
   const double fin_energy = a.GetGridFunctionEnergy(x) /
                             (hradaptivity ? mesh->GetNE() : 1);
   double fin_metric_energy = fin_energy;
@@ -1233,7 +1232,7 @@ int main(int argc, char *argv[])
   cout << "The strain energy decreased by: "
        << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;

-   // Visualize the final mesh and metric values.
+   // 16. Visualize the final mesh and metric values.
   if (visualization)
   {
      char title[] = "Final metric values";
@@ -1247,7 +1246,6 @@ int main(int argc, char *argv[])
                             600, 600, 300, 300);
   }

-   // Visualize fitting surfaces and report fitting errors.
   if (surface_fit_const > 0.0)
   {
      if (visualization)
@@ -1264,7 +1262,7 @@ int main(int argc, char *argv[])
                << "Max fitting error: " << err_max << std::endl;
   }

-   // Visualize the mesh displacement.
+   // 17. Visualize the mesh displacement.
   if (visualization)
   {
      osockstream sock(19916, "localhost");
@@ -84,6 +84,24 @@ double discrete_ori_2d(const Vector &x)
   return M_PI * x(1) * (1.0 - x(1)) * cos(2 * M_PI * x(0));
 }

+double discrete_aspr_2d(const Vector &x)
+{
+   double xc = x(0)-0.5, yc = x(1)-0.5;
+   double th = 22.5*M_PI/180.;
+   double xn =  cos(th)*xc + sin(th)*yc;
+   double yn = -sin(th)*xc + cos(th)*yc;
+   xc = xn; yc = yn;
+
+   double tfac = 20;
+   double s1 = 3;
+   double s2 = 2;
+   double wgt = std::tanh((tfac*(yc) + s2*std::sin(s1*M_PI*xc)) + 1)
+                - std::tanh((tfac*(yc) + s2*std::sin(s1*M_PI*xc)) - 1);
+   if (wgt > 1) { wgt = 1; }
+   if (wgt < 0) { wgt = 0; }
+   return 0.1 + 1*(1-wgt)*(1-wgt);
+}
+
 void discrete_aspr_3d(const Vector &x, Vector &v)
 {
   int dim = x.Size();
@@ -77,6 +77,7 @@ constexpr Element::Type QUAD = Element::QUADRILATERAL;
 constexpr double NL_DMAX = std::numeric_limits<double>::max();

 // Static variables for GLVis
+static socketstream glvis;
 constexpr int GLVIZ_W = 1024;
 constexpr int GLVIZ_H = 1024;
 constexpr int  visport = 19916;
@@ -117,10 +118,8 @@ protected:
   Opt &opt;
   Mesh *mesh;
   Array<int> bc;
-   socketstream glvis;
   H1_FECollection *fec;
   FiniteElementSpace *fes;
-
 public:
   // Reading from mesh file
   Surface(Opt &opt, const char *file): Mesh(file, true), opt(opt) { }
@@ -158,7 +157,7 @@ public:
      // Initialize GLVis server if 'visualization' is set
      if (opt.vis) { opt.vis = glvis.open(vishost, visport) == 0; }
      // Send to GLVis the first mesh
-      if (opt.vis) { Visualize(glvis, opt, mesh, GLVIZ_W, GLVIZ_H); }
+      if (opt.vis) { Visualize(opt, mesh, GLVIZ_W, GLVIZ_H); }
      // Create and launch the surface solver
      if (opt.by_vdim)
      {
@@ -171,7 +170,7 @@ public:
      if (opt.vis && opt.snapshot)
      {
         opt.keys = "Sq";
-         Visualize(glvis, opt, mesh, mesh->GetNodes());
+         Visualize(opt, mesh, mesh->GetNodes());
      }
      return 0;
   }
@@ -244,8 +243,7 @@ public:
   }

   // Initialize visualization of some given mesh
-   static void Visualize(socketstream &glvis,
-                         Opt &opt, const Mesh *mesh,
+   static void Visualize(Opt &opt, const Mesh *mesh,
                         const int w, const int h,
                         const GridFunction *sol = nullptr)
   {
@@ -261,8 +259,7 @@ public:
   }

   // Visualize some solution on the given mesh
-   static void Visualize(socketstream &glvis,
-                         const Opt &opt, const Mesh *mesh,
+   static void Visualize(const Opt &opt, const Mesh *mesh,
                         const GridFunction *sol = nullptr)
   {
      const GridFunction &solution = sol ? *sol : *mesh->GetNodes();
@@ -327,7 +324,7 @@ public:
         for (int i=0; i < opt.niters; ++i)
         {
            if (opt.amr) { Amr(); }
-            if (opt.vis) { Surface::Visualize(S.glvis, opt, S.mesh); }
+            if (opt.vis) { Surface::Visualize(opt, S.mesh); }
            if (!opt.id) { mfem::out << "Iteration " << i << ": "; }
            S.mesh->NodesUpdated();
            a.Update();
@@ -1240,9 +1237,8 @@ static int Problem1(Opt &opt)
   GridFunction uold(&fes), u(&fes), b(&fes);
   FunctionCoefficient u0_fc(u0);
   u.ProjectCoefficient(u0_fc);
-   socketstream glvis;
   if (opt.vis) { opt.vis = glvis.open(vishost, visport) == 0; }
-   if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
+   if (opt.vis) { Surface::Visualize(opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
   CGSolver cg;
   cg.SetRelTol(EPS);
   cg.SetAbsTol(EPS*EPS);
@@ -1274,7 +1270,7 @@ static int Problem1(Opt &opt)
         mfem::out << "Iteration " << i << ", norm: " << norm
                   << ", area: " << area << std::endl;
      }
-      if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, &u); }
+      if (opt.vis) { Surface::Visualize(opt, &mesh, &u); }
      if (opt.print) { Surface::Print(opt, &mesh, &u); }
      if (norm < NRM) { break; }
   }
@@ -57,8 +57,10 @@
 //   Adapted discrete size+aspect_ratio:
 //     mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100
 //     mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100 -qo 6 -ex -st 1 -nor
-//   Adapted discrete size+orientation:
-//     mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -nor
+//   Adapted discrete size+orientation (requires GSLIB):
+//   * mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -ae 1 -nor
+//   Adapted discrete aspect-ratio+orientation (requires GSLIB):
+//   * mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 85 -tid 8 -ni 10 -bnd -qt 1 -qo 8 -fd -ae 1
 //   Adapted discrete aspect ratio (3D):
 //     mpirun -np 4 pmesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 302 -tid 7 -ni 20 -bnd -qt 1 -qo 8
 //
@@ -84,7 +86,7 @@
 //   Blade limited shape:
 //     mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -bnd -qt 1 -qo 8 -lc 5000
 //   ICF shape and equal size:
-//     mpirun -np 4 pmesh-optimizer -o 3 -mid 80 -bec -tid 2 -ni 25 -ls 3 -art 2 -qo 5
+//     mpirun -np 4 pmesh-optimizer -o 3 -mid 9 -tid 2 -ni 25 -ls 3 -art 2 -qo 5
 //   ICF shape and initial size:
 //     mpirun -np 4 pmesh-optimizer -o 3 -mid 9 -tid 3 -ni 30 -ls 3 -bnd -qt 1 -qo 8
 //   ICF shape:
@@ -148,7 +150,6 @@ int main (int argc, char *argv[])
   int max_lin_iter      = 100;
   bool move_bnd         = true;
   int combomet          = 0;
-   bool bal_expl_combo   = false;
   bool hradaptivity     = false;
   int h_metric_id       = -1;
   bool normalization    = false;
@@ -269,9 +270,6 @@ int main (int argc, char *argv[])
                  "0: Use single metric\n\t"
                  "1: Shape + space-dependent size given analytically\n\t"
                  "2: Shape + adapted size given discretely; shared target");
-   args.AddOption(&bal_expl_combo, "-bec", "--balance-explicit-combo",
-                  "-no-bec", "--balance-explicit-combo",
-                  "Automatic balancing of explicit combo metrics.");
   args.AddOption(&hradaptivity, "-hr", "--hr-adaptivity", "-no-hr",
                  "--no-hr-adaptivity",
                  "Enable hr-adaptivity.");
@@ -374,6 +372,9 @@ int main (int argc, char *argv[])
   //    transformation of the reference element.
   pmesh->SetNodalFESpace(pfespace);

+   // 6. Set up an empty right-hand side vector b, which is equivalent to b=0.
+   Vector b(0);
+
   // 7. Get the mesh nodes (vertices and other degrees of freedom in the finite
   //    element space) as a finite element grid function in fespace. Note that
   //    changing x automatically changes the shapes of the mesh elements.
@@ -773,9 +774,20 @@ int main (int argc, char *argv[])
 #endif
         }

-         ConstantCoefficient size_coeff(0.1*0.1);
-         size.ProjectCoefficient(size_coeff);
-         tc->SetParDiscreteTargetSize(size);
+         if (metric_id == 14 || metric_id == 36)
+         {
+            ConstantCoefficient size_coeff(0.1*0.1);
+            size.ProjectCoefficient(size_coeff);
+            tc->SetParDiscreteTargetSize(size);
+         }
+
+         if (metric_id == 85)
+         {
+            FunctionCoefficient aspr_coeff(discrete_aspr_2d);
+            aspr.ProjectCoefficient(aspr_coeff);
+            DiffuseField(aspr,2);
+            tc->SetParDiscreteTargetAspectRatio(aspr);
+         }

         FunctionCoefficient ori_coeff(discrete_ori_2d);
         ori.ProjectCoefficient(ori_coeff);
@@ -799,21 +811,12 @@ int main (int argc, char *argv[])
         if (myid == 0) { cout << "Unknown target_id: " << target_id << endl; }
         return 3;
   }
+
   if (target_c == NULL)
   {
      target_c = new TargetConstructor(target_t, MPI_COMM_WORLD);
   }
   target_c->SetNodes(x0);
-
-   // Automatically balanced gamma in composite metrics.
-   auto metric_combo = dynamic_cast<TMOP_Combo_QualityMetric *>(metric);
-   if (metric_combo && bal_expl_combo)
-   {
-      Vector bal_weights;
-      metric_combo->ComputeBalancedWeights(x, *target_c, bal_weights);
-      metric_combo->SetWeights(bal_weights);
-   }
-
   TMOP_QualityMetric *metric_to_use = barrier_type > 0 || worst_case_type > 0
                                       ? untangler_metric
                                       : metric;
@@ -824,6 +827,7 @@ int main (int argc, char *argv[])
      tmop_integ->ComputeUntangleMetricQuantiles(x, *pfespace);
   }

+
   // Finite differences for computations of derivatives.
   if (fdscheme)
   {
@@ -1252,7 +1256,7 @@ int main (int argc, char *argv[])
      pmesh->PrintAsOne(mesh_ofs);
   }

-   // Report the final energy of the functional.
+   // Compute the final energy of the functional.
   const double fin_energy = a.GetParGridFunctionEnergy(x) /
                             (hradaptivity ? pmesh->GetGlobalNE() : 1);
   double fin_metric_energy = fin_energy;
@@ -1280,7 +1284,7 @@ int main (int argc, char *argv[])
           << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
   }

-   // Visualize the final mesh and metric values.
+   // 18. Visualize the final mesh and metric values.
   if (visualization)
   {
      char title[] = "Final metric values";
@@ -1294,7 +1298,6 @@ int main (int argc, char *argv[])
                             600, 600, 300, 300);
   }

-   // Visualize fitting surfaces and report fitting errors.
   if (surface_fit_const > 0.0)
   {
      if (visualization)
@@ -1314,7 +1317,7 @@ int main (int argc, char *argv[])
      }
   }

-   // Visualize the mesh displacement.
+   // 19. Visualize the mesh displacement.
   if (visualization)
   {
      x0 -= x;
@@ -1335,6 +1338,7 @@ int main (int argc, char *argv[])
      }
   }

+   // 20. Free the used memory.
   delete S;
   delete S_prec;
   delete target_c2;
@@ -77,6 +77,7 @@ constexpr Element::Type QUAD = Element::QUADRILATERAL;
 constexpr double NL_DMAX = std::numeric_limits<double>::max();

 // Static variables for GLVis
+static socketstream glvis;
 constexpr int GLVIZ_W = 1024;
 constexpr int GLVIZ_H = 1024;
 constexpr int  visport = 19916;
@@ -117,7 +118,6 @@ protected:
   Opt &opt;
   ParMesh *mesh;
   Array<int> bc;
-   socketstream glvis;
   H1_FECollection *fec;
   ParFiniteElementSpace *fes;
 public:
@@ -157,7 +157,7 @@ public:
      // Initialize GLVis server if 'visualization' is set
      if (opt.vis) { opt.vis = glvis.open(vishost, visport) == 0; }
      // Send to GLVis the first mesh
-      if (opt.vis) { Visualize(glvis, opt, mesh, GLVIZ_W, GLVIZ_H); }
+      if (opt.vis) { Visualize(opt, mesh, GLVIZ_W, GLVIZ_H); }
      // Create and launch the surface solver
      if (opt.by_vdim)
      {
@@ -170,7 +170,7 @@ public:
      if (opt.vis && opt.snapshot)
      {
         opt.keys = "Sq";
-         Visualize(glvis, opt, mesh, mesh->GetNodes());
+         Visualize(opt, mesh, mesh->GetNodes());
      }
      return 0;
   }
@@ -243,8 +243,7 @@ public:
   }

   // Initialize visualization of some given mesh
-   static void Visualize(socketstream &glvis,
-                         Opt &opt, const Mesh *mesh,
+   static void Visualize(Opt &opt, const Mesh *mesh,
                         const int w, const int h,
                         const GridFunction *sol = nullptr)
   {
@@ -260,8 +259,7 @@ public:
   }

   // Visualize some solution on the given mesh
-   static void Visualize(socketstream &glvis,
-                         const Opt &opt, const Mesh *mesh,
+   static void Visualize(const Opt &opt, const Mesh *mesh,
                         const GridFunction *sol = nullptr)
   {
      glvis << "parallel " << opt.sz << " " << opt.id << "\n";
@@ -330,7 +328,7 @@ public:
         for (int i=0; i < opt.niters; ++i)
         {
            if (opt.amr) { Amr(); }
-            if (opt.vis) { Surface::Visualize(S.glvis, opt, S.mesh); }
+            if (opt.vis) { Surface::Visualize(opt, S.mesh); }
            if (!opt.id) { mfem::out << "Iteration " << i << ": "; }
            S.mesh->NodesUpdated();
            a.Update();
@@ -1248,9 +1246,8 @@ static int Problem1(Opt &opt)
   ParGridFunction uold(&fes), u(&fes), b(&fes);
   FunctionCoefficient u0_fc(u0);
   u.ProjectCoefficient(u0_fc);
-   socketstream glvis;
   if (opt.vis) { opt.vis = glvis.open(vishost, visport) == 0; }
-   if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
+   if (opt.vis) { Surface::Visualize(opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
   Vector B, X;
   OperatorPtr A;
   CGSolver cg(MPI_COMM_WORLD);
@@ -1282,7 +1279,7 @@ static int Problem1(Opt &opt)
         mfem::out << "Iteration " << i << ", norm: " << norm
                   << ", area: " << area << std::endl;
      }
-      if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, &u); }
+      if (opt.vis) { Surface::Visualize(opt, &mesh, &u); }
      if (opt.print) { Surface::Print(opt, &mesh, &u); }
      if (norm < NRM) { break; }
   }
@@ -12,8 +12,6 @@
 #ifndef MFEM_LOR_MMS_HPP
 #define MFEM_LOR_MMS_HPP

-extern bool grad_div_problem;
-
 namespace mfem
 {

@@ -23,34 +21,36 @@ static constexpr double pi = M_PI, pi2 = M_PI*M_PI;
 // defined below.
 double u(const Vector &xvec)
 {
-   int dim = xvec.Size();
-   double x = pi*xvec[0], y = pi*xvec[1];
+   const int dim = xvec.Size();
+   const double x = pi*xvec[0], y = pi*xvec[1];
   if (dim == 2) { return sin(x)*sin(y); }
-   else { double z = pi*xvec[2]; return sin(x)*sin(y)*sin(z); }
+   else { const double z = pi*xvec[2]; return sin(x)*sin(y)*sin(z); }
 }

-double f(const Vector &xvec)
+std::function<double(const Vector &)> f(double mass_coeff)
 {
-   int dim = xvec.Size();
-   double x = pi*xvec[0], y = pi*xvec[1];
-
-   if (dim == 2)
+   return [mass_coeff](const Vector &xvec)
   {
-      return sin(x)*sin(y) + 2*pi2*sin(x)*sin(y);
-   }
-   else // dim == 3
-   {
-      double z = pi*xvec[2];
-      return sin(x)*sin(y)*sin(z) + 3*pi2*sin(x)*sin(y)*sin(z);
-   }
+      const int dim = xvec.Size();
+      const double x = pi*xvec[0], y = pi*xvec[1];
+      if (dim == 2)
+      {
+         return mass_coeff*sin(x)*sin(y) + 2*pi2*sin(x)*sin(y);
+      }
+      else // dim == 3
+      {
+         const double z = pi*xvec[2];
+         return mass_coeff*sin(x)*sin(y)*sin(z) + 3*pi2*sin(x)*sin(y)*sin(z);
+      }
+   };
 }

 // Exact solution for definite Maxwell and grad-div problems with RHS
 // corresponding to f_vec below.
 void u_vec(const Vector &xvec, Vector &u)
 {
-   int dim = xvec.Size();
-   double x = pi*xvec[0], y = pi*xvec[1];
+   const int dim = xvec.Size();
+   const double x = pi*xvec[0], y = pi*xvec[1];
   if (dim == 2)
   {
      u[0] = cos(x)*sin(y);
@@ -58,47 +58,50 @@ void u_vec(const Vector &xvec, Vector &u)
   }
   else // dim == 3
   {
-      double z = pi*xvec[2];
+      const double z = pi*xvec[2];
      u[0] = cos(x)*sin(y)*sin(z);
      u[1] = sin(x)*cos(y)*sin(z);
      u[2] = sin(x)*sin(y)*cos(z);
   }
 }

-void f_vec(const Vector &xvec, Vector &f)
+std::function<void(const Vector &, Vector &)> f_vec(bool grad_div_problem)
 {
-   int dim = xvec.Size();
-   double x = pi*xvec[0], y = pi*xvec[1];
-   if (grad_div_problem)
+   return [grad_div_problem](const Vector &xvec, Vector &f)
   {
-      if (dim == 2)
+      const int dim = xvec.Size();
+      const double x = pi*xvec[0], y = pi*xvec[1];
+      if (grad_div_problem)
      {
-         f[0] = (1 + 2*pi2)*cos(x)*sin(y);
-         f[1] = (1 + 2*pi2)*cos(y)*sin(x);
+         if (dim == 2)
+         {
+            f[0] = (1 + 2*pi2)*cos(x)*sin(y);
+            f[1] = (1 + 2*pi2)*cos(y)*sin(x);
+         }
+         else // dim == 3
+         {
+            const double z = pi*xvec[2];
+            f[0] = (1 + 3*pi2)*cos(x)*sin(y)*sin(z);
+            f[1] = (1 + 3*pi2)*cos(y)*sin(x)*sin(z);
+            f[2] = (1 + 3*pi2)*cos(z)*sin(x)*sin(y);
+         }
      }
-      else // dim == 3
+      else
      {
-         double z = pi*xvec[2];
-         f[0] = (1 + 3*pi2)*cos(x)*sin(y)*sin(z);
-         f[1] = (1 + 3*pi2)*cos(y)*sin(x)*sin(z);
-         f[2] = (1 + 3*pi2)*cos(z)*sin(x)*sin(y);
+         if (dim == 2)
+         {
+            f[0] = cos(x)*sin(y);
+            f[1] = sin(x)*cos(y);
+         }
+         else // dim == 3
+         {
+            const double z = pi*xvec[2];
+            f[0] = cos(x)*sin(y)*sin(z);
+            f[1] = sin(x)*cos(y)*sin(z);
+            f[2] = sin(x)*sin(y)*cos(z);
+         }
      }
-   }
-   else
-   {
-      if (dim == 2)
-      {
-         f[0] = cos(x)*sin(y);
-         f[1] = sin(x)*cos(y);
-      }
-      else // dim == 3
-      {
-         double z = pi*xvec[2];
-         f[0] = cos(x)*sin(y)*sin(z);
-         f[1] = sin(x)*cos(y)*sin(z);
-         f[2] = sin(x)*sin(y)*cos(z);
-      }
-   }
+   };
 }

 } // namespace mfem
@@ -74,8 +74,6 @@
 using namespace std;
 using namespace mfem;

-bool grad_div_problem = false;
-
 int main(int argc, char *argv[])
 {
   const char *mesh_file = "../../data/star.mesh";
@@ -109,7 +107,6 @@ int main(int argc, char *argv[])
   else if (string(fe) == "l") { L2 = true; }
   else { MFEM_ABORT("Bad FE type. Must be 'h', 'n', 'r', or 'l'."); }

-   if (RT) { grad_div_problem = true; }
   double kappa = (order+1)*(order+1); // Penalty used for DG discretizations

   Mesh mesh(mesh_file, 1, 1);
@@ -117,8 +114,8 @@ int main(int argc, char *argv[])
   MFEM_VERIFY(dim == 2 || dim == 3, "Spatial dimension must be 2 or 3.");
   for (int l = 0; l < ref_levels; l++) { mesh.UniformRefinement(); }

-   FunctionCoefficient f_coeff(f), u_coeff(u);
-   VectorFunctionCoefficient f_vec_coeff(dim, f_vec), u_vec_coeff(dim, u_vec);
+   FunctionCoefficient f_coeff(f(1.0)), u_coeff(u);
+   VectorFunctionCoefficient f_vec_coeff(dim, f_vec(RT)), u_vec_coeff(dim, u_vec);

   int b1 = BasisType::GaussLobatto, b2 = BasisType::IntegratedGLL;
   unique_ptr<FiniteElementCollection> fec;
@@ -72,8 +72,6 @@
 using namespace std;
 using namespace mfem;

-bool grad_div_problem = false;
-
 int main(int argc, char *argv[])
 {
   Mpi::Init();
@@ -112,7 +110,6 @@ int main(int argc, char *argv[])
   else if (string(fe) == "l") { L2 = true; }
   else { MFEM_ABORT("Bad FE type. Must be 'h', 'n', 'r', or 'l'."); }

-   if (RT) { grad_div_problem = true; }
   double kappa = (order+1)*(order+1); // Penalty used for DG discretizations

   Mesh serial_mesh(mesh_file, 1, 1);
@@ -126,8 +123,8 @@ int main(int argc, char *argv[])
   if (mesh.ncmesh && (RT || ND))
   { MFEM_ABORT("LOR AMS and ADS solvers are not supported with AMR meshes."); }

-   FunctionCoefficient f_coeff(f), u_coeff(u);
-   VectorFunctionCoefficient f_vec_coeff(dim, f_vec), u_vec_coeff(dim, u_vec);
+   FunctionCoefficient f_coeff(f(1.0)), u_coeff(u);
+   VectorFunctionCoefficient f_vec_coeff(dim, f_vec(RT)), u_vec_coeff(dim, u_vec);

   int b1 = BasisType::GaussLobatto, b2 = BasisType::IntegratedGLL;
   unique_ptr<FiniteElementCollection> fec;
@@ -221,8 +221,6 @@ int main(int argc, char *argv[])
         if (k > 0)
         {
            double r = log2(err_old / err_k);
-            // Error is zero (2nd derivative is exact) -> put rate 2 (optimal).
-            if (err_k < 1e-14) { r = 2.0; }
            rate_sum += r;
            if (verbose)
            {
@@ -190,7 +190,7 @@ int main(int argc, char *argv[])
   src_dc->SetPadDigitsRank(src_pad_digits_rank);
   src_dc->Load(src_cycle);

-   if (src_dc->Error() != DataCollection::No_Error)
+   if (src_dc->Error() != DataCollection::NO_ERROR)
   {
      mfem::out << "Error loading data collection: "
                << src_coll_name
@@ -227,7 +227,7 @@ int main(int argc, char *argv[])

   out_dc->Save();

-   if (out_dc->Error() != DataCollection::No_Error)
+   if (out_dc->Error() != DataCollection::NO_ERROR)
   {
      mfem::out << "Error saving data collection: "
                << out_coll_name
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Will Pazner	a7c92ac238	RZ example with Robin conditions	2023-10-09 14:57:28 -07:00
Will Pazner	2462e7d591	Add check using IsIdentityProlongation	2023-04-03 15:24:08 -07:00
Will Pazner	d80e3d796b	Fix issue in grad-div mode with map type VALUE	2023-04-03 15:21:47 -07:00
Will Pazner	cdacbfb827	Add rz coordinate Darcy example	2023-03-15 13:00:13 -07:00
Will Pazner	9bcd366d28	Add Robin condition to Darcy example	2023-03-14 15:18:36 -07:00
Will Pazner	957109fe78	Add support for Robin-type conditions Temporarily this means disabling partial assembly for the RT mass term. The PA functionality is implemented in PR #3539.	2023-03-14 15:18:20 -07:00
Will Pazner	789a8dea13	Don't require SetBC on partitions with no boundary DOFs	2023-03-08 21:02:56 -08:00
Will Pazner	2aa41a06dc	Fix parallel bug in HdivSaddlePointSolver::EliminateBC	2023-03-08 16:56:05 -08:00
Will Pazner	4ea8e8a208	Make sure to reset size of intermediate vector HdivSaddlePointSolver::EliminateBC was resizing the temporary vector z. When no basis change is required, the line basis_l2.Mult(z, xE); would set xE = z. If z had the wrong size, this would resize xE. But xE needed to be an alias (view) into the global x vector, so this was a bug.	2023-03-07 16:05:59 -08:00
Will Pazner	67b7caeb2c	Properly handle map type VALUE in Darcy solver The diagonal L_diag_unweighted (added to the approximate Schur complement) needs to incorporate the mesh Jacobian determinant.	2023-03-07 16:04:07 -08:00
Will Pazner	908e025f7a	Use less oscillatory coefficients in residual example	2023-02-25 16:01:38 -08:00
Will Pazner	fd6363cd57	Fix degraded convergence in grad-div mode	2023-02-25 15:54:05 -08:00
Will Pazner	aec5511c7c	Improve the H(div) solver residual example	2023-02-25 15:48:12 -08:00
Will Pazner	d7e9c426e7	Add H(div) solver residual example	2023-02-25 15:34:31 -08:00
Will Pazner	2a6153c640	Improve conversion from map type VALUE to INTEGRAL	2023-02-25 15:25:56 -08:00
Will Pazner	8fbcda2419	Support map type VALUE in H(div) saddle-point solver	2023-02-17 14:06:43 -08:00
Will Pazner	a21d9b4895	Support non-nodal basis types in ChangeOfBasis_RT	2023-02-07 14:45:08 -08:00
Will Pazner	4a0a0e9d25	Handle non-nodal basis in ChangeOfBasis_L2	2023-02-07 14:29:49 -08:00
Will Pazner	da802fc1ca	Construct diagonal matrix directly on device	2023-01-31 16:55:36 -08:00
Will Pazner	968858dec2	Better handle variable L2 coefficients in Darcy mode HdivSaddlePointSolver	2023-01-27 12:45:06 -08:00
Will Pazner	65b6aa3a86	Add DGMassInverse::MultTranspose	2023-01-27 12:16:07 -08:00
Will Pazner	d41f5d8f04	Improve HdivSaddlePointSolver comments	2023-01-26 20:46:24 -08:00
Will Pazner	227a3c2c98	Add H(div) saddle-point solver miniapps Included are grad-div and Darcy/Poisson miniapps.	2023-01-26 19:19:11 -08:00
Will Pazner	7a7355643a	Parameterize lor_mms coefficients using std::function	2023-01-26 19:17:36 -08:00
Will Pazner	6d58074dd4	Make ElementRestriction low-level array accessors public	2023-01-26 19:17:15 -08:00