minor bug

changes to enums to avoid windows macro conflicts

.github/workflows/builds-and-tests.yml

@@ -141,7 +141,7 @@ jobs:
 
     - name: get MPI (Windows)
       if: matrix.mpi == 'par' && matrix.os == 'windows-latest'
-      uses: mpi4py/setup-mpi@v1.1.2
+      uses: mpi4py/setup-mpi@v1.1.4
 
     # Get Hypre through cache, or build it.
     # Install will only run on cache miss.

.gitignore

@@ -131,6 +131,12 @@ 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.*
@@ -203,6 +209,7 @@ 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
@@ -219,6 +226,7 @@ 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
@@ -278,6 +286,7 @@ 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

.gitlab/quartz-baseline.yml

@@ -93,7 +93,7 @@ report_baseline:
           git pull && \
           git add ${rundir} && \
           git commit -m "${msg}" && \
-          git push origin master
+          ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
         else
           for file in ${rundir}/*; do
             echo "------------------------------"

.gitlab/scripts/git_try_to_push

@@ -0,0 +1,41 @@
+#!/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

.gitlab/scripts/report_build_and_test_failure

@@ -32,7 +32,7 @@ if [[ "$AUTOTEST_COMMIT" != "NO" ]]; then
   git pull && \
   git add ${rundir} && \
   git commit -m "${msg}" && \
-  git push origin master
+  ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
 else
   for file in ${rundir}/*; do
     echo "------------------------------"

.gitlab/scripts/report_build_and_test_success

@@ -29,7 +29,7 @@ if [[ "$AUTOTEST_COMMIT" != "NO" ]]; then
   git pull && \
   git add ${rundir} && \
   git commit -m "${msg}" && \
-  git push origin master
+  ${CI_PROJECT_DIR}/.gitlab/scripts/git_try_to_push
 else
   for file in ${rundir}/*; do
     echo "------------------------------"

CHANGELOG

@@ -10,12 +10,23 @@
 
 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
@@ -27,6 +38,9 @@ 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.
@@ -102,6 +116,9 @@ 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.
 

CMakeLists.txt

@@ -134,8 +134,7 @@ if (MFEM_USE_CUDA)
       set(CUDA_FLAGS "-ccbin=${CMAKE_CXX_COMPILER} ${CUDA_FLAGS}")
       set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CMAKE_CXX_COMPILER})
    endif()
-   set(CMAKE_CUDA_FLAGS "${CUDA_FLAGS}" CACHE STRING
-       "CUDA flags set for MFEM" FORCE)
+   set(CMAKE_CUDA_FLAGS ${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS})
    set(CUSPARSE_FOUND TRUE)
    set(CUSPARSE_LIBRARIES "cusparse")
    set(CUBLAS_FOUND TRUE)
@@ -405,6 +404,15 @@ 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)
@@ -500,7 +508,7 @@ 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 POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
+    NETCDF MPFR PUMI HIOP IPOPT 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)
 

CONTRIBUTING.md

@@ -112,6 +112,7 @@ The MFEM source code has the following structure:
   │   ├── caliper
   │   ├── ginkgo
   │   ├── hiop
+  │   ├── ipopt
   │   ├── jupyter
   │   ├── moonolith
   │   ├── petsc

INSTALL

@@ -471,6 +471,9 @@ 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/
@@ -738,6 +741,11 @@ 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
@@ -972,6 +980,7 @@ MFEM_USE_MPFR
 MFEM_USE_ZLIB
 MFEM_USE_PUMI
 MFEM_USE_HIOP
+MFEM_USE_IPOPT
 MFEM_USE_CODIPACK
 MFEM_USE_ADFORWARD
 MFEM_USE_CUDA
@@ -1035,6 +1044,7 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - POSIXCLOCKS
  - PUMI
  - HIOP
+ - IPOPT
  - CoDiPack
  - OCCA
  - RAJA

config/cmake/MFEMConfig.cmake.in

@@ -36,6 +36,7 @@ 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@)

config/cmake/config.hpp.in

@@ -131,6 +131,9 @@
 // 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

config/cmake/modules/FindIPOPT.cmake

@@ -0,0 +1,23 @@
+# 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.")
+

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -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_GSLIB MFEM_USE_CUDA
+      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_IPOPT 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

config/config.hpp.in

@@ -141,6 +141,9 @@
 // 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
 

config/config.mk.in

@@ -46,6 +46,7 @@ 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@

config/defaults.cmake

@@ -48,6 +48,7 @@ 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)
@@ -220,6 +221,10 @@ 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")

config/defaults.mk

@@ -148,6 +148,7 @@ 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
@@ -447,6 +448,11 @@ 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)

config/sample-runs.sh

@@ -58,6 +58,10 @@ groups_serial=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp"'
+'"ipopt"
+   "IpOpt examples:"
+   "examples/ipopt"
+   "ex10.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
@@ -215,6 +219,10 @@ groups_all=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp ex9p.cpp"'
+'"ipopt"
+   "IpOpt examples:"
+   "examples/ipopt"
+   "ex10.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"

doc/CodeDocumentation.conf.in

@@ -785,6 +785,7 @@ 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 \

examples/CMakeLists.txt

@@ -178,6 +178,11 @@ 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)

examples/contact.cpp

@@ -0,0 +1,810 @@
+//                                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;
+}

examples/ipopt/CMakeLists.txt

@@ -0,0 +1,60 @@
+# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+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()

examples/ipopt/README

@@ -0,0 +1,19 @@
+                    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.

examples/ipopt/block1.mesh

@@ -0,0 +1,103 @@
+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

examples/ipopt/block2.mesh

@@ -0,0 +1,68 @@
+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

examples/ipopt/contact.cpp

@@ -0,0 +1,742 @@
+//                                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;
+}

examples/ipopt/exContactBlockTL.hpp

@@ -0,0 +1,230 @@
+//                                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

examples/ipopt/makefile

@@ -0,0 +1,68 @@
+# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ipopt/,)
+CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+# Use the MFEM install directory
+# MFEM_INSTALL_DIR = ../../mfem
+# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_EXAMPLES = exContactBlockTL
+EXAMPLES = $(SEQ_EXAMPLES)
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all clean clean-build clean-exec
+
+# Remove built-in rule
+%: %.cpp
+
+# Replace the default implicit rule for *.cpp files
+%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+
+all: $(EXAMPLES)
+
+ifeq ($(MFEM_USE_IPOPT),NO)
+$(EXAMPLES):
+	$(error MFEM is not configured with IPOPT)
+endif
+
+MFEM_TESTS = EXAMPLES
+include $(MFEM_TEST_MK)
+
+# Testing: Parallel vs. serial runs
+RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
+%-test-par: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
+%-test-seq: %
+	@$(call mfem-test,$<,, Serial example)
+
+# Testing: "test" target and mfem-test* variables are defined in config/test.mk
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean: clean-build clean-exec
+
+clean-build:
+	rm -f *.o *~ $(SEQ_EXAMPLES)
+	rm -rf *.dSYM *.TVD.*breakpoints
+
+clean-exec:
+	@rm -f exContactBlockTL.mesh exContactBlockTL-mesh.* exContactBlockTL-init.* exContactBlockTL-final.* ExampleContactBlockTL*

examples/ipopt/nodepair.hpp

@@ -0,0 +1,888 @@
+
+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);
+   }
+};
+

examples/makefile

@@ -46,6 +46,9 @@ 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

examples/nodepair.hpp

@@ -0,0 +1,888 @@
+
+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);
+   }
+};
+

fem/bilininteg_mass_pa.cpp

@@ -56,8 +56,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
    dim = mesh->Dimension();
    ne = fes.GetMesh()->GetNE();
    nq = ir->GetNPoints();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
-                                    GeometricFactors::JACOBIANS, mt);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::DETERMINANTS, mt);
    maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
@@ -74,7 +73,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
       const bool const_c = coeff.Size() == 1;
       const bool by_val = map_type == FiniteElement::VALUE;
       const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
-      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
+      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,NE);
       const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
                      Reshape(coeff.Read(), Q1D,Q1D,NE);
       auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
@@ -84,11 +83,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
          {
             MFEM_FOREACH_THREAD(qy,y,Q1D)
             {
-               const double J11 = J(qx,qy,0,0,e);
-               const double J12 = J(qx,qy,1,0,e);
-               const double J21 = J(qx,qy,0,1,e);
-               const double J22 = J(qx,qy,1,1,e);
-               const double detJ = (J11*J22)-(J21*J12);
+               const double detJ = J(qx,qy,e);
                const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
                v(qx,qy,e) =  W(qx,qy) * coeff * (by_val ? detJ : 1.0/detJ);
             }
@@ -102,7 +97,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
       const bool const_c = coeff.Size() == 1;
       const bool by_val = map_type == FiniteElement::VALUE;
       const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
-      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
+      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,Q1D,NE);
       const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
                      Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
       auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
@@ -114,18 +109,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
             {
                MFEM_FOREACH_THREAD(qz,z,Q1D)
                {
-                  const double J11 = J(qx,qy,qz,0,0,e);
-                  const double J21 = J(qx,qy,qz,1,0,e);
-                  const double J31 = J(qx,qy,qz,2,0,e);
-                  const double J12 = J(qx,qy,qz,0,1,e);
-                  const double J22 = J(qx,qy,qz,1,1,e);
-                  const double J32 = J(qx,qy,qz,2,1,e);
-                  const double J13 = J(qx,qy,qz,0,2,e);
-                  const double J23 = J(qx,qy,qz,1,2,e);
-                  const double J33 = J(qx,qy,qz,2,2,e);
-                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
-                  /* */               J21 * (J12 * J33 - J32 * J13) +
-                  /* */               J31 * (J12 * J23 - J22 * J13);
+                  const double detJ = J(qx,qy,qz,e);
                   const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
                   v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * (by_val ? detJ : 1.0/detJ);
                }

fem/datacollection.cpp

@@ -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) +

fem/datacollection.hpp

@@ -378,12 +378,24 @@ public:
    virtual ~DataCollection();
 
    /// Errors returned by Error()
-   enum { NO_ERROR = 0, READ_ERROR = 1, WRITE_ERROR = 2 };
+   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
+   };
 
    /// 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;

fem/fe/fe_base.cpp

@@ -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(
@@ -239,7 +239,6 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
    }
 }
 
-
 // Assume a linear mapping
 void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
                                          Vector &Laplacian) const
@@ -250,7 +249,7 @@ 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)
@@ -283,7 +282,6 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
          Laplacian[nd] += hess(nd,ii)*scale[ii];
       }
    }
-
 }
 
 void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
@@ -363,11 +361,128 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
    Mult( hess, lhm, Hessian);
 }
 
-const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &,
-                                             DofToQuad::Mode) const
+const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &ir,
+                                             DofToQuad::Mode mode) const
 {
-   MFEM_ABORT("method is not implemented for this element");
-   return *dof2quad_array[0]; // suppress a warning
+   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;
 }
 
 FiniteElement::~FiniteElement()
@@ -379,16 +494,19 @@ 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 c_shape(dof);
+   Vector shape(dof);
+#else
+   Vector shape;
+   vshape.GetColumnReference(0, shape);
 #endif
 
    MFEM_ASSERT(map_type == fine_fe.GetMapType(), "");
@@ -398,10 +516,10 @@ void ScalarFiniteElement::NodalLocalInterpolation (
    {
       Trans.Transform(fine_fe.Nodes.IntPoint(i), vv);
       f_ip.Set(v, dim);
-      CalcShape(f_ip, c_shape);
+      CalcShape(f_ip, shape);
       for (int j = 0; j < dof; j++)
       {
-         if (fabs(I(i,j) = c_shape(j)) < 1.0e-12)
+         if (fabs(I(i,j) = shape(j)) < 1.0e-12)
          {
             I(i,j) = 0.0;
          }
@@ -422,7 +540,7 @@ 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();
@@ -456,14 +574,13 @@ void ScalarFiniteElement::ScalarLocalInterpolation(
    }
 }
 
-void ScalarFiniteElement::ScalarLocalRestriction(
+void ScalarFiniteElement::ScalarLocalL2Restriction(
    ElementTransformation &Trans, DenseMatrix &R,
    const ScalarFiniteElement &coarse_fe) const
 {
    // General "restriction", defined by L2 projection
    double v[Geometry::MaxDim];
-   Vector vv (v, dim);
-   IntegrationPoint f_ip;
+   Vector vv(v, dim);
 
    const int cs = coarse_fe.GetDof(), fs = this->GetDof();
    R.SetSize(cs, fs);
@@ -472,16 +589,27 @@ void ScalarFiniteElement::ScalarLocalRestriction(
    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 &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);
+      const IntegrationPoint &c_ip = ir.IntPoint(i);
+      coarse_fe.CalcShape(c_ip, coarse_shape);
+      AddMult_a_VVt(c_ip.weight, coarse_shape, coarse_mass);
+   }
 
-      AddMult_a_VVt(ip.weight, coarse_shape, coarse_mass);
-      AddMult_a_VWt(ip.weight, coarse_shape, fine_shape, coarse_fine_mass);
+   // 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);
    }
 
    DenseMatrixInverse coarse_mass_inv(coarse_mass);
@@ -494,95 +622,6 @@ void ScalarFiniteElement::ScalarLocalRestriction(
       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,
@@ -631,7 +670,10 @@ void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
    Vector pt(&ipt.x, dim);
 
 #ifdef MFEM_THREAD_SAFE
-   Vector c_shape(dof);
+   Vector shape(dof);
+#else
+   Vector shape;
+   vshape.GetColumnReference(0, shape);
 #endif
 
    Trans.SetIntPoint(&Nodes[0]);
@@ -641,8 +683,8 @@ void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
       InvertLinearTrans(Trans, Nodes[j], pt);
       if (Geometries.CheckPoint(geom_type, ipt)) // do we need an epsilon here?
       {
-         CalcShape(ipt, c_shape);
-         R.SetRow(j, c_shape);
+         CalcShape(ipt, shape);
+         R.SetRow(j, shape);
       }
       else
       {
@@ -653,7 +695,7 @@ 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++)
@@ -662,7 +704,7 @@ 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();
@@ -670,7 +712,7 @@ void NodalFiniteElement::Project (
    }
 }
 
-void NodalFiniteElement::Project (
+void NodalFiniteElement::Project(
    VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 {
    MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
@@ -849,18 +891,18 @@ 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()
@@ -900,7 +942,7 @@ void VectorFiniteElement::SetDerivMembers()
    }
 }
 
-void VectorFiniteElement::CalcVShape_RT (
+void VectorFiniteElement::CalcVShape_RT(
    ElementTransformation &Trans, DenseMatrix &shape) const
 {
    MFEM_ASSERT(map_type == H_DIV, "");
@@ -912,7 +954,7 @@ 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, "");
@@ -2402,6 +2444,46 @@ 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,
@@ -2436,8 +2518,7 @@ VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                                                      const DofMapType dmtype)
    : VectorFiniteElement(dims, GetTensorProductGeometry(dims), d,
                          p, M, FunctionSpace::Qk),
-     TensorBasisElement(dims, p, VerifyNodal(cbtype), dmtype),
-     cbasis1d(poly1d.GetBasis(p, VerifyClosed(cbtype))),
+     TensorBasisElement(dims, p, VerifyNodal(VerifyClosed(cbtype)), dmtype),
      obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(obtype)))
 {
    MFEM_VERIFY(dims > 1, "Constructor for VectorTensorFiniteElement with both "
@@ -2452,93 +2533,13 @@ VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                                                      const DofMapType dmtype)
    : VectorFiniteElement(dims, GetTensorProductGeometry(dims), d,
                          p, M, FunctionSpace::Pk),
-     TensorBasisElement(dims, p, obtype, dmtype),
-     cbasis1d(poly1d.GetBasis(p, VerifyOpen(obtype))),
+     TensorBasisElement(dims, p, VerifyOpen(obtype), dmtype),
      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++)

fem/fe/fe_base.hpp

@@ -127,7 +127,6 @@ 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. */
@@ -157,8 +156,7 @@ 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
-          (TODO). */
+          are used to describe the "closed" and "open" 1D basis functions. */
       TENSOR
    };
 
@@ -176,7 +174,7 @@ 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, (TODO)
+       - #nqpt x dim x #ndof, for vector elements,
 
        where
 
@@ -187,15 +185,15 @@ 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 (TODO). */
+       - #ndof x #nqpt x dim, for vector elements. */
    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 (TODO), or
-       - #nqpt x cdim x #ndof, for H(curl) vector elements (TODO),
+       - #nqpt x #ndof, for H(div) vector elements, or
+       - #nqpt x cdim x #ndof, for H(curl) vector elements,
 
        where
 
@@ -208,12 +206,11 @@ 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 (TODO), or
-       - #ndof x #nqpt x cdim, for H(curl) vector elements (TODO). */
+       - #ndof x #nqpt, for H(div) vector elements, or
+       - #ndof x #nqpt x cdim, for H(curl) vector elements. */
    Array<double> Gt;
 };
 
-
 /// Describes the function space on each element
 class FunctionSpace
 {
@@ -247,7 +244,7 @@ protected:
    mutable int orders[Geometry::MaxDim]; ///< Anisotropic orders
    IntegrationRule Nodes;
 #ifndef MFEM_THREAD_SAFE
-   mutable DenseMatrix vshape; // Dof x VDim
+   mutable DenseMatrix vshape; // Dof x Dim
 #endif
    /// Container for all DofToQuad objects created by the FiniteElement.
    /** Multiple DofToQuad objects may be needed when different quadrature rules
@@ -350,7 +347,6 @@ 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}. */
@@ -457,8 +453,8 @@ 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. */
@@ -579,6 +575,7 @@ 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();
 
@@ -625,16 +622,11 @@ 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,
@@ -642,10 +634,6 @@ 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
@@ -656,13 +644,8 @@ 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
@@ -674,7 +657,6 @@ 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,
@@ -695,15 +677,11 @@ 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 ScalarLocalRestriction(ElementTransformation &Trans,
-                               DenseMatrix &R,
-                               const ScalarFiniteElement &coarse_fe) const;
-
-   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
-                                         DofToQuad::Mode mode) const;
+   void ScalarLocalL2Restriction(ElementTransformation &Trans,
+                                 DenseMatrix &R,
+                                 const ScalarFiniteElement &coarse_fe) const;
 };
 
-
 /// Class for standard nodal finite elements.
 class NodalFiniteElement : public ScalarFiniteElement
 {
@@ -725,38 +703,38 @@ public:
                       int F = FunctionSpace::Pk)
       : ScalarFiniteElement(D, G, Do, O, F) { }
 
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
    { NodalLocalInterpolation(Trans, I, *this); }
 
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const;
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override;
 
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
    { CheckScalarFE(fe).NodalLocalInterpolation(Trans, I, *this); }
 
-   virtual void Project (Coefficient &coeff,
-                         ElementTransformation &Trans, Vector &dofs) const;
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 
-   virtual void Project (VectorCoefficient &vc,
-                         ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;
 
    // (mc.height x mc.width) @ DOFs -> (Dof x mc.width x mc.height) in dofs
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
+   void ProjectMatrixCoefficient(
+      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override;
 
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override;
 
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const;
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override;
 
-   virtual void ProjectDiv(const FiniteElement &fe,
-                           ElementTransformation &Trans,
-                           DenseMatrix &div) const;
+   void ProjectDiv(const FiniteElement &fe,
+                   ElementTransformation &Trans,
+                   DenseMatrix &div) const override;
 
    /** @brief Get an Array<int> that maps lexicographically ordered indices to
        the indices of the respective nodes/dofs/basis functions.
@@ -790,12 +768,12 @@ class VectorFiniteElement : public FiniteElement
    // Hide the scalar functions CalcShape and CalcDShape.
 private:
    /// Overrides the scalar CalcShape function to print an error.
-   virtual void CalcShape(const IntegrationPoint &ip,
-                          Vector &shape) const;
+   void CalcShape(const IntegrationPoint &ip,
+                  Vector &shape) const override;
 
    /// Overrides the scalar CalcDShape function to print an error.
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 
 protected:
    bool is_nodal;
@@ -954,11 +932,10 @@ 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
@@ -1179,7 +1156,6 @@ public:
 
 extern Poly_1D poly1d;
 
-
 /// An element defined as an ND tensor product of 1D elements on a segment,
 /// square, or cube
 class TensorBasisElement
@@ -1203,7 +1179,7 @@ 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
@@ -1235,6 +1211,11 @@ 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,
@@ -1245,18 +1226,18 @@ public:
                             const DofMapType dmtype);
 
    const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
-                                 DofToQuad::Mode mode) const
+                                 DofToQuad::Mode mode) const override
    {
       return (mode == DofToQuad::FULL) ?
-             ScalarFiniteElement::GetDofToQuad(ir, mode) :
-             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+             FiniteElement::GetDofToQuad(ir, mode) :
+             GetTensorDofToQuad(*this, ir, mode, basis1d, true, dof2quad_array);
    }
 
-   virtual void SetMapType(const int map_type_);
+   void SetMapType(const int map_type_) override;
 
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
    {
       if (basis1d.IsIntegratedType())
       {
@@ -1276,7 +1257,7 @@ private:
    mutable Array<DofToQuad*> dof2quad_array_open;
 
 protected:
-   Poly_1D::Basis &cbasis1d, &obasis1d;
+   Poly_1D::Basis &obasis1d;
 
 public:
    VectorTensorFiniteElement(const int dims, const int d, const int p,
@@ -1289,16 +1270,22 @@ public:
                              const DofMapType dmtype);
 
    const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
-                                 DofToQuad::Mode mode) const;
+                                 DofToQuad::Mode mode) const override
+   {
+      MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
+      return GetTensorDofToQuad(*this, ir, mode, basis1d, true,
+                                dof2quad_array);
+   }
 
    const DofToQuad &GetDofToQuadOpen(const IntegrationRule &ir,
-                                     DofToQuad::Mode mode) const;
+                                     DofToQuad::Mode mode) const
+   {
+      MFEM_VERIFY(mode != DofToQuad::FULL, "invalid mode requested");
+      return GetTensorDofToQuad(*this, ir, mode, obasis1d, false,
+                                dof2quad_array_open);
+   }
 
-   const DofToQuad &GetTensorDofToQuad(const IntegrationRule &ir,
-                                       DofToQuad::Mode mode,
-                                       const bool closed) const;
-
-   ~VectorTensorFiniteElement();
+   virtual ~VectorTensorFiniteElement();
 };
 
 void InvertLinearTrans(ElementTransformation &trans,

fem/fe/fe_l2.hpp

@@ -32,6 +32,11 @@ 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); }
+
 };
 
 
@@ -55,6 +60,11 @@ 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,
@@ -80,6 +90,11 @@ 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,
@@ -111,6 +126,11 @@ public:
                             ElementTransformation &Trans,
                             DenseMatrix &curl) const
    { ProjectCurl_2D(fe, Trans, curl); }
+
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { ScalarLocalL2Restriction(Trans, R, *this); }
+
 };
 
 
@@ -133,6 +153,11 @@ 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); }
+
 };
 
 

fem/fe/fe_nd.cpp

@@ -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
-      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
-      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
+      basis1d.Eval(ip.x, shape_cx, dshape_cx);
+      basis1d.Eval(ip.y, shape_cy, dshape_cy);
+      basis1d.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
    {
-      cbasis1d.Eval(ip.x, shape_cx);
-      cbasis1d.Eval(ip.y, shape_cy);
-      cbasis1d.Eval(ip.z, shape_cz);
+      basis1d.Eval(ip.x, shape_cx);
+      basis1d.Eval(ip.y, shape_cy);
+      basis1d.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
 
-   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
-   cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
+   basis1d.Eval(ip.x, shape_cx, dshape_cx);
+   basis1d.Eval(ip.y, shape_cy, dshape_cy);
+   basis1d.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
-      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+      basis1d.Eval(ip.x, shape_cx, dshape_cx);
+      basis1d.Eval(ip.y, shape_cy, dshape_cy);
       obasis1d.ScaleIntegrated(false);
       obasis1d.EvalIntegrated(dshape_cx, shape_ox);
       obasis1d.EvalIntegrated(dshape_cy, shape_oy);
    }
    else
    {
-      cbasis1d.Eval(ip.x, shape_cx);
-      cbasis1d.Eval(ip.y, shape_cy);
+      basis1d.Eval(ip.x, shape_cx);
+      basis1d.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
 
-   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+   basis1d.Eval(ip.x, shape_cx, dshape_cx);
+   basis1d.Eval(ip.y, shape_cy, dshape_cy);
    if (obasis1d.IsIntegratedType())
    {
       obasis1d.ScaleIntegrated(false);

fem/fe/fe_pos.cpp

@@ -13,6 +13,7 @@
 
 #include "fe_pos.hpp"
 #include "../bilininteg.hpp"
+#include "../lininteg.hpp"
 #include "../coefficient.hpp"
 
 namespace mfem

fem/fe/fe_pos.hpp

@@ -40,7 +40,7 @@ public:
 
    virtual void GetLocalRestriction(ElementTransformation &Trans,
                                     DenseMatrix &R) const
-   { ScalarLocalRestriction(Trans, R, *this); }
+   { ScalarLocalL2Restriction(Trans, R, *this); }
 
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
@@ -73,8 +73,8 @@ public:
                                  DofToQuad::Mode mode) const
    {
       return (mode == DofToQuad::FULL) ?
-             ScalarFiniteElement::GetDofToQuad(ir, mode) :
-             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+             FiniteElement::GetDofToQuad(ir, mode) :
+             GetTensorDofToQuad(*this, ir, mode, basis1d, true, dof2quad_array);
    }
 };
 

fem/fe/fe_rt.cpp

@@ -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
-      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+      basis1d.Eval(ip.x, shape_cx, dshape_cx);
+      basis1d.Eval(ip.y, shape_cy, dshape_cy);
       obasis1d.ScaleIntegrated(false);
       obasis1d.EvalIntegrated(dshape_cx, shape_ox);
       obasis1d.EvalIntegrated(dshape_cy, shape_oy);
    }
    else
    {
-      cbasis1d.Eval(ip.x, shape_cx);
-      cbasis1d.Eval(ip.y, shape_cy);
+      basis1d.Eval(ip.x, shape_cx);
+      basis1d.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
 
-   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
+   basis1d.Eval(ip.x, shape_cx, dshape_cx);
+   basis1d.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
-      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
-      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
+      basis1d.Eval(ip.x, shape_cx, dshape_cx);
+      basis1d.Eval(ip.y, shape_cy, dshape_cy);
+      basis1d.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
    {
-      cbasis1d.Eval(ip.x, shape_cx);
-      cbasis1d.Eval(ip.y, shape_cy);
-      cbasis1d.Eval(ip.z, shape_cz);
+      basis1d.Eval(ip.x, shape_cx);
+      basis1d.Eval(ip.y, shape_cy);
+      basis1d.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
 
-   cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
-   cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
-   cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
+   basis1d.Eval(ip.x, shape_cx, dshape_cx);
+   basis1d.Eval(ip.y, shape_cy, dshape_cy);
+   basis1d.Eval(ip.z, shape_cz, dshape_cz);
    if (obasis1d.IsIntegratedType())
    {
       obasis1d.ScaleIntegrated(false);

fem/fe_coll.cpp

@@ -25,15 +25,16 @@ 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++)
    {
-      const FiniteElement *fe = FiniteElementForGeometry((Geometry::Type)g);
-      if (fe != NULL)
-      {
-         return fe;
-      }
+      fe = FiniteElementForGeometry((Geometry::Type)g);
+      if (fe != nullptr) { break; }
    }
-   return NULL;
+   error_mode = save_error_mode;
+   return fe;
 }
 
 int FiniteElementCollection::GetRangeType(int dim) const
@@ -643,6 +644,7 @@ 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
@@ -686,6 +688,7 @@ 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
@@ -726,6 +729,7 @@ 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
@@ -766,6 +770,7 @@ 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
@@ -832,6 +837,7 @@ 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
@@ -869,6 +875,7 @@ 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
@@ -911,6 +918,7 @@ 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
@@ -952,6 +960,7 @@ 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
@@ -993,6 +1002,7 @@ 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
@@ -1028,6 +1038,7 @@ 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
@@ -1063,6 +1074,7 @@ 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.");
    }
@@ -1097,6 +1109,7 @@ 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;
@@ -1131,6 +1144,7 @@ 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
@@ -1166,6 +1180,7 @@ 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
@@ -1196,6 +1211,7 @@ 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.");
    }
@@ -1234,6 +1250,7 @@ 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
@@ -1271,6 +1288,7 @@ 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
@@ -1311,6 +1329,7 @@ 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
@@ -1352,6 +1371,7 @@ 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
@@ -1391,6 +1411,7 @@ 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
@@ -1432,6 +1453,7 @@ 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
@@ -1472,6 +1494,7 @@ 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
@@ -1521,6 +1544,7 @@ 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
@@ -1570,6 +1594,7 @@ 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
@@ -1931,6 +1956,7 @@ 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;
@@ -2311,6 +2337,7 @@ 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;
@@ -2566,6 +2593,7 @@ 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;
@@ -2851,6 +2879,7 @@ 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;
@@ -3453,6 +3482,7 @@ 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

fem/fe_coll.hpp

@@ -233,6 +233,19 @@ 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.

fem/fespace.cpp

@@ -2056,10 +2056,7 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
       GetLocalDerefinementMatrices(elem_geoms[i], localR[elem_geoms[i]]);
    }
 
-   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());
+   SparseMatrix *R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim);
 
    Array<int> mark(R->Height());
    mark = 0;
@@ -2069,6 +2066,7 @@ 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++)
    {
@@ -2091,10 +2089,11 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
             int r = DofToVDof(dofs[i], vd);
             int m = (r >= 0) ? r : (-1 - r);
 
-            if (!mark[m])
+            if (is_dg || !mark[m])
             {
                lR.GetRow(i, row);
                R->SetRow(r, old_vdofs, row);
+
                mark[m] = 1;
                num_marked++;
             }
@@ -2102,8 +2101,11 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
       }
    }
 
-   MFEM_VERIFY(num_marked == R->Height(),
-               "internal error: not all rows of R were set.");
+   if (!is_dg)
+   {
+      MFEM_VERIFY(num_marked == R->Height(),
+                  "internal error: not all rows of R were set.");
+   }
 
    R->Finalize(); // no-op if fixed width
    return R;

fem/fespacehierarchy.hpp

@@ -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() { }
+   FiniteElementSpaceHierarchy() = default;
 
    /// @brief Constructs a space hierarchy with the given mesh and space on the
    /// coarsest level.
@@ -91,6 +91,7 @@ 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

fem/gridfunc.cpp

@@ -1441,21 +1441,13 @@ void GridFunction::GetDerivative(int comp, int der_comp, GridFunction &der)
    }
 }
 
-
 void GridFunction::GetVectorGradientHat(
    ElementTransformation &T, DenseMatrix &gh) const
 {
-   int elNo = T.ElementNo;
-   const FiniteElement *FElem = fes->GetFE(elNo);
+   const FiniteElement *FElem = fes->GetFE(T.ElementNo);
    int dim = FElem->GetDim(), dof = FElem->GetDof();
-   Array<int> vdofs;
-   DofTransformation * doftrans = fes->GetElementVDofs(elNo, vdofs);
    Vector loc_data;
-   GetSubVector(vdofs, loc_data);
-   if (doftrans)
-   {
-      doftrans->InvTransformPrimal(loc_data);
-   }
+   GetElementDofValues(T.ElementNo, loc_data);
    // assuming scalar FE
    int vdim = fes->GetVDim();
    DenseMatrix dshape(dof, dim);
@@ -1660,6 +1652,7 @@ 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);
@@ -1728,13 +1721,8 @@ 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;
-   Array<int> dofs;
-   DofTransformation * doftrans = fes->GetElementDofs(elNo, dofs);
-   GetSubVector(dofs, lval);
-   if (doftrans)
-   {
-      doftrans->InvTransformPrimal(lval);
-   }
+
+   GetElementDofValues(tr.ElementNo, lval);
    grad.SetSize(fe->GetDim(), ir.GetNPoints());
    for (int i = 0; i < ir.GetNPoints(); i++)
    {

fem/gridfunc.hpp

@@ -48,8 +48,6 @@ 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,
@@ -329,17 +327,34 @@ 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. */

fem/gslib.cpp

@@ -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)
+     avgtype(AvgType::ARITHMETIC), bdr_tol(1e-8)
 {
    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)
+     avgtype(AvgType::ARITHMETIC), bdr_tol(1e-8)
 {
    mesh_split.SetSize(4);
    ir_split.SetSize(4);
@@ -223,10 +223,12 @@ 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)
+      if (gsl_code[i] == 2 ||
+          (gsl_code[i] == 1 && gsl_dist(i) > bdr_tol))
       {
          gsl_elem[i] = 0;
          for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
+         gsl_code[i] = 2;
       }
    }
 
@@ -571,7 +573,7 @@ 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;
+   node_vals = 0.0;
 
    int gsl_mesh_pt_index = 0;
 
@@ -1153,7 +1155,7 @@ void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
    distfint.SetSize(pts_cnt);
    if (!gfmax)
    {
-      distfint = 0.;
+      distfint = 0.0;
    }
    else
    {
@@ -1248,10 +1250,12 @@ 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)
+      if (gsl_code[i] == 2 ||
+          (gsl_code[i] == 1 && gsl_dist(i) > bdr_tol))
       {
          gsl_elem[i] = 0;
          for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
+         gsl_code[i] = 2;
       }
    }
 

fem/gslib.hpp

@@ -38,6 +38,11 @@ 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.
  *
@@ -70,6 +75,8 @@ 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);
@@ -181,6 +188,14 @@ 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. */

fem/pbilinearform.cpp

@@ -347,14 +347,12 @@ ParallelEliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
 void ParBilinearForm::TrueAddMult(const Vector &x, Vector &y, const double a)
 const
 {
-   if (Xaux.ParFESpace() != pfes)
-   {
-      Xaux.SetSpace(pfes);
-      Yaux.SetSpace(pfes);
-      Ytmp.SetSize(pfes->GetTrueVSize());
-   }
+   const Operator *P = pfes->GetProlongationMatrix();
+   Xaux.SetSize(P->Height());
+   Yaux.SetSize(P->Height());
+   Ytmp.SetSize(P->Width());
 
-   Xaux.Distribute(&x);
+   P->Mult(x, Xaux);
    if (ext)
    {
       ext->Mult(Xaux, Yaux);
@@ -366,8 +364,8 @@ const
                   " implemented");
       mat->Mult(Xaux, Yaux);
    }
-   pfes->GetProlongationMatrix()->MultTranspose(Yaux, Ytmp);
-   y.Add(a,Ytmp);
+   P->MultTranspose(Yaux, Ytmp);
+   y.Add(a, Ytmp);
 }
 
 void ParBilinearForm::FormLinearSystem(

fem/pbilinearform.hpp

@@ -31,9 +31,8 @@ class ParBilinearForm : public BilinearForm
 protected:
    ParFiniteElementSpace *pfes; ///< Points to the same object as #fes
 
-   /// Auxiliary objects used in TrueAddMult().
-   mutable ParGridFunction Xaux, Yaux;
-   mutable Vector Ytmp;
+   /// Auxiliary vectors used in TrueAddMult(): L-, L-, and T-vector, resp.
+   mutable Vector Xaux, Yaux, Ytmp;
 
    OperatorHandle p_mat, p_mat_e;
 

fem/pfespace.cpp

@@ -3025,6 +3025,8 @@ 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];
@@ -3053,7 +3055,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
                int r = DofToVDof(dofs[i], vd);
                int m = (r >= 0) ? r : (-1 - r);
 
-               if (!mark[m])
+               if (is_dg || !mark[m])
                {
                   lR.GetRow(i, row);
                   diag->SetRow(r, old_vdofs, row);
@@ -3105,7 +3107,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
                int r = DofToVDof(dofs[i], vd);
                int m = (r >= 0) ? r : (-1 - r);
 
-               if (!mark[m])
+               if (is_dg || !mark[m])
                {
                   lR.GetRow(i, row);
                   MFEM_ASSERT(ldof[geom] == row.Size(), "");
@@ -3122,6 +3124,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
          }
       }
    }
+
    messages.clear();
    offd->Finalize(0);
    offd->SetWidth(col_map.size());

fem/tmop.cpp

@@ -48,8 +48,7 @@ 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);
-      Pt *= wt_arr[i];
-      P += Pt;
+      P.Add(wt_arr[i], Pt);
    }
 }
 
@@ -62,12 +61,109 @@ 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, At);
-      At *= wt_arr[i];
+      tmop_q_arr[i]->AssembleH(Jpt, DS, weight * wt_arr[i], At);
       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
 {
@@ -728,30 +824,30 @@ 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) [ (I2b/I1b)*dI1b + dI2b ]
+   // 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 ]
    //
    // dI1b x dz2 + dI2b x dz1 =
-   //    (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)
+   //    (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.
    //
    // z1 = I1b/sqrt(I1b*I2b), z2 = I2b/sqrt(I1b*I2b)
 
    ie.SetJacobian(Jpt.GetData());
    ie.SetDerivativeMatrix(DS.Height(), DS.GetData());
-   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);
+   double X_data[9];
+   DenseMatrix X(X_data, 3, 3);
+   Add(- ie.Get_I2b(), ie.Get_dI1b(), ie.Get_I1b(), ie.Get_dI2b(), X);
    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), d_I1b_I2b_data, A.GetData());
+   ie.Assemble_TProd(-a/(2*I1b_I2b), X_data, A.GetData());
 }
 
 double TMOP_Metric_302::EvalWMatrixForm(const DenseMatrix &Jpt) const
@@ -2798,8 +2894,6 @@ 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; }
@@ -2809,6 +2903,9 @@ 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
 }
 
@@ -3997,6 +4094,14 @@ 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());
@@ -4011,6 +4116,14 @@ 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());

fem/tmop.hpp

@@ -78,11 +78,14 @@ public:
    virtual int Id() const { return 0; }
 };
 
-/// Abstract class used to define combination of metrics with constant coefficients.
+class TargetConstructor;
+
+/// Abstract class used to define explicit combination of metrics with constant
+/// coefficients.
 class TMOP_Combo_QualityMetric : public TMOP_QualityMetric
 {
 protected:
-   Array<TMOP_QualityMetric *> tmop_q_arr; //not owned
+   Array<TMOP_QualityMetric *> tmop_q_arr; //the metrics are not owned
    Array<double> wt_arr;
 
 public:
@@ -108,6 +111,25 @@ 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
@@ -272,6 +294,7 @@ public:
 };
 
 /// 2D barrier shape (S) metric (polyconvex).
+/// Grade - A.
 class TMOP_Metric_002 : public TMOP_QualityMetric
 {
 protected:
@@ -293,6 +316,7 @@ public:
 };
 
 /// 2D non-barrier shape (S) metric.
+/// Grade - F.
 class TMOP_Metric_004 : public TMOP_QualityMetric
 {
 protected:
@@ -378,7 +402,8 @@ public:
                           const double weight, DenseMatrix &A) const;
 };
 
-/// 2D barrier (not a shape) metric (polyconvex).
+/// 2D barrier shape metric (polyconvex).
+/// Grade - A.
 class TMOP_Metric_050 : public TMOP_QualityMetric
 {
 protected:
@@ -395,6 +420,7 @@ public:
 };
 
 /// 2D non-barrier size (V) metric (not polyconvex).
+/// Grade - F.
 class TMOP_Metric_055 : public TMOP_QualityMetric
 {
 protected:
@@ -412,6 +438,7 @@ public:
 };
 
 /// 2D barrier size (V) metric (polyconvex).
+/// Grade - C.
 class TMOP_Metric_056 : public TMOP_QualityMetric
 {
 protected:
@@ -449,29 +476,29 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_004),
-      sz_metric(new TMOP_Metric_055)
+   TMOP_Metric_066(double 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 gamma; }
+   double GetGamma() const { return wt_arr[1]; }
 
    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:
@@ -490,24 +517,24 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_002),
-      sz_metric(new TMOP_Metric_077)
+   TMOP_Metric_080(double gamma)
+      : sh_metric(new TMOP_Metric_002), sz_metric(new TMOP_Metric_077)
    {
       // (1-gamma) mu_2 + gamma mu_77
-      AddQualityMetric(sh_metric, 1.-gamma_);
-      AddQualityMetric(sz_metric, gamma_);
+      AddQualityMetric(sh_metric, 1.0 - gamma);
+      AddQualityMetric(sz_metric, gamma);
    }
+
    virtual int Id() const { return 80; }
-   double GetGamma() const { return gamma; }
+   double GetGamma() const { return wt_arr[1]; }
 
    virtual ~TMOP_Metric_080() { delete sh_metric; delete sz_metric; }
 };
@@ -808,17 +835,15 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_301),
-      sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_328(double 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; }
@@ -828,21 +853,19 @@ public:
 class TMOP_Metric_332 : public TMOP_Combo_QualityMetric
 {
 protected:
-   double gamma;
    TMOP_QualityMetric *sh_metric, *sz_metric;
 
 public:
-   TMOP_Metric_332(double gamma_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_302),
-      sz_metric(new TMOP_Metric_315)
+   TMOP_Metric_332(double 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 gamma; }
+   double GetGamma() const { return wt_arr[1]; }
 
    virtual ~TMOP_Metric_332() { delete sh_metric; delete sz_metric; }
 };
@@ -852,17 +875,15 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_302),
-      sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_333(double 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; }
@@ -873,21 +894,19 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_303),
-      sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_334(double 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 gamma; }
+   double GetGamma() const { return wt_arr[1]; }
 
    virtual ~TMOP_Metric_334() { delete sh_metric; delete sz_metric; }
 };
@@ -897,21 +916,19 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_304),
-      sz_metric(new TMOP_Metric_316)
+   TMOP_Metric_347(double 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 gamma; }
+   double GetGamma() const { return wt_arr[1]; }
 
    virtual ~TMOP_Metric_347() { delete sh_metric; delete sz_metric; }
 };
@@ -1034,17 +1051,15 @@ 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_) : gamma(gamma_),
-      sh_metric(new TMOP_AMetric_011),
-      sz_metric(new TMOP_AMetric_014a)
+   TMOP_AMetric_126(double 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; }
@@ -1551,6 +1566,11 @@ 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; }

fem/tmop_tools.hpp

@@ -68,6 +68,11 @@ public:
                                      Vector &new_field,
                                      int new_nodes_ordering = Ordering::byNODES);
 
+   const FindPointsGSLIB *GetFindPointsGSLIB() const
+   {
+      return finder;
+   }
+
    ~InterpolatorFP()
    {
       finder->FreeData();

fem/transfer.cpp

@@ -291,6 +291,10 @@ 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; }
 
@@ -319,8 +323,11 @@ 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]);
-   // P will contain the corresponding prolongation operator
-   P.SetSize(offsets[nel_ho]);
+   if (build_P)
+   {
+      // P will contain the corresponding prolongation operator
+      P.SetSize(offsets[nel_ho]);
+   }
 
    IntegrationPointTransformation ip_tr;
    IsoparametricTransformation &emb_tr = ip_tr.Transf;
@@ -341,7 +348,6 @@ 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);
@@ -385,10 +391,15 @@ L2ProjectionGridTransfer::L2ProjectionL2Space::L2ProjectionL2Space(
       }
       mfem::Mult(Minv_lor, M_mixed, R_iho);
 
-      mfem::MultAtB(R_iho, M_lor, RtMlor);
-      mfem::Mult(RtMlor, R_iho, RtMlorR);
-      RtMlorR_inv.Factor();
-      RtMlorR_inv.Mult(RtMlor, P_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);
+      }
    }
 }
 
@@ -462,6 +473,8 @@ 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;
@@ -497,6 +510,8 @@ 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;
@@ -898,6 +913,11 @@ void L2ProjectionGridTransfer::BuildF()
    }
 }
 
+bool L2ProjectionGridTransfer::SupportsBackwardsOperator() const
+{
+   return ran_fes.GetTrueVSize() >= dom_fes.GetTrueVSize();
+}
+
 
 TransferOperator::TransferOperator(const FiniteElementSpace& lFESpace_,
                                    const FiniteElementSpace& hFESpace_)

fem/transfer.hpp

@@ -98,6 +98,8 @@ public:
    {
       return MakeTrueOperator(ran_fes, dom_fes, BackwardOperator(), bw_t_oper);
    }
+
+   virtual bool SupportsBackwardsOperator() const { return true; }
 };
 
 
@@ -346,6 +348,8 @@ public:
    virtual const Operator &ForwardOperator();
 
    virtual const Operator &BackwardOperator();
+
+   virtual bool SupportsBackwardsOperator() const;
 private:
    void BuildF();
 };

general/backends.hpp

@@ -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 double atomicAdd(double *add, double val)
+MFEM_DEVICE inline double atomicAdd(double *add, double val)
 {
    unsigned long long int *ptr = (unsigned long long int *) add;
    unsigned long long int old = *ptr, reg;

general/mem_manager.cpp

@@ -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)

general/mem_manager.hpp

@@ -165,8 +165,16 @@ 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() */
@@ -211,6 +219,8 @@ 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;
@@ -972,7 +982,7 @@ 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)
@@ -1008,7 +1018,7 @@ 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);
@@ -1019,7 +1029,7 @@ 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;
 
@@ -1038,7 +1048,7 @@ 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);
@@ -1098,7 +1108,7 @@ 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,
@@ -1111,7 +1121,7 @@ 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,
@@ -1124,7 +1134,7 @@ 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,
@@ -1136,12 +1146,12 @@ 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));
@@ -1151,9 +1161,9 @@ 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);
 }
@@ -1168,7 +1178,7 @@ 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);
 }
 
@@ -1188,7 +1198,7 @@ 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)
       {
@@ -1208,7 +1218,7 @@ 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)
       {
@@ -1235,7 +1245,7 @@ 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)
       {

general/version.cpp

@@ -97,6 +97,9 @@ 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

linalg/constraints.cpp

@@ -352,6 +352,7 @@ 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();
 
@@ -485,6 +486,7 @@ 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();
 
@@ -616,6 +618,7 @@ 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;
 }

linalg/hypre.cpp

@@ -292,13 +292,14 @@ HypreParVector& HypreParVector::operator=(const HypreParVector &y)
 
 HypreParVector& HypreParVector::operator=(HypreParVector &&y)
 {
-   // 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
+   Vector::operator=(std::move(y));
+   // Self-assignment-safe way to move for 'own_ParVector' and 'x':
+   const auto own_tmp = y.own_ParVector;
    y.own_ParVector = 0;
+   own_ParVector = own_tmp;
+   const auto x_tmp = y.x;
    y.x = nullptr;
-   y.data.Reset();
-   y.size = 0;
+   x = x_tmp;
    return *this;
 }
 

linalg/solvers.cpp

@@ -583,6 +583,7 @@ 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)
    {
@@ -735,6 +736,7 @@ 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)
    {
@@ -752,6 +754,7 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
       }
       converged = false;
       final_iter = 0;
+      initial_norm = nom;
       final_norm = nom;
       return;
    }
@@ -1015,7 +1018,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
          r = b;
       }
    }
-   double beta = Norm(r);  // beta = ||r||
+   double beta = initial_norm = Norm(r);  // beta = ||r||
    MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
 
    final_norm = std::max(rel_tol*beta, abs_tol);
@@ -1175,7 +1178,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
       x = 0.;
       r = b;
    }
-   double beta = Norm(r);  // beta = ||r||
+   double beta = initial_norm = Norm(r);  // beta = ||r||
    // We need to preallocate this to report the correct result in the case of
    // no convergence.
    double resid;
@@ -1391,7 +1394,7 @@ void BiCGSTABSolver::Mult(const Vector &b, Vector &x) const
    }
    rtilde = r;
 
-   resid = Norm(r);
+   resid = initial_norm = Norm(r);
    MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
    if (print_options.iterations || print_options.first_and_last)
    {
@@ -1638,7 +1641,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
    {
       prec->Mult(v1, u1);
    }
-   eta = beta = sqrt(Dot(*z, v1));
+   eta = beta = initial_norm = sqrt(Dot(*z, v1));
    MFEM_ASSERT(IsFinite(eta), "eta = " << eta);
    gamma0 = gamma1 = 1.;
    sigma0 = sigma1 = 0.;
@@ -1833,7 +1836,7 @@ void NewtonSolver::Mult(const Vector &b, Vector &x) const
       r -= b;
    }
 
-   norm0 = norm = Norm(r);
+   norm0 = norm = initial_norm = Norm(r);
    if (print_options.first_and_last && !print_options.iterations)
    {
       mfem::out << "Newton iteration " << setw(2) << 0
@@ -2031,7 +2034,7 @@ void LBFGSSolver::Mult(const Vector &b, Vector &x) const
 
    c = r;           // initial descent direction
 
-   norm0 = norm = Norm(r);
+   norm0 = norm = initial_norm = Norm(r);
    if (print_options.first_and_last && !print_options.iterations)
    {
       mfem::out << "LBFGS iteration " << setw(2) << 0
@@ -2404,7 +2407,7 @@ void SLBQPOptimizer::Mult(const Vector& xt, Vector& x) const
    }
 
    // Solve QP with fixed Lagrange multiplier
-   r = solve(l,xt,x,nclip);
+   r = initial_norm = solve(l,xt,x,nclip);
    print_iteration(nclip, r, l);
 
 

linalg/solvers.hpp

@@ -159,11 +159,12 @@ protected:
    ///@}
 
    /// @name Solver statistics (protected attributes)
+   /// Every IterativeSolver is expected to define these in its Mult() call.
    ///@{
 
-   mutable int final_iter;
-   mutable bool converged;
-   mutable double final_norm;
+   mutable int final_iter = -1;
+   mutable bool converged = false;
+   mutable double initial_norm = -1.0, final_norm = -1.0;
 
    ///@}
 
@@ -241,11 +242,38 @@ public:
    virtual void SetPrintLevel(PrintLevel);
    ///@}
 
-   /// @name Solver statistics
+   /// @name Solver statistics.
+   /// These are valid after the call to Mult().
    ///@{
+
+   /// 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

linalg/vector.cpp

@@ -149,9 +149,10 @@ Vector &Vector::operator=(const Vector &v)
 Vector &Vector::operator=(Vector &&v)
 {
    data = std::move(v.data);
-   size = v.size;
-   v.data.Reset();
+   // Self-assignment-safe way to move v.size to size:
+   const auto size_tmp = v.size;
    v.size = 0;
+   size = size_tmp;
    return *this;
 }
 
@@ -593,7 +594,7 @@ 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());
 
@@ -638,7 +639,7 @@ 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());
 
@@ -682,7 +683,7 @@ 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());
 

makefile

@@ -119,7 +119,7 @@ $(if $(word 2,$(SRC)),$(error Spaces in SRC = "$(SRC)" are not supported))
 MFEM_GIT_STRING = $(shell [ -d $(MFEM_DIR)/.git ] && git -C $(MFEM_DIR) \
    describe --all --long --abbrev=40 --dirty --always 2> /dev/null)
 
-EXAMPLE_SUBDIRS = amgx caliper ginkgo hiop petsc pumi sundials superlu moonolith
+EXAMPLE_SUBDIRS = amgx caliper ginkgo hiop ipopt 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\
+ SUITESPARSE STRUMPACK GINKGO GNUTLS NETCDF PETSC SLEPC MPFR PUMI HIOP IPOPT\
  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_GSLIB MFEM_USE_CUDA MFEM_USE_HIP\
+ MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_IPOPT 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\
@@ -690,6 +690,7 @@ 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))

mesh/mesh.cpp

@@ -1467,6 +1467,7 @@ 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()
@@ -1489,6 +1490,9 @@ void Mesh::DestroyTables()
 
    delete face_edge;
    delete edge_vertex;
+
+   delete face_to_elem;
+   face_to_elem = NULL;
 }
 
 void Mesh::DestroyPointers()
@@ -1550,6 +1554,7 @@ 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;
@@ -3632,6 +3637,7 @@ 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;
@@ -6175,6 +6181,34 @@ 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;
@@ -9152,8 +9186,9 @@ void Mesh::NonconformingRefinement(const Array<Refinement> &refinements,
 double Mesh::AggregateError(const Array<double> &elem_error,
                             const int *fine, int nfine, int op)
 {
-   double error = 0.0;
-   for (int i = 0; i < nfine; i++)
+   double error = elem_error[fine[0]];
+
+   for (int i = 1; i < nfine; i++)
    {
       MFEM_VERIFY(fine[i] < elem_error.Size(), "");
 
@@ -9317,6 +9352,7 @@ 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);

mesh/mesh.hpp

@@ -223,8 +223,13 @@ protected:
    Array<int> be_to_edge;  // for 2D
    Table *bel_to_edge;     // for 3D
    Array<int> be_to_face;
-   mutable Table *face_edge;
-   mutable Table *edge_vertex;
+
+   // 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().
 
    IsoparametricTransformation Transformation, Transformation2;
    IsoparametricTransformation BdrTransformation;
@@ -1182,6 +1187,10 @@ 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;
 
@@ -1226,24 +1235,32 @@ public:
 
    static FiniteElement *GetTransformationFEforElementType(Element::Type);
 
-   /** Builds the transformation defining the i-th element in the user-defined
-       variable. */
+   /// 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.
    void GetElementTransformation(int i, IsoparametricTransformation *ElTr);
 
-   /// Returns the transformation defining the i-th element
+   /// 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.
    ElementTransformation *GetElementTransformation(int i);
 
-   /** Return the transformation defining the i-th element assuming
-       the position of the vertices/nodes are given by 'nodes'. */
+   /// 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.
    void GetElementTransformation(int i, const Vector &nodes,
                                  IsoparametricTransformation *ElTr);
 
-   /// Returns the transformation defining the i-th boundary element
-   ElementTransformation * GetBdrElementTransformation(int i);
+   /// 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.
    void GetBdrElementTransformation(int i, IsoparametricTransformation *ElTr);
 
-   /** @brief Returns the transformation defining the given face element in a
-       user-defined variable. */
+   /// 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.
    void GetFaceTransformation(int i, IsoparametricTransformation *FTr);
 
    /** @brief A helper method that constructs a transformation from the
@@ -1255,14 +1272,18 @@ public:
                                    IsoparametricTransformation &Transf,
                                    int info);
 
-   /// Returns the transformation defining the given face element
+   /// 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.
    ElementTransformation *GetFaceTransformation(int FaceNo);
 
-   /** Returns the transformation defining the given edge element.
-       The transformation is stored in a user-defined variable. */
+   /// 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.
    void GetEdgeTransformation(int i, IsoparametricTransformation *EdTr);
 
-   /// Returns the transformation defining the given face element
+   /// 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.
    ElementTransformation *GetEdgeTransformation(int EdgeNo);
 
    /// Returns (a pointer to an object containing) the following data:
@@ -1295,16 +1316,22 @@ 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.
@@ -1576,6 +1603,10 @@ 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.
@@ -1603,15 +1634,22 @@ 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;
-   /** 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). */
+   /** @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(). */
    void EnsureNodes();
 
-   /** 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). */
+   /// 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). */
    virtual void SetCurvature(int order, bool discont = false, int space_dim = -1,
                              int ordering = 1);
 

mesh/mesh_readers.cpp

@@ -2107,8 +2107,6 @@ 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)
@@ -2121,7 +2119,7 @@ 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>;
@@ -2131,7 +2129,6 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                            }
                            break;
                         }
-                     */
                      case 15: // 1-node point
                      {
                         elements_0D.push_back(
@@ -2336,8 +2333,6 @@ 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)
@@ -2350,7 +2345,7 @@ 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>;
@@ -2360,7 +2355,6 @@ void Mesh::ReadGmshMesh(std::istream &input, int &curved, int &read_gf)
                         }
                         break;
                      }
-                  */
                   case 15: // 1-node point
                   {
                      elements_0D.push_back(
@@ -2563,16 +2557,16 @@ 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;

mesh/ncmesh.cpp

@@ -3706,20 +3706,28 @@ void NCMesh::FindSetNeighbors(const Array<char> &elem_set,
 
 static bool sorted_lists_intersect(const int* a, const int* b, int na, int nb)
 {
-   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;
+   // 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
 }
 
+
 void NCMesh::FindNeighbors(int elem, Array<int> &neighbors,
                            const Array<int> *search_set)
 {
@@ -4480,6 +4488,19 @@ 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

mesh/pmesh.cpp

@@ -2689,6 +2689,20 @@ 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
@@ -2796,6 +2810,61 @@ 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

mesh/pmesh.hpp

@@ -501,6 +501,9 @@ 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;
@@ -509,7 +512,9 @@ 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. */
+       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. */
    FaceElementTransformations *
    GetSharedFaceTransformations(int sf, bool fill2 = true);
 
@@ -517,12 +522,16 @@ 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. */
+       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. */
    FaceElementTransformations *
    GetSharedFaceTransformationsByLocalIndex(int FaceNo, bool fill2 = true);
 
-   ElementTransformation *
-   GetFaceNbrElementTransformation(int i)
+   /// 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)
    {
       GetFaceNbrElementTransformation(i, &FaceNbrTransformation);
 

miniapps/meshing/CMakeLists.txt

@@ -62,6 +62,10 @@ 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)

miniapps/meshing/makefile

@@ -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
+	shaper extruder mesh-optimizer minimal-surface polar-nc reflector
 PAR_MINIAPPS = pmesh-optimizer pminimal-surface
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -91,6 +91,8 @@ minimal-surface-test-seq: minimal-surface
 	@$(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:
@@ -108,14 +110,14 @@ clean: clean-build clean-exec
 
 clean-build:
 	rm -f *.o *~ mobius-strip klein-bottle toroid twist
-	rm -f mesh-explorer shaper extruder trimmer
+	rm -f mesh-explorer shaper extruder trimmer reflector
 	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
+	@rm -f toroid-*.mesh twist-*.mesh trimmer.mesh reflected.mesh
 	@rm -f partitioning.txt shaper.mesh extruder.mesh
 	@rm -f optimized* perturbed* polar-nc.mesh
 	@rm -rf mesh-explorer-{visit,paraview}*

miniapps/meshing/mesh-optimizer.cpp

@@ -57,10 +57,8 @@
 //   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 (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 size+orientation:
+//      mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -nor
 //   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
 //
@@ -86,7 +84,7 @@
 //   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 9 -tid 2 -ni 25 -ls 3 -art 2 -qo 5
+//     mesh-optimizer -o 3 -mid 80 -bec -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:
@@ -140,6 +138,7 @@ 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;
@@ -258,6 +257,9 @@ 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.");
@@ -740,20 +742,9 @@ int main(int argc, char *argv[])
 #endif
          }
 
-         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);
-         }
+         ConstantCoefficient size_coeff(0.1*0.1);
+         size.ProjectCoefficient(size_coeff);
+         tc->SetSerialDiscreteTargetSize(size);
 
          FunctionCoefficient ori_coeff(discrete_ori_2d);
          ori.ProjectCoefficient(ori_coeff);
@@ -780,6 +771,16 @@ 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;
@@ -790,7 +791,6 @@ int main(int argc, char *argv[])
       tmop_integ->ComputeUntangleMetricQuantiles(x, *fespace);
    }
 
-
    // Finite differences for computations of derivatives.
    if (fdscheme)
    {
@@ -1208,6 +1208,7 @@ 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;
@@ -1232,7 +1233,7 @@ int main(int argc, char *argv[])
    cout << "The strain energy decreased by: "
         << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
 
-   // 16. Visualize the final mesh and metric values.
+   // Visualize the final mesh and metric values.
    if (visualization)
    {
       char title[] = "Final metric values";
@@ -1246,6 +1247,7 @@ 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)
@@ -1262,7 +1264,7 @@ int main(int argc, char *argv[])
                 << "Max fitting error: " << err_max << std::endl;
    }
 
-   // 17. Visualize the mesh displacement.
+   // Visualize the mesh displacement.
    if (visualization)
    {
       osockstream sock(19916, "localhost");

miniapps/meshing/mesh-optimizer.hpp

@@ -84,24 +84,6 @@ 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();

miniapps/meshing/minimal-surface.cpp

@@ -77,7 +77,6 @@ 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;
@@ -118,8 +117,10 @@ 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) { }
@@ -157,7 +158,7 @@ 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(opt, mesh, GLVIZ_W, GLVIZ_H); }
+      if (opt.vis) { Visualize(glvis, opt, mesh, GLVIZ_W, GLVIZ_H); }
       // Create and launch the surface solver
       if (opt.by_vdim)
       {
@@ -170,7 +171,7 @@ public:
       if (opt.vis && opt.snapshot)
       {
          opt.keys = "Sq";
-         Visualize(opt, mesh, mesh->GetNodes());
+         Visualize(glvis, opt, mesh, mesh->GetNodes());
       }
       return 0;
    }
@@ -243,7 +244,8 @@ public:
    }
 
    // Initialize visualization of some given mesh
-   static void Visualize(Opt &opt, const Mesh *mesh,
+   static void Visualize(socketstream &glvis,
+                         Opt &opt, const Mesh *mesh,
                          const int w, const int h,
                          const GridFunction *sol = nullptr)
    {
@@ -259,7 +261,8 @@ public:
    }
 
    // Visualize some solution on the given mesh
-   static void Visualize(const Opt &opt, const Mesh *mesh,
+   static void Visualize(socketstream &glvis,
+                         const Opt &opt, const Mesh *mesh,
                          const GridFunction *sol = nullptr)
    {
       const GridFunction &solution = sol ? *sol : *mesh->GetNodes();
@@ -324,7 +327,7 @@ public:
          for (int i=0; i < opt.niters; ++i)
          {
             if (opt.amr) { Amr(); }
-            if (opt.vis) { Surface::Visualize(opt, S.mesh); }
+            if (opt.vis) { Surface::Visualize(S.glvis, opt, S.mesh); }
             if (!opt.id) { mfem::out << "Iteration " << i << ": "; }
             S.mesh->NodesUpdated();
             a.Update();
@@ -1237,8 +1240,9 @@ 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(opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
+   if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
    CGSolver cg;
    cg.SetRelTol(EPS);
    cg.SetAbsTol(EPS*EPS);
@@ -1270,7 +1274,7 @@ static int Problem1(Opt &opt)
          mfem::out << "Iteration " << i << ", norm: " << norm
                    << ", area: " << area << std::endl;
       }
-      if (opt.vis) { Surface::Visualize(opt, &mesh, &u); }
+      if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, &u); }
       if (opt.print) { Surface::Print(opt, &mesh, &u); }
       if (norm < NRM) { break; }
    }

miniapps/meshing/pmesh-optimizer.cpp

@@ -57,10 +57,8 @@
 //   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 (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 size+orientation:
+//     mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -nor
 //   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
 //
@@ -86,7 +84,7 @@
 //   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 9 -tid 2 -ni 25 -ls 3 -art 2 -qo 5
+//     mpirun -np 4 pmesh-optimizer -o 3 -mid 80 -bec -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:
@@ -150,6 +148,7 @@ 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;
@@ -270,6 +269,9 @@ 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.");
@@ -372,9 +374,6 @@ 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.
@@ -774,20 +773,9 @@ int main (int argc, char *argv[])
 #endif
          }
 
-         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);
-         }
+         ConstantCoefficient size_coeff(0.1*0.1);
+         size.ProjectCoefficient(size_coeff);
+         tc->SetParDiscreteTargetSize(size);
 
          FunctionCoefficient ori_coeff(discrete_ori_2d);
          ori.ProjectCoefficient(ori_coeff);
@@ -811,12 +799,21 @@ 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;
@@ -827,7 +824,6 @@ int main (int argc, char *argv[])
       tmop_integ->ComputeUntangleMetricQuantiles(x, *pfespace);
    }
 
-
    // Finite differences for computations of derivatives.
    if (fdscheme)
    {
@@ -1256,7 +1252,7 @@ int main (int argc, char *argv[])
       pmesh->PrintAsOne(mesh_ofs);
    }
 
-   // Compute the final energy of the functional.
+   // Report the final energy of the functional.
    const double fin_energy = a.GetParGridFunctionEnergy(x) /
                              (hradaptivity ? pmesh->GetGlobalNE() : 1);
    double fin_metric_energy = fin_energy;
@@ -1284,7 +1280,7 @@ int main (int argc, char *argv[])
            << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
    }
 
-   // 18. Visualize the final mesh and metric values.
+   // Visualize the final mesh and metric values.
    if (visualization)
    {
       char title[] = "Final metric values";
@@ -1298,6 +1294,7 @@ 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)
@@ -1317,7 +1314,7 @@ int main (int argc, char *argv[])
       }
    }
 
-   // 19. Visualize the mesh displacement.
+   // Visualize the mesh displacement.
    if (visualization)
    {
       x0 -= x;
@@ -1338,7 +1335,6 @@ int main (int argc, char *argv[])
       }
    }
 
-   // 20. Free the used memory.
    delete S;
    delete S_prec;
    delete target_c2;

miniapps/meshing/pminimal-surface.cpp

@@ -77,7 +77,6 @@ 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;
@@ -118,6 +117,7 @@ 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(opt, mesh, GLVIZ_W, GLVIZ_H); }
+      if (opt.vis) { Visualize(glvis, 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(opt, mesh, mesh->GetNodes());
+         Visualize(glvis, opt, mesh, mesh->GetNodes());
       }
       return 0;
    }
@@ -243,7 +243,8 @@ public:
    }
 
    // Initialize visualization of some given mesh
-   static void Visualize(Opt &opt, const Mesh *mesh,
+   static void Visualize(socketstream &glvis,
+                         Opt &opt, const Mesh *mesh,
                          const int w, const int h,
                          const GridFunction *sol = nullptr)
    {
@@ -259,7 +260,8 @@ public:
    }
 
    // Visualize some solution on the given mesh
-   static void Visualize(const Opt &opt, const Mesh *mesh,
+   static void Visualize(socketstream &glvis,
+                         const Opt &opt, const Mesh *mesh,
                          const GridFunction *sol = nullptr)
    {
       glvis << "parallel " << opt.sz << " " << opt.id << "\n";
@@ -328,7 +330,7 @@ public:
          for (int i=0; i < opt.niters; ++i)
          {
             if (opt.amr) { Amr(); }
-            if (opt.vis) { Surface::Visualize(opt, S.mesh); }
+            if (opt.vis) { Surface::Visualize(S.glvis, opt, S.mesh); }
             if (!opt.id) { mfem::out << "Iteration " << i << ": "; }
             S.mesh->NodesUpdated();
             a.Update();
@@ -1246,8 +1248,9 @@ 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(opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
+   if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, GLVIZ_W, GLVIZ_H, &u); }
    Vector B, X;
    OperatorPtr A;
    CGSolver cg(MPI_COMM_WORLD);
@@ -1279,7 +1282,7 @@ static int Problem1(Opt &opt)
          mfem::out << "Iteration " << i << ", norm: " << norm
                    << ", area: " << area << std::endl;
       }
-      if (opt.vis) { Surface::Visualize(opt, &mesh, &u); }
+      if (opt.vis) { Surface::Visualize(glvis, opt, &mesh, &u); }
       if (opt.print) { Surface::Print(opt, &mesh, &u); }
       if (norm < NRM) { break; }
    }

miniapps/tools/check-tmop-metric.cpp

@@ -221,6 +221,8 @@ 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)
             {

miniapps/tools/convert-dc.cpp

@@ -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

miniapps/tools/get-values.cpp

@@ -117,7 +117,7 @@ int main(int argc, char *argv[])
    dc.SetPadDigitsRank(pad_digits_rank);
    dc.Load(cycle);
 
-   if (dc.Error() != DataCollection::NO_ERROR)
+   if (dc.Error() != DataCollection::No_Error)
    {
       mfem::out << "Error loading VisIt data collection: " << coll_name << endl;
       return 1;

miniapps/tools/load-dc.cpp

@@ -73,7 +73,7 @@ int main(int argc, char *argv[])
    dc.SetPadDigitsRank(pad_digits_rank);
    dc.Load(cycle);
 
-   if (dc.Error() != DataCollection::NO_ERROR)
+   if (dc.Error() != DataCollection::No_Error)
    {
       mfem::out << "Error loading VisIt data collection: " << coll_name << endl;
       return 1;

miniapps/tools/lor-transfer.cpp

@@ -170,7 +170,6 @@ int main(int argc, char *argv[])
       gt = new L2ProjectionGridTransfer(fespace, fespace_lor);
    }
    const Operator &R = gt->ForwardOperator();
-   const Operator &P = gt->BackwardOperator();
 
    // HO->LOR restriction
    direction = "HO -> LOR @ LOR";
@@ -178,24 +177,29 @@ int main(int argc, char *argv[])
    compute_mass(&fespace_lor, ho_mass, LOR_dc, "R(HO)    ");
    if (vis) { visualize(LOR_dc, "R(HO)", Wx, Wy); Wx += offx; }
 
-   // LOR->HO prolongation
-   direction = "HO -> LOR @ HO";
-   GridFunction rho_prev = rho;
-   P.Mult(rho_lor, rho);
-   compute_mass(&fespace, ho_mass, HO_dc, "P(R(HO)) ");
-   if (vis) { visualize(HO_dc, "P(R(HO))", Wx, Wy); Wx = 0; Wy += offy; }
+   if (gt->SupportsBackwardsOperator())
+   {
+      const Operator &P = gt->BackwardOperator();
+      // LOR->HO prolongation
+      direction = "HO -> LOR @ HO";
+      GridFunction rho_prev = rho;
+      P.Mult(rho_lor, rho);
+      compute_mass(&fespace, ho_mass, HO_dc, "P(R(HO)) ");
+      if (vis) { visualize(HO_dc, "P(R(HO))", Wx, Wy); Wx = 0; Wy += offy; }
 
-   rho_prev -= rho;
-   cout.precision(12);
-   cout << "|HO - P(R(HO))|_∞   = " << rho_prev.Normlinf() << endl;
+      rho_prev -= rho;
+      cout.precision(12);
+      cout << "|HO - P(R(HO))|_∞   = " << rho_prev.Normlinf() << endl;
+   }
 
    // HO* to LOR* dual fields
    GridFunction ones(&fespace), ones_lor(&fespace_lor);
    ones = 1.0;
    ones_lor = 1.0;
    LinearForm M_rho(&fespace), M_rho_lor(&fespace_lor);
-   if (!use_pointwise_transfer)
+   if (!use_pointwise_transfer && gt->SupportsBackwardsOperator())
    {
+      const Operator &P = gt->BackwardOperator();
       M_ho.Mult(rho, M_rho);
       P.MultTranspose(M_rho, M_rho_lor);
       cout << "HO -> LOR dual field: " << fabs(M_rho(ones)-M_rho_lor(ones_lor))
@@ -209,22 +213,26 @@ int main(int argc, char *argv[])
    double lor_mass = compute_mass(&fespace_lor, -1.0, LOR_dc, "LOR      ");
    if (vis) { visualize(LOR_dc, "LOR", Wx, Wy); Wx += offx; }
 
-   // Prolongate to HO space
-   direction = "LOR -> HO @ HO";
-   P.Mult(rho_lor, rho);
-   compute_mass(&fespace, lor_mass, HO_dc, "P(LOR)   ");
-   if (vis) { visualize(HO_dc, "P(LOR)", Wx, Wy); Wx += offx; }
+   if (gt->SupportsBackwardsOperator())
+   {
+      const Operator &P = gt->BackwardOperator();
+      // Prolongate to HO space
+      direction = "LOR -> HO @ HO";
+      P.Mult(rho_lor, rho);
+      compute_mass(&fespace, lor_mass, HO_dc, "P(LOR)   ");
+      if (vis) { visualize(HO_dc, "P(LOR)", Wx, Wy); Wx += offx; }
 
-   // Restrict back to LOR space. This won't give the original function because
-   // the rho_lor doesn't necessarily live in the range of R.
-   direction = "LOR -> HO @ LOR";
-   R.Mult(rho, rho_lor);
-   compute_mass(&fespace_lor, lor_mass, LOR_dc, "R(P(LOR))");
-   if (vis) { visualize(LOR_dc, "R(P(LOR))", Wx, Wy); }
+      // Restrict back to LOR space. This won't give the original function because
+      // the rho_lor doesn't necessarily live in the range of R.
+      direction = "LOR -> HO @ LOR";
+      R.Mult(rho, rho_lor);
+      compute_mass(&fespace_lor, lor_mass, LOR_dc, "R(P(LOR))");
+      if (vis) { visualize(LOR_dc, "R(P(LOR))", Wx, Wy); }
 
-   rho_lor_prev -= rho_lor;
-   cout.precision(12);
-   cout << "|LOR - R(P(LOR))|_∞ = " << rho_lor_prev.Normlinf() << endl;
+      rho_lor_prev -= rho_lor;
+      cout.precision(12);
+      cout << "|LOR - R(P(LOR))|_∞ = " << rho_lor_prev.Normlinf() << endl;
+   }
 
    // LOR* to HO* dual fields
    if (!use_pointwise_transfer)

miniapps/tools/makefile

@@ -25,7 +25,9 @@ include $(DEFAULTS_MK)
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
-SEQ_MINIAPPS = display-basis load-dc convert-dc get-values lor-transfer
+
+SEQ_MINIAPPS = display-basis load-dc convert-dc get-values lor-transfer \
+	check-tmop-metric tmop-metric-magnitude
 PAR_MINIAPPS =
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -60,6 +62,10 @@ display-basis: %: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK) | lib-common
 	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<)
 	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $(COMMON_LIB) $(MFEM_LIBS)
 
+tmop-metric-magnitude: %: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK) | lib-common
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<)
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $(COMMON_LIB) $(MFEM_LIBS)
+
 # Rule for building lib-common
 lib-common:
 	$(MAKE) -C $(MFEM_BUILD_DIR)/miniapps/common
@@ -76,7 +82,8 @@ RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
 
 # Testing: Specific execution options
 # Do not test: display-basis, load-dc, convert-dc, get-values, lor-transfer
-NO_TEST_APPS = display-basis load-dc convert-dc get-values lor-transfer
+NO_TEST_APPS = display-basis load-dc convert-dc get-values lor-transfer \
+	check-tmop-metric tmop-metric-magnitude
 $(foreach app,$(NO_TEST_APPS),$(app)-test-seq $(app)-test-par):
 	@true
 

miniapps/tools/tmop-metric-magnitude.cpp

@@ -0,0 +1,204 @@
+// 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.
+//
+// Checks evaluation / 1st derivative / 2nd derivative for TMOP metrics. Serial.
+//   ./tmop-metric-magnitude -mid 2 -p 2.0
+//
+
+#include "mfem.hpp"
+#include "../common/mfem-common.hpp"
+#include <iostream>
+
+using namespace mfem;
+using namespace std;
+
+void Form2DJac(double perturb_v, double perturb_ar, double perturb_s,
+               DenseMatrix &J);
+void Form3DJac(double perturb_v, double perturb_ar, double perturb_s,
+               DenseMatrix &J);
+
+int main(int argc, char *argv[])
+{
+   int metric_id = 2;
+   double perturb_v = 1.0;
+   double perturb_ar = 1.0;
+   double perturb_s  = 1.0;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&metric_id, "-mid", "--metric-id", "Metric id");
+   args.AddOption(&perturb_v, "-pv", "--perturb-factor-volume",
+                  "Volume perturbation factor w.r.t. the ideal element.");
+   args.AddOption(&perturb_ar, "-par", "--perturb-factor-aspect-ratio",
+                  "Aspect ratio perturbation factor w.r.t. the ideal element.");
+   args.AddOption(&perturb_s, "-ps", "--perturb-factor-skew",
+                  "Skew perturbation factor w.r.t. the ideal element.");
+   args.Parse();
+   if (!args.Good()) { args.PrintUsage(cout); return 1; }
+   args.PrintOptions(cout);
+
+   // Setup metric.
+   TMOP_QualityMetric *metric = NULL;
+   switch (metric_id)
+   {
+      // T-metrics
+      case 1: metric = new TMOP_Metric_001; break;
+      case 2: metric = new TMOP_Metric_002; break;
+      case 7: metric = new TMOP_Metric_007; break;
+      case 9: metric = new TMOP_Metric_009; break;
+      case 14: metric = new TMOP_Metric_014; break;
+      case 50: metric = new TMOP_Metric_050; break;
+      case 55: metric = new TMOP_Metric_055; break;
+      case 56: metric = new TMOP_Metric_056; break;
+      case 58: metric = new TMOP_Metric_058; break;
+      case 77: metric = new TMOP_Metric_077; break;
+      case 85: metric = new TMOP_Metric_085; break;
+      case 98: metric = new TMOP_Metric_098; break;
+      // case 211: metric = new TMOP_Metric_211; break;
+      // case 252: metric = new TMOP_Metric_252(tauval); break;
+      case 301: metric = new TMOP_Metric_301; break;
+      case 302: metric = new TMOP_Metric_302; break;
+      case 303: metric = new TMOP_Metric_303; break;
+      case 304: metric = new TMOP_Metric_304; break;
+      // case 311: metric = new TMOP_Metric_311; break;
+      case 315: metric = new TMOP_Metric_315; break;
+      case 316: metric = new TMOP_Metric_316; break;
+      case 321: metric = new TMOP_Metric_321; break;
+      case 322: metric = new TMOP_Metric_322; break;
+      case 323: metric = new TMOP_Metric_323; break;
+      // case 352: metric = new TMOP_Metric_352(tauval); break;
+      case 360: metric = new TMOP_Metric_360; break;
+      // A-metrics
+      case 11: metric = new TMOP_AMetric_011; break;
+      case 36: metric = new TMOP_AMetric_036; break;
+      case 107: metric = new TMOP_AMetric_107a; break;
+      default: cout << "Unknown metric_id: " << metric_id << endl; return 3;
+   }
+
+   const int dim = (metric_id < 300) ? 2 : 3;
+
+   Mesh *mesh;
+   if (dim == 2)
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(1, 1, Element::QUADRILATERAL));
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian3D(1, 1, 1, Element::HEXAHEDRON));
+   }
+   H1_FECollection fec(1, dim);
+   FiniteElementSpace fespace(mesh, &fec, dim);
+   mesh->SetNodalFESpace(&fespace);
+   GridFunction x(&fespace);
+   mesh->SetNodalGridFunction(&x);
+
+   socketstream sock1;
+   common::VisualizeMesh(sock1, "localhost", 19916, *mesh, "ideal", 0, 0);
+
+   DenseMatrix J;
+   (dim == 2) ? Form2DJac(perturb_v, perturb_ar, perturb_s, J)
+   /* */      : Form3DJac(perturb_v, perturb_ar, perturb_s, J);
+
+   const int nodes_cnt = x.Size() / dim;
+   for (int i = 0; i < nodes_cnt; i++)
+   {
+      Vector X(dim);
+      for (int d = 0; d < dim; d++) { X(d) = x(i + d * nodes_cnt); }
+      Vector Jx(dim);
+      J.Mult(X, Jx);
+      for (int d = 0; d < dim; d++) { x(i + d * nodes_cnt) = Jx(d); }
+   }
+
+   socketstream sock2;
+   common::VisualizeMesh(sock2, "localhost", 19916, *mesh, "perturbed", 400, 0);
+
+   // Target is always identity -> Jpt = Jpr.
+   cout << "Magnitude of metric " << metric_id << ": " << metric->EvalW(J)
+        << "\n  volume perturbation factor: " << perturb_v
+        << "\n  aspect ratio pert factor:   " << perturb_ar
+        << "\n  skew perturbation factor:   " << perturb_s << endl;
+
+   delete metric;
+   delete mesh;
+   return 0;
+}
+
+void Form2DJac(double perturb_v, double perturb_ar, double perturb_s,
+               DenseMatrix &J)
+{
+   // Volume.
+   const double volume = 1.0 * perturb_v;
+
+   // Aspect Ratio.
+   const double a_r = 1.0 * perturb_ar;
+   DenseMatrix M_ar(2); M_ar = 0.0;
+   M_ar(0, 0) = 1.0 / sqrt(a_r);
+   M_ar(1, 1) = sqrt(a_r);
+
+   // Skew.
+   const double skew_angle = M_PI / 2.0 / perturb_s;
+   DenseMatrix M_skew(2);
+   M_skew(0, 0) = 1.0; M_skew(0, 1) = cos(skew_angle);
+   M_skew(1, 0) = 0.0; M_skew(1, 1) = sin(skew_angle);
+
+   // Rotation.
+   const double rot_angle = 0.0; // not sure how to choose
+   DenseMatrix M_rot(2);
+   M_rot(0, 0) = cos(rot_angle); M_rot(0, 1) = -sin(rot_angle);
+   M_rot(1, 0) = sin(rot_angle); M_rot(1, 1) =  cos(rot_angle);
+
+   // Form J.
+   J.SetSize(2);
+   DenseMatrix TMP(2);
+   Mult(M_rot, M_skew, TMP);
+   Mult(TMP, M_ar, J);
+   J *= sqrt(volume / sin(skew_angle));
+}
+
+void Form3DJac(double perturb_v, double perturb_ar, double perturb_s,
+               DenseMatrix &J)
+{
+   MFEM_ABORT("The 3D case is still not complete.");
+
+   // Volume.
+   const double volume = 1.0 * perturb_v;
+
+   // Aspect Ratio - only in one direction, the others are uniform.
+   const double ar_1 = 1.0 * perturb_ar,
+                ar_2 = 1.0 * perturb_ar;
+
+   // Skew - only in one direction, the others are pi/2.
+   const double skew_angle_12 = M_PI / 2.0 / perturb_s,
+                skew_angle_13 = M_PI / 2.0 / perturb_s,
+                skew_angle_23 = M_PI / 2.0 / perturb_s;
+   const double sin3 = sin(skew_angle_12)*sin(skew_angle_13)*sin(skew_angle_23);
+
+   // Rotation - not done yet.
+
+   J.SetSize(3);
+   //
+   J(0, 0) = ar_1;
+   J(0, 1) = ar_2 * cos(skew_angle_12);
+   J(0, 2) = cos(skew_angle_13) / (ar_1 * ar_2) *
+             sqrt(sin3 / volume);
+   //
+   J(1, 0) = 0.0;
+   J(1, 1) = ar_2 * sin(skew_angle_12);
+   J(1, 2) = sin(skew_angle_13) * cos(skew_angle_23) / (ar_1 * ar_2) *
+             sqrt(sin3 / volume);
+   //
+   J(2, 0) = 0.0;
+   J(2, 1) = 0.0;
+   J(2, 2) = sin(skew_angle_13) * sin(skew_angle_23) / (ar_1 * ar_2) *
+             sqrt(sin3/ volume);
+   //
+   J *= sqrt(volume / sin3);
+}
+

tests/unit/CMakeLists.txt

@@ -14,6 +14,8 @@ project(mfem-unit-tests NONE)
 # Include the source directory for the unit tests - catch.hpp is there.
 include_directories(BEFORE ${CMAKE_CURRENT_SOURCE_DIR})
 
+# The following list can be updated using (in bash):
+#    for d in general linalg mesh fem enzyme; do ls -1 $d/*.cpp; done
 set(UNIT_TESTS_SRCS
   general/test_array.cpp
   general/test_mem.cpp
@@ -22,8 +24,8 @@ set(UNIT_TESTS_SRCS
   general/test_zlib.cpp
   linalg/test_cg_indefinite.cpp
   linalg/test_chebyshev.cpp
-  linalg/test_complex_operator.cpp
   linalg/test_complex_dense_matrix.cpp
+  linalg/test_complex_operator.cpp
   linalg/test_constrainedsolver.cpp
   linalg/test_direct_solvers.cpp
   linalg/test_hypre_ilu.cpp
@@ -42,57 +44,71 @@ set(UNIT_TESTS_SRCS
   mesh/test_fms.cpp
   mesh/test_mesh.cpp
   mesh/test_ncmesh.cpp
-  mesh/test_pmesh.cpp
-  mesh/test_submesh.cpp
-  mesh/test_psubmesh.cpp
   mesh/test_periodic_mesh.cpp
+  mesh/test_pmesh.cpp
+  mesh/test_psubmesh.cpp
+  mesh/test_submesh.cpp
   mesh/test_vtu.cpp
   fem/test_1d_bilininteg.cpp
   fem/test_2d_bilininteg.cpp
   fem/test_3d_bilininteg.cpp
-  fem/test_r1d_bilininteg.cpp
-  fem/test_r2d_bilininteg.cpp
   fem/test_assemblediagonalpa.cpp
   fem/test_assembly_levels.cpp
   fem/test_bilinearform.cpp
   fem/test_blocknonlinearform.cpp
-  fem/test_calcshape.cpp
-  fem/test_calcvshape.cpp
-  fem/test_calcdshape.cpp
+  fem/test_build_dof_to_arrays.cpp
   fem/test_calccurlshape.cpp
   fem/test_calcdivshape.cpp
+  fem/test_calcdshape.cpp
+  fem/test_calcshape.cpp
+  fem/test_calcvshape.cpp
   fem/test_coefficient.cpp
   fem/test_datacollection.cpp
   fem/test_derefine.cpp
   fem/test_dgmassinv.cpp
+  fem/test_doftrans.cpp
+  fem/test_domain_int.cpp
+  fem/test_eigs.cpp
   fem/test_estimator.cpp
+  fem/test_fa_determinism.cpp
   fem/test_face_elem_trans.cpp
   fem/test_face_permutation.cpp
   fem/test_fe.cpp
   fem/test_get_value.cpp
   fem/test_getderivative.cpp
+  fem/test_getgradient.cpp
   fem/test_intrules.cpp
   fem/test_intruletypes.cpp
   fem/test_inversetransform.cpp
   fem/test_lexicographic_ordering.cpp
   fem/test_lin_interp.cpp
   fem/test_linear_fes.cpp
+  fem/test_linearform_ext.cpp
   fem/test_lor.cpp
   fem/test_lor_batched.cpp
   fem/test_operatorjacobismoother.cpp
+  fem/test_oscillation.cpp
   fem/test_pa_coeff.cpp
   fem/test_pa_grad.cpp
   fem/test_pa_idinterp.cpp
   fem/test_pa_kernels.cpp
+  fem/test_project_bdr.cpp
   fem/test_quadf_coef.cpp
+  fem/test_quadinterpolator.cpp
   fem/test_quadraturefunc.cpp
+  fem/test_r1d_bilininteg.cpp
+  fem/test_r2d_bilininteg.cpp
   fem/test_sparse_matrix.cpp
   fem/test_sum_bilin.cpp
+  fem/test_surf_blf.cpp
   fem/test_tet_reorder.cpp
   fem/test_transfer.cpp
   fem/test_var_order.cpp
   fem/test_white_noise.cpp
-  # The following are tested separately (keep the comment as a reminder):
+  enzyme/compatibility.cpp
+  # The following are tested separately (keep the comment as a reminder).
+  # This list can be updated using (in bash):
+  #    for d in miniapps ceed; do ls -1 $d/*.cpp; done
   # miniapps/test_debug_device.cpp
   # miniapps/test_sedov.cpp
   # miniapps/test_tmop_pa.cpp

tests/unit/fem/test_derefine.cpp

@@ -112,7 +112,377 @@ TEST_CASE("Derefine")
    }
 }
 
+
+double integrate(GridFunction* gf)
+{
+   ConstantCoefficient one(1.0);
+   LinearForm lf(gf->FESpace());
+   LinearFormIntegrator* lfi = new DomainLFIntegrator(one);
+   lf.AddDomainIntegrator(lfi);
+   lf.Assemble();
+   double integral = lf(*gf);
+   return integral;
+}
+
+struct PolyCoeff
+{
+   static int order_;
+
+   static double poly_coeff(const Vector& x)
+   {
+      int& o{order_};
+
+      double f = 0.0;
+      for (int d = 0; d < dimension; d++)
+      {
+         f += pow(x[d],o);
+      }
+      return f;
+   }
+};
+int PolyCoeff::order_ = -1;
+
+void test_derefine_L2_element(int order, Element::Type el_type, int basis_type)
+{
+   Mesh mesh;
+   if (dimension == 1)
+   {
+      mesh = Mesh::MakeCartesian1D(1, 1.0);
+   }
+   if (dimension == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(1, 1, el_type, true, 1.0, 1.0);
+   }
+   if (dimension == 3)
+   {
+      mesh = Mesh::MakeCartesian3D(1, 1, 1, el_type, true, 1.0, 1.0, 1.0);
+   }
+   mesh.EnsureNCMesh(true);
+
+   L2_FECollection fec(order, dimension, basis_type);
+   FiniteElementSpace fespace(&mesh, &fec);
+   GridFunction x(&fespace);
+
+   PolyCoeff pcoeff;
+   pcoeff.order_ = order+1; // raise order so it isn't exact
+   FunctionCoefficient c(PolyCoeff::poly_coeff);
+
+   Array<Refinement> refinements;
+   refinements.Append(Refinement(0));
+   mesh.GeneralRefinement(refinements);
+
+   fespace.Update();
+   x.Update();
+
+   // project to get function that isn't exactly representable in the
+   // fine space.
+   x.ProjectCoefficient(c);
+
+   // deep copy the fine solution
+   Vector xf = x;
+   GridFunction x_fine(x.FESpace());
+   x_fine.SetData(xf.GetData());
+
+   double mass_fine = integrate(&x_fine);
+
+   Vector local_err(mesh.GetNE());
+   local_err = 0.;
+   double threshold = 1.0;
+   mesh.DerefineByError(local_err, threshold);
+   fespace.Update();
+   x.Update();
+
+   Vector coarse_soln_v{x};
+
+   double mass_coarse = integrate(&x);
+
+   // conservation check
+   REQUIRE( fabs(mass_fine-mass_coarse) < 1.e-12 );
+
+   // re-refine to get everything on the same grid
+   mesh.GeneralRefinement(refinements);
+   fespace.Update();
+   x.Update();
+
+   // Compute error of coarse L2 projection against fine solution
+   GridFunctionCoefficient gfc(&x);
+
+   double err0 = x_fine.ComputeL2Error(gfc);
+
+   // test for local L2 optimality by shifting dofs by +/-epsilon and
+   // recomputing error wrt fine solution. maybe there is a more
+   // clever way to do this.
+   double eps = 1.e-3;
+
+   // limit to max 20 dofs for efficiency in 3D
+   int test_ndofs = std::min(coarse_soln_v.Size(), 20);
+   for (int i = 0; i < test_ndofs; i++)
+   {
+      for (int f = -1; f <= 1; f += 2)
+      {
+         mesh.DerefineByError(local_err, threshold);
+         fespace.Update();
+         x.Update();
+         x = coarse_soln_v;
+         x(i) += f*eps;
+
+         mesh.GeneralRefinement(refinements);
+         fespace.Update();
+         x.Update();
+
+         double err = x_fine.ComputeL2Error(gfc);
+         REQUIRE(err > err0);
+      }
+   }
+}
+
+TEST_CASE("AMR Coarsen L2 Element","[AMR][Coarsen]")
+{
+   std::vector<int> orders_1d{0,1,2,3};
+   std::vector<int> orders_2d{0,1,2,3};
+   std::vector<int> orders_3d{0,1,2};
+
+   std::vector<int> basis_types
+   {
+      BasisType::Positive,
+      BasisType::GaussLegendre,
+      BasisType::GaussLobatto};
+
+   std::vector<Element::Type> el_types_1d;
+   el_types_1d.push_back(Element::SEGMENT);
+
+   std::vector<Element::Type> el_types_2d;
+   el_types_2d.push_back(Element::QUADRILATERAL);
+   el_types_2d.push_back(Element::TRIANGLE); // (nonconforming only)
+
+   std::vector<Element::Type> el_types_3d;
+   el_types_3d.push_back(Element::HEXAHEDRON);
+   el_types_3d.push_back(Element::TETRAHEDRON); // (nonconforming only)
+   // el_types_3d.push_back(Element::WEDGE); // derefinement not supported
+
+   dimension = 1;
+   for (auto el_type: el_types_1d)
+   {
+      for (auto order: orders_1d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            test_derefine_L2_element(order, el_type, basis_type);
+         }
+      }
+   }
+
+   dimension = 2;
+   for (auto el_type: el_types_2d)
+   {
+      for (auto order: orders_2d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            test_derefine_L2_element(order, el_type, basis_type);
+         }
+      }
+   }
+
+   dimension = 3;
+   for (auto el_type: el_types_3d)
+   {
+      for (auto order: orders_3d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            test_derefine_L2_element(order, el_type, basis_type);
+         }
+      }
+   }
+}
+
 #ifdef MFEM_USE_MPI
+
+void RefineRandomly(ParMesh& pmesh,
+                    ParFiniteElementSpace& fespace, ParGridFunction& u)
+{
+   double freq = 0.3;
+
+   Array<Refinement> refinements;
+   for (int k = 0; k < pmesh.GetNE(); k++)
+   {
+      double a = rand()/double(RAND_MAX);
+      if (a < freq)
+      {
+         refinements.Append(Refinement(k));
+      }
+   }
+
+   pmesh.GeneralRefinement(refinements);
+   fespace.Update();
+   u.Update();
+}
+
+
+void CoarsenRandomly(ParMesh& pmesh,
+                     ParFiniteElementSpace& fespace, ParGridFunction& u)
+{
+   double freq = 0.2;
+
+   Vector local_err(pmesh.GetNE());
+   local_err = 1.1;
+   double threshold = 1.0;
+
+   for (int k = 0; k < pmesh.GetNE(); k++)
+   {
+      double a = rand()/double(RAND_MAX);
+      if (a < freq)
+      {
+         local_err(k) = 0.0;
+      }
+   }
+
+   int op = 0; // take min
+   int nc_limit = 0;
+   pmesh.DerefineByError(local_err, threshold, nc_limit, op);
+   fespace.Update();
+   u.Update();
+}
+
+// stress test parallel correctness by:
+// initializing with an exact polynomial
+// loop:
+//   refine randomly
+//   rebalance
+//   coarsen randomly
+//   rebalance
+// representation should remain exact throughout
+
+void stress_parallel_coarsen(int order, Element::Type el_type, int basis_type)
+{
+   // This is deactivated until we have a way to exactly project onto
+   // positive finite elements.
+#if 0
+   int myid = Mpi::WorldRank();
+
+   Mesh mesh;
+   if (dimension == 1)
+   {
+      mesh = Mesh::MakeCartesian1D(4, 1.0);
+   }
+   if (dimension == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(2, 2, el_type, true, 1.0, 1.0);
+   }
+   if (dimension == 3)
+   {
+      mesh = Mesh::MakeCartesian3D(2, 2, 2, el_type, true, 1.0, 1.0, 1.0);
+   }
+   mesh.EnsureNCMesh(true);
+
+   ParMesh *pmeshp = new ParMesh(MPI_COMM_WORLD, mesh);
+   ParMesh& pmesh{*pmeshp};
+
+   L2_FECollection fec(order, dimension, basis_type);
+   ParFiniteElementSpace fespace(&pmesh, &fec);
+   ParGridFunction x(&fespace);
+
+   PolyCoeff pcoeff;
+   pcoeff.order_ = order; // exact
+   FunctionCoefficient c(PolyCoeff::poly_coeff);
+
+   x.ProjectCoefficient(c);
+
+   srand( (unsigned)time( NULL )+myid );
+
+   int total_it = 10;
+   for (int it = 0; it < total_it; it++)
+   {
+      RefineRandomly(pmesh, fespace, x);
+
+      double err = x.ComputeL2Error(c);
+      REQUIRE( err < 1.e-12 );
+
+      pmesh.Rebalance();
+      fespace.Update();
+      x.Update();
+
+      err = x.ComputeL2Error(c);
+      REQUIRE( err < 1.e-12 );
+
+      CoarsenRandomly(pmesh, fespace, x);
+
+      err = x.ComputeL2Error(c);
+      REQUIRE( err < 1.e-12 );
+
+      pmesh.Rebalance();
+      fespace.Update();
+      x.Update();
+
+      err = x.ComputeL2Error(c);
+      REQUIRE( err < 1.e-12 );
+   }
+#endif
+}
+
+TEST_CASE("Parallel AMR Coarsen Stress Test", "[AMR][Coarsen][Parallel]")
+{
+   std::vector<int> orders_1d{0,1,2,3};
+   std::vector<int> orders_2d{0,1,2,3};
+   std::vector<int> orders_3d{0,1,2};
+
+   std::vector<int> basis_types
+   {
+      BasisType::Positive,
+      BasisType::GaussLegendre,
+      BasisType::GaussLobatto};
+
+   std::vector<Element::Type> el_types_1d;
+   el_types_1d.push_back(Element::SEGMENT);
+
+   std::vector<Element::Type> el_types_2d;
+   el_types_2d.push_back(Element::QUADRILATERAL);
+   // el_types_2d.push_back(Element::TRIANGLE); // derefinement not supported
+
+   std::vector<Element::Type> el_types_3d;
+   el_types_3d.push_back(Element::HEXAHEDRON);
+   // el_types_3d.push_back(Element::TETRAHEDRON); // derefinement not supported
+   // el_types_3d.push_back(Element::WEDGE); // derefinement not supported
+
+   dimension = 1;
+   for (auto el_type: el_types_1d)
+   {
+      for (auto order: orders_1d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            stress_parallel_coarsen(order, el_type, basis_type);
+         }
+      }
+   }
+
+   dimension = 2;
+   for (auto el_type: el_types_2d)
+   {
+      for (auto order: orders_2d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            stress_parallel_coarsen(order, el_type, basis_type);
+         }
+      }
+   }
+
+   dimension = 3;
+   for (auto el_type: el_types_3d)
+   {
+      for (auto order: orders_3d)
+      {
+         for (auto basis_type: basis_types)
+         {
+            stress_parallel_coarsen(order, el_type, basis_type);
+         }
+      }
+   }
+
+}
+
 TEST_CASE("ParDerefine", "[Parallel]")
 {
    for (dimension = 2; dimension <= 3; ++dimension)

tests/unit/fem/test_getderivative.cpp

@@ -14,6 +14,9 @@
 
 using namespace mfem;
 
+namespace test_GetDerivative_parallel
+{
+
 double func(const Vector &coord)
 {
    if (coord.Size() == 1) { return std::sin(coord(0)); }
@@ -74,3 +77,5 @@ TEST_CASE("GetDerivative", "[Parallel]")
 }
 
 #endif
+
+}

tests/unit/fem/test_getgradient.cpp

@@ -0,0 +1,153 @@
+// 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 "unit_tests.hpp"
+#include "mfem.hpp"
+
+using namespace mfem;
+
+namespace test_GetGradient_shared_faces
+{
+
+int dim;
+
+double func(const Vector &coord)
+{
+   double x = coord(0),
+          y = (dim > 1) ? coord(1) : 0.0,
+          z = (dim > 2) ? coord(2) : 0.0;
+   return x * x + y * y + z * z;
+}
+
+void func_grad(const Vector &coord, Vector &grad)
+{
+   grad.SetSize(coord.Size());
+   grad(0) = 2.0 * coord(0);
+   if (dim > 1) { grad(1) = 2.0 * coord(1); }
+   if (dim > 2) { grad(2) = 2.0 * coord(2); }
+}
+
+void vec_func(const Vector &coord, Vector &res)
+{
+   double x = coord(0),
+          y = (dim > 1) ? coord(1) : 0.0,
+          z = (dim > 2) ? coord(2) : 0.0;
+
+   res(0) = (x + 1.0) * (y + 1.0) * (z + 1.0);
+   res(1) = x * x + y * y + z * z;
+}
+
+void vec_func_grad(const Vector &coord, DenseMatrix &grad)
+{
+   grad.SetSize(2, dim);
+   double x = coord(0),
+          y = (dim > 1) ? coord(1) : 0.0,
+          z = (dim> 2) ? coord(2) : 0.0;
+
+   grad(0, 0) = (y + 1.0) * (z + 1.0);
+   grad(1, 0) = 2.0 * x;
+   if (dim > 1)
+   {
+      grad(0, 1) = (x + 1.0) * (z + 1.0);
+      grad(1, 1) = 2.0 * y;
+   }
+   if (dim > 2)
+   {
+      grad(0, 2) = (x + 1.0) * (y + 1.0);
+      grad(1, 2) = 2.0 * z;
+   }
+}
+
+#ifdef MFEM_USE_MPI
+
+TEST_CASE("GetGradient Shared Faces", "[ParGridFunction][Parallel]")
+{
+   const int fe_order = 3;
+   for (dim = 1; dim <= 3; dim++)
+   {
+      int num_procs;
+      MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+      int myid;
+      MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+      Mesh mesh;
+      if (dim == 1)
+      {
+         mesh = Mesh::MakeCartesian1D(100, 1.0);
+      }
+      else if (dim == 2)
+      {
+         mesh = Mesh::LoadFromFile("../../data/star-mixed.mesh");
+      }
+      else
+      {
+         mesh = Mesh::LoadFromFile("../../data/fichera-mixed.mesh");
+      }
+      for (int i = 0; i < 2; i++) { mesh.UniformRefinement(); }
+      ParMesh pmesh(MPI_COMM_WORLD, mesh);
+
+      FunctionCoefficient func_coeff(func);
+      VectorFunctionCoefficient vec_func_coeff(2, vec_func);
+      H1_FECollection fec(fe_order, dim);
+      ParFiniteElementSpace pfes(&pmesh, &fec), pfes_vec(&pmesh, &fec, 2);
+      ParGridFunction pgf(&pfes), pgf_vec(&pfes_vec);
+      pgf.ProjectCoefficient(func_coeff);
+      pgf_vec.ProjectCoefficient(vec_func_coeff);
+      pgf.ExchangeFaceNbrData();
+      pgf_vec.ExchangeFaceNbrData();
+
+      double max_error_grad = 0.0, max_error_grads = 0.0,
+             max_error_vec_grad = 0.0;
+      for (int f = 0; f < pmesh.GetNSharedFaces(); f++)
+      {
+         auto tr_f  = pmesh.GetSharedFaceTransformations(f);
+         ElementTransformation &tr_e2 = tr_f->GetElement2Transformation();
+         const IntegrationRule &ir_f = IntRules.Get(tr_f->GetGeometryType(),
+                                                    2*fe_order + 2);
+         IntegrationRule ir_e2(ir_f.GetNPoints());
+         tr_f->Loc2.Transform(ir_f, ir_e2);
+
+         Vector grad_e2, grad_exact, coord(dim);
+
+         DenseMatrix grads_e2, vec_grad_e2, vec_grad_exact;
+         pgf.GetGradients(tr_e2, ir_e2, grads_e2);
+
+         for (int q = 0; q < ir_f.GetNPoints(); q++)
+         {
+            const IntegrationPoint &ip_f = ir_f.IntPoint(q);
+            tr_f->SetIntPoint(&ip_f);
+            tr_f->Transform(ip_f, coord);
+            func_grad(coord, grad_exact);
+
+            pgf.GetGradient(tr_e2, grad_e2);
+            grad_e2 -= grad_exact;
+            max_error_grad = fmax(max_error_grad, grad_e2.Norml2());
+
+            grads_e2.GetColumn(q, grad_e2);
+            grad_e2 -= grad_exact;
+            max_error_grads = fmax(max_error_grads, grad_e2.Norml2());
+
+            pgf_vec.GetVectorGradient(tr_e2, vec_grad_e2);
+            vec_func_grad(coord, vec_grad_exact);
+            vec_grad_e2 -= vec_grad_exact;
+            max_error_vec_grad = fmax(max_error_vec_grad, vec_grad_e2.FNorm2());
+         }
+      }
+
+      REQUIRE(max_error_grad == MFEM_Approx(0.0));
+      REQUIRE(max_error_grads == MFEM_Approx(0.0));
+      REQUIRE(max_error_vec_grad == MFEM_Approx(0.0));
+   }
+}
+
+#endif
+
+}

tests/unit/general/test_mem.cpp

@@ -44,8 +44,8 @@ TEST_CASE("MemoryManager/Scopes",
       REQUIRE(h_x == x.GetData());
       REQUIRE(mem->capacity == x.Size());
       REQUIRE(mem->h_mt == Device::GetHostMemoryType());
-      constexpr unsigned REGISTERED = 1 << 0;
-      const bool registered = mem->flags & REGISTERED;
+      constexpr unsigned Registered = 1 << 0;
+      const bool registered = mem->flags & Registered;
       const bool registered_is_known = registered == mm.IsKnown(h_x);
       REQUIRE(registered_is_known);
    }