including an obstacle problem variant wherein the essential dofs are not given to the optimizer as free variables that it must choose the values for.

Change Array::MakeRef to use MakeAlias

.appveyor.yml

@@ -31,7 +31,7 @@ install:
 - ps: ( get-content "GKlib\gk_arch.h") | % { If ($_.ReadCount -ge 52) {$_ -replace "#ifdef __MSC__","#ifdef DISABLE_THIS_ANCIENT_MSC_CHECK"} Else {$_} } | set-content "GKlib\gk_arch.h"
 - cmake -H. -Bbuild
 # -DCMAKE_BUILD_TYPE=Release
-- cmake --build build
+- cmake --build build --target metis -j 4
 - set METIS_PATH=%cd%
 - cd ..
 
@@ -40,7 +40,7 @@ install:
 - 7z x v2.19.0.tar.gz -so | 7z x -si -ttar > nul
 - cd hypre-2.19.0/src
 - cmake -H. -Bbuild
-- cmake --build build
+- cmake --build build -j 4
 - cmake --build build --target install
 - cd ../..
 
@@ -49,14 +49,20 @@ install:
 
 # MFEM
 before_build:
-- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DHYPRE_DIR=%cd%\..\hypre-2.19.0\src\hypre -DMETIS_LIBRARIES=%METIS_PATH%\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%METIS_PATH%\include
-- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_serial -DMFEM_USE_MPI=FALSE
+- cmake . -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DHYPRE_DIR=%cd%\..\hypre-2.19.0\src\hypre -DMETIS_LIBRARIES=%METIS_PATH%\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%METIS_PATH%\include
+# - cmake . -Bbuild_serial -DMFEM_USE_MPI=FALSE
+- cmake . -Bbuild_shared_serial -DMFEM_USE_MPI=FALSE -DBUILD_SHARED_LIBS=ON
 
 build_script:
-- cmake --build build_parallel --config Release -j 4
-- cmake --build build_serial --config Release -j 4
-- cmake --build build_serial --target exec --config Release -j 4
+- cmake --build build_parallel --config Debug -j 4
+# - cmake --build build_serial --config Release -j 4
+# - cmake --build build_serial --target exec --config Release -j 4
+- cmake --build build_shared_serial --config Release -j 4
+- cmake --build build_shared_serial --target exec --config Release -j 4
 
 after_build:
-- cd build_serial
+# - cd build_serial
+# - ctest -C Release --output-on-failure
+# - cd ..
+- cd build_shared_serial
 - ctest -C Release --output-on-failure

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

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -74,12 +74,19 @@ jobs:
             codecov: YES
           - os: windows-latest
             codecov: NO
+          - os: windows-latest
+            target: opt
+            mpi: par
+            config-opts: '-DBUILD_SHARED_LIBS=ON'
           - os: ubuntu-latest
             target: opt
             codecov: NO
             mpi: par
             build-system: cmake
             hypre-target: int32
+            # This option can be set to pass additional configuration options to
+            # the MFEM configuration command.
+            # config-opts: '-DCMAKE_VERBOSE_MAKEFILE=ON'
           - os: ubuntu-latest
             target: opt
             codecov: NO
@@ -210,7 +217,7 @@ jobs:
 
     # MFEM build and test
     - name: build
-      uses: mfem/github-actions/build-mfem@v2.2
+      uses: mfem/github-actions/build-mfem@v2.3
       env:
         VCPKG_DEFAULT_BINARY_CACHE: ${{ github.workspace }}/vcpkg_cache
       with:
@@ -222,7 +229,7 @@ jobs:
         hypre-dir: ${{ env.HYPRE_TOP_DIR }}
         metis-dir: ${{ env.METIS_TOP_DIR }}
         mfem-dir: ${{ env.MFEM_TOP_DIR }}
-        config-options: ${{ env.MFEM_EXTRA_CONFIG }}
+        config-options: ${{ matrix.config-opts }}
         library-only: ${{ matrix.target == 'dbg' }}
 
     # Run checks (and only checks) on debug targets

.github/workflows/mfem-analysis.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.github/workflows/repo-check.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitignore

@@ -21,6 +21,9 @@ CMakeFiles/
 # Default install location
 /mfem/
 
+# Typical build directory
+/build/
+
 # Generated files in main directory, config/ and docs/
 /deps.mk
 config/_config.hpp
@@ -118,11 +121,9 @@ examples/amgx/sol.gf
 examples/amgx/mesh.*
 examples/amgx/sol.*
 
-examples/gingko/ex1
-examples/gingko/refined.mesh
-examples/gingko/sol.gf
-examples/gingko/mesh.*
-examples/gingko/sol.*
+examples/ginkgo/ex1
+examples/ginkgo/refined.mesh
+examples/ginkgo/sol.gf
 
 examples/hiop/ex9
 examples/hiop/ex9p
@@ -148,8 +149,8 @@ examples/petsc/velocity.*
 examples/petsc/elastic_energy.*
 examples/petsc/mode_*
 
-examples/pumi/ex1
-examples/pumi/ex[126]p
+examples/pumi/ex[12]
+examples/pumi/ex[16]p
 examples/pumi/refined.mesh
 examples/pumi/sol.gf
 examples/pumi/mesh.*
@@ -194,6 +195,9 @@ miniapps/gslib/field-diff
 miniapps/gslib/field-interp
 miniapps/gslib/findpts
 miniapps/gslib/pfindpts
+miniapps/gslib/schwarz_ex1
+miniapps/gslib/schwarz_ex1p
+miniapps/gslib/interpolated.gf
 
 miniapps/meshing/mobius-strip
 miniapps/meshing/klein-bottle
@@ -206,6 +210,7 @@ miniapps/meshing/trimmer
 miniapps/meshing/reflector
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
+miniapps/meshing/pmesh-fitting
 miniapps/meshing/minimal-surface
 miniapps/meshing/pminimal-surface
 miniapps/meshing/polar-nc
@@ -245,6 +250,7 @@ miniapps/navier/navier_tgv
 miniapps/navier/navier_shear
 miniapps/navier/navier_3dfoc
 miniapps/navier/navier_turbchan
+miniapps/navier/navier_cht
 miniapps/navier/tgv_out*.txt
 miniapps/navier/*_output
 

.gitlab-ci.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/common.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/corona-config.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/lassen-config.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/quartz-config.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/report-build-and-test.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/setup-baseline.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/configs/setup-build-and-test.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/corona-build-and-test.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/lassen-build-and-test.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/quartz-baseline.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/quartz-build-and-test.yml

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -27,11 +27,6 @@ allocate_resource:
   timeout: 6h
 
 # GitLab jobs for the Quartz machine at LLNL
-debug_ser_gcc_4_9_3:
-  variables:
-    SPEC: "%gcc@4.9.3 +debug~mpi"
-  extends: .build_and_test_on_quartz
-
 debug_ser_gcc_6_1_0:
   variables:
     SPEC: "%gcc@6.1.0 +debug~mpi"

.gitlab/scripts/baseline

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/scripts/git_try_to_push

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/scripts/rebaseline

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/scripts/report_build_and_test_failure

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/scripts/report_build_and_test_success

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

.gitlab/scripts/safe_create_rundir

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

CHANGELOG

@@ -8,61 +8,69 @@
                                https://mfem.org
 
 
-Version 4.5.1 (development)
+Version 4.5.3 (development)
 ===========================
-- When using discontinuous (L2) spaces, use local (element-wise) L2 projection
-  as the coarsening operator for non-conforming AMR meshes.
 
-Meshing improvements
---------------------
+- Added new methods in the Mesh class to set and get attributes on NURBS patches
+  and patch boundaries.
+
+New and updated examples and miniapps
+-------------------------------------
+- Added a miniapp pmesh-fitting in miniapps/meshing for interface and boundary fitting to implicit domains defined using level-set functions.
+
+- Moved the distance solver methods from miniapps/shifted to miniapps/common. 
+
+Discretization improvements
+---------------------------
+- Face restriction operators for Nedelec and Raviart-Thomas finite element
+  spaces are now supported through the ConformingFaceRestriction class.
+
+- VectorFEBoundaryFluxLFIntegrator is now supported on device/GPU.
+
+
+Version 4.5.2, released on March 23, 2023
+=========================================
+
 - Added support for pyramids in non-conforming meshes. Currently only isotropic
   refinement is supported in this case.
 
+- Removed the support for the Mesquite toolkit. We recommend using MFEM's TMOP
+  functionality instead for mesh optimization. See the mesh-optimizer miniapp.
+
+- Added a fast normalization-based distance solver, see the Distance miniapp
+  in the miniapps/shifted/ directory.
+
+- Added a new meshing miniapp, Reflector, which reflects a high-order or NURBS
+  hexahedral mesh about a plane.
+
 - Updated logic in FindPointsGSLIB to ignore points found near (but outside) the
   domain boundary.
 
-- Added support for pyramids in Gmsh meshes.
+- Added an option to auto-balance compound TMOP metrics.
 
 - Fixed a bug in TMOP metric 301.
 
-- Added an option to auto-balance compound TMOP metrics.
+- When using discontinuous (L2) spaces, use local (element-wise) L2 projection
+  as the coarsening operator for non-conforming AMR meshes.
 
-Discretization improvements
----------------------------
-- TBD
+- Added support for GridFunction::GetGradients() and GetVectorGradient() on
+  face-neighbor elements.
 
-Linear and nonlinear solvers
-----------------------------
-- Added a fast normalization-based distance solver, see the Distance miniapp
-  in the miniapps/shifted/ directory.
+- Added support for pyramids in Gmsh meshes.
 
-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. See option 'D' in the menu.
 
-- 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.
+- VisItDataCollection now correctly handles data collection names containing
+  underscores.
 
-Integrations, testing and documentation
----------------------------------------
-- Removed the support for the Mesquite toolkit. We recommend using MFEM's TMOP
-  functionality instead for mesh optimization. See the mesh-optimizer miniapp.
+- Added support for shared Windows builds with MSVC through CMake.
+  Developers note: this enhancement is facilitated by the addition of the macro
+  MFEM_EXPORT, see config.hpp for more details on its usage.
 
 - The following integrations have updated minimum version requirements:
   * RAJA >= 2022.10.3
 
-Miscellaneous
--------------
-- VisItDataCollection now correctly handles collection names containing
-  underscores.
-
-- VisItDataCollection::SetPadDigits() no longer alters the number of digits
-  used to represent the MPI rank because VisIt seems to require 6 digits.
-  This parameter can still be explicitly overridden with
-  VisItDataCollection::SetPadDigitsRank().
-
 API changes
 -----------
 - The implicit cast methods of class Vector to 'double *' and 'const double *'
@@ -73,6 +81,11 @@ API changes
   deprecated, and Mesh::GetFaceGeometry (which provides identical functionality)
   should be used instead.
 
+- VisItDataCollection::SetPadDigits() no longer alters the number of digits
+  used to represent the MPI rank because VisIt seems to require 6 digits.
+  This parameter can still be explicitly overridden with SetPadDigitsRank().
+
+
 Version 4.5, released on October 22, 2022
 =========================================
 
@@ -116,9 +129,6 @@ Discretization improvements
 - Added a class CoefficientVector for efficient access of variable coefficient
   values at quadrature points (in particular for GPU/device kernels).
 
-- Added support for GridFunction::GetGradients() and
-  GriFunction::GetVectorGradient() on face-neighbor elements.
-
 - Added WhiteGaussianNoiseDomainLFIntegrator: a LinearFormIntegrator class for
   spatial Gaussian white noise.
 

CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -13,6 +13,7 @@
 # Version 3.8 fixes the handling of CMAKE_CXX_STANDARD for try_compile.
 # Version 3.8 or newer is required for direct CUDA support.
 cmake_minimum_required(VERSION 3.8)
+message(STATUS "CMake version: ${CMAKE_VERSION}")
 set(USER_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}/config/user.cmake" CACHE PATH
   "Path to optional user configuration file.")
 
@@ -24,8 +25,11 @@ set(CMAKE_CXX_EXTENSIONS OFF)
 # Load user settings before the defaults - this way the defaults will not
 # overwrite the user set options. If the user has not set all options, we still
 # have the defaults.
-message(STATUS "(optional) USER_CONFIG = ${USER_CONFIG}")
-include("${USER_CONFIG}" OPTIONAL)
+include("${USER_CONFIG}" OPTIONAL RESULT_VARIABLE USER_CONFIG_LOADED)
+if (USER_CONFIG_LOADED)
+  set(USER_CONFIG_LOADED "LOADED")
+endif()
+message(STATUS "Loading USER_CONFIG = ${USER_CONFIG} (${USER_CONFIG_LOADED})")
 include("${CMAKE_CURRENT_SOURCE_DIR}/config/defaults.cmake")
 
 # Allow overwriting of the compiler by setting CXX/MPICXX on the command line or
@@ -53,7 +57,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 4.5.1)
+set(${PROJECT_NAME}_VERSION 4.5.3)
 
 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -183,6 +187,23 @@ else()
   set(MFEM_DEBUG OFF)
 endif()
 
+# Shared build on Windows
+if (WIN32 AND BUILD_SHARED_LIBS)
+  # CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS works only with MSVC?
+  set(CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS ON CACHE BOOL
+      "Automatically export symbols for shared Windows DLL build")
+  # Place all .dll and .exe files in the same sub-directory, 'bin/<config>', of
+  # the build directory, so that the .exe files can find the .dll files at
+  # runtime:
+  set(CMAKE_RUNTIME_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin")
+  # Note: CMake tests are run from the build-tree sub-directory where the test
+  # is defined, e.g. <build-dir>/tests/unit, so hard coded paths to meshes still
+  # work fine.
+  # Not strictly necessary:
+  # set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
+  # set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
+endif()
+
 # AMD HIP
 if (MFEM_USE_HIP)
   if (HIP_ARCH)
@@ -519,6 +540,7 @@ list(REVERSE TPL_LIBRARIES)
 list(REMOVE_DUPLICATES TPL_INCLUDE_DIRS)
 # message(STATUS "TPL_INCLUDE_DIRS = ${TPL_INCLUDE_DIRS}")
 
+message(STATUS "MFEM shared library: BUILD_SHARED_LIBS = ${BUILD_SHARED_LIBS}")
 message(STATUS "MFEM build type: CMAKE_BUILD_TYPE = ${CMAKE_BUILD_TYPE}")
 message(STATUS "MFEM version: v${MFEM_VERSION_STRING}")
 message(STATUS "MFEM git string: ${MFEM_GIT_STRING}")
@@ -574,7 +596,19 @@ target_include_directories(mfem
   PUBLIC
     $<BUILD_INTERFACE:${CMAKE_CURRENT_BINARY_DIR}>
     $<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
+    # The INSTALL_INTERFACE is handled below
     ${TPL_INCLUDE_DIRS})
+if (MFEM_USE_MPI)
+  if (MPI_CXX_COMPILE_FLAGS)
+    separate_arguments(MPI_CXX_COMPILE_ARGS UNIX_COMMAND
+      "${MPI_CXX_COMPILE_FLAGS}")
+    target_compile_options(mfem PUBLIC ${MPI_CXX_COMPILE_ARGS})
+  endif()
+  if (MPI_CXX_LINK_FLAGS)
+    target_link_libraries(mfem PUBLIC ${MPI_CXX_LINK_FLAGS})
+  endif()
+endif()
+
 set_target_properties(mfem PROPERTIES VERSION "${mfem_VERSION}")
 set_target_properties(mfem PROPERTIES SOVERSION "${mfem_VERSION}")
 
@@ -586,6 +620,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
 endif()
 
 # Generate configuration file in the build directory: config/_config.hpp.
+set(MFEM_SHARED_BUILD ${BUILD_SHARED_LIBS})
 configure_file(
   "${PROJECT_SOURCE_DIR}/config/cmake/config.hpp.in"
   "${PROJECT_BINARY_DIR}/config/_config.hpp")
@@ -705,7 +740,7 @@ set(INSTALL_LIB_DIR lib
 set(INSTALL_CMAKE_DIR lib/cmake/mfem
   CACHE PATH "Relative path for installing cmake config files.")
 
-target_include_directories(mfem
+target_include_directories(mfem BEFORE
   PUBLIC
     $<INSTALL_INTERFACE:${INSTALL_INCLUDE_DIR}>)
 
@@ -757,10 +792,8 @@ endif()
 
 # Install the configuration header files
 install(FILES ${PROJECT_BINARY_DIR}/config/_config.hpp
-  DESTINATION ${INSTALL_INCLUDE_DIR}/mfem/config
-  RENAME config.hpp)
-
-install(FILES ${PROJECT_SOURCE_DIR}/config/tconfig.hpp
+  ${PROJECT_SOURCE_DIR}/config/config.hpp
+  ${PROJECT_SOURCE_DIR}/config/tconfig.hpp
   DESTINATION ${INSTALL_INCLUDE_DIR}/mfem/config)
 
 # Package the whole thing up nicely

LICENSE

@@ -1,6 +1,6 @@
 BSD 3-Clause License
 
-Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC
+Copyright (c) 2010-2023, Lawrence Livermore National Security, LLC
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without

config/CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/MFEMConfig.cmake.in

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/config.hpp.in

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //
@@ -39,6 +39,9 @@
 // Description of the git commit used to build MFEM.
 #cmakedefine MFEM_GIT_STRING "@MFEM_GIT_STRING@"
 
+// Enable shared library build of MFEM.
+#cmakedefine MFEM_SHARED_BUILD
+
 // Build the parallel MFEM library.
 // Requires an MPI compiler, and the libraries HYPRE and METIS.
 #cmakedefine MFEM_USE_MPI

config/cmake/modules/FindAMGX.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindAlgoim.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindAxom.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindBenchmark.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindBlitz.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindCODIPACK.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindCXXABIDemangle.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindCaliper.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindConduit.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -21,8 +21,15 @@ if(EXISTS ${CONDUIT_DIR}/include/conduit/conduit_relay_hdf5.hpp)
   # we only need  HDF5 if Conduit was built with HDF5 support
   set(Conduit_REQUIRED_PACKAGES "HDF5" CACHE STRING
       "Additional packages required by Conduit.")
-  else()
-    message(STATUS "Conduit Relay HDF5 Support is DISABLED")
+  # Suppress warning about HDF5_ROOT being set
+  if (POLICY CMP0074)
+    cmake_policy(SET CMP0074 NEW)
+  endif()
+  # HDF5_ROOT is needed in some cases, e.g. when HDF5_TARGET_NAMES is set and
+  # MFEM's FindHDF5.cmake is not used.
+  set(HDF5_ROOT ${HDF5_DIR} CACHE PATH "")
+else()
+  message(STATUS "Conduit Relay HDF5 Support is DISABLED")
 endif()
 
 include(MfemCmakeUtilities)
@@ -32,4 +39,4 @@ mfem_find_package(Conduit CONDUIT CONDUIT_DIR
   ADD_COMPONENT relay
     "include;include/conduit" conduit_relay.hpp "lib" conduit_relay
   ADD_COMPONENT blueprint
-      "include;include/conduit" conduit_blueprint.hpp "lib" conduit_blueprint)
+    "include;include/conduit" conduit_blueprint.hpp "lib" conduit_blueprint)

config/cmake/modules/FindENZYME.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindFMS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindGSLIB.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindHDF5.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindHIOP.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindHYPRE.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindLIBDL.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindLibunwind.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindMETIS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindMFEMBacktrace.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindMKL_CPARDISO.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindMPFR.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindMUMPS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindNetCDF.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -14,11 +14,17 @@
 #   - NETCDF_LIBRARIES
 #   - NETCDF_INCLUDE_DIRS
 
+# Suppress warning about HDF5_ROOT being set
+if (POLICY CMP0074)
+  cmake_policy(SET CMP0074 NEW)
+endif()
+
 include(MfemCmakeUtilities)
 
 # FindHDF5.cmake uses HDF5_ROOT, so we "translate" from the MFEM convention
-# (MFEM's FindHDF5.cmake does not need HDF5_ROOT)
-# set(HDF5_ROOT ${HDF5_DIR} CACHE PATH "")
+# (Needed in some cases, e.g. when HDF5_TARGET_NAMES is set and MFEM's
+# FindHDF5.cmake is not used.)
+set(HDF5_ROOT ${HDF5_DIR} CACHE PATH "")
 
 # We need to guard against the case where HDF5 was already found but without
 # the HL extensions (in which case mfem_find_package will treat the package
@@ -35,6 +41,11 @@ mfem_find_package(NetCDF NETCDF NETCDF_DIR "include" netcdf.h "lib" netcdf
 # The netcdf library will always be the first element of NETCDF_LIBRARIES
 # and we need to insert after that library but before the hdf5 library, so
 # position 1 is used
-# (MFEM's FindHDF5.cmake does not set HDF5_C_LIBRARY_hdf5_hl and the HL library
-# is already added to NETCDF_LIBRARIES)
-# list(INSERT NETCDF_LIBRARIES 1 ${HDF5_C_LIBRARY_hdf5_hl})
+# (Needed in some cases, e.g. when HDF5_TARGET_NAMES is set and MFEM's
+# FindHDF5.cmake is not used.)
+if (HDF5_C_LIBRARY_hdf5_hl)
+  list(INSERT NETCDF_LIBRARIES 1 ${HDF5_C_LIBRARY_hdf5_hl})
+  if (NOT NetCDF_FIND_QUIETLY)
+    message(STATUS "Updated NetCDF libraries: ${NETCDF_LIBRARIES}")
+  endif()
+endif()

config/cmake/modules/FindOCCA.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindPARELAG.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindPOSIXClocks.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindParMETIS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindRAJA.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindSLEPc.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindSTRUMPACK.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindSUNDIALS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindScotch.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindSuiteSparse.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindSuperLUDist.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindUMPIRE.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/Find_GnuTLS.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/FindlibCEED.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -103,25 +103,6 @@ macro(add_mfem_examples EXE_SRCS)
       ${MFEM_EXEC_PREREQUISITES_TARGET_NAME} ${EXE_PREREQUISITE})
 
     target_link_libraries(${EXE_NAME} mfem)
-    if (MFEM_USE_MPI)
-      # Not needed: (mfem already links with MPI_CXX_LIBRARIES)
-      # target_link_libraries(${EXE_NAME} ${MPI_CXX_LIBRARIES})
-
-      # Language-specific include directories:
-      if (MPI_CXX_INCLUDE_PATH)
-        target_include_directories(${EXE_NAME} PRIVATE "${MPI_CXX_INCLUDE_PATH}")
-      endif()
-      if (MPI_CXX_COMPILE_FLAGS)
-        separate_arguments(MPI_CXX_COMPILE_ARGS UNIX_COMMAND
-          "${MPI_CXX_COMPILE_FLAGS}")
-        target_compile_options(${EXE_NAME} PRIVATE ${MPI_CXX_COMPILE_ARGS})
-      endif()
-
-      if (MPI_CXX_LINK_FLAGS)
-        set_target_properties(${EXE_NAME} PROPERTIES
-          LINK_FLAGS "${MPI_CXX_LINK_FLAGS}")
-      endif()
-    endif()
   endforeach(SRC_FILE)
 endmacro()
 
@@ -172,26 +153,6 @@ macro(add_mfem_miniapp MFEM_EXE_NAME)
   if (EXTRA_DEFINES_LIST)
     target_compile_definitions(${MFEM_EXE_NAME} PRIVATE ${EXTRA_DEFINES_LIST})
   endif()
-
-  # Handle the MPI separately
-  if (MFEM_USE_MPI)
-    # Add MPI_CXX_LIBRARIES, in case this target does not link with mfem.
-    target_link_libraries(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_LIBRARIES})
-
-    if (MPI_CXX_INCLUDE_PATH)
-      target_include_directories(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_INCLUDE_PATH})
-    endif()
-    if (MPI_CXX_COMPILE_FLAGS)
-      separate_arguments(MPI_CXX_COMPILE_ARGS UNIX_COMMAND
-        "${MPI_CXX_COMPILE_FLAGS}")
-      target_compile_options(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_COMPILE_ARGS})
-    endif()
-
-    if (MPI_CXX_LINK_FLAGS)
-      set_target_properties(${MFEM_EXE_NAME} PROPERTIES
-        LINK_FLAGS "${MPI_CXX_LINK_FLAGS}")
-    endif()
-  endif()
 endmacro()
 
 
@@ -436,9 +397,9 @@ function(mfem_find_package Name Prefix DirVar IncSuffixes Header LibSuffixes
               break()
             endif()
           endforeach()
-          if (${Required} AND NOT ${ReqPack}_FOUND)
+          if (Required AND NOT ${ReqPack}_FOUND)
             message(FATAL_ERROR " *** Required package ${ReqPack} not found."
-              "Checked target names: ${ReqPack} ${${ReqPack}_TARGET_NAMES}")
+              " Checked target names: ${ReqPack} ${${ReqPack}_TARGET_NAMES}")
           endif()
         endif()
       endif()
@@ -504,14 +465,18 @@ function(mfem_find_package Name Prefix DirVar IncSuffixes Header LibSuffixes
           endif()
           get_target_property(IsImported ${TargetName} IMPORTED)
           if (IsImported)
+            get_target_property(ImpConfigs ${TargetName} IMPORTED_CONFIGURATIONS)
+            # message(STATUS "${ReqPack} imported configs: ${ImpConfigs}")
             set(ImportConfig ${${ReqPack}_IMPORT_CONFIG})
             if (NOT ImportConfig)
               set(ImportConfig RELEASE)
+              list(FIND ImpConfigs ${ImportConfig} _Index)
+              if (_Index EQUAL -1)
+                list(GET ImpConfigs 0 ImportConfig)
+              endif()
             endif()
             set(ImportConfigSuffix "_${ImportConfig}")
-            get_target_property(ImpConfigs ${TargetName} IMPORTED_CONFIGURATIONS)
-            list(FIND ImpConfigs ${ImportConfig} _Index)
-            if ((_Index EQUAL -1) OR ("${ImportConfig}" STREQUAL "NO_CONFIG"))
+            if ((NOT ImportConfig) OR ("${ImportConfig}" STREQUAL "NO_CONFIG"))
               set(ImportConfig "NO_CONFIG")
               set(ImportConfigSuffix "")
               # message(FATAL_ERROR " *** ${ReqPack}: configuration "
@@ -529,7 +494,8 @@ function(mfem_find_package Name Prefix DirVar IncSuffixes Header LibSuffixes
           else()
             # Set _Pack_LIBS from the target properties for ImportConfig
             foreach (_prop IMPORTED_LOCATION${ImportConfigSuffix}
-                IMPORTED_LINK_INTERFACE_LIBRARIES${ImportConfigSuffix})
+                IMPORTED_LINK_INTERFACE_LIBRARIES${ImportConfigSuffix}
+                INTERFACE_LINK_LIBRARIES)
               get_target_property(_value ${TargetName} ${_prop})
               if (_value)
                 list(APPEND _Pack_LIBS ${_value})
@@ -780,6 +746,7 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
       list(APPEND CompileOpts "-isystem \"${SysDir}\"")
     endforeach()
   endif()
+  set(AddInterfaceLinkLibs TRUE)
   if ("${type}" STREQUAL "STATIC_LIBRARY")
     get_target_property(Location ${tgt} LOCATION)
     if (Location)
@@ -801,18 +768,7 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
       message(STATUS " *** Warning: [${tgt}] LOCATION not defined!")
     endif()
   elseif ("${type}" STREQUAL "INTERFACE_LIBRARY")
-    get_target_property(Libs ${tgt} INTERFACE_LINK_LIBRARIES)
-    if (Libs)
-      foreach(Lib ${Libs})
-        if (NOT (TARGET ${Lib}))
-          list(APPEND LinkOpts "${Lib}")
-        else()
-          mfem_get_target_options(${Lib} COpts LOpts)
-          list(APPEND CompileOpts ${COpts})
-          list(APPEND LinkOpts ${LOpts})
-        endif()
-      endforeach()
-    endif()
+    # The INTERFACE_LINK_LIBRARIES property is handled below.
     # Other properties we may need to handle:
     # INTERFACE_LINK_DEPENDS
     # INTERFACE_LINK_DIRECTORIES
@@ -820,6 +776,26 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
   else()
     message(STATUS " *** Warning: [${tgt}] uses target type '${type}'"
       " which is not supported!")
+    set(AddInterfaceLinkLibs FALSE)
+  endif()
+  if (AddInterfaceLinkLibs)
+    get_target_property(Libs ${tgt} INTERFACE_LINK_LIBRARIES)
+    # message(STATUS "${tgt}[INTERFACE_LINK_LIBRARIES]: ${Libs}")
+    if (Libs)
+      foreach(Lib ${Libs})
+        if (NOT (TARGET ${Lib}))
+          # message(STATUS "Lib = ${Lib}")
+          # Filter-out generator expressions
+          if (NOT ("${Lib}" MATCHES "^\\$"))
+            list(APPEND LinkOpts "${Lib}")
+          endif()
+        else()
+          mfem_get_target_options(${Lib} COpts LOpts)
+          list(APPEND CompileOpts ${COpts})
+          list(APPEND LinkOpts ${LOpts})
+        endif()
+      endforeach()
+    endif()
   endif()
 
   # Other potentially relevant properties:
@@ -843,6 +819,9 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
   set(${CompileOptsVar} "${CompileOpts}" PARENT_SCOPE)
   set(${LinkOptsVar} "${LinkOpts}" PARENT_SCOPE)
 
+  # message(STATUS "${tgt}[CompileOpts]: ${CompileOpts}")
+  # message(STATUS "${tgt}[LinkOpts]: ${LinkOpts}")
+
 endfunction(mfem_get_target_options)
 
 
@@ -894,7 +873,7 @@ function(mfem_export_mk_files)
          "${cxx_std_flag} ${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"
          MFEM_CXXFLAGS)
   set(MFEM_TPLFLAGS "")
-  foreach(dir ${MFEM_TPL_INCLUDE_DIRS})
+  foreach(dir ${TPL_INCLUDE_DIRS})
     set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} -I${dir}")
   endforeach()
   # TODO: MFEM_TPLFLAGS: add other TPL flags, in addition to the -I flags.

config/config.hpp

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //
@@ -30,11 +30,30 @@
 #endif
 
 // Windows specific options
-#ifdef _WIN32
-#ifndef _USE_MATH_DEFINES
+#if defined(_WIN32) && !defined(_USE_MATH_DEFINES)
 // Macro needed to get defines like M_PI from <cmath>. (Visual Studio C++ only?)
 #define _USE_MATH_DEFINES
 #endif
+// Macro MFEM_EXPORT: this macro is used when declaring exported global
+// variables and static class variables in public header files, e.g.:
+//    extern MFEM_EXPORT Geometry Geometries;
+//    static MFEM_EXPORT Device device_singleton;
+// In cases where a class contains multiple static variables, instead of marking
+// all such variables with MFEM_EXPORT, one can mark the class with MFEM_EXPORT,
+// e.g.:
+//    class MFEM_EXPORT MemoryManager ...
+// Note: MFEM's GitHub CI includes a shared MSVC build that will fail if a
+// variable that needs MFEM_EXPORT does not have it. However, builds with
+// optional external libraries are not tested and may require separate checks to
+// determine the necessity of MFEM_EXPORT.
+#if defined(_MSC_VER) && defined(MFEM_SHARED_BUILD)
+#ifdef mfem_EXPORTS
+#define MFEM_EXPORT __declspec(dllexport)
+#else
+#define MFEM_EXPORT __declspec(dllimport)
+#endif
+#else
+#define MFEM_EXPORT
 #endif
 // On Cygwin the option -std=c++11 prevents the definition of M_PI. Defining
 // the following macro allows us to get M_PI and some needed functions, e.g.

config/config.hpp.in

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //
@@ -39,6 +39,9 @@
 // Description of the git commit used to build MFEM.
 // #define MFEM_GIT_STRING "@MFEM_GIT_STRING@"
 
+// Enable shared library build of MFEM.
+// #define MFEM_SHARED_BUILD
+
 // Build the parallel MFEM library.
 // Requires an MPI compiler, and the libraries HYPRE and METIS.
 // #define MFEM_USE_MPI

config/config.mk.in

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/defaults.cmake

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -19,6 +19,7 @@ if (NOT CMAKE_BUILD_TYPE)
 endif()
 
 # MFEM options. Set to mimic the default "defaults.mk" file.
+option(BUILD_SHARED_LIBS "Enable shared library build of MFEM" OFF)
 option(MFEM_USE_MPI "Enable MPI parallel build" OFF)
 option(MFEM_USE_METIS "Enable METIS usage" ${MFEM_USE_MPI})
 option(MFEM_USE_EXCEPTIONS "Enable the use of exceptions" OFF)

config/defaults.mk

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -58,7 +58,7 @@ HIP_CXX = hipcc
 # example: gfx600 (tahiti), gfx700 (kaveri), gfx701 (hawaii), gfx801 (carrizo),
 # gfx900, gfx1010, etc.
 HIP_ARCH = gfx900
-HIP_FLAGS = --amdgpu-target=$(HIP_ARCH)
+HIP_FLAGS = --offload-arch=$(HIP_ARCH)
 HIP_XCOMPILER =
 HIP_XLINKER   = -Wl,
 

config/get_hypre_version.cpp

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //

config/get_mumps_version.cpp

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //

config/githooks/pre-push

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -35,8 +35,8 @@ cd $(git rev-parse --show-toplevel)
 # copyright check
 copyright=true
 if [[ "${option}" == "--copyright" || "${option}" == "" ]]; then
-  if git grep -l "^\(#\|//\).*\(\-2021\|\ 2010,\)" > matches.txt; then
-    echo "Please update the following files to Copyright (c) 2010-2022:"
+  if git grep -n "^\(#\|//\).*Copyright.*2010-20\(2[^3]\|[^2].\)" > matches.txt; then
+    echo "Please update the following files to Copyright (c) 2010-2023:"
     cat matches.txt
     copyright=false
   fi

config/makefile

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

config/sample-runs.sh

@@ -1,6 +1,6 @@
 #!/bin/bash
 
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #
@@ -138,7 +138,7 @@ groups_parallel=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "pmesh-optimizer.cpp pminimal-surface.cpp"'
+   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
@@ -227,7 +227,7 @@ groups_all=(
    "Meshing miniapps:"
    "miniapps/meshing"
    "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    {,p}mesh-optimizer.cpp {,p}minimal-surface.cpp"'
+    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"

config/tconfig.hpp

@@ -1,4 +1,4 @@
-// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// Copyright (c) 2010-2023, 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.
 //

config/test.mk

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

data/disk.mesh

@@ -0,0 +1,109 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+2
+
+elements
+5
+1 3 4 5 6 7
+1 3 0 1 5 4
+1 3 1 2 6 5
+1 3 3 7 6 2
+1 3 0 4 7 3
+
+boundary
+4
+1 1 0 1
+1 1 2 3
+1 1 1 2
+1 1 3 0
+
+edges
+12
+0 0 1
+0 4 5
+0 7 6
+0 3 2
+1 1 2
+1 5 6
+1 4 7
+1 0 3
+2 0 4
+2 1 5
+2 2 6
+2 3 7
+
+vertices
+8
+
+knotvectors
+3
+2 3 0 0 0 1 1 1
+2 3 0 0 0 1 1 1
+2 3 0 0 0 1 1 1
+
+weights
+1
+1
+1
+1
+1
+1
+1
+1
+0.70710678118655
+1
+1
+0.70710678118655
+0.70710678118655
+1
+1
+0.70710678118655
+1
+1
+1
+1
+1
+0.85355339059327
+0.85355339059327
+0.85355339059327
+0.85355339059327
+
+FiniteElementSpace
+FiniteElementCollection: NURBS2
+VDim: 2
+Ordering: 1
+
+-0.70710678118 -0.70710678118
+0.70710678118 -0.70710678118
+0.70710678118 0.70710678118
+-0.70710678118 0.70710678118
+-0.35355339059 -0.35355339059
+0.35355339059 -0.35355339059
+0.35355339059 0.35355339059
+-0.35355339059 0.35355339059
+0 -1.41421356236
+0 -0.35355339059
+0 0.35355339059
+0 1.41421356236
+1.41421356236 0
+0.35355339059 0
+-0.35355339059 0
+-1.41421356236 0
+-0.530330085885 -0.530330085885
+0.530330085885 -0.530330085885
+0.530330085885 0.530330085885
+-0.530330085885 0.530330085885
+0 0
+0 -0.883883476475
+0.883883476475 0
+0 0.883883476475
+-0.883883476475 0

data/segment-nurbs.mesh

@@ -0,0 +1,46 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+elements
+1
+1 1 0 1
+
+boundary
+2
+1 0 0
+2 0 1
+
+edges
+1
+0 0 1
+
+vertices
+2
+
+knotvectors
+1
+1 2 0 0 1 1
+
+weights
+1
+1
+
+FiniteElementSpace
+FiniteElementCollection: NURBS1
+VDim: 1
+Ordering: 1
+
+0
+1
+
+

doc/CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

doc/CodeDocumentation.conf.in

@@ -38,7 +38,7 @@ PROJECT_NAME           = "MFEM"
 # could be handy for archiving the generated documentation or if some version
 # control system is used.
 
-PROJECT_NUMBER         = v4.5.1
+PROJECT_NUMBER         = v4.5.3
 
 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a

doc/makefile

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/amgx/CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/amgx/makefile

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/caliper/CMakeLists.txt

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/caliper/makefile

@@ -1,4 +1,4 @@
-# Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+# Copyright (c) 2010-2023, 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.
 #

examples/contact/DirichletObstacleProblem.cpp

@@ -0,0 +1,141 @@
+#include "mfem.hpp"
+#include "Problems.hpp"
+#include "IPsolver.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+
+
+double fRhs(const Vector &pt);
+double obstacle(const Vector &pt);
+double dmanufacturedFun(const Vector &pt);
+
+int main(int argc, char *argv[])
+{
+  int FEorder = 1; // order of the finite elements
+  int linSolver = 0;
+  int maxIPMiters = 30;
+  bool iAmRoot = true;
+  int ref_levels = 3; 
+  OptionsParser args(argc, argv);
+  args.AddOption(&FEorder, "-o", "--order",\
+		  "Order of the finite elements.");
+  args.AddOption(&linSolver, "-linSolver", "--linearSolver", \
+       "IP-Newton linear system solution strategy.");
+  args.AddOption(&maxIPMiters, "-IPMiters", "--IPMiters",\
+		  "Maximum number of IPM iterations");
+  args.AddOption(&ref_levels, "-r", "--mesh_refinement", \
+		  "Mesh Refinement");
+  
+  args.Parse();
+  if(!args.Good())
+  {
+    args.PrintUsage(cout);
+    return 1;
+  }
+  else
+  {
+    if( iAmRoot )
+    {
+      args.PrintOptions(cout);
+    }
+  }
+
+  const char *meshFile = "../../data/inline-quad.mesh";
+  Mesh *mesh = new Mesh(meshFile, 1, 1);
+  int dim = mesh->Dimension(); // geometric dimension of the domain
+  for (int l = 0; l < ref_levels; l++)
+  {
+      mesh->UniformRefinement();
+  }
+
+  FiniteElementCollection *fec = new H1_FECollection(FEorder, dim);
+  FiniteElementSpace      *Vh  = new FiniteElementSpace(mesh, fec);
+  Array<int> ess_tdof_list;
+  if (mesh->bdr_attributes.Size())
+  {
+     Array<int> ess_bdr(mesh->bdr_attributes.Max());
+     ess_bdr = 1;
+     Vh->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+  }
+  
+  double DC_val = 0.0;
+  int dimD = Vh->GetTrueVSize();
+  Vector x0(dimD); x0 = DC_val;
+  Vector xf(dimD); xf = 0.0;
+
+  ObstacleProblem problem(Vh, x0, &fRhs, &obstacle, ess_tdof_list);
+  
+
+  InteriorPointSolver optimizer(&problem); 
+  optimizer.SetTol(1.e-7);
+  optimizer.SetLinearSolver(linSolver);
+  optimizer.SetMaxIter(maxIPMiters);
+  optimizer.Mult(x0, xf);
+  
+  double Einitial = problem.E(x0);
+  double Efinal = problem.E(xf);
+  cout << "Energy objective at initial point = " << Einitial << endl;
+  cout << "Energy objective at optimizer = " << Efinal << endl;
+
+  GridFunction d_gf(Vh);
+
+  d_gf = xf;
+  
+  FunctionCoefficient dm_fc(dmanufacturedFun); // pseudo-manufactured solution
+  GridFunction dm_gf(Vh);
+  dm_gf.ProjectCoefficient(dm_fc);
+
+  
+  ParaViewDataCollection paraview_dc("BarrierProblemSolution", mesh);
+  paraview_dc.SetPrefixPath("ParaView");
+  paraview_dc.SetLevelsOfDetail(FEorder);
+  paraview_dc.SetDataFormat(VTKFormat::BINARY);
+  paraview_dc.SetHighOrderOutput(true);
+  paraview_dc.SetCycle(0);
+  paraview_dc.SetTime(0.0);
+  paraview_dc.RegisterField("d(x) (numerical)", &d_gf);
+  paraview_dc.RegisterField("d(x) (pseudo-manufactured)", &dm_gf);
+  paraview_dc.Save();
+  
+
+  delete Vh;
+  delete fec;
+  delete mesh;
+  return 0;
+}
+
+
+
+double dmanufacturedFun(const Vector &pt)
+{
+  double alpha = 16.5;
+  return sin(M_PI * pt(1)) * (sin(M_PI * pt(0)) - alpha * pow(pt(0) * (1. - pt(0)), 2));
+}
+
+
+// f(x) forcing term... which enters the objective energy functional
+// E(d) = 0.5 d^T K d - f^T d, where f is a discrete vector representation
+// of f(x). f(x) is such that in the absence of bound-constraints then
+// the solution of the optimization problem satisfies the PDE
+// -div(grad(d)) + d = f + homogeneous Neumann conditions on the unit interval,
+// for d(x) = cos(2 \pi x) + a0 + a3 (x^3 - 1.5 x^2), a2 = 0.2, a3 = -2
+
+double fRhs(const Vector &pt)
+{
+  double alpha = 16.5;
+  double fx;
+  fx = pow(M_PI, 2) * sin(M_PI * pt(0));
+  fx += alpha * (2. * pow(pt(0), 2) + 2. * pow(1.-pt(0), 2) - 8. * pt(0) * (1.-pt(0)));
+  fx += pow(M_PI, 2) * sin(M_PI * pt(0)) * dmanufacturedFun(pt);
+  fx *= sin(M_PI * pt(1));
+  return fx;
+}
+
+double obstacle(const Vector &pt)
+{
+  return 0.0;
+}

examples/contact/DirichletObstacleProblemVariant.cpp

@@ -0,0 +1,156 @@
+#include "mfem.hpp"
+#include "Problems.hpp"
+#include "IPsolver.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+
+
+double fRhs(const Vector &pt);
+double obstacle(const Vector &pt);
+double dmanufacturedFun(const Vector &pt);
+
+int main(int argc, char *argv[])
+{
+  int FEorder = 1; // order of the finite elements
+  int linSolver = 0;
+  int maxIPMiters = 30;
+  bool iAmRoot = true;
+  int ref_levels = 3; 
+  OptionsParser args(argc, argv);
+  args.AddOption(&FEorder, "-o", "--order",\
+		  "Order of the finite elements.");
+  args.AddOption(&linSolver, "-linSolver", "--linearSolver", \
+       "IP-Newton linear system solution strategy.");
+  args.AddOption(&maxIPMiters, "-IPMiters", "--IPMiters",\
+		  "Maximum number of IPM iterations");
+  args.AddOption(&ref_levels, "-r", "--mesh_refinement", \
+		  "Mesh Refinement");
+  
+  args.Parse();
+  if(!args.Good())
+  {
+    args.PrintUsage(cout);
+    return 1;
+  }
+  else
+  {
+    if( iAmRoot )
+    {
+      args.PrintOptions(cout);
+    }
+  }
+
+  const char *meshFile = "../../data/inline-quad.mesh";
+  Mesh *mesh = new Mesh(meshFile, 1, 1);
+  int dim = mesh->Dimension(); // geometric dimension of the domain
+  for (int l = 0; l < ref_levels; l++)
+  {
+      mesh->UniformRefinement();
+  }
+
+  FiniteElementCollection *fec = new H1_FECollection(FEorder, dim);
+  FiniteElementSpace      *Vh  = new FiniteElementSpace(mesh, fec);
+  Array<int> ess_tdof_list;
+  if (mesh->bdr_attributes.Size())
+  {
+     Array<int> ess_bdr(mesh->bdr_attributes.Max());
+     ess_bdr = 1;
+     Vh->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+  }
+  
+  double DC_val = 0.06;
+  Vector x0DC(Vh->GetTrueVSize()); x0DC = DC_val;
+  int dimD = Vh->GetTrueVSize() - ess_tdof_list.Size();
+  Vector x0(dimD); x0 = 0.0;
+  Vector xf(dimD); xf = 0.0;
+
+  ObstacleProblemVariant problem(Vh, x0DC, &fRhs, &obstacle, ess_tdof_list);
+
+  InteriorPointSolver optimizer(&problem); 
+  optimizer.SetTol(1.e-7);
+  optimizer.SetLinearSolver(linSolver);
+  optimizer.SetMaxIter(maxIPMiters);
+  optimizer.Mult(x0, xf);
+  
+  double Einitial = problem.E(x0);
+  double Efinal = problem.E(xf);
+  cout << "Energy objective at initial point = " << Einitial << endl;
+  cout << "Energy objective at optimizer = " << Efinal << endl;
+
+  Array<int> noness_tdof_list;
+  noness_tdof_list.SetSize(dimD);
+  int i = 0;
+  for(int j = 0; j < Vh->GetTrueVSize(); j++)
+  {
+     if(ess_tdof_list.Find(j) == -1)
+     {
+        noness_tdof_list[i] = j;
+        i += 1;
+     }
+  }
+
+
+  GridFunction d_gf(Vh);
+  d_gf.Set(1.0, x0DC);
+  d_gf.SetSubVector(noness_tdof_list, xf);
+
+
+
+  FunctionCoefficient dm_fc(dmanufacturedFun); // pseudo-manufactured solution
+  GridFunction dm_gf(Vh);
+  dm_gf.ProjectCoefficient(dm_fc);
+
+  
+  ParaViewDataCollection paraview_dc("BarrierProblemSolution", mesh);
+  paraview_dc.SetPrefixPath("ParaView");
+  paraview_dc.SetLevelsOfDetail(FEorder);
+  paraview_dc.SetDataFormat(VTKFormat::BINARY);
+  paraview_dc.SetHighOrderOutput(true);
+  paraview_dc.SetCycle(0);
+  paraview_dc.SetTime(0.0);
+  paraview_dc.RegisterField("d(x) (numerical)", &d_gf);
+  paraview_dc.RegisterField("d(x) (pseudo-manufactured)", &dm_gf);
+  paraview_dc.Save();
+ 
+
+  delete Vh;
+  delete fec;
+  delete mesh;
+  return 0;
+}
+
+
+
+double dmanufacturedFun(const Vector &pt)
+{
+  double alpha = 16.5;
+  return sin(M_PI * pt(1)) * (sin(M_PI * pt(0)) - alpha * pow(pt(0) * (1. - pt(0)), 2));
+}
+
+
+// f(x) forcing term... which enters the objective energy functional
+// E(d) = 0.5 d^T K d - f^T d, where f is a discrete vector representation
+// of f(x). f(x) is such that in the absence of bound-constraints then
+// the solution of the optimization problem satisfies the PDE
+// -div(grad(d)) + d = f + homogeneous Neumann conditions on the unit interval,
+// for d(x) = cos(2 \pi x) + a0 + a3 (x^3 - 1.5 x^2), a2 = 0.2, a3 = -2
+
+double fRhs(const Vector &pt)
+{
+  double alpha = 16.5;
+  double fx;
+  fx = pow(M_PI, 2) * sin(M_PI * pt(0));
+  fx += alpha * (2. * pow(pt(0), 2) + 2. * pow(1.-pt(0), 2) - 8. * pt(0) * (1.-pt(0)));
+  fx += pow(M_PI, 2) * sin(M_PI * pt(0)) * dmanufacturedFun(pt);
+  fx *= sin(M_PI * pt(1));
+  return fx;
+}
+
+double obstacle(const Vector &pt)
+{
+  return 0.0;
+}

examples/contact/IPsolver.cpp

@@ -0,0 +1,827 @@
+#include "mfem.hpp"
+#include "IPsolver.hpp"
+#include "Problems.hpp"
+#include <fstream>
+#include <iostream>
+#include <cstdlib>
+
+using namespace std;
+using namespace mfem;
+
+
+
+InteriorPointSolver::InteriorPointSolver(GeneralOptProblem * Problem) : optProblem(Problem), block_offsetsumlz(5), block_offsetsuml(4), block_offsetsx(3),
+Huu(nullptr), Hum(nullptr), Hmu(nullptr), Hmm(nullptr), Wmm(nullptr), D(nullptr), Ju(nullptr), Jm(nullptr), JuT(nullptr), JmT(nullptr), Huucl(nullptr), HLuu(nullptr), saveLogBarrierIterates(false)
+{
+  rel_tol  = 1.e-2;
+  max_iter = 20;
+  mu_k     = 1.0;
+
+  sMax     = 1.e2;
+  kSig     = 1.e10;   // control deviation from primal Hessian
+  tauMin   = 0.8;     // control rate at which iterates can approach the boundary
+  eta      = 1.e-4;   // backtracking constant
+  thetaMin = 1.e-4;   // allowed violation of the equality constraints
+
+  // constants in line-step A-5.4
+  delta    = 1.0;
+  sTheta   = 1.1;
+  sPhi     = 2.3;
+
+  // control the rate at which the penalty parameter is decreased
+  kMu     = 0.2;
+  thetaMu = 1.5;
+
+  // TO DO -- include the filter
+
+  thetaMax = 1.e6; // maximum constraint violation
+  // data for the second order correction
+  kSoc     = 0.99;
+
+  // equation (18)
+  gTheta = 1.e-5;
+  gPhi   = 1.e-5;
+
+  kEps   = 1.e1;
+
+  dimU = optProblem->GetDimU();
+  dimM = optProblem->GetDimM();
+  dimC = optProblem->GetDimC();
+  ckSoc.SetSize(dimC);
+  
+  block_offsetsumlz[0] = 0;
+  block_offsetsumlz[1] = dimU; // u
+  block_offsetsumlz[2] = dimM; // m
+  block_offsetsumlz[3] = dimC; // lambda
+  block_offsetsumlz[4] = dimM; // zl
+  block_offsetsumlz.PartialSum();
+
+  for(int i = 0; i < block_offsetsuml.Size(); i++)  { block_offsetsuml[i] = block_offsetsumlz[i]; }
+  for(int i = 0; i < block_offsetsx.Size(); i++)    { block_offsetsx[i]   = block_offsetsuml[i] ; }
+
+  // lower-bound for the inequality constraint m >= ml
+  ml = optProblem->Getml();
+  
+  lk.SetSize(dimC);  lk  = 0.0;
+  zlk.SetSize(dimM); zlk = 0.0;
+
+  linSolver = 0;
+  MyRank = 0;
+  iAmRoot = MyRank == 0 ? true : false;
+}
+
+double InteriorPointSolver::MaxStepSize(Vector &x, Vector &xl, Vector &xhat, double tau)
+{
+  double alphaMaxloc = 1.0;
+  double alphaTmp;
+  for(int i = 0; i < x.Size(); i++)
+  {
+    if( xhat(i) < 0. )
+    {
+      alphaTmp = -1. * tau * (x(i) - xl(i)) / xhat(i);
+      alphaMaxloc = min(alphaMaxloc, alphaTmp);
+    } 
+  }
+
+  // alphaMaxloc is the local maximum step size which is
+  // distinct on each MPI process. Need to compute
+  // the global maximum step size 
+  double alphaMaxglb;
+  alphaMaxglb = alphaMaxloc;
+  return alphaMaxglb;
+}
+
+double InteriorPointSolver::MaxStepSize(Vector &x, Vector &xhat, double tau)
+{
+  Vector zero(x.Size()); zero = 0.0;
+  return MaxStepSize(x, zero, xhat, tau);
+}
+
+
+void InteriorPointSolver::Mult(const Vector &x0, Vector &xf)
+{
+  BlockVector x0block(block_offsetsx); x0block = 0.0;
+  x0block.GetBlock(0).Set(1.0, x0);
+  // To do: give options for user specificiation of initialization m0
+  x0block.GetBlock(1) = 100.;
+  x0block.GetBlock(1).Add(1.0, ml);
+  BlockVector xfblock(block_offsetsx); xfblock = 0.0;
+  Mult(x0block, xfblock);
+  xf.Set(1.0, xfblock.GetBlock(0));
+}
+
+void InteriorPointSolver::Mult(const BlockVector &x0, BlockVector &xf)
+{
+  converged = false;
+  
+  BlockVector xk(block_offsetsx), xhat(block_offsetsx); xk = 0; xhat = 0.0;
+  BlockVector Xk(block_offsetsumlz), Xhat(block_offsetsumlz); Xk = 0.0; Xhat = 0.0;
+  BlockVector Xhatuml(block_offsetsuml); Xhatuml = 0.0;
+  Vector zlhat(dimM); zlhat = 0.0;
+
+  xk.GetBlock(0).Set(1.0, x0.GetBlock(0));
+  xk.GetBlock(1).Set(1.0, x0.GetBlock(1));
+  // running estimate of the final values of the Lagrange multipliers
+  lk  = 0.0;
+  zlk = 0.0;
+
+  for(int i = 0; i < dimM; i++)
+  {
+    zlk(i) = 1.e1 * mu_k / (xk(i+dimU) - ml(i));
+  }
+
+  Xk.GetBlock(0).Set(1.0, xk.GetBlock(0));
+  Xk.GetBlock(1).Set(1.0, xk.GetBlock(1));
+  Xk.GetBlock(2).Set(1.0, lk);
+  Xk.GetBlock(3).Set(1.0, zlk);
+
+  /* set theta0 = theta(x0)
+   *     thetaMin
+   *     thetaMax
+   * when theta(xk) < thetaMin and the switching condition holds
+   * then we ask for the Armijo sufficient decrease of the barrier
+   * objective to be satisfied, in order to accept the trial step length alphakl
+   * 
+   * thetaMax controls how the filter is initialized for each log-barrier subproblem
+   * F0 = {(th, phi) s.t. th > thetaMax}
+   * that is the filter does not allow for iterates where the constraint violation
+   * is larger than that of thetaMax
+   */
+  double theta0 = theta(xk);
+  thetaMin = 1.e-4 * max(1.0, theta0);
+  thetaMax = 1.e8  * thetaMin;
+
+  double Eeval, maxBarrierSolves, Eevalmu0;
+  bool printOptimalityError; // control optimality error print to console for log-barrier subproblems
+  
+  maxBarrierSolves = 10;
+
+  for(jOpt = 0; jOpt < max_iter; jOpt++)
+  {
+    mfem::out << "interior-point solve step " << jOpt << endl;
+    // A-2. Check convergence of overall optimization problem
+    printOptimalityError = false;
+    Eevalmu0 = E(xk, lk, zlk, printOptimalityError);
+    if(Eevalmu0 < rel_tol)
+    {
+      converged = true;
+      mfem::out << "solved optimization problem :)\n";
+      break;
+    }
+    
+    if(jOpt > 0) { maxBarrierSolves = 1; }
+    
+    for(int i = 0; i < maxBarrierSolves; i++)
+    {
+      // A-3. Check convergence of the barrier subproblem
+      printOptimalityError = true;
+      Eeval = E(xk, lk, zlk, mu_k, printOptimalityError);
+      if(Eeval < kEps * mu_k)
+      {
+        mfem::out << "solved barrier subproblem, for mu = " << mu_k << endl;
+        // A-3.1. Recompute the barrier parameter
+        mu_k  = max(rel_tol / 10., min(kMu * mu_k, pow(mu_k, thetaMu)));
+        // A-3.2. Re-initialize the filter
+        F1.DeleteAll();
+        F2.DeleteAll();
+      }
+      else
+      {
+        break;
+      }
+    }
+    
+    // A-4. Compute the search direction
+    // solve for (uhat, mhat, lhat)
+    mfem::out << "\n** A-4. IP-Newton solve **\n";
+    zlhat = 0.0; Xhatuml = 0.0;
+    // why do we have Xhatuml ....???
+    // TO DO: remove Xhatuml in favor of passing Xhat
+    IPNewtonSolve(xk, lk, zlk, zlhat, Xhatuml, mu_k, false); 
+
+
+    // assign data stack, X = (u, m, l, zl)
+    Xk = 0.0;
+    Xk.GetBlock(0).Set(1.0, xk.GetBlock(0));
+    Xk.GetBlock(1).Set(1.0, xk.GetBlock(1));
+    Xk.GetBlock(2).Set(1.0, lk);
+    Xk.GetBlock(3).Set(1.0, zlk);
+
+    // assign data stack, Xhat = (uhat, mhat, lhat, zlhat)
+    Xhat = 0.0;
+    for(int i = 0; i < 3; i++)
+    {
+      Xhat.GetBlock(i).Set(1.0, Xhatuml.GetBlock(i));
+    }
+    Xhat.GetBlock(3).Set(1.0, zlhat);
+
+
+    // A-5. Backtracking line search.
+    mfem::out << "\n** A-5. Linesearch **\n";
+    mfem::out << "mu = " << mu_k << endl;
+    
+    lineSearch(Xk, Xhat, mu_k);
+    
+    if(lineSearchSuccess)
+    {
+      if(!switchCondition || !sufficientDecrease)
+      {
+        F1.Append( (1. - gTheta) * thx0);
+        F2.Append( phx0 - gPhi * thx0);
+      }
+      // ----- A-6: Accept the trial point
+      // print info regarding zl...
+      xk.GetBlock(0).Add(alpha, Xhat.GetBlock(0));
+      xk.GetBlock(1).Add(alpha, Xhat.GetBlock(1));
+      lk.Add(alpha,   Xhat.GetBlock(2));
+      zlk.Add(alphaz, Xhat.GetBlock(3));
+      projectZ(xk, zlk, mu_k);
+    }
+    else
+    {
+      mfem::out << "lineSearch not successful :(\n";
+      mfem::out << "attempting feasibility restoration with theta = " << thx0 << endl;
+      mfem::out << "no feasibility restoration implemented, exiting now \n";
+      break;
+    }
+    //
+    if(jOpt + 1 == max_iter) 
+    { 
+      mfem::out << "maximum optimization iterations :(\n";
+    }
+  }
+  // done with optimization routine, just reassign data to xf reference so
+  // that the application code has access to the optimal point
+  xf = 0.0;
+  xf.GetBlock(0).Set(1.0, xk.GetBlock(0));
+  xf.GetBlock(1).Set(1.0, xk.GetBlock(1));
+}
+
+void InteriorPointSolver::FormIPNewtonMat(BlockVector & x, Vector & l, Vector &zl, BlockOperator &Ak)
+{
+  // WARNING: Huu, Hum, Hmu, Hmm should all be Hessian terms of the Lagrangian, currently we 
+  //          them by Hessian terms of the objective function and neglect the Hessian of l^T c
+
+  Huu = optProblem->Duuf(x); Hum = optProblem->Dumf(x);
+  Hmu = optProblem->Dmuf(x); Hmm = optProblem->Dmmf(x);
+
+  Vector DiagLogBar(dimM); DiagLogBar = 0.0;
+  for(int ii = 0; ii < dimM; ii++)
+  {
+    DiagLogBar(ii) = zl(ii) / (x(ii+dimU) - ml(ii));
+  }
+  if(saveLogBarrierIterates)
+  {
+    std::ofstream diagStream;
+    char diagString[100];
+    snprintf(diagString, 100, "logBarrierHessiandata/D%d.dat", jOpt);
+    diagStream.open(diagString, ios::out | ios::trunc);
+    for(int ii = 0; ii < dimM; ii++)
+    {
+      diagStream << setprecision(30) << DiagLogBar(ii) << endl;
+    }
+    diagStream.close();
+  } 
+
+
+  D = new SparseMatrix(DiagLogBar);
+  
+  if(Hmm != nullptr)
+  {
+    Wmm = new SparseMatrix(*Hmm);
+    Wmm->Add(1.0, *D);
+  }
+  else
+  {
+    Wmm = D;
+  }
+
+  Ju = optProblem->Duc(x); JuT = Transpose(*Ju);
+  Jm = optProblem->Dmc(x); JmT = Transpose(*Jm);
+ 
+  Huucl = optProblem->lDuuc(x, l);
+  if(Huucl != nullptr)
+  {
+    HLuu = Add(*Huucl, *Huu);
+    Ak.SetBlock(0, 0, HLuu);
+  } 
+  else
+  {
+    Ak.SetBlock(0, 0, Huu);
+  }
+
+  //         IP-Newton system matrix
+  //    Ak = [[H_(u,u)  H_(u,m)   J_u^T]
+  //          [H_(m,u)  W_(m,m)   J_m^T]
+  //          [ J_u      J_m       0  ]]
+
+  Ak.SetBlock(0, 2, JuT);
+  Ak.SetBlock(1, 1, Wmm); Ak.SetBlock(1, 2, JmT);
+  Ak.SetBlock(2, 0,  Ju); Ak.SetBlock(2, 1,  Jm);
+
+  if(Hum != nullptr) { Ak.SetBlock(0, 1, Hum); Ak.SetBlock(1, 0, Hmu); }
+}
+
+
+// perturbed KKT system solve
+// determine the search direction
+void InteriorPointSolver::IPNewtonSolve(BlockVector &x, Vector &l, Vector &zl, Vector &zlhat, BlockVector &Xhat, double mu, bool socSolve)
+{
+  // solve A x = b, where A is the IP-Newton matrix
+  BlockOperator A(block_offsetsuml, block_offsetsuml); BlockVector b(block_offsetsuml); b = 0.0;
+  FormIPNewtonMat(x, l, zl, A);
+
+  //       [grad_u phi + Ju^T l]
+  // b = - [grad_m phi + Jm^T l]
+  //       [          c        ]
+  BlockVector gradphi(block_offsetsx); gradphi = 0.0;
+  BlockVector JTl(block_offsetsx); JTl = 0.0;
+  Dxphi(x, mu, gradphi);
+  
+  (A.GetBlock(0,2)).Mult(l, JTl.GetBlock(0));
+  (A.GetBlock(1,2)).Mult(l, JTl.GetBlock(1));
+
+  for(int ii = 0; ii < 2; ii++)
+  {
+    b.GetBlock(ii).Set(1.0, gradphi.GetBlock(ii));
+    b.GetBlock(ii).Add(1.0, JTl.GetBlock(ii));
+  }
+  if(!socSolve) 
+  {
+    optProblem->c(x, b.GetBlock(2));
+  }
+  else
+  {
+    b.GetBlock(2).Set(1.0, ckSoc);
+  }
+  b *= -1.0; 
+  Xhat = 0.0;
+
+
+  #ifdef MFEM_USE_SUITESPARSE
+    // Direct solve for IP-Newton saddle-point system
+    // A = [ [ Huu   0    Ju^T]
+    //       [  0    D     -I ]
+    //       [ Ju   -I      0 ]]
+    if(linSolver == 0)
+    {
+      BlockMatrix ABlockMatrix(block_offsetsuml, block_offsetsuml);
+      for(int ii = 0; ii < 3; ii++)
+      {
+        for(int jj = 0; jj < 3; jj++)
+        {
+          if(!A.IsZeroBlock(ii, jj))
+          {
+            ABlockMatrix.SetBlock(ii, jj, dynamic_cast<SparseMatrix *>(&(A.GetBlock(ii, jj))));
+          }
+        }
+      }
+      /* direct solve of the 3x3 IP-Newton linear system */
+      UMFPackSolver ASolver;
+      SparseMatrix *ASparse = ABlockMatrix.CreateMonolithic();
+      ASolver.SetOperator(*ASparse);
+      ASolver.Mult(b, Xhat);
+
+      Vector residual(Xhat.Size());
+      ASparse->Mult(Xhat, residual);
+      residual.Add(-1.0, b);
+      delete ASparse;
+    }
+    else if(linSolver == 1)
+    {
+      // Direct solve for 0,0 Schur complement of IP-Newton system, Huu + Ju^T Wmm Ju,
+      // where Wmm = D for contact problems
+      SparseMatrix * Huuloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(0, 0)));
+      SparseMatrix * Wmmloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(1, 1)));
+      SparseMatrix * Juloc  = dynamic_cast<SparseMatrix *>(&(A.GetBlock(2, 0)));
+      SparseMatrix * JuTloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(0, 2)));
+      Vector DVec(dimM); DVec = 0.0;
+      Vector one(dimM); one = 1.0;
+      D->Mult(one, DVec);
+      SparseMatrix *JuTDJu = Mult_AtDA(*Juloc, DVec);     // Ju^T D Ju
+      SparseMatrix *Areduced = Add(*Huuloc, *JuTDJu);  // Huu + Ju^T D Ju
+
+      
+      /* prepare the reduced rhs */
+      // breduced = bu + Ju^T (bm + Wmm bl)
+      Vector breduced(dimU); breduced = 0.0;
+      Vector tempVec(dimM); tempVec = 0.0;
+      Wmmloc->Mult(b.GetBlock(2), tempVec);
+      tempVec.Add(1.0, b.GetBlock(1));
+      JuTloc->Mult(tempVec, breduced);
+      breduced.Add(1.0, b.GetBlock(0));
+
+      // solve the reduced linear system
+      UMFPackSolver AreducedSolver;
+      AreducedSolver.SetOperator(*Areduced);
+      AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+
+      // now propagate solved uhat to obtain mhat and lhat
+      // xm = Ju xu - bl
+      Juloc->Mult(Xhat.GetBlock(0), Xhat.GetBlock(1));
+      Xhat.GetBlock(1).Add(-1.0, b.GetBlock(2));
+
+      // xl = Wmm xm - bm
+      Wmmloc->Mult(Xhat.GetBlock(1), Xhat.GetBlock(2));
+      Xhat.GetBlock(2).Add(-1.0, b.GetBlock(1));
+
+      delete JuTDJu;
+      delete Areduced;
+    }
+  #else
+    MFEM_VERIFY(linSolver > 1, "linSolver = 0, 1 require MFEM_USE_SUITESPARSE=YES");
+  #endif
+  if(linSolver > 1)
+  { 
+    // Iterative solve for 0,0 Schur complement of IP-Newton system, Huu + Ju^T Wmm Ju,
+    // where Wmm = D for contact problems
+    // here the iterative solver is a Jacobi-preconditioned CG-solve
+    SparseMatrix * Huuloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(0, 0)));
+    SparseMatrix * Wmmloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(1, 1)));
+    SparseMatrix * Juloc  = dynamic_cast<SparseMatrix *>(&(A.GetBlock(2, 0)));
+    SparseMatrix * JuTloc = dynamic_cast<SparseMatrix *>(&(A.GetBlock(0, 2)));
+    Vector DVec(dimM); DVec = 0.0;
+    Vector one(dimM); one = 1.0;
+    D->Mult(one, DVec);
+    SparseMatrix *JuTDJu   = Mult_AtDA(*Juloc, DVec);     // Ju^T D Ju
+    SparseMatrix *Areduced = Add(*Huuloc, *JuTDJu);  // Huu + Ju^T D Ju
+
+    /* prepare the reduced rhs */
+    // breduced = bu + Ju^T (bm + Wmm bl)
+    Vector breduced(dimU); breduced = 0.0;
+    Vector tempVec(dimM); tempVec = 0.0;
+    Wmmloc->Mult(b.GetBlock(2), tempVec);
+    tempVec.Add(1.0, b.GetBlock(1));
+    JuTloc->Mult(tempVec, breduced);
+    breduced.Add(1.0, b.GetBlock(0));
+    
+    if (linSolver == 2)
+    {
+      /* Jacobi preconditioned conjugate-gradient solve */
+      DSmoother AreducedPrec((SparseMatrix &)(*Areduced));
+      CGSolver AreducedSolver;
+      AreducedSolver.SetOperator(*Areduced);
+      AreducedSolver.SetAbsTol(1.e-12);
+      AreducedSolver.SetRelTol(1.e-8);
+      AreducedSolver.SetMaxIter(500);
+      AreducedSolver.SetPreconditioner(AreducedPrec);
+      AreducedSolver.SetPrintLevel(1);
+      AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+    }
+    else
+    {
+      /* Gauss-Seidel preconditioned GMRES solve */
+      GSSmoother AreducedPrec((SparseMatrix &)(*Areduced));
+      GMRESSolver AreducedSolver;
+      AreducedSolver.SetOperator(*Areduced);
+      AreducedSolver.SetAbsTol(1.e-12);
+      AreducedSolver.SetRelTol(1.e-8);
+      AreducedSolver.SetMaxIter(500);
+      AreducedSolver.SetPreconditioner(AreducedPrec);
+      AreducedSolver.SetPrintLevel(1);
+      AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+    }
+    
+    // now propagate solved uhat to obtain mhat and lhat
+    // xm = Ju xu - bl
+    Juloc->Mult(Xhat.GetBlock(0), Xhat.GetBlock(1));
+    Xhat.GetBlock(1).Add(-1.0, b.GetBlock(2));
+
+    // xl = Wmm xm - bm
+    Wmmloc->Mult(Xhat.GetBlock(1), Xhat.GetBlock(2));
+    Xhat.GetBlock(2).Add(-1.0, b.GetBlock(1));
+
+    delete JuTDJu;
+    delete Areduced;
+  }
+    
+  
+  /* backsolve to determine zlhat */
+  for(int ii = 0; ii < dimM; ii++)
+  {
+    zlhat(ii) = -1.*(zl(ii) + (zl(ii) * Xhat(ii + dimU) - mu) / (x(ii + dimU) - ml(ii)) );
+  }
+
+  // free memory
+  if(Hmm != nullptr)
+  {
+    delete Wmm;
+  }
+  if( Huucl != nullptr)
+  {
+    delete HLuu; HLuu = nullptr;
+  }
+  delete D;
+  delete JuT;
+  delete JmT;
+}
+
+// here Xhat, X will be BlockVectors w.r.t. the 4 partitioning X = (u, m, l, zl)
+
+void InteriorPointSolver::lineSearch(BlockVector& X0, BlockVector& Xhat, double mu)
+{
+  double tau  = max(tauMin, 1.0 - mu);
+  Vector u0   = X0.GetBlock(0);
+  Vector m0   = X0.GetBlock(1);
+  Vector l0   = X0.GetBlock(2);
+  Vector z0   = X0.GetBlock(3);
+  Vector uhat = Xhat.GetBlock(0);
+  Vector mhat = Xhat.GetBlock(1);
+  Vector lhat = Xhat.GetBlock(2);
+  Vector zhat = Xhat.GetBlock(3);
+  double alphaMax  = MaxStepSize(m0, ml, mhat, tau);
+  double alphaMaxz = MaxStepSize(z0, zhat, tau);
+  alphaz = alphaMaxz;
+
+
+  BlockVector x0(block_offsetsx); x0 = 0.0;
+  x0.GetBlock(0).Set(1.0, u0);
+  x0.GetBlock(1).Set(1.0, m0);
+  
+  BlockVector xhat(block_offsetsx); xhat = 0.0;
+  xhat.GetBlock(0).Set(1.0, uhat);
+  xhat.GetBlock(1).Set(1.0, mhat);
+  
+  BlockVector xtrial(block_offsetsx); xtrial = 0.0;
+  BlockVector Dxphi0(block_offsetsx); Dxphi0 = 0.0;
+  int maxBacktrack = 20;
+  alpha = alphaMax;
+
+
+  Vector ck0(dimC); ck0 = 0.0;
+  Vector zhatsoc(dimM); zhatsoc = 0.0;
+  BlockVector Xhatumlsoc(block_offsetsuml); Xhatumlsoc = 0.0;
+  BlockVector xhatsoc(block_offsetsx); xhatsoc = 0.0;
+  Vector uhatsoc(dimU); uhatsoc = 0.0;
+  Vector mhatsoc(dimM); mhatsoc = 0.0;
+
+  Dxphi(x0, mu, Dxphi0);
+  Dxphi0_xhat = InnerProduct(Dxphi0, xhat);
+  descentDirection = Dxphi0_xhat < 0. ? true : false;
+  if(descentDirection)
+  {
+    mfem::out << "is a descent direction for the log-barrier objective\n";
+  }
+  else
+  {
+    mfem::out << "is not a descent direction for the log-barrier objective\n";
+  }
+  mfem::out << "Dxphi^T xhat / (|| Dxphi||_2 * || xhat ||_2) = " << Dxphi0_xhat / (xhat.Norml2() * Dxphi0.Norml2()) << endl;
+  thx0 = theta(x0);
+  phx0 = phi(x0, mu);
+
+  lineSearchSuccess = false;
+  for(int i = 0; i < maxBacktrack; i++)
+  {
+    mfem::out << "\n--------- alpha = " << alpha << " ---------\n";
+
+    // ----- A-5.2. Compute trial point: xtrial = x0 + alpha_i xhat
+    xtrial.Set(1.0, x0);
+    xtrial.Add(alpha, xhat);
+
+    // ------ A-5.3. if not in filter region go to A.5.4 otherwise go to A-5.5.
+    thxtrial = theta(xtrial);
+    phxtrial = phi(xtrial, mu);
+
+    filterCheck(thxtrial, phxtrial);    
+    if(!inFilterRegion)
+    {
+      mfem::out << "not in filter region :)\n";
+      // ------ A.5.4: Check sufficient decrease
+      if(!descentDirection)
+      {
+        switchCondition = false;
+      }
+      else
+      {
+        switchCondition = (alpha * pow(abs(Dxphi0_xhat), sPhi) > delta * pow(thx0, sTheta)) ? true : false;
+      }
+      mfem::out << "theta(x0) = "     << thx0     << ", thetaMin = "                  << thetaMin             << endl;
+      mfem::out << "theta(xtrial) = " << thxtrial << ", (1-gTheta) *theta(x0) = "     << (1. - gTheta) * thx0 << endl;
+      mfem::out << "phi(xtrial) = "   << phxtrial << ", phi(x0) - gPhi *theta(x0) = " << phx0 - gPhi * thx0   << endl;
+      
+      // Case I      
+      if(thx0 <= thetaMin && switchCondition)
+      {
+        sufficientDecrease = phxtrial <= phx0 + eta * alpha * Dxphi0_xhat ? true : false;
+        if(sufficientDecrease)
+        {
+          mfem::out << "Accepted step length -- sufficient decrease in log-barrier objective.\n"; 
+          // accept the trial step
+          lineSearchSuccess = true;
+          break;
+        }
+      }
+      else
+      {
+        if(thxtrial <= (1. - gTheta) * thx0 || phxtrial <= phx0 - gPhi * thx0)
+        {
+          mfem::out << "Accepted step length -- decrease in either constraint violation or log-barrier objective.\n"; 
+          // accept the trial step
+          lineSearchSuccess = true;
+          break;
+        }
+      }
+      // A-5.5: Initialize the second-order correction
+      if((!(thx0 < thxtrial)) && i == 0)
+      {
+        mfem::out << "second order correction\n";
+        optProblem->c(xtrial, ckSoc);
+        optProblem->c(x0, ck0);
+        ckSoc.Add(alphaMax, ck0);
+        // A-5.6 Compute the second-order correction.
+        IPNewtonSolve(x0, l0, z0, zhatsoc, Xhatumlsoc, mu, true);
+        mhatsoc.Set(1.0, Xhatumlsoc.GetBlock(1));
+        // alphasoc = MaxStepSize(m0, ml, mhatsoc, tau);
+        //WARNING: not complete but currently solver isn't entering this region
+      }
+    }
+    else
+    {
+      mfem::out << "in filter region\n";
+    }
+
+    // include more if needed
+    alpha *= 0.5;
+
+  } 
+}
+
+
+void InteriorPointSolver::projectZ(const Vector &x, Vector &z, double mu)
+{
+  double zi;
+  double mudivmml;
+  for(int i = 0; i < dimM; i++)
+  {
+    zi = z(i);
+    mudivmml = mu / (x(i + dimU) - ml(i));
+    z(i) = max(min(zi, kSig * mudivmml), mudivmml / kSig);
+  }
+}
+
+void InteriorPointSolver::filterCheck(double th, double ph)
+{
+  inFilterRegion = false;
+  if(th > thetaMax)
+  {
+    inFilterRegion = true;
+  }
+  else
+  {
+    for(int i = 0; i < F1.Size(); i++)
+    {
+      if(th >= F1[i] && ph >= F2[i])
+      {
+        inFilterRegion = true;
+        break;
+      }
+    }
+  }
+}
+
+double InteriorPointSolver::E(const BlockVector &x, const Vector &l, const Vector &zl, double mu, bool print)
+{
+  double E1, E2, E3;
+  double sc, sd;
+  BlockVector gradL(block_offsetsx); gradL = 0.0; // stationarity grad L = grad f + J^T l - z
+  Vector cx(dimC); cx = 0.0;     // feasibility c = c(x)
+  Vector comp(dimM); comp = 0.0; // complementarity M Z - mu 1
+
+  DxL(x, l, zl, gradL);
+  E1 = gradL.Normlinf();
+
+  optProblem->c(x, cx);
+  E2 = cx.Normlinf();
+
+  for(int ii = 0; ii < dimM; ii++) 
+  { 
+    comp(ii) = x(dimU + ii) * zl(ii) - mu;
+  }
+  E3 = comp.Normlinf();
+
+  double ll1, zl1;
+  zl1 = zl.Norml1() / double(dimC + dimM);
+  ll1 =  l.Norml1();
+  sc = max(sMax, zl1 / (double(dimM)) ) / sMax;
+  sd = max(sMax, (ll1 + zl1) / (double(dimC + dimM))) / sMax;
+  if(print)
+  {
+    mfem::out << "evaluating optimality error for mu = " << mu << endl;
+    mfem::out << "stationarity measure = "    << E1 / sd << endl;
+    mfem::out << "feasibility measure  = "    << E2      << endl;
+    mfem::out << "complimentarity measure = " << E3 / sc << endl;
+  }
+  return max(max(E1 / sd, E2), E3 / sc);
+}
+
+double InteriorPointSolver::E(const BlockVector &x, const Vector &l, const Vector &zl, bool print)
+{
+  return E(x, l, zl, 0.0, print);
+}
+
+double InteriorPointSolver::theta(const BlockVector &x)
+{
+  Vector cx(dimC); cx = 0.0;
+  optProblem->c(x, cx);
+  return cx.Norml2();
+}
+
+// log-barrier objective
+double InteriorPointSolver::phi(const BlockVector &x, double mu)
+{
+  double fx = optProblem->CalcObjective(x); 
+  double logBarrierLoc = 0.0;
+  for(int i = 0; i < dimM; i++) 
+  { 
+    logBarrierLoc += log(x(dimU+i)-ml(i));
+  }
+  double logBarrierGlb = 0.0;
+  logBarrierGlb = logBarrierLoc;
+  return fx - mu * logBarrierGlb;
+}
+
+
+
+
+// gradient of log-barrier objective with respect to x = (u, m)
+void InteriorPointSolver::Dxphi(const BlockVector &x, double mu, BlockVector &y)
+{
+  optProblem->CalcObjectiveGrad(x, y);
+  for(int i = 0; i < dimM; i++) 
+  { 
+    y(dimU + i) -= mu / (x(dimU + i));
+  } 
+}
+
+
+// Lagrangian function evaluation
+// L(x, l, zl) = f(x) + l^T c(x) - zl^T m
+double InteriorPointSolver::L(const BlockVector &x, const Vector &l, const Vector &zl)
+{
+  double fx = optProblem->CalcObjective(x);
+  Vector cx(dimC); optProblem->c(x, cx);
+  return (fx + InnerProduct(cx, l) - InnerProduct(x.GetBlock(1), zl));
+}
+
+void InteriorPointSolver::DxL(const BlockVector &x, const Vector &l, const Vector &zl, BlockVector &y)
+{
+  // evaluate the gradient of the objective with respect to the primal variables x = (u, m)
+  BlockVector gradxf(block_offsetsx); gradxf = 0.0;
+  optProblem->CalcObjectiveGrad(x, gradxf);
+  
+  SparseMatrix *Jacu, *Jacm, *JacuT, *JacmT;
+  Jacu = optProblem->Duc(x); Jacm = optProblem->Dmc(x);
+  JacuT = Transpose(*Jacu);
+  JacmT = Transpose(*Jacm);
+  JacuT->Mult(l, y.GetBlock(0));
+  JacmT->Mult(l, y.GetBlock(1));
+  delete JacuT; 
+  delete JacmT;
+  y.Add(1.0, gradxf);
+  (y.GetBlock(1)).Add(-1.0, zl);
+}
+
+
+bool InteriorPointSolver::GetConverged() const
+{
+  return converged;
+}
+
+void InteriorPointSolver::SetTol(double Tol)
+{
+  rel_tol = Tol;
+}
+
+void InteriorPointSolver::SetMaxIter(int max_it)
+{
+  max_iter = max_it;
+}
+
+void InteriorPointSolver::SetBarrierParameter(double mu_0)
+{
+  mu_k = mu_0;
+}
+
+void InteriorPointSolver::SaveLogBarrierHessianIterates(bool save)
+{
+  MFEM_ASSERT(MyRank == 0 || save == false, "currently can only save logbarrier hessian in serial codes");
+  saveLogBarrierIterates = save;
+}
+
+void InteriorPointSolver::SetLinearSolver(int LinSolver)
+{
+  linSolver = LinSolver;
+}
+
+
+
+InteriorPointSolver::~InteriorPointSolver() 
+{
+  F1.DeleteAll();
+  F2.DeleteAll();
+  block_offsetsx.DeleteAll();
+  block_offsetsumlz.DeleteAll();
+  block_offsetsuml.DeleteAll();
+  ml.SetSize(0);
+}

examples/contact/IPsolver.hpp

@@ -0,0 +1,80 @@
+#include "mfem.hpp"
+#include "Problems.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+
+#ifndef IPSOLVER 
+#define IPSOLVER
+
+class InteriorPointSolver
+{
+protected:
+    GeneralOptProblem* optProblem;
+    double rel_tol;
+    int  max_iter;
+    double mu_k; // \mu_k
+    Vector lk, zlk;
+
+    double sMax, kSig, tauMin, eta, thetaMin, delta, sTheta, sPhi, kMu, thetaMu;
+    double thetaMax, kSoc, gTheta, gPhi, kEps;
+	
+    // filter
+    Array<double> F1, F2;
+	
+    // quantities computed in lineSearch
+    double alpha, alphaz;
+    double thx0, thxtrial;
+    double phx0, phxtrial;
+    bool descentDirection, switchCondition, sufficientDecrease, lineSearchSuccess, inFilterRegion;
+    double Dxphi0_xhat;
+
+    int dimU, dimM, dimC;
+    Array<int> block_offsetsumlz, block_offsetsuml, block_offsetsx;
+    Vector ml;
+
+    Vector ckSoc;
+    SparseMatrix * Huu, * Hum, * Hmu, * Hmm, * Wmm, *D, * Ju, * Jm, * JuT, * JmT;
+    SparseMatrix * Huucl, *HLuu;    
+    int jOpt;
+    bool converged;
+    
+    int MyRank;
+    bool iAmRoot;
+
+    bool saveLogBarrierIterates;
+
+    int linSolver;
+
+public:
+    InteriorPointSolver(GeneralOptProblem*);
+    void Mult(const BlockVector& , BlockVector&); // used when the user wants to be aware of bound-constrained variable m >= ml
+    void Mult(const Vector&, Vector &); // useful when the user doesn't need to know about bound-constrained variable   m >= ml, e.g., when m is a slack variable
+    double MaxStepSize(Vector& , Vector& , Vector& , double);
+    double MaxStepSize(Vector& , Vector& , double);
+    void FormIPNewtonMat(BlockVector& , Vector& , Vector& , BlockOperator &);
+    void IPNewtonSolve(BlockVector& , Vector& , Vector& , Vector&, BlockVector& , double, bool);
+    void lineSearch(BlockVector& , BlockVector& , double);
+    void projectZ(const Vector & , Vector &, double);
+    void filterCheck(double, double);
+    double E(const BlockVector &, const Vector &, const Vector &, double, bool);
+    double E(const BlockVector &, const Vector &, const Vector &, bool);
+    bool GetConverged() const;
+    // TO DO: include Hessian of Lagrangian
+    double theta(const BlockVector &);
+    double phi(const BlockVector &, double);
+    void Dxphi(const BlockVector &, double, BlockVector &);
+    double L(const BlockVector &, const Vector &, const Vector &);
+    void DxL(const BlockVector &, const Vector &, const Vector &, BlockVector &);
+    void SetTol(double);
+    void SetMaxIter(int);
+    void SetBarrierParameter(double);    
+    void SaveLogBarrierHessianIterates(bool);
+    void SetLinearSolver(int);
+    virtual ~InteriorPointSolver();
+};
+
+#endif

examples/contact/ObstacleProblem.cpp

@@ -0,0 +1,125 @@
+#include "mfem.hpp"
+#include "Problems.hpp"
+#include "IPsolver.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+
+
+double dmanufacturedFun(const Vector &);
+double fRhs(const Vector &);
+double obstacle(const Vector &);
+
+int main(int argc, char *argv[])
+{
+  int FEorder = 1; // order of the finite elements
+  int linSolver = 0;
+  int maxIPMiters = 30;
+  bool iAmRoot = true;
+  
+  OptionsParser args(argc, argv);
+  args.AddOption(&FEorder, "-o", "--order",\
+		  "Order of the finite elements.");
+  args.AddOption(&linSolver, "-linSolver", "--linearSolver", \
+       "IP-Newton linear system solution strategy.");
+  args.AddOption(&maxIPMiters, "-IPMiters", "--IPMiters",\
+		  "Maximum number of IPM iterations");
+  
+  args.Parse();
+  if(!args.Good())
+  {
+    args.PrintUsage(cout);
+    return 1;
+  }
+  else
+  {
+    if( iAmRoot )
+    {
+      args.PrintOptions(cout);
+    }
+  }
+
+  const char *meshFile = "../../data/inline-quad.mesh";
+  Mesh *mesh = new Mesh(meshFile, 1, 1);
+  int dim = mesh->Dimension(); // geometric dimension of the domain
+  {
+     int ref_levels = 3;
+     for (int l = 0; l < ref_levels; l++)
+     {
+        mesh->UniformRefinement();
+     }
+  }
+
+  FiniteElementCollection *fec = new H1_FECollection(FEorder, dim);
+  FiniteElementSpace      *Vh  = new FiniteElementSpace(mesh, fec);
+  ObstacleProblem problem(Vh, &fRhs, &obstacle);
+  
+  int dimD = problem.GetDimD();
+  Vector x0(dimD); x0 = 0.0;
+  Vector xf(dimD); xf = 0.0;
+
+  InteriorPointSolver optimizer(&problem); 
+  optimizer.SetTol(1.e-7);
+  optimizer.SetLinearSolver(linSolver);
+  optimizer.SetMaxIter(maxIPMiters);
+  optimizer.Mult(x0, xf);
+
+  double Einitial = problem->E(x0);
+  double Efinal = problem->E(xf);
+  cout << "Energy objective at initial point = " << Einitial << endl;
+  cout << "Energy objective at QP optimizer = " << Efinal << endl;
+
+
+  GridFunction d_gf(Vh);
+
+  d_gf = xf;
+
+  FunctionCoefficient dm_fc(dmanufacturedFun); // pseudo-manufactured solution
+  GridFunction dm_gf(Vh);
+  dm_gf.ProjectCoefficient(dm_fc);
+  
+  ParaViewDataCollection paraview_dc("BarrierProblemSolution", mesh);
+  paraview_dc.SetPrefixPath("ParaView");
+  paraview_dc.SetLevelsOfDetail(FEorder);
+  paraview_dc.SetDataFormat(VTKFormat::BINARY);
+  paraview_dc.SetHighOrderOutput(true);
+  paraview_dc.SetCycle(0);
+  paraview_dc.SetTime(0.0);
+  paraview_dc.RegisterField("d(x) (numerical)", &d_gf);
+  paraview_dc.RegisterField("d(x) (pseudo-manufactured)", &dm_gf);
+  paraview_dc.Save();
+  
+  
+  delete Vh;
+  delete fec;
+  delete mesh;
+  return 0;
+}
+
+
+double dmanufacturedFun(const Vector &x)
+{
+  return cos(2*M_PI*x(0)) + 0.2 - 2.0*(pow(x(0),3) - 1.5*pow(x(0),2));
+}
+
+
+// f(x) forcing term... which enters the objective energy functional
+// E(d) = 0.5 d^T K d - f^T d, where f is a discrete vector representation
+// of f(x). f(x) is such that in the absence of bound-constraints then
+// the solution of the optimization problem satisfies the PDE
+// -div(grad(d)) + d = f + homogeneous Neumann conditions on the unit interval,
+// for d(x) = cos(2 \pi x) + a0 + a3 (x^3 - 1.5 x^2), a2 = 0.2, a3 = -2
+double fRhs(const Vector &x)
+{
+  double fx = 0.;
+  fx = 0.2 - 2.0 * (pow(x(0),3)- 1.5*pow(x(0),2.) - 6 * x(0) + 3.) + (1. + pow(2.*M_PI,2))*cos(2.*M_PI*x(0));
+  return fx;
+}
+
+double obstacle(const Vector &x)
+{
+  return 0.0;
+}

examples/contact/ParIPsolver.cpp

@@ -0,0 +1,834 @@
+#include "mfem.hpp"
+#include "ParIPsolver.hpp"
+#include "ParProblems.hpp"
+#include <fstream>
+#include <iostream>
+#include <cstdlib>
+
+using namespace std;
+using namespace mfem;
+
+
+ParInteriorPointSolver::ParInteriorPointSolver(ParGeneralOptProblem * problem_) 
+                     : problem(problem_), 
+                       block_offsetsumlz(5), block_offsetsuml(4), block_offsetsx(3),
+                       Huu(nullptr), Hum(nullptr), Hmu(nullptr), 
+                       Hmm(nullptr), Wmm(nullptr), D(nullptr), 
+                       Ju(nullptr), Jm(nullptr), JuT(nullptr), JmT(nullptr), 
+                       saveLogBarrierIterates(false)
+{
+   OptTol  = 1.e-2;
+   max_iter = 20;
+   mu_k     = 1.0;
+
+   sMax     = 1.e2;
+   kSig     = 1.e10;   // control deviation from primal Hessian
+   tauMin   = 0.8;     // control rate at which iterates can approach the boundary
+   eta      = 1.e-4;   // backtracking constant
+   thetaMin = 1.e-4;   // allowed violation of the equality constraints
+
+   // constants in line-step A-5.4
+   delta    = 1.0;
+   sTheta   = 1.1;
+   sPhi     = 2.3;
+
+   // control the rate at which the penalty parameter is decreased
+   kMu     = 0.2;
+   thetaMu = 1.5;
+
+   thetaMax = 1.e6; // maximum constraint violation
+   // data for the second order correction
+   kSoc     = 0.99;
+
+   // equation (18)
+   gTheta = 1.e-5;
+   gPhi   = 1.e-5;
+
+   kEps   = 1.e1;
+
+   dimU = problem->GetDimU();
+   dimM = problem->GetDimM();
+   dimC = problem->GetDimC();
+   MPI_Allreduce(&dimU, &dimUglb, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+   MPI_Allreduce(&dimM, &dimMglb, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+   MPI_Allreduce(&dimC, &dimCglb, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+   ckSoc.SetSize(dimC);
+  
+   block_offsetsumlz[0] = 0;
+   block_offsetsumlz[1] = dimU; // u
+   block_offsetsumlz[2] = dimM; // m
+   block_offsetsumlz[3] = dimC; // lambda
+   block_offsetsumlz[4] = dimM; // zl
+   block_offsetsumlz.PartialSum();
+
+   for(int i = 0; i < block_offsetsuml.Size(); i++)  
+   { 
+      block_offsetsuml[i] = block_offsetsumlz[i]; 
+   }
+   for(int i = 0; i < block_offsetsx.Size(); i++)    
+   { 
+      block_offsetsx[i] = block_offsetsuml[i] ; 
+   }
+
+  
+   ml = problem->Getml();
+  
+   lk.SetSize(dimC);  lk  = 0.0;
+   zlk.SetSize(dimM); zlk = 0.0;
+
+   linSolver = 0;
+   linSolveTol = 1.e-8;
+   MyRank = Mpi::WorldRank();
+   iAmRoot = MyRank == 0 ? true : false;
+}
+
+double ParInteriorPointSolver::MaxStepSize(Vector &x, Vector &xl, Vector &xhat, double tau)
+{
+   double alphaMaxloc = 1.0;
+   double alphaTmp;
+   for(int i = 0; i < x.Size(); i++)
+   {   
+      if( xhat(i) < 0. )
+      {
+         alphaTmp = -1. * tau * (x(i) - xl(i)) / xhat(i);
+         alphaMaxloc = min(alphaMaxloc, alphaTmp);
+      } 
+   }
+
+   // alphaMaxloc is the local maximum step size which is
+   // distinct on each MPI process. Need to compute
+   // the global maximum step size 
+   double alphaMaxglb;
+   MPI_Allreduce(&alphaMaxloc, &alphaMaxglb, 1, MPI_DOUBLE, MPI_MIN, MPI_COMM_WORLD);
+   return alphaMaxglb;
+}
+
+double ParInteriorPointSolver::MaxStepSize(Vector &x, Vector &xhat, double tau)
+{
+   Vector zero(x.Size()); zero = 0.0;
+   return MaxStepSize(x, zero, xhat, tau);
+}
+
+
+void ParInteriorPointSolver::Mult(const Vector &x0, Vector &xf)
+{
+   BlockVector x0block(block_offsetsx); x0block = 0.0;
+   x0block.GetBlock(0).Set(1.0, x0);
+   x0block.GetBlock(1) = 100.;
+   x0block.GetBlock(1).Add(1.0, ml);
+   BlockVector xfblock(block_offsetsx); xfblock = 0.0;
+   Mult(x0block, xfblock);
+   xf.Set(1.0, xfblock.GetBlock(0));
+}
+
+
+void ParInteriorPointSolver::Mult(const BlockVector &x0, BlockVector &xf)
+{
+   converged = false;
+   
+   BlockVector xk(block_offsetsx), xhat(block_offsetsx); xk = 0; xhat = 0.0;
+   BlockVector Xk(block_offsetsumlz), Xhat(block_offsetsumlz); Xk = 0.0; Xhat = 0.0;
+   BlockVector Xhatuml(block_offsetsuml); Xhatuml = 0.0;
+   Vector zlhat(dimM); zlhat = 0.0;
+
+   xk.GetBlock(0).Set(1.0, x0.GetBlock(0));
+   xk.GetBlock(1).Set(1.0, x0.GetBlock(1));
+   // running estimate of the final values of the Lagrange multipliers
+   lk  = 0.0;
+   zlk = 0.0;
+
+   for(int i = 0; i < dimM; i++)
+   {
+      zlk(i) = 1.e1 * mu_k / (xk(i+dimU) - ml(i));
+   }
+
+   Xk.GetBlock(0).Set(1.0, xk.GetBlock(0));
+   Xk.GetBlock(1).Set(1.0, xk.GetBlock(1));
+   Xk.GetBlock(2).Set(1.0, lk);
+   Xk.GetBlock(3).Set(1.0, zlk);
+
+  /* set theta0 = theta(x0)
+   *     thetaMin
+   *     thetaMax
+   * when theta(xk) < thetaMin and the switching condition holds
+   * then we ask for the Armijo sufficient decrease of the barrier
+   * objective to be satisfied, in order to accept the trial step length alphakl
+   * 
+   * thetaMax controls how the filter is initialized for each log-barrier subproblem
+   * F0 = {(th, phi) s.t. th > thetaMax}
+   * that is the filter does not allow for iterates where the constraint violation
+   * is larger than that of thetaMax
+   */
+   double theta0 = theta(xk);
+   thetaMin = 1.e-4 * max(1.0, theta0);
+   thetaMax = 1.e8  * thetaMin; // 1.e4 * max(1.0, theta0)
+
+   double Eeval, maxBarrierSolves, Eevalmu0;
+   bool printOptimalityError; // control optimality error print to console for log-barrier subproblems
+   
+   maxBarrierSolves = 10;
+
+   for(jOpt = 0; jOpt < max_iter; jOpt++)
+   {
+      if(iAmRoot)
+      {
+         cout << "interior-point solve step " << jOpt << endl;
+      }
+      // A-2. Check convergence of overall optimization problem
+      printOptimalityError = false;
+      Eevalmu0 = E(xk, lk, zlk, printOptimalityError);
+      if(Eevalmu0 < OptTol)
+      {
+         converged = true;
+         if(iAmRoot)
+         {
+            cout << "solved optimization problem :)\n";
+         }
+         break;
+      }
+      
+      if(jOpt > 0) { maxBarrierSolves = 1; }
+      
+      for(int i = 0; i < maxBarrierSolves; i++)
+      {
+         // A-3. Check convergence of the barrier subproblem
+         printOptimalityError = true;
+         Eeval = E(xk, lk, zlk, mu_k, printOptimalityError);
+         if(iAmRoot)
+         {
+            cout << "E = " << Eeval << endl;
+         }
+         if(Eeval < kEps * mu_k)
+         {
+            if(iAmRoot)
+            {
+               cout << "solved barrier subproblem :), for mu = " << mu_k << endl;
+            }
+            // A-3.1. Recompute the barrier parameter
+            mu_k  = max(OptTol / 10., min(kMu * mu_k, pow(mu_k, thetaMu)));
+            // A-3.2. Re-initialize the filter
+            F1.DeleteAll();
+            F2.DeleteAll();
+         }
+         else
+         {
+            break;
+         }
+      }
+    
+      // A-4. Compute the search direction
+      // solve for (uhat, mhat, lhat)
+      if(iAmRoot)
+      {
+         cout << "\n** A-4. IP-Newton solve **\n";
+      }
+      zlhat = 0.0; Xhatuml = 0.0;
+      // why do we have Xhatuml ....???
+      // TO DO: remove Xhatuml in favor of passing Xhat
+      IPNewtonSolve(xk, lk, zlk, zlhat, Xhatuml, mu_k, false); 
+
+      // assign data stack, X = (u, m, l, zl)
+      Xk = 0.0;
+      Xk.GetBlock(0).Set(1.0, xk.GetBlock(0));
+      Xk.GetBlock(1).Set(1.0, xk.GetBlock(1));
+      Xk.GetBlock(2).Set(1.0, lk);
+      Xk.GetBlock(3).Set(1.0, zlk);
+
+      // assign data stack, Xhat = (uhat, mhat, lhat, zlhat)
+      Xhat = 0.0;
+      for(int i = 0; i < 3; i++)
+      {
+         Xhat.GetBlock(i).Set(1.0, Xhatuml.GetBlock(i));
+      }
+      Xhat.GetBlock(3).Set(1.0, zlhat);
+
+      // A-5. Backtracking line search.
+      if(iAmRoot)
+      {
+         cout << "\n** A-5. Linesearch **\n";
+         cout << "mu = " << mu_k << endl;
+      }
+      lineSearch(Xk, Xhat, mu_k);
+
+      if(lineSearchSuccess)
+      {
+         if(iAmRoot)
+         {
+            cout << "lineSearch successful :)\n";
+         }
+         if(!switchCondition || !sufficientDecrease)
+         {
+            F1.Append( (1. - gTheta) * thx0);
+            F2.Append( phx0 - gPhi * thx0);
+         }
+         // ----- A-6: Accept the trial point
+         // print info regarding zl...
+         xk.GetBlock(0).Add(alpha, Xhat.GetBlock(0));
+         xk.GetBlock(1).Add(alpha, Xhat.GetBlock(1));
+         lk.Add(alpha,   Xhat.GetBlock(2));
+         zlk.Add(alphaz, Xhat.GetBlock(3));
+         projectZ(xk, zlk, mu_k);
+      }
+      else
+      {
+         if(iAmRoot)
+         {
+            cout << "lineSearch not successful :(\n";
+            cout << "attempting feasibility restoration with theta = " << thx0 << endl;
+            cout << "no feasibility restoration implemented, exiting now \n";
+         }
+         break;
+      }
+      if(jOpt + 1 == max_iter && iAmRoot) 
+      {  
+         cout << "maximum optimization iterations :(\n";
+      }
+   }
+   // done with optimization routine, just reassign data to xf reference so
+   // that the application code has access to the optimal point
+   xf = 0.0;
+   xf.GetBlock(0).Set(1.0, xk.GetBlock(0));
+   xf.GetBlock(1).Set(1.0, xk.GetBlock(1));
+}
+
+void ParInteriorPointSolver::FormIPNewtonMat(BlockVector & x, Vector & l, Vector &zl, BlockOperator &Ak)
+{
+   // WARNING: Huu, Hum, Hmu, Hmm should all be Hessian terms of the Lagrangian, currently we 
+   //          them by Hessian terms of the objective function and neglect the Hessian of l^T c
+
+   Huu = problem->Duuf(x); 
+   Hum = problem->Dumf(x);
+   Hmu = problem->Dmuf(x);
+   Hmm = problem->Dmmf(x);
+
+   Vector DiagLogBar(dimM); DiagLogBar = 0.0;
+   for(int ii = 0; ii < dimM; ii++)
+   {
+      DiagLogBar(ii) = zl(ii) / (x(ii+dimU) - ml(ii));
+   }
+   if(saveLogBarrierIterates)
+   {
+      std::ofstream diagStream;
+      char diagString[100];
+      snprintf(diagString, 100, "logBarrierHessiandata/D%d.dat", jOpt);
+      diagStream.open(diagString, ios::out | ios::trunc);
+      for(int ii = 0; ii < dimM; ii++)
+      {
+         diagStream << setprecision(30) << DiagLogBar(ii) << endl;
+      }
+      diagStream.close();
+   } 
+
+   SparseMatrix * Ds = new SparseMatrix(DiagLogBar);
+   ParFiniteElementSpace * fes = problem->GetfesM();
+   D = new HypreParMatrix(fes->GetComm(), fes->GlobalTrueVSize(), fes->GetTrueDofOffsets(), Ds);
+   HypreStealOwnership(*D,*Ds);
+   delete Ds;
+  
+   if(Hmm != nullptr)
+   {
+      Wmm = Hmm;
+      Wmm->Add(1.0, *D);
+   }
+   else
+   {
+      Wmm = D;
+   }
+
+   Ju = problem->Duc(x); JuT = Ju->Transpose();
+   Jm = problem->Dmc(x); JmT = Jm->Transpose();
+  
+   //         IP-Newton system matrix
+   //    Ak = [[H_(u,u)  H_(u,m)   J_u^T]
+   //          [H_(m,u)  W_(m,m)   J_m^T]
+   //          [ J_u      J_m       0  ]]
+
+   Ak.SetBlock(0, 0, Huu);                         Ak.SetBlock(0, 2, JuT);
+                           Ak.SetBlock(1, 1, Wmm); Ak.SetBlock(1, 2, JmT);
+   Ak.SetBlock(2, 0,  Ju); Ak.SetBlock(2, 1,  Jm);
+
+   if(Hum != nullptr) { Ak.SetBlock(0, 1, Hum); Ak.SetBlock(1, 0, Hmu); }
+}
+
+// perturbed KKT system solve
+// determine the search direction
+void ParInteriorPointSolver::IPNewtonSolve(BlockVector &x, Vector &l, Vector &zl, Vector &zlhat, BlockVector &Xhat, double mu, bool socSolve)
+{
+   // solve A x = b, where A is the IP-Newton matrix
+   BlockOperator A(block_offsetsuml, block_offsetsuml); BlockVector b(block_offsetsuml); b = 0.0;
+   FormIPNewtonMat(x, l, zl, A);
+
+   //       [grad_u phi + Ju^T l]
+   // b = - [grad_m phi + Jm^T l]
+   //       [          c        ]
+   BlockVector gradphi(block_offsetsx); gradphi = 0.0;
+   BlockVector JTl(block_offsetsx); JTl = 0.0;
+   Dxphi(x, mu, gradphi);
+   
+   (A.GetBlock(0,2)).Mult(l, JTl.GetBlock(0));
+   (A.GetBlock(1,2)).Mult(l, JTl.GetBlock(1));
+
+   for(int ii = 0; ii < 2; ii++)
+   {
+      b.GetBlock(ii).Set(1.0, gradphi.GetBlock(ii));
+      b.GetBlock(ii).Add(1.0, JTl.GetBlock(ii));
+   }
+   if(!socSolve) 
+   {
+      problem->c(x, b.GetBlock(2));
+   }
+   else
+   {
+      b.GetBlock(2).Set(1.0, ckSoc);
+   }
+   b *= -1.0; 
+   Xhat = 0.0;
+
+
+   // Direct solver (default)
+   if(linSolver == 0)
+   {
+      Array2D<HypreParMatrix *> ABlockMatrix(3,3);
+      for(int ii = 0; ii < 3; ii++)
+      {
+      for(int jj = 0; jj < 3; jj++)
+      {
+         if(!A.IsZeroBlock(ii, jj))
+         {
+            ABlockMatrix(ii, jj) = dynamic_cast<HypreParMatrix *>(&(A.GetBlock(ii, jj)));
+	 }
+	 else
+	 {
+	    ABlockMatrix(ii, jj) = nullptr;
+	 }
+      }
+      }
+      
+      HypreParMatrix * Ah = HypreParMatrixFromBlocks(ABlockMatrix);   
+      
+      /* direct solve of the 3x3 IP-Newton linear system */
+      #ifdef MFEM_USE_MUMPS
+        MUMPSSolver ASolver;
+        ASolver.SetPrintLevel(0);
+        ASolver.SetMatrixSymType(MUMPSSolver::MatType::SYMMETRIC_INDEFINITE);
+        ASolver.SetOperator(*Ah);
+        ASolver.Mult(b, Xhat);
+      #else 
+        #ifdef MFEM_USE_MKL_CPARDISO
+          CPardisoSolver ASolver(MPI_COMM_WORLD);
+          ASolver.SetOperator(*Ah);
+          ASolver.Mult(b, Xhat);
+	#else
+	  MFEM_VERIFY(false, "linSolver 0 will not work unless compiled with MUMPS or MKL");
+        #endif
+      #endif
+
+      delete Ah;
+   }
+   else if(linSolver == 1 || linSolver == 2)
+   {
+      // form A = Huu + Ju^T D Ju, Wmm = D for contact
+      HypreParMatrix * Huuloc = dynamic_cast<HypreParMatrix *>(&(A.GetBlock(0, 0)));
+      HypreParMatrix * Wmmloc = dynamic_cast<HypreParMatrix *>(&(A.GetBlock(1, 1)));
+      HypreParMatrix * Juloc  = dynamic_cast<HypreParMatrix *>(&(A.GetBlock(2, 0)));
+      HypreParMatrix * JuTloc = dynamic_cast<HypreParMatrix *>(&(A.GetBlock(0, 2)));
+      
+      
+      HypreParMatrix *JuTDJu   = RAP(Wmmloc, Juloc);     // Ju^T D Ju
+      HypreParMatrix *Areduced = ParAdd(Huuloc, JuTDJu);  // Huu + Ju^T D Ju
+      /* prepare the reduced rhs */
+      // breduced = bu + Ju^T (bm + Wmm bl)
+      Vector breduced(dimU); breduced = 0.0;
+      Vector tempVec(dimM); tempVec = 0.0;
+      Wmmloc->Mult(b.GetBlock(2), tempVec);
+      tempVec.Add(1.0, b.GetBlock(1));
+      JuTloc->Mult(tempVec, breduced);
+      breduced.Add(1.0, b.GetBlock(0));
+      
+      if(linSolver == 1)
+      {
+         // setup the solver for the reduced linear system
+         #ifdef MFEM_USE_MUMPS
+	   MUMPSSolver AreducedSolver;   
+           AreducedSolver.SetPrintLevel(0);
+           AreducedSolver.SetMatrixSymType(MUMPSSolver::MatType::SYMMETRIC_INDEFINITE);
+	   AreducedSolver.SetOperator(*Areduced);
+	   AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+         #else 
+           #ifdef MFEM_USE_MKL_CPARDISO
+	     CPardisoSolver AreducedSolver(MPI_COMM_WORLD);
+	     AreducedSolver.SetOperator(*Areduced);
+	     AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+           #else
+	     MFEM_VERIFY(false, "linSolver 1 will not work unless compiled with MUMPS or MKL");
+           #endif
+         #endif
+      }
+      else
+      {
+         HyprePCG AreducedSolver(MPI_COMM_WORLD);
+	 AreducedSolver.SetOperator(*Areduced);
+	 HypreBoomerAMG AreducedPrec;
+         AreducedSolver.SetTol(linSolveTol);
+         AreducedSolver.SetMaxIter(500);
+         AreducedSolver.SetPreconditioner(AreducedPrec);
+         AreducedSolver.SetResidualConvergenceOptions(); // convergence criteria based on residual norm
+	 AreducedSolver.SetPrintLevel(2);
+         AreducedSolver.Mult(breduced, Xhat.GetBlock(0));
+      }
+
+      // now propagate solved uhat to obtain mhat and lhat
+      // xm = Ju xu - bl
+      Juloc->Mult(Xhat.GetBlock(0), Xhat.GetBlock(1));
+      Xhat.GetBlock(1).Add(-1.0, b.GetBlock(2));
+
+      // xl = Wmm xm - bm
+      Wmmloc->Mult(Xhat.GetBlock(1), Xhat.GetBlock(2));
+      Xhat.GetBlock(2).Add(-1.0, b.GetBlock(1));
+
+      delete JuTDJu;
+      delete Areduced;
+   }
+
+   /* backsolve to determine zlhat */
+   for(int ii = 0; ii < dimM; ii++)
+   {
+      zlhat(ii) = -1.*(zl(ii) + (zl(ii) * Xhat(ii + dimU) - mu) / (x(ii + dimU) - ml(ii)) );
+   }
+
+   // free memory
+   delete D;
+   delete JuT;
+   delete JmT;
+   if(Hmm != nullptr)
+   {
+      delete Wmm;
+   }
+}
+
+// here Xhat, X will be BlockVectors w.r.t. the 4 partitioning X = (u, m, l, zl)
+
+void ParInteriorPointSolver::lineSearch(BlockVector& X0, BlockVector& Xhat, double mu)
+{
+   double tau  = max(tauMin, 1.0 - mu);
+   Vector u0   = X0.GetBlock(0);
+   Vector m0   = X0.GetBlock(1);
+   Vector l0   = X0.GetBlock(2);
+   Vector z0   = X0.GetBlock(3);
+   Vector uhat = Xhat.GetBlock(0);
+   Vector mhat = Xhat.GetBlock(1);
+   Vector lhat = Xhat.GetBlock(2);
+   Vector zhat = Xhat.GetBlock(3);
+   double alphaMax  = MaxStepSize(m0, ml, mhat, tau);
+   double alphaMaxz = MaxStepSize(z0, zhat, tau);
+   alphaz = alphaMaxz;
+
+   BlockVector x0(block_offsetsx); x0 = 0.0;
+   x0.GetBlock(0).Set(1.0, u0);
+   x0.GetBlock(1).Set(1.0, m0);
+   
+   BlockVector xhat(block_offsetsx); xhat = 0.0;
+   xhat.GetBlock(0).Set(1.0, uhat);
+   xhat.GetBlock(1).Set(1.0, mhat);
+   
+   BlockVector xtrial(block_offsetsx); xtrial = 0.0;
+   BlockVector Dxphi0(block_offsetsx); Dxphi0 = 0.0;
+   int maxBacktrack = 20;
+   alpha = alphaMax;
+
+   Vector ck0(dimC); ck0 = 0.0;
+   Vector zhatsoc(dimM); zhatsoc = 0.0;
+   BlockVector Xhatumlsoc(block_offsetsuml); Xhatumlsoc = 0.0;
+   BlockVector xhatsoc(block_offsetsx); xhatsoc = 0.0;
+   Vector uhatsoc(dimU); uhatsoc = 0.0;
+   Vector mhatsoc(dimM); mhatsoc = 0.0;
+
+   Dxphi(x0, mu, Dxphi0);
+
+   Dxphi0_xhat = InnerProduct(MPI_COMM_WORLD, Dxphi0, xhat);
+   descentDirection = Dxphi0_xhat < 0. ? true : false;
+   if(descentDirection)
+   {
+      if (iAmRoot)
+      {
+         cout << "is a descent direction for the log-barrier objective\n";
+      }
+   }
+   else
+   {
+      cout << "is not a descent direction for the log-barrier objective\n";
+   }
+   thx0 = theta(x0);
+   phx0 = phi(x0, mu);
+
+   lineSearchSuccess = false;
+   for(int i = 0; i < maxBacktrack; i++)
+   {
+      if (iAmRoot)
+      {
+         cout << "\n--------- alpha = " << alpha << " ---------\n";
+      }
+      // ----- A-5.2. Compute trial point: xtrial = x0 + alpha_i xhat
+      xtrial.Set(1.0, x0);
+      xtrial.Add(alpha, xhat);
+
+      // ------ A-5.3. if not in filter region go to A.5.4 otherwise go to A-5.5.
+      thxtrial = theta(xtrial);
+      phxtrial = phi(xtrial, mu);
+      filterCheck(thxtrial, phxtrial);    
+      if(!inFilterRegion)
+      {
+         if (iAmRoot)
+         {
+            cout << "not in filter region :)\n";
+         }
+         // ------ A.5.4: Check sufficient decrease
+         if(!descentDirection)
+         {
+            switchCondition = false;
+         }
+         else
+         {
+            switchCondition = (alpha * pow(abs(Dxphi0_xhat), sPhi) > delta * pow(thx0, sTheta)) ? true : false;
+         }
+         if (iAmRoot)
+         {
+            cout << "theta(x0) = "     << thx0     << ", thetaMin = "                  << thetaMin             << endl;
+            cout << "theta(xtrial) = " << thxtrial << ", (1-gTheta) *theta(x0) = "     << (1. - gTheta) * thx0 << endl;
+            cout << "phi(xtrial) = "   << phxtrial << ", phi(x0) - gPhi *theta(x0) = " << phx0 - gPhi * thx0   << endl;
+         }      
+         // Case I      
+         if(thx0 <= thetaMin && switchCondition)
+         {
+            sufficientDecrease = (phxtrial <= phx0 + eta * alpha * Dxphi0_xhat) ? true : false;
+            if(sufficientDecrease)
+            {
+               if(iAmRoot) { cout << "Line search successful: sufficient decrease in log-barrier objective.\n"; } 
+               // accept the trial step
+               lineSearchSuccess = true;
+               break;
+            }
+         }
+         else
+         {
+            if(thxtrial <= (1. - gTheta) * thx0 || phxtrial <= phx0 - gPhi * thx0)
+            {
+               if(iAmRoot) { cout << "Line search successful: infeasibility or log-barrier objective decreased.\n"; } 
+               // accept the trial step
+               lineSearchSuccess = true;
+               break;
+            }
+         }
+         // A-5.5: Initialize the second-order correction
+         if((!(thx0 < thxtrial)) && i == 0)
+         {
+            if (iAmRoot)
+            {
+               cout << "second order correction\n";
+            }
+            problem->c(xtrial, ckSoc);
+            problem->c(x0, ck0);
+            ckSoc.Add(alphaMax, ck0);
+            // A-5.6 Compute the second-order correction.
+            IPNewtonSolve(x0, l0, z0, zhatsoc, Xhatumlsoc, mu, true);
+            mhatsoc.Set(1.0, Xhatumlsoc.GetBlock(1));
+            //WARNING: not complete but currently solver isn't entering this region
+         }
+      }
+      else
+      {
+         if (iAmRoot)
+         {
+            cout << "in filter region :(\n"; 
+         }
+      }
+      // include more if needed
+      alpha *= 0.5;
+
+   } 
+}
+
+
+void ParInteriorPointSolver::projectZ(const Vector &x, Vector &z, double mu)
+{
+   double zi;
+   double mudivmml;
+   for(int i = 0; i < dimM; i++)
+   {
+      zi = z(i);
+      mudivmml = mu / (x(i + dimU) - ml(i));
+      z(i) = max(min(zi, kSig * mudivmml), mudivmml / kSig);
+   }
+}
+
+void ParInteriorPointSolver::filterCheck(double th, double ph)
+{
+   inFilterRegion = false;
+   if(th > thetaMax)
+   {
+      inFilterRegion = true;
+   }
+   else
+   {
+      for(int i = 0; i < F1.Size(); i++)
+      {
+         if(th >= F1[i] && ph >= F2[i])
+         {
+            inFilterRegion = true;
+            break;
+         }
+      }
+   }
+}
+
+double ParInteriorPointSolver::E(const BlockVector &x, const Vector &l, const Vector &zl, double mu, bool printEeval)
+{
+   double E1, E2, E3;
+   double sc, sd;
+   BlockVector gradL(block_offsetsx); gradL = 0.0; // stationarity grad L = grad f + J^T l - z
+   Vector cx(dimC); cx = 0.0;     // feasibility c = c(x)
+   Vector comp(dimM); comp = 0.0; // complementarity M Z - mu 1
+
+   DxL(x, l, zl, gradL);
+   E1 = GlobalLpNorm(infinity(), gradL.Normlinf(), MPI_COMM_WORLD); 
+
+   problem->c(x, cx);
+   E2 = GlobalLpNorm(infinity(), cx.Normlinf(), MPI_COMM_WORLD); 
+
+
+   for(int ii = 0; ii < dimM; ii++) 
+   { 
+      comp(ii) = x(dimU + ii) * zl(ii) - mu;
+   }
+   E3 = GlobalLpNorm(infinity(), comp.Normlinf(), MPI_COMM_WORLD); 
+
+   double ll1, zl1;
+
+   zl1 = GlobalLpNorm(1, zl.Norml1(), MPI_COMM_WORLD)/ double(dimCglb + dimMglb); 
+   ll1 = GlobalLpNorm(1, l.Norml1(), MPI_COMM_WORLD);
+   sc = max(sMax, zl1 / (double(dimMglb)) ) / sMax;
+   sd = max(sMax, (ll1 + zl1) / (double(dimCglb + dimMglb))) / sMax;
+   if(iAmRoot && printEeval)
+   {
+      cout << "evaluating optimality error for mu = " << mu << endl;
+      cout << "stationarity measure = "    << E1 / sd << endl;
+      cout << "feasibility measure  = "    << E2      << endl;
+      cout << "complimentarity measure = " << E3 / sc << endl;
+   }
+   return max(max(E1 / sd, E2), E3 / sc);
+}
+
+double ParInteriorPointSolver::E(const BlockVector &x, const Vector &l, const Vector &zl, bool printEeval)
+{
+  return E(x, l, zl, 0.0, printEeval);
+}
+
+double ParInteriorPointSolver::theta(const BlockVector &x)
+{
+  Vector cx(dimC); cx = 0.0;
+  problem->c(x, cx);
+  return sqrt(InnerProduct(MPI_COMM_WORLD,cx, cx));
+}
+
+// log-barrier objective
+double ParInteriorPointSolver::phi(const BlockVector &x, double mu)
+{
+   double fx = problem->CalcObjective(x); 
+   double logBarrierLoc = 0.0;
+   for(int i = 0; i < dimM; i++) 
+   { 
+     logBarrierLoc += log(x(dimU+i)-ml(i));
+   }
+   double logBarrierGlb;
+   MPI_Allreduce(&logBarrierLoc, &logBarrierGlb, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+   return fx - mu * logBarrierGlb;
+}
+
+// gradient of log-barrier objective with respect to x = (u, m)
+void ParInteriorPointSolver::Dxphi(const BlockVector &x, double mu, BlockVector &y)
+{
+   problem->CalcObjectiveGrad(x, y);
+   
+   for(int i = 0; i < dimM; i++) 
+   { 
+      y(dimU + i) -= mu / (x(dimU + i));
+   } 
+}
+
+// Lagrangian function evaluation
+// L(x, l, zl) = f(x) + l^T c(x) - zl^T m
+double ParInteriorPointSolver::L(const BlockVector &x, const Vector &l, const Vector &zl)
+{
+   double fx = problem->CalcObjective(x);
+   Vector cx(dimC); problem->c(x, cx);
+   return (fx + InnerProduct(MPI_COMM_WORLD,cx, l) - InnerProduct(MPI_COMM_WORLD, x.GetBlock(1), zl));
+}
+
+void ParInteriorPointSolver::DxL(const BlockVector &x, const Vector &l, const Vector &zl, BlockVector &y)
+{
+   // evaluate the gradient of the objective with respect to the primal variables x = (u, m)
+   BlockVector gradxf(block_offsetsx); gradxf = 0.0;
+   problem->CalcObjectiveGrad(x, gradxf);
+   
+   HypreParMatrix *Jacu, *Jacm, *JacuT, *JacmT;
+   Jacu = problem->Duc(x); 
+   Jacm = problem->Dmc(x);
+   JacuT = Jacu->Transpose();
+   JacmT = Jacm->Transpose();
+   
+   JacuT->Mult(l, y.GetBlock(0));
+   JacmT->Mult(l, y.GetBlock(1));
+   
+   delete JacuT;
+   delete JacmT;
+   
+   y.Add(1.0, gradxf);
+   (y.GetBlock(1)).Add(-1.0, zl);
+}
+
+bool ParInteriorPointSolver::GetConverged() const
+{
+   return converged;
+}
+
+void ParInteriorPointSolver::SetTol(double Tol)
+{
+   OptTol = Tol;
+}
+
+void ParInteriorPointSolver::SetMaxIter(int max_it)
+{
+   max_iter = max_it;
+}
+
+void ParInteriorPointSolver::SetBarrierParameter(double mu_0)
+{
+   mu_k = mu_0;
+}
+
+void ParInteriorPointSolver::SaveLogBarrierHessianIterates(bool save)
+{
+   MFEM_ASSERT(MyRank == 0 || save == false, "currently can only save logbarrier hessian in serial codes");
+   saveLogBarrierIterates = save;
+}
+
+void ParInteriorPointSolver::SetLinearSolver(int LinSolver)
+{
+   linSolver = LinSolver;
+}
+
+void ParInteriorPointSolver::SetLinearSolveTol(double Tol)
+{
+  linSolveTol = Tol;
+}
+
+
+ParInteriorPointSolver::~ParInteriorPointSolver() 
+{
+   F1.DeleteAll();
+   F2.DeleteAll();
+   block_offsetsx.DeleteAll();
+   block_offsetsumlz.DeleteAll();
+   block_offsetsuml.DeleteAll();
+   ml.SetSize(0);
+}

examples/contact/ParIPsolver.hpp

@@ -0,0 +1,82 @@
+#include "mfem.hpp"
+#include "ParProblems.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+
+#ifndef PARIPSOLVER 
+#define PARIPSOLVER
+
+class ParInteriorPointSolver
+{
+protected:
+    ParGeneralOptProblem* problem;
+    double OptTol;
+    int  max_iter;
+    double mu_k; // \mu_k
+    Vector lk, zlk;
+
+    double sMax, kSig, tauMin, eta, thetaMin, delta, sTheta, sPhi, kMu, thetaMu;
+    double thetaMax, kSoc, gTheta, gPhi, kEps;
+	
+    // filter
+    Array<double> F1, F2;
+	
+    // quantities computed in lineSearch
+    double alpha, alphaz;
+    double thx0, thxtrial;
+    double phx0, phxtrial;
+    bool descentDirection, switchCondition, sufficientDecrease, lineSearchSuccess, inFilterRegion;
+    double Dxphi0_xhat;
+
+    int dimU, dimM, dimC;
+    int dimUglb, dimMglb, dimCglb;
+    Array<int> block_offsetsumlz, block_offsetsuml, block_offsetsx;
+    Vector ml;
+
+    Vector ckSoc;
+    HypreParMatrix * Huu, * Hum, * Hmu, * Hmm, * Wmm, *D, * Ju, * Jm, * JuT, * JmT;
+    
+    int jOpt;
+    bool converged;
+    
+    int MyRank;
+    bool iAmRoot;
+
+    bool saveLogBarrierIterates;
+
+    int linSolver;
+    double linSolveTol;
+public:
+    ParInteriorPointSolver(ParGeneralOptProblem*);
+    double MaxStepSize(Vector& , Vector& , Vector& , double);
+    double MaxStepSize(Vector& , Vector& , double);
+    void Mult(const BlockVector& , BlockVector&);
+    void Mult(const Vector&, Vector &); 
+    void FormIPNewtonMat(BlockVector& , Vector& , Vector& , BlockOperator &);
+    void IPNewtonSolve(BlockVector& , Vector& , Vector& , Vector&, BlockVector& , double, bool);
+    void lineSearch(BlockVector& , BlockVector& , double);
+    void projectZ(const Vector & , Vector &, double);
+    void filterCheck(double, double);
+    double E(const BlockVector &, const Vector &, const Vector &, double, bool);
+    double E(const BlockVector &, const Vector &, const Vector &, bool);
+    bool GetConverged() const;
+    // TO DO: include Hessian of Lagrangian
+    double theta(const BlockVector &);
+    double phi(const BlockVector &, double);
+    void Dxphi(const BlockVector &, double, BlockVector &);
+    double L(const BlockVector &, const Vector &, const Vector &);
+    void DxL(const BlockVector &, const Vector &, const Vector &, BlockVector &);
+    void SetTol(double);
+    void SetMaxIter(int);
+    void SetBarrierParameter(double);    
+    void SaveLogBarrierHessianIterates(bool);
+    void SetLinearSolver(int);
+    void SetLinearSolveTol(double);
+    virtual ~ParInteriorPointSolver();
+};
+
+#endif

examples/contact/ParObstacleProblem.cpp

@@ -0,0 +1,129 @@
+//                         Obstacle Problem
+//
+//
+// Compile with: make ParObstacleProblem
+//
+// Sample runs: mpirun -np 4 ./ParObstacleProblem
+//
+//
+// Description: This example code demonstrates the use of MFEM to solve the
+//              bound-constrained energy minimization problem
+//
+//                      minimize (||∇u||² + ||u||²) subject to u ≥ ϕ in H¹.
+
+#include "mfem.hpp"
+#include "ParProblems.hpp"
+#include "ParIPsolver.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+double dmanufacturedFun(const Vector &);
+double fRhs(const Vector &);
+
+int main(int argc, char *argv[])
+{
+  // Initialize MPI
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   int FEorder = 1; // order of the finite elements
+   int linSolver = 2;
+   int maxIPMiters = 30;
+   int ref_levels = 3;
+   OptionsParser args(argc, argv);
+   args.AddOption(&FEorder, "-o", "--order",\
+	 	  "Order of the finite elements.");
+   args.AddOption(&linSolver, "-linSolver", "--linearSolver", \
+        "IP-Newton linear system solution strategy.");
+   args.AddOption(&maxIPMiters, "-IPMiters", "--IPMiters",\
+	 	  "Maximum number of IPM iterations");
+   args.AddOption(&ref_levels, "-r", "--mesh_refinement", \
+		  "Mesh Refinement");
+  
+   args.Parse();
+   if(!args.Good())
+   {
+     args.PrintUsage(cout);
+     return 1;
+   }
+   else
+   {
+     if(Mpi::Root())
+     {  
+       args.PrintOptions(cout);
+     }
+   }
+
+   const char *meshFile = "../../data/inline-quad.mesh";
+   Mesh mesh(meshFile, 1, 1);
+   int dim = mesh.Dimension(); // geometric dimension of the meshed domain
+   {
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh.UniformRefinement();
+      }
+   }
+
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+
+   FiniteElementCollection *fec = new H1_FECollection(FEorder, dim);
+   ParFiniteElementSpace   *Vh  = new ParFiniteElementSpace(&pmesh, fec);
+
+   ParObstacleProblem problem(Vh,Vh,&fRhs);
+  
+   int dimD = problem.GetDimD();
+   Vector x0(dimD); x0 = 100.0;
+   Vector xf(dimD); xf = 0.0;
+
+   ParInteriorPointSolver optimizer(&problem); 
+   optimizer.SetTol(1.e-8);
+   optimizer.SetLinearSolveTol(1.e-10);
+   optimizer.SetLinearSolver(linSolver);
+   optimizer.SetMaxIter(maxIPMiters);
+   optimizer.Mult(x0, xf);
+
+   ParGridFunction d_gf(Vh);
+
+   d_gf.SetFromTrueDofs(xf);
+
+
+   FunctionCoefficient dm_fc(dmanufacturedFun); // manufactured solution
+   ParGridFunction dm_gf(Vh);
+   dm_gf.ProjectCoefficient(dm_fc);
+
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream exact_sock(vishost, visport);
+   exact_sock.precision(8);
+   exact_sock << "parallel " << num_procs << " " << myid << "\n";
+   exact_sock << "solution\n" << pmesh << dm_gf
+              << "window_title 'Manufactured solution'" << flush;
+
+   socketstream sol_sock(vishost, visport);
+   sol_sock.precision(8);
+   sol_sock << "parallel " << num_procs << " " << myid << "\n";
+   sol_sock << "solution\n" << pmesh << d_gf 
+            << "window_title 'Numerical solution'" << flush;
+
+   delete Vh;
+   delete fec;
+   return 0;
+}
+
+
+double dmanufacturedFun(const Vector &x)
+{
+  return cos(2*M_PI*x(0)) + 0.2 - 2.0*(pow(x(0),3) - 1.5*pow(x(0),2));
+}
+
+double fRhs(const Vector &x)
+{
+  double fx = 0.;
+  fx = 0.2 - 2.0 * (pow(x(0),3)- 1.5*pow(x(0),2.) - 6 * x(0) + 3.) + (1. + pow(2.*M_PI,2))*cos(2.*M_PI*x(0));
+  return fx;
+}

examples/contact/ParProblems.cpp

@@ -0,0 +1,212 @@
+#include "mfem.hpp"
+#include "ParProblems.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+ParGeneralOptProblem::ParGeneralOptProblem(ParFiniteElementSpace * fesU_, ParFiniteElementSpace * fesM_) 
+: fesU(fesU_), fesM(fesM_) 
+{ 
+   dimU = fesU->GetTrueVSize();
+   dimM = fesM->GetTrueVSize();
+   dimC = fesM->GetTrueVSize();
+}
+
+void ParGeneralOptProblem::CalcObjectiveGrad(const BlockVector &x, BlockVector &y) const
+{
+   Duf(x, y.GetBlock(0));
+   Dmf(x, y.GetBlock(1));
+}
+
+ParGeneralOptProblem::~ParGeneralOptProblem()
+{
+   block_offsetsx.DeleteAll();
+}
+
+
+// min E(d) s.t. g(d) >= 0
+// min_(d,s) E(d) s.t. c(d,s) := g(d) - s = 0, s >= 0
+ParOptProblem::ParOptProblem(ParFiniteElementSpace * fesU_, 
+                                     ParFiniteElementSpace * fesM_)
+ : ParGeneralOptProblem(fesU_, fesM_), block_offsetsx(3)
+{
+   block_offsetsx[0] = 0;
+   block_offsetsx[1] = dimU;
+   block_offsetsx[2] = dimM;
+   block_offsetsx.PartialSum();
+   ml.SetSize(dimM); ml = 0.0;
+   Vector negIdentDiag(dimM);
+   negIdentDiag = -1.0;
+   SparseMatrix * diag = new SparseMatrix(negIdentDiag);
+   Ih = new HypreParMatrix(fesM->GetComm(), fesM->GlobalTrueVSize(),
+                                             fesM->GetTrueDofOffsets(), diag);
+   HypreStealOwnership(*Ih, *diag);
+   delete diag;
+}
+
+double ParOptProblem::CalcObjective(const BlockVector &x) const { return E(x.GetBlock(0)); }
+
+void ParOptProblem::Duf(const BlockVector &x, Vector &y) const { DdE(x.GetBlock(0), y); }
+
+void ParOptProblem::Dmf(const BlockVector &x, Vector &y) const { y = 0.0; }
+
+HypreParMatrix * ParOptProblem::Duuf(const BlockVector &x) 
+{ 
+   return DddE(x.GetBlock(0)); 
+}
+
+HypreParMatrix * ParOptProblem::Dumf(const BlockVector &x) { return nullptr; }
+
+HypreParMatrix * ParOptProblem::Dmuf(const BlockVector &x) { return nullptr; }
+
+HypreParMatrix * ParOptProblem::Dmmf(const BlockVector &x) { return nullptr; }
+
+void ParOptProblem::c(const BlockVector &x, Vector &y) const // c(u,m) = g(u) - m 
+{
+   g(x.GetBlock(0), y);
+   y.Add(-1.0, x.GetBlock(1));  
+}
+
+HypreParMatrix * ParOptProblem::Duc(const BlockVector &x) 
+{ 
+   return Ddg(x.GetBlock(0)); 
+}
+
+HypreParMatrix * ParOptProblem::Dmc(const BlockVector &x) 
+{ 
+   return Ih;
+} 
+
+ParOptProblem::~ParOptProblem() 
+{
+   delete Ih;
+}
+
+
+// Obstacle Problem, no essential boundary conditions enforced
+// Hessian of energy term is K + M (stiffness + mass)
+ParObstacleProblem::ParObstacleProblem(ParFiniteElementSpace *fesU_, 
+                                       ParFiniteElementSpace *fesM_, 
+                                       double (*fSource)(const Vector &)) : 
+                                       ParOptProblem(fesU_,fesM_), f(dimU), psi(dimU), J(nullptr)
+{
+   Kform = new ParBilinearForm(fesU);
+   Kform->AddDomainIntegrator(new MassIntegrator);
+   Kform->AddDomainIntegrator(new DiffusionIntegrator);
+   Kform->Assemble();
+   Kform->Finalize();
+   Kform->FormSystemMatrix(ess_tdof_list, K);
+
+   FunctionCoefficient fcoeff(fSource);
+   fform = new ParLinearForm(fesU);
+   fform->AddDomainIntegrator(new DomainLFIntegrator(fcoeff));
+   fform->Assemble();
+   Vector F(dimU);
+   fform->ParallelAssemble(F);
+   f.SetSize(dimU);
+   f.Set(1.0, F);
+
+   psi = 0.0;
+   
+   Vector iDiag(dimU); iDiag = 1.0;
+   SparseMatrix * Jacg = new SparseMatrix(iDiag);
+   
+   J = new HypreParMatrix(fesU->GetComm(),fesU->GlobalTrueVSize(),fesU->GetTrueDofOffsets(),Jacg);
+   HypreStealOwnership(*J, *Jacg);
+   delete Jacg;
+}
+
+// Obstacle Problem, essential boundary conditions enforced
+// Hessian of energy term is K (stiffness)
+ParObstacleProblem::ParObstacleProblem(ParFiniteElementSpace *fesU_, 
+                                       ParFiniteElementSpace *fesM_, 
+				       double (*fSource)(const Vector &),
+				       double (*obstacleSource)(const Vector &),
+				       Array<int> tdof_list, Vector &xDC) : ParOptProblem(fesU_,fesM_), f(dimU), psi(dimU), J(nullptr)
+{
+   // elastic energy functional terms	
+   ess_tdof_list = tdof_list;
+   Kform = new ParBilinearForm(fesU);
+   Kform->AddDomainIntegrator(new DiffusionIntegrator);
+   Kform->Assemble();
+   Kform->Finalize();
+   Kform->FormSystemMatrix(ess_tdof_list, K);
+
+   FunctionCoefficient fcoeff(fSource);
+   fform = new ParLinearForm(fesU);
+   fform->AddDomainIntegrator(new DomainLFIntegrator(fcoeff));
+   fform->Assemble();
+   Vector F(dimU);
+   fform->ParallelAssemble(F);
+   f.SetSize(dimU);
+   f.Set(1.0, F);
+   Kform->EliminateVDofsInRHS(ess_tdof_list, xDC, f);
+   
+   // obstacle constraints --  
+   Vector iDiag(dimU); iDiag = 1.0;
+   for(int i = 0; i < ess_tdof_list.Size(); i++)
+   {
+     iDiag(ess_tdof_list[i]) = 0.0;
+   }
+   SparseMatrix * Jacg = new SparseMatrix(iDiag);
+
+   J = new HypreParMatrix(fesU->GetComm(),fesU->GlobalTrueVSize(),fesU->GetTrueDofOffsets(),Jacg);
+   HypreStealOwnership(*J, *Jacg);
+   delete Jacg;
+
+   FunctionCoefficient psi_fc(obstacleSource);
+   ParGridFunction psi_gf(fesU);
+   psi_gf.ProjectCoefficient(psi_fc);
+   psi.Set(1.0, (*psi_gf.GetTrueDofs()));
+   for(int i = 0; i < ess_tdof_list.Size(); i++)
+   {
+     psi(ess_tdof_list[i]) -= 1.e-8;
+   }
+}
+
+
+
+double ParObstacleProblem::E(const Vector &d) const
+{
+   Vector Kd(K.Height()); Kd = 0.0;
+   MFEM_VERIFY(d.Size() == K.Width(), "ParObstacleProblem::E - Inconsistent dimensions");
+   K.Mult(d, Kd);
+   return 0.5 * InnerProduct(MPI_COMM_WORLD, d, Kd) - InnerProduct(MPI_COMM_WORLD, f, d);
+}
+
+void ParObstacleProblem::DdE(const Vector &d, Vector &gradE) const
+{
+   gradE.SetSize(K.Height());
+   MFEM_VERIFY(d.Size() == K.Width(), "ParObstacleProblem::DdE - Inconsistent dimensions");
+   K.Mult(d, gradE);
+   MFEM_VERIFY(f.Size() == K.Height(), "ParObstacleProblem::DdE - Inconsistent dimensions");
+   gradE.Add(-1.0, f);
+}
+
+HypreParMatrix * ParObstacleProblem::DddE(const Vector &d)
+{
+   return &K; 
+}
+
+// g(d) = d >= \psi
+void ParObstacleProblem::g(const Vector &d, Vector &gd) const
+{
+   MFEM_VERIFY(d.Size() == J->Width(), "ParObstacleProblem::g - Inconsistent dimensions");
+   J->Mult(d, gd);
+   MFEM_VERIFY(gd.Size() == J->Height(), "ParObstacleProblem::g - Inconsistent dimensions");
+   gd.Add(-1.0, psi);
+}
+
+HypreParMatrix * ParObstacleProblem::Ddg(const Vector &d)
+{
+   return J;
+}
+
+ParObstacleProblem::~ParObstacleProblem()
+{
+   delete Kform;
+   delete fform;
+   delete J;
+}

examples/contact/ParProblems.hpp

@@ -0,0 +1,107 @@
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+#ifndef PARPROBLEM_DEFS
+#define PARPROBLEM_DEFS
+
+// abstract ParGeneralOptProblem class
+// of the form
+// min_(u,m) f(u,m) s.t. c(u,m)=0 and m>=ml
+// the primal variable (u, m) is represented as a BlockVector
+// think about supporting general lower and upper bounds (see HiOP user manual) 
+
+class ParGeneralOptProblem
+{
+protected:
+    int dimU, dimM, dimC;
+    ParFiniteElementSpace * fesU = nullptr;
+    ParFiniteElementSpace * fesM = nullptr;
+    Array<int> block_offsetsx;
+    Vector ml;
+public:
+    ParGeneralOptProblem(ParFiniteElementSpace * fesU_, ParFiniteElementSpace * fesM_); // constructor
+    virtual double CalcObjective(const BlockVector &) const = 0;
+    virtual void Duf(const BlockVector &, Vector &) const = 0;
+    virtual void Dmf(const BlockVector &, Vector &) const = 0;
+    void CalcObjectiveGrad(const BlockVector &, BlockVector &) const;
+    virtual HypreParMatrix * Duuf(const BlockVector &) = 0;
+    virtual HypreParMatrix * Dumf(const BlockVector &) = 0;
+    virtual HypreParMatrix * Dmuf(const BlockVector &) = 0;
+    virtual HypreParMatrix * Dmmf(const BlockVector &) = 0;
+    virtual HypreParMatrix * Duc(const BlockVector &) = 0;
+    virtual HypreParMatrix * Dmc(const BlockVector &) = 0;
+    // TO DO: include Hessian terms of constraint c
+    virtual void c(const BlockVector &, Vector &) const = 0;
+    int GetDimU() const { return dimU; };
+    int GetDimM() const { return dimM; }; 
+    int GetDimC() const { return dimC; };
+    ParFiniteElementSpace * GetfesU() {return fesU;}
+    ParFiniteElementSpace * GetfesM() {return fesM;}
+    Vector Getml() const { return ml; };
+    ~ParGeneralOptProblem(); // destructor
+};
+
+
+// abstract ContactProblem class
+// of the form
+// min_d e(d) s.t. g(d) >= 0
+class ParOptProblem : public ParGeneralOptProblem
+{
+protected:
+    Array<int> block_offsetsx;
+    HypreParMatrix * Ih;
+public:
+    ParOptProblem(ParFiniteElementSpace * fesU_, ParFiniteElementSpace * fesM_);        // constructor
+    double CalcObjective(const BlockVector &) const; // objective e
+    void Duf(const BlockVector &, Vector &) const;
+    void Dmf(const BlockVector &, Vector &) const;
+
+    HypreParMatrix * Duuf(const BlockVector &);
+    HypreParMatrix * Dumf(const BlockVector &);
+    HypreParMatrix * Dmuf(const BlockVector &);
+    HypreParMatrix * Dmmf(const BlockVector &);
+    HypreParMatrix * Duc(const BlockVector &);
+    HypreParMatrix * Dmc(const BlockVector &);
+
+    void c(const BlockVector &, Vector &) const;
+    virtual double E(const Vector &) const = 0;               // objective e(d) (energy function)
+    virtual void DdE(const Vector &, Vector &) const = 0;      // gradient of objective De / Dd
+    virtual HypreParMatrix * DddE(const Vector &) = 0;
+    // Hessian of objective D^2 e / D d^2
+    virtual HypreParMatrix * Ddg(const Vector &) = 0;
+    // Jacobian of inequality constraint Dg / Dd
+    virtual void g(const Vector &, Vector &) const = 0;       // inequality constraint g(d) >= 0 (gap function)
+    int GetDimD() const { return fesU->GetTrueVSize(); };
+    int GetDimS() const { return fesM->GetTrueVSize(); };
+    virtual ~ParOptProblem();
+};
+
+class ParObstacleProblem : public ParOptProblem
+{
+protected:
+   // data to define energy objective function e(d) = 0.5 d^T K d - f^T d, g(d) = d >= \psi
+   // stiffness matrix used to define objective
+   ParBilinearForm *Kform;
+   ParLinearForm   *fform;
+   Array<int> ess_tdof_list; // needed for calls to FormSystemMatrix
+   HypreParMatrix  K;
+   HypreParMatrix  *J;
+   ParFiniteElementSpace *Vh;
+   Vector f;
+   Vector psi;
+public :
+   ParObstacleProblem(ParFiniteElementSpace*, ParFiniteElementSpace*, double (*fSource)(const Vector &));
+   ParObstacleProblem(ParFiniteElementSpace*, ParFiniteElementSpace*, double (*fSource)(const Vector &), double (*obstacleSource)(const Vector &), Array<int> tdof_list, Vector &);
+   double E(const Vector &) const;
+   void DdE(const Vector &, Vector &) const;
+   HypreParMatrix* DddE(const Vector &);
+   void g(const Vector &, Vector &) const;
+   HypreParMatrix* Ddg(const Vector &);
+   virtual ~ParObstacleProblem();
+};
+
+#endif

examples/contact/ParSphericalObstacleProblem.cpp

@@ -0,0 +1,173 @@
+//                       Spherical Obstacle Problem
+//
+//
+// Compile with: make ParSphericalObstacleProblem
+//
+// Sample runs: mpirun -np 4 ./ParSphericalObstacleProblem -linSolver 0
+//              mpirun -np 4 ./ParSphericalObstacleProblem -linSolver 1
+//              mpirun -np 4 ./ParSphericalObstacleProblem -linSolver 2
+//
+//
+// Description: This example code demonstrates the use of MFEM to solve the
+//              bound-constrained energy minimization problem
+//
+//                      minimize ||∇u||² subject to u ≥ ϕ in H¹₀.
+
+#include "mfem.hpp"
+#include "ParProblems.hpp"
+#include "ParIPsolver.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+double fRhs(const Vector &);
+double spherical_obstacle(const Vector &);
+double exact_solution_obstacle(const Vector &);
+
+
+int main(int argc, char *argv[])
+{
+  // Initialize MPI
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   int FEorder = 1; // order of the finite elements
+   int linSolver = 2;
+   int maxIPMiters = 30;
+   int ref_levels = 3;
+   OptionsParser args(argc, argv);
+   args.AddOption(&FEorder, "-o", "--order",\
+	 	  "Order of the finite elements.");
+   args.AddOption(&linSolver, "-linSolver", "--linearSolver", \
+        "IP-Newton linear system solution strategy.");
+   args.AddOption(&maxIPMiters, "-IPMiters", "--IPMiters",\
+	 	  "Maximum number of IPM iterations");
+   args.AddOption(&ref_levels, "-r", "--mesh_refinement", \
+		  "Mesh Refinement");
+  
+   args.Parse();
+   if(!args.Good())
+   {
+     args.PrintUsage(cout);
+     return 1;
+   }
+   else
+   {
+     if(myid == 0)
+     {  
+       args.PrintOptions(cout);
+     }
+   }
+
+   const char *meshFile = "../../data/disk.mesh";
+   Mesh mesh(meshFile, 1, 1);
+   int dim = mesh.Dimension(); // geometric dimension of the meshed domain
+   {
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh.UniformRefinement();
+      }
+   }
+
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   
+   FiniteElementCollection *fec = new H1_FECollection(FEorder, dim);
+   ParFiniteElementSpace   *Vh  = new ParFiniteElementSpace(&pmesh, fec);
+   Array<int> boundary_dofs;
+   Vh->GetBoundaryTrueDofs(boundary_dofs);
+   int dimD = Vh->GetTrueVSize();
+   Vector xDC(dimD); xDC = 0.0;
+
+   ParObstacleProblem problem(Vh, Vh, &fRhs, &spherical_obstacle, boundary_dofs, xDC);
+   Vector x0(dimD); x0.Set(1.0, xDC);
+   Vector xf(dimD); xf = 0.0;
+
+   ParInteriorPointSolver optimizer(&problem); 
+   optimizer.SetTol(1.e-7);
+   optimizer.SetLinearSolveTol(1.e-10);
+   optimizer.SetLinearSolver(linSolver);
+   optimizer.SetMaxIter(maxIPMiters);
+   optimizer.Mult(x0, xf);
+
+   ParGridFunction d_gf(Vh);
+
+   d_gf.SetFromTrueDofs(xf);
+
+
+   FunctionCoefficient dtrue_fc(exact_solution_obstacle); // analytic solution
+   ParGridFunction dtrue_gf(Vh);
+   dtrue_gf.ProjectCoefficient(dtrue_fc);
+
+   double L2error = d_gf.ComputeL2Error(dtrue_fc);
+   if (myid == 0)
+   {
+     cout << "\n|| u_h - u ||_{L^2} = " << L2error << '\n' << endl;
+   } 
+   
+   ParaViewDataCollection paraview_dc("SphericalObstacleProblem", &pmesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(FEorder);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetTime(0.0);
+   paraview_dc.RegisterField("u(x,y) (analytic)", &dtrue_gf);
+   paraview_dc.RegisterField("u(x,y) (numerical)", &d_gf);
+   paraview_dc.Save();
+
+   delete Vh;
+   delete fec;
+   return 0;
+}
+
+
+double fRhs(const Vector &x)
+{
+  return 0.;
+}
+
+
+double spherical_obstacle(const Vector &pt)
+{
+   double x = pt(0), y = pt(1);
+   double r = sqrt(x*x + y*y);
+   double r0 = 0.5;
+   double beta = 0.9;
+
+   double b = r0*beta;
+   double tmp = sqrt(r0*r0 - b*b);
+   double B = tmp + b*b/tmp;
+   double C = -b/tmp;
+
+   if (r > b)
+   {
+      return B + r * C;
+   }
+   else
+   {
+      return sqrt(r0*r0 - r*r);
+   }
+}
+
+double exact_solution_obstacle(const Vector &pt)
+{
+   double x = pt(0), y = pt(1);
+   double r = sqrt(x*x + y*y);
+   double r0 = 0.5;
+   double a =  0.348982574111686;
+   double A = -0.340129705945858;
+
+   if (r > a)
+   {
+      return A * log(r);
+   }
+   else
+   {
+      return sqrt(r0*r0-r*r);
+   }
+} 
+