minor cleanup

Improve support for out-of-tree installations

.gitignore

@@ -272,16 +272,27 @@ miniapps/navier/*_output
 
 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
+miniapps/nurbs/nurbs_ex3
+miniapps/nurbs/nurbs_ex5
 miniapps/nurbs/nurbs_ex11p
+miniapps/nurbs/nurbs_ex24
+miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
+miniapps/nurbs/sol_?.gf
 miniapps/nurbs/sol.*
 miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
+miniapps/nurbs/Example3*
+miniapps/nurbs/Example5*
+miniapps/nurbs/Solenoidal*
+miniapps/nurbs/ParaView
 miniapps/nurbs/sin-fit.mesh
+miniapps/nurbs/ex5.mesh
+miniapps/nurbs/exsol.mesh
 miniapps/nurbs/CurveInt
 miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh

.gitlab-ci.yml

@@ -22,7 +22,7 @@ include:
 # the "needs" keyword and express the DAG of jobs for more efficiency.
 # - We use setup and setup_baseline phases to download content outside of mfem
 #   directory.
-# - Allocate/Release is where quartz resource are allocated/released once for all.
+# - Allocate/Release is where ruby resource are allocated/released once for all.
 # - Build and Test is where we build and MFEM for multiple toolchains.
 # - Baseline_checks gathers baseline-type test suites execution
 # - Baseline_publish, only available on master, allows to update baseline
@@ -53,7 +53,7 @@ variables:
   AUTOTEST_COMMIT: "YES"
 
 # Trigger subpipelines:
-quartz-build-and-test:
+ruby-build-and-test:
   stage: sub-pipelines
   variables:
     # Explicitly pass down values that we want to be able to set when triggering
@@ -61,10 +61,10 @@ quartz-build-and-test:
     AUTOTEST: "${AUTOTEST}"
     AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
   trigger:
-    include: .gitlab/quartz-build-and-test.yml
+    include: .gitlab/ruby-build-and-test.yml
     strategy: depend
 
-quartz-baseline:
+ruby-baseline:
   stage: sub-pipelines
   variables:
     # Explicitly pass down values that we want to be able to set when triggering
@@ -73,7 +73,7 @@ quartz-baseline:
     AUTOTEST: "${AUTOTEST}"
     AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
   trigger:
-    include: .gitlab/quartz-baseline.yml
+    include: .gitlab/ruby-baseline.yml
     strategy: depend
 
 lassen-build-and-test:

.gitlab/README.md

@@ -24,7 +24,7 @@ and `test type`.
 
 Machines typically include:
 
-* Quartz: Intel bi-socket x86
+* Ruby: 2nd Gen Intel Xeon (Cascade Lake)
 * Lassen: Power9 + Nvidia GPU
 * Corona: AMD GPU
 
@@ -76,13 +76,13 @@ with a spack spec of MFEM, within the limits permitted by the MFEM spack
 package.
 
 In any build-and-test sub-pipeline a job basically consists in defining the
-spack spec to use. Adding a job on quartz for example resumes to:
+spack spec to use. Adding a job on ruby for example resumes to:
 
 ```yaml
 <job_name>:
   variables:
     SPEC: "<spack_spec>"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 ```
 
 The remaining and non trivial work is to make sure this spec is working. To

.gitlab/configs/common.yml

@@ -24,7 +24,7 @@ variables:
 # TODO: add a clean-up mechanism
   BUILD_ROOT: ${USER_CI_TOP_DIR}/${CI_PROJECT_NAME}-${MACHINE_NAME}-pipeline-${CI_PIPELINE_ID}
 
-# On LLNL's quartz, there is only one allocation shared among jobs in order to
+# On LLNL's ruby, there is only one allocation shared among jobs in order to
 # save time and resource. This allocation has to be uniquely named so that we
 # are sure to retrieve it.
   ALLOC_NAME: ${CI_PROJECT_NAME}_ci_${CI_PIPELINE_ID}

.gitlab/configs/ruby-config.yml

@@ -9,17 +9,17 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-# GitLab pipelines configurations for the Quartz machine at LLNL
+# GitLab pipelines configurations for the Ruby machine at LLNL
 variables:
-  MACHINE_NAME: quartz
+  MACHINE_NAME: ruby
 
-.on_quartz:
+.on_ruby:
   tags:
     - shell
-    - quartz
+    - ruby
   rules:
-    # Don't run quartz jobs if...
-    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"'
+    # Don't run ruby jobs if...
+    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_RUBY == "OFF"'
       when: never
     # Don't run autotest update if...
     - if: '$CI_JOB_NAME =~ /report/ && $AUTOTEST != "YES"'
@@ -40,13 +40,13 @@ variables:
     - when: on_success
 
 # Spack helped builds
-# Generic quartz build job, extending build script
-.build_and_test_on_quartz:
-  extends: [.on_quartz]
+# Generic ruby build job, extending build script
+.build_and_test_on_ruby:
+  extends: [.on_ruby]
   stage: build_and_test
   script:
     # THREADS is used by 'tests/gitlab/build_and_test', run below
-    - export THREADS=12
+    - export THREADS=16
     - echo ${ALLOC_NAME}
     - export JOBID=$(squeue -h --name=${ALLOC_NAME} --format=%A)
     - echo ${JOBID}

.gitlab/configs/setup-baseline.yml

@@ -18,7 +18,7 @@
 setup_baseline:
   tags:
     - shell
-    - quartz
+    - ruby
   stage: setup
   variables:
     GIT_STRATEGY: none

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

@@ -16,7 +16,7 @@
 setup:
   tags:
     - shell
-    - quartz
+    - ruby
   stage: setup
   variables:
     GIT_STRATEGY: none

.gitlab/ruby-baseline.yml

@@ -19,8 +19,8 @@ stages:
   - cleanup
   - baseline_publish
 
-baselinecheck_mfem_intel_quartz:
-  extends: [.on_quartz]
+baselinecheck_mfem_intel_ruby:
+  extends: [.on_ruby]
   stage: baseline_check
   variables:
     # TPLS_DIR is used in .gitlab/scripts/baseline to provide the tpls location
@@ -32,7 +32,7 @@ baselinecheck_mfem_intel_quartz:
     - echo ${BUILD_ROOT}
     - echo ${TPLS_DIR}
     # Used by the tests in MFEM/tests:
-    - export MFEM_TEST_NP=32
+    - export MFEM_TEST_NP=48
     # The next script uses the following environment variables:
     # * BASELINE_TEST, SYS_TYPE, CI_PROJECT_DIR, ARTIFACTS_DIR,
     # * BUILD_ROOT, TPLS_DIR, MACHINE_NAME
@@ -44,18 +44,16 @@ baselinecheck_mfem_intel_quartz:
   allow_failure: true
 
 cleanup:
-  extends: .on_quartz
+  extends: .on_ruby
   stage: cleanup
   variables:
     GIT_STRATEGY: none
   script:
     - echo "BUILD_ROOT=${BUILD_ROOT}"
     - rm -rf "${BUILD_ROOT}" || true
-    - echo "CI_PROJECT_DIR=${CI_PROJECT_DIR}"
-    - make -C "${CI_PROJECT_DIR}" distclean
 
 report_baseline:
-  extends: [.on_quartz]
+  extends: [.on_ruby]
   stage: baseline_report
   script:
     - echo ${MACHINE_NAME}
@@ -115,8 +113,8 @@ report_baseline:
         exit $err
       ) 9> autotest.lock
 
-baselinepublish_mfem_quartz:
-  extends: [.on_quartz]
+baselinepublish_mfem_ruby:
+  extends: [.on_ruby]
   stage: baseline_publish
   rules:
     # - if: '$CI_COMMIT_BRANCH == "master" || $REBASELINE == "YES"'
@@ -131,5 +129,5 @@ baselinepublish_mfem_quartz:
 
 include:
   - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-config.yml
+  - local: .gitlab/configs/ruby-config.yml
   - local: .gitlab/configs/setup-baseline.yml

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

@@ -19,54 +19,54 @@ stages:
 allocate_resource:
   variables:
     GIT_STRATEGY: none
-  extends: .on_quartz
+  extends: .on_ruby
   stage: allocate_resource
   script:
     - echo ${ALLOC_NAME}
     - salloc --exclusive --nodes=1 --reservation=ci --time=60 --no-shell --job-name=${ALLOC_NAME}
   timeout: 6h
 
-# GitLab jobs for the Quartz machine at LLNL
+# GitLab jobs for the Ruby machine at LLNL
 debug_ser_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 +debug~mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 debug_par_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 +debug+mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_ser_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1 ~mpi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10:
   variables:
     SPEC: "%gcc@10.3.1"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_sundials:
   variables:
     SPEC: "%gcc@10.3.1 +sundials"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_petsc:
   variables:
     SPEC: "%gcc@10.3.1 +petsc ^petsc+mumps~superlu-dist"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 opt_par_gcc_10_pumi:
   variables:
     SPEC: "%gcc@10.3.1 +pumi"
-  extends: .build_and_test_on_quartz
+  extends: .build_and_test_on_ruby
 
 # Release
 release_resource:
   variables:
     GIT_STRATEGY: none
-  extends: .on_quartz
+  extends: .on_ruby
   stage: release_resource_and_report
   script:
     - echo ${ALLOC_NAME}
@@ -78,17 +78,17 @@ release_resource:
 report_job_success:
   stage: release_resource_and_report
   extends:
-    - .on_quartz
+    - .on_ruby
     - .report_job_success
 
 report_job_failure:
   stage: release_resource_and_report
   extends:
-    - .on_quartz
+    - .on_ruby
     - .report_job_failure
 
 include:
   - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-config.yml
+  - local: .gitlab/configs/ruby-config.yml
   - local: .gitlab/configs/setup-build-and-test.yml
   - local: .gitlab/configs/report-build-and-test.yml

.gitlab/scripts/baseline

@@ -14,7 +14,7 @@
 # locals
 glob_err=${BASELINE_TEST}.err
 base=${BASELINE_TEST}-${SYS_TYPE}
-if [[ "${MACHINE_NAME}" == "quartz" ]]; then
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
   base="${BASELINE_TEST}-${MACHINE_NAME}"
 fi
 base_diff=${base}.diff
@@ -31,8 +31,8 @@ cd tests
 mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}
 
 # run
-if [[ "${MACHINE_NAME}" == "quartz" || "${MACHINE_NAME}" == "ruby" ]]; then
-  salloc --nodes=1 --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
+  salloc --nodes=1 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 elif [[ ${MACHINE_NAME} == "corona" ]]; then
   salloc --nodes=1 -t 60 -p pbatch ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 elif [[ ${MACHINE_NAME} == "lassen" ]]; then
@@ -41,11 +41,11 @@ else
   echo "Unknown machine: MACHINE_NAME=$MACHINE_NAME"
   exit 1
 fi
+status="$?"
 
 # post
 mkdir ${artifacts_path}
 
-status=0
 if [[ -f ${BASELINE_TEST}.out ]]; then
   cp ${BASELINE_TEST}.out ${artifacts_path}
 fi

.gitlab/scripts/rebaseline

@@ -11,7 +11,7 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-# There will be collision between corona and quartz baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 ARTIFACT_PATH=${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/baseline-${SYS_TYPE}
@@ -21,7 +21,7 @@ PATCH_FILE=${ARTIFACT_PATH}.patch
 FULL_FILE=${ARTIFACT_PATH}.out
 DIFF_FILE=${ARTIFACT_PATH}.diff
 
-# There will be collision between corona and quartz baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 SAVED_NAME=baseline-${SYS_TYPE}.saved

CHANGELOG

@@ -11,9 +11,28 @@
 Version 4.7.1 (development)
 ===========================
 
+- Refactored the `ARKStepSolver` class (ARKODE interface) to use
+  `TimeDependentOperator::Mult` only when the associated ODE operator is
+  expressed in explicit form (i.e., `TimeDependentOperator::isExplicit()`),
+  otherwise `TimeDependentOperator::ExplicitMult` is used. A check has been
+  added to `ARKStepSolver` to verify that the associated ODE operator is not in
+  explicit form when a mass matrix solver is enabled via a call to either the
+  `UseMFEMMassLinearSolver` or `UseSundialsMassLinearSolver` methods. This is
+  because enabling a mass matrix solver assumes that F(u,k,t) = M k in the
+  associated ODE operator.
+
+- Added support for custom interpolation procedure in FindPointsGSLIB.
+
+- Added NURBS-based H(div) and H(curl) elements in 2D and 3D. Only on single
+  patch meshes. Only implemented for serial computations.
+
+- Added miniapps to demonstrate the H(div) and H(curl) NURBS elements.
+
 - Added an MFEM example for the eikonal equation. This new solver is based on
   the proximal Galerkin method introduced by Keith and Surowiec.
 
+- API change: in class GridFunction, 'fec' was renamed to 'fec_owned'.
+
 
 Version 4.7, released on May 7, 2024
 ====================================
@@ -38,6 +57,9 @@ Meshing improvements
 
 - Added support for internal boundary elements in nonconforming meshes.
 
+- Added ExodusII output capability. The writer can handle first-order (Pyramid5,
+  Wedge6, Hex8, Tet4) and second-order FE types (Pyramid14, Wedge18, Hex27, Tet10).
+
 - The ReadCubit Genesis mesh importer has been rewritten to improve readability.
 
 Discretization improvements

INSTALL

@@ -273,7 +273,13 @@ Installation options:
    PREFIX  - Specify the installation directory. The library (libmfem.a) will be
              installed in $(PREFIX)/lib, the headers in $(PREFIX)/include, and
              the configuration makefile (config.mk) in $(PREFIX)/share/mfem.
-   INSTALL - Specify the install program, e.g /usr/bin/install
+   INSTALL - Specify the install program, default = /usr/bin/install
+   INSTALL_DEF_PERM - Specify the default install permissions. This affects
+                      headers and configuration makefiles, default = 644
+   INSTALL_BIN_PERM - Specify the install permissions for binaries. This only
+                      affects the shared version of the library, default = 755
+   INSTALL_DIR_PERM - Specify the install permissions for directories and,
+                      on macOS/BSD, for symlinks as well, default = 755
 
 MFEM library features/options (GNU make)
 ----------------------------------------

config/defaults.mk

@@ -95,6 +95,10 @@ else
    # Silence unused command line argument warnings when generating dependencies
    # with mpicxx and clang
    DEP_FLAGS := -Wno-unused-command-line-argument $(DEP_FLAGS)
+   # Silence "ignoring duplicate libraries" warnings on new (Xcode 15) linker
+   ifneq (,$(findstring PROJECT:dyld,$(shell ld -v 2>&1)))
+      LDFLAGS_INTERNAL = -Xlinker -no_warn_duplicate_libraries
+   endif
 endif
 
 # Set CXXFLAGS to overwrite the default selection of DEBUG_FLAGS/OPTIM_FLAGS

config/sample-runs.sh

@@ -32,7 +32,7 @@ groups_serial=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1,2,3}[0-9].cpp"'
+   "ex{,[1-9]}[0-9].cpp"'
 #   "ex1.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -58,6 +58,10 @@ groups_serial=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
@@ -66,25 +70,38 @@ groups_serial=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
     mesh-optimizer.cpp minimal-surface.cpp"'
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
    "cvsRoberts_ASAi_dns.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp"' # 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp "'
+# todo: miniapps/mtop
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
    "nurbs_ex1.cpp"'
+# todo: add other nurbs miniapps
+# todo: miniapps/solvers (serial)
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
    "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
     lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
    "Toys miniapps:"
    "miniapps/toys"
@@ -100,7 +117,7 @@ groups_parallel=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1,2,3}[0-9]p.cpp"'
+   "ex{,[1-9]}[0-9]p.cpp"'
 #   "ex1p.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -126,6 +143,10 @@ groups_parallel=(
    "HiOp examples:"
    "examples/hiop"
    "ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex{1,2}p.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
@@ -138,24 +159,41 @@ groups_parallel=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp"'
+   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
    "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
    "adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "par_example.cpp"'
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "p{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "pfindpts.cpp schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
    "Navier miniapps:"
    "miniapps/navier"
    "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
@@ -164,14 +202,18 @@ groups_parallel=(
    "Shifted miniapps:"
    "miniapps/shifted"
    "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
    "Solvers miniapps:"
    "miniapps/solvers"
    "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
-   "convert-cd.cpp get-values.cpp load-dc.cpp"'
+   "convert-dc.cpp get-values.cpp load-dc.cpp"'
+# todo: add other tools miniapps
 '"convergence"
    "Convergence tests:"
    "tests/convergence"
@@ -186,7 +228,7 @@ groups_all=(
 '"examples"
    "Examples:"
    "examples"
-   "ex\"{,1,2,3}[0-9]\"{,p}.cpp"'
+   "ex\"{,[1-9]}[0-9]\"{,p}.cpp"'
 '"sundials"
    "SUNDIALS examples:"
    "examples/sundials"
@@ -215,10 +257,14 @@ groups_all=(
    "HiOp examples:"
    "examples/hiop"
    "ex9.cpp ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp ex{1,2}p.cpp"'
 '"pumi"
    "PUMI examples:"
    "examples/pumi"
-   "ex1.cpp ex1p.cpp ex2.cpp ex6p.cpp"'
+   "ex1.cpp ex2.cpp ex1p.cpp ex6p.cpp"'
 '"superlu"
    "Superlu examples:"
    "examples/superlu"
@@ -226,43 +272,67 @@ groups_all=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp"'
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
+    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
    "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
    "Adjoint miniapps:"
    "miniapps/adjoint"
-   "adjoint_advection_diffusion.cpp cvsRoberts_ASAi_dns.cpp"'
+   "cvsRoberts_ASAi_dns.cpp adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp par_example.cpp"'
+# 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{,p}{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
    "GSLIB miniapps:"
    "miniapps/gslib"
    "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp pfindpts.cpp
     schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
    "Navier miniapps:"
    "miniapps/navier"
    "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
    "NURBS miniapps:"
    "miniapps/nurbs"
    "nurbs_ex1.cpp nurbs_ex1p.cpp nurbs_ex11p.cpp"'
+# todo: add other nurbs miniapps
 '"shifted"
    "Shifted miniapps:"
    "miniapps/shifted"
    "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
    "Solvers miniapps:"
    "miniapps/solvers"
    "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
    "Tools miniapps:"
    "miniapps/tools"
    "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
     lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
    "Toys miniapps:"
    "miniapps/toys"
@@ -386,7 +456,7 @@ function help_message()
       mfem_config [${mfem_config}]
          Set MFEM configuration options
       make [${make}], mpiexec [${mpiexec}], mpiexec_np [${mpiexec_np}]
-         Their values can also set using the respective uppercase environment
+         Their values can also be set using the respective uppercase environment
          variable
       mfem_build_dir [${mfem_build_dir}]
          Same as '-d': set this variable to something different from <mfem_dir>

data/pipe-nurbs-2d.mesh

@@ -18,9 +18,9 @@ elements
 boundary
 4
 1 1 0 1
-1 1 2 3
-1 1 3 0
-1 1 1 2
+2 1 2 3
+3 1 3 0
+4 1 1 2
 
 edges
 4

doc/CodeDocumentation.conf.in

@@ -1049,7 +1049,8 @@ RECURSIVE              = NO
 EXCLUDE                = @MFEM_SOURCE_DIR@/config/_config.hpp \
                          @MFEM_SOURCE_DIR@/config/get_hypre_version.cpp \
                          @MFEM_SOURCE_DIR@/general/tinyxml2.h \
-                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp
+                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp \
+                         @MFEM_SOURCE_DIR@/linalg/lapack.hpp
 
 # The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
 # directories that are symbolic links (a Unix file system feature) are excluded

doc/CodeDocumentation.dox

@@ -182,6 +182,21 @@ namespace mfem {
  *   <a class="el" href="examples_2superlu_2ex1p_8cpp_source.html">1p</a>,
  *   demonstrating the use of MFEM's \link superlu.hpp SuperLU integration\endlink.
  *
+ * <H4>NURBS Examples</H4>
+ * - Variants of Examples
+ *  <a class="el" href="nurbs__ex1_8cpp_source.html">1</a>,
+ *  <a class="el" href="nurbs__ex1p_8cpp_source.html">1p</a>,
+ *  <a class="el" href="nurbs__ex3_8cpp_source.html">3</a>,
+ *  <a class="el" href="nurbs__ex5_8cpp_source.html">5</a>,
+ *  <a class="el" href="nurbs__ex11p_8cpp_source.html">11p</a>, and
+ *  <a class="el" href="nurbs__ex24_8cpp_source.html">24</a>,
+ *   demonstrating howto perform NURBS-based Isogeometric Analysis.
+ * - Variant of Example <a class="el" href="nurbs__patch__ex1_8cpp_source.html">1</a>: demonstrates the use of patch integration
+ * - <a class="el" href="nurbs__solenoidal_8cpp_source.html">NURBS Divergence-free</a>: solve a solenoidal vector projection with NURBS-based H(div) elements
+ * - <a class="el" href="nurbs__curveint_8cpp_source.html">NURBS Interpolation</a>: NURBS interpolation of given geometry
+ * - <a class="el" href="nurbs__naca__cmesh_8cpp_source.html">NURBS NACA Mesher</a>: generate NURBS based mesh around a NACA foil
+ * - <a class="el" href="nurbs__printfunc_8cpp_source.html">NURBS Printer</a>: print the NURBS-basis
+ *
  * <H3>Miniapps</H3>
  * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
  * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code

examples/amgx/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/amgx/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/caliper/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/caliper,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/ex23.cpp

@@ -44,7 +44,7 @@ protected:
    BilinearForm *M;
    BilinearForm *K;
 
-   SparseMatrix Mmat, Kmat, Kmat0;
+   SparseMatrix Mmat, Kmat;
    SparseMatrix *T; // T = M + dt K
    real_t current_dt;
 
@@ -83,25 +83,24 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
    : SecondOrderTimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0),
      fespace(f), M(NULL), K(NULL), T(NULL), current_dt(0.0), z(height)
 {
-   const real_t rel_tol = 1e-8;
-
-   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-
+   // Assemble Laplace matrix
    c2 = new ConstantCoefficient(speed*speed);
-
    K = new BilinearForm(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(*c2));
    K->Assemble();
 
-   Array<int> dummy;
-   K->FormSystemMatrix(dummy, Kmat0);
-   K->FormSystemMatrix(ess_tdof_list, Kmat);
-
+   // Assemble Mass matrix
    M = new BilinearForm(&fespace);
    M->AddDomainIntegrator(new MassIntegrator());
    M->Assemble();
+
+   // Apply Bcs
+   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   K->FormSystemMatrix(ess_tdof_list, Kmat);
    M->FormSystemMatrix(ess_tdof_list, Mmat);
 
+   // Configure preconditioner
+   const real_t rel_tol = 1e-8;
    M_solver.iterative_mode = false;
    M_solver.SetRelTol(rel_tol);
    M_solver.SetAbsTol(0.0);
@@ -110,14 +109,13 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
+   // Configure solver
    T_solver.iterative_mode = false;
    T_solver.SetRelTol(rel_tol);
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
-
-   T = NULL;
 }
 
 void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
@@ -126,9 +124,11 @@ void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
    // Compute:
    //    d2udt2 = M^{-1}*-K(u)
    // for d2udt2
-   Kmat.Mult(u, z);
+   K->FullMult(u, z);
    z.Neg(); // z = -z
+   z.SetSubVector(ess_tdof_list, 0.0);
    M_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }
 
 void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
@@ -142,14 +142,11 @@ void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
       T = Add(1.0, Mmat, fac0, Kmat);
       T_solver.SetOperator(*T);
    }
-   Kmat0.Mult(u, z);
+   K->FullMult(u, z);
    z.Neg();
-
-   for (int i = 0; i < ess_tdof_list.Size(); i++)
-   {
-      z[ess_tdof_list[i]] = 0.0;
-   }
+   z.SetSubVector(ess_tdof_list, 0.0);
    T_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }
 
 void WaveOperator::SetParameters(const Vector &u)
@@ -314,7 +311,6 @@ int main(int argc, char *argv[])
          ess_bdr = 0;
       }
    }
-
    WaveOperator oper(fespace, ess_bdr, speed);
 
    u_gf.SetFromTrueDofs(u);

examples/ginkgo/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ginkgo/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/hiop/ex9p.cpp

@@ -96,6 +96,7 @@ public:
    {
       Vector w_glob(width);
       pfes.Dof_TrueDof_Matrix()->MultTranspose(w, w_glob);
+      w_glob.HostReadWrite(); // read+write -> can use w_glob(i) (non-const)
       for (int i = 0; i < width; i++) { grad(0, i) = w_glob(i); }
    }
 

examples/hiop/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/hiop/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ..
 MFEM_BUILD_DIR ?= ..
+MFEM_INSTALL_DIR ?= ../mfem
 SRC = $(if $(MFEM_DIR:..=),$(MFEM_DIR)/examples/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/moonolith/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/moonolith/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/petsc/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/petsc/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/pumi/ex1.cpp

@@ -66,7 +66,6 @@ int main(int argc, char *argv[])
 {
    // 1. Initialize MPI (required by PUMI) and HYPRE.
    Mpi::Init(argc, argv);
-   int num_procs = Mpi::WorldSize();
    int myid = Mpi::WorldRank();
    Hypre::Init();
 

examples/pumi/ex2.cpp

@@ -80,8 +80,6 @@ int main(int argc, char *argv[])
 {
    // 1. Initialize MPI (required by PUMI) and HYPRE.
    Mpi::Init(argc, argv);
-   int num_proc = Mpi::WorldSize();
-   int myId = Mpi::WorldRank();
    Hypre::Init();
 
    // 2. Parse command-line options.

examples/pumi/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/pumi/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

examples/sundials/CMakeLists.txt

@@ -31,11 +31,21 @@ include_directories(BEFORE ${PROJECT_BINARY_DIR})
 add_custom_target(test_sundials
   ${CMAKE_CTEST_COMMAND} -R sundials USES_TERMINAL)
 
-# Add one executable per cpp file, adding "sundials_" as prefix. Sets
-# "test_sundials" as a target that depends on the given examples.
+# Add one executable per cpp file, adding "sundials_" as prefix so the CMake
+# target is unique from those in the non-SUNDIALS examples. Also sets
+# "test_sundials" as a target that depends on the given SUNDIALS examples.
 set(PFX sundials_)
 add_mfem_examples(SUNDIALS_EXAMPLES_SRCS ${PFX} "" test_sundials)
 
+# Remove "sundials_" prefix from exectuable name for consistency with GNU build
+# system.
+foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})
+  get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
+  string(REPLACE ".cpp" "" TARGET_NAME "${PFX}${SRC_FILENAME}")
+  string(REPLACE ${PFX} "" EXE_NAME ${TARGET_NAME})
+  set_target_properties(${TARGET_NAME} PROPERTIES OUTPUT_NAME ${EXE_NAME})
+endforeach()
+
 # Testing.
 # The SUNDIALS tests can be run separately using the target "test_sundials"
 # which builds the examples and runs:
@@ -51,7 +61,10 @@ if (MFEM_ENABLE_TESTING)
   set(EX10_COMMON_OPTS -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -tf 6 -vs 10)
   set(EX10_TEST_OPTS ${EX10_COMMON_OPTS}  -r  2)
   set(EX10P_TEST_OPTS ${EX10_COMMON_OPTS} -rp 1)
-  # Example 16: use the default options
+  # Example 16: test ARKODE with implicit time stepping using mass form
+  set(EX16_COMMON_OPTS -s 15)
+  set(EX16_TEST_OPTS ${EX16_COMMON_OPTS})
+  set(EX16P_TEST_OPTS ${EX16_COMMON_OPTS})
 
   # Add the tests: one test per source file.
   foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})

examples/sundials/ex10.cpp

@@ -1,7 +1,9 @@
 //                                MFEM Example 10
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10
+// Compile with:
+//    make ex10             (GNU make)
+//    make sundials_ex10    (CMake)
 //
 // Sample runs:
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10

examples/sundials/ex10p.cpp

@@ -1,7 +1,9 @@
 //                       MFEM Example 10 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10p
+// Compile with:
+//    make ex10p            (GNU make)
+//    make sundials_ex10p   (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10

examples/sundials/ex16.cpp

@@ -1,15 +1,21 @@
 //                                MFEM Example 16
 //                             SUNDIALS Modification
 //
-// Compile with: make ex16
+// Compile with:
+//    make ex16             (GNU make)
+//    make sundials_ex16    (CMake)
 //
 // Sample runs:  ex16
 //               ex16 -m ../../data/inline-tri.mesh
 //               ex16 -m ../../data/disc-nurbs.mesh -tf 2
 //               ex16 -s 12 -a 0.0 -k 1.0
+//               ex16 -s 15 -a 0.0 -k 1.0
 //               ex16 -s 8 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
+//               ex16 -s 11 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
 //               ex16 -s 9 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
+//               ex16 -s 12 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
 //               ex16 -s 10 -dt 1.0e-4 -tf 4.0e-2 -vs 40
+//               ex16 -s 13 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               ex16 -m ../../data/fichera-q2.mesh
 //               ex16 -m ../../data/escher.mesh
 //               ex16 -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -37,75 +43,102 @@
 using namespace std;
 using namespace mfem;
 
-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
  *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
  *
  *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
  *  (\kappa + \alpha u).
  *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
  */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
    FiniteElementSpace &fespace;
    Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.
 
-   BilinearForm *M;
-   BilinearForm *K;
+   BilinearForm M;
+   SparseMatrix Mmat;
 
-   SparseMatrix Mmat, Kmat;
-   SparseMatrix *T; // T = M + dt K
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
+   SparseMatrix Kmat;
+
+   std::unique_ptr<SparseMatrix> T; // T = M + gam K(u)
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
    DSmoother M_prec;  // Preconditioner for the mass matrix M
 
-   CGSolver T_solver; // Implicit solver for T = M + dt K
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
    DSmoother T_prec;  // Preconditioner for the implicit solver
 
-   double alpha, kappa;
-
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(FiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);
 
-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(FiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);
 
-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);
 
-   /// Custom Jacobian system solver for the SUNDIALS time integrators.
-   /** For the ODE system represented by ConductionOperator
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+    operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+      approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;
 
-           M du/dt = -K(u),
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;
 
-       this class facilitates the solution of linear systems of the form
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;
 
-           (M + γK) y = M b,
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;
 
-       for given b, u (not used), and γ = GetTimeStep(). */
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;
 
-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   int SUNMassSetup() override;
 
-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;
 
-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
-
-   virtual ~ConductionOperator();
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+
 
 int main(int argc, char *argv[])
 {
@@ -117,16 +150,16 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 2;
    int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;
 
    int precision = 8;
    cout.precision(precision);
@@ -151,7 +184,10 @@ int main(int argc, char *argv[])
                   "9  - CVODE (implicit BDF),\n\t"
                   "10 - ARKODE (default explicit),\n\t"
                   "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -174,16 +210,13 @@ int main(int argc, char *argv[])
       args.PrintUsage(cout);
       return 1;
    }
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      return 3;
-   }
    args.PrintOptions(cout);
 
+   bool use_mass_solver = ode_solver_type >= 13;
+
    // 2. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 1));
    int dim = mesh->Dimension();
 
    // 3. Refine the mesh to increase the resolution. In this example we do
@@ -197,7 +230,7 @@ int main(int argc, char *argv[])
    // 4. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
    H1_FECollection fe_coll(order, dim);
-   FiniteElementSpace fespace(mesh, &fe_coll);
+   FiniteElementSpace fespace(mesh.get(), &fe_coll);
 
    int fe_size = fespace.GetTrueVSize();
    cout << "Number of temperature unknowns: " << fe_size << endl;
@@ -211,8 +244,17 @@ int main(int argc, char *argv[])
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 6. Initialize the conduction operator and the visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 6. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -224,7 +266,7 @@ int main(int argc, char *argv[])
       u_gf.Save(osol);
    }
 
-   VisItDataCollection visit_dc("Example16", mesh);
+   VisItDataCollection visit_dc("Example16", mesh.get());
    visit_dc.RegisterField("temperature", &u_gf);
    if (visit)
    {
@@ -258,52 +300,75 @@ int main(int argc, char *argv[])
    }
 
    // 7. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
    switch (ode_solver_type)
    {
       // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
       // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
       // CVODE
       case 8:
-         cvode = new CVODESolver(CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
       case 9:
-         cvode = new CVODESolver(CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(new CVODESolver(cvode_solver_type));
          cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
       // ARKODE
       case 10:
       case 11:
-         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(arkode_solver_type));
          arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
          {
             arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
          }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -311,8 +376,14 @@ int main(int argc, char *argv[])
 
    // Since we want to update the diffusion coefficient after every time step,
    // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }
 
    // 8. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
@@ -323,7 +394,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       // Note that since we are using the "one-step" mode of the SUNDIALS
       // solvers, they will, generally, step over the final time and will not
@@ -337,8 +408,14 @@ int main(int argc, char *argv[])
       if (last_step || (ti % vis_steps) == 0)
       {
          cout << "step " << ti << ", t = " << t << endl;
-         if (cvode) { cvode->PrintInfo(); }
-         if (arkode) { arkode->PrintInfo(); }
+         if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+         {
+            cvode->PrintInfo();
+         }
+         else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+         {
+            arkode->PrintInfo();
+         }
 
          u_gf.SetFromTrueDofs(u);
          if (visualization)
@@ -353,137 +430,153 @@ int main(int argc, char *argv[])
             visit_dc.Save();
          }
       }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
    }
    tic_toc.Stop();
    cout << "Done, " << tic_toc.RealTime() << "s." << endl;
 
    // 9. Save the final solution. This output can be viewed later using GLVis:
    //    "glvis -m ex16.mesh -g ex16-final.gf".
-   {
-      ofstream osol("ex16-final.gf");
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 10. Free the used memory.
-   delete ode_solver;
-   delete mesh;
+   u_gf.Save("ex16-final.gf", precision);
 
    return 0;
 }
 
-ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), z(height)
+ConductionOperator::ConductionOperator(FiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;
 
-   M = new BilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble();
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble();
+   M.FormSystemMatrix(ess_tdof_list, Mmat);
 
    M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    M_solver.SetAbsTol(0.0);
    M_solver.SetMaxIter(50);
    M_solver.SetPrintLevel(0);
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
-   alpha = al;
-   kappa = kap;
-
    T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
 
-   SetParameters(u);
+   SetConductionTensor(u);
 }
 
-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
    GridFunction u_alpha_gf(&fespace);
    u_alpha_gf.SetFromTrueDofs(u);
    for (int i = 0; i < u_alpha_gf.Size(); i++)
    {
       u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
    }
-
-   delete K;
-   K = new BilinearForm(&fespace);
-
    GridFunctionCoefficient u_coeff(&u_alpha_gf);
 
+   K = std::make_unique<BilinearForm>(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
    K->Assemble();
    K->FormSystemMatrix(ess_tdof_list, Kmat);
 }
 
-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
+}
+
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
+{
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
    T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
+   T_solver.Mult(z, k);
 }
 
-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
 {
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
 }
 
-ConductionOperator::~ConductionOperator()
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
 {
-   delete T;
-   delete M;
-   delete K;
-}
-
-double InitialTemperature(const Vector &x)
-{
-   if (x.Norml2() < 0.5)
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
    {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
    }
    else
    {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
    }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}
+

examples/sundials/ex16p.cpp

@@ -1,16 +1,22 @@
 //                         MFEM Example 16 - Parallel Version
 //                              SUNDIALS Modification
 //
-// Compile with: make ex16p
+// Compile with:
+//    make ex16p            (GNU make)
+//    make sundials_ex16p   (CMake)
 //
 // Sample runs:
 //     mpirun -np 4 ex16p
 //     mpirun -np 4 ex16p -m ../../data/inline-tri.mesh
 //     mpirun -np 4 ex16p -m ../../data/disc-nurbs.mesh -tf 2
 //     mpirun -np 4 ex16p -s 12 -a 0.0 -k 1.0
+//     mpirun -np 4 ex16p -s 15 -a 0.0 -k 1.0
 //     mpirun -np 4 ex16p -s 8 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
+//     mpirun -np 4 ex16p -s 11 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
 //     mpirun -np 8 ex16p -s 9 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
+//     mpirun -np 8 ex16p -s 12 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
 //     mpirun -np 4 ex16p -s 10 -dt 2.0e-4 -tf 4.0e-2
+//     mpirun -np 4 ex16p -s 13 -dt 2.0e-4 -tf 4.0e-2
 //     mpirun -np 16 ex16p -m ../../data/fichera-q2.mesh
 //     mpirun -np 16 ex16p -m ../../data/escher-p2.mesh
 //     mpirun -np 8 ex16p -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -38,66 +44,102 @@
 using namespace std;
 using namespace mfem;
 
-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
  *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
  *
  *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
  *  (\kappa + \alpha u).
  *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where either
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
  */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
    ParFiniteElementSpace &fespace;
    Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.
 
-   ParBilinearForm *M;
-   ParBilinearForm *K;
-
+   ParBilinearForm M;
    HypreParMatrix Mmat;
+
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
    HypreParMatrix Kmat;
-   HypreParMatrix *T; // T = M + dt K
-   double current_dt;
 
-   CGSolver M_solver;    // Krylov solver for inverting the mass matrix M
-   HypreSmoother M_prec; // Preconditioner for the mass matrix M
+   std::unique_ptr<HypreParMatrix> T; // T = M + gam K(u)
 
-   CGSolver T_solver;    // Implicit solver for T = M + dt K
-   HypreSmoother T_prec; // Preconditioner for the implicit solver
+   CGSolver M_solver; // Krylov solver for inverting the mass matrix M
+   HypreSmoother M_prec;  // Preconditioner for the mass matrix M
 
-   double alpha, kappa;
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
+   HypreSmoother T_prec;  // Preconditioner for the implicit solver
 
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(ParFiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);
 
-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(ParFiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);
 
-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);
 
-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+       operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+       approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;
 
-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;
 
-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;
 
-   virtual ~ConductionOperator();
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;
+
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;
+
+   int SUNMassSetup() override;
+
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;
+
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+
 
 int main(int argc, char *argv[])
 {
@@ -114,16 +156,16 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 2;
    int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
 
    // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;
 
    int precision = 8;
    cout.precision(precision);
@@ -150,7 +192,10 @@ int main(int argc, char *argv[])
                   "9  - CVODE (implicit BDF),\n\t"
                   "10 - ARKODE (default explicit),\n\t"
                   "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -174,40 +219,33 @@ int main(int argc, char *argv[])
       return 1;
    }
 
-   if (myid == 0)
+   if (Mpi::Root())
    {
       args.PrintOptions(cout);
    }
 
-   // check for valid ODE solver option
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      if (myid == 0)
-      {
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      }
-      return 1;
-   }
+   bool use_mass_solver = ode_solver_type >= 13;
 
-   // 3. Read the serial mesh from the given mesh file on all processors. We can
+   // 3. Define a parallel mesh by a partitioning of a serial mesh. Read the
+   //    serial mesh from the given mesh file on all processors. We can
    //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-
-   // 4. Refine the mesh in serial to increase the resolution. In this example
-   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
-   //    a command-line parameter.
-   for (int lev = 0; lev < ser_ref_levels; lev++)
+   std::unique_ptr<ParMesh> pmesh;
    {
-      mesh->UniformRefinement();
-   }
+      std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 1));
 
-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
-   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted.
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
+      // 4. Refine the mesh in serial to increase the resolution. In this example
+      //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
+      //    a command-line parameter.
+      for (int lev = 0; lev < ser_ref_levels; lev++)
+      {
+         mesh->UniformRefinement();
+      }
+
+      // 5. Refine this mesh further in parallel to increase the resolution.
+      //    Once the parallel mesh is defined, the serial mesh can be deleted.
+      pmesh = std::make_unique<ParMesh>(MPI_COMM_WORLD, *mesh);
+   }
    for (int lev = 0; lev < par_ref_levels; lev++)
    {
       pmesh->UniformRefinement();
@@ -215,8 +253,9 @@ int main(int argc, char *argv[])
 
    // 6. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
+   int dim = pmesh->Dimension();
    H1_FECollection fe_coll(order, dim);
-   ParFiniteElementSpace fespace(pmesh, &fe_coll);
+   ParFiniteElementSpace fespace(pmesh.get(), &fe_coll);
 
    int fe_size = fespace.GlobalTrueVSize();
    if (myid == 0)
@@ -233,8 +272,17 @@ int main(int argc, char *argv[])
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 8. Initialize the conduction operator and the VisIt visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 8. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -249,7 +297,7 @@ int main(int argc, char *argv[])
       u_gf.Save(osol);
    }
 
-   VisItDataCollection visit_dc("Example16-Parallel", pmesh);
+   VisItDataCollection visit_dc("Example16-Parallel", pmesh.get());
    visit_dc.RegisterField("temperature", &u_gf);
    if (visit)
    {
@@ -293,52 +341,76 @@ int main(int argc, char *argv[])
    }
 
    // 9. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
    switch (ode_solver_type)
    {
       // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
       // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
       // CVODE
       case 8:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
       case 9:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(
+            new CVODESolver(MPI_COMM_WORLD, cvode_solver_type));
          cvode->Init(oper);
          cvode->SetSStolerances(reltol, abstol);
          cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
       // ARKODE
       case 10:
       case 11:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(MPI_COMM_WORLD, arkode_solver_type));
          arkode->Init(oper);
          arkode->SetSStolerances(reltol, abstol);
          arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
          {
             arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
          }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
    }
 
    // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -346,12 +418,18 @@ int main(int argc, char *argv[])
 
    // Since we want to update the diffusion coefficient after every time step,
    // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }
 
    // 10. Perform time-integration (looping over the time iterations, ti, with a
    //     time-step dt).
-   if (myid == 0)
+   if (Mpi::Root())
    {
       cout << "Integrating the ODE ..." << endl;
    }
@@ -361,7 +439,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       // Note that since we are using the "one-step" mode of the SUNDIALS
       // solvers, they will, generally, step over the final time and will not
@@ -377,8 +455,14 @@ int main(int argc, char *argv[])
          if (myid == 0)
          {
             cout << "step " << ti << ", t = " << t << endl;
-            if (cvode) { cvode->PrintInfo(); }
-            if (arkode) { arkode->PrintInfo(); }
+            if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+            {
+               cvode->PrintInfo();
+            }
+            else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+            {
+               arkode->PrintInfo();
+            }
          }
 
          u_gf.SetFromTrueDofs(u);
@@ -395,46 +479,38 @@ int main(int argc, char *argv[])
             visit_dc.Save();
          }
       }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
    }
    tic_toc.Stop();
-   if (myid == 0)
+   if (Mpi::Root())
    {
       cout << "Done, " << tic_toc.RealTime() << "s." << endl;
    }
 
    // 11. Save the final solution in parallel. This output can be viewed later
    //     using GLVis: "glvis -np <np> -m ex16-mesh -g ex16-final".
-   {
-      ostringstream sol_name;
-      sol_name << "ex16-final." << setfill('0') << setw(6) << myid;
-      ofstream osol(sol_name.str().c_str());
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 12. Free the used memory.
-   delete ode_solver;
-   delete pmesh;
+   u_gf.Save("ex16-final", precision);
 
    return 0;
 }
 
-ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL),
-     M_solver(f.GetComm()), T_solver(f.GetComm()), z(height)
+ConductionOperator::ConductionOperator(ParFiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace),
+     M_solver(fes.GetComm()), T_solver(fes.GetComm()), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;
 
-   M = new ParBilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble(0); // keep sparsity pattern of M and K the same
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
+   M.FormSystemMatrix(ess_tdof_list, Mmat);
 
    M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    M_solver.SetAbsTol(0.0);
    M_solver.SetMaxIter(100);
    M_solver.SetPrintLevel(0);
@@ -442,97 +518,118 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
    M_solver.SetPreconditioner(M_prec);
    M_solver.SetOperator(Mmat);
 
-   alpha = al;
-   kappa = kap;
-
    T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
    T_solver.SetAbsTol(0.0);
    T_solver.SetMaxIter(100);
    T_solver.SetPrintLevel(0);
    T_solver.SetPreconditioner(T_prec);
 
-   SetParameters(u);
+   SetConductionTensor(u);
 }
 
-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
-{
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
-   T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
-}
-
-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
-{
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
    ParGridFunction u_alpha_gf(&fespace);
    u_alpha_gf.SetFromTrueDofs(u);
    for (int i = 0; i < u_alpha_gf.Size(); i++)
    {
       u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
    }
-
-   delete K;
-   K = new ParBilinearForm(&fespace);
-
    GridFunctionCoefficient u_coeff(&u_alpha_gf);
 
+   K = std::make_unique<ParBilinearForm>(&fespace);
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
-   K->Assemble(0); // keep sparsity pattern of M and K the same
+   K->Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
    K->FormSystemMatrix(ess_tdof_list, Kmat);
 }
 
-ConductionOperator::~ConductionOperator()
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   delete T;
-   delete M;
-   delete K;
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
 }
 
-double InitialTemperature(const Vector &x)
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
 {
-   if (x.Norml2() < 0.5)
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   T_solver.Mult(z, k);
+}
+
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
+{
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
+{
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
    {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
    }
    else
    {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
    }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}

examples/sundials/ex9.cpp

@@ -1,7 +1,9 @@
 //                                MFEM Example 9
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9
+// Compile with:
+//    make ex9              (GNU make)
+//    make sundials_ex9     (CMake)
 //
 // Sample runs:
 //    ex9 -m ../../data/periodic-segment.mesh -p 0 -r 2 -s 7 -dt 0.005

examples/sundials/ex9p.cpp

@@ -1,7 +1,9 @@
 //                       MFEM Example 9 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9p
+// Compile with:
+//    make ex9p             (GNU make)
+//    make sundials_ex9p    (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex9p -m ../../data/periodic-segment.mesh -p 1 -rp 1 -s 7 -dt 0.0025

examples/sundials/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/sundials/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -100,6 +99,12 @@ ex10-test-seq: ex10
 	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX10_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX10P_ARGS))
+# Example 16: test ARKODE with implicit time stepping using mass form
+EX16_COMMON_ARGS := -s 15
+ex16-test-seq: ex16
+	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX16_COMMON_ARGS))
+ex16p-test-par: ex16p
+	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX16_COMMON_ARGS))
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

examples/superlu/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/superlu/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

fem/eltrans.hpp

@@ -52,6 +52,15 @@ protected:
    const DenseMatrix &EvalTransAdjugateJ();
    const DenseMatrix &EvalInverseJ();
 
+   /// @name Tolerance used for point comparisons
+   ///@{
+#ifdef MFEM_USE_DOUBLE
+   static constexpr real_t tol_0 = 1e-15;
+#elif defined(MFEM_USE_SINGLE)
+   static constexpr real_t tol_0 = 1e-7;
+#endif
+   ///@}
+
 public:
 
    /** This enumeration declares the values stored in
@@ -176,7 +185,7 @@ public:
        returned. This method is not 100 percent reliable for non-linear
        transformations. */
    virtual int TransformBack(const Vector &pt, IntegrationPoint &ip,
-                             const real_t phys_tol = 1e-15) = 0;
+                             const real_t phys_tol = tol_0) = 0;
 
    virtual ~ElementTransformation() { }
 };
@@ -281,9 +290,15 @@ public:
         rel_qpts_order(-1),
         solver_type(NewtonElementProject),
         max_iter(16),
+#ifdef MFEM_USE_DOUBLE
         ref_tol(1e-15),
         phys_rtol(1e-15),
         ip_tol(1e-8),
+#elif defined(MFEM_USE_SINGLE)
+        ref_tol(1e-7),
+        phys_rtol(1e-7),
+        ip_tol(1e-4),
+#endif
         print_level(-1)
    { }
 
@@ -449,7 +464,7 @@ public:
        returned. This method is not 100 percent reliable for non-linear
        transformations. */
    virtual int TransformBack(const Vector & v, IntegrationPoint & ip,
-                             const real_t phys_rel_tol = 1e-15)
+                             const real_t phys_rel_tol = tol_0)
    {
       InverseElementTransformation inv_tr(this);
       inv_tr.SetPhysicalRelTol(phys_rel_tol);

fem/fe/fe_base.hpp

@@ -394,7 +394,32 @@ public:
    /// Get a const reference to the nodes of the element
    const IntegrationRule & GetNodes() const { return Nodes; }
 
-   // virtual functions for finite elements on vector spaces
+   /** @brief Evaluate the Hessians of all shape functions of a scalar finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
+       part of the Hessian of one shape function.
+       The order in 2D is {u_xx, u_xy, u_yy}.
+       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
+
+   /** @brief Evaluate the Hessian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof, #dim*(#dim+1)/2) of @a Hessian must be set in advance. */
+   void CalcPhysHessian(ElementTransformation &Trans,
+                        DenseMatrix& Hessian) const;
+
+   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof) of @a Laplacian must be set in advance. */
+   void CalcPhysLaplacian(ElementTransformation &Trans,
+                          Vector& Laplacian) const;
+
+   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof) of @a Laplacian must be set in advance. */
+   void CalcPhysLinLaplacian(ElementTransformation &Trans,
+                             Vector& Laplacian) const;
 
    /** @brief Evaluate the values of all shape functions of a *vector* finite
        element in reference space at the given point @a ip. */
@@ -454,30 +479,6 @@ public:
    */
    virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
 
-   /** @brief Evaluate the Hessians of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
-       part of the Hessian of one shape function.
-       The order in 2D is {u_xx, u_xy, u_yy}.
-       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
-
-   /** @brief Evaluate the Hessian of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** The size (#dof, #dim*(#dim+1)/2) of @a Hessian must be set in advance. */
-   virtual void CalcPhysHessian(ElementTransformation &Trans,
-                                DenseMatrix& Hessian) const;
-
-   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** The size (#dof) of @a Laplacian must be set in advance. */
-   virtual void CalcPhysLaplacian(ElementTransformation &Trans,
-                                  Vector& Laplacian) const;
-
-   virtual void CalcPhysLinLaplacian(ElementTransformation &Trans,
-                                     Vector& Laplacian) const;
-
    /** @brief Return the local interpolation matrix @a I (Dof x Dof) where the
        fine element is the image of the base geometry under the given
        transformation. */

fem/fe/fe_nurbs.cpp

@@ -398,8 +398,621 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
       hessian(o,5) = hessian(o,5)*sum
                      - 2*du(o,1)*sum*dsum[1]
                      + u[o]*sum*(2*dsum[1]*dsum[1] - d2sum[5]);
-
    }
 }
 
+
+void NURBS_HDiv2DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+
+   order = max(orders[0]+1, orders[1]+1);
+   dof = (orders[0] + 2)*(orders[1] + 1)
+         + (orders[1] + 1)*(orders[1] + 2);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HDiv2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                           DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         shape(o,0) = shape1_x(i)*sy;
+         shape(o,1) = 0.0;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t sy1 = shape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         shape(o,0) = 0.0;
+         shape(o,1) = shape_x(i)*sy1;
+      }
+   }
+}
+
+void NURBS_HDiv2DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                           DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & J = Trans.Jacobian();
+   MFEM_ASSERT(J.Width() == 2 && J.Height() == 2,
+               "NURBS_HDiv2DFiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      shape(i, 0) = sx * J(0, 0) + sy * J(0, 1);
+      shape(i, 1) = sx * J(1, 0) + sy * J(1, 1);
+   }
+   shape *= (1.0 / Trans.Weight());
+}
+
+void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
+                                             Vector &divshape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         divshape(o) = dshape1_x(i)*sy;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t dsy1 = dshape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         divshape(o) = shape_x(i)*dsy1;
+      }
+   }
+}
+
+NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+}
+
+
+void NURBS_HDiv3DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+   orders[2] = kv[2]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+   kv1[2] = kv[2]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+   shape_z.SetSize(orders[2]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+   dshape_z.SetSize(orders[2]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+   d2shape_z.SetSize(orders[2]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+   shape1_z.SetSize(orders[2]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+   dshape1_z.SetSize(orders[2]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+   d2shape1_z.SetSize(orders[2]+2);
+
+   order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
+   dof = (orders[0] + 2)*(orders[1] + 1)*(orders[2] + 1) +
+         (orders[0] + 1)*(orders[1] + 2)*(orders[2] + 1) +
+         (orders[0] + 1)*(orders[1] + 1)*(orders[2] + 2);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HDiv3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                           DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape(shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   shape = 0.0;
+   int o = 0;
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz = shape_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,0) = shape1_x(i)*sy_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,1) = shape_x(i)*sy1_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,2) = shape_x(i)*sy_sz1;
+         }
+      }
+   }
+}
+
+void NURBS_HDiv3DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                           DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & J = Trans.Jacobian();
+   MFEM_ASSERT(J.Width() == 3 && J.Height() == 3,
+               "RT_R2D_FiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      real_t sz = shape(i, 2);
+      shape(i, 0) = sx * J(0, 0) + sy * J(0, 1) + sz * J(0, 2);
+      shape(i, 1) = sx * J(1, 0) + sy * J(1, 1) + sz * J(1, 2);
+      shape(i, 2) = sx * J(2, 0) + sy * J(2, 1) + sz * J(2, 2);
+   }
+   shape *= (1.0 / Trans.Weight());
+}
+
+void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
+                                             Vector &divshape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+   kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
+
+   int o = 0;
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz = shape_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            divshape(o) = dshape1_x(i)*sy_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t dy1_sz = dshape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            divshape(o) = shape_x(i)*dy1_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t dz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_dz1 = shape_y(j)*dz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            divshape(o) = shape_x(i)*sy_dz1;
+         }
+      }
+   }
+}
+
+NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+}
+
+void NURBS_HCurl2DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+
+   order = max(orders[0]+1, orders[1]+1);
+   dof = (orders[0] + 1)*(orders[1] + 2)
+         + (orders[1] + 2)*(orders[1] + 1);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HCurl2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                            DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t sy1 = shape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         shape(o,0) = shape_x(i)*sy1;
+         shape(o,1) = 0.0;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         shape(o,0) = 0.0;
+         shape(o,1) = shape1_x(i)*sy;
+      }
+   }
+}
+
+void NURBS_HCurl2DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                            DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & JI = Trans.InverseJacobian();
+   MFEM_ASSERT(JI.Width() == 2 && JI.Height() == 2,
+               "NURBS_HCurl2DFiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0);
+      shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1);
+   }
+}
+
+void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
+                                               DenseMatrix &curl_shape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t dsy1 = dshape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         curl_shape(o,0) = -shape_x(i)*dsy1;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         curl_shape(o,0) = dshape1_x(i)*sy;
+      }
+   }
+}
+
+NURBS_HCurl2DFiniteElement::~NURBS_HCurl2DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+}
+
+
+void NURBS_HCurl3DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+   orders[2] = kv[2]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+   kv1[2] = kv[2]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+   shape_z.SetSize(orders[2]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+   dshape_z.SetSize(orders[2]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+   d2shape_z.SetSize(orders[2]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+   shape1_z.SetSize(orders[2]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+   dshape1_z.SetSize(orders[2]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+   d2shape1_z.SetSize(orders[2]+2);
+
+   order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
+   dof = (orders[0] + 1)*(orders[1] + 2)*(orders[2] + 2) +
+         (orders[0] + 2)*(orders[1] + 1)*(orders[2] + 2) +
+         (orders[0] + 2)*(orders[1] + 2)*(orders[2] + 1);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HCurl3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                            DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape(shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   shape = 0.0;
+   int o = 0;
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz1 = shape1_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,0) = shape_x(i)*sy1_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,1) = shape1_x(i)*sy_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,2) = shape1_x(i)*sy1_sz;
+         }
+      }
+   }
+}
+
+void NURBS_HCurl3DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                            DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & JI = Trans.InverseJacobian();
+   MFEM_ASSERT(JI.Width() == 3 && JI.Height() == 3,
+               "NURBS_HCurl3DFiniteElement must be in a"
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      real_t sz = shape(i, 2);
+      shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0) + sz * JI(2, 0);
+      shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1) + sz * JI(2, 1);
+      shape(i, 2) = sx * JI(0, 2) + sy * JI(1, 2) + sz * JI(2, 2);
+   }
+}
+
+void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
+                                               DenseMatrix &curl_shape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+   kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
+
+   int o = 0;
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_dsz1 = shape1_y(j)*dsz1,
+                      dsy1_sz1 = dshape1_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            curl_shape(o,0) = 0.0;
+            curl_shape(o,1) =  shape_x(i)*sy1_dsz1;
+            curl_shape(o,2) = -shape_x(i)*dsy1_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_dsz1 = shape_y(j)*dsz1,
+                      sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            curl_shape(o,0) = -shape1_x(i)*sy_dsz1;
+            curl_shape(o,1) = 0.0;
+            curl_shape(o,2) = dshape1_x(i)*sy_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz,
+                      dsy1_sz = dshape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            curl_shape(o,0) = shape1_x(i)*dsy1_sz;
+            curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
+            curl_shape(o,2) = 0.0;
+         }
+      }
+   }
+}
+
+NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+}
+
 }

fem/fe/fe_nurbs.hpp

@@ -20,7 +20,7 @@ namespace mfem
 class KnotVector;
 
 /// An arbitrary order and dimension NURBS element
-class NURBSFiniteElement : public ScalarFiniteElement
+class NURBSFiniteElement
 {
 protected:
    mutable Array <const KnotVector*> kv;
@@ -30,31 +30,34 @@ protected:
 
 public:
    /** @brief Construct NURBSFiniteElement with given
-       @param D    Reference space dimension
-       @param G    Geometry type (of type Geometry::Type)
-       @param Do   Number of degrees of freedom in the FiniteElement
-       @param O    Order/degree of the FiniteElement
-       @param F    FunctionSpace type of the FiniteElement
+       @param dim    Reference space dimension
     */
-   NURBSFiniteElement(int D, Geometry::Type G, int Do, int O, int F)
-      : ScalarFiniteElement(D, G, Do, O, F)
+   NURBSFiniteElement(int dim)
    {
       ijk = NULL;
       patch = elem = -1;
       kv.SetSize(dim);
-      weights.SetSize(dof);
-      weights = 1.0;
    }
 
+   /// Resets the patch and element data stored in the element
    void                 Reset      ()         const { patch = elem = -1; }
+   /// Set which IJK in patch should be evaluated
    void                 SetIJK     (const int *IJK) const { ijk = IJK; }
+   /// Get which patch is currently considered
    int                  GetPatch   ()         const { return patch; }
+   /// Set which patch should be evaluated
    void                 SetPatch   (int p)    const { patch = p; }
+   /// Set which elemenet should be evaluated
    int                  GetElement ()         const { return elem; }
+   /// Get which element is currently considered
    void                 SetElement (int e)    const { elem = e; }
+   /// Get the KnotVectors
    Array <const KnotVector*> &KnotVectors()   const { return kv; }
+   /// Get the Weights
    Vector              &Weights    ()         const { return weights; }
-   /// Update the NURBSFiniteElement according to the currently set knot vectors
+   /// Update the polynomial order according to the currently set knotvectors
+   /// Resizes all internal data members to have the correct size
+   /// related to the polynomial order
    virtual void         SetOrder   ()         const { }
 
    /// Returns the indices (i,j) in 2D or (i,j,k) in 3D of this element in the
@@ -64,7 +67,8 @@ public:
 
 
 /// An arbitrary order 1D NURBS element on a segment
-class NURBS1DFiniteElement : public NURBSFiniteElement
+class NURBS1DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
    mutable Vector shape_x;
@@ -72,7 +76,8 @@ protected:
 public:
    /// Construct the NURBS1DFiniteElement of order @a p
    NURBS1DFiniteElement(int p)
-      : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
+      : ScalarFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
+        NURBSFiniteElement(1),
         shape_x(p + 1) { }
 
    virtual void SetOrder() const;
@@ -84,7 +89,8 @@ public:
 };
 
 /// An arbitrary order 2D NURBS element on a square
-class NURBS2DFiniteElement : public NURBSFiniteElement
+class NURBS2DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
    mutable Vector u, shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
@@ -93,16 +99,18 @@ protected:
 public:
    /// Construct the NURBS2DFiniteElement of order @a p
    NURBS2DFiniteElement(int p)
-      : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
-                           FunctionSpace::Qk),
+      : ScalarFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
+                            FunctionSpace::Qk),
+        NURBSFiniteElement(2),
         u(dof), shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
         dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1), du(dof,2)
    { orders[0] = orders[1] = p; }
 
    /// Construct the NURBS2DFiniteElement with x-order @a px and y-order @a py
    NURBS2DFiniteElement(int px, int py)
-      : NURBSFiniteElement(2, Geometry::SQUARE, (px + 1)*(py + 1),
-                           std::max(px, py), FunctionSpace::Qk),
+      : ScalarFiniteElement(2, Geometry::SQUARE, (px + 1)*(py + 1),
+                            std::max(px, py), FunctionSpace::Qk),
+        NURBSFiniteElement(2),
         u(dof), shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
         dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1), du(dof,2)
    { orders[0] = px; orders[1] = py; }
@@ -116,7 +124,8 @@ public:
 };
 
 /// An arbitrary order 3D NURBS element on a cube
-class NURBS3DFiniteElement : public NURBSFiniteElement
+class NURBS3DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
    mutable Vector u, shape_x, shape_y, shape_z;
@@ -127,8 +136,9 @@ protected:
 public:
    /// Construct the NURBS3DFiniteElement of order @a p
    NURBS3DFiniteElement(int p)
-      : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
-                           FunctionSpace::Qk),
+      : ScalarFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
+                            FunctionSpace::Qk),
+        NURBSFiniteElement(3),
         u(dof), shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
         dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
         d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1), du(dof,3)
@@ -137,8 +147,9 @@ public:
    /// Construct the NURBS3DFiniteElement with x-order @a px and y-order @a py
    /// and z-order @a pz
    NURBS3DFiniteElement(int px, int py, int pz)
-      : NURBSFiniteElement(3, Geometry::CUBE, (px + 1)*(py + 1)*(pz + 1),
-                           std::max(std::max(px,py),pz), FunctionSpace::Qk),
+      : ScalarFiniteElement(3, Geometry::CUBE, (px + 1)*(py + 1)*(pz + 1),
+                            std::max(std::max(px,py),pz), FunctionSpace::Qk),
+        NURBSFiniteElement(2),
         u(dof), shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
         dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
         d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1), du(dof,3)
@@ -152,6 +163,352 @@ public:
                              DenseMatrix &hessian) const;
 };
 
+
+/** An arbitrary order H(div)-conforming 2D NURBS element on a square.
+    More details in the following papers:
+
+[1] Annalisa Buffa, Carlo De Falco, Giancarlo Sangalli
+"Isogeometric analysis: stable elements for the 2D Stokes equation."
+International Journal for Numerical Methods in Fluids 65 (11‐12) 1407-1422
+
+[2] John A Evans, Thomas JR Hughes
+"Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations."
+Journal of Computational Physics (241) 141-167
+*/
+class NURBS_HDiv2DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
+   mutable Vector shape1_x, shape1_y, dshape1_x, dshape1_y, d2shape1_x, d2shape1_y;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HDiv2DFiniteElement of order @a p
+   NURBS_HDiv2DFiniteElement(int p)
+      : VectorFiniteElement(2, Geometry::SQUARE, 2*(p + 1)*(p + 2), p,
+                            H_DIV,FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
+        dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), dshape1_x(p + 2),
+        dshape1_y(p + 2), d2shape1_x(p + 2), d2shape1_y(p + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = orders[1] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   /// Construct the NURBS_HDiv2DFiniteElement with x-order @a px and y-order @a py
+   NURBS_HDiv2DFiniteElement(int px, int py)
+      : VectorFiniteElement(2, Geometry::SQUARE,
+                            (px + 2)*(py + 1)+(px + 1)*(py + 2),
+                            std::max(px, py), H_DIV, FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
+        dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1),
+        shape1_x(px + 2), shape1_y(py + 2), dshape1_x(px + 2),
+        dshape1_y(py + 2), d2shape1_x(px + 2), d2shape1_y(py + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = px; orders[1] = py;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   virtual void SetOrder() const;
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the divergence of all shape functions of a *vector*
+       finite element in reference space at the given point @a ip. */
+   /** The size (#dof) of the result Vector @a divshape must be set in advance.
+    */
+   virtual void CalcDivShape(const IntegrationPoint &ip,
+                             Vector &divshape) const;
+
+   ~NURBS_HDiv2DFiniteElement();
+};
+
+
+/** An arbitrary order H(div)-conforming 3D NURBS element on a cube
+    More details in the following papers:
+
+    [1] Annalisa Buffa, Carlo De Falco, Giancarlo Sangalli
+    "Isogeometric analysis: stable elements for the 2D Stokes equation."
+    International Journal for Numerical Methods in Fluids 65 (11‐12) 1407-1422
+
+    [2] John A Evans, Thomas JR Hughes
+    "Isogeometric divergence-conforming B-splines for the unsteady
+    Navier–Stokes equations."
+    Journal of Computational Physics (241) 141-167 */
+class NURBS_HDiv3DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, shape_z;
+   mutable Vector dshape_x, dshape_y, dshape_z;
+   mutable Vector d2shape_x, d2shape_y, d2shape_z;
+   mutable Vector shape1_x, shape1_y, shape1_z;
+   mutable Vector dshape1_x, dshape1_y, dshape1_z;
+   mutable Vector d2shape1_x, d2shape1_y, d2shape1_z;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HDiv3DFiniteElement of order @a p
+   NURBS_HDiv3DFiniteElement(int p)
+      : VectorFiniteElement(3, Geometry::CUBE, 3*(p + 1)*(p + 1)*(p + 2),
+                            p, H_DIV,FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
+        dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
+        d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), shape1_z(p + 2),
+        dshape1_x(p + 2), dshape1_y(p + 2),dshape1_z(p + 2),
+        d2shape1_x(p + 2), d2shape1_y(p + 2), d2shape1_z(p + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = orders[1] = orders[2] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   /// Construct the NURBS_HDiv3DFiniteElement with x-order @a px, y-order @a py and z-order @a pz
+   NURBS_HDiv3DFiniteElement(int px, int py, int pz)
+      : VectorFiniteElement(3, Geometry::CUBE,
+                            (px + 2)*(py + 1)*(pz + 1) +
+                            (px + 1)*(py + 2)*(pz + 1) +
+                            (px + 1)*(py + 1)*(pz + 2),
+                            std::max(px, py), H_DIV, FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
+        dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
+        d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1),
+        shape1_x(px + 2), shape1_y(py + 2), shape1_z(pz + 2),
+        dshape1_x(px + 2), dshape1_y(py + 2),dshape1_z(pz + 2),
+        d2shape1_x(px + 2), d2shape1_y(py + 2), d2shape1_z(pz + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = px; orders[1] = py; orders[2] = pz;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   virtual void SetOrder() const;
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the divergence of all shape functions of a *vector*
+       finite element in reference space at the given point @a ip. */
+   /** The size (#dof) of the result Vector @a divshape must be set in advance.
+    */
+   virtual void CalcDivShape(const IntegrationPoint &ip,
+                             Vector &divshape) const;
+
+   ~NURBS_HDiv3DFiniteElement();
+};
+
+
+/** An arbitrary order H(curl)-conforming 2D NURBS element on a square
+    More details in the following paper:
+
+    [1] Annalisa Buffa, Giancarlo Sangalli, Rafael Vázquez
+    "Isogeometric analysis in electromagnetics: B-splines approximation."
+    Computer Methods in Applied Mechanics and Engineering (199) 1143-1152 */
+class NURBS_HCurl2DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
+   mutable Vector shape1_x, shape1_y, dshape1_x, dshape1_y, d2shape1_x, d2shape1_y;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HCurl2DFiniteElement of order @a p
+   NURBS_HCurl2DFiniteElement(int p)
+      : VectorFiniteElement(2, Geometry::SQUARE, 2*(p + 1)*(p + 2), p,
+                            H_CURL,FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
+        dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), dshape1_x(p + 2),
+        dshape1_y(p + 2), d2shape1_x(p + 2), d2shape1_y(p + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = orders[1] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   /// Construct the NURBS_HCurl2DFiniteElement with x-order @a px and y-order @a py
+   NURBS_HCurl2DFiniteElement(int px, int py)
+      : VectorFiniteElement(2, Geometry::SQUARE,
+                            (px + 1)*(py + 2)+(px + 2)*(py + 1),
+                            std::max(px, py), H_CURL, FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
+        dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1),
+        shape1_x(px + 2), shape1_y(py + 2), dshape1_x(px + 2),
+        dshape1_y(py + 2), d2shape1_x(px + 2), d2shape1_y(py + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = px; orders[1] = py;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   virtual void SetOrder() const;
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the curl of all shape functions of a *vector* finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a curl_shape contains the components
+       of the curl of one vector shape function. The size (#dof x CDim) of
+       @a curl_shape must be set in advance, where CDim = 3 for #dim = 3 and
+       CDim = 1 for #dim = 2. */
+   virtual void CalcCurlShape(const IntegrationPoint &ip,
+                              DenseMatrix &curl_shape) const;
+
+   ~NURBS_HCurl2DFiniteElement();
+};
+
+
+/** An arbitrary order H(curl)-conforming 3D NURBS element on a cube
+    More details in the following paper:
+
+    [1] Annalisa Buffa, Giancarlo Sangalli, Rafael Vázquez
+    "Isogeometric analysis in electromagnetics: B-splines approximation."
+    Computer Methods in Applied Mechanics and Engineering (199) 1143-1152 */
+class NURBS_HCurl3DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, shape_z;
+   mutable Vector dshape_x, dshape_y, dshape_z;
+   mutable Vector d2shape_x, d2shape_y, d2shape_z;
+   mutable Vector shape1_x, shape1_y, shape1_z;
+   mutable Vector dshape1_x, dshape1_y, dshape1_z;
+   mutable Vector d2shape1_x, d2shape1_y, d2shape1_z;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HCurl3DFiniteElement of order @a p
+   NURBS_HCurl3DFiniteElement(int p)
+      : VectorFiniteElement(3, Geometry::CUBE, 3*(p + 1)*(p + 2)*(p + 2), p,
+                            H_CURL,FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
+        dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
+        d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), shape1_z(p + 2),
+        dshape1_x(p + 2), dshape1_y(p + 2),dshape1_z(p + 2),
+        d2shape1_x(p + 2), d2shape1_y(p + 2), d2shape1_z(p + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = orders[1] = orders[2] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   /// Construct the NURBS_HCurl3DFiniteElement with x-order @a px, y-order @a py and z-order @a pz
+   NURBS_HCurl3DFiniteElement(int px, int py, int pz)
+      : VectorFiniteElement(3, Geometry::CUBE,
+                            (px + 1)*(py + 2)*(pz + 2) +
+                            (px + 2)*(py + 1)*(pz + 2) +
+                            (px + 2)*(py + 2)*(pz + 1),
+                            std::max(std::max(px, py), pz), H_CURL, FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
+        dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
+        d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1),
+        shape1_x(px + 2), shape1_y(py + 2), shape1_z(pz + 2),
+        dshape1_x(px + 2), dshape1_y(py + 2),dshape1_z(pz + 2),
+        d2shape1_x(px + 2), d2shape1_y(py + 2), d2shape1_z(pz + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = px; orders[1] = py; orders[2] = pz;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   virtual void SetOrder() const;
+
+   virtual void CalcVShape(const IntegrationPoint &ip,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   virtual void CalcVShape(ElementTransformation &Trans,
+                           DenseMatrix &shape) const;
+
+   /** @brief Evaluate the curl of all shape functions of a *vector* finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a curl_shape contains the components
+       of the curl of one vector shape function. The size (#dof x CDim) of
+       @a curl_shape must be set in advance, where CDim = 3 for #dim = 3 and
+       CDim = 1 for #dim = 2. */
+   virtual void CalcCurlShape(const IntegrationPoint &ip,
+                              DenseMatrix &curl_shape) const;
+
+   ~NURBS_HCurl3DFiniteElement();
+};
+
 } // namespace mfem
 
 #endif

fem/fe_coll.cpp

@@ -344,6 +344,32 @@ FiniteElementCollection *FiniteElementCollection::New(const char *name)
    {
       fec = new Local_FECollection(name + 6);
    }
+   else if (!strncmp(name, "NURBS_HDiv", 10))
+   {
+      if (name[10] != '\0')
+      {
+         // "NURBS" + "number" --> fixed order nurbs collection
+         fec = new NURBS_HDivFECollection(atoi(name + 10));
+      }
+      else
+      {
+         // "NURBS" --> variable order nurbs collection
+         fec = new NURBS_HDivFECollection();
+      }
+   }
+   else if (!strncmp(name, "NURBS_HCurl", 11))
+   {
+      if (name[11] != '\0')
+      {
+         // "NURBS" + "number" --> fixed order nurbs collection
+         fec = new NURBS_HCurlFECollection(atoi(name + 11));
+      }
+      else
+      {
+         // "NURBS" --> variable order nurbs collection
+         fec = new NURBS_HCurlFECollection();
+      }
+   }
    else if (!strncmp(name, "NURBS", 5))
    {
       if (name[5] != '\0')
@@ -3533,4 +3559,192 @@ FiniteElementCollection *NURBSFECollection::GetTraceCollection() const
    return NULL;
 }
 
+
+NURBS_HDivFECollection::NURBS_HDivFECollection(int Order, const int dim)
+   : NURBSFECollection((Order == VariableOrder) ? 1 : Order)
+{
+   const int order = (Order == VariableOrder) ? 1 : Order;
+
+   SegmentFE       = new NURBS1DFiniteElement(order);
+   QuadrilateralFE = new NURBS2DFiniteElement(order);
+
+   QuadrilateralVFE  = new NURBS_HDiv2DFiniteElement(order);
+   ParallelepipedVFE = new NURBS_HDiv3DFiniteElement(order);
+
+   if (dim != -1) { SetDim(dim); }
+   SetOrder(Order);
+}
+
+void NURBS_HDivFECollection::SetDim(int dim)
+{
+   if (dim == 2)
+   {
+      sFE = SegmentFE;
+      qFE = QuadrilateralVFE;
+      hFE = nullptr;
+   }
+   else if (dim == 3)
+   {
+      sFE = nullptr;
+      qFE = QuadrilateralFE;
+      hFE = ParallelepipedVFE;
+   }
+   else
+   {
+      mfem::err<<"Dimension = "<<dim<<endl;
+      mfem_error ("NURBS_HDivFECollection: wrong dimension!");
+   }
+}
+
+NURBS_HDivFECollection::~NURBS_HDivFECollection()
+{
+   delete SegmentFE;
+   delete QuadrilateralFE;
+   delete QuadrilateralVFE;
+   delete ParallelepipedVFE;
+}
+
+const FiniteElement *
+NURBS_HDivFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   switch (GeomType)
+   {
+      case Geometry::SEGMENT:     return sFE;
+      case Geometry::SQUARE:      return qFE;
+      case Geometry::CUBE:        return hFE;
+      default:
+         if (error_mode == RETURN_NULL) { return nullptr; }
+         mfem_error ("NURBS_HDivFECollection: unknown geometry type.");
+   }
+   return QuadrilateralFE; // Make some compilers happy
+}
+
+void NURBS_HDivFECollection::SetOrder(int Order) const
+{
+   mOrder = Order;
+   if (Order != VariableOrder)
+   {
+      snprintf(name, 16, "NURBS_HDiv%i", Order);
+   }
+   else
+   {
+      snprintf(name, 16, "NURBS_HDiv");
+   }
+}
+
+int NURBS_HDivFECollection::DofForGeometry(Geometry::Type GeomType) const
+{
+   mfem_error("NURBS_HDivFECollection::DofForGeometry");
+   return 0; // Make some compilers happy
+}
+
+const int *NURBS_HDivFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType,
+   int Or) const
+{
+   mfem_error("NURBS_HDivFECollection::DofOrderForOrientation");
+   return NULL;
+}
+
+FiniteElementCollection *NURBS_HDivFECollection::GetTraceCollection() const
+{
+   MFEM_ABORT("NURBS finite elements can not be statically condensed!");
+   return NULL;
+}
+
+NURBS_HCurlFECollection::NURBS_HCurlFECollection(int Order, const int dim)
+   : NURBSFECollection((Order == VariableOrder) ? 1 : Order)
+{
+   const int order = (Order == VariableOrder) ? 1 : Order;
+
+   SegmentFE       = new NURBS1DFiniteElement(order+1);
+   QuadrilateralFE = new NURBS2DFiniteElement(order+1);
+
+   QuadrilateralVFE  = new NURBS_HCurl2DFiniteElement(order);
+   ParallelepipedVFE = new NURBS_HCurl3DFiniteElement(order);
+   if (dim != -1) { SetDim(dim); }
+   SetOrder(Order);
+}
+
+void NURBS_HCurlFECollection::SetDim(int dim)
+{
+   if (dim == 2)
+   {
+      sFE = SegmentFE;
+      qFE = QuadrilateralVFE;
+      hFE = nullptr;
+   }
+   else if (dim == 3)
+   {
+      sFE = nullptr;
+      qFE = QuadrilateralFE;
+      hFE = ParallelepipedVFE;
+   }
+   else
+   {
+      mfem::err<<"Dimension = "<<dim<<endl;
+      mfem_error ("NURBS_HCurlFECollection: wrong dimension!");
+   }
+}
+
+
+
+NURBS_HCurlFECollection::~NURBS_HCurlFECollection()
+{
+   delete SegmentFE;
+   delete QuadrilateralFE;
+   delete QuadrilateralVFE;
+   delete ParallelepipedVFE;
+}
+
+const FiniteElement *
+NURBS_HCurlFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   switch (GeomType)
+   {
+      case Geometry::SEGMENT:     return sFE;
+      case Geometry::SQUARE:      return qFE;
+      case Geometry::CUBE:        return hFE;
+      default:
+         if (error_mode == RETURN_NULL) { return nullptr; }
+         mfem_error ("NURBS_HCurlFECollection: unknown geometry type.");
+   }
+   return QuadrilateralFE; // Make some compilers happy
+}
+
+void NURBS_HCurlFECollection::SetOrder(int Order) const
+{
+   mOrder = Order;
+   if (Order != VariableOrder)
+   {
+      snprintf(name, 16, "NURBS_HCurl%i", Order);
+   }
+   else
+   {
+      snprintf(name, 16, "NURBS_HCurl");
+   }
+}
+
+int NURBS_HCurlFECollection::DofForGeometry(Geometry::Type GeomType) const
+{
+   mfem_error("NURBS_HCurlFECollection::DofForGeometry");
+   return 0; // Make some compilers happy
+}
+
+const int *NURBS_HCurlFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType,
+   int Or) const
+{
+   mfem_error("NURBS_HCurlFECollection::DofOrderForOrientation");
+   return NULL;
+}
+
+FiniteElementCollection *NURBS_HCurlFECollection::GetTraceCollection() const
+{
+   MFEM_ABORT("NURBS finite elements can not be statically condensed!");
+   return NULL;
+}
+
+
+
 }

fem/fe_coll.hpp

@@ -680,8 +680,8 @@ public:
 /// Arbitrary order non-uniform rational B-splines (NURBS) finite elements.
 class NURBSFECollection : public FiniteElementCollection
 {
-private:
-   PointFiniteElement   *PointFE;
+protected:
+   PointFiniteElement *PointFE;
    NURBS1DFiniteElement *SegmentFE;
    NURBS2DFiniteElement *QuadrilateralFE;
    NURBS3DFiniteElement *ParallelepipedFE;
@@ -701,13 +701,15 @@ public:
       order, or VariableOrder (default). */
    explicit NURBSFECollection(int Order = VariableOrder);
 
-   void Reset() const
+   virtual void Reset() const
    {
       SegmentFE->Reset();
       QuadrilateralFE->Reset();
       ParallelepipedFE->Reset();
    }
 
+   virtual void SetDim(const int dim) {};
+
    /** @brief Get the order of the NURBS collection: either a positive number,
        when using fixed order, or VariableOrder. */
    /** @note Not to be confused with FiniteElementCollection::GetOrder(). */
@@ -715,7 +717,7 @@ public:
 
    /** @brief Set the order and the name, based on the given @a Order: either a
        positive number for fixed order, or VariableOrder. */
-   void SetOrder(int Order) const;
+   virtual void SetOrder(int Order) const;
 
    const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const override;
@@ -734,6 +736,109 @@ public:
    virtual ~NURBSFECollection();
 };
 
+/// Arbitrary order H(div) NURBS finite elements.
+class NURBS_HDivFECollection : public NURBSFECollection
+{
+private:
+
+   NURBS1DFiniteElement *SegmentFE;
+   NURBS2DFiniteElement *QuadrilateralFE;
+
+   NURBS_HDiv2DFiniteElement *QuadrilateralVFE;
+   NURBS_HDiv3DFiniteElement *ParallelepipedVFE;
+
+   FiniteElement *sFE;
+   FiniteElement *qFE;
+   FiniteElement *hFE;
+
+public:
+
+   /** @brief The parameter @a Order must be either a positive number, for fixed
+      order, or VariableOrder (default). */
+   explicit NURBS_HDivFECollection(int Order = VariableOrder, const int vdim = -1);
+
+   virtual void Reset() const override
+   {
+      SegmentFE->Reset();
+      QuadrilateralFE->Reset();
+      QuadrilateralVFE->Reset();
+      ParallelepipedVFE->Reset();
+   }
+
+   virtual void SetDim(const int dim) override;
+
+   /** @brief Set the order and the name, based on the given @a Order: either a
+       positive number for fixed order, or VariableOrder. */
+   virtual void SetOrder(int Order) const override;
+
+   const FiniteElement *
+   FiniteElementForGeometry(Geometry::Type GeomType) const override;
+
+   int DofForGeometry(Geometry::Type GeomType) const override;
+
+   const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                     int Or) const override;
+
+   const char *Name() const override { return name; }
+
+   int GetContType() const override { return CONTINUOUS; }
+
+   FiniteElementCollection *GetTraceCollection() const override;
+
+   virtual ~NURBS_HDivFECollection();
+};
+
+/// Arbitrary order H(curl) NURBS finite elements.
+class NURBS_HCurlFECollection : public NURBSFECollection
+{
+private:
+   NURBS1DFiniteElement *SegmentFE;
+   NURBS2DFiniteElement *QuadrilateralFE;
+
+   NURBS_HCurl2DFiniteElement *QuadrilateralVFE;
+   NURBS_HCurl3DFiniteElement *ParallelepipedVFE;
+
+   FiniteElement *sFE;
+   FiniteElement *qFE;
+   FiniteElement *hFE;
+public:
+
+   /** @brief The parameter @a Order must be either a positive number, for fixed
+      order, or VariableOrder (default). */
+   explicit NURBS_HCurlFECollection(int Order = VariableOrder,
+                                    const int vdim = -1);
+
+   virtual void Reset() const override
+   {
+      SegmentFE->Reset();
+      QuadrilateralFE->Reset();
+      QuadrilateralVFE->Reset();
+      ParallelepipedVFE->Reset();
+   }
+
+   virtual void SetDim(const int dim) override;
+
+   /** @brief Set the order and the name, based on the given @a Order: either a
+       positive number for fixed order, or VariableOrder. */
+   virtual void SetOrder(int Order) const override;
+
+   const FiniteElement *
+   FiniteElementForGeometry(Geometry::Type GeomType) const override;
+
+   int DofForGeometry(Geometry::Type GeomType) const override;
+
+   const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                     int Or) const override;
+
+   const char *Name() const override { return name; }
+
+   int GetContType() const override { return CONTINUOUS; }
+
+   FiniteElementCollection *GetTraceCollection() const override;
+
+   virtual ~NURBS_HCurlFECollection();
+};
+
 /// Piecewise-(bi/tri)linear continuous finite elements.
 class LinearFECollection : public FiniteElementCollection
 {

fem/fespace.cpp

@@ -1525,6 +1525,67 @@ SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    return P;
 }
 
+SparseMatrix *FiniteElementSpace::VariableOrderRefinementMatrix(
+   const int coarse_ndofs, const Table &coarse_elem_dof) const
+{
+   MFEM_VERIFY(mesh->GetLastOperation() == Mesh::REFINE, "");
+
+   Array<int> dofs, coarse_dofs, coarse_vdofs;
+   Vector row;
+
+   Mesh::GeometryList elem_geoms(*mesh);
+
+   SparseMatrix *P = new SparseMatrix(GetVSize(), coarse_ndofs*vdim);
+
+   Array<int> mark(P->Height());
+   mark = 0;
+
+   const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
+   DenseMatrix lP;
+   IsoparametricTransformation isotr;
+   for (int k = 0; k < mesh->GetNE(); k++)
+   {
+      const Embedding &emb = rtrans.embeddings[k];
+      const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
+
+      const FiniteElement *fe = GetFE(k);
+      isotr.SetIdentityTransformation(geom);
+      const int ldof = fe->GetDof();
+      lP.SetSize(ldof, ldof);
+      const DenseTensor &pmats = rtrans.point_matrices[geom];
+      isotr.SetPointMat(pmats(emb.matrix));
+      fe->GetLocalInterpolation(isotr, lP);
+
+      const int fine_ldof = lP.Height();
+
+      elem_dof->GetRow(k, dofs);
+      coarse_elem_dof.GetRow(emb.parent, coarse_dofs);
+
+      for (int vd = 0; vd < vdim; vd++)
+      {
+         coarse_dofs.Copy(coarse_vdofs);
+         DofsToVDofs(vd, coarse_vdofs, coarse_ndofs);
+
+         for (int i = 0; i < fine_ldof; i++)
+         {
+            const int r = DofToVDof(dofs[i], vd);
+            int m = (r >= 0) ? r : (-1 - r);
+
+            if (!mark[m])
+            {
+               lP.GetRow(i, row);
+               P->SetRow(r, coarse_vdofs, row);
+               mark[m] = 1;
+            }
+         }
+      }
+   }
+
+   MFEM_VERIFY(mark.Sum() == P->Height(), "Not all rows of P set.");
+   P->Finalize();
+   return P;
+}
+
 void FiniteElementSpace::GetLocalRefinementMatrices(
    Geometry::Type geom, DenseTensor &localP) const
 {
@@ -1556,15 +1617,20 @@ SparseMatrix* FiniteElementSpace::RefinementMatrix(int old_ndofs,
                "Previous mesh is not coarser.");
 
    Mesh::GeometryList elem_geoms(*mesh);
-
-   DenseTensor localP[Geometry::NumGeom];
-   for (int i = 0; i < elem_geoms.Size(); i++)
+   if (!IsVariableOrder())
    {
-      GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+      DenseTensor localP[Geometry::NumGeom];
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+      }
+      return RefinementMatrix_main(old_ndofs, *old_elem_dof, old_elem_fos,
+                                   localP);
+   }
+   else
+   {
+      return VariableOrderRefinementMatrix(old_ndofs, *old_elem_dof);
    }
-
-   return RefinementMatrix_main(old_ndofs, *old_elem_dof, old_elem_fos,
-                                localP);
 }
 
 FiniteElementSpace::RefinementOperator::RefinementOperator(
@@ -1582,9 +1648,12 @@ FiniteElementSpace::RefinementOperator::RefinementOperator(
 
    Mesh::GeometryList elem_geoms(*fespace->GetMesh());
 
-   for (int i = 0; i < elem_geoms.Size(); i++)
+   if (!fespace->IsVariableOrder())
    {
-      fespace->GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         fespace->GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+      }
    }
 
    ConstructDoFTransArray();
@@ -1597,10 +1666,13 @@ FiniteElementSpace::RefinementOperator::RefinementOperator(
 {
    Mesh::GeometryList elem_geoms(*fespace->GetMesh());
 
-   for (int i = 0; i < elem_geoms.Size(); i++)
+   if (!fespace->IsVariableOrder())
    {
-      fespace->GetLocalRefinementMatrices(*coarse_fes, elem_geoms[i],
-                                          localP[elem_geoms[i]]);
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         fespace->GetLocalRefinementMatrices(*coarse_fes, elem_geoms[i],
+                                             localP[elem_geoms[i]]);
+      }
    }
 
    // Make a copy of the coarse elem_dof Table.
@@ -1676,11 +1748,25 @@ void FiniteElementSpace::RefinementOperator::Mult(const Vector &x,
 
    Vector subY, subX;
 
+   DenseMatrix eP;
+   IsoparametricTransformation isotr;
+
    for (int k = 0; k < mesh_ref->GetNE(); k++)
    {
       const Embedding &emb = trans_ref.embeddings[k];
       const Geometry::Type geom = mesh_ref->GetElementBaseGeometry(k);
-      const DenseMatrix &lP = localP[geom](emb.matrix);
+      if (fespace->IsVariableOrder())
+      {
+         const FiniteElement *fe = fespace->GetFE(k);
+         isotr.SetIdentityTransformation(geom);
+         const int ldof = fe->GetDof();
+         eP.SetSize(ldof, ldof);
+         const DenseTensor &pmats = trans_ref.point_matrices[geom];
+         isotr.SetPointMat(pmats(emb.matrix));
+         fe->GetLocalInterpolation(isotr, eP);
+      }
+      const DenseMatrix &lP = (fespace->IsVariableOrder()) ? eP : localP[geom](
+                                 emb.matrix);
 
       subY.SetSize(lP.Height());
 
@@ -1745,11 +1831,28 @@ void FiniteElementSpace::RefinementOperator::MultTranspose(const Vector &x,
 
    Vector subY, subX, subYt;
 
+   DenseMatrix eP;
+   IsoparametricTransformation isotr;
+   const FiniteElement *fe = nullptr;
+
    for (int k = 0; k < mesh_ref->GetNE(); k++)
    {
       const Embedding &emb = trans_ref.embeddings[k];
       const Geometry::Type geom = mesh_ref->GetElementBaseGeometry(k);
-      const DenseMatrix &lP = localP[geom](emb.matrix);
+
+      if (fespace->IsVariableOrder())
+      {
+         fe = fespace->GetFE(k);
+         isotr.SetIdentityTransformation(geom);
+         const int ldof = fe->GetDof();
+         eP.SetSize(ldof);
+         const DenseTensor &pmats = trans_ref.point_matrices[geom];
+         isotr.SetPointMat(pmats(emb.matrix));
+         fe->GetLocalInterpolation(isotr, eP);
+      }
+
+      const DenseMatrix &lP = (fespace->IsVariableOrder()) ? eP : localP[geom](
+                                 emb.matrix);
 
       DofTransformation *doftrans = fespace->GetElementDofs(k, f_dofs);
       old_elem_dof->GetRow(emb.parent, c_dofs);
@@ -2108,9 +2211,12 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
    Mesh::GeometryList elem_geoms(*mesh);
 
    DenseTensor localR[Geometry::NumGeom];
-   for (int i = 0; i < elem_geoms.Size(); i++)
+   if (!IsVariableOrder())
    {
-      GetLocalDerefinementMatrices(elem_geoms[i], localR[elem_geoms[i]]);
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         GetLocalDerefinementMatrices(elem_geoms[i], localR[elem_geoms[i]]);
+      }
    }
 
    SparseMatrix *R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim);
@@ -2125,14 +2231,34 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
 
    bool is_dg = FEColl()->GetContType() == FiniteElementCollection::DISCONTINUOUS;
    int num_marked = 0;
+   const FiniteElement *fe = nullptr;
+   DenseMatrix localRVO; //for variable order only
    for (int k = 0; k < dtrans.embeddings.Size(); k++)
    {
       const Embedding &emb = dtrans.embeddings[k];
       Geometry::Type geom = mesh->GetElementBaseGeometry(emb.parent);
-      DenseMatrix &lR = localR[geom](emb.matrix);
+
+      if (IsVariableOrder())
+      {
+         fe = GetFE(emb.parent);
+         const DenseTensor &pmats = dtrans.point_matrices[geom];
+         const int ldof = fe->GetDof();
+
+         IsoparametricTransformation isotr;
+         isotr.SetIdentityTransformation(geom);
+
+         localRVO.SetSize(ldof, ldof);
+         isotr.SetPointMat(pmats(emb.matrix));
+         // Local restriction is size ldofxldof assuming that the parent and
+         // child are of same polynomial order.
+         fe->GetLocalRestriction(isotr, localRVO);
+      }
+      DenseMatrix &lR = IsVariableOrder() ? localRVO : localR[geom](emb.matrix);
 
       elem_dof->GetRow(emb.parent, dofs);
       old_elem_dof->GetRow(k, old_dofs);
+      MFEM_VERIFY(old_dofs.Size() == dofs.Size(),
+                  "Parent and child must have same #dofs.");
 
       for (int vd = 0; vd < vdim; vd++)
       {
@@ -2158,7 +2284,7 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
       }
    }
 
-   if (!is_dg)
+   if (!is_dg && !IsVariableOrder())
    {
       MFEM_VERIFY(num_marked == R->Height(),
                   "internal error: not all rows of R were set.");
@@ -2216,6 +2342,7 @@ void FiniteElementSpace::Constructor(Mesh *mesh_, NURBSExtension *NURBSext_,
 
    const NURBSFECollection *nurbs_fec =
       dynamic_cast<const NURBSFECollection *>(fec_);
+
    if (nurbs_fec)
    {
       MFEM_VERIFY(mesh_->NURBSext, "NURBS FE space requires a NURBS mesh.");
@@ -2312,12 +2439,63 @@ void FiniteElementSpace::UpdateNURBS()
    face_dof = NULL;
    face_to_be.DeleteAll();
 
+   // Depending on the element type create the appropriate extensions
+   // for the individual components.
    dynamic_cast<const NURBSFECollection *>(fec)->Reset();
 
-   ndofs = NURBSext->GetNDof();
-   elem_dof = NURBSext->GetElementDofTable();
-   bdr_elem_dof = NURBSext->GetBdrElementDofTable();
+   if (dynamic_cast<const NURBS_HDivFECollection *>(fec))
+   {
+      VNURBSext.SetSize(mesh->Dimension());
+      for (int d = 0; d < mesh->Dimension(); d++)
+      {
+         VNURBSext[d] = NURBSext->GetDivExtension(d);
+      }
+   }
 
+   if (dynamic_cast<const NURBS_HCurlFECollection *>(fec))
+   {
+      VNURBSext.SetSize(mesh->Dimension());
+      for (int d = 0; d < mesh->Dimension(); d++)
+      {
+         VNURBSext[d] = NURBSext->GetCurlExtension(d);
+      }
+   }
+
+   // If required: concatenate the dof tables of the individual components into
+   // one dof table for the vector fespace.
+   if (VNURBSext.Size() == 2)
+   {
+      int offset1 = VNURBSext[0]->GetNDof();
+      ndofs = VNURBSext[0]->GetNDof() + VNURBSext[1]->GetNDof();
+
+      // Merge Tables
+      elem_dof = new Table(*VNURBSext[0]->GetElementDofTable(),
+                           *VNURBSext[1]->GetElementDofTable(),offset1 );
+
+      bdr_elem_dof = new Table(*VNURBSext[0]->GetBdrElementDofTable(),
+                               *VNURBSext[1]->GetBdrElementDofTable(),offset1);
+   }
+   else if (VNURBSext.Size() == 3)
+   {
+      int offset1 = VNURBSext[0]->GetNDof();
+      int offset2 = offset1 + VNURBSext[1]->GetNDof();
+      ndofs = offset2 + VNURBSext[2]->GetNDof();
+
+      // Merge Tables
+      elem_dof = new Table(*VNURBSext[0]->GetElementDofTable(),
+                           *VNURBSext[1]->GetElementDofTable(),offset1,
+                           *VNURBSext[2]->GetElementDofTable(),offset2);
+
+      bdr_elem_dof = new Table(*VNURBSext[0]->GetBdrElementDofTable(),
+                               *VNURBSext[1]->GetBdrElementDofTable(),offset1,
+                               *VNURBSext[2]->GetBdrElementDofTable(),offset2);
+   }
+   else
+   {
+      ndofs = NURBSext->GetNDof();
+      elem_dof = NURBSext->GetElementDofTable();
+      bdr_elem_dof = NURBSext->GetBdrElementDofTable();
+   }
    mesh_sequence = mesh->GetSequence();
    sequence++;
 }
@@ -3319,11 +3497,21 @@ void FiniteElementSpace::Destroy()
    dof_elem_array.DeleteAll();
    dof_ldof_array.DeleteAll();
 
+   for (int i = 0; i < VNURBSext.Size(); i++)
+   {
+      delete VNURBSext[i];
+   }
+
    if (NURBSext)
    {
       if (own_ext) { delete NURBSext; }
       delete face_dof;
       face_to_be.DeleteAll();
+      if (VNURBSext.Size() > 0 )
+      {
+         delete elem_dof;
+         delete bdr_elem_dof;
+      }
    }
    else
    {
@@ -3335,6 +3523,8 @@ void FiniteElementSpace::Destroy()
       delete [] bdofs;
    }
    ceed::RemoveBasisAndRestriction(this);
+
+
 }
 
 void FiniteElementSpace::DestroyDoFTransArray()
@@ -3353,19 +3543,27 @@ void FiniteElementSpace::GetTransferOperator(
 
    if (T.Type() == Operator::MFEM_SPARSEMAT)
    {
-      Mesh::GeometryList elem_geoms(*mesh);
-
-      DenseTensor localP[Geometry::NumGeom];
-      for (int i = 0; i < elem_geoms.Size(); i++)
+      if (!IsVariableOrder())
       {
-         GetLocalRefinementMatrices(coarse_fes, elem_geoms[i],
-                                    localP[elem_geoms[i]]);
+         Mesh::GeometryList elem_geoms(*mesh);
+
+         DenseTensor localP[Geometry::NumGeom];
+         for (int i = 0; i < elem_geoms.Size(); i++)
+         {
+            GetLocalRefinementMatrices(coarse_fes, elem_geoms[i],
+                                       localP[elem_geoms[i]]);
+         }
+         T.Reset(RefinementMatrix_main(coarse_fes.GetNDofs(),
+                                       coarse_fes.GetElementToDofTable(),
+                                       coarse_fes.
+                                       GetElementToFaceOrientationTable(),
+                                       localP));
+      }
+      else
+      {
+         T.Reset(VariableOrderRefinementMatrix(coarse_fes.GetNDofs(),
+                                               coarse_fes.GetElementToDofTable()));
       }
-      T.Reset(RefinementMatrix_main(coarse_fes.GetNDofs(),
-                                    coarse_fes.GetElementToDofTable(),
-                                    coarse_fes.
-                                    GetElementToFaceOrientationTable(),
-                                    localP));
    }
    else
    {
@@ -3416,19 +3614,33 @@ void FiniteElementSpace::GetTrueTransferOperator(
 
 void FiniteElementSpace::UpdateElementOrders()
 {
-   const CoarseFineTransformations &cf_tr = mesh->GetRefinementTransforms();
-
    Array<char> new_order(mesh->GetNE());
    switch (mesh->GetLastOperation())
    {
       case Mesh::REFINE:
       {
+         const CoarseFineTransformations &cf_tr = mesh->GetRefinementTransforms();
          for (int i = 0; i < mesh->GetNE(); i++)
          {
             new_order[i] = elem_order[cf_tr.embeddings[i].parent];
          }
          break;
       }
+      case Mesh::DEREFINE:
+      {
+         const CoarseFineTransformations &cf_tr =
+            mesh->ncmesh->GetDerefinementTransforms();
+         Table coarse_to_fine;
+         cf_tr.MakeCoarseToFineTable(coarse_to_fine);
+         Array<int> tabrow;
+         for (int i = 0; i < coarse_to_fine.Size(); i++)
+         {
+            coarse_to_fine.GetRow(i, tabrow);
+            //For now we require that all children are of same polynomial order.
+            new_order[i] = elem_order[tabrow[0]];
+         }
+         break;
+      }
       default:
          MFEM_ABORT("not implemented yet");
    }
@@ -3523,11 +3735,23 @@ void FiniteElementSpace::Update(bool want_transform)
          {
             BuildConformingInterpolation();
             Th.Reset(DerefinementMatrix(old_ndofs, old_elem_dof, old_elem_fos));
-            if (cP && cR)
+            if (IsVariableOrder())
             {
-               Th.SetOperatorOwner(false);
-               Th.Reset(new TripleProductOperator(cP.get(), cR.get(), Th.Ptr(),
-                                                  false, false, true));
+               if (cP && cR_hp)
+               {
+                  Th.SetOperatorOwner(false);
+                  Th.Reset(new TripleProductOperator(cP.get(), cR_hp.get(), Th.Ptr(),
+                                                     false, false, true));
+               }
+            }
+            else
+            {
+               if (cP && cR)
+               {
+                  Th.SetOperatorOwner(false);
+                  Th.Reset(new TripleProductOperator(cP.get(), cR.get(), Th.Ptr(),
+                                                     false, false, true));
+               }
             }
             break;
          }
@@ -3640,6 +3864,7 @@ FiniteElementCollection *FiniteElementSpace::Load(Mesh *m, std::istream &input)
    input >> ord;
 
    NURBSFECollection *nurbs_fec = dynamic_cast<NURBSFECollection*>(r_fec);
+   if (nurbs_fec) { nurbs_fec->SetDim(m->Dimension()); }
    NURBSExtension *nurbs_ext = NULL;
    if (fes_format == 90) // original format, v0.9
    {

fem/fespace.hpp

@@ -268,6 +268,10 @@ protected:
    Array<int> dof_elem_array, dof_ldof_array;
 
    NURBSExtension *NURBSext;
+   /** array of NURBS extension for H(div) and H(curl) vector elements.
+       For each direction an extension is created from the base NURBSext,
+       with an increase in order in the appropriate direction. */
+   Array<NURBSExtension*> VNURBSext;
    int own_ext;
    mutable Array<int> face_to_be; // NURBS FE space only
 
@@ -469,6 +473,11 @@ protected:
                                        const Table *coarse_elem_fos,
                                        const DenseTensor localP[]) const;
 
+   /* This method returns the Refinement matrix (i.e., the embedding)
+      from a coarse variable-order fes to a fine fes (after a geometric refinement) */
+   SparseMatrix *VariableOrderRefinementMatrix(const int coarse_ndofs,
+                                               const Table &coarse_elem_dof) const;
+
    void GetLocalRefinementMatrices(Geometry::Type geom,
                                    DenseTensor &localP) const;
    void GetLocalDerefinementMatrices(Geometry::Type geom,
@@ -517,6 +526,8 @@ protected:
                                                const Array<int> *perm);
 
 public:
+
+
    /** @brief Default constructor: the object is invalid until initialized using
        the method Load(). */
    FiniteElementSpace();
@@ -644,7 +655,10 @@ public:
    const ElementRestrictionOperator *GetElementRestriction(
       ElementDofOrdering e_ordering) const;
 
-   /// Return an Operator that converts L-vectors to E-vectors on each face.
+   /** @brief Return an Operator that converts L-vectors to E-vectors on each
+       face. */
+   /** @warning only meshes with tensor-product elements are currently
+       supported. */
    virtual const FaceRestriction *GetFaceRestriction(
       ElementDofOrdering f_ordering, FaceType,
       L2FaceValues mul = L2FaceValues::DoubleValued) const;

fem/gridfunc.cpp

@@ -12,6 +12,8 @@
 // Implementation of GridFunction
 
 #include "gridfunc.hpp"
+#include "linearform.hpp"
+#include "bilinearform.hpp"
 #include "quadinterpolator.hpp"
 #include "../mesh/nurbs.hpp"
 #include "../general/text.hpp"
@@ -39,7 +41,7 @@ GridFunction::GridFunction(Mesh *m, std::istream &input)
    UseDevice(true);
 
    fes = new FiniteElementSpace;
-   fec = fes->Load(m, input);
+   fec_owned = fes->Load(m, input);
 
    skip_comment_lines(input, '#');
    istream::int_type next_char = input.peek();
@@ -81,10 +83,10 @@ GridFunction::GridFunction(Mesh *m, GridFunction *gf_array[], int num_pieces)
    int vdim, ordering;
 
    fes = gf_array[0]->FESpace();
-   fec = FiniteElementCollection::New(fes->FEColl()->Name());
+   fec_owned = FiniteElementCollection::New(fes->FEColl()->Name());
    vdim = fes->GetVDim();
    ordering = fes->GetOrdering();
-   fes = new FiniteElementSpace(m, fec, vdim, ordering);
+   fes = new FiniteElementSpace(m, fec_owned, vdim, ordering);
    SetSize(fes->GetVSize());
 
    if (m->NURBSext)
@@ -153,11 +155,11 @@ GridFunction::GridFunction(Mesh *m, GridFunction *gf_array[], int num_pieces)
 
 void GridFunction::Destroy()
 {
-   if (fec)
+   if (fec_owned)
    {
       delete fes;
-      delete fec;
-      fec = NULL;
+      delete fec_owned;
+      fec_owned = NULL;
    }
 }
 
@@ -325,10 +327,9 @@ int GridFunction::VectorDim() const
    const FiniteElement *fe;
    if (!fes->GetNE())
    {
-      const FiniteElementCollection *fe_coll = fes->FEColl();
       static const Geometry::Type geoms[3] =
       { Geometry::SEGMENT, Geometry::TRIANGLE, Geometry::TETRAHEDRON };
-      fe = fe_coll->
+      fe = fes->FEColl()->
            FiniteElementForGeometry(geoms[fes->GetMesh()->Dimension()-1]);
    }
    else
@@ -350,7 +351,8 @@ int GridFunction::CurlDim() const
    {
       static const Geometry::Type geoms[3] =
       { Geometry::SEGMENT, Geometry::TRIANGLE, Geometry::TETRAHEDRON };
-      fe = fec->FiniteElementForGeometry(geoms[fes->GetMesh()->Dimension()-1]);
+      fe = fes->FEColl()->
+           FiniteElementForGeometry(geoms[fes->GetMesh()->Dimension()-1]);
    }
    else
    {
@@ -2372,19 +2374,48 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff)
 
    if (delta_c == NULL)
    {
-      Array<int> vdofs;
-      Vector vals;
-
-      for (int i = 0; i < fes->GetNE(); i++)
+      if (fes->GetNURBSext() == NULL)
       {
-         doftrans = fes->GetElementVDofs(i, vdofs);
-         vals.SetSize(vdofs.Size());
-         fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
-         if (doftrans)
+         Array<int> vdofs;
+         Vector vals;
+
+         for (int i = 0; i < fes->GetNE(); i++)
          {
-            doftrans->TransformPrimal(vals);
+            doftrans = fes->GetElementVDofs(i, vdofs);
+            vals.SetSize(vdofs.Size());
+            fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+            if (doftrans)
+            {
+               doftrans->TransformPrimal(vals);
+            }
+            SetSubVector(vdofs, vals);
          }
-         SetSubVector(vdofs, vals);
+      }
+      else
+      {
+         // Define and assemble linear form
+         LinearForm b(fes);
+         b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+         b.Assemble();
+
+         // Define and assemble bilinear form
+         BilinearForm a(fes);
+         a.AddDomainIntegrator(new MassIntegrator());
+         a.Assemble();
+
+         // Set solver and preconditioner
+         SparseMatrix A(a.SpMat());
+         GSSmoother  prec(A);
+         CGSolver cg;
+         cg.SetOperator(A);
+         cg.SetPreconditioner(prec);
+         cg.SetRelTol(1e-12);
+         cg.SetMaxIter(1000);
+         cg.SetPrintLevel(0);
+
+         // Solve and get solution
+         *this = 0.0;
+         cg.Mult(b,*this);
       }
    }
    else
@@ -2425,22 +2456,54 @@ void GridFunction::ProjectCoefficient(
 
 void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
 {
-   int i;
-   Array<int> vdofs;
-   Vector vals;
-
-   DofTransformation * doftrans = NULL;
-
-   for (i = 0; i < fes->GetNE(); i++)
+   if (fes->GetNURBSext() == NULL)
    {
-      doftrans = fes->GetElementVDofs(i, vdofs);
-      vals.SetSize(vdofs.Size());
-      fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-      if (doftrans)
+
+      int i;
+      Array<int> vdofs;
+      Vector vals;
+
+      DofTransformation * doftrans = NULL;
+
+      for (i = 0; i < fes->GetNE(); i++)
       {
-         doftrans->TransformPrimal(vals);
+         doftrans = fes->GetElementVDofs(i, vdofs);
+         vals.SetSize(vdofs.Size());
+         fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+         if (doftrans)
+         {
+            doftrans->TransformPrimal(vals);
+         }
+         SetSubVector(vdofs, vals);
       }
-      SetSubVector(vdofs, vals);
+
+   }
+
+   else
+   {
+      // Define and assemble linear form
+      LinearForm b(fes);
+      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
+      b.Assemble();
+
+      // Define and assemble bilinear form
+      BilinearForm a(fes);
+      a.AddDomainIntegrator(new VectorFEMassIntegrator());
+      a.Assemble();
+
+      // Set solver and preconditioner
+      SparseMatrix A(a.SpMat());
+      GSSmoother  prec(A);
+      CGSolver cg;
+      cg.SetOperator(A);
+      cg.SetPreconditioner(prec);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(1000);
+      cg.SetPrintLevel(0);
+
+      // Solve and get solution
+      *this = 0.0;
+      cg.Mult(b,*this);
    }
 }
 
@@ -3926,7 +3989,7 @@ void GridFunction::LegacyNCReorder()
       mesh->GetEdgeVertices(i, ev);
       if (old_vertex[ev[0]] > old_vertex[ev[1]])
       {
-         const int *ind = fec->DofOrderForOrientation(Geometry::SEGMENT, -1);
+         const int *ind = fes->FEColl()->DofOrderForOrientation(Geometry::SEGMENT, -1);
 
          fes->GetEdgeInteriorDofs(i, dofs);
          for (int k = 0; k < dofs.Size(); k++)

fem/gridfunc.hpp

@@ -30,14 +30,14 @@ namespace mfem
 class GridFunction : public Vector
 {
 protected:
-   /// FE space on which the grid function lives. Owned if #fec is not NULL.
+   /// FE space on which the grid function lives. Owned if #fec_owned is not NULL.
    FiniteElementSpace *fes;
 
    /** @brief Used when the grid function is read from a file. It can also be
        set explicitly, see MakeOwner().
 
        If not NULL, this pointer is owned by the GridFunction. */
-   FiniteElementCollection *fec;
+   FiniteElementCollection *fec_owned;
 
    long fes_sequence; // see FiniteElementSpace::sequence, Mesh::sequence
 
@@ -72,16 +72,16 @@ protected:
 
 public:
 
-   GridFunction() { fes = NULL; fec = NULL; fes_sequence = 0; UseDevice(true); }
+   GridFunction() { fes = NULL; fec_owned = NULL; fes_sequence = 0; UseDevice(true); }
 
    /// Copy constructor. The internal true-dof vector #t_vec is not copied.
    GridFunction(const GridFunction &orig)
-      : Vector(orig), fes(orig.fes), fec(NULL), fes_sequence(orig.fes_sequence)
+      : Vector(orig), fes(orig.fes), fec_owned(NULL), fes_sequence(orig.fes_sequence)
    { UseDevice(true); }
 
    /// Construct a GridFunction associated with the FiniteElementSpace @a *f.
    GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
-   { fes = f; fec = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
+   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction using previously allocated array @a data.
    /** The GridFunction does not assume ownership of @a data which is assumed to
@@ -91,13 +91,13 @@ public:
     */
    GridFunction(FiniteElementSpace *f, real_t *data)
       : Vector(data, f->GetVSize())
-   { fes = f; fec = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
+   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
 
    /** @brief Construct a GridFunction using previously allocated Vector @a base
        starting at the given offset, @a base_offset. */
    GridFunction(FiniteElementSpace *f, Vector &base, int base_offset = 0)
       : Vector(base, base_offset, f->GetVSize())
-   { fes = f; fec = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
+   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction on the given Mesh, using the data from @a input.
    /** The content of @a input should be in the format created by the method
@@ -116,12 +116,12 @@ public:
    GridFunction &operator=(const GridFunction &rhs)
    { return operator=((const Vector &)rhs); }
 
-   /// Make the GridFunction the owner of #fec and #fes.
-   /** If the new FiniteElementCollection, @a fec_, is NULL, ownership of #fec
+   /// Make the GridFunction the owner of #fec_owned and #fes.
+   /** If the new FiniteElementCollection, @a fec_, is NULL, ownership of #fec_owned
        and #fes is taken away. */
-   void MakeOwner(FiniteElementCollection *fec_) { fec = fec_; }
+   void MakeOwner(FiniteElementCollection *fec_) { fec_owned = fec_; }
 
-   FiniteElementCollection *OwnFEC() { return fec; }
+   FiniteElementCollection *OwnFEC() { return fec_owned; }
 
    int VectorDim() const;
    int CurlDim() const;
@@ -387,7 +387,8 @@ public:
    /** @brief Project @a coeff Coefficient to @a this GridFunction. The
        projection computation depends on the choice of the FiniteElementSpace
        #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). */
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
    virtual void ProjectCoefficient(Coefficient &coeff);
 
    /** @brief Project @a coeff Coefficient to @a this GridFunction, using one
@@ -398,7 +399,8 @@ public:
    /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction. The
        projection computation depends on the choice of the FiniteElementSpace
        #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection).*/
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
    void ProjectCoefficient(VectorCoefficient &vcoeff);
 
    /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction, using

fem/gslib.cpp

@@ -1168,6 +1168,120 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
    } // parallel
 }
 
+void FindPointsGSLIB::DistributePointInfoToOwningMPIRanks(
+   Array<unsigned int> &recv_elem, Vector &recv_ref,
+   Array<unsigned int> &recv_code)
+{
+   MFEM_VERIFY(points_cnt,
+               "Invalid size. Please make sure to call FindPoints method "
+               "before calling this function.");
+
+   // Pack data to send via crystal router
+   struct gslib::array *outpt = new gslib::array;
+
+   struct out_pt { double rst[3]; uint index, elem, proc, code; };
+   struct out_pt *pt;
+   array_init(struct out_pt, outpt, points_cnt);
+   outpt->n=points_cnt;
+   pt = (struct out_pt *)outpt->ptr;
+
+   for (int index = 0; index < points_cnt; index++)
+   {
+      pt->index = index;
+      pt->elem = gsl_mfem_elem[index];
+      pt->proc  = gsl_proc[index];
+      pt->code = gsl_code[index];
+      for (int d = 0; d < dim; ++d)
+      {
+         pt->rst[d]= gsl_mfem_ref(index*dim + d);
+      }
+      ++pt;
+   }
+
+   // Transfer data to target MPI ranks
+   sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+
+   // Store received data
+   const int points_recv = outpt->n;
+   recv_proc.SetSize(points_recv);
+   recv_elem.SetSize(points_recv);
+   recv_index.SetSize(points_recv);
+   recv_code.SetSize(points_recv);
+   recv_ref.SetSize(points_recv*dim);
+
+   pt = (struct out_pt *)outpt->ptr;
+   for (int index = 0; index < points_recv; index++)
+   {
+      recv_index[index] = pt->index;
+      recv_elem[index] = pt->elem;
+      recv_proc[index] = pt->proc;
+      recv_code[index] = pt->code;
+      for (int d = 0; d < dim; ++d)
+      {
+         recv_ref(index*dim + d)= pt->rst[d];
+      }
+      ++pt;
+   }
+
+   array_free(outpt);
+   delete outpt;
+}
+
+void FindPointsGSLIB::DistributeInterpolatedValues(const Vector &int_vals,
+                                                   const int vdim,
+                                                   const int ordering,
+                                                   Vector &field_out) const
+{
+   const int points_recv = recv_index.Size();;
+   MFEM_VERIFY(points_recv == 0 ||
+               int_vals.Size() % points_recv == 0,
+               "Incompatible size. Please return interpolated values"
+               "corresponding to points received using"
+               "SendCoordinatesToOwningProcessors.");
+   field_out.SetSize(points_cnt*vdim);
+
+   for (int v = 0; v < vdim; v++)
+   {
+      // Pack data to send via crystal router
+      struct gslib::array *outpt = new gslib::array;
+      struct out_pt { double val; uint index, proc; };
+      struct out_pt *pt;
+      array_init(struct out_pt, outpt, points_recv);
+      outpt->n=points_recv;
+      pt = (struct out_pt *)outpt->ptr;
+      for (int index = 0; index < points_recv; index++)
+      {
+         pt->index = recv_index[index];
+         pt->proc  = recv_proc[index];
+         pt->val = ordering == Ordering::byNODES ?
+                   int_vals(index + v*points_recv) :
+                   int_vals(index*vdim + v);
+         ++pt;
+      }
+
+      // Transfer data to target MPI ranks
+      sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+
+      // Store received data
+      MFEM_VERIFY(outpt->n == points_cnt, "Incompatible size. Number of points "
+                  "received does not match the number of points originally "
+                  "found using FindPoints.");
+
+      pt = (struct out_pt *)outpt->ptr;
+      for (int index = 0; index < points_cnt; index++)
+      {
+         int idx = ordering == Ordering::byNODES ?
+                   pt->index + v*points_cnt :
+                   pt->index*vdim + v;
+         field_out(idx) = pt->val;
+         ++pt;
+      }
+
+      array_free(outpt);
+      delete outpt;
+   }
+}
+
 void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
                                    GridFunction *gfmax,
                                    const double bb_t, const double newt_tol,

fem/gslib.hpp

@@ -34,7 +34,7 @@ namespace mfem
  *
  *  There are three key functions in FindPointsGSLIB:
  *
- *  1. Setup - constructs the internal data structures of gslib.
+ *  1. Setup - constructs the internal data structures of gslib. See \ref Setup.
  *
  *  2. FindPoints - for any given arbitrary set of points in physical space,
  *     gslib finds the element number, MPI rank, and the reference space
@@ -45,12 +45,23 @@ namespace mfem
  *     on an element edge/face or near the domain boundary, and gslib also
  *     returns a distance to the border. Points near (but outside) the domain
  *     boundary must then be marked as not found using the distance returned
- *     by gslib.
+ *     by gslib. See \ref FindPoints.
  *
  *  3. Interpolate - Interpolates any grid function at the points found using 2.
+ *     For functions in L2 finite element space, use \ref SetL2AvgType to
+ *     specify how to interpolate values at points located at element boundaries
+ *     where the function might be multi-valued. See \ref Interpolate.
  *
- *  FindPointsGSLIB provides interface to use these functions individually or
- *  using a single call.
+ *  FindPointsGSLIB also provides interface to use these functions through a
+ *  single call.
+ *
+ *  For custom interpolation (e.g., evaluating strain rate tensor), we provide
+ *  functions that use gslib to send element index and corresponding
+ *  reference-space coordinates for each point to the mpi rank that the element
+ *  is located on. Then, custom interpolation can be defined locally by the user
+ *  before sending the values back to mpi ranks where the query originated from.
+ *  See \ref DistributePointInfoToOwningMPIRanks and
+ *  \ref DistributeInterpolatedValues.
  */
 class FindPointsGSLIB
 {
@@ -74,7 +85,8 @@ protected:
    int dim, points_cnt;
    Array<unsigned int> gsl_code, gsl_proc, gsl_elem, gsl_mfem_elem;
    Vector gsl_mesh, gsl_ref, gsl_dist, gsl_mfem_ref;
-   bool setupflag;              // flag to indicate whether gslib data has been setup
+   Array<unsigned int> recv_proc, recv_index; // data for custom interpolation
+   bool setupflag;              // flag to indicate if gslib data has been setup
    double default_interp_value; // used for points that are not found in the mesh
    AvgType avgtype;             // average type used for L2 functions
    Array<int> split_element_map;
@@ -118,9 +130,9 @@ public:
    virtual ~FindPointsGSLIB();
 
    /** Initializes the internal mesh in gslib, by sending the positions of the
-       Gauss-Lobatto nodes of the input Mesh object @a m.
+       Gauss-Lobatto nodes of the input Mesh object \p m.
        Note: not tested with periodic (L2).
-       Note: the input mesh @a m must have Nodes set.
+       Note: the input mesh \p m must have Nodes set.
 
        @param[in] m         Input mesh.
        @param[in] bb_t      (Optional) Relative size of bounding box around
@@ -133,9 +145,9 @@ public:
    void Setup(Mesh &m, const double bb_t = 0.1,
               const double newt_tol = 1.0e-12,
               const int npt_max = 256);
-   /** Searches positions given in physical space by @a point_pos.
+   /** Searches positions given in physical space by \p point_pos.
        These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
-       byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering.
+       byVDim: (XYZ,XYZ,....XYZ) specified by \p point_pos_ordering.
        This function populates the following member variables:
        #gsl_code        Return codes for each point: inside element (0),
                         element boundary (1), not found (2).
@@ -164,20 +176,20 @@ public:
    /** Interpolation of field values at prescribed reference space positions.
        @param[in] field_in    Function values that will be interpolated on the
                               reference positions. Note: it is assumed that
-                              @a field_in is in H1 and in the same space as the
+                              \p field_in is in H1 and in the same space as the
                               mesh that was given to Setup().
        @param[out] field_out  Interpolated values. For points that are not found
                               the value is set to #default_interp_value. */
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
    /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
-       the output values in @a field_out corresponds to the ordering used
-       in the input GridFunction @a field_in. */
+       the output values in \p field_out corresponds to the ordering used
+       in the input GridFunction \p field_in. */
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                     Vector &field_out,
                     int point_pos_ordering = Ordering::byNODES);
    /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
-       or byVDIM) of the output values in @a field_out corresponds to the
-       ordering used in the input GridFunction @a field_in. */
+       or byVDIM) of the output values in \p field_out corresponds to the
+       ordering used in the input GridFunction \p field_in. */
    void Interpolate(Mesh &m, const Vector &point_pos,
                     const GridFunction &field_in, Vector &field_out,
                     int point_pos_ordering = Ordering::byNODES);
@@ -225,6 +237,41 @@ public:
    /// Return reference coordinates in [-1,1] (internal range in GSLIB) for each
    /// point found by FindPoints.
    virtual const Vector &GetGSLIBReferencePosition() const { return gsl_ref; }
+
+   /** @name Methods to support a custom interpolation procedure.
+       \brief The physical-space point that the user seeks to interpolate at
+       could be located inside an element on another mpi rank.
+       To enable a custom interpolation procedure (e.g., strain tensor computation)
+       we need a mechanism to first send element indices and reference-space
+       coordinates to the mpi-ranks where each point is found. Then the custom
+       interpolation can be done locally by the user before sending the
+       interpolated values back to the mpi-ranks that the query originated from.
+       Example usage looks something like this:
+
+       FindPoints() -> DistributePointInfoToOwningMPIRanks() -> Computation by
+       user -> DistributeInterpolatedValues().
+   */
+   ///@{
+   /// Distribute element indices in #gsl_mfem_elem, the reference coordinates
+   /// #gsl_mfem_ref, and the code #gsl_code to the corresponding mpi-rank
+   /// #gsl_proc for each point. The received information is provided locally
+   /// in \p recv_elem, \p recv_ref (ordered by vdim), and \p recv_code.
+   /// Note: The user can send empty Array/Vectors to the method as they are
+   /// appropriately sized and filled internally.
+   virtual void DistributePointInfoToOwningMPIRanks(
+      Array<unsigned int> &recv_elem, Vector &recv_ref,
+      Array<unsigned int> &recv_code);
+   /// Return interpolated values back to the mpi-ranks #recv_proc that had
+   /// sent the element indices and corresponding reference-space coordinates.
+   /// Specify \p vdim and \p ordering (by nodes or by vdim) based on how the
+   /// \p int_vals are structured. The received values are filled in
+   /// \p field_out consistent with the original ordering of the points that
+   /// were used in \ref FindPoints.
+   virtual void DistributeInterpolatedValues(const Vector &int_vals,
+                                             const int vdim,
+                                             const int ordering,
+                                             Vector &field_out) const;
+   ///@}
 };
 
 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -249,9 +296,9 @@ public:
 #endif
 
    /** Initializes the internal mesh in gslib, by sending the positions of the
-       Gauss-Lobatto nodes of the input Mesh object @a m.
+       Gauss-Lobatto nodes of the input Mesh object \p m.
        Note: not tested with periodic meshes (L2).
-       Note: the input mesh @a m must have Nodes set.
+       Note: the input mesh \p m must have Nodes set.
 
        @param[in] m         Input mesh.
        @param[in] meshid    A unique # for each overlapping mesh. This id is
@@ -274,12 +321,12 @@ public:
               const double bb_t = 0.1, const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
-   /** Searches positions given in physical space by @a point_pos. All output
+   /** Searches positions given in physical space by \p point_pos. All output
        Arrays and Vectors are expected to have the correct size.
 
        @param[in]  point_pos           Positions to be found.
        @param[in]  point_id            Index of the mesh that the point belongs
-                                       to (corresponding to @a meshid in Setup).
+                                       to (corresponding to \p meshid in Setup).
        @param[in]  point_pos_ordering  Ordering of the points:
                                        byNodes: (XXX...,YYY...,ZZZ) or
                                        byVDim: (XYZ,XYZ,....XYZ) */
@@ -342,7 +389,7 @@ public:
    enum GSOp {ADD, MUL, MIN, MAX};
 
    /// Update the identifiers used for the gather-scatter operator.
-   /// Same @a ids get grouped together and id == 0 does not participate.
+   /// Same \p ids get grouped together and id == 0 does not participate.
    /// See class description.
    void UpdateIdentifiers(const Array<long long> &ids);
 

fem/intrules_cut.cpp

@@ -220,8 +220,8 @@ void MomentFittingIntRules::ComputeSurfaceWeights1D(ElementTransformation& Tr)
    {
       IntegrationPoint ip2;
       ip2.x = .5;
-      while (LvlSet->Eval(Tr, ip2) > 1e-12
-             || LvlSet->Eval(Tr, ip2) < -1e-12)
+      while (LvlSet->Eval(Tr, ip2) > tol_1
+             || LvlSet->Eval(Tr, ip2) < -tol_1)
       {
          if (LvlSet->Eval(Tr, ip0) * LvlSet->Eval(Tr, ip2) < 0.)
          {
@@ -237,12 +237,12 @@ void MomentFittingIntRules::ComputeSurfaceWeights1D(ElementTransformation& Tr)
       intp.x = ip2.x;
       intp.weight = 1. / Tr.Weight();
    }
-   else if (LvlSet->Eval(Tr, ip0) > 0. && LvlSet->Eval(Tr, ip1) <= 1e-12)
+   else if (LvlSet->Eval(Tr, ip0) > 0. && LvlSet->Eval(Tr, ip1) <= tol_1)
    {
       intp.x = 1.;
       intp.weight = 1. / Tr.Weight();
    }
-   else if (LvlSet->Eval(Tr, ip1) > 0. && LvlSet->Eval(Tr, ip0) <= 1e-12)
+   else if (LvlSet->Eval(Tr, ip1) > 0. && LvlSet->Eval(Tr, ip0) <= tol_1)
    {
       intp.x = 0.;
       intp.weight = 1. / Tr.Weight();
@@ -290,8 +290,8 @@ void MomentFittingIntRules::ComputeVolumeWeights1D(ElementTransformation& Tr,
          }
       }
    }
-   else if (LvlSet->Eval(Tr, ip0) <= -1e-12
-            || LvlSet->Eval(Tr, ip1) <= -1e-12)
+   else if (LvlSet->Eval(Tr, ip0) <= -tol_1
+            || LvlSet->Eval(Tr, ip1) <= -tol_1)
    {
       for (int ip = 0; ip < ir.GetNPoints(); ip++)
       {
@@ -356,24 +356,24 @@ void MomentFittingIntRules::ComputeSurfaceWeights2D(ElementTransformation& Tr)
       IntegrationPoint ipB;
       Trafo.TransformBack(pointB, ipB);
 
-      if (LvlSet->Eval(Trafo, ipA) < -1e-12
-          || LvlSet->Eval(Trafo, ipB) < -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) < -tol_1
+          || LvlSet->Eval(Trafo, ipB) < -tol_1)
       {
          interior = false;
       }
 
-      if (LvlSet->Eval(Trafo, ipA) > -1e-12
-          && LvlSet->Eval(Trafo, ipB) > -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) > -tol_1
+          && LvlSet->Eval(Trafo, ipB) > -tol_1)
       {
          layout = Layout::inside;
       }
-      else if (LvlSet->Eval(Trafo, ipA) > 1e-15
+      else if (LvlSet->Eval(Trafo, ipA) > tol_2
                && LvlSet->Eval(Trafo, ipB) <= 0.)
       {
          layout = Layout::intersected;
       }
       else if (LvlSet->Eval(Trafo, ipA) <= 0.
-               && LvlSet->Eval(Trafo, ipB) > 1e-15)
+               && LvlSet->Eval(Trafo, ipB) > tol_2)
       {
          layout = Layout::intersected;
          Vector temp(pointA.Size());
@@ -399,10 +399,10 @@ void MomentFittingIntRules::ComputeSurfaceWeights2D(ElementTransformation& Tr)
          IntegrationPoint ip;
          Trafo.TransformBack(mid, ip);
 
-         while (LvlSet->Eval(Trafo, ip) > 1e-12
-                || LvlSet->Eval(Trafo, ip) < -1e-12)
+         while (LvlSet->Eval(Trafo, ip) > tol_1
+                || LvlSet->Eval(Trafo, ip) < -tol_1)
          {
-            if (LvlSet->Eval(Trafo, ip) > 1e-12)
+            if (LvlSet->Eval(Trafo, ip) > tol_1)
             {
                pointC = mid;
             }
@@ -539,7 +539,7 @@ void MomentFittingIntRules::ComputeSurfaceWeights2D(ElementTransformation& Tr)
       temp2 = 0.;
       for (int i = 0; i < nBasis; i++)
       {
-         if (SVD.Singularvalue(i) > 1e-12)
+         if (SVD.Singularvalue(i) > tol_1)
          {
             temp2(i) = temp(i) / SVD.Singularvalue(i);
          }
@@ -606,24 +606,24 @@ void MomentFittingIntRules::ComputeVolumeWeights2D(ElementTransformation& Tr,
       IntegrationPoint ipB;
       Trafo.TransformBack(pointB, ipB);
 
-      if (LvlSet->Eval(Trafo, ipA) < -1e-12
-          || LvlSet->Eval(Trafo, ipB) < -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) < -tol_1
+          || LvlSet->Eval(Trafo, ipB) < -tol_1)
       {
          interior = false;
       }
 
-      if (LvlSet->Eval(Trafo, ipA) > -1e-12
-          && LvlSet->Eval(Trafo, ipB) > -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) > -tol_1
+          && LvlSet->Eval(Trafo, ipB) > -tol_1)
       {
          layout = Layout::inside;
       }
-      else if (LvlSet->Eval(Trafo, ipA) > 1e-15
+      else if (LvlSet->Eval(Trafo, ipA) > tol_2
                && LvlSet->Eval(Trafo, ipB) <= 0.)
       {
          layout = Layout::intersected;
       }
       else if (LvlSet->Eval(Trafo, ipA) <= 0.
-               && LvlSet->Eval(Trafo, ipB) > 1e-15)
+               && LvlSet->Eval(Trafo, ipB) > tol_2)
       {
          layout = Layout::intersected;
          Vector temp(pointA.Size());
@@ -648,10 +648,10 @@ void MomentFittingIntRules::ComputeVolumeWeights2D(ElementTransformation& Tr,
          IntegrationPoint ip;
          Trafo.TransformBack(mid, ip);
 
-         while (LvlSet->Eval(Trafo, ip) > 1e-12
-                || LvlSet->Eval(Trafo, ip) < -1e-12)
+         while (LvlSet->Eval(Trafo, ip) > tol_1
+                || LvlSet->Eval(Trafo, ip) < -tol_1)
          {
-            if (LvlSet->Eval(Trafo, ip) > 1e-12)
+            if (LvlSet->Eval(Trafo, ip) > tol_1)
             {
                pointC = mid;
             }
@@ -786,7 +786,7 @@ void MomentFittingIntRules::ComputeVolumeWeights2D(ElementTransformation& Tr,
       VolumeSVD->LeftSingularvectors().MultTranspose(RHS, temp);
       for (int i = 0; i < nBasisVolume; i++)
       {
-         if (VolumeSVD->Singularvalue(i) > 1e-12)
+         if (VolumeSVD->Singularvalue(i) > tol_1)
          {
             temp2(i) = temp(i) / VolumeSVD->Singularvalue(i);
          }
@@ -865,18 +865,18 @@ void MomentFittingIntRules::ComputeSurfaceWeights3D(ElementTransformation& Tr)
       IntegrationPoint ipD;
       Trafo.TransformBack(pointD, ipD);
 
-      if (LvlSet->Eval(Trafo, ipA) < -1e-12
-          || LvlSet->Eval(Trafo, ipB) < -1e-12
-          || LvlSet->Eval(Trafo, ipC) < -1e-12
-          || LvlSet->Eval(Trafo, ipD) < -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) < -tol_1
+          || LvlSet->Eval(Trafo, ipB) < -tol_1
+          || LvlSet->Eval(Trafo, ipC) < -tol_1
+          || LvlSet->Eval(Trafo, ipD) < -tol_1)
       {
          interior = false;
       }
 
-      if (LvlSet->Eval(Trafo, ipA) > -1e-12
-          || LvlSet->Eval(Trafo, ipB) > -1e-12
-          || LvlSet->Eval(Trafo, ipC) > -1e-12
-          || LvlSet->Eval(Trafo, ipD) > -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) > -tol_1
+          || LvlSet->Eval(Trafo, ipB) > -tol_1
+          || LvlSet->Eval(Trafo, ipC) > -tol_1
+          || LvlSet->Eval(Trafo, ipD) > -tol_1)
       {
          element_int = true;
       }
@@ -978,7 +978,7 @@ void MomentFittingIntRules::ComputeSurfaceWeights3D(ElementTransformation& Tr)
       temp2 = 0.;
       for (int i = 0; i < nBasis; i++)
       {
-         if (SVD.Singularvalue(i) > 1e-12)
+         if (SVD.Singularvalue(i) > tol_1)
          {
             temp2(i) = temp(i) / SVD.Singularvalue(i);
          }
@@ -1047,18 +1047,18 @@ void MomentFittingIntRules::ComputeVolumeWeights3D(ElementTransformation& Tr,
       IntegrationPoint ipD;
       Trafo.TransformBack(pointD, ipD);
 
-      if (LvlSet->Eval(Trafo, ipA) < -1e-12
-          || LvlSet->Eval(Trafo, ipB) < -1e-12
-          || LvlSet->Eval(Trafo, ipC) < -1e-12
-          || LvlSet->Eval(Trafo, ipD) < -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) < -tol_1
+          || LvlSet->Eval(Trafo, ipB) < -tol_1
+          || LvlSet->Eval(Trafo, ipC) < -tol_1
+          || LvlSet->Eval(Trafo, ipD) < -tol_1)
       {
          interior = false;
       }
 
-      if (LvlSet->Eval(Trafo, ipA) > -1e-12
-          || LvlSet->Eval(Trafo, ipB) > -1e-12
-          || LvlSet->Eval(Trafo, ipC) > -1e-12
-          || LvlSet->Eval(Trafo, ipD) > -1e-12)
+      if (LvlSet->Eval(Trafo, ipA) > -tol_1
+          || LvlSet->Eval(Trafo, ipB) > -tol_1
+          || LvlSet->Eval(Trafo, ipC) > -tol_1
+          || LvlSet->Eval(Trafo, ipD) > -tol_1)
       {
          element_int = true;
       }
@@ -1159,7 +1159,7 @@ void MomentFittingIntRules::ComputeVolumeWeights3D(ElementTransformation& Tr,
       VolumeSVD->LeftSingularvectors().MultTranspose(RHS, temp);
       temp2 = 0.;
       for (int i = 0; i < nBasisVolume; i++)
-         if (VolumeSVD->Singularvalue(i) > 1e-12)
+         if (VolumeSVD->Singularvalue(i) > tol_1)
          {
             temp2(i) = temp(i) / VolumeSVD->Singularvalue(i);
          }

fem/intrules_cut.hpp

@@ -36,6 +36,17 @@ protected:
    /// Space order for the LS projection.
    int lsOrder;
 
+   /// @name Tolerances used for point comparisons
+   ///@{
+#ifdef MFEM_USE_DOUBLE
+   static constexpr real_t tol_1 = 1e-12;
+   static constexpr real_t tol_2 = 1e-15;
+#elif defined(MFEM_USE_SINGLE)
+   static constexpr real_t tol_1 = 1e-5;
+   static constexpr real_t tol_2 = 1e-7;
+#endif
+   ///@}
+
    /** @brief Constructor to set up the generated cut IntegrationRules.
 
        @param [in] order  Order of the constructed IntegrationRule.

fem/pgridfunc.cpp

@@ -39,9 +39,10 @@ ParGridFunction::ParGridFunction(ParMesh *pmesh, const GridFunction *gf,
 {
    const FiniteElementSpace *glob_fes = gf->FESpace();
    // duplicate the FiniteElementCollection from 'gf'
-   fec = FiniteElementCollection::New(glob_fes->FEColl()->Name());
+   fec_owned = FiniteElementCollection::New(glob_fes->FEColl()->Name());
    // create a local ParFiniteElementSpace from the global one:
-   fes = pfes = new ParFiniteElementSpace(pmesh, glob_fes, partitioning, fec);
+   fes = pfes = new ParFiniteElementSpace(pmesh, glob_fes, partitioning,
+                                          fec_owned);
    SetSize(pfes->GetVSize());
 
    if (partitioning)
@@ -81,7 +82,7 @@ ParGridFunction::ParGridFunction(ParMesh *pmesh, std::istream &input)
    : GridFunction(pmesh, input)
 {
    // Convert the FiniteElementSpace, fes, to a ParFiniteElementSpace:
-   pfes = new ParFiniteElementSpace(pmesh, fec, fes->GetVDim(),
+   pfes = new ParFiniteElementSpace(pmesh, fec_owned, fes->GetVDim(),
                                     fes->GetOrdering());
    delete fes;
    fes = pfes;

fem/restriction.cpp

@@ -751,11 +751,11 @@ void ConformingFaceRestriction::CheckFESpace(const ElementDofOrdering
 #ifdef MFEM_DEBUG
    const FiniteElement *fe0 = fes.GetFE(0);
    const TensorBasisElement *tfe = dynamic_cast<const TensorBasisElement*>(fe0);
-   MFEM_VERIFY(tfe != NULL &&
-               (tfe->GetBasisType()==BasisType::GaussLobatto ||
-                tfe->GetBasisType()==BasisType::Positive),
-               "Only Gauss-Lobatto and Bernstein basis are supported in "
-               "ConformingFaceRestriction.");
+   MFEM_VERIFY(tfe != NULL,
+               "ConformingFaceRestriction only supports TensorBasisElements");
+   MFEM_VERIFY(tfe->GetBasisType()==BasisType::GaussLobatto ||
+               tfe->GetBasisType()==BasisType::Positive,
+               "ConformingFaceRestriction only supports Gauss-Lobatto and Bernstein bases");
 
    // Assuming all finite elements are using Gauss-Lobatto.
    const bool dof_reorder = (f_ordering == ElementDofOrdering::LEXICOGRAPHIC);
@@ -855,7 +855,8 @@ void ConformingFaceRestriction::SetFaceDofsScatterIndices(
                "This method should not be used on nonconforming coarse faces.");
    MFEM_ASSERT(face.element[0].orientation==0,
                "FaceRestriction used on degenerated mesh.");
-   MFEM_CONTRACT_VAR(f_ordering); // not supported yet
+   MFEM_VERIFY(f_ordering == ElementDofOrdering::LEXICOGRAPHIC,
+               "NATIVE ordering is not supported yet");
 
    fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
 
@@ -883,7 +884,8 @@ void ConformingFaceRestriction::SetFaceDofsGatherIndices(
 {
    MFEM_ASSERT(!(face.IsNonconformingCoarse()),
                "This method should not be used on nonconforming coarse faces.");
-   MFEM_CONTRACT_VAR(f_ordering); // not supported yet
+   MFEM_VERIFY(f_ordering == ElementDofOrdering::LEXICOGRAPHIC,
+               "NATIVE ordering is not supported yet");
 
    fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
 

fem/tmop.cpp

@@ -3390,11 +3390,12 @@ real_t TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
 
          const IntegrationPoint &ip_s = ir_s->IntPoint(s);
          Tpr->SetIntPoint(&ip_s);
+         double w = surf_fit_coeff->Eval(*Tpr, ip_s) * surf_fit_normal *
+                    1.0 / surf_fit_dof_count[scalar_dof_id];
 
          if (surf_fit_gf)
          {
-            energy += surf_fit_coeff->Eval(*Tpr, ip_s) * surf_fit_normal *
-                      sigma_e(s) * sigma_e(s);
+            energy += w * sigma_e(s) * sigma_e(s);
          }
          if (surf_fit_pos)
          {
@@ -3405,8 +3406,7 @@ real_t TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
                pos(d) = PMatI(s, d);
                pos_target(d) = (*surf_fit_pos)(vdofs[d*dof + s]);
             }
-            energy += surf_fit_coeff->Eval(*Tpr, ip_s) * surf_fit_normal *
-                      surf_fit_limiter->Eval(pos, pos_target, 1.0);
+            energy += w * surf_fit_limiter->Eval(pos, pos_target, 1.0);
          }
       }
    }

fem/tmop.hpp

@@ -217,6 +217,21 @@ public:
    virtual WorstCaseType GetWorstCaseType() { return wctype; }
 };
 
+/// 0 metric
+class TMOP_Metric_000 : public TMOP_QualityMetric
+{
+public:
+   // W = 0.
+   virtual real_t EvalW(const DenseMatrix &Jpt) const {return 0.0;}
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const {P = 0.0;}
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const {A = 0.0;}
+
+   virtual int Id() const { return 0; }
+};
+
 /// 2D non-barrier metric without a type.
 class TMOP_Metric_001 : public TMOP_QualityMetric
 {

fem/transfer.cpp

@@ -1233,6 +1233,8 @@ void PRefinementTransferOperator::Mult(const Vector& x, Vector& y) const
 
    int vdim = lFESpace.GetVDim();
 
+   y = 0.0;
+
    for (int i = 0; i < mesh->GetNE(); i++)
    {
       DofTransformation * doftrans_h = hFESpace.GetElementDofs(i, h_dofs);

general/backends.hpp

@@ -63,9 +63,9 @@
 #define MFEM_FOREACH_THREAD(i,k,N) for(int i=0; i<N; i++)
 #endif
 
-// 'double' atomicAdd implementation for previous versions of CUDA
+// 'double' and 'float' atomicAdd implementation for previous versions of CUDA
 #if defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ < 600
-MFEM_DEVICE inline real_t atomicAdd(real_t *add, real_t val)
+MFEM_DEVICE inline mfem::real_t atomicAdd(mfem::real_t *add, mfem::real_t val)
 {
    unsigned long long int *ptr = (unsigned long long int *) add;
    unsigned long long int old = *ptr, reg;

general/isockstream.cpp

@@ -51,7 +51,7 @@ int isockstream::establish()
 {
    // char myname[129];
    char   myname[] = "localhost";
-   int    sfd;
+   int    sfd = -1;
    struct addrinfo hints, *res, *rp;
 
    memset(&hints, 0, sizeof(hints));

general/table.cpp

@@ -37,6 +37,78 @@ Table::Table(const Table &table)
    }
 }
 
+Table::Table(const Table &table1,
+             const Table &table2, int offset)
+{
+   MFEM_ASSERT(table1.size == table2.size,
+               "Tables have different sizes can not merge.");
+   size = table1.size;
+
+   const int nnz = table1.I[size] + table2.I[size];
+   I.New(size+1, table1.I.GetMemoryType());
+   J.New(nnz, table1.J.GetMemoryType());
+
+   I[0] = 0;
+   Array<int> row;
+   for (int i = 0; i < size; i++)
+   {
+      I[i+1] = I[i];
+
+      table1.GetRow(i, row);
+      for (int r = 0; r < row.Size(); r++,  I[i+1] ++)
+      {
+         J[ I[i+1] ] = row[r];
+      }
+
+      table2.GetRow(i, row);
+      for (int r = 0; r < row.Size(); r++,  I[i+1] ++)
+      {
+         J[ I[i+1] ] = (row[r] < 0) ? row[r] - offset : row[r] + offset;
+      }
+
+   }
+}
+
+Table::Table(const Table &table1,
+             const Table &table2, int offset2,
+             const Table &table3, int offset3)
+{
+   MFEM_ASSERT(table1.size == table2.size,
+               "Tables have different sizes can not merge.");
+   MFEM_ASSERT(table1.size == table3.size,
+               "Tables have different sizes can not merge.");
+   size = table1.size;
+
+   const int nnz = table1.I[size] + table2.I[size] + table3.I[size];
+   I.New(size+1, table1.I.GetMemoryType());
+   J.New(nnz, table1.J.GetMemoryType());
+
+   I[0] = 0;
+   Array<int> row;
+   for (int i = 0; i < size; i++)
+   {
+      I[i+1] = I[i];
+
+      table1.GetRow(i, row);
+      for (int r = 0; r < row.Size(); r++,  I[i+1] ++)
+      {
+         J[ I[i+1] ] = row[r];
+      }
+
+      table2.GetRow(i, row);
+      for (int r = 0; r < row.Size(); r++,  I[i+1] ++)
+      {
+         J[ I[i+1] ] = (row[r] < 0) ? row[r] - offset2 : row[r] + offset2;
+      }
+
+      table3.GetRow(i, row);
+      for (int r = 0; r < row.Size(); r++,  I[i+1] ++)
+      {
+         J[ I[i+1] ] = (row[r] < 0) ? row[r] - offset3 : row[r] + offset3;
+      }
+   }
+}
+
 Table& Table::operator=(const Table &rhs)
 {
    Clear();

general/table.hpp

@@ -58,6 +58,14 @@ public:
    /// Copy constructor
    Table(const Table &);
 
+   /** Merge constructors
+       This is used to combine two or three tables into one table.*/
+   Table(const Table &table1,
+         const Table &table2, int offset2);
+   Table(const Table &table1,
+         const Table &table2, int offset2,
+         const Table &table3, int offset3);
+
    /// Assignment operator: deep copy
    Table& operator=(const Table &rhs);
 

linadvmcl/.gitignore

@@ -0,0 +1,2 @@
+linadv
+output

linadvmcl/makefile

@@ -0,0 +1,204 @@
+# Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ..
+MFEM_BUILD_DIR ?= ..
+MFEM_INSTALL_DIR ?= ../mfem
+SRC = $(if $(MFEM_DIR:..=),$(MFEM_DIR)/linadvmcl/,)
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
+   ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
+   ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40
+PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
+   ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
+   ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
+   ex37p ex39p ex40p
+SEQ_DEVICE_EXAMPLES = ex1 ex3 ex4 ex5 ex6 ex9 ex14 ex22 ex24 ex25 ex26 ex34
+PAR_DEVICE_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex14p \
+   ex22p ex24p ex25p ex26p ex34p ex35p
+
+ifeq ($(MFEM_USE_LAPACK),YES)
+   SEQ_EXAMPLES += ex38
+endif
+
+ifeq ($(MFEM_USE_MPI),NO)
+   EXAMPLES = $(SEQ_EXAMPLES)
+else
+   EXAMPLES = $(PAR_EXAMPLES) $(SEQ_EXAMPLES)
+endif
+SUBDIRS =
+ifeq ($(MFEM_USE_AMGX),YES)
+   SUBDIRS += amgx
+endif
+ifeq ($(MFEM_USE_GINKGO),YES)
+   SUBDIRS += ginkgo
+endif
+ifeq ($(MFEM_USE_HIOP),YES)
+   SUBDIRS += hiop
+endif
+ifeq ($(MFEM_USE_PETSC),YES)
+   SUBDIRS += petsc
+endif
+ifeq ($(MFEM_USE_PUMI),YES)
+   SUBDIRS += pumi
+endif
+ifeq ($(MFEM_USE_SUNDIALS),YES)
+   SUBDIRS += sundials
+endif
+ifeq ($(MFEM_USE_SUPERLU),YES)
+   SUBDIRS += superlu
+endif
+ifeq ($(MFEM_USE_MOONOLITH),YES)
+   SUBDIRS += moonolith
+endif
+ifeq ($(MFEM_USE_CALIPER),YES)
+   SUBDIRS += caliper
+endif
+
+SUBDIRS_ALL = $(addsuffix /all,$(SUBDIRS))
+SUBDIRS_TEST = $(addsuffix /test,$(SUBDIRS))
+SUBDIRS_CLEAN = $(addsuffix /clean,$(SUBDIRS))
+SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all clean clean-build clean-exec
+
+# Remove built-in rule
+%: %.cpp
+
+# Replace the default implicit rule for *.cpp files
+%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+
+all: $(EXAMPLES) $(SUBDIRS_ALL)
+
+.PHONY: $(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_CLEAN) $(SUBDIRS_TPRINT)
+$(SUBDIRS_ALL) $(SUBDIRS_TEST) $(SUBDIRS_CLEAN):
+	$(MAKE) -C $(@D) $(@F)
+$(SUBDIRS_TPRINT):
+	@$(MAKE) -C $(@D) $(@F)
+
+# Additional dependencies
+ex18: $(SRC)ex18.hpp
+ex33: $(SRC)ex33.hpp
+ex37: $(SRC)ex37.hpp
+
+ifeq ($(MFEM_USE_MPI),YES)
+ex18p: $(SRC)ex18.hpp
+ex33p: $(SRC)ex33.hpp
+ex37p: $(SRC)ex37.hpp
+endif
+
+MFEM_TESTS = EXAMPLES
+include $(MFEM_TEST_MK)
+test: $(SUBDIRS_TEST)
+test-print: $(SUBDIRS_TPRINT)
+
+# Testing: Parallel vs. serial runs
+RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
+%-test-par: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
+%-test-seq: %
+	@$(call mfem-test,$<,, Serial example)
+%-test-par-cuda: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel CUDA example,-d cuda)
+%-test-seq-cuda: %
+	@$(call mfem-test,$<,, Serial CUDA example,-d cuda)
+%-test-par-hip: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel HIP example,-d hip)
+%-test-seq-hip: %
+	@$(call mfem-test,$<,, Serial HIP example,-d hip)
+
+# Testing: Specific execution options
+ex0-test-seq: ex0
+	@$(call mfem-test,$<,, Serial example,,1)
+ex0p-test-par: ex0p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,,1)
+ex1-test-seq: ex1
+	@$(call mfem-test,$<,, Serial example)
+ex1p-test-par: ex1p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
+ex10-test-seq: ex10
+	@$(call mfem-test,$<,, Serial example,-tf 5)
+ex10p-test-par: ex10p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-tf 5)
+ex14-test-seq-cuda: ex14
+	@$(call mfem-test,$<,, Serial CUDA example,-r 2 -pa -d cuda)
+ex14p-test-par-cuda: ex14p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel CUDA example,-rs 2 -rp 0 -pa -d cuda)
+ex14-test-seq-hip: ex14
+	@$(call mfem-test,$<,, Serial HIP example,-r 2 -pa -d hip)
+ex14p-test-par-hip: ex14p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel HIP example,-rs 2 -rp 0 -pa -d hip)
+ex15-test-seq: ex15
+	@$(call mfem-test,$<,, Serial example,-e 1)
+ex15p-test-par: ex15p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-e 1)
+ex27-test-seq: ex27
+	@$(call mfem-test,$<,, Serial example,-dg)
+ex27p-test-par: ex27p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-dg)
+ex37-test-seq: ex37
+	@$(call mfem-test,$<,, Serial example,-mi 3)
+ex37p-test-par: ex37p
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-mi 3)
+# Testing: optional tests
+ifeq ($(MFEM_USE_STRUMPACK),YES)
+ex11p-test-strumpack: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), STRUMPACK example,--strumpack)
+test-par-YES: ex11p-test-strumpack
+endif
+ifeq ($(MFEM_USE_SUPERLU),YES)
+ex11p-test-superlu: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), SuperLU_DIST example,--superlu)
+test-par-YES: ex11p-test-superlu
+endif
+ifeq ($(MFEM_USE_MKL_CPARDISO),YES)
+ex11p-test-cpardiso: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), MKL_CPARDISO example,--cpardiso)
+test-par-YES: ex11p-test-cpardiso
+endif
+
+# Testing: "test" target and mfem-test* variables are defined in config/test.mk
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean: clean-build clean-exec $(SUBDIRS_CLEAN)
+
+clean-build:
+	rm -f *.o *~ $(SEQ_EXAMPLES) $(PAR_EXAMPLES)
+	rm -rf *.dSYM *.TVD.*breakpoints
+
+clean-exec:
+	@rm -f refined.mesh displaced.mesh mesh.* ex5.mesh ex6p-checkpoint.*
+	@rm -rf Example5* Example9* Example15* Example16* Example23* ParaView
+	@rm -f sphere_refined.* sol.* sol_u.* sol_p.* sol_r.* sol_i.*
+	@rm -f ex9.mesh ex9-mesh.* ex9-init.* ex9-final.*
+	@rm -f deformed.* velocity.* elastic_energy.* mode_* mode_deriv_* flux.*
+	@rm -f ex5-p-*.bp ex9-p-*.bp ex12-p-*.bp ex16-p-*.bp
+	@rm -f ex16.mesh ex16-mesh.* ex16-init.* ex16-final.*
+	@rm -f deformation.* pressure.*
+	@rm -f ex20.dat ex20p_?????.dat gnuplot_ex20.inp gnuplot_ex20p.inp
+	@rm -f ex21*.mesh ex21*.sol ex21p_*.*
+	@rm -f ex23.mesh ex23-*.gf
+	@rm -f ex25.mesh ex25-*.gf ex25p-*.*
+	@rm -f euler-?-final.* euler-?-init.* euler-mesh-final.* euler-mesh.*
+	@rm -rf ex28_* ex28p_*
+	@rm -rf cond.* cond_mesh.* cond_j.* dsol.* port_mesh.* port_mode.*

linalg/CMakeLists.txt

@@ -44,6 +44,7 @@ list(APPEND HDRS
   handle.hpp
   invariants.hpp
   kernels.hpp
+  lapack.hpp
   linalg.hpp
   matrix.hpp
   ode.hpp

linalg/complex_densemat.cpp

@@ -10,60 +10,9 @@
 // CONTRIBUTING.md for details.
 
 #include "complex_densemat.hpp"
+#include "lapack.hpp"
 #include <complex>
 
-#ifdef MFEM_USE_LAPACK
-#ifdef MFEM_USE_SINGLE
-extern "C" void
-cgetrf_(int *, int *, std::complex<float> *, int *, int *, int *);
-extern "C" void
-cgetrs_(char *, int *, int *, std::complex<float> *, int *, int *,
-        std::complex<float> *, int *, int *);
-extern "C" void
-cgetri_(int *, std::complex<float> *, int *, int *,
-        std::complex<float> *, int *, int *);
-extern "C" void
-ctrsm_(char *, char *, char *, char *, int *, int *, std::complex<float> *,
-       std::complex<float> *, int *, std::complex<float> *, int *);
-extern "C" void
-cpotrf_(char *, int *, std::complex<float> *, int *, int *);
-
-extern "C" void
-ctrtrs_(char *, char*, char *, int *, int *, std::complex<float> *, int *,
-        std::complex<float> *, int *, int *);
-extern "C" void
-cpotri_(char *, int *, std::complex<float> *, int*, int *);
-
-extern "C" void
-cpotrs_(char *, int *, int *, std::complex<float> *, int *,
-        std::complex<float> *, int *, int *);
-#elif defined MFEM_USE_DOUBLE
-extern "C" void
-zgetrf_(int *, int *, std::complex<double> *, int *, int *, int *);
-extern "C" void
-zgetrs_(char *, int *, int *, std::complex<double> *, int *, int *,
-        std::complex<double> *, int *, int *);
-extern "C" void
-zgetri_(int *, std::complex<double> *, int *, int *,
-        std::complex<double> *, int *, int *);
-extern "C" void
-ztrsm_(char *, char *, char *, char *, int *, int *, std::complex<double> *,
-       std::complex<double> *, int *, std::complex<double> *, int *);
-extern "C" void
-zpotrf_(char *, int *, std::complex<double> *, int *, int *);
-
-extern "C" void
-ztrtrs_(char *, char*, char *, int *, int *, std::complex<double> *, int *,
-        std::complex<double> *, int *, int *);
-extern "C" void
-zpotri_(char *, int *, std::complex<double> *, int*, int *);
-
-extern "C" void
-zpotrs_(char *, int *, int *, std::complex<double> *, int *,
-        std::complex<double> *, int *, int *);
-#endif
-#endif
-
 namespace mfem
 {
 
@@ -175,35 +124,17 @@ ComplexDenseMatrix * ComplexDenseMatrix::ComputeInverse()
    std::complex<real_t> qwork, *work;
    int    info;
 
-#ifdef MFEM_USE_SINGLE
-   cgetrf_(&w, &w, data, &w, ipiv, &info);
-#elif defined MFEM_USE_DOUBLE
-   zgetrf_(&w, &w, data, &w, ipiv, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(getrf_)(&w, &w, data, &w, ipiv, &info);
    if (info)
    {
       mfem_error("DenseMatrix::Invert() : Error in ZGETRF");
    }
 
-#ifdef MFEM_USE_SINGLE
-   cgetri_(&w, data, &w, ipiv, &qwork, &lwork, &info);
-#elif defined MFEM_USE_DOUBLE
-   zgetri_(&w, data, &w, ipiv, &qwork, &lwork, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(getri_)(&w, data, &w, ipiv, &qwork, &lwork, &info);
    lwork = (int) qwork.real();
    work = new std::complex<real_t>[lwork];
 
-#ifdef MFEM_USE_SINGLE
-   cgetri_(&w, data, &w, ipiv, work, &lwork, &info);
-#elif defined MFEM_USE_DOUBLE
-   zgetri_(&w, data, &w, ipiv, work, &lwork, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(getri_)(&w, data, &w, ipiv, work, &lwork, &info);
    if (info)
    {
       mfem_error("DenseMatrix::Invert() : Error in ZGETRI");
@@ -493,11 +424,7 @@ bool ComplexLUFactors::Factor(int m, real_t TOL)
 #ifdef MFEM_USE_LAPACK
    int info = 0;
    MFEM_VERIFY(data, "Matrix data not set");
-#ifdef MFEM_USE_SINGLE
-   if (m) { cgetrf_(&m, &m, data, &m, ipiv, &info); }
-#elif defined MFEM_USE_DOUBLE
-   if (m) { zgetrf_(&m, &m, data, &m, ipiv, &info); }
-#endif
+   if (m) { MFEM_LAPACK_COMPLEX(getrf_)(&m, &m, data, &m, ipiv, &info); }
    return info == 0;
 #else
    // compiling without LAPACK
@@ -659,13 +586,10 @@ void ComplexLUFactors::Solve(int m, int n, real_t *X_r, real_t * X_i) const
    std::complex<real_t> * x = ComplexFactors::RealToComplex(m*n,X_r,X_i);
    char trans = 'N';
    int  info = 0;
-#ifdef MFEM_USE_SINGLE
-   if (m > 0 && n > 0) { cgetrs_(&trans, &m, &n, data, &m, ipiv, x, &m, &info); }
-#elif defined MFEM_USE_DOUBLE
-   if (m > 0 && n > 0) { zgetrs_(&trans, &m, &n, data, &m, ipiv, x, &m, &info); }
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   if (m > 0 && n > 0)
+   {
+      MFEM_LAPACK_COMPLEX(getrs_)(&trans, &m, &n, data, &m, ipiv, x, &m, &info);
+   }
    MFEM_VERIFY(!info, "LAPACK: error in ZGETRS");
    ComplexFactors::ComplexToReal(m*n,x,X_r,X_i);
    delete [] x;
@@ -685,15 +609,8 @@ void ComplexLUFactors::RightSolve(int m, int n, real_t *X_r, real_t * X_i) const
    if (m > 0 && n > 0)
    {
       std::complex<real_t> alpha(1.0,0.0);
-#ifdef MFEM_USE_SINGLE
-      ctrsm_(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
-      ctrsm_(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
-#elif defined MFEM_USE_DOUBLE
-      ztrsm_(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
-      ztrsm_(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
-#else
-      MFEM_ABORT("Floating point type undefined");
-#endif
+      MFEM_LAPACK_COMPLEX(trsm_)(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
+      MFEM_LAPACK_COMPLEX(trsm_)(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
    }
 #else
    // compiling without LAPACK
@@ -815,13 +732,7 @@ bool ComplexCholeskyFactors::Factor(int m, real_t TOL)
    int info = 0;
    char uplo = 'L';
    MFEM_VERIFY(data, "Matrix data not set");
-#ifdef MFEM_USE_SINGLE
-   if (m) {cpotrf_(&uplo, &m, data, &m, &info);}
-#elif defined MFEM_USE_DOUBLE
-   if (m) {zpotrf_(&uplo, &m, data, &m, &info);}
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   if (m) { MFEM_LAPACK_COMPLEX(potrf_)(&uplo, &m, data, &m, &info); }
    return info == 0;
 #else
    // Cholesky–Crout algorithm
@@ -921,13 +832,8 @@ void ComplexCholeskyFactors::LSolve(int m, int n, real_t * X_r,
    char diag = 'N';
    int info = 0;
 
-#ifdef MFEM_USE_SINGLE
-   ctrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, x, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   ztrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, x, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(trtrs_)(&uplo, &trans, &diag, &m, &n, data, &m, x, &m,
+                               &info);
    MFEM_VERIFY(!info, "ComplexCholeskyFactors:LSolve:: info");
 #else
    for (int k = 0; k < n; k++)
@@ -960,13 +866,8 @@ void ComplexCholeskyFactors::USolve(int m, int n, real_t * X_r,
    char diag = 'N';
    int info = 0;
 
-#ifdef MFEM_USE_SINGLE
-   ctrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, x, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   ztrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, x, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(trtrs_)(&uplo, &trans, &diag, &m, &n, data, &m, x, &m,
+                               &info);
    MFEM_VERIFY(!info, "ComplexCholeskyFactors:USolve:: info");
 #else
    // X <- L^{-t} X
@@ -994,13 +895,7 @@ void ComplexCholeskyFactors::Solve(int m, int n, real_t * X_r,
    char uplo = 'L';
    int info = 0;
    std::complex<real_t> *x = ComplexFactors::RealToComplex(m*n,X_r,X_i);
-#ifdef MFEM_USE_SINGLE
-   cpotrs_(&uplo, &m, &n, data, &m, x, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   zpotrs_(&uplo, &m, &n, data, &m, x, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(potrs_)(&uplo, &m, &n, data, &m, x, &m, &info);
    MFEM_VERIFY(!info, "ComplexCholeskyFactors:Solve:: info");
    ComplexFactors::ComplexToReal(m*n,x,X_r,X_i);
    delete x;
@@ -1026,15 +921,8 @@ void ComplexCholeskyFactors::RightSolve(int m, int n, real_t * X_r,
    std::complex<real_t> alpha(1.0,0.0);
    if (m > 0 && n > 0)
    {
-#ifdef MFEM_USE_SINGLE
-      ctrsm_(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,x,&n);
-      ctrsm_(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,x,&n);
-#elif defined MFEM_USE_DOUBLE
-      ztrsm_(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,x,&n);
-      ztrsm_(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,x,&n);
-#else
-      MFEM_ABORT("Floating point type undefined");
-#endif
+      MFEM_LAPACK_COMPLEX(trsm_)(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,x,&n);
+      MFEM_LAPACK_COMPLEX(trsm_)(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,x,&n);
    }
 #else
    // X <- X L^{-H}
@@ -1085,13 +973,7 @@ void ComplexCholeskyFactors::GetInverseMatrix(int m, real_t * X_r,
    }
    char uplo = 'L';
    int info = 0;
-#ifdef MFEM_USE_SINGLE
-   cpotri_(&uplo, &m, X, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   zpotri_(&uplo, &m, X, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_COMPLEX(potri_)(&uplo, &m, X, &m, &info);
    MFEM_VERIFY(!info, "ComplexCholeskyFactors:GetInverseMatrix:: info");
    // fill in the upper triangular part
    for (int i = 0; i<m; i++)

linalg/densemat.cpp

@@ -17,6 +17,7 @@
 #include "vector.hpp"
 #include "matrix.hpp"
 #include "densemat.hpp"
+#include "lapack.hpp"
 #include "../general/forall.hpp"
 #include "../general/table.hpp"
 #include "../general/globals.hpp"
@@ -32,103 +33,6 @@
 #endif
 
 
-#ifdef MFEM_USE_LAPACK
-#ifdef MFEM_USE_SINGLE
-extern "C" void
-sgemm_(char *, char *, int *, int *, int *, float *, float *,
-       int *, float *, int *, float *, float *, int *);
-extern "C" void
-sgetrf_(int *, int *, float *, int *, int *, int *);
-extern "C" void
-sgetrs_(char *, int *, int *, float *, int *, int *, float *, int *, int *);
-extern "C" void
-sgetri_(int *N, float *A, int *LDA, int *IPIV, float *WORK,
-        int *LWORK, int *INFO);
-extern "C" void
-ssyevr_(char *JOBZ, char *RANGE, char *UPLO, int *N, float *A, int *LDA,
-        float *VL, float *VU, int *IL, int *IU, float *ABSTOL, int *M,
-        float *W, float *Z, int *LDZ, int *ISUPPZ, float *WORK, int *LWORK,
-        int *IWORK, int *LIWORK, int *INFO);
-extern "C" void
-ssyev_(char *JOBZ, char *UPLO, int *N, float *A, int *LDA, float *W,
-       float *WORK, int *LWORK, int *INFO);
-extern "C" void
-ssygv_ (int *ITYPE, char *JOBZ, char *UPLO, int * N, float *A, int *LDA,
-        float *B, int *LDB, float *W,  float *WORK, int *LWORK, int *INFO);
-extern "C" void
-sgesvd_(char *JOBU, char *JOBVT, int *M, int *N, float *A, int *LDA,
-        float *S, float *U, int *LDU, float *VT, int *LDVT, float *WORK,
-        int *LWORK, int *INFO);
-extern "C" void
-strsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       float *alpha, float *a, int *lda, float *b, int *ldb);
-extern "C" void
-sggev_(char *jobvl, char *jobvr, int *n, float *a, int *lda, float *B,
-       int *ldb, float *alphar, float *alphai, float *beta, float *vl,
-       int * ldvl, float * vr, int * ldvr, float * work, int * lwork, int* info);
-
-// Cholesky factorizations/solves
-extern "C" void
-spotrf_(char *, int *, float *, int *, int *);
-// Solve
-extern "C" void
-spotrs_(char *, int *, int *, float *, int *, float *, int *, int *);
-// Triangular Solves
-extern "C" void
-strtrs_(char *, char*, char *, int *, int *, float *, int *, float *, int *,
-        int *);
-extern "C" void
-spotri_(char *, int *, float *, int*, int *);
-#elif defined MFEM_USE_DOUBLE
-extern "C" void
-dgemm_(char *, char *, int *, int *, int *, double *, double *,
-       int *, double *, int *, double *, double *, int *);
-extern "C" void
-dgetrf_(int *, int *, double *, int *, int *, int *);
-extern "C" void
-dgetrs_(char *, int *, int *, double *, int *, int *, double *, int *, int *);
-extern "C" void
-dgetri_(int *N, double *A, int *LDA, int *IPIV, double *WORK,
-        int *LWORK, int *INFO);
-extern "C" void
-dsyevr_(char *JOBZ, char *RANGE, char *UPLO, int *N, double *A, int *LDA,
-        double *VL, double *VU, int *IL, int *IU, double *ABSTOL, int *M,
-        double *W, double *Z, int *LDZ, int *ISUPPZ, double *WORK, int *LWORK,
-        int *IWORK, int *LIWORK, int *INFO);
-extern "C" void
-dsyev_(char *JOBZ, char *UPLO, int *N, double *A, int *LDA, double *W,
-       double *WORK, int *LWORK, int *INFO);
-extern "C" void
-dsygv_ (int *ITYPE, char *JOBZ, char *UPLO, int * N, double *A, int *LDA,
-        double *B, int *LDB, double *W,  double *WORK, int *LWORK, int *INFO);
-extern "C" void
-dgesvd_(char *JOBU, char *JOBVT, int *M, int *N, double *A, int *LDA,
-        double *S, double *U, int *LDU, double *VT, int *LDVT, double *WORK,
-        int *LWORK, int *INFO);
-extern "C" void
-dtrsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       double *alpha, double *a, int *lda, double *b, int *ldb);
-extern "C" void
-dggev_(char *jobvl, char *jobvr, int *n, double *a, int *lda, double *B,
-       int *ldb, double *alphar, double *alphai, double *beta, double *vl,
-       int * ldvl, double * vr, int * ldvr, double * work, int * lwork, int* info);
-
-// Cholesky factorizations/solves
-extern "C" void
-dpotrf_(char *, int *, double *, int *, int *);
-// Solve
-extern "C" void
-dpotrs_(char *, int *, int *, double *, int *, double *, int *, int *);
-// Triangular Solves
-extern "C" void
-dtrtrs_(char *, char*, char *, int *, int *, double *, int *, double *, int *,
-        int *);
-extern "C" void
-dpotri_(char *, int *, double *, int*, int *);
-#endif
-#endif
-
-
 namespace mfem
 {
 
@@ -801,36 +705,19 @@ void DenseMatrix::Invert()
    real_t qwork, *work;
    int    info;
 
-#ifdef MFEM_USE_SINGLE
-   sgetrf_(&width, &width, data, &width, ipiv, &info);
-#elif defined MFEM_USE_DOUBLE
-   dgetrf_(&width, &width, data, &width, ipiv, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(getrf_)(&width, &width, data, &width, ipiv, &info);
 
    if (info)
    {
       mfem_error("DenseMatrix::Invert() : Error in DGETRF");
    }
 
-#ifdef MFEM_USE_SINGLE
-   sgetri_(&width, data, &width, ipiv, &qwork, &lwork, &info);
+   MFEM_LAPACK_PREFIX(getri_)(&width, data, &width, ipiv, &qwork, &lwork, &info);
 
    lwork = (int) qwork;
-   work = new float[lwork];
+   work = new real_t[lwork];
 
-   sgetri_(&width, data, &width, ipiv, work, &lwork, &info);
-#elif defined MFEM_USE_DOUBLE
-   dgetri_(&width, data, &width, ipiv, &qwork, &lwork, &info);
-
-   lwork = (int) qwork;
-   work = new double[lwork];
-
-   dgetri_(&width, data, &width, ipiv, work, &lwork, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(getri_)(&width, data, &width, ipiv, work, &lwork, &info);
 
    if (info)
    {
@@ -1066,15 +953,9 @@ void dsyevr_Eigensystem(DenseMatrix &a, Vector &ev, DenseMatrix *evect)
       A[i] = data[i];
    }
 
-#ifdef MFEM_USE_SINGLE
-   ssyevr_( &JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL, &IU,
-#elif defined MFEM_USE_DOUBLE
-   dsyevr_( &JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL, &IU,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-            &ABSTOL, &M, W, Z, &LDZ, ISUPPZ, &QWORK, &LWORK,
-            &QIWORK, &LIWORK, &INFO );
+   MFEM_LAPACK_PREFIX(syevr_)(&JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL,
+                              &IU, &ABSTOL, &M, W, Z, &LDZ, ISUPPZ, &QWORK,
+                              &LWORK, &QIWORK, &LIWORK, &INFO);
 
    LWORK  = (int) QWORK;
    LIWORK = QIWORK;
@@ -1082,15 +963,9 @@ void dsyevr_Eigensystem(DenseMatrix &a, Vector &ev, DenseMatrix *evect)
    WORK  = new real_t[LWORK];
    IWORK = new int[LIWORK];
 
-#ifdef MFEM_USE_SINGLE
-   ssyevr_( &JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL, &IU,
-#elif defined MFEM_USE_DOUBLE
-   dsyevr_( &JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL, &IU,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-            &ABSTOL, &M, W, Z, &LDZ, ISUPPZ, WORK, &LWORK,
-            IWORK, &LIWORK, &INFO );
+   MFEM_LAPACK_PREFIX(syevr_)(&JOBZ, &RANGE, &UPLO, &N, A, &LDA, &VL, &VU, &IL,
+                              &IU, &ABSTOL, &M, W, Z, &LDZ, ISUPPZ, WORK,
+                              &LWORK, IWORK, &LIWORK, &INFO);
 
    if (INFO != 0)
    {
@@ -1230,24 +1105,12 @@ void dsyev_Eigensystem(DenseMatrix &a, Vector &ev, DenseMatrix *evect)
       A[i] = data[i];
    }
 
-#ifdef MFEM_USE_SINGLE
-   ssyev_(&JOBZ, &UPLO, &N, A, &LDA, W, &QWORK, &LWORK, &INFO);
-#elif defined MFEM_USE_DOUBLE
-   dsyev_(&JOBZ, &UPLO, &N, A, &LDA, W, &QWORK, &LWORK, &INFO);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(syev_)(&JOBZ, &UPLO, &N, A, &LDA, W, &QWORK, &LWORK, &INFO);
 
    LWORK = (int) QWORK;
    WORK = new real_t[LWORK];
 
-#ifdef MFEM_USE_SINGLE
-   ssyev_(&JOBZ, &UPLO, &N, A, &LDA, W, WORK, &LWORK, &INFO);
-#elif defined MFEM_USE_DOUBLE
-   dsyev_(&JOBZ, &UPLO, &N, A, &LDA, W, WORK, &LWORK, &INFO);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(syev_)(&JOBZ, &UPLO, &N, A, &LDA, W, WORK, &LWORK, &INFO);
 
    if (INFO != 0)
    {
@@ -1322,24 +1185,14 @@ void dsygv_Eigensystem(DenseMatrix &a, DenseMatrix &b, Vector &ev,
       B[i] = b_data[i];
    }
 
-#ifdef MFEM_USE_SINGLE
-   ssygv_(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W, &QWORK, &LWORK, &INFO);
-#elif defined MFEM_USE_DOUBLE
-   dsygv_(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W, &QWORK, &LWORK, &INFO);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(sygv_)(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W,
+                             &QWORK, &LWORK, &INFO);
 
    LWORK = (int) QWORK;
    WORK = new real_t[LWORK];
 
-#ifdef MFEM_USE_SINGLE
-   ssygv_(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W, WORK, &LWORK, &INFO);
-#elif defined MFEM_USE_DOUBLE
-   dsygv_(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W, WORK, &LWORK, &INFO);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(sygv_)(&ITYPE, &JOBZ, &UPLO, &N, A, &LDA, B, &LDB, W, WORK,
+                             &LWORK, &INFO);
 
    if (INFO != 0)
    {
@@ -1391,26 +1244,14 @@ void DenseMatrix::SingularValues(Vector &sv) const
    int         info;
    real_t      qwork;
 
-#ifdef MFEM_USE_SINGLE
-   sgesvd_(&jobu, &jobvt, &m, &n, a, &m,
-#elif defined MFEM_USE_DOUBLE
-   dgesvd_(&jobu, &jobvt, &m, &n, a, &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-           s, u, &m, vt, &n, &qwork, &lwork, &info);
+   MFEM_LAPACK_PREFIX(gesvd_)(&jobu, &jobvt, &m, &n, a, &m, s, u, &m, vt, &n,
+                              &qwork, &lwork, &info);
 
    lwork = (int) qwork;
    work = new real_t[lwork];
 
-#ifdef MFEM_USE_SINGLE
-   sgesvd_(&jobu, &jobvt, &m, &n, a, &m,
-#elif defined MFEM_USE_DOUBLE
-   dgesvd_(&jobu, &jobvt, &m, &n, a, &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-           s, u, &m, vt, &n, work, &lwork, &info);
+   MFEM_LAPACK_PREFIX(gesvd_)(&jobu, &jobvt, &m, &n, a, &m, s, u, &m, vt, &n,
+                              work, &lwork, &info);
 
    delete [] work;
    if (info)
@@ -2573,14 +2414,8 @@ void Mult(const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
    static real_t alpha = 1.0, beta = 0.0;
    int m = b.Height(), n = c.Width(), k = b.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          c.Data(), &k, &beta, a.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
+                             c.Data(), &k, &beta, a.Data(), &m);
 #else
    const int ah = a.Height();
    const int aw = a.Width();
@@ -2603,14 +2438,8 @@ void AddMult_a(real_t alpha, const DenseMatrix &b, const DenseMatrix &c,
    static real_t beta = 1.0;
    int m = b.Height(), n = c.Width(), k = b.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          c.Data(), &k, &beta, a.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
+                             c.Data(), &k, &beta, a.Data(), &m);
 #else
    const int ah = a.Height();
    const int aw = a.Width();
@@ -2641,12 +2470,8 @@ void AddMult(const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
    static real_t alpha = 1.0, beta = 1.0;
    int m = b.Height(), n = c.Width(), k = b.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
-#endif
-          c.Data(), &k, &beta, a.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, b.Data(), &m,
+                             c.Data(), &k, &beta, a.Data(), &m);
 #else
    const int ah = a.Height();
    const int aw = a.Width();
@@ -2965,12 +2790,8 @@ void MultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
    static real_t alpha = 1.0, beta = 0.0;
    int m = A.Height(), n = B.Height(), k = A.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#endif
-          B.Data(), &n, &beta, ABt.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
+                             B.Data(), &n, &beta, ABt.Data(), &m);
 #elif 1
    const int ah = A.Height();
    const int bh = B.Height();
@@ -3074,12 +2895,8 @@ void AddMultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
    static real_t alpha = 1.0, beta = 1.0;
    int m = A.Height(), n = B.Height(), k = A.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#endif
-          B.Data(), &n, &beta, ABt.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
+                             B.Data(), &n, &beta, ABt.Data(), &m);
 #elif 1
    const int ah = A.Height();
    const int bh = B.Height();
@@ -3173,12 +2990,8 @@ void AddMult_a_ABt(real_t a, const DenseMatrix &A, const DenseMatrix &B,
    static real_t beta = 1.0;
    int m = A.Height(), n = B.Height(), k = A.Width();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
-#endif
-          B.Data(), &n, &beta, ABt.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &m,
+                             B.Data(), &n, &beta, ABt.Data(), &m);
 #elif 1
    const int ah = A.Height();
    const int bh = B.Height();
@@ -3234,12 +3047,8 @@ void MultAtB(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &AtB)
    static real_t alpha = 1.0, beta = 0.0;
    int m = A.Width(), n = B.Width(), k = A.Height();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#endif
-          B.Data(), &k, &beta, AtB.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
+                             B.Data(), &k, &beta, AtB.Data(), &m);
 #elif 1
    const int ah = A.Height();
    const int aw = A.Width();
@@ -3291,12 +3100,8 @@ void AddMultAtB(const DenseMatrix &A, const DenseMatrix &B,
    static real_t alpha = 1.0, beta = 1.0;
    int m = A.Width(), n = B.Width(), k = A.Height();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#endif
-          B.Data(), &k, &beta, AtB.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
+                             B.Data(), &k, &beta, AtB.Data(), &m);
 #else
    const int ah = A.Height();
    const int aw = A.Width();
@@ -3335,12 +3140,8 @@ void AddMult_a_AtB(real_t a, const DenseMatrix &A, const DenseMatrix &B,
    static real_t beta = 1.0;
    int m = A.Width(), n = B.Width(), k = A.Height();
 
-#ifdef MFEM_USE_SINGLE
-   sgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#elif defined MFEM_USE_DOUBLE
-   dgemm_(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
-#endif
-          B.Data(), &k, &beta, AtB.Data(), &m);
+   MFEM_LAPACK_PREFIX(gemm_)(&transa, &transb, &m, &n, &k, &alpha, A.Data(), &k,
+                             B.Data(), &k, &beta, AtB.Data(), &m);
 #else
    const int ah = A.Height();
    const int aw = A.Width();
@@ -3545,13 +3346,7 @@ bool LUFactors::Factor(int m, real_t TOL)
 {
 #ifdef MFEM_USE_LAPACK
    int info = 0;
-#ifdef MFEM_USE_SINGLE
-   if (m) { sgetrf_(&m, &m, data, &m, ipiv, &info); }
-#elif defined MFEM_USE_DOUBLE
-   if (m) { dgetrf_(&m, &m, data, &m, ipiv, &info); }
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   if (m) { MFEM_LAPACK_PREFIX(getrf_)(&m, &m, data, &m, ipiv, &info); }
    return info == 0;
 #else
    // compiling without LAPACK
@@ -3703,13 +3498,10 @@ void LUFactors::Solve(int m, int n, real_t *X) const
 #ifdef MFEM_USE_LAPACK
    char trans = 'N';
    int  info = 0;
-#ifdef MFEM_USE_SINGLE
-   if (m > 0 && n > 0) { sgetrs_(&trans, &m, &n, data, &m, ipiv, X, &m, &info); }
-#elif defined MFEM_USE_DOUBLE
-   if (m > 0 && n > 0) { dgetrs_(&trans, &m, &n, data, &m, ipiv, X, &m, &info); }
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   if (m > 0 && n > 0)
+   {
+      MFEM_LAPACK_PREFIX(getrs_)(&trans, &m, &n, data, &m, ipiv, X, &m, &info);
+   }
    MFEM_VERIFY(!info, "LAPACK: error in DGETRS");
 #else
    // compiling without LAPACK
@@ -3726,15 +3518,8 @@ void LUFactors::RightSolve(int m, int n, real_t *X) const
    real_t alpha = 1.0;
    if (m > 0 && n > 0)
    {
-#ifdef MFEM_USE_SINGLE
-      strsm_(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
-      strsm_(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
-#elif defined MFEM_USE_DOUBLE
-      dtrsm_(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
-      dtrsm_(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
-#else
-      MFEM_ABORT("Floating point type undefined");
-#endif
+      MFEM_LAPACK_PREFIX(trsm_)(&side,&u_ch,&n_ch,&n_ch,&n,&m,&alpha,data,&m,X,&n);
+      MFEM_LAPACK_PREFIX(trsm_)(&side,&l_ch,&n_ch,&u_ch,&n,&m,&alpha,data,&m,X,&n);
    }
 #else
    // compiling without LAPACK
@@ -3911,13 +3696,7 @@ bool CholeskyFactors::Factor(int m, real_t TOL)
    int info = 0;
    char uplo = 'L';
    MFEM_VERIFY(data, "Matrix data not set");
-#ifdef MFEM_USE_SINGLE
-   if (m) {spotrf_(&uplo, &m, data, &m, &info);}
-#elif defined MFEM_USE_DOUBLE
-   if (m) {dpotrf_(&uplo, &m, data, &m, &info);}
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   if (m) { MFEM_LAPACK_PREFIX(potrf_)(&uplo, &m, data, &m, &info); }
    return info == 0;
 #else
    // Cholesky–Crout algorithm
@@ -4009,13 +3788,8 @@ void CholeskyFactors::LSolve(int m, int n, real_t * X) const
    char diag = 'N';
    int info = 0;
 
-#ifdef MFEM_USE_SINGLE
-   strtrs_(&uplo, &trans, &diag, &m, &n, data, &m, X, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   dtrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, X, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(trtrs_)(&uplo, &trans, &diag, &m, &n, data, &m, X, &m,
+                              &info);
    MFEM_VERIFY(!info, "CholeskyFactors:LSolve:: info");
 
 #else
@@ -4045,13 +3819,8 @@ void CholeskyFactors::USolve(int m, int n, real_t * X) const
    char diag = 'N';
    int info = 0;
 
-#ifdef MFEM_USE_SINGLE
-   strtrs_(&uplo, &trans, &diag, &m, &n, data, &m, X, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   dtrtrs_(&uplo, &trans, &diag, &m, &n, data, &m, X, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(trtrs_)(&uplo, &trans, &diag, &m, &n, data, &m, X, &m,
+                              &info);
    MFEM_VERIFY(!info, "CholeskyFactors:USolve:: info");
 
 #else
@@ -4077,13 +3846,7 @@ void CholeskyFactors::Solve(int m, int n, real_t * X) const
 #ifdef MFEM_USE_LAPACK
    char uplo = 'L';
    int info = 0;
-#ifdef MFEM_USE_SINGLE
-   spotrs_(&uplo, &m, &n, data, &m, X, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   dpotrs_(&uplo, &m, &n, data, &m, X, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(potrs_)(&uplo, &m, &n, data, &m, X, &m, &info);
    MFEM_VERIFY(!info, "CholeskyFactors:Solve:: info");
 
 #else
@@ -4104,15 +3867,8 @@ void CholeskyFactors::RightSolve(int m, int n, real_t * X) const
    real_t alpha = 1.0;
    if (m > 0 && n > 0)
    {
-#ifdef MFEM_USE_SINGLE
-      strsm_(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,X,&n);
-      strsm_(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,X,&n);
-#elif defined MFEM_USE_DOUBLE
-      dtrsm_(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,X,&n);
-      dtrsm_(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,X,&n);
-#else
-      MFEM_ABORT("Floating point type undefined");
-#endif
+      MFEM_LAPACK_PREFIX(trsm_)(&side,&uplo,&transt,&diag,&n,&m,&alpha,data,&m,X,&n);
+      MFEM_LAPACK_PREFIX(trsm_)(&side,&uplo,&trans,&diag,&n,&m,&alpha,data,&m,X,&n);
    }
 #else
    // X <- X L^{-t}
@@ -4160,13 +3916,7 @@ void CholeskyFactors::GetInverseMatrix(int m, real_t * X) const
    }
    char uplo = 'L';
    int info = 0;
-#ifdef MFEM_USE_SINGLE
-   spotri_(&uplo, &m, X, &m, &info);
-#elif defined MFEM_USE_DOUBLE
-   dpotri_(&uplo, &m, X, &m, &info);
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
+   MFEM_LAPACK_PREFIX(potri_)(&uplo, &m, X, &m, &info);
    MFEM_VERIFY(!info, "CholeskyFactors:GetInverseMatrix:: info");
    // fill in the upper triangular part
    for (int i = 0; i<m; i++)
@@ -4350,14 +4100,8 @@ DenseMatrixEigensystem::DenseMatrixEigensystem(DenseMatrix &m)
    uplo = 'U';
    lwork = -1;
    real_t qwork;
-#ifdef MFEM_USE_SINGLE
-   ssyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-#elif defined MFEM_USE_DOUBLE
-   dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          &qwork, &lwork, &info);
+   MFEM_LAPACK_PREFIX(syev_)(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
+                             &qwork, &lwork, &info);
 
    lwork = (int) qwork;
    work = new real_t[lwork];
@@ -4385,14 +4129,8 @@ void DenseMatrixEigensystem::Eval()
 #endif
 
    EVect = mat;
-#ifdef MFEM_USE_SINGLE
-   ssyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-#elif defined MFEM_USE_DOUBLE
-   dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          work, &lwork, &info);
+   MFEM_LAPACK_PREFIX(syev_)(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
+                             work, &lwork, &info);
 
    if (info != 0)
    {
@@ -4444,15 +4182,9 @@ DenseMatrixGeneralizedEigensystem::DenseMatrixGeneralizedEigensystem(
    int nl = max(1,Vl.Height());
    int nr = max(1,Vr.Height());
 
-#ifdef MFEM_USE_SINGLE
-   sggev_(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,alphar,
-#elif defined MFEM_USE_DOUBLE
-   dggev_(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,alphar,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          alphai, beta, Vl.Data(), &nl, Vr.Data(), &nr,
-          &qwork, &lwork, &info);
+   MFEM_LAPACK_PREFIX(ggev_)(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,
+                             alphar, alphai, beta, Vl.Data(), &nl, Vr.Data(),
+                             &nr, &qwork, &lwork, &info);
 
    lwork = (int) qwork;
    work = new real_t[lwork];
@@ -4465,15 +4197,9 @@ void DenseMatrixGeneralizedEigensystem::Eval()
 
    A_copy = A;
    B_copy = B;
-#ifdef MFEM_USE_SINGLE
-   sggev_(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,alphar,
-#elif defined MFEM_USE_DOUBLE
-   dggev_(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,alphar,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-          alphai, beta, Vl.Data(), &nl, Vr.Data(), &nr,
-          work, &lwork, &info);
+   MFEM_LAPACK_PREFIX(ggev_)(&jobvl,&jobvr,&n,A_copy.Data(),&n,B_copy.Data(),&n,
+                             alphar, alphai, beta, Vl.Data(), &nl, Vr.Data(),
+                             &nr, work, &lwork, &info);
    if (info != 0)
    {
       mfem::err << "DenseMatrixGeneralizedEigensystem::Eval(): DGGEV error code: "
@@ -4554,14 +4280,8 @@ void DenseMatrixSVD::Init()
    sv.SetSize(min(m, n));
    real_t qwork;
    lwork = -1;
-#ifdef MFEM_USE_SINGLE
-   sgesvd_(&jobu, &jobvt, &m, &n, NULL, &m, sv.GetData(), NULL, &m,
-#elif defined MFEM_USE_DOUBLE
-   dgesvd_(&jobu, &jobvt, &m, &n, NULL, &m, sv.GetData(), NULL, &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-           NULL, &n, &qwork, &lwork, &info);
+   MFEM_LAPACK_PREFIX(gesvd_)(&jobu, &jobvt, &m, &n, NULL, &m, sv.GetData(),
+                              NULL, &m, NULL, &n, &qwork, &lwork, &info);
    lwork = (int) qwork;
    work = new real_t[lwork];
 }
@@ -4597,14 +4317,8 @@ void DenseMatrixSVD::Eval(DenseMatrix &M)
       datavt = Vt.Data();
    }
    Mc = M;
-#ifdef MFEM_USE_SINGLE
-   sgesvd_(&jobu, &jobvt, &m, &n, Mc.Data(), &m, sv.GetData(), datau, &m,
-#elif defined MFEM_USE_DOUBLE
-   dgesvd_(&jobu, &jobvt, &m, &n, Mc.Data(), &m, sv.GetData(), datau, &m,
-#else
-   MFEM_ABORT("Floating point type undefined");
-#endif
-           datavt, &n, work, &lwork, &info);
+   MFEM_LAPACK_PREFIX(gesvd_)(&jobu, &jobvt, &m, &n, Mc.Data(), &m, sv.GetData(),
+                              datau, &m, datavt, &n, work, &lwork, &info);
 
    if (info)
    {

linalg/lapack.hpp

@@ -0,0 +1,134 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_LAPACK_HPP
+#define MFEM_LAPACK_HPP
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_USE_LAPACK
+
+#ifdef MFEM_USE_SINGLE
+#define MFEM_LAPACK_PREFIX(stub) s##stub
+#define MFEM_LAPACK_COMPLEX(stub) c##stub
+#elif defined(MFEM_USE_DOUBLE)
+#define MFEM_LAPACK_PREFIX(stub) d##stub
+#define MFEM_LAPACK_COMPLEX(stub) z##stub
+#endif
+
+namespace mfem
+{
+
+extern "C" void
+MFEM_LAPACK_PREFIX(gemm_)(char *, char *, int *, int *, int *, real_t *,
+                          real_t *, int *, real_t *, int *, real_t *, real_t *,
+                          int *);
+extern "C" void
+MFEM_LAPACK_PREFIX(getrf_)(int *, int *, real_t *, int *, int *, int *);
+extern "C" void
+MFEM_LAPACK_PREFIX(getrs_)(char *, int *, int *, real_t *, int *, int *,
+                           real_t *, int *, int *);
+extern "C" void
+MFEM_LAPACK_PREFIX(getri_)(int *N, real_t *A, int *LDA, int *IPIV, real_t *WORK,
+                           int *LWORK, int *INFO);
+extern "C" void
+MFEM_LAPACK_PREFIX(syevr_)(char *JOBZ, char *RANGE, char *UPLO, int *N,
+                           real_t *A, int *LDA, real_t *VL, real_t *VU, int *IL,
+                           int *IU, real_t *ABSTOL, int *M, real_t *W,
+                           real_t *Z, int *LDZ, int *ISUPPZ, real_t *WORK,
+                           int *LWORK, int *IWORK, int *LIWORK, int *INFO);
+extern "C" void
+MFEM_LAPACK_PREFIX(syev_)(char *JOBZ, char *UPLO, int *N, real_t *A, int *LDA,
+                          real_t *W, real_t *WORK, int *LWORK, int *INFO);
+extern "C" void
+MFEM_LAPACK_PREFIX(sygv_) (int *ITYPE, char *JOBZ, char *UPLO, int * N,
+                           real_t *A, int *LDA, real_t *B, int *LDB, real_t *W,
+                           real_t *WORK, int *LWORK, int *INFO);
+extern "C" void
+MFEM_LAPACK_PREFIX(gesvd_)(char *JOBU, char *JOBVT, int *M, int *N, real_t *A,
+                           int *LDA, real_t *S, real_t *U, int *LDU, real_t *VT,
+                           int *LDVT, real_t *WORK, int *LWORK, int *INFO);
+extern "C" void
+MFEM_LAPACK_PREFIX(trsm_)(char *side, char *uplo, char *transa, char *diag,
+                          int *m, int *n, real_t *alpha, real_t *a, int *lda,
+                          real_t *b, int *ldb);
+extern "C" void
+MFEM_LAPACK_PREFIX(ggev_)(char *jobvl, char *jobvr, int *n, real_t *a, int *lda,
+                          real_t *B, int *ldb, real_t *alphar, real_t *alphai,
+                          real_t *beta, real_t *vl, int * ldvl, real_t * vr,
+                          int * ldvr, real_t * work, int * lwork, int* info);
+
+// Cholesky factorizations/solves
+extern "C" void
+MFEM_LAPACK_PREFIX(potrf_)(char *, int *, real_t *, int *, int *);
+// Solve
+extern "C" void
+MFEM_LAPACK_PREFIX(potrs_)(char *, int *, int *, real_t *, int *, real_t *,
+                           int *, int *);
+// Triangular Solves
+extern "C" void
+MFEM_LAPACK_PREFIX(trtrs_)(char *, char*, char *, int *, int *, real_t *, int *,
+                           real_t *, int *, int *);
+extern "C" void
+MFEM_LAPACK_PREFIX(potri_)(char *, int *, real_t *, int*, int *);
+
+// LAPACK routines for NNLSSolver
+extern "C" void
+MFEM_LAPACK_PREFIX(ormqr_)(char *, char *, int *, int *, int *, real_t *, int*,
+                           real_t *, real_t *, int *, real_t *, int*, int*);
+
+extern "C" void
+MFEM_LAPACK_PREFIX(geqrf_)(int *, int *, real_t *, int *, real_t *, real_t *,
+                           int *, int *);
+
+extern "C" void
+MFEM_LAPACK_PREFIX(gemv_)(char *, int *, int *, real_t *, real_t *, int *,
+                          real_t *, int *, real_t *, real_t *, int *);
+
+extern "C" void
+MFEM_LAPACK_PREFIX(trsm_)(char *side, char *uplo, char *transa, char *diag,
+                          int *m, int *n, real_t *alpha, real_t *a, int *lda,
+                          real_t *b, int *ldb);
+
+// Complex
+extern "C" void
+MFEM_LAPACK_COMPLEX(getrf_)(int *, int *, std::complex<real_t> *, int *, int *,
+                            int *);
+extern "C" void
+MFEM_LAPACK_COMPLEX(getrs_)(char *, int *, int *, std::complex<real_t> *, int *,
+                            int *, std::complex<real_t> *, int *, int *);
+extern "C" void
+MFEM_LAPACK_COMPLEX(getri_)(int *, std::complex<real_t> *, int *, int *,
+                            std::complex<real_t> *, int *, int *);
+extern "C" void
+MFEM_LAPACK_COMPLEX(trsm_)(char *, char *, char *, char *, int *, int *,
+                           std::complex<real_t> *, std::complex<real_t> *,
+                           int *, std::complex<real_t> *, int *);
+extern "C" void
+MFEM_LAPACK_COMPLEX(potrf_)(char *, int *, std::complex<real_t> *, int *,
+                            int *);
+
+extern "C" void
+MFEM_LAPACK_COMPLEX(trtrs_)(char *, char*, char *, int *, int *,
+                            std::complex<real_t> *, int *,
+                            std::complex<real_t> *, int *, int *);
+extern "C" void
+MFEM_LAPACK_COMPLEX(potri_)(char *, int *, std::complex<real_t> *, int*, int *);
+
+extern "C" void
+MFEM_LAPACK_COMPLEX(potrs_)(char *, int *, int *, std::complex<real_t> *, int *,
+                            std::complex<real_t> *, int *, int *);
+
+}
+
+#endif
+
+#endif

linalg/operator.hpp

@@ -420,8 +420,9 @@ public:
    /** @brief Perform the action of the explicit part of the operator, G:
        @a v = G(@a u, t) where t is the current time.
 
-       Presently, this method is used by some PETSc ODE solvers, for more
-       details, see the PETSc Manual. */
+       Presently, this method is used by some PETSc ODE solvers and the
+       SUNDIALS ARKStep integrator, for more details, see either the PETSc
+       Manual or the ARKode User Guide, respectively. */
    virtual void ExplicitMult(const Vector &u, Vector &v) const;
 
    /** @brief Perform the action of the implicit part of the operator, F:
@@ -445,7 +446,7 @@ public:
 
        Regardless of the choice of F and G, this function should always compute
        @a k = inv(M) g(@a u, t). */
-   virtual void Mult(const Vector &u, Vector &v) const override;
+   virtual void Mult(const Vector &u, Vector &k) const override;
 
    /** @brief Solve for the unknown @a k, at the current time t, the following
        equation:
@@ -496,7 +497,17 @@ public:
        details, see the PETSc Manual. */
    virtual Operator& GetExplicitGradient(const Vector &u) const;
 
-   /** @brief Setup a linear system as needed by some SUNDIALS ODE solvers.
+   /** @brief Setup a linear system as needed by some SUNDIALS ODE solvers to
+       perform a similar action to ImplicitSolve, i.e., solve for k, at the
+       current time t, in F(u + gamma k, k, t) = G(u + gamma k, t).
+
+       The SUNDIALS ODE solvers iteratively solve for k, as knew = kold + dk.
+       The linear system here is for dk, obtained by linearizing the nonlinear
+       system F(u + gamma knew, knew, t) = G(u + gamma knew, t) about dk = 0:
+          F(u + gamma (kold + dk), kold + dk, t) = G(u + gamma (kold + dk), t)
+          => [dF/dk + gamma (dF/du - dG/du)] dk = G - F + O(dk^2)
+       In other words, the linear system to be setup here is A dk = r, where
+       A = [dF/dk + gamma (dF/du - dG/du)] and r = G - F.
 
        For solving an ordinary differential equation of the form
        $ M \frac{dy}{dt} = g(y,t) $, recall that F and G can be defined as one
@@ -506,7 +517,7 @@ public:
          2. F(u,k,t) = M k and G(u,t) = g(u,t)
          3. F(u,k,t) = M k - g(u,t) and G(u,t) = 0
 
-       This function performs setup to solve $ A x = b $ where A is either
+       This function performs setup to solve $ A dk = r $ where A is either
 
          1. A(@a y,t) = I - @a gamma inv(M) J(@a y,t)
          2. A(@a y,t) = M - @a gamma J(@a y,t)
@@ -527,18 +538,26 @@ public:
    virtual int SUNImplicitSetup(const Vector &y, const Vector &v,
                                 int jok, int *jcur, real_t gamma);
 
-   /** @brief Solve the ODE linear system A @a x = @a b, where A is defined by
-       the method SUNImplicitSetup().
+   /** @brief Solve the ODE linear system A @a dk = @a r , where A and r are
+       defined by the method SUNImplicitSetup().
 
-       @param[in]      b   The linear system right-hand side.
-       @param[in,out]  x   On input, the initial guess. On output, the solution.
+       For solving an ordinary differential equation of the form
+       $ M \frac{dy}{dt} = g(y,t) $, recall that F and G can be defined as one
+       of the following:
+
+         1. F(u,k,t) = k and G(u,t) = inv(M) g(u,t)
+         2. F(u,k,t) = M k and G(u,t) = g(u,t)
+         3. F(u,k,t) = M k - g(u,t) and G(u,t) = 0
+
+       @param[in]      r   inv(M) g(y,t) - k for 1 or g(y,t) - M k for 2 & 3.
+       @param[in,out]  dk  On input, the initial guess. On output, the solution.
        @param[in]      tol Linear solve tolerance.
 
        If not re-implemented, this method simply generates an error.
 
        Presently, this method is used by SUNDIALS ODE solvers, for more
        details, see the SUNDIALS User Guides. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, real_t tol);
+   virtual int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol);
 
    /** @brief Setup the mass matrix in the ODE system
        $ M \frac{dy}{dt} = g(y,t) $ .

linalg/solvers.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "linalg.hpp"
+#include "lapack.hpp"
 #include "../general/annotation.hpp"
 #include "../general/forall.hpp"
 #include "../general/globals.hpp"
@@ -263,7 +264,7 @@ void OperatorJacobiSmoother::SetOperator(const Operator &op)
       oper = &op;
       height = op.Height();
       width = op.Width();
-      MFEM_ASSERT(height == width, "not a square matrix!");
+      MFEM_VERIFY(height == width, "not a square matrix!");
       // ess_tdof_list is only used with BilinearForm
       ess_tdof_list = nullptr;
    }
@@ -304,8 +305,8 @@ void OperatorJacobiSmoother::Mult(const Vector &x, Vector &y) const
 {
    // For empty MPI ranks, height may be 0:
    // MFEM_VERIFY(Height() > 0, "The diagonal hasn't been computed.");
-   MFEM_ASSERT(x.Size() == Width(), "invalid input vector");
-   MFEM_ASSERT(y.Size() == Height(), "invalid output vector");
+   MFEM_VERIFY(x.Size() == Width(), "invalid input vector");
+   MFEM_VERIFY(y.Size() == Height(), "invalid output vector");
 
    if (iterative_mode)
    {
@@ -591,7 +592,7 @@ void SLISolver::Mult(const Vector &b, Vector &x) const
    }
    initial_norm = nom0;
 
-   if (print_options.iterations | print_options.first_and_last)
+   if (print_options.iterations || print_options.first_and_last)
    {
       mfem::out << "   Iteration : " << setw(3) << right << 0 << "  ||Br|| = "
                 << nom << (print_options.first_and_last ? " ..." : "") << '\n';
@@ -743,7 +744,7 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
    }
    nom0 = nom = Dot(d, r);
    if (nom0 >= 0.0) { initial_norm = sqrt(nom0); }
-   MFEM_ASSERT(IsFinite(nom), "nom = " << nom);
+   MFEM_VERIFY(IsFinite(nom), "nom = " << nom);
    if (print_options.iterations || print_options.first_and_last)
    {
       mfem::out << "   Iteration : " << setw(3) << 0 << "  (B r, r) = "
@@ -775,7 +776,7 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
 
    oper->Mult(d, z);  // z = A d
    den = Dot(z, d);
-   MFEM_ASSERT(IsFinite(den), "den = " << den);
+   MFEM_VERIFY(IsFinite(den), "den = " << den);
    if (den <= 0.0)
    {
       if (Dot(d, d) > 0.0 && print_options.warnings)
@@ -810,7 +811,7 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
       {
          betanom = Dot(r, r);
       }
-      MFEM_ASSERT(IsFinite(betanom), "betanom = " << betanom);
+      MFEM_VERIFY(IsFinite(betanom), "betanom = " << betanom);
       if (betanom < 0.0)
       {
          if (print_options.warnings)
@@ -854,7 +855,7 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
       }
       oper->Mult(d, z);       //  z = A d
       den = Dot(d, z);
-      MFEM_ASSERT(IsFinite(den), "den = " << den);
+      MFEM_VERIFY(IsFinite(den), "den = " << den);
       if (den <= 0.0)
       {
          if (Dot(d, d) > 0.0 && print_options.warnings)
@@ -1024,7 +1025,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
       }
    }
    real_t beta = initial_norm = Norm(r);  // beta = ||r||
-   MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
+   MFEM_VERIFY(IsFinite(beta), "beta = " << beta);
 
    final_norm = std::max(rel_tol*beta, abs_tol);
 
@@ -1074,7 +1075,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
          }
 
          H(i+1,i) = Norm(w);           // H(i+1,i) = ||w||
-         MFEM_ASSERT(IsFinite(H(i+1,i)), "Norm(w) = " << H(i+1,i));
+         MFEM_VERIFY(IsFinite(H(i+1,i)), "Norm(w) = " << H(i+1,i));
          if (v[i+1] == NULL) { v[i+1] = new Vector(n); }
          v[i+1]->Set(1.0/H(i+1,i), w); // v[i+1] = w / H(i+1,i)
 
@@ -1088,7 +1089,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
          ApplyPlaneRotation(s(i), s(i+1), cs(i), sn(i));
 
          const real_t resid = fabs(s(i+1));
-         MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
+         MFEM_VERIFY(IsFinite(resid), "resid = " << resid);
 
          if (resid <= final_norm)
          {
@@ -1127,7 +1128,7 @@ void GMRESSolver::Mult(const Vector &b, Vector &x) const
          subtract(b, r, r);
       }
       beta = Norm(r);         // beta = ||r||
-      MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
+      MFEM_VERIFY(IsFinite(beta), "beta = " << beta);
       if (beta <= final_norm)
       {
          final_norm = beta;
@@ -1184,7 +1185,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
       r = b;
    }
    real_t beta = initial_norm = Norm(r);  // beta = ||r||
-   MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
+   MFEM_VERIFY(IsFinite(beta), "beta = " << beta);
 
    final_norm = std::max(rel_tol*beta, abs_tol);
 
@@ -1261,7 +1262,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
          ApplyPlaneRotation(s(i), s(i+1), cs(i), sn(i));
 
          const real_t resid = fabs(s(i+1));
-         MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
+         MFEM_VERIFY(IsFinite(resid), "resid = " << resid);
          if (print_options.iterations || (print_options.first_and_last &&
                                           resid <= final_norm))
          {
@@ -1302,7 +1303,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
       oper->Mult(x, r);
       subtract(b,r,r);
       beta = Norm(r);
-      MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
+      MFEM_VERIFY(IsFinite(beta), "beta = " << beta);
       if (beta <= final_norm)
       {
          converged = true;
@@ -1399,7 +1400,7 @@ void BiCGSTABSolver::Mult(const Vector &b, Vector &x) const
    rtilde = r;
 
    resid = initial_norm = Norm(r);
-   MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
+   MFEM_VERIFY(IsFinite(resid), "resid = " << resid);
    if (print_options.iterations || print_options.first_and_last)
    {
       mfem::out << "   Iteration : " << setw(3) << 0
@@ -1466,7 +1467,7 @@ void BiCGSTABSolver::Mult(const Vector &b, Vector &x) const
       alpha = rho_1 / Dot(rtilde, v);
       add(r, -alpha, v, s); //  s = r - alpha * v
       resid = Norm(s);
-      MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
+      MFEM_VERIFY(IsFinite(resid), "resid = " << resid);
       if (resid < tol_goal)
       {
          x.Add(alpha, phat);  //  x = x + alpha * phat
@@ -1506,7 +1507,7 @@ void BiCGSTABSolver::Mult(const Vector &b, Vector &x) const
 
       rho_2 = rho_1;
       resid = Norm(r);
-      MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
+      MFEM_VERIFY(IsFinite(resid), "resid = " << resid);
       if (print_options.iterations)
       {
          mfem::out << "   ||r|| = " << resid << '\n';
@@ -1646,7 +1647,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
       prec->Mult(v1, u1);
    }
    eta = beta = initial_norm = sqrt(Dot(*z, v1));
-   MFEM_ASSERT(IsFinite(eta), "eta = " << eta);
+   MFEM_VERIFY(IsFinite(eta), "eta = " << eta);
    gamma0 = gamma1 = 1.;
    sigma0 = sigma1 = 0.;
 
@@ -1674,7 +1675,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
       }
       oper->Mult(*z, q);
       alpha = Dot(*z, q);
-      MFEM_ASSERT(IsFinite(alpha), "alpha = " << alpha);
+      MFEM_VERIFY(IsFinite(alpha), "alpha = " << alpha);
       if (it > 1) // (v0 == 0) for (it == 1)
       {
          q.Add(-beta, v0);
@@ -1693,7 +1694,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
          prec->Mult(v0, q);
          beta = sqrt(Dot(v0, q));
       }
-      MFEM_ASSERT(IsFinite(beta), "beta = " << beta);
+      MFEM_VERIFY(IsFinite(beta), "beta = " << beta);
       rho1 = std::hypot(delta, beta);
 
       if (it == 1)
@@ -1719,7 +1720,7 @@ void MINRESSolver::Mult(const Vector &b, Vector &x) const
       sigma1 = beta/rho1;
 
       eta = -sigma1*eta;
-      MFEM_ASSERT(IsFinite(eta), "eta = " << eta);
+      MFEM_VERIFY(IsFinite(eta), "eta = " << eta);
 
       if (fabs(eta) <= norm_goal)
       {
@@ -1812,7 +1813,7 @@ void NewtonSolver::SetOperator(const Operator &op)
    oper = &op;
    height = op.Height();
    width = op.Width();
-   MFEM_ASSERT(height == width, "square Operator is required.");
+   MFEM_VERIFY(height == width, "square Operator is required.");
 
    r.SetSize(width);
    c.SetSize(width);
@@ -1820,8 +1821,8 @@ void NewtonSolver::SetOperator(const Operator &op)
 
 void NewtonSolver::Mult(const Vector &b, Vector &x) const
 {
-   MFEM_ASSERT(oper != NULL, "the Operator is not set (use SetOperator).");
-   MFEM_ASSERT(prec != NULL, "the Solver is not set (use SetSolver).");
+   MFEM_VERIFY(oper != NULL, "the Operator is not set (use SetOperator).");
+   MFEM_VERIFY(prec != NULL, "the Solver is not set (use SetSolver).");
 
    int it;
    real_t norm0, norm, norm_goal;
@@ -1853,7 +1854,7 @@ void NewtonSolver::Mult(const Vector &b, Vector &x) const
    // x_{i+1} = x_i - [DF(x_i)]^{-1} [F(x_i)-b]
    for (it = 0; true; it++)
    {
-      MFEM_ASSERT(IsFinite(norm), "norm = " << norm);
+      MFEM_VERIFY(IsFinite(norm), "norm = " << norm);
       if (print_options.iterations)
       {
          mfem::out << "Newton iteration " << setw(2) << it
@@ -2047,7 +2048,7 @@ void LBFGSSolver::Mult(const Vector &b, Vector &x) const
    norm_goal = std::max(rel_tol*norm, abs_tol);
    for (it = 0; true; it++)
    {
-      MFEM_ASSERT(IsFinite(norm), "norm = " << norm);
+      MFEM_VERIFY(IsFinite(norm), "norm = " << norm);
       if (print_options.iterations)
       {
          mfem::out << "LBFGS iteration " <<  it
@@ -2309,14 +2310,14 @@ OptimizationProblem::OptimizationProblem(const int insize,
    : C(C_), D(D_), c_e(NULL), d_lo(NULL), d_hi(NULL), x_lo(NULL), x_hi(NULL),
      input_size(insize)
 {
-   if (C) { MFEM_ASSERT(C->Width() == input_size, "Wrong width of C."); }
-   if (D) { MFEM_ASSERT(D->Width() == input_size, "Wrong width of D."); }
+   if (C) { MFEM_VERIFY(C->Width() == input_size, "Wrong width of C."); }
+   if (D) { MFEM_VERIFY(D->Width() == input_size, "Wrong width of D."); }
 }
 
 void OptimizationProblem::SetEqualityConstraint(const Vector &c)
 {
-   MFEM_ASSERT(C, "The C operator is unspecified -- can't set constraints.");
-   MFEM_ASSERT(c.Size() == C->Height(), "Wrong size of the constraint.");
+   MFEM_VERIFY(C, "The C operator is unspecified -- can't set constraints.");
+   MFEM_VERIFY(c.Size() == C->Height(), "Wrong size of the constraint.");
 
    c_e = &c;
 }
@@ -2324,8 +2325,8 @@ void OptimizationProblem::SetEqualityConstraint(const Vector &c)
 void OptimizationProblem::SetInequalityConstraint(const Vector &dl,
                                                   const Vector &dh)
 {
-   MFEM_ASSERT(D, "The D operator is unspecified -- can't set constraints.");
-   MFEM_ASSERT(dl.Size() == D->Height() && dh.Size() == D->Height(),
+   MFEM_VERIFY(D, "The D operator is unspecified -- can't set constraints.");
+   MFEM_VERIFY(dl.Size() == D->Height() && dh.Size() == D->Height(),
                "Wrong size of the constraint.");
 
    d_lo = &dl; d_hi = &dh;
@@ -2333,7 +2334,7 @@ void OptimizationProblem::SetInequalityConstraint(const Vector &dl,
 
 void OptimizationProblem::SetSolutionBounds(const Vector &xl, const Vector &xh)
 {
-   MFEM_ASSERT(xl.Size() == input_size && xh.Size() == input_size,
+   MFEM_VERIFY(xl.Size() == input_size && xh.Size() == input_size,
                "Wrong size of the constraint.");
 
    x_lo = &xl; x_hi = &xh;
@@ -2354,8 +2355,8 @@ void SLBQPOptimizer::SetOptimizationProblem(const OptimizationProblem &prob)
       MFEM_WARNING("Objective functional is ignored as SLBQP always minimizes"
                    "the l2 norm of (x - x_target).");
    }
-   MFEM_ASSERT(prob.GetC(), "Linear constraint is not set.");
-   MFEM_ASSERT(prob.GetC()->Height() == 1, "Solver expects scalar constraint.");
+   MFEM_VERIFY(prob.GetC(), "Linear constraint is not set.");
+   MFEM_VERIFY(prob.GetC()->Height() == 1, "Solver expects scalar constraint.");
 
    problem = &prob;
 }
@@ -2786,7 +2787,7 @@ void BlockILU::SetOperator(const Operator &op)
    }
    height = op.Height();
    width = op.Width();
-   MFEM_ASSERT(A->Finalized(), "Matrix must be finalized.");
+   MFEM_VERIFY(A->Finalized(), "Matrix must be finalized.");
    CreateBlockPattern(*A);
    Factorize();
 }
@@ -2997,7 +2998,7 @@ void BlockILU::Factorize()
 
 void BlockILU::Mult(const Vector &b, Vector &x) const
 {
-   MFEM_ASSERT(height > 0, "BlockILU(0) preconditioner is not constructed");
+   MFEM_VERIFY(height > 0, "BlockILU(0) preconditioner is not constructed");
    int nblockrows = Height()/block_size;
    y.SetSize(Height());
 
@@ -3292,7 +3293,7 @@ void KLUSolver::SetOperator(const Operator &op)
 {
    if (Numeric)
    {
-      MFEM_ASSERT(Symbolic != 0,
+      MFEM_VERIFY(Symbolic != 0,
                   "Had Numeric pointer in KLU, but not Symbolic");
       klu_free_symbolic(&Symbolic, &Common);
       Symbolic = 0;
@@ -3543,38 +3544,6 @@ void AuxSpaceSmoother::Mult(const Vector &x, Vector &y, bool transpose) const
 #endif // MFEM_USE_MPI
 
 #ifdef MFEM_USE_LAPACK
-// LAPACK routines for NNLSSolver
-#ifdef MFEM_USE_SINGLE
-extern "C" void
-sormqr_(char *, char *, int *, int *, int *, float *, int*, float *,
-        float *, int *, float *, int*, int*);
-
-extern "C" void
-sgeqrf_(int *, int *, float *, int *, float *, float *, int *, int *);
-
-extern "C" void
-sgemv_(char *, int *, int *, float *, float *, int *, float *, int *,
-       float *, float *, int *);
-
-extern "C" void
-strsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       float *alpha, float *a, int *lda, float *b, int *ldb);
-#elif defined MFEM_USE_DOUBLE
-extern "C" void
-dormqr_(char *, char *, int *, int *, int *, double *, int*, double *,
-        double *, int *, double *, int*, int*);
-
-extern "C" void
-dgeqrf_(int *, int *, double *, int *, double *, double *, int *, int *);
-
-extern "C" void
-dgemv_(char *, int *, int *, double *, double *, int *, double *, int *,
-       double *, double *, int *);
-
-extern "C" void
-dtrsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       double *alpha, double *a, int *lda, double *b, int *ldb);
-#endif
 
 NNLSSolver::NNLSSolver()
    : Solver(0), mat(nullptr), const_tol_(1.0e-14), min_nnz_(0),
@@ -3938,25 +3907,19 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             lwork = -1;
             work.resize(10);
 
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    mat_qr_data.GetData() + (i_qr_start * m), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &n_update,
+                                       &i_qr_start, mat_qr_data.GetData(), &m,
+                                       tau.GetData(),
+                                       mat_qr_data.GetData() + (i_qr_start * m),
+                                       &m, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T A update work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    mat_qr_data.GetData() + (i_qr_start * m), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &n_update,
+                                       &i_qr_start, mat_qr_data.GetData(), &m,
+                                       tau.GetData(),
+                                       mat_qr_data.GetData() + (i_qr_start * m),
+                                       &m, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T A update failed
             // Compute QR factorization of the submatrix
             lwork = -1;
@@ -3977,24 +3940,16 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
                sub_tau[j] = tau[i_qr_start + j];
             }
 
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m_update, &n_update,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m_update, &n_update,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m_update, &n_update, submat_data.GetData(),
+                                       &m_update, sub_tau.GetData(), work.data(),
+                                       &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR update factorization work calc
             lwork = static_cast<int>(work[0]);
             if (lwork == 0) { lwork = 1; }
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m_update, &n_update,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m_update, &n_update,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m_update, &n_update, submat_data.GetData(),
+                                       &m_update, sub_tau.GetData(), work.data(),
+                                       &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR update factorization failed
 
             // Copy result back
@@ -4023,23 +3978,13 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             // perform qr)
             lwork = -1;
             work.resize(10);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m, &n_glob, mat_qr_data.GetData(), &m,
+                                       tau.GetData(), work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR factorization work calculation
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m, &n_glob, mat_qr_data.GetData(), &m,
+                                       tau.GetData(), work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR factorization failed
          }
 
@@ -4067,25 +4012,17 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
 
             sub_tau[0] = tau[i_qr_start];
 
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m_update, &ione, &ione,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m_update, &ione, &ione,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    sub_qt.GetData(), &m_update,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m_update, &ione, &ione,
+                                       submat_data.GetData(), &m_update,
+                                       sub_tau.GetData(), sub_qt.GetData(),
+                                       &m_update, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // H_last y work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m_update, &ione, &ione,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m_update, &ione, &ione,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    sub_qt.GetData(), &m_update,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m_update, &ione, &ione,
+                                       submat_data.GetData(), &m_update,
+                                       sub_tau.GetData(), sub_qt.GetData(),
+                                       &m_update, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // H_last y failed
             // Copy result back
             for (int i=0; i<m_update; ++i)
@@ -4099,25 +4036,17 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             qt_rhs_glob = rhs_avg_glob;
             lwork = -1;
             work.resize(10);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &ione, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &ione, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    qt_rhs_glob.GetData(), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &ione, &n_glob,
+                                       mat_qr_data.GetData(), &m, tau.GetData(),
+                                       qt_rhs_glob.GetData(), &m,
+                                       work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T b work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &ione, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &ione, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    qt_rhs_glob.GetData(), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &ione, &n_glob,
+                                       mat_qr_data.GetData(), &m, tau.GetData(),
+                                       qt_rhs_glob.GetData(), &m,
+                                       work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T b failed
          }
 
@@ -4130,14 +4059,10 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
          char upper = 'U';
          char nounit = 'N';
          vec1 = qt_rhs_glob;
-#ifdef MFEM_USE_SINGLE
-         strsm_(&lside, &upper, &notrans, &nounit,
-#elif defined MFEM_USE_DOUBLE
-         dtrsm_(&lside, &upper, &notrans, &nounit,
-#endif
-                &n_glob, &ione, &fone,
-                mat_qr_data.GetData(), &m,
-                vec1.GetData(), &n_glob);
+         MFEM_LAPACK_PREFIX(trsm_)(&lside, &upper, &notrans, &nounit,
+                                   &n_glob, &ione, &fone,
+                                   mat_qr_data.GetData(), &m,
+                                   vec1.GetData(), &n_glob);
 
          if (verbosity_ > 2)
          {
@@ -4360,14 +4285,10 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
       {
          res_glob = rhs_avg_glob;
          real_t fmone = -1.0;
-#ifdef MFEM_USE_SINGLE
-         sgemv_(&notrans, &m, &n_glob, &fmone,
-#elif defined MFEM_USE_DOUBLE
-         dgemv_(&notrans, &m, &n_glob, &fmone,
-#endif
-                mat_0_data.GetData(), &m,
-                soln_nz_glob.GetData(), &ione, &fone,
-                res_glob.GetData(), &ione);
+         MFEM_LAPACK_PREFIX(gemv_)(&notrans, &m, &n_glob, &fmone,
+                                   mat_0_data.GetData(), &m,
+                                   soln_nz_glob.GetData(), &ione, &fone,
+                                   res_glob.GetData(), &ione);
       }
       else
       {
@@ -4381,24 +4302,18 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             qqt_rhs_glob(i) = qt_rhs_glob(i);
          }
 
-#ifdef MFEM_USE_SINGLE
-         sormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#elif defined MFEM_USE_DOUBLE
-         dormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#endif
-                 tau.GetData(), qqt_rhs_glob.GetData(), &m,
-                 work.data(), &lwork, &info);
+         MFEM_LAPACK_PREFIX(ormqr_)(&lside, &notrans, &m, &ione, &n_glob,
+                                    mat_qr_data.GetData(), &m,
+                                    tau.GetData(), qqt_rhs_glob.GetData(), &m,
+                                    work.data(), &lwork, &info);
 
          MFEM_VERIFY(info == 0, ""); // Q Q^T b work calculation failed.
          lwork = static_cast<int>(work[0]);
          work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-         sormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#elif defined MFEM_USE_DOUBLE
-         dormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#endif
-                 tau.GetData(), qqt_rhs_glob.GetData(), &m,
-                 work.data(), &lwork, &info);
+         MFEM_LAPACK_PREFIX(ormqr_)(&lside, &notrans, &m, &ione, &n_glob,
+                                    mat_qr_data.GetData(), &m,
+                                    tau.GetData(), qqt_rhs_glob.GetData(), &m,
+                                    work.data(), &lwork, &info);
          MFEM_VERIFY(info == 0, ""); // Q Q^T b calculation failed.
          res_glob = rhs_avg_glob;
          res_glob -= qqt_rhs_glob;

linalg/sparsemat.cpp

@@ -1267,24 +1267,32 @@ real_t SparseMatrix::InnerProduct(const Vector &x, const Vector &y) const
 
 void SparseMatrix::GetRowSums(Vector &x) const
 {
-   for (int i = 0; i < height; i++)
+   if (Finalized())
    {
-      real_t a = 0.0;
-      if (A)
+      auto d_I = ReadI();
+      auto d_A = ReadData();
+      auto d_x = x.Write();
+      mfem::forall(height, [=] MFEM_HOST_DEVICE (int i)
       {
-         for (int j = I[i], end = I[i+1]; j < end; j++)
+         real_t sum = 0.0;
+         for (int j = d_I[i], end = d_I[i+1]; j < end; j++)
          {
-            a += A[j];
+            sum += d_A[j];
          }
-      }
-      else
+         d_x[i] = sum;
+      });
+   }
+   else
+   {
+      for (int i = 0; i < height; i++)
       {
+         real_t a = 0.0;
          for (RowNode *np = Rows[i]; np != NULL; np = np->Prev)
          {
             a += np->Value;
          }
+         x(i) = a;
       }
-      x(i) = a;
    }
 }
 
@@ -3300,7 +3308,7 @@ void SparseMatrix::Print(std::ostream & os, int width_) const
 {
    int i, j;
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)
@@ -3354,7 +3362,7 @@ void SparseMatrix::PrintMatlab(std::ostream & os) const
    os.setf(ios::scientific);
    std::streamsize old_prec = os.precision(14);
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)
@@ -3385,6 +3393,61 @@ void SparseMatrix::PrintMatlab(std::ostream & os) const
    os.flags(old_fmt);
 }
 
+void SparseMatrix::PrintMathematica(std::ostream & os) const
+{
+   int i, j;
+   ios::fmtflags old_fmt = os.flags();
+   os.setf(ios::scientific);
+   std::streamsize old_prec = os.precision(14);
+
+   os << "(* Read file into Mathematica using: "
+      << "my_mat = Get[\"this_file_name\"] *)\n";
+   os << "SparseArray[";
+
+   if (A == NULL)
+   {
+      RowNode *nd;
+      int c = 0;
+      os << "{\n";
+      for (i = 0; i < height; i++)
+      {
+         for (nd = Rows[i], j = 0; nd != NULL; nd = nd->Prev, j++, c++)
+         {
+            os << "{"<< i+1 << ", " << nd->Column+1
+               << "} -> Internal`StringToMReal[\"" << nd->Value << "\"]";
+            if (c < NumNonZeroElems() - 1) { os << ","; }
+            os << '\n';
+         }
+      }
+      os << "}\n";
+   }
+   else
+   {
+      // HostRead forces synchronization
+      HostReadI();
+      HostReadJ();
+      HostReadData();
+      int c = 0;
+      os << "{\n";
+      for (i = 0; i < height; i++)
+      {
+         for (j = I[i]; j < I[i+1]; j++, c++)
+         {
+            os << "{" << i+1 << ", " << J[j]+1
+               << "} -> Internal`StringToMReal[\"" << A[j] << "\"]";
+            if (c < NumNonZeroElems() - 1) { os << ","; }
+            os << '\n';
+         }
+      }
+      os << "}";
+   }
+
+   os << ",{" << height << "," << width << "}]\n";
+
+   os.precision(old_prec);
+   os.flags(old_fmt);
+}
+
 void SparseMatrix::PrintMM(std::ostream & os) const
 {
    int i, j;
@@ -3397,7 +3460,7 @@ void SparseMatrix::PrintMM(std::ostream & os) const
 
    os << height << " " << width << " " << NumNonZeroElems() << '\n';
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)

linalg/sparsemat.hpp

@@ -216,7 +216,7 @@ public:
    void ClearCuSparse() { ClearGPUSparse(); }
 
    /// Check if the SparseMatrix is empty.
-   bool Empty() const { return (A == NULL) && (Rows == NULL); }
+   bool Empty() const { return A.Empty() && (Rows == NULL); }
 
    /// Return the array #I.
    inline int *GetI() { return I; }
@@ -657,6 +657,19 @@ public:
    /** @note The host in synchronized when the finalized matrix is on the device. */
    virtual void PrintMatlab(std::ostream &out = mfem::out) const;
 
+   /// Prints matrix as a SparseArray for importing into Mathematica.
+   /** The resulting file can be read into Mathematica using an expression such
+       as: my_mat = Get["output_file_name"]
+       The Mathematica variable "my_mat" will then be assigned to a new
+       SparseArray object containing the data from this MFEM SparseMatrix.
+
+       @note Mathematica uses 1-based indexing so the MFEM row and column
+       indices will be sifted up by one in the Mathematica output.
+
+       @note The host in synchronized when the finalized matrix is on the
+       device. */
+   virtual void PrintMathematica(std::ostream &out = mfem::out) const;
+
    /// Prints matrix in Matrix Market sparse format.
    /** @note The host in synchronized when the finalized matrix is on the device. */
    void PrintMM(std::ostream &out = mfem::out) const;

linalg/sundials.cpp

@@ -1341,38 +1341,59 @@ CVODESSolver::~CVODESSolver()
 // ARKStep interface
 // ---------------------------------------------------------------------------
 
-int ARKStepSolver::RHS1(realtype t, const N_Vector y, N_Vector ydot,
+int ARKStepSolver::RHS1(realtype t, const N_Vector y, N_Vector result,
                         void *user_data)
 {
    // Get data from N_Vectors
    const SundialsNVector mfem_y(y);
-   SundialsNVector mfem_ydot(ydot);
+   SundialsNVector mfem_result(result);
    ARKStepSolver *self = static_cast<ARKStepSolver*>(user_data);
 
-   // Compute f(t, y) in y' = f(t, y) or fe(t, y) in y' = fe(t, y) + fi(t, y)
+   // Compute either f(t, y) in one of
+   //   1. y' = f(t, y)
+   //   2. M y' = f(t, y)
+   // or fe(t, y) in one of
+   //   1. y' = fe(t, y) + fi(t, y)
+   //   2. M y' = fe(t, y) + fi(t, y)
    self->f->SetTime(t);
    if (self->rk_type == IMEX)
    {
       self->f->SetEvalMode(TimeDependentOperator::ADDITIVE_TERM_1);
    }
-   self->f->Mult(mfem_y, mfem_ydot);
+   if (self->f->isExplicit()) // ODE is in form 1
+   {
+      self->f->Mult(mfem_y, mfem_result);
+   }
+   else // ODE is in form 2
+   {
+      self->f->ExplicitMult(mfem_y, mfem_result);
+   }
 
    // Return success
    return (0);
 }
 
-int ARKStepSolver::RHS2(realtype t, const N_Vector y, N_Vector ydot,
+int ARKStepSolver::RHS2(realtype t, const N_Vector y, N_Vector result,
                         void *user_data)
 {
    // Get data from N_Vectors
    const SundialsNVector mfem_y(y);
-   SundialsNVector mfem_ydot(ydot);
+   SundialsNVector mfem_result(result);
    ARKStepSolver *self = static_cast<ARKStepSolver*>(user_data);
 
-   // Compute fi(t, y) in y' = fe(t, y) + fi(t, y)
+   // Compute fi(t, y) in one of
+   //   1. y' = fe(t, y) + fi(t, y)       (ODE is expressed in EXPLICIT form)
+   //   2. M y' = fe(t, y) + fi(y, t)     (ODE is expressed in IMPLICIT form)
    self->f->SetTime(t);
    self->f->SetEvalMode(TimeDependentOperator::ADDITIVE_TERM_2);
-   self->f->Mult(mfem_y, mfem_ydot);
+   if (self->f->isExplicit())
+   {
+      self->f->Mult(mfem_y, mfem_result);
+   }
+   else
+   {
+      self->f->ExplicitMult(mfem_y, mfem_result);
+   }
 
    // Return success
    return (0);
@@ -1567,7 +1588,7 @@ void ARKStepSolver::Init(TimeDependentOperator &f_)
    reinit = true;
 }
 
-void ARKStepSolver::Step(Vector &x, double &t, double &dt)
+void ARKStepSolver::Step(Vector &x, real_t &t, real_t &dt)
 {
    Y->MakeRef(x, 0, x.Size());
    MFEM_VERIFY(Y->Size() == x.Size(), "size mismatch");
@@ -1666,7 +1687,7 @@ void ARKStepSolver::UseMFEMMassLinearSolver(int tdep)
    LSM->content      = this;
    LSM->ops->gettype = LSGetType;
    LSM->ops->solve   = ARKStepSolver::MassSysSolve;
-   LSA->ops->free    = LSFree;
+   LSM->ops->free    = LSFree;
 
    M = SUNMatNewEmpty(Sundials::GetContext());
    MFEM_VERIFY(M, "error in SUNMatNewEmpty()");
@@ -1683,6 +1704,9 @@ void ARKStepSolver::UseMFEMMassLinearSolver(int tdep)
    // Set the linear system function
    flag = ARKStepSetMassFn(sundials_mem, ARKStepSolver::MassSysSetup);
    MFEM_VERIFY(flag == ARK_SUCCESS, "error in ARKStepSetMassFn()");
+
+   // Check that the ODE is not expressed in EXPLICIT form
+   MFEM_VERIFY(!f->isExplicit(), "ODE operator is expressed in EXPLICIT form")
 }
 
 void ARKStepSolver::UseSundialsMassLinearSolver(int tdep)
@@ -1703,6 +1727,9 @@ void ARKStepSolver::UseSundialsMassLinearSolver(int tdep)
    flag = ARKStepSetMassTimes(sundials_mem, NULL, ARKStepSolver::MassMult2,
                               this);
    MFEM_VERIFY(flag == ARK_SUCCESS, "error in ARKStepSetMassTimes()");
+
+   // Check that the ODE is not expressed in EXPLICIT form
+   MFEM_VERIFY(!f->isExplicit(), "ODE operator is expressed in EXPLICIT form")
 }
 
 void ARKStepSolver::SetStepMode(int itask)

linalg/sundials.hpp

@@ -763,7 +763,7 @@ public:
        @note On input, the values of @a t and @a dt are used to compute desired
        output time for the integration, tout = @a t + @a dt.
    */
-   virtual void Step(Vector &x, double &t, double &dt);
+   virtual void Step(Vector &x, real_t &t, real_t &dt) override;
 
    /** @brief Attach the linear system setup and solve methods from the
        TimeDependentOperator i.e., SUNImplicitSetup() and SUNImplicitSolve() to

makefile

@@ -193,7 +193,8 @@ endif
 
 # Compile flags used by MFEM: CPPFLAGS, CXXFLAGS, plus library flags
 INCFLAGS =
-# Link flags used by MFEM: library link flags plus LDFLAGS (added last)
+# Link flags used by MFEM: library link flags plus LDFLAGS and LDFLAGS_INTERNAL
+# (added at the end)
 ALL_LIBS =
 
 # Building static and/or shared libraries:
@@ -372,7 +373,7 @@ MFEM_TPLFLAGS  ?= $(INCFLAGS)
 MFEM_INCFLAGS  ?= -I@MFEM_INC_DIR@ @MFEM_TPLFLAGS@
 MFEM_PICFLAG   ?= $(if $(shared),$(PICFLAG))
 MFEM_FLAGS     ?= @MFEM_CPPFLAGS@ @MFEM_CXXFLAGS@ @MFEM_INCFLAGS@
-MFEM_EXT_LIBS  ?= $(ALL_LIBS) $(LDFLAGS)
+MFEM_EXT_LIBS  ?= $(ALL_LIBS) $(LDFLAGS) $(LDFLAGS_INTERNAL)
 MFEM_LIBS      ?= $(if $(shared),$(BUILD_RPATH)) -L@MFEM_LIB_DIR@ -lmfem\
    @MFEM_EXT_LIBS@
 MFEM_LIB_FILE  ?= @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_VER),a)
@@ -581,53 +582,77 @@ clean: $(addsuffix /clean,$(EM_DIRS) $(TEST_DIRS))
 distclean: clean config/clean doc/clean
 	rm -rf mfem/
 
+# User-definable install permissions.
+# Install permissions for everything except directories and binaries:
+INSTALL_DEF_PERM ?= 644
+# Install permissions for binaries:
+INSTALL_BIN_PERM ?= 755
+# Install permissions for directories (and symlinks on macOS/BSD):
+INSTALL_DIR_PERM ?= 755
+
+# Shortcuts, not to be modified by the user on the command line.
+# We use 'umask' because 'mkdir -p' (and 'install -d') do not use the mode
+# specified with the '-m' flag when creating non-existent parent directories.
+# WARNING: $(MKINSTALLDIR) changes the umask for commands following it as part
+#          of the same shell expression unless it is placed inside '()' to be
+#          executed in a sub-shell.
+override INSTALLDEF   = $(INSTALL) -m $(INSTALL_DEF_PERM)
+override INSTALLMASK  = $(shell printf "%o" $$((~0$(INSTALL_DIR_PERM) & 0777)))
+override MKINSTALLDIR = umask $(INSTALLMASK) && mkdir -p
+
 INSTALL_SHARED_LIB = $(MFEM_CXX) $(MFEM_LINK_FLAGS) $(INSTALL_SOFLAGS)\
    $(OBJECT_FILES) $(EXT_LIBS) -o $(PREFIX_LIB)/libmfem.$(SO_VER) && \
-   cd $(PREFIX_LIB) && ln -sf libmfem.$(SO_VER) libmfem.$(SO_EXT)
+   cd $(PREFIX_LIB) && chmod $(INSTALL_BIN_PERM) libmfem.$(SO_VER) && \
+   ( umask $(INSTALLMASK) && ln -sf libmfem.$(SO_VER) libmfem.$(SO_EXT) )
 
 install: $(if $(static),$(BLD)libmfem.a) $(if $(shared),$(BLD)libmfem.$(SO_EXT))
-	mkdir -p $(PREFIX_LIB)
+	$(MKINSTALLDIR) $(PREFIX_LIB)
 # install static and/or shared library
-	$(if $(static),$(INSTALL) -m 640 $(BLD)libmfem.a $(PREFIX_LIB))
+	$(if $(static),$(INSTALLDEF) $(BLD)libmfem.a $(PREFIX_LIB))
 	$(if $(shared),$(INSTALL_SHARED_LIB))
 # install top level includes
-	mkdir -p $(PREFIX_INC)/mfem
-	$(INSTALL) -m 640 $(SRC)mfem.hpp $(SRC)mfem-performance.hpp \
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem
+	$(INSTALLDEF) $(SRC)mfem.hpp $(SRC)mfem-performance.hpp \
 	   $(PREFIX_INC)/mfem
 	for hdr in mfem.hpp mfem-performance.hpp; do \
 	   printf '// Auto-generated file.\n#include "mfem/'$$hdr'"\n' \
-	      > $(PREFIX_INC)/$$hdr && chmod 640 $(PREFIX_INC)/$$hdr; done
+	      > $(PREFIX_INC)/$$hdr && \
+	   chmod $(INSTALL_DEF_PERM) $(PREFIX_INC)/$$hdr; done
 # install config include
-	mkdir -p $(PREFIX_INC)/mfem/config
-	$(INSTALL) -m 640 $(BLD)config/_config.hpp $(PREFIX_INC)/mfem/config/_config.hpp
-	$(INSTALL) -m 640 $(SRC)config/config.hpp $(PREFIX_INC)/mfem/config/config.hpp
-	$(INSTALL) -m 640 $(SRC)config/tconfig.hpp $(PREFIX_INC)/mfem/config
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem/config
+	$(INSTALLDEF) $(BLD)config/_config.hpp $(PREFIX_INC)/mfem/config
+	$(INSTALLDEF) $(SRC)config/config.hpp $(PREFIX_INC)/mfem/config
+	$(INSTALLDEF) $(SRC)config/tconfig.hpp $(PREFIX_INC)/mfem/config
 # install remaining includes in each subdirectory
 	for dir in $(DIRS); do \
-	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
-	   $(INSTALL) -m 640 $(SRC)$$dir/*.hpp $(PREFIX_INC)/mfem/$$dir; \
+	   ( $(MKINSTALLDIR) $(PREFIX_INC)/mfem/$$dir ) && \
+	   $(INSTALLDEF) $(SRC)$$dir/*.hpp $(PREFIX_INC)/mfem/$$dir; \
 	done
 # install *.okl files
 	for dir in $(OKL_DIRS); do \
-	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
-	   $(INSTALL) -m 640 $(SRC)$$dir/*.okl $(PREFIX_INC)/mfem/$$dir; \
+	   ( $(MKINSTALLDIR) $(PREFIX_INC)/mfem/$$dir ) && \
+	   $(INSTALLDEF) $(SRC)$$dir/*.okl $(PREFIX_INC)/mfem/$$dir; \
 	done
 # install libCEED q-function headers
-	mkdir -p $(PREFIX_INC)/mfem/fem/ceed/integrators/mass
-	$(INSTALL) -m 640 $(SRC)fem/ceed/integrators/mass/*.h $(PREFIX_INC)/mfem/fem/ceed/integrators/mass
-	mkdir -p $(PREFIX_INC)/mfem/fem/ceed/integrators/convection
-	$(INSTALL) -m 640 $(SRC)fem/ceed/integrators/convection/*.h $(PREFIX_INC)/mfem/fem/ceed/integrators/convection
-	mkdir -p $(PREFIX_INC)/mfem/fem/ceed/integrators/diffusion
-	$(INSTALL) -m 640 $(SRC)fem/ceed/integrators/diffusion/*.h $(PREFIX_INC)/mfem/fem/ceed/integrators/diffusion
-	mkdir -p $(PREFIX_INC)/mfem/fem/ceed/integrators/nlconvection
-	$(INSTALL) -m 640 $(SRC)fem/ceed/integrators/nlconvection/*.h $(PREFIX_INC)/mfem/fem/ceed/integrators/nlconvection
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem/fem/ceed/integrators/mass
+	$(INSTALLDEF) $(SRC)fem/ceed/integrators/mass/*.h \
+	   $(PREFIX_INC)/mfem/fem/ceed/integrators/mass
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem/fem/ceed/integrators/convection
+	$(INSTALLDEF) $(SRC)fem/ceed/integrators/convection/*.h \
+	   $(PREFIX_INC)/mfem/fem/ceed/integrators/convection
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem/fem/ceed/integrators/diffusion
+	$(INSTALLDEF) $(SRC)fem/ceed/integrators/diffusion/*.h \
+	   $(PREFIX_INC)/mfem/fem/ceed/integrators/diffusion
+	$(MKINSTALLDIR) $(PREFIX_INC)/mfem/fem/ceed/integrators/nlconvection
+	$(INSTALLDEF) $(SRC)fem/ceed/integrators/nlconvection/*.h \
+	   $(PREFIX_INC)/mfem/fem/ceed/integrators/nlconvection
 # install config.mk in $(PREFIX_SHARE)
-	mkdir -p $(PREFIX_SHARE)
+	$(MKINSTALLDIR) $(PREFIX_SHARE)
 	$(MAKE) -C $(BLD)config config-mk CONFIG_MK=config-install.mk
-	$(INSTALL) -m 640 $(BLD)config/config-install.mk $(PREFIX_SHARE)/config.mk
+	$(INSTALLDEF) $(BLD)config/config-install.mk $(PREFIX_SHARE)/config.mk
 	rm -f $(BLD)config/config-install.mk
 # install test.mk in $(PREFIX_SHARE)
-	$(INSTALL) -m 640 $(SRC)config/test.mk $(PREFIX_SHARE)/test.mk
+	$(INSTALLDEF) $(SRC)config/test.mk $(PREFIX_SHARE)
 
 $(CONFIG_MK):
 # Skip the error message when '-B' make flag is used (unconditionally

mesh/CMakeLists.txt

@@ -12,6 +12,7 @@
 set(SRCS
   attribute_sets.cpp
   element.cpp
+  exodus_writer.cpp
   face_nbr_geom.cpp
   gmsh.cpp
   hexahedron.cpp

mesh/mesh.cpp

@@ -466,7 +466,8 @@ void Mesh::GetBdrElementTransformation(int i,
          {
             for (int j = 0; j < n; j++)
             {
-               pm(k,j) = nodes(vdofs[n*k+j]);
+               int idx = vdofs[n*k+j];
+               pm(k,j) = nodes((idx<0)? -1-idx:idx);
             }
          }
          ElTr->SetFE(bdr_el);
@@ -7131,17 +7132,15 @@ Table *Mesh::GetEdgeVertexTable() const
 
 Table *Mesh::GetVertexToElementTable()
 {
-   int i, j, nv, *v;
-
    Table *vert_elem = new Table;
 
    vert_elem->MakeI(NumOfVertices);
 
-   for (i = 0; i < NumOfElements; i++)
+   for (int i = 0; i < NumOfElements; i++)
    {
-      nv = elements[i]->GetNVertices();
-      v  = elements[i]->GetVertices();
-      for (j = 0; j < nv; j++)
+      const int nv = elements[i]->GetNVertices();
+      const int *v = elements[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
       {
          vert_elem->AddAColumnInRow(v[j]);
       }
@@ -7149,11 +7148,11 @@ Table *Mesh::GetVertexToElementTable()
 
    vert_elem->MakeJ();
 
-   for (i = 0; i < NumOfElements; i++)
+   for (int i = 0; i < NumOfElements; i++)
    {
-      nv = elements[i]->GetNVertices();
-      v  = elements[i]->GetVertices();
-      for (j = 0; j < nv; j++)
+      const int nv = elements[i]->GetNVertices();
+      const int *v = elements[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
       {
          vert_elem->AddConnection(v[j], i);
       }
@@ -7164,6 +7163,39 @@ Table *Mesh::GetVertexToElementTable()
    return vert_elem;
 }
 
+Table *Mesh::GetVertexToBdrElementTable()
+{
+   Table *vert_bdr_elem = new Table;
+
+   vert_bdr_elem->MakeI(NumOfVertices);
+
+   for (int i = 0; i < NumOfBdrElements; i++)
+   {
+      const int nv = boundary[i]->GetNVertices();
+      const int *v = boundary[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
+      {
+         vert_bdr_elem->AddAColumnInRow(v[j]);
+      }
+   }
+
+   vert_bdr_elem->MakeJ();
+
+   for (int i = 0; i < NumOfBdrElements; i++)
+   {
+      const int nv = boundary[i]->GetNVertices();
+      const int *v = boundary[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
+      {
+         vert_bdr_elem->AddConnection(v[j], i);
+      }
+   }
+
+   vert_bdr_elem->ShiftUpI();
+
+   return vert_bdr_elem;
+}
+
 Table *Mesh::GetFaceToElementTable() const
 {
    Table *face_elem = new Table;
@@ -13600,22 +13632,23 @@ Mesh &MeshPart::GetMesh()
 
 MeshPartitioner::MeshPartitioner(Mesh &mesh_,
                                  int num_parts_,
-                                 int *partitioning_,
+                                 const int *partitioning_,
                                  int part_method)
    : mesh(mesh_)
 {
    if (partitioning_)
    {
-      partitioning.MakeRef(partitioning_, mesh.GetNE(), false);
+      partitioning.MakeRef(const_cast<int *>(partitioning_), mesh.GetNE(),
+                           false);
    }
    else
    {
-      partitioning_ = mesh.GeneratePartitioning(num_parts_, part_method);
       // Mesh::GeneratePartitioning always uses new[] to allocate the,
       // partitioning, so we need to tell the memory manager to free it with
       // delete[] (even if a different host memory type has been selected).
-      const MemoryType mt = MemoryType::HOST;
-      partitioning.MakeRef(partitioning_, mesh.GetNE(), mt, true);
+      constexpr MemoryType mt = MemoryType::HOST;
+      partitioning.MakeRef(mesh.GeneratePartitioning(num_parts_, part_method),
+                           mesh.GetNE(), mt, true);
    }
 
    Transpose(partitioning, part_to_element, num_parts_);

mesh/mesh.hpp

@@ -1537,6 +1537,9 @@ public:
    /// @note The returned Table should be deleted by the caller
    Table *GetVertexToElementTable();
 
+   /// @note The returned Table should be deleted by the caller
+   Table *GetVertexToBdrElementTable();
+
    /// Return the "face"-element Table. Here "face" refers to face (3D),
    /// edge (2D), or vertex (1D).
    ///
@@ -2331,6 +2334,11 @@ public:
                     bool high_order_output=false,
                     int compression_level=0);
 
+#ifdef MFEM_USE_NETCDF
+   /// @brief Export a mesh to an Exodus II file.
+   void PrintExodusII(const std::string fpath);
+#endif
+
    /** @brief Prints the mesh with boundary elements given by the boundary of
        the subdomains, so that the boundary of subdomain i has boundary
        attribute i+1. */
@@ -2728,8 +2736,8 @@ public:
                                 Mesh::GeneratePartitioning() when the provided
                                 input partitioning is NULL.
    */
-   MeshPartitioner(Mesh &mesh_, int num_parts_, int *partitioning_ = NULL,
-                   int part_method = 1);
+   MeshPartitioner(Mesh &mesh_, int num_parts_,
+                   const int *partitioning_ = nullptr, int part_method = 1);
 
    /** @brief Construct a MeshPart corresponding to the given @a part_id.
 

mesh/nurbs.cpp

@@ -1857,7 +1857,7 @@ NURBSPatch *Revolve3D(NURBSPatch &patch, real_t n[], real_t ang, int times)
 {
    if (patch.Dim != 4)
    {
-      mfem_error("Revolve3D(NURBSPatch &, double [], double)");
+      mfem_error("Revolve3D(NURBSPatch &, real_t [], real_t)");
    }
 
    int size = 1, ns;
@@ -2008,23 +2008,23 @@ NURBSExtension::NURBSExtension(std::istream &input, bool spacing)
          input >> numSpacing;
          for (int j = 0; j < numSpacing; j++)
          {
-            int ki, spacingType, numIntParam, numDoubleParam;
-            input >> ki >> spacingType >> numIntParam >> numDoubleParam;
+            int ki, spacingType, numIntParam, numRealParam;
+            input >> ki >> spacingType >> numIntParam >> numRealParam;
 
             MFEM_VERIFY(0 <= ki && ki < NumOfKnotVectors,
                         "Invalid knotvector index");
-            MFEM_VERIFY(numIntParam >= 0 && numDoubleParam >= 0,
+            MFEM_VERIFY(numIntParam >= 0 && numRealParam >= 0,
                         "Invalid number of parameters in KnotVector");
 
             Array<int> ipar(numIntParam);
-            Vector dpar(numDoubleParam);
+            Vector dpar(numRealParam);
 
             for (int i=0; i<numIntParam; ++i)
             {
                input >> ipar[i];
             }
 
-            for (int i=0; i<numDoubleParam; ++i)
+            for (int i=0; i<numRealParam; ++i)
             {
                input >> dpar[i];
             }
@@ -2064,7 +2064,7 @@ NURBSExtension::NURBSExtension(std::istream &input, bool spacing)
                   new KnotVector(*patches[p]->GetKV(0));
             }
          }
-         if (Dimension() == 2)
+         else if (Dimension() == 2)
          {
             patchTopo->GetElementEdges(p, edges, oedge);
             if (knotVectors[KnotInd(edges[0])] == NULL)
@@ -2230,7 +2230,8 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent, int newOrder)
 }
 
 NURBSExtension::NURBSExtension(NURBSExtension *parent,
-                               const Array<int> &newOrders)
+                               const Array<int> &newOrders, Mode mode)
+   : mode(mode)
 {
    newOrders.Copy(mOrders);
    SetOrderFromOrders();
@@ -3891,7 +3892,16 @@ void NURBSExtension::GenerateBdrElementDofTable()
    int ndof = bel_dof->Size_of_connections();
    for (int i = 0; i < ndof; i++)
    {
-      dof[i] = activeDof[dof[i]] - 1;
+      int idx = dof[i];
+      if (idx < 0)
+      {
+         dof[i] = -1 - (activeDof[-1-idx] - 1);
+         dof[i] = -activeDof[-1-idx];
+      }
+      else
+      {
+         dof[i] = activeDof[idx] - 1;
+      }
    }
 }
 
@@ -3943,6 +3953,22 @@ void NURBSExtension::Generate2DBdrElementDofTable()
       // Load dofs
       const int nks0 = kv[0]->GetNKS();
       const int ord0 = kv[0]->GetOrder();
+
+      bool add_dofs = true;
+      int  s = 1;
+
+      if (mode == Mode::H_DIV)
+      {
+         int fn = patchTopo->GetBdrElementFaceIndex(b);
+         if (ord0 == mOrders.Max()) { add_dofs = false; }
+         if (fn == 0) { s = -1; }
+         if (fn == 2) { s = -1; }
+      }
+      else if (mode == Mode::H_CURL)
+      {
+         if (ord0 == mOrders.Max()) { add_dofs = false; }
+      }
+
       for (int i = 0; i < nks0; i++)
       {
          if (kv[0]->isElement(i))
@@ -3950,10 +3976,14 @@ void NURBSExtension::Generate2DBdrElementDofTable()
             if (activeBdrElem[gbe])
             {
                Connection conn(lbe,0);
-               for (int ii = 0; ii <= ord0; ii++)
+               if (add_dofs)
                {
-                  conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
-                  bel_dof_list.Append(conn);
+                  for (int ii = 0; ii <= ord0; ii++)
+                  {
+                     conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
+                     if (s == -1) { conn.to = -1 -conn.to; }
+                     bel_dof_list.Append(conn);
+                  }
                }
                bel_to_patch[lbe] = b;
                bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : (-1-i);
@@ -3990,6 +4020,25 @@ void NURBSExtension::Generate3DBdrElementDofTable()
       const int ord0 = kv[0]->GetOrder();
       const int nks1 = kv[1]->GetNKS();
       const int ord1 = kv[1]->GetOrder();
+
+      // Check if dofs are actually defined on boundary
+      bool add_dofs = true;
+      int  s = 1;
+
+      if (mode == Mode::H_DIV)
+      {
+         int fn = patchTopo->GetBdrElementFaceIndex(b);
+         if (ord0 != ord1) { add_dofs = false; }
+         if (fn == 4) { s = -1; }
+         if (fn == 1) { s = -1; }
+         if (fn == 0) { s = -1; }
+      }
+      else if (mode == Mode::H_CURL)
+      {
+         if (ord0 == ord1) { add_dofs = false; }
+      }
+
+
       for (int j = 0; j < nks1; j++)
       {
          if (kv[1]->isElement(j))
@@ -4001,14 +4050,18 @@ void NURBSExtension::Generate3DBdrElementDofTable()
                   if (activeBdrElem[gbe])
                   {
                      Connection conn(lbe,0);
-                     for (int jj = 0; jj <= ord1; jj++)
+                     if (add_dofs)
                      {
-                        const int jj_ = (okv[1] >= 0) ? (j+jj) : (ny-j-jj);
-                        for (int ii = 0; ii <= ord0; ii++)
+                        for (int jj = 0; jj <= ord1; jj++)
                         {
-                           const int ii_ = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
-                           conn.to = DofMap(p2g(ii_, jj_));
-                           bel_dof_list.Append(conn);
+                           const int jj_ = (okv[1] >= 0) ? (j+jj) : (ny-j-jj);
+                           for (int ii = 0; ii <= ord0; ii++)
+                           {
+                              const int ii_ = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
+                              conn.to = DofMap(p2g(ii_, jj_));
+                              if (s == -1) { conn.to = -1 -conn.to; }
+                              bel_dof_list.Append(conn);
+                           }
                         }
                      }
                      bel_to_patch[lbe] = b;
@@ -4241,6 +4294,38 @@ void NURBSExtension::DegreeElevate(int rel_degree, int degree)
    }
 }
 
+NURBSExtension* NURBSExtension::GetDivExtension(int component)
+{
+   // Smarter routine
+   if (GetNP() > 1)
+   {
+      mfem_error("NURBSExtension::GetDivExtension currently "
+                 "only works for single patch NURBS meshes ");
+   }
+
+   Array<int> newOrders  = GetOrders();
+   newOrders[component] += 1;
+
+   return new NURBSExtension(this, newOrders, Mode::H_DIV);
+}
+
+NURBSExtension* NURBSExtension::GetCurlExtension(int component)
+{
+   // Smarter routine
+   if (GetNP() > 1)
+   {
+      mfem_error("NURBSExtension::GetCurlExtension currently "
+                 "only works for single patch NURBS meshes ");
+   }
+
+   Array<int> newOrders  = GetOrders();
+   for (int c = 0; c < newOrders.Size(); c++) { newOrders[c]++; }
+   newOrders[component] -= 1;
+
+   return new NURBSExtension(this, newOrders, Mode::H_CURL);
+}
+
+
 void NURBSExtension::UniformRefinement(Array<int> const& rf)
 {
    for (int p = 0; p < patches.Size(); p++)
@@ -4722,19 +4807,15 @@ const Array<int>& NURBSExtension::GetPatchBdrElements(int patch)
 #ifdef MFEM_USE_MPI
 ParNURBSExtension::ParNURBSExtension(const ParNURBSExtension &orig)
    : NURBSExtension(orig),
-     partitioning(orig.partitioning ? new int[orig.GetGNE()] : NULL),
+     partitioning(orig.partitioning),
      gtopo(orig.gtopo),
      ldof_group(orig.ldof_group)
 {
-   // Copy the partitioning, if not NULL
-   if (partitioning)
-   {
-      std::memcpy(partitioning, orig.partitioning, orig.GetGNE()*sizeof(int));
-   }
 }
 
 ParNURBSExtension::ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
-                                     int *part, const Array<bool> &active_bel)
+                                     const int *partitioning_,
+                                     const Array<bool> &active_bel)
    : gtopo(comm)
 {
    if (parent->NumOfActiveElems < parent->NumOfElements)
@@ -4772,11 +4853,11 @@ ParNURBSExtension::ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
    CountElements();
    CountBdrElements();
 
-   // copy 'part' to 'partitioning'
-   partitioning = new int[GetGNE()];
+   // copy 'partitioning_' to 'partitioning'
+   partitioning.SetSize(GetGNE());
    for (int i = 0; i < GetGNE(); i++)
    {
-      partitioning[i] = part[i];
+      partitioning[i] = partitioning_[i];
    }
    SetActive(partitioning, active_bel);
 
@@ -4867,8 +4948,6 @@ ParNURBSExtension::ParNURBSExtension(NURBSExtension *parent,
 
    delete parent;
 
-   partitioning = NULL;
-
    MFEM_VERIFY(par_parent->partitioning,
                "parent ParNURBSExtension has no partitioning!");
 

mesh/nurbs.hpp

@@ -426,6 +426,16 @@ class NURBSExtension
    friend class NURBSPatchMap;
 
 protected:
+
+   /// Flag for indicating what type of NURBS fespace this extension is used for.
+   enum class Mode
+   {
+      H_1,    ///> Extension for a standard scalar-valued space
+      H_DIV,  ///> Extension for a divergence conforming vector-valued space
+      H_CURL, ///> Extension for a curl conforming vector-valued space
+   };
+   Mode mode = Mode::H_1;
+
    /// Order of KnotVectors, see GetOrder() for description.
    int mOrder;
 
@@ -655,8 +665,10 @@ public:
    /** @a note If a KnotVector in @a parent already has order greater than or
        equal to the corresponding entry in @a newOrder, it will be used
        unmodified. */
-   NURBSExtension(NURBSExtension *parent, const Array<int> &newOrders);
+   NURBSExtension(NURBSExtension *parent, const Array<int> &newOrders,
+                  Mode mode = Mode::H_1);
    /// Construct a NURBSExtension by merging a partitioned NURBS mesh.
+
    NURBSExtension(Mesh *mesh_array[], int num_pieces);
 
    /// Copy assignment not supported.
@@ -841,6 +853,16 @@ public:
    void KnotInsert(Array<KnotVector *> &kv);
    void KnotInsert(Array<Vector *> &kv);
 
+   /** Returns the NURBSExtension to be used for @a component of
+       an H(div) conforming NURBS space. Caller gets ownership of
+       the returned object, and is responsible for deletion.*/
+   NURBSExtension* GetDivExtension(int component);
+
+   /** Returns the NURBSExtension to be used for @a component of
+       an H(curl) conforming NURBS space. Caller gets ownership of
+       the returned object, and is responsible for deletion.*/
+   NURBSExtension* GetCurlExtension(int component);
+
    void KnotRemove(Array<Vector *> &kv, real_t tol = 1.0e-12);
 
    /** Calls GetCoarseningFactors for each patch and finds the minimum factor
@@ -848,6 +870,7 @@ public:
        non-nested spacing functions. */
    void GetCoarseningFactors(Array<int> & f) const;
 
+
    /// Returns the index of the patch containing element @a elem.
    int GetElementPatch(int elem) const { return el_to_patch[elem]; }
 
@@ -872,7 +895,7 @@ class ParNURBSExtension : public NURBSExtension
 {
 private:
    /// Partitioning of the global elements by MPI rank
-   int *partitioning;
+   mfem::Array<int> partitioning;
 
    /// Construct and return a table of DOFs for each global element.
    Table *GetGlobalElementDofTable();
@@ -882,9 +905,10 @@ private:
 
    /** @brief Set active global elements and boundary elements based on MPI
        ranks in @a partition and the array @a active_bel. */
-   void SetActive(const int *partition, const Array<bool> &active_bel);
+   void SetActive(const int *partitioning_, const Array<bool> &active_bel);
+
    /// Set up GroupTopology @a gtopo for MPI communication.
-   void BuildGroups(const int *partition, const Table &elem_dof);
+   void BuildGroups(const int *partitioning_, const Table &elem_dof);
 
 public:
    GroupTopology gtopo;
@@ -895,11 +919,12 @@ public:
    ParNURBSExtension(const ParNURBSExtension &orig);
 
    /** @brief Constructor for an MPI communicator @a comm, a global
-       NURBSExtension @a parent, a partitioning @a part of the global elements
-       by MPI rank, and a marker @a active_bel of active global boundary
-       elements on this rank. The partitioning is deep-copied and will not be
-       deleted by this object. */
-   ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent, int *part,
+       NURBSExtension @a parent, a partitioning @a partitioning_ of the global
+       elements by MPI rank, and a marker @a active_bel of active global
+       boundary elements on this rank. The partitioning is deep-copied and will
+       not be deleted by this object. */
+   ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
+                     const int *partitioning_,
                      const Array<bool> &active_bel);
 
    /** @brief Create a parallel version of @a parent with partitioning as in
@@ -907,8 +932,6 @@ public:
        The @a parent can be either a local NURBSExtension or a global one. */
    ParNURBSExtension(NURBSExtension *parent,
                      const ParNURBSExtension *par_parent);
-
-   virtual ~ParNURBSExtension() { delete [] partitioning; }
 };
 #endif
 

mesh/pmesh.cpp

@@ -103,29 +103,32 @@ ParMesh& ParMesh::operator=(ParMesh &&mesh)
    return *this;
 }
 
-ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
+ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, const int *partitioning_,
                  int part_method)
    : glob_elem_offset(-1)
    , glob_offset_sequence(-1)
    , gtopo(comm)
 {
-   int *partitioning = NULL;
-   Array<bool> activeBdrElem;
-
    MyComm = comm;
    MPI_Comm_size(MyComm, &NRanks);
    MPI_Comm_rank(MyComm, &MyRank);
 
+   Array<int> partitioning;
+   Array<bool> activeBdrElem;
+
+   if (partitioning_)
+   {
+      partitioning.MakeRef(const_cast<int *>(partitioning_), mesh.GetNE(),
+                           false);
+   }
+
    if (mesh.Nonconforming())
    {
-      if (partitioning_)
+      ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning_);
+
+      if (!partitioning_)
       {
-         partitioning = partitioning_;
-      }
-      ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning);
-      if (!partitioning)
-      {
-         partitioning = new int[mesh.GetNE()];
+         partitioning.SetSize(mesh.GetNE());
          for (int i = 0; i < mesh.GetNE(); i++)
          {
             partitioning[i] = pncmesh->InitialPartition(i);
@@ -158,13 +161,14 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
 
       ncmesh = pncmesh = NULL;
 
-      if (partitioning_)
+      if (!partitioning_)
       {
-         partitioning = partitioning_;
-      }
-      else
-      {
-         partitioning = mesh.GeneratePartitioning(NRanks, part_method);
+         // Mesh::GeneratePartitioning always uses new[] to allocate the,
+         // partitioning, so we need to tell the memory manager to free it with
+         // delete[] (even if a different host memory type has been selected).
+         constexpr MemoryType mt = MemoryType::HOST;
+         partitioning.MakeRef(mesh.GeneratePartitioning(NRanks, part_method),
+                              mesh.GetNE(), mt, true);
       }
 
       // re-enumerate the partitions to better map to actual processor
@@ -306,11 +310,6 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
       SetVerticesFromNodes(Nodes);
    }
 
-   if (partitioning != partitioning_)
-   {
-      delete [] partitioning;
-   }
-
    have_face_nbr_data = false;
 }
 
@@ -730,7 +729,7 @@ void ParMesh::BuildVertexGroup(int ngroups, const Table &vert_element)
 }
 
 void ParMesh::BuildSharedFaceElems(int ntri_faces, int nquad_faces,
-                                   const Mesh& mesh, int *partitioning,
+                                   const Mesh& mesh, const int *partitioning,
                                    const STable3D *faces_tbl,
                                    const Array<int> &face_group,
                                    const Array<int> &vert_global_local)

mesh/pmesh.hpp

@@ -241,7 +241,7 @@ protected:
    void BuildVertexGroup(int ngroups, const Table& vert_element);
 
    void BuildSharedFaceElems(int ntri_faces, int nquad_faces,
-                             const Mesh &mesh, int *partitioning,
+                             const Mesh &mesh, const int *partitioning,
                              const STable3D *faces_tbl,
                              const Array<int> &face_group,
                              const Array<int> &vert_global_local);
@@ -343,7 +343,7 @@ public:
        meshes and quick space-filling curve equipartitioning for nonconforming
        meshes (elements of nonconforming meshes should ideally be ordered as a
        sequence of face-neighbors). */
-   ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_ = NULL,
+   ParMesh(MPI_Comm comm, Mesh &mesh, const int *partitioning_ = nullptr,
            int part_method = 1);
 
    /** Copy constructor. Performs a deep copy of (almost) all data, so that the
@@ -438,8 +438,6 @@ public:
 
    ParNCMesh* pncmesh;
 
-   int *partitioning_cache = nullptr;
-
    int GetNGroups() const { return gtopo.NGroups(); }
 
    ///@{ @name These methods require group > 0

mesh/pncmesh.cpp

@@ -28,7 +28,8 @@ namespace mfem
 
 using namespace bin_io;
 
-ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, int *part)
+ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh,
+                     const int *partitioning)
    : NCMesh(ncmesh)
 {
    MyComm = comm;
@@ -39,7 +40,8 @@ ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, int *part)
    // sequence of leaf elements into 'NRanks' parts
    for (int i = 0; i < leaf_elements.Size(); i++)
    {
-      elements[leaf_elements[i]].rank = part ? part[i] : InitialPartition(i);
+      elements[leaf_elements[i]].rank =
+         partitioning ? partitioning[i] : InitialPartition(i);
    }
 
    Update();

mesh/pncmesh.hpp

@@ -67,7 +67,8 @@ public:
    /// Construct by partitioning a serial NCMesh.
    /** SFC partitioning is used by default. A user-specified partition can be
        passed in 'part', where part[i] is the desired MPI rank for element i. */
-   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh, int* part = NULL);
+   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh,
+             const int *partitioning = nullptr);
 
    /** Load from a stream, parallel version. See the serial NCMesh::NCMesh
        counterpart for a description of the parameters. */
@@ -81,7 +82,8 @@ public:
 
    /** An override of NCMesh::Refine, which is called eventually, after making
        sure that refinements that occur on the processor boundary are sent to
-       the neighbor processors so they can keep their ghost layers up to date.*/
+       the neighbor processors so they can keep their ghost layers up to
+       date. */
    void Refine(const Array<Refinement> &refinements) override;
 
    /// Parallel version of NCMesh::LimitNCLevel.
@@ -229,8 +231,8 @@ public:
                                     const Table &deref_table);
 
    /** Extension of NCMesh::GetBoundaryClosure. Filters out ghost vertices and
-       ghost edges from 'bdr_vertices' and 'bdr_edges', and uncovers hidden internal
-       boundary faces. */
+       ghost edges from 'bdr_vertices' and 'bdr_edges', and uncovers hidden
+       internal boundary faces. */
    void GetBoundaryClosure(const Array<int> &bdr_attr_is_ess,
                            Array<int> &bdr_vertices,
                            Array<int> &bdr_edges, Array<int> &bdr_faces) override;
@@ -252,8 +254,9 @@ protected: // interface for ParMesh
    friend class ParMesh;
 
    /** For compatibility with conforming code in ParMesh and ParFESpace.
-       Initializes shared structures in ParMesh: gtopo, shared_*, group_s*, s*_l*.
-       The ParMesh then acts as a parallel mesh cut along the NC interfaces. */
+       Initializes shared structures in ParMesh: gtopo, shared_*, group_s*,
+       s*_l*. The ParMesh then acts as a parallel mesh cut along the NC
+       interfaces. */
    void GetConformingSharedStructures(class ParMesh &pmesh);
 
    /** Populate face neighbor members of ParMesh from the ghost layer, without
@@ -519,8 +522,9 @@ protected: // implementation
        owners, keeping the ghost layer up to date. Used by Rebalance() and
        Derefine(). 'target_elements' is the number of elements this rank
        is supposed to own after the exchange. If this number is not known
-       a priori, the parameter can be set to -1, but more expensive communication
-       (synchronous sends and a barrier) will be used in that case. */
+       a priori, the parameter can be set to -1, but more expensive
+       communication (synchronous sends and a barrier) will be used in that
+       case. */
    void RedistributeElements(Array<int> &new_ranks, int target_elements,
                              bool record_comm);
 

mesh/pumi.cpp

@@ -819,7 +819,7 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh,
          apf::Downward verts;
          apf_mesh->getDownward(ent,0,verts);
 
-         int *v, nv = 0;
+         int *v = nullptr, nv = 0;
          apf::Mesh::Type ftype = apf_mesh->getType(ent);
          if (ftype == apf::Mesh::TRIANGLE)
          {
@@ -890,9 +890,9 @@ GridFunctionPumi::GridFunctionPumi(Mesh* m, apf::Mesh2* PumiM,
 {
    int spDim = m->SpaceDimension();
    // Note: default BasisType for 'fec' is GaussLobatto.
-   fec = new H1_FECollection(mesh_order, m->Dimension());
+   fec_owned = new H1_FECollection(mesh_order, m->Dimension());
    int ordering = Ordering::byVDIM; // x1y1z1/x2y2z2/...
-   fes = new FiniteElementSpace(m, fec, spDim, ordering);
+   fes = new FiniteElementSpace(m, fec_owned, spDim, ordering);
    int data_size = fes->GetVSize();
 
    // Read PUMI mesh data

mesh/submesh/submesh.cpp

@@ -31,7 +31,7 @@ SubMesh SubMesh::CreateFromBoundary(const Mesh &parent,
 SubMesh::SubMesh(const Mesh &parent, From from,
                  Array<int> attributes) : parent_(parent), from_(from), attributes_(attributes)
 {
-   if (Nonconforming())
+   if (parent.Nonconforming())
    {
       MFEM_ABORT("SubMesh does not support non-conforming meshes");
    }
@@ -193,8 +193,6 @@ SubMesh::SubMesh(const Mesh &parent, From from,
    Finalize();
 }
 
-SubMesh::~SubMesh() {}
-
 void SubMesh::Transfer(const GridFunction &src, GridFunction &dst)
 {
    TransferMap map(src, dst);

mesh/submesh/submesh.hpp

@@ -174,8 +174,6 @@ public:
       return dynamic_cast<const SubMesh *>(m) != nullptr;
    }
 
-   ~SubMesh();
-
 private:
    /// Private constructor
    SubMesh(const Mesh &parent, From from, Array<int> attributes);

mesh/submesh/submesh_utils.cpp

@@ -174,7 +174,8 @@ void BuildVdofToVdofMap(const FiniteElementSpace& subfes,
       Array<int> sub_vdofs;
       subfes.GetElementVDofs(i, sub_vdofs);
 
-      MFEM_ASSERT(parent_vdofs.Size() == sub_vdofs.Size(), "internal error");
+      MFEM_ASSERT(parent_vdofs.Size() == sub_vdofs.Size(),
+                  "elem " << i << ' ' << parent_vdofs.Size() << ' ' << sub_vdofs.Size());
       for (int j = 0; j < parent_vdofs.Size(); j++)
       {
          real_t sub_sign = 1.0;

mesh/submesh/transfermap.cpp

@@ -92,10 +92,13 @@ TransferMap::TransferMap(const GridFunction &src,
 
          if (!root_fes_reset)
          {
+            const FiniteElementCollection *src_fec = src.FESpace()->FEColl();
+            const FiniteElementCollection *dst_fec = dst.FESpace()->FEColl();
+            auto *root_fec = src_sm_dim == parent_dim ? src_fec : dst_fec;
+
             root_fes_.reset(new FiniteElementSpace(
-                               *src.FESpace(),
                                const_cast<Mesh *>(
-                                  SubMeshUtils::GetRootParent(*src_sm))));
+                                  SubMeshUtils::GetRootParent(*src_sm)), root_fec));
          }
       }
 

miniapps/adjoint/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/adjoint/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

miniapps/autodiff/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/autodiff/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 # Include defaults.mk to get XLINKER
 DEFAULTS_MK = $(MFEM_DIR)/config/defaults.mk

miniapps/common/makefile

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/common/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 # Default target
 all: lib-common

miniapps/dpg/CMakeLists.txt

@@ -42,42 +42,42 @@ set(DPG_COMMON_FILES
 add_mfem_miniapp(diffusion-dpg
   MAIN diffusion.cpp
   ${DPG_COMMON_FILES}
-  LIBRARIES mfem mfem-common)
+  LIBRARIES mfem-common)
 
 add_mfem_miniapp(convection-diffusion-dpg
 MAIN convection-diffusion.cpp
 ${DPG_COMMON_FILES}
-LIBRARIES mfem mfem-common )
+LIBRARIES mfem-common)
 
 add_mfem_miniapp(acoustics-dpg
 MAIN acoustics.cpp
 ${DPG_COMMON_FILES}
-LIBRARIES mfem mfem-common)
+LIBRARIES mfem-common)
 
 add_mfem_miniapp(maxwell-dpg
 MAIN maxwell.cpp
 ${DPG_COMMON_FILES}
-LIBRARIES mfem mfem-common)
+LIBRARIES mfem-common)
 
 if (MFEM_USE_MPI)
   add_mfem_miniapp(pdiffusion-dpg
     MAIN pdiffusion.cpp
     ${DPG_COMMON_FILES}
-    LIBRARIES mfem mfem-common)
+    LIBRARIES mfem-common)
 
   add_mfem_miniapp(pconvection-diffusion-dpg
   MAIN pconvection-diffusion.cpp
   ${DPG_COMMON_FILES}
-  LIBRARIES mfem mfem-common)
+  LIBRARIES mfem-common)
 
   add_mfem_miniapp(pacoustics-dpg
   MAIN pacoustics.cpp
   ${DPG_COMMON_FILES}
-  LIBRARIES mfem mfem-common)
+  LIBRARIES mfem-common)
 
   add_mfem_miniapp(pmaxwell-dpg
   MAIN pmaxwell.cpp
   ${DPG_COMMON_FILES}
-  LIBRARIES mfem mfem-common)
+  LIBRARIES mfem-common)
 endif ()
 

miniapps/dpg/acoustics.cpp

@@ -15,11 +15,11 @@
 //
 // Sample runs
 //
-// acoustics -ref 4 -o 1 -rnum 1.0
-// acoustics -m ../../data/inline-tri.mesh -ref 4 -o 2 -sc -rnum 3.0
-// acoustics -m ../../data/amr-quad.mesh -ref 3 -o 3 -sc -rnum 4.5 -prob 1
-// acoustics -m ../../data/inline-quad.mesh -ref 2 -o 4 -sc -rnum 11.5 -prob 1
-// acoustics -m ../../data/inline-hex.mesh -ref 1 -o 2 -sc -rnum 1.0
+//  acoustics -ref 4 -o 1 -rnum 1.0
+//  acoustics -m ../../data/inline-tri.mesh -ref 4 -o 2 -sc -rnum 3.0
+//  acoustics -m ../../data/amr-quad.mesh -ref 3 -o 3 -sc -rnum 4.5 -prob 1
+//  acoustics -m ../../data/inline-quad.mesh -ref 2 -o 4 -sc -rnum 11.5 -prob 1
+//  acoustics -m ../../data/inline-hex.mesh -ref 1 -o 2 -sc -rnum 1.0
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve

miniapps/dpg/convection-diffusion.cpp

@@ -14,14 +14,14 @@
 // Compile with: make convection-diffusion
 //
 // sample runs
-// convection-diffusion -m ../../data/star.mesh -o 2 -ref 2 -theta 0.0 -eps 1e-1 -beta '2 3'
-// convection-diffusion -m ../../data/beam-hex.mesh -o 2 -ref 2 -theta 0.0 -eps 1e0 -beta '1 0 2'
-// convection-diffusion -m ../../data/inline-tri.mesh -o 3 -ref 2 -theta 0.0 -eps 1e-2 -beta '4 2' -sc
+//  convection-diffusion -m ../../data/star.mesh -o 2 -ref 2 -theta 0.0 -eps 1e-1 -beta '2 3'
+//  convection-diffusion -m ../../data/beam-hex.mesh -o 2 -ref 2 -theta 0.0 -eps 1e0 -beta '1 0 2'
+//  convection-diffusion -m ../../data/inline-tri.mesh -o 3 -ref 2 -theta 0.0 -eps 1e-2 -beta '4 2' -sc
 
 // AMR runs
-// convection-diffusion  -o 3 -ref 5 -prob 1 -eps 1e-1 -theta 0.75
-// convection-diffusion  -o 2 -ref 9 -prob 1 -eps 1e-2 -theta 0.75
-// convection-diffusion  -o 3 -ref 9 -prob 1 -eps 1e-3 -theta 0.75 -sc
+//  convection-diffusion -o 3 -ref 5 -prob 1 -eps 1e-1 -theta 0.75
+//  convection-diffusion -o 2 -ref 9 -prob 1 -eps 1e-2 -theta 0.75
+//  convection-diffusion -o 3 -ref 9 -prob 1 -eps 1e-3 -theta 0.75 -sc
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve

miniapps/dpg/makefile

@@ -12,8 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/miniapps/dpg/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))
 
 # Include defaults.mk to get XLINKER
 DEFAULTS_MK = $(MFEM_DIR)/config/defaults.mk

miniapps/dpg/maxwell.cpp

@@ -14,10 +14,10 @@
 // Compile with: make maxwell
 //
 // Sample runs
-// maxwell -m ../../data/inline-tri.mesh -ref 4 -o 1 -rnum 1.0
-// maxwell -m ../../data/amr-quad.mesh -ref 3 -o 2 -rnum 1.6 -sc
-// maxwell -m ../../data/inline-quad.mesh -ref 2 -o 3 -rnum 4.2 -sc
-// maxwell -m ../../data/inline-hex.mesh -ref 1 -o 2 -sc -rnum 1.0
+//  maxwell -m ../../data/inline-tri.mesh -ref 4 -o 1 -rnum 1.0
+//  maxwell -m ../../data/amr-quad.mesh -ref 3 -o 2 -rnum 1.6 -sc
+//  maxwell -m ../../data/inline-quad.mesh -ref 2 -o 3 -rnum 4.2 -sc
+//  maxwell -m ../../data/inline-hex.mesh -ref 1 -o 2 -sc -rnum 1.0
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve

miniapps/dpg/pacoustics.cpp

@@ -15,19 +15,19 @@
 //
 // sample runs
 
-// mpirun -np 4 pacoustics -o 3 -m ../../data/star.mesh -sref 1 -pref 2 -rnum 1.9 -sc -prob 0
-// mpirun -np 4 pacoustics -o 3 -m ../../data/inline-quad.mesh -sref 1 -pref 2  -rnum 5.2 -sc -prob 1
-// mpirun -np 4 pacoustics -o 4 -m ../../data/inline-tri.mesh -sref 1 -pref 2  -rnum 7.1 -sc -prob 1
-// mpirun -np 4 pacoustics -o 2 -m ../../data/inline-hex.mesh -sref 0 -pref 1 -rnum 1.9 -sc -prob 0
-// mpirun -np 4 pacoustics -o 3 -m ../../data/inline-quad.mesh -sref 2 -pref 1 -rnum 7.1 -sc -prob 2
-// mpirun -np 4 pacoustics -o 2 -m ../../data/inline-hex.mesh -sref 0 -pref 1  -rnum 4.1 -sc -prob 2
-// mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 7.1 -sc -prob 3
-// mpirun -np 4 pacoustics -o 4 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 10.1 -sc -prob 4
-// mpirun -np 4 pacoustics -o 4 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 12.1 -sc -prob 5
+//  mpirun -np 4 pacoustics -o 3 -m ../../data/star.mesh -sref 1 -pref 2 -rnum 1.9 -sc -prob 0
+//  mpirun -np 4 pacoustics -o 3 -m ../../data/inline-quad.mesh -sref 1 -pref 2  -rnum 5.2 -sc -prob 1
+//  mpirun -np 4 pacoustics -o 4 -m ../../data/inline-tri.mesh -sref 1 -pref 2  -rnum 7.1 -sc -prob 1
+//  mpirun -np 4 pacoustics -o 2 -m ../../data/inline-hex.mesh -sref 0 -pref 1 -rnum 1.9 -sc -prob 0
+//  mpirun -np 4 pacoustics -o 3 -m ../../data/inline-quad.mesh -sref 2 -pref 1 -rnum 7.1 -sc -prob 2
+//  mpirun -np 4 pacoustics -o 2 -m ../../data/inline-hex.mesh -sref 0 -pref 1  -rnum 4.1 -sc -prob 2
+//  mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 7.1 -sc -prob 3
+//  mpirun -np 4 pacoustics -o 4 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 10.1 -sc -prob 4
+//  mpirun -np 4 pacoustics -o 4 -m meshes/scatter.mesh -sref 1 -pref 1  -rnum 12.1 -sc -prob 5
 
 // AMR runs
-// mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 0 -pref 7 -theta 0.75 -rnum 10.1 -sc -prob 3
-// mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 0 -pref 12 -theta 0.75 -rnum 20.1 -sc -prob 3
+//  mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 0 -pref 7 -theta 0.75 -rnum 10.1 -sc -prob 3
+//  mpirun -np 4 pacoustics -o 3 -m meshes/scatter.mesh -sref 0 -pref 12 -theta 0.75 -rnum 20.1 -sc -prob 3
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve