complex-jacobi minor cleanup

Starting ComplexOperatorJacobiSmoother
Updating changelog.
2020-07-30 17:01:53 -07:00 · 2020-07-29 14:41:31 -07:00 · 2020-07-29 12:33:18 -05:00 · 2020-07-29 12:11:16 -05:00 · 2020-07-29 12:09:58 -05:00 · 2020-07-29 11:21:17 -05:00
228 changed files with 10825 additions and 33080 deletions
@@ -16,7 +16,7 @@ install:
 - set PATH=C:\Program Files\Microsoft MPI\Bin;%PATH%

 # Install METIS
- ps: Start-FileDownload 'http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/metis-5.1.0.tar.gz'
+- ps: Start-FileDownload 'https://mfem.github.io/tpls/metis-5.1.0.tar.gz'
 - 7z x metis-5.1.0.tar.gz -so | 7z x -si -ttar > nul
 - cd metis-5.1.0
 - ps: ( get-content "GKlib\gk_arch.h") | % { If ($_.ReadCount -ge 52) {$_ -replace "#ifdef __MSC__","#ifdef DISABLE_THIS_ANCIENT_MSC_CHECK"} Else {$_} } | set-content "GKlib\gk_arch.h"
@@ -26,17 +26,17 @@ install:
 - cd ..

 # Install hypre
- ps: Start-FileDownload 'https://github.com/hypre-space/hypre/archive/V2-10-0b.tar.gz'
- 7z x V2-10-0b.tar.gz -so | 7z x -si -ttar > nul
- cd hypre-2-10-0b
- cmake -H. -Bbuild -DHYPRE_USING_FEI=OFF -DMPI_C_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DMPI_C_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include"
+- ps: Start-FileDownload 'https://github.com/hypre-space/hypre/archive/v2.19.0.tar.gz'
+- 7z x v2.19.0.tar.gz -so | 7z x -si -ttar > nul
+- cd hypre-2.19.0/src
+- cmake -H. -Bbuild -DMPI_C_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DMPI_C_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include"
 - cmake --build build
 - cmake --build build --target install
- cd ..
+- cd ../..

 # MFEM
 before_build:
- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DHYPRE_LIBRARIES=%cd%\hypre-2-10-0b\hypre\lib\HYPRE.lib -DHYPRE_INCLUDE_DIRS=%cd%\hypre-2-10-0b\hypre\include -DHYPRE_VERSION=21000 -DMETIS_LIBRARIES=%cd%\metis-5.1.0\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%cd%\metis-5.1.0\include
+- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DHYPRE_DIR=%cd%\hypre-2.19.0\src\hypre -DMETIS_LIBRARIES=%cd%\metis-5.1.0\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%cd%\metis-5.1.0\include
 - cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_serial -DMFEM_USE_MPI=FALSE

 build_script:
@@ -50,6 +50,7 @@ examples/ex1[04-9]
 examples/ex1[0-9]p
 examples/ex2[0-9]
 examples/ex2[0-9]p
+examples/ex25-gpu

 examples/refined.mesh
 examples/displaced.mesh
@@ -163,20 +164,6 @@ miniapps/electromagnetics/Tesla-AMR*
 miniapps/electromagnetics/Maxwell-Parallel*
 miniapps/electromagnetics/Joule_*

-miniapps/hypsys/build
-miniapps/hypsys/errors.txt
-miniapps/hypsys/grid*
-miniapps/hypsys/hypsys
-miniapps/hypsys/initial*
-miniapps/hypsys/output
-miniapps/hypsys/phypsys
-miniapps/hypsys/pressure*
-miniapps/hypsys/results
-miniapps/hypsys/scripts/gridfunc-scatter
-miniapps/hypsys/ultimate*
-miniapps/hypsys/velocity*
-miniapps/hypsys/various
-
 miniapps/meshing/mobius-strip
 miniapps/meshing/klein-bottle
 miniapps/meshing/toroid
@@ -258,6 +245,9 @@ miniapps/navier/navier_3dfoc
 miniapps/navier/tgv_out*.txt
 miniapps/navier/*_output

+miniapps/adjoint/cvsRoberts_ASAi_dns
+miniapps/adjoint/adjoint_advection_diffusion
+
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests
@@ -16,6 +16,12 @@ stages:
  - tests
  - optional

+env:
+  global:
+    - HYPRE_ARCHIVE=v2.19.0.tar.gz
+      HYPRE_URL=https://github.com/hypre-space/hypre/archive/$HYPRE_ARCHIVE
+      HYPRE_TOP_DIR=hypre-2.19.0
+
 jobs:
  include:

@@ -138,8 +144,7 @@ jobs:
           NPROCS=2
      cache:
        directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
      before_cache:
        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -169,8 +174,7 @@ jobs:
           NPROCS=2
      cache:
        directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
      before_cache:
        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -193,7 +197,7 @@ jobs:
        - cd ${TRAVIS_BUILD_DIR}/build
        - cmake ..
             -DMFEM_USE_MPI=ON
-             -DHYPRE_DIR=${TRAVIS_BUILD_DIR}/../hypre-2.10.0b/src/hypre
+             -DHYPRE_DIR=${TRAVIS_BUILD_DIR}/../$HYPRE_TOP_DIR/src/hypre
             -DMFEM_MPI_NP=$NPROCS
        - make -j3 mfem examples
        - cd ${TRAVIS_BUILD_DIR}/build/tests/unit
@@ -201,8 +205,7 @@ jobs:
        - ctest --output-on-failure
      cache:
        directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
      before_cache:
        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -247,8 +250,7 @@ jobs:
           TMPDIR=/tmp
      cache:
        directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
          - $HOME/local-cached
      before_cache:
@@ -268,8 +270,7 @@ jobs:
           TMPDIR=/tmp
      cache:
        directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
          - $HOME/local-cached
      before_cache:
@@ -335,18 +336,18 @@ install:

   # hypre
   - if [ $MPI == "YES" ]; then
-        if [ ! -e hypre-2.10.0b/src/hypre/lib/libHYPRE.a ]; then
-           wget https://computation.llnl.gov/project/linear_solvers/download/hypre-2.10.0b.tar.gz --no-check-certificate;
-           rm -rf hypre-2.10.0b;
-           tar xvzf hypre-2.10.0b.tar.gz;
-           cd hypre-2.10.0b/src;
-           ./configure --disable-fortran --without-fei CC=mpicc CXX=mpic++;
+        if [ ! -e $HYPRE_TOP_DIR/src/hypre/lib/libHYPRE.a ]; then
+           wget $HYPRE_URL;
+           rm -rf $HYPRE_TOP_DIR;
+           tar xvzf $HYPRE_ARCHIVE;
+           cd $HYPRE_TOP_DIR/src;
+           ./configure --disable-fortran CC=mpicc CXX=mpic++;
           make -j3;
           cd ../..;
        else
-            echo "Reusing cached hypre-2.10.0b/";
+            echo "Reusing cached $HYPRE_TOP_DIR/";
        fi;
-        ln -s hypre-2.10.0b hypre;
+        ln -s $HYPRE_TOP_DIR hypre;
     else
        echo "Serial build, not using hypre";
     fi
@@ -354,7 +355,7 @@ install:
   # METIS
   - if [ $MPI == "YES" ]; then
        if [ ! -e metis-4.0/libmetis.a ]; then
-           wget http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/OLD/metis-4.0.3.tar.gz;
+           wget https://mfem.github.io/tpls/metis-4.0.3.tar.gz;
           tar xvzf metis-4.0.3.tar.gz;
           make -j3 -C metis-4.0.3/Lib CC="$CC" OPTFLAGS="-O2";
           rm -rf metis-4.0;
@@ -33,6 +33,9 @@ Meshing improvements
  for example the periodic-annulus-sector and periodic-torus-sector files in
  the data directory.

+- Added complete action of the TMOP Integrator to account for the spatial
+  derivatives of discrete and analytic targets.
+
 Performance improvements
 ------------------------
 - Added support for explicit vectorization in the high-performance templated
@@ -48,6 +51,19 @@ Improved GPU capabilities
 -------------------------
 - Added support for Chebyshev accelerated polynomial smoother on GPU.

+- Optimized AMD/HIP kernel support.
+
+- Added a Full Assembly mode compatible with Device kernel execution. This
+  assembly level builds on top of the current Element Assembly kernels to
+  compute a global sparse matrix. All integrators supported by element assembly
+  are also supported by full assembly. See the '-fa' option in Example 9.
+
+- Added support for BlockOperator on GPU. See the updated Example 5.
+
+- Added partial assembly and GPU support for ComplexOperator,
+  [Par]ComplexGridFunction, [Par]ComplexLinearForm, and [Par]SesquilinearForm.
+  See the updated Example 22.
+
 Discretization improvements
 ---------------------------
 - Added support for matrix-free interpolation and restriction operators between
@@ -71,7 +87,7 @@ Discretization improvements
  and, in the continuous field case, arbitrary mesh edges and faces.

 - Added new coefficient and vector coefficient classes for QuadratureFunctions.
-  Additionaly, new LinearForm integrators were also added which make use of
+  Additionally, new LinearForm integrators were also added which make use of
  these new QuadratureFunction coefficient classes.

 - Added support face integrals on the boundaries of NURBS meshes.
@@ -88,6 +104,10 @@ Linear and nonlinear solvers
  and solution during the solving process of an IterativeSolver after every
  iteration.

+- Added support for the CVODES package in SUNDIALS which provides ODE
+  solvers with sensitivity analysis capabilities. See the CVODESSolver
+  class and the new adjoint miniapps below.
+
 - Block arrays of parallel matrices can now be merged into a single parallel
  matrix with the function HypreParMatrixFromBlocks. This could be useful for
  solving block systems with parallel direct solvers such as STRUMPACK.
@@ -115,6 +135,14 @@ New and updated examples and miniapps
  equations of incompressible fluid dynamics. See the miniapps/navier directory
  for more details.

+- Added a new miniapps/adjoint directory with two miniapps demonstrating how to
+  solve adjoint problems in MFEM using the CVODES package in SUNDIALS. Both of
+  these miniapps require the MFEM_USE_SUNDIALS configuration option.
+  * The cvsRoberts_ASAi_dns miniapp solves a backward adjoint problem for a
+    system of ODEs, evaluating both forward and adjoint quadratures in serial.
+  * The adjoint_advection_diffusion miniapp solves a backward adjoint problem
+    for an advection diffusion PDE, evaluating adjoint quadratures in parallel.
+
 - Ported Example 11p to SLEPc, to demonstrate solving the Laplace eigenvalue
  equation with the shift-and-invert spectral transformation method.

@@ -125,11 +153,10 @@ New and updated examples and miniapps
 - Added a new meshing miniapp, Minimal Surface, which solves Plateau's problem:
  the Dirichlet problem for the minimal surface equation.

- Added partial assembly support to examples 4/4p and 5/5p, with diagonal
-  preconditioning.
+- Added full assembly support in Example 9/9p.

- Added a new test problem in example 24/24p, demonstrating a mixed bilinear
-  form for H(div) and L_2, with partial assembly support.
+- Added a new test problem in Example 24/24p, demonstrating a mixed bilinear
+  form for H1, H(curl), H(div) and L_2, with partial assembly support.

 - Added weak Dirichlet boundary conditions (Nitsche) to the NURBS miniapp.

@@ -137,6 +164,9 @@ New and updated examples and miniapps
  mesh based on element attributes. Any newly exposed boundary elements are
  assigned attribute numbers related to the trimmed element attributes.

+- Added partial assembly and device support to Example 4/4p, Example 5/5p,
+  Example 22/22p, and Example 25/25p, with diagonal preconditioning.
+
 Improved testing
 ----------------
 - Added a GitLab pipeline that automates PR testing on supercomputing systems
@@ -211,10 +211,10 @@ endif()
 # SUNDIALS
 if (MFEM_USE_SUNDIALS)
  if (NOT MFEM_USE_MPI)
-    find_package(SUNDIALS REQUIRED NVector_Serial CVODE ARKODE KINSOL)
+    find_package(SUNDIALS REQUIRED NVector_Serial CVODES ARKODE KINSOL)
  else()
    find_package(SUNDIALS REQUIRED
-      NVector_Serial NVector_Parallel NVector_ParHyp CVODE ARKODE KINSOL)
+      NVector_Serial NVector_Parallel NVector_ParHyp CVODES ARKODE KINSOL)
  endif()
 endif()

@@ -109,6 +109,7 @@ The MFEM source code has the following structure:
  ├── linalg
  ├── mesh
  ├── miniapps
+  │   ├── adjoint
  │   ├── common
  │   ├── electromagnetics
  │   ├── gslib
@@ -25,5 +25,6 @@ mfem_find_package(SUNDIALS SUNDIALS SUNDIALS_DIR
  ADD_COMPONENT NVector_ParHyp
    "include" nvector/nvector_parhyp.h "lib" sundials_nvecparhyp
  ADD_COMPONENT CVODE "include" cvode/cvode.h "lib" sundials_cvode
+  ADD_COMPONENT CVODES "include" cvodes/cvodes.h "lib" sundials_cvodes
  ADD_COMPONENT ARKODE "include" arkode/arkode.h "lib" sundials_arkode
  ADD_COMPONENT KINSOL "include" kinsol/kinsol.h "lib" sundials_kinsol)
@@ -88,6 +88,8 @@ set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library."

 set(LIBUNWIND_DIR "" CACHE PATH "Path to Libunwind.")

+# For sundials_nvecparhyp and nvecparallel remember to build with MPI_ENABLED=ON
+# and modify cmake variables for hypre for sundials
 set(SUNDIALS_DIR "${MFEM_DIR}/../sundials-5.0.0/instdir" CACHE PATH
    "Path to the SUNDIALS library.")
 # The following may be necessary, if SUNDIALS was built with KLU:
@@ -189,10 +189,12 @@ OPENMP_LIB =
 POSIX_CLOCKS_LIB = -lrt

 # SUNDIALS library configuration
+# For sundials_nvecparhyp and nvecparallel remember to build with MPI_ENABLED=ON
+# and modify cmake variables for hypre for sundials
 SUNDIALS_DIR = @MFEM_DIR@/../sundials-5.0.0/instdir
 SUNDIALS_OPT = -I$(SUNDIALS_DIR)/include
 SUNDIALS_LIB = -Wl,-rpath,$(SUNDIALS_DIR)/lib64 -L$(SUNDIALS_DIR)/lib64\
- -lsundials_arkode -lsundials_cvode -lsundials_nvecserial -lsundials_kinsol
+ -lsundials_arkode -lsundials_cvodes -lsundials_nvecserial -lsundials_kinsol

 ifeq ($(MFEM_USE_MPI),YES)
   SUNDIALS_LIB += -lsundials_nvecparhyp -lsundials_nvecparallel
@@ -770,6 +770,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/examples/pumi \
                         @MFEM_SOURCE_DIR@/examples/hiop \
                         @MFEM_SOURCE_DIR@/examples/sundials \
+                         @MFEM_SOURCE_DIR@/miniapps/adjoint \			 
                         @MFEM_SOURCE_DIR@/miniapps/common \
                         @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
                         @MFEM_SOURCE_DIR@/miniapps/gslib \
@@ -88,8 +88,8 @@ namespace mfem {
 * - <a class="el" href="ex24p_8cpp_source.html">Example 24p</a>: parallel mixed finite element spaces and interpolators
 * - <a class="el" href="ex25_8cpp_source.html">Example 25</a>: simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
 * - <a class="el" href="ex25p_8cpp_source.html">Example 25p</a>: parallel simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
- * - <a class="el" href="ex26_8cpp_source.html">Example 26</a>: multigrid preconditioner for the Laplace problem using nodal H1 FEM 
- * - <a class="el" href="ex26p_8cpp_source.html">Example 26p</a>: parallel multigrid preconditioner for the Laplace problem using nodal H1 FEM 
+ * - <a class="el" href="ex26_8cpp_source.html">Example 26</a>: multigrid preconditioner for the Laplace problem using nodal H1 FEM
+ * - <a class="el" href="ex26p_8cpp_source.html">Example 26p</a>: parallel multigrid preconditioner for the Laplace problem using nodal H1 FEM
 *
 * <H4>SUNDIALS Examples</H4>
 * - Variants of Examples
@@ -101,6 +101,9 @@ namespace mfem {
 *   and
 *   <a class="el" href="sundials_2ex16p_8cpp_source.html">16p</a>
 *   demonstrating the use of MFEM's \link sundials.hpp SUNDIALS classes\endlink
+ * - CVODES adjoint examples:
+ *   <a class="el" href="cvsRoberts__ASAi__dns_8cpp_source.html">serial ODE system</a>,
+ *   <a class="el" href="adjoint__advection__diffusion_8cpp_source.html">parallel advection-diffusion</a>
 *
 * <H4>PETSc Examples</H4>
 * - Variants of Examples
@@ -140,7 +143,9 @@ namespace mfem {
 * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code
 * - <a class="el" href="maxwell_8cpp_source.html">Maxwell</a>: simple transient full-wave electromagnetics simulation code
 * - <a class="el" href="joule_8cpp_source.html">Joule</a>: transient magnetics and Joule heating miniapp
- * - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
+ * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
+
+* - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
 * - <a class="el" href="klein-bottle_8cpp_source.html">Klein Bottle</a>: generate three types of Klein bottle surfaces
 * - <a class="el" href="toroid_8cpp_source.html">Toroid</a>: generate simple toroidal meshes
 * - <a class="el" href="twist_8cpp_source.html">Twist</a>: generate simple periodic meshes
@@ -157,7 +162,6 @@ namespace mfem {
 * - <a class="el" href="lor-transfer_8cpp_source.html">LOR Transfer</a>: map functions between high-order and low-order refined spaces
 * - <a class="el" href="findpts_8cpp_source.html">Find Points</a>: evaluate grid function in physical space, <a class="el" href="findpts_8cpp_source.html">serial</a> and <a class="el" href="pfindpts_8cpp_source.html">parallel</a> versions
 * - <a class="el" href="field-diff_8cpp_source.html">Field Diff</a>: compare grid functions on different meshes
- * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
 * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Laplace problem
 * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Laplace problem
 *
@@ -103,8 +103,8 @@ int main(int argc, char *argv[])
   // 3. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();

   // 4. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
@@ -112,10 +112,10 @@ int main(int argc, char *argv[])
   //    elements.
   {
      int ref_levels =
-         (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+         (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
      }
   }

@@ -123,66 +123,70 @@ int main(int argc, char *argv[])
   //    Lagrange finite elements of the specified order. If order < 1, we
   //    instead use an isoparametric/isogeometric space.
   FiniteElementCollection *fec;
+   bool delete_fec;
   if (order > 0)
   {
      fec = new H1_FECollection(order, dim);
+      delete_fec = true;
   }
-   else if (mesh->GetNodes())
+   else if (mesh.GetNodes())
   {
-      fec = mesh->GetNodes()->OwnFEC();
+      fec = mesh.GetNodes()->OwnFEC();
+      delete_fec = false;
      cout << "Using isoparametric FEs: " << fec->Name() << endl;
   }
   else
   {
      fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
   }
-   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
+   FiniteElementSpace fespace(&mesh, fec);
   cout << "Number of finite element unknowns: "
-        << fespace->GetTrueVSize() << endl;
+        << fespace.GetTrueVSize() << endl;

   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined by marking all
   //    the boundary attributes from the mesh as essential (Dirichlet) and
   //    converting them to a list of true dofs.
   Array<int> ess_tdof_list;
-   if (mesh->bdr_attributes.Size())
+   if (mesh.bdr_attributes.Size())
   {
-      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      Array<int> ess_bdr(mesh.bdr_attributes.Max());
      ess_bdr = 1;
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
-   LinearForm *b = new LinearForm(fespace);
+   LinearForm b(&fespace);
   ConstantCoefficient one(1.0);
-   b->AddDomainIntegrator(new DomainLFIntegrator(one));
-   b->Assemble();
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();

   // 8. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero,
   //    which satisfies the boundary conditions.
-   GridFunction x(fespace);
+   GridFunction x(&fespace);
   x = 0.0;

   // 9. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //    domain integrator.
-   BilinearForm *a = new BilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   BilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));

   // 10. Assemble the bilinear form and the corresponding linear system,
   //     applying any necessary transformations such as: eliminating boundary
   //     conditions, applying conforming constraints for non-conforming AMR,
   //     static condensation, etc.
-   if (static_cond) { a->EnableStaticCondensation(); }
-   a->Assemble();
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();

   OperatorPtr A;
   Vector B, X;
-   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);

   cout << "Size of linear system: " << A->Height() << endl;

@@ -203,9 +207,9 @@ int main(int argc, char *argv[])
   }
   else // Jacobi preconditioning in partial assembly mode
   {
-      if (UsesTensorBasis(*fespace))
+      if (UsesTensorBasis(fespace))
      {
-         OperatorJacobiSmoother M(*a, ess_tdof_list);
+         OperatorJacobiSmoother M(a, ess_tdof_list);
         PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
      }
      else
@@ -215,13 +219,13 @@ int main(int argc, char *argv[])
   }

   // 12. Recover the solution as a finite element grid function.
-   a->RecoverFEMSolution(X, *b, x);
+   a.RecoverFEMSolution(X, b, x);

   // 13. Save the refined mesh and the solution. This output can be viewed later
   //     using GLVis: "glvis -m refined.mesh -g sol.gf".
   ofstream mesh_ofs("refined.mesh");
   mesh_ofs.precision(8);
-   mesh->Print(mesh_ofs);
+   mesh.Print(mesh_ofs);
   ofstream sol_ofs("sol.gf");
   sol_ofs.precision(8);
   x.Save(sol_ofs);
@@ -233,15 +237,14 @@ int main(int argc, char *argv[])
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
-      sol_sock << "solution\n" << *mesh << x << flush;
+      sol_sock << "solution\n" << mesh << x << flush;
   }

   // 15. Free the used memory.
-   delete a;
-   delete b;
-   delete fespace;
-   if (order > 0) { delete fec; }
-   delete mesh;
+   if (delete_fec)
+   {
+      delete fec;
+   }

   return 0;
 }
@@ -112,8 +112,8 @@ int main(int argc, char *argv[])
   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();

   // 5. Refine the serial mesh on all processors to increase the resolution. In
   //    this example we do 'ref_levels' of uniform refinement. We choose
@@ -121,23 +121,23 @@ int main(int argc, char *argv[])
   //    more than 10,000 elements.
   {
      int ref_levels =
-         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
      }
   }

   // 6. 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;
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
   {
      int par_ref_levels = 2;
      for (int l = 0; l < par_ref_levels; l++)
      {
-         pmesh->UniformRefinement();
+         pmesh.UniformRefinement();
      }
   }

@@ -145,13 +145,16 @@ int main(int argc, char *argv[])
   //    use continuous Lagrange finite elements of the specified order. If
   //    order < 1, we instead use an isoparametric/isogeometric space.
   FiniteElementCollection *fec;
+   bool delete_fec;
   if (order > 0)
   {
      fec = new H1_FECollection(order, dim);
+      delete_fec = true;
   }
-   else if (pmesh->GetNodes())
+   else if (pmesh.GetNodes())
   {
-      fec = pmesh->GetNodes()->OwnFEC();
+      fec = pmesh.GetNodes()->OwnFEC();
+      delete_fec = false;
      if (myid == 0)
      {
         cout << "Using isoparametric FEs: " << fec->Name() << endl;
@@ -160,9 +163,10 @@ int main(int argc, char *argv[])
   else
   {
      fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
   }
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
+   ParFiniteElementSpace fespace(&pmesh, fec);
+   HYPRE_Int size = fespace.GlobalTrueVSize();
   if (myid == 0)
   {
      cout << "Number of finite element unknowns: " << size << endl;
@@ -173,44 +177,44 @@ int main(int argc, char *argv[])
   //    by marking all the boundary attributes from the mesh as essential
   //    (Dirichlet) and converting them to a list of true dofs.
   Array<int> ess_tdof_list;
-   if (pmesh->bdr_attributes.Size())
+   if (pmesh.bdr_attributes.Size())
   {
-      Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+      Array<int> ess_bdr(pmesh.bdr_attributes.Max());
      ess_bdr = 1;
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

   // 9. Set up the parallel linear form b(.) which corresponds to the
   //    right-hand side of the FEM linear system, which in this case is
   //    (1,phi_i) where phi_i are the basis functions in fespace.
-   ParLinearForm *b = new ParLinearForm(fespace);
+   ParLinearForm b(&fespace);
   ConstantCoefficient one(1.0);
-   b->AddDomainIntegrator(new DomainLFIntegrator(one));
-   b->Assemble();
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();

   // 10. Define the solution vector x as a parallel finite element grid function
   //     corresponding to fespace. Initialize x with initial guess of zero,
   //     which satisfies the boundary conditions.
-   ParGridFunction x(fespace);
+   ParGridFunction x(&fespace);
   x = 0.0;

   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
   //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //     domain integrator.
-   ParBilinearForm *a = new ParBilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   ParBilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));

   // 12. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, static condensation, etc.
-   if (static_cond) { a->EnableStaticCondensation(); }
-   a->Assemble();
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();

   OperatorPtr A;
   Vector B, X;
-   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);

   // 13. Solve the linear system A X = B.
   //     * With full assembly, use the BoomerAMG preconditioner from hypre.
@@ -218,9 +222,9 @@ int main(int argc, char *argv[])
   Solver *prec = NULL;
   if (pa)
   {
-      if (UsesTensorBasis(*fespace))
+      if (UsesTensorBasis(fespace))
      {
-         prec = new OperatorJacobiSmoother(*a, ess_tdof_list);
+         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
      }
   }
   else
@@ -238,7 +242,7 @@ int main(int argc, char *argv[])

   // 14. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
-   a->RecoverFEMSolution(X, *b, x);
+   a.RecoverFEMSolution(X, b, x);

   // 15. Save the refined mesh and the solution in parallel. This output can
   //     be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
@@ -249,7 +253,7 @@ int main(int argc, char *argv[])

      ofstream mesh_ofs(mesh_name.str().c_str());
      mesh_ofs.precision(8);
-      pmesh->Print(mesh_ofs);
+      pmesh.Print(mesh_ofs);

      ofstream sol_ofs(sol_name.str().c_str());
      sol_ofs.precision(8);
@@ -264,16 +268,14 @@ int main(int argc, char *argv[])
      socketstream sol_sock(vishost, visport);
      sol_sock << "parallel " << num_procs << " " << myid << "\n";
      sol_sock.precision(8);
-      sol_sock << "solution\n" << *pmesh << x << flush;
+      sol_sock << "solution\n" << pmesh << x << flush;
   }

   // 17. Free the used memory.
-   delete a;
-   delete b;
-   delete fespace;
-   if (order > 0) { delete fec; }
-   delete pmesh;
-
+   if (delete_fec)
+   {
+      delete fec;
+   }
   MPI_Finalize();

   return 0;
@@ -13,6 +13,11 @@
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2
 //               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0
 //
+// Device sample runs:
+//               ex22 -m ../data/inline-quad.mesh -o 3 -p 1 -pa -d cuda
+//               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa -d cuda
+//               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0 -pa -d cuda
+//
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
 //               variants of a damped harmonic oscillator:
@@ -76,6 +81,8 @@ int main(int argc, char *argv[])
   bool visualization = 1;
   bool herm_conv = true;
   bool exact_sol = true;
+   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -106,6 +113,10 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -135,13 +146,18 @@ int main(int argc, char *argv[])
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes
   //    with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 3. Refine the mesh to increase resolution. In this example we do
+   // 4. Refine the mesh to increase resolution. In this example we do
   //    'ref_levels' of uniform refinement where the user specifies
   //    the number of levels with the '-r' option.
   for (int l = 0; l < ref_levels; l++)
@@ -149,7 +165,7 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 4. Define a finite element space on the mesh. Here we use continuous
+   // 5. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange, Nedelec, or Raviart-Thomas finite elements of the specified
   //    order.
   if (dim == 1 && prob != 0 )
@@ -171,7 +187,7 @@ int main(int argc, char *argv[])
   cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
        << endl;

-   // 5. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined based on the type
   //    of mesh and the problem type.
   Array<int> ess_tdof_list;
@@ -183,12 +199,12 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system.
   ComplexLinearForm b(fespace, conv);
   b.Vector::operator=(0.0);

-   // 7. Define the solution vector u as a complex finite element grid function
+   // 8. Define the solution vector u as a complex finite element grid function
   //    corresponding to fespace. Initialize u with initial guess of 1+0i or
   //    the exact solution if it is known.
   ComplexGridFunction u(fespace);
@@ -210,7 +226,6 @@ int main(int argc, char *argv[])
   VectorConstantCoefficient zeroVecCoef(zeroVec);
   VectorConstantCoefficient oneVecCoef(oneVec);

-   u = 0.0;
   switch (prob)
   {
      case 0:
@@ -263,7 +278,7 @@ int main(int argc, char *argv[])
                 << "window_title 'Exact: Imaginary Part'" << flush;
   }

-   // 8. Set up the sesquilinear form a(.,.) on the finite element space
+   // 9. Set up the sesquilinear form a(.,.) on the finite element space
   //    corresponding to the damped harmonic oscillator operator of the
   //    appropriate type:
   //
@@ -282,6 +297,7 @@ int main(int argc, char *argv[])
   ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);

   SesquilinearForm *a = new SesquilinearForm(fespace, conv);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   switch (prob)
   {
      case 0:
@@ -305,7 +321,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 8a. Set up the bilinear form for the preconditioner corresponding to the
+   // 9a. Set up the bilinear form for the preconditioner corresponding to the
   //     appropriate operator
   //
   //      0) A scalar H1 field
@@ -318,6 +334,8 @@ int main(int argc, char *argv[])
   //         -Grad(a Div) - omega^2 b + omega c
   //
   BilinearForm *pcOp = new BilinearForm(fespace);
+   if (pa) { pcOp->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
   switch (prob)
   {
      case 0:
@@ -338,9 +356,9 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 9. Assemble the form and the corresponding linear system, applying any
-   //    necessary transformations such as: assembly, eliminating boundary
-   //    conditions, conforming constraints for non-conforming AMR, etc.
+   // 10. Assemble the form and the corresponding linear system, applying any
+   //     necessary transformations such as: assembly, eliminating boundary
+   //     conditions, conforming constraints for non-conforming AMR, etc.
   a->Assemble();
   pcOp->Assemble();

@@ -348,28 +366,17 @@ int main(int argc, char *argv[])
   Vector B, U;

   a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;

-   OperatorHandle PCOp;
-   pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
+   cout << "Size of linear system: " << A->Width() << endl << endl;

-   {
-      ComplexSparseMatrix * Asp =
-         dynamic_cast<ComplexSparseMatrix*>(A.Ptr());
-
-      cout << "Size of linear system: "
-           << 2 * Asp->real().Width() << endl << endl;
-   }
-
-   // 10. Define and apply a GMRES solver for AU=B with a block diagonal
+   // 11. Define and apply a GMRES solver for AU=B with a block diagonal
   //     preconditioner based on the appropriate sparse smoother.
   {
      Array<int> blockOffsets;
      blockOffsets.SetSize(3);
      blockOffsets[0] = 0;
-      blockOffsets[1] = PCOp.Ptr()->Height();
-      blockOffsets[2] = PCOp.Ptr()->Height();
+      blockOffsets[1] = A->Height() / 2;
+      blockOffsets[2] = A->Height() / 2;
      blockOffsets.PartialSum();

      BlockDiagonalPreconditioner BDP(blockOffsets);
@@ -377,22 +384,31 @@ int main(int argc, char *argv[])
      Operator * pc_r = NULL;
      Operator * pc_i = NULL;

-      double s = 1.0;
-      switch (prob)
+      if (pa)
      {
-         case 0:
-            pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
-            break;
-         case 1:
-            pc_r = new GSSmoother(*PCOp.As<SparseMatrix>());
-            s = -1.0;
-            break;
-         case 2:
-            pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
-            break;
-
-         default: break; // This should be unreachable
+         pc_r = new OperatorJacobiSmoother(*pcOp, ess_tdof_list);
      }
+      else
+      {
+         OperatorHandle PCOp;
+         pcOp->SetDiagonalPolicy(mfem::Operator::DIAG_ONE);
+         pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
+         switch (prob)
+         {
+            case 0:
+               pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            case 1:
+               pc_r = new GSSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            case 2:
+               pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            default:
+               break; // This should be unreachable
+         }
+      }
+      double s = (prob != 1) ? 1.0 : -1.0;
      pc_i = new ScaledOperator(pc_r,
                                (conv == ComplexOperator::HERMITIAN) ?
                                s:-s);
@@ -410,9 +426,11 @@ int main(int argc, char *argv[])
      gmres.Mult(B, U);
   }

-   // 11. Recover the solution as a finite element grid function and compute the
+   // 12. Recover the solution as a finite element grid function and compute the
   //     errors if the exact solution is known.
   a->RecoverFEMSolution(U, b, u);
+   u.real().SyncMemory(u);
+   u.imag().SyncMemory(u);

   if (exact_sol)
   {
@@ -442,7 +460,7 @@ int main(int argc, char *argv[])
      cout << endl;
   }

-   // 12. Save the refined mesh and the solution. This output can be viewed
+   // 13. Save the refined mesh and the solution. This output can be viewed
   //     later using GLVis: "glvis -m mesh -g sol".
   {
      ofstream mesh_ofs("refined.mesh");
@@ -457,7 +475,7 @@ int main(int argc, char *argv[])
      u.imag().Save(sol_i_ofs);
   }

-   // 13. Send the solution by socket to a GLVis server.
+   // 14. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -516,7 +534,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 14. Free the used memory.
+   // 15. Free the used memory.
   delete a;
   delete u_exact;
   delete pcOp;
@@ -13,6 +13,11 @@
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 2
 //               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0
 //
+// Device sample runs:
+//               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 1 -p 1 -pa -d cuda
+//               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa -d cuda
+//               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0 -pa -d cuda
+//
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
 //               variants of a damped harmonic oscillator:
@@ -41,7 +46,6 @@
 //               We recommend viewing examples 1, 3 and 4 before viewing this
 //               example.

-
 #include "mfem.hpp"
 #include <fstream>
 #include <iostream>
@@ -84,6 +88,8 @@ int main(int argc, char *argv[])
   bool visualization = 1;
   bool herm_conv = true;
   bool exact_sol = true;
+   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -116,6 +122,10 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -152,19 +162,24 @@ int main(int argc, char *argv[])
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

-   // 3. Read the (serial) mesh from the given mesh file on all processors. We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors. We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 4. Refine the serial mesh on all processors to increase the resolution.
+   // 5. Refine the serial mesh on all processors to increase the resolution.
   for (int l = 0; l < ser_ref_levels; l++)
   {
      mesh->UniformRefinement();
   }

-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. 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);
@@ -174,7 +189,7 @@ int main(int argc, char *argv[])
      pmesh->UniformRefinement();
   }

-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use continuous Lagrange, Nedelec, or Raviart-Thomas finite elements of
   //    the specified order.
   if (dim == 1 && prob != 0 )
@@ -202,7 +217,7 @@ int main(int argc, char *argv[])
      cout << "Number of finite element unknowns: " << size << endl;
   }

-   // 7. Determine the list of true (i.e. parallel conforming) essential
+   // 8. Determine the list of true (i.e. parallel conforming) essential
   //    boundary dofs. In this example, the boundary conditions are defined
   //    based on the type of mesh and the problem type.
   Array<int> ess_tdof_list;
@@ -214,14 +229,14 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 8. Set up the parallel linear form b(.) which corresponds to the
+   // 9. Set up the parallel linear form b(.) which corresponds to the
   //    right-hand side of the FEM linear system.
   ParComplexLinearForm b(fespace, conv);
   b.Vector::operator=(0.0);

-   // 9. Define the solution vector u as a parallel complex finite element grid
-   //    function corresponding to fespace. Initialize u with initial guess of
-   //    1+0i or the exact solution if it is known.
+   // 10. Define the solution vector u as a parallel complex finite element grid
+   //     function corresponding to fespace. Initialize u with initial guess of
+   //     1+0i or the exact solution if it is known.
   ParComplexGridFunction u(fespace);
   ParComplexGridFunction * u_exact = NULL;
   if (exact_sol) { u_exact = new ParComplexGridFunction(fespace); }
@@ -241,7 +256,6 @@ int main(int argc, char *argv[])
   VectorConstantCoefficient zeroVecCoef(zeroVec);
   VectorConstantCoefficient oneVecCoef(oneVec);

-   u = 0.0;
   switch (prob)
   {
      case 0:
@@ -296,7 +310,7 @@ int main(int argc, char *argv[])
                 << "window_title 'Exact: Imaginary Part'" << flush;
   }

-   // 10. Set up the parallel sesquilinear form a(.,.) on the finite element
+   // 11. Set up the parallel sesquilinear form a(.,.) on the finite element
   //     space corresponding to the damped harmonic oscillator operator of the
   //     appropriate type:
   //
@@ -315,6 +329,7 @@ int main(int argc, char *argv[])
   ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);

   ParSesquilinearForm *a = new ParSesquilinearForm(fespace, conv);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   switch (prob)
   {
      case 0:
@@ -338,7 +353,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 10a. Set up the parallel bilinear form for the preconditioner
+   // 11a. Set up the parallel bilinear form for the preconditioner
   //      corresponding to the appropriate operator
   //
   //      0) A scalar H1 field
@@ -351,6 +366,7 @@ int main(int argc, char *argv[])
   //         -Grad(a Div) - omega^2 b + omega c
   //
   ParBilinearForm *pcOp = new ParBilinearForm(fespace);
+   if (pa) { pcOp->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   switch (prob)
   {
      case 0:
@@ -371,7 +387,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 11. Assemble the parallel bilinear form and the corresponding linear
+   // 12. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, etc.
@@ -382,30 +398,22 @@ int main(int argc, char *argv[])
   Vector B, U;

   a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;
-
-   OperatorHandle PCOp;
-   pcOp->FormSystemMatrix(ess_tdof_list, PCOp);

   if (myid == 0)
   {
-      ComplexHypreParMatrix * Ahyp =
-         dynamic_cast<ComplexHypreParMatrix*>(A.Ptr());
-
      cout << "Size of linear system: "
-           << 2 * Ahyp->real().GetGlobalNumRows() << endl << endl;
+           << 2 * fespace->GlobalTrueVSize() << endl << endl;
   }

-   // 12. Define and apply a parallel FGMRES solver for AU=B with a block
+   // 13. Define and apply a parallel FGMRES solver for AU=B with a block
   //     diagonal preconditioner based on the appropriate multigrid
   //     preconditioner from hypre.
   {
      Array<int> blockTrueOffsets;
      blockTrueOffsets.SetSize(3);
      blockTrueOffsets[0] = 0;
-      blockTrueOffsets[1] = PCOp.Ptr()->Height();
-      blockTrueOffsets[2] = PCOp.Ptr()->Height();
+      blockTrueOffsets[1] = A->Height() / 2;
+      blockTrueOffsets[2] = A->Height() / 2;
      blockTrueOffsets.PartialSum();

      BlockDiagonalPreconditioner BDP(blockTrueOffsets);
@@ -413,25 +421,34 @@ int main(int argc, char *argv[])
      Operator * pc_r = NULL;
      Operator * pc_i = NULL;

-      switch (prob)
+      if (pa)
      {
-         case 0:
-            pc_r = new HypreBoomerAMG(*PCOp.As<HypreParMatrix>());
-            break;
-         case 1:
-            pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
-            break;
-         case 2:
-            if (dim == 2 )
-            {
+         pc_r = new OperatorJacobiSmoother(*pcOp, ess_tdof_list);
+      }
+      else
+      {
+         OperatorHandle PCOp;
+         pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
+         switch (prob)
+         {
+            case 0:
+               pc_r = new HypreBoomerAMG(*PCOp.As<HypreParMatrix>());
+               break;
+            case 1:
               pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
-            }
-            else
-            {
-               pc_r = new HypreADS(*PCOp.As<HypreParMatrix>(), fespace);
-            }
-            break;
-         default: break; // This should be unreachable
+               break;
+            case 2:
+               if (dim == 2 )
+               {
+                  pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
+               }
+               else
+               {
+                  pc_r = new HypreADS(*PCOp.As<HypreParMatrix>(), fespace);
+               }
+               break;
+            default: break; // This should be unreachable
+         }
      }
      pc_i = new ScaledOperator(pc_r,
                                (conv == ComplexOperator::HERMITIAN) ?
@@ -449,9 +466,11 @@ int main(int argc, char *argv[])
      fgmres.SetPrintLevel(1);
      fgmres.Mult(B, U);
   }
-   // 13. Recover the parallel grid function corresponding to U. This is the
+   // 14. Recover the parallel grid function corresponding to U. This is the
   //     local finite element solution on each processor.
   a->RecoverFEMSolution(U, b, u);
+   u.real().SyncMemory(u);
+   u.imag().SyncMemory(u);

   if (exact_sol)
   {
@@ -484,7 +503,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 14. Save the refined mesh and the solution in parallel. This output can be
+   // 15. Save the refined mesh and the solution in parallel. This output can be
   //     viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
   {
      ostringstream mesh_name, sol_r_name, sol_i_name;
@@ -504,7 +523,7 @@ int main(int argc, char *argv[])
      u.imag().Save(sol_i_ofs);
   }

-   // 15. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -569,7 +588,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 16. Free the used memory.
+   // 17. Free the used memory.
   delete a;
   delete u_exact;
   delete pcOp;
@@ -7,6 +7,7 @@
 //               ex24 -m ../data/beam-tet.mesh
 //               ex24 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 1
+//               ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 2
 //               ex24 -m ../data/escher.mesh
 //               ex24 -m ../data/escher.mesh -o 2
 //               ex24 -m ../data/fichera.mesh
@@ -24,12 +25,13 @@
 //               ex24 -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces, with three variants:
 //
 //               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
+//               2) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               3) (div v, q) for v in H(div) tested against q in L_2
 //
-//               Using different approaches, we project the gradient or
+//               Using different approaches, we project the gradient, curl, or
 //               divergence to the appropriate space.
 //
 //               We recommend viewing examples 1, 3, and 5 before viewing this
@@ -45,8 +47,11 @@ using namespace mfem;
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
 double div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);

 int dim;
+double freq = 1.0, kappa;

 int main(int argc, char *argv[])
 {
@@ -65,7 +70,7 @@ int main(int argc, char *argv[])
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -83,6 +88,7 @@ int main(int argc, char *argv[])
      return 1;
   }
   args.PrintOptions(cout);
+   kappa = freq * M_PI;

   // 2. Enable hardware devices such as GPUs, and programming models such as
   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
@@ -119,10 +125,15 @@ int main(int argc, char *argv[])
      trial_fec = new H1_FECollection(order, dim);
      test_fec = new ND_FECollection(order, dim);
   }
+   else if (prob == 1)
+   {
+      trial_fec = new ND_FECollection(order, dim);
+      test_fec = new RT_FECollection(order-1, dim);
+   }
   else
   {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
+      trial_fec = new RT_FECollection(order-1, dim);
+      test_fec = new L2_FECollection(order-1, dim);
   }

   FiniteElementSpace trial_fes(mesh, trial_fec);
@@ -136,6 +147,12 @@ int main(int argc, char *argv[])
      cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
      cout << "Number of H1 finite element unknowns: " << trial_size << endl;
   }
+   else if (prob == 1)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+      cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+           endl;
+   }
   else
   {
      cout << "Number of Raviart-Thomas finite element unknowns: "
@@ -150,12 +167,18 @@ int main(int argc, char *argv[])
   GridFunction x(&test_fes);
   FunctionCoefficient p_coef(p_exact);
   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
   FunctionCoefficient divgradp_coef(div_gradp_exact);

   if (prob == 0)
   {
      gftrial.ProjectCoefficient(p_coef);
   }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
   else
   {
      gftrial.ProjectCoefficient(gradp_coef);
@@ -179,6 +202,11 @@ int main(int argc, char *argv[])
      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
   }
+   else if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
+   }
   else
   {
      a.AddDomainIntegrator(new MassIntegrator(one));
@@ -244,6 +272,10 @@ int main(int argc, char *argv[])
   {
      dlo.AddDomainInterpolator(new GradientInterpolator());
   }
+   else if (prob == 1)
+   {
+      dlo.AddDomainInterpolator(new CurlInterpolator());
+   }
   else
   {
      dlo.AddDomainInterpolator(new DivergenceInterpolator());
@@ -258,6 +290,10 @@ int main(int argc, char *argv[])
   {
      exact_proj.ProjectCoefficient(gradp_coef);
   }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
   else
   {
      exact_proj.ProjectCoefficient(divgradp_coef);
@@ -276,10 +312,23 @@ int main(int argc, char *argv[])
      cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
           "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
      cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-           "||_{L_2} = " << errInterp << '\n' << endl;
+           " ||_{L_2} = " << errInterp << '\n' << endl;
      cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
           "||_{L_2} = " << errProj << '\n' << endl;
   }
+   else if (prob == 1)
+   {
+      double errSol = x.ComputeL2Error(curlv_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
+           "|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+      cout << " Curl interpolant E_h = curl v_h in H(div): || E_h - curl v "
+           "||_{L_2} = " << errInterp << '\n' << endl;
+      cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
   else
   {
      int order_quad = max(2, 2*order+1);
@@ -295,7 +344,7 @@ int main(int argc, char *argv[])

      cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
           "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
-      cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
+      cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v "
           "||_{L_2} = " << errInterp << '\n' << endl;
      cout << " Projection f_h of exact div v in L_2: || f_h - div v "
           "||_{L_2} = " << errProj << '\n' << endl;
@@ -371,3 +420,33 @@ double div_gradp_exact(const Vector &x)

   return 0.0;
 }
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}
@@ -6,7 +6,8 @@
 //               mpirun -np 4 ex24p -m ../data/square-disc.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa
-//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -p 1 -pa
+//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa -p 1
+//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa -p 2
 //               mpirun -np 4 ex24p -m ../data/escher.mesh
 //               mpirun -np 4 ex24p -m ../data/escher.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/fichera.mesh
@@ -24,12 +25,13 @@
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces, with three variants:
 //
 //               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
+//               2) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               3) (div v, q) for v in H(div) tested against q in L_2
 //
-//               Using different approaches, we project the gradient or
+//               Using different approaches, we project the gradient, curl, or
 //               divergence to the appropriate space.
 //
 //               We recommend viewing examples 1, 3, and 5 before viewing this
@@ -45,8 +47,11 @@ using namespace mfem;
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
 double div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);

 int dim;
+double freq = 1.0, kappa;

 int main(int argc, char *argv[])
 {
@@ -71,7 +76,7 @@ int main(int argc, char *argv[])
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -96,6 +101,7 @@ int main(int argc, char *argv[])
   {
      args.PrintOptions(cout);
   }
+   kappa = freq * M_PI;

   // 3. Enable hardware devices such as GPUs, and programming models such as
   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
@@ -147,10 +153,15 @@ int main(int argc, char *argv[])
      trial_fec = new H1_FECollection(order, dim);
      test_fec = new ND_FECollection(order, dim);
   }
+   else if (prob == 1)
+   {
+      trial_fec = new ND_FECollection(order, dim);
+      test_fec = new RT_FECollection(order-1, dim);
+   }
   else
   {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
+      trial_fec = new RT_FECollection(order-1, dim);
+      test_fec = new L2_FECollection(order-1, dim);
   }

   ParFiniteElementSpace trial_fes(pmesh, trial_fec);
@@ -166,6 +177,12 @@ int main(int argc, char *argv[])
         cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
         cout << "Number of H1 finite element unknowns: " << trial_size << endl;
      }
+      else if (prob == 1)
+      {
+         cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+         cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+              endl;
+      }
      else
      {
         cout << "Number of Raviart-Thomas finite element unknowns: "
@@ -181,12 +198,18 @@ int main(int argc, char *argv[])
   ParGridFunction x(&test_fes);
   FunctionCoefficient p_coef(p_exact);
   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
   FunctionCoefficient divgradp_coef(div_gradp_exact);

   if (prob == 0)
   {
      gftrial.ProjectCoefficient(p_coef);
   }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
   else
   {
      gftrial.ProjectCoefficient(gradp_coef);
@@ -210,6 +233,11 @@ int main(int argc, char *argv[])
      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
   }
+   else if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
+   }
   else
   {
      a.AddDomainIntegrator(new MassIntegrator(one));
@@ -293,6 +321,10 @@ int main(int argc, char *argv[])
   {
      dlo.AddDomainInterpolator(new GradientInterpolator());
   }
+   else if (prob == 1)
+   {
+      dlo.AddDomainInterpolator(new CurlInterpolator());
+   }
   else
   {
      dlo.AddDomainInterpolator(new DivergenceInterpolator());
@@ -307,6 +339,10 @@ int main(int argc, char *argv[])
   {
      exact_proj.ProjectCoefficient(gradp_coef);
   }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
   else
   {
      exact_proj.ProjectCoefficient(divgradp_coef);
@@ -324,14 +360,30 @@ int main(int argc, char *argv[])

      if (myid == 0)
      {
-         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
-              "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
-         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-              "||_{L_2} = " << errInterp << '\n' << endl;
+         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl)"
+              ": || E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
+         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad"
+              " p ||_{L_2} = " << errInterp << '\n' << endl;
         cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
              "||_{L_2} = " << errProj << '\n' << endl;
      }
   }
+   else if (prob == 1)
+   {
+      double errSol = x.ComputeL2Error(curlv_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      if (myid == 0)
+      {
+         cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in "
+              "H(div): || E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+         cout << " Curl interpolant E_h = curl v_h in H(div): || E_h - curl v "
+              "||_{L_2} = " << errInterp << '\n' << endl;
+         cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+              "||_{L_2} = " << errProj << '\n' << endl;
+      }
+   }
   else
   {
      int order_quad = max(2, 2*order+1);
@@ -350,7 +402,7 @@ int main(int argc, char *argv[])
         cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
              "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
         cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
-              "||_{L_2} = " << errInterp << '\n' << endl;
+              " ||_{L_2} = " << errInterp << '\n' << endl;
         cout << " Projection f_h of exact div v in L_2: || f_h - div v "
              "||_{L_2} = " << errProj << '\n' << endl;
      }
@@ -436,3 +488,33 @@ double div_gradp_exact(const Vector &x)

   return 0.0;
 }
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}
@@ -10,6 +10,10 @@
 //               ex25 -o 2 -f 8.0 -ref 3 -prob 4 -m ../data/inline-quad.mesh
 //               ex25 -o 2 -f 2.0 -ref 1 -prob 4 -m ../data/inline-hex.mesh
 //
+// Device sample runs:
+//               ex25 -o 2 -f 8.0 -ref 3 -prob 4 -m ../data/inline-quad.mesh -pa -d cuda
+//               ex25 -o 2 -f 2.0 -ref 1 -prob 4 -m ../data/inline-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple electromagnetic wave
 //               propagation problem corresponding to the second order
 //               indefinite Maxwell equation
@@ -82,24 +86,24 @@ public:
 };

 // Class for returning the PML coefficients of the bilinear form
-class PMLMatrixCoefficient : public MatrixCoefficient
+class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
   CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , DenseMatrix &);
+   void (*Function)(const Vector &, CartesianPML * , Vector &);
 public:
-   PMLMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
-                                          DenseMatrix &),
-                        CartesianPML * pml_)
-      : MatrixCoefficient(dim), pml(pml_), Function(F)
+   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
+                                              Vector &),
+                            CartesianPML * pml_)
+      : VectorCoefficient(dim), pml(pml_), Function(F)
   {}
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+   virtual void Eval(Vector &K, ElementTransformation &T,
                     const IntegrationPoint &ip)
   {
      double x[3];
      Vector transip(x, 3);
      T.Transform(ip, transip);
-      K.SetSize(height, width);
+      K.SetSize(vdim);
      (*Function)(transip, pml, K);
   }
 };
@@ -116,13 +120,13 @@ void source(const Vector &x, Vector & f);

 // Functions for computing the necessary coefficients after PML stretching.
 // J is the Jacobian matrix of the stretching function
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector &D);

-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector &D);

 Array2D<double> comp_domain_bdr;
 Array2D<double> domain_bdr;
@@ -153,6 +157,8 @@ int main(int argc, char *argv[])
   double freq = 5.0;
   bool herm_conv = true;
   bool visualization = 1;
+   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -174,12 +180,21 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();

   if (iprob > 4) { iprob = 4; }
   prob = (prob_type)iprob;

-   // 2. Setup the mesh
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Setup the mesh
   if (!mesh_file)
   {
      exact_known = true;
@@ -220,7 +235,7 @@ int main(int argc, char *argv[])
   // Setup PML length
   Array2D<double> length(dim, 2); length = 0.0;

-   // 3. Setup the Cartesian PML region.
+   // 4. Setup the Cartesian PML region.
   switch (prob)
   {
      case disc:
@@ -246,19 +261,19 @@ int main(int argc, char *argv[])
   comp_domain_bdr = pml->GetCompDomainBdr();
   domain_bdr = pml->GetDomainBdr();

-   // 4. Refine the mesh to increase the resolution.
+   // 5. Refine the mesh to increase the resolution.
   for (int l = 0; l < ref_levels; l++)
   {
      mesh->UniformRefinement();
   }

-   // 5. Reorient mesh in case of a tet mesh
+   // 6. Reorient mesh in case of a tet mesh
   mesh->ReorientTetMesh();

   // Set element attributes in order to distinguish elements in the PML region
   pml->SetAttributes(mesh);

-   // 6. Define a finite element space on the mesh. Here we use the Nedelec
+   // 7. Define a finite element space on the mesh. Here we use the Nedelec
   //    finite elements of the specified order.
   FiniteElementCollection *fec = new ND_FECollection(order, dim);
   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
@@ -266,7 +281,7 @@ int main(int argc, char *argv[])

   cout << "Number of finite element unknowns: " << size << endl;

-   // 7. Determine the list of true essential boundary dofs. In this example,
+   // 8. Determine the list of true essential boundary dofs. In this example,
   //    the boundary conditions are defined based on the specific mesh and the
   //    problem type.
   Array<int> ess_tdof_list;
@@ -308,12 +323,12 @@ int main(int argc, char *argv[])
   }
   fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);

-   // 8. Setup Complex Operator convention
+   // 9. Setup Complex Operator convention
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

-   // 9. Set up the linear form b(.) which corresponds to the right-hand side of
-   //    the FEM linear system.
+   // 10. Set up the linear form b(.) which corresponds to the right-hand side of
+   //     the FEM linear system.
   VectorFunctionCoefficient f(dim, source);
   ComplexLinearForm b(fespace, conv);
   if (prob == load_src)
@@ -323,7 +338,7 @@ int main(int argc, char *argv[])
   b.Vector::operator=(0.0);
   b.Assemble();

-   // 10. Define the solution vector x as a complex finite element grid function
+   // 11. Define the solution vector x as a complex finite element grid function
   //     corresponding to fespace.
   ComplexGridFunction x(fespace);
   x = 0.0;
@@ -331,7 +346,7 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient E_Im(dim, E_bdr_data_Im);
   x.ProjectBdrCoefficientTangent(E_Re, E_Im, ess_bdr);

-   // 11. Set up the sesquilinear form a(.,.)
+   // 12. Set up the sesquilinear form a(.,.)
   //
   //     In Comp
   //     Domain:   1/mu (Curl E, Curl F) - omega^2 * epsilon (E,F)
@@ -365,19 +380,19 @@ int main(int argc, char *argv[])
   a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_omeg),NULL);

   int cdim = (dim == 2) ? 1 : dim;
-   PMLMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
-   PMLMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
-   ScalarMatrixProductCoefficient c1_Re(muinv,pml_c1_Re);
-   ScalarMatrixProductCoefficient c1_Im(muinv,pml_c1_Im);
-   MatrixRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
+   PMLDiagMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
+   ScalarVectorProductCoefficient c1_Re(muinv,pml_c1_Re);
+   ScalarVectorProductCoefficient c1_Im(muinv,pml_c1_Im);
+   VectorRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
+   VectorRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);

-   PMLMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
-   PMLMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
-   ScalarMatrixProductCoefficient c2_Re(omeg,pml_c2_Re);
-   ScalarMatrixProductCoefficient c2_Im(omeg,pml_c2_Im);
-   MatrixRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
+   PMLDiagMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
+   ScalarVectorProductCoefficient c2_Re(omeg,pml_c2_Re);
+   ScalarVectorProductCoefficient c2_Im(omeg,pml_c2_Im);
+   VectorRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
+   VectorRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);

   // Integrators inside the PML region
   a.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_Re),
@@ -385,30 +400,29 @@ int main(int argc, char *argv[])
   a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_Re),
                         new VectorFEMassIntegrator(restr_c2_Im));

-   // 12. Assemble the bilinear form and the corresponding linear system,
+   // 13. Assemble the bilinear form and the corresponding linear system,
   //     applying any necessary transformations such as: assembly, eliminating
   //     boundary conditions, applying conforming constraints for
   //     non-conforming AMR, etc.
-   a.Assemble();
+#ifndef MFEM_USE_SUITESPARSE
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+#endif
+   a.Assemble(0);

-   OperatorHandle Ah;
+   OperatorPtr A;
   Vector B, X;
-   a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);
-
-   // 13. Transform to monolithic SparseMatrix
-   SparseMatrix *A = Ah.As<ComplexSparseMatrix>()->GetSystemMatrix();
-
-   cout << "Size of linear system: " << A->Height() << endl;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);

   // 14. Solve using a direct or an iterative solver
 #ifdef MFEM_USE_SUITESPARSE
   {
-      UMFPackSolver  solver(*A);
-      solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-      solver.Mult(B, X);
+      if (pa) { cout << "PA not available with MFEM_USE_SUITESPARSE" << endl; }
+      ComplexUMFPackSolver csolver(*A.As<ComplexSparseMatrix>());
+      csolver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      csolver.SetPrintLevel(1);
+      csolver.Mult(B, X);
   }
 #else
-
   // 14a. Set up the Bilinear form a(.,.) for the preconditioner
   //
   //    In Comp
@@ -424,45 +438,64 @@ int main(int argc, char *argv[])
      prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_muinv));
      prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_absomeg));

-      PMLMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
-      ScalarMatrixProductCoefficient c1_abs(muinv,pml_c1_abs);
-      MatrixRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
+      ScalarVectorProductCoefficient c1_abs(muinv,pml_c1_abs);
+      VectorRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);

-      PMLMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
-      ScalarMatrixProductCoefficient c2_abs(absomeg,pml_c2_abs);
-      MatrixRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
+      ScalarVectorProductCoefficient c2_abs(absomeg,pml_c2_abs);
+      VectorRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);

      prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_abs));
      prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_abs));

+      if (pa) { prec.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
      prec.Assemble();

-      OperatorHandle PCOpAh;
-      prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
-
      // 14b. Define and apply a GMRES solver for AU=B with a block diagonal
-      //      preconditioner based on the Gauss-Seidel sparse smoother.
+      //      preconditioner based on the Gauss-Seidel or Jacobi sparse smoother.
      Array<int> offsets(3);
      offsets[0] = 0;
      offsets[1] = fespace->GetTrueVSize();
      offsets[2] = fespace->GetTrueVSize();
      offsets.PartialSum();

-      GSSmoother gs00(*PCOpAh.As<SparseMatrix>());
-      BlockDiagonalPreconditioner BlockGS(offsets);
-      ScaledOperator gs11(&gs00,
-                          (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0);
-      BlockGS.SetDiagonalBlock(0,&gs00);
-      BlockGS.SetDiagonalBlock(1,&gs11);
+      Operator *pc_r = nullptr;
+      Operator *pc_i = nullptr;
+      int s = (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0;
+      if (pa)
+      {
+         // Jacobi Smoother
+         OperatorJacobiSmoother *d00 = new OperatorJacobiSmoother(prec, ess_tdof_list);
+         ScaledOperator *d11 = new ScaledOperator(d00, s);
+         pc_r = d00;
+         pc_i = d11;
+      }
+      else
+      {
+         OperatorPtr PCOpAh;
+         prec.SetDiagonalPolicy(mfem::Operator::DIAG_ONE);
+         prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
+
+         // Gauss-Seidel Smoother
+         GSSmoother *gs00 = new GSSmoother(*PCOpAh.As<SparseMatrix>());
+         ScaledOperator *gs11 = new ScaledOperator(gs00, s);
+         pc_r = gs00;
+         pc_i = gs11;
+      }
+
+      BlockDiagonalPreconditioner BlockDP(offsets);
+      BlockDP.SetDiagonalBlock(0, pc_r);
+      BlockDP.SetDiagonalBlock(1, pc_i);

      GMRESSolver gmres;
      gmres.SetPrintLevel(1);
      gmres.SetKDim(200);
-      gmres.SetMaxIter(2000);
+      gmres.SetMaxIter(pa ? 5000 : 2000);
      gmres.SetRelTol(1e-5);
      gmres.SetAbsTol(0.0);
      gmres.SetOperator(*A);
-      gmres.SetPreconditioner(BlockGS);
+      gmres.SetPreconditioner(BlockDP);
      gmres.Mult(B, X);
   }
 #endif
@@ -474,10 +507,8 @@ int main(int argc, char *argv[])
   // If exact is known compute the error
   if (exact_known)
   {
-      ComplexGridFunction x_gf(fespace);
      VectorFunctionCoefficient E_ex_Re(dim, E_exact_Re);
      VectorFunctionCoefficient E_ex_Im(dim, E_exact_Im);
-      x_gf.ProjectCoefficient(E_ex_Re, E_ex_Im);
      int order_quad = max(2, 2 * order + 1);
      const IntegrationRule *irs[Geometry::NumGeom];
      for (int i = 0; i < Geometry::NumGeom; ++i)
@@ -573,7 +604,6 @@ int main(int argc, char *argv[])
   }

   // 18. Free the used memory.
-   delete A;
   delete pml;
   delete fespace;
   delete fec;
@@ -771,7 +801,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
   }
 }

-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det(1.0, 0.0);
@@ -782,14 +812,13 @@ void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], 2)).real();
   }
 }

-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -800,14 +829,13 @@ void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], 2)).imag();
   }
 }

-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -818,14 +846,13 @@ void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], 2));
   }
 }

-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det(1.0, 0.0);
@@ -839,19 +866,18 @@ void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
   // in the 2D case the coefficient is scalar 1/det(J)
   if (dim == 2)
   {
-      M = (1.0 / det).real();
+      D = (1.0 / det).real();
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], 2) / det).real();
      }
   }
 }

-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -864,19 +890,18 @@ void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)

   if (dim == 2)
   {
-      M = (1.0 / det).imag();
+      D = (1.0 / det).imag();
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], 2) / det).imag();
      }
   }
 }

-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector &D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -889,14 +914,13 @@ void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)

   if (dim == 2)
   {
-      M = abs(1.0 / det);
+      D = abs(1.0 / det);
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], 2) / det);
      }
   }
 }
@@ -10,6 +10,10 @@
 //               mpirun -np 4 ex25p -o 2 -f 8.0 -rs 2 -rp 2 -prob 4 -m ../data/inline-quad.mesh
 //               mpirun -np 4 ex25p -o 2 -f 2.0 -rs 1 -rp 1 -prob 4 -m ../data/inline-hex.mesh
 //
+// Device sample runs:
+//               mpirun -np 4 ex25p -o 1 -f 3.0 -rs 3 -rp 1 -prob 2 -pa -d cuda
+//               mpirun -np 4 ex25p -o 2 -f 1.0 -rs 1 -rp 1 -prob 3 -pa -d cuda
+//
 // Description:  This example code solves a simple electromagnetic wave
 //               propagation problem corresponding to the second order
 //               indefinite Maxwell equation
@@ -82,24 +86,24 @@ public:
 };

 // Class for returning the PML coefficients of the bilinear form
-class PMLMatrixCoefficient : public MatrixCoefficient
+class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
   CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , DenseMatrix &);
+   void (*Function)(const Vector &, CartesianPML * , Vector &);
 public:
-   PMLMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
-                                          DenseMatrix &),
-                        CartesianPML * pml_)
-      : MatrixCoefficient(dim), pml(pml_), Function(F)
+   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
+                                              Vector &),
+                            CartesianPML * pml_)
+      : VectorCoefficient(dim), pml(pml_), Function(F)
   {}
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+   virtual void Eval(Vector &K, ElementTransformation &T,
                     const IntegrationPoint &ip)
   {
      double x[3];
      Vector transip(x, 3);
      T.Transform(ip, transip);
-      K.SetSize(height, width);
+      K.SetSize(vdim);
      (*Function)(transip, pml, K);
   }
 };
@@ -116,13 +120,13 @@ void source(const Vector &x, Vector & f);

 // Functions for computing the necessary coefficients after PML stretching.
 // J is the Jacobian matrix of the stretching function
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector & D);

-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector & D);

 Array2D<double> comp_domain_bdr;
 Array2D<double> domain_bdr;
@@ -160,6 +164,8 @@ int main(int argc, char *argv[])
   double freq = 5.0;
   bool herm_conv = true;
   bool visualization = 1;
+   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -183,12 +189,21 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();

   if (iprob > 4) { iprob = 4; }
   prob = (prob_type)iprob;

-   // 3. Setup the (serial) mesh on all processors.
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 4. Setup the (serial) mesh on all processors.
   if (!mesh_file)
   {
      exact_known = true;
@@ -236,7 +251,7 @@ int main(int argc, char *argv[])
   // Setup PML length
   Array2D<double> length(dim, 2); length = 0.0;

-   // 4. Setup the Cartesian PML region.
+   // 5. Setup the Cartesian PML region.
   switch (prob)
   {
      case disc:
@@ -262,13 +277,13 @@ int main(int argc, char *argv[])
   comp_domain_bdr = pml->GetCompDomainBdr();
   domain_bdr = pml->GetDomainBdr();

-   // 5. Refine the serial mesh on all processors to increase the resolution.
+   // 6. Refine the serial mesh on all processors to increase the resolution.
   for (int l = 0; l < ref_levels; l++)
   {
      mesh->UniformRefinement();
   }

-   // 6. Define a parallel mesh by a partitioning of the serial mesh.
+   // 7. Define a parallel mesh by a partitioning of the serial mesh.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -278,13 +293,13 @@ int main(int argc, char *argv[])
      }
   }

-   // 6a. Reorient mesh in case of a tet mesh
+   // 7a. Reorient mesh in case of a tet mesh
   pmesh->ReorientTetMesh();

-   // 7. Set element attributes in order to distinguish elements in the PML
+   // 8. Set element attributes in order to distinguish elements in the PML
   pml->SetAttributes(pmesh);

-   // 8. Define a parallel finite element space on the parallel mesh. Here we
+   // 9. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
   FiniteElementCollection *fec = new ND_FECollection(order, dim);
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
@@ -294,9 +309,9 @@ int main(int argc, char *argv[])
      cout << "Number of finite element unknowns: " << size << endl;
   }

-   // 9. Determine the list of true (i.e. parallel conforming) essential
-   //    boundary dofs. In this example, the boundary conditions are defined
-   //    based on the specific mesh and the problem type.
+   // 10. Determine the list of true (i.e. parallel conforming) essential
+   //     boundary dofs. In this example, the boundary conditions are defined
+   //     based on the specific mesh and the problem type.
   Array<int> ess_tdof_list;
   Array<int> ess_bdr;
   if (pmesh->bdr_attributes.Size())
@@ -336,11 +351,11 @@ int main(int argc, char *argv[])
   }
   fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);

-   // 10. Setup Complex Operator convention
+   // 11. Setup Complex Operator convention
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

-   // 11. Set up the parallel linear form b(.) which corresponds to the
+   // 12. Set up the parallel linear form b(.) which corresponds to the
   //     right-hand side of the FEM linear system.
   VectorFunctionCoefficient f(dim, source);
   ParComplexLinearForm b(fespace, conv);
@@ -351,7 +366,7 @@ int main(int argc, char *argv[])
   b.Vector::operator=(0.0);
   b.Assemble();

-   // 12. Define the solution vector x as a parallel complex finite element grid
+   // 13. Define the solution vector x as a parallel complex finite element grid
   //     function corresponding to fespace.
   ParComplexGridFunction x(fespace);
   x = 0.0;
@@ -359,7 +374,7 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient E_Im(dim, E_bdr_data_Im);
   x.ProjectBdrCoefficientTangent(E_Re, E_Im, ess_bdr);

-   // 13. Set up the parallel sesquilinear form a(.,.)
+   // 14. Set up the parallel sesquilinear form a(.,.)
   //
   //     In Comp
   //     Domain:   1/mu (Curl E, Curl F) - omega^2 * epsilon (E,F)
@@ -393,19 +408,19 @@ int main(int argc, char *argv[])
   a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_omeg),NULL);

   int cdim = (dim == 2) ? 1 : dim;
-   PMLMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
-   PMLMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
-   ScalarMatrixProductCoefficient c1_Re(muinv,pml_c1_Re);
-   ScalarMatrixProductCoefficient c1_Im(muinv,pml_c1_Im);
-   MatrixRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
+   PMLDiagMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
+   ScalarVectorProductCoefficient c1_Re(muinv,pml_c1_Re);
+   ScalarVectorProductCoefficient c1_Im(muinv,pml_c1_Im);
+   VectorRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
+   VectorRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);

-   PMLMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
-   PMLMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
-   ScalarMatrixProductCoefficient c2_Re(omeg,pml_c2_Re);
-   ScalarMatrixProductCoefficient c2_Im(omeg,pml_c2_Im);
-   MatrixRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
+   PMLDiagMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
+   ScalarVectorProductCoefficient c2_Re(omeg,pml_c2_Re);
+   ScalarVectorProductCoefficient c2_Im(omeg,pml_c2_Im);
+   VectorRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
+   VectorRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);

   // Integrators inside the PML region
   a.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_Re),
@@ -413,27 +428,25 @@ int main(int argc, char *argv[])
   a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_Re),
                         new VectorFEMassIntegrator(restr_c2_Im));

-   // 14. Assemble the parallel bilinear form and the corresponding linear
+   // 15. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, etc.
+#ifndef MFEM_USE_SUPERLU
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+#endif
   a.Assemble();

-   OperatorHandle Ah;
+   OperatorPtr Ah;
   Vector B, X;
   a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);

-   // 15. Transform to monolithic HypreParMatrix
-   HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
-
-   if (myid == 0)
-   {
-      cout << "Size of linear system: " << A->GetGlobalNumRows() << endl;
-   }
-
   // 16. Solve using a direct or an iterative solver
 #ifdef MFEM_USE_SUPERLU
   {
+      if (pa) { cout << "PA not available with MFEM_USE_SUPERLU" << endl; }
+      // Transform to monolithic HypreParMatrix
+      HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
      SuperLURowLocMatrix SA(*A);
      SuperLUSolver superlu(MPI_COMM_WORLD);
      superlu.SetPrintStatistics(false);
@@ -441,9 +454,9 @@ int main(int argc, char *argv[])
      superlu.SetColumnPermutation(superlu::PARMETIS);
      superlu.SetOperator(SA);
      superlu.Mult(B, X);
+      delete A;
   }
 #else
-
   // 16a. Set up the parallel Bilinear form a(.,.) for the preconditioner
   //
   //    In Comp
@@ -459,22 +472,20 @@ int main(int argc, char *argv[])
      prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_muinv));
      prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_absomeg));

-      PMLMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
-      ScalarMatrixProductCoefficient c1_abs(muinv,pml_c1_abs);
-      MatrixRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
+      ScalarVectorProductCoefficient c1_abs(muinv,pml_c1_abs);
+      VectorRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);

-      PMLMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
-      ScalarMatrixProductCoefficient c2_abs(absomeg,pml_c2_abs);
-      MatrixRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
+      ScalarVectorProductCoefficient c2_abs(absomeg,pml_c2_abs);
+      VectorRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);

      prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_abs));
      prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_abs));

+      if (pa) { prec.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
      prec.Assemble();

-      OperatorHandle PCOpAh;
-      prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
-
      // 16b. Define and apply a parallel GMRES solver for AU=B with a block
      //      diagonal preconditioner based on hypre's AMS preconditioner.
      Array<int> offsets(3);
@@ -483,21 +494,41 @@ int main(int argc, char *argv[])
      offsets[2] = fespace->GetTrueVSize();
      offsets.PartialSum();

-      HypreAMS ams00(*PCOpAh.As<HypreParMatrix>(),fespace);
-      BlockDiagonalPreconditioner BlockAMS(offsets);
-      ScaledOperator ams11(&ams00,
-                           (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0);
-      BlockAMS.SetDiagonalBlock(0,&ams00);
-      BlockAMS.SetDiagonalBlock(1,&ams11);
+      Operator *pc_r = nullptr;
+      Operator *pc_i = nullptr;
+      int s = (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0;
+      if (pa)
+      {
+         // Jacobi Smoother
+         OperatorJacobiSmoother *d00 = new OperatorJacobiSmoother(prec, ess_tdof_list);
+         ScaledOperator *d11 = new ScaledOperator(d00, s);
+         pc_r = d00;
+         pc_i = d11;
+      }
+      else
+      {
+         OperatorPtr PCOpAh;
+         prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
+
+         // Hypre AMS
+         HypreAMS *ams00 = new HypreAMS(*PCOpAh.As<HypreParMatrix>(), fespace);
+         ScaledOperator *ams11 = new ScaledOperator(ams00, s);
+         pc_r = ams00;
+         pc_i = ams11;
+      }
+
+      BlockDiagonalPreconditioner BlockDP(offsets);
+      BlockDP.SetDiagonalBlock(0, pc_r);
+      BlockDP.SetDiagonalBlock(1, pc_i);

      GMRESSolver gmres(MPI_COMM_WORLD);
      gmres.SetPrintLevel(1);
      gmres.SetKDim(200);
-      gmres.SetMaxIter(2000);
+      gmres.SetMaxIter(pa ? 5000 : 2000);
      gmres.SetRelTol(1e-5);
      gmres.SetAbsTol(0.0);
-      gmres.SetOperator(*A);
-      gmres.SetPreconditioner(BlockAMS);
+      gmres.SetOperator(*Ah);
+      gmres.SetPreconditioner(BlockDP);
      gmres.Mult(B, X);
   }
 #endif
@@ -509,10 +540,8 @@ int main(int argc, char *argv[])
   // If exact is known compute the error
   if (exact_known)
   {
-      ParComplexGridFunction x_gf(fespace);
      VectorFunctionCoefficient E_ex_Re(dim, E_exact_Re);
      VectorFunctionCoefficient E_ex_Im(dim, E_exact_Im);
-      x_gf.ProjectCoefficient(E_ex_Re, E_ex_Im);
      int order_quad = max(2, 2 * order + 1);
      const IntegrationRule *irs[Geometry::NumGeom];
      for (int i = 0; i < Geometry::NumGeom; ++i)
@@ -629,7 +658,6 @@ int main(int argc, char *argv[])
   }

   // 20. Free the used memory.
-   delete A;
   delete pml;
   delete fespace;
   delete fec;
@@ -828,7 +856,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
   }
 }

-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det(1.0, 0.0);
@@ -839,14 +867,13 @@ void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], 2)).real();
   }
 }

-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -857,14 +884,13 @@ void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], 2)).imag();
   }
 }

-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -875,14 +901,13 @@ void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
      det *= dxs[i];
   }

-   M = 0.0;
   for (int i = 0; i < dim; ++i)
   {
-      M(i, i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], 2));
   }
 }

-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det(1.0, 0.0);
@@ -896,19 +921,18 @@ void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
   // in the 2D case the coefficient is scalar 1/det(J)
   if (dim == 2)
   {
-      M = (1.0 / det).real();
+      D = (1.0 / det).real();
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], 2) / det).real();
      }
   }
 }

-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -921,19 +945,18 @@ void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)

   if (dim == 2)
   {
-      M = (1.0 / det).imag();
+      D = (1.0 / det).imag();
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], 2) / det).imag();
      }
   }
 }

-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector & D)
 {
   vector<complex<double>> dxs(dim);
   complex<double> det = 1.0;
@@ -946,14 +969,13 @@ void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)

   if (dim == 2)
   {
-      M = abs(1.0 / det);
+      D = abs(1.0 / det);
   }
   else
   {
-      M = 0.0;
      for (int i = 0; i < dim; ++i)
      {
-         M(i, i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], 2) / det);
      }
   }
 }
@@ -11,6 +11,12 @@
 //               ex5 -m ../data/escher.mesh
 //               ex5 -m ../data/fichera.mesh
 //
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D mixed Darcy problem
 //               corresponding to the saddle point system
 //                                 k*u + grad p = f
@@ -50,6 +56,7 @@ int main(int argc, char *argv[])
   const char *mesh_file = "../data/star.mesh";
   int order = 1;
   bool pa = false;
+   const char *device_config = "cpu";
   bool visualization = 1;

   OptionsParser args(argc, argv);
@@ -59,6 +66,8 @@ int main(int argc, char *argv[])
                  "Finite element order (polynomial degree).");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -70,13 +79,18 @@ int main(int argc, char *argv[])
   }
   args.PrintOptions(cout);

-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
   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
+   // 4. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
   //    largest number that gives a final mesh with no more than 10,000
   //    elements.
@@ -89,7 +103,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 4. Define a finite element space on the mesh. Here we use the
+   // 5. Define a finite element space on the mesh. Here we use the
   //    Raviart-Thomas finite elements of the specified order.
   FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
   FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
@@ -97,7 +111,7 @@ int main(int argc, char *argv[])
   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, hdiv_coll);
   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, l2_coll);

-   // 5. Define the BlockStructure of the problem, i.e. define the array of
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
   //    offsets for each variable. The last component of the Array is the sum
   //    of the dimensions of each block.
   Array<int> block_offsets(3); // number of variables + 1
@@ -112,7 +126,7 @@ int main(int argc, char *argv[])
   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
   std::cout << "***********************************************************\n";

-   // 6. Define the coefficients, analytical solution, and rhs of the PDE.
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
   ConstantCoefficient k(1.0);

   VectorFunctionCoefficient fcoeff(dim, fFun);
@@ -122,25 +136,28 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient ucoeff(dim, uFun_ex);
   FunctionCoefficient pcoeff(pFun_ex);

-   // 7. Allocate memory (x, rhs) for the analytical solution and the right hand
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
   //    side.  Define the GridFunction u,p for the finite element solution and
   //    linear forms fform and gform for the right hand side.  The data
   //    allocated by x and rhs are passed as a reference to the grid functions
   //    (u,p) and the linear forms (fform, gform).
-   BlockVector x(block_offsets), rhs(block_offsets);
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);

   LinearForm *fform(new LinearForm);
   fform->Update(R_space, rhs.GetBlock(0), 0);
   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
   fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
   fform->Assemble();
+   fform->SyncAliasMemory(rhs);

   LinearForm *gform(new LinearForm);
   gform->Update(W_space, rhs.GetBlock(1), 0);
   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
   gform->Assemble();
+   gform->SyncAliasMemory(rhs);

-   // 8. Assemble the finite element matrices for the Darcy operator
+   // 9. Assemble the finite element matrices for the Darcy operator
   //
   //                            D = [ M  B^T ]
   //                                [ B   0  ]
@@ -185,7 +202,7 @@ int main(int argc, char *argv[])
      darcyOp.SetBlock(1,0, &B);
   }

-   // 9. Construct the operators for preconditioner
+   // 10. Construct the operators for preconditioner
   //
   //                 P = [ diag(M)         0         ]
   //                     [  0       B diag(M)^-1 B^T ]
@@ -202,10 +219,11 @@ int main(int argc, char *argv[])
   if (pa)
   {
      mVarf->AssembleDiagonal(Md);
+      auto Md_host = Md.HostRead();
      Vector invMd(mVarf->Height());
      for (int i=0; i<mVarf->Height(); ++i)
      {
-         invMd(i) = 1.0 / Md(i);
+         invMd(i) = 1.0 / Md_host[i];
      }

      Vector BMBt_diag(bVarf->Height());
@@ -246,7 +264,7 @@ int main(int argc, char *argv[])
   darcyPrec.SetDiagonalBlock(0, invM);
   darcyPrec.SetDiagonalBlock(1, invS);

-   // 10. Solve the linear system with MINRES.
+   // 11. Solve the linear system with MINRES.
   //     Check the norm of the unpreconditioned residual.
   int maxIter(1000);
   double rtol(1.e-6);
@@ -263,6 +281,7 @@ int main(int argc, char *argv[])
   solver.SetPrintLevel(1);
   x = 0.0;
   solver.Mult(rhs, x);
+   if (device.IsEnabled()) { x.HostRead(); }
   chrono.Stop();

   if (solver.GetConverged())
@@ -273,7 +292,7 @@ int main(int argc, char *argv[])
                << " iterations. Residual norm is " << solver.GetFinalNorm() << ".\n";
   std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";

-   // 11. Create the grid functions u and p. Compute the L2 error norms.
+   // 12. Create the grid functions u and p. Compute the L2 error norms.
   GridFunction u, p;
   u.MakeRef(R_space, x.GetBlock(0), 0);
   p.MakeRef(W_space, x.GetBlock(1), 0);
@@ -293,7 +312,7 @@ int main(int argc, char *argv[])
   std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
   std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";

-   // 12. Save the mesh and the solution. This output can be viewed later using
+   // 13. Save the mesh and the solution. This output can be viewed later using
   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
   //     sol_p.gf".
   {
@@ -310,13 +329,13 @@ int main(int argc, char *argv[])
      p.Save(p_ofs);
   }

-   // 13. Save data in the VisIt format
+   // 14. Save data in the VisIt format
   VisItDataCollection visit_dc("Example5", mesh);
   visit_dc.RegisterField("velocity", &u);
   visit_dc.RegisterField("pressure", &p);
   visit_dc.Save();

-   // 14. Save data in the ParaView format
+   // 15. Save data in the ParaView format
   ParaViewDataCollection paraview_dc("Example5", mesh);
   paraview_dc.SetPrefixPath("ParaView");
   paraview_dc.SetLevelsOfDetail(order);
@@ -328,7 +347,7 @@ int main(int argc, char *argv[])
   paraview_dc.RegisterField("pressure",&p);
   paraview_dc.Save();

-   // 15. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -341,7 +360,7 @@ int main(int argc, char *argv[])
      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
   }

-   // 16. Free the used memory.
+   // 17. Free the used memory.
   delete fform;
   delete gform;
   delete invM;
@@ -11,6 +11,12 @@
 //               mpirun -np 4 ex5p -m ../data/escher.mesh
 //               mpirun -np 4 ex5p -m ../data/fichera.mesh
 //
+// Device sample runs:
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d cuda
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-cuda
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-omp
+//               mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D mixed Darcy problem
 //               corresponding to the saddle point system
 //                                 k*u + grad p = f
@@ -60,6 +66,7 @@ int main(int argc, char *argv[])
   int order = 1;
   bool par_format = false;
   bool pa = false;
+   const char *device_config = "cpu";
   bool visualization = 1;
   bool adios2 = false;

@@ -75,6 +82,8 @@ int main(int argc, char *argv[])
                  "Format to use when saving the results for VisIt.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -96,13 +105,18 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
   //    this example we do 'ref_levels' of uniform refinement. We choose
   //    'ref_levels' to be the largest number that gives a final mesh with no
   //    more than 10,000 elements, unless the user specifies it as input.
@@ -118,7 +132,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. 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);
@@ -131,7 +145,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Raviart-Thomas finite elements of the specified order.
   FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
   FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
@@ -151,7 +165,7 @@ int main(int argc, char *argv[])
      std::cout << "***********************************************************\n";
   }

-   // 7. Define the two BlockStructure of the problem.  block_offsets is used
+   // 8. Define the two BlockStructure of the problem.  block_offsets is used
   //    for Vector based on dof (like ParGridFunction or ParLinearForm),
   //    block_trueOffstes is used for Vector based on trueDof (HypreParVector
   //    for the rhs and solution of the linear system).  The offsets computed
@@ -168,7 +182,7 @@ int main(int argc, char *argv[])
   block_trueOffsets[2] = W_space->TrueVSize();
   block_trueOffsets.PartialSum();

-   // 8. Define the coefficients, analytical solution, and rhs of the PDE.
+   // 9. Define the coefficients, analytical solution, and rhs of the PDE.
   ConstantCoefficient k(1.0);

   VectorFunctionCoefficient fcoeff(dim, fFun);
@@ -178,25 +192,30 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient ucoeff(dim, uFun_ex);
   FunctionCoefficient pcoeff(pFun_ex);

-   // 9. Define the parallel grid function and parallel linear forms, solution
-   //    vector and rhs.
-   BlockVector x(block_offsets), rhs(block_offsets);
-   BlockVector trueX(block_trueOffsets), trueRhs(block_trueOffsets);
+   // 10. Define the parallel grid function and parallel linear forms, solution
+   //     vector and rhs.
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+   BlockVector trueX(block_trueOffsets, mt), trueRhs(block_trueOffsets, mt);

   ParLinearForm *fform(new ParLinearForm);
   fform->Update(R_space, rhs.GetBlock(0), 0);
   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
   fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
   fform->ParallelAssemble(trueRhs.GetBlock(0));
+   trueRhs.GetBlock(0).SyncAliasMemory(trueRhs);

   ParLinearForm *gform(new ParLinearForm);
   gform->Update(W_space, rhs.GetBlock(1), 0);
   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
   gform->ParallelAssemble(trueRhs.GetBlock(1));
+   trueRhs.GetBlock(1).SyncAliasMemory(trueRhs);

-   // 10. Assemble the finite element matrices for the Darcy operator
+   // 11. Assemble the finite element matrices for the Darcy operator
   //
   //                            D = [ M  B^T ]
   //                                [ B   0  ]
@@ -249,7 +268,7 @@ int main(int argc, char *argv[])
      darcyOp->SetBlock(1,0, B);
   }

-   // 11. Construct the operators for preconditioner
+   // 12. Construct the operators for preconditioner
   //
   //                 P = [ diag(M)         0         ]
   //                     [  0       B diag(M)^-1 B^T ]
@@ -266,10 +285,11 @@ int main(int argc, char *argv[])
   {
      Md_PA.SetSize(R_space->GetTrueVSize());
      mVarf->AssembleDiagonal(Md_PA);
+      auto Md_host = Md_PA.HostRead();
      Vector invMd(Md_PA.Size());
      for (int i=0; i<Md_PA.Size(); ++i)
      {
-         invMd(i) = 1.0 / Md_PA(i);
+         invMd(i) = 1.0 / Md_host[i];
      }

      Vector BMBt_diag(W_space->GetTrueVSize());
@@ -302,7 +322,7 @@ int main(int argc, char *argv[])
   darcyPr->SetDiagonalBlock(0, invM);
   darcyPr->SetDiagonalBlock(1, invS);

-   // 12. Solve the linear system with MINRES.
+   // 13. Solve the linear system with MINRES.
   //     Check the norm of the unpreconditioned residual.
   int maxIter(pa ? 1000 : 500);
   double rtol(1.e-6);
@@ -319,6 +339,7 @@ int main(int argc, char *argv[])
   solver.SetPrintLevel(verbose);
   trueX = 0.0;
   solver.Mult(trueRhs, trueX);
+   if (device.IsEnabled()) { trueX.HostRead(); }
   chrono.Stop();

   if (verbose)
@@ -332,7 +353,7 @@ int main(int argc, char *argv[])
      std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";
   }

-   // 13. Extract the parallel grid function corresponding to the finite element
+   // 14. Extract the parallel grid function corresponding to the finite element
   //     approximation X. This is the local solution on each processor. Compute
   //     L2 error norms.
   ParGridFunction *u(new ParGridFunction);
@@ -360,7 +381,7 @@ int main(int argc, char *argv[])
      std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
   }

-   // 14. Save the refined mesh and the solution in parallel. This output can be
+   // 15. Save the refined mesh and the solution in parallel. This output can be
   //     viewed later using GLVis: "glvis -np <np> -m mesh -g sol_*".
   {
      ostringstream mesh_name, u_name, p_name;
@@ -381,7 +402,7 @@ int main(int argc, char *argv[])
      p->Save(p_ofs);
   }

-   // 15. Save data in the VisIt format
+   // 16. Save data in the VisIt format
   VisItDataCollection visit_dc("Example5-Parallel", pmesh);
   visit_dc.RegisterField("velocity", u);
   visit_dc.RegisterField("pressure", p);
@@ -390,7 +411,7 @@ int main(int argc, char *argv[])
                      DataCollection::PARALLEL_FORMAT);
   visit_dc.Save();

-   // 16. Save data in the ParaView format
+   // 17. Save data in the ParaView format
   ParaViewDataCollection paraview_dc("Example5P", pmesh);
   paraview_dc.SetPrefixPath("ParaView");
   paraview_dc.SetLevelsOfDetail(order);
@@ -402,7 +423,7 @@ int main(int argc, char *argv[])
   paraview_dc.RegisterField("pressure",p);
   paraview_dc.Save();

-   // 17. Optionally output a BP (binary pack) file using ADIOS2. This can be
+   // 18. Optionally output a BP (binary pack) file using ADIOS2. This can be
   //     visualized with the ParaView VTX reader.
 #ifdef MFEM_USE_ADIOS2
   if (adios2)
@@ -422,7 +443,7 @@ int main(int argc, char *argv[])
   }
 #endif

-   // 18. Send the solution by socket to a GLVis server.
+   // 19. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -442,7 +463,7 @@ int main(int argc, char *argv[])
             << endl;
   }

-   // 19. Free the used memory.
+   // 20. Free the used memory.
   delete fform;
   delete gform;
   delete u;
@@ -20,8 +20,11 @@
 // Device sample runs:
 //    ex9 -pa
 //    ex9 -ea
+//    ex9 -fa
 //    ex9 -pa -m ../data/periodic-cube.mesh
 //    ex9 -pa -m ../data/periodic-cube.mesh -d cuda
+//    ex9 -ea -m ../data/periodic-cube.mesh -d cuda
+//    ex9 -fa -m ../data/periodic-cube.mesh -d cuda
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -144,6 +147,7 @@ int main(int argc, char *argv[])
   int order = 3;
   bool pa = false;
   bool ea = false;
+   bool fa = false;
   const char *device_config = "cpu";
   int ode_solver_type = 4;
   double t_final = 10.0;
@@ -170,6 +174,8 @@ int main(int argc, char *argv[])
                  "--no-partial-assembly", "Enable Partial Assembly.");
   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
                  "--no-element-assembly", "Enable Element Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
   args.AddOption(&device_config, "-d", "--device",
                  "Device configuration string, see Device::Configure().");
   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -254,7 +260,7 @@ int main(int argc, char *argv[])

   // 5. Define the discontinuous DG finite element space of the given
   //    polynomial order on the refined mesh.
-   DG_FECollection fec(order, dim, BasisType::Positive);
+   DG_FECollection fec(order, dim, BasisType::GaussLobatto);
   FiniteElementSpace fes(&mesh, &fec);

   cout << "Number of unknowns: " << fes.GetVSize() << endl;
@@ -278,6 +284,11 @@ int main(int argc, char *argv[])
      m.SetAssemblyLevel(AssemblyLevel::ELEMENT);
      k.SetAssemblyLevel(AssemblyLevel::ELEMENT);
   }
+   else if (fa)
+   {
+      m.SetAssemblyLevel(AssemblyLevel::FULL);
+      k.SetAssemblyLevel(AssemblyLevel::FULL);
+   }
   m.AddDomainIntegrator(new MassIntegrator);
   k.AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
   k.AddInteriorFaceIntegrator(
@@ -378,10 +389,6 @@ int main(int argc, char *argv[])
   //    iterations, ti, with a time-step dt).
   FE_Evolution adv(m, k, b);

-   Vector masses(u.Size());
-   m.SpMat().Mult(u, masses);
-   double mass = masses.Sum();
-
   double t = 0.0;
   adv.SetTime(t);
   ode_solver->Init(adv);
@@ -428,9 +435,6 @@ int main(int argc, char *argv[])
      u.Save(osol);
   }

-   m.SpMat().Mult(u, masses);
-   cout << "Mass difference:" << abs(mass - masses.Sum()) << endl;
-
   // 10. Free the used memory.
   delete ode_solver;
   delete pd;
@@ -444,21 +448,19 @@ int main(int argc, char *argv[])
 FE_Evolution::FE_Evolution(BilinearForm &_M, BilinearForm &_K, const Vector &_b)
   : TimeDependentOperator(_M.Height()), M(_M), K(_K), b(_b), z(_M.Height())
 {
-   bool pa = M.GetAssemblyLevel() == AssemblyLevel::PARTIAL;
-   bool ea = M.GetAssemblyLevel() == AssemblyLevel::ELEMENT;
   Array<int> ess_tdof_list;
-   if (pa || ea)
+   if (M.GetAssemblyLevel() == AssemblyLevel::LEGACYFULL)
+   {
+      M_prec = new DSmoother(M.SpMat());
+      M_solver.SetOperator(M.SpMat());
+      dg_solver = new DG_Solver(M.SpMat(), K.SpMat(), *M.FESpace());
+   }
+   else
   {
      M_prec = new OperatorJacobiSmoother(M, ess_tdof_list);
      M_solver.SetOperator(M);
      dg_solver = NULL;
   }
-   else
-   {
-      M_prec = new DSmoother(M.SpMat());
-      dg_solver = new DG_Solver(M.SpMat(), K.SpMat(), *M.FESpace());
-      M_solver.SetOperator(M.SpMat());
-   }
   M_solver.SetPreconditioner(*M_prec);
   M_solver.iterative_mode = false;
   M_solver.SetRelTol(1e-9);
@@ -21,8 +21,11 @@
 // Device sample runs:
 //    mpirun -np 4 ex9p -pa
 //    mpirun -np 4 ex9p -ea
+//    mpirun -np 4 ex9p -fa
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh -d cuda
+//    mpirun -np 4 ex9p -ea -m ../data/periodic-cube.mesh -d cuda
+//    mpirun -np 4 ex9p -fa -m ../data/periodic-cube.mesh -d cuda
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -164,6 +167,7 @@ int main(int argc, char *argv[])
   int order = 3;
   bool pa = false;
   bool ea = false;
+   bool fa = false;
   const char *device_config = "cpu";
   int ode_solver_type = 4;
   double t_final = 10.0;
@@ -193,6 +197,8 @@ int main(int argc, char *argv[])
                  "--no-partial-assembly", "Enable Partial Assembly.");
   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
                  "--no-element-assembly", "Enable Element Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
   args.AddOption(&device_config, "-d", "--device",
                  "Device configuration string, see Device::Configure().");
   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -329,6 +335,12 @@ int main(int argc, char *argv[])
      m->SetAssemblyLevel(AssemblyLevel::ELEMENT);
      k->SetAssemblyLevel(AssemblyLevel::ELEMENT);
   }
+   else if (fa)
+   {
+      m->SetAssemblyLevel(AssemblyLevel::FULL);
+      k->SetAssemblyLevel(AssemblyLevel::FULL);
+   }
+
   m->AddDomainIntegrator(new MassIntegrator);
   k->AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
   k->AddInteriorFaceIntegrator(
@@ -565,29 +577,21 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
     M_solver(_M.ParFESpace()->GetComm()),
     z(_M.Height())
 {
-   bool pa = _M.GetAssemblyLevel()==AssemblyLevel::PARTIAL;
-   bool ea = _M.GetAssemblyLevel()==AssemblyLevel::ELEMENT;
-
-   if (pa || ea)
-   {
-      M.Reset(&_M, false);
-      K.Reset(&_K, false);
-   }
-   else
+   if (_M.GetAssemblyLevel()==AssemblyLevel::LEGACYFULL)
   {
      M.Reset(_M.ParallelAssemble(), true);
      K.Reset(_K.ParallelAssemble(), true);
   }
+   else
+   {
+      M.Reset(&_M, false);
+      K.Reset(&_K, false);
+   }

   M_solver.SetOperator(*M);

   Array<int> ess_tdof_list;
-   if (pa || ea)
-   {
-      M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
-      dg_solver = NULL;
-   }
-   else
+   if (_M.GetAssemblyLevel()==AssemblyLevel::LEGACYFULL)
   {
      HypreParMatrix &M_mat = *M.As<HypreParMatrix>();
      HypreParMatrix &K_mat = *K.As<HypreParMatrix>();
@@ -596,6 +600,11 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,

      dg_solver = new DG_Solver(M_mat, K_mat, *_M.FESpace());
   }
+   else
+   {
+      M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
+      dg_solver = NULL;
+   }

   M_solver.SetPreconditioner(*M_prec);
   M_solver.iterative_mode = false;
@@ -76,7 +76,7 @@ BilinearForm::BilinearForm(FiniteElementSpace * f)
   precompute_sparsity = 0;
   diag_policy = DIAG_KEEP;

-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
   batch = 1;
   ext = NULL;
 }
@@ -94,7 +94,7 @@ BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
   precompute_sparsity = ps;
   diag_policy = DIAG_KEEP;

-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
   batch = 1;
   ext = NULL;

@@ -121,9 +121,10 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
   assembly = assembly_level;
   switch (assembly)
   {
+      case AssemblyLevel::LEGACYFULL:
+         break;
      case AssemblyLevel::FULL:
-         // ext = new FABilinearFormExtension(this);
-         // Use the original BilinearForm implementation for now
+         ext = new FABilinearFormExtension(this);
         break;
      case AssemblyLevel::ELEMENT:
         ext = new EABilinearFormExtension(this);
@@ -143,7 +144,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
 void BilinearForm::EnableStaticCondensation()
 {
   delete static_cond;
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
   {
      static_cond = NULL;
      MFEM_WARNING("Static condensation not supported for this assembly level");
@@ -168,7 +169,7 @@ void BilinearForm::EnableHybridization(FiniteElementSpace *constr_space,
                                       const Array<int> &ess_tdof_list)
 {
   delete hybridization;
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
   {
      delete constr_integ;
      hybridization = NULL;
@@ -223,7 +224,7 @@ MatrixInverse * BilinearForm::Inverse() const

 void BilinearForm::Finalize (int skip_zeros)
 {
-   if (assembly == AssemblyLevel::FULL)
+   if (assembly == AssemblyLevel::LEGACYFULL)
   {
      if (!static_cond) { mat->Finalize(skip_zeros); }
      if (mat_e) { mat_e->Finalize(skip_zeros); }
@@ -639,8 +640,7 @@ void BilinearForm::AssembleDiagonal(Vector &diag) const
   }
   else
   {
-      MFEM_ABORT("Not implemented. Maybe assemble your bilinear form into a "
-                 "matrix and use SparseMatrix::GetDiag?");
+      mat->GetDiag(diag);
   }
 }

@@ -1083,7 +1083,7 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
   mat = NULL;
   mat_e = NULL;
   extern_bfs = 0;
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
   ext = NULL;
 }

@@ -1108,7 +1108,7 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
   bbfi_marker = mbf->bbfi_marker;
   btfbfi_marker = mbf->btfbfi_marker;

-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
   ext = NULL;
 }

@@ -1121,6 +1121,8 @@ void MixedBilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
   assembly = assembly_level;
   switch (assembly)
   {
+      case AssemblyLevel::LEGACYFULL:
+         break;
      case AssemblyLevel::FULL:
         // ext = new FAMixedBilinearFormExtension(this);
         // Use the original BilinearForm implementation for now
@@ -1191,7 +1193,7 @@ void MixedBilinearForm::AddMultTranspose(const Vector & x, Vector & y,

 MatrixInverse * MixedBilinearForm::Inverse() const
 {
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
   {
      MFEM_WARNING("MixedBilinearForm::Inverse not possible with this assembly level!");
      return NULL;
@@ -1204,7 +1206,7 @@ MatrixInverse * MixedBilinearForm::Inverse() const

 void MixedBilinearForm::Finalize (int skip_zeros)
 {
-   if (assembly == AssemblyLevel::FULL)
+   if (assembly == AssemblyLevel::LEGACYFULL)
   {
      mat -> Finalize (skip_zeros);
   }
@@ -1481,7 +1483,7 @@ void MixedBilinearForm::AssembleDiagonal_ADAt(const Vector &D,

 void MixedBilinearForm::ConformingAssemble()
 {
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
   {
      MFEM_WARNING("Conforming assemble not supported for this assembly level!");
      return;
@@ -29,8 +29,11 @@ namespace mfem
    form classes derived from Operator. */
 enum class AssemblyLevel
 {
-   /// Fully assembled form, i.e. a global sparse matrix in MFEM, Hypre or PETSC
-   /// format.
+   /// Legacy fully assembled form, i.e. a global sparse matrix in MFEM, Hypre
+   /// or PETSC format. This assembly is ALWAYS performed on the host.
+   LEGACYFULL = 0,
+   /// Fully assembled form, i.e. a global sparse matrix in MFEM format. This
+   /// assembly is compatible with device execution.
   FULL,
   /// Form assembled at element level, which computes and stores dense element
   /// matrices.
@@ -119,7 +122,7 @@ protected:
      static_cond = NULL; hybridization = NULL;
      precompute_sparsity = 0;
      diag_policy = DIAG_KEEP;
-      assembly = AssemblyLevel::FULL;
+      assembly = AssemblyLevel::LEGACYFULL;
      batch = 1;
      ext = NULL;
   }
@@ -15,6 +15,7 @@
 #include "../general/forall.hpp"
 #include "bilinearform.hpp"
 #include "libceed/ceed.hpp"
+#include "pgridfunc.hpp"

 namespace mfem
 {
@@ -292,7 +293,8 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const

 // Data and methods for element-assembled bilinear forms
 EABilinearFormExtension::EABilinearFormExtension(BilinearForm *form)
-   : PABilinearFormExtension(form)
+   : PABilinearFormExtension(form),
+     factorize_face_terms(form->FESpace()->IsDGSpace())
 {
 }

@@ -347,6 +349,17 @@ void EABilinearFormExtension::Assemble()
   {
      bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr);
   }
+
+   if (factorize_face_terms && int_face_restrict_lex)
+   {
+      auto restFint = dynamic_cast<const L2FaceRestriction&>(*int_face_restrict_lex);
+      restFint.AddFaceMatricesToElementMatrices(ea_data_int, ea_data);
+   }
+   if (factorize_face_terms && bdr_face_restrict_lex)
+   {
+      auto restFbdr = dynamic_cast<const L2FaceRestriction&>(*bdr_face_restrict_lex);
+      restFbdr.AddFaceMatricesToElementMatrices(ea_data_bdr, ea_data);
+   }
 }

 void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
@@ -399,24 +412,27 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
         const int NDOFS = faceDofs;
         auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
         auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
+         if (!factorize_face_terms)
         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
+            auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
+            MFEM_FORALL(glob_j, nf_int*NDOFS,
            {
-               res += A_int(i, j, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(i, j, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
+               const int f = glob_j/NDOFS;
+               const int j = glob_j%NDOFS;
+               double res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(i, j, 0, f)*X(i, 0, f);
+               }
+               Y(j, 0, f) += res;
+               res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(i, j, 1, f)*X(i, 1, f);
+               }
+               Y(j, 1, f) += res;
+            });
+         }
         auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
         MFEM_FORALL(glob_j, nf_int*NDOFS,
         {
@@ -443,7 +459,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
   // Treatment of boundary faces
   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
   const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
+   if (!factorize_face_terms && bdr_face_restrict_lex && bFISz>0)
   {
      // Apply the Boundary Face Restriction
      bdr_face_restrict_lex->Mult(x, faceBdrX);
@@ -522,24 +538,27 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         const int NDOFS = faceDofs;
         auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
         auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
+         if (!factorize_face_terms)
         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
+            auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
+            MFEM_FORALL(glob_j, nf_int*NDOFS,
            {
-               res += A_int(j, i, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(j, i, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
+               const int f = glob_j/NDOFS;
+               const int j = glob_j%NDOFS;
+               double res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(j, i, 0, f)*X(i, 0, f);
+               }
+               Y(j, 0, f) += res;
+               res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(j, i, 1, f)*X(i, 1, f);
+               }
+               Y(j, 1, f) += res;
+            });
+         }
         auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
         MFEM_FORALL(glob_j, nf_int*NDOFS,
         {
@@ -566,7 +585,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
   // Treatment of boundary faces
   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
   const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
+   if (!factorize_face_terms && bdr_face_restrict_lex && bFISz>0)
   {
      // Apply the Boundary Face Restriction
      bdr_face_restrict_lex->Mult(x, faceBdrX);
@@ -595,6 +614,139 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
   }
 }

+// Data and methods for fully-assembled bilinear forms
+FABilinearFormExtension::FABilinearFormExtension(BilinearForm *form)
+   : EABilinearFormExtension(form),
+     mat(form->FESpace()->GetVSize(),form->FESpace()->GetVSize(),0),
+     face_mat(form->FESpace()->GetVSize(),0,0),
+     use_face_mat(false)
+{
+#ifdef MFEM_USE_MPI
+   if ( ParFiniteElementSpace* pfes =
+           dynamic_cast<ParFiniteElementSpace*>(form->FESpace()) )
+   {
+      if (pfes->IsDGSpace())
+      {
+         use_face_mat = true;
+         pfes->ExchangeFaceNbrData();
+         face_mat.SetWidth(pfes->GetFaceNbrVSize());
+      }
+   }
+#endif
+}
+
+void FABilinearFormExtension::Assemble()
+{
+   EABilinearFormExtension::Assemble();
+   FiniteElementSpace &fes = *a->FESpace();
+   if (fes.IsDGSpace())
+   {
+      const L2ElementRestriction *restE =
+         static_cast<const L2ElementRestriction*>(elem_restrict);
+      const L2FaceRestriction *restF =
+         static_cast<const L2FaceRestriction*>(int_face_restrict_lex);
+      // 1. Fill I
+      //  1.1 Increment with restE
+      restE->FillI(mat);
+      //  1.2 Increment with restF
+      if (restF) { restF->FillI(mat, face_mat); }
+      //  1.3 Sum the non-zeros in I
+      auto h_I = mat.HostReadWriteI();
+      int cpt = 0;
+      const int vd = fes.GetVDim();
+      const int ndofs = ne*elemDofs*vd;
+      for (int i = 0; i < ndofs; i++)
+      {
+         const int nnz = h_I[i];
+         h_I[i] = cpt;
+         cpt += nnz;
+      }
+      const int nnz = cpt;
+      h_I[ndofs] = nnz;
+      mat.GetMemoryJ().New(nnz, mat.GetMemoryJ().GetMemoryType());
+      mat.GetMemoryData().New(nnz, mat.GetMemoryData().GetMemoryType());
+      if (use_face_mat && restF)
+      {
+         auto h_I_face = face_mat.HostReadWriteI();
+         int cpt = 0;
+         for (int i = 0; i < ndofs; i++)
+         {
+            const int nnz = h_I_face[i];
+            h_I_face[i] = cpt;
+            cpt += nnz;
+         }
+         const int nnz_face = cpt;
+         h_I_face[ndofs] = nnz_face;
+         face_mat.GetMemoryJ().New(nnz_face,
+                                   face_mat.GetMemoryJ().GetMemoryType());
+         face_mat.GetMemoryData().New(nnz_face,
+                                      face_mat.GetMemoryData().GetMemoryType());
+      }
+      // 2. Fill J and Data
+      // 2.1 Fill J and Data with Elem ea_data
+      restE->FillJAndData(ea_data, mat);
+      // 2.2 Fill J and Data with Face ea_data_ext
+      if (restF) { restF->FillJAndData(ea_data_ext, mat, face_mat); }
+      // 2.3 Shift indirections in I back to original
+      auto I = mat.HostReadWriteI();
+      for (int i = ndofs; i > 0; i--)
+      {
+         I[i] = I[i-1];
+      }
+      I[0] = 0;
+      if (use_face_mat && restF)
+      {
+         auto I_face = face_mat.HostReadWriteI();
+         for (int i = ndofs; i > 0; i--)
+         {
+            I_face[i] = I_face[i-1];
+         }
+         I_face[0] = 0;
+      }
+   }
+   else // continuous Galerkin case
+   {
+      const ElementRestriction &rest =
+         static_cast<const ElementRestriction&>(*elem_restrict);
+      rest.FillSparseMatrix(ea_data, mat);
+   }
+}
+
+void FABilinearFormExtension::Mult(const Vector &x, Vector &y) const
+{
+   mat.Mult(x, y);
+#ifdef MFEM_USE_MPI
+   if (const ParFiniteElementSpace *pfes =
+          dynamic_cast<const ParFiniteElementSpace*>(testFes))
+   {
+      ParGridFunction x_gf;
+      x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(pfes),
+                   const_cast<Vector&>(x),0);
+      x_gf.ExchangeFaceNbrData();
+      Vector &shared_x = x_gf.FaceNbrData();
+      if (shared_x.Size()) { face_mat.AddMult(shared_x, y); }
+   }
+#endif
+}
+
+void FABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
+{
+   mat.MultTranspose(x, y);
+#ifdef MFEM_USE_MPI
+   if (const ParFiniteElementSpace *pfes =
+          dynamic_cast<const ParFiniteElementSpace*>(testFes))
+   {
+      ParGridFunction x_gf;
+      x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(pfes),
+                   const_cast<Vector&>(x),0);
+      x_gf.ExchangeFaceNbrData();
+      Vector &shared_x = x_gf.FaceNbrData();
+      if (shared_x.Size()) { face_mat.AddMultTranspose(shared_x, y); }
+   }
+#endif
+}
+
+
 MixedBilinearFormExtension::MixedBilinearFormExtension(MixedBilinearForm *form)
   : Operator(form->Height(), form->Width()), a(form)
 {
@@ -62,27 +62,6 @@ public:
   virtual void Update() = 0;
 };

-/** @brief Data and methods for fully-assembled bilinear forms.
-    Not yet implemented!  Use the BilinearForm Class instead. */
-class FABilinearFormExtension : public BilinearFormExtension
-{
-public:
-   FABilinearFormExtension(BilinearForm *form)
-      : BilinearFormExtension(form) { }
-
-   /// TODO
-   void Assemble() {}
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A) {}
-   void FormLinearSystem(const Array<int> &ess_tdof_list,
-                         Vector &x, Vector &b,
-                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0) {}
-   void Mult(const Vector &x, Vector &y) const {}
-   void MultTranspose(const Vector &x, Vector &y) const {}
-   void Update() {}
-   ~FABilinearFormExtension() {}
-};
-
 /// Data and methods for partially-assembled bilinear forms
 class PABilinearFormExtension : public BilinearFormExtension
 {
@@ -119,10 +98,12 @@ class EABilinearFormExtension : public PABilinearFormExtension
 protected:
   int ne;
   int elemDofs;
+   // The element matrices are stored row major
   Vector ea_data;
   int nf_int, nf_bdr;
   int faceDofs;
   Vector ea_data_int, ea_data_ext, ea_data_bdr;
+   bool factorize_face_terms;

 public:
   EABilinearFormExtension(BilinearForm *form);
@@ -132,6 +113,23 @@ public:
   void MultTranspose(const Vector &x, Vector &y) const;
 };

+/// Data and methods for fully-assembled bilinear forms
+class FABilinearFormExtension : public EABilinearFormExtension
+{
+private:
+   SparseMatrix mat;
+   /// face_mat handles parallelism for DG face terms.
+   SparseMatrix face_mat;
+   bool use_face_mat;
+
+public:
+   FABilinearFormExtension(BilinearForm *form);
+
+   void Assemble();
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+};
+
 /// Data and methods for matrix-free bilinear forms NOT YET IMPLEMENTED.
 class MFBilinearFormExtension : public BilinearFormExtension
 {
@@ -1522,6 +1522,7 @@ void CurlCurlIntegrator::AssembleElementMatrix
   double w;

 #ifdef MFEM_THREAD_SAFE
+   Vector D;
   DenseMatrix curlshape(nd,dimc), curlshape_dFt(nd,dimc), M;
 #else
   curlshape.SetSize(nd,dimc);
@@ -1529,6 +1530,7 @@ void CurlCurlIntegrator::AssembleElementMatrix
 #endif
   elmat.SetSize(nd);
   if (MQ) { M.SetSize(dimc); }
+   if (DQ) { D.SetSize(dimc); }

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
@@ -1572,6 +1574,12 @@ void CurlCurlIntegrator::AssembleElementMatrix
         Mult(curlshape_dFt, M, curlshape);
         AddMultABt(curlshape, curlshape_dFt, elmat);
      }
+      else if (DQ)
+      {
+         DQ->Eval(D, Trans, ip);
+         D *= w;
+         AddMultADAt(curlshape_dFt, D, elmat);
+      }
      else if (Q)
      {
         w *= Q->Eval(Trans, ip);
@@ -20,6 +20,13 @@
 namespace mfem
 {

+// Local maximum size of dofs and quads in 1D
+constexpr int HCURL_MAX_D1D = 5;
+constexpr int HCURL_MAX_Q1D = 6;
+
+constexpr int HDIV_MAX_D1D = 5;
+constexpr int HDIV_MAX_Q1D = 6;
+
 /// Abstract base class BilinearFormIntegrator
 class BilinearFormIntegrator : public NonlinearFormIntegrator
 {
@@ -1685,6 +1692,22 @@ protected:
   {
      trial_fe.CalcPhysCurlShape(Trans, shape);
   }
+
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, dofs1Dtest,quad1D, testType, trialType, coeffDim;
 };

 /** Class for integrating the bilinear form a(u,v) := (Q u, curl v) in 3D and
@@ -1724,6 +1747,20 @@ protected:
   {
      test_fe.CalcPhysCurlShape(Trans, shape);
   }
+
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, quad1D, testType, trialType, coeffDim;
 };

 /** Class for integrating the bilinear form a(u,v) := - (Q u, grad v) in either
@@ -2263,12 +2300,14 @@ class CurlCurlIntegrator: public BilinearFormIntegrator
 private:
   Vector vec, pointflux;
 #ifndef MFEM_THREAD_SAFE
+   Vector D;
   DenseMatrix curlshape, curlshape_dFt, M;
   DenseMatrix vshape, projcurl;
 #endif

 protected:
   Coefficient *Q;
+   VectorCoefficient *DQ;
   MatrixCoefficient *MQ;

   // PA extension
@@ -2277,12 +2316,17 @@ protected:
   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
   const GeometricFactors *geom;   ///< Not owned
   int dim, ne, nq, dofs1D, quad1D;
+   bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient

 public:
-   CurlCurlIntegrator() { Q = NULL; MQ = NULL; }
+   CurlCurlIntegrator() { Q = NULL; DQ = NULL; MQ = NULL; }
   /// Construct a bilinear form integrator for Nedelec elements
-   CurlCurlIntegrator(Coefficient &q) : Q(&q) { MQ = NULL; }
-   CurlCurlIntegrator(MatrixCoefficient &m) : MQ(&m) { Q = NULL; }
+   CurlCurlIntegrator(Coefficient &q, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), Q(&q) { DQ = NULL; MQ = NULL; }
+   CurlCurlIntegrator(VectorCoefficient &dq, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), DQ(&dq) { Q = NULL; MQ = NULL; }
+   CurlCurlIntegrator(MatrixCoefficient &mq, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), MQ(&mq) { Q = NULL; DQ = NULL; }

   /* Given a particular Finite Element, compute the
      element curl-curl matrix elmat */
@@ -2360,8 +2404,11 @@ protected:
   Vector pa_data;
   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
   const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, nq, dofs1D, quad1D, fetype;
+   int dim, ne, nq, dofs1D, dofs1Dtest, quad1D, trial_fetype, test_fetype;
+   bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient

 public:
   VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
@@ -2382,6 +2429,8 @@ public:

   using BilinearFormIntegrator::AssemblePA;
   virtual void AssemblePA(const FiniteElementSpace &fes);
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
   virtual void AddMultPA(const Vector &x, Vector &y) const;
   virtual void AssembleDiagonalPA(Vector& diag);
 };
@@ -32,7 +32,7 @@ static void EAConvectionAssemble1D(const int NE,
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -54,7 +54,7 @@ static void EAConvectionAssemble1D(const int NE,
            {
               val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
            }
-            A(i1, j1, e) = val;
+            A(i1, j1, e) += val;
         }
      }
   });
@@ -76,7 +76,7 @@ static void EAConvectionAssemble2D(const int NE,
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, 2, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -121,7 +121,7 @@ static void EAConvectionAssemble2D(const int NE,
                               * r_B[k1][j1]* r_B[k2][j2];
                     }
                  }
-                  A(i1, i2, j1, j2, e) = val;
+                  A(i1, i2, j1, j2, e) += val;
               }
            }
         }
@@ -145,7 +145,7 @@ static void EAConvectionAssemble3D(const int NE,
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -191,7 +191,7 @@ static void EAConvectionAssemble3D(const int NE,
                              }
                           }
                        }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                        A(i1, i2, i3, j1, j2, j3, e) += val;
                     }
                  }
               }
@@ -788,6 +788,20 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   {
      vel = cQ->GetVec();
   }
+   else if (VectorQuadratureFunctionCoefficient* cQ =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == dim * nq * ne,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+
+      qFun.Read();
+      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
   else
   {
      vel.SetSize(dim * nq * ne);
@@ -167,6 +167,19 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
      r.SetSize(1);
      r(0) = c_rho->constant;
   }
+   else if (QuadratureFunctionCoefficient* c_rho =
+               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
+   {
+      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
   else
   {
      r.SetSize(nq * nf);
@@ -200,6 +213,20 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
   {
      vel = c_u->GetVec();
   }
+   else if (VectorQuadratureFunctionCoefficient* c_u =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(u))
+   {
+      // Assumed to be in lexicographical ordering
+      const QuadratureFunction &qFun = c_u->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == dim * nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
   else
   {
      vel.SetSize(dim * nq * nf);
@@ -31,7 +31,7 @@ static void EADiffusionAssemble1D(const int NE,
   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -53,7 +53,7 @@ static void EADiffusionAssemble1D(const int NE,
            {
               val += r_Gj[k1] * D(k1, e) * r_Gi[k1];
            }
-            A(i1, j1, e) = val;
+            A(i1, j1, e) += val;
         }
      }
   });
@@ -75,7 +75,7 @@ static void EADiffusionAssemble2D(const int NE,
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -120,7 +120,7 @@ static void EADiffusionAssemble2D(const int NE,
                               + gbi * D11 * gbj;
                     }
                  }
-                  A(i1, i2, j1, j2, e) = val;
+                  A(i1, i2, j1, j2, e) += val;
               }
            }
         }
@@ -144,7 +144,7 @@ static void EADiffusionAssemble3D(const int NE,
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 6, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -208,7 +208,7 @@ static void EADiffusionAssemble3D(const int NE,
                              }
                           }
                        }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                        A(i1, i2, i3, j1, j2, j3, e) += val;
                     }
                  }
               }
@@ -296,6 +296,19 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
      coeff.SetSize(1);
      coeff(0) = cQ->constant;
   }
+   else if (QuadratureFunctionCoefficient* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == ne*nq,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
   else
   {
      coeff.SetSize(nq * ne);
@@ -1307,7 +1320,33 @@ static void PADiffusionApply3D(const int NE,
   });
 }

-// Shared memory PA Diffusion Apply 3D kernel
+// Half of B and G are stored in shared to get B, Bt, G and Gt.
+// Indices computation for SmemPADiffusionApply3D.
+static MFEM_HOST_DEVICE inline int qi(const int q, const int d, const int Q)
+{
+   return (q<=d) ? q : Q-1-q;
+}
+
+static MFEM_HOST_DEVICE inline int dj(const int q, const int d, const int D)
+{
+   return (q<=d) ? d : D-1-d;
+}
+
+static MFEM_HOST_DEVICE inline int qk(const int q, const int d, const int Q)
+{
+   return (q<=d) ? Q-1-q : q;
+}
+
+static MFEM_HOST_DEVICE inline int dl(const int q, const int d, const int D)
+{
+   return (q<=d) ? D-1-d : d;
+}
+
+static MFEM_HOST_DEVICE inline double sign(const int q, const int d)
+{
+   return (q<=d) ? -1.0 : 1.0;
+}
+
 template<int T_D1D = 0, int T_Q1D = 0>
 static void SmemPADiffusionApply3D(const int NE,
                                   const Array<double> &b_,
@@ -1320,28 +1359,27 @@ static void SmemPADiffusionApply3D(const int NE,
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-   MFEM_VERIFY(D1D <= MD1, "");
-   MFEM_VERIFY(Q1D <= MQ1, "");
+   constexpr int M1Q = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int M1D = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= M1D, "");
+   MFEM_VERIFY(Q1D <= M1Q, "");
   auto b = Reshape(b_.Read(), Q1D, D1D);
   auto g = Reshape(g_.Read(), Q1D, D1D);
-   auto d = Reshape(d_.Read(), Q1D*Q1D*Q1D, 6, NE);
+   auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, 6, NE);
   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, 1,
   {
-      const int tidz = MFEM_THREAD_ID(z);
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
-      MFEM_SHARED double sBG[2][MQ1*MD1];
-      double (*B)[MD1] = (double (*)[MD1]) (sBG+0);
-      double (*G)[MD1] = (double (*)[MD1]) (sBG+1);
-      double (*Bt)[MQ1] = (double (*)[MQ1]) (sBG+0);
-      double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double sBG[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) sBG;
+      double (*G)[MD1] = (double (*)[MD1]) sBG;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) sBG;
+      double (*Gt)[MQ1] = (double (*)[MQ1]) sBG;
      MFEM_SHARED double sm0[3][MDQ*MDQ*MDQ];
      MFEM_SHARED double sm1[3][MDQ*MDQ*MDQ];
      double (*X)[MD1][MD1]    = (double (*)[MD1][MD1]) (sm0+2);
@@ -1359,108 +1397,127 @@ static void SmemPADiffusionApply3D(const int NE,
      double (*QDD0)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+0);
      double (*QDD1)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+1);
      double (*QDD2)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+2);
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD(dy,y,D1D)
      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD(dx,x,D1D)
         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
            {
               X[dz][dy][dx] = x(dx,dy,dz,e);
            }
         }
-      }
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B[q][d] = b(q,d);
-               G[q][d] = g(q,d);
-            }
+            const int i = qi(qx,dy,Q1D);
+            const int j = dj(qx,dy,D1D);
+            const int k = qk(qx,dy,Q1D);
+            const int l = dl(qx,dy,D1D);
+            B[i][j] = b(qx,dy);
+            G[k][l] = g(qx,dy) * sign(qx,dy);
         }
      }
      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD(dy,y,D1D)
      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            double u[D1D], v[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++) { u[dz] = v[dz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dx = 0; dx < D1D; ++dx)
            {
-               double u = 0.0;
-               double v = 0.0;
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const double coords = X[dz][dy][dx];
-                  u += coords * B[qx][dx];
-                  v += coords * G[qx][dx];
-               }
-               DDQ0[dz][dy][qx] = u;
-               DDQ1[dz][dy][qx] = v;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int dy = 0; dy < D1D; ++dy)
-               {
-                  u += DDQ1[dz][dy][qx] * B[qy][dy];
-                  v += DDQ0[dz][dy][qx] * G[qy][dy];
-                  w += DDQ0[dz][dy][qx] * B[qy][dy];
-               }
-               DQQ0[dz][qy][qx] = u;
-               DQQ1[dz][qy][qx] = v;
-               DQQ2[dz][qy][qx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
+               const int i = qi(qx,dx,Q1D);
+               const int j = dj(qx,dx,D1D);
+               const int k = qk(qx,dx,Q1D);
+               const int l = dl(qx,dx,D1D);
+               const double s = sign(qx,dx);
+               MFEM_UNROLL(MD1)
               for (int dz = 0; dz < D1D; ++dz)
               {
-                  u += DQQ0[dz][qy][qx] * B[qz][dz];
-                  v += DQQ1[dz][qy][qx] * B[qz][dz];
-                  w += DQQ2[dz][qy][qx] * G[qz][dz];
+                  const double coords = X[dz][dy][dx];
+                  u[dz] += coords * B[i][j];
+                  v[dz] += coords * G[k][l] * s;
               }
-               QQQ0[qz][qy][qx] = u;
-               QQQ1[qz][qy][qx] = v;
-               QQQ2[qz][qy][qx] = w;
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               DDQ0[dz][dy][qx] = u[dz];
+               DDQ1[dz][dy][qx] = v[dz];
            }
         }
      }
      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            double u[D1D], v[D1D], w[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++) { u[dz] = v[dz] = w[dz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dy = 0; dy < D1D; ++dy)
            {
-               const int q = qx + ((qy*Q1D) + (qz*Q1D*Q1D));
-               const double O11 = d(q,0,e);
-               const double O12 = d(q,1,e);
-               const double O13 = d(q,2,e);
-               const double O22 = d(q,3,e);
-               const double O23 = d(q,4,e);
-               const double O33 = d(q,5,e);
-               const double gX = QQQ0[qz][qy][qx];
-               const double gY = QQQ1[qz][qy][qx];
-               const double gZ = QQQ2[qz][qy][qx];
+               const int i = qi(qy,dy,Q1D);
+               const int j = dj(qy,dy,D1D);
+               const int k = qk(qy,dy,Q1D);
+               const int l = dl(qy,dy,D1D);
+               const double s = sign(qy,dy);
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < D1D; dz++)
+               {
+                  u[dz] += DDQ1[dz][dy][qx] * B[i][j];
+                  v[dz] += DDQ0[dz][dy][qx] * G[k][l] * s;
+                  w[dz] += DDQ0[dz][dy][qx] * B[i][j];
+               }
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++)
+            {
+               DQQ0[dz][qy][qx] = u[dz];
+               DQQ1[dz][qy][qx] = v[dz];
+               DQQ2[dz][qy][qx] = w[dz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; qz++) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; qz++)
+               {
+                  const int i = qi(qz,dz,Q1D);
+                  const int j = dj(qz,dz,D1D);
+                  const int k = qk(qz,dz,Q1D);
+                  const int l = dl(qz,dz,D1D);
+                  const double s = sign(qz,dz);
+                  u[qz] += DQQ0[dz][qy][qx] * B[i][j];
+                  v[qz] += DQQ1[dz][qy][qx] * B[i][j];
+                  w[qz] += DQQ2[dz][qy][qx] * G[k][l] * s;
+               }
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; qz++)
+            {
+               const double O11 = d(qx,qy,qz,0,e);
+               const double O12 = d(qx,qy,qz,1,e);
+               const double O13 = d(qx,qy,qz,2,e);
+               const double O22 = d(qx,qy,qz,3,e);
+               const double O23 = d(qx,qy,qz,4,e);
+               const double O33 = d(qx,qy,qz,5,e);
+               const double gX = u[qz];
+               const double gY = v[qz];
+               const double gZ = w[qz];
               QQQ0[qz][qy][qx] = (O11*gX) + (O12*gY) + (O13*gZ);
               QQQ1[qz][qy][qx] = (O12*gX) + (O22*gY) + (O23*gZ);
               QQQ2[qz][qy][qx] = (O13*gX) + (O23*gY) + (O33*gZ);
@@ -1468,78 +1525,112 @@ static void SmemPADiffusionApply3D(const int NE,
         }
      }
      MFEM_SYNC_THREAD;
-      if (tidz == 0)
+      MFEM_FOREACH_THREAD(d,y,D1D)
      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
+         MFEM_FOREACH_THREAD(q,x,Q1D)
         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               Bt[d][q] = b(q,d);
-               Gt[d][q] = g(q,d);
-            }
+            const int i = qi(q,d,Q1D);
+            const int j = dj(q,d,D1D);
+            const int k = qk(q,d,Q1D);
+            const int l = dl(q,d,D1D);
+            Bt[j][i] = b(q,d);
+            Gt[l][k] = g(q,d) * sign(q,d);
         }
      }
      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD(dx,x,D1D)
         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qx = 0; qx < Q1D; ++qx)
            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  u += QQQ0[qz][qy][qx] * Gt[dx][qx];
-                  v += QQQ1[qz][qy][qx] * Bt[dx][qx];
-                  w += QQQ2[qz][qy][qx] * Bt[dx][qx];
-               }
-               QQD0[qz][qy][dx] = u;
-               QQD1[qz][qy][dx] = v;
-               QQD2[qz][qy][dx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int qy = 0; qy < Q1D; ++qy)
-               {
-                  u += QQD0[qz][qy][dx] * Bt[dy][qy];
-                  v += QQD1[qz][qy][dx] * Gt[dy][qy];
-                  w += QQD2[qz][qy][dx] * Bt[dy][qy];
-               }
-               QDD0[qz][dy][dx] = u;
-               QDD1[qz][dy][dx] = v;
-               QDD2[qz][dy][dx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
+               const int i = qi(qx,dx,Q1D);
+               const int j = dj(qx,dx,D1D);
+               const int k = qk(qx,dx,Q1D);
+               const int l = dl(qx,dx,D1D);
+               const double s = sign(qx,dx);
+               MFEM_UNROLL(MQ1)
               for (int qz = 0; qz < Q1D; ++qz)
               {
-                  u += QDD0[qz][dy][dx] * Bt[dz][qz];
-                  v += QDD1[qz][dy][dx] * Bt[dz][qz];
-                  w += QDD2[qz][dy][dx] * Gt[dz][qz];
+                  u[qz] += QQQ0[qz][qy][qx] * Gt[l][k] * s;
+                  v[qz] += QQQ1[qz][qy][qx] * Bt[j][i];
+                  w[qz] += QQQ2[qz][qy][qx] * Bt[j][i];
               }
-               y(dx,dy,dz,e) += (u + v + w);
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               QQD0[qz][qy][dx] = u[qz];
+               QQD1[qz][qy][dx] = v[qz];
+               QQD2[qz][qy][dx] = w[qz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const int i = qi(qy,dy,Q1D);
+               const int j = dj(qy,dy,D1D);
+               const int k = qk(qy,dy,Q1D);
+               const int l = dl(qy,dy,D1D);
+               const double s = sign(qy,dy);
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  u[qz] += QQD0[qz][qy][dx] * Bt[j][i];
+                  v[qz] += QQD1[qz][qy][dx] * Gt[l][k] * s;
+                  w[qz] += QQD2[qz][qy][dx] * Bt[j][i];
+               }
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               QDD0[qz][dy][dx] = u[qz];
+               QDD1[qz][dy][dx] = v[qz];
+               QDD2[qz][dy][dx] = w[qz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u[D1D], v[D1D], w[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz) { u[dz] = v[dz] = w[dz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < D1D; ++dz)
+               {
+                  const int i = qi(qz,dz,Q1D);
+                  const int j = dj(qz,dz,D1D);
+                  const int k = qk(qz,dz,Q1D);
+                  const int l = dl(qz,dz,D1D);
+                  const double s = sign(qz,dz);
+                  u[dz] += QDD0[qz][dy][dx] * Bt[j][i];
+                  v[dz] += QDD1[qz][dy][dx] * Bt[j][i];
+                  w[dz] += QDD2[qz][dy][dx] * Gt[l][k] * s;
+               }
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               y(dx,dy,dz,e) += (u[dz] + v[dz] + w[dz]);
            }
         }
      }
@@ -1574,9 +1665,11 @@ static void PADiffusionApply(const int dim,
      MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
   }
 #endif // MFEM_USE_OCCA
+   const int ID = (D1D << 4 ) | Q1D;
+
   if (dim == 2)
   {
-      switch ((D1D << 4 ) | Q1D)
+      switch (ID)
      {
         case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,D,X,Y);
         case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,D,X,Y);
@@ -1589,9 +1682,10 @@ static void PADiffusionApply(const int dim,
         default:   return PADiffusionApply2D(NE,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
      }
   }
-   else if (dim == 3)
+
+   if (dim == 3)
   {
-      switch ((D1D << 4 ) | Q1D)
+      switch (ID)
      {
         case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,D,X,Y);
         case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,D,X,Y);
@@ -23,11 +23,6 @@ using namespace std;
 namespace mfem
 {

-// Local maximum size of dofs and quads in 1D
-constexpr int HDIV_MAX_D1D = 5;
-constexpr int HDIV_MAX_Q1D = 6;
-
-
 // PA H(div) Mass Assemble 2D kernel
 void PAHdivSetup2D(const int Q1D,
                   const int NE,
@@ -114,6 +109,8 @@ void PAHdivMassApply2D(const int D1D,
                       Vector &_y)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
@@ -238,6 +235,7 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
                                  Vector &_diag)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
@@ -614,6 +612,8 @@ static void PADivDivApply2D(const int D1D,
                            Vector &_y)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
   auto Bot = Reshape(_Bot.Read(), D1D-1, Q1D);
@@ -977,6 +977,7 @@ static void PADivDivAssembleDiagonal2D(const int D1D,
                                       Vector &_diag)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
   auto Gc = Reshape(_Gc.Read(), Q1D, D1D);
@@ -1400,6 +1401,8 @@ static void PAHdivL2Apply2D(const int D1D,
                            Vector &_y)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
   auto Gc = Reshape(_Gc.Read(), Q1D, D1D);
@@ -1666,6 +1669,8 @@ static void PAHdivL2ApplyTranspose2D(const int D1D,
                                     Vector &_y)
 {
   constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;

   auto L2Bo = Reshape(_L2Bo.Read(), Q1D, L2D1D);
   auto Gct = Reshape(_Gct.Read(), D1D, Q1D);
@@ -1724,7 +1729,7 @@ static void PAHdivL2ApplyTranspose2D(const int D1D,

      for (int qy = 0; qy < Q1D; ++qy)
      {
-         double aX[HDIV_MAX_D1D];
+         double aX[MAX_D1D];

         int osc = 0;
         for (int c = 0; c < VDIM; ++c)  // loop over x, y components
@@ -30,7 +30,7 @@ static void EAMassAssemble1D(const int NE,
   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
   auto B = Reshape(basis.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -52,7 +52,7 @@ static void EAMassAssemble1D(const int NE,
            {
               val += r_Bi[k1] * r_Bj[k1] * D(k1, e);
            }
-            M(i1, j1, e) = val;
+            M(i1, j1, e) += val;
         }
      }
   });
@@ -72,7 +72,7 @@ static void EAMassAssemble2D(const int NE,
   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
   auto B = Reshape(basis.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -114,7 +114,7 @@ static void EAMassAssemble2D(const int NE,
                               * s_D[k1][k2];
                     }
                  }
-                  M(i1, i2, j1, j2, e) = val;
+                  M(i1, i2, j1, j2, e) += val;
               }
            }
         }
@@ -136,7 +136,7 @@ static void EAMassAssemble3D(const int NE,
   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
   auto B = Reshape(basis.Read(), Q1D, D1D);
   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
@@ -189,7 +189,7 @@ static void EAMassAssemble3D(const int NE,
                              }
                           }
                        }
-                        M(i1, i2, i3, j1, j2, j3, e) = val;
+                        M(i1, i2, i3, j1, j2, j3, e) += val;
                     }
                  }
               }
@@ -41,6 +41,8 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
      InitCeedCoeff(Q, ptr);
      return CeedPAMassAssemble(fes, *ir, *ptr);
   }
+#else
+   MFEM_CONTRACT_VAR(force);
 #endif
   dim = mesh->Dimension();
   ne = fes.GetMesh()->GetNE();
@@ -62,6 +64,19 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
      coeff.SetSize(1);
      coeff(0) = cQ->constant;
   }
+   else if (QuadratureFunctionCoefficient* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * ne,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
   else
   {
      coeff.SetSize(nq * ne);
@@ -639,6 +654,7 @@ static void SmemPAMassApply2D(const int NE,
                              const int d1d = 0,
                              const int q1d = 0)
 {
+   MFEM_CONTRACT_VAR(bt_);
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
@@ -902,6 +918,7 @@ static void SmemPAMassApply3D(const int NE,
                              const int d1d = 0,
                              const int q1d = 0)
 {
+   MFEM_CONTRACT_VAR(bt_);
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   constexpr int M1Q = T_Q1D ? T_Q1D : MAX_Q1D;
@@ -25,7 +25,7 @@ void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
   if (ne == 0) { return; }
   const int dofs = fes.GetFE(0)->GetDof();
   auto A = Reshape(ea_data_tmp.Write(), dofs, dofs, ne);
-   auto AT = Reshape(ea_data.Write(), dofs, dofs, ne);
+   auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
   MFEM_FORALL(e, ne,
   {
      for (int i = 0; i < dofs; i++)
@@ -9,12 +9,14 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.

+#include "../general/forall.hpp"
 #include "bilininteg.hpp"

 namespace mfem
 {

 void PAHcurlSetup2D(const int Q1D,
+                    const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
@@ -22,6 +24,7 @@ void PAHcurlSetup2D(const int Q1D,
                    Vector &op);

 void PAHcurlSetup3D(const int Q1D,
+                    const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
@@ -31,6 +34,7 @@ void PAHcurlSetup3D(const int Q1D,
 void PAHcurlMassAssembleDiagonal2D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                   const bool symmetric,
                                   const Array<double> &_Bo,
                                   const Array<double> &_Bc,
                                   const Vector &_op,
@@ -39,6 +43,7 @@ void PAHcurlMassAssembleDiagonal2D(const int D1D,
 void PAHcurlMassAssembleDiagonal3D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                   const bool symmetric,
                                   const Array<double> &_Bo,
                                   const Array<double> &_Bc,
                                   const Vector &_op,
@@ -47,6 +52,7 @@ void PAHcurlMassAssembleDiagonal3D(const int D1D,
 void PAHcurlMassApply2D(const int D1D,
                        const int Q1D,
                        const int NE,
+                        const bool symmetric,
                        const Array<double> &_Bo,
                        const Array<double> &_Bc,
                        const Array<double> &_Bot,
@@ -58,6 +64,7 @@ void PAHcurlMassApply2D(const int D1D,
 void PAHcurlMassApply3D(const int D1D,
                        const int Q1D,
                        const int NE,
+                        const bool symmetric,
                        const Array<double> &_Bo,
                        const Array<double> &_Bc,
                        const Array<double> &_Bot,
@@ -140,20 +147,573 @@ void PAHdivMassApply3D(const int D1D,
                       const Vector &_x,
                       Vector &_y);

+void PAHcurlL2Setup(const int NQ,
+                    const int coeffDim,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &_coeff,
+                    Vector &op);
+
+// PA H(curl) x H(div) mass assemble 3D kernel, with factor
+// dF^{-1} C dF for a vector or matrix coefficient C.
+// If transpose, use dF^T C dF^{-T} for H(div) x H(curl).
+void PAHcurlHdivSetup3D(const int Q1D,
+                        const int coeffDim,
+                        const int NE,
+                        const bool transpose,
+                        const Array<double> &_w,
+                        const Vector &j,
+                        Vector &_coeff,
+                        Vector &op)
+{
+   const int NQ = Q1D*Q1D*Q1D;
+   const bool symmetric = (coeffDim != 9);
+   auto W = _w.Read();
+   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
+   auto coeff = Reshape(_coeff.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), 9, NQ, NE);
+
+   const int i11 = 0;
+   const int i12 = transpose ? 3 : 1;
+   const int i13 = transpose ? 6 : 2;
+   const int i21 = transpose ? 1 : 3;
+   const int i22 = 4;
+   const int i23 = transpose ? 7 : 5;
+   const int i31 = transpose ? 2 : 6;
+   const int i32 = transpose ? 5 : 7;
+   const int i33 = 8;
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J31 = J(q,2,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double J32 = J(q,2,1,e);
+         const double J13 = J(q,0,2,e);
+         const double J23 = J(q,1,2,e);
+         const double J33 = J(q,2,2,e);
+         const double detJ = J11 * (J22 * J33 - J32 * J23) -
+         /* */               J21 * (J12 * J33 - J32 * J13) +
+         /* */               J31 * (J12 * J23 - J22 * J13);
+         const double w_detJ = W[q] / detJ;
+         // adj(J)
+         const double A11 = (J22 * J33) - (J23 * J32);
+         const double A12 = (J32 * J13) - (J12 * J33);
+         const double A13 = (J12 * J23) - (J22 * J13);
+         const double A21 = (J31 * J23) - (J21 * J33);
+         const double A22 = (J11 * J33) - (J13 * J31);
+         const double A23 = (J21 * J13) - (J11 * J23);
+         const double A31 = (J21 * J32) - (J31 * J22);
+         const double A32 = (J31 * J12) - (J11 * J32);
+         const double A33 = (J11 * J22) - (J12 * J21);
+
+         if (coeffDim == 6 || coeffDim == 9) // Matrix coefficient version
+         {
+            // First compute entries of R = MJ
+            const double M11 = (!symmetric) ? coeff(i11, q, e) : coeff(0, q, e);
+            const double M12 = (!symmetric) ? coeff(i12, q, e) : coeff(1, q, e);
+            const double M13 = (!symmetric) ? coeff(i13, q, e) : coeff(2, q, e);
+            const double M21 = (!symmetric) ? coeff(i21, q, e) : M12;
+            const double M22 = (!symmetric) ? coeff(i22, q, e) : coeff(3, q, e);
+            const double M23 = (!symmetric) ? coeff(i23, q, e) : coeff(4, q, e);
+            const double M31 = (!symmetric) ? coeff(i31, q, e) : M13;
+            const double M32 = (!symmetric) ? coeff(i32, q, e) : M23;
+            const double M33 = (!symmetric) ? coeff(i33, q, e) : coeff(5, q, e);
+
+            const double R11 = M11*J11 + M12*J12 + M13*J13;
+            const double R12 = M11*J21 + M12*J22 + M13*J23;
+            const double R13 = M11*J31 + M12*J32 + M13*J33;
+            const double R21 = M21*J11 + M22*J12 + M23*J13;
+            const double R22 = M21*J21 + M22*J22 + M23*J23;
+            const double R23 = M21*J31 + M22*J32 + M23*J33;
+            const double R31 = M31*J11 + M32*J12 + M33*J13;
+            const double R32 = M31*J21 + M32*J22 + M33*J23;
+            const double R33 = M31*J31 + M32*J32 + M33*J33;
+
+            // Now set y to detJ J^{-1} R = adj(J) R
+            y(i11,q,e) = w_detJ * (A11*R11 + A12*R21 + A13*R31); // 1,1
+            y(i12,q,e) = w_detJ * (A11*R12 + A12*R22 + A13*R32); // 1,2
+            y(i13,q,e) = w_detJ * (A11*R13 + A12*R23 + A13*R33); // 1,3
+            y(i21,q,e) = w_detJ * (A21*R11 + A22*R21 + A23*R31); // 2,1
+            y(i22,q,e) = w_detJ * (A21*R12 + A22*R22 + A23*R32); // 2,2
+            y(i23,q,e) = w_detJ * (A21*R13 + A22*R23 + A23*R33); // 2,3
+            y(i31,q,e) = w_detJ * (A31*R11 + A32*R21 + A33*R31); // 3,1
+            y(i32,q,e) = w_detJ * (A31*R12 + A32*R22 + A33*R32); // 3,2
+            y(i33,q,e) = w_detJ * (A31*R13 + A32*R23 + A33*R33); // 3,3
+         }
+         else if (coeffDim == 3)  // Vector coefficient version
+         {
+            const double D1 = coeff(0, q, e);
+            const double D2 = coeff(1, q, e);
+            const double D3 = coeff(2, q, e);
+            // detJ J^{-1} DJ = adj(J) DJ
+            y(i11,q,e) = w_detJ * (D1*A11*J11 + D2*A12*J21 + D3*A13*J31); // 1,1
+            y(i12,q,e) = w_detJ * (D1*A11*J12 + D2*A12*J22 + D3*A13*J32); // 1,2
+            y(i13,q,e) = w_detJ * (D1*A11*J13 + D2*A12*J23 + D3*A13*J33); // 1,3
+            y(i21,q,e) = w_detJ * (D1*A21*J11 + D2*A22*J21 + D3*A23*J31); // 2,1
+            y(i22,q,e) = w_detJ * (D1*A21*J12 + D2*A22*J22 + D3*A23*J32); // 2,2
+            y(i23,q,e) = w_detJ * (D1*A21*J13 + D2*A22*J23 + D3*A23*J33); // 2,3
+            y(i31,q,e) = w_detJ * (D1*A31*J11 + D2*A32*J21 + D3*A33*J31); // 3,1
+            y(i32,q,e) = w_detJ * (D1*A31*J12 + D2*A32*J22 + D3*A33*J32); // 3,2
+            y(i33,q,e) = w_detJ * (D1*A31*J13 + D2*A32*J23 + D3*A33*J33); // 3,3
+         }
+      }
+   });
+}
+
+// PA H(curl) x H(div) mass assemble 2D kernel, with factor
+// dF^{-1} C dF for a vector or matrix coefficient C.
+// If transpose, use dF^T C dF^{-T} for H(div) x H(curl).
+void PAHcurlHdivSetup2D(const int Q1D,
+                        const int coeffDim,
+                        const int NE,
+                        const bool transpose,
+                        const Array<double> &_w,
+                        const Vector &j,
+                        Vector &_coeff,
+                        Vector &op)
+{
+   const int NQ = Q1D*Q1D;
+   const bool symmetric = (coeffDim != 4);
+   auto W = _w.Read();
+   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
+   auto coeff = Reshape(_coeff.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), 4, NQ, NE);
+
+   const int i11 = 0;
+   const int i12 = transpose ? 2 : 1;
+   const int i21 = transpose ? 1 : 2;
+   const int i22 = 3;
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double w_detJ = W[q] / (J11*J22) - (J21*J12);
+
+         if (coeffDim == 3 || coeffDim == 4) // Matrix coefficient version
+         {
+            // First compute entries of R = MJ
+            const double M11 = coeff(i11, q, e);
+            const double M12 = (!symmetric) ? coeff(i12, q, e) : coeff(1, q, e);
+            const double M21 = (!symmetric) ? coeff(i21, q, e) : M12;
+            const double M22 = (!symmetric) ? coeff(i22, q, e) : coeff(2, q, e);
+
+            const double R11 = M11*J11 + M12*J21;
+            const double R12 = M11*J12 + M12*J22;
+            const double R21 = M21*J11 + M22*J21;
+            const double R22 = M21*J12 + M22*J22;
+
+            // Now set y to J^{-1} R
+            y(i11,q,e) = w_detJ * ( J22*R11 - J12*R21); // 1,1
+            y(i12,q,e) = w_detJ * ( J22*R12 - J12*R22); // 1,2
+            y(i21,q,e) = w_detJ * (-J21*R11 + J11*R21); // 2,1
+            y(i22,q,e) = w_detJ * (-J21*R12 + J11*R22); // 2,2
+         }
+         else if (coeffDim == 2) // Vector coefficient version
+         {
+            const double D1 = coeff(0, q, e);
+            const double D2 = coeff(1, q, e);
+            const double R11 = D1*J11;
+            const double R12 = D1*J12;
+            const double R21 = D2*J21;
+            const double R22 = D2*J22;
+            y(i11,q,e) = w_detJ * ( J22*R11 - J12*R21); // 1,1
+            y(i12,q,e) = w_detJ * ( J22*R12 - J12*R22); // 1,2
+            y(i21,q,e) = w_detJ * (-J21*R11 + J11*R21); // 2,1
+            y(i22,q,e) = w_detJ * (-J21*R12 + J11*R22); // 2,2
+         }
+      }
+   });
+}
+
+// Mass operator for H(curl) and H(div) functions, using Piola transformations
+// u = dF^{-T} \hat{u} in H(curl), v = (1 / det dF) dF \hat{v} in H(div).
+void PAHcurlHdivMassApply3D(const int D1D,
+                            const int D1Dtest,
+                            const int Q1D,
+                            const int NE,
+                            const bool scalarCoeff,
+                            const bool trialHcurl,
+                            const Array<double> &_Bo,
+                            const Array<double> &_Bc,
+                            const Array<double> &_Bot,
+                            const Array<double> &_Bct,
+                            const Vector &_op,
+                            const Vector &_x,
+                            Vector &_y)
+{
+   constexpr static int MAX_D1D = HCURL_MAX_D1D;
+   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
+
+   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
+   constexpr static int VDIM = 3;
+
+   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
+   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
+   auto Bot = Reshape(_Bot.Read(), D1Dtest-1, Q1D);
+   auto Bct = Reshape(_Bct.Read(), D1Dtest, Q1D);
+   auto op = Reshape(_op.Read(), scalarCoeff ? 1 : 9, Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), 3*(D1D-1)*D1D*(trialHcurl ? D1D : D1D-1), NE);
+   auto y = Reshape(_y.ReadWrite(), 3*(D1Dtest-1)*D1Dtest*
+                    (trialHcurl ? D1Dtest-1 : D1Dtest), NE);
+
+   MFEM_FORALL(e, NE,
+   {
+      double mass[MAX_Q1D][MAX_Q1D][MAX_Q1D][VDIM];
+
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               for (int c = 0; c < VDIM; ++c)
+               {
+                  mass[qz][qy][qx][c] = 0.0;
+               }
+            }
+         }
+      }
+
+      int osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y, z trial components
+      {
+         const int D1Dz = trialHcurl ? ((c == 2) ? D1D - 1 : D1D) :
+                          ((c == 2) ? D1D : D1D - 1);
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1D - 1 : D1D) :
+                          ((c == 1) ? D1D : D1D - 1);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1D - 1 : D1D) :
+                          ((c == 0) ? D1D : D1D - 1);
+
+         for (int dz = 0; dz < D1Dz; ++dz)
+         {
+            double massXY[MAX_Q1D][MAX_Q1D];
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massXY[qy][qx] = 0.0;
+               }
+            }
+
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               double massX[MAX_Q1D];
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massX[qx] = 0.0;
+               }
+
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  const double t = x(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e);
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     massX[qx] += t * (trialHcurl ? ((c == 0) ? Bo(qx,dx) : Bc(qx,dx)) :
+                                       ((c == 0) ? Bc(qx,dx) : Bo(qx,dx)));
+                  }
+               }
+
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  const double wy = trialHcurl ? ((c == 1) ? Bo(qy,dy) : Bc(qy,dy)) :
+                                    ((c == 1) ? Bc(qy,dy) : Bo(qy,dy));
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     const double wx = massX[qx];
+                     massXY[qy][qx] += wx * wy;
+                  }
+               }
+            }
+
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               const double wz = trialHcurl ? ((c == 2) ? Bo(qz,dz) : Bc(qz,dz)) :
+                                 ((c == 2) ? Bc(qz,dz) : Bo(qz,dz));
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     mass[qz][qy][qx][c] += massXY[qy][qx] * wz;
+                  }
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy * D1Dz;
+      }  // loop (c) over components
+
+      // Apply D operator.
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const double O11 = op(0,qx,qy,qz,e);
+               const double O12 = scalarCoeff ? 0.0 : op(1,qx,qy,qz,e);
+               const double O13 = scalarCoeff ? 0.0 : op(2,qx,qy,qz,e);
+               const double O21 = scalarCoeff ? 0.0 : op(3,qx,qy,qz,e);
+               const double O22 = scalarCoeff ? O11 : op(4,qx,qy,qz,e);
+               const double O23 = scalarCoeff ? 0.0 : op(5,qx,qy,qz,e);
+               const double O31 = scalarCoeff ? 0.0 : op(6,qx,qy,qz,e);
+               const double O32 = scalarCoeff ? 0.0 : op(7,qx,qy,qz,e);
+               const double O33 = scalarCoeff ? O11 : op(8,qx,qy,qz,e);
+               const double massX = mass[qz][qy][qx][0];
+               const double massY = mass[qz][qy][qx][1];
+               const double massZ = mass[qz][qy][qx][2];
+               mass[qz][qy][qx][0] = (O11*massX)+(O12*massY)+(O13*massZ);
+               mass[qz][qy][qx][1] = (O21*massX)+(O22*massY)+(O23*massZ);
+               mass[qz][qy][qx][2] = (O31*massX)+(O32*massY)+(O33*massZ);
+            }
+         }
+      }
+
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         double massXY[HDIV_MAX_D1D][HDIV_MAX_D1D];
+
+         osc = 0;
+         for (int c = 0; c < VDIM; ++c)  // loop over x, y, z test components
+         {
+            const int D1Dz = trialHcurl ? ((c == 2) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 2) ? D1Dtest - 1 : D1Dtest);
+            const int D1Dy = trialHcurl ? ((c == 1) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 1) ? D1Dtest - 1 : D1Dtest);
+            const int D1Dx = trialHcurl ? ((c == 0) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 0) ? D1Dtest - 1 : D1Dtest);
+
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massXY[dy][dx] = 0.0;
+               }
+            }
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               double massX[HDIV_MAX_D1D];
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massX[dx] = 0.0;
+               }
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     massX[dx] += mass[qz][qy][qx][c] * (trialHcurl ?
+                                                         ((c == 0) ? Bct(dx,qx) : Bot(dx,qx)) :
+                                                         ((c == 0) ? Bot(dx,qx) : Bct(dx,qx)));
+                  }
+               }
+               for (int dy = 0; dy < D1Dy; ++dy)
+               {
+                  const double wy = trialHcurl ? ((c == 1) ? Bct(dy,qy) : Bot(dy,qy)) :
+                                    ((c == 1) ? Bot(dy,qy) : Bct(dy,qy));
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     massXY[dy][dx] += massX[dx] * wy;
+                  }
+               }
+            }
+
+            for (int dz = 0; dz < D1Dz; ++dz)
+            {
+               const double wz = trialHcurl ? ((c == 2) ? Bct(dz,qz) : Bot(dz,qz)) :
+                                 ((c == 2) ? Bot(dz,qz) : Bct(dz,qz));
+               for (int dy = 0; dy < D1Dy; ++dy)
+               {
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     y(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e) +=
+                        massXY[dy][dx] * wz;
+                  }
+               }
+            }
+
+            osc += D1Dx * D1Dy * D1Dz;
+         }  // loop c
+      }  // loop qz
+   }); // end of element loop
+}
+
+// Mass operator for H(curl) and H(div) functions, using Piola transformations
+// u = dF^{-T} \hat{u} in H(curl), v = (1 / det dF) dF \hat{v} in H(div).
+void PAHcurlHdivMassApply2D(const int D1D,
+                            const int D1Dtest,
+                            const int Q1D,
+                            const int NE,
+                            const bool scalarCoeff,
+                            const bool trialHcurl,
+                            const Array<double> &_Bo,
+                            const Array<double> &_Bc,
+                            const Array<double> &_Bot,
+                            const Array<double> &_Bct,
+                            const Vector &_op,
+                            const Vector &_x,
+                            Vector &_y)
+{
+   constexpr static int MAX_D1D = HCURL_MAX_D1D;
+   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
+
+   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
+   constexpr static int VDIM = 2;
+
+   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
+   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
+   auto Bot = Reshape(_Bot.Read(), D1Dtest-1, Q1D);
+   auto Bct = Reshape(_Bct.Read(), D1Dtest, Q1D);
+   auto op = Reshape(_op.Read(), scalarCoeff ? 1 : 4, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), 2*(D1D-1)*D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), 2*(D1Dtest-1)*D1Dtest, NE);
+
+   MFEM_FORALL(e, NE,
+   {
+      double mass[MAX_Q1D][MAX_Q1D][VDIM];
+
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            for (int c = 0; c < VDIM; ++c)
+            {
+               mass[qy][qx][c] = 0.0;
+            }
+         }
+      }
+
+      int osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y trial components
+      {
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1D - 1 : D1D) :
+                          ((c == 1) ? D1D : D1D - 1);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1D - 1 : D1D) :
+                          ((c == 0) ? D1D : D1D - 1);
+
+         for (int dy = 0; dy < D1Dy; ++dy)
+         {
+            double massX[MAX_Q1D];
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               massX[qx] = 0.0;
+            }
+
+            for (int dx = 0; dx < D1Dx; ++dx)
+            {
+               const double t = x(dx + (dy * D1Dx) + osc, e);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massX[qx] += t * (trialHcurl ? ((c == 0) ? Bo(qx,dx) : Bc(qx,dx)) :
+                                    ((c == 0) ? Bc(qx,dx) : Bo(qx,dx)));
+               }
+            }
+
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const double wy = trialHcurl ? ((c == 1) ? Bo(qy,dy) : Bc(qy,dy)) :
+                                 ((c == 1) ? Bc(qy,dy) : Bo(qy,dy));
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  mass[qy][qx][c] += massX[qx] * wy;
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy;
+      }  // loop (c) over components
+
+      // Apply D operator.
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double O11 = op(0,qx,qy,e);
+            const double O12 = scalarCoeff ? 0.0 : op(1,qx,qy,e);
+            const double O21 = scalarCoeff ? 0.0 : op(2,qx,qy,e);
+            const double O22 = scalarCoeff ? O11 : op(3,qx,qy,e);
+            const double massX = mass[qy][qx][0];
+            const double massY = mass[qy][qx][1];
+            mass[qy][qx][0] = (O11*massX)+(O12*massY);
+            mass[qy][qx][1] = (O21*massX)+(O22*massY);
+         }
+      }
+
+      osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y test components
+      {
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1Dtest : D1Dtest - 1) :
+                          ((c == 1) ? D1Dtest - 1 : D1Dtest);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1Dtest : D1Dtest - 1) :
+                          ((c == 0) ? D1Dtest - 1 : D1Dtest);
+
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            double massX[HDIV_MAX_D1D];
+            for (int dx = 0; dx < D1Dx; ++dx)
+            {
+               massX[dx] = 0.0;
+            }
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massX[dx] += mass[qy][qx][c] * (trialHcurl ?
+                                                  ((c == 0) ? Bct(dx,qx) : Bot(dx,qx)) :
+                                                  ((c == 0) ? Bot(dx,qx) : Bct(dx,qx)));
+               }
+            }
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               const double wy = trialHcurl ? ((c == 1) ? Bct(dy,qy) : Bot(dy,qy)) :
+                                 ((c == 1) ? Bot(dy,qy) : Bct(dy,qy));
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  y(dx + (dy * D1Dx) + osc, e) += massX[dx] * wy;
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy;
+      }  // loop c
+   }); // end of element loop
+}
+
 void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
-   // Assumes tensor-product elements
-   Mesh *mesh = fes.GetMesh();
-   const FiniteElement *fel = fes.GetFE(0);
+   AssemblePA(fes, fes);
+}

-   const VectorTensorFiniteElement *el =
-      dynamic_cast<const VectorTensorFiniteElement*>(fel);
-   MFEM_VERIFY(el != NULL, "Only VectorTensorFiniteElement is supported!");
+void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
+                                        const FiniteElementSpace &test_fes)
+{
+   // Assumes tensor-product elements
+   Mesh *mesh = trial_fes.GetMesh();
+
+   const FiniteElement *trial_fel = trial_fes.GetFE(0);
+   const VectorTensorFiniteElement *trial_el =
+      dynamic_cast<const VectorTensorFiniteElement*>(trial_fel);
+   MFEM_VERIFY(trial_el != NULL, "Only VectorTensorFiniteElement is supported!");
+
+   const FiniteElement *test_fel = test_fes.GetFE(0);
+   const VectorTensorFiniteElement *test_el =
+      dynamic_cast<const VectorTensorFiniteElement*>(test_fel);
+   MFEM_VERIFY(test_el != NULL, "Only VectorTensorFiniteElement is supported!");

   const IntegrationRule *ir
-      = IntRule ? IntRule : &MassIntegrator::GetRule(*el, *el,
+      = IntRule ? IntRule : &MassIntegrator::GetRule(*trial_el, *trial_el,
                                                     *mesh->GetElementTransformation(0));
-   const int dims = el->GetDim();
+   const int dims = trial_el->GetDim();
   MFEM_VERIFY(dims == 2 || dims == 3, "");

   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
@@ -161,53 +721,160 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dim = mesh->Dimension();
   MFEM_VERIFY(dim == 2 || dim == 3, "");

-   ne = fes.GetNE();
+   ne = trial_fes.GetNE();
+   MFEM_VERIFY(ne == test_fes.GetNE(),
+               "Different meshes for test and trial spaces");
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   mapsC = &trial_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsO = &trial_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
   dofs1D = mapsC->ndof;
   quad1D = mapsC->nqpt;

+   mapsCtest = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsOtest = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   dofs1Dtest = mapsCtest->ndof;
+
   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");

-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+   trial_fetype = trial_el->GetDerivType();
+   test_fetype = test_el->GetDerivType();

-   Vector coeff(ne * nq);
+   const int MQsymmDim = MQ ? (MQ->GetWidth() * (MQ->GetWidth() + 1)) / 2 : 0;
+   const int MQfullDim = MQ ? (MQ->GetHeight() * MQ->GetWidth()) : 0;
+   const int MQdim = MQ ? (MQ->IsSymmetric() ? MQsymmDim : MQfullDim) : 0;
+   const int coeffDim = MQ ? MQdim : (VQ ? VQ->GetVDim() : 1);
+
+   symmetric = MQ ? MQ->IsSymmetric() : true;
+
+   if ((trial_fetype == mfem::FiniteElement::CURL &&
+        test_fetype == mfem::FiniteElement::DIV) ||
+       (trial_fetype == mfem::FiniteElement::DIV &&
+        test_fetype == mfem::FiniteElement::CURL))
+      pa_data.SetSize((coeffDim == 1 ? 1 : dim*dim) * nq * ne,
+                      Device::GetMemoryType());
+   else
+      pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne,
+                      Device::GetMemoryType());
+
+   Vector coeff(coeffDim * ne * nq);
   coeff = 1.0;
-   if (Q)
+   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
+   if (Q || VQ || MQ)
   {
+      Vector D(VQ ? coeffDim : 0);
+      DenseMatrix M;
+      Vector Msymm;
+      if (MQ)
+      {
+         if (symmetric)
+         {
+            Msymm.SetSize(MQsymmDim);
+         }
+         else
+         {
+            M.SetSize(dim);
+         }
+      }
+
+      if (VQ)
+      {
+         MFEM_VERIFY(coeffDim == dim, "");
+      }
+      if (MQ)
+      {
+         MFEM_VERIFY(coeffDim == MQdim, "");
+         MFEM_VERIFY(MQ->GetHeight() == dim && MQ->GetWidth() == dim, "");
+      }
+
      for (int e=0; e<ne; ++e)
      {
         ElementTransformation *tr = mesh->GetElementTransformation(e);
         for (int p=0; p<nq; ++p)
         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
+            if (MQ)
+            {
+               if (MQ->IsSymmetric())
+               {
+                  MQ->EvalSymmetric(Msymm, *tr, ir->IntPoint(p));
+
+                  for (int i=0; i<MQsymmDim; ++i)
+                  {
+                     coeffh(i, p, e) = Msymm[i];
+                  }
+               }
+               else
+               {
+                  MQ->Eval(M, *tr, ir->IntPoint(p));
+
+                  for (int i=0; i<dim; ++i)
+                     for (int j=0; j<dim; ++j)
+                     {
+                        coeffh(j+(i*dim), p, e) = M(i,j);
+                     }
+               }
+            }
+            else if (VQ)
+            {
+               VQ->Eval(D, *tr, ir->IntPoint(p));
+               for (int i=0; i<coeffDim; ++i)
+               {
+                  coeffh(i, p, e) = D[i];
+               }
+            }
+            else
+            {
+               coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
+            }
         }
      }
   }

-   fetype = el->GetDerivType();
-
-   if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
+   if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype
+       && dim == 3)
   {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
-   else if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
+   else if (trial_fetype == mfem::FiniteElement::CURL
+            && test_fetype == trial_fetype && dim == 2)
   {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup2D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
+   else if (trial_fetype == mfem::FiniteElement::DIV
+            && test_fetype == trial_fetype && dim == 3)
   {
      PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 2)
+   else if (trial_fetype == mfem::FiniteElement::DIV
+            && test_fetype == trial_fetype && dim == 2)
   {
      PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
+   else if (((trial_fetype == mfem::FiniteElement::CURL &&
+              test_fetype == mfem::FiniteElement::DIV) ||
+             (trial_fetype == mfem::FiniteElement::DIV &&
+              test_fetype == mfem::FiniteElement::CURL)) &&
+            test_fel->GetOrder() == trial_fel->GetOrder())
+   {
+      if (coeffDim == 1)
+      {
+         PAHcurlL2Setup(nq, coeffDim, ne, ir->GetWeights(), coeff, pa_data);
+      }
+      else
+      {
+         const bool tr = (trial_fetype == mfem::FiniteElement::DIV &&
+                          test_fetype == mfem::FiniteElement::CURL);
+         if (dim == 3)
+            PAHcurlHdivSetup3D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+                               geom->J, coeff, pa_data);
+         else
+            PAHcurlHdivSetup2D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+                               geom->J, coeff, pa_data);
+      }
+   }
   else
   {
      MFEM_ABORT("Unknown kernel.");
@@ -218,12 +885,13 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
 {
   if (dim == 3)
   {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
      {
-         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne,
+         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
                                       mapsO->B, mapsC->B, pa_data, diag);
      }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
      {
         PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne,
                                      mapsO->B, mapsC->B, pa_data, diag);
@@ -235,12 +903,13 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
   }
   else
   {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
      {
-         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne,
+         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne, symmetric,
                                       mapsO->B, mapsC->B, pa_data, diag);
      }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
      {
         PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne,
                                      mapsO->B, mapsC->B, pa_data, diag);
@@ -256,16 +925,33 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 {
   if (dim == 3)
   {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
      {
-         PAHcurlMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
+         PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
+                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
      }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
      {
         PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                           mapsC->Bt, pa_data, x, y);
      }
+      else if (trial_fetype == mfem::FiniteElement::CURL &&
+               test_fetype == mfem::FiniteElement::DIV)
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                true, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == mfem::FiniteElement::CURL)
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                false, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
      else
      {
         MFEM_ABORT("Unknown kernel.");
@@ -273,16 +959,28 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
   }
   else
   {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
      {
-         PAHcurlMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
+         PAHcurlMassApply2D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
+                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
      }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
      {
         PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                           mapsC->Bt, pa_data, x, y);
      }
+      else if ((trial_fetype == mfem::FiniteElement::CURL &&
+                test_fetype == mfem::FiniteElement::DIV) ||
+               (trial_fetype == mfem::FiniteElement::DIV &&
+                test_fetype == mfem::FiniteElement::CURL))
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         const bool trialHcurl = (trial_fetype == mfem::FiniteElement::CURL);
+         PAHcurlHdivMassApply2D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                trialHcurl, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
      else
      {
         MFEM_ABORT("Unknown kernel.");
@@ -348,12 +1046,12 @@ void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
   // Use the same setup functions as VectorFEMassIntegrator.
   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
   {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup3D(quad1D, 1, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
   else if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
   {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup2D(quad1D, 1, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
   else
@@ -319,6 +319,31 @@ void MatrixFunctionCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
   }
 }

+void MatrixFunctionCoefficient::EvalSymmetric(Vector &K,
+                                              ElementTransformation &T,
+                                              const IntegrationPoint &ip)
+{
+   MFEM_VERIFY(symmetric && height == width && height < 4 && SymmFunction,
+               "MatrixFunctionCoefficient is not symmetric");
+
+   double x[3];
+   Vector transip(x, 3);
+
+   T.Transform(ip, transip);
+
+   K.SetSize((width * (width + 1)) / 2); // 1x1: 1, 2x2: 3, 3x3: 6
+
+   if (SymmFunction)
+   {
+      (*SymmFunction)(transip, K);
+   }
+
+   if (Q)
+   {
+      K *= Q->Eval(T, ip, GetTime());
+   }
+}
+
 MatrixArrayCoefficient::MatrixArrayCoefficient (int dim)
   : MatrixCoefficient (dim)
 {
@@ -30,7 +30,10 @@ class ParMesh;
 /** @brief Base class Coefficients that optionally depend on space and time.
    These are used by the BilinearFormIntegrator, LinearFormIntegrator, and
    NonlinearFormIntegrator classes to represent the physical coefficients in
-    the PDEs that are being discretized. */
+    the PDEs that are being discretized. This class can also be used in a more
+    general way to represent functions that don't necessarily belong to a FE
+    space, e.g., to project onto GridFunctions to use as initial conditions,
+    exact solutions, etc. See, e.g., ex4 or ex22 for these uses. */
 class Coefficient
 {
 protected:
@@ -692,13 +695,16 @@ class MatrixCoefficient
 protected:
   int height, width;
   double time;
+   bool symmetric;

 public:
   /// Construct a dim x dim matrix coefficient.
-   explicit MatrixCoefficient(int dim) { height = width = dim; time = 0.; }
+   explicit MatrixCoefficient(int dim, bool symm=false)
+   { height = width = dim; time = 0.; symmetric = symm; }

   /// Construct a h x w matrix coefficient.
-   MatrixCoefficient(int h, int w) : height(h), width(w), time(0.) { }
+   MatrixCoefficient(int h, int w, bool symm=false) :
+      height(h), width(w), time(0.), symmetric(symm) { }

   /// Set the time for time dependent coefficients
   void SetTime(double t) { time = t; }
@@ -715,6 +721,9 @@ public:
   /// For backward compatibility get the width of the matrix.
   int GetVDim() const { return width; }

+   void SetSymmetric(bool s) { symmetric = s; }
+   bool IsSymmetric() const { return symmetric; }
+
   /** @brief Evaluate the matrix coefficient in the element described by @a T
       at the point @a ip, storing the result in @a K. */
   /** @note When this method is called, the caller must make sure that the
@@ -723,6 +732,15 @@ public:
   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip) = 0;

+   /** @brief Evaluate the upper triangular entries of the matrix coefficient
+       in the symmetric case, similarly to Eval. Matrix entry (i,j) is stored
+       in K[j - i + os_i] for 0 <= i <= j < width, os_0 = 0,
+       os_{i+1} = os_i + width - i. That is, K = {M(0,0), ..., M(0,w-1),
+       M(1,1), ..., M(1,w-1), ..., M(w-1,w-1) with w = width. */
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip)
+   { mfem_error("MatrixCoefficient::EvalSymmetric"); }
+
   virtual ~MatrixCoefficient() { }
 };

@@ -750,6 +768,7 @@ class MatrixFunctionCoefficient : public MatrixCoefficient
 {
 private:
   void (*Function)(const Vector &, DenseMatrix &);
+   void (*SymmFunction)(const Vector &, Vector &);
   void (*TDFunction)(const Vector &, double, DenseMatrix &);
   Coefficient *Q;
   DenseMatrix mat;
@@ -787,10 +806,26 @@ public:
      mat.SetSize(0);
   }

+   /// Construct a symmetric square matrix coefficient from a C-function
+   /// defining a vector function used by EvalSymmetric
+   MatrixFunctionCoefficient(int dim, void (*F)(const Vector &, Vector &),
+                             Coefficient *q = NULL)
+      : MatrixCoefficient(dim, true), Q(q)
+   {
+      SymmFunction = F;
+      Function = NULL;
+      TDFunction = NULL;
+      mat.SetSize(0);
+   }
+
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip);

+   /// Evaluate the symmetric matrix coefficient at @a ip.
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip);
+
   virtual ~MatrixFunctionCoefficient() { }
 };

@@ -99,8 +99,8 @@ public:
                     ComplexOperator::Convention
                     convention = ComplexOperator::HERMITIAN);

-   /** @brief Create a ComplexLinearForm on the FiniteElementSpace @a f, using
-       the same integrators as the LinearForms @a lfr (real) and @a lfi (imag) .
+   /** @brief Create a ComplexLinearForm on the FiniteElementSpace @a fes, using
+       the same integrators as the LinearForms @a lf_r (real) and @a lf_i (imag).

       The pointer @a fes is not owned by the newly constructed object.

@@ -195,8 +195,8 @@ private:
   BilinearForm *blfr;
   BilinearForm *blfi;

-   /* These methods check if the real/imag parts of the sesqulinear form are not
-      empty */
+   /* These methods check if the real/imag parts of the sesquilinear form are
+      not empty */
   bool RealInteg();
   bool ImagInteg();

@@ -204,7 +204,7 @@ public:
   SesquilinearForm(FiniteElementSpace *fes,
                    ComplexOperator::Convention
                    convention = ComplexOperator::HERMITIAN);
-   /** @brief Create a SesquilinearForm on the FiniteElementSpace @a f, using
+   /** @brief Create a SesquilinearForm on the FiniteElementSpace @a fes, using
       the same integrators as the BilinearForms @a bfr and @a bfi .

       The pointer @a fes is not owned by the newly constructed object.
@@ -219,6 +219,21 @@ public:
   void SetConvention(const ComplexOperator::Convention &
                      convention) { conv = convention; }

+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::FULL  (default)
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      blfr->SetAssemblyLevel(assembly_level);
+      blfi->SetAssemblyLevel(assembly_level);
+   }
+
   BilinearForm & real() { return *blfr; }
   BilinearForm & imag() { return *blfi; }
   const BilinearForm & real() const { return *blfr; }
@@ -309,7 +324,7 @@ protected:
 public:

   /* @brief Construct a ParComplexGridFunction associated with the
-      ParFiniteElementSpace @a *f. */
+      ParFiniteElementSpace @a *pf. */
   ParComplexGridFunction(ParFiniteElementSpace *pf);

   void Update();
@@ -401,8 +416,8 @@ public:
                        convention = ComplexOperator::HERMITIAN);

   /** @brief Create a ParComplexLinearForm on the ParFiniteElementSpace @a pf,
-       using the same integrators as the LinearForms @a plfr (real) and @a plfi
-       (imag) .
+       using the same integrators as the LinearForms @a plf_r (real) and
+       @a plf_i (imag).

      The pointer @a fes is not owned by the newly constructed object.

@@ -478,7 +493,7 @@ public:
 /** Class for a parallel sesquilinear form

    A sesquilinear form is a generalization of a bilinear form to complex-valued
-    fields. Sesquilinear forms are linear in the second argument but but the
+    fields. Sesquilinear forms are linear in the second argument but the
    first argument involves a complex conjugate in the sense that:

                a(alpha u, beta v) = conj(alpha) beta a(u, v)
@@ -524,6 +539,21 @@ public:
   void SetConvention(const ComplexOperator::Convention &
                      convention) { conv = convention; }

+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::FULL  (default)
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      pblfr->SetAssemblyLevel(assembly_level);
+      pblfi->SetAssemblyLevel(assembly_level);
+   }
+
   ParBilinearForm & real() { return *pblfr; }
   ParBilinearForm & imag() { return *pblfi; }
   const ParBilinearForm & real() const { return *pblfr; }
@@ -415,9 +415,6 @@ void VisItDataCollection::SetMesh(MPI_Comm comm, Mesh *new_mesh)
 void VisItDataCollection::RegisterField(const std::string& name,
                                        GridFunction *gf)
 {
-   DataCollection::RegisterField(name, gf);
-   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim());
-
   int LOD = 1;
   if (gf->FESpace()->GetNURBSext())
   {
@@ -431,6 +428,27 @@ void VisItDataCollection::RegisterField(const std::string& name,
      }
   }

+   DataCollection::RegisterField(name, gf);
+   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim(), LOD);
+   visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
+}
+
+void VisItDataCollection::RegisterQField(const std::string& name,
+                                         QuadratureFunction *qf)
+{
+   int LOD = -1;
+   Mesh *mesh = qf->GetSpace()->GetMesh();
+   for (int e=0; e<qf->GetSpace()->GetNE(); e++)
+   {
+      int locLOD = GlobGeometryRefiner.GetRefinementLevelFromElems(
+                      mesh->GetElementBaseGeometry(e),
+                      qf->GetElementIntRule(e).GetNPoints());
+
+      LOD = std::max(LOD,locLOD);
+   }
+
+   DataCollection::RegisterQField(name, qf);
+   field_info_map[name] = VisItFieldInfo("elements", 1, LOD);
   visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
 }

@@ -598,14 +616,28 @@ void VisItDataCollection::LoadFields()
      // TODO: 1) load parallel GridFunction on one processor
      if (serial)
      {
-         field_map.Register(it->first, new GridFunction(mesh, file), own_data);
+         if ((it->second).association == "nodes")
+         {
+            field_map.Register(it->first, new GridFunction(mesh, file), own_data);
+         }
+         else if ((it->second).association == "elements")
+         {
+            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
+         }
      }
      else
      {
 #ifdef MFEM_USE_MPI
-         field_map.Register(
-            it->first,
-            new ParGridFunction(dynamic_cast<ParMesh*>(mesh), file), own_data);
+         if ((it->second).association == "nodes")
+         {
+            field_map.Register(
+               it->first,
+               new ParGridFunction(dynamic_cast<ParMesh*>(mesh), file), own_data);
+         }
+         else if ((it->second).association == "elements")
+         {
+            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
+         }
 #else
         error = READ_ERROR;
         MFEM_WARNING("Reading parallel format in serial is not supported");
@@ -640,7 +672,7 @@ std::string VisItDataCollection::GetVisItRootString()
   {
      ftags["assoc"] = picojson::value((it->second).association);
      ftags["comps"] = picojson::value(to_string((it->second).num_components));
-      ftags["lod"] = picojson::value(to_string(visit_levels_of_detail));
+      ftags["lod"] = picojson::value(to_string((it->second).lod));
      field["path"] = picojson::value(path_str + it->first + file_ext_format);
      field["tags"] = picojson::value(ftags);
      fields[it->first] = picojson::value(field);
@@ -391,9 +391,10 @@ class VisItFieldInfo
 public:
   std::string association;
   int num_components;
-   VisItFieldInfo() { association = ""; num_components = 0; }
-   VisItFieldInfo(std::string _association, int _num_components)
-   { association = _association; num_components = _num_components; }
+   int lod;
+   VisItFieldInfo() { association = ""; num_components = 0; lod = 1;}
+   VisItFieldInfo(std::string _association, int _num_components, int _lod = 1)
+   { association = _association; num_components = _num_components; lod =_lod;}
 };

 /// Data collection with VisIt I/O routines
@@ -445,6 +446,12 @@ public:
   /// Add a grid function to the collection and update the root file
   virtual void RegisterField(const std::string& field_name, GridFunction *gf);

+   /// Add a quadrature function to the collection and update the root file.
+   /** Visualization of quadrature function is not supported in VisIt(3.12).
+       A patch has been sent to VisIt developers in June 2020. */
+   virtual void RegisterQField(const std::string& q_field_name,
+                               QuadratureFunction *qf);
+
   /// Set VisIt parameter: default levels of detail for the MultiresControl
   void SetLevelsOfDetail(int levels_of_detail);

@@ -37,7 +37,8 @@ public:
      ClosedUniform   = 4,  ///< Nodes: x_i = i/(n-1),     i=0,...,n-1
      OpenHalfUniform = 5,  ///< Nodes: x_i = (i+1/2)/n,   i=0,...,n-1
      Serendipity     = 6,  ///< Serendipity basis (squares / cubes)
-      NumBasisTypes   = 7   /**< Keep track of maximum types to prevent
+      ClosedGL        = 7,  ///< Closed GaussLegendre
+      NumBasisTypes   = 8   /**< Keep track of maximum types to prevent
                                 hard-coding */
   };
   /** @brief If the input does not represents a valid BasisType, abort with an
@@ -69,6 +70,7 @@ public:
         case ClosedUniform:   return Quadrature1D::ClosedUniform;
         case OpenHalfUniform: return Quadrature1D::OpenHalfUniform;
         case Serendipity:     return Quadrature1D::GaussLobatto;
+         case ClosedGL:        return Quadrature1D::ClosedGL;
      }
      return Quadrature1D::Invalid;
   }
@@ -82,6 +84,7 @@ public:
         case Quadrature1D::OpenUniform:     return OpenUniform;
         case Quadrature1D::ClosedUniform:   return ClosedUniform;
         case Quadrature1D::OpenHalfUniform: return OpenHalfUniform;
+         case Quadrature1D::ClosedGL:        return ClosedGL;
      }
      return Invalid;
   }
@@ -756,6 +756,12 @@ public:
   /// Return the total number of quadrature points.
   int GetSize() const { return size; }

+   /// Returns the mesh
+   inline Mesh *GetMesh() const { return mesh; }
+
+   /// Returns number of elements in the mesh.
+   inline int GetNE() const { return mesh->GetNE(); }
+
   /// Get the IntegrationRule associated with mesh element @a idx.
   const IntegrationRule &GetElementIntRule(int idx) const
   { return *int_rule[mesh->GetElementBaseGeometry(idx)]; }
@@ -1344,15 +1344,14 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
            return NULL;
         }
         ir = FindInIntPts(Geom, Times-1);
-         if (ir == NULL)
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule(Times-1);
+         for (int i = 1; i < Times; i++)
         {
-            ir = new IntegrationRule(Times-1);
-            for (int i = 1; i < Times; i++)
-            {
-               IntegrationPoint &ip = ir->IntPoint(i-1);
-               ip.x = double(i) / Times;
-               ip.y = ip.z = 0.0;
-            }
+            IntegrationPoint &ip = ir->IntPoint(i-1);
+            ip.x = double(i) / Times;
+            ip.y = ip.z = 0.0;
         }
      }
      break;
@@ -1364,18 +1363,17 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
            return NULL;
         }
         ir = FindInIntPts(Geom, ((Times-1)*(Times-2))/2);
-         if (ir == NULL)
-         {
-            ir = new IntegrationRule(((Times-1)*(Times-2))/2);
-            for (int k = 0, j = 1; j < Times-1; j++)
-               for (int i = 1; i < Times-j; i++, k++)
-               {
-                  IntegrationPoint &ip = ir->IntPoint(k);
-                  ip.x = double(i) / Times;
-                  ip.y = double(j) / Times;
-                  ip.z = 0.0;
-               }
-         }
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule(((Times-1)*(Times-2))/2);
+         for (int k = 0, j = 1; j < Times-1; j++)
+            for (int i = 1; i < Times-j; i++, k++)
+            {
+               IntegrationPoint &ip = ir->IntPoint(k);
+               ip.x = double(i) / Times;
+               ip.y = double(j) / Times;
+               ip.z = 0.0;
+            }
      }
      break;

@@ -1386,18 +1384,17 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
            return NULL;
         }
         ir = FindInIntPts(Geom, (Times-1)*(Times-1));
-         if (ir == NULL)
-         {
-            ir = new IntegrationRule((Times-1)*(Times-1));
-            for (int k = 0, j = 1; j < Times; j++)
-               for (int i = 1; i < Times; i++, k++)
-               {
-                  IntegrationPoint &ip = ir->IntPoint(k);
-                  ip.x = double(i) / Times;
-                  ip.y = double(j) / Times;
-                  ip.z = 0.0;
-               }
-         }
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule((Times-1)*(Times-1));
+         for (int k = 0, j = 1; j < Times; j++)
+            for (int i = 1; i < Times; i++, k++)
+            {
+               IntegrationPoint &ip = ir->IntPoint(k);
+               ip.x = double(i) / Times;
+               ip.y = double(j) / Times;
+               ip.z = 0.0;
+            }
      }
      break;

@@ -1405,10 +1402,121 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
         mfem_error("GeometryRefiner::RefineInterior(...)");
   }

-   if (ir) { IntPts[Geom].Append(ir); }
+   MFEM_ASSERT(ir != NULL, "Failed to construct the refined IntegrationRule.");
+   IntPts[Geom].Append(ir);
+
   return ir;
 }

+
+int GeometryRefiner::GetRefinementLevelFromPoints(Geometry::Type geom, int Npts)
+{
+   switch (geom)
+   {
+      case Geometry::POINT:
+      {
+         return -1;
+      }
+      case Geometry::SEGMENT:
+      {
+         return Npts -1;
+      }
+      case Geometry::TRIANGLE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+2)/2;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::SQUARE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1);
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::CUBE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1)*(n+1);
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::TETRAHEDRON:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+3)*(n+2)*(n+1)/6;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::PRISM:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1)*(n+2)/2;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      default:
+      {
+         mfem_error("Non existing Geometry.");
+      }
+   }
+
+   return -1;
+}
+
+
+int GeometryRefiner::GetRefinementLevelFromElems(Geometry::Type geom, int Nels)
+{
+   switch (geom)
+   {
+      case Geometry::POINT:
+      {
+         return -1;
+      }
+      case Geometry::SEGMENT:
+      {
+         return Nels;
+      }
+      case Geometry::TRIANGLE:
+      case Geometry::SQUARE:
+      {
+         for (int n = 0; (n < 15) && (n*n < Nels+1) ; n++)
+         {
+            if (n*n == Nels) { return n-1; }
+         }
+         return -1;
+      }
+      case Geometry::CUBE:
+      case Geometry::TETRAHEDRON:
+      case Geometry::PRISM:
+      {
+         for (int n = 0; (n < 15) && (n*n*n < Nels+1) ; n++)
+         {
+            if (n*n*n == Nels) { return n-1; }
+         }
+         return -1;
+      }
+      default:
+      {
+         mfem_error("Non existing Geometry.");
+      }
+   }
+
+   return -1;
+}
+
+
 GeometryRefiner GlobGeometryRefiner;

 }
@@ -273,6 +273,12 @@ public:
   /// @note This method always uses Quadrature1D::OpenUniform points.
   const IntegrationRule *RefineInterior(Geometry::Type Geom, int Times);

+   /// Get the Refinement level based on number of points
+   virtual int GetRefinementLevelFromPoints(Geometry::Type Geom, int Npts);
+
+   /// Get the Refinement level based on number of elements
+   virtual int GetRefinementLevelFromElems(Geometry::Type geom, int Npts);
+
   ~GeometryRefiner();
 };

@@ -199,8 +199,7 @@ void GridFunction::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
   if (f != fes) { Destroy(); }
   fes = f;
   v.UseDevice(true);
-   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, fes->GetVSize()),
-                    fes->GetVSize(), true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
   sequence = fes->GetSequence();
 }

@@ -2984,7 +2983,7 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 1; // <----------
+         int intorder = 2*fe->GetOrder() + 3; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      GetValues(i, *ir, vals);
@@ -3117,7 +3116,7 @@ double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 1; // <----------
+         int intorder = 2*fe->GetOrder() + 3; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      T = fes->GetElementTransformation(i);
@@ -105,7 +105,7 @@ public:
       have the same size.

       @note Defining this method overwrites the implicitly defined copy
-       assignemnt operator. */
+       assignment operator. */
   GridFunction &operator=(const GridFunction &rhs)
   { return operator=((const Vector &)rhs); }

@@ -714,7 +714,7 @@ public:
       the same size.

       @note Defining this method overwrites the implicitly defined copy
-       assignemnt operator. */
+       assignment operator. */
   QuadratureFunction &operator=(const QuadratureFunction &v);

   /// Get the IntegrationRule associated with mesh element @a idx.
@@ -618,6 +618,26 @@ void QuadratureFunctions1D::OpenHalfUniform(const int np, IntegrationRule* ir)
   CalculateUniformWeights(ir, Quadrature1D::OpenHalfUniform);
 }

+void QuadratureFunctions1D::ClosedGL(const int np, IntegrationRule* ir)
+{
+   ir->SetSize(np);
+   ir->IntPoint(0).x = 0.0;
+   ir->IntPoint(np-1).x = 1.0;
+
+   if ( np > 2 )
+   {
+      IntegrationRule gl_ir;
+      GaussLegendre(np-1, &gl_ir);
+
+      for (int i = 1; i < np-1; ++i)
+      {
+         ir->IntPoint(i).x = (gl_ir.IntPoint(i-1).x + gl_ir.IntPoint(i).x)/2;
+      }
+   }
+
+   CalculateUniformWeights(ir, Quadrature1D::ClosedGL);
+}
+
 void QuadratureFunctions1D::GivePolyPoints(const int np, double *pts,
                                           const int type)
 {
@@ -650,6 +670,11 @@ void QuadratureFunctions1D::GivePolyPoints(const int np, double *pts,
         OpenHalfUniform(np, &ir);
         break;
      }
+      case Quadrature1D::ClosedGL:
+      {
+         ClosedGL(np, &ir);
+         break;
+      }
      default:
      {
         MFEM_ABORT("Asking for an unknown type of 1D Quadrature points, "
@@ -272,6 +272,7 @@ public:
   void OpenUniform(const int np, IntegrationRule *ir);
   void ClosedUniform(const int np, IntegrationRule *ir);
   void OpenHalfUniform(const int np, IntegrationRule *ir);
+   void ClosedGL(const int np, IntegrationRule *ir);
   ///@}

   /// A helper function that will play nice with Poly_1D::OpenPoints and
@@ -293,7 +294,8 @@ public:
      GaussLobatto    = 1,
      OpenUniform     = 2,  ///< aka open Newton-Cotes
      ClosedUniform   = 3,  ///< aka closed Newton-Cotes
-      OpenHalfUniform = 4   ///< aka "open half" Newton-Cotes
+      OpenHalfUniform = 4,  ///< aka "open half" Newton-Cotes
+      ClosedGL        = 5   ///< aka closed Gauss Legendre
   };
   /** @brief If the Quadrature1D type is not closed return Invalid; otherwise
       return type. */
@@ -199,10 +199,19 @@ void LinearForm::Assemble()
 void LinearForm::Update(FiniteElementSpace *f, Vector &v, int v_offset)
 {
   fes = f;
-   NewDataAndSize((double *)v + v_offset, fes->GetVSize());
+   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, f->GetVSize()),
+                    f->GetVSize(), false);
   ResetDeltaLocations();
 }

+void LinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
+{
+   MFEM_ASSERT(v.Size() >= v_offset + f->GetVSize(), "");
+   fes = f;
+   v.UseDevice(true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
+}
+
 void LinearForm::AssembleDelta()
 {
   if (dlfi_delta.Size() == 0) { return; }
@@ -26,7 +26,7 @@ protected:
   /// FE space on which the LinearForm lives. Not owned.
   FiniteElementSpace *fes;

-   /** @brief Indicates the LinerFormIntegrator%s stored in #dlfi, #dlfi_delta,
+   /** @brief Indicates the LinearFormIntegrator%s stored in #dlfi, #dlfi_delta,
       #blfi, and #flfi are owned by another LinearForm. */
   int extern_lfs;

@@ -175,6 +175,15 @@ public:
       @note This method does not perform assembly. */
   void Update(FiniteElementSpace *f, Vector &v, int v_offset);

+   /** @brief Make the LinearForm reference external data on a new
+       FiniteElementSpace. */
+   /** This method changes the FiniteElementSpace associated with the LinearForm
+       @a *f and sets the data of the Vector @a v (plus the @a v_offset)
+       as external data in the LinearForm.
+       @note This version of the method will also perform bounds checks when
+       the build option MFEM_DEBUG is enabled. */
+   virtual void MakeRef(FiniteElementSpace *f, Vector &v, int v_offset);
+
   /// Return the action of the LinearForm as a linear mapping.
   /** Linear forms are linear functionals which map GridFunctions to
       the real numbers.  This method performs this mapping which in
@@ -135,11 +135,18 @@ void Multigrid::SetOperator(const Operator& op)
   MFEM_ABORT("SetOperator not supported in Multigrid");
 }

-void Multigrid::SmoothingStep(int level) const
+void Multigrid::SmoothingStep(int level, bool transpose) const
 {
   GetOperatorAtLevel(level)->Mult(*Y[level], *R[level]); // r = A x
   subtract(*X[level], *R[level], *R[level]);             // r = b - A x
-   GetSmootherAtLevel(level)->Mult(*R[level], *Z[level]); // z = S r
+   if (transpose)
+   {
+      GetSmootherAtLevel(level)->MultTranspose(*R[level], *Z[level]); // z = S r
+   }
+   else
+   {
+      GetSmootherAtLevel(level)->Mult(*R[level], *Z[level]); // z = S r
+   }
   add(*Y[level], 1.0, *Z[level], *Y[level]);             // x = x + S (b - A x)
 }

@@ -153,7 +160,7 @@ void Multigrid::Cycle(int level) const

   for (int i = 0; i < preSmoothingSteps; i++)
   {
-      SmoothingStep(level);
+      SmoothingStep(level, false);
   }

   // Compute residual
@@ -187,7 +194,7 @@ void Multigrid::Cycle(int level) const
   // Post-smooth
   for (int i = 0; i < postSmoothingSteps; i++)
   {
-      SmoothingStep(level);
+      SmoothingStep(level, true);
   }
 }

@@ -108,7 +108,7 @@ public:

 private:
   /// Application of a smoothing step at particular level
-   void SmoothingStep(int level) const;
+   void SmoothingStep(int level, bool transpose) const;

   /// Application of a cycle at particular level
   void Cycle(int level) const;
@@ -933,6 +933,17 @@ Operator &BlockNonlinearForm::GetGradientBlocked(const BlockVector &bx) const
      }
   }

+   if (!Grads(0,0)->Finalized())
+   {
+      for (int i=0; i<fes.Size(); ++i)
+      {
+         for (int j=0; j<fes.Size(); ++j)
+         {
+            Grads(i,j)->Finalize(skip_zeros);
+         }
+      }
+   }
+
   for (int s=0; s<fes.Size(); ++s)
   {
      for (int i = 0; i < ess_vdofs[s]->Size(); ++i)
@@ -952,17 +963,6 @@ Operator &BlockNonlinearForm::GetGradientBlocked(const BlockVector &bx) const
      }
   }

-   if (!Grads(0,0)->Finalized())
-   {
-      for (int i=0; i<fes.Size(); ++i)
-      {
-         for (int j=0; j<fes.Size(); ++j)
-         {
-            Grads(i,j)->Finalize(skip_zeros);
-         }
-      }
-   }
-
   for (int i=0; i<fes.Size(); ++i)
   {
      for (int j=0; j<fes.Size(); ++j)
@@ -241,7 +241,7 @@ void ParBilinearForm::Assemble(int skip_zeros)

   BilinearForm::Assemble(skip_zeros);

-   if (fbfi.Size() > 0)
+   if (!ext && fbfi.Size() > 0)
   {
      AssembleSharedFaces(skip_zeros);
   }
@@ -711,7 +711,9 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
   int *nfdofs = new int[NRanks];
   int *nrdofs = new int[NRanks];

-   values[0] = data;
+   double * h_data = const_cast<double *>(this->HostRead());
+
+   values[0] = h_data;
   nv[0]     = pfes -> GetVSize();
   nvdofs[0] = pfes -> GetNVDofs();
   nedofs[0] = pfes -> GetNEDofs();
@@ -812,7 +814,7 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
      MPI_Send(&nvdofs[0], 1, MPI_INT, 0, 456, MyComm);
      MPI_Send(&nedofs[0], 1, MPI_INT, 0, 457, MyComm);
      MPI_Send(&nfdofs[0], 1, MPI_INT, 0, 458, MyComm);
-      MPI_Send(data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
+      MPI_Send(h_data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
   }

   delete [] values;
@@ -21,7 +21,6 @@ namespace mfem
 void ParLinearForm::Update(ParFiniteElementSpace *pf)
 {
   if (pf) { pfes = pf; }
-
   LinearForm::Update(pfes);
 }

@@ -31,6 +30,18 @@ void ParLinearForm::Update(ParFiniteElementSpace *pf, Vector &v, int v_offset)
   LinearForm::Update(pf,v,v_offset);
 }

+void ParLinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
+{
+   LinearForm::MakeRef(f, v, v_offset);
+   pfes = dynamic_cast<ParFiniteElementSpace*>(f);
+}
+
+void ParLinearForm::MakeRef(ParFiniteElementSpace *pf, Vector &v, int v_offset)
+{
+   LinearForm::MakeRef(pf, v, v_offset);
+   pfes = pf;
+}
+
 void ParLinearForm::ParallelAssemble(Vector &tv)
 {
   const Operator* prolong = pfes->GetProlongationMatrix();
@@ -92,6 +92,25 @@ public:
       @note This method does not perform assembly. */
   void Update(ParFiniteElementSpace *pf, Vector &v, int v_offset);

+
+   /** @brief Make the ParLinearForm reference external data on a new
+       FiniteElementSpace. */
+   /** This method changes the FiniteElementSpace associated with the ParLinearForm
+       to @a *f and sets the data of the Vector @a v (plus the @a v_offset) as external
+       data in the ParLinearForm.
+       @note This version of the method will also perform bounds checks when
+       the build option MFEM_DEBUG is enabled. */
+   virtual void MakeRef(FiniteElementSpace *f, Vector &v, int v_offset);
+
+   /** @brief Make the ParLinearForm reference external data on a new
+       ParFiniteElementSpace. */
+   /** This method changes the ParFiniteElementSpace associated with the ParLinearForm
+       to @a *pf and sets the data of the Vector @a v (plus the @a v_offset) as external
+       data in the ParLinearForm.
+       @note This version of the method will also perform bounds checks when
+       the build option MFEM_DEBUG is enabled. */
+   void MakeRef(ParFiniteElementSpace *pf, Vector &v, int v_offset);
+
   /// Assemble the vector on the true dofs, i.e. P^t v.
   void ParallelAssemble(Vector &tv);

@@ -27,35 +27,24 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
                                           ElementDofOrdering e_ordering,
                                           FaceType type,
                                           L2FaceValues m)
-   : fes(fes),
-     nf(fes.GetNFbyType(type)),
-     vdim(fes.GetVDim()),
-     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     ndofs(fes.GetNDofs()),
-     dof(nf>0 ?
-         fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof()
-         : 0),
-     m(m),
-     nfdofs(nf*dof),
-     scatter_indices1(nf*dof),
-     scatter_indices2(m==L2FaceValues::DoubleValued?nf*dof:0),
-     offsets(ndofs+1),
-     gather_indices((m==L2FaceValues::DoubleValued? 2 : 1)*nf*dof)
+   : L2FaceRestriction(fes, type, m)
 {
   if (nf==0) { return; }
   // If fespace == L2
-   const FiniteElement *fe = fes.GetFE(0);
+   const ParFiniteElementSpace &pfes =
+      static_cast<const ParFiniteElementSpace&>(this->fes);
+   const FiniteElement *fe = pfes.GetFE(0);
   const TensorBasisElement *tfe = dynamic_cast<const TensorBasisElement*>(fe);
   MFEM_VERIFY(tfe != NULL &&
               (tfe->GetBasisType()==BasisType::GaussLobatto ||
                tfe->GetBasisType()==BasisType::Positive),
               "Only Gauss-Lobatto and Bernstein basis are supported in "
               "ParL2FaceRestriction.");
-   MFEM_VERIFY(fes.GetMesh()->Conforming(),
+   MFEM_VERIFY(pfes.GetMesh()->Conforming(),
               "Non-conforming meshes not yet supported with partial assembly.");
   // Assuming all finite elements are using Gauss-Lobatto dofs
   height = (m==L2FaceValues::DoubleValued? 2 : 1)*vdim*nf*dof;
-   width = fes.GetVSize();
+   width = pfes.GetVSize();
   const bool dof_reorder = (e_ordering == ElementDofOrdering::LEXICOGRAPHIC);
   if (!dof_reorder)
   {
@@ -63,32 +52,32 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
   }
   if (dof_reorder && nf > 0)
   {
-      for (int f = 0; f < fes.GetNF(); ++f)
+      for (int f = 0; f < pfes.GetNF(); ++f)
      {
         const FiniteElement *fe =
-            fes.GetTraceElement(f, fes.GetMesh()->GetFaceBaseGeometry(f));
+            pfes.GetTraceElement(f, pfes.GetMesh()->GetFaceBaseGeometry(f));
         const TensorBasisElement* el =
            dynamic_cast<const TensorBasisElement*>(fe);
         if (el) { continue; }
         mfem_error("Finite element not suitable for lexicographic ordering");
      }
   }
-   const Table& e2dTable = fes.GetElementToDofTable();
+   const Table& e2dTable = pfes.GetElementToDofTable();
   const int* elementMap = e2dTable.GetJ();
   Array<int> faceMap1(dof), faceMap2(dof);
   int e1, e2;
   int inf1, inf2;
   int face_id1, face_id2;
   int orientation;
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
-   const int elem_dofs = fes.GetFE(0)->GetDof();
-   const int dim = fes.GetMesh()->SpaceDimension();
+   const int dof1d = pfes.GetFE(0)->GetOrder()+1;
+   const int elem_dofs = pfes.GetFE(0)->GetDof();
+   const int dim = pfes.GetMesh()->SpaceDimension();
   // Computation of scatter indices
   int f_ind=0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
   {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
      if (dof_reorder)
      {
         orientation = inf1 % 64;
@@ -136,7 +125,7 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
            {
               const int se2 = -1 - e2;
               Array<int> sharedDofs;
-               fes.GetFaceNbrElementVDofs(se2, sharedDofs);
+               pfes.GetFaceNbrElementVDofs(se2, sharedDofs);
               for (int d = 0; d < dof; ++d)
               {
                  const int pd = PermuteFaceL2(dim, face_id1, face_id2,
@@ -180,10 +169,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
      offsets[i] = 0;
   }
   f_ind = 0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
   {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
      if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
          (type==FaceType::Boundary && e2<0 && inf2<0) )
      {
@@ -222,10 +211,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
      offsets[i] += offsets[i - 1];
   }
   f_ind = 0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
   {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
      if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
          (type==FaceType::Boundary && e2<0 && inf2<0) )
      {
@@ -272,8 +261,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,

 void ParL2FaceRestriction::Mult(const Vector& x, Vector& y) const
 {
+   const ParFiniteElementSpace &pfes =
+      static_cast<const ParFiniteElementSpace&>(this->fes);
   ParGridFunction x_gf;
-   x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(&fes),
+   x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(&pfes),
                const_cast<Vector&>(x), 0);
   x_gf.ExchangeFaceNbrData();

@@ -337,34 +328,122 @@ void ParL2FaceRestriction::Mult(const Vector& x, Vector& y) const
   }
 }

-void ParL2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
+static MFEM_HOST_DEVICE int AddNnz(const int iE, int *I, const int dofs)
 {
-   // Assumes all elements have the same number of dofs
-   const int nd = dof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   const int dofs = nfdofs;
-   auto d_offsets = offsets.Read();
-   auto d_indices = gather_indices.Read();
-   auto d_x = Reshape(x.Read(), nd, vd, 2, nf);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
-   MFEM_FORALL(i, ndofs,
+   int val = AtomicAdd(I[iE],dofs);
+   return val;
+}
+
+void ParL2FaceRestriction::FillI(SparseMatrix &mat,
+                                 SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   const int Ndofs = ndofs;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   auto I_face = face_mat.ReadWriteI();
+   MFEM_FORALL(i, ne*elemDofs*vdim+1,
   {
-      const int offset = d_offsets[i];
-      const int nextOffset = d_offsets[i + 1];
-      for (int c = 0; c < vd; ++c)
+      I_face[i] = 0;
+   });
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int f  = fdof/face_dofs;
+      const int iF = fdof%face_dofs;
+      const int iE1 = d_indices1[f*face_dofs+iF];
+      if (iE1 < Ndofs)
      {
-         double dofValue = 0;
-         for (int j = offset; j < nextOffset; ++j)
+         for (int jF = 0; jF < face_dofs; jF++)
         {
-            int idx_j = d_indices[j];
-            bool isE1 = idx_j < dofs;
-            idx_j = isE1 ? idx_j : idx_j - dofs;
-            dofValue +=  isE1 ?
-            d_x(idx_j % nd, c, 0, idx_j / nd)
-            :d_x(idx_j % nd, c, 1, idx_j / nd);
+            const int jE2 = d_indices2[f*face_dofs+jF];
+            if (jE2 < Ndofs)
+            {
+               AddNnz(iE1,I,1);
+            }
+            else
+            {
+               AddNnz(iE1,I_face,1);
+            }
+         }
+      }
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      if (iE2 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE1 = d_indices1[f*face_dofs+jF];
+            if (jE1 < Ndofs)
+            {
+               AddNnz(iE2,I,1);
+            }
+            else
+            {
+               AddNnz(iE2,I_face,1);
+            }
+         }
+      }
+   });
+}
+
+void ParL2FaceRestriction::FillJAndData(const Vector &ea_data,
+                                        SparseMatrix &mat,
+                                        SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   const int Ndofs = ndofs;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto mat_fea = Reshape(ea_data.Read(), face_dofs, face_dofs, 2, nf);
+   auto I = mat.ReadWriteI();
+   auto I_face = face_mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto J_face = face_mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto Data_face = face_mat.WriteData();
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int f  = fdof/face_dofs;
+      const int iF = fdof%face_dofs;
+      const int iE1 = d_indices1[f*face_dofs+iF];
+      if (iE1 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE2 = d_indices2[f*face_dofs+jF];
+            if (jE2 < Ndofs)
+            {
+               const int offset = AddNnz(iE1,I,1);
+               J[offset] = jE2;
+               Data[offset] = mat_fea(jF,iF,1,f);
+            }
+            else
+            {
+               const int offset = AddNnz(iE1,I_face,1);
+               J_face[offset] = jE2-Ndofs;
+               Data_face[offset] = mat_fea(jF,iF,1,f);
+            }
+         }
+      }
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      if (iE2 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE1 = d_indices1[f*face_dofs+jF];
+            if (jE1 < Ndofs)
+            {
+               const int offset = AddNnz(iE2,I,1);
+               J[offset] = jE1;
+               Data[offset] = mat_fea(jF,iF,0,f);
+            }
+            else
+            {
+               const int offset = AddNnz(iE2,I_face,1);
+               J_face[offset] = jE1-Ndofs;
+               Data_face[offset] = mat_fea(jF,iF,0,f);
+            }
         }
-         d_y(t?c:i,t?i:c) += dofValue;
      }
   });
 }
@@ -26,28 +26,21 @@ class ParFiniteElementSpace;
 /// Operator that extracts Face degrees of freedom in parallel.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetFaceRestriction(). */
-class ParL2FaceRestriction : public Operator
+class ParL2FaceRestriction : public L2FaceRestriction
 {
-protected:
-   const ParFiniteElementSpace &fes;
-   const int nf;
-   const int vdim;
-   const bool byvdim;
-   const int ndofs;
-   const int dof;
-   const L2FaceValues m;
-   const int nfdofs;
-   Array<int> scatter_indices1;
-   Array<int> scatter_indices2;
-   Array<int> offsets;
-   Array<int> gather_indices;
-
 public:
   ParL2FaceRestriction(const ParFiniteElementSpace&, ElementDofOrdering,
                        FaceType type,
                        L2FaceValues m = L2FaceValues::DoubleValued);
   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this ParL2FaceRestriction. */
+   void FillI(SparseMatrix &mat, SparseMatrix &face_mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this ParL2FaceRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data,
+                     SparseMatrix &mat,
+                     SparseMatrix &face_mat) const;
 };

 }
@@ -17,55 +17,6 @@
 namespace mfem
 {

-L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
-   : ne(fes.GetNE()),
-     vdim(fes.GetVDim()),
-     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     ndof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
-     ndofs(fes.GetNDofs())
-{
-   height = vdim*ne*ndof;
-   width = vdim*ne*ndof;
-}
-
-void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
-{
-   const int nd = ndof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
-   auto d_y = Reshape(y.Write(), nd, vd, ne);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int idx = i;
-      const int dof = idx % nd;
-      const int e = idx / nd;
-      for (int c = 0; c < vd; ++c)
-      {
-         d_y(dof, c, e) = d_x(t?c:idx, t?idx:c);
-      }
-   });
-}
-
-void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
-{
-   const int nd = ndof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   auto d_x = Reshape(x.Read(), nd, vd, ne);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int idx = i;
-      const int dof = idx % nd;
-      const int e = idx / nd;
-      for (int c = 0; c < vd; ++c)
-      {
-         d_y(t?c:idx,t?idx:c) = d_x(dof, c, e);
-      }
-   });
-}
-
 ElementRestriction::ElementRestriction(const FiniteElementSpace &f,
                                       ElementDofOrdering e_ordering)
   : fes(f),
@@ -281,7 +232,309 @@ void ElementRestriction::BooleanMask(Vector& y) const
   }
 }

-/// Return the face degrees of freedom returned in Lexicographic order.
+void ElementRestriction::FillSparseMatrix(const Vector &mat_ea,
+                                          SparseMatrix &mat) const
+{
+   mat.GetMemoryI().New(mat.Height()+1, mat.GetMemoryI().GetMemoryType());
+   const int nnz = FillI(mat);
+   mat.GetMemoryJ().New(nnz, mat.GetMemoryJ().GetMemoryType());
+   mat.GetMemoryData().New(nnz, mat.GetMemoryData().GetMemoryType());
+   FillJAndData(mat_ea, mat);
+}
+
+template <int MaxNbNbr>
+static MFEM_HOST_DEVICE int GetMinElt(const int *my_elts, const int nbElts,
+                                      const int *nbr_elts, const int nbrNbElts)
+{
+   // Building the intersection
+   int inter[MaxNbNbr];
+   int cpt = 0;
+   for (int i = 0; i < nbElts; i++)
+   {
+      const int e_i = my_elts[i];
+      for (int j = 0; j < nbrNbElts; j++)
+      {
+         if (e_i==nbr_elts[j])
+         {
+            inter[cpt] = e_i;
+            cpt++;
+         }
+      }
+   }
+   // Finding the minimum
+   int min = inter[0];
+   for (int i = 1; i < cpt; i++)
+   {
+      if (inter[i] < min)
+      {
+         min = inter[i];
+      }
+   }
+   return min;
+}
+
+/** Returns the index where a non-zero entry should be added and increment the
+    number of non-zeros for the row i_L. */
+static MFEM_HOST_DEVICE int GetAndIncrementNnzIndex(const int i_L, int* I)
+{
+   int ind = AtomicAdd(I[i_L],1);
+   return ind;
+}
+
+int ElementRestriction::FillI(SparseMatrix &mat) const
+{
+   static constexpr int Max = MaxNbNbr;
+   const int all_dofs = ndofs;
+   const int vd = vdim;
+   const int elt_dofs = dof;
+   auto I = mat.ReadWriteI();
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_gatherMap = gatherMap.Read();
+   MFEM_FORALL(i_L, vd*all_dofs+1,
+   {
+      I[i_L] = 0;
+   });
+   MFEM_FORALL(e, ne,
+   {
+      for (int i = 0; i < elt_dofs; i++)
+      {
+         int i_elts[Max];
+         const int i_E = e*elt_dofs + i;
+         const int i_L = d_gatherMap[i_E];
+         const int i_offset = d_offsets[i_L];
+         const int i_nextOffset = d_offsets[i_L+1];
+         const int i_nbElts = i_nextOffset - i_offset;
+         for (int e_i = 0; e_i < i_nbElts; ++e_i)
+         {
+            const int i_E = d_indices[i_offset+e_i];
+            i_elts[e_i] = i_E/elt_dofs;
+         }
+         for (int j = 0; j < elt_dofs; j++)
+         {
+            const int j_E = e*elt_dofs + j;
+            const int j_L = d_gatherMap[j_E];
+            const int j_offset = d_offsets[j_L];
+            const int j_nextOffset = d_offsets[j_L+1];
+            const int j_nbElts = j_nextOffset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1) // no assembly required
+            {
+               GetAndIncrementNnzIndex(i_L, I);
+            }
+            else // assembly required
+            {
+               int j_elts[Max];
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_E = d_indices[j_offset+e_j];
+                  const int elt = j_E/elt_dofs;
+                  j_elts[e_j] = elt;
+               }
+               int min_e = GetMinElt<Max>(i_elts, i_nbElts, j_elts, j_nbElts);
+               if (e == min_e) // add the nnz only once
+               {
+                  GetAndIncrementNnzIndex(i_L, I);
+               }
+            }
+         }
+      }
+   });
+   // We need to sum the entries of I, we do it on CPU as it is very sequential.
+   auto h_I = mat.HostReadWriteI();
+   const int nTdofs = vd*all_dofs;
+   int sum = 0;
+   for (int i = 0; i < nTdofs; i++)
+   {
+      const int nnz = h_I[i];
+      h_I[i] = sum;
+      sum+=nnz;
+   }
+   h_I[nTdofs] = sum;
+   // We return the number of nnz
+   return h_I[nTdofs];
+}
+
+void ElementRestriction::FillJAndData(const Vector &ea_data,
+                                      SparseMatrix &mat) const
+{
+   static constexpr int Max = MaxNbNbr;
+   const int all_dofs = ndofs;
+   const int vd = vdim;
+   const int elt_dofs = dof;
+   auto I = mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_gatherMap = gatherMap.Read();
+   auto mat_ea = Reshape(ea_data.Read(), elt_dofs, elt_dofs, ne);
+   MFEM_FORALL(e, ne,
+   {
+      for (int i = 0; i < elt_dofs; i++)
+      {
+         int i_elts[Max];
+         int i_B[Max];
+         const int i_E = e*elt_dofs + i;
+         const int i_L = d_gatherMap[i_E];
+         const int i_offset = d_offsets[i_L];
+         const int i_nextOffset = d_offsets[i_L+1];
+         const int i_nbElts = i_nextOffset - i_offset;
+         for (int e_i = 0; e_i < i_nbElts; ++e_i)
+         {
+            const int i_E = d_indices[i_offset+e_i];
+            i_elts[e_i] = i_E/elt_dofs;
+            i_B[e_i]    = i_E%elt_dofs;
+         }
+         for (int j = 0; j < elt_dofs; j++)
+         {
+            const int j_E = e*elt_dofs + j;
+            const int j_L = d_gatherMap[j_E];
+            const int j_offset = d_offsets[j_L];
+            const int j_nextOffset = d_offsets[j_L+1];
+            const int j_nbElts = j_nextOffset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1) // no assembly required
+            {
+               const int nnz = GetAndIncrementNnzIndex(i_L, I);
+               J[nnz] = j_L;
+               Data[nnz] = mat_ea(j,i,e);
+            }
+            else // assembly required
+            {
+               int j_elts[Max];
+               int j_B[Max];
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_E = d_indices[j_offset+e_j];
+                  const int elt = j_E/elt_dofs;
+                  j_elts[e_j] = elt;
+                  j_B[e_j]    = j_E%elt_dofs;
+               }
+               int min_e = GetMinElt<Max>(i_elts, i_nbElts, j_elts, j_nbElts);
+               if (e == min_e) // add the nnz only once
+               {
+                  double val = 0.0;
+                  for (int i = 0; i < i_nbElts; i++)
+                  {
+                     const int e_i = i_elts[i];
+                     const int i_Bloc = i_B[i];
+                     for (int j = 0; j < j_nbElts; j++)
+                     {
+                        const int e_j = j_elts[j];
+                        const int j_Bloc = j_B[j];
+                        if (e_i == e_j)
+                        {
+                           val += mat_ea(j_Bloc, i_Bloc, e_i);
+                        }
+                     }
+                  }
+                  const int nnz = GetAndIncrementNnzIndex(i_L, I);
+                  J[nnz] = j_L;
+                  Data[nnz] = val;
+               }
+            }
+         }
+      }
+   });
+   // We need to shift again the entries of I, we do it on CPU as it is very
+   // sequential.
+   auto h_I = mat.HostReadWriteI();
+   const int size = vd*all_dofs;
+   for (int i = 0; i < size; i++)
+   {
+      h_I[size-i] = h_I[size-(i+1)];
+   }
+   h_I[0] = 0;
+}
+
+L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
+   : ne(fes.GetNE()),
+     vdim(fes.GetVDim()),
+     byvdim(fes.GetOrdering() == Ordering::byVDIM),
+     ndof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
+     ndofs(fes.GetNDofs())
+{
+   height = vdim*ne*ndof;
+   width = vdim*ne*ndof;
+}
+
+void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
+{
+   const int nd = ndof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.Write(), nd, vd, ne);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int idx = i;
+      const int dof = idx % nd;
+      const int e = idx / nd;
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(dof, c, e) = d_x(t?c:idx, t?idx:c);
+      }
+   });
+}
+
+void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
+{
+   const int nd = ndof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_x = Reshape(x.Read(), nd, vd, ne);
+   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int idx = i;
+      const int dof = idx % nd;
+      const int e = idx / nd;
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(t?c:idx,t?idx:c) = d_x(dof, c, e);
+      }
+   });
+}
+
+void L2ElementRestriction::FillI(SparseMatrix &mat) const
+{
+   const int elem_dofs = ndof;
+   const int vd = vdim;
+   auto I = mat.WriteI();
+   MFEM_FORALL(dof, ne*elem_dofs*vd,
+   {
+      I[dof] = elem_dofs;
+   });
+}
+
+static MFEM_HOST_DEVICE int AddNnz(const int iE, int *I, const int dofs)
+{
+   int val = AtomicAdd(I[iE],dofs);
+   return val;
+}
+
+void L2ElementRestriction::FillJAndData(const Vector &ea_data,
+                                        SparseMatrix &mat) const
+{
+   const int elem_dofs = ndof;
+   const int vd = vdim;
+   auto I = mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto mat_ea = Reshape(ea_data.Read(), elem_dofs, elem_dofs, ne);
+   MFEM_FORALL(iE, ne*elem_dofs*vd,
+   {
+      const int offset = AddNnz(iE,I,elem_dofs);
+      const int e = iE/elem_dofs;
+      const int i = iE%elem_dofs;
+      for (int j = 0; j < elem_dofs; j++)
+      {
+         J[offset+j] = e*elem_dofs+j;
+         Data[offset+j] = mat_ea(j,i,e);
+      }
+   });
+}
+
+// Return the face degrees of freedom returned in Lexicographic order.
 void GetFaceDofs(const int dim, const int face_id,
                 const int dof1d, Array<int> &faceMap)
 {
@@ -700,7 +953,7 @@ static int PermuteFace3D(const int face_id1, const int face_id2,
   return ToLexOrdering3D(face_id2, size1d, new_i, new_j);
 }

-/// Permute dofs or quads on a face for e2 to match with the ordering of e1
+// Permute dofs or quads on a face for e2 to match with the ordering of e1
 int PermuteFaceL2(const int dim, const int face_id1,
                  const int face_id2, const int orientation,
                  const int size1d, const int index)
@@ -720,23 +973,32 @@ int PermuteFaceL2(const int dim, const int face_id1,
 }

 L2FaceRestriction::L2FaceRestriction(const FiniteElementSpace &fes,
-                                     const ElementDofOrdering e_ordering,
                                     const FaceType type,
                                     const L2FaceValues m)
   : fes(fes),
     nf(fes.GetNFbyType(type)),
+     ne(fes.GetNE()),
     vdim(fes.GetVDim()),
     byvdim(fes.GetOrdering() == Ordering::byVDIM),
     ndofs(fes.GetNDofs()),
     dof(nf > 0 ?
         fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof()
         : 0),
+     elemDofs(fes.GetFE(0)->GetDof()),
     m(m),
     nfdofs(nf*dof),
     scatter_indices1(nf*dof),
     scatter_indices2(m==L2FaceValues::DoubleValued?nf*dof:0),
     offsets(ndofs+1),
     gather_indices((m==L2FaceValues::DoubleValued? 2 : 1)*nf*dof)
+{
+}
+
+L2FaceRestriction::L2FaceRestriction(const FiniteElementSpace &fes,
+                                     const ElementDofOrdering e_ordering,
+                                     const FaceType type,
+                                     const L2FaceValues m)
+   : L2FaceRestriction(fes, type, m)
 {
   // If fespace == L2
   const FiniteElement *fe = fes.GetFE(0);
@@ -1034,6 +1296,113 @@ void L2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
   }
 }

+void L2FaceRestriction::FillI(SparseMatrix &mat,
+                              SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int iE1 = d_indices1[fdof];
+      const int iE2 = d_indices2[fdof];
+      AddNnz(iE1,I,face_dofs);
+      AddNnz(iE2,I,face_dofs);
+   });
+}
+
+void L2FaceRestriction::FillJAndData(const Vector &ea_data,
+                                     SparseMatrix &mat,
+                                     SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   auto mat_fea = Reshape(ea_data.Read(), face_dofs, face_dofs, 2, nf);
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int f  = fdof/face_dofs;
+      const int iF = fdof%face_dofs;
+      const int iE1 = d_indices1[f*face_dofs+iF];
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      const int offset1 = AddNnz(iE1,I,face_dofs);
+      const int offset2 = AddNnz(iE2,I,face_dofs);
+      for (int jF = 0; jF < face_dofs; jF++)
+      {
+         const int jE1 = d_indices1[f*face_dofs+jF];
+         const int jE2 = d_indices2[f*face_dofs+jF];
+         J[offset2+jF] = jE1;
+         J[offset1+jF] = jE2;
+         Data[offset2+jF] = mat_fea(jF,iF,0,f);
+         Data[offset1+jF] = mat_fea(jF,iF,1,f);
+      }
+   });
+}
+
+void L2FaceRestriction::AddFaceMatricesToElementMatrices(Vector &fea_data,
+                                                         Vector &ea_data) const
+{
+   const int face_dofs = dof;
+   const int elem_dofs = elemDofs;
+   const int NE = ne;
+   if (m==L2FaceValues::DoubleValued)
+   {
+      auto d_indices1 = scatter_indices1.Read();
+      auto d_indices2 = scatter_indices2.Read();
+      auto mat_fea = Reshape(fea_data.Read(), face_dofs, face_dofs, 2, nf);
+      auto mat_ea = Reshape(ea_data.ReadWrite(), elem_dofs, elem_dofs, ne);
+      MFEM_FORALL(f, nf,
+      {
+         const int e1 = d_indices1[f*face_dofs]/elem_dofs;
+         const int e2 = d_indices2[f*face_dofs]/elem_dofs;
+         for (int j = 0; j < face_dofs; j++)
+         {
+            const int jB1 = d_indices1[f*face_dofs+j]%elem_dofs;
+            for (int i = 0; i < face_dofs; i++)
+            {
+               const int iB1 = d_indices1[f*face_dofs+i]%elem_dofs;
+               AtomicAdd(mat_ea(iB1,jB1,e1), mat_fea(i,j,0,f));
+            }
+         }
+         if (e2 < NE)
+         {
+            for (int j = 0; j < face_dofs; j++)
+            {
+               const int jB2 = d_indices2[f*face_dofs+j]%elem_dofs;
+               for (int i = 0; i < face_dofs; i++)
+               {
+                  const int iB2 = d_indices2[f*face_dofs+i]%elem_dofs;
+                  AtomicAdd(mat_ea(iB2,jB2,e2), mat_fea(i,j,1,f));
+               }
+            }
+         }
+      });
+   }
+   else
+   {
+      auto d_indices = scatter_indices1.Read();
+      auto mat_fea = Reshape(fea_data.Read(), face_dofs, face_dofs, nf);
+      auto mat_ea = Reshape(ea_data.ReadWrite(), elem_dofs, elem_dofs, ne);
+      MFEM_FORALL(f, nf,
+      {
+         const int e = d_indices[f*face_dofs]/elem_dofs;
+         for (int j = 0; j < face_dofs; j++)
+         {
+            const int jE = d_indices[f*face_dofs+j]%elem_dofs;
+            for (int i = 0; i < face_dofs; i++)
+            {
+               const int iE = d_indices[f*face_dofs+i]%elem_dofs;
+               AtomicAdd(mat_ea(iE,jE,e), mat_fea(i,j,f));
+            }
+         }
+      });
+   }
+}
+
 int ToLexOrdering(const int dim, const int face_id, const int size1d,
                  const int index)
 {
@@ -30,6 +30,11 @@ enum class L2FaceValues : bool {SingleValued, DoubleValued};
    objects, see FiniteElementSpace::GetElementRestriction(). */
 class ElementRestriction : public Operator
 {
+private:
+   /** This number defines the maximum number of elements any dof can belong to
+       for the FillSparseMatrix method. */
+   static const int MaxNbNbr = 16;
+
 protected:
   const FiniteElementSpace &fes;
   const int ne;
@@ -59,6 +64,16 @@ public:
       emulate SetSubVector and its transpose on GPUs. This method is running on
       the host, since the `processed` array requires a large shared memory. */
   void BooleanMask(Vector& y) const;
+
+   /// Fill a Sparse Matrix with Element Matrices.
+   void FillSparseMatrix(const Vector &mat_ea, SparseMatrix &mat) const;
+
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this ElementRestriction. */
+   int FillI(SparseMatrix &mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this ElementRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
 };

 /// Operator that converts L2 FiniteElementSpace L-vectors to E-vectors.
@@ -77,6 +92,12 @@ public:
   L2ElementRestriction(const FiniteElementSpace&);
   void Mult(const Vector &x, Vector &y) const;
   void MultTranspose(const Vector &x, Vector &y) const;
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this ElementRestriction. */
+   void FillI(SparseMatrix &mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this L2FaceRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
 };

 /// Operator that extracts Face degrees of freedom.
@@ -111,10 +132,12 @@ class L2FaceRestriction : public Operator
 protected:
   const FiniteElementSpace &fes;
   const int nf;
+   const int ne;
   const int vdim;
   const bool byvdim;
   const int ndofs;
   const int dof;
+   const int elemDofs;
   const L2FaceValues m;
   const int nfdofs;
   Array<int> scatter_indices1;
@@ -122,12 +145,27 @@ protected:
   Array<int> offsets;
   Array<int> gather_indices;

+   L2FaceRestriction(const FiniteElementSpace&,
+                     const FaceType,
+                     const L2FaceValues m = L2FaceValues::DoubleValued);
+
 public:
   L2FaceRestriction(const FiniteElementSpace&, const ElementDofOrdering,
                     const FaceType,
                     const L2FaceValues m = L2FaceValues::DoubleValued);
-   void Mult(const Vector &x, Vector &y) const;
+   virtual void Mult(const Vector &x, Vector &y) const;
   void MultTranspose(const Vector &x, Vector &y) const;
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this L2FaceRestriction. */
+   virtual void FillI(SparseMatrix &mat, SparseMatrix &face_mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this L2FaceRestriction, and the values of ea_data. */
+   virtual void FillJAndData(const Vector &ea_data,
+                             SparseMatrix &mat,
+                             SparseMatrix &face_mat) const;
+   /// This methods adds the DG face matrices to the element matrices.
+   void AddFaceMatricesToElementMatrices(Vector &fea_data,
+                                         Vector &ea_data) const;
 };

 // Return the face degrees of freedom returned in Lexicographic order.
@@ -927,9 +927,20 @@ void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
   }
 }

+void TargetConstructor::ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                                      const Vector &elfun,
+                                                      IsoparametricTransformation &Tpr,
+                                                      DenseTensor &dJtr) const
+{
+   MFEM_ASSERT(target_type == IDEAL_SHAPE_UNIT_SIZE || nodes != NULL, "");
+
+   // TODO: Compute derivative for targets with GIVEN_SHAPE or/and GIVEN_SIZE
+   for (int i = 0; i < Tpr.GetFE()->GetDim()*ir.GetNPoints(); i++) { dJtr(i) = 0.; }
+}
+
 void AnalyticAdaptTC::SetAnalyticTargetSpec(Coefficient *sspec,
                                            VectorCoefficient *vspec,
-                                            MatrixCoefficient *mspec)
+                                            TMOPMatrixCoefficient *mspec)
 {
   scalar_tspec = sspec;
   vector_tspec = vspec;
@@ -970,6 +981,39 @@ void AnalyticAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
   }
 }

+void AnalyticAdaptTC::ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                                    const Vector &elfun,
+                                                    IsoparametricTransformation &Tpr,
+                                                    DenseTensor &dJtr) const
+{
+   const FiniteElement *fe = Tpr.GetFE();
+   DenseMatrix point_mat;
+   point_mat.UseExternalData(elfun.GetData(), fe->GetDof(), fe->GetDim());
+
+   switch (target_type)
+   {
+      case GIVEN_FULL:
+      {
+         MFEM_VERIFY(matrix_tspec != NULL,
+                     "Target type GIVEN_FULL requires a TMOPMatrixCoefficient.");
+
+         for (int d = 0; d < fe->GetDim(); d++)
+         {
+            for (int i = 0; i < ir.GetNPoints(); i++)
+            {
+               const IntegrationPoint &ip = ir.IntPoint(i);
+               Tpr.SetIntPoint(&ip);
+               DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+               matrix_tspec->EvalGrad(dJtr_i, Tpr, ip, d);
+            }
+         }
+         break;
+      }
+      default:
+         MFEM_ABORT("Incompatible target type for analytic adaptation!");
+   }
+}
+
 #ifdef MFEM_USE_MPI
 void DiscreteAdaptTC::FinalizeParDiscreteTargetSpec(const ParGridFunction
                                                    &tspec_)
@@ -1168,7 +1212,7 @@ void DiscreteAdaptTC::UpdateTargetSpecificationAtNode(const FiniteElement &el,

   Array<int> dofs;
   tspec_fes->GetElementDofs(T.ElementNo, dofs);
-   const int cnt = tspec.Size()/ncomp; //dofs per scalar-field
+   const int cnt = tspec.Size()/ncomp; // dofs per scalar-field

   for (int i = 0; i < ncomp; i++)
   {
@@ -1196,6 +1240,9 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
                                            DenseTensor &Jtr) const
 {
   MFEM_VERIFY(tspec_fesv, "No target specifications have been set.");
+   const int dim = fe.GetDim(),
+             nqp = ir.GetNPoints();
+   Jtrcomp.SetSize(dim, dim, 4*nqp);

   switch (target_type)
   {
@@ -1205,7 +1252,7 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
         const DenseMatrix &Wideal =
            Geometries.GetGeomToPerfGeomJac(fe.GetGeomType());
         const int dim = Wideal.Height(),
-                   ndofs = tspec_fes->GetFE(0)->GetDof(),
+                   ndofs = tspec_fes->GetFE(e_id)->GetDof(),
                   ntspec_dofs = ndofs*ncomp;

         Vector shape(ndofs), tspec_vals(ntspec_dofs), par_vals,
@@ -1216,25 +1263,32 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
         tspec_fesv->GetElementVDofs(e_id, dofs);
         tspec.GetSubVector(dofs, tspec_vals);

-         for (int i = 0; i < ir.GetNPoints(); i++)
+         for (int q = 0; q < nqp; q++)
         {
-            const IntegrationPoint &ip = ir.IntPoint(i);
+            const IntegrationPoint &ip = ir.IntPoint(q);
            tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
-            Jtr(i) = Wideal; //Initialize to identity
+            Jtr(q) = Wideal; // Initialize to identity
+            for (int d = 0; d < 4; d++)
+            {
+               DenseMatrix Jtrcomp_q(Jtrcomp.GetData(d + 4*q), dim, dim);
+               Jtrcomp_q = Wideal; // Initialize to identity
+            }

-            if (sizeidx != -1) //Set size
+            if (sizeidx != -1) // Set size
            {
               par_vals.SetDataAndSize(tspec_vals.GetData()+sizeidx*ndofs, ndofs);
               const double min_size = par_vals.Min();
               MFEM_VERIFY(min_size > 0.0,
                           "Non-positive size propagated in the target definition.");
               const double size = std::max(shape * par_vals, min_size);
-               Jtr(i).Set(std::pow(size, 1.0/dim), Jtr(i));
-            } //Done size
+               Jtr(q).Set(std::pow(size, 1.0/dim), Jtr(q));
+               DenseMatrix Jtrcomp_q(Jtrcomp.GetData(0 + 4*q), dim, dim);
+               Jtrcomp_q = Jtr(q);
+            } // Done size

            if (target_type == IDEAL_SHAPE_GIVEN_SIZE) { continue; }

-            if (aspectratioidx != -1) //Set aspect ratio
+            if (aspectratioidx != -1) // Set aspect ratio
            {
               if (dim == 2)
               {
@@ -1262,12 +1316,13 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
                  D_rho(1,1) = pow(rho2,2./3.);
                  D_rho(2,2) = pow(rho3,2./3.);
               }
+               DenseMatrix Jtrcomp_q(Jtrcomp.GetData(1 + 4*q), dim, dim);
+               Jtrcomp_q = D_rho;
+               DenseMatrix Temp = Jtr(q);
+               Mult(D_rho, Temp, Jtr(q));
+            } // Done aspect ratio

-               DenseMatrix Temp = Jtr(i);
-               Mult(D_rho, Temp, Jtr(i));
-            } //Done aspect ratio
-
-            if (skewidx != -1) //Set skew
+            if (skewidx != -1) // Set skew
            {
               if (dim == 2)
               {
@@ -1303,12 +1358,13 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,

                  Q_phi(2,2) = sin(phi13)*sin(chi);
               }
+               DenseMatrix Jtrcomp_q(Jtrcomp.GetData(2 + 4*q), dim, dim);
+               Jtrcomp_q = Q_phi;
+               DenseMatrix Temp = Jtr(q);
+               Mult(Q_phi, Temp, Jtr(q));
+            } // Done skew

-               DenseMatrix Temp = Jtr(i);
-               Mult(Q_phi, Temp, Jtr(i));
-            } // done skew
-
-            if (orientationidx != -1) //Set orientation
+            if (orientationidx != -1) // Set orientation
            {
               if (dim == 2)
               {
@@ -1333,33 +1389,28 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
                  const double psi   = shape * par_vals_c2;
                  const double beta  = shape * par_vals_c3;

-                  DenseMatrix R_tp(dim), R_beta(dim), R_theta(dim);
                  double ct = cos(theta), st = sin(theta),
-                         cp = cos(psi),   sp = sin(psi);
-                  R_tp(0,0) = ct*sp;
-                  R_tp(1,0) = st*sp;
-                  R_tp(2,0) = cp;
+                         cp = cos(psi),   sp = sin(psi),
+                         cb = cos(beta),  sb = sin(beta);

-                  R_tp(0,1) = -(ct*st*sp*sp)/(1+cp);
-                  R_tp(1,1) = cp+(pow(ct,2.)*pow(sp,2.))/(1+cp);
-                  R_tp(2,1) = -st*sp;
+                  R_theta = 0.;
+                  R_theta(0,0) = ct*sp;
+                  R_theta(1,0) = st*sp;
+                  R_theta(2,0) = cp;

-                  R_tp(0,2) = -cp-(pow(st,2.)*pow(sp,2.))/(1+cp);
-                  R_tp(1,2) = -R_tp(0,1);
-                  R_tp(2,2) =  ct*sp;
+                  R_theta(0,1) = -st*cb + ct*cp*sb;
+                  R_theta(1,1) = ct*cb + st*cp*sb;
+                  R_theta(2,1) = -sp*sb;

-                  R_beta = 0.;
-                  R_beta(0,0) = 1.;
-                  R_beta(1,1) =  cos(beta);
-                  R_beta(1,2) = -sin(beta);
-                  R_beta(2,1) =  sin(beta);
-                  R_beta(2,2) =  cos(beta);
-
-                  Mult(R_tp, R_beta, R_theta);
+                  R_theta(0,0) = -st*sb - ct*cp*cb;
+                  R_theta(1,0) = ct*sb - st*cp*cb;
+                  R_theta(2,0) = sp*cb;
               }
-               DenseMatrix Temp = Jtr(i);
-               Mult(R_theta, Temp, Jtr(i));
-            } // done orientation
+               DenseMatrix Jtrcomp_q(Jtrcomp.GetData(3 + 4*q), dim, dim);
+               Jtrcomp_q = R_theta;
+               DenseMatrix Temp = Jtr(q);
+               Mult(R_theta, Temp, Jtr(q));
+            } // Done orientation
         }
         break;
      }
@@ -1368,6 +1419,353 @@ void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
   }
 }

+void DiscreteAdaptTC::ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                                    const Vector &elfun,
+                                                    IsoparametricTransformation &Tpr,
+                                                    DenseTensor &dJtr) const
+{
+   MFEM_ASSERT(target_type == IDEAL_SHAPE_UNIT_SIZE || nodes != NULL, "");
+
+   MFEM_VERIFY(tspec_fesv, "No target specifications have been set.");
+
+   dJtr = 0.;
+   const int e_id = Tpr.ElementNo;
+   const FiniteElement *fe = Tpr.GetFE();
+
+   switch (target_type)
+   {
+      case IDEAL_SHAPE_GIVEN_SIZE:
+      case GIVEN_SHAPE_AND_SIZE:
+      {
+         const DenseMatrix &Wideal =
+            Geometries.GetGeomToPerfGeomJac(fe->GetGeomType());
+         const int dim = Wideal.Height(),
+                   ndofs = fe->GetDof(),
+                   ntspec_dofs = ndofs*ncomp;
+
+         Vector shape(ndofs), tspec_vals(ntspec_dofs), par_vals,
+                par_vals_c1(ndofs), par_vals_c2(ndofs), par_vals_c3(ndofs);
+
+         Array<int> dofs;
+         DenseMatrix dD_rho(dim), dQ_phi(dim), dR_theta(dim);
+         DenseMatrix dQ_phi13(dim), dQ_phichi(dim); // dQ_phi is used for dQ/dphi12 in 3D
+         DenseMatrix dR_psi(dim), dR_beta(dim);
+         tspec_fesv->GetElementVDofs(e_id, dofs);
+         tspec.GetSubVector(dofs, tspec_vals);
+
+         DenseMatrix grad_e_c1(ndofs, dim),
+                     grad_e_c2(ndofs, dim),
+                     grad_e_c3(ndofs, dim);
+         Vector grad_ptr_c1(grad_e_c1.GetData(), ndofs*dim),
+                grad_ptr_c2(grad_e_c2.GetData(), ndofs*dim),
+                grad_ptr_c3(grad_e_c3.GetData(), ndofs*dim);
+
+         DenseMatrix grad_phys; // This will be (dof x dim, dof).
+         fe->ProjectGrad(*fe, Tpr, grad_phys);
+
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+            DenseMatrix Jtrcomp_s(Jtrcomp.GetData(0 + 4*i), dim, dim); // size
+            DenseMatrix Jtrcomp_d(Jtrcomp.GetData(1 + 4*i), dim, dim); // aspect-ratio
+            DenseMatrix Jtrcomp_q(Jtrcomp.GetData(2 + 4*i), dim, dim); // skew
+            DenseMatrix Jtrcomp_r(Jtrcomp.GetData(3 + 4*i), dim, dim); // orientation
+            DenseMatrix work1(dim), work2(dim), work3(dim);
+
+            if (sizeidx != -1) // Set size
+            {
+               par_vals.SetDataAndSize(tspec_vals.GetData()+sizeidx*ndofs, ndofs);
+
+               grad_phys.Mult(par_vals, grad_ptr_c1);
+               Vector grad_q(dim);
+               tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+               grad_e_c1.MultTranspose(shape, grad_q);
+
+               const double min_size = par_vals.Min();
+               MFEM_VERIFY(min_size > 0.0,
+                           "Non-positive size propagated in the target definition.");
+               const double size = std::max(shape * par_vals, min_size);
+               double dz_dsize = (1./dim)*pow(size, 1./dim - 1.);
+
+               Mult(Jtrcomp_q, Jtrcomp_d, work1); // Q*D
+               Mult(Jtrcomp_r, work1, work2);     // R*Q*D
+
+               for (int d = 0; d < dim; d++)
+               {
+                  DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                  work1 = Wideal;
+                  work1.Set(dz_dsize, work1);    // dz/dsize
+                  work1 *= grad_q(d);            // dz/dsize*dsize/dx
+                  AddMult(work1, work2, dJtr_i); // dz/dx*R*Q*D
+               }
+            } // Done size
+
+            if (target_type == IDEAL_SHAPE_GIVEN_SIZE) { continue; }
+
+            if (aspectratioidx != -1) // Set aspect ratio
+            {
+               if (dim == 2)
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          aspectratioidx*ndofs, ndofs);
+
+                  grad_phys.Mult(par_vals, grad_ptr_c1);
+                  Vector grad_q(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q);
+
+                  const double aspectratio = shape * par_vals;
+                  dD_rho = 0.;
+                  dD_rho(0,0) = -0.5*pow(aspectratio,-1.5);
+                  dD_rho(1,1) = 0.5*pow(aspectratio,-0.5);
+
+                  Mult(Jtrcomp_s, Jtrcomp_r, work1); // z*R
+                  Mult(work1, Jtrcomp_q, work2);     // z*R*Q
+
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dD_rho;
+                     work1 *= grad_q(d); // work1 = dD/drho*drho/dx
+                     AddMult(work2, work1, dJtr_i); // z*R*Q*dD/dx
+                  }
+               }
+               else // 3D
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          aspectratioidx*ndofs, ndofs*3);
+                  par_vals_c1.SetData(par_vals.GetData());
+                  par_vals_c2.SetData(par_vals.GetData()+ndofs);
+                  par_vals_c3.SetData(par_vals.GetData()+2*ndofs);
+
+                  grad_phys.Mult(par_vals_c1, grad_ptr_c1);
+                  grad_phys.Mult(par_vals_c2, grad_ptr_c2);
+                  grad_phys.Mult(par_vals_c3, grad_ptr_c3);
+                  Vector grad_q1(dim), grad_q2(dim), grad_q3(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q1);
+                  grad_e_c2.MultTranspose(shape, grad_q2);
+                  grad_e_c3.MultTranspose(shape, grad_q3);
+
+                  const double rho1 = shape * par_vals_c1;
+                  const double rho2 = shape * par_vals_c2;
+                  const double rho3 = shape * par_vals_c3;
+                  dD_rho = 0.;
+                  dD_rho(0,0) = (2./3.)*pow(rho1,-1./3.);
+                  dD_rho(1,1) = (2./3.)*pow(rho2,-1./3.);
+                  dD_rho(2,2) = (2./3.)*pow(rho3,-1./3.);
+
+                  Mult(Jtrcomp_s, Jtrcomp_r, work1); // z*R
+                  Mult(work1, Jtrcomp_q, work2);     // z*R*Q
+
+
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dD_rho;
+                     work1(0,0) *= grad_q1(d);
+                     work1(1,2) *= grad_q2(d);
+                     work1(2,2) *= grad_q3(d);
+                     // work1 = dD/dx = dD/drho1*drho1/dx + dD/drho2*drho2/dx
+                     AddMult(work2, work1, dJtr_i); // z*R*Q*dD/dx
+                  }
+               }
+            } // Done aspect ratio
+
+            if (skewidx != -1) // Set skew
+            {
+               if (dim == 2)
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          skewidx*ndofs, ndofs);
+
+                  grad_phys.Mult(par_vals, grad_ptr_c1);
+                  Vector grad_q(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q);
+
+                  const double skew = shape * par_vals;
+
+                  dQ_phi = 0.;
+                  dQ_phi(0,0) = 1.;
+                  dQ_phi(0,1) = -sin(skew);
+                  dQ_phi(1,1) = cos(skew);
+
+                  Mult(Jtrcomp_s, Jtrcomp_r, work2); // z*R
+
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dQ_phi;
+                     work1 *= grad_q(d); // work1 = dQ/dphi*dphi/dx
+                     Mult(work1, Jtrcomp_d, work3); // dQ/dx*D
+                     AddMult(work2, work3, dJtr_i); // z*R*dQ/dx*D
+                  }
+               }
+               else
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          skewidx*ndofs, ndofs*3);
+                  par_vals_c1.SetData(par_vals.GetData());
+                  par_vals_c2.SetData(par_vals.GetData()+ndofs);
+                  par_vals_c3.SetData(par_vals.GetData()+2*ndofs);
+
+                  grad_phys.Mult(par_vals_c1, grad_ptr_c1);
+                  grad_phys.Mult(par_vals_c2, grad_ptr_c2);
+                  grad_phys.Mult(par_vals_c3, grad_ptr_c3);
+                  Vector grad_q1(dim), grad_q2(dim), grad_q3(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q1);
+                  grad_e_c2.MultTranspose(shape, grad_q2);
+                  grad_e_c3.MultTranspose(shape, grad_q3);
+
+                  const double phi12  = shape * par_vals_c1;
+                  const double phi13  = shape * par_vals_c2;
+                  const double chi = shape * par_vals_c3;
+
+                  dQ_phi = 0.;
+                  dQ_phi(0,0) = 1.;
+                  dQ_phi(0,1) = -sin(phi12);
+                  dQ_phi(1,1) = cos(phi12);
+
+                  dQ_phi13 = 0.;
+                  dQ_phi13(0,2) = -sin(phi13);
+                  dQ_phi13(1,2) = cos(phi13)*cos(chi);
+                  dQ_phi13(2,2) = cos(phi13)*sin(chi);
+
+                  dQ_phichi = 0.;
+                  dQ_phichi(1,2) = -sin(phi13)*sin(chi);
+                  dQ_phichi(2,2) =  sin(phi13)*cos(chi);
+
+                  Mult(Jtrcomp_s, Jtrcomp_r, work2); // z*R
+
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dQ_phi;
+                     work1 *= grad_q1(d); // work1 = dQ/dphi12*dphi12/dx
+                     work1.Add(grad_q2(d), dQ_phi13);  // + dQ/dphi13*dphi13/dx
+                     work1.Add(grad_q3(d), dQ_phichi); // + dQ/dchi*dchi/dx
+                     Mult(work1, Jtrcomp_d, work3); // dQ/dx*D
+                     AddMult(work2, work3, dJtr_i); // z*R*dQ/dx*D
+                  }
+               }
+            } // Done skew
+
+            if (orientationidx != -1) // Set orientation
+            {
+               if (dim == 2)
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          orientationidx*ndofs, ndofs);
+
+                  grad_phys.Mult(par_vals, grad_ptr_c1);
+                  Vector grad_q(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q);
+
+                  const double theta = shape * par_vals;
+                  dR_theta(0,0) = -sin(theta);
+                  dR_theta(0,1) = -cos(theta);
+                  dR_theta(1,0) =  cos(theta);
+                  dR_theta(1,1) = -sin(theta);
+
+                  Mult(Jtrcomp_q, Jtrcomp_d, work1); // Q*D
+                  Mult(Jtrcomp_s, work1, work2);     // z*Q*D
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dR_theta;
+                     work1 *= grad_q(d); // work1 = dR/dtheta*dtheta/dx
+                     AddMult(work1, work2, dJtr_i);  // z*dR/dx*Q*D
+                  }
+               }
+               else
+               {
+                  par_vals.SetDataAndSize(tspec_vals.GetData()+
+                                          orientationidx*ndofs, ndofs*3);
+                  par_vals_c1.SetData(par_vals.GetData());
+                  par_vals_c2.SetData(par_vals.GetData()+ndofs);
+                  par_vals_c3.SetData(par_vals.GetData()+2*ndofs);
+
+                  grad_phys.Mult(par_vals_c1, grad_ptr_c1);
+                  grad_phys.Mult(par_vals_c2, grad_ptr_c2);
+                  grad_phys.Mult(par_vals_c3, grad_ptr_c3);
+                  Vector grad_q1(dim), grad_q2(dim), grad_q3(dim);
+                  tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+                  grad_e_c1.MultTranspose(shape, grad_q1);
+                  grad_e_c2.MultTranspose(shape, grad_q2);
+                  grad_e_c3.MultTranspose(shape, grad_q3);
+
+                  const double theta = shape * par_vals_c1;
+                  const double psi   = shape * par_vals_c2;
+                  const double beta  = shape * par_vals_c3;
+
+                  const double ct = cos(theta), st = sin(theta),
+                               cp = cos(psi),   sp = sin(psi),
+                               cb = cos(beta),  sb = sin(beta);
+
+                  dR_theta = 0.;
+                  dR_theta(0,0) = -st*sp;
+                  dR_theta(1,0) = ct*sp;
+                  dR_theta(2,0) = 0;
+
+                  dR_theta(0,1) = -ct*cb - st*cp*sb;
+                  dR_theta(1,1) = -st*cb + ct*cp*sb;
+                  dR_theta(2,1) = 0.;
+
+                  dR_theta(0,0) = -ct*sb + st*cp*cb;
+                  dR_theta(1,0) = -st*sb - ct*cp*cb;
+                  dR_theta(2,0) = 0.;
+
+                  dR_beta = 0.;
+                  dR_beta(0,0) = 0.;
+                  dR_beta(1,0) = 0.;
+                  dR_beta(2,0) = 0.;
+
+                  dR_beta(0,1) = st*sb + ct*cp*cb;
+                  dR_beta(1,1) = -ct*sb + st*cp*cb;
+                  dR_beta(2,1) = -sp*cb;
+
+                  dR_beta(0,0) = -st*cb + ct*cp*sb;
+                  dR_beta(1,0) = ct*cb + st*cp*sb;
+                  dR_beta(2,0) = 0.;
+
+                  dR_psi = 0.;
+                  dR_psi(0,0) = ct*cp;
+                  dR_psi(1,0) = st*cp;
+                  dR_psi(2,0) = -sp;
+
+                  dR_psi(0,1) = 0. - ct*sp*sb;
+                  dR_psi(1,1) = 0. + st*sp*sb;
+                  dR_psi(2,1) = -cp*sb;
+
+                  dR_psi(0,0) = 0. + ct*sp*cb;
+                  dR_psi(1,0) = 0. + st*sp*cb;
+                  dR_psi(2,0) = cp*cb;
+
+                  Mult(Jtrcomp_q, Jtrcomp_d, work1); // Q*D
+                  Mult(Jtrcomp_s, work1, work2);     // z*Q*D
+                  for (int d = 0; d < dim; d++)
+                  {
+                     DenseMatrix &dJtr_i = dJtr(i + d*ir.GetNPoints());
+                     work1 = dR_theta;
+                     work1 *= grad_q1(d); // work1 = dR/dtheta*dtheta/dx
+                     work1.Add(grad_q2(d), dR_psi);  // +dR/dpsi*dpsi/dx
+                     work1.Add(grad_q3(d), dR_beta); // +dR/dbeta*dbeta/dx
+                     AddMult(work1, work2, dJtr_i);  // z*dR/dx*Q*D
+                  }
+               }
+            } // Done orientation
+         }
+         break;
+      }
+      default:
+         MFEM_ABORT("Incompatible target type for discrete adaptation!");
+   }
+   Jtrcomp.Clear();
+}
+
 void DiscreteAdaptTC::UpdateGradientTargetSpecification(const Vector &x,
                                                        const double dx,
                                                        bool use_flag)
@@ -1697,6 +2095,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
 {
   const int dof = el.GetDof(), dim = el.GetDim();

+   DenseMatrix Amat(dim), work1(dim), work2(dim);
   DSh.SetSize(dof, dim);
   DS.SetSize(dof, dim);
   Jrt.SetSize(dim);
@@ -1712,14 +2111,15 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
   elvect = 0.0;
   Vector weights(nqp);
   DenseTensor Jtr(dim, dim, nqp);
+   DenseTensor dJtr(dim, dim, dim*nqp);
   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);

   // Limited case.
   DenseMatrix pos0;
   Vector shape, p, p0, d_vals, grad;
+   shape.SetSize(dof);
   if (coeff0)
   {
-      shape.SetSize(dof);
      p.SetSize(dim);
      p0.SetSize(dim);
      pos0.SetSize(dof, dim);
@@ -1739,16 +2139,23 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,

   // Define ref->physical transformation, when a Coefficient is specified.
   IsoparametricTransformation *Tpr = NULL;
-   if (coeff1 || coeff0 || zeta)
+   if (coeff1 || coeff0 || zeta || exact_action)
   {
      Tpr = new IsoparametricTransformation;
      Tpr->SetFE(&el);
      Tpr->ElementNo = T.ElementNo;
-      Tpr->ElementType = ElementTransformation::ELEMENT;
      Tpr->Attribute = T.Attribute;
      Tpr->GetPointMat().Transpose(PMatI); // PointMat = PMatI^T
+      if (exact_action)
+      {
+         targetC->ComputeElementTargetsGradient(*ir, elfun, *Tpr, dJtr);
+      }
   }

+
+   Vector d_detW_dx(dim);
+   Vector d_Winv_dx(dim);
+
   for (int q = 0; q < nqp; q++)
   {
      const IntegrationPoint &ip = ir->IntPoint(q);
@@ -1767,13 +2174,44 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
      if (coeff1) { weight_m *= coeff1->Eval(*Tpr, ip); }

      P *= weight_m;
-      AddMultABt(DS, P, PMatO);
+      AddMultABt(DS, P, PMatO); // w_q det(W) dmu/dx : dA/dx Winv

-      // TODO: derivatives of adaptivity-based targets.
+      if (exact_action)
+      {
+         el.CalcShape(ip, shape);
+         // Derivatives of adaptivity-based targets.
+         // First term: w_q d*(Det W)/dx * mu(T)
+         // d(Det W)/dx = det(W)*Tr[Winv*dW/dx]
+         DenseMatrix dwdx(dim);
+         for (int d = 0; d < dim; d++)
+         {
+            const DenseMatrix &dJtr_q = dJtr(q + d*ir->GetNPoints());
+            Mult(Jrt, dJtr_q, dwdx );
+            d_detW_dx(d) = dwdx.Trace();
+         }
+         d_detW_dx *= weight_m*metric->EvalW(Jpt); // *[w_q*det(W)]*mu(T)
+
+         // Second term: w_q det(W) dmu/dx : AdWinv/dx
+         // dWinv/dx = -Winv*dW/dx*Winv
+         MultAtB(PMatI, DSh, Amat);
+         for (int d = 0; d < dim; d++)
+         {
+            const DenseMatrix &dJtr_q = dJtr(q + d*nqp);
+            Mult(Jrt, dJtr_q, work1); // Winv*dw/dx
+            Mult(work1, Jrt, work2);  // Winv*dw/dx*Winv
+            Mult(Amat, work2, work1); // A*Winv*dw/dx*Winv
+            MultAtB(P, work1, work2); // dmu/dT^T*A*Winv*dw/dx*Winv
+            d_Winv_dx(d) = work2.Trace(); // Tr[dmu/dT : AWinv*dw/dx*Winv]
+         }
+         d_Winv_dx *= -weight_m; // Include (-) factor as well
+
+         d_detW_dx += d_Winv_dx;
+         AddMultVWt(shape, d_detW_dx, PMatO);
+      }

      if (coeff0)
      {
-         el.CalcShape(ip, shape);
+         if (!exact_action) { el.CalcShape(ip, shape); }
         PMatI.MultTranspose(shape, p);
         pos0.MultTranspose(shape, p0);
         lim_func->Eval_d1(p, p0, d_vals(q), grad);
@@ -2214,7 +2652,8 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
   Jpt.SetSize(dim);

   const IntegrationRule *ir = EnergyIntegrationRule(*fe);
-   DenseTensor Jtr(dim, dim, ir->GetNPoints());
+   const int nqp =  ir->GetNPoints();
+   DenseTensor Jtr(dim, dim, nqp);

   metric_energy = 0.0;
   lim_energy = 0.0;
@@ -2227,12 +2666,12 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,

      targetC->ComputeElementTargets(i, *fe, *ir, x_vals, Jtr);

-      for (int i = 0; i < ir->GetNPoints(); i++)
+      for (int q = 0; q < nqp; q++)
      {
-         const IntegrationPoint &ip = ir->IntPoint(i);
-         metric->SetTargetJacobian(Jtr(i));
-         CalcInverse(Jtr(i), Jrt);
-         const double weight = ip.weight * Jtr(i).Det();
+         const IntegrationPoint &ip = ir->IntPoint(q);
+         metric->SetTargetJacobian(Jtr(q));
+         CalcInverse(Jtr(q), Jrt);
+         const double weight = ip.weight * Jtr(q).Det();

         fe->CalcDShape(ip, DSh);
         MultAtB(PMatI, DSh, Jpr);
@@ -677,6 +677,25 @@ public:
                                      const IntegrationRule &ir,
                                      const Vector &elfun,
                                      DenseTensor &Jtr) const;
+
+   virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                              const Vector &elfun,
+                                              IsoparametricTransformation &Tpr,
+                                              DenseTensor &dJtr) const;
+};
+
+class TMOPMatrixCoefficient  : public MatrixCoefficient
+{
+public:
+   explicit TMOPMatrixCoefficient(int dim) : MatrixCoefficient(dim, dim) { }
+
+   /** @brief Evaluate the derivative of the matrix coefficient with respect to
+       @a comp in the element described by @a T at the point @a ip, storing the
+       result in @a K. */
+   virtual void EvalGrad(DenseMatrix &K, ElementTransformation &T,
+                         const IntegrationPoint &ip, int comp) = 0;
+
+   virtual ~TMOPMatrixCoefficient() { }
 };

 class AnalyticAdaptTC : public TargetConstructor
@@ -685,7 +704,7 @@ protected:
   // Analytic target specification.
   Coefficient *scalar_tspec;
   VectorCoefficient *vector_tspec;
-   MatrixCoefficient *matrix_tspec;
+   TMOPMatrixCoefficient *matrix_tspec;

 public:
   AnalyticAdaptTC(TargetType ttype)
@@ -694,7 +713,7 @@ public:

   virtual void SetAnalyticTargetSpec(Coefficient *sspec,
                                      VectorCoefficient *vspec,
-                                      MatrixCoefficient *mspec);
+                                      TMOPMatrixCoefficient *mspec);

   /** @brief Given an element and quadrature rule, computes ref->target
       transformation Jacobians for each quadrature point in the element.
@@ -703,6 +722,11 @@ public:
                                      const IntegrationRule &ir,
                                      const Vector &elfun,
                                      DenseTensor &Jtr) const;
+
+   virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                              const Vector &elfun,
+                                              IsoparametricTransformation &Tpr,
+                                              DenseTensor &dJtr) const;
 };

 #ifdef MFEM_USE_MPI
@@ -724,13 +748,17 @@ protected:
   // eta1(x+h,y), eta2(x+h,y) ... etan(x+h,y), eta1(x,y+h), eta2(x,y+h) ...
   // same for tspec_pert2h and tspec_pertmix.

+   // Components of Target Jacobian at each quadrature point of an element. This
+   // is required for computation of the derivative using chain rule.
+   mutable DenseTensor Jtrcomp;
+
   // Note: do not use the Nodes of this space as they may not be on the
   // positions corresponding to the values of tspec.
   const FiniteElementSpace *tspec_fes;
   const FiniteElementSpace *tspec_fesv;

-   // These flags can be used by outside functions to avoid recomputing
-   // the tspec and tspec_perth fields again on the same mesh.
+   // These flags can be used by outside functions to avoid recomputing the
+   // tspec and tspec_perth fields again on the same mesh.
   bool good_tspec, good_tspec_grad, good_tspec_hess;

   // Evaluation of the discrete target specification on different meshes.
@@ -837,6 +865,11 @@ public:
                                      const IntegrationRule &ir,
                                      const Vector &elfun,
                                      DenseTensor &Jtr) const;
+
+   virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
+                                              const Vector &elfun,
+                                              IsoparametricTransformation &Tpr,
+                                              DenseTensor &dJtr) const;
 };

 class TMOPNewtonSolver;
@@ -889,6 +922,9 @@ protected:
   // Specifies that ComputeElementTargets is being called by a FD function.
   // It's used to skip terms that have exact derivative calculations.
   bool fd_call_flag;
+   // Compute the exact action of the Integrator (includes derivative of the
+   // target with respect to spatial position)
+   bool exact_action;

   Array <Vector *> ElemDer;        //f'(x)
   Array <Vector *> ElemPertEnergy; //f(x+h)
@@ -978,7 +1014,7 @@ public:
        lim_dist(NULL), lim_func(NULL), lim_normal(1.0),
        zeta_0(NULL), zeta(NULL), coeff_zeta(NULL), adapt_eval(NULL),
        discr_tc(dynamic_cast<DiscreteAdaptTC *>(tc)),
-        fdflag(false), dxscale(1.0e3), fd_call_flag(false)
+        fdflag(false), dxscale(1.0e3), fd_call_flag(false), exact_action(false)
   { }

   ~TMOP_Integrator();
@@ -1066,6 +1102,9 @@ public:
   void   SetFDhScale(double _dxscale) { dxscale = _dxscale; }
   bool   GetFDFlag() const { return fdflag; }
   double GetFDh()    const { return dx; }
+
+   /** @brief Flag to control if exact action of Integration is effected. */
+   void SetExactActionFlag(bool flag_) { exact_action = flag_; }
 };

 class TMOPComboIntegrator : public NonlinearFormIntegrator
@@ -32,6 +32,7 @@ list(APPEND SRCS

 list(APPEND HDRS
  array.hpp
+  backends.hpp
  binaryio.hpp
  cuda.hpp
  device.hpp
@@ -36,9 +36,9 @@ void Swap(Array<T> &, Array<T> &);
   Abstract data type Array.

   Array<T> is an automatically increasing array containing elements of the
-   generic type T. The allocated size may be larger then the logical size
-   of the array.
-   The elements can be accessed by the [] operator, the range is 0 to size-1.
+   generic type T, which must be a POD (plain old data) type. The allocated size
+   may be larger then the logical size of the array. The elements can be
+   accessed by the [] operator, the range is 0 to size-1.
 */
 template <class T>
 class Array
@@ -0,0 +1,72 @@
+// Copyright (c) 2010-2020, 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_BACKENDS_HPP
+#define MFEM_BACKENDS_HPP
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_USE_CUDA
+#include <cuda_runtime.h>
+#include <cuda.h>
+#endif
+#include "cuda.hpp"
+
+#ifdef MFEM_USE_HIP
+#include <hip/hip_runtime.h>
+#endif
+#include "hip.hpp"
+
+#ifdef MFEM_USE_OCCA
+#include <occa.hpp>
+#include "occa.hpp"
+#endif
+
+#ifdef MFEM_USE_RAJA
+#include "RAJA/RAJA.hpp"
+#if defined(RAJA_ENABLE_CUDA) && !defined(MFEM_USE_CUDA)
+#error When RAJA is built with CUDA, MFEM_USE_CUDA=YES is required
+#endif
+#endif
+
+#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
+#define MFEM_DEVICE
+#define MFEM_LAMBDA
+#define MFEM_HOST_DEVICE
+// MFEM_DEVICE_SYNC is made available for debugging purposes
+#define MFEM_DEVICE_SYNC
+// MFEM_STREAM_SYNC is used for UVM and MPI GPU-Aware kernels
+#define MFEM_STREAM_SYNC
+#endif
+
+#if !((defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__)) || \
+      (defined(MFEM_USE_HIP)  && defined(__HIP_DEVICE_COMPILE__)))
+#define MFEM_SHARED
+#define MFEM_SYNC_THREAD
+#define MFEM_THREAD_ID(k) 0
+#define MFEM_THREAD_SIZE(k) 1
+#define MFEM_FOREACH_THREAD(i,k,N) for(int i=0; i<N; i++)
+#endif
+
+template <typename T>
+MFEM_HOST_DEVICE T AtomicAdd(T &add, const T val)
+{
+#if ((defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__)) || \
+     (defined(MFEM_USE_HIP)  && defined(__HIP_DEVICE_COMPILE__)))
+   return atomicAdd(&add,val);
+#else
+   T old = add;
+   add += val;
+   return old;
+#endif
+}
+
+#endif // MFEM_BACKENDS_HPP
@@ -9,7 +9,7 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.

-#include "cuda.hpp"
+#include "backends.hpp"
 #include "globals.hpp"

 namespace mfem
@@ -15,17 +15,15 @@
 #include "../config/config.hpp"
 #include "error.hpp"

-#ifdef MFEM_USE_CUDA
-#include <cuda_runtime.h>
-#include <cuda.h>
-#endif
-
 // CUDA block size used by MFEM.
 #define MFEM_CUDA_BLOCKS 256

 #ifdef MFEM_USE_CUDA
 #define MFEM_DEVICE __device__
+#define MFEM_LAMBDA __host__
 #define MFEM_HOST_DEVICE __host__ __device__
+#define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(cudaDeviceSynchronize())
+#define MFEM_STREAM_SYNC MFEM_GPU_CHECK(cudaStreamSynchronize(0))
 // Define a CUDA error check macro, MFEM_GPU_CHECK(x), where x returns/is of
 // type 'cudaError_t'. This macro evaluates 'x' and raises an error if the
 // result is not cudaSuccess.
@@ -39,8 +37,6 @@
      } \
   } \
   while (0)
-#define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(cudaDeviceSynchronize())
-#define MFEM_STREAM_SYNC MFEM_GPU_CHECK(cudaStreamSynchronize(0))
 #endif // MFEM_USE_CUDA

 // Define the MFEM inner threading macros
@@ -52,22 +48,6 @@
 #define MFEM_FOREACH_THREAD(i,k,N) for(int i=threadIdx.k; i<N; i+=blockDim.k)
 #endif

-#if !(defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP))
-#define MFEM_DEVICE
-#define MFEM_HOST_DEVICE
-#define MFEM_DEVICE_SYNC
-#define MFEM_STREAM_SYNC
-#endif
-
-#if !((defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__)) || \
-      (defined(MFEM_USE_HIP)  && defined(__ROCM_ARCH__)))
-#define MFEM_SHARED
-#define MFEM_SYNC_THREAD
-#define MFEM_THREAD_ID(k) 0
-#define MFEM_THREAD_SIZE(k) 1
-#define MFEM_FOREACH_THREAD(i,k,N) for(int i=0; i<N; i++)
-#endif
-
 namespace mfem
 {

@@ -144,4 +144,15 @@ void mfem_warning(const char *msg = NULL);
   "invalid index " #i << " = " << (i) << \
   ", valid range is [" << (imin) << ',' << (imax) << ')')

+// Abort inside a device kernel
+#if defined(__CUDA_ARCH__)
+#define MFEM_ABORT_KERNEL(msg) \
+   {                           \
+      printf(msg);             \
+      asm("trap;");            \
+   }
+#else
+#define MFEM_ABORT_KERNEL(msg) MFEM_ABORT(msg)
+#endif
+
 #endif
@@ -14,20 +14,11 @@

 #include "../config/config.hpp"
 #include "error.hpp"
-#include "cuda.hpp"
-#include "hip.hpp"
-#include "occa.hpp"
+#include "backends.hpp"
 #include "device.hpp"
 #include "mem_manager.hpp"
 #include "../linalg/dtensor.hpp"

-#ifdef MFEM_USE_RAJA
-#include "RAJA/RAJA.hpp"
-#if defined(RAJA_ENABLE_CUDA) && !defined(MFEM_USE_CUDA)
-#error When RAJA is built with CUDA, MFEM_USE_CUDA=YES is required
-#endif
-#endif
-
 namespace mfem
 {

@@ -52,20 +43,20 @@ const int MAX_Q1D = 14;
 #define MFEM_FORALL(i,N,...)                             \
   ForallWrap<1>(true,N,                                 \
                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
-                 [&]             (int i) {__VA_ARGS__})
+                 [&] MFEM_LAMBDA (int i) {__VA_ARGS__})

 // MFEM_FORALL with a 2D CUDA block
 #define MFEM_FORALL_2D(i,N,X,Y,BZ,...)                   \
   ForallWrap<2>(true,N,                                 \
                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
-                 [&]             (int i) {__VA_ARGS__},  \
+                 [&] MFEM_LAMBDA (int i) {__VA_ARGS__},\
                 X,Y,BZ)

 // MFEM_FORALL with a 3D CUDA block
 #define MFEM_FORALL_3D(i,N,X,Y,Z,...)                    \
   ForallWrap<3>(true,N,                                 \
                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
-                 [&]             (int i) {__VA_ARGS__},  \
+                 [&] MFEM_LAMBDA (int i) {__VA_ARGS__},\
                 X,Y,Z)

 // MFEM_FORALL that uses the basic CPU backend when use_dev is false. See for
@@ -74,7 +65,7 @@ const int MAX_Q1D = 14;
 #define MFEM_FORALL_SWITCH(use_dev,i,N,...)              \
   ForallWrap<1>(use_dev,N,                              \
                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
-                 [&]             (int i) {__VA_ARGS__})
+                 [&] MFEM_LAMBDA (int i) {__VA_ARGS__})


 /// OpenMP backend
@@ -125,5 +125,4 @@ void SetGlobalMPI_Comm(MPI_Comm comm);
 #define MFEM_DEPRECATED
 #endif

-
 #endif
@@ -9,7 +9,7 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.

-#include "hip.hpp"
+#include "backends.hpp"
 #include "globals.hpp"

 namespace mfem
@@ -15,16 +15,15 @@
 #include "../config/config.hpp"
 #include "error.hpp"

-#ifdef MFEM_USE_HIP
-#include <hip/hip_runtime.h>
-#endif
-
 // HIP block size used by MFEM.
 #define MFEM_HIP_BLOCKS 256

 #ifdef MFEM_USE_HIP
 #define MFEM_DEVICE __device__
+#define MFEM_LAMBDA __host__ __device__
 #define MFEM_HOST_DEVICE __host__ __device__
+#define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(hipDeviceSynchronize())
+#define MFEM_STREAM_SYNC MFEM_GPU_CHECK(hipStreamSynchronize(0))
 // Define a HIP error check macro, MFEM_GPU_CHECK(x), where x returns/is of
 // type 'hipError_t'. This macro evaluates 'x' and raises an error if the
 // result is not hipSuccess.
@@ -38,17 +37,16 @@
      } \
   } \
   while (0)
-#define MFEM_DEVICE_SYNC MFEM_GPU_CHECK(hipDeviceSynchronize())
-#define MFEM_STREAM_SYNC MFEM_GPU_CHECK(hipStreamSynchronize(0))
 #endif // MFEM_USE_HIP

 // Define the MFEM inner threading macros
-#if defined(MFEM_USE_HIP) && defined(__ROCM_ARCH__)
+#if defined(MFEM_USE_HIP) && defined(__HIP_DEVICE_COMPILE__)
 #define MFEM_SHARED __shared__
 #define MFEM_SYNC_THREAD __syncthreads()
 #define MFEM_THREAD_ID(k) hipThreadIdx_ ##k
 #define MFEM_THREAD_SIZE(k) hipBlockDim_ ##k
-#define MFEM_FOREACH_THREAD(i,k,N) for(int i=hipThreadIdx_ ##k; i<N; i+=hipBlockDim_ ##k)
+#define MFEM_FOREACH_THREAD(i,k,N) \
+    for(int i=hipThreadIdx_ ##k; i<N; i+=hipBlockDim_ ##k)
 #endif

 namespace mfem
@@ -16,8 +16,8 @@

 #ifdef MFEM_USE_OCCA
 #include "mem_manager.hpp"
+#include "backends.hpp"
 #include "device.hpp"
-#include <occa.hpp>

 namespace mfem
 {
@@ -13,8 +13,7 @@
 #define MFEM_TEMPLATE_ASSIGN

 #include "../config/tconfig.hpp"
-#include "../general/cuda.hpp"
-#include "../general/hip.hpp"
+#include "backends.hpp"

 namespace mfem
 {
@@ -74,10 +74,12 @@ void BlockOperator::Mult (const Vector & x, Vector & y) const
   MFEM_ASSERT(x.Size() == width, "incorrect input Vector size");
   MFEM_ASSERT(y.Size() == height, "incorrect output Vector size");

-   yblock.Update(y.GetData(),row_offsets);
-   xblock.Update(x.GetData(),col_offsets);
+   x.Read();
+   y.Write(); y = 0.0;
+
+   xblock.Update(const_cast<Vector&>(x),col_offsets);
+   yblock.Update(y,row_offsets);

-   y = 0.0;
   for (int iRow=0; iRow < nRowBlocks; ++iRow)
   {
      tmp.SetSize(row_offsets[iRow+1] - row_offsets[iRow]);
@@ -90,6 +92,16 @@ void BlockOperator::Mult (const Vector & x, Vector & y) const
         }
      }
   }
+
+   for (int iRow=0; iRow < nRowBlocks; ++iRow)
+   {
+      yblock.GetBlock(iRow).SyncAliasMemory(y);
+   }
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   for (int i=0; i < xblock.NumBlocks(); ++i) { xblock.GetBlock(i).Destroy(); }
+   for (int i=0; i < yblock.NumBlocks(); ++i) { yblock.GetBlock(i).Destroy(); }
 }

 // Action of the transpose operator
@@ -98,10 +110,11 @@ void BlockOperator::MultTranspose (const Vector & x, Vector & y) const
   MFEM_ASSERT(x.Size() == height, "incorrect input Vector size");
   MFEM_ASSERT(y.Size() == width, "incorrect output Vector size");

-   y = 0.0;
+   x.Read();
+   y.Write(); y = 0.0;

-   xblock.Update(x.GetData(),row_offsets);
-   yblock.Update(y.GetData(),col_offsets);
+   xblock.Update(const_cast<Vector&>(x),row_offsets);
+   yblock.Update(y,col_offsets);

   for (int iRow=0; iRow < nColBlocks; ++iRow)
   {
@@ -116,6 +129,15 @@ void BlockOperator::MultTranspose (const Vector & x, Vector & y) const
      }
   }

+   for (int iRow=0; iRow < nColBlocks; ++iRow)
+   {
+      yblock.GetBlock(iRow).SyncAliasMemory(y);
+   }
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   for (int i=0; i < xblock.NumBlocks(); ++i) { xblock.GetBlock(i).Destroy(); }
+   for (int i=0; i < yblock.NumBlocks(); ++i) { yblock.GetBlock(i).Destroy(); }
 }

 BlockOperator::~BlockOperator()
@@ -140,7 +162,6 @@ BlockDiagonalPreconditioner::BlockDiagonalPreconditioner(
   nBlocks(offsets_.Size() - 1),
   offsets(0),
   op(nBlocks)
-
 {
   op = static_cast<Operator *>(NULL);
   offsets.MakeRef(offsets_);
@@ -165,8 +186,11 @@ void BlockDiagonalPreconditioner::Mult (const Vector & x, Vector & y) const
   MFEM_ASSERT(x.Size() == width, "incorrect input Vector size");
   MFEM_ASSERT(y.Size() == height, "incorrect output Vector size");

-   yblock.Update(y.GetData(), offsets);
-   xblock.Update(x.GetData(), offsets);
+   x.Read();
+   y.Write(); y = 0.0;
+
+   xblock.Update(const_cast<Vector&>(x),offsets);
+   yblock.Update(y,offsets);

   for (int i=0; i<nBlocks; ++i)
   {
@@ -179,6 +203,16 @@ void BlockDiagonalPreconditioner::Mult (const Vector & x, Vector & y) const
         yblock.GetBlock(i) = xblock.GetBlock(i);
      }
   }
+
+   for (int i=0; i<nBlocks; ++i)
+   {
+      yblock.GetBlock(i).SyncAliasMemory(y);
+   }
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   for (int i=0; i < xblock.NumBlocks(); ++i) { xblock.GetBlock(i).Destroy(); }
+   for (int i=0; i < yblock.NumBlocks(); ++i) { yblock.GetBlock(i).Destroy(); }
 }

 // Action of the transpose operator
@@ -188,8 +222,11 @@ void BlockDiagonalPreconditioner::MultTranspose (const Vector & x,
   MFEM_ASSERT(x.Size() == height, "incorrect input Vector size");
   MFEM_ASSERT(y.Size() == width, "incorrect output Vector size");

-   yblock.Update(y.GetData(), offsets);
-   xblock.Update(x.GetData(), offsets);
+   x.Read();
+   y.Write(); y = 0.0;
+
+   xblock.Update(const_cast<Vector&>(x),offsets);
+   yblock.Update(y,offsets);

   for (int i=0; i<nBlocks; ++i)
   {
@@ -202,6 +239,16 @@ void BlockDiagonalPreconditioner::MultTranspose (const Vector & x,
         yblock.GetBlock(i) = xblock.GetBlock(i);
      }
   }
+
+   for (int i=0; i<nBlocks; ++i)
+   {
+      yblock.GetBlock(i).SyncAliasMemory(y);
+   }
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   for (int i=0; i < xblock.NumBlocks(); ++i) { xblock.GetBlock(i).Destroy(); }
+   for (int i=0; i < yblock.NumBlocks(); ++i) { yblock.GetBlock(i).Destroy(); }
 }

 BlockDiagonalPreconditioner::~BlockDiagonalPreconditioner()
@@ -87,6 +87,22 @@ void BlockVector::Update(double *data, const Array<int> & bOffsets)
   SetBlocks();
 }

+void BlockVector::Update(Vector & data, const Array<int> & bOffsets)
+{
+   blockOffsets = bOffsets.GetData();
+   if (numBlocks != bOffsets.Size()-1)
+   {
+      delete [] blocks;
+      numBlocks = bOffsets.Size()-1;
+      blocks = new Vector[numBlocks];
+   }
+
+   for (int i = 0; i < numBlocks; ++i)
+   {
+      blocks[i].MakeRef(data, blockOffsets[i], BlockSize(i));
+   }
+}
+
 void BlockVector::Update(const Array<int> &bOffsets)
 {
   Update(bOffsets, data.GetMemoryType());
@@ -102,6 +102,8 @@ public:
    */
   void Update(double *data, const Array<int> & bOffsets);

+   void Update(Vector & data, const Array<int> & bOffsets);
+
   /// Update a BlockVector with new @a bOffsets and make sure it owns its data.
   /** The block-vector will be re-allocated if either:
       - the offsets @a bOffsets are different from the current offsets, or
@@ -26,10 +26,10 @@ ComplexOperator::ComplexOperator(Operator * Op_Real, Operator * Op_Imag,
   , ownReal_(ownReal)
   , ownImag_(ownImag)
   , convention_(convention)
-   , x_r_(NULL, width / 2)
-   , x_i_(NULL, width / 2)
-   , y_r_(NULL, height / 2)
-   , y_i_(NULL, height / 2)
+   , x_r_()
+   , x_i_()
+   , y_r_()
+   , y_i_()
   , u_(NULL)
   , v_(NULL)
 {}
@@ -68,14 +68,26 @@ const Operator & ComplexOperator::imag() const

 void ComplexOperator::Mult(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   x_r_.SetData(x_data);
-   x_i_.SetData(&x_data[width / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;

-   y_r_.SetData(&y[0]);
-   y_i_.SetData(&y[height / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, width/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), width/2, width/2);
+
+   y_r_.MakeRef(y, 0, height/2);
+   y_i_.MakeRef(y, height/2, height/2);

   this->Mult(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }

 void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
@@ -91,31 +103,47 @@ void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
      y_r = 0.0;
      y_i = 0.0;
   }
+
   if (Op_Imag_)
   {
-      if (!v_) { v_ = new Vector(Op_Imag_->Height()); }
+      if (!v_) { v_ = new Vector(); }
+      v_->UseDevice(true);
+      v_->SetSize(Op_Imag_->Height());
+
      Op_Imag_->Mult(x_i, *v_);
-      y_r_ -= *v_;
+      y_r.Add(-1.0, *v_);
      Op_Imag_->Mult(x_r, *v_);
-      y_i_ += *v_;
+      y_i.Add(1.0, *v_);
   }

   if (convention_ == BLOCK_SYMMETRIC)
   {
-      y_i_ *= -1.0;
+      y_i *= -1.0;
   }
 }

 void ComplexOperator::MultTranspose(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   y_r_.SetData(x_data);
-   y_i_.SetData(&x_data[height / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;

-   x_r_.SetData(&y[0]);
-   x_i_.SetData(&y[width / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, height/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), height/2, height/2);

-   this->MultTranspose(y_r_, y_i_, x_r_, x_i_);
+   y_r_.MakeRef(y, 0, width/2);
+   y_i_.MakeRef(y, width/2, width/2);
+
+   this->MultTranspose(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }

 void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
@@ -136,13 +164,17 @@ void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
      y_r = 0.0;
      y_i = 0.0;
   }
+
   if (Op_Imag_)
   {
-      if (!u_) { u_ = new Vector(Op_Imag_->Width()); }
+      if (!u_) { u_ = new Vector(); }
+      u_->UseDevice(true);
+      u_->SetSize(Op_Imag_->Width());
+
      Op_Imag_->MultTranspose(x_i, *u_);
-      y_r_.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
+      y_r.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
      Op_Imag_->MultTranspose(x_r, *u_);
-      y_i_ -= *u_;
+      y_i.Add(-1.0, *u_);
   }
 }

@@ -235,6 +267,261 @@ SparseMatrix * ComplexSparseMatrix::GetSystemMatrix() const
   return new SparseMatrix(I, J, D, this->Height(), this->Width());
 }

+
+#ifdef MFEM_USE_SUITESPARSE
+
+void ComplexUMFPackSolver::Init()
+{
+   mat = NULL;
+   Numeric = NULL;
+   AI = AJ = NULL;
+   if (!use_long_ints)
+   {
+      umfpack_zi_defaults(Control);
+   }
+   else
+   {
+      umfpack_zl_defaults(Control);
+   }
+}
+
+void ComplexUMFPackSolver::SetOperator(const Operator &op)
+{
+   int *Ap, *Ai;
+   void *Symbolic;
+   double *Ax;
+   double *Az;
+
+   if (Numeric)
+   {
+      if (!use_long_ints)
+      {
+         umfpack_zi_free_numeric(&Numeric);
+      }
+      else
+      {
+         umfpack_zl_free_numeric(&Numeric);
+      }
+   }
+
+   mat = const_cast<ComplexSparseMatrix *>
+         (dynamic_cast<const ComplexSparseMatrix *>(&op));
+   MFEM_VERIFY(mat, "not a ComplexSparseMatrix");
+
+   MFEM_VERIFY(mat->real().NumNonZeroElems() == mat->imag().NumNonZeroElems(),
+               "Real and imag Sparsity pattern mismatch: Try setting Assemble (skip_zeros = 0)");
+
+   // UMFPack requires that the column-indices in mat corresponding to each
+   // row be sorted.
+   // Generally, this will modify the ordering of the entries of mat.
+
+   mat->real().SortColumnIndices();
+   mat->imag().SortColumnIndices();
+
+   height = mat->real().Height();
+   width = mat->real().Width();
+   MFEM_VERIFY(width == height, "not a square matrix");
+
+   Ap = mat->real().GetI(); // assuming real and imag have the same sparsity
+   Ai = mat->real().GetJ();
+   Ax = mat->real().GetData();
+   Az = mat->imag().GetData();
+
+   if (!use_long_ints)
+   {
+      int status = umfpack_zi_symbolic(width,width,Ap,Ai,Ax,Az,&Symbolic,
+                                       Control,Info);
+      if (status < 0)
+      {
+         umfpack_zi_report_info(Control, Info);
+         umfpack_zi_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::SetOperator :"
+                    " umfpack_zi_symbolic() failed!");
+      }
+
+      status = umfpack_zi_numeric(Ap, Ai, Ax, Az, Symbolic, &Numeric,
+                                  Control, Info);
+      if (status < 0)
+      {
+         umfpack_zi_report_info(Control, Info);
+         umfpack_zi_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::SetOperator :"
+                    " umfpack_zi_numeric() failed!");
+      }
+      umfpack_zi_free_symbolic(&Symbolic);
+   }
+   else
+   {
+      SuiteSparse_long status;
+
+      delete [] AJ;
+      delete [] AI;
+      AI = new SuiteSparse_long[width + 1];
+      AJ = new SuiteSparse_long[Ap[width]];
+      for (int i = 0; i <= width; i++)
+      {
+         AI[i] = (SuiteSparse_long)(Ap[i]);
+      }
+      for (int i = 0; i < Ap[width]; i++)
+      {
+         AJ[i] = (SuiteSparse_long)(Ai[i]);
+      }
+
+      status = umfpack_zl_symbolic(width, width, AI, AJ, Ax, Az, &Symbolic,
+                                   Control, Info);
+      if (status < 0)
+      {
+         umfpack_zl_report_info(Control, Info);
+         umfpack_zl_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::SetOperator :"
+                    " umfpack_zl_symbolic() failed!");
+      }
+
+      status = umfpack_zl_numeric(AI, AJ, Ax, Az, Symbolic, &Numeric,
+                                  Control, Info);
+      if (status < 0)
+      {
+         umfpack_zl_report_info(Control, Info);
+         umfpack_zl_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::SetOperator :"
+                    " umfpack_zl_numeric() failed!");
+      }
+      umfpack_zl_free_symbolic(&Symbolic);
+   }
+}
+
+void ComplexUMFPackSolver::Mult(const Vector &b, Vector &x) const
+{
+   if (mat == NULL)
+      mfem_error("ComplexUMFPackSolver::Mult : matrix is not set!"
+                 " Call SetOperator first!");
+   int n = b.Size()/2;
+   double * datax = x.GetData();
+   double * datab = b.GetData();
+
+   // For the Block Symmetric case data the imaginary part
+   // has to be scaled by -1
+   ComplexOperator::Convention conv = mat->GetConvention();
+   Vector bimag;
+   if (conv == ComplexOperator::Convention::BLOCK_SYMMETRIC)
+   {
+      bimag.SetDataAndSize(&datab[n],n);
+      bimag *=-1.0;
+   }
+
+   // Solve the transpose, since UMFPack expects CCS instead of CRS format
+   if (!use_long_ints)
+   {
+      int status =
+         umfpack_zi_solve(UMFPACK_Aat, mat->real().GetI(), mat->real().GetJ(),
+                          mat->real().GetData(), mat->imag().GetData(),
+                          datax, &datax[n], datab, &datab[n], Numeric, Control, Info);
+      umfpack_zi_report_info(Control, Info);
+      if (status < 0)
+      {
+         umfpack_zi_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::Mult : umfpack_zi_solve() failed!");
+      }
+   }
+   else
+   {
+      SuiteSparse_long status =
+         umfpack_zl_solve(UMFPACK_Aat,AI,AJ,mat->real().GetData(),
+                          mat->imag().GetData(),
+                          datax,&datax[n],datab,&datab[n],Numeric,Control,Info);
+
+      umfpack_zl_report_info(Control, Info);
+      if (status < 0)
+      {
+         umfpack_zl_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::Mult : umfpack_zl_solve() failed!");
+      }
+   }
+   if (conv == ComplexOperator::Convention::BLOCK_SYMMETRIC)
+   {
+      bimag *=-1.0;
+   }
+}
+
+void ComplexUMFPackSolver::MultTranspose(const Vector &b, Vector &x) const
+{
+   if (mat == NULL)
+      mfem_error("ComplexUMFPackSolver::Mult : matrix is not set!"
+                 " Call SetOperator first!");
+   int n = b.Size()/2;
+   double * datax = x.GetData();
+   double * datab = b.GetData();
+
+   ComplexOperator::Convention conv = mat->GetConvention();
+   Vector bimag;
+   bimag.SetDataAndSize(&datab[n],n);
+   // Solve the Adjoint A^H x = b by solving
+   // the conjugate problem A^T \bar{x} = \bar{b}
+   if ((!transa && conv == ComplexOperator::HERMITIAN) ||
+       ( transa && conv == ComplexOperator::BLOCK_SYMMETRIC))
+   {
+      bimag *=-1.0;
+   }
+
+   if (!use_long_ints)
+   {
+      int status =
+         umfpack_zi_solve(UMFPACK_A, mat->real().GetI(), mat->real().GetJ(),
+                          mat->real().GetData(), mat->imag().GetData(),
+                          datax, &datax[n], datab, &datab[n], Numeric, Control, Info);
+      umfpack_zi_report_info(Control, Info);
+      if (status < 0)
+      {
+         umfpack_zi_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::Mult : umfpack_zi_solve() failed!");
+      }
+   }
+   else
+   {
+      SuiteSparse_long status =
+         umfpack_zl_solve(UMFPACK_A,AI,AJ,mat->real().GetData(),
+                          mat->imag().GetData(),
+                          datax,&datax[n],datab,&datab[n],Numeric,Control,Info);
+
+      umfpack_zl_report_info(Control, Info);
+      if (status < 0)
+      {
+         umfpack_zl_report_status(Control, status);
+         mfem_error("ComplexUMFPackSolver::Mult : umfpack_zl_solve() failed!");
+      }
+   }
+   if (!transa)
+   {
+      Vector ximag;
+      ximag.SetDataAndSize(&datax[n],n);
+      ximag *=-1.0;
+   }
+   if ((!transa && conv == ComplexOperator::HERMITIAN) ||
+       ( transa && conv == ComplexOperator::BLOCK_SYMMETRIC))
+   {
+      bimag *=-1.0;
+   }
+}
+
+ComplexUMFPackSolver::~ComplexUMFPackSolver()
+{
+   delete [] AJ;
+   delete [] AI;
+   if (Numeric)
+   {
+      if (!use_long_ints)
+      {
+         umfpack_zi_free_numeric(&Numeric);
+      }
+      else
+      {
+         umfpack_zl_free_numeric(&Numeric);
+      }
+   }
+}
+
+#endif
+
 #ifdef MFEM_USE_MPI

 ComplexHypreParMatrix::ComplexHypreParMatrix(HypreParMatrix * A_Real,
@@ -18,6 +18,10 @@
 #include "hypre.hpp"
 #endif

+#ifdef MFEM_USE_SUITESPARSE
+#include <umfpack.h>
+#endif
+
 namespace mfem
 {

@@ -109,6 +113,8 @@ public:

   virtual Type GetType() const { return Complex_Operator; }

+   Convention GetConvention() const { return convention_; }
+
 protected:
   // Let this be hidden from the public interface since the implementation
   // depends on internal members
@@ -168,6 +174,71 @@ public:
   virtual Type GetType() const { return MFEM_ComplexSparseMat; }
 };

+#ifdef MFEM_USE_SUITESPARSE
+/** @brief Interface with UMFPack solver specialized for ComplexSparseMatrix
+    This approach avoids forming a monolithic SparseMatrix which leads
+    to increased memory and flops
+ */
+class ComplexUMFPackSolver : public Solver
+{
+protected:
+   bool use_long_ints;
+   bool transa;
+   ComplexSparseMatrix *mat;
+
+   void *Numeric;
+   SuiteSparse_long *AI, *AJ;
+
+   void Init();
+
+public:
+   double Control[UMFPACK_CONTROL];
+   mutable double Info[UMFPACK_INFO];
+
+   /** @brief For larger matrices, if the solver fails, set the parameter @a
+       _use_long_ints = true. */
+   ComplexUMFPackSolver(bool _use_long_ints = false, bool transa_ = false)
+      : use_long_ints(_use_long_ints), transa(transa_) { Init(); }
+   /** @brief Factorize the given ComplexSparseMatrix using the defaults.
+       For larger matrices, if the solver fails, set the parameter
+       @a _use_long_ints = true. */
+   ComplexUMFPackSolver(ComplexSparseMatrix &A, bool _use_long_ints = false,
+                        bool transa_ = false)
+      : use_long_ints(_use_long_ints), transa(transa_) { Init(); SetOperator(A); }
+
+   /** @brief Factorize the given Operator @a op which must be
+       a ComplexSparseMatrix.
+
+       The factorization uses the parameters set in the #Control data member.
+       @note This method calls SparseMatrix::SortColumnIndices()
+       for real and imag parts of the ComplexSparseMatrix,
+       modifying the matrices if the column indices are not already sorted. */
+   virtual void SetOperator(const Operator &op);
+
+   // Set the print level field in the #Control data member.
+   void SetPrintLevel(int print_lvl) { Control[UMFPACK_PRL] = print_lvl; }
+
+   // This determines the action of MultTranspose (see below for details)
+   void SetTransposeSolve(bool transa_) { transa = transa_; }
+
+   /** @brief This is solving the system A x = b */
+   virtual void Mult(const Vector &b, Vector &x) const;
+
+   /** @brief
+      This is solving the system:
+      A^H x = b (when transa = false)
+      This is equivalent to solving the transpose block system for the
+      case of Convention = HERMITIAN
+      A^T x = b (when transa = true)
+      This is equivalent to solving the transpose block system for the
+      case of Convention = BLOCK_SYMMETRIC */
+   virtual void MultTranspose(const Vector &b, Vector &x) const;
+
+   virtual ~ComplexUMFPackSolver();
+};
+
+#endif
+
 #ifdef MFEM_USE_MPI

 /** @brief Specialization of the ComplexOperator built from a pair of
@@ -12,7 +12,7 @@
 #ifndef MFEM_DTENSOR
 #define MFEM_DTENSOR

-#include "../general/cuda.hpp"
+#include "../general/backends.hpp"

 namespace mfem
 {
@@ -21,6 +21,10 @@
 #include <cmath>
 #include <cstdlib>

+#ifdef MFEM_USE_SUNDIALS
+#include <nvector/nvector_parallel.h>
+#endif
+
 using namespace std;

 namespace mfem
@@ -179,16 +183,9 @@ HypreParVector::~HypreParVector()

 #ifdef MFEM_USE_SUNDIALS

-void HypreParVector::ToNVector(N_Vector &nv)
+N_Vector HypreParVector::ToNVector()
 {
-   MFEM_ASSERT(nv && N_VGetVectorID(nv) == SUNDIALS_NVEC_PARHYP,
-               "invalid N_Vector");
-   N_VectorContent_ParHyp nv_c = (N_VectorContent_ParHyp)(nv->content);
-   MFEM_ASSERT(nv_c->own_parvector == SUNFALSE, "invalid N_Vector");
-   nv_c->local_length = x->local_vector->size;
-   nv_c->global_length = x->global_size;
-   nv_c->comm = x->comm;
-   nv_c->x = x;
+   return N_VMake_Parallel(GetComm(), Size(), GlobalSize(), GetData());
 }

 #endif // MFEM_USE_SUNDIALS
@@ -34,9 +34,6 @@

 #include "sparsemat.hpp"
 #include "hypre_parcsr.hpp"
-#ifdef MFEM_USE_SUNDIALS
-#include <nvector/nvector_parhyp.h>
-#endif

 namespace mfem
 {
@@ -163,13 +160,9 @@ public:
   ~HypreParVector();

 #ifdef MFEM_USE_SUNDIALS
-   /// Return a new wrapper SUNDIALS N_Vector of type SUNDIALS_NVEC_PARHYP.
+   /// Return a new wrapper SUNDIALS N_Vector of type SUNDIALS_NVEC_PARALLEL.
   /** The returned N_Vector must be destroyed by the caller. */
-   virtual N_Vector ToNVector() { return N_VMake_ParHyp(x); }
-
-   /** @brief Update an existing wrapper SUNDIALS N_Vector of type
-       SUNDIALS_NVEC_PARHYP to point to this Vector. */
-   virtual void ToNVector(N_Vector &nv);
+   virtual N_Vector ToNVector();
 #endif
 };

@@ -18,7 +18,7 @@
 #endif

 #include "../config/config.hpp"
-#include "../general/cuda.hpp"
+#include "../general/backends.hpp"
 #include "../general/globals.hpp"

 #include "matrix.hpp"
@@ -28,13 +28,6 @@ class Matrix : public Operator
 {
   friend class MatrixInverse;
 public:
-   /// Defines matrix diagonal policy upon elimination of rows and/or columns.
-   enum DiagonalPolicy
-   {
-      DIAG_ZERO, ///< Set the diagonal value to zero
-      DIAG_ONE,  ///< Set the diagonal value to one
-      DIAG_KEEP  ///< Keep the diagonal value
-   };

   /// Creates a square matrix of size s.
   explicit Matrix(int s) : Operator(s) { }
@@ -346,7 +346,6 @@ const double RK8Solver::c[] =

 AdamsBashforthSolver::AdamsBashforthSolver(int _s, const double *_a)
 {
-   s = 0;
   smax = std::min(_s,5);
   a = _a;
   k = new Vector[5];
@@ -365,6 +364,34 @@ AdamsBashforthSolver::AdamsBashforthSolver(int _s, const double *_a)
   }
 }

+void AdamsBashforthSolver::GetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < s ),
+                " AdamsBashforthSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+
+   state = k[idx[i]];
+}
+
+const Vector &AdamsBashforthSolver::GetStateVector(int i)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < s ),
+                " AdamsBashforthSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+
+   return k[idx[i]];
+}
+
+
+void AdamsBashforthSolver::SetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < smax ),
+                " AdamsBashforthSolver::SetStateVector \n" <<
+                " - Tried to set non-existent state "<<i);
+   k[idx[i]] = state;
+   s = std::max(i,s);
+}
+
 void AdamsBashforthSolver::Init(TimeDependentOperator &_f)
 {
   ODESolver::Init(_f);
@@ -430,6 +457,31 @@ AdamsMoultonSolver::AdamsMoultonSolver(int _s, const double *_a)
   }
 }

+const Vector &AdamsMoultonSolver::GetStateVector(int i)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < s ),
+                " AdamsMoultonSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   return k[idx[i+1]];
+}
+
+void AdamsMoultonSolver::GetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < s ),
+                " AdamsMoultonSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   state = k[idx[i+1]];
+}
+
+void AdamsMoultonSolver::SetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i >= 0) && ( i < smax ),
+                " AdamsMoultonSolver::SetStateVector \n" <<
+                " - Tried to set non-existent state "<<i);
+   k[idx[i+1]] = state;
+   s = std::max(i,s);
+}
+
 void AdamsMoultonSolver::Init(TimeDependentOperator &_f)
 {
   ODESolver::Init(_f);
@@ -641,7 +693,32 @@ void GeneralizedAlphaSolver::Init(TimeDependentOperator &_f)
   y.SetSize(f->Width(), mem_type);
   xdot.SetSize(f->Width(), mem_type);
   xdot = 0.0;
-   first = true;
+   nstate = 0;
+}
+
+const Vector &GeneralizedAlphaSolver::GetStateVector(int i)
+{
+   MFEM_ASSERT( (i == 0) && (nstate == 1),
+                "GeneralizedAlphaSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   return xdot;
+}
+
+void GeneralizedAlphaSolver::GetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i == 0) && (nstate == 1),
+                "GeneralizedAlphaSolver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   state = xdot;
+}
+
+void GeneralizedAlphaSolver::SetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i == 0),
+                "GeneralizedAlphaSolver::SetStateVector \n" <<
+                " - Tried to set non-existent state "<<i);
+   xdot = state;
+   nstate = 1;
 }

 void GeneralizedAlphaSolver::SetRhoInf(double rho_inf)
@@ -684,10 +761,10 @@ void GeneralizedAlphaSolver::PrintProperties(std::ostream &out)
 // This routine assumes xdot is initialized.
 void GeneralizedAlphaSolver::Step(Vector &x, double &t, double &dt)
 {
-   if (first)
+   if (nstate == 0)
   {
      f->Mult(x,xdot);
-      first = false;
+      nstate = 1;
   }

   // Set y = x + alpha_f*(1.0 - (gamma/alpha_m))*dt*xdot
@@ -892,7 +969,33 @@ void GeneralizedAlpha2Solver::Init(SecondOrderTimeDependentOperator &_f)
   aa.SetSize(f->Width());
   d2xdt2.SetSize(f->Width());
   d2xdt2 = 0.0;
-   first = true;
+   nstate = 0;
+}
+
+const Vector &GeneralizedAlpha2Solver::GetStateVector(int i)
+{
+   MFEM_ASSERT( (i == 0) && (nstate == 1),
+                "GeneralizedAlpha2Solver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   return d2xdt2;
+}
+
+
+void GeneralizedAlpha2Solver::GetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i == 0) && (nstate == 1),
+                "GeneralizedAlpha2Solver::GetStateVector \n" <<
+                " - Tried to get non-existent state "<<i);
+   state = d2xdt2;
+}
+
+void GeneralizedAlpha2Solver::SetStateVector(int i, Vector &state)
+{
+   MFEM_ASSERT( (i == 0),
+                "GeneralizedAlpha2Solver::SetStateVector \n" <<
+                " - Tried to set non-existent state "<<i);
+   d2xdt2 = state;
+   nstate = 1;
 }

 void GeneralizedAlpha2Solver::PrintProperties(std::ostream &out)
@@ -935,13 +1038,12 @@ void GeneralizedAlpha2Solver::Step(Vector &x, Vector &dxdt,
   double fac5 = alpha_m;

   // In the first pass compute d2xdt2 directy from operator.
-   if (first)
+   if (nstate == 0)
   {
      f->Mult(x, dxdt, d2xdt2);
-      first = false;
+      nstate = 1;
   }

-
   // Predict alpha levels
   add(dxdt, fac0*dt, d2xdt2, va);
   add(x, fac1*dt, va, xa);
@@ -91,6 +91,23 @@ public:
      while (t < tf) { Step(x, t, dt); }
   }

+   /// Function for getting and setting the state vectors
+   virtual int   GetMaxStateSize() { return 0; }
+   virtual int   GetStateSize() { return 0; }
+   virtual const Vector &GetStateVector(int i)
+   {
+      mfem_error("ODESolver has no state vectors");
+      Vector *s = NULL; return *s; // Make some compiler happy
+   }
+   virtual void  GetStateVector(int i, Vector &state)
+   {
+      mfem_error("ODESolver has no state vectors");
+   }
+   virtual void  SetStateVector(int i, Vector &state)
+   {
+      mfem_error("ODESolver has no state vectors");
+   }
+
   virtual ~ODESolver() { }
 };

@@ -102,9 +119,9 @@ private:
   Vector dxdt;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -122,9 +139,9 @@ private:
 public:
   RK2Solver(const double _a = 2./3.) : a(_a) { }

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -135,9 +152,9 @@ private:
   Vector y, k;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -148,9 +165,9 @@ private:
   Vector y, k, z;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -174,9 +191,9 @@ public:
   ExplicitRKSolver(int _s, const double *_a, const double *_b,
                    const double *_c);

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;

   virtual ~ExplicitRKSolver();
 };
@@ -219,9 +236,15 @@ private:
 public:
   AdamsBashforthSolver(int _s, const double *_a);

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
+
+   int  GetMaxStateSize() override { return smax; };
+   int  GetStateSize() override { return s; };
+   const Vector &GetStateVector(int i) override;
+   void GetStateVector(int i, Vector &state) override;
+   void SetStateVector(int i, Vector &state) override;

   ~AdamsBashforthSolver()
   {
@@ -294,9 +317,15 @@ private:
 public:
   AdamsMoultonSolver(int _s, const double *_a);

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
+
+   int  GetMaxStateSize() override { return smax-1; };
+   int  GetStateSize() override { return s-1; };
+   const Vector &GetStateVector(int i) override;
+   void GetStateVector(int i, Vector &state) override;
+   void SetStateVector(int i, Vector &state) override;

   ~AdamsMoultonSolver()
   {
@@ -363,9 +392,9 @@ protected:
   Vector k;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -376,9 +405,9 @@ protected:
   Vector k;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -397,9 +426,9 @@ protected:
 public:
   SDIRK23Solver(int gamma_opt = 1);

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -411,9 +440,9 @@ protected:
   Vector k, y, z;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -425,9 +454,9 @@ protected:
   Vector k, y;

 public:
-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
 };


@@ -439,7 +468,7 @@ class GeneralizedAlphaSolver : public ODESolver
 protected:
   mutable Vector xdot,k,y;
   double alpha_f, alpha_m, gamma;
-   bool first;
+   int  nstate;

   void SetRhoInf(double rho_inf);
   void PrintProperties(std::ostream &out = mfem::out);
@@ -447,9 +476,15 @@ public:

   GeneralizedAlphaSolver(double rho = 1.0) { SetRhoInf(rho); };

-   virtual void Init(TimeDependentOperator &_f);
+   void Init(TimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, double &t, double &dt);
+   void Step(Vector &x, double &t, double &dt) override;
+
+   int  GetMaxStateSize() override { return 1; };
+   int  GetStateSize() override { return nstate; };
+   const Vector &GetStateVector(int i) override;
+   void GetStateVector(int i, Vector &state) override;
+   void SetStateVector(int i, Vector &state) override;
 };


@@ -497,7 +532,7 @@ class SIA1Solver : public SIASolver
 {
 public:
   SIA1Solver() {}
-   void Step(Vector &q, Vector &p, double &t, double &dt);
+   void Step(Vector &q, Vector &p, double &t, double &dt) override;
 };

 /// Second Order Symplectic Integration Algorithm
@@ -505,7 +540,7 @@ class SIA2Solver : public SIASolver
 {
 public:
   SIA2Solver() {}
-   void Step(Vector &q, Vector &p, double &t, double &dt);
+   void Step(Vector &q, Vector &p, double &t, double &dt) override;
 };

 /// Variable order Symplectic Integration Algorithm (orders 1-4)
@@ -513,7 +548,7 @@ class SIAVSolver : public SIASolver
 {
 public:
   SIAVSolver(int order);
-   void Step(Vector &q, Vector &p, double &t, double &dt);
+   void Step(Vector &q, Vector &p, double &t, double &dt) override;

 private:
   int order_;
@@ -606,11 +641,26 @@ public:
      while (t < tf) { Step(x, dxdt, t, dt); }
   }

+   /// Function for getting and setting the state vectors
+   virtual int   GetMaxStateSize() { return 0; };
+   virtual int   GetStateSize() { return 0; }
+   virtual const Vector &GetStateVector(int i)
+   {
+      mfem_error("ODESolver has no state vectors");
+      Vector *s = NULL; return *s; // Make some compiler happy
+   }
+   virtual void  GetStateVector(int i, Vector &state)
+   {
+      mfem_error("ODESolver has no state vectors");
+   }
+   virtual void  SetStateVector(int i, Vector &state)
+   {
+      mfem_error("ODESolver has no state vectors");
+   }
+
   virtual ~SecondOrderODESolver() { }
 };

-
-
 /// The classical newmark method.
 /// Newmark, N. M. (1959) A method of computation for structural dynamics.
 /// Journal of Engineering Mechanics, ASCE, 85 (EM3) 67-94.
@@ -625,11 +675,11 @@ private:
 public:
   NewmarkSolver(double beta_ = 0.25, double gamma_ = 0.5) { beta = beta_; gamma = gamma_; };

-   virtual void PrintProperties(std::ostream &out = mfem::out);
+   void PrintProperties(std::ostream &out = mfem::out);

-   virtual void Init(SecondOrderTimeDependentOperator &_f);
+   void Init(SecondOrderTimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, Vector &dxdt, double &t, double &dt);
+   void Step(Vector &x, Vector &dxdt, double &t, double &dt) override;
 };

 class LinearAccelerationSolver : public NewmarkSolver
@@ -661,7 +711,7 @@ class GeneralizedAlpha2Solver : public SecondOrderODESolver
 protected:
   Vector xa,va,aa,d2xdt2;
   double alpha_f, alpha_m, beta, gamma;
-   bool first;
+   int nstate;

 public:
   GeneralizedAlpha2Solver(double rho_inf = 1.0)
@@ -675,11 +725,17 @@ public:
      gamma   = 0.5 + alpha_m - alpha_f;
   };

-   virtual void PrintProperties(std::ostream &out = mfem::out);
+   void PrintProperties(std::ostream &out = mfem::out);

-   virtual void Init(SecondOrderTimeDependentOperator &_f);
+   void Init(SecondOrderTimeDependentOperator &_f) override;

-   virtual void Step(Vector &x, Vector &dxdt, double &t, double &dt);
+   void Step(Vector &x, Vector &dxdt, double &t, double &dt) override;
+
+   int  GetMaxStateSize() override { return 1; };
+   int  GetStateSize() override { return nstate; };
+   const Vector &GetStateVector(int i) override;
+   void GetStateVector(int i, Vector &state) override;
+   void SetStateVector(int i, Vector &state) override;
 };

 /// The classical midpoint method.
@@ -403,8 +403,10 @@ TripleProductOperator::~TripleProductOperator()


 ConstrainedOperator::ConstrainedOperator(Operator *A, const Array<int> &list,
-                                         bool _own_A)
-   : Operator(A->Height(), A->Width()), A(A), own_A(_own_A)
+                                         bool _own_A,
+                                         DiagonalPolicy _diag_policy)
+   : Operator(A->Height(), A->Width()), A(A), own_A(_own_A),
+     diag_policy(_diag_policy)
 {
   // 'mem_class' should work with A->Mult() and MFEM_FORALL():
   mem_class = A->GetMemoryClass()*Device::GetDeviceMemoryClass();
@@ -464,11 +466,30 @@ void ConstrainedOperator::Mult(const Vector &x, Vector &y) const
   auto d_x = x.Read();
   // Use read+write access - we are modifying sub-vector of y
   auto d_y = y.ReadWrite();
-   MFEM_FORALL(i, csz,
+   switch (diag_policy)
   {
-      const int id = idx[i];
-      d_y[id] = d_x[id];
-   });
+      case DIAG_ONE:
+         MFEM_FORALL(i, csz,
+         {
+            const int id = idx[i];
+            d_y[id] = d_x[id];
+         });
+         break;
+      case DIAG_ZERO:
+         MFEM_FORALL(i, csz,
+         {
+            const int id = idx[i];
+            d_y[id] = 0.0;
+         });
+         break;
+      case DIAG_KEEP:
+         // Needs action of the operator diagonal on vector
+         mfem_error("ConstrainedOperator::Mult #1");
+         break;
+      default:
+         mfem_error("ConstrainedOperator::Mult #2");
+         break;
+   }
 }

 RectangularConstrainedOperator::RectangularConstrainedOperator(
@@ -41,6 +41,14 @@ protected:
   Operator *SetupRAP(const Operator *Pi, const Operator *Po);

 public:
+   /// Defines operator diagonal policy upon elimination of rows and/or columns.
+   enum DiagonalPolicy
+   {
+      DIAG_ZERO, ///< Set the diagonal value to zero
+      DIAG_ONE,  ///< Set the diagonal value to one
+      DIAG_KEEP  ///< Keep the diagonal value
+   };
+
   /// Initializes memory for true vectors of linear system
   void InitTVectors(const Operator *Po, const Operator *Ri, const Operator *Pi,
                     Vector &x, Vector &b,
@@ -442,6 +450,132 @@ public:
   virtual ~TimeDependentOperator() { }
 };

+
+/** TimeDependentAdjointOperator is a TimeDependentOperator with Adjoint rate
+    equations to be used with CVODESSolver. */
+class TimeDependentAdjointOperator : public TimeDependentOperator
+{
+public:
+
+   /**
+      \brief The TimedependentAdjointOperator extends the TimeDependentOperator
+      class to use features in SUNDIALS CVODESSolver for computing quadratures
+      and solving adjoint problems.
+
+      To solve adjoint problems one needs to implement the AdjointRateMult
+      method to tell CVODES what the adjoint rate equation is.
+
+      QuadratureIntegration (optional) can be used to compute values over the
+      forward problem
+
+      QuadratureSensitivityMult (optional) can be used to find the sensitivity
+      of the quadrature using the adjoint solution in part.
+
+      SUNImplicitSetupB (optional) can be used to setup custom solvers for the
+      newton solve for the adjoint problem.
+
+      SUNImplicitSolveB (optional) actually uses the solvers from
+      SUNImplicitSetupB to solve the adjoint problem.
+
+      See SUNDIALS user manuals for specifics.
+
+      \param[in] dim Dimension of the forward operator
+      \param[in] adjdim Dimension of the adjoint operator. Typically it is the
+      same size as dim. However, SUNDIALS allows users to specify the size if
+      one wants to perform custom operations.
+      \param[in] t Starting time to set
+      \param[in] type The TimeDependentOperator type
+   */
+   TimeDependentAdjointOperator(int dim, int adjdim, double t = 0.,
+                                Type type = EXPLICIT) :
+      TimeDependentOperator(dim, t, type),
+      adjoint_height(adjdim)
+   {}
+
+   /// Destructor
+   virtual ~TimeDependentAdjointOperator() {};
+
+   /**
+      \brief Provide the operator integration of a quadrature equation
+
+      \param[in] y The current value at time t
+      \param[out] qdot The current quadrature rate value at t
+   */
+   virtual void QuadratureIntegration(const Vector &y, Vector &qdot) const {};
+
+   /** @brief Perform the action of the operator:
+       @a yBdot = k = f(@a y,@2 yB, t), where
+
+       @param[in] y The primal solution at time t
+       @param[in] yB The adjoint solution at time t
+       @param[out] yBdot the rate at time t
+   */
+   virtual void AdjointRateMult(const Vector &y, Vector & yB,
+                                Vector &yBdot) const = 0;
+
+   /**
+      \brief Provides the sensitivity of the quadrature w.r.t to primal and
+      adjoint solutions
+
+      \param[in] y the value of the primal solution at time t
+      \param[in] yB the value of the adjoint solution at time t
+      \param[out] qBdot the value of the sensitivity of the quadrature rate at
+      time t
+   */
+   virtual void QuadratureSensitivityMult(const Vector &y, const Vector &yB,
+                                          Vector &qBdot) const {}
+
+   /** @brief Setup the ODE linear system \f$ A(x,t) = (I - gamma J) \f$ or
+       \f$ A = (M - gamma J) \f$, where \f$ J(x,t) = \frac{df}{dt(x,t)} \f$.
+
+       @param[in]  t     The current time
+       @param[in]  x     The state at which \f$A(x,xB,t)\f$ should be evaluated.
+       @param[in]  xB    The state at which \f$A(x,xB,t)\f$ should be evaluated.
+       @param[in]  fxB   The current value of the ODE rhs function, \f$f(x,t)\f$.
+       @param[in]  jokB   Flag indicating if the Jacobian should be updated.
+       @param[out] jcurB  Flag to signal if the Jacobian was updated.
+       @param[in]  gammaB The scaled time step value.
+
+       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 SUNImplicitSetupB(const double t, const Vector &x,
+                                 const Vector &xB, const Vector &fxB,
+                                 int jokB, int *jcurB, double gammaB)
+   {
+      mfem_error("TimeDependentAdjointOperator::SUNImplicitSetupB() is not "
+                 "overridden!");
+      return (-1);
+   }
+
+   /** @brief Solve the ODE linear system \f$ A(x,xB,t) xB = b \f$ as setup 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.
+       @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 SUNImplicitSolveB(Vector &x, const Vector &b, double tol)
+   {
+      mfem_error("TimeDependentAdjointOperator::SUNImplicitSolveB() is not "
+                 "overridden!");
+      return (-1);
+   }
+
+   /// Returns the size of the adjoint problem state space
+   int GetAdjointHeight() {return adjoint_height;}
+
+protected:
+   int adjoint_height; /// Size of the adjoint problem
+};
+
+
 /// Base abstract class for second order time dependent operators.
 /** Operator of the form: (x,dxdt,t) -> f(x,dxdt,t), where k = f(x,dxdt,t)
    generally solves the algebraic equation F(x,dxdt,k,t) = G(x,dxdt,t).
@@ -671,20 +805,27 @@ protected:
   bool own_A;                  ///< Ownership flag for A.
   mutable Vector z, w;         ///< Auxiliary vectors.
   MemoryClass mem_class;
+   DiagonalPolicy diag_policy;  ///< Diagonal policy for constrained dofs

 public:
   /** @brief Constructor from a general Operator and a list of essential
       indices/dofs.

       Specify the unconstrained operator @a *A and a @a list of indices to
-       constrain, i.e. each entry @a list[i] represents an essential-dof. If the
+       constrain, i.e. each entry @a list[i] represents an essential dof. If the
       ownership flag @a own_A is true, the operator @a *A will be destroyed
-       when this object is destroyed. */
-   ConstrainedOperator(Operator *A, const Array<int> &list, bool own_A = false);
+       when this object is destroyed. The @a diag_policy determines how the
+       operator sets entries corresponding to essential dofs. */
+   ConstrainedOperator(Operator *A, const Array<int> &list, bool own_A = false,
+                       DiagonalPolicy diag_policy = DIAG_ONE);

   /// Returns the type of memory in which the solution and temporaries are stored.
   virtual MemoryClass GetMemoryClass() const { return mem_class; }

+   /// Set the diagonal policy for the constrained operator.
+   void SetDiagonalPolicy(const DiagonalPolicy _diag_policy)
+   { diag_policy = _diag_policy; }
+
   /** @brief Eliminate "essential boundary condition" values specified in @a x
       from the given right-hand side @a b.

@@ -134,7 +134,7 @@ OperatorJacobiSmoother::OperatorJacobiSmoother(const BilinearForm &a,

 OperatorJacobiSmoother::OperatorJacobiSmoother(const Vector &d,
                                               const Array<int> &ess_tdofs,
-                                               const double dmpng)
+                                               const double dmpng, const bool inverse)
   :
   Solver(d.Size()),
   N(d.Size()),
@@ -143,16 +143,30 @@ OperatorJacobiSmoother::OperatorJacobiSmoother(const Vector &d,
   ess_tdof_list(ess_tdofs),
   residual(N)
 {
-   Setup(d);
+   Setup(d, inverse);
 }

-void OperatorJacobiSmoother::Setup(const Vector &diag)
+void OperatorJacobiSmoother::Setup(const Vector &diag, const bool inverse)
 {
   residual.UseDevice(true);
   const double delta = damping;
   auto D = diag.Read();
   auto DI = dinv.Write();
-   MFEM_FORALL(i, N, DI[i] = delta / D[i]; );
+   if (inverse)
+   {
+      if (delta > 0.0)
+      {
+         MFEM_FORALL(i, N, DI[i] = delta * D[i]; );
+      }
+      else
+      {
+         MFEM_FORALL(i, N, DI[i] = D[i]; );
+      }
+   }
+   else
+   {
+      MFEM_FORALL(i, N, DI[i] = delta / D[i]; );
+   }
   auto I = ess_tdof_list.Read();
   MFEM_FORALL(i, ess_tdof_list.Size(), DI[I[i]] = delta; );
 }
@@ -114,23 +114,25 @@ public:
   /** Setup a Jacobi smoother with the diagonal of @a a obtained by calling
       a.AssembleDiagonal(). It is assumed that the underlying operator acts as
       the identity on entries in ess_tdof_list, corresponding to (assembled)
-       DIAG_ONE policy or ConstratinedOperator in the matrix-free setting. */
+       DIAG_ONE policy or ConstrainedOperator in the matrix-free setting. */
   OperatorJacobiSmoother(const BilinearForm &a,
                          const Array<int> &ess_tdof_list,
                          const double damping=1.0);

   /** Application is by the *inverse* of the given vector. It is assumed that
       the underlying operator acts as the identity on entries in ess_tdof_list,
-       corresponding to (assembled) DIAG_ONE policy or ConstratinedOperator in
+       corresponding to (assembled) DIAG_ONE policy or ConstrainedOperator in
       the matrix-free setting. */
   OperatorJacobiSmoother(const Vector &d,
                          const Array<int> &ess_tdof_list,
-                          const double damping=1.0);
+                          const double damping=1.0, 
+                          const bool inverse=false);
   ~OperatorJacobiSmoother() {}

   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const { Mult(x, y); }
   void SetOperator(const Operator &op) { oper = &op; }
-   void Setup(const Vector &diag);
+   void Setup(const Vector &diag, const bool inverse=false);

 private:
   const int N;
@@ -181,6 +183,8 @@ public:

   void Mult(const Vector&x, Vector &y) const;

+   void MultTranspose(const Vector &x, Vector &y) const { Mult(x, y); }
+
   void SetOperator(const Operator &op_)
   {
      oper = &op_;
@@ -494,24 +494,29 @@ void SparseMatrix::GetDiag(Vector & d) const

   d.SetSize(height);

-   int j, end;
-   for (int i = 0; i < height; i++)
-   {
+   auto I = this->ReadI();
+   auto J = this->ReadJ();
+   auto A = this->ReadData();
+   auto dd = d.Write();

-      end = I[i+1];
-      for (j = I[i]; j < end; j++)
+   MFEM_FORALL(i, height,
+   {
+      const int begin = I[i];
+      const int end = I[i+1];
+      int j;
+      for (j = begin; j < end; j++)
      {
         if (J[j] == i)
         {
-            d[i] = A[j];
+            dd[i] = A[j];
            break;
         }
      }
      if (j == end)
      {
-         d[i] = 0.;
+         dd[i] = 0.;
      }
-   }
+   });
 }

 /// Produces a DenseMatrix from a SparseMatrix
@@ -2145,31 +2150,46 @@ void SparseMatrix::DiagScale(const Vector &b, Vector &x, double sc) const
 {
   MFEM_VERIFY(Finalized(), "Matrix must be finalized.");

+   const int nnz = J.Capacity();
+
+   const bool use_dev = b.UseDevice() || x.UseDevice();
+
+   auto bp = b.Read(use_dev);
+   auto xp = x.Write(use_dev);
+
+   auto Ap = Read(A, nnz);
+   auto Ip = Read(I, height+1);
+   auto Jp = Read(J, nnz);
+
   bool scale = (sc != 1.0);
-   for (int i = 0, j = 0; i < height; i++)
+   MFEM_FORALL(i, height,
   {
-      int end = I[i+1];
-      for ( ; true; j++)
+      int end = Ip[i+1];
+      for (int j = Ip[i]; true; j++)
      {
-         MFEM_VERIFY(j != end, "Couldn't find diagonal in row. i = " << i
-                     << ", j = " << j
-                     << ", I[i+1] = " << end );
-         if (J[j] == i)
+         if (j == end)
         {
-            MFEM_VERIFY(std::abs(A[j]) > 0.0, "Diagonal " << j << " must be nonzero");
+            MFEM_ABORT_KERNEL("Diagonal not found in SparseMatrix::DiagScale");
+         }
+         if (Jp[j] == i)
+         {
+            if (!(std::abs(Ap[j]) > 0.0))
+            {
+               MFEM_ABORT_KERNEL("Zero diagonal in SparseMatrix::DiagScale");
+            }
+
            if (scale)
            {
-               x(i) = sc * b(i) / A[j];
+               xp[i] = sc * bp[i] / Ap[j];
            }
            else
            {
-               x(i) = b(i) / A[j];
+               xp[i] = bp[i] / Ap[j];
            }
            break;
         }
      }
-      j = end;
-   }
+   });
   return;
 }

@@ -2749,6 +2769,10 @@ void SparseMatrix::Print(std::ostream & out, int _width) const
      return;
   }

+   // HostRead forces synchronization
+   HostReadI();
+   HostReadJ();
+   HostReadData();
   for (i = 0; i < height; i++)
   {
      out << "[row " << i << "]\n";
@@ -578,6 +578,12 @@ public:
   Type GetType() const { return MFEM_SPARSEMAT; }
 };

+inline std::ostream& operator<<(std::ostream& os, SparseMatrix const& mat)
+{
+   mat.Print(os);
+   return os;
+}
+
 /// Applies f() to each element of the matrix (after it is finalized).
 void SparseMatrixFunction(SparseMatrix &S, double (*f)(double));

--- a/Show More
+++ b/Show More