Removing experimental example codes

# Conflicts:
#	examples/ex21p.cpp
#	fem/complex_fem.cpp
#	miniapps/electromagnetics/makefile

.gitignore

@@ -29,6 +29,8 @@ config/sample-runs-build.log
 doc/CodeDocumentation.conf
 doc/CodeDocumentation.html
 doc/CodeDocumentation
+doc/undoc.log
+doc/warnings.log
 
 # Temporary files created by the tests.
 *.stderr
@@ -167,6 +169,7 @@ miniapps/meshing/twist
 miniapps/meshing/mesh-explorer
 miniapps/meshing/shaper
 miniapps/meshing/extruder
+miniapps/meshing/trimmer
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
 miniapps/meshing/minimal-surface
@@ -180,6 +183,7 @@ miniapps/meshing/mesh-explorer.mesh
 miniapps/meshing/partitioning.txt
 miniapps/meshing/shaper.mesh
 miniapps/meshing/extruder.mesh
+miniapps/meshing/trimmer.mesh
 miniapps/meshing/optimized*
 miniapps/meshing/perturbed*
 

.travis.yml

@@ -11,8 +11,6 @@
 
 language: cpp
 
-sudo: false
-
 stages:
   - checks
   - tests
@@ -370,8 +368,10 @@ script:
    # Compiler
    - if [ $MPI == "YES" ]; then
         export MYCXX=mpic++;
+        export MAKE_CXX_FLAG=MPICXX=$MYCXX;
      else
         export MYCXX="$CXX";
+        export MAKE_CXX_FLAG=CXX=$MYCXX;
      fi
 
    # Print the compiler version
@@ -384,12 +384,9 @@ script:
      if [ "$CODECOV" == "YES" ]; then
         CPPFLAGS="--coverage -g";
      fi;
-     if [ "$CXX" == "clang++" ]; then
-        export MFEM_PERF_SW=clang;
-     fi
 
    # Configure the library
-   - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG MFEM_CXX="$MYCXX"
+   - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG $MAKE_CXX_FLAG
         MFEM_MPI_NP=$NPROCS CPPFLAGS="$CPPFLAGS"
    # Show the configuration
    - make info

CHANGELOG

@@ -23,6 +23,27 @@ Meshing improvements
   Hessian for r-adaptivity using discrete fields, and allows use of skewness
   and orientation based metrics.
 
+- Added support for r-adaptivity with more than one discrete field. This allows
+  the user to specify different discrete functions for controlling the
+  size, aspect-ratio, orientation, and skew of elements in the mesh.
+
+- Added TMOP capability for approximate tangential mesh relaxation.
+
+- Added support for reading periodic meshes in Gmsh format (version 2.2). See
+  for example the periodic-annulus-sector and periodic-torus-sector files in
+  the data directory.
+
+Performance improvements
+------------------------
+- Added support for explicit vectorization in the high-performance templated
+  code, which can now take advantage of specific intrinsics classes on the
+  following architectures:
+    - x86 (SSE/AVX/AVX2/AVX512),
+    - Power8 & Power9 (VSX),
+    - BG/Q (QPX).
+  These are now enabled by default, and can be disabled with MFEM_USE_SIMD=NO.
+  See the new file linalg/simd.hpp and the new directory linalg/simd.
+
 Improved GPU capabilities
 -------------------------
 - Added support for Chebyshev accelerated polynomial smoother on GPU.
@@ -35,6 +56,26 @@ Discretization improvements
 
 - Added support for simplices in GSLIB-FindPoints.
 
+- Added support for H1 and L2 element matrix assembly in the mass, convection,
+  diffusion, transpose, and the face DG trace integrators. This is compatible
+  with GPU device execution and is illustrated in Example 9/9p, see the option
+  '-ea'. When enabled, this level of assembly stores independent dense matrices
+  for the elements, and independent dense matrices for the faces in the DG case.
+
+- Added new partial assembly kernels for H(div) bilinear forms, as well as
+  VectorFEDivergenceIntegrator.
+
+- Improved the documentation of the GridFunction GetValue and GetVectorValue
+  methods. Expanded the GetValue and GetVectorValue methods which accept an
+  ElementTransformation argument to support evaluation on boundary elements
+  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
+  these new QuadratureFunction coefficient classes.
+
+- Added support face integrals on the boundaries of NURBS meshes.
+
 Linear and nonlinear solvers
 ----------------------------
 - Added power method to iteratively estimate the largest eigenvalue and the
@@ -43,6 +84,17 @@ Linear and nonlinear solvers
 - Added initial support for h- and p-multigrid solvers and preconditioners for
   matrix-based and matrix-free discretizations with basic GPU capability.
 
+- Added a new IterativeSolverMonitor class that allows to monitor the residual
+  and solution during the solving process of an IterativeSolver after every
+  iteration.
+
+- 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.
+
+- In SLISolver, changed the residual inner product from (Br,r) to (Br,Br) so the
+  solver can work with non-SPD preconditioner B.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
@@ -52,11 +104,10 @@ New and updated examples and miniapps
 - Added a new Example 26/26p to demonstrate the construction of a matrix-free
   geometric and p-multigrid preconditioner for the Laplace problem.
 
-- Added a new example, Example 27/27p, to demonstrate the enforcement of
-  various boundary conditions with the Laplace operator.  The example shows the
-  procedures for applying Dirichlet, Neumann (both homogeneous and
-  inhomogeneous), Robin, and periodic boundary conditions with either H1 or DG
-  discretizations.
+- Added a new example, Example 27/27p, to demonstrate the enforcement of various
+  boundary conditions with the Laplace operator. The example shows the procedure
+  for applying Dirichlet, Neumann (both homogeneous and inhomogeneous), Robin,
+  and periodic boundary conditions with either H1 or DG discretizations.
 
 - Added a simple meshing miniapp, Twist, which demonstrates MFEM's strategy of
   stitching together opposite surfaces of a mesh to create a topologically
@@ -65,6 +116,18 @@ 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 a new test problem in example 24/24p, demonstrating a mixed bilinear
+  form for H(div) and L_2, with partial assembly support.
+
+- Added weak Dirichlet boundary conditions (Nitsche) to the NURBS miniapp.
+
+- Added a simple mesh editing miniapp, Trimmer, which trims away portions of a
+  mesh based on element attributes. Any newly exposed boundary elements are
+  assigned attribute numbers related to the trimmed element attributes.
+
 Improved testing
 ----------------
 - Added a GitLab pipeline that automates PR testing on supercomputing systems
@@ -74,15 +137,17 @@ Improved testing
 
 Miscellaneous
 -------------
-- In SLISolver, changed the residual inner product from (Br,r) to (Br,Br) so the
-  solver can work with non-SPD preconditioner B.
-
 - Added support for ADIOS2 for parallel I/O with ParaView visualization. The
   classes adios2stream and ADIOS2DataCollection are introduced in mfem as the
   interfaces to generate ADIOS2 Binary Pack (BP4) directory datasets for the
   entire spatial and temporal data. In addition, ADIOS2 allows for setting a
   user-defined number of data substreams/subfiles. See examples 5, 9, 12, 16.
 
+- The integration order used in the ComputeLpError and ComputeElementLpError
+  methods of class GridFunction has been increased.
+
+- Various other simplifications, extensions, and bugfixes in the code.
+
 
 Version 4.1, released on March 10, 2020
 =======================================

INSTALL

@@ -396,6 +396,12 @@ MFEM_USE_SIDRE = YES/NO
    blueprint specification. When enabled, this option requires installation of
    HDF5 (see also MFEM_USE_NETCDF), Conduit and LLNL's axom project.
 
+MFEM_USE_SIMD = YES/NO
+   Enables the high performance templated classes to use architecture dependent
+   SIMD intrinsics instead of the generic implementation of class AutoSIMD in
+   linalg/simd/auto.hpp. This option should be combined with suitable
+   compiler options, such as -march=native, to enable optimal vectorization.
+
 MFEM_USE_CONDUIT = YES/NO
    Enables support for converting MFEM Mesh and Grid Function objects to and
    from Conduit Mesh Blueprint Descriptions (https://github.com/LLNL/conduit/)
@@ -426,6 +432,8 @@ MFEM_USE_PUMI = YES/NO
    data management system that is capable of handling general non-manifold
    models and effectively supports automated adaptive analysis. PUMI enables
    support for parallel unstructured mesh modifications in MFEM.
+   The develop branch of PUMI repository (https://github.com/SCOREC/core)
+   should be used for most updated features.
 
 MFEM_USE_UMPIRE = YES/NO
    Enables support for Umpire, a resource management library that allows the
@@ -609,8 +617,9 @@ The specific libraries and their options are:
 
 - PUMI (optional), used when MFEM_USE_PUMI = YES.
   URL: https://scorec.rpi.edu/pumi
+       https://github.com/SCOREC/core
   Options: PUMI_OPT, PUMI_LIB.
-  Versions: PUMI >= 2.2.0.
+  Versions: PUMI >= 2.2.3.
 
 - HiOp (optional), used when MFEM_USE_HIOP = YES.
   URL: https://github.com/LLNL/hiop

config/cmake/MFEMConfig.cmake.in

@@ -47,6 +47,7 @@ set(MFEM_USE_OCCA @MFEM_USE_OCCA@)
 set(MFEM_USE_RAJA @MFEM_USE_RAJA@)
 set(MFEM_USE_CEED @MFEM_USE_CEED@)
 set(MFEM_USE_UMPIRE @MFEM_USE_UMPIRE@)
+set(MFEM_USE_SIMD @MFEM_USE_SIMD@)
 set(MFEM_USE_ADIOS2 @MFEM_USE_ADIOS2@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")

config/cmake/config.hpp.in

@@ -107,6 +107,9 @@
 // Enable MFEM functionality based on the Sidre library
 #cmakedefine MFEM_USE_SIDRE
 
+// Enable the use of SIMD in the high performance templated classes
+#cmakedefine MFEM_USE_SIMD
+
 // Enable MFEM functionality based on Conduit
 #cmakedefine MFEM_USE_CONDUIT
 

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -733,7 +733,7 @@ function(mfem_export_mk_files)
       MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GNUTLS
       MFEM_USE_GSLIB MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE
       MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_CUDA MFEM_USE_OCCA MFEM_USE_RAJA
-      MFEM_USE_UMPIRE)
+      MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)
@@ -743,6 +743,7 @@ function(mfem_export_mk_files)
   endforeach()
   # TODO: Add support for MFEM_USE_CUDA=YES
   set(MFEM_CXX ${CMAKE_CXX_COMPILER})
+  set(MFEM_HOST_CXX ${MFEM_CXX})
   set(MFEM_CPPFLAGS "")
   string(STRIP "${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"
          MFEM_CXXFLAGS)

config/config.hpp.in

@@ -106,6 +106,9 @@
 // Enable Sidre support
 // #define MFEM_USE_SIDRE
 
+// Enable the use of SIMD in the high performance templated classes
+// #define MFEM_USE_SIMD
+
 // Enable Conduit support
 // #define MFEM_USE_CONDUIT
 

config/config.mk.in

@@ -49,10 +49,12 @@ MFEM_USE_RAJA          = @MFEM_USE_RAJA@
 MFEM_USE_OCCA          = @MFEM_USE_OCCA@
 MFEM_USE_CEED          = @MFEM_USE_CEED@
 MFEM_USE_UMPIRE        = @MFEM_USE_UMPIRE@
+MFEM_USE_SIMD          = @MFEM_USE_SIMD@
 MFEM_USE_ADIOS2        = @MFEM_USE_ADIOS2@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@
+MFEM_HOST_CXX  = @MFEM_HOST_CXX@
 MFEM_CPPFLAGS  = @MFEM_CPPFLAGS@
 MFEM_CXXFLAGS  = @MFEM_CXXFLAGS@
 MFEM_TPLFLAGS  = @MFEM_TPLFLAGS@

config/defaults.cmake

@@ -49,6 +49,7 @@ option(MFEM_USE_OCCA "Enable OCCA" OFF)
 option(MFEM_USE_RAJA "Enable RAJA" OFF)
 option(MFEM_USE_CEED "Enable CEED" OFF)
 option(MFEM_USE_UMPIRE "Enable Umpire" OFF)
+option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" ON)
 option(MFEM_USE_ADIOS2 "Enable ADIOS2" OFF)
 
 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")

config/defaults.mk

@@ -137,6 +137,7 @@ MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
 MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
+MFEM_USE_SIMD          = YES
 MFEM_USE_ADIOS2        = NO
 
 # Compile and link options for zlib.

config/tconfig.hpp

@@ -29,8 +29,20 @@
 #define MFEM_ALWAYS_INLINE
 #endif
 
+// --- MFEM_VECTORIZE_LOOP (disabled)
+#if (__cplusplus >= 201103L) && !defined(MFEM_DEBUG) && defined(__GNUC__)
+//#define MFEM_VECTORIZE_LOOP _Pragma("GCC ivdep")
+#define MFEM_VECTORIZE_LOOP
+#else
+#define MFEM_VECTORIZE_LOOP
+#endif
+
+// MFEM_TEMPLATE_BLOCK_SIZE is the block size used by the template matrix-matrix
+// multiply, Mult_AB, defined in tmatrix.hpp. This parameter will generally
+// require tuning to determine good value. It is probably highly influenced by
+// the SIMD width when Mult_AB is used with a SIMD type like AutoSIMD.
 #define MFEM_TEMPLATE_BLOCK_SIZE 4
-#define MFEM_SIMD_SIZE 32
+
 #define MFEM_TEMPLATE_ENABLE_SERIALIZE
 
 // #define MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
@@ -38,11 +50,6 @@
 // #define MFEM_TEMPLATE_FIELD_EVAL_DATA_HAS_DOFS
 #define MFEM_TEMPLATE_INTRULE_COEFF_PRECOMP
 
-// derived macros
-#define MFEM_ROUNDUP(val,base) ((((val)+(base)-1)/(base))*(base))
-#define MFEM_ALIGN_SIZE(size,type) \
-   MFEM_ROUNDUP(size,(MFEM_SIMD_SIZE)/sizeof(type))
-
 #ifdef MFEM_COUNT_FLOPS
 namespace mfem
 {

data/periodic-annulus-sector.geo

@@ -0,0 +1,37 @@
+SetFactory("OpenCASCADE");
+
+R1 = 1.0;
+R2 = 2.0;
+
+Point(1) = {0.0, 0, 0, 1.0};
+Point(2) = {R1, 0, 0, 1.0};
+Point(3) = {R2, 0, 0, 1.0};
+Point(4) = {R1*Cos(Pi/3), R1*Sin(Pi/3), 0, 1.0};
+Point(5) = {R2*Cos(Pi/3), R2*Sin(Pi/3), 0, 1.0};
+Line(1) = {2, 3};
+Line(2) = {4, 5};
+Circle(3) = {2, 1, 4};
+Circle(4) = {3, 1, 5};
+Curve Loop(5) = {1, 4, -2, -3};
+Plane Surface(1) = {5};
+
+Transfinite Curve{1} = 7;
+Transfinite Curve{2} = 7;
+Transfinite Curve{3} = 4;
+Transfinite Curve{4} = 10;
+
+// Set a rotation periodicity constraint:
+Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Pi/3};
+
+// Tag surfaces and volumes with positive integers
+Physical Curve(1) = {3};
+Physical Curve(2) = {4};
+Physical Curve(3) = {1};
+Physical Curve(4) = {2};
+Physical Surface(1) = {1};
+
+// Generate 2D mesh
+Mesh 2;
+Mesh.MshFileVersion = 2.2;
+
+Save "periodic-annulus-sector.msh";

data/periodic-annulus-sector.msh

@@ -0,0 +1,185 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
+55
+1 1 0 0
+2 2 0 0
+3 0.5000000000000001 0.8660254037844386 0
+4 1 1.732050807568877 0
+5 1.166666666666667 0 0
+6 1.333333333333333 0 0
+7 1.5 0 0
+8 1.666666666666667 0 0
+9 1.833333333333333 0 0
+10 0.5833333333333335 1.010362971081845 0
+11 0.6666666666666667 1.154700538379251 0
+12 0.7500000000000002 1.299038105676658 0
+13 0.8333333333333335 1.443375672974064 0
+14 0.9166666666666669 1.587713240271471 0
+15 0.9396926207859085 0.3420201433256683 0
+16 0.7660444431189786 0.6427876096865386 0
+17 1.986476715483886 0.2321858282504602 0
+18 1.946089741159648 0.4612317414848793 0
+19 1.879385241571817 0.6840402866513365 0
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+21 1.670975622825874 1.09901795614161 0
+22 1.532088886237958 1.285575219373077 0
+23 1.372483275737469 1.454747283146095 0
+24 1.194317183405575 1.604246385510085 0
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+26 0.8788667344146573 1.13917645290495 0
+27 1.630372059110754 0.7154531062316609 0
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+29 1.081023776188756 0.6241293681829633 0
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+37 1.066623110765233 1.061857005744772 0
+38 1.587029716281926 0.1355955181472859 0
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+40 1.25 0.1443375672974065 0
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+47 0.7499999999999998 1.010362971081845 0
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+53 1.079645953234324 1.246963713711438 0
+54 1.877063966817811 0.1348974588243076 0
+55 1.055356609656722 1.558136350380461 0
+$EndNodes
+$Elements
+108
+1 1 2 3 1 1 5
+2 1 2 3 1 5 6
+3 1 2 3 1 6 7
+4 1 2 3 1 7 8
+5 1 2 3 1 8 9
+6 1 2 3 1 9 2
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+9 1 2 4 2 11 12
+10 1 2 4 2 12 13
+11 1 2 4 2 13 14
+12 1 2 4 2 14 4
+13 1 2 1 3 1 15
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+15 1 2 1 3 16 3
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+87 2 2 1 1 31 52 39
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+99 2 2 1 1 26 45 12
+100 2 2 1 1 11 47 26
+101 2 2 1 1 27 50 42
+102 2 2 1 1 40 44 5
+103 2 2 1 1 43 51 28
+104 2 2 1 1 10 48 47
+105 2 2 1 1 9 54 39
+106 2 2 1 1 46 55 14
+107 2 2 1 1 1 44 15
+108 2 2 1 1 16 48 3
+$EndElements
+$Periodic
+1
+1 1 2
+Affine 0.5000000000000001 0.8660254037844386 0 0 -0.8660254037844386 0.5000000000000001 0 0 0 0 1 0 0 0 0 1
+7
+9 14
+6 11
+8 13
+5 10
+7 12
+2 4
+1 3
+$EndPeriodic

data/periodic-torus-sector.geo

@@ -0,0 +1,25 @@
+SetFactory("OpenCASCADE");
+
+R = 1.5;
+r = 0.5;
+
+Torus(1) = {0,0,0, R, r, Pi/3};
+
+pts() = PointsOf{ Volume{1}; };
+
+Characteristic Length{ pts() } = 0.25;
+
+// Set a rotation periodicity constraint:
+Periodic Surface{3} = {2} Rotate{{0,0,1}, {0,0,0}, Pi/3};
+
+// Tag surfaces and volumes with positive integers
+Physical Surface(1) = {1};
+Physical Surface(2) = {2};
+Physical Surface(3) = {3};
+Physical Volume(1) = {1};
+
+// Generate 3D mesh
+Mesh 3;
+
+Mesh.MshFileVersion = 2.2;
+Save "periodic-torus-sector.msh";

data/square-disc-nurbs-patch.mesh

@@ -0,0 +1,155 @@
+MFEM NURBS mesh v1.0
+
+dimension
+2
+
+elements
+5
+1 3 0 3 7 4
+1 3 3 2 6 7
+1 3 2 1 5 6
+1 3 1 0 4 5
+1 3 2 8 9 1
+
+boundary
+10
+1 1 0 3
+2 1 3 2
+2 1 1 0
+2 1 2 8
+2 1 9 1
+3 1 7 4
+3 1 6 7
+3 1 5 6
+3 1 4 5
+4 1 8 9
+
+edges
+15
+0 0 4
+0 3 7
+0 1 5
+0 2 6
+1 0 3
+1 4 7
+2 3 2
+2 7 6
+2 1 0
+2 5 4
+1 2 1
+1 6 5
+1 8 9
+3 2 8
+3 1 9
+
+vertices
+10
+
+patches
+
+knotvectors
+2
+2 3 0 0 0 1 1 1
+2 4 0 0 0 0.5 1 1 1
+
+dimension
+2
+
+controlpoints_cartesian
+-5 5 1
+-5 3.92523e-16 1
+-5 -5 1
+-2.47593 2.47593 1
+-4.95187 6.06429e-16 0.707107
+-2.47593 -2.47593 1
+-0.424264 0.424264 1
+-0.848528 1.03915e-16 0.707107
+-0.424264 -0.424264 1
+-0.353553 0.353553 1
+-0.707107 8.65956e-17 0.707107
+-0.353553 -0.353553 1
+
+knotvectors
+2
+2 3 0 0 0 1 1 1
+2 4 0 0 0 0.5 1 1 1
+
+dimension
+2
+
+controlpoints_cartesian
+-5 -5 1
+-1.17757e-15 -5 1
+5 -5 1
+-2.47593 -2.47593 1
+-9.09644e-16 -4.95187 0.707107
+2.47593 -2.47593 1
+-0.424264 -0.424264 1
+-1.55872e-16 -0.848528 0.707107
+0.424264 -0.424264 1
+-0.353553 -0.353553 1
+-1.29893e-16 -0.707107 0.707107
+0.353553 -0.353553 1
+
+knotvectors
+2
+2 3 0 0 0 1 1 1
+2 4 0 0 0 0.5 1 1 1
+
+dimension
+2
+
+controlpoints_cartesian
+5 -5 1
+5 -1.17757e-15 1
+5 5 1
+2.47593 -2.47593 1
+4.95187 -1.21286e-15 0.707107
+2.47593 2.47593 1
+0.424264 -0.424264 1
+0.848528 -2.07829e-16 0.707107
+0.424264 0.424264 1
+0.353553 -0.353553 1
+0.707107 -1.73191e-16 0.707107
+0.353553 0.353553 1
+
+knotvectors
+2
+2 3 0 0 0 1 1 1
+2 4 0 0 0 0.5 1 1 1
+
+dimension
+2
+
+controlpoints_cartesian
+5 5 1
+3.92523e-16 5 1
+-5 5 1
+2.47593 2.47593 1
+3.03215e-16 4.95187 0.707107
+-2.47593 2.47593 1
+0.424264 0.424264 1
+5.19574e-17 0.848528 0.707107
+-0.424264 0.424264 1
+0.353553 0.353553 1
+4.32978e-17 0.707107 0.707107
+-0.353553 0.353553 1
+
+knotvectors
+2
+2 3 0 0 0 1 1 1
+2 3 0 0 0 1 1 1
+
+dimension
+2
+
+controlpoints_cartesian
+5 -5 1
+10 -5 1
+15 -5 1
+5 0 1
+10 0 1
+15 0 1
+5 5 1
+10 5 1
+15 5 1

doc/CMakeLists.txt

@@ -16,36 +16,21 @@ if (DOXYGEN_FOUND)
   configure_file(${CMAKE_CURRENT_SOURCE_DIR}/CodeDocumentation.conf.in
     ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf @ONLY)
 
-  if (UNIX)
-    # Only create symlinks if UNIX operating system
-    add_custom_target(doc
-      COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
-      COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
-      COMMAND ${CMAKE_COMMAND} -E create_symlink
-      ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
-      ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
-      BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
-      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
-      COMMENT "Generating API documentation with Doxygen to CodeDocumentation.html"
-      VERBATIM)
 
-    add_custom_target(clean-doc
-      COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
-      COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
-      COMMENT "Removing API documentation"
-      VERBATIM)
+  add_custom_target(doc
+    COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
+    COMMAND echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
+    BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
+    WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+    COMMENT "Generating API documentation with Doxygen to CodeDocumentation.html"
+    VERBATIM)
+
+  add_custom_target(clean-doc
+    COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
+    COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/warnings.log
+    COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
+    COMMENT "Removing API documentation"
+    VERBATIM)
 
-  else (UNIX)
-    add_custom_target(doc
-      COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
-      BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
-      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
-      COMMENT "Generating API documentation with Doxygen to CodeDocumentation/html/index.html"
-      VERBATIM)
 
-    add_custom_target(clean-doc
-      COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
-      COMMENT "Removing API documentation"
-      VERBATIM)
-  endif (UNIX)
 endif (DOXYGEN_FOUND)

doc/CodeDocumentation.conf.in

@@ -51,7 +51,7 @@ PROJECT_BRIEF          = "Finite element discretization library"
 # pixels and the maximum width should not exceed 200 pixels. Doxygen will copy
 # the logo to the output directory.
 
-PROJECT_LOGO           =
+PROJECT_LOGO           = web/logo-small.png
 
 # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
 # into which the generated documentation will be written. If a relative path is
@@ -746,7 +746,7 @@ WARN_FORMAT            = "$file:$line: $text"
 # messages should be written. If left blank the output is written to standard
 # error (stderr).
 
-WARN_LOGFILE           =
+WARN_LOGFILE           = warnings.log
 
 #---------------------------------------------------------------------------
 # Configuration options related to the input files
@@ -1470,7 +1470,7 @@ MATHJAX_FORMAT         = HTML-CSS
 # The default value is: http://cdn.mathjax.org/mathjax/latest.
 # This tag requires that the tag USE_MATHJAX is set to YES.
 
-MATHJAX_RELPATH        = https://cdn.llnl.gov/mathjax/2.7.2
+MATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest
 
 # The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax
 # extension names that should be enabled during MathJax rendering. For example

doc/CodeDocumentation.dox

@@ -149,6 +149,7 @@ namespace mfem {
  * - <a class="el" href="extruder_8cpp_source.html">Extruder</a>: extrude a low-dimensional mesh into a higher dimension
  * - <a class="el" href="mesh-explorer_8cpp_source.html">Mesh Explorer</a>: visualize and manipulate meshes
  * - <a class="el" href="mesh-optimizer_8cpp_source.html">Mesh Optimizer</a>: optimize high-order meshes, <a class="el" href="mesh-optimizer_8cpp_source.html">serial</a> and <a class="el" href="pmesh-optimizer_8cpp_source.html">parallel</a> versions
+ * - <a class="el" href="trimmer_8cpp_source.html">Trimmer</a>: trim elements from existing meshes
  * - <a class="el" href="display-basis_8cpp_source.html">Display Basis</a>: visualize finite element basis functions
  * - <a class="el" href="get-values_8cpp_source.html">Get Values</a>: extract field values via DataCollection classes
  * - <a class="el" href="load-dc_8cpp_source.html">Load DC</a>: visualize fields saved via DataCollection classes

doc/makefile

@@ -9,18 +9,25 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
+SHELL = /bin/bash
 MFEM_DIR ?= ..
 DOXYGEN_CONF = CodeDocumentation.conf
 
+
 # doxygen uses: graphviz, latex
 html: $(DOXYGEN_CONF)
-	doxygen $(DOXYGEN_CONF)
-	rm -f CodeDocumentation.html
-	ln -s CodeDocumentation/html/index.html CodeDocumentation.html
+	@# Generate the html documentation
+	@doxygen $(DOXYGEN_CONF)
+	@echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > CodeDocumentation.html
+	@cat warnings.log
+	@# Generate the log of undocumented methods
+	@( cat $(DOXYGEN_CONF) ; echo "GENERATE_HTML=NO" ; echo "EXTRACT_ALL=NO" ; echo "WARN_LOGFILE=undoc.log" ; echo "QUIET=YES" ) | doxygen - &> /dev/null
 
 clean:
 	rm -rf $(DOXYGEN_CONF) CodeDocumentation CodeDocumentation.html *~
+	rm -rf  undoc.log warnings.log
 
 $(DOXYGEN_CONF): $(MFEM_DIR)/doc/$(DOXYGEN_CONF).in
-	sed -e 's%@MFEM_SOURCE_DIR@%$(MFEM_DIR)%g' $(<) \
+	@sed -e 's%@MFEM_SOURCE_DIR@%$(MFEM_DIR)%g' $(<) \
 	  > $(DOXYGEN_CONF)
+

examples/ex1.cpp

@@ -9,6 +9,8 @@
 //               ex1 -m ../data/fichera.mesh
 //               ex1 -m ../data/fichera-mixed.mesh
 //               ex1 -m ../data/toroid-wedge.mesh
+//               ex1 -m ../data/periodic-annulus-sector.msh
+//               ex1 -m ../data/periodic-torus-sector.msh
 //               ex1 -m ../data/square-disc-p2.vtk -o 2
 //               ex1 -m ../data/square-disc-p3.mesh -o 3
 //               ex1 -m ../data/square-disc-nurbs.mesh -o -1

examples/ex11p.cpp

@@ -8,6 +8,8 @@
 //               mpirun -np 4 ex11p -m ../data/escher.mesh
 //               mpirun -np 4 ex11p -m ../data/fichera.mesh
 //               mpirun -np 4 ex11p -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex11p -m ../data/periodic-annulus-sector.msh
+//               mpirun -np 4 ex11p -m ../data/periodic-torus-sector.msh -rs 1
 //               mpirun -np 4 ex11p -m ../data/toroid-wedge.mesh -o 2
 //               mpirun -np 4 ex11p -m ../data/square-disc-p2.vtk -o 2
 //               mpirun -np 4 ex11p -m ../data/square-disc-p3.mesh -o 3

examples/ex14p.cpp

@@ -35,6 +35,38 @@
 using namespace std;
 using namespace mfem;
 
+class CustomSolverMonitor : public IterativeSolverMonitor
+{
+public:
+   CustomSolverMonitor(const ParMesh *m,
+                       ParGridFunction *f) :
+      pmesh(m),
+      pgf(f) {}
+
+   void MonitorSolution(int i, double norm, const Vector &x, bool final)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      int  num_procs, myid;
+
+      MPI_Comm_size(pmesh->GetComm(),&num_procs);
+      MPI_Comm_rank(pmesh->GetComm(),&myid);
+
+      pgf->SetFromTrueDofs(x);
+
+      socketstream sol_sock(vishost, visport);
+      sol_sock << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *pmesh << *pgf
+               << "window_title 'Iteration no " << i << "'"
+               << "keys rRjlc\n" << flush;
+   }
+
+private:
+   const ParMesh *pmesh;
+   ParGridFunction *pgf;
+};
+
 int main(int argc, char *argv[])
 {
    // 1. Initialize MPI.
@@ -188,6 +220,7 @@ int main(int argc, char *argv[])
    }
    else
    {
+      CustomSolverMonitor monitor(pmesh, &x);
       GMRESSolver gmres(MPI_COMM_WORLD);
       gmres.SetAbsTol(0.0);
       gmres.SetRelTol(1e-12);
@@ -196,6 +229,7 @@ int main(int argc, char *argv[])
       gmres.SetPrintLevel(1);
       gmres.SetOperator(*A);
       gmres.SetPreconditioner(*amg);
+      gmres.SetMonitor(monitor);
       gmres.Mult(*B, *X);
    }
    delete amg;

examples/ex18.hpp

@@ -418,7 +418,7 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
    {
       intorder++;
    }
-   const IntegrationRule *ir = &IntRules.Get(Tr.FaceGeom, intorder);
+   const IntegrationRule *ir = &IntRules.Get(Tr.GetGeometryType(), intorder);
 
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
@@ -435,10 +435,10 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
       elfun1_mat.MultTranspose(shape1, funval1);
       elfun2_mat.MultTranspose(shape2, funval2);
 
-      Tr.Face->SetIntPoint(&ip);
+      Tr.SetIntPoint(&ip);
 
       // Get the normal vector and the flux on the face
-      CalcOrtho(Tr.Face->Jacobian(), nor);
+      CalcOrtho(Tr.Jacobian(), nor);
       const double mcs = rsolver.Eval(funval1, funval2, nor, fluxN);
 
       // Update max char speed

examples/ex19.cpp

@@ -38,6 +38,42 @@
 using namespace std;
 using namespace mfem;
 
+class GeneralResidualMonitor : public IterativeSolverMonitor
+{
+public:
+   GeneralResidualMonitor(const std::string& prefix_, int print_lvl)
+      : prefix(prefix_)
+   {
+      print_level = print_lvl;
+   }
+
+   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
+
+private:
+   const std::string prefix;
+   int print_level;
+   mutable double norm0;
+};
+
+void GeneralResidualMonitor::MonitorResidual(int it, double norm,
+                                             const Vector &r, bool final)
+{
+   if (print_level == 1 || (print_level == 3 && (final || it == 0)))
+   {
+      mfem::out << prefix << " iteration " << setw(2) << it
+                << " : ||r|| = " << norm;
+      if (it > 0)
+      {
+         mfem::out << ",  ||r||/||r_0|| = " << norm/norm0;
+      }
+      else
+      {
+         norm0 = norm;
+      }
+      mfem::out << '\n';
+   }
+}
+
 // Custom block preconditioner for the Jacobian of the incompressible nonlinear
 // elasticity operator. It has the form
 //
@@ -103,9 +139,11 @@ protected:
 
    // Newton solver for the hyperelastic operator
    NewtonSolver newton_solver;
+   GeneralResidualMonitor newton_monitor;
 
    // Solver for the Jacobian solve in the Newton method
    Solver *j_solver;
+   GeneralResidualMonitor j_monitor;
 
    // Preconditioner for the Jacobian
    Solver *j_prec;
@@ -410,7 +448,8 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
                                int iter,
                                Coefficient &c_mu)
    : Operator(fes[0]->GetVSize() + fes[1]->GetVSize()),
-     newton_solver(), mu(c_mu), block_offsets(offsets)
+     newton_solver(), newton_monitor("Newton", 1),
+     j_monitor("  GMRES", 3), mu(c_mu), block_offsets(offsets)
 {
    Array<Vector *> rhs(2);
    rhs = NULL; // Set all entries in the array
@@ -446,7 +485,8 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
    j_gmres->SetRelTol(1e-12);
    j_gmres->SetAbsTol(1e-12);
    j_gmres->SetMaxIter(300);
-   j_gmres->SetPrintLevel(0);
+   j_gmres->SetPrintLevel(-1);
+   j_gmres->SetMonitor(j_monitor);
    j_gmres->SetPreconditioner(*j_prec);
    j_solver = j_gmres;
 
@@ -454,7 +494,8 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
    newton_solver.iterative_mode = true;
    newton_solver.SetSolver(*j_solver);
    newton_solver.SetOperator(*this);
-   newton_solver.SetPrintLevel(1);
+   newton_solver.SetPrintLevel(-1);
+   newton_solver.SetMonitor(newton_monitor);
    newton_solver.SetRelTol(rel_tol);
    newton_solver.SetAbsTol(abs_tol);
    newton_solver.SetMaxIter(iter);

examples/ex19p.cpp

@@ -38,6 +38,56 @@
 using namespace std;
 using namespace mfem;
 
+class GeneralResidualMonitor : public IterativeSolverMonitor
+{
+public:
+   GeneralResidualMonitor(MPI_Comm comm, const std::string& prefix_,
+                          int print_lvl)
+      : prefix(prefix_)
+   {
+#ifndef MFEM_USE_MPI
+      print_level = print_lvl;
+#else
+      int rank;
+      MPI_Comm_rank(comm, &rank);
+      if (rank == 0)
+      {
+         print_level = print_lvl;
+      }
+      else
+      {
+         print_level = -1;
+      }
+#endif
+   }
+
+   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
+
+private:
+   const std::string prefix;
+   int print_level;
+   mutable double norm0;
+};
+
+void GeneralResidualMonitor::MonitorResidual(int it, double norm,
+                                             const Vector &r, bool final)
+{
+   if (print_level == 1 || (print_level == 3 && (final || it == 0)))
+   {
+      mfem::out << prefix << " iteration " << setw(2) << it
+                << " : ||r|| = " << norm;
+      if (it > 0)
+      {
+         mfem::out << ",  ||r||/||r_0|| = " << norm/norm0;
+      }
+      else
+      {
+         norm0 = norm;
+      }
+      mfem::out << '\n';
+   }
+}
+
 // Custom block preconditioner for the Jacobian of the incompressible nonlinear
 // elasticity operator. It has the form
 //
@@ -103,9 +153,11 @@ protected:
 
    // Newton solver for the hyperelastic operator
    NewtonSolver newton_solver;
+   GeneralResidualMonitor newton_monitor;
 
    // Solver for the Jacobian solve in the Newton method
    Solver *j_solver;
+   GeneralResidualMonitor j_monitor;
 
    // Preconditioner for the Jacobian
    Solver *j_prec;
@@ -459,7 +511,10 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
                                int iter,
                                Coefficient &c_mu)
    : Operator(fes[0]->TrueVSize() + fes[1]->TrueVSize()),
-     newton_solver(fes[0]->GetComm()), mu(c_mu), block_trueOffsets(trueOffsets)
+     newton_solver(fes[0]->GetComm()),
+     newton_monitor(fes[0]->GetComm(), "Newton", 1),
+     j_monitor(fes[0]->GetComm(), "  GMRES", 3),
+     mu(c_mu), block_trueOffsets(trueOffsets)
 {
    Array<Vector *> rhs(2);
    rhs = NULL; // Set all entries in the array
@@ -499,7 +554,8 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
    j_gmres->SetRelTol(1e-12);
    j_gmres->SetAbsTol(1e-12);
    j_gmres->SetMaxIter(300);
-   j_gmres->SetPrintLevel(0);
+   j_gmres->SetPrintLevel(-1);
+   j_gmres->SetMonitor(j_monitor);
    j_gmres->SetPreconditioner(*j_prec);
    j_solver = j_gmres;
 
@@ -507,7 +563,8 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
    newton_solver.iterative_mode = true;
    newton_solver.SetSolver(*j_solver);
    newton_solver.SetOperator(*this);
-   newton_solver.SetPrintLevel(1);
+   newton_solver.SetPrintLevel(-1);
+   newton_solver.SetMonitor(newton_monitor);
    newton_solver.SetRelTol(rel_tol);
    newton_solver.SetAbsTol(abs_tol);
    newton_solver.SetMaxIter(iter);

examples/ex1p.cpp

@@ -9,6 +9,8 @@
 //               mpirun -np 4 ex1p -m ../data/fichera.mesh
 //               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
 //               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../data/periodic-annulus-sector.msh
+//               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
 //               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
 //               mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
 //               mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1

examples/ex24.cpp

@@ -6,6 +6,7 @@
 //               ex24 -m ../data/square-disc.mesh -o 2
 //               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/escher.mesh
 //               ex24 -m ../data/escher.mesh -o 2
 //               ex24 -m ../data/fichera.mesh
@@ -23,11 +24,15 @@
 //               ex24 -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces. Using two different approaches, we project a gradient
-//               of a function in H^1 to H(curl). Other spaces and example
-//               computations are to be added in the future.
+//               spaces, with two variants:
 //
-//               We recommend viewing examples 1 and 3 before viewing this
+//               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
+//
+//               Using different approaches, we project the gradient or
+//               divergence to the appropriate space.
+//
+//               We recommend viewing examples 1, 3, and 5 before viewing this
 //               example.
 
 #include "mfem.hpp"
@@ -39,6 +44,7 @@ using namespace mfem;
 
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
+double div_gradp_exact(const Vector &x);
 
 int dim;
 
@@ -47,6 +53,7 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    const char *mesh_file = "../data/beam-hex.mesh";
    int order = 1;
+   int prob = 0;
    bool static_cond = false;
    bool pa = false;
    const char *device_config = "cpu";
@@ -57,6 +64,8 @@ int main(int argc, char *argv[])
                   "Mesh file to use.");
    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)");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -100,72 +109,107 @@ int main(int argc, char *argv[])
    }
    mesh->ReorientTetMesh();
 
-   // 5. 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);
-   FiniteElementCollection *H1fec = new H1_FECollection(order, dim);
-   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
-   FiniteElementSpace *H1fespace = new FiniteElementSpace(mesh, H1fec);
+   // 5. Define a finite element space on the mesh. Here we use Nedelec or
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *trial_fec = NULL;
+   FiniteElementCollection *test_fec = NULL;
 
-   int size = fespace->GetTrueVSize();
-   int H1size = H1fespace->GetTrueVSize();
-   cout << "Number of Nedelec finite element unknowns: " << size << endl;
-   cout << "Number of H1 finite element unknowns: " << H1size << endl;
-
-   // 6. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x by projecting the exact
-   //    solution. Note that only values from the boundary edges will be used
-   //    when eliminating the non-homogeneous boundary condition to modify the
-   //    r.h.s. vector b.
-   GridFunction x(fespace);
-   FunctionCoefficient p_coef(p_exact);
-   GridFunction p(H1fespace);
-   p.ProjectCoefficient(p_coef);
-   p.SetTrueVector();
-   p.SetFromTrueVector();
-
-   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
-
-   // 7. Set up the bilinear forms.
-   Coefficient *muinv = new ConstantCoefficient(1.0);
-   Coefficient *sigma = new ConstantCoefficient(1.0);
-   BilinearForm *a = new BilinearForm(fespace);
-   MixedBilinearForm *a_NDH1 = new MixedBilinearForm(H1fespace, fespace);
-   if (pa)
+   if (prob == 0)
    {
-      a->SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      a_NDH1->SetAssemblyLevel(AssemblyLevel::PARTIAL);
-   }
-
-   // First approach: L2 projection
-   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
-   a_NDH1->AddDomainIntegrator(new MixedVectorGradientIntegrator(*muinv));
-
-   // 8. 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 (!pa) { a->Finalize(); }
-
-   a_NDH1->Assemble();
-   if (!pa) { a_NDH1->Finalize(); }
-
-   if (pa)
-   {
-      a_NDH1->Mult(p, x);
+      trial_fec = new H1_FECollection(order, dim);
+      test_fec = new ND_FECollection(order, dim);
    }
    else
    {
-      SparseMatrix& NDH1 = a_NDH1->SpMat();
-      NDH1.Mult(p, x);
+      trial_fec = new RT_FECollection(order - 1, dim);
+      test_fec = new L2_FECollection(order - 1, dim);
+   }
+
+   FiniteElementSpace trial_fes(mesh, trial_fec);
+   FiniteElementSpace test_fes(mesh, test_fec);
+
+   int trial_size = trial_fes.GetTrueVSize();
+   int test_size = test_fes.GetTrueVSize();
+
+   if (prob == 0)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
+      cout << "Number of H1 finite element unknowns: " << trial_size << endl;
+   }
+   else
+   {
+      cout << "Number of Raviart-Thomas finite element unknowns: "
+           << trial_size << endl;
+      cout << "Number of L2 finite element unknowns: " << test_size << endl;
+   }
+
+   // 6. Define the solution vector as a finite element grid function
+   //    corresponding to the trial fespace.
+   GridFunction gftest(&test_fes);
+   GridFunction gftrial(&trial_fes);
+   GridFunction x(&test_fes);
+   FunctionCoefficient p_coef(p_exact);
+   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   FunctionCoefficient divgradp_coef(div_gradp_exact);
+
+   if (prob == 0)
+   {
+      gftrial.ProjectCoefficient(p_coef);
+   }
+   else
+   {
+      gftrial.ProjectCoefficient(gradp_coef);
+   }
+
+   gftrial.SetTrueVector();
+   gftrial.SetFromTrueVector();
+
+   // 7. Set up the bilinear forms for L2 projection.
+   ConstantCoefficient one(1.0);
+   BilinearForm a(&test_fes);
+   MixedBilinearForm a_mixed(&trial_fes, &test_fes);
+   if (pa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   }
+
+   if (prob == 0)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
+   }
+   else
+   {
+      a.AddDomainIntegrator(new MassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
+   }
+
+   // 8. 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 (!pa) { a.Finalize(); }
+
+   a_mixed.Assemble();
+   if (!pa) { a_mixed.Finalize(); }
+
+   if (pa)
+   {
+      a_mixed.Mult(gftrial, x);
+   }
+   else
+   {
+      SparseMatrix& mixed = a_mixed.SpMat();
+      mixed.Mult(gftrial, x);
    }
 
    // 9. Define and apply a PCG solver for Ax = b with Jacobi preconditioner.
    {
-      GridFunction rhs(fespace);
+      GridFunction rhs(&test_fes);
       rhs = x;
       x = 0.0;
 
@@ -176,15 +220,15 @@ int main(int argc, char *argv[])
       if (pa)
       {
          Array<int> ess_tdof_list; // empty
-         OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);
+         OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
 
-         cg.SetOperator(*a);
+         cg.SetOperator(a);
          cg.SetPreconditioner(Jacobi);
          cg.Mult(rhs, x);
       }
       else
       {
-         SparseMatrix& Amat = a->SpMat();
+         SparseMatrix& Amat = a.SpMat();
          DSmoother Jacobi(Amat);
 
          cg.SetOperator(Amat);
@@ -193,33 +237,68 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 10. Second approach: compute the same solution by applying
-   //     GradientInterpolator in H(curl).
-   DiscreteLinearOperator grad(H1fespace, fespace);
-   grad.AddDomainInterpolator(new GradientInterpolator());
-   grad.Assemble();
+   // 10. Compute the same field by applying a DiscreteInterpolator.
+   GridFunction discreteInterpolant(&test_fes);
+   DiscreteLinearOperator dlo(&trial_fes, &test_fes);
+   if (prob == 0)
+   {
+      dlo.AddDomainInterpolator(new GradientInterpolator());
+   }
+   else
+   {
+      dlo.AddDomainInterpolator(new DivergenceInterpolator());
+   }
 
-   GridFunction gradp(fespace);
-   grad.Mult(p, gradp);
+   dlo.Assemble();
+   dlo.Mult(gftrial, discreteInterpolant);
 
-   // 11. Compute the projection of the exact grad p.
-   GridFunction exact_gradp(fespace);
-   exact_gradp.ProjectCoefficient(gradp_coef);
-   exact_gradp.SetTrueVector();
-   exact_gradp.SetFromTrueVector();
+   // 11. Compute the projection of the exact field.
+   GridFunction exact_proj(&test_fes);
+   if (prob == 0)
+   {
+      exact_proj.ProjectCoefficient(gradp_coef);
+   }
+   else
+   {
+      exact_proj.ProjectCoefficient(divgradp_coef);
+   }
 
-   // 12. Compute and print the L^2 norm of the error.
+   exact_proj.SetTrueVector();
+   exact_proj.SetFromTrueVector();
+
+   // 12. Compute and print the L_2 norm of the error.
+   if (prob == 0)
    {
       double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = gradp.ComputeL2Error(gradp_coef);
-      double errProj = exact_gradp.ComputeL2Error(gradp_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
+      double errProj = exact_proj.ComputeL2Error(gradp_coef);
 
       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;
+           "|| 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;
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+   else
+   {
+      int order_quad = max(2, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      double errSol = x.ComputeL2Error(divgradp_coef, irs);
+      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
+      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
+
+      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;
+      cout << " Projection f_h of exact div v in L_2: || f_h - div v "
+           "||_{L_2} = " << errProj << '\n' << endl;
    }
 
    // 13. Save the refined mesh and the solution. This output can be viewed
@@ -242,14 +321,8 @@ int main(int argc, char *argv[])
    }
 
    // 15. Free the used memory.
-   delete a;
-   delete a_NDH1;
-   delete sigma;
-   delete muinv;
-   delete fespace;
-   delete H1fespace;
-   delete fec;
-   delete H1fec;
+   delete trial_fec;
+   delete test_fec;
    delete mesh;
 
    return 0;
@@ -284,3 +357,17 @@ void gradp_exact(const Vector &x, Vector &f)
       if (x.Size() == 3) { f(2) = 0.0; }
    }
 }
+
+double div_gradp_exact(const Vector &x)
+{
+   if (dim == 3)
+   {
+      return -3.0 * sin(x(0)) * sin(x(1)) * sin(x(2));
+   }
+   else if (dim == 2)
+   {
+      return -2.0 * sin(x(0)) * sin(x(1));
+   }
+
+   return 0.0;
+}

examples/ex24p.cpp

@@ -6,6 +6,7 @@
 //               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/escher.mesh
 //               mpirun -np 4 ex24p -m ../data/escher.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/fichera.mesh
@@ -23,11 +24,15 @@
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces. Using two different approaches, we project a gradient
-//               of a function in H^1 to H(curl). Other spaces and example
-//               computations are to be added in the future.
+//               spaces, with two variants:
 //
-//               We recommend viewing examples 1 and 3 before viewing this
+//               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
+//
+//               Using different approaches, we project the gradient or
+//               divergence to the appropriate space.
+//
+//               We recommend viewing examples 1, 3, and 5 before viewing this
 //               example.
 
 #include "mfem.hpp"
@@ -39,6 +44,7 @@ using namespace mfem;
 
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
+double div_gradp_exact(const Vector &x);
 
 int dim;
 
@@ -53,6 +59,7 @@ int main(int argc, char *argv[])
    // 2. Parse command-line options.
    const char *mesh_file = "../data/beam-hex.mesh";
    int order = 1;
+   int prob = 0;
    bool static_cond = false;
    bool pa = false;
    const char *device_config = "cpu";
@@ -63,6 +70,8 @@ int main(int argc, char *argv[])
                   "Mesh file to use.");
    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)");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -129,80 +138,115 @@ int main(int argc, char *argv[])
    pmesh->ReorientTetMesh();
 
    // 7. 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);
-   FiniteElementCollection *H1fec = new H1_FECollection(order, dim);
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   ParFiniteElementSpace *H1fespace = new ParFiniteElementSpace(pmesh, H1fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
-   HYPRE_Int H1size = H1fespace->GlobalTrueVSize();
+   //    use Nedelec or Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *trial_fec = NULL;
+   FiniteElementCollection *test_fec = NULL;
+
+   if (prob == 0)
+   {
+      trial_fec = new H1_FECollection(order, dim);
+      test_fec = new ND_FECollection(order, dim);
+   }
+   else
+   {
+      trial_fec = new RT_FECollection(order - 1, dim);
+      test_fec = new L2_FECollection(order - 1, dim);
+   }
+
+   ParFiniteElementSpace trial_fes(pmesh, trial_fec);
+   ParFiniteElementSpace test_fes(pmesh, test_fec);
+
+   HYPRE_Int trial_size = trial_fes.GlobalTrueVSize();
+   HYPRE_Int test_size = test_fes.GlobalTrueVSize();
+
    if (myid == 0)
    {
-      cout << "Number of Nedelec finite element unknowns: " << size << endl;
-      cout << "Number of H1 finite element unknowns: " << H1size << endl;
+      if (prob == 0)
+      {
+         cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
+         cout << "Number of H1 finite element unknowns: " << trial_size << endl;
+      }
+      else
+      {
+         cout << "Number of Raviart-Thomas finite element unknowns: "
+              << trial_size << endl;
+         cout << "Number of L2 finite element unknowns: " << test_size << endl;
+      }
    }
 
-   // 8. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x by projecting the exact
-   //    solution. Note that only values from the boundary edges will be used
-   //    when eliminating the non-homogeneous boundary condition to modify the
-   //    r.h.s. vector b.
-   ParGridFunction x(fespace);
+   // 8. Define the solution vector as a parallel finite element grid function
+   //    corresponding to the trial fespace.
+   ParGridFunction gftest(&test_fes);
+   ParGridFunction gftrial(&trial_fes);
+   ParGridFunction x(&test_fes);
    FunctionCoefficient p_coef(p_exact);
-   ParGridFunction p(H1fespace);
-   p.ProjectCoefficient(p_coef);
-   p.SetTrueVector();
-   p.SetFromTrueVector();
-
    VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   FunctionCoefficient divgradp_coef(div_gradp_exact);
 
-   // 9. Set up the parallel bilinear forms.
-   Coefficient *muinv = new ConstantCoefficient(1.0);
-   Coefficient *sigma = new ConstantCoefficient(1.0);
-   ParBilinearForm *a = new ParBilinearForm(fespace);
-   ParMixedBilinearForm *a_NDH1 = new ParMixedBilinearForm(H1fespace, fespace);
+   if (prob == 0)
+   {
+      gftrial.ProjectCoefficient(p_coef);
+   }
+   else
+   {
+      gftrial.ProjectCoefficient(gradp_coef);
+   }
+
+   gftrial.SetTrueVector();
+   gftrial.SetFromTrueVector();
+
+   // 9. Set up the parallel bilinear forms for L2 projection.
+   ConstantCoefficient one(1.0);
+   ParBilinearForm a(&test_fes);
+   ParMixedBilinearForm a_mixed(&trial_fes, &test_fes);
    if (pa)
    {
-      a->SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      a_NDH1->SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
    }
 
-   // First approach: L2 projection
-   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
-   a_NDH1->AddDomainIntegrator(new MixedVectorGradientIntegrator(*muinv));
+   if (prob == 0)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
+   }
+   else
+   {
+      a.AddDomainIntegrator(new MassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
+   }
 
    // 10. 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(); }
+   if (static_cond) { a.EnableStaticCondensation(); }
 
-   a->Assemble();
-   if (!pa) { a->Finalize(); }
+   a.Assemble();
+   if (!pa) { a.Finalize(); }
 
-   a_NDH1->Assemble();
-   if (!pa) { a_NDH1->Finalize(); }
+   a_mixed.Assemble();
+   if (!pa) { a_mixed.Finalize(); }
 
-   Vector B(fespace->GetTrueVSize());
-   Vector X(fespace->GetTrueVSize());
+   Vector B(test_fes.GetTrueVSize());
+   Vector X(test_fes.GetTrueVSize());
 
    if (pa)
    {
-      ParLinearForm *b = new ParLinearForm(fespace); // used as a vector
-      a_NDH1->Mult(p, *b); // process-local multiplication
-      b->ParallelAssemble(B);
-      delete b;
+      ParLinearForm b(&test_fes); // used as a vector
+      a_mixed.Mult(gftrial, b); // process-local multiplication
+      b.ParallelAssemble(B);
    }
    else
    {
-      HypreParMatrix *NDH1 = a_NDH1->ParallelAssemble();
+      HypreParMatrix *mixed = a_mixed.ParallelAssemble();
 
-      Vector P(H1fespace->GetTrueVSize());
-      p.GetTrueDofs(P);
+      Vector P(trial_fes.GetTrueVSize());
+      gftrial.GetTrueDofs(P);
 
-      NDH1->Mult(P,B);
+      mixed->Mult(P,B);
 
-      delete NDH1;
+      delete mixed;
    }
 
    // 11. Define and apply a parallel PCG solver for AX=B with Jacobi
@@ -212,9 +256,9 @@ int main(int argc, char *argv[])
       Array<int> ess_tdof_list; // empty
 
       OperatorPtr A;
-      a->FormSystemMatrix(ess_tdof_list, A);
+      a.FormSystemMatrix(ess_tdof_list, A);
 
-      OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);
+      OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
 
       CGSolver cg(MPI_COMM_WORLD);
       cg.SetRelTol(1e-12);
@@ -227,7 +271,7 @@ int main(int argc, char *argv[])
    }
    else
    {
-      HypreParMatrix *Amat = a->ParallelAssemble();
+      HypreParMatrix *Amat = a.ParallelAssemble();
       HypreDiagScale Jacobi(*Amat);
       HyprePCG pcg(*Amat);
       pcg.SetTol(1e-12);
@@ -242,35 +286,73 @@ int main(int argc, char *argv[])
 
    x.SetFromTrueDofs(X);
 
-   // 12. Second approach: compute the same solution by applying
-   //     GradientInterpolator in H(curl).
-   ParDiscreteLinearOperator grad(H1fespace, fespace);
-   grad.AddDomainInterpolator(new GradientInterpolator());
-   grad.Assemble();
+   // 12. Compute the same field by applying a DiscreteInterpolator.
+   ParGridFunction discreteInterpolant(&test_fes);
+   ParDiscreteLinearOperator dlo(&trial_fes, &test_fes);
+   if (prob == 0)
+   {
+      dlo.AddDomainInterpolator(new GradientInterpolator());
+   }
+   else
+   {
+      dlo.AddDomainInterpolator(new DivergenceInterpolator());
+   }
 
-   ParGridFunction gradp(fespace);
-   grad.Mult(p, gradp);
+   dlo.Assemble();
+   dlo.Mult(gftrial, discreteInterpolant);
 
-   // 13. Compute the projection of the exact grad p.
-   ParGridFunction exact_gradp(fespace);
-   exact_gradp.ProjectCoefficient(gradp_coef);
-   exact_gradp.SetTrueVector();
-   exact_gradp.SetFromTrueVector();
+   // 13. Compute the projection of the exact field.
+   ParGridFunction exact_proj(&test_fes);
+   if (prob == 0)
+   {
+      exact_proj.ProjectCoefficient(gradp_coef);
+   }
+   else
+   {
+      exact_proj.ProjectCoefficient(divgradp_coef);
+   }
 
-   // 14. Compute and print the L^2 norm of the error.
+   exact_proj.SetTrueVector();
+   exact_proj.SetFromTrueVector();
+
+   // 14. Compute and print the L_2 norm of the error.
+   if (prob == 0)
    {
       double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = gradp.ComputeL2Error(gradp_coef);
-      double errProj = exact_gradp.ComputeL2Error(gradp_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
+      double errProj = exact_proj.ComputeL2Error(gradp_coef);
 
       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;
+              "||_{L_2} = " << errProj << '\n' << endl;
+      }
+   }
+   else
+   {
+      int order_quad = max(2, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      double errSol = x.ComputeL2Error(divgradp_coef, irs);
+      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
+      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
+
+      if (myid == 0)
+      {
+         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;
+         cout << " Projection f_h of exact div v in L_2: || f_h - div v "
+              "||_{L_2} = " << errProj << '\n' << endl;
       }
    }
 
@@ -302,14 +384,8 @@ int main(int argc, char *argv[])
    }
 
    // 17. Free the used memory.
-   delete a;
-   delete a_NDH1;
-   delete sigma;
-   delete muinv;
-   delete fespace;
-   delete H1fespace;
-   delete fec;
-   delete H1fec;
+   delete trial_fec;
+   delete test_fec;
    delete pmesh;
 
    MPI_Finalize();
@@ -346,3 +422,17 @@ void gradp_exact(const Vector &x, Vector &f)
       if (x.Size() == 3) { f(2) = 0.0; }
    }
 }
+
+double div_gradp_exact(const Vector &x)
+{
+   if (dim == 3)
+   {
+      return -3.0 * sin(x(0)) * sin(x(1)) * sin(x(2));
+   }
+   else if (dim == 2)
+   {
+      return -2.0 * sin(x(0)) * sin(x(1));
+   }
+
+   return 0.0;
+}

examples/ex4.cpp

@@ -6,6 +6,7 @@
 //               ex4 -m ../data/star.mesh
 //               ex4 -m ../data/beam-tet.mesh
 //               ex4 -m ../data/beam-hex.mesh
+//               ex4 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex4 -m ../data/escher.mesh
 //               ex4 -m ../data/fichera.mesh -o 2 -hb
 //               ex4 -m ../data/fichera-q2.vtk
@@ -20,6 +21,12 @@
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
 //               ex4 -m ../data/star-surf.mesh -o 1
 //
+// Device sample runs:
+//               ex4 -m ../data/star.mesh -pa -d cuda
+//               ex4 -m ../data/star.mesh -pa -d raja-cuda
+//               ex4 -m ../data/star.mesh -pa -d raja-omp
+//               ex4 -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D H(div) diffusion
 //               problem corresponding to the second order definite equation
 //               -grad(alpha div F) + beta F = f with boundary condition F dot n
@@ -55,6 +62,8 @@ int main(int argc, char *argv[])
    bool set_bc = true;
    bool static_cond = false;
    bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -70,6 +79,10 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
                   "--no-hybridization", "Enable hybridization.");
+   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.");
@@ -82,14 +95,19 @@ int main(int argc, char *argv[])
    args.PrintOptions(cout);
    kappa = freq * M_PI;
 
-   // 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, as well as
    //    periodic meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
 
-   // 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 25,000
    //    elements.
@@ -102,14 +120,14 @@ 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 *fec = new RT_FECollection(order-1, dim);
    FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
    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 by marking all
    //    the boundary attributes from the mesh as essential (Dirichlet) and
    //    converting them to a list of true dofs.
@@ -121,7 +139,7 @@ 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
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side
    //    of the FEM linear system, which in this case is (f,phi_i) where f is
    //    given by the function f_exact and phi_i are the basis functions in the
    //    finite element fespace.
@@ -130,7 +148,7 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
    b->Assemble();
 
-   // 7. Define the solution vector x as a finite element grid function
+   // 8. Define the solution vector x as a finite element grid function
    //    corresponding to fespace. Initialize x by projecting the exact
    //    solution. Note that only values from the boundary faces will be used
    //    when eliminating the non-homogeneous boundary condition to modify the
@@ -139,16 +157,17 @@ int main(int argc, char *argv[])
    VectorFunctionCoefficient F(sdim, F_exact);
    x.ProjectCoefficient(F);
 
-   // 8. Set up the bilinear form corresponding to the H(div) diffusion operator
+   // 9. Set up the bilinear form corresponding to the H(div) diffusion operator
    //    grad alpha div + beta I, by adding the div-div and the mass domain
    //    integrators.
    Coefficient *alpha = new ConstantCoefficient(1.0);
    Coefficient *beta  = new ConstantCoefficient(1.0);
    BilinearForm *a = new BilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
    a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));
 
-   // 9. Assemble the bilinear form and the corresponding linear system,
+   // 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, hybridization, etc.
@@ -167,32 +186,47 @@ int main(int argc, char *argv[])
    }
    a->Assemble();
 
-   SparseMatrix A;
+   OperatorPtr A;
    Vector B, X;
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
 
-   cout << "Size of linear system: " << A.Height() << endl;
+   cout << "Size of linear system: " << A->Height() << endl;
 
+   // 11. Solve the linear system A X = B.
+   if (!pa)
+   {
 #ifndef MFEM_USE_SUITESPARSE
-   // 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
-   //     solve the system A X = B with PCG.
-   GSSmoother M(A);
-   PCG(A, M, B, X, 1, 10000, 1e-20, 0.0);
+      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
+      GSSmoother M((SparseMatrix&)(*A));
+      PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
 #else
-   // 10. If compiled with SuiteSparse support, use UMFPACK to solve the system.
-   UMFPackSolver umf_solver;
-   umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-   umf_solver.SetOperator(A);
-   umf_solver.Mult(B, X);
+      // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
+      UMFPackSolver umf_solver;
+      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver.SetOperator(*A);
+      umf_solver.Mult(B, X);
 #endif
+   }
+   else // Jacobi preconditioning in partial assembly mode
+   {
+      if (UsesTensorBasis(*fespace))
+      {
+         OperatorJacobiSmoother M(*a, ess_tdof_list);
+         PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
+      }
+      else
+      {
+         CG(*A, B, X, 1, 10000, 1e-20, 0.0);
+      }
+   }
 
-   // 11. Recover the solution as a finite element grid function.
+   // 12. Recover the solution as a finite element grid function.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 12. Compute and print the L^2 norm of the error.
+   // 13. Compute and print the L^2 norm of the error.
    cout << "\n|| F_h - F ||_{L^2} = " << x.ComputeL2Error(F) << '\n' << endl;
 
-   // 13. Save the refined mesh and the solution. This output can be viewed
+   // 14. 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");
@@ -203,7 +237,7 @@ int main(int argc, char *argv[])
       x.Save(sol_ofs);
    }
 
-   // 14. Send the solution by socket to a GLVis server.
+   // 15. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -213,7 +247,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *mesh << x << flush;
    }
 
-   // 15. Free the used memory.
+   // 16. Free the used memory.
    delete hfes;
    delete hfec;
    delete a;
@@ -235,7 +269,7 @@ void F_exact(const Vector &p, Vector &F)
 
    double x = p(0);
    double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0;
+   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
 
    F(0) = cos(kappa*x)*sin(kappa*y);
    F(1) = cos(kappa*y)*sin(kappa*x);
@@ -252,7 +286,7 @@ void f_exact(const Vector &p, Vector &f)
 
    double x = p(0);
    double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0;
+   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
 
    double temp = 1 + 2*kappa*kappa;
 

examples/ex4p.cpp

@@ -6,6 +6,7 @@
 //               mpirun -np 4 ex4p -m ../data/star.mesh
 //               mpirun -np 4 ex4p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex4p -m ../data/escher.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/fichera-q2.vtk
@@ -19,6 +20,12 @@
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
+// Device sample runs:
+//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d cuda
+//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-cuda
+//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-omp
+//               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D H(div) diffusion
 //               problem corresponding to the second order definite equation
 //               -grad(alpha div F) + beta F = f with boundary condition F dot n
@@ -60,6 +67,8 @@ int main(int argc, char *argv[])
    bool set_bc = true;
    bool static_cond = false;
    bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -75,6 +84,10 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
                   "--no-hybridization", "Enable hybridization.");
+   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.");
@@ -94,14 +107,19 @@ int main(int argc, char *argv[])
    }
    kappa = freq * M_PI;
 
-   // 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, as well as periodic meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
 
-   // 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 1,000 elements.
@@ -114,7 +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. Tetrahedral
    //    meshes need to be reoriented before we can define high-order Nedelec
@@ -130,7 +148,7 @@ int main(int argc, char *argv[])
    }
    pmesh->ReorientTetMesh();
 
-   // 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 *fec = new RT_FECollection(order-1, dim);
    ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
@@ -140,7 +158,7 @@ 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
    //    by marking all the boundary attributes from the mesh as essential
    //    (Dirichlet) and converting them to a list of true dofs.
@@ -152,7 +170,7 @@ 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, which in this case is
    //    (f,phi_i) where f is given by the function f_exact and phi_i are the
    //    basis functions in the finite element fespace.
@@ -161,7 +179,7 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
    b->Assemble();
 
-   // 9. Define the solution vector x as a parallel finite element grid function
+   // 10. Define the solution vector x as a parallel finite element grid function
    //    corresponding to fespace. Initialize x by projecting the exact
    //    solution. Note that only values from the boundary faces will be used
    //    when eliminating the non-homogeneous boundary condition to modify the
@@ -170,16 +188,17 @@ int main(int argc, char *argv[])
    VectorFunctionCoefficient F(sdim, F_exact);
    x.ProjectCoefficient(F);
 
-   // 10. Set up the parallel bilinear form corresponding to the H(div)
+   // 11. Set up the parallel bilinear form corresponding to the H(div)
    //     diffusion operator grad alpha div + beta I, by adding the div-div and
    //     the mass domain integrators.
    Coefficient *alpha = new ConstantCoefficient(1.0);
    Coefficient *beta  = new ConstantCoefficient(1.0);
    ParBilinearForm *a = new ParBilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
    a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));
 
-   // 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, static condensation,
@@ -199,41 +218,43 @@ int main(int argc, char *argv[])
    }
    a->Assemble();
 
-   HypreParMatrix A;
+   OperatorPtr A;
    Vector B, X;
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
 
-   HYPRE_Int glob_size = A.GetGlobalNumRows();
-   if (myid == 0)
+   if (myid == 0 && !pa)
    {
-      cout << "Size of linear system: " << glob_size << endl;
+      cout << "Size of linear system: "
+           << A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
    }
 
-   // 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
+   // 13. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
    //     the 3D ADS preconditioners from hypre. If using hybridization, the
-   //     system is preconditioned with hypre's BoomerAMG.
-   HypreSolver *prec = NULL;
-   CGSolver *pcg = new CGSolver(A.GetComm());
-   pcg->SetOperator(A);
+   //     system is preconditioned with hypre's BoomerAMG. In the partial
+   //     assembly case, use Jacobi preconditioning.
+   Solver *prec = NULL;
+   CGSolver *pcg = new CGSolver(MPI_COMM_WORLD);
+   pcg->SetOperator(*A);
    pcg->SetRelTol(1e-12);
-   pcg->SetMaxIter(500);
+   pcg->SetMaxIter(2000);
    pcg->SetPrintLevel(1);
-   if (hybridization) { prec = new HypreBoomerAMG(A); }
+   if (hybridization) { prec = new HypreBoomerAMG(*A.As<HypreParMatrix>()); }
+   else if (pa) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
    else
    {
       ParFiniteElementSpace *prec_fespace =
          (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
-      if (dim == 2)   { prec = new HypreAMS(A, prec_fespace); }
-      else            { prec = new HypreADS(A, prec_fespace); }
+      if (dim == 2)   { prec = new HypreAMS(*A.As<HypreParMatrix>(), prec_fespace); }
+      else            { prec = new HypreADS(*A.As<HypreParMatrix>(), prec_fespace); }
    }
    pcg->SetPreconditioner(*prec);
    pcg->Mult(B, X);
 
-   // 13. Recover the parallel grid function corresponding to X. This is the
+   // 14. Recover the parallel grid function corresponding to X. This is the
    //     local finite element solution on each processor.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 14. Compute and print the L^2 norm of the error.
+   // 15. Compute and print the L^2 norm of the error.
    {
       double err = x.ComputeL2Error(F);
       if (myid == 0)
@@ -242,7 +263,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 15. Save the refined mesh and the solution in parallel. This output can
+   // 16. 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_name;
@@ -258,7 +279,7 @@ int main(int argc, char *argv[])
       x.Save(sol_ofs);
    }
 
-   // 16. Send the solution by socket to a GLVis server.
+   // 17. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -269,7 +290,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *pmesh << x << flush;
    }
 
-   // 17. Free the used memory.
+   // 18. Free the used memory.
    delete pcg;
    delete prec;
    delete hfes;
@@ -295,7 +316,7 @@ void F_exact(const Vector &p, Vector &F)
 
    double x = p(0);
    double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0;
+   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
 
    F(0) = cos(kappa*x)*sin(kappa*y);
    F(1) = cos(kappa*y)*sin(kappa*x);
@@ -312,7 +333,7 @@ void f_exact(const Vector &p, Vector &f)
 
    double x = p(0);
    double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0;
+   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
 
    double temp = 1 + 2*kappa*kappa;
 

examples/ex5.cpp

@@ -4,8 +4,10 @@
 //
 // Sample runs:  ex5 -m ../data/square-disc.mesh
 //               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
 //               ex5 -m ../data/beam-tet.mesh
 //               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
 //               ex5 -m ../data/escher.mesh
 //               ex5 -m ../data/fichera.mesh
 //
@@ -47,6 +49,7 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
+   bool pa = false;
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -54,6 +57,8 @@ int main(int argc, char *argv[])
                   "Mesh file to use.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -146,22 +151,39 @@ int main(int argc, char *argv[])
    BilinearForm *mVarf(new BilinearForm(R_space));
    MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
 
+   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
    mVarf->Assemble();
-   mVarf->Finalize();
-   SparseMatrix &M(mVarf->SpMat());
+   if (!pa) { mVarf->Finalize(); }
 
+   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
    bVarf->Assemble();
-   bVarf->Finalize();
-   SparseMatrix & B(bVarf->SpMat());
-   B *= -1.;
-   SparseMatrix *BT = Transpose(B);
+   if (!pa) { bVarf->Finalize(); }
 
-   BlockMatrix darcyMatrix(block_offsets);
-   darcyMatrix.SetBlock(0,0, &M);
-   darcyMatrix.SetBlock(0,1, BT);
-   darcyMatrix.SetBlock(1,0, &B);
+   BlockOperator darcyOp(block_offsets);
+
+   TransposeOperator *Bt = NULL;
+
+   if (pa)
+   {
+      Bt = new TransposeOperator(bVarf);
+
+      darcyOp.SetBlock(0,0, mVarf);
+      darcyOp.SetBlock(0,1, Bt, -1.0);
+      darcyOp.SetBlock(1,0, bVarf, -1.0);
+   }
+   else
+   {
+      SparseMatrix &M(mVarf->SpMat());
+      SparseMatrix &B(bVarf->SpMat());
+      B *= -1.;
+      Bt = new TransposeOperator(&B);
+
+      darcyOp.SetBlock(0,0, &M);
+      darcyOp.SetBlock(0,1, Bt);
+      darcyOp.SetBlock(1,0, &B);
+   }
 
    // 9. Construct the operators for preconditioner
    //
@@ -170,27 +192,57 @@ int main(int argc, char *argv[])
    //
    //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
    //     pressure Schur Complement
-   SparseMatrix *MinvBt = Transpose(B);
-   Vector Md(M.Height());
-   M.GetDiag(Md);
-   for (int i = 0; i < Md.Size(); i++)
-   {
-      MinvBt->ScaleRow(i, 1./Md(i));
-   }
-   SparseMatrix *S = Mult(B, *MinvBt);
+   SparseMatrix *MinvBt = NULL;
+   Vector Md(mVarf->Height());
 
+   BlockDiagonalPreconditioner darcyPrec(block_offsets);
    Solver *invM, *invS;
-   invM = new DSmoother(M);
+   SparseMatrix *S = NULL;
+
+   if (pa)
+   {
+      mVarf->AssembleDiagonal(Md);
+      Vector invMd(mVarf->Height());
+      for (int i=0; i<mVarf->Height(); ++i)
+      {
+         invMd(i) = 1.0 / Md(i);
+      }
+
+      Vector BMBt_diag(bVarf->Height());
+      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+      Array<int> ess_tdof_list;  // empty
+
+      invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+   }
+   else
+   {
+      SparseMatrix &M(mVarf->SpMat());
+      M.GetDiag(Md);
+
+      SparseMatrix &B(bVarf->SpMat());
+      MinvBt = Transpose(B);
+
+      for (int i = 0; i < Md.Size(); i++)
+      {
+         MinvBt->ScaleRow(i, 1./Md(i));
+      }
+
+      S = Mult(B, *MinvBt);
+
+      invM = new DSmoother(M);
+
 #ifndef MFEM_USE_SUITESPARSE
-   invS = new GSSmoother(*S);
+      invS = new GSSmoother(*S);
 #else
-   invS = new UMFPackSolver(*S);
+      invS = new UMFPackSolver(*S);
 #endif
+   }
 
    invM->iterative_mode = false;
    invS->iterative_mode = false;
 
-   BlockDiagonalPreconditioner darcyPrec(block_offsets);
    darcyPrec.SetDiagonalBlock(0, invM);
    darcyPrec.SetDiagonalBlock(1, invS);
 
@@ -206,7 +258,7 @@ int main(int argc, char *argv[])
    solver.SetAbsTol(atol);
    solver.SetRelTol(rtol);
    solver.SetMaxIter(maxIter);
-   solver.SetOperator(darcyMatrix);
+   solver.SetOperator(darcyOp);
    solver.SetPreconditioner(darcyPrec);
    solver.SetPrintLevel(1);
    x = 0.0;
@@ -295,8 +347,8 @@ int main(int argc, char *argv[])
    delete invM;
    delete invS;
    delete S;
+   delete Bt;
    delete MinvBt;
-   delete BT;
    delete mVarf;
    delete bVarf;
    delete W_space;

examples/ex5p.cpp

@@ -4,8 +4,10 @@
 //
 // Sample runs:  mpirun -np 4 ex5p -m ../data/square-disc.mesh
 //               mpirun -np 4 ex5p -m ../data/star.mesh
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa
 //               mpirun -np 4 ex5p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex5p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa
 //               mpirun -np 4 ex5p -m ../data/escher.mesh
 //               mpirun -np 4 ex5p -m ../data/fichera.mesh
 //
@@ -54,19 +56,25 @@ int main(int argc, char *argv[])
 
    // 2. Parse command-line options.
    const char *mesh_file = "../data/star.mesh";
+   int ref_levels = -1;
    int order = 1;
    bool par_format = false;
+   bool pa = false;
    bool visualization = 1;
    bool adios2 = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of times to refine the mesh uniformly.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
                   "--serial-format",
                   "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(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -97,10 +105,13 @@ int main(int argc, char *argv[])
    // 4. 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.
+   //    more than 10,000 elements, unless the user specifies it as input.
    {
-      int ref_levels =
-         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      if (ref_levels == -1)
+      {
+         ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      }
+
       for (int l = 0; l < ref_levels; l++)
       {
          mesh->UniformRefinement();
@@ -196,25 +207,47 @@ int main(int argc, char *argv[])
    ParBilinearForm *mVarf(new ParBilinearForm(R_space));
    ParMixedBilinearForm *bVarf(new ParMixedBilinearForm(R_space, W_space));
 
-   HypreParMatrix *M, *B;
+   HypreParMatrix *M = NULL;
+   HypreParMatrix *B = NULL;
 
+   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
    mVarf->Assemble();
-   mVarf->Finalize();
-   M = mVarf->ParallelAssemble();
+   if (!pa) { mVarf->Finalize(); }
 
+   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
    bVarf->Assemble();
-   bVarf->Finalize();
-   B = bVarf->ParallelAssemble();
-   (*B) *= -1;
-
-   HypreParMatrix *BT = B->Transpose();
+   if (!pa) { bVarf->Finalize(); }
 
    BlockOperator *darcyOp = new BlockOperator(block_trueOffsets);
-   darcyOp->SetBlock(0,0, M);
-   darcyOp->SetBlock(0,1, BT);
-   darcyOp->SetBlock(1,0, B);
+
+   Array<int> empty_tdof_list;  // empty
+   OperatorPtr opM, opB;
+
+   TransposeOperator *Bt = NULL;
+
+   if (pa)
+   {
+      mVarf->FormSystemMatrix(empty_tdof_list, opM);
+      bVarf->FormRectangularSystemMatrix(empty_tdof_list, empty_tdof_list, opB);
+      Bt = new TransposeOperator(opB.Ptr());
+
+      darcyOp->SetBlock(0,0, opM.Ptr());
+      darcyOp->SetBlock(0,1, Bt, -1.0);
+      darcyOp->SetBlock(1,0, opB.Ptr(), -1.0);
+   }
+   else
+   {
+      M = mVarf->ParallelAssemble();
+      B = bVarf->ParallelAssemble();
+      (*B) *= -1;
+      Bt = new TransposeOperator(B);
+
+      darcyOp->SetBlock(0,0, M);
+      darcyOp->SetBlock(0,1, Bt);
+      darcyOp->SetBlock(1,0, B);
+   }
 
    // 11. Construct the operators for preconditioner
    //
@@ -223,17 +256,43 @@ int main(int argc, char *argv[])
    //
    //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
    //     pressure Schur Complement.
-   HypreParMatrix *MinvBt = B->Transpose();
-   HypreParVector *Md = new HypreParVector(MPI_COMM_WORLD, M->GetGlobalNumRows(),
-                                           M->GetRowStarts());
-   M->GetDiag(*Md);
+   HypreParMatrix *MinvBt = NULL;
+   HypreParVector *Md = NULL;
+   HypreParMatrix *S = NULL;
+   Vector Md_PA;
+   Solver *invM, *invS;
 
-   MinvBt->InvScaleRows(*Md);
-   HypreParMatrix *S = ParMult(B, MinvBt);
+   if (pa)
+   {
+      Md_PA.SetSize(R_space->GetTrueVSize());
+      mVarf->AssembleDiagonal(Md_PA);
+      Vector invMd(Md_PA.Size());
+      for (int i=0; i<Md_PA.Size(); ++i)
+      {
+         invMd(i) = 1.0 / Md_PA(i);
+      }
 
-   HypreSolver *invM, *invS;
-   invM = new HypreDiagScale(*M);
-   invS = new HypreBoomerAMG(*S);
+      Vector BMBt_diag(W_space->GetTrueVSize());
+      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+      Array<int> ess_tdof_list;  // empty
+
+      invM = new OperatorJacobiSmoother(Md_PA, ess_tdof_list);
+      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+   }
+   else
+   {
+      Md = new HypreParVector(MPI_COMM_WORLD, M->GetGlobalNumRows(),
+                              M->GetRowStarts());
+      M->GetDiag(*Md);
+
+      MinvBt = B->Transpose();
+      MinvBt->InvScaleRows(*Md);
+      S = ParMult(B, MinvBt);
+
+      invM = new HypreDiagScale(*M);
+      invS = new HypreBoomerAMG(*S);
+   }
 
    invM->iterative_mode = false;
    invS->iterative_mode = false;
@@ -245,7 +304,7 @@ int main(int argc, char *argv[])
 
    // 12. Solve the linear system with MINRES.
    //     Check the norm of the unpreconditioned residual.
-   int maxIter(500);
+   int maxIter(pa ? 1000 : 500);
    double rtol(1.e-6);
    double atol(1.e-10);
 
@@ -395,7 +454,7 @@ int main(int argc, char *argv[])
    delete S;
    delete Md;
    delete MinvBt;
-   delete BT;
+   delete Bt;
    delete B;
    delete M;
    delete mVarf;

examples/ex9.cpp

@@ -19,6 +19,7 @@
 //
 // Device sample runs:
 //    ex9 -pa
+//    ex9 -ea
 //    ex9 -pa -m ../data/periodic-cube.mesh
 //    ex9 -pa -m ../data/periodic-cube.mesh -d cuda
 //
@@ -142,6 +143,7 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 3;
    bool pa = false;
+   bool ea = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
    double t_final = 10.0;
@@ -166,6 +168,8 @@ int main(int argc, char *argv[])
                   "Order (degree) of the finite elements.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
+                  "--no-element-assembly", "Enable Element Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -269,6 +273,11 @@ int main(int argc, char *argv[])
       m.SetAssemblyLevel(AssemblyLevel::PARTIAL);
       k.SetAssemblyLevel(AssemblyLevel::PARTIAL);
    }
+   else if (ea)
+   {
+      m.SetAssemblyLevel(AssemblyLevel::ELEMENT);
+      k.SetAssemblyLevel(AssemblyLevel::ELEMENT);
+   }
    m.AddDomainIntegrator(new MassIntegrator);
    k.AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
    k.AddInteriorFaceIntegrator(
@@ -429,8 +438,9 @@ 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)
+   if (pa || ea)
    {
       M_prec = new OperatorJacobiSmoother(M, ess_tdof_list);
       M_solver.SetOperator(M);

examples/ex9p.cpp

@@ -19,6 +19,7 @@
 //
 // Device sample runs:
 //    mpirun -np 4 ex9p -pa
+//    mpirun -np 4 ex9p -ea
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh -d cuda
 //
@@ -161,6 +162,7 @@ int main(int argc, char *argv[])
    int par_ref_levels = 0;
    int order = 3;
    bool pa = false;
+   bool ea = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
    double t_final = 10.0;
@@ -188,6 +190,8 @@ int main(int argc, char *argv[])
                   "Order (degree) of the finite elements.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
+                  "--no-element-assembly", "Enable Element Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -319,6 +323,11 @@ int main(int argc, char *argv[])
       m->SetAssemblyLevel(AssemblyLevel::PARTIAL);
       k->SetAssemblyLevel(AssemblyLevel::PARTIAL);
    }
+   else if (ea)
+   {
+      m->SetAssemblyLevel(AssemblyLevel::ELEMENT);
+      k->SetAssemblyLevel(AssemblyLevel::ELEMENT);
+   }
    m->AddDomainIntegrator(new MassIntegrator);
    k->AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
    k->AddInteriorFaceIntegrator(
@@ -556,8 +565,9 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
      z(_M.Height())
 {
    bool pa = _M.GetAssemblyLevel()==AssemblyLevel::PARTIAL;
+   bool ea = _M.GetAssemblyLevel()==AssemblyLevel::ELEMENT;
 
-   if (pa)
+   if (pa || ea)
    {
       M.Reset(&_M, false);
       K.Reset(&_K, false);
@@ -571,7 +581,7 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
    M_solver.SetOperator(*M);
 
    Array<int> ess_tdof_list;
-   if (pa)
+   if (pa || ea)
    {
       M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
       dg_solver = NULL;

examples/pumi/ex1.cpp

@@ -32,6 +32,13 @@
 //               is used for the Finite Element order and "-go" is used for the
 //               geometry order. Note that they can be used independently, i.e.
 //               "-o 8 -go 3" solves for 8th order FE on a third order geometry.
+//
+// NOTE:         Model/Mesh files for this example are in the (large) data file
+//               repository of MFEM here https://github.com/mfem/data under the
+//               folder named "pumi", which consists of the following sub-folders:
+//               a) geom -->  model files
+//               b) parallel --> parallel pumi mesh files
+//               c) serial --> serial pumi mesh files
 
 #include "mfem.hpp"
 #include <fstream>

examples/pumi/ex1p.cpp

@@ -36,6 +36,14 @@
 //               option "-o" is used for the Finite Element order and "-go" for
 //               the geometry order. Note that they can be used independently:
 //               "-o 8 -go 3" solves for 8th order FE on third order geometry.
+//
+// NOTE:         Model/Mesh files for this example are in the (large) data file
+//               repository of MFEM here https://github.com/mfem/data under the
+//               folder named "pumi", which consists of the following sub-folders:
+//               a) geom -->  model files
+//               b) parallel --> parallel pumi mesh files
+//               c) serial --> serial pumi mesh files
+
 
 #include "mfem.hpp"
 #include <fstream>

examples/pumi/ex2.cpp

@@ -43,6 +43,14 @@
 //               also illustrated.
 //
 //               We recommend viewing Example 1 before viewing this example.
+//
+// NOTE:         Model/Mesh files for this example are in the (large) data file
+//               repository of MFEM here https://github.com/mfem/data under the
+//               folder named "pumi", which consists of the following sub-folders:
+//               a) geom -->  model files
+//               b) parallel --> parallel pumi mesh files
+//               c) serial --> serial pumi mesh files
+
 
 #include "mfem.hpp"
 #include <fstream>

examples/pumi/ex6p.cpp

@@ -1,7 +1,7 @@
 //                       MFEM Example 6 - Parallel Version
 //                              PUMI Modification
 //
-// Compile with: make ex1p
+// Compile with: make ex6p
 //
 // Sample runs:  mpirun -np 8 ex6p
 //
@@ -18,6 +18,13 @@
 //               is added to modify the "adapt_ratio" which is the fraction of
 //               allowable error that scales the output size field of the error
 //               estimator.
+//
+// NOTE:         Model/Mesh files for this example are in the (large) data file
+//               repository of MFEM here https://github.com/mfem/data under the
+//               folder named "pumi", which consists of the following sub-folders:
+//               a) geom -->  model files
+//               b) parallel --> parallel pumi mesh files
+//               c) serial --> serial pumi mesh files
 
 #include "mfem.hpp"
 #include <fstream>
@@ -332,7 +339,6 @@ int main(int argc, char *argv[])
 
       apf::destroyField(Tmag_field);
       apf::destroyField(ipfield);
-      apf::destroyNumbering(pumi_mesh->findNumbering("LocalVertexNumbering"));
 
       // 18. Perform MesAdapt.
       ma::Input* erinput = ma::configure(pumi_mesh, sizefield);

fem/CMakeLists.txt

@@ -13,13 +13,20 @@ set(SRCS
   bilinearform.cpp
   bilinearform_ext.cpp
   bilininteg.cpp
-  bilininteg_convection.cpp
-  bilininteg_dgtrace.cpp
-  bilininteg_diffusion.cpp
+  bilininteg_convection_pa.cpp
+  bilininteg_convection_ea.cpp
+  bilininteg_dgtrace_pa.cpp
+  bilininteg_dgtrace_ea.cpp
+  bilininteg_diffusion_pa.cpp
+  bilininteg_diffusion_ea.cpp
   bilininteg_divergence.cpp
   bilininteg_hcurl.cpp
+  bilininteg_hdiv.cpp
+  bilininteg_vectorfe.cpp
   bilininteg_gradient.cpp
-  bilininteg_mass.cpp
+  bilininteg_mass_pa.cpp
+  bilininteg_mass_ea.cpp
+  bilininteg_transpose_ea.cpp
   bilininteg_vecdiffusion.cpp
   bilininteg_vecmass.cpp
   coefficient.cpp

fem/adios2datacollection.cpp

@@ -15,6 +15,8 @@
 
 #include "adios2datacollection.hpp"
 
+#ifdef MFEM_USE_ADIOS2
+
 namespace mfem
 {
 
@@ -87,4 +89,4 @@ noexcept
 
 } //end namespace mfem
 
-
+#endif // MFEM_USE_ADIOS2

fem/adios2datacollection.hpp

@@ -17,6 +17,9 @@
 #define MFEM_ADIOS2DATACOLLECTION
 
 #include "../config/config.hpp"
+
+#ifdef MFEM_USE_ADIOS2
+
 #include "../general/adios2stream.hpp"
 #include "datacollection.hpp"
 
@@ -85,4 +88,6 @@ private:
 
 }  // namespace mfem
 
+#endif // MFEM_USE_ADIOS2
+
 #endif /* MFEM_ADIOS2DATACOLLECTION */

fem/bilinearform.cpp

@@ -126,8 +126,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
          // Use the original BilinearForm implementation for now
          break;
       case AssemblyLevel::ELEMENT:
-         mfem_error("Element assembly not supported yet... stay tuned!");
-         // ext = new EABilinearFormExtension(this);
+         ext = new EABilinearFormExtension(this);
          break;
       case AssemblyLevel::PARTIAL:
          ext = new PABilinearFormExtension(this);
@@ -1432,6 +1431,54 @@ void MixedBilinearForm::Assemble (int skip_zeros)
    }
 }
 
+void MixedBilinearForm::AssembleDiagonal_ADAt(const Vector &D,
+                                              Vector &diag) const
+{
+   if (ext)
+   {
+      MFEM_ASSERT(diag.Size() == test_fes->GetTrueVSize(),
+                  "Vector for holding diagonal has wrong size!");
+      MFEM_ASSERT(D.Size() == trial_fes->GetTrueVSize(),
+                  "Vector for holding diagonal has wrong size!");
+      const Operator *P_trial = trial_fes->GetProlongationMatrix();
+      const Operator *P_test = test_fes->GetProlongationMatrix();
+      if (!IsIdentityProlongation(P_trial))
+      {
+         Vector local_D(P_trial->Height());
+         P_trial->Mult(D, local_D);
+
+         if (!IsIdentityProlongation(P_test))
+         {
+            Vector local_diag(P_test->Height());
+            ext->AssembleDiagonal_ADAt(local_D, local_diag);
+            P_test->MultTranspose(local_diag, diag);
+         }
+         else
+         {
+            ext->AssembleDiagonal_ADAt(local_D, diag);
+         }
+      }
+      else
+      {
+         if (!IsIdentityProlongation(P_test))
+         {
+            Vector local_diag(P_test->Height());
+            ext->AssembleDiagonal_ADAt(D, local_diag);
+            P_test->MultTranspose(local_diag, diag);
+         }
+         else
+         {
+            ext->AssembleDiagonal_ADAt(D, diag);
+         }
+      }
+   }
+   else
+   {
+      MFEM_ABORT("Not implemented. Maybe assemble your bilinear form into a "
+                 "matrix and use SparseMatrix functions?");
+   }
+}
+
 void MixedBilinearForm::ConformingAssemble()
 {
    if (assembly != AssemblyLevel::FULL)

fem/bilinearform.hpp

@@ -25,8 +25,8 @@
 namespace mfem
 {
 
-/// Enumeration defining the assembly level for bilinear and nonlinear form
-/// classes derived from Operator.
+/** @brief Enumeration defining the assembly level for bilinear and nonlinear
+    form classes derived from Operator. */
 enum class AssemblyLevel
 {
    /// Fully assembled form, i.e. a global sparse matrix in MFEM, Hypre or PETSC
@@ -44,15 +44,19 @@ enum class AssemblyLevel
 };
 
 
-/** Class for bilinear form - "Matrix" with associated FE space and
-    BLFIntegrators. */
+/** @brief A "square matrix" operator for the associated FE space and
+    BLFIntegrators The sum of all the BLFIntegrators can be used form the matrix
+    M. This class also supports other assembly levels specified via the
+    SetAssemblyLevel() function. */
 class BilinearForm : public Matrix
 {
 protected:
-   /// Sparse matrix to be associated with the form. Owned.
+   /// Sparse matrix \f$ M \f$ to be associated with the form. Owned.
    SparseMatrix *mat;
 
-   /// Matrix used to eliminate b.c. Owned.
+   /** @brief Sparse Matrix \f$ M_e \f$ used to store the eliminations
+        from the b.c.  Owned.
+       \f$ M + M_e = M_{original} \f$ */
    SparseMatrix *mat_e;
 
    /// FE space on which the form lives. Not owned.
@@ -62,12 +66,12 @@ protected:
    AssemblyLevel assembly;
    /// Element batch size used in the form action (1, 8, num_elems, etc.)
    int batch;
-   /** Extension for supporting Full Assembly (FA), Element Assembly (EA),
+   /** @brief Extension for supporting Full Assembly (FA), Element Assembly (EA),
        Partial Assembly (PA), or Matrix Free assembly (MF). */
    BilinearFormExtension *ext;
 
-   /// Indicates the Mesh::sequence corresponding to the current state of the
-   /// BilinearForm.
+   /** @brief Indicates the Mesh::sequence corresponding to the current state of
+       the BilinearForm. */
    long sequence;
 
    /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
@@ -147,35 +151,43 @@ public:
    /// Get the size of the BilinearForm as a square matrix.
    int Size() const { return height; }
 
-   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
-   /** This method must be called before assembly. */
+   /// 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);
 
    /// Returns the assembly level
    AssemblyLevel GetAssemblyLevel() const { return assembly; }
 
-   /** Enable the use of static condensation. For details see the description
-       for class StaticCondensation in fem/staticcond.hpp This method should be
-       called before assembly. If the number of unknowns after static
+   /** @brief Enable the use of static condensation. For details see the
+       description for class StaticCondensation in fem/staticcond.hpp This method
+       should be called before assembly. If the number of unknowns after static
        condensation is not reduced, it is not enabled. */
    void EnableStaticCondensation();
 
-   /** Check if static condensation was actually enabled by a previous call to
-       EnableStaticCondensation(). */
+   /** @brief Check if static condensation was actually enabled by a previous
+       call to EnableStaticCondensation(). */
    bool StaticCondensationIsEnabled() const { return static_cond; }
 
    /// Return the trace FE space associated with static condensation.
    FiniteElementSpace *SCFESpace() const
    { return static_cond ? static_cond->GetTraceFESpace() : NULL; }
 
-   /** Enable hybridization; for details see the description for class
+   /// Enable hybridization.
+   /** For details see the description for class
        Hybridization in fem/hybridization.hpp. This method should be called
        before assembly. */
    void EnableHybridization(FiniteElementSpace *constr_space,
                             BilinearFormIntegrator *constr_integ,
                             const Array<int> &ess_tdof_list);
 
-   /** For scalar FE spaces, precompute the sparsity pattern of the matrix
+   /** @brief For scalar FE spaces, precompute the sparsity pattern of the matrix
        (assuming dense element matrices) based on the types of integrators
        present in the bilinear form. */
    void UsePrecomputedSparsity(int ps = 1) { precompute_sparsity = ps; }
@@ -194,15 +206,16 @@ public:
    /// Use the sparsity of @a A to allocate the internal SparseMatrix.
    void UseSparsity(SparseMatrix &A);
 
-   /** Pre-allocate the internal SparseMatrix before assembly. If the flag
-       'precompute sparsity' is set, the matrix is allocated in CSR format (i.e.
+   /// Pre-allocate the internal SparseMatrix before assembly.
+   /**  If the flag 'precompute sparsity'
+       is set, the matrix is allocated in CSR format (i.e.
        finalized) and the entries are initialized with zeros. */
    void AllocateMatrix() { if (mat == NULL) { AllocMat(); } }
 
-   /// Access all integrators added with AddDomainIntegrator().
+   /// Access all the integrators added with AddDomainIntegrator().
    Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }
 
-   /// Access all integrators added with AddBoundaryIntegrator().
+   /// Access all the integrators added with AddBoundaryIntegrator().
    Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
    /** @brief Access all boundary markers added with AddBoundaryIntegrator().
        If no marker was specified when the integrator was added, the
@@ -219,64 +232,85 @@ public:
        corresponding pointer (to Array<int>) will be NULL. */
    Array<Array<int>*> *GetBFBFI_Marker() { return &bfbfi_marker; }
 
+   /// Returns a reference to: \f$ M_{ij} \f$
    const double &operator()(int i, int j) { return (*mat)(i,j); }
 
-   /// Returns reference to a_{ij}.
+   /// Returns a reference to: \f$ M_{ij} \f$
    virtual double &Elem(int i, int j);
 
-   /// Returns constant reference to a_{ij}.
+   /// Returns constant reference to: \f$ M_{ij} \f$
    virtual const double &Elem(int i, int j) const;
 
-   /// Matrix vector multiplication.
+   /// Matrix vector multiplication:  \f$ y = M x \f$
    virtual void Mult(const Vector &x, Vector &y) const;
 
+   /** @brief Matrix vector multiplication with the original uneliminated
+       matrix.  The original matrix is \f$ M + M_e \f$ so we have:
+       \f$ y = M x + M_e x \f$ */
    void FullMult(const Vector &x, Vector &y) const
    { mat->Mult(x, y); mat_e->AddMult(x, y); }
 
+   /// Add the matrix vector multiple to a vector:  \f$ y += a M x \f$
    virtual void AddMult(const Vector &x, Vector &y, const double a = 1.0) const
    { mat -> AddMult (x, y, a); }
 
+   /** @brief Add the original uneliminated matrix vector multiple to a vector.
+       The original matrix is \f$ M + Me \f$ so we have:
+       \f$ y += M x + M_e x \f$ */
    void FullAddMult(const Vector &x, Vector &y) const
    { mat->AddMult(x, y); mat_e->AddMult(x, y); }
 
+   /// Add the matrix transpose vector multiplication:  \f$ y += a M^T x \f$
    virtual void AddMultTranspose(const Vector & x, Vector & y,
                                  const double a = 1.0) const
    { mat->AddMultTranspose(x, y, a); }
 
+   /** @brief Add the original uneliminated matrix transpose vector
+       multiple to a vector. The original matrix is \f$ M + M_e \f$
+       so we have: \f$ y += M^T x + {M_e}^T x \f$ */
    void FullAddMultTranspose(const Vector & x, Vector & y) const
    { mat->AddMultTranspose(x, y); mat_e->AddMultTranspose(x, y); }
 
+   /// Matrix transpose vector multiplication:  \f$ y = M^T x \f$
    virtual void MultTranspose(const Vector & x, Vector & y) const
    { y = 0.0; AddMultTranspose (x, y); }
 
+   /// Compute \f$ y^T M x \f$
    double InnerProduct(const Vector &x, const Vector &y) const
    { return mat->InnerProduct (x, y); }
 
-   /// Returns a pointer to (approximation) of the matrix inverse.
+   /// Returns a pointer to (approximation) of the matrix inverse:  \f$ M^{-1} \f$
    virtual MatrixInverse *Inverse() const;
 
    /// Finalizes the matrix initialization.
    virtual void Finalize(int skip_zeros = 1);
 
-   /// Returns a reference to the sparse matrix
+   /// Returns a const reference to the sparse matrix.
    const SparseMatrix &SpMat() const
    {
       MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
       return *mat;
    }
+
+   /// Returns a reference to the sparse matrix:  \f$ M \f$
    SparseMatrix &SpMat()
    {
       MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
       return *mat;
    }
+
+   /**  @brief Nullifies the internal matrix \f$ M \f$ and returns a pointer
+        to it.  Used for transfering ownership. */
    SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }
 
-   /// Returns a reference to the sparse matrix of eliminated b.c.
+   /// Returns a const reference to the sparse matrix of eliminated b.c.: \f$ M_e \f$
    const SparseMatrix &SpMatElim() const
    {
       MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
       return *mat_e;
    }
+
+   /// Returns a reference to the sparse matrix of eliminated b.c.: \f$ M_e \f$
    SparseMatrix &SpMatElim()
    {
       MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
@@ -311,6 +345,7 @@ public:
    void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
                              Array<int> &bdr_marker);
 
+   /// Sets all sparse values of \f$ M \f$ and \f$ M_e \f$ to 'a'.
    void operator=(const double a)
    {
       if (mat != NULL) { *mat = a; }
@@ -328,10 +363,10 @@ public:
        for an AMR mesh. */
    void AssembleDiagonal(Vector &diag) const;
 
-   /// Get the finite element space prolongation matrix
+   /// Get the finite element space prolongation operator.
    virtual const Operator *GetProlongation() const
    { return fes->GetConformingProlongation(); }
-   /// Get the finite element space restriction matrix
+   /// Get the finite element space restriction operator
    virtual const Operator *GetRestriction() const
    { return fes->GetConformingRestriction(); }
    /// Get the output finite element space prolongation matrix
@@ -491,10 +526,12 @@ public:
                                  double value);
 
    /// Eliminate the given @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
+   /** In this case the eliminations are applied to the internal \f$ M \f$
+       and @a rhs without storing the elimination matrix \f$ M_e \f$. */
    void EliminateVDofs(const Array<int> &vdofs, const Vector &sol, Vector &rhs,
                        DiagonalPolicy dpolicy = DIAG_ONE);
 
-   /// Eliminate the given @a vdofs, storing the eliminated part internally.
+   /// Eliminate the given @a vdofs, storing the eliminated part internally in \f$ M_e \f$.
    /** This method works in conjunction with EliminateVDofsInRHS() and allows
        elimination of boundary conditions in multiple right-hand sides. In this
        method, @a vdofs is a list of DOFs. */
@@ -523,9 +560,11 @@ public:
    void EliminateVDofsInRHS(const Array<int> &vdofs, const Vector &x,
                             Vector &b);
 
+   /// Compute inner product for full uneliminated matrix \f$ y^T M x + y^T M_e x \f$
    double FullInnerProduct(const Vector &x, const Vector &y) const
    { return mat->InnerProduct(x, y) + mat_e->InnerProduct(x, y); }
 
+   /// Update the @a FiniteElementSpace and delete all data associated with the old one.
    virtual void Update(FiniteElementSpace *nfes = NULL);
 
    /// (DEPRECATED) Return the FE space associated with the BilinearForm.
@@ -537,7 +576,13 @@ public:
    /// Read-only access to the associated FiniteElementSpace.
    const FiniteElementSpace *FESpace() const { return fes; }
 
-   /// Sets diagonal policy used upon construction of the linear system
+   /// Sets diagonal policy used upon construction of the linear system.
+   /** Policies include:
+
+       - DIAG_ZERO (Set the diagonal values to zero)
+       - DIAG_ONE  (Set the diagonal values to one)
+       - DIAG_KEEP (Keep the diagonal values)
+   */
    void SetDiagonalPolicy(DiagonalPolicy policy);
 
    /// Indicate that integrators are not owned by the BilinearForm
@@ -550,16 +595,16 @@ public:
 
 /**
    Class for assembling of bilinear forms `a(u,v)` defined on different
-   trial and test spaces. The assembled matrix `A` is such that
+   trial and test spaces. The assembled matrix `M` is such that
 
-       a(u,v) = V^t A U
+       a(u,v) = V^t M U
 
    where `U` and `V` are the vectors representing the functions `u` and `v`,
    respectively.  The first argument, `u`, of `a(,)` is in the trial space
    and the second argument, `v`, is in the test space. Thus,
 
-       # of rows of A = dimension of the test space and
-       # of cols of A = dimension of the trial space.
+       # of rows of M = dimension of the test space and
+       # of cols of M = dimension of the trial space.
 
    Both trial and test spaces should be defined on the same mesh.
 */
@@ -628,11 +673,15 @@ public:
                      FiniteElementSpace *te_fes,
                      MixedBilinearForm *mbf);
 
+   /// Returns a reference to: \f$ M_{ij} \f$
    virtual double &Elem(int i, int j);
 
+   /// Returns a reference to: \f$ M_{ij} \f$
    virtual const double &Elem(int i, int j) const;
 
+   /// Matrix multiplication: \f$ y = M x \f$
    virtual void Mult(const Vector & x, Vector & y) const;
+
    virtual void AddMult(const Vector & x, Vector & y,
                         const double a = 1.0) const;
 
@@ -642,6 +691,7 @@ public:
 
    virtual MatrixInverse *Inverse() const;
 
+   /// Finalizes the matrix initialization.
    virtual void Finalize(int skip_zeros = 1);
 
    /** Extract the associated matrix as SparseMatrix blocks. The number of
@@ -649,8 +699,14 @@ public:
        test and trial spaces, respectively. */
    void GetBlocks(Array2D<SparseMatrix *> &blocks) const;
 
+   /// Returns a const reference to the sparse matrix:  \f$ M \f$
    const SparseMatrix &SpMat() const { return *mat; }
+
+   /// Returns a reference to the sparse matrix:  \f$ M \f$
    SparseMatrix &SpMat() { return *mat; }
+
+   /**  @brief Nullifies the internal matrix \f$ M \f$ and returns a pointer
+        to it.  Used for transfering ownership. */
    SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }
 
    /// Adds a domain integrator. Assumes ownership of @a bfi.
@@ -697,6 +753,7 @@ public:
        corresponding pointer (to Array<int>) will be NULL. */
    Array<Array<int>*> *GetBTFBFI_Marker() { return &btfbfi_marker; }
 
+   /// Sets all sparse values of \f$ M \f$ to @a a.
    void operator=(const double a) { *mat = a; }
 
    /// Set the desired assembly level. The default is AssemblyLevel::FULL.
@@ -705,6 +762,10 @@ public:
 
    void Assemble(int skip_zeros = 1);
 
+   /** @brief Assemble the diagonal of ADA^T into diag, where A is this mixed
+       bilinear form and D is a diagonal. */
+   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
+
    /// Get the input finite element space prolongation matrix
    virtual const Operator *GetProlongation() const
    { return trial_fes->GetProlongationMatrix(); }

fem/bilinearform_ext.cpp

@@ -47,7 +47,7 @@ PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
    bdr_face_restrict_lex = NULL;
 }
 
-void PABilinearFormExtension::SetupRestrictionOperators()
+void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
 {
    ElementDofOrdering ordering = UsesTensorBasis(*a->FESpace())?
                                  ElementDofOrdering::LEXICOGRAPHIC:
@@ -65,7 +65,8 @@ void PABilinearFormExtension::SetupRestrictionOperators()
    if (int_face_restrict_lex == NULL && a->GetFBFI()->Size() > 0)
    {
       int_face_restrict_lex = trialFes->GetFaceRestriction(
-                                 ElementDofOrdering::LEXICOGRAPHIC, FaceType::Interior);
+                                 ElementDofOrdering::LEXICOGRAPHIC,
+                                 FaceType::Interior);
       faceIntX.SetSize(int_face_restrict_lex->Height(), Device::GetMemoryType());
       faceIntY.SetSize(int_face_restrict_lex->Height(), Device::GetMemoryType());
       faceIntY.UseDevice(true); // ensure 'faceIntY = 0.0' is done on device
@@ -74,7 +75,9 @@ void PABilinearFormExtension::SetupRestrictionOperators()
    if (bdr_face_restrict_lex == NULL && a->GetBFBFI()->Size() > 0)
    {
       bdr_face_restrict_lex = trialFes->GetFaceRestriction(
-                                 ElementDofOrdering::LEXICOGRAPHIC, FaceType::Boundary);
+                                 ElementDofOrdering::LEXICOGRAPHIC,
+                                 FaceType::Boundary,
+                                 m);
       faceBdrX.SetSize(bdr_face_restrict_lex->Height(), Device::GetMemoryType());
       faceBdrY.SetSize(bdr_face_restrict_lex->Height(), Device::GetMemoryType());
       faceBdrY.UseDevice(true); // ensure 'faceBoundY = 0.0' is done on device
@@ -83,7 +86,7 @@ void PABilinearFormExtension::SetupRestrictionOperators()
 
 void PABilinearFormExtension::Assemble()
 {
-   SetupRestrictionOperators();
+   SetupRestrictionOperators(L2FaceValues::DoubleValued);
 
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
    const int integratorCount = integrators.Size();
@@ -287,6 +290,311 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
    }
 }
 
+// Data and methods for element-assembled bilinear forms
+EABilinearFormExtension::EABilinearFormExtension(BilinearForm *form)
+   : PABilinearFormExtension(form)
+{
+}
+
+void EABilinearFormExtension::Assemble()
+{
+   SetupRestrictionOperators(L2FaceValues::SingleValued);
+
+   ne = trialFes->GetMesh()->GetNE();
+   elemDofs = trialFes->GetFE(0)->GetDof();
+
+   ea_data.SetSize(ne*elemDofs*elemDofs, Device::GetMemoryType());
+   ea_data.UseDevice(true);
+   ea_data = 0.0;
+
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int integratorCount = integrators.Size();
+   for (int i = 0; i < integratorCount; ++i)
+   {
+      integrators[i]->AssembleEA(*a->FESpace(), ea_data);
+   }
+
+   faceDofs = trialFes ->
+              GetTraceElement(0, trialFes->GetMesh()->GetFaceBaseGeometry(0)) ->
+              GetDof();
+
+   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
+   const int intFaceIntegratorCount = intFaceIntegrators.Size();
+   if (intFaceIntegratorCount>0)
+   {
+      nf_int = trialFes->GetNFbyType(FaceType::Interior);
+      ea_data_int.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
+      ea_data_ext.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
+      ea_data_int = 0.0;
+      ea_data_ext = 0.0;
+   }
+   for (int i = 0; i < intFaceIntegratorCount; ++i)
+   {
+      intFaceIntegrators[i]->AssembleEAInteriorFaces(*a->FESpace(),
+                                                     ea_data_int,
+                                                     ea_data_ext);
+   }
+
+   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
+   const int boundFaceIntegratorCount = bdrFaceIntegrators.Size();
+   if (boundFaceIntegratorCount>0)
+   {
+      nf_bdr = trialFes->GetNFbyType(FaceType::Boundary);
+      ea_data_bdr.SetSize(nf_bdr*faceDofs*faceDofs, Device::GetMemoryType());
+      ea_data_bdr = 0.0;
+   }
+   for (int i = 0; i < boundFaceIntegratorCount; ++i)
+   {
+      bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr);
+   }
+}
+
+void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
+{
+   // Apply the Element Restriction
+   const bool useRestrict = !DeviceCanUseCeed() && elem_restrict;
+   if (!useRestrict)
+   {
+      y.UseDevice(true); // typically this is a large vector, so store on device
+      y = 0.0;
+   }
+   else
+   {
+      elem_restrict->Mult(x, localX);
+      localY = 0.0;
+   }
+   // Apply the Element Matrices
+   const int NDOFS = elemDofs;
+   auto X = Reshape(useRestrict?localX.Read():x.Read(), NDOFS, ne);
+   auto Y = Reshape(useRestrict?localY.ReadWrite():y.ReadWrite(), NDOFS, ne);
+   auto A = Reshape(ea_data.Read(), NDOFS, NDOFS, ne);
+   MFEM_FORALL(glob_j, ne*NDOFS,
+   {
+      const int e = glob_j/NDOFS;
+      const int j = glob_j%NDOFS;
+      double res = 0.0;
+      for (int i = 0; i < NDOFS; i++)
+      {
+         res += A(i, j, e)*X(i, e);
+      }
+      Y(j, e) += res;
+   });
+   // Apply the Element Restriction transposed
+   if (useRestrict)
+   {
+      elem_restrict->MultTranspose(localY, y);
+   }
+
+   // Treatment of interior faces
+   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
+   const int iFISz = intFaceIntegrators.Size();
+   if (int_face_restrict_lex && iFISz>0)
+   {
+      // Apply the Interior Face Restriction
+      int_face_restrict_lex->Mult(x, faceIntX);
+      if (faceIntX.Size()>0)
+      {
+         faceIntY = 0.0;
+         // Apply the interior face matrices
+         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,
+         {
+            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,
+         {
+            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_ext(i, j, 0, f)*X(i, 0, f);
+            }
+            Y(j, 1, f) += res;
+            res = 0.0;
+            for (int i = 0; i < NDOFS; i++)
+            {
+               res += A_ext(i, j, 1, f)*X(i, 1, f);
+            }
+            Y(j, 0, f) += res;
+         });
+         // Apply the Interior Face Restriction transposed
+         int_face_restrict_lex->MultTranspose(faceIntY, y);
+      }
+   }
+
+   // Treatment of boundary faces
+   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
+   const int bFISz = bdrFaceIntegrators.Size();
+   if (bdr_face_restrict_lex && bFISz>0)
+   {
+      // Apply the Boundary Face Restriction
+      bdr_face_restrict_lex->Mult(x, faceBdrX);
+      if (faceBdrX.Size()>0)
+      {
+         faceBdrY = 0.0;
+         // Apply the boundary face matrices
+         const int NDOFS = faceDofs;
+         auto X = Reshape(faceBdrX.Read(), NDOFS, nf_bdr);
+         auto Y = Reshape(faceBdrY.ReadWrite(), NDOFS, nf_bdr);
+         auto A = Reshape(ea_data_bdr.Read(), NDOFS, NDOFS, nf_bdr);
+         MFEM_FORALL(glob_j, nf_bdr*NDOFS,
+         {
+            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(i, j, f)*X(i, f);
+            }
+            Y(j, f) += res;
+         });
+         // Apply the Boundary Face Restriction transposed
+         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+      }
+   }
+}
+
+void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
+{
+   // Apply the Element Restriction
+   const bool useRestrict = DeviceCanUseCeed() || !elem_restrict;
+   if (!useRestrict)
+   {
+      y.UseDevice(true); // typically this is a large vector, so store on device
+      y = 0.0;
+   }
+   else
+   {
+      elem_restrict->Mult(x, localX);
+      localY = 0.0;
+   }
+   // Apply the Element Matrices transposed
+   const int NDOFS = elemDofs;
+   auto X = Reshape(useRestrict?localX.Read():x.Read(), NDOFS, ne);
+   auto Y = Reshape(useRestrict?localY.ReadWrite():y.ReadWrite(), NDOFS, ne);
+   auto A = Reshape(ea_data.Read(), NDOFS, NDOFS, ne);
+   MFEM_FORALL(glob_j, ne*NDOFS,
+   {
+      const int e = glob_j/NDOFS;
+      const int j = glob_j%NDOFS;
+      double res = 0.0;
+      for (int i = 0; i < NDOFS; i++)
+      {
+         res += A(j, i, e)*X(i, e);
+      }
+      Y(j, e) += res;
+   });
+   // Apply the Element Restriction transposed
+   if (useRestrict)
+   {
+      elem_restrict->MultTranspose(localY, y);
+   }
+
+   // Treatment of interior faces
+   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
+   const int iFISz = intFaceIntegrators.Size();
+   if (int_face_restrict_lex && iFISz>0)
+   {
+      // Apply the Interior Face Restriction
+      int_face_restrict_lex->Mult(x, faceIntX);
+      if (faceIntX.Size()>0)
+      {
+         faceIntY = 0.0;
+         // Apply the interior face matrices transposed
+         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,
+         {
+            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,
+         {
+            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_ext(j, i, 0, f)*X(i, 0, f);
+            }
+            Y(j, 1, f) += res;
+            res = 0.0;
+            for (int i = 0; i < NDOFS; i++)
+            {
+               res += A_ext(j, i, 1, f)*X(i, 1, f);
+            }
+            Y(j, 0, f) += res;
+         });
+         // Apply the Interior Face Restriction transposed
+         int_face_restrict_lex->MultTranspose(faceIntY, y);
+      }
+   }
+
+   // Treatment of boundary faces
+   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
+   const int bFISz = bdrFaceIntegrators.Size();
+   if (bdr_face_restrict_lex && bFISz>0)
+   {
+      // Apply the Boundary Face Restriction
+      bdr_face_restrict_lex->Mult(x, faceBdrX);
+      if (faceBdrX.Size()>0)
+      {
+         faceBdrY = 0.0;
+         // Apply the boundary face matrices transposed
+         const int NDOFS = faceDofs;
+         auto X = Reshape(faceBdrX.Read(), NDOFS, nf_bdr);
+         auto Y = Reshape(faceBdrY.ReadWrite(), NDOFS, nf_bdr);
+         auto A = Reshape(ea_data_bdr.Read(), NDOFS, NDOFS, nf_bdr);
+         MFEM_FORALL(glob_j, nf_bdr*NDOFS,
+         {
+            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(j, i, f)*X(i, f);
+            }
+            Y(j, f) += res;
+         });
+         // Apply the Boundary Face Restriction transposed
+         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+      }
+   }
+}
+
 MixedBilinearFormExtension::MixedBilinearFormExtension(MixedBilinearForm *form)
    : Operator(form->Height(), form->Width()), a(form)
 {
@@ -487,4 +795,68 @@ void PAMixedBilinearFormExtension::AddMultTranspose(const Vector &x, Vector &y,
    }
 }
 
+void PAMixedBilinearFormExtension::AssembleDiagonal_ADAt(const Vector &D,
+                                                         Vector &diag) const
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+
+   const int iSz = integrators.Size();
+
+   if (elem_restrict_trial)
+   {
+      const ElementRestriction* H1elem_restrict_trial =
+         dynamic_cast<const ElementRestriction*>(elem_restrict_trial);
+      if (H1elem_restrict_trial)
+      {
+         H1elem_restrict_trial->MultUnsigned(D, localTrial);
+      }
+      else
+      {
+         elem_restrict_trial->Mult(D, localTrial);
+      }
+   }
+
+   if (elem_restrict_test)
+   {
+      localTest = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         if (elem_restrict_trial)
+         {
+            integrators[i]->AssembleDiagonalPA_ADAt(localTrial, localTest);
+         }
+         else
+         {
+            integrators[i]->AssembleDiagonalPA_ADAt(D, localTest);
+         }
+      }
+      const ElementRestriction* H1elem_restrict_test =
+         dynamic_cast<const ElementRestriction*>(elem_restrict_test);
+      if (H1elem_restrict_test)
+      {
+         H1elem_restrict_test->MultTransposeUnsigned(localTest, diag);
+      }
+      else
+      {
+         elem_restrict_test->MultTranspose(localTest, diag);
+      }
+   }
+   else
+   {
+      diag.UseDevice(true); // typically this is a large vector, so store on device
+      diag = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         if (elem_restrict_trial)
+         {
+            integrators[i]->AssembleDiagonalPA_ADAt(localTrial, diag);
+         }
+         else
+         {
+            integrators[i]->AssembleDiagonalPA_ADAt(D, diag);
+         }
+      }
+   }
+}
+
 } // namespace mfem

fem/bilinearform_ext.hpp

@@ -22,9 +22,12 @@ namespace mfem
 class BilinearForm;
 class MixedBilinearForm;
 
-
-/** @brief Class extending the BilinearForm class to support the different
-    AssemblyLevel%s. */
+/// Class extending the BilinearForm class to support different AssemblyLevels.
+/**  FA - Full Assembly
+     PA - Partial Assembly
+     EA - Element Assembly
+     MF - Matrix Free
+*/
 class BilinearFormExtension : public Operator
 {
 protected:
@@ -42,6 +45,7 @@ public:
    /// Get the finite element space restriction matrix
    virtual const Operator *GetRestriction() const;
 
+   /// Assemble at the level given for the BilinearFormExtension subclass
    virtual void Assemble() = 0;
 
    virtual void AssembleDiagonal(Vector &diag) const
@@ -58,7 +62,8 @@ public:
    virtual void Update() = 0;
 };
 
-/// Data and methods for fully-assembled bilinear forms
+/** @brief Data and methods for fully-assembled bilinear forms.
+    Not yet implemented!  Use the BilinearForm Class instead. */
 class FABilinearFormExtension : public BilinearFormExtension
 {
 public:
@@ -78,26 +83,6 @@ public:
    ~FABilinearFormExtension() {}
 };
 
-/// Data and methods for element-assembled bilinear forms
-class EABilinearFormExtension : public BilinearFormExtension
-{
-public:
-   EABilinearFormExtension(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() {}
-   ~EABilinearFormExtension() {}
-};
-
 /// Data and methods for partially-assembled bilinear forms
 class PABilinearFormExtension : public BilinearFormExtension
 {
@@ -113,7 +98,6 @@ protected:
 public:
    PABilinearFormExtension(BilinearForm*);
 
-   void SetupRestrictionOperators();
    void Assemble();
    void AssembleDiagonal(Vector &diag) const;
    void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
@@ -121,14 +105,34 @@ public:
                          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();
+
+protected:
+   void SetupRestrictionOperators(const L2FaceValues m);
 };
 
+/// Data and methods for element-assembled bilinear forms
+class EABilinearFormExtension : public PABilinearFormExtension
+{
+protected:
+   int ne;
+   int elemDofs;
+   Vector ea_data;
+   int nf_int, nf_bdr;
+   int faceDofs;
+   Vector ea_data_int, ea_data_ext, ea_data_bdr;
 
-/// Data and methods for matrix-free bilinear forms
+public:
+   EABilinearFormExtension(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
 {
 public:
@@ -148,8 +152,12 @@ public:
    ~MFBilinearFormExtension() {}
 };
 
-/** @brief Class extending the MixedBilinearForm class to support the different
-    AssemblyLevel%s. */
+/// Class extending the MixedBilinearForm class to support different AssemblyLevels.
+/**  FA - Full Assembly
+     PA - Partial Assembly
+     EA - Element Assembly
+     MF - Matrix Free
+*/
 class MixedBilinearFormExtension : public Operator
 {
 protected:
@@ -186,6 +194,8 @@ public:
    virtual void AddMultTranspose(const Vector &x, Vector &y,
                                  const double c=1.0) const = 0;
 
+   virtual void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const = 0;
+
    virtual void Update() = 0;
 };
 
@@ -236,6 +246,9 @@ public:
    void MultTranspose(const Vector &x, Vector &y) const;
    /// y += c*A^T*x
    void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;
+   /// Assemble the diagonal of ADA^T for a diagonal vector D.
+   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
+
    /// Update internals for when a new MixedBilinearForm is given to this class
    void Update();
 };

fem/bilininteg.cpp

@@ -47,7 +47,37 @@ void BilinearFormIntegrator::AssemblePABoundaryFaces(const FiniteElementSpace&)
 
 void BilinearFormIntegrator::AssembleDiagonalPA(Vector &)
 {
-   MFEM_ABORT("BilinearFormIntegrator::AssembleDiagonalPA(...)\n"
+   mfem_error ("BilinearFormIntegrator::AssembleDiagonalPA(...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AssembleEA(const FiniteElementSpace &fes,
+                                        Vector &emat)
+{
+   mfem_error ("BilinearFormIntegrator::AssembleEA(...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace
+                                                     &fes,
+                                                     Vector &ea_data_int,
+                                                     Vector &ea_data_ext)
+{
+   mfem_error ("BilinearFormIntegrator::AssembleEAInteriorFaces(...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace
+                                                     &fes,
+                                                     Vector &ea_data_bdr)
+{
+   mfem_error ("BilinearFormIntegrator::AssembleEABoundaryFaces(...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AssembleDiagonalPA_ADAt(const Vector &, Vector &)
+{
+   MFEM_ABORT("BilinearFormIntegrator::AssembleDiagonalPA_ADAt(...)\n"
               "   is not implemented for this class.");
 }
 
@@ -889,7 +919,7 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
    {
       int order = 2 * el1.GetOrder();
 
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    elmat = 0.0;
@@ -900,11 +930,11 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
       Trans.Loc1.Transform(ip, eip);
       el1.CalcShape(eip, shape);
 
-      Trans.Face->SetIntPoint(&ip);
-      w = Trans.Face->Weight() * ip.weight;
+      Trans.SetIntPoint(&ip);
+      w = Trans.Weight() * ip.weight;
       if (Q)
       {
-         w *= Q -> Eval(*Trans.Face, ip);
+         w *= Q -> Eval(Trans, ip);
       }
 
       AddMult_a_VVt(w, shape, elmat);
@@ -1974,7 +2004,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
       D.SetSize(VQ ? VQ->GetVDim() : 0);
       K.SetSize(MQ ? MQ->GetVDim() : 0, MQ ? MQ->GetVDim() : 0);
 #endif
-      DenseMatrix tmp(trial_vshape.Height(), K.Width());
+      DenseMatrix tmp(test_vshape.Height(), K.Width());
 
       elmat.SetSize (test_dof, trial_dof);
 
@@ -2535,7 +2565,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
       {
          order++;
       }
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    for (int p = 0; p < ir->GetNPoints(); p++)
@@ -2549,8 +2579,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
       }
       el1.CalcShape(eip1, shape1);
 
-      Trans.Face->SetIntPoint(&ip);
-      Trans.Elem1->SetIntPoint(&eip1);
+      Trans.SetIntPoint(&ip);
 
       u->Eval(vu, *Trans.Elem1, eip1);
 
@@ -2560,7 +2589,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
       }
       else
       {
-         CalcOrtho(Trans.Face->Jacobian(), nor);
+         CalcOrtho(Trans.Jacobian(), nor);
       }
 
       un = vu * nor;
@@ -2575,7 +2604,6 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
          double rho_p;
          if (un >= 0.0 && ndof2)
          {
-            Trans.Elem2->SetIntPoint(&eip2);
             rho_p = rho->Eval(*Trans.Elem2, eip2);
          }
          else
@@ -2691,7 +2719,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
       {
          order = 2*el1.GetOrder();
       }
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    // assemble: < {(Q \nabla u).n},[v] >      --> elmat
@@ -2702,19 +2730,18 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
       IntegrationPoint eip1, eip2;
 
       Trans.Loc1.Transform(ip, eip1);
-      Trans.Face->SetIntPoint(&ip);
+      Trans.SetIntPoint(&ip);
       if (dim == 1)
       {
          nor(0) = 2*eip1.x - 1.0;
       }
       else
       {
-         CalcOrtho(Trans.Face->Jacobian(), nor);
+         CalcOrtho(Trans.Jacobian(), nor);
       }
 
       el1.CalcShape(eip1, shape1);
       el1.CalcDShape(eip1, dshape1);
-      Trans.Elem1->SetIntPoint(&eip1);
       w = ip.weight/Trans.Elem1->Weight();
       if (ndof2)
       {
@@ -2763,7 +2790,6 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
          Trans.Loc2.Transform(ip, eip2);
          el2.CalcShape(eip2, shape2);
          el2.CalcDShape(eip2, dshape2);
-         Trans.Elem2->SetIntPoint(&eip2);
          w = ip.weight/2/Trans.Elem2->Weight();
          if (!MQ)
          {
@@ -2973,7 +2999,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
    {
       // a simple choice for the integration order; is this OK?
       const int order = 2 * max(el1.GetOrder(), ndofs2 ? el2.GetOrder() : 0);
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    for (int pind = 0; pind < ir->GetNPoints(); ++pind)
@@ -2981,8 +3007,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       const IntegrationPoint &ip = ir->IntPoint(pind);
       IntegrationPoint eip1, eip2; // integration point in the reference space
       Trans.Loc1.Transform(ip, eip1);
-      Trans.Face->SetIntPoint(&ip);
-      Trans.Elem1->SetIntPoint(&eip1);
+      Trans.SetIntPoint(&ip);
 
       el1.CalcShape(eip1, shape1);
       el1.CalcDShape(eip1, dshape1);
@@ -2996,14 +3021,13 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       }
       else
       {
-         CalcOrtho(Trans.Face->Jacobian(), nor);
+         CalcOrtho(Trans.Jacobian(), nor);
       }
 
       double w, wLM;
       if (ndofs2)
       {
          Trans.Loc2.Transform(ip, eip2);
-         Trans.Elem2->SetIntPoint(&eip2);
          el2.CalcShape(eip2, shape2);
          el2.CalcDShape(eip2, dshape2);
          CalcAdjugate(Trans.Elem2->Jacobian(), adjJ);
@@ -3133,9 +3157,9 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
       order += trial_face_fe.GetOrder();
       if (trial_face_fe.GetMapType() == FiniteElement::VALUE)
       {
-         order += Trans.Face->OrderW();
+         order += Trans.OrderW();
       }
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    for (int p = 0; p < ir->GetNPoints(); p++)
@@ -3143,23 +3167,21 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
       const IntegrationPoint &ip = ir->IntPoint(p);
       IntegrationPoint eip1, eip2;
       // Trace finite element shape function
-      Trans.Face->SetIntPoint(&ip);
+      Trans.SetIntPoint(&ip);
       trial_face_fe.CalcShape(ip, face_shape);
       // Side 1 finite element shape function
       Trans.Loc1.Transform(ip, eip1);
       test_fe1.CalcShape(eip1, shape1);
-      Trans.Elem1->SetIntPoint(&eip1);
       if (ndof2)
       {
          // Side 2 finite element shape function
          Trans.Loc2.Transform(ip, eip2);
          test_fe2.CalcShape(eip2, shape2);
-         Trans.Elem2->SetIntPoint(&eip2);
       }
       w = ip.weight;
       if (trial_face_fe.GetMapType() == FiniteElement::VALUE)
       {
-         w *= Trans.Face->Weight();
+         w *= Trans.Weight();
       }
       face_shape *= w;
       for (i = 0; i < ndof1; i++)
@@ -3224,7 +3246,7 @@ void NormalTraceJumpIntegrator::AssembleFaceMatrix(
          order = test_fe1.GetOrder() - 1;
       }
       order += trial_face_fe.GetOrder();
-      ir = &IntRules.Get(Trans.FaceGeom, order);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
    }
 
    for (int p = 0; p < ir->GetNPoints(); p++)

fem/bilininteg.hpp

@@ -57,6 +57,9 @@ public:
    /// Assemble diagonal and add it to Vector @a diag.
    virtual void AssembleDiagonalPA(Vector &diag);
 
+   /// Assemble diagonal of ADA^T (A is this integrator) and add it to @a diag.
+   virtual void AssembleDiagonalPA_ADAt(const Vector &D, Vector &diag);
+
    /// Method for partially assembled action.
    /** Perform the action of integrator on the input @a x and add the result to
        the output @a y. Both @a x and @a y are E-vectors, i.e. they represent
@@ -75,6 +78,22 @@ public:
        called. */
    virtual void AddMultTransposePA(const Vector &x, Vector &y) const;
 
+   /// Method defining element assembly.
+   /** The result of the element assembly is added and stored in the @a emat
+       Vector. */
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   /** Used with BilinearFormIntegrators that have different spaces. */
+   // virtual void AssembleEA(const FiniteElementSpace &trial_fes,
+   //                         const FiniteElementSpace &test_fes,
+   //                         Vector &emat);
+
+   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
+                                        Vector &ea_data_int,
+                                        Vector &ea_data_ext);
+
+   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
+                                        Vector &ea_data_bdr);
+
    /// Given a particular Finite Element computes the element matrix elmat.
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,
@@ -180,6 +199,8 @@ public:
    virtual ~BilinearFormIntegrator() { }
 };
 
+/** Wraps a given @a BilinearFormIntegrator and transposes the resulting element
+    matrices. See for example ex9, ex9p. */
 class TransposeIntegrator : public BilinearFormIntegrator
 {
 private:
@@ -234,6 +255,15 @@ public:
       bfi->AddMultTransposePA(x, y);
    }
 
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+
+   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
+                                        Vector &ea_data_int,
+                                        Vector &ea_data_ext);
+
+   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
+                                        Vector &ea_data_bdr);
+
    virtual ~TransposeIntegrator() { if (own_bfi) { delete bfi; } }
 };
 
@@ -1535,7 +1565,7 @@ public:
 };
 
 /** Class for integrating the bilinear form a(u,v) := (-V u, Grad v) in 2D or 3D
-    and where V is a vector coefficient, u is in H1 and v is in H1. */
+    and where V is a vector coefficient, u is in H1 or L2 and v is in H1. */
 class MixedScalarWeakDivergenceIntegrator : public MixedScalarVectorIntegrator
 {
 public:
@@ -1885,6 +1915,8 @@ public:
 
    virtual void AssemblePA(const FiniteElementSpace &fes);
 
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+
    virtual void AssembleDiagonalPA(Vector &diag);
 
    virtual void AddMultPA(const Vector&, Vector&) const;
@@ -1958,6 +1990,8 @@ public:
 
    virtual void AssemblePA(const FiniteElementSpace &fes);
 
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+
    virtual void AssembleDiagonalPA(Vector &diag);
 
    virtual void AddMultPA(const Vector&, Vector&) const;
@@ -1969,6 +2003,7 @@ public:
    void SetupPA(const FiniteElementSpace &fes, const bool force = false);
 };
 
+/** Mass integrator (u, v) restricted to the boundary of a domain */
 class BoundaryMassIntegrator : public MassIntegrator
 {
 public:
@@ -2011,6 +2046,8 @@ public:
 
    virtual void AssemblePA(const FiniteElementSpace&);
 
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+
    virtual void AddMultPA(const Vector&, Vector&) const;
 
    static const IntegrationRule &GetRule(const FiniteElement &el,
@@ -2110,11 +2147,25 @@ class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
 protected:
    Coefficient *Q;
 
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+   virtual void AddMultTransposePA(const Vector&, Vector&) const;
+
 private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape, shape;
 #endif
 
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *L2mapsO;       ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   int dim, ne, dofs1D, L2dofs1D, quad1D;
+
 public:
    VectorFEDivergenceIntegrator() { Q = NULL; }
    VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -2125,6 +2176,8 @@ public:
                                        const FiniteElement &test_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
+
+   virtual void AssembleDiagonalPA_ADAt(const Vector &D, Vector &diag);
 };
 
 
@@ -2308,7 +2361,7 @@ protected:
    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, nq, dofs1D, quad1D;
+   int dim, ne, nq, dofs1D, quad1D, fetype;
 
 public:
    VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
@@ -2387,11 +2440,23 @@ class DivDivIntegrator: public BilinearFormIntegrator
 protected:
    Coefficient *Q;
 
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &fes);
+   virtual void AddMultPA(const Vector &x, Vector &y) const;
+   virtual void AssembleDiagonalPA(Vector& diag);
+
 private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape;
 #endif
 
+   // 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;
+
 public:
    DivDivIntegrator() { Q = NULL; }
    DivDivIntegrator(Coefficient &q) : Q(&q) { }
@@ -2544,6 +2609,13 @@ public:
 
    virtual void AddMultPA(const Vector&, Vector&) const;
 
+   virtual void AssembleEAInteriorFaces(const FiniteElementSpace& fes,
+                                        Vector &ea_data_int,
+                                        Vector &ea_data_ext);
+
+   virtual void AssembleEABoundaryFaces(const FiniteElementSpace& fes,
+                                        Vector &ea_data_bdr);
+
    static const IntegrationRule &GetRule(Geometry::Type geom, int order,
                                          FaceElementTransformations &T);
 

fem/bilininteg_convection_ea.cpp

@@ -0,0 +1,258 @@
+// 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.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+namespace mfem
+{
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAConvectionAssemble1D(const int NE,
+                                   const Array<double> &b,
+                                   const Array<double> &g,
+                                   const Vector &padata,
+                                   Vector &eadata,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      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;
+      double r_Gi[MQ1];
+      double r_Bj[MQ1];
+      for (int q = 0; q < Q1D; q++)
+      {
+         r_Gi[q] = G(q,MFEM_THREAD_ID(x));
+         r_Bj[q] = B(q,MFEM_THREAD_ID(y));
+      }
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(j1,y,D1D)
+         {
+            double val = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
+            }
+            A(i1, j1, e) = val;
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAConvectionAssemble2D(const int NE,
+                                   const Array<double> &b,
+                                   const Array<double> &g,
+                                   const Vector &padata,
+                                   Vector &eadata,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      double r_G[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+            r_G[q][d] = G(q,d);
+         }
+      }
+      MFEM_SHARED double s_D[MQ1][MQ1][2];
+      MFEM_FOREACH_THREAD(k1,x,Q1D)
+      {
+         MFEM_FOREACH_THREAD(k2,y,Q1D)
+         {
+            s_D[k1][k2][0] = D(k1,k2,0,e);
+            s_D[k1][k2][1] = D(k1,k2,1,e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            for (int j1 = 0; j1 < D1D; ++j1)
+            {
+               for (int j2 = 0; j2 < D1D; ++j2)
+               {
+                  double val = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        val += (r_G[k1][i1] * r_B[k2][i2] * s_D[k1][k2][0]
+                                + r_B[k1][i1] * r_G[k2][i2] * s_D[k1][k2][1])
+                               * r_B[k1][j1]* r_B[k2][j2];
+                     }
+                  }
+                  A(i1, i2, j1, j2, e) = val;
+               }
+            }
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAConvectionAssemble3D(const int NE,
+                                   const Array<double> &b,
+                                   const Array<double> &g,
+                                   const Vector &padata,
+                                   Vector &eadata,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      double r_G[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+            r_G[q][d] = G(q,d);
+         }
+      }
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(i3,z,D1D)
+            {
+               for (int j1 = 0; j1 < D1D; ++j1)
+               {
+                  for (int j2 = 0; j2 < D1D; ++j2)
+                  {
+                     for (int j3 = 0; j3 < D1D; ++j3)
+                     {
+                        double val = 0.0;
+                        for (int k1 = 0; k1 < Q1D; ++k1)
+                        {
+                           for (int k2 = 0; k2 < Q1D; ++k2)
+                           {
+                              for (int k3 = 0; k3 < Q1D; ++k3)
+                              {
+                                 double D0 = D(k1,k2,k3,0,e);
+                                 double D1 = D(k1,k2,k3,1,e);
+                                 double D2 = D(k1,k2,k3,2,e);
+                                 val += (r_G[k1][i1] * r_B[k2][i2] * r_B[k3][i3] * D0
+                                         + r_B[k1][i1] * r_G[k2][i2] * r_B[k3][i3] * D1
+                                         + r_B[k1][i1] * r_B[k2][i2] * r_G[k3][i3] * D2)
+                                        * r_B[k1][j1] * r_B[k2][j2] * r_B[k3][j3];
+                              }
+                           }
+                        }
+                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                     }
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
+void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
+                                      Vector &ea_data)
+{
+   AssemblePA(fes);
+   const int ne = fes.GetMesh()->GetNE();
+   const Array<double> &B = maps->B;
+   const Array<double> &G = maps->G;
+   if (dim == 1)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
+         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
+         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
+         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
+         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
+         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
+         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
+         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
+         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 2)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
+         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
+         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
+         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
+         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
+         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
+         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
+         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
+         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
+         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
+         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
+         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
+         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
+         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
+         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
+         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+}

fem/bilininteg_dgtrace_ea.cpp

@@ -0,0 +1,414 @@
+// 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.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+namespace mfem
+{
+
+static void EADGTraceAssemble1DInt(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_int,
+                                   Vector &eadata_ext)
+{
+   auto D = Reshape(padata.Read(), 2, 2, NF);
+   auto A_int = Reshape(eadata_int.ReadWrite(), 2, NF);
+   auto A_ext = Reshape(eadata_ext.ReadWrite(), 2, NF);
+   MFEM_FORALL(f, NF,
+   {
+      double val_int0, val_int1, val_ext01, val_ext10;
+      val_int0  = D(0, 0, f);
+      val_ext10 = D(1, 0, f);
+      val_ext01 = D(0, 1, f);
+      val_int1  = D(1, 1, f);
+      A_int(0, f) += val_int0;
+      A_int(1, f) += val_int1;
+      A_ext(0, f) += val_ext01;
+      A_ext(1, f) += val_ext10;
+   });
+}
+
+static void EADGTraceAssemble1DBdr(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_bdr)
+{
+   auto D = Reshape(padata.Read(), 2, 2, NF);
+   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), NF);
+   MFEM_FORALL(f, NF,
+   {
+      A_bdr(f) += D(0, 0, f);
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADGTraceAssemble2DInt(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_int,
+                                   Vector &eadata_ext,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, 2, 2, NF);
+   auto A_int = Reshape(eadata_int.ReadWrite(), D1D, D1D, 2, NF);
+   auto A_ext = Reshape(eadata_ext.ReadWrite(), D1D, D1D, 2, NF);
+   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(j1,y,D1D)
+         {
+            double val_int0 = 0.0;
+            double val_int1 = 0.0;
+            double val_ext01 = 0.0;
+            double val_ext10 = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val_int0  += B(k1,i1) * B(k1,j1) * D(k1, 0, 0, f);
+               val_ext01 += B(k1,i1) * B(k1,j1) * D(k1, 0, 1, f);
+               val_ext10 += B(k1,i1) * B(k1,j1) * D(k1, 1, 0, f);
+               val_int1  += B(k1,i1) * B(k1,j1) * D(k1, 1, 1, f);
+            }
+            A_int(i1, j1, 0, f) += val_int0;
+            A_int(i1, j1, 1, f) += val_int1;
+            A_ext(i1, j1, 0, f) += val_ext01;
+            A_ext(i1, j1, 1, f) += val_ext10;
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADGTraceAssemble2DBdr(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_bdr,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, 2, 2, NF);
+   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), D1D, D1D, NF);
+   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(j1,y,D1D)
+         {
+            double val_bdr = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val_bdr  += B(k1,i1) * B(k1,j1) * D(k1, 0, 0, f);
+            }
+            A_bdr(i1, j1, f) += val_bdr;
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADGTraceAssemble3DInt(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_int,
+                                   Vector &eadata_ext,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, Q1D, 2, 2, NF);
+   auto A_int = Reshape(eadata_int.ReadWrite(), D1D, D1D, D1D, D1D, 2, NF);
+   auto A_ext = Reshape(eadata_ext.ReadWrite(), D1D, D1D, D1D, D1D, 2, NF);
+   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+         }
+      }
+      MFEM_SHARED double s_D[MQ1][MQ1][2][2];
+      for (int i=0; i < 2; i++)
+      {
+         for (int j=0; j < 2; j++)
+         {
+            MFEM_FOREACH_THREAD(k1,x,Q1D)
+            {
+               MFEM_FOREACH_THREAD(k2,y,Q1D)
+               {
+                  s_D[k1][k2][i][j] = D(k1,k2,i,j,f);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            for (int j1 = 0; j1 < D1D; ++j1)
+            {
+               for (int j2 = 0; j2 < D1D; ++j2)
+               {
+                  double val_int0 = 0.0;
+                  double val_int1 = 0.0;
+                  double val_ext01 = 0.0;
+                  double val_ext10 = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        val_int0 += r_B[k1][i1] * r_B[k1][j1]
+                                    * r_B[k2][i2] * r_B[k2][j2]
+                                    * s_D[k1][k2][0][0];
+                        val_int1 += r_B[k1][i1] * r_B[k1][j1]
+                                    * r_B[k2][i2] * r_B[k2][j2]
+                                    * s_D[k1][k2][1][1];
+                        val_ext01+= r_B[k1][i1] * r_B[k1][j1]
+                                    * r_B[k2][i2] * r_B[k2][j2]
+                                    * s_D[k1][k2][0][1];
+                        val_ext10+= r_B[k1][i1] * r_B[k1][j1]
+                                    * r_B[k2][i2] * r_B[k2][j2]
+                                    * s_D[k1][k2][1][0];
+                     }
+                  }
+                  A_int(i1, i2, j1, j2, 0, f) += val_int0;
+                  A_int(i1, i2, j1, j2, 1, f) += val_int1;
+                  A_ext(i1, i2, j1, j2, 0, f) += val_ext01;
+                  A_ext(i1, i2, j1, j2, 1, f) += val_ext10;
+               }
+            }
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADGTraceAssemble3DBdr(const int NF,
+                                   const Array<double> &basis,
+                                   const Vector &padata,
+                                   Vector &eadata_bdr,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(basis.Read(), Q1D, D1D);
+   auto D = Reshape(padata.Read(), Q1D, Q1D, 2, 2, NF);
+   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), D1D, D1D, D1D, D1D, NF);
+   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+         }
+      }
+      MFEM_SHARED double s_D[MQ1][MQ1][2][2];
+      for (int i=0; i < 2; i++)
+      {
+         for (int j=0; j < 2; j++)
+         {
+            MFEM_FOREACH_THREAD(k1,x,Q1D)
+            {
+               MFEM_FOREACH_THREAD(k2,y,Q1D)
+               {
+                  s_D[k1][k2][i][j] = D(k1,k2,i,j,f);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            for (int j1 = 0; j1 < D1D; ++j1)
+            {
+               for (int j2 = 0; j2 < D1D; ++j2)
+               {
+                  double val_bdr = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        val_bdr += r_B[k1][i1] * r_B[k1][j1]
+                                   * r_B[k2][i2] * r_B[k2][j2]
+                                   * s_D[k1][k2][0][0];
+                     }
+                  }
+                  A_bdr(i1, i2, j1, j2, f) += val_bdr;
+               }
+            }
+         }
+      }
+   });
+}
+
+void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
+                                                Vector &ea_data_int,
+                                                Vector &ea_data_ext)
+{
+   SetupPA(fes, FaceType::Interior);
+   nf = fes.GetNFbyType(FaceType::Interior);
+   if (nf==0) { return; }
+   const Array<double> &B = maps->B;
+   if (dim == 1)
+   {
+      return EADGTraceAssemble1DInt(nf,B,pa_data,ea_data_int,ea_data_ext);
+   }
+   else if (dim == 2)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22:
+            return EADGTraceAssemble2DInt<2,2>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x33:
+            return EADGTraceAssemble2DInt<3,3>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x44:
+            return EADGTraceAssemble2DInt<4,4>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x55:
+            return EADGTraceAssemble2DInt<5,5>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x66:
+            return EADGTraceAssemble2DInt<6,6>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x77:
+            return EADGTraceAssemble2DInt<7,7>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x88:
+            return EADGTraceAssemble2DInt<8,8>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x99:
+            return EADGTraceAssemble2DInt<9,9>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         default:
+            return EADGTraceAssemble2DInt(nf,B,pa_data,ea_data_int,
+                                          ea_data_ext,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23:
+            return EADGTraceAssemble3DInt<2,3>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x34:
+            return EADGTraceAssemble3DInt<3,4>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x45:
+            return EADGTraceAssemble3DInt<4,5>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x56:
+            return EADGTraceAssemble3DInt<5,6>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x67:
+            return EADGTraceAssemble3DInt<6,7>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x78:
+            return EADGTraceAssemble3DInt<7,8>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         case 0x89:
+            return EADGTraceAssemble3DInt<8,9>(nf,B,pa_data,ea_data_int,
+                                               ea_data_ext);
+         default:
+            return EADGTraceAssemble3DInt(nf,B,pa_data,ea_data_int,
+                                          ea_data_ext,dofs1D,quad1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+void DGTraceIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
+                                                Vector &ea_data_bdr)
+{
+   SetupPA(fes, FaceType::Boundary);
+   nf = fes.GetNFbyType(FaceType::Boundary);
+   if (nf==0) { return; }
+   const Array<double> &B = maps->B;
+   if (dim == 1)
+   {
+      return EADGTraceAssemble1DBdr(nf,B,pa_data,ea_data_bdr);
+   }
+   else if (dim == 2)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EADGTraceAssemble2DBdr<2,2>(nf,B,pa_data,ea_data_bdr);
+         case 0x33: return EADGTraceAssemble2DBdr<3,3>(nf,B,pa_data,ea_data_bdr);
+         case 0x44: return EADGTraceAssemble2DBdr<4,4>(nf,B,pa_data,ea_data_bdr);
+         case 0x55: return EADGTraceAssemble2DBdr<5,5>(nf,B,pa_data,ea_data_bdr);
+         case 0x66: return EADGTraceAssemble2DBdr<6,6>(nf,B,pa_data,ea_data_bdr);
+         case 0x77: return EADGTraceAssemble2DBdr<7,7>(nf,B,pa_data,ea_data_bdr);
+         case 0x88: return EADGTraceAssemble2DBdr<8,8>(nf,B,pa_data,ea_data_bdr);
+         case 0x99: return EADGTraceAssemble2DBdr<9,9>(nf,B,pa_data,ea_data_bdr);
+         default:
+            return EADGTraceAssemble2DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23: return EADGTraceAssemble3DBdr<2,3>(nf,B,pa_data,ea_data_bdr);
+         case 0x34: return EADGTraceAssemble3DBdr<3,4>(nf,B,pa_data,ea_data_bdr);
+         case 0x45: return EADGTraceAssemble3DBdr<4,5>(nf,B,pa_data,ea_data_bdr);
+         case 0x56: return EADGTraceAssemble3DBdr<5,6>(nf,B,pa_data,ea_data_bdr);
+         case 0x67: return EADGTraceAssemble3DBdr<6,7>(nf,B,pa_data,ea_data_bdr);
+         case 0x78: return EADGTraceAssemble3DBdr<7,8>(nf,B,pa_data,ea_data_bdr);
+         case 0x89: return EADGTraceAssemble3DBdr<8,9>(nf,B,pa_data,ea_data_bdr);
+         default:
+            return EADGTraceAssemble3DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+}

fem/bilininteg_diffusion_ea.cpp

@@ -0,0 +1,275 @@
+// 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.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+namespace mfem
+{
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADiffusionAssemble1D(const int NE,
+                                  const Array<double> &b,
+                                  const Array<double> &g,
+                                  const Vector &padata,
+                                  Vector &eadata,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      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;
+      double r_Gi[MQ1];
+      double r_Gj[MQ1];
+      for (int q = 0; q < Q1D; q++)
+      {
+         r_Gi[q] = G(q,MFEM_THREAD_ID(x));
+         r_Gj[q] = G(q,MFEM_THREAD_ID(y));
+      }
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(j1,y,D1D)
+         {
+            double val = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val += r_Gj[k1] * D(k1, e) * r_Gi[k1];
+            }
+            A(i1, j1, e) = val;
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADiffusionAssemble2D(const int NE,
+                                  const Array<double> &b,
+                                  const Array<double> &g,
+                                  const Vector &padata,
+                                  Vector &eadata,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      double r_G[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+            r_G[q][d] = G(q,d);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            for (int j1 = 0; j1 < D1D; ++j1)
+            {
+               for (int j2 = 0; j2 < D1D; ++j2)
+               {
+                  double val = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        double bgi = r_G[k1][i1] * r_B[k2][i2];
+                        double gbi = r_B[k1][i1] * r_G[k2][i2];
+                        double bgj = r_G[k1][j1] * r_B[k2][j2];
+                        double gbj = r_B[k1][j1] * r_G[k2][j2];
+                        double D00 = D(k1,k2,0,e);
+                        double D10 = D(k1,k2,1,e);
+                        double D01 = D10;
+                        double D11 = D(k1,k2,2,e);
+                        val += bgi * D00 * bgj
+                               + gbi * D01 * bgj
+                               + bgi * D10 * gbj
+                               + gbi * D11 * gbj;
+                     }
+                  }
+                  A(i1, i2, j1, j2, e) = val;
+               }
+            }
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EADiffusionAssemble3D(const int NE,
+                                  const Array<double> &g,
+                                  const Array<double> &b,
+                                  const Vector &padata,
+                                  Vector &eadata,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      double r_G[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+            r_G[q][d] = G(q,d);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(i3,z,D1D)
+            {
+               for (int j1 = 0; j1 < D1D; ++j1)
+               {
+                  for (int j2 = 0; j2 < D1D; ++j2)
+                  {
+                     for (int j3 = 0; j3 < D1D; ++j3)
+                     {
+                        double val = 0.0;
+                        for (int k1 = 0; k1 < Q1D; ++k1)
+                        {
+                           for (int k2 = 0; k2 < Q1D; ++k2)
+                           {
+                              for (int k3 = 0; k3 < Q1D; ++k3)
+                              {
+                                 double bbgi = r_G[k1][i1] * r_B[k2][i2] * r_B[k3][i3];
+                                 double bgbi = r_B[k1][i1] * r_G[k2][i2] * r_B[k3][i3];
+                                 double gbbi = r_B[k1][i1] * r_B[k2][i2] * r_G[k3][i3];
+                                 double bbgj = r_G[k1][j1] * r_B[k2][j2] * r_B[k3][j3];
+                                 double bgbj = r_B[k1][j1] * r_G[k2][j2] * r_B[k3][j3];
+                                 double gbbj = r_B[k1][j1] * r_B[k2][j2] * r_G[k3][j3];
+                                 double D00 = D(k1,k2,k3,0,e);
+                                 double D10 = D(k1,k2,k3,1,e);
+                                 double D20 = D(k1,k2,k3,2,e);
+                                 double D01 = D10;
+                                 double D11 = D(k1,k2,k3,3,e);
+                                 double D21 = D(k1,k2,k3,4,e);
+                                 double D02 = D20;
+                                 double D12 = D21;
+                                 double D22 = D(k1,k2,k3,5,e);
+                                 val += bbgi * D00 * bbgj
+                                        + bgbi * D10 * bbgj
+                                        + gbbi * D20 * bbgj
+                                        + bbgi * D01 * bgbj
+                                        + bgbi * D11 * bgbj
+                                        + gbbi * D21 * bgbj
+                                        + bbgi * D02 * gbbj
+                                        + bgbi * D12 * gbbj
+                                        + gbbi * D22 * gbbj;
+                              }
+                           }
+                        }
+                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                     }
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
+void DiffusionIntegrator::AssembleEA(const FiniteElementSpace &fes,
+                                     Vector &ea_data)
+{
+   AssemblePA(fes);
+   const int ne = fes.GetMesh()->GetNE();
+   const Array<double> &B = maps->B;
+   const Array<double> &G = maps->G;
+   if (dim == 1)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EADiffusionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
+         case 0x33: return EADiffusionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
+         case 0x44: return EADiffusionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
+         case 0x55: return EADiffusionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
+         case 0x66: return EADiffusionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
+         case 0x77: return EADiffusionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
+         case 0x88: return EADiffusionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
+         case 0x99: return EADiffusionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
+         default:   return EADiffusionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 2)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EADiffusionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
+         case 0x33: return EADiffusionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
+         case 0x44: return EADiffusionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
+         case 0x55: return EADiffusionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
+         case 0x66: return EADiffusionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
+         case 0x77: return EADiffusionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
+         case 0x88: return EADiffusionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
+         case 0x99: return EADiffusionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
+         default:   return EADiffusionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23: return EADiffusionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
+         case 0x34: return EADiffusionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
+         case 0x45: return EADiffusionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
+         case 0x56: return EADiffusionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
+         case 0x67: return EADiffusionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
+         case 0x78: return EADiffusionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
+         case 0x89: return EADiffusionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
+         default:   return EADiffusionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+}

fem/bilininteg_hcurl.cpp

@@ -24,12 +24,12 @@ constexpr int HCURL_MAX_D1D = 5;
 constexpr int HCURL_MAX_Q1D = 6;
 
 // PA H(curl) Mass Assemble 2D kernel
-static void PAHcurlSetup2D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           const Vector &j,
-                           Vector &_coeff,
-                           Vector &op)
+void PAHcurlSetup2D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    const Vector &j,
+                    Vector &_coeff,
+                    Vector &op)
 {
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
@@ -55,12 +55,12 @@ static void PAHcurlSetup2D(const int Q1D,
 }
 
 // PA H(curl) Mass Assemble 3D kernel
-static void PAHcurlSetup3D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           const Vector &j,
-                           Vector &_coeff,
-                           Vector &op)
+void PAHcurlSetup3D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    const Vector &j,
+                    Vector &_coeff,
+                    Vector &op)
 {
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
@@ -106,78 +106,16 @@ static void PAHcurlSetup3D(const int Q1D,
    });
 }
 
-void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
-{
-   // Assumes tensor-product elements
-   Mesh *mesh = fes.GetMesh();
-   const FiniteElement *fel = fes.GetFE(0);
-
-   const VectorTensorFiniteElement *el =
-      dynamic_cast<const VectorTensorFiniteElement*>(fel);
-   MFEM_VERIFY(el != NULL, "Only VectorTensorFiniteElement is supported!");
-
-   const IntegrationRule *ir
-      = IntRule ? IntRule : &MassIntegrator::GetRule(*el, *el,
-                                                     *mesh->GetElementTransformation(0));
-   const int dims = el->GetDim();
-   MFEM_VERIFY(dims == 2 || dims == 3, "");
-
-   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
-   const int nq = ir->GetNPoints();
-   dim = mesh->Dimension();
-   MFEM_VERIFY(dim == 2 || dim == 3, "");
-
-   ne = fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   dofs1D = mapsC->ndof;
-   quad1D = mapsC->nqpt;
-
-   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
-
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
-
-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      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 (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
-   {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
-   {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else
-   {
-      MFEM_ABORT("Unknown kernel.");
-   }
-}
-
-static void PAHcurlMassApply2D(const int D1D,
-                               const int Q1D,
-                               const int NE,
-                               const Array<double> &_Bo,
-                               const Array<double> &_Bc,
-                               const Array<double> &_Bot,
-                               const Array<double> &_Bct,
-                               const Vector &_op,
-                               const Vector &_x,
-                               Vector &_y)
+void PAHcurlMassApply2D(const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        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 VDIM = 2;
 
@@ -294,13 +232,13 @@ static void PAHcurlMassApply2D(const int D1D,
    }); // end of element loop
 }
 
-static void PAHcurlMassAssembleDiagonal2D(const int D1D,
-                                          const int Q1D,
-                                          const int NE,
-                                          const Array<double> &_Bo,
-                                          const Array<double> &_Bc,
-                                          const Vector &_op,
-                                          Vector &_diag)
+void PAHcurlMassAssembleDiagonal2D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &_Bo,
+                                   const Array<double> &_Bc,
+                                   const Vector &_op,
+                                   Vector &_diag)
 {
    constexpr static int VDIM = 2;
 
@@ -348,15 +286,17 @@ static void PAHcurlMassAssembleDiagonal2D(const int D1D,
    }); // end of element loop
 }
 
-template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlMassAssembleDiagonal3D(const int D1D,
-                                          const int Q1D,
-                                          const int NE,
-                                          const Array<double> &_Bo,
-                                          const Array<double> &_Bc,
-                                          const Vector &_op,
-                                          Vector &_diag)
+void PAHcurlMassAssembleDiagonal3D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &_Bo,
+                                   const Array<double> &_Bc,
+                                   const Vector &_op,
+                                   Vector &_diag)
 {
+   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;
@@ -416,28 +356,20 @@ static void PAHcurlMassAssembleDiagonal3D(const int D1D,
    }); // end of element loop
 }
 
-void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
+void PAHcurlMassApply3D(const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &_Bo,
+                        const Array<double> &_Bc,
+                        const Array<double> &_Bot,
+                        const Array<double> &_Bct,
+                        const Vector &_op,
+                        const Vector &_x,
+                        Vector &_y)
 {
-   if (dim == 3)
-      PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne,
-                                    mapsO->B, mapsC->B, pa_data, diag);
-   else
-      PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne,
-                                    mapsO->B, mapsC->B, pa_data, diag);
-}
+   constexpr static int MAX_D1D = HCURL_MAX_D1D;
+   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
 
-template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlMassApply3D(const int D1D,
-                               const int Q1D,
-                               const int NE,
-                               const Array<double> &_Bo,
-                               const Array<double> &_Bc,
-                               const Array<double> &_Bot,
-                               const Array<double> &_Bct,
-                               const Vector &_op,
-                               const Vector &_x,
-                               Vector &_y)
-{
    MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
    MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
    constexpr static int VDIM = 3;
@@ -615,20 +547,6 @@ static void PAHcurlMassApply3D(const int D1D,
    }); // end of element loop
 }
 
-void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (dim == 3)
-   {
-      PAHcurlMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                         mapsC->Bt, pa_data, x, y);
-   }
-   else
-   {
-      PAHcurlMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                         mapsC->Bt, pa_data, x, y);
-   }
-}
-
 // PA H(curl) curl-curl assemble 2D kernel
 static void PACurlCurlSetup2D(const int Q1D,
                               const int NE,
@@ -1678,92 +1596,25 @@ void CurlCurlIntegrator::AssembleDiagonalPA(Vector& diag)
    }
 }
 
-void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
-                                               &trial_fes,
-                                               const FiniteElementSpace &test_fes)
-{
-   // Assumes tensor-product elements, with a vector test space and H^1 trial space.
-   Mesh *mesh = trial_fes.GetMesh();
-   const FiniteElement *trial_fel = trial_fes.GetFE(0);
-   const FiniteElement *test_fel = test_fes.GetFE(0);
-
-   const NodalTensorFiniteElement *trial_el =
-      dynamic_cast<const NodalTensorFiniteElement*>(trial_fel);
-   MFEM_VERIFY(trial_el != NULL, "Only NodalTensorFiniteElement is supported!");
-
-   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(*trial_el, *trial_el,
-                                                     *mesh->GetElementTransformation(0));
-   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
-   const int nq = ir->GetNPoints();
-   dim = mesh->Dimension();
-   MFEM_VERIFY(dim == 2 || dim == 3, "");
-
-   MFEM_VERIFY(trial_el->GetOrder() == test_el->GetOrder(), "");
-
-   ne = trial_fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   dofs1D = mapsC->ndof;
-   quad1D = mapsC->nqpt;
-
-   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
-
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
-
-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      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));
-         }
-      }
-   }
-
-   // Use the same setup functions as VectorFEMassIntegrator.
-   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
-   {
-      PAHcurlSetup3D(quad1D, 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,
-                     coeff, pa_data);
-   }
-   else
-   {
-      MFEM_ABORT("Unknown kernel.");
-   }
-}
-
 // Apply to x corresponding to DOF's in H^1 (trial), whose gradients are integrated
 // against H(curl) test functions corresponding to y.
-template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PAHcurlH1Apply3D(const int D1D,
-                             const int Q1D,
-                             const int NE,
-                             const Array<double> &_Bc,
-                             const Array<double> &_Gc,
-                             const Array<double> &_Bot,
-                             const Array<double> &_Bct,
-                             const Vector &_op,
-                             const Vector &_x,
-                             Vector &_y)
+void PAHcurlH1Apply3D(const int D1D,
+                      const int Q1D,
+                      const int NE,
+                      const Array<double> &_Bc,
+                      const Array<double> &_Gc,
+                      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 Bc = Reshape(_Bc.Read(), Q1D, D1D);
@@ -1937,16 +1788,16 @@ static void PAHcurlH1Apply3D(const int D1D,
 
 // Apply to x corresponding to DOF's in H^1 (trial), whose gradients are integrated
 // against H(curl) test functions corresponding to y.
-static void PAHcurlH1Apply2D(const int D1D,
-                             const int Q1D,
-                             const int NE,
-                             const Array<double> &_Bc,
-                             const Array<double> &_Gc,
-                             const Array<double> &_Bot,
-                             const Array<double> &_Bct,
-                             const Vector &_op,
-                             const Vector &_x,
-                             Vector &_y)
+void PAHcurlH1Apply2D(const int D1D,
+                      const int Q1D,
+                      const int NE,
+                      const Array<double> &_Bc,
+                      const Array<double> &_Gc,
+                      const Array<double> &_Bot,
+                      const Array<double> &_Bct,
+                      const Vector &_op,
+                      const Vector &_x,
+                      Vector &_y)
 {
    constexpr static int VDIM = 2;
 
@@ -2057,18 +1908,4 @@ static void PAHcurlH1Apply2D(const int D1D,
    }); // end of element loop
 }
 
-void MixedVectorGradientIntegrator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (dim == 3)
-      PAHcurlH1Apply3D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
-                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
-   else if (dim == 2)
-      PAHcurlH1Apply2D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
-                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
-   else
-   {
-      MFEM_ABORT("Unsupported dimension!");
-   }
-}
-
 } // namespace mfem

fem/bilininteg_mass_ea.cpp

@@ -0,0 +1,255 @@
+// 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.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+namespace mfem
+{
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAMassAssemble1D(const int NE,
+                             const Array<double> &basis,
+                             const Vector &padata,
+                             Vector &eadata,
+                             const int d1d = 0,
+                             const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      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;
+      double r_Bi[MQ1];
+      double r_Bj[MQ1];
+      for (int q = 0; q < Q1D; q++)
+      {
+         r_Bi[q] = B(q,MFEM_THREAD_ID(x));
+         r_Bj[q] = B(q,MFEM_THREAD_ID(y));
+      }
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(j1,y,D1D)
+         {
+            double val = 0.0;
+            for (int k1 = 0; k1 < Q1D; ++k1)
+            {
+               val += r_Bi[k1] * r_Bj[k1] * D(k1, e);
+            }
+            M(i1, j1, e) = val;
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAMassAssemble2D(const int NE,
+                             const Array<double> &basis,
+                             const Vector &padata,
+                             Vector &eadata,
+                             const int d1d = 0,
+                             const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+         }
+      }
+      MFEM_SHARED double s_D[MQ1][MQ1];
+      MFEM_FOREACH_THREAD(k1,x,Q1D)
+      {
+         MFEM_FOREACH_THREAD(k2,y,Q1D)
+         {
+            s_D[k1][k2] = D(k1,k2,e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            for (int j1 = 0; j1 < D1D; ++j1)
+            {
+               for (int j2 = 0; j2 < D1D; ++j2)
+               {
+                  double val = 0.0;
+                  for (int k1 = 0; k1 < Q1D; ++k1)
+                  {
+                     for (int k2 = 0; k2 < Q1D; ++k2)
+                     {
+                        val += r_B[k1][i1] * r_B[k1][j1]
+                               * r_B[k2][i2] * r_B[k2][j2]
+                               * s_D[k1][k2];
+                     }
+                  }
+                  M(i1, i2, j1, j2, e) = val;
+               }
+            }
+         }
+      }
+   });
+}
+
+template<int T_D1D = 0, int T_Q1D = 0>
+static void EAMassAssemble3D(const int NE,
+                             const Array<double> &basis,
+                             const Vector &padata,
+                             Vector &eadata,
+                             const int d1d = 0,
+                             const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   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);
+   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      double r_B[MQ1][MD1];
+      for (int d = 0; d < D1D; d++)
+      {
+         for (int q = 0; q < Q1D; q++)
+         {
+            r_B[q][d] = B(q,d);
+         }
+      }
+      MFEM_SHARED double s_D[MQ1][MQ1][MQ1];
+      MFEM_FOREACH_THREAD(k1,x,Q1D)
+      {
+         MFEM_FOREACH_THREAD(k2,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(k3,z,Q1D)
+            {
+               s_D[k1][k2][k3] = D(k1,k2,k3,e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(i1,x,D1D)
+      {
+         MFEM_FOREACH_THREAD(i2,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(i3,z,D1D)
+            {
+               for (int j1 = 0; j1 < D1D; ++j1)
+               {
+                  for (int j2 = 0; j2 < D1D; ++j2)
+                  {
+                     for (int j3 = 0; j3 < D1D; ++j3)
+                     {
+                        double val = 0.0;
+                        for (int k1 = 0; k1 < Q1D; ++k1)
+                        {
+                           for (int k2 = 0; k2 < Q1D; ++k2)
+                           {
+                              for (int k3 = 0; k3 < Q1D; ++k3)
+                              {
+                                 val += r_B[k1][i1] * r_B[k1][j1]
+                                        * r_B[k2][i2] * r_B[k2][j2]
+                                        * r_B[k3][i3] * r_B[k3][j3]
+                                        * s_D[k1][k2][k3];
+                              }
+                           }
+                        }
+                        M(i1, i2, i3, j1, j2, j3, e) = val;
+                     }
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
+void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
+                                Vector &ea_data)
+{
+   AssemblePA(fes);
+   const int ne = fes.GetMesh()->GetNE();
+   const Array<double> &B = maps->B;
+   if (dim == 1)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EAMassAssemble1D<2,2>(ne,B,pa_data,ea_data);
+         case 0x33: return EAMassAssemble1D<3,3>(ne,B,pa_data,ea_data);
+         case 0x44: return EAMassAssemble1D<4,4>(ne,B,pa_data,ea_data);
+         case 0x55: return EAMassAssemble1D<5,5>(ne,B,pa_data,ea_data);
+         case 0x66: return EAMassAssemble1D<6,6>(ne,B,pa_data,ea_data);
+         case 0x77: return EAMassAssemble1D<7,7>(ne,B,pa_data,ea_data);
+         case 0x88: return EAMassAssemble1D<8,8>(ne,B,pa_data,ea_data);
+         case 0x99: return EAMassAssemble1D<9,9>(ne,B,pa_data,ea_data);
+         default:   return EAMassAssemble1D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 2)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x22: return EAMassAssemble2D<2,2>(ne,B,pa_data,ea_data);
+         case 0x33: return EAMassAssemble2D<3,3>(ne,B,pa_data,ea_data);
+         case 0x44: return EAMassAssemble2D<4,4>(ne,B,pa_data,ea_data);
+         case 0x55: return EAMassAssemble2D<5,5>(ne,B,pa_data,ea_data);
+         case 0x66: return EAMassAssemble2D<6,6>(ne,B,pa_data,ea_data);
+         case 0x77: return EAMassAssemble2D<7,7>(ne,B,pa_data,ea_data);
+         case 0x88: return EAMassAssemble2D<8,8>(ne,B,pa_data,ea_data);
+         case 0x99: return EAMassAssemble2D<9,9>(ne,B,pa_data,ea_data);
+         default:   return EAMassAssemble2D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((dofs1D << 4 ) | quad1D)
+      {
+         case 0x23: return EAMassAssemble3D<2,3>(ne,B,pa_data,ea_data);
+         case 0x34: return EAMassAssemble3D<3,4>(ne,B,pa_data,ea_data);
+         case 0x45: return EAMassAssemble3D<4,5>(ne,B,pa_data,ea_data);
+         case 0x56: return EAMassAssemble3D<5,6>(ne,B,pa_data,ea_data);
+         case 0x67: return EAMassAssemble3D<6,7>(ne,B,pa_data,ea_data);
+         case 0x78: return EAMassAssemble3D<7,8>(ne,B,pa_data,ea_data);
+         case 0x89: return EAMassAssemble3D<8,9>(ne,B,pa_data,ea_data);
+         default:   return EAMassAssemble3D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+}

fem/bilininteg_transpose_ea.cpp

@@ -0,0 +1,103 @@
+// 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.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+
+namespace mfem
+{
+
+void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
+                                     Vector &ea_data)
+{
+   Vector ea_data_tmp(ea_data.Size());
+   ea_data_tmp = 0.0;
+   bfi->AssembleEA(fes, ea_data_tmp);
+   const int ne = fes.GetNE();
+   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);
+   MFEM_FORALL(e, ne,
+   {
+      for (int i = 0; i < dofs; i++)
+      {
+         for (int j = 0; j < dofs; j++)
+         {
+            const double a = A(i, j, e);
+            AT(j, i, e) += a;
+         }
+      }
+   });
+}
+
+void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
+                                                  Vector &ea_data_int,
+                                                  Vector &ea_data_ext)
+{
+   const int nf = fes.GetNFbyType(FaceType::Interior);
+   if (nf == 0) { return; }
+   Vector ea_data_int_tmp(ea_data_int.Size());
+   Vector ea_data_ext_tmp(ea_data_ext.Size());
+   ea_data_int_tmp = 0.0;
+   ea_data_ext_tmp = 0.0;
+   bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp);
+   const int faceDofs = fes.GetTraceElement(0,
+                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+   auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
+   auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
+   auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
+   auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
+   MFEM_FORALL(f, nf,
+   {
+      for (int i = 0; i < faceDofs; i++)
+      {
+         for (int j = 0; j < faceDofs; j++)
+         {
+            const double a_int0 = A_int(i, j, 0, f);
+            const double a_int1 = A_int(i, j, 1, f);
+            const double a_ext0 = A_ext(i, j, 0, f);
+            const double a_ext1 = A_ext(i, j, 1, f);
+            AT_int(j, i, 0, f) += a_int0;
+            AT_int(j, i, 1, f) += a_int1;
+            AT_ext(j, i, 0, f) += a_ext1;
+            AT_ext(j, i, 1, f) += a_ext0;
+         }
+      }
+   });
+}
+
+void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
+                                                  Vector &ea_data_bdr)
+{
+   const int nf = fes.GetNFbyType(FaceType::Boundary);
+   if (nf == 0) { return; }
+   Vector ea_data_bdr_tmp(ea_data_bdr.Size());
+   ea_data_bdr_tmp = 0.0;
+   bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp);
+   const int faceDofs = fes.GetTraceElement(0,
+                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+   auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
+   auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
+   MFEM_FORALL(f, nf,
+   {
+      for (int i = 0; i < faceDofs; i++)
+      {
+         for (int j = 0; j < faceDofs; j++)
+         {
+            const double a_bdr = A_bdr(i, j, f);
+            AT_bdr(j, i, f) += a_bdr;
+         }
+      }
+   });
+}
+
+}

fem/bilininteg_vectorfe.cpp

@@ -0,0 +1,379 @@
+// 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.
+
+#include "bilininteg.hpp"
+
+namespace mfem
+{
+
+void PAHcurlSetup2D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    const Vector &j,
+                    Vector &_coeff,
+                    Vector &op);
+
+void PAHcurlSetup3D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    const Vector &j,
+                    Vector &_coeff,
+                    Vector &op);
+
+void PAHcurlMassAssembleDiagonal2D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &_Bo,
+                                   const Array<double> &_Bc,
+                                   const Vector &_op,
+                                   Vector &_diag);
+
+void PAHcurlMassAssembleDiagonal3D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &_Bo,
+                                   const Array<double> &_Bc,
+                                   const Vector &_op,
+                                   Vector &_diag);
+
+void PAHcurlMassApply2D(const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &_Bo,
+                        const Array<double> &_Bc,
+                        const Array<double> &_Bot,
+                        const Array<double> &_Bct,
+                        const Vector &_op,
+                        const Vector &_x,
+                        Vector &_y);
+
+void PAHcurlMassApply3D(const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &_Bo,
+                        const Array<double> &_Bc,
+                        const Array<double> &_Bot,
+                        const Array<double> &_Bct,
+                        const Vector &_op,
+                        const Vector &_x,
+                        Vector &_y);
+
+void PAHdivSetup2D(const int Q1D,
+                   const int NE,
+                   const Array<double> &w,
+                   const Vector &j,
+                   Vector &_coeff,
+                   Vector &op);
+
+void PAHdivSetup3D(const int Q1D,
+                   const int NE,
+                   const Array<double> &w,
+                   const Vector &j,
+                   Vector &_coeff,
+                   Vector &op);
+
+void PAHcurlH1Apply2D(const int D1D,
+                      const int Q1D,
+                      const int NE,
+                      const Array<double> &_Bc,
+                      const Array<double> &_Gc,
+                      const Array<double> &_Bot,
+                      const Array<double> &_Bct,
+                      const Vector &_op,
+                      const Vector &_x,
+                      Vector &_y);
+
+void PAHcurlH1Apply3D(const int D1D,
+                      const int Q1D,
+                      const int NE,
+                      const Array<double> &_Bc,
+                      const Array<double> &_Gc,
+                      const Array<double> &_Bot,
+                      const Array<double> &_Bct,
+                      const Vector &_op,
+                      const Vector &_x,
+                      Vector &_y);
+
+void PAHdivMassAssembleDiagonal2D(const int D1D,
+                                  const int Q1D,
+                                  const int NE,
+                                  const Array<double> &_Bo,
+                                  const Array<double> &_Bc,
+                                  const Vector &_op,
+                                  Vector &_diag);
+
+void PAHdivMassAssembleDiagonal3D(const int D1D,
+                                  const int Q1D,
+                                  const int NE,
+                                  const Array<double> &_Bo,
+                                  const Array<double> &_Bc,
+                                  const Vector &_op,
+                                  Vector &_diag);
+
+void PAHdivMassApply2D(const int D1D,
+                       const int Q1D,
+                       const int NE,
+                       const Array<double> &_Bo,
+                       const Array<double> &_Bc,
+                       const Array<double> &_Bot,
+                       const Array<double> &_Bct,
+                       const Vector &_op,
+                       const Vector &_x,
+                       Vector &_y);
+
+void PAHdivMassApply3D(const int D1D,
+                       const int Q1D,
+                       const int NE,
+                       const Array<double> &_Bo,
+                       const Array<double> &_Bc,
+                       const Array<double> &_Bot,
+                       const Array<double> &_Bct,
+                       const Vector &_op,
+                       const Vector &_x,
+                       Vector &_y);
+
+void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
+{
+   // Assumes tensor-product elements
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fel = fes.GetFE(0);
+
+   const VectorTensorFiniteElement *el =
+      dynamic_cast<const VectorTensorFiniteElement*>(fel);
+   MFEM_VERIFY(el != NULL, "Only VectorTensorFiniteElement is supported!");
+
+   const IntegrationRule *ir
+      = IntRule ? IntRule : &MassIntegrator::GetRule(*el, *el,
+                                                     *mesh->GetElementTransformation(0));
+   const int dims = el->GetDim();
+   MFEM_VERIFY(dims == 2 || dims == 3, "");
+
+   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
+   const int nq = ir->GetNPoints();
+   dim = mesh->Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "");
+
+   ne = fes.GetNE();
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsO = &el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   dofs1D = mapsC->ndof;
+   quad1D = mapsC->nqpt;
+
+   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
+
+   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+
+   Vector coeff(ne * nq);
+   coeff = 1.0;
+   if (Q)
+   {
+      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));
+         }
+      }
+   }
+
+   fetype = el->GetDerivType();
+
+   if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
+   {
+      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+                     coeff, pa_data);
+   }
+   else if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
+   {
+      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+                     coeff, pa_data);
+   }
+   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
+   {
+      PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+                    coeff, pa_data);
+   }
+   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 2)
+   {
+      PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+                    coeff, pa_data);
+   }
+   else
+   {
+      MFEM_ABORT("Unknown kernel.");
+   }
+}
+
+void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
+{
+   if (dim == 3)
+   {
+      if (fetype == mfem::FiniteElement::CURL)
+      {
+         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne,
+                                       mapsO->B, mapsC->B, pa_data, diag);
+      }
+      else if (fetype == mfem::FiniteElement::DIV)
+      {
+         PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne,
+                                      mapsO->B, mapsC->B, pa_data, diag);
+      }
+      else
+      {
+         MFEM_ABORT("Unknown kernel.");
+      }
+   }
+   else
+   {
+      if (fetype == mfem::FiniteElement::CURL)
+      {
+         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne,
+                                       mapsO->B, mapsC->B, pa_data, diag);
+      }
+      else if (fetype == mfem::FiniteElement::DIV)
+      {
+         PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne,
+                                      mapsO->B, mapsC->B, pa_data, diag);
+      }
+      else
+      {
+         MFEM_ABORT("Unknown kernel.");
+      }
+   }
+}
+
+void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   if (dim == 3)
+   {
+      if (fetype == mfem::FiniteElement::CURL)
+      {
+         PAHcurlMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
+                            mapsC->Bt, pa_data, x, y);
+      }
+      else if (fetype == mfem::FiniteElement::DIV)
+      {
+         PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
+                           mapsC->Bt, pa_data, x, y);
+      }
+      else
+      {
+         MFEM_ABORT("Unknown kernel.");
+      }
+   }
+   else
+   {
+      if (fetype == mfem::FiniteElement::CURL)
+      {
+         PAHcurlMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
+                            mapsC->Bt, pa_data, x, y);
+      }
+      else if (fetype == mfem::FiniteElement::DIV)
+      {
+         PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
+                           mapsC->Bt, pa_data, x, y);
+      }
+      else
+      {
+         MFEM_ABORT("Unknown kernel.");
+      }
+   }
+}
+
+void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
+                                               &trial_fes,
+                                               const FiniteElementSpace &test_fes)
+{
+   // Assumes tensor-product elements, with a vector test space and H^1 trial space.
+   Mesh *mesh = trial_fes.GetMesh();
+   const FiniteElement *trial_fel = trial_fes.GetFE(0);
+   const FiniteElement *test_fel = test_fes.GetFE(0);
+
+   const NodalTensorFiniteElement *trial_el =
+      dynamic_cast<const NodalTensorFiniteElement*>(trial_fel);
+   MFEM_VERIFY(trial_el != NULL, "Only NodalTensorFiniteElement is supported!");
+
+   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(*trial_el, *trial_el,
+                                                     *mesh->GetElementTransformation(0));
+   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
+   const int nq = ir->GetNPoints();
+   dim = mesh->Dimension();
+   MFEM_VERIFY(dim == 2 || dim == 3, "");
+
+   MFEM_VERIFY(trial_el->GetOrder() == test_el->GetOrder(), "");
+
+   ne = trial_fes.GetNE();
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   mapsC = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsO = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   dofs1D = mapsC->ndof;
+   quad1D = mapsC->nqpt;
+
+   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
+
+   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+
+   Vector coeff(ne * nq);
+   coeff = 1.0;
+   if (Q)
+   {
+      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));
+         }
+      }
+   }
+
+   // Use the same setup functions as VectorFEMassIntegrator.
+   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
+   {
+      PAHcurlSetup3D(quad1D, 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,
+                     coeff, pa_data);
+   }
+   else
+   {
+      MFEM_ABORT("Unknown kernel.");
+   }
+}
+
+void MixedVectorGradientIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   if (dim == 3)
+      PAHcurlH1Apply3D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
+                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
+   else if (dim == 2)
+      PAHcurlH1Apply2D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
+                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
+   else
+   {
+      MFEM_ABORT("Unsupported dimension!");
+   }
+}
+
+} // namespace mfem

fem/coefficient.cpp

@@ -49,7 +49,7 @@ double FunctionCoefficient::Eval(ElementTransformation & T,
 double GridFunctionCoefficient::Eval (ElementTransformation &T,
                                       const IntegrationPoint &ip)
 {
-   return GridF -> GetValue (T.ElementNo, ip, Component);
+   return GridF -> GetValue (T, ip, Component);
 }
 
 double TransformedCoefficient::Eval(ElementTransformation &T,
@@ -160,13 +160,13 @@ void VectorArrayCoefficient::Eval(Vector &V, ElementTransformation &T,
 }
 
 VectorGridFunctionCoefficient::VectorGridFunctionCoefficient (
-   GridFunction *gf)
+   const GridFunction *gf)
    : VectorCoefficient ((gf) ? gf -> VectorDim() : 0)
 {
    GridFunc = gf;
 }
 
-void VectorGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+void VectorGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
 {
    GridFunc = gf; vdim = (gf) ? gf -> VectorDim() : 0;
 }
@@ -174,24 +174,7 @@ void VectorGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
 void VectorGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
                                          const IntegrationPoint &ip)
 {
-   Mesh *mesh = GridFunc->FESpace()->GetMesh();
-   if (mesh->Dimension() == T.GetDimension())
-   {
-      GridFunc->GetVectorValue(T.ElementNo, ip, V);
-   }
-   else // Assuming T is a boundary element transformation
-   {
-      int el_id, el_info;
-      mesh->GetBdrElementAdjacentElement(T.ElementNo, el_id, el_info);
-      IntegrationPointTransformation loc_T;
-      mesh->GetLocalFaceTransformation(mesh->GetBdrElementType(T.ElementNo),
-                                       mesh->GetElementType(el_id),
-                                       loc_T.Transf,
-                                       el_info);
-      IntegrationPoint eip;
-      loc_T.Transform(ip, eip);
-      GridFunc->GetVectorValue(el_id, eip, V);
-   }
+   GridFunc->GetVectorValue(T, ip, V);
 }
 
 void VectorGridFunctionCoefficient::Eval(
@@ -201,14 +184,14 @@ void VectorGridFunctionCoefficient::Eval(
 }
 
 GradientGridFunctionCoefficient::GradientGridFunctionCoefficient (
-   GridFunction *gf)
+   const GridFunction *gf)
    : VectorCoefficient((gf) ?
                        gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
 {
    GridFunc = gf;
 }
 
-void GradientGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+void GradientGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
 {
    GridFunc = gf; vdim = (gf) ?
                          gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
@@ -227,14 +210,14 @@ void GradientGridFunctionCoefficient::Eval(
 }
 
 CurlGridFunctionCoefficient::CurlGridFunctionCoefficient (
-   GridFunction *gf)
+   const GridFunction *gf)
    : VectorCoefficient ((gf) ?
                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
 {
    GridFunc = gf;
 }
 
-void CurlGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+void CurlGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
 {
    GridFunc = gf; vdim = (gf) ?
                          gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
@@ -247,7 +230,7 @@ void CurlGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
 }
 
 DivergenceGridFunctionCoefficient::DivergenceGridFunctionCoefficient (
-   GridFunction *gf) : Coefficient()
+   const GridFunction *gf) : Coefficient()
 {
    GridFunc = gf;
 }
@@ -302,6 +285,22 @@ void VectorRestrictedCoefficient::Eval(
    }
 }
 
+void UnitNormalCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                 const IntegrationPoint &ip)
+{
+   V.SetSize(vdim);
+   V = 0.0;
+
+   const DenseMatrix & J = T.Jacobian();
+   if (J.Width() == J.Height() - 1)
+   {
+      CalcOrtho(J, V);
+      double norm = V.Norml2();
+      MFEM_ASSERT(norm > 0.0, "Length of normal vector is non-positive!");
+      V /= norm;
+   }
+}
+
 void MatrixFunctionCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
                                      const IntegrationPoint &ip)
 {
@@ -775,4 +774,61 @@ double ComputeGlobalLpNorm(double p, VectorCoefficient &coeff, ParMesh &pmesh,
 }
 #endif
 
+VectorQuadratureFunctionCoefficient::VectorQuadratureFunctionCoefficient(
+   QuadratureFunction &qf)
+   : VectorCoefficient(qf.GetVDim()), QuadF(qf), index(0) { }
+
+void VectorQuadratureFunctionCoefficient::SetComponent(int _index, int _length)
+{
+   MFEM_VERIFY(_index >= 0, "Index must be >= 0");
+   MFEM_VERIFY(_index < QuadF.GetVDim(),
+               "Index must be < QuadratureFunction length");
+   index = _index;
+
+   MFEM_VERIFY(_length > 0, "Length must be > 0");
+   MFEM_VERIFY(_length <= QuadF.GetVDim() - index,
+               "Length must be <= (QuadratureFunction length - index)");
+
+   vdim = _length;
+}
+
+void VectorQuadratureFunctionCoefficient::Eval(Vector &V,
+                                               ElementTransformation &T,
+                                               const IntegrationPoint &ip)
+{
+   QuadF.HostRead();
+
+   if (index == 0 && vdim == QuadF.GetVDim())
+   {
+      QuadF.GetElementValues(T.ElementNo, ip.index, V);
+   }
+   else
+   {
+      Vector temp;
+      QuadF.GetElementValues(T.ElementNo, ip.index, temp);
+      V.SetSize(vdim);
+      for (int i = 0; i < vdim; i++)
+      {
+         V(i) = temp(index + i);
+      }
+   }
+
+   return;
+}
+
+QuadratureFunctionCoefficient::QuadratureFunctionCoefficient(
+   QuadratureFunction &qf) : QuadF(qf)
+{
+   MFEM_VERIFY(qf.GetVDim() == 1, "QuadratureFunction's vdim must be 1");
+}
+
+double QuadratureFunctionCoefficient::Eval(ElementTransformation &T,
+                                           const IntegrationPoint &ip)
+{
+   QuadF.HostRead();
+   Vector temp(1);
+   QuadF.GetElementValues(T.ElementNo, ip.index, temp);
+   return temp[0];
+}
+
 }

fem/datacollection.cpp

@@ -739,12 +739,6 @@ ParaViewDataCollection::ParaViewDataCollection(const std::string&
 #endif
 }
 
-void ParaViewDataCollection::RegisterField(const std::string& field_name,
-                                           mfem::GridFunction *gf)
-{
-   DataCollection::RegisterField(field_name,gf);
-}
-
 void ParaViewDataCollection::SetLevelsOfDetail(int levels_of_detail_)
 {
    levels_of_detail = levels_of_detail_;
@@ -815,7 +809,7 @@ void ParaViewDataCollection::Save()
    // the directory is created
 
    // create pvd file if needed
-   if (!pvd_stream.is_open())
+   if (myid == 0 && !pvd_stream.is_open())
    {
       std::string dpath=GenerateCollectionPath();
       std::string pvdname=dpath+"/"+GeneratePVDFileName();

fem/datacollection.hpp

@@ -501,10 +501,6 @@ public:
    ParaViewDataCollection(const std::string& collection_name,
                           mfem::Mesh *mesh_ = NULL);
 
-   /// Add a grid function to the collection
-   virtual void RegisterField(const std::string& field_name,
-                              mfem::GridFunction *gf) override;
-
    /// Set refinement levels - every element is uniformly split based on
    /// levels_of_detail_
    void SetLevelsOfDetail(int levels_of_detail_);

fem/eltrans.cpp

@@ -19,6 +19,7 @@ namespace mfem
 ElementTransformation::ElementTransformation()
    : IntPoint(static_cast<IntegrationPoint *>(NULL)),
      EvalState(0),
+     geom(Geometry::INVALID),
      Attribute(-1),
      ElementNo(-1)
 { }
@@ -551,4 +552,76 @@ void IntegrationPointTransformation::Transform (const IntegrationRule &ir1,
    }
 }
 
+void FaceElementTransformations::SetIntPoint(const IntegrationPoint *ip)
+{
+   IsoparametricTransformation::SetIntPoint(ip);
+
+   if (Elem1)
+   {
+      Loc1.Transform(*ip, eip1);
+      Elem1->SetIntPoint(&eip1);
+   }
+   if (Elem2)
+   {
+      Loc2.Transform(*ip, eip2);
+      Elem2->SetIntPoint(&eip2);
+   }
+}
+
+ElementTransformation &
+FaceElementTransformations::GetElement1Transformation()
+{
+   MFEM_VERIFY(mask & 1 && Elem1 != NULL, "The ElementTransformation "
+               "for the element has not been configured for side 1.");
+   return *Elem1;
+}
+
+ElementTransformation &
+FaceElementTransformations::GetElement2Transformation()
+{
+   MFEM_VERIFY(mask & 2 && Elem2 != NULL, "The ElementTransformation "
+               "for the element has not been configured for side 2.");
+   return *Elem2;
+}
+
+IntegrationPointTransformation &
+FaceElementTransformations::GetIntPoint1Transformation()
+{
+   MFEM_VERIFY(mask & 4, "The IntegrationPointTransformation "
+               "for the element has not been configured for side 1.");
+   return Loc1;
+}
+
+IntegrationPointTransformation &
+FaceElementTransformations::GetIntPoint2Transformation()
+{
+   MFEM_VERIFY(mask & 8, "The IntegrationPointTransformation "
+               "for the element has not been configured for side 2.");
+   return Loc2;
+}
+
+void FaceElementTransformations::Transform(const IntegrationPoint &ip,
+                                           Vector &trans)
+{
+   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+               "for the face has not been configured.");
+   IsoparametricTransformation::Transform(ip, trans);
+}
+
+void FaceElementTransformations::Transform(const IntegrationRule &ir,
+                                           DenseMatrix &tr)
+{
+   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+               "for the face has not been configured.");
+   IsoparametricTransformation::Transform(ir, tr);
+}
+
+void FaceElementTransformations::Transform(const DenseMatrix &matrix,
+                                           DenseMatrix &result)
+{
+   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+               "for the face has not been configured.");
+   IsoparametricTransformation::Transform(matrix, result);
+}
+
 }

fem/eltrans.hpp

@@ -38,9 +38,12 @@ protected:
    };
    Geometry::Type geom;
 
-   // Evaluate the Jacobian of the transformation at the IntPoint and store it
-   // in dFdx.
+   /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
+       store it in dFdx. */
    virtual const DenseMatrix &EvalJacobian() = 0;
+
+   /** @brief Evaluate the Hessian of the transformation at the IntPoint and
+       store it in d2Fdx2. */
    virtual const DenseMatrix &EvalHessian() = 0;
 
    double EvalWeight();
@@ -48,18 +51,53 @@ protected:
    const DenseMatrix &EvalInverseJ();
 
 public:
-   int Attribute, ElementNo;
+
+   /** This enumeration declares the values stored in
+       ElementTransformation::ElementType and indicates which group of objects
+       the index stored in ElementTransformation::ElementNo refers:
+
+       | ElementType | Range of ElementNo
+       +-------------+-------------------------
+       | ELEMENT     | [0, Mesh::GetNE()     )
+       | BDR_ELEMENT | [0, Mesh::GetNBE()    )
+       | EDGE        | [0, Mesh::GetNEdges() )
+       | FACE        | [0, Mesh::GetNFaces() )
+       | BDR_FACE    | [0, Mesh::GetNBE()    )
+   */
+   enum
+   {
+      ELEMENT     = 1,
+      BDR_ELEMENT = 2,
+      EDGE        = 3,
+      FACE        = 4,
+      BDR_FACE    = 5
+   };
+
+   int Attribute, ElementNo, ElementType;
 
    ElementTransformation();
 
+   /** @brief Set the integration point @a ip that weights and Jacobians will
+       be evaluated at. */
    void SetIntPoint(const IntegrationPoint *ip)
    { IntPoint = ip; EvalState = 0; }
+
+   /** @brief Get a const reference to the currently set integration point.  This
+       will return NULL if no integration point is set. */
    const IntegrationPoint &GetIntPoint() { return *IntPoint; }
 
+   /** @brief Transform integration point from reference coordinates to
+       physical coordinates and store them in the vector. */
    virtual void Transform(const IntegrationPoint &, Vector &) = 0;
+
+   /** @brief Transform all the integration points from the integration rule
+       from reference coordinates to physical
+       coordinates and store them as column vectors in the matrix. */
    virtual void Transform(const IntegrationRule &, DenseMatrix &) = 0;
 
-   /// Transform columns of 'matrix', store result in 'result'.
+   /** @brief Transform all the integration points from the column vectors
+       of @a matrix from reference coordinates to physical
+       coordinates and store them as column vectors in @a result. */
    virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result) = 0;
 
    /** @brief Return the Jacobian matrix of the transformation at the currently
@@ -70,27 +108,44 @@ public:
    const DenseMatrix &Jacobian()
    { return (EvalState & JACOBIAN_MASK) ? dFdx : EvalJacobian(); }
 
+
+   /** @brief Return the Hessian matrix of the transformation at the currently
+       set IntegrationPoint, using the method SetIntPoint(). */
    const DenseMatrix &Hessian()
    { return (EvalState & HESSIAN_MASK) ? d2Fdx2 : EvalHessian(); }
 
+   /** @brief Return the weight of the Jacobian matrix of the transformation
+       at the currently set IntegrationPoint.
+       The Weight evaluates to \f$ \sqrt{\lvert J^T J \rvert} \f$. */
    double Weight() { return (EvalState & WEIGHT_MASK) ? Wght : EvalWeight(); }
 
+   /** @brief Return the adjugate of the Jacobian matrix of the transformation
+        at the currently set IntegrationPoint. */
    const DenseMatrix &AdjugateJacobian()
    { return (EvalState & ADJUGATE_MASK) ? adjJ : EvalAdjugateJ(); }
 
+   /** @brief Return the inverse of the Jacobian matrix of the transformation
+        at the currently set IntegrationPoint. */
    const DenseMatrix &InverseJacobian()
    { return (EvalState & INVERSE_MASK) ? invJ : EvalInverseJ(); }
 
+   /// Return the order of the current element we are using for the transformation.
    virtual int Order() const = 0;
+
+   /// Return the order of the elements of the Jacobian of the transformation.
    virtual int OrderJ() const = 0;
+
+   /** @brief Return the order of the determinant of the Jacobian (weight)
+       of the transformation. */
    virtual int OrderW() const = 0;
-   /// Order of adj(J)^t.grad(fi)
+
+   /// Return the order of \f$ adj(J)^T \nabla fi \f$
    virtual int OrderGrad(const FiniteElement *fe) const = 0;
 
    /// Return the Geometry::Type of the reference element.
    Geometry::Type GetGeometryType() const { return geom; }
 
-   /// Return the dimension of the reference element.
+   /// Return the topological dimension of the reference element.
    int GetDimension() const { return Geometry::Dimension[geom]; }
 
    /// Get the dimension of the target (physical) space.
@@ -286,7 +341,7 @@ public:
    virtual int Transform(const Vector &pt, IntegrationPoint &ip);
 };
 
-
+/// A standard isoparametric element transformation
 class IsoparametricTransformation : public ElementTransformation
 {
 private:
@@ -296,26 +351,29 @@ private:
    const FiniteElement *FElem;
    DenseMatrix PointMat; // dim x dof
 
-   // Evaluate the Jacobian of the transformation at the IntPoint and store it
-   // in dFdx.
+   /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
+       store it in dFdx. */
    virtual const DenseMatrix &EvalJacobian();
    // Evaluate the Hessian of the transformation at the IntPoint and store it
    // in d2Fdx2.
    virtual const DenseMatrix &EvalHessian();
 public:
+   /// Set the element that will be used to compute the transformations
    void SetFE(const FiniteElement *FE) { FElem = FE; geom = FE->GetGeomType(); }
+
+   /// Get the current element used to compute the transformations
    const FiniteElement* GetFE() const { return FElem; }
 
    /// @brief Set the underlying point matrix describing the transformation.
    /** The dimensions of the matrix are space-dim x dof. The transformation is
        defined as
+           \f$ x = F( \hat x ) = P \phi( \hat x ) \f$
 
-           x = F(xh) = P . phi(xh),
-
-       where xh (x hat) is the reference point, x is the corresponding physical
-       point, P is the point matrix, and phi(xh) is the column-vector of all
-       basis functions evaluated at xh. The columns of P represent the control
-       points in physical space defining the transformation. */
+       where \f$ \hat x \f$  is the reference point, @a x is the corresponding
+       physical point, @a P is the point matrix, and \f$ \phi( \hat x ) \f$ is
+       the column-vector of all basis functions evaluated at \f$ \hat x \f$ .
+       The columns of @a P represent the control points in physical space
+       defining the transformation. */
    void SetPointMat(const DenseMatrix &pm) { PointMat = pm; }
 
    /// Return the stored point matrix.
@@ -324,19 +382,44 @@ public:
    /// Write access to the stored point matrix. Use with caution.
    DenseMatrix &GetPointMat() { return PointMat; }
 
+   /// Set the FiniteElement Geometry for the reference elements being used.
    void SetIdentityTransformation(Geometry::Type GeomType);
 
+   /** @brief Transform integration point from reference coordinates to
+       physical coordinates and store them in the vector. */
    virtual void Transform(const IntegrationPoint &, Vector &);
+
+   /** @brief Transform all the integration points from the integration rule
+       from reference coordinates to physical
+      coordinates and store them as column vectors in the matrix. */
    virtual void Transform(const IntegrationRule &, DenseMatrix &);
+
+   /** @brief Transform all the integration points from the column vectors
+       of @a matrix from reference coordinates to physical
+       coordinates and store them as column vectors in @a result. */
    virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
 
+   /// Return the order of the current element we are using for the transformation.
    virtual int Order() const { return FElem->GetOrder(); }
+
+   /// Return the order of the elements of the Jacobian of the transformation.
    virtual int OrderJ() const;
+
+   /** @brief Return the order of the determinant of the Jacobian (weight)
+       of the transformation. */
    virtual int OrderW() const;
+
+   /// Return the order of \f$ adj(J)^T \nabla fi \f$
    virtual int OrderGrad(const FiniteElement *fe) const;
 
    virtual int GetSpaceDim() const { return PointMat.Height(); }
 
+   /** @brief Transform a point @a pt from physical space to a point @a ip in
+       reference space. */
+   /** Attempt to find the IntegrationPoint that is transformed into the given
+       point in physical space. If the inversion fails a non-zero value is
+       returned. This method is not 100 percent reliable for non-linear
+       transformations. */
    virtual int TransformBack(const Vector & v, IntegrationPoint & ip)
    {
       InverseElementTransformation inv_tr(this);
@@ -356,15 +439,62 @@ public:
    void Transform (const IntegrationRule  &, IntegrationRule  &);
 };
 
-class FaceElementTransformations
+
+class FaceElementTransformations : public IsoparametricTransformation
 {
+private:
+   int mask;
+
+   IntegrationPoint eip1, eip2;
+
 public:
-   int Elem1No, Elem2No, FaceGeom;
-   ElementTransformation *Elem1, *Elem2, *Face;
+   int Elem1No, Elem2No;
+   Geometry::Type &FaceGeom; ///< @deprecated Use GetGeometryType instead
+   ElementTransformation *Elem1, *Elem2;
+   ElementTransformation *Face; ///< @deprecated No longer necessary
    IntegrationPointTransformation Loc1, Loc2;
+
+   FaceElementTransformations() : FaceGeom(geom), Face(this) {}
+
+   /** @brief Method to set the geometry type of the face.
+
+       @note This method is designed to be used when
+       [Par]Mesh::GetFaceTransformation will not be called i.e. when the face
+       transformation will not be needed but the neighboring element
+       transformations will be.  Using this method to override the GeometryType
+       should only be done with great care.
+   */
+   void SetGeometryType(Geometry::Type g) { geom = g; }
+
+   /// Set the mask indicating which portions of the object have been setup
+   /** The argument @a m is a bitmask used in
+       Mesh::GetFaceElementTransformations to indicate which portions of the
+       FaceElement Transformations object have been configured.
+
+       mask &  1: Elem1 is configured
+       mask &  2: Elem2 is configured
+       mask &  4: Loc1 is configured
+       mask &  8: Loc2 is configured
+       mask & 16: The Face transformation itself is configured
+   */
+   void SetConfigurationMask(int m) { mask = m; }
+   int  GetConfigurationMask() const { return mask; }
+
+   /** @brief Set the integration point in the Face and the two neighboring
+       elements, if present. */
+   void SetIntPoint(const IntegrationPoint *ip);
+
+   virtual void Transform(const IntegrationPoint &, Vector &);
+   virtual void Transform(const IntegrationRule &, DenseMatrix &);
+   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
+
+   ElementTransformation & GetElement1Transformation();
+   ElementTransformation & GetElement2Transformation();
+   IntegrationPointTransformation & GetIntPoint1Transformation();
+   IntegrationPointTransformation & GetIntPoint2Transformation();
 };
 
-/*                 Elem1(Loc1(x)) = Face(x) = Elem2(Loc2(x))
+/**                Elem1(Loc1(x)) = Face(x) = Elem2(Loc2(x))
 
 
                                 Physical Space

fem/estimators.cpp

@@ -50,4 +50,21 @@ void L2ZienkiewiczZhuEstimator::ComputeEstimates()
 
 #endif // MFEM_USE_MPI
 
+void LpErrorEstimator::ComputeEstimates()
+{
+   MFEM_VERIFY(coef != NULL || vcoef != NULL,
+               "LpErrorEstimator has no coefficient!  Call SetCoef first.");
+
+   error_estimates.SetSize(sol->FESpace()->GetMesh()->GetNE());
+   if (coef)
+   {
+      sol->ComputeElementLpErrors(local_norm_p, *coef, error_estimates);
+   }
+   else
+   {
+      sol->ComputeElementLpErrors(local_norm_p, *vcoef, error_estimates);
+   }
+   current_sequence = sol->FESpace()->GetMesh()->GetSequence();
+}
+
 } // namespace mfem

fem/estimators.hpp

@@ -45,6 +45,7 @@ public:
    /// Force recomputation of the estimates on the next call to GetLocalErrors.
    virtual void Reset() = 0;
 
+   /// Destruct the error estimator
    virtual ~ErrorEstimator() { }
 };
 
@@ -66,6 +67,14 @@ public:
 /** @brief The ZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu
     error estimation procedure.
 
+    Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery
+    and a posteriori error estimates. Part 1: The recovery technique.
+    Int. J. Num. Meth. Engng. 33, 1331-1364 (1992).
+
+    Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery
+    and a posteriori error estimates. Part 2: Error estimates and adaptivity.
+    Int. J. Num. Meth. Engng. 33, 1365-1382 (1992).
+
     The required BilinearFormIntegrator must implement the methods
     ComputeElementFlux() and ComputeFluxEnergy().
  */
@@ -217,6 +226,7 @@ protected:
       class when needed.*/
    bool own_flux_fes; ///< Ownership flag for flux_space and smooth_flux_space.
 
+   /// Initialize with the integrator, solution, and flux finite element spaces.
    void Init(BilinearFormIntegrator &integ,
              ParGridFunction &sol,
              ParFiniteElementSpace *flux_fes,
@@ -304,6 +314,88 @@ public:
 
 #endif // MFEM_USE_MPI
 
+/** @brief The LpErrorEstimator class compares the solution to a known
+    coefficient.
+
+    This class can be used, for example, to adapt a mesh to a non-trivial
+    initial condition in a time-dependent simulation. It can also be used to
+    force refinement in the neighborhood of small features before switching to a
+    more traditional error estimator.
+
+    The LpErrorEstimator supports either scalar or vector coefficients and works
+    both in serial and in parallel.
+*/
+class LpErrorEstimator : public ErrorEstimator
+{
+protected:
+   long current_sequence;
+   int local_norm_p;
+   Vector error_estimates;
+
+   Coefficient * coef;
+   VectorCoefficient * vcoef;
+   GridFunction * sol;
+
+   /// Check if the mesh of the solution was modified.
+   bool MeshIsModified()
+   {
+      long mesh_sequence = sol->FESpace()->GetMesh()->GetSequence();
+      MFEM_ASSERT(mesh_sequence >= current_sequence, "");
+      return (mesh_sequence > current_sequence);
+   }
+
+   /// Compute the element error estimates.
+   void ComputeEstimates();
+
+public:
+   /** @brief Construct a new LpErrorEstimator object for a scalar field.
+       @param p    Integer which selects which Lp norm to use.
+       @param sol  The GridFunction representation of the scalar field.
+       Note: the coefficient must be set before use with the SetCoef method.
+   */
+   LpErrorEstimator(int p, GridFunction &sol)
+      : current_sequence(-1), local_norm_p(p),
+        error_estimates(0), coef(NULL), vcoef(NULL), sol(&sol) { }
+
+   /** @brief Construct a new LpErrorEstimator object for a scalar field.
+       @param p    Integer which selects which Lp norm to use.
+       @param coef The scalar Coefficient to compare to the solution.
+       @param sol  The GridFunction representation of the scalar field.
+   */
+   LpErrorEstimator(int p, Coefficient &coef, GridFunction &sol)
+      : current_sequence(-1), local_norm_p(p),
+        error_estimates(0), coef(&coef), vcoef(NULL), sol(&sol) { }
+
+   /** @brief Construct a new LpErrorEstimator object for a vector field.
+       @param p    Integer which selects which Lp norm to use.
+       @param coef The vector VectorCoefficient to compare to the solution.
+       @param sol  The GridFunction representation of the vector field.
+   */
+   LpErrorEstimator(int p, VectorCoefficient &coef, GridFunction &sol)
+      : current_sequence(-1), local_norm_p(p),
+        error_estimates(0), coef(NULL), vcoef(&coef), sol(&sol) { }
+
+   /** @brief Set the exponent, p, of the Lp norm used for computing the local
+       element errors. */
+   void SetLocalErrorNormP(int p) { local_norm_p = p; }
+
+   void SetCoef(Coefficient &A) { coef = &A; }
+   void SetCoef(VectorCoefficient &A) { vcoef = &A; }
+
+   /// Reset the error estimator.
+   virtual void Reset() { current_sequence = -1; }
+
+   /// Get a Vector with all element errors.
+   virtual const Vector &GetLocalErrors()
+   {
+      if (MeshIsModified()) { ComputeEstimates(); }
+      return error_estimates;
+   }
+
+   /// Destructor
+   virtual ~LpErrorEstimator() {}
+};
+
 } // namespace mfem
 
 #endif // MFEM_ERROR_ESTIMATORS

fem/fe_coll.cpp

@@ -311,10 +311,10 @@ GetEdge(int &nv, v_t &v, int &ne, int &e, int &eo, const int edge_info)
    eo = edge_info%64;
    MFEM_ASSERT(0 <= e && e < g_consts::NumEdges, "");
    MFEM_ASSERT(0 <= eo && eo < e_consts::NumOrient, "");
-   v[0] = g_consts::Edges[e][0];
-   v[1] = g_consts::Edges[e][1];
-   v[0] = e_consts::Orient[eo][v[0]];
-   v[1] = e_consts::Orient[eo][v[1]];
+   v[0] = e_consts::Orient[eo][0];
+   v[1] = e_consts::Orient[eo][1];
+   v[0] = g_consts::Edges[e][v[0]];
+   v[1] = g_consts::Edges[e][v[1]];
 }
 
 template <Geometry::Type geom, Geometry::Type f_geom,

fem/fe_coll.hpp

@@ -19,10 +19,10 @@
 namespace mfem
 {
 
-/** Collection of finite elements from the same family in multiple dimensions.
-    This class is used to match the degrees of freedom of a FiniteElementSpace
-    between elements, and to provide the finite element restriction from an
-    element to its boundary. */
+/** @brief Collection of finite elements from the same family in multiple
+    dimensions. This class is used to match the degrees of freedom of a
+    FiniteElementSpace between elements, and to provide the finite element
+    restriction from an element to its boundary. */
 class FiniteElementCollection
 {
 protected:
@@ -40,6 +40,14 @@ protected:
                               const int face_info);
 
 public:
+   /** @brief Enumeration for ContType: defines the continuity of the field
+       across element interfaces. */
+   enum { CONTINUOUS,   ///< Field is continuous across element interfaces
+          TANGENTIAL,   ///< Tangential components of vector field
+          NORMAL,       ///< Normal component of vector field
+          DISCONTINUOUS ///< Field is discontinuous across element interfaces
+        };
+
    virtual const FiniteElement *
    FiniteElementForGeometry(Geometry::Type GeomType) const = 0;
 
@@ -52,6 +60,8 @@ public:
 
    virtual const char * Name() const { return "Undefined"; }
 
+   virtual int GetContType() const = 0;
+
    int HasFaceDofs(Geometry::Type GeomType) const;
 
    virtual const FiniteElement *TraceFiniteElementForGeometry(
@@ -66,15 +76,81 @@ public:
 
    /** @brief Factory method: return a newly allocated FiniteElementCollection
        according to the given name. */
+   /**
+   | FEC Name | Space | Order | BasisType | FiniteElement::MapT | Notes |
+   | :------: | :---: | :---: | :-------: | :-----: | :---: |
+   | H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
+   | H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
+   | H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
+   | H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
+   | ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
+   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
+   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
+   | RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
+   | RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
+   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
+   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
+   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
+   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
+   | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
+   | NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
+   | LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
+   | CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
+   | Local_[FENAME] | - | - | - | - | Special collection that builds a local version out of the FENAME collection |
+   |-|-|-|-|-|-|
+   | Linear | H1 | 1 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
+   | Quadratic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
+   | QuadraticPos | H1 | 2 | 2 | VALUE | Left in for backward compatibility, consider using H1_ |
+   | Cubic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
+   | Const2D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | Const3D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | LinearDiscont2D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | GaussLinearDiscont2D | L2 | 1 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | P1OnQuad | H1 | 1 | 1 | VALUE | Linear P1 element with 3 nodes on a square |
+   | QuadraticDiscont2D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | QuadraticPosDiscont2D | L2 | 2 | 2 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | GaussQuadraticDiscont2D | L2 | 2 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | CubicDiscont2D | L2 | 3 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | LinearDiscont3D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | QuadraticDiscont3D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
+   | ND1_3D | H(Curl) | 1 | 1 / 0 | H_CURL | Left in for backward compatibility, consider using ND_ |
+   | RT0_2D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
+   | RT1_2D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
+   | RT2_2D | H(Div) | 3 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
+   | RT0_3D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
+   | RT1_3D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
+
+   | Tag | Description |
+   | :------: | :--------: |
+   | [DIM]    | Dimension of the elements (1D, 2D, 3D) |
+   | [ORDER]  | Approximation order of the elements (P0, P1, P2, ...) |
+   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
+   | [OBTYPE] | Open BasisType of the element for elements which have both types |
+   | [CBTYPE] | Closed BasisType of the element for elements which have both types |
+
+   [FENAME]  Is a special case for the Local FEC which generates a local version of a given
+   FEC.  It is selected from one of (BiCubic2DFiniteElement, Quad_Q3, Nedelec1HexFiniteElement,
+      Hex_ND1, H1_[DIM]_[ORDER],H1Pos_[DIM]_[ORDER], L2_[DIM]_[ORDER] )
+   */
    static FiniteElementCollection *New(const char *name);
 
    /** @brief Get the local dofs for a given sub-manifold.
 
-      Return the local dofs for a SDim-dimensional sub-manifold (0D - vertex,
-      1D - edge, 2D - face) including those on its boundary. The local index of
-      the sub-manifold (inside Geom) and its orientation are given by the
-      parameter Info = 64 * SubIndex + SubOrientation. Naturally, it is assumed
-      that 0 <= SDim <= Dim(Geom). */
+      Return the local dofs for a SDim-dimensional sub-manifold (0D - vertex, 1D
+      - edge, 2D - face) including those on its boundary. The local index of the
+      sub-manifold (inside Geom) and its orientation are given by the parameter
+      Info = 64 * SubIndex + SubOrientation. Naturally, it is assumed that 0 <=
+      SDim <= Dim(Geom). */
    void SubDofOrder(Geometry::Type Geom, int SDim, int Info,
                     Array<int> &dofs) const;
 };
@@ -102,6 +178,7 @@ public:
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                              int Or) const;
    virtual const char *Name() const { return h1_name; }
+   virtual int GetContType() const { return CONTINUOUS; }
    FiniteElementCollection *GetTraceCollection() const;
 
    int GetBasisType() const { return b_type; }
@@ -111,8 +188,8 @@ public:
    virtual ~H1_FECollection();
 };
 
-/** Arbitrary order H1-conforming (continuous) finite elements with positive
-    basis functions. */
+/** @brief Arbitrary order H1-conforming (continuous) finite elements with
+    positive basis functions. */
 class H1Pos_FECollection : public H1_FECollection
 {
 public:
@@ -120,6 +197,7 @@ public:
       : H1_FECollection(p, dim, BasisType::Positive) { }
 };
 
+
 /** Arbitrary order H1-conforming (continuous) serendipity finite elements;
     Current implementation works in 2D only; 3D version is in development. */
 class H1Ser_FECollection : public H1_FECollection
@@ -129,9 +207,9 @@ public:
       : H1_FECollection(p, dim, BasisType::Serendipity) { };
 };
 
-/** Arbitrary order "H^{1/2}-conforming" trace finite elements defined on the
-    interface between mesh elements (faces,edges,vertices); these are the trace
-    FEs of the H1-conforming FEs. */
+/** @brief Arbitrary order "H^{1/2}-conforming" trace finite elements defined on
+    the interface between mesh elements (faces,edges,vertices); these are the
+    trace FEs of the H1-conforming FEs. */
 class H1_Trace_FECollection : public H1_FECollection
 {
 public:
@@ -174,6 +252,8 @@ public:
                                              int Or) const;
    virtual const char *Name() const { return d_name; }
 
+   virtual int GetContType() const { return DISCONTINUOUS; }
+
    virtual const FiniteElement *TraceFiniteElementForGeometry(
       Geometry::Type GeomType) const
    {
@@ -221,14 +301,15 @@ public:
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                              int Or) const;
    virtual const char *Name() const { return rt_name; }
+   virtual int GetContType() const { return NORMAL; }
    FiniteElementCollection *GetTraceCollection() const;
 
    virtual ~RT_FECollection();
 };
 
-/** Arbitrary order "H^{-1/2}-conforming" face finite elements defined on the
-    interface between mesh elements (faces); these are the normal trace FEs of
-    the H(div)-conforming FEs. */
+/** @brief Arbitrary order "H^{-1/2}-conforming" face finite elements defined on
+    the interface between mesh elements (faces); these are the normal trace FEs
+    of the H(div)-conforming FEs. */
 class RT_Trace_FECollection : public RT_FECollection
 {
 public:
@@ -270,14 +351,15 @@ public:
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                              int Or) const;
    virtual const char *Name() const { return nd_name; }
+   virtual int GetContType() const { return TANGENTIAL; }
    FiniteElementCollection *GetTraceCollection() const;
 
    virtual ~ND_FECollection();
 };
 
-/** Arbitrary order H(curl)-trace finite elements defined on the interface
-    between mesh elements (faces,edges); these are the tangential trace FEs of
-    the H(curl)-conforming FEs. */
+/** @brief Arbitrary order H(curl)-trace finite elements defined on the
+    interface between mesh elements (faces,edges); these are the tangential
+    trace FEs of the H(curl)-conforming FEs. */
 class ND_Trace_FECollection : public ND_FECollection
 {
 public:
@@ -334,13 +416,15 @@ public:
 
    virtual const char *Name() const { return name; }
 
+   virtual int GetContType() const { return CONTINUOUS; }
+
    FiniteElementCollection *GetTraceCollection() const;
 
    virtual ~NURBSFECollection();
 };
 
 
-/// Piecewise-(bi)linear continuous finite elements.
+/// Piecewise-(bi/tri)linear continuous finite elements.
 class LinearFECollection : public FiniteElementCollection
 {
 private:
@@ -363,6 +447,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "Linear"; }
+
+   virtual int GetContType() const { return CONTINUOUS; }
 };
 
 /// Piecewise-(bi)quadratic continuous finite elements.
@@ -389,6 +475,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "Quadratic"; }
+
+   virtual int GetContType() const { return CONTINUOUS; }
 };
 
 /// Version of QuadraticFECollection with positive basis functions.
@@ -410,6 +498,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "QuadraticPos"; }
+
+   virtual int GetContType() const { return CONTINUOUS; }
 };
 
 /// Piecewise-(bi)cubic continuous finite elements.
@@ -437,6 +527,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "Cubic"; }
+
+   virtual int GetContType() const { return CONTINUOUS; }
 };
 
 /// Crouzeix-Raviart nonconforming elements in 2D.
@@ -458,6 +550,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "CrouzeixRaviart"; }
+
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Piecewise-linear nonconforming finite elements in 3D.
@@ -481,11 +575,13 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "LinearNonConf3D"; }
+
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 
-/** First order Raviart-Thomas finite elements in 2D. This class is kept only
-    for backward compatibility, consider using RT_FECollection instead. */
+/** @brief First order Raviart-Thomas finite elements in 2D. This class is kept
+    only for backward compatibility, consider using RT_FECollection instead. */
 class RT0_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -504,10 +600,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RT0_2D"; }
+
+   virtual int GetContType() const { return NORMAL; }
 };
 
-/** Second order Raviart-Thomas finite elements in 2D. This class is kept only
-    for backward compatibility, consider using RT_FECollection instead. */
+/** @brief Second order Raviart-Thomas finite elements in 2D. This class is kept
+    only for backward compatibility, consider using RT_FECollection instead. */
 class RT1_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -526,10 +624,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RT1_2D"; }
+
+   virtual int GetContType() const { return NORMAL; }
 };
 
-/** Third order Raviart-Thomas finite elements in 2D. This class is kept only
-    for backward compatibility, consider using RT_FECollection instead. */
+/** @brief Third order Raviart-Thomas finite elements in 2D. This class is kept
+    only for backward compatibility, consider using RT_FECollection instead. */
 class RT2_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -548,10 +648,13 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RT2_2D"; }
+
+   virtual int GetContType() const { return NORMAL; }
 };
 
-/** Piecewise-constant discontinuous finite elements in 2D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-constant discontinuous finite elements in 2D. This class is
+    kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class Const2DFECollection : public FiniteElementCollection
 {
 private:
@@ -569,10 +672,13 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "Const2D"; }
+
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-linear discontinuous finite elements in 2D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-linear discontinuous finite elements in 2D. This class is
+    kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class LinearDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -591,6 +697,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "LinearDiscont2D"; }
+
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Version of LinearDiscont2DFECollection with dofs in the Gaussian points.
@@ -613,6 +721,8 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "GaussLinearDiscont2D"; }
+
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Linear (P1) finite elements on quadrilaterals.
@@ -628,10 +738,12 @@ public:
    virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                              int Or) const;
    virtual const char * Name() const { return "P1OnQuad"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-quadratic discontinuous finite elements in 2D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-quadratic discontinuous finite elements in 2D. This class
+    is kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class QuadraticDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -650,6 +762,7 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "QuadraticDiscont2D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Version of QuadraticDiscont2DFECollection with positive basis functions.
@@ -667,6 +780,7 @@ public:
                                              int Or) const
    { return NULL; }
    virtual const char * Name() const { return "QuadraticPosDiscont2D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Version of QuadraticDiscont2DFECollection with dofs in the Gaussian points.
@@ -689,10 +803,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "GaussQuadraticDiscont2D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-cubic discontinuous finite elements in 2D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-cubic discontinuous finite elements in 2D. This class is
+    kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class CubicDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -711,10 +827,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "CubicDiscont2D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-constant discontinuous finite elements in 3D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-constant discontinuous finite elements in 3D. This class is
+    kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class Const3DFECollection : public FiniteElementCollection
 {
 private:
@@ -734,10 +852,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "Const3D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-linear discontinuous finite elements in 3D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-linear discontinuous finite elements in 3D. This class is
+    kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class LinearDiscont3DFECollection : public FiniteElementCollection
 {
 private:
@@ -756,10 +876,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "LinearDiscont3D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
-/** Piecewise-quadratic discontinuous finite elements in 3D. This class is kept
-    only for backward compatibility, consider using L2_FECollection instead. */
+/** @brief Piecewise-quadratic discontinuous finite elements in 3D. This class
+    is kept only for backward compatibility, consider using L2_FECollection
+    instead. */
 class QuadraticDiscont3DFECollection : public FiniteElementCollection
 {
 private:
@@ -778,6 +900,7 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "QuadraticDiscont3D"; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 /// Finite element collection on a macro-element.
@@ -803,10 +926,12 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RefinedLinear"; }
+   virtual int GetContType() const { return CONTINUOUS; }
 };
 
-/** Lowest order Nedelec finite elements in 3D. This class is kept only for
-    backward compatibility, consider using the new ND_FECollection instead. */
+/** @brief Lowest order Nedelec finite elements in 3D. This class is kept only
+    for backward compatibility, consider using the new ND_FECollection
+    instead. */
 class ND1_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -825,10 +950,11 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "ND1_3D"; }
+   virtual int GetContType() const { return TANGENTIAL; }
 };
 
-/** First order Raviart-Thomas finite elements in 3D. This class is kept only
-    for backward compatibility, consider using RT_FECollection instead. */
+/** @brief First order Raviart-Thomas finite elements in 3D. This class is kept
+    only for backward compatibility, consider using RT_FECollection instead. */
 class RT0_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -848,10 +974,11 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RT0_3D"; }
+   virtual int GetContType() const { return NORMAL; }
 };
 
-/** Second order Raviart-Thomas finite elements in 3D. This class is kept only
-    for backward compatibility, consider using RT_FECollection instead. */
+/** @brief Second order Raviart-Thomas finite elements in 3D. This class is kept
+    only for backward compatibility, consider using RT_FECollection instead. */
 class RT1_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -870,6 +997,7 @@ public:
                                              int Or) const;
 
    virtual const char * Name() const { return "RT1_3D"; }
+   virtual int GetContType() const { return NORMAL; }
 };
 
 /// Discontinuous collection defined locally by a given finite element.
@@ -894,6 +1022,7 @@ public:
    virtual const char *Name() const { return d_name; }
 
    virtual ~Local_FECollection() { delete Local_Element; }
+   virtual int GetContType() const { return DISCONTINUOUS; }
 };
 
 }

fem/fespace.cpp

@@ -60,7 +60,7 @@ FiniteElementSpace::FiniteElementSpace()
    : mesh(NULL), fec(NULL), vdim(0), ordering(Ordering::byNODES),
      ndofs(0), nvdofs(0), nedofs(0), nfdofs(0), nbdofs(0),
      fdofs(NULL), bdofs(NULL),
-     elem_dof(NULL), bdrElem_dof(NULL),
+     elem_dof(NULL), bdrElem_dof(NULL), face_dof(NULL),
      NURBSext(NULL), own_ext(false),
      cP(NULL), cR(NULL), cP_is_set(false),
      Th(Operator::ANY_TYPE),
@@ -233,6 +233,54 @@ void FiniteElementSpace::BuildElementToDofTable() const
    elem_dof = el_dof;
 }
 
+void FiniteElementSpace::BuildBdrElementToDofTable() const
+{
+   if (bdrElem_dof) { return; }
+
+   Table *bel_dof = new Table;
+   Array<int> dofs;
+   bel_dof->MakeI(mesh->GetNBE());
+   for (int i = 0; i < mesh->GetNBE(); i++)
+   {
+      GetBdrElementDofs(i, dofs);
+      bel_dof->AddColumnsInRow(i, dofs.Size());
+   }
+   bel_dof->MakeJ();
+   for (int i = 0; i < mesh->GetNBE(); i++)
+   {
+      GetBdrElementDofs(i, dofs);
+      bel_dof->AddConnections(i, (int *)dofs, dofs.Size());
+   }
+   bel_dof->ShiftUpI();
+   bdrElem_dof = bel_dof;
+}
+
+void FiniteElementSpace::BuildFaceToDofTable() const
+{
+   // Here, "face" == (dim-1)-dimensional mesh entity.
+
+   if (face_dof) { return; }
+
+   if (NURBSext) { BuildNURBSFaceToDofTable(); return; }
+
+   Table *fc_dof = new Table;
+   Array<int> dofs;
+   fc_dof->MakeI(mesh->GetNumFaces());
+   for (int i = 0; i < fc_dof->Size(); i++)
+   {
+      GetFaceDofs(i, dofs);
+      fc_dof->AddColumnsInRow(i, dofs.Size());
+   }
+   fc_dof->MakeJ();
+   for (int i = 0; i < fc_dof->Size(); i++)
+   {
+      GetFaceDofs(i, dofs);
+      fc_dof->AddConnections(i, (int *)dofs, dofs.Size());
+   }
+   fc_dof->ShiftUpI();
+   face_dof = fc_dof;
+}
+
 void FiniteElementSpace::RebuildElementToDofTable()
 {
    delete elem_dof;
@@ -1456,6 +1504,7 @@ void FiniteElementSpace::Constructor(Mesh *mesh, NURBSExtension *NURBSext,
    this->ordering = (Ordering::Type) ordering;
 
    elem_dof = NULL;
+   face_dof = NULL;
    sequence = mesh->GetSequence();
    Th.SetType(Operator::ANY_TYPE);
 
@@ -1505,6 +1554,8 @@ NURBSExtension *FiniteElementSpace::StealNURBSext()
 
 void FiniteElementSpace::UpdateNURBS()
 {
+   MFEM_VERIFY(NURBSext, "NURBSExt not defined.");
+
    nvdofs = 0;
    nedofs = 0;
    nfdofs = 0;
@@ -1512,6 +1563,10 @@ void FiniteElementSpace::UpdateNURBS()
    fdofs = NULL;
    bdofs = NULL;
 
+   delete face_dof;
+   face_dof = NULL;
+   face_to_be.DeleteAll();
+
    dynamic_cast<const NURBSFECollection *>(fec)->Reset();
 
    ndofs = NURBSext->GetNDof();
@@ -1519,6 +1574,55 @@ void FiniteElementSpace::UpdateNURBS()
    bdrElem_dof = NURBSext->GetBdrElementDofTable();
 }
 
+void FiniteElementSpace::BuildNURBSFaceToDofTable() const
+{
+   if (face_dof) { return; }
+
+   const int dim = mesh->Dimension();
+
+   // Find bdr to face mapping
+   face_to_be.SetSize(GetNF());
+   face_to_be = -1;
+   for (int b = 0; b < GetNBE(); b++)
+   {
+      int f = mesh->GetBdrElementEdgeIndex(b);
+      face_to_be[f] = b;
+   }
+
+   // Loop over faces in correct order, to prevent a sort
+   // Sort will destroy orientation info in ordering of dofs
+   Array<Connection> face_dof_list;
+   Array<int> row;
+   for (int f = 0; f < GetNF(); f++)
+   {
+      int b = face_to_be[f];
+      if (b == -1) { continue; }
+      // FIXME: this assumes the boundary element and the face element have the
+      //        same orientation.
+      if (dim > 1)
+      {
+         const Element *fe = mesh->GetFace(f);
+         const Element *be = mesh->GetBdrElement(b);
+         const int nv = be->GetNVertices();
+         const int *fv = fe->GetVertices();
+         const int *bv = be->GetVertices();
+         for (int i = 0; i < nv; i++)
+         {
+            MFEM_VERIFY(fv[i] == bv[i],
+                        "non-matching face and boundary elements detected!");
+         }
+      }
+      GetBdrElementDofs(b, row);
+      Connection conn(f,0);
+      for (int i = 0; i < row.Size(); i++)
+      {
+         conn.to = row[i];
+         face_dof_list.Append(conn);
+      }
+   }
+   face_dof = new Table(GetNF(), face_dof_list);
+}
+
 void FiniteElementSpace::Construct()
 {
    // This method should be used only for non-NURBS spaces.
@@ -1526,6 +1630,7 @@ void FiniteElementSpace::Construct()
 
    elem_dof = NULL;
    bdrElem_dof = NULL;
+   face_dof = NULL;
 
    ndofs = 0;
    nedofs = nfdofs = nbdofs = 0;
@@ -1788,59 +1893,68 @@ void FiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
 
 void FiniteElementSpace::GetFaceDofs(int i, Array<int> &dofs) const
 {
-   int j, k, nv, ne, nf, nd, dim = mesh->Dimension();
-   Array<int> V, E, Eo;
-   const int *ind;
+   // If face_dof is already built, use it.
+   // If it is not and we have a NURBS space, build the face_dof and use it.
+   if (face_dof || (NURBSext && (BuildNURBSFaceToDofTable(), true)))
+   {
+      face_dof->GetRow(i, dofs);
+   }
+   else
+   {
+      int j, k, nv, ne, nf, nd, dim = mesh->Dimension();
+      Array<int> V, E, Eo;
+      const int *ind;
 
-   // for 1D, 2D and 3D faces
-   nv = fec->DofForGeometry(Geometry::POINT);
-   ne = (dim > 1) ? fec->DofForGeometry(Geometry::SEGMENT) : 0;
-   if (nv > 0)
-   {
-      mesh->GetFaceVertices(i, V);
-   }
-   if (ne > 0)
-   {
-      mesh->GetFaceEdges(i, E, Eo);
-   }
-   nf = (fdofs) ? (fdofs[i+1]-fdofs[i]) : (0);
-   nd = V.Size() * nv + E.Size() * ne + nf;
-   dofs.SetSize(nd);
-   if (nv > 0)
-   {
-      for (k = 0; k < V.Size(); k++)
+      // for 1D, 2D and 3D faces
+      nv = fec->DofForGeometry(Geometry::POINT);
+      ne = (dim > 1) ? fec->DofForGeometry(Geometry::SEGMENT) : 0;
+      if (nv > 0)
       {
-         for (j = 0; j < nv; j++)
-         {
-            dofs[k*nv+j] = V[k]*nv+j;
-         }
+         mesh->GetFaceVertices(i, V);
       }
-   }
-   nv *= V.Size();
-   if (ne > 0)
-   {
-      for (k = 0; k < E.Size(); k++)
+      if (ne > 0)
       {
-         ind = fec->DofOrderForOrientation(Geometry::SEGMENT, Eo[k]);
-         for (j = 0; j < ne; j++)
+         mesh->GetFaceEdges(i, E, Eo);
+      }
+      nf = (fdofs) ? (fdofs[i+1]-fdofs[i]) : (0);
+      nd = V.Size() * nv + E.Size() * ne + nf;
+      dofs.SetSize(nd);
+      if (nv > 0)
+      {
+         for (k = 0; k < V.Size(); k++)
          {
-            if (ind[j] < 0)
+            for (j = 0; j < nv; j++)
             {
-               dofs[nv+k*ne+j] = -1 - ( nvdofs+E[k]*ne+(-1-ind[j]) );
-            }
-            else
-            {
-               dofs[nv+k*ne+j] = nvdofs+E[k]*ne+ind[j];
+               dofs[k*nv+j] = V[k]*nv+j;
             }
          }
       }
-   }
-   ne = nv + ne * E.Size();
-   if (nf > 0)
-   {
-      for (j = nvdofs+nedofs+fdofs[i], k = 0; k < nf; j++, k++)
+      nv *= V.Size();
+      if (ne > 0)
       {
-         dofs[ne+k] = j;
+         for (k = 0; k < E.Size(); k++)
+         {
+            ind = fec->DofOrderForOrientation(Geometry::SEGMENT, Eo[k]);
+            for (j = 0; j < ne; j++)
+            {
+               if (ind[j] < 0)
+               {
+                  dofs[nv+k*ne+j] = -1 - ( nvdofs+E[k]*ne+(-1-ind[j]) );
+               }
+               else
+               {
+                  dofs[nv+k*ne+j] = nvdofs+E[k]*ne+ind[j];
+               }
+            }
+         }
+      }
+      ne = nv + ne * E.Size();
+      if (nf > 0)
+      {
+         for (j = nvdofs+nedofs+fdofs[i], k = 0; k < nf; j++, k++)
+         {
+            dofs[ne+k] = j;
+         }
       }
    }
 }
@@ -1969,14 +2083,21 @@ const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
          fe = fec->FiniteElementForGeometry(mesh->GetFaceBaseGeometry(i));
    }
 
-   // if (NURBSext)
-   //    NURBSext->LoadFaceElement(i, fe);
+   if (NURBSext)
+   {
+      // Ensure 'face_to_be' is built:
+      if (!face_dof) { BuildNURBSFaceToDofTable(); }
+      MFEM_ASSERT(face_to_be[i] >= 0,
+                  "NURBS mesh: only boundary faces are supported!");
+      NURBSext->LoadBE(face_to_be[i], fe);
+   }
 
    return fe;
 }
 
 const FiniteElement *FiniteElementSpace::GetEdgeElement(int i) const
 {
+   MFEM_ASSERT(mesh->Dimension() > 1, "No edges with a mesh dimension < 2");
    return fec->FiniteElementForGeometry(Geometry::SEGMENT);
 }
 
@@ -2024,11 +2145,14 @@ void FiniteElementSpace::Destroy()
    if (NURBSext)
    {
       if (own_ext) { delete NURBSext; }
+      delete face_dof;
+      face_to_be.DeleteAll();
    }
    else
    {
       delete elem_dof;
       delete bdrElem_dof;
+      delete face_dof;
 
       delete [] bdofs;
       delete [] fdofs;
@@ -2615,7 +2739,9 @@ const Operator &InterpolationGridTransfer::BackwardOperator()
 
 L2ProjectionGridTransfer::L2Projection::L2Projection(
    const FiniteElementSpace &fes_ho_, const FiniteElementSpace &fes_lor_)
-   : fes_ho(fes_ho_), fes_lor(fes_lor_)
+   : Operator(fes_lor_.GetVSize(), fes_ho_.GetVSize()),
+     fes_ho(fes_ho_),
+     fes_lor(fes_lor_)
 {
    Mesh *mesh_ho = fes_ho.GetMesh();
    MFEM_VERIFY(mesh_ho->GetNumGeometries(mesh_ho->Dimension()) <= 1,

fem/fespace.hpp

@@ -111,7 +111,9 @@ protected:
    int *fdofs, *bdofs;
 
    mutable Table *elem_dof; // if NURBS FE space, not owned; otherwise, owned.
-   Table *bdrElem_dof; // used only with NURBS FE spaces; not owned.
+   mutable Table *bdrElem_dof; // not owned only if NURBS FE space.
+   mutable Table *face_dof; // owned
+   mutable Array<int> face_to_be; // used only with NURBS FE spaces; owned.
 
    Array<int> dof_elem_array, dof_ldof_array;
 
@@ -158,6 +160,14 @@ protected:
    void Destroy();
 
    void BuildElementToDofTable() const;
+   void BuildBdrElementToDofTable() const;
+   void BuildFaceToDofTable() const;
+
+   /** @brief  Generates partial face_dof table for a NURBS space.
+
+       The table is only defined for exterior faces that coincide with a
+       boundary. */
+   void BuildNURBSFaceToDofTable() const;
 
    /// Helpers to remove encoded sign from a DOF
    static inline int DecodeDof(int dof)
@@ -206,7 +216,7 @@ protected:
       virtual ~RefinementOperator();
    };
 
-   // Derefinement operator, used by the friend class InterpolationGridTransfer.
+   /// Derefinement operator, used by the friend class InterpolationGridTransfer.
    class DerefinementOperator : public Operator
    {
       const FiniteElementSpace *fine_fes; // Not owned.
@@ -225,12 +235,12 @@ protected:
       virtual ~DerefinementOperator();
    };
 
-   // This method makes the same assumptions as the method:
-   //    void GetLocalRefinementMatrices(
-   //       const FiniteElementSpace &coarse_fes, Geometry::Type geom,
-   //       DenseTensor &localP) const
-   // which is defined below. It also assumes that the coarse fes and this have
-   // the same vector dimension, vdim.
+   /** This method makes the same assumptions as the method:
+       void GetLocalRefinementMatrices(
+           const FiniteElementSpace &coarse_fes, Geometry::Type geom,
+           DenseTensor &localP) const
+       which is defined below. It also assumes that the coarse fes and this have
+       the same vector dimension, vdim. */
    SparseMatrix *RefinementMatrix_main(const int coarse_ndofs,
                                        const Table &coarse_elem_dof,
                                        const DenseTensor localP[]) const;
@@ -248,11 +258,13 @@ protected:
    /// Calculate GridFunction restriction matrix after mesh derefinement.
    SparseMatrix* DerefinementMatrix(int old_ndofs, const Table* old_elem_dof);
 
-   // This method assumes that this->mesh is a refinement of coarse_fes->mesh
-   // and that the CoarseFineTransformations of this->mesh are set accordingly.
-   // Another assumption is that the FEs of this use the same MapType as the FEs
-   // of coarse_fes. Finally, it assumes that the spaces this and coarse_fes are
-   // NOT variable-order spaces.
+   /** @brief Return in @a localP the local refinement matrices that map
+       between fespaces after mesh refinement. */
+   /** This method assumes that this->mesh is a refinement of coarse_fes->mesh
+       and that the CoarseFineTransformations of this->mesh are set accordingly.
+       Another assumption is that the FEs of this use the same MapType as the FEs
+       of coarse_fes. Finally, it assumes that the spaces this and coarse_fes are
+       NOT variable-order spaces. */
    void GetLocalRefinementMatrices(const FiniteElementSpace &coarse_fes,
                                    Geometry::Type geom,
                                    DenseTensor &localP) const;
@@ -467,11 +479,11 @@ public:
    /// Returns indexes of degrees of freedom for i'th boundary element.
    virtual void GetBdrElementDofs(int i, Array<int> &dofs) const;
 
-   /** Returns the indexes of the degrees of freedom for i'th face
+   /** @brief eturns the indexes of the degrees of freedom for i'th face
        including the dofs for the edges and the vertices of the face. */
    virtual void GetFaceDofs(int i, Array<int> &dofs) const;
 
-   /** Returns the indexes of the degrees of freedom for i'th edge
+   /** @brief Returns the indexes of the degrees of freedom for i'th edge
        including the dofs for the vertices of the edge. */
    void GetEdgeDofs(int i, Array<int> &dofs) const;
 
@@ -526,28 +538,59 @@ public:
        is preserved. */
    void ReorderElementToDofTable();
 
+   /** @brief Return a reference to the internal Table that stores the lists of
+       scalar dofs, for each mesh element, as returned by GetElementDofs(). */
+   const Table &GetElementToDofTable() const { return *elem_dof; }
+
+   /** @brief Return a reference to the internal Table that stores the lists of
+       scalar dofs, for each boundary mesh element, as returned by
+       GetBdrElementDofs(). */
+   const Table &GetBdrElementToDofTable() const
+   { if (!bdrElem_dof) { BuildBdrElementToDofTable(); } return *bdrElem_dof; }
+
+   /** @brief Return a reference to the internal Table that stores the lists of
+       scalar dofs, for each face in the mesh, as returned by GetFaceDofs(). In
+       this context, "face" refers to a (dim-1)-dimensional mesh entity. */
+   /** @note In the case of a NURBS space, the rows corresponding to interior
+       faces will be empty. */
+   const Table &GetFaceToDofTable() const
+   { if (!face_dof) { BuildFaceToDofTable(); } return *face_dof; }
+
+   /** @brief Initialize internal data that enables the use of the methods
+       GetElementForDof() and GetLocalDofForDof(). */
    void BuildDofToArrays();
 
-   const Table &GetElementToDofTable() const { return *elem_dof; }
-   const Table &GetBdrElementToDofTable() const { return *bdrElem_dof; }
-
+   /// Return the index of the first element that contains dof @a i.
+   /** This method can be called only after setup is performed using the method
+       BuildDofToArrays(). */
    int GetElementForDof(int i) const { return dof_elem_array[i]; }
+   /// Return the local dof index in the first element that contains dof @a i.
+   /** This method can be called only after setup is performed using the method
+       BuildDofToArrays(). */
    int GetLocalDofForDof(int i) const { return dof_ldof_array[i]; }
 
-   /// Returns pointer to the FiniteElement associated with i'th element.
+   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
+        associated with i'th element in the mesh object. */
    const FiniteElement *GetFE(int i) const;
 
-   /// Returns pointer to the FiniteElement for the i'th boundary element.
+   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
+        associated with i'th boundary face in the mesh object. */
    const FiniteElement *GetBE(int i) const;
 
+   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
+        associated with i'th face in the mesh object.  Faces in this case refer
+        to the MESHDIM-1 primitive so in 2D they are segments and in 1D they are
+        points.*/
    const FiniteElement *GetFaceElement(int i) const;
 
+   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
+        associated with i'th edge in the mesh object. */
    const FiniteElement *GetEdgeElement(int i) const;
 
    /// Return the trace element from element 'i' to the given 'geom_type'
    const FiniteElement *GetTraceElement(int i, Geometry::Type geom_type) const;
 
-   /** Mark degrees of freedom associated with boundary elements with
+   /** @brief Mark degrees of freedom associated with boundary elements with
        the specified boundary attributes (marked in 'bdr_attr_is_ess').
        For spaces with 'vdim' > 1, the 'component' parameter can be used
        to restricts the marked vDOFs to the specified component. */
@@ -555,7 +598,7 @@ public:
                                   Array<int> &ess_vdofs,
                                   int component = -1) const;
 
-   /** Get a list of essential true dofs, ess_tdof_list, corresponding to the
+   /** @brief Get a list of essential true dofs, ess_tdof_list, corresponding to the
        boundary attributes marked in the array bdr_attr_is_ess.
        For spaces with 'vdim' > 1, the 'component' parameter can be used
        to restricts the marked tDOFs to the specified component. */
@@ -566,19 +609,19 @@ public:
    /// Convert a Boolean marker array to a list containing all marked indices.
    static void MarkerToList(const Array<int> &marker, Array<int> &list);
 
-   /** Convert an array of indices (list) to a Boolean marker array where all
+   /** @brief Convert an array of indices (list) to a Boolean marker array where all
        indices in the list are marked with the given value and the rest are set
        to zero. */
    static void ListToMarker(const Array<int> &list, int marker_size,
                             Array<int> &marker, int mark_val = -1);
 
-   /** For a partially conforming FE space, convert a marker array (nonzero
+   /** @brief For a partially conforming FE space, convert a marker array (nonzero
        entries are true) on the partially conforming dofs to a marker array on
        the conforming dofs. A conforming dofs is marked iff at least one of its
        dependent dofs is marked. */
    void ConvertToConformingVDofs(const Array<int> &dofs, Array<int> &cdofs);
 
-   /** For a partially conforming FE space, convert a marker array (nonzero
+   /** @brief For a partially conforming FE space, convert a marker array (nonzero
        entries are true) on the conforming dofs to a marker array on the
        (partially conforming) dofs. A dof is marked iff it depends on a marked
        conforming dofs, where dependency is defined by the ConformingRestriction
@@ -586,15 +629,15 @@ public:
        conforming dof. */
    void ConvertFromConformingVDofs(const Array<int> &cdofs, Array<int> &dofs);
 
-   /** Generate the global restriction matrix from a discontinuous
+   /** @brief Generate the global restriction matrix from a discontinuous
        FE space to the continuous FE space of the same polynomial degree. */
    SparseMatrix *D2C_GlobalRestrictionMatrix(FiniteElementSpace *cfes);
 
-   /** Generate the global restriction matrix from a discontinuous
+   /** @brief Generate the global restriction matrix from a discontinuous
        FE space to the piecewise constant FE space. */
    SparseMatrix *D2Const_GlobalRestrictionMatrix(FiniteElementSpace *cfes);
 
-   /** Construct the restriction matrix from the FE space given by
+   /** @brief Construct the restriction matrix from the FE space given by
        (*this) to the lower degree FE space given by (*lfes) which
        is defined on the same mesh. */
    SparseMatrix *H2L_GlobalRestrictionMatrix(FiniteElementSpace *lfes);
@@ -631,7 +674,7 @@ public:
    virtual void GetTrueTransferOperator(const FiniteElementSpace &coarse_fes,
                                         OperatorHandle &T) const;
 
-   /** Reflect changes in the mesh: update number of DOFs, etc. Also, calculate
+   /** @brief Reflect changes in the mesh: update number of DOFs, etc. Also, calculate
        GridFunction transformation operator (unless want_transform is false).
        Safe to call multiple times, does nothing if space already up to date. */
    virtual void Update(bool want_transform = true);
@@ -669,6 +712,7 @@ public:
       return dynamic_cast<const L2_FECollection*>(fec) != NULL;
    }
 
+   /// Save finite element space to output stream @a out.
    void Save(std::ostream &out) const;
 
    /** @brief Read a FiniteElementSpace from a stream. The returned
@@ -906,7 +950,8 @@ protected:
       const L2Projection &l2proj;
 
    public:
-      L2Prolongation(const L2Projection &l2proj_) : l2proj(l2proj_) { }
+      L2Prolongation(const L2Projection &l2proj_)
+         : Operator(l2proj_.Width(), l2proj_.Height()), l2proj(l2proj_) { }
       void Mult(const Vector &x, Vector &y) const
       {
          l2proj.Prolongate(x, y);

fem/gridfunc.cpp

@@ -236,7 +236,6 @@ void GridFunction::MakeTRef(FiniteElementSpace *f, Vector &tv, int tv_offset)
    }
 }
 
-
 void GridFunction::SumFluxAndCount(BilinearFormIntegrator &blfi,
                                    GridFunction &flux,
                                    Array<int>& count,
@@ -617,17 +616,354 @@ int GridFunction::GetFaceValues(int i, int side, const IntegrationRule &ir,
    return dir;
 }
 
+void GridFunction::GetVectorValues(int i, const IntegrationRule &ir,
+                                   DenseMatrix &vals, DenseMatrix &tr) const
+{
+   ElementTransformation *Tr = fes->GetElementTransformation(i);
+   Tr->Transform(ir, tr);
+
+   GetVectorValues(*Tr, ir, vals);
+}
+
+void be_to_bfe(Geometry::Type geom, int o, const IntegrationPoint &ip,
+               IntegrationPoint &fip)
+{
+   if (geom == Geometry::TRIANGLE)
+   {
+      if (o == 2)
+      {
+         fip.x = 1.0 - ip.x - ip.y;
+         fip.y = ip.x;
+      }
+      else if (o == 4)
+      {
+         fip.x = ip.y;
+         fip.y = 1.0 - ip.x - ip.y;
+      }
+      else
+      {
+         fip.x = ip.x;
+         fip.y = ip.y;
+      }
+      fip.z = ip.z;
+   }
+   else
+   {
+      if (o == 2)
+      {
+         fip.x = ip.y;
+         fip.y = 1.0 - ip.x;
+      }
+      else if (o == 4)
+      {
+         fip.x = 1.0 - ip.x;
+         fip.y = 1.0 - ip.y;
+      }
+      else if (o == 6)
+      {
+         fip.x = 1.0 - ip.y;
+         fip.y = ip.x;
+      }
+      else
+      {
+         fip.x = ip.x;
+         fip.y = ip.y;
+      }
+      fip.z = ip.z;
+   }
+   fip.weight = ip.weight;
+   fip.index  = ip.index;
+}
+
+double GridFunction::GetValue(ElementTransformation &T,
+                              const IntegrationPoint &ip,
+                              int comp, Vector *tr) const
+{
+   if (tr)
+   {
+      T.SetIntPoint(&ip);
+      T.Transform(ip, *tr);
+   }
+
+   const FiniteElement * fe = NULL;
+   Array<int> dofs;
+
+   switch (T.ElementType)
+   {
+      case ElementTransformation::ELEMENT:
+         fe = fes->GetFE(T.ElementNo);
+         fes->GetElementDofs(T.ElementNo, dofs);
+         break;
+      case ElementTransformation::EDGE:
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            fe = fes->GetEdgeElement(T.ElementNo);
+            fes->GetEdgeDofs(T.ElementNo, dofs);
+         }
+         else
+         {
+            MFEM_ABORT("GridFunction::GetValue: Field continuity type \""
+                       << fes->FEColl()->GetContType() << "\" not supported "
+                       << "on mesh edges.");
+            return NAN;
+         }
+         break;
+      case ElementTransformation::FACE:
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            fe = fes->GetFaceElement(T.ElementNo);
+            fes->GetFaceDofs(T.ElementNo, dofs);
+         }
+         else
+         {
+            MFEM_ABORT("GridFunction::GetValue: Field continuity type \""
+                       << fes->FEColl()->GetContType() << "\" not supported "
+                       << "on mesh faces.");
+            return NAN;
+         }
+         break;
+      case ElementTransformation::BDR_ELEMENT:
+      {
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            // This is a continuous field so we can evaluate it on the boundary.
+            fe = fes->GetBE(T.ElementNo);
+            fes->GetBdrElementDofs(T.ElementNo, dofs);
+         }
+         else
+         {
+            // This is a discontinuous field which cannot be evaluated on the
+            // boundary so we'll evaluate it in the neighboring element.
+            FaceElementTransformations * FET =
+               fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+            // Boundary elements and Boundary Faces may have different
+            // orientations so adjust the integration point if necessary.
+            int o = 0;
+            if (fes->GetMesh()->Dimension() == 3)
+            {
+               int f;
+               fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+            }
+
+            IntegrationPoint fip;
+            be_to_bfe(FET->GetGeometryType(), o, ip, fip);
+
+            FET->SetIntPoint(&fip);
+            ElementTransformation & T1 = FET->GetElement1Transformation();
+            return GetValue(T1, T1.GetIntPoint(), comp);
+         }
+         break;
+      }
+      case ElementTransformation::BDR_FACE:
+      {
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element for both continuous and
+         // discontinuous fields.
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         return GetValue(T1, T1.GetIntPoint(), comp);
+      }
+      default:
+      {
+         MFEM_ABORT("GridFunction::GetValue: Unsupported element type \""
+                    << T.ElementType << "\"");
+         return NAN;
+      }
+   }
+
+   fes->DofsToVDofs(comp-1, dofs);
+   Vector DofVal(dofs.Size()), LocVec;
+   if (fe->GetMapType() == FiniteElement::VALUE)
+   {
+      fe->CalcShape(ip, DofVal);
+   }
+   else
+   {
+      fe->CalcPhysShape(T, DofVal);
+   }
+   GetSubVector(dofs, LocVec);
+
+   return (DofVal * LocVec);
+}
+
+void GridFunction::GetValues(ElementTransformation &T,
+                             const IntegrationRule &ir,
+                             Vector &vals, int comp,
+                             DenseMatrix *tr) const
+{
+   if (tr)
+   {
+      T.Transform(ir, *tr);
+   }
+
+   int nip = ir.GetNPoints();
+   vals.SetSize(nip);
+   for (int j = 0; j < nip; j++)
+   {
+      const IntegrationPoint &ip = ir.IntPoint(j);
+      T.SetIntPoint(&ip);
+      vals[j] = GetValue(T, ip, comp);
+   }
+}
+
+void GridFunction::GetVectorValue(ElementTransformation &T,
+                                  const IntegrationPoint &ip,
+                                  Vector &val, Vector *tr) const
+{
+   if (tr)
+   {
+      T.SetIntPoint(&ip);
+      T.Transform(ip, *tr);
+   }
+
+   Array<int> vdofs;
+   const FiniteElement *fe = NULL;
+
+   switch (T.ElementType)
+   {
+      case ElementTransformation::ELEMENT:
+         fes->GetElementVDofs(T.ElementNo, vdofs);
+         fe = fes->GetFE(T.ElementNo);
+         break;
+      case ElementTransformation::EDGE:
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            fe = fes->GetEdgeElement(T.ElementNo);
+            fes->GetEdgeVDofs(T.ElementNo, vdofs);
+         }
+         else
+         {
+            MFEM_ABORT("GridFunction::GetVectorValue: Field continuity type \""
+                       << fes->FEColl()->GetContType() << "\" not supported "
+                       << "on mesh edges.");
+            return;
+         }
+         break;
+      case ElementTransformation::FACE:
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            fe = fes->GetFaceElement(T.ElementNo);
+            fes->GetFaceVDofs(T.ElementNo, vdofs);
+         }
+         else
+         {
+            MFEM_ABORT("GridFunction::GetVectorValue: Field continuity type \""
+                       << fes->FEColl()->GetContType() << "\" not supported "
+                       << "on mesh faces.");
+            return;
+         }
+         break;
+      case ElementTransformation::BDR_ELEMENT:
+      {
+         if (fes->FEColl()->GetContType() ==
+             FiniteElementCollection::CONTINUOUS)
+         {
+            // This is a continuous field so we can evaluate it on the boundary.
+            fes->GetBdrElementVDofs(T.ElementNo, vdofs);
+            fe = fes->GetBE(T.ElementNo);
+         }
+         else
+         {
+            // This is a discontinuous vector field which cannot be evaluated on
+            // the boundary so we'll evaluate it in the neighboring element.
+            FaceElementTransformations * FET =
+               fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+            // Boundary elements and Boundary Faces may have different
+            // orientations so adjust the integration point if necessary.
+            int o = 0;
+            if (fes->GetMesh()->Dimension() == 3)
+            {
+               int f;
+               fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+            }
+
+            IntegrationPoint fip;
+            be_to_bfe(FET->GetGeometryType(), o, ip, fip);
+
+            FET->SetIntPoint(&fip);
+            ElementTransformation & T1 = FET->GetElement1Transformation();
+            return GetVectorValue(T1, T1.GetIntPoint(), val);
+         }
+         break;
+      }
+      case ElementTransformation::BDR_FACE:
+      {
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element for both continuous and
+         // discontinuous fields.
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         return GetVectorValue(T1, T1.GetIntPoint(), val);
+      }
+      default:
+      {
+         MFEM_ABORT("GridFunction::GetVectorValue: Unsupported element type \""
+                    << T.ElementType << "\"");
+         if (val.Size() > 0) { val = NAN; }
+         return;
+      }
+   }
+
+   int dof = fe->GetDof();
+   Vector loc_data;
+   GetSubVector(vdofs, loc_data);
+   if (fe->GetRangeType() == FiniteElement::SCALAR)
+   {
+      Vector shape(dof);
+      if (fe->GetMapType() == FiniteElement::VALUE)
+      {
+         fe->CalcShape(ip, shape);
+      }
+      else
+      {
+         fe->CalcPhysShape(T, shape);
+      }
+      int vdim = fes->GetVDim();
+      val.SetSize(vdim);
+      for (int k = 0; k < vdim; k++)
+      {
+         val(k) = shape * ((const double *)loc_data + dof * k);
+      }
+   }
+   else
+   {
+      int spaceDim = fes->GetMesh()->SpaceDimension();
+      DenseMatrix vshape(dof, spaceDim);
+      fe->CalcVShape(T, vshape);
+      val.SetSize(spaceDim);
+      vshape.MultTranspose(loc_data, val);
+   }
+}
+
 void GridFunction::GetVectorValues(ElementTransformation &T,
                                    const IntegrationRule &ir,
-                                   DenseMatrix &vals) const
+                                   DenseMatrix &vals,
+                                   DenseMatrix *tr) const
 {
+   if (tr)
+   {
+      T.Transform(ir, *tr);
+   }
+
    const FiniteElement *FElem = fes->GetFE(T.ElementNo);
    int dof = FElem->GetDof();
+
    Array<int> vdofs;
    fes->GetElementVDofs(T.ElementNo, vdofs);
+
    Vector loc_data;
    GetSubVector(vdofs, loc_data);
    int nip = ir.GetNPoints();
+
    if (FElem->GetRangeType() == FiniteElement::SCALAR)
    {
       MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
@@ -639,6 +975,7 @@ void GridFunction::GetVectorValues(ElementTransformation &T,
       {
          const IntegrationPoint &ip = ir.IntPoint(j);
          FElem->CalcShape(ip, shape);
+
          for (int k = 0; k < vdim; k++)
          {
             vals(k,j) = shape * ((const double *)loc_data + dof * k);
@@ -649,28 +986,22 @@ void GridFunction::GetVectorValues(ElementTransformation &T,
    {
       int spaceDim = fes->GetMesh()->SpaceDimension();
       DenseMatrix vshape(dof, spaceDim);
+
       vals.SetSize(spaceDim, nip);
       Vector val_j;
+
       for (int j = 0; j < nip; j++)
       {
          const IntegrationPoint &ip = ir.IntPoint(j);
          T.SetIntPoint(&ip);
          FElem->CalcVShape(T, vshape);
+
          vals.GetColumnReference(j, val_j);
          vshape.MultTranspose(loc_data, val_j);
       }
    }
 }
 
-void GridFunction::GetVectorValues(int i, const IntegrationRule &ir,
-                                   DenseMatrix &vals, DenseMatrix &tr) const
-{
-   ElementTransformation *Tr = fes->GetElementTransformation(i);
-   Tr->Transform(ir, tr);
-
-   GetVectorValues(*Tr, ir, vals);
-}
-
 int GridFunction::GetFaceVectorValues(
    int i, int side, const IntegrationRule &ir,
    DenseMatrix &vals, DenseMatrix &tr) const
@@ -702,13 +1033,13 @@ int GridFunction::GetFaceVectorValues(
    {
       Transf = fes->GetMesh()->GetFaceElementTransformations(i, 4);
       Transf->Loc1.Transform(ir, eir);
-      GetVectorValues(Transf->Elem1No, eir, vals, tr);
+      GetVectorValues(*Transf->Elem1, eir, vals, &tr);
    }
    else
    {
       Transf = fes->GetMesh()->GetFaceElementTransformations(i, 8);
       Transf->Loc2.Transform(ir, eir);
-      GetVectorValues(Transf->Elem2No, eir, vals, tr);
+      GetVectorValues(*Transf->Elem2, eir, vals, &tr);
    }
 
    return di;
@@ -1716,6 +2047,8 @@ void GridFunction::ProjectCoefficient(
    ElementTransformation *T = NULL;
    const FiniteElement *fe = NULL;
 
+   fes->BuildDofToArrays(); // ensures GetElementForDof(), GetLocalDofForDof() initialized.
+
    for (int i = 0; i < dofs.Size(); i++)
    {
       int dof = dofs[i], j = fes->GetElementForDof(dof);
@@ -1757,6 +2090,8 @@ void GridFunction::ProjectCoefficient(
 
    Vector val;
 
+   fes->BuildDofToArrays(); // ensures GetElementForDof(), GetLocalDofForDof() initialized.
+
    for (int i = 0; i < dofs.Size(); i++)
    {
       int dof = dofs[i], j = fes->GetElementForDof(dof);
@@ -2009,7 +2344,7 @@ double GridFunction::ComputeL2Error(
       fdof = fe->GetDof();
       transf = fes->GetElementTransformation(i);
       shape.SetSize(fdof);
-      intorder = 2*fe->GetOrder() + 1; // <----------
+      intorder = 2*fe->GetOrder() + 3; // <----------
       const IntegrationRule *ir;
       if (irs)
       {
@@ -2064,7 +2399,7 @@ double GridFunction::ComputeL2Error(
    {
       if (elems != NULL && (*elems)[i] == 0) { continue; }
       fe = fes->GetFE(i);
-      int intorder = 2*fe->GetOrder() + 1; // <----------
+      int intorder = 2*fe->GetOrder() + 3; // <----------
       const IntegrationRule *ir;
       if (irs)
       {
@@ -2168,7 +2503,7 @@ double GridFunction::ComputeH1Error(
             }
          intorder = 2 * intorder;  // <-------------
          const IntegrationRule &ir =
-            IntRules.Get(face_elem_transf->FaceGeom, intorder);
+            IntRules.Get(face_elem_transf->GetGeometryType(), intorder);
          err_val.SetSize(ir.GetNPoints());
          ell_coeff_val.SetSize(ir.GetNPoints());
          // side 1
@@ -2225,7 +2560,7 @@ double GridFunction::ComputeH1Error(
             }
          }
          face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
-         transf = face_elem_transf->Face;
+         transf = face_elem_transf;
          for (j = 0; j < ir.GetNPoints(); j++)
          {
             const IntegrationPoint &ip = ir.IntPoint(j);
@@ -2259,7 +2594,7 @@ double GridFunction::ComputeMaxError(
       fdof = fe->GetDof();
       transf = fes->GetElementTransformation(i);
       shape.SetSize(fdof);
-      intorder = 2*fe->GetOrder() + 1; // <----------
+      intorder = 2*fe->GetOrder() + 3; // <----------
       const IntegrationRule *ir;
       if (irs)
       {
@@ -2425,7 +2760,7 @@ 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);
@@ -2472,10 +2807,13 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
 }
 
 void GridFunction::ComputeElementLpErrors(const double p, Coefficient &exsol,
-                                          GridFunction &error,
+                                          Vector &error,
                                           Coefficient *weight,
                                           const IntegrationRule *irs[]) const
 {
+   MFEM_ASSERT(error.Size() == fes->GetNE(),
+               "Incorrect size for result vector");
+
    error = 0.0;
    const FiniteElement *fe;
    ElementTransformation *T;
@@ -2491,7 +2829,7 @@ void GridFunction::ComputeElementLpErrors(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);
@@ -2555,7 +2893,7 @@ 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);
@@ -2627,11 +2965,14 @@ double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,
 
 void GridFunction::ComputeElementLpErrors(const double p,
                                           VectorCoefficient &exsol,
-                                          GridFunction &error,
+                                          Vector &error,
                                           Coefficient *weight,
                                           VectorCoefficient *v_weight,
                                           const IntegrationRule *irs[]) const
 {
+   MFEM_ASSERT(error.Size() == fes->GetNE(),
+               "Incorrect size for result vector");
+
    error = 0.0;
    const FiniteElement *fe;
    ElementTransformation *T;
@@ -2648,7 +2989,7 @@ void GridFunction::ComputeElementLpErrors(const double p,
       }
       else
       {
-         int intorder = 2*fe->GetOrder() + 1; // <----------
+         int intorder = 2*fe->GetOrder() + 3; // <----------
          ir = &(IntRules.Get(fe->GetGeomType(), intorder));
       }
       T = fes->GetElementTransformation(i);
@@ -2658,15 +2999,15 @@ void GridFunction::ComputeElementLpErrors(const double p,
       loc_errs.SetSize(vals.Width());
       if (!v_weight)
       {
-         // compute the lengths of the errors at the integration points
-         // thus the vector norm is rotationally invariant
+         // compute the lengths of the errors at the integration points thus the
+         // vector norm is rotationally invariant
          vals.Norm2(loc_errs);
       }
       else
       {
          v_weight->Eval(exact_vals, *T, *ir);
-         // column-wise dot product of the vector error (in vals) and the
-         // vector weight (in exact_vals)
+         // column-wise dot product of the vector error (in vals) and the vector
+         // weight (in exact_vals)
          for (int j = 0; j < vals.Width(); j++)
          {
             double err = 0.0;
@@ -2798,7 +3139,9 @@ void GridFunction::SaveVTK(std::ostream &out, const std::string &field_name,
          RefG = GlobGeometryRefiner.Refine(
                    mesh->GetElementBaseGeometry(i), ref, 1);
 
-         GetVectorValues(i, RefG->RefPts, vval, pmat);
+         // GetVectorValues(i, RefG->RefPts, vval, pmat);
+         ElementTransformation * T = mesh->GetElementTransformation(i);
+         GetVectorValues(*T, RefG->RefPts, vval, &pmat);
 
          for (int j = 0; j < vval.Width(); j++)
          {

fem/gridfunc.hpp

@@ -144,17 +144,133 @@ public:
    /// Returns the values in the vertices of i'th element for dimension vdim.
    void GetNodalValues(int i, Array<double> &nval, int vdim = 1) const;
 
+   /** @name Element index Get Value Methods
+
+       These methods take an element index and return the interpolated value of
+       the field at a given reference point within the element.
+
+       @warning These methods retrieve and use the ElementTransformation object
+       from the mfem::Mesh. This can alter the state of the element
+       transformation object and can also lead to unexpected results when the
+       ElementTransformation object is already in use such as when these methods
+       are called from within an integration loop. Consider using
+       GetValue(ElementTransformation &T, ...) instead.
+   */
+   ///@{
+   /** Return a scalar value from within the given element. */
    virtual double GetValue(int i, const IntegrationPoint &ip,
                            int vdim = 1) const;
 
+   /** Return a vector value from within the given element. */
    void GetVectorValue(int i, const IntegrationPoint &ip, Vector &val) const;
+   ///@}
 
+   /** @name Element Index Get Values Methods
+
+       These are convenience methods for repeatedly calling GetValue for
+       multiple points within a given element. The GetValues methods are
+       optimized and should perform better than repeatedly calling GetValue. The
+       GetVectorValues method simply calls GetVectorValue repeatedly.
+
+       @warning These methods retrieve and use the ElementTransformation object
+       from the mfem::Mesh. This can alter the state of the element
+       transformation object and can also lead to unexpected results when the
+       ElementTransformation object is already in use such as when these methods
+       are called from within an integration loop. Consider using
+       GetValues(ElementTransformation &T, ...) instead.
+   */
+   ///@{
+   /** Compute a collection of scalar values from within the element indicated
+       by the index i. */
    void GetValues(int i, const IntegrationRule &ir, Vector &vals,
                   int vdim = 1) const;
 
+   /** Compute a collection of vector values from within the element indicated
+       by the index i. */
    void GetValues(int i, const IntegrationRule &ir, Vector &vals,
                   DenseMatrix &tr, int vdim = 1) const;
 
+   void GetVectorValues(int i, const IntegrationRule &ir,
+                        DenseMatrix &vals, DenseMatrix &tr) const;
+   ///@}
+
+   /** @name ElementTransformation Get Value Methods
+
+       These member functions are designed for use within
+       GridFunctionCoefficient objects. These can be used with
+       ElementTransformation objects coming from either
+       Mesh::GetElementTransformation() or Mesh::GetBdrElementTransformation().
+
+       @note These methods do not reset the ElementTransformation object so they
+       should be safe to use within integration loops or other contexts where
+       the ElementTransformation is already in use.
+   */
+   ///@{
+   /** Return a scalar value from within the element indicated by the
+       ElementTransformation Object. */
+   double GetValue(ElementTransformation &T, const IntegrationPoint &ip,
+                   int comp = 0, Vector *tr = NULL) const;
+
+   /** Return a vector value from within the element indicated by the
+       ElementTransformation Object. */
+   void GetVectorValue(ElementTransformation &T, const IntegrationPoint &ip,
+                       Vector &val, Vector *tr = NULL) const;
+   ///@}
+
+   /** @name ElementTransformation Get Values Methods
+
+       These are convenience methods for repeatedly calling GetValue for
+       multiple points within a given element. They work by calling either the
+       ElementTransformation or FaceElementTransformations versions described
+       above. Consequently, these methods should not be expected to run faster
+       than calling the above methods in an external loop.
+
+       @note These methods do not reset the ElementTransformation object so they
+       should be safe to use within integration loops or other contexts where
+       the ElementTransformation is already in use.
+
+       @note These methods can also be used with FaceElementTransformations
+       objects.
+    */
+   ///@{
+   /** Compute a collection of scalar values from within the element indicated
+       by the ElementTransformation object. */
+   void GetValues(ElementTransformation &T, const IntegrationRule &ir,
+                  Vector &vals, int comp = 0, DenseMatrix *tr = NULL) const;
+
+   /** Compute a collection of vector values from within the element indicated
+       by the ElementTransformation object. */
+   void GetVectorValues(ElementTransformation &T, const IntegrationRule &ir,
+                        DenseMatrix &vals, DenseMatrix *tr = NULL) const;
+   ///@}
+
+   /** @name Face Index Get Values Methods
+
+       These methods are designed to work with Discontinuous Galerkin basis
+       functions. They compute field values on the interface between elements,
+       or on boundary elements, by interpolating the field in a neighboring
+       element. The \a side argument indices which neighboring element should be
+       used: 0, 1, or 2 (automatically chosen).
+
+       @warning These methods retrieve and use the FaceElementTransformations
+       object from the mfem::Mesh. This can alter the state of the face element
+       transformations object and can also lead to unexpected results when the
+       FaceElementTransformations object is already in use such as when these
+       methods are called from within an integration loop. Consider using
+       GetValues(ElementTransformation &T, ...) instead.
+    */
+   ///@{
+   /** Compute a collection of scalar values from within the face
+       indicated by the index i. */
+   int GetFaceValues(int i, int side, const IntegrationRule &ir, Vector &vals,
+                     DenseMatrix &tr, int vdim = 1) const;
+
+   /** Compute a collection of vector values from within the face
+       indicated by the index i. */
+   int GetFaceVectorValues(int i, int side, const IntegrationRule &ir,
+                           DenseMatrix &vals, DenseMatrix &tr) const;
+   ///@}
+
    void GetLaplacians(int i, const IntegrationRule &ir, Vector &laps,
                       int vdim = 1) const;
 
@@ -167,18 +283,6 @@ public:
    void GetHessians(int i, const IntegrationRule &ir, DenseMatrix &hess,
                     DenseMatrix &tr, int vdim = 1) const;
 
-   int GetFaceValues(int i, int side, const IntegrationRule &ir, Vector &vals,
-                     DenseMatrix &tr, int vdim = 1) const;
-
-   void GetVectorValues(ElementTransformation &T, const IntegrationRule &ir,
-                        DenseMatrix &vals) const;
-
-   void GetVectorValues(int i, const IntegrationRule &ir,
-                        DenseMatrix &vals, DenseMatrix &tr) const;
-
-   int GetFaceVectorValues(int i, int side, const IntegrationRule &ir,
-                           DenseMatrix &vals, DenseMatrix &tr) const;
-
    void GetValuesFrom(const GridFunction &orig_func);
 
    void GetBdrValuesFrom(const GridFunction &orig_func);
@@ -236,12 +340,10 @@ public:
 
    virtual void ProjectCoefficient(Coefficient &coeff);
 
-   // call fes -> BuildDofToArrays() before using this projection
    void ProjectCoefficient(Coefficient &coeff, Array<int> &dofs, int vd = 0);
 
    void ProjectCoefficient(VectorCoefficient &vcoeff);
 
-   // call fes -> BuildDofToArrays() before using this projection
    void ProjectCoefficient(VectorCoefficient &vcoeff, Array<int> &dofs);
 
    void ProjectCoefficient(Coefficient *coeff[]);
@@ -365,28 +467,28 @@ public:
                                  const IntegrationRule *irs[] = NULL) const;
 
    /** Compute the Lp error in each element of the mesh and store the results in
-       the GridFunction @a error. The result should be an L2 GridFunction of
-       order zero using map type VALUE. */
+       the Vector @a error. The result should be of length number of elements,
+       for example an L2 GridFunction of order zero using map type VALUE. */
    virtual void ComputeElementLpErrors(const double p, Coefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        Coefficient *weight = NULL,
                                        const IntegrationRule *irs[] = NULL
                                       ) const;
 
    virtual void ComputeElementL1Errors(Coefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
    { ComputeElementLpErrors(1.0, exsol, error, NULL, irs); }
 
    virtual void ComputeElementL2Errors(Coefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
    { ComputeElementLpErrors(2.0, exsol, error, NULL, irs); }
 
    virtual void ComputeElementMaxErrors(Coefficient &exsol,
-                                        GridFunction &error,
+                                        Vector &error,
                                         const IntegrationRule *irs[] = NULL
                                        ) const
    { ComputeElementLpErrors(infinity(), exsol, error, NULL, irs); }
@@ -400,29 +502,29 @@ public:
                                  const IntegrationRule *irs[] = NULL) const;
 
    /** Compute the Lp error in each element of the mesh and store the results in
-       the GridFunction @ error. The result should be an L2 GridFunction of
-       order zero using map type VALUE. */
+       the Vector @ error. The result should be of length number of elements,
+       for example an L2 GridFunction of order zero using map type VALUE. */
    virtual void ComputeElementLpErrors(const double p, VectorCoefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        Coefficient *weight = NULL,
                                        VectorCoefficient *v_weight = NULL,
                                        const IntegrationRule *irs[] = NULL
                                       ) const;
 
    virtual void ComputeElementL1Errors(VectorCoefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
    { ComputeElementLpErrors(1.0, exsol, error, NULL, NULL, irs); }
 
    virtual void ComputeElementL2Errors(VectorCoefficient &exsol,
-                                       GridFunction &error,
+                                       Vector &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
    { ComputeElementLpErrors(2.0, exsol, error, NULL, NULL, irs); }
 
    virtual void ComputeElementMaxErrors(VectorCoefficient &exsol,
-                                        GridFunction &error,
+                                        Vector &error,
                                         const IntegrationRule *irs[] = NULL
                                        ) const
    { ComputeElementLpErrors(infinity(), exsol, error, NULL, NULL, irs); }
@@ -496,11 +598,13 @@ public:
                      type = adios2stream::data_type::point_data) const;
 #endif
 
-   /** Write the GridFunction in VTK format. Note that Mesh::PrintVTK must be
-       called first. The parameter ref > 0 must match the one used in
+   /** @brief Write the GridFunction in VTK format. Note that Mesh::PrintVTK
+       must be called first. The parameter ref > 0 must match the one used in
        Mesh::PrintVTK. */
    void SaveVTK(std::ostream &out, const std::string &field_name, int ref);
 
+   /** @brief Write the GridFunction in STL format. Note that the mesh dimension
+       must be 2 and that quad elements will be broken into two triangles.*/
    void SaveSTL(std::ostream &out, int TimesToRefine = 1);
 
    /// Destroys grid function.
@@ -633,6 +737,16 @@ public:
     */
    inline void GetElementValues(int idx, Vector &values) const;
 
+   /// Return the quadrature function values at an integration point.
+   /** The result is stored in the Vector @a values as a reference to the
+       global values. */
+   inline void GetElementValues(int idx, const int ip_num, Vector &values);
+
+   /// Return the quadrature function values at an integration point.
+   /** The result is stored in the Vector @a values as a copy to the
+       global values. */
+   inline void GetElementValues(int idx, const int ip_num, Vector &values) const;
+
    /// Return all values associated with mesh element @a idx in a DenseMatrix.
    /** The result is stored in the DenseMatrix @a values as a reference to the
        global values.
@@ -737,6 +851,25 @@ inline void QuadratureFunction::GetElementValues(int idx, Vector &values) const
    }
 }
 
+inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
+                                                 Vector &values)
+{
+   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
+   values.NewDataAndSize(data + s_offset, vdim);
+}
+
+inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
+                                                 Vector &values) const
+{
+   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
+   values.SetSize(vdim);
+   const double *q = data + s_offset;
+   for (int i = 0; i < values.Size(); i++)
+   {
+      values(i) = *(q++);
+   }
+}
+
 inline void QuadratureFunction::GetElementValues(int idx, DenseMatrix &values)
 {
    const int s_offset = qspace->element_offsets[idx];

fem/gslib.cpp

@@ -29,12 +29,14 @@ namespace mfem
 {
 
 FindPointsGSLIB::FindPointsGSLIB()
-   : mesh(NULL), ir_simplex(NULL), gsl_mesh(), fdata2D(NULL), fdata3D(NULL),
-     dim(-1)
+   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
+     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
 {
    gsl_comm = new comm;
 #ifdef MFEM_USE_MPI
-   MPI_Init(NULL, NULL);
+   int initialized;
+   MPI_Initialized(&initialized);
+   if (!initialized) { MPI_Init(NULL, NULL); }
    MPI_Comm comm = MPI_COMM_WORLD;;
    comm_init(gsl_comm, comm);
 #else
@@ -50,28 +52,29 @@ FindPointsGSLIB::~FindPointsGSLIB()
 
 #ifdef MFEM_USE_MPI
 FindPointsGSLIB::FindPointsGSLIB(MPI_Comm _comm)
-   : mesh(NULL), ir_simplex(NULL), gsl_mesh(), fdata2D(NULL), fdata3D(NULL),
-     dim(-1)
+   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
+     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
 {
    gsl_comm = new comm;
    comm_init(gsl_comm, _comm);
 }
 #endif
 
-void FindPointsGSLIB::Setup(Mesh &m, double bb_t, double newt_tol, int npt_max)
+void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
+                            const int npt_max)
 {
    MFEM_VERIFY(m.GetNodes() != NULL, "Mesh nodes are required.");
    MFEM_VERIFY(m.GetNumGeometries(m.Dimension()) == 1,
                "Mixed meshes are not currently supported in FindPointsGSLIB.");
 
+   // call FreeData if FindPointsGSLIB::Setup has been called already
+   if (setupflag) { FreeData(); }
+
    mesh = &m;
    dim  = mesh->Dimension();
    const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
    unsigned dof1D = fe->GetOrder() + 1;
-   int NE      = mesh->GetNE(),
-       dof_cnt = fe->GetDof(),
-       pts_cnt = NE * dof_cnt,
-       gt      = fe->GetGeomType();
+   const int gt   = fe->GetGeomType();
 
    if (gt == Geometry::TRIANGLE || gt == Geometry::TETRAHEDRON ||
        gt == Geometry::PRISM)
@@ -87,8 +90,8 @@ void FindPointsGSLIB::Setup(Mesh &m, double bb_t, double newt_tol, int npt_max)
       MFEM_ABORT("Element type not currently supported in FindPointsGSLIB.");
    }
 
-   pts_cnt = gsl_mesh.Size()/dim;
-   int NEtot = pts_cnt/(int)pow(dof1D, dim);
+   const int pts_cnt = gsl_mesh.Size()/dim,
+             NEtot = pts_cnt/(int)pow(dof1D, dim);
 
    if (dim == 2)
    {
@@ -107,6 +110,7 @@ void FindPointsGSLIB::Setup(Mesh &m, double bb_t, double newt_tol, int npt_max)
       fdata3D = findpts_setup_3(gsl_comm, elx, nr, NEtot, mr, bb_t,
                                 pts_cnt, pts_cnt, npt_max, newt_tol);
    }
+   setupflag = true;
 }
 
 void FindPointsGSLIB::FindPoints(const Vector &point_pos,
@@ -115,6 +119,7 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
                                  Array<unsigned int> &elem_ids,
                                  Vector &ref_pos, Vector &dist)
 {
+   MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
    const int points_cnt = point_pos.Size() / dim;
    if (dim == 2)
    {
@@ -150,36 +155,92 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
    }
 }
 
+void FindPointsGSLIB::FindPoints(const Vector &point_pos)
+{
+   const int points_cnt = point_pos.Size() / dim;
+   gsl_code.SetSize(points_cnt);
+   gsl_proc.SetSize(points_cnt);
+   gsl_elem.SetSize(points_cnt);
+   gsl_ref.SetSize(points_cnt * dim);
+   gsl_dist.SetSize(points_cnt);
+
+   FindPoints(point_pos, gsl_code, gsl_proc, gsl_elem, gsl_ref, gsl_dist);
+}
+
+void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
+                                 const double bb_t, const double newt_tol,
+                                 const int npt_max)
+{
+   if (!setupflag || (mesh != &m) )
+   {
+      Setup(m, bb_t, newt_tol, npt_max);
+   }
+   FindPoints(point_pos);
+}
+
 void FindPointsGSLIB::Interpolate(Array<unsigned int> &codes,
                                   Array<unsigned int> &proc_ids,
                                   Array<unsigned int> &elem_ids,
                                   Vector &ref_pos, const GridFunction &field_in,
                                   Vector &field_out)
 {
-   Vector node_vals;
-   GetNodeValues(field_in, node_vals);
 
-   const int points_cnt = ref_pos.Size() / dim;
-   if (dim==2)
+   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
+   GridFunction field_in_scalar(&ind_fes);
+   Vector node_vals;
+
+   const int ncomp      = field_in.FESpace()->GetVDim(),
+             points_fld = field_in.Size() / ncomp,
+             points_cnt = codes.Size();
+
+   for (int i = 0; i < ncomp; i++)
    {
-      findpts_eval_2(field_out.GetData(), sizeof(double),
-                     codes.GetData(), sizeof(unsigned int),
-                     proc_ids.GetData(), sizeof(unsigned int),
-                     elem_ids.GetData(), sizeof(unsigned int),
-                     ref_pos.GetData(), sizeof(double) * dim,
-                     points_cnt, node_vals.GetData(), fdata2D);
-   }
-   else
-   {
-      findpts_eval_3(field_out.GetData(), sizeof(double),
-                     codes.GetData(), sizeof(unsigned int),
-                     proc_ids.GetData(), sizeof(unsigned int),
-                     elem_ids.GetData(), sizeof(unsigned int),
-                     ref_pos.GetData(), sizeof(double) * dim,
-                     points_cnt, node_vals.GetData(), fdata3D);
+      const int dataptrin  = i*points_fld,
+                dataptrout = i*points_cnt;
+      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
+      GetNodeValues(field_in_scalar, node_vals);
+
+      if (dim==2)
+      {
+         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
+                        codes.GetData(),       sizeof(unsigned int),
+                        proc_ids.GetData(),    sizeof(unsigned int),
+                        elem_ids.GetData(),    sizeof(unsigned int),
+                        ref_pos.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata2D);
+      }
+      else
+      {
+         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
+                        codes.GetData(),       sizeof(unsigned int),
+                        proc_ids.GetData(),    sizeof(unsigned int),
+                        elem_ids.GetData(),    sizeof(unsigned int),
+                        ref_pos.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata3D);
+      }
    }
 }
 
+void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
+                                  Vector &field_out)
+{
+   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+}
+
+void FindPointsGSLIB::Interpolate(const Vector &point_pos,
+                                  const GridFunction &field_in, Vector &field_out)
+{
+   FindPoints(point_pos);
+   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+}
+
+void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
+                                  const GridFunction &field_in, Vector &field_out)
+{
+   FindPoints(m, point_pos);
+   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+}
+
 void FindPointsGSLIB::FreeData()
 {
    if (dim == 2)
@@ -190,7 +251,13 @@ void FindPointsGSLIB::FreeData()
    {
       findpts_free_3(fdata3D);
    }
+   setupflag = false;
+   gsl_code.DeleteAll();
+   gsl_proc.DeleteAll();
+   gsl_elem.DeleteAll();
    gsl_mesh.Destroy();
+   gsl_ref.Destroy();
+   gsl_dist.Destroy();
 }
 
 void FindPointsGSLIB::GetNodeValues(const GridFunction &gf_in,
@@ -292,7 +359,7 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
    const GridFunction *nodes = mesh->GetNodes();
    Mesh *meshsplit           = NULL;
    const int NE              = mesh->GetNE();
-   int NEsplit;
+   int NEsplit = -1;
 
    // Split the reference element into a reference submesh of quads or hexes.
    if (gt == Geometry::TRIANGLE)
@@ -386,6 +453,7 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
       }
       meshsplit->FinalizeHexMesh(1, 1, true);
    }
+   else { MFEM_ABORT("Unsupported geometry type."); }
 
    // Curve the reference submesh.
    H1_FECollection fec(fe->GetOrder(), dim);

fem/gslib.hpp

@@ -29,10 +29,12 @@ class FindPointsGSLIB
 protected:
    Mesh *mesh;
    IntegrationRule *ir_simplex;
-   Vector gsl_mesh;
    struct findpts_data_2 *fdata2D;
    struct findpts_data_3 *fdata3D;
    int dim;
+   Array<unsigned int> gsl_code, gsl_proc, gsl_elem;
+   Vector gsl_mesh, gsl_ref, gsl_dist;
+   bool setupflag;
 
    struct comm *gsl_comm;
 
@@ -59,7 +61,8 @@ public:
        @param[in] newt_tol  Newton tolerance for the gslib search methods.
        @param[in] npt_max   Number of points for simultaneous iteration. This
                             alters performance and memory footprint. */
-   void Setup(Mesh &m, double bb_t, double newt_tol, int npt_max);
+   void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
+              const int npt_max = 256);
 
    /** Searches positions given in physical space by @a point_pos. All output
        Arrays and Vectors are expected to have the correct size.
@@ -73,11 +76,15 @@ public:
        @param[out] ref_pos    Reference coordinates of the found point. Ordered
                               by vdim (XYZ,XYZ,XYZ...).
                               Note: the gslib reference frame is [-1,1].
-       @param[out] dist       Distance between the seeked and the found point
+       @param[out] dist       Distance between the sought and the found point
                               in physical space. */
    void FindPoints(const Vector &point_pos, Array<unsigned int> &codes,
                    Array<unsigned int> &proc_ids, Array<unsigned int> &elem_ids,
                    Vector &ref_pos, Vector &dist);
+   void FindPoints(const Vector &point_pos);
+   /// Setup FindPoints and search positions
+   void FindPoints(Mesh &m, const Vector &point_pos, const double bb_t = 0.1,
+                   const double newt_tol = 1.0e-12,  const int npt_max = 256);
 
    /** Interpolation of field values at prescribed reference space positions.
 
@@ -96,11 +103,31 @@ public:
    void Interpolate(Array<unsigned int> &codes, Array<unsigned int> &proc_ids,
                     Array<unsigned int> &elem_ids, Vector &ref_pos,
                     const GridFunction &field_in, Vector &field_out);
+   void Interpolate(const GridFunction &field_in, Vector &field_out);
+   /** Search positions and interpolate */
+   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
+                    Vector &field_out);
+   /** Setup FindPoints, search positions and interpolate */
+   void Interpolate(Mesh &m, const Vector &point_pos,
+                    const GridFunction &field_in, Vector &field_out);
 
    /** Cleans up memory allocated internally by gslib.
        Note that in parallel, this must be called before MPI_Finalize(), as
        it calls MPI_Comm_free() for internal gslib communicators. */
    void FreeData();
+
+   /// Return code for each point searched by FindPoints: inside element (0), on
+   /// element boundary (1), or not found (2).
+   const Array<unsigned int> &GetCode() const { return gsl_code; }
+   /// Return element number for each point found by FindPoints.
+   const Array<unsigned int> &GetElem() const { return gsl_elem; }
+   /// Return MPI rank on which each point was found by FindPoints.
+   const Array<unsigned int> &GetProc() const { return gsl_proc; }
+   /// Return reference coordinates for each point found by FindPoints.
+   const Vector &GetReferencePosition() const { return gsl_ref;  }
+   /// Return distance Distance between the sought and the found point
+   /// in physical space, for each point found by FindPoints.
+   const Vector &GetDist()              const { return gsl_dist; }
 };
 
 } // namespace mfem

fem/libceed/ceed.hpp

@@ -40,7 +40,7 @@ struct CeedConstCoeff
 
 struct CeedGridCoeff
 {
-   GridFunction* coeff;
+   const GridFunction* coeff;
    CeedBasis basis;
    CeedElemRestriction restr;
    CeedVector coeffVector;

fem/linearform.hpp

@@ -19,7 +19,7 @@
 namespace mfem
 {
 
-/// Class for linear form - Vector with associated FE space and LFIntegrators.
+/// Vector with associated FE space and LinearFormIntegrators.
 class LinearForm : public Vector
 {
 protected:

fem/lininteg.cpp

@@ -307,7 +307,7 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    if (ir == NULL)
    {
       int intorder = 2*el.GetOrder();
-      ir = &IntRules.Get(Tr.FaceGeom, intorder);
+      ir = &IntRules.Get(Tr.GetGeometryType(), intorder);
    }
 
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -316,9 +316,11 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
       IntegrationPoint eip;
       Tr.Loc1.Transform(ip, eip);
 
-      Tr.Face->SetIntPoint(&ip);
-      Q.Eval(vec, *Tr.Face, ip);
-      vec *= Tr.Face->Weight() * ip.weight;
+      Tr.SetIntPoint(&ip);
+
+      // Use Tr transformation in case Q depends on boundary attribute
+      Q.Eval(vec, Tr, ip);
+      vec *= Tr.Weight() * ip.weight;
       el.CalcShape(eip, shape);
       for (int k = 0; k < vdim; k++)
       {
@@ -510,7 +512,7 @@ void BoundaryFlowIntegrator::AssembleRHSElementVect(
       {
          order++;
       }
-      ir = &IntRules.Get(Tr.FaceGeom, order);
+      ir = &IntRules.Get(Tr.GetGeometryType(), order);
    }
 
    shape.SetSize(ndof);
@@ -524,8 +526,10 @@ void BoundaryFlowIntegrator::AssembleRHSElementVect(
       Tr.Loc1.Transform(ip, eip);
       el.CalcShape(eip, shape);
 
-      Tr.Face->SetIntPoint(&ip);
+      Tr.SetIntPoint(&ip);
 
+      // Use Tr.Elem1 transformation for u so that it matches the coefficient
+      // used with the ConvectionIntegrator and/or the DGTraceIntegrator.
       u->Eval(vu, *Tr.Elem1, eip);
 
       if (dim == 1)
@@ -534,12 +538,12 @@ void BoundaryFlowIntegrator::AssembleRHSElementVect(
       }
       else
       {
-         CalcOrtho(Tr.Face->Jacobian(), nor);
+         CalcOrtho(Tr.Jacobian(), nor);
       }
 
       un = vu * nor;
       w = 0.5*alpha*un - beta*fabs(un);
-      w *= ip.weight*f->Eval(*Tr.Elem1, eip);
+      w *= ip.weight*f->Eval(Tr, ip);
       elvect.Add(w, shape);
    }
 }
@@ -582,7 +586,7 @@ void DGDirichletLFIntegrator::AssembleRHSElementVect(
    {
       // a simple choice for the integration order; is this OK?
       int order = 2*el.GetOrder();
-      ir = &IntRules.Get(Tr.FaceGeom, order);
+      ir = &IntRules.Get(Tr.GetGeometryType(), order);
    }
 
    for (int p = 0; p < ir->GetNPoints(); p++)
@@ -591,33 +595,33 @@ void DGDirichletLFIntegrator::AssembleRHSElementVect(
       IntegrationPoint eip;
 
       Tr.Loc1.Transform(ip, eip);
-      Tr.Face->SetIntPoint(&ip);
+      Tr.SetIntPoint(&ip);
       if (dim == 1)
       {
          nor(0) = 2*eip.x - 1.0;
       }
       else
       {
-         CalcOrtho(Tr.Face->Jacobian(), nor);
+         CalcOrtho(Tr.Jacobian(), nor);
       }
 
       el.CalcShape(eip, shape);
       el.CalcDShape(eip, dshape);
-      Tr.Elem1->SetIntPoint(&eip);
+
       // compute uD through the face transformation
-      w = ip.weight * uD->Eval(*Tr.Face, ip) / Tr.Elem1->Weight();
+      w = ip.weight * uD->Eval(Tr, ip) / Tr.Elem1->Weight();
       if (!MQ)
       {
          if (Q)
          {
-            w *= Q->Eval(*Tr.Elem1, eip);
+            w *= Q->Eval(Tr, ip);
          }
          ni.Set(w, nor);
       }
       else
       {
          nh.Set(w, nor);
-         MQ->Eval(mq, *Tr.Elem1, eip);
+         MQ->Eval(mq, Tr, ip);
          mq.MultTranspose(nh, ni);
       }
       CalcAdjugate(Tr.Elem1->Jacobian(), adjJ);
@@ -676,7 +680,7 @@ void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
    if (ir == NULL)
    {
       const int order = 2*el.GetOrder(); // <-----
-      ir = &IntRules.Get(Tr.FaceGeom, order);
+      ir = &IntRules.Get(Tr.GetGeometryType(), order);
    }
 
    for (int pi = 0; pi < ir->GetNPoints(); ++pi)
@@ -684,11 +688,10 @@ void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
       const IntegrationPoint &ip = ir->IntPoint(pi);
       IntegrationPoint eip;
       Tr.Loc1.Transform(ip, eip);
-      Tr.Face->SetIntPoint(&ip);
-      Tr.Elem1->SetIntPoint(&eip);
+      Tr.SetIntPoint(&ip);
 
       // Evaluate the Dirichlet b.c. using the face transformation.
-      uD.Eval(u_dir, *Tr.Face, ip);
+      uD.Eval(u_dir, Tr, ip);
 
       el.CalcShape(eip, shape);
       el.CalcDShape(eip, dshape);
@@ -702,7 +705,7 @@ void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
       }
       else
       {
-         CalcOrtho(Tr.Face->Jacobian(), nor);
+         CalcOrtho(Tr.Jacobian(), nor);
       }
 
       double wL, wM, jcoef;
@@ -768,4 +771,58 @@ void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
    }
 }
 
+void VectorQuadratureLFIntegrator::AssembleRHSElementVect(
+   const FiniteElement &fe, ElementTransformation &Tr, Vector &elvect)
+{
+   const IntegrationRule *ir =
+      &vqfc.GetQuadFunction().GetSpace()->GetElementIntRule(Tr.ElementNo);
+
+   const int nqp = ir->GetNPoints();
+   const int vdim = vqfc.GetVDim();
+   const int ndofs = fe.GetDof();
+   Vector shape(ndofs);
+   Vector temp(vdim);
+   elvect.SetSize(vdim * ndofs);
+   elvect = 0.0;
+   for (int q = 0; q < nqp; q++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(q);
+      Tr.SetIntPoint(&ip);
+      const double w = Tr.Weight() * ip.weight;
+      vqfc.Eval(temp, Tr, ip);
+      fe.CalcShape(ip, shape);
+      for (int ind = 0; ind < vdim; ind++)
+      {
+         for (int nd = 0; nd < ndofs; nd++)
+         {
+            elvect(nd + ind * ndofs) += w * shape(nd) * temp(ind);
+         }
+      }
+   }
+}
+
+void QuadratureLFIntegrator::AssembleRHSElementVect(const FiniteElement &fe,
+                                                    ElementTransformation &Tr,
+                                                    Vector &elvect)
+{
+   const IntegrationRule *ir =
+      &qfc.GetQuadFunction().GetSpace()->GetElementIntRule(Tr.ElementNo);
+
+   const int nqp = ir->GetNPoints();
+   const int ndofs = fe.GetDof();
+   Vector shape(ndofs);
+   elvect.SetSize(ndofs);
+   elvect = 0.0;
+   for (int q = 0; q < nqp; q++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(q);
+      Tr.SetIntPoint (&ip);
+      const double w = Tr.Weight() * ip.weight;
+      double temp = qfc.Eval(Tr, ip);
+      fe.CalcShape(ip, shape);
+      shape *= (w * temp);
+      elvect += shape;
+   }
+}
+
 }

fem/lininteg.hpp

@@ -36,7 +36,7 @@ public:
                                        FaceElementTransformations &Tr,
                                        Vector &elvect);
 
-   void SetIntRule(const IntegrationRule *ir) { IntRule = ir; }
+   virtual void SetIntRule(const IntegrationRule *ir) { IntRule = ir; }
    const IntegrationRule* GetIntRule() { return IntRule; }
 
    virtual ~LinearFormIntegrator() { }
@@ -426,6 +426,69 @@ public:
                                        Vector &elvect);
 };
 
+/** Class for domain integration of L(v) := (f, v), where
+    f=(f1,...,fn) and v=(v1,...,vn). that makes use of
+    VectorQuadratureFunctionCoefficient*/
+class VectorQuadratureLFIntegrator : public LinearFormIntegrator
+{
+private:
+   VectorQuadratureFunctionCoefficient &vqfc;
+
+public:
+   VectorQuadratureLFIntegrator(VectorQuadratureFunctionCoefficient &vqfc,
+                                const IntegrationRule *ir)
+      : LinearFormIntegrator(ir), vqfc(vqfc)
+   {
+      if (ir)
+      {
+         MFEM_WARNING("Integration rule not used in this class. "
+                      "The QuadratureFunction integration rules are used instead");
+      }
+   }
+
+   using LinearFormIntegrator::AssembleRHSElementVect;
+   virtual void AssembleRHSElementVect(const FiniteElement &fe,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect);
+
+   virtual void SetIntRule(const IntegrationRule *ir)
+   {
+      MFEM_WARNING("Integration rule not used in this class. "
+                   "The QuadratureFunction integration rules are used instead");
+   }
+};
+
+/** Class for domain integration L(v) := (f, v) that makes use
+    of QuadratureFunctionCoefficient. */
+class QuadratureLFIntegrator : public LinearFormIntegrator
+{
+private:
+   QuadratureFunctionCoefficient &qfc;
+
+public:
+   QuadratureLFIntegrator(QuadratureFunctionCoefficient &qfc,
+                          const IntegrationRule *ir)
+      : LinearFormIntegrator(ir), qfc(qfc)
+   {
+      if (ir)
+      {
+         MFEM_WARNING("Integration rule not used in this class. "
+                      "The QuadratureFunction integration rules are used instead");
+      }
+   }
+
+   using LinearFormIntegrator::AssembleRHSElementVect;
+   virtual void AssembleRHSElementVect(const FiniteElement &fe,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect);
+
+   virtual void SetIntRule(const IntegrationRule *ir)
+   {
+      MFEM_WARNING("Integration rule not used in this class. "
+                   "The QuadratureFunction integration rules are used instead");
+   }
+};
+
 }
 
 #endif

fem/nonlininteg.hpp

@@ -20,10 +20,9 @@
 namespace mfem
 {
 
-/** The abstract base class NonlinearFormIntegrator is used to express the
-    local action of a general nonlinear finite element operator. In addition
-    it may provide the capability to assemble the local gradient operator
-    and to compute the local energy. */
+/** @brief This class is used to express the local action of a general nonlinear
+    finite element operator. In addition it may provide the capability to
+    assemble the local gradient operator and to compute the local energy. */
 class NonlinearFormIntegrator
 {
 protected:

fem/pfespace.cpp

@@ -487,6 +487,11 @@ void ParFiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
 
 void ParFiniteElementSpace::GetFaceDofs(int i, Array<int> &dofs) const
 {
+   if (face_dof)
+   {
+      face_dof->GetRow(i, dofs);
+      return;
+   }
    FiniteElementSpace::GetFaceDofs(i, dofs);
    if (Conforming())
    {

fem/pfespace.hpp

@@ -376,7 +376,7 @@ public:
 
    void PrintPartitionStats();
 
-   // Obsolete, kept for backward compatibility
+   /// Obsolete, kept for backward compatibility
    int TrueVSize() const { return ltdof_size; }
 };
 

fem/pgridfunc.cpp

@@ -232,7 +232,8 @@ void ParGridFunction::ExchangeFaceNbrData()
    auto d_send_data = send_data.Write();
    MFEM_FORALL(i, send_data.Size(),
    {
-      d_send_data[i] = d_data[d_send_ldof[i]];
+      const int ldof = d_send_ldof[i];
+      d_send_data[i] = d_data[ldof >= 0 ? ldof : -1-ldof];
    });
 
    bool mpi_gpu_aware = Device::GetGPUAwareMPI();

fem/restriction.cpp

@@ -168,6 +168,27 @@ void ElementRestriction::Mult(const Vector& x, Vector& y) const
    });
 }
 
+void ElementRestriction::MultUnsigned(const Vector& x, Vector& y) const
+{
+   // Assumes all elements have the same number of dofs
+   const int nd = dof;
+   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);
+   auto d_gatherMap = gatherMap.Read();
+
+   MFEM_FORALL(i, dof*ne,
+   {
+      const int gid = d_gatherMap[i];
+      const int j = gid >= 0 ? gid : -1-gid;
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(i % nd, c, i / nd) = d_x(t?c:j, t?j:c);
+      }
+   });
+}
+
 void ElementRestriction::MultTranspose(const Vector& x, Vector& y) const
 {
    // Assumes all elements have the same number of dofs
@@ -966,27 +987,51 @@ void L2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
    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,
+
+   if (m == L2FaceValues::DoubleValued)
    {
-      const int offset = d_offsets[i];
-      const int nextOffset = d_offsets[i + 1];
-      for (int c = 0; c < vd; ++c)
+      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,
       {
-         double dofValue = 0;
-         for (int j = offset; j < nextOffset; ++j)
+         const int offset = d_offsets[i];
+         const int nextOffset = d_offsets[i + 1];
+         for (int c = 0; c < vd; ++c)
          {
-            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);
+            double dofValue = 0;
+            for (int j = offset; j < nextOffset; ++j)
+            {
+               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);
+            }
+            d_y(t?c:i,t?i:c) += dofValue;
          }
-         d_y(t?c:i,t?i:c) += dofValue;
-      }
-   });
+      });
+   }
+   else
+   {
+      auto d_x = Reshape(x.Read(), nd, vd, nf);
+      auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+      MFEM_FORALL(i, ndofs,
+      {
+         const int offset = d_offsets[i];
+         const int nextOffset = d_offsets[i + 1];
+         for (int c = 0; c < vd; ++c)
+         {
+            double dofValue = 0;
+            for (int j = offset; j < nextOffset; ++j)
+            {
+               int idx_j = d_indices[j];
+               dofValue +=  d_x(idx_j % nd, c, idx_j / nd);
+            }
+            d_y(t?c:i,t?i:c) += dofValue;
+         }
+      });
+   }
 }
 
 int ToLexOrdering(const int dim, const int face_id, const int size1d,

fem/restriction.hpp

@@ -47,6 +47,8 @@ public:
    void Mult(const Vector &x, Vector &y) const;
    void MultTranspose(const Vector &x, Vector &y) const;
 
+   /// Compute Mult without applying signs based on DOF orientations.
+   void MultUnsigned(const Vector &x, Vector &y) const;
    /// Compute MultTranspose without applying signs based on DOF orientations.
    void MultTransposeUnsigned(const Vector &x, Vector &y) const;
 

fem/tbilinearform.hpp

@@ -13,6 +13,7 @@
 #define MFEM_TEMPLATE_BILINEAR_FORM
 
 #include "../config/tconfig.hpp"
+#include "../linalg/simd.hpp"
 #include "../linalg/ttensor.hpp"
 #include "bilinearform.hpp"
 #include "tevaluator.hpp"
@@ -23,16 +24,32 @@
 namespace mfem
 {
 
-// Templated bilinear form class, cf. bilinearform.?pp
+/** @brief Templated bilinear form class, cf. bilinearform.?pp
 
 // complex_t - sol dof data type
+    @tparam meshType typically TMesh, which is templated on FE type
 // real_t - mesh nodes, sol basis, mesh basis data type
+    @tparam solFESpace eg. H1_FiniteElementSpace
+    @tparam IR integration rule, typically TIntegrationRule, which is further
+               templated on element geometry
+    @tparam IntegratorType typically a TIntegrator, which is templated on a
+                           kernel, eg. TDiffusionKernel or TMassKernel. This
+                           describes what actual problem you solve.
+    @tparam solVecLayout_t describes how degrees of freedom are laid out,
+                           scalar or vector, column/row major, etc.
+    @tparam complex_t data type for solution dofs
+    @tparam real_t data type for mesh nodes, solution basis, and mesh basis
+*/
 template <typename meshType, typename solFESpace,
           typename IR, typename IntegratorType,
           typename solVecLayout_t = ScalarLayout,
-          typename complex_t = double, typename real_t = double>
+          typename complex_t = double, typename real_t = double,
+          typename impl_traits_t = AutoSIMDTraits<complex_t,real_t> >
 class TBilinearForm : public Operator
 {
+public:
+   typedef impl_traits_t impl_traits_type;
+
 protected:
    typedef complex_t complex_type;
    typedef real_t    real_type;
@@ -48,26 +65,47 @@ protected:
    static const int dofs = solFE_type::dofs;
    static const int vdim = solVecLayout_t::vec_dim;
    static const int qpts = IR::qpts;
+   static const int AB   = impl_traits_t::align_bytes;
+   static const int SS   = impl_traits_t::simd_size;
+   static const int BE   = impl_traits_t::batch_size;
+   static const int TE   = SS*BE;
 
+   typedef typename impl_traits_t::vcomplex_t vcomplex_t;
+   typedef typename impl_traits_t::vreal_t    vreal_t;
+
+   /// @name IntegratorType defines several internal types
+   ///@{
    typedef IntegratorType integ_t;
+   /// coeff_t might be TConstantCoefficient or TFunctionCoefficient, for example
    typedef typename integ_t::coefficient_type coeff_t;
-   typedef typename integ_t::template kernel<sdim,dim,complex_t>::type kernel_t;
+   /// kernel_t may be TDiffusionKernel or TMassKernel
+   typedef typename integ_t::template kernel<sdim,dim,vcomplex_t>::type kernel_t;
+   /// p_assembled_t is something like a TTensor or TMatrix for partial assembly
    typedef typename kernel_t::template p_asm_data<qpts>::type p_assembled_t;
+   /// f_assembled_t is something like a TTensor or TMatrix for full assembly
    typedef typename kernel_t::template f_asm_data<qpts>::type f_assembled_t;
+   ///@}
+
+   typedef typename kernel_t::template
+   CoefficientEval<IR,coeff_t,impl_traits_t>::Type coeff_eval_t;
+
 
    typedef TElementTransformation<meshType,IR,real_t> Trans_t;
-   template <int NE> struct T_result
+   struct T_result
    {
       static const int EvalOps =
          Trans_t::template Get<coeff_t,kernel_t>::EvalOps;
-      typedef typename Trans_t::template Result<EvalOps,NE> Type;
+      typedef typename Trans_t::template Result<EvalOps,impl_traits_t> Type;
    };
 
    typedef FieldEvaluator<solFESpace,solVecLayout_t,IR,
            complex_t,real_t> solFieldEval;
-   template <int BE> struct S_spec
+
+   /** @brief Contains matrix sizes, type of kernel (ElementMatrix is templated
+       on a kernel, e.g. ElementMatrix::Compute may be AssembleGradGrad()). */
+   struct S_spec
    {
-      typedef typename solFieldEval::template Spec<kernel_t,BE> Spec;
+      typedef typename solFieldEval::template Spec<kernel_t,impl_traits_t> Spec;
       typedef typename Spec::DataType DataType;
       typedef typename Spec::ElementMatrix ElementMatrix;
    };
@@ -86,7 +124,7 @@ protected:
 
    coeff_t coeff;
 
-   p_assembled_t *assembled_data;
+   Memory<p_assembled_t> assembled_data;
 
    const FiniteElementSpace &in_fes;
 
@@ -101,13 +139,17 @@ public:
         solVecLayout(sol_fes),
         int_rule(),
         coeff(integ.coeff),
-        assembled_data(NULL),
+        assembled_data(),
         in_fes(sol_fes)
-   { }
+   {
+      assembled_data.Reset(AB == 64 ? MemoryType::HOST_64 :
+                           AB == 32 ? MemoryType::HOST_32 :
+                           MemoryType::HOST);
+   }
 
    virtual ~TBilinearForm()
    {
-      delete [] assembled_data;
+      assembled_data.Delete();
    }
 
    /// Get the input finite element space prolongation matrix
@@ -119,10 +161,9 @@ public:
 
    virtual void Mult(const Vector &x, Vector &y) const
    {
-      if (assembled_data)
+      if (!assembled_data.Empty())
       {
-         const int num_elem = 1;
-         MultAssembled<num_elem>(x, y);
+         MultAssembled(x, y);
       }
       else
       {
@@ -135,10 +176,6 @@ public:
    {
       y = 0.0;
 
-      const int BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
       // For better performance, create stack copies of solFES, and solEval
       // inside 'solFEval'. The element-transformation 'T' also copies the
       // meshFES, meshEval, etc internally.
@@ -149,49 +186,49 @@ public:
       coeff_eval_t wQ(int_rule, coeff);
 
       const int NE = mesh.GetNE();
-      for (int el = 0; el < NE; el++)
+      for (int el = 0; el < NE; el += TE)
       {
 #if 0
-         typename S_spec<BE>::DataType R;
+         typename S_spec::DataType R;
          solFEval.Eval(el, R);
 
-         typename T_result<BE>::Type F;
+         typename T_result::Type F;
          T.Eval(el, F);
 #else
-         typename T_result<BE>::Type F;
+         typename T_result::Type F;
          T.Eval(el, F);
 
-         typename S_spec<BE>::DataType R;
+         typename S_spec::DataType R;
          solFEval.Eval(el, R);
 #endif
 
          typename coeff_eval_t::result_t res;
          wQ.Eval(F, res);
 
-         kernel_t::Action(0, F, wQ, res, R);
+         for (int k = 0; k < BE; k++)
+         {
+            kernel_t::Action(k, F, wQ, res, R);
+         }
 
          solFEval.template Assemble<true>(R);
       }
    }
 
-   // Partial assembly of quadrature point data
+   /// Partial assembly of quadrature point data
    void Assemble()
    {
-      const int BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
       Trans_t T(mesh, meshEval);
       coeff_eval_t wQ(int_rule, coeff);
 
       const int NE = mesh.GetNE();
-      if (!assembled_data)
+      if (assembled_data.Empty())
       {
-         assembled_data = new p_assembled_t[NE];
+         const int size = ((NE+TE-1)/TE)*BE;
+         assembled_data.New(size, assembled_data.GetMemoryType());
       }
-      for (int el = 0; el < NE; el++) // BE == 1
+      for (int el = 0; el < NE; el += TE)
       {
-         typename T_result<BE>::Type F;
+         typename T_result::Type F;
          T.Eval(el, F);
 
          typename coeff_eval_t::result_t res;
@@ -199,28 +236,26 @@ public:
 
          for (int k = 0; k < BE; k++)
          {
-            kernel_t::Assemble(k, F, wQ, res, assembled_data[el+k]);
+            kernel_t::Assemble(k, F, wQ, res, assembled_data[el/SS+k]);
          }
       }
    }
 
-   template <int num_elem>
    inline MFEM_ALWAYS_INLINE
    void ElementAddMultAssembled(int el, solFieldEval &solFEval) const
    {
-      typename S_spec<num_elem>::DataType R;
+      typename S_spec::DataType R;
       solFEval.Eval(el, R);
 
-      for (int k = 0; k < num_elem; k++)
+      for (int k = 0; k < BE; k++)
       {
-         kernel_t::MultAssembled(k, assembled_data[el+k], R);
+         kernel_t::MultAssembled(k, assembled_data[el/SS+k], R);
       }
 
       solFEval.template Assemble<true>(R);
    }
 
    // complex_t = double
-   template <int num_elem>
    void MultAssembled(const Vector &x, Vector &y) const
    {
       y = 0.0;
@@ -229,14 +264,9 @@ public:
                             x.GetData(), y.GetData());
 
       const int NE = mesh.GetNE();
-      const int bNE = NE-NE%num_elem;
-      for (int el = 0; el < bNE; el += num_elem)
+      for (int el = 0; el < NE; el += TE)
       {
-         ElementAddMultAssembled<num_elem>(el, solFEval);
-      }
-      for (int el = bNE; el < NE; el++)
-      {
-         ElementAddMultAssembled<1>(el, solFEval);
+         ElementAddMultAssembled(el, solFEval);
       }
    }
 
@@ -249,10 +279,10 @@ public:
       solVecLayout_type solVecLayout(this->solVecLayout);
       solFESpace solFES(this->solFES);
 
-      TTensor3<dofs,vdim,1,complex_t> xy_dof;
+      TTensor3<dofs,vdim,BE,vcomplex_t> xy_dof;
 
       const int NE = mesh.GetNE();
-      for (int el = 0; el < NE; el++)
+      for (int el = 0; el < NE; el += TE)
       {
          solFES.SetElement(el);
 
@@ -266,98 +296,108 @@ public:
    {
       typedef typename meshType::FESpace_type meshFESpace;
       meshFESpace meshFES(mesh.t_fes);
-      typedef TTensor3<meshFE_type::dofs,sdim,1,real_t> lnodes_t;
+      typedef TTensor3<meshFE_type::dofs,sdim,BE,vreal_t> lnodes_t;
 
       const int NE = mesh.GetNE();
-      sNodes.SetSize(lnodes_t::size*NE);
-      real_t *lNodes = sNodes.GetData();
-      for (int el = 0; el < NE; el++)
+      // TODO: How do we make sure that this array is aligned properly, AND the
+      //       compiler knows that it is aligned? => ALIGN_32|ALIGN_64 when ready
+      const int NVE = (NE+TE-1)/TE;
+      vreal_t *vsNodes = new vreal_t[lnodes_t::size*NVE];
+      sNodes.NewDataAndSize(vsNodes[0].vec, (lnodes_t::size*SS)*NVE);
+      sNodes.MakeDataOwner();
+      for (int el = 0; el < NE; el += TE)
       {
          meshFES.SetElement(el);
          meshFES.VectorExtract(mesh.node_layout, mesh.Nodes,
-                               lnodes_t::layout, lNodes);
-         lNodes += lnodes_t::size;
+                               lnodes_t::layout, vsNodes);
+         vsNodes += lnodes_t::size;
       }
    }
 
-   // partial assembly from "serialized" nodes
+   /// Partial assembly from "serialized" nodes
    // real_t = double
    void AssembleFromSerializedNodes(const Vector &sNodes)
    {
-      const int  BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
-      Trans_t T(this->mesh, this->meshEval);
+      Trans_t T(mesh, meshEval);
       coeff_eval_t wQ(int_rule, coeff);
 
       const int NE = mesh.GetNE();
-      if (!assembled_data)
+      if (assembled_data.Empty())
       {
-         assembled_data = new p_assembled_t[NE];
+         const int size = ((NE+TE-1)/TE)*BE;
+         assembled_data.New(size, assembled_data.GetMemoryType());
       }
-      for (int el = 0; el < NE; el++)
+      const vreal_t *vsNodes = (const vreal_t*)(sNodes.GetData());
+      for (int el = 0; el < NE; el += TE)
       {
-         typename T_result<BE>::Type F;
-         T.EvalSerialized(el, sNodes.GetData(), F);
+         typename T_result::Type F;
+         T.EvalSerialized(el, vsNodes, F);
 
          typename coeff_eval_t::result_t res;
          wQ.Eval(F, res);
 
-         kernel_t::Assemble(0, F, wQ, res, assembled_data[el]);
+         for (int k = 0; k < BE; k++)
+         {
+            kernel_t::Assemble(k, F, wQ, res, assembled_data[el/SS+k]);
+         }
       }
    }
 
    // complex_t = double
    void Serialize(const Vector &x, Vector &sx) const
    {
+      typedef TTensor3<dofs,vdim,BE,vcomplex_t> vdof_data_t;
+
       solVecLayout_t solVecLayout(this->solVecLayout);
-      typedef TTensor3<dofs,vdim,1,complex_t> vdof_data_t;
       solFESpace solFES(this->solFES);
 
       const int NE = mesh.GetNE();
-      sx.SetSize(vdim*dofs*NE);
-      complex_t *loc_sx = sx.GetData();
-      for (int el = 0; el < NE; el++)
+      // TODO: How do we make sure that this array is aligned properly, AND
+      //       the compiler knows that it is aligned? => ALIGN_32|ALIGN_64 when ready
+      const int NVE = (NE+TE-1)/TE;
+      vreal_t *vsx = new vreal_t[vdof_data_t::size*NVE];
+      sx.NewDataAndSize(vsx[0].vec, (vdof_data_t::size*SS)*NVE);
+      sx.MakeDataOwner();
+      for (int el = 0; el < NE; el += TE)
       {
          solFES.SetElement(el);
-         solFES.VectorExtract(solVecLayout, x, vdof_data_t::layout, loc_sx);
-         loc_sx += vdim*dofs;
+         solFES.VectorExtract(solVecLayout, x, vdof_data_t::layout, vsx);
+         vsx += vdof_data_t::size;
       }
    }
 
-   // serialized vector sx --> serialized vector 'sy'
+   /// serialized vector sx --> serialized vector 'sy'
    // complex_t = double
    void MultAssembledSerialized(const Vector &sx, Vector &sy) const
    {
       solFieldEval solFEval(solFES, solEval, solVecLayout, NULL, NULL);
 
       const int NE = mesh.GetNE();
-      const complex_t *loc_sx = sx.GetData();
-      complex_t *loc_sy = sy.GetData();
-      for (int el = 0; el < NE; el++)
+      const vreal_t *vsx = (const vreal_t*)(sx.GetData());
+      vreal_t *vsy = (vreal_t*)(sy.GetData());
+
+      for (int el = 0; el < NE; el += TE)
       {
-         typename S_spec<1>::DataType R;
-         solFEval.EvalSerialized(loc_sx, R);
+         typename S_spec::DataType R;
+         solFEval.EvalSerialized(vsx, R);
 
-         kernel_t::MultAssembled(0, assembled_data[el], R);
+         for (int k = 0; k < BE; k++)
+         {
+            kernel_t::MultAssembled(k, assembled_data[el/SS+k], R);
+         }
 
-         solFEval.template AssembleSerialized<false>(R, loc_sy);
+         solFEval.template AssembleSerialized<false>(R, vsy);
 
-         loc_sx += vdim*dofs;
-         loc_sy += vdim*dofs;
+         vsx += vdim*dofs*BE;
+         vsy += vdim*dofs*BE;
       }
    }
 #endif // MFEM_TEMPLATE_ENABLE_SERIALIZE
 
-   // Assemble the operator in a SparseMatrix.
+   /// Assemble the operator in a SparseMatrix.
    // complex_t = double
    void AssembleMatrix(SparseMatrix &M) const
    {
-      const int BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
       Trans_t T(mesh, meshEval);
       solFESpace solFES(this->solFES);
       solShapeEval solEval(this->solEval);
@@ -365,79 +405,100 @@ public:
       coeff_eval_t wQ(int_rule, coeff);
 
       const int NE = mesh.GetNE();
-      for (int el = 0; el < NE; el++)
+      for (int el = 0; el < NE; el += TE)
       {
-         f_assembled_t asm_qpt_data;
+         f_assembled_t asm_qpt_data[BE];
          {
-            typename T_result<BE>::Type F;
+            typename T_result::Type F;
             T.Eval(el, F);
 
             typename coeff_eval_t::result_t res;
             wQ.Eval(F, res);
 
-            kernel_t::Assemble(0, F, wQ, res, asm_qpt_data);
+            for (int k = 0; k < BE; k++)
+            {
+               kernel_t::Assemble(k, F, wQ, res, asm_qpt_data[k]);
+            }
          }
 
          // For now, when vdim > 1, assume block-diagonal matrix with the same
          // diagonal block for all components.
-         TMatrix<dofs,dofs> M_loc;
-         S_spec<BE>::ElementMatrix::Compute(
-            asm_qpt_data.layout, asm_qpt_data, M_loc.layout, M_loc, solEval);
-
-         solFES.SetElement(el);
-         for (int bi = 0; bi < vdim; bi++)
+         for (int k = 0; k < BE; k++)
          {
-            solFES.AssembleBlock(bi, bi, solVecLayout, M_loc, M);
+            const int el_k = el+SS*k;
+            if (el_k >= NE) { break; }
+
+            TMatrix<dofs,dofs,vcomplex_t> M_loc;
+            S_spec::ElementMatrix::Compute(
+               asm_qpt_data[k].layout, asm_qpt_data[k], M_loc.layout, M_loc,
+               solEval);
+
+            solFES.SetElement(el_k);
+            for (int bi = 0; bi < vdim; bi++)
+            {
+               solFES.AssembleBlock(bi, bi, solVecLayout, M_loc, M);
+            }
          }
       }
    }
 
-   // Assemble element matrices and store them as a DenseTensor object.
+   /// Assemble element matrices and store them as a DenseTensor object.
    // complex_t = double
    void AssembleMatrix(DenseTensor &M) const
    {
-      const int BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
       Trans_t T(mesh, meshEval);
       solShapeEval solEval(this->solEval);
       coeff_eval_t wQ(int_rule, coeff);
 
       const int NE = mesh.GetNE();
-      for (int el = 0; el < NE; el++)
+      for (int el = 0; el < NE; el += TE)
       {
-         f_assembled_t asm_qpt_data;
+         f_assembled_t asm_qpt_data[BE];
          {
-            typename T_result<BE>::Type F;
+            typename T_result::Type F;
             T.Eval(el, F);
 
             typename coeff_eval_t::result_t res;
             wQ.Eval(F, res);
 
-            kernel_t::Assemble(0, F, wQ, res, asm_qpt_data);
+            for (int k = 0; k < BE; k++)
+            {
+               kernel_t::Assemble(k, F, wQ, res, asm_qpt_data[k]);
+            }
          }
 
          // For now, when vdim > 1, assume block-diagonal matrix with the same
          // diagonal block for all components.
          // M is assumed to be (dof x dof x NE).
-         TMatrix<dofs,dofs> M_loc;
-         S_spec<BE>::ElementMatrix::Compute(
-            asm_qpt_data.layout, asm_qpt_data, M_loc.layout, M_loc, solEval);
+         for (int k = 0; k < BE; k++)
+         {
+            const int el_k = el+SS*k;
+            if (el_k >= NE) { break; }
 
-         complex_t *M_data = M.GetData(el);
-         M_loc.template AssignTo<AssignOp::Set>(M_data);
+            TMatrix<dofs,dofs,vcomplex_t> M_loc;
+            S_spec::ElementMatrix::Compute(
+               asm_qpt_data[k].layout, asm_qpt_data[k], M_loc.layout, M_loc,
+               solEval);
+
+            for (int s = 0; s < SS && el_k+s < NE; s++)
+            {
+               complex_t *M_data = M.GetData(el_k+s);
+               for (int j = 0; j < dofs; j++)
+               {
+                  for (int i = 0; i < dofs; i++)
+                  {
+                     M_data[j+dofs*i] = M_loc(i,j)[s];
+                  }
+               }
+            }
+         }
       }
    }
 
-   // Assemble element matrices and add them to the bilinear form
+   /// Assemble element matrices and add them to the bilinear form
    // complex_t = double
    void AssembleBilinearForm(BilinearForm &a) const
    {
-      const int BE = 1; // batch-size of elements
-      typedef typename kernel_t::template
-      CoefficientEval<IR,coeff_t,BE>::Type coeff_eval_t;
-
       Trans_t T(mesh, meshEval);
       solShapeEval solEval(this->solEval);
       coeff_eval_t wQ(int_rule, coeff);
@@ -448,61 +509,93 @@ public:
       DenseMatrix M_loc_perm(dofs*vdim,dofs*vdim); // initialized with zeros
 
       const int NE = mesh.GetNE();
-      for (int el = 0; el < NE; el++)
+      for (int el = 0; el < NE; el += TE)
       {
-         f_assembled_t asm_qpt_data;
+         f_assembled_t asm_qpt_data[BE];
          {
-            typename T_result<BE>::Type F;
+            typename T_result::Type F;
             T.Eval(el, F);
 
             typename coeff_eval_t::result_t res;
             wQ.Eval(F, res);
 
-            kernel_t::Assemble(0, F, wQ, res, asm_qpt_data);
+            for (int k = 0; k < BE; k++)
+            {
+               kernel_t::Assemble(k, F, wQ, res, asm_qpt_data[k]);
+            }
          }
 
          // For now, when vdim > 1, assume block-diagonal matrix with the same
          // diagonal block for all components.
-         TMatrix<dofs,dofs> M_loc;
-         S_spec<BE>::ElementMatrix::Compute(
-            asm_qpt_data.layout, asm_qpt_data, M_loc.layout, M_loc, solEval);
-
-         if (dof_map) // switch from tensor-product ordering
+         for (int k = 0; k < BE; k++)
          {
-            for (int i = 0; i < dofs; i++)
+            const int el_k = el+SS*k;
+            if (el_k >= NE) { break; }
+
+            TMatrix<dofs,dofs,vcomplex_t> M_loc;
+            S_spec::ElementMatrix::Compute(
+               asm_qpt_data[k].layout, asm_qpt_data[k], M_loc.layout, M_loc,
+               solEval);
+
+            if (dof_map) // switch from tensor-product ordering
             {
-               for (int j = 0; j < dofs; j++)
+               for (int s = 0; s < SS && el_k+s < NE; s++)
                {
-                  M_loc_perm(dof_map_[i],dof_map_[j]) = M_loc(i,j);
+                  for (int i = 0; i < dofs; i++)
+                  {
+                     for (int j = 0; j < dofs; j++)
+                     {
+                        M_loc_perm(dof_map_[i],dof_map_[j]) = M_loc(i,j)[s];
+                     }
+                  }
+                  for (int bi = 1; bi < vdim; bi++)
+                  {
+                     M_loc_perm.CopyMN(M_loc_perm, dofs, dofs, 0, 0,
+                                       bi*dofs, bi*dofs);
+                  }
+                  a.AssembleElementMatrix(el_k+s, M_loc_perm, vdofs);
                }
             }
-            for (int bi = 1; bi < vdim; bi++)
+            else if (SS == 1)
             {
-               M_loc_perm.CopyMN(M_loc_perm, dofs, dofs, 0, 0,
-                                 bi*dofs, bi*dofs);
-            }
-            a.AssembleElementMatrix(el, M_loc_perm, vdofs);
-         }
-         else
-         {
-            DenseMatrix DM(M_loc.data, dofs, dofs);
-            if (vdim == 1)
-            {
-               a.AssembleElementMatrix(el, DM, vdofs);
+               DenseMatrix DM(M_loc.data[0].vec, dofs, dofs);
+               if (vdim == 1)
+               {
+                  a.AssembleElementMatrix(el_k, DM, vdofs);
+               }
+               else
+               {
+                  for (int bi = 0; bi < vdim; bi++)
+                  {
+                     M_loc_perm.CopyMN(DM, dofs, dofs, 0, 0, bi*dofs, bi*dofs);
+                  }
+                  a.AssembleElementMatrix(el_k, M_loc_perm, vdofs);
+               }
             }
             else
             {
-               for (int bi = 0; bi < vdim; bi++)
+               for (int s = 0; s < SS && el_k+s < NE; s++)
                {
-                  M_loc_perm.CopyMN(DM, dofs, dofs, 0, 0, bi*dofs, bi*dofs);
+                  for (int i = 0; i < dofs; i++)
+                  {
+                     for (int j = 0; j < dofs; j++)
+                     {
+                        M_loc_perm(i,j) = M_loc(i,j)[s];
+                     }
+                  }
+                  for (int bi = 1; bi < vdim; bi++)
+                  {
+                     M_loc_perm.CopyMN(M_loc_perm, dofs, dofs, 0, 0,
+                                       bi*dofs, bi*dofs);
+                  }
+                  a.AssembleElementMatrix(el_k+s, M_loc_perm, vdofs);
                }
-               a.AssembleElementMatrix(el, M_loc_perm, vdofs);
             }
          }
       }
    }
 
-   // Multiplication using assembled element matrices stored as a DenseTensor.
+   /// Multiplication using assembled element matrices stored as a DenseTensor.
    // complex_t = double
    void AddMult(DenseTensor &M, const Vector &x, Vector &y) const
    {
@@ -513,7 +606,7 @@ public:
       const int NE = mesh.GetNE();
       for (int el = 0; el < NE; el++)
       {
-         TTensor3<dofs,vdim,1,complex_t> x_dof, y_dof;
+         TTensor3<dofs,vdim,1,AutoSIMD<complex_t,1,1> > x_dof, y_dof;
 
          solFES.SetElement(el);
          solFES.VectorExtract(solVecLayout, x, x_dof.layout, x_dof);

fem/tbilininteg.hpp

@@ -21,8 +21,7 @@ namespace mfem
 
 // Templated local bilinear form integrator kernels, cf. bilininteg.?pp
 
-// The Integrator class combines a kernel and a coefficient
-
+/// The Integrator class combines a kernel and a coefficient
 template <typename coeff_t, template<int,int,typename> class kernel_t>
 class TIntegrator
 {
@@ -38,46 +37,48 @@ public:
 };
 
 
-// Mass kernel
-
+/// Mass kernel
 template <int SDim, int Dim, typename complex_t>
 struct TMassKernel
 {
    typedef complex_t complex_type;
 
-   // needed for the TElementTransformation::Result class
+   /// Needed for the TElementTransformation::Result class
    static const bool uses_Jacobians = true;
 
-   // needed for the FieldEvaluator::Data class
+   /// @name Needed for the FieldEvaluator::Data class
+   ///@{
    static const bool in_values     = true;
    static const bool in_gradients  = false;
    static const bool out_values    = true;
    static const bool out_gradients = false;
+   ///@}
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in partial assembly, and partially
-   // assembled action.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in partial assembly, and partially
+       assembled action. */
    template <int qpts>
    struct p_asm_data { typedef TVector<qpts,complex_t> type; };
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in full element matrix assembly.
+   /** @brief Partially assembled data type for one element with the given
+       number of quadrature points. This type is used in full element matrix
+       assembly. */
    template <int qpts>
    struct f_asm_data { typedef TVector<qpts,complex_t> type; };
 
-   template <typename IR, typename coeff_t, int NE>
+   template <typename IR, typename coeff_t, typename impl_traits_t>
    struct CoefficientEval
    {
-      typedef typename IntRuleCoefficient<IR,coeff_t,NE>::Type Type;
+      typedef typename IntRuleCoefficient<IR,coeff_t,impl_traits_t>::Type Type;
    };
 
-   // Method used for un-assembled (matrix free) action.
-   // Jt       [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                              - CoefficientEval<>::Type
-   // q                              - CoefficientEval<>::Type::result_t
-   // val_qpts [M x NC x NE]         - in/out data member in R
-   //
-   // val_qpts *= w det(J)
+   /** @brief Method used for un-assembled (matrix free) action.
+       @param k the element number
+       @param F  Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q  CoefficientEval<>::Type
+       @param q  CoefficientEval<>::Type::result_t
+       @param R  val_qpts [M x NC x NE] - in/out data member in R
+       val_qpts *= w det(J) */
    template <typename T_result_t, typename Q_t, typename q_t,
              typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
@@ -101,13 +102,16 @@ struct TMassKernel
       }
    }
 
-   // Method defining partial assembly.
-   // Jt   [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                          - CoefficientEval<>::Type
-   // q                          - CoefficientEval<>::Type::result_t
-   // A    [M]                   - partially assembled scalars
-   //
-   // A = w det(J)
+   /** @brief Method defining partial assembly.
+       Result in A is the quadrature-point dependent part of element matrix
+       assembly (as opposed to part that is same for all elements),
+       A = w det(J)
+       @param k the element number
+       @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q CoefficientEval<>::Type
+       @param q CoefficientEval<>::Type::result_t
+       @param A [M] - partially assembled scalars
+   */
    template <typename T_result_t, typename Q_t, typename q_t, int qpts>
    static inline MFEM_ALWAYS_INLINE
    void Assemble(const int k, const T_result_t &F,
@@ -124,11 +128,12 @@ struct TMassKernel
       }
    }
 
-   // Method for partially assembled action.
-   // A        [M]           - partially assembled scalars
-   // val_qpts [M x NC x NE] - in/out data member in R
-   //
-   // val_qpts *= A
+   /** @brief Method for partially assembled action.
+       @param k the element number
+       @param A  [M] - partially assembled scalars
+       @param R  val_qpts [M x NC x NE] - in/out data member in R
+       val_qpts *= A
+   */
    template <int qpts, typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
    void MultAssembled(const int k, const TVector<qpts,complex_t> &A, S_data_t &R)
@@ -148,51 +153,54 @@ struct TMassKernel
 };
 
 
-// Diffusion kernel
-
-// complex_t - type for the assembled data
+/** @brief Diffusion kernel
+    @tparam complex_t - type for the assembled data
+*/
 template <int SDim, int Dim, typename complex_t>
 struct TDiffusionKernel;
 
-// Diffusion kernel in 1D
+/// Diffusion kernel in 1D
 template <typename complex_t>
 struct TDiffusionKernel<1,1,complex_t>
 {
    typedef complex_t complex_type;
 
-   // needed for the TElementTransformation::Result class
+   /// Needed for the TElementTransformation::Result class
    static const bool uses_Jacobians = true;
 
-   // needed for the FieldEvaluator::Data class
+   /// Needed for the FieldEvaluator::Data class
+   ///@{
    static const bool in_values     = false;
    static const bool in_gradients  = true;
    static const bool out_values    = false;
    static const bool out_gradients = true;
+   ///@}
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in partial assembly, and partially
-   // assembled action.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in partial assembly, and partially
+       assembled action. */
    template <int qpts>
    struct p_asm_data { typedef TMatrix<qpts,1,complex_t> type; };
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in full element matrix assembly.
+
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in full element matrix assembly. */
    template <int qpts>
    struct f_asm_data { typedef TTensor3<qpts,1,1,complex_t> type; };
 
-   template <typename IR, typename coeff_t, int NE>
+   template <typename IR, typename coeff_t, typename impl_traits_t>
    struct CoefficientEval
    {
-      typedef typename IntRuleCoefficient<IR,coeff_t,NE>::Type Type;
+      typedef typename IntRuleCoefficient<IR,coeff_t,impl_traits_t>::Type Type;
    };
 
-   // Method used for un-assembled (matrix free) action.
-   // Jt        [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                               - CoefficientEval<>::Type
-   // q                               - CoefficientEval<>::Type::result_t
-   // grad_qpts [M x SDim x NC x NE]  - in/out data member in R
-   //
-   // grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts
+   /** @brief Method used for un-assembled (matrix free) action.
+       @param k the element number
+       @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q - CoefficientEval<>::Type
+       @param q - CoefficientEval<>::Type::result_t
+       @param R grad_qpts [M x SDim x NC x NE]  - in/out data member in R
+       grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts */
    template <typename T_result_t, typename Q_t, typename q_t,
              typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
@@ -214,17 +222,20 @@ struct TDiffusionKernel<1,1,complex_t>
       }
    }
 
-   // Method defining partial assembly. The pointwise Dim x Dim matrices are
-   // stored as symmetric (when asm_type == p_asm_data, i.e. A.layout.rank == 2)
-   // or non-symmetric (when asm_type == f_asm_data, i.e. A.layout.rank == 3)
-   // matrices.
-   // Jt   [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                          - CoefficientEval<>::Type
-   // q                          - CoefficientEval<>::Type::result_t
-   // A    [M x Dim*(Dim+1)/2]   - partially assembled Dim x Dim symm. matrices
-   // A    [M x Dim x Dim]       - partially assembled Dim x Dim matrices
-   //
-   // A = (w/det(J)) adj(J) adj(J)^t
+
+   /** @brief Method defining partial assembly.
+       The pointwise Dim x Dim matrices are stored as symmetric (when
+       asm_type == p_asm_data, i.e. A.layout.rank == 2) or
+       non-symmetric (when asm_type == f_asm_data, i.e. A.layout.rank
+       == 3) matrices.
+       @param k the element number
+       @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q CoefficientEval<>::Type
+       @param q CoefficientEval<>::Type::result_t
+       @param A [M x Dim*(Dim+1)/2] - partially assembled Dim x Dim symm. matrices
+              A [M x Dim x Dim]     - partially assembled Dim x Dim matrices
+       A = (w/det(J)) adj(J) adj(J)^t
+   */
    template <typename T_result_t, typename Q_t, typename q_t, typename asm_type>
    static inline MFEM_ALWAYS_INLINE
    void Assemble(const int k, const T_result_t &F,
@@ -240,13 +251,13 @@ struct TDiffusionKernel<1,1,complex_t>
          A[i] = Q.get(q,i,k) / F.Jt(i,0,0,k);
       }
    }
-
-   // Method for partially assembled action.
-   // A         [M x Dim*(Dim+1)/2]  - partially assembled Dim x Dim symmetric
-   //                                  matrices
-   // grad_qpts [M x SDim x NC x NE] - in/out data member in R
-   //
-   // grad_qpts = A grad_qpts
+   /** @brief Method for partially assembled action.
+       @param k the element number
+       @param A  [M x Dim*(Dim+1)/2] partially assembled Dim x Dim symmetric
+                                     matrices
+       @param R  grad_qpts [M x SDim x NC x NE] - in/out data member in R
+       grad_qpts = A grad_qpts
+   */
    template <int qpts, typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
    void MultAssembled(const int k, const TMatrix<qpts,1,complex_t> &A,
@@ -266,46 +277,49 @@ struct TDiffusionKernel<1,1,complex_t>
    }
 };
 
-// Diffusion kernel in 2D
+/// Diffusion kernel in 2D
 template <typename complex_t>
 struct TDiffusionKernel<2,2,complex_t>
 {
    typedef complex_t complex_type;
 
-   // needed for the TElementTransformation::Result class
+   /// Needed for the TElementTransformation::Result class
    static const bool uses_Jacobians = true;
 
-   // needed for the FieldEvaluator::Data class
+   /// Needed for the FieldEvaluator::Data class
+   ///@{
    static const bool in_values     = false;
    static const bool in_gradients  = true;
    static const bool out_values    = false;
    static const bool out_gradients = true;
+   ///@}
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in partial assembly, and partially
-   // assembled action. Stores one symmetric 2 x 2 matrix per point.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in partial assembly, and partially
+       assembled action. Stores one symmetric 2 x 2 matrix per point. */
    template <int qpts>
    struct p_asm_data { typedef TMatrix<qpts,3,complex_t> type; };
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in full element matrix assembly.
-   // Stores one general (non-symmetric) 2 x 2 matrix per point.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in full element matrix assembly.
+       Stores one general (non-symmetric) 2 x 2 matrix per point. */
    template <int qpts>
    struct f_asm_data { typedef TTensor3<qpts,2,2,complex_t> type; };
 
-   template <typename IR, typename coeff_t, int NE>
+   template <typename IR, typename coeff_t, typename impl_traits_t>
    struct CoefficientEval
    {
-      typedef typename IntRuleCoefficient<IR,coeff_t,NE>::Type Type;
+      typedef typename IntRuleCoefficient<IR,coeff_t,impl_traits_t>::Type Type;
    };
 
-   // Method used for un-assembled (matrix free) action.
-   // Jt        [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                               - CoefficientEval<>::Type
-   // q                               - CoefficientEval<>::Type::result_t
-   // grad_qpts [M x SDim x NC x NE]  - in/out data member in R
-   //
-   // grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts
+   /** @brief Method used for un-assembled (matrix free) action.
+       @param k the element number
+       @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q CoefficientEval<>::Type
+       @param q CoefficientEval<>::Type::result_t
+       @param R grad_qpts [M x SDim x NC x NE]  - in/out data member in R
+       grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts
+   */
    template <typename T_result_t, typename Q_t, typename q_t,
              typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
@@ -338,17 +352,18 @@ struct TDiffusionKernel<2,2,complex_t>
       }
    }
 
-   // Method defining partial assembly. The pointwise Dim x Dim matrices are
-   // stored as symmetric (when asm_type == p_asm_data, i.e. A.layout.rank == 2)
-   // or non-symmetric (when asm_type == f_asm_data, i.e. A.layout.rank == 3)
-   // matrices.
-   // Jt   [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                          - CoefficientEval<>::Type
-   // q                          - CoefficientEval<>::Type::result_t
-   // A    [M x Dim*(Dim+1)/2]   - partially assembled Dim x Dim symm. matrices
-   // A    [M x Dim x Dim]       - partially assembled Dim x Dim matrices
-   //
-   // A = (w/det(J)) adj(J) adj(J)^t
+   /** @brief Method defining partial assembly.
+       The pointwise Dim x Dim matrices are stored as symmetric (when
+       asm_type == p_asm_data, i.e. A.layout.rank == 2) or non-symmetric
+       (when asm_type == f_asm_data, i.e. A.layout.rank == 3) matrices.
+       A = (w/det(J)) adj(J) adj(J)^t
+       @param k the element number
+       @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       @param Q CoefficientEval<>::Type
+       @param q CoefficientEval<>::Type::result_t
+       @param A [M x Dim*(Dim+1)/2] partially assembled Dim x Dim symm. matrices
+       @param A [M x Dim x Dim]       partially assembled Dim x Dim matrices
+   */
    template <typename T_result_t, typename Q_t, typename q_t, typename asm_type>
    static inline MFEM_ALWAYS_INLINE
    void Assemble(const int k, const T_result_t &F,
@@ -376,12 +391,13 @@ struct TDiffusionKernel<2,2,complex_t>
       }
    }
 
-   // Method for partially assembled action.
-   // A         [M x Dim*(Dim+1)/2]  - partially assembled Dim x Dim symmetric
-   //                                  matrices
-   // grad_qpts [M x SDim x NC x NE] - in/out data member in R
-   //
-   // grad_qpts = A grad_qpts
+   /** @brief  Method for partially assembled action.
+       @param k the element number
+       @param  A  [M x Dim*(Dim+1)/2]  - partially assembled Dim x Dim symmetric
+                                         matrices
+       @param R grad_qpts [M x SDim x NC x NE] - in/out data member in R
+       grad_qpts = A grad_qpts
+   */
    template <int qpts, typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
    void MultAssembled(const int k, const TMatrix<qpts,3,complex_t> &A,
@@ -407,46 +423,48 @@ struct TDiffusionKernel<2,2,complex_t>
    }
 };
 
-// Diffusion kernel in 3D
+/// Diffusion kernel in 3D
 template <typename complex_t>
 struct TDiffusionKernel<3,3,complex_t>
 {
    typedef complex_t complex_type;
 
-   // needed for the TElementTransformation::Result class
+   /// Needed for the TElementTransformation::Result class
    static const bool uses_Jacobians = true;
 
-   // needed for the FieldEvaluator::Data class
+   /// Needed for the FieldEvaluator::Data class
+   ///@{
    static const bool in_values     = false;
    static const bool in_gradients  = true;
    static const bool out_values    = false;
    static const bool out_gradients = true;
+   ///@}
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in partial assembly, and partially
-   // assembled action. Stores one symmetric 3 x 3 matrix per point.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in partial assembly, and partially
+       assembled action. Stores one symmetric 3 x 3 matrix per point. */
    template <int qpts>
    struct p_asm_data { typedef TMatrix<qpts,6,complex_t> type; };
 
-   // Partially assembled data type for one element with the given number of
-   // quadrature points. This type is used in full element matrix assembly.
-   // Stores one general (non-symmetric) 3 x 3 matrix per point.
+   /** @brief Partially assembled data type for one element with the given number of
+       quadrature points. This type is used in full element matrix assembly.
+       Stores one general (non-symmetric) 3 x 3 matrix per point. */
    template <int qpts>
    struct f_asm_data { typedef TTensor3<qpts,3,3,complex_t> type; };
 
-   template <typename IR, typename coeff_t, int NE>
+   template <typename IR, typename coeff_t, typename impl_traits_t>
    struct CoefficientEval
    {
-      typedef typename IntRuleCoefficient<IR,coeff_t,NE>::Type Type;
+      typedef typename IntRuleCoefficient<IR,coeff_t,impl_traits_t>::Type Type;
    };
 
-   // Method used for un-assembled (matrix free) action.
-   // Jt        [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                               - CoefficientEval<>::Type
-   // q                               - CoefficientEval<>::Type::result_t
-   // grad_qpts [M x SDim x NC x NE]  - in/out data member in R
-   //
-   // grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts
+   /** @brief Method used for un-assembled (matrix free) action.
+       grad_qpts = (w/det(J)) adj(J) adj(J)^t grad_qpts
+       Jt        [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+       Q                               - CoefficientEval<>::Type
+       q                               - CoefficientEval<>::Type::result_t
+       grad_qpts [M x SDim x NC x NE]  - in/out data member in R
+   */
    template <typename T_result_t, typename Q_t, typename q_t,
              typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
@@ -477,17 +495,18 @@ struct TDiffusionKernel<3,3,complex_t>
       }
    }
 
-   // Method defining partial assembly. The pointwise Dim x Dim matrices are
-   // stored as symmetric (when asm_type == p_asm_data, i.e. A.layout.rank == 2)
-   // or non-symmetric (when asm_type == f_asm_data, i.e. A.layout.rank == 3)
-   // matrices.
-   // Jt   [M x Dim x SDim x NE] - Jacobian transposed, data member in F
-   // Q                          - CoefficientEval<>::Type
-   // q                          - CoefficientEval<>::Type::result_t
-   // A    [M x Dim*(Dim+1)/2]   - partially assembled Dim x Dim symm. matrices
-   // A    [M x Dim x Dim]       - partially assembled Dim x Dim matrices
-   //
-   // A = (w/det(J)) adj(J) adj(J)^t
+   /** @brief Method defining partial assembly.
+      The pointwise Dim x Dim matrices are stored as symmetric (when
+      asm_type == p_asm_data, i.e. A.layout.rank == 2) or
+      non-symmetric (when asm_type == f_asm_data, i.e. A.layout.rank
+      == 3) matrices.
+      A = (w/det(J)) adj(J) adj(J)^t
+      Jt   [M x Dim x SDim x NE] - Jacobian transposed, data member in F
+      Q                          - CoefficientEval<>::Type
+      q                          - CoefficientEval<>::Type::result_t
+      A    [M x Dim*(Dim+1)/2]   - partially assembled Dim x Dim symm. matrices
+      A    [M x Dim x Dim]       - partially assembled Dim x Dim matrices
+   */
    template <typename T_result_t, typename Q_t, typename q_t, typename asm_type>
    static inline MFEM_ALWAYS_INLINE
    void Assemble(const int k, const T_result_t &F,
@@ -518,12 +537,12 @@ struct TDiffusionKernel<3,3,complex_t>
       }
    }
 
-   // Method for partially assembled action.
-   // A         [M x Dim*(Dim+1)/2]  - partially assembled Dim x Dim symmetric
-   //                                  matrices
-   // grad_qpts [M x SDim x NC x NE] - in/out data member in R
-   //
-   // grad_qpts = A grad_qpts
+   /** @brief Method for partially assembled action.
+       A         [M x Dim*(Dim+1)/2]  - partially assembled Dim x Dim symmetric
+                                        matrices
+       grad_qpts [M x SDim x NC x NE] - in/out data member in R
+       grad_qpts = A grad_qpts
+   */
    template <int qpts, typename S_data_t>
    static inline MFEM_ALWAYS_INLINE
    void MultAssembled(const int k, const TMatrix<qpts,6,complex_t> &A,

fem/tcoefficient.hpp

@@ -21,7 +21,7 @@
 namespace mfem
 {
 
-// Templated coefficient classes, cf. coefficient.?pp
+/// Templated coefficient classes, cf. coefficient.?pp
 
 class TCoefficient
 {
@@ -56,12 +56,13 @@ public:
 };
 
 
-// Function coefficient. The template class 'Func' has to implement at least one
-// of the following methods, depending on the dimension that will be used:
-// complex_t Eval1D(real_t);
-// complex_t Eval2D(real_t,real_t);
-// complex_t Eval3D(real_t,real_t,real_t);
-// Use MFEM_FLOPS_ADD() to count flops inside Eval*D.
+/** @brief Function coefficient.
+    @tparam Func has to implement at least one of the following methods,
+    depending on the dimension that will be used:
+    complex_t Eval1D(real_t);
+    complex_t Eval2D(real_t,real_t);
+    complex_t Eval3D(real_t,real_t,real_t);
+    Use MFEM_FLOPS_ADD() to count flops inside Eval*D. */
 template <typename Func, typename complex_t = double>
 class TFunctionCoefficient : public TCoefficient
 {
@@ -81,11 +82,15 @@ protected:
       {
          const int qpts = T_result_t::x_type::layout_type::dim_1;
          const int ne   = T_result_t::x_type::layout_type::dim_3;
+         const int vs   = sizeof(T.x[0])/sizeof(T.x[0][0]);
          for (int k = 0; k < ne; k++)
          {
             for (int i = 0; i < qpts; i++)
             {
-               c[l.ind(i,k)] = F.Eval1D(T.x(i,0,k));
+               for (int s = 0; s < vs; s++)
+               {
+                  c[l.ind(i,k)][s] = F.Eval1D(T.x(i,0,k)[s]);
+               }
             }
          }
       }
@@ -98,11 +103,15 @@ protected:
       {
          const int qpts = T_result_t::x_type::layout_type::dim_1;
          const int ne   = T_result_t::x_type::layout_type::dim_3;
+         const int vs   = sizeof(T.x[0])/sizeof(T.x[0][0]);
          for (int k = 0; k < ne; k++)
          {
             for (int i = 0; i < qpts; i++)
             {
-               c[l.ind(i,k)] = F.Eval2D(T.x(i,0,k), T.x(i,1,k));
+               for (int s = 0; s < vs; s++)
+               {
+                  c[l.ind(i,k)][s] = F.Eval2D(T.x(i,0,k)[s], T.x(i,1,k)[s]);
+               }
             }
          }
       }
@@ -115,20 +124,25 @@ protected:
       {
          const int qpts = T_result_t::x_type::layout_type::dim_1;
          const int ne   = T_result_t::x_type::layout_type::dim_3;
+         const int vs   = sizeof(T.x[0])/sizeof(T.x[0][0]);
          for (int k = 0; k < ne; k++)
          {
             for (int i = 0; i < qpts; i++)
             {
-               c[l.ind(i,k)] = F.Eval3D(T.x(i,0,k), T.x(i,1,k), T.x(i,2,k));
+               for (int s = 0; s < vs; s++)
+               {
+                  c[l.ind(i,k)][s] =
+                     F.Eval3D(T.x(i,0,k)[s], T.x(i,1,k)[s], T.x(i,2,k)[s]);
+               }
             }
          }
       }
    };
 
 public:
-   // Constructor for the case when Func has no data members.
+   /// Constructor for the case when Func has no data members.
    TFunctionCoefficient() : F() { }
-   // Constructor for the case when Func has data members.
+   /// Constructor for the case when Func has data members.
    TFunctionCoefficient(Func &F_) : F(F_) { }
    // Default copy constructor, Func has to have copy constructor.
 
@@ -170,14 +184,21 @@ public:
    void Eval(const T_result_t &T, const c_layout_t &l, c_data_t &c)
    {
       const int ne = T_result_t::ne;
+      const int vs = sizeof(T.attrib[0])/sizeof(T.attrib[0][0]);
+      MFEM_STATIC_ASSERT(vs == sizeof(c[0])/sizeof(c[0][0]), "");
       for (int i = 0; i < ne; i++)
       {
-         TAssign<AssignOp::Set>(l.ind2(i), c, constants(T.attrib[i]-1));
+         typename c_data_t::data_type ci;
+         for (int s = 0; s < vs; s++)
+         {
+            ci[s] = constants(T.attrib[i][s]-1);
+         }
+         TAssign<AssignOp::Set>(l.ind2(i), c, ci);
       }
    }
 };
 
-
+/// GridFunction coefficient class.
 template <typename FieldEval>
 class TGridFunctionCoefficient : public TCoefficient
 {
@@ -243,12 +264,13 @@ public:
 
 /// Auxiliary class that is used to simplify the evaluation of a coefficient and
 /// scaling it by the weights of a quadrature rule.
-template <typename IR, typename coeff_t, int NE>
+template <typename IR, typename coeff_t, typename impl_traits_t>
 struct IntRuleCoefficient
 {
    static const int qpts = IR::qpts;
-   static const int ne   = NE;
+   static const int ne   = impl_traits_t::batch_size;
    typedef typename coeff_t::complex_type complex_type;
+   typedef typename impl_traits_t::vcomplex_t vcomplex_t;
 
    template <bool is_const, bool dummy> struct Aux;
 
@@ -277,7 +299,7 @@ struct IntRuleCoefficient
    // non-constant coefficient
    template <bool dummy> struct Aux<false,dummy>
    {
-      typedef TMatrix<qpts,ne,complex_type> result_t;
+      typedef TMatrix<qpts,ne,vcomplex_t> result_t;
 #ifdef MFEM_TEMPLATE_INTRULE_COEFF_PRECOMP
       TMatrix<qpts,1,typename IR::real_type> w;
 #else
@@ -312,7 +334,7 @@ struct IntRuleCoefficient
       }
 
       inline MFEM_ALWAYS_INLINE
-      const complex_type &get(const result_t &res, int i, int k) const
+      const vcomplex_t &get(const result_t &res, int i, int k) const
       {
          return res(i,k);
       }

fem/teltrans.hpp

@@ -21,12 +21,14 @@ namespace mfem
 
 // Templated element transformation classes, cf. eltrans.?pp
 
-// Element transformation class, templated on a mesh type and an integration
-// rule. It is constructed from a mesh (e.g. class TMesh) and shape evaluator
-// (e.g. class ShapeEvaluator) objects. Allows computation of physical
-// coordinates and Jacobian matrices corresponding to the reference integration
-// points. The desired result is specified through the template subclass Result
-// and stored in an object of the same type.
+/** @brief Element transformation class, templated on a mesh type and an
+    integration rule.
+    It is constructed from a mesh (e.g. class TMesh) and shape evaluator
+    (e.g. class ShapeEvaluator) objects. Allows computation of physical
+    coordinates and Jacobian matrices corresponding to the reference integration
+    points. The desired result is specified through the template subclass Result
+    and stored in an object of the same type.
+*/
 template <typename Mesh_t, typename IR, typename real_t = double>
 class TElementTransformation
 {
@@ -39,9 +41,9 @@ public:
 
    typedef TElementTransformation<Mesh_t,IR,real_t> T_type;
 
-   // Enumeration for the result type of the TElementTransformation::Eval()
-   // method. The types can obtained by summing constants from this enumeration
-   // and used as a template parameter in struct Result.
+   /// Enumeration for the result type of the TElementTransformation::Eval()
+   /// method. The types can obtained by summing constants from this enumeration
+   /// and used as a template parameter in struct Result.
    enum EvalOperations
    {
       EvalNone        = 0,
@@ -51,6 +53,8 @@ public:
       LoadElementIdxs = 8
    };
 
+   /// Determines at compile-time the operations needed for given coefficient
+   /// and kernel
    template <typename coeff_t, typename kernel_t> struct Get
    {
       static const int EvalOps =
@@ -61,12 +65,14 @@ public:
          (EvalJacobians   * kernel_t::uses_Jacobians);
    };
 
-   // Templated struct Result, used to specify the type result that is computed
-   // by the TElementTransformation::Eval() method and stored in this structure.
-   // The template parameter EvalOps is a sum (bitwise or) of constants from
-   // the enum EvalOperations. The parameter NE is the number of elements to be
-   // processed in the Eval() method.
-   template<int EvalOps, int NE> struct Result;
+   /** @brief Templated struct Result, used to specify the type result that is
+       computed by the TElementTransformation::Eval() method and stored in this
+       structure.
+       @tparam EvalOps is a sum (bitwise or) of constants from the enum EvalOperations
+       @tparam NE is the number of elements to be processed in the Eval() method.
+       @tparam impl_traits_t specifies additional parameters and types to be used by the Eval() method
+   */
+   template<int EvalOps, typename impl_traits_t> struct Result;
 
    static const int dim  = Mesh_t::dim;
    static const int sdim = Mesh_t::space_dim;
@@ -85,13 +91,17 @@ protected:
 
    const Element* const *elements;
 
-   template <int NE>
+   template <typename vint_t, int NE>
    inline MFEM_ALWAYS_INLINE
-   void SetAttributes(int el, int (&attrib)[NE]) const
+   void SetAttributes(int el, vint_t (&attrib)[NE]) const
    {
+      const int vsize = sizeof(vint_t)/sizeof(attrib[0][0]);
       for (int i = 0; i < NE; i++)
       {
-         attrib[i] = elements[el+i]->GetAttribute();
+         for (int j = 0; j < vsize; i++)
+         {
+            attrib[i][j] = elements[el+j+i*vsize]->GetAttribute();
+         }
       }
    }
 
@@ -105,26 +115,31 @@ public:
         elements(mesh.m_mesh.GetElementsArray())
    { }
 
-   // Evaluate coordinates and/or Jacobian matrices at quadrature points.
-   template<int EvalOps, int NE>
+   /// Evaluate coordinates and/or Jacobian matrices at quadrature points.
+   template<int EvalOps, typename impl_traits_t>
    inline MFEM_ALWAYS_INLINE
-   void Eval(int el, Result<EvalOps,NE> &F)
+   void Eval(int el, Result<EvalOps,impl_traits_t> &F)
    {
       F.Eval(el, *this);
    }
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
-   template<int EvalOps, int NE>
+   template<int EvalOps, typename impl_traits_t>
    inline MFEM_ALWAYS_INLINE
-   void EvalSerialized(int el, const real_t *nodeData, Result<EvalOps,NE> &F)
+   void EvalSerialized(int el, const typename impl_traits_t::vreal_t *nodeData,
+                       Result<EvalOps,impl_traits_t> &F)
    {
       F.EvalSerialized(el, *this, nodeData);
    }
 #endif
 
-   template <int NE> struct Result<0,NE> // 0 = EvalNone
+   // Specialization of the Result<> class
+
+   // Case EvalOps = 0 = EvalNone
+   template <typename it_t> struct Result<0,it_t>
    {
-      static const int ne = NE;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
       // x_type x;
       // Jt_type Jt;
       // int attrib[NE];
@@ -137,20 +152,23 @@ public:
       }
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData) { }
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData) { }
 #endif
    };
-   template <int NE> struct Result<1,NE> // 1 = EvalCoordinates
+
+   // Case EvalOps = 1 = EvalCoordinates
+   template <typename it_t> struct Result<1,it_t>
    {
-      static const int ne = NE;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
-      typedef TTensor3<qpts,sdim,NE,real_t,true> x_type;
+      typedef TTensor3<qpts,sdim,NE,vreal_t,true> x_type;
 #else
-      typedef TTensor3<qpts,sdim,NE,real_t/*,true*/> x_type;
+      typedef TTensor3<qpts,sdim,ne,vreal_t/*,true*/> x_type;
 #endif
       x_type x;
 
-      typedef TTensor3<dofs,sdim,NE,real_t> nodes_dof_t;
+      typedef TTensor3<dofs,sdim,ne,vreal_t> nodes_dof_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
       nodes_dof_t nodes_dof;
 #endif
@@ -159,8 +177,8 @@ public:
       void Eval(int el, T_type &T)
       {
 #ifdef MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
-         MFEM_STATIC_ASSERT(NE == 1, "only NE == 1 is supported");
-         TTensor3<dofs,sdim,1,real_t> &nodes_dof = T.nodes_dof;
+         MFEM_STATIC_ASSERT(ne == 1, "only ne == 1 is supported");
+         TTensor3<dofs,sdim,1,vreal_t> &nodes_dof = T.nodes_dof;
 #elif !defined(MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES)
          nodes_dof_t nodes_dof;
 #endif
@@ -173,25 +191,30 @@ public:
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData)
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData)
       {
+         const int SS = sizeof(nodeData[0])/sizeof(nodeData[0][0]);
+         MFEM_ASSERT(el % (SS*ne) == 0, "invalid element index: " << el);
          T.evaluator.Calc(nodes_dof_t::layout.merge_23(),
-                          &nodeData[el*nodes_dof_t::size],
+                          &nodeData[el/SS*nodes_dof_t::size],
                           x.layout.merge_23(), x);
       }
 #endif
    };
-   template <int NE> struct Result<2,NE> // 2 = EvalJacobians
+
+   // Case EvalOps = 2 = EvalJacobians
+   template <typename it_t> struct Result<2,it_t>
    {
-      static const int ne = NE;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
-      typedef TTensor4<qpts,dim,sdim,NE,real_t,true> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t,true> Jt_type;
 #else
-      typedef TTensor4<qpts,dim,sdim,NE,real_t/*,true*/> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t/*,true*/> Jt_type;
 #endif
       Jt_type Jt;
 
-      typedef TTensor3<dofs,sdim,NE,real_t> nodes_dof_t;
+      typedef TTensor3<dofs,sdim,ne,vreal_t> nodes_dof_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
       nodes_dof_t nodes_dof;
 #endif
@@ -200,8 +223,8 @@ public:
       void Eval(int el, T_type &T)
       {
 #ifdef MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
-         MFEM_STATIC_ASSERT(NE == 1, "only NE == 1 is supported");
-         TTensor3<dofs,sdim,1,real_t> &nodes_dof = T.nodes_dof;
+         MFEM_STATIC_ASSERT(ne == 1, "only ne == 1 is supported");
+         TTensor3<dofs,sdim,1,vreal_t> &nodes_dof = T.nodes_dof;
 #elif !defined(MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES)
          nodes_dof_t nodes_dof;
 #endif
@@ -214,27 +237,32 @@ public:
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData)
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData)
       {
+         const int SS = sizeof(nodeData[0])/sizeof(nodeData[0][0]);
+         MFEM_ASSERT(el % (SS*ne) == 0, "invalid element index: " << el);
          T.evaluator.CalcGrad(nodes_dof_t::layout.merge_23(),
-                              &nodeData[el*nodes_dof_t::size],
+                              &nodeData[el/SS*nodes_dof_t::size],
                               Jt.layout.merge_34(), Jt);
       }
 #endif
    };
-   template <int NE> struct Result<3,NE> // 3 = EvalCoordinates|EvalJacobians
+
+   // Case EvalOps = 3 = EvalCoordinates|EvalJacobians
+   template <typename it_t> struct Result<3,it_t>
    {
-      static const int ne = NE;
-      typedef TTensor3<qpts,sdim,NE,real_t,true> x_type;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
+      typedef TTensor3<qpts,sdim,ne,vreal_t,true> x_type;
       x_type x;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
-      typedef TTensor4<qpts,dim,sdim,NE,real_t,true> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t,true> Jt_type;
 #else
-      typedef TTensor4<qpts,dim,sdim,NE,real_t/*,true*/> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t/*,true*/> Jt_type;
 #endif
       Jt_type Jt;
 
-      typedef TTensor3<dofs,sdim,NE,real_t> nodes_dof_t;
+      typedef TTensor3<dofs,sdim,ne,vreal_t> nodes_dof_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
       nodes_dof_t nodes_dof;
 #endif
@@ -243,8 +271,8 @@ public:
       void Eval(int el, T_type &T)
       {
 #ifdef MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
-         MFEM_STATIC_ASSERT(NE == 1, "only NE == 1 is supported");
-         TTensor3<dofs,sdim,1,real_t> &nodes_dof = T.nodes_dof;
+         MFEM_STATIC_ASSERT(ne == 1, "only ne == 1 is supported");
+         TTensor3<dofs,sdim,1,vreal_t> &nodes_dof = T.nodes_dof;
 #elif !defined(MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES)
          nodes_dof_t nodes_dof;
 #endif
@@ -259,39 +287,45 @@ public:
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData)
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData)
       {
+         const int SS = sizeof(nodeData[0])/sizeof(nodeData[0][0]);
+         MFEM_ASSERT(el % (SS*ne) == 0, "invalid element index: " << el);
          T.evaluator.Calc(nodes_dof_t::layout.merge_23(),
-                          &nodeData[el*nodes_dof_t::size],
+                          &nodeData[el/SS*nodes_dof_t::size],
                           x.layout.merge_23(), x);
          T.evaluator.CalcGrad(nodes_dof_t::layout.merge_23(),
-                              &nodeData[el*nodes_dof_t::size],
+                              &nodeData[el/SS*nodes_dof_t::size],
                               Jt.layout.merge_34(), Jt);
       }
 #endif
    };
-   template <int NE> struct Result<6,NE> // 6 = EvalJacobians|LoadAttributes
+
+   // Case EvalOps = 6 = EvalJacobians|LoadAttributes
+   template <typename it_t> struct Result<6,it_t>
    {
-      static const int ne = NE;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
+      typedef typename it_t::vint_t  vint_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
-      typedef TTensor4<qpts,dim,sdim,NE,real_t,true> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t,true> Jt_type;
 #else
-      typedef TTensor4<qpts,dim,sdim,NE,real_t/*,true*/> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t/*,true*/> Jt_type;
 #endif
       Jt_type Jt;
 
-      typedef TTensor3<dofs,sdim,NE,real_t> nodes_dof_t;
+      typedef TTensor3<dofs,sdim,ne,vreal_t> nodes_dof_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
       nodes_dof_t nodes_dof;
 #endif
-      int attrib[NE];
+      vint_t attrib[ne];
 
       inline MFEM_ALWAYS_INLINE
       void Eval(int el, T_type &T)
       {
 #ifdef MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
-         MFEM_STATIC_ASSERT(NE == 1, "only NE == 1 is supported");
-         TTensor3<dofs,sdim,1,real_t> &nodes_dof = T.nodes_dof;
+         MFEM_STATIC_ASSERT(ne == 1, "only ne == 1 is supported");
+         TTensor3<dofs,sdim,1,vreal_t> &nodes_dof = T.nodes_dof;
 #elif !defined(MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES)
          nodes_dof_t nodes_dof;
 #endif
@@ -305,26 +339,31 @@ public:
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData)
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData)
       {
+         const int SS = sizeof(nodeData[0])/sizeof(nodeData[0][0]);
+         MFEM_ASSERT(el % (SS*ne) == 0, "invalid element index: " << el);
          T.evaluator.CalcGrad(nodes_dof_t::layout.merge_23(),
-                              &nodeData[el*nodes_dof_t::size],
+                              &nodeData[el/SS*nodes_dof_t::size],
                               Jt.layout.merge_34(), Jt);
          T.SetAttributes(el, attrib);
       }
 #endif
    };
-   template <int NE> struct Result<10,NE> // 10 = EvalJacobians|LoadElementIdxs
+
+   // Case EvalOps = 10 = EvalJacobians|LoadElementIdxs
+   template <typename it_t> struct Result<10,it_t>
    {
-      static const int ne = NE;
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vreal_t vreal_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
-      typedef TTensor4<qpts,dim,sdim,NE,real_t,true> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t,true> Jt_type;
 #else
-      typedef TTensor4<qpts,dim,sdim,NE,real_t/*,true*/> Jt_type;
+      typedef TTensor4<qpts,dim,sdim,ne,vreal_t/*,true*/> Jt_type;
 #endif
       Jt_type Jt;
 
-      typedef TTensor3<dofs,sdim,NE,real_t> nodes_dof_t;
+      typedef TTensor3<dofs,sdim,ne,vreal_t> nodes_dof_t;
 #ifdef MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES
       nodes_dof_t nodes_dof;
 #endif
@@ -334,8 +373,8 @@ public:
       void Eval(int el, T_type &T)
       {
 #ifdef MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
-         MFEM_STATIC_ASSERT(NE == 1, "only NE == 1 is supported");
-         TTensor3<dofs,sdim,1,real_t> &nodes_dof = T.nodes_dof;
+         MFEM_STATIC_ASSERT(ne == 1, "only ne == 1 is supported");
+         TTensor3<dofs,sdim,1,vreal_t> &nodes_dof = T.nodes_dof;
 #elif !defined(MFEM_TEMPLATE_ELTRANS_RESULT_HAS_NODES)
          nodes_dof_t nodes_dof;
 #endif
@@ -349,10 +388,12 @@ public:
 
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(int el, T_type &T, const real_t *nodeData)
+      void EvalSerialized(int el, T_type &T, const vreal_t *nodeData)
       {
+         const int SS = sizeof(nodeData[0])/sizeof(nodeData[0][0]);
+         MFEM_ASSERT(el % (SS*ne) == 0, "invalid element index: " << el);
          T.evaluator.CalcGrad(nodes_dof_t::layout.merge_23(),
-                              &nodeData[el*nodes_dof_t::size],
+                              &nodeData[el/SS*nodes_dof_t::size],
                               Jt.layout.merge_34(), Jt);
          first_elem_idx = el;
       }

fem/tevaluator.hpp

@@ -23,12 +23,16 @@ namespace mfem
 // Templated classes for transitioning between degrees of freedom and quadrature
 // points values.
 
-// Shape evaluators -- values of basis functions on the reference element
-
+/** @brief Shape evaluators -- values of basis functions on the reference element
+    @tparam FE some form of TFiniteElement, probably got from TMesh::FE_type
+    @tparam IR some form of TIntegrationRule
+    @tparam TP tensor product or not
+    @tparam real_t data type for mesh nodes, solution basis, mesh basis
+*/
 template <class FE, class IR, bool TP, typename real_t>
 class ShapeEvaluator_base;
 
-// ShapeEvaluator without tensor-product structure
+/// ShapeEvaluator without tensor-product structure
 template <class FE, class IR, typename real_t>
 class ShapeEvaluator_base<FE, IR, false, real_t>
 {
@@ -54,11 +58,11 @@ public:
 
    // default copy constructor
 
-   // Multi-component shape evaluation from DOFs to quadrature points.
-   // dof_layout is (DOF x NumComp) and qpt_layout is (NIP x NumComp).
+   /** @brief Multi-component shape evaluation from DOFs to quadrature points.
+       dof_layout is (DOF x NumComp) and qpt_layout is (NIP x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
@@ -76,12 +80,12 @@ public:
                      qpt_layout, qpt_data);
    }
 
-   // Multi-component shape evaluation transpose from quadrature points to DOFs.
-   // qpt_layout is (NIP x NumComp) and dof_layout is (DOF x NumComp).
+   /** @brief Multi-component shape evaluation transpose from quadrature points to
+       DOFs.  qpt_layout is (NIP x NumComp) and dof_layout is (DOF x NumComp). */
    template <bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
@@ -99,11 +103,11 @@ public:
                    dof_layout, dof_data);
    }
 
-   // Multi-component gradient evaluation from DOFs to quadrature points.
-   // dof_layout is (DOF x NumComp) and grad_layout is (NIP x DIM x NumComp).
+   /** @brief Multi-component gradient evaluation from DOFs to quadrature points.
+      dof_layout is (DOF x NumComp) and grad_layout is (NIP x DIM x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename grad_layout_t, typename grad_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGrad(const dof_layout_t  &dof_layout,
                  const dof_data_t    &dof_data,
                  const grad_layout_t &grad_layout,
@@ -124,12 +128,12 @@ public:
                      grad_layout.merge_12(), grad_data);
    }
 
-   // Multi-component gradient evaluation transpose from quadrature points to
-   // DOFs. grad_layout is (NIP x DIM x NumComp), dof_layout is (DOF x NumComp).
+   /** @brief Multi-component gradient evaluation transpose from quadrature points to
+      DOFs. grad_layout is (NIP x DIM x NumComp), dof_layout is (DOF x NumComp). */
    template <bool Add,
              typename grad_layout_t, typename grad_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGradT(const grad_layout_t &grad_layout,
                   const grad_data_t   &grad_data,
                   const dof_layout_t  &dof_layout,
@@ -150,11 +154,12 @@ public:
                    dof_layout, dof_data);
    }
 
-   // Multi-component assemble.
-   // qpt_layout is (NIP x NumComp), M_layout is (DOF x DOF x NumComp)
+   /** @brief Multi-component assemble.
+       qpt_layout is (NIP x NumComp),
+       M_layout is (DOF x DOF x NumComp) */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename M_layout_t, typename M_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
                  const M_layout_t &M_layout, M_data_t &M_data) const
    {
@@ -173,19 +178,20 @@ public:
 #endif
    }
 
-   // Multi-component assemble of grad-grad element matrices.
-   // qpt_layout is (NIP x DIM x DIM x NumComp), and
-   // D_layout is (DOF x DOF x NumComp).
+   /** @brief Multi-component assemble of grad-grad element matrices.
+       qpt_layout is (NIP x DIM x DIM x NumComp), and
+       D_layout is (DOF x DOF x NumComp). */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void AssembleGradGrad(const qpt_layout_t &qpt_layout,
                          const qpt_data_t   &qpt_data,
                          const D_layout_t   &D_layout,
                          D_data_t           &D_data) const
    {
       const int NC = qpt_layout_t::dim_4;
-      TTensor4<NIP,DIM,DOF,NC> F;
+      typedef typename qpt_data_t::data_type entry_type;
+      TTensor4<NIP,DIM,DOF,NC,entry_type> F;
       for (int k = 0; k < NC; k++)
       {
          // Next loop performs a batch of matrix-matrix products of size
@@ -207,7 +213,7 @@ public:
 template <int Dim, int DOF, int NIP, typename real_t>
 class TProductShapeEvaluator;
 
-// ShapeEvaluator with 1D tensor-product structure
+/// ShapeEvaluator with 1D tensor-product structure
 template <int DOF, int NIP, typename real_t>
 class TProductShapeEvaluator<1, DOF, NIP, real_t>
 {
@@ -220,11 +226,11 @@ protected:
 public:
    TProductShapeEvaluator() { }
 
-   // Multi-component shape evaluation from DOFs to quadrature points.
-   // dof_layout is (DOF x NumComp) and qpt_layout is (NIP x NumComp).
+   /** @brief Multi-component shape evaluation from DOFs to quadrature points.
+       dof_layout is (DOF x NumComp) and qpt_layout is (NIP x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
@@ -233,12 +239,12 @@ public:
                      qpt_layout, qpt_data);
    }
 
-   // Multi-component shape evaluation transpose from quadrature points to DOFs.
-   // qpt_layout is (NIP x NumComp) and dof_layout is (DOF x NumComp).
+   /** @brief Multi-component shape evaluation transpose from quadrature points
+       to DOFs.  qpt_layout is (NIP x NumComp) and dof_layout is (DOF x NumComp). */
    template <bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
@@ -247,11 +253,11 @@ public:
                    dof_layout, dof_data);
    }
 
-   // Multi-component gradient evaluation from DOFs to quadrature points.
-   // dof_layout is (DOF x NumComp) and grad_layout is (NIP x DIM x NumComp).
+   /** @brief Multi-component gradient evaluation from DOFs to quadrature points.
+       dof_layout is (DOF x NumComp) and grad_layout is (NIP x DIM x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename grad_layout_t, typename grad_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGrad(const dof_layout_t  &dof_layout,
                  const dof_data_t    &dof_data,
                  const grad_layout_t &grad_layout,
@@ -263,12 +269,12 @@ public:
                      grad_layout.merge_12(), grad_data);
    }
 
-   // Multi-component gradient evaluation transpose from quadrature points to
-   // DOFs. grad_layout is (NIP x DIM x NumComp), dof_layout is (DOF x NumComp).
+   /** @brief Multi-component gradient evaluation transpose from quadrature points to
+       DOFs. grad_layout is (NIP x DIM x NumComp), dof_layout is (DOF x NumComp). */
    template <bool Add,
              typename grad_layout_t, typename grad_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGradT(const grad_layout_t &grad_layout,
                   const grad_data_t   &grad_data,
                   const dof_layout_t  &dof_layout,
@@ -281,11 +287,11 @@ public:
                    dof_layout, dof_data);
    }
 
-   // Multi-component assemble.
-   // qpt_layout is (NIP x NumComp), M_layout is (DOF x DOF x NumComp)
+   /** @brief Multi-component assemble.
+       qpt_layout is (NIP x NumComp), M_layout is (DOF x DOF x NumComp) */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename M_layout_t, typename M_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
                  const M_layout_t &M_layout, M_data_t &M_data) const
    {
@@ -304,12 +310,12 @@ public:
 #endif
    }
 
-   // Multi-component assemble of grad-grad element matrices.
-   // qpt_layout is (NIP x DIM x DIM x NumComp), and
-   // D_layout is (DOF x DOF x NumComp).
+   /** @brief Multi-component assemble of grad-grad element matrices.
+       qpt_layout is (NIP x DIM x DIM x NumComp), and
+       D_layout is (DOF x DOF x NumComp). */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void AssembleGradGrad(const qpt_layout_t &qpt_layout,
                          const qpt_data_t   &qpt_data,
                          const D_layout_t   &D_layout,
@@ -331,7 +337,7 @@ public:
    }
 };
 
-// ShapeEvaluator with 2D tensor-product structure
+/// ShapeEvaluator with 2D tensor-product structure
 template <int DOF, int NIP, typename real_t>
 class TProductShapeEvaluator<2, DOF, NIP, real_t>
 {
@@ -348,13 +354,14 @@ public:
    template <bool Dx, bool Dy,
              typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
       const int NC = dof_layout_t::dim_2;
+      typedef typename qpt_data_t::data_type entry_type;
       // DOF x DOF x NC --> NIP x DOF x NC --> NIP x NIP x NC
-      TTensor3<NIP,DOF,NC> A;
+      TTensor3<NIP,DOF,NC,entry_type> A;
 
       // (1) A_{i,j,k} = \sum_s B_1d_{i,s} dof_data_{s,j,k}
       Mult_2_1<false>(B_1d.layout, Dx ? G_1d : B_1d,
@@ -366,11 +373,11 @@ public:
                       qpt_layout.template split_1<NIP,NIP>(), qpt_data);
    }
 
-   // Multi-component shape evaluation from DOFs to quadrature points.
-   // dof_layout is (TDOF x NumComp) and qpt_layout is (TNIP x NumComp).
+   /** @brief Multi-component shape evaluation from DOFs to quadrature points.
+       dof_layout is (TDOF x NumComp) and qpt_layout is (TNIP x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
@@ -380,13 +387,14 @@ public:
    template <bool Dx, bool Dy, bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
       const int NC = dof_layout_t::dim_2;
+      typedef typename qpt_data_t::data_type entry_type;
       // NIP x NIP X NC --> NIP x DOF x NC --> DOF x DOF x NC
-      TTensor3<NIP,DOF,NC> A;
+      TTensor3<NIP,DOF,NC,entry_type> A;
 
       // (1) A_{i,j,k} = \sum_s B_1d_{s,j} qpt_data_{i,s,k}
       Mult_1_2<false>(B_1d.layout, Dy ? G_1d : B_1d,
@@ -398,23 +406,23 @@ public:
                     dof_layout.template split_1<DOF,DOF>(), dof_data);
    }
 
-   // Multi-component shape evaluation transpose from quadrature points to DOFs.
-   // qpt_layout is (TNIP x NumComp) and dof_layout is (TDOF x NumComp).
+   /** @brief Multi-component shape evaluation transpose from quadrature points to DOFs.
+       qpt_layout is (TNIP x NumComp) and dof_layout is (TDOF x NumComp). */
    template <bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
       CalcT<false,false,Add>(qpt_layout, qpt_data, dof_layout, dof_data);
    }
 
-   // Multi-component gradient evaluation from DOFs to quadrature points.
-   // dof_layout is (TDOF x NumComp) and grad_layout is (TNIP x DIM x NumComp).
+   /** @brief Multi-component gradient evaluation from DOFs to quadrature points.
+       dof_layout is (TDOF x NumComp) and grad_layout is (TNIP x DIM x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename grad_layout_t, typename grad_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGrad(const dof_layout_t  &dof_layout,
                  const dof_data_t    &dof_data,
                  const grad_layout_t &grad_layout,
@@ -426,13 +434,13 @@ public:
                        grad_layout.ind2(1), grad_data);
    }
 
-   // Multi-component gradient evaluation transpose from quadrature points to
-   // DOFs. grad_layout is (TNIP x DIM x NumComp), dof_layout is
-   // (TDOF x NumComp).
+   /** @brief Multi-component gradient evaluation transpose from quadrature points to
+       DOFs. grad_layout is (TNIP x DIM x NumComp), dof_layout is
+       (TDOF x NumComp). */
    template <bool Add,
              typename grad_layout_t, typename grad_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGradT(const grad_layout_t &grad_layout,
                   const grad_data_t   &grad_data,
                   const dof_layout_t  &dof_layout,
@@ -444,15 +452,16 @@ public:
                              dof_layout, dof_data);
    }
 
-   // Multi-component assemble.
-   // qpt_layout is (TNIP x NumComp), M_layout is (TDOF x TDOF x NumComp)
+   /** @brief Multi-component assemble.
+       qpt_layout is (TNIP x NumComp), M_layout is (TDOF x TDOF x NumComp) */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename M_layout_t, typename M_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
                  const M_layout_t &M_layout, M_data_t &M_data) const
    {
       const int NC = qpt_layout_t::dim_2;
+      typedef typename qpt_data_t::data_type entry_type;
 
       // Using TensorAssemble: <I,NIP,J> --> <DOF,I,DOF,J>
 
@@ -469,7 +478,7 @@ public:
          TTensor3<DOF,NIP,DOF*NC>::layout, A,
          M_layout.merge_23().template split_12<DOF,DOF,DOF,DOF*NC>(), M_data);
 #elif 1
-      TTensor4<DOF,NIP,DOF,NC> A;
+      TTensor4<DOF,NIP,DOF,NC,entry_type> A;
       // qpt_data<NIP1,NIP2,NC> --> A<DOF2,NIP1,DOF2,NC>
       TensorAssemble<false>(
          Bt_1d.layout, Bt_1d, B_1d.layout, B_1d,
@@ -510,14 +519,15 @@ public:
    template <int D1, int D2, bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout,
                  const qpt_data_t   &qpt_data,
                  const D_layout_t   &D_layout,
                  D_data_t           &D_data) const
    {
       const int NC = qpt_layout_t::dim_2;
-      TTensor4<DOF,NIP,DOF,NC> A;
+      typedef typename qpt_data_t::data_type entry_type;
+      TTensor4<DOF,NIP,DOF,NC,entry_type> A;
 
       // Using TensorAssemble: <I,NIP,J> --> <DOF,I,DOF,J>
 
@@ -531,16 +541,16 @@ public:
       TensorAssemble<Add>(
          Bt_1d.layout, D1 == 1 ? Bt_1d : Gt_1d,
          B_1d.layout, D2 == 1 ? B_1d : G_1d,
-         TTensor3<DOF,NIP,DOF*NC>::layout, A,
+         A.layout.merge_34(), A,
          D_layout.merge_23().template split_12<DOF,DOF,DOF,DOF*NC>(), D_data);
    }
 
-   // Multi-component assemble of grad-grad element matrices.
-   // qpt_layout is (TNIP x DIM x DIM x NumComp), and
-   // D_layout is (TDOF x TDOF x NumComp).
+   /** @brief Multi-component assemble of grad-grad element matrices.
+      qpt_layout is (TNIP x DIM x DIM x NumComp), and
+      D_layout is (TDOF x TDOF x NumComp). */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void AssembleGradGrad(const qpt_layout_t &qpt_layout,
                          const qpt_data_t   &qpt_data,
                          const D_layout_t   &D_layout,
@@ -607,7 +617,7 @@ public:
    }
 };
 
-// ShapeEvaluator with 3D tensor-product structure
+/// ShapeEvaluator with 3D tensor-product structure
 template <int DOF, int NIP, typename real_t>
 class TProductShapeEvaluator<3, DOF, NIP, real_t>
 {
@@ -624,13 +634,14 @@ public:
    template <bool Dx, bool Dy, bool Dz,
              typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
       const int NC = dof_layout_t::dim_2;
-      TVector<NIP*DOF*DOF*NC> QDD;
-      TVector<NIP*NIP*DOF*NC> QQD;
+      typedef typename qpt_data_t::data_type entry_type;
+      TVector<NIP*DOF*DOF*NC,entry_type> QDD;
+      TVector<NIP*NIP*DOF*NC,entry_type> QQD;
 
       // QDD_{i,jj,k} = \sum_s B_1d_{i,s} dof_data_{s,jj,k}
       Mult_2_1<false>(B_1d.layout, Dx ? G_1d : B_1d,
@@ -646,11 +657,11 @@ public:
                       qpt_layout.template split_1<NIP*NIP,NIP>(), qpt_data);
    }
 
-   // Multi-component shape evaluation from DOFs to quadrature points.
-   // dof_layout is (TDOF x NumComp) and qpt_layout is (TNIP x NumComp).
+   /** @brief Multi-component shape evaluation from DOFs to quadrature points.
+       dof_layout is (TDOF x NumComp) and qpt_layout is (TNIP x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename qpt_layout_t, typename qpt_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Calc(const dof_layout_t &dof_layout, const dof_data_t &dof_data,
              const qpt_layout_t &qpt_layout, qpt_data_t &qpt_data) const
    {
@@ -660,13 +671,14 @@ public:
    template <bool Dx, bool Dy, bool Dz, bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
       const int NC = dof_layout_t::dim_2;
-      TVector<NIP*DOF*DOF*NC> QDD;
-      TVector<NIP*NIP*DOF*NC> QQD;
+      typedef typename qpt_data_t::data_type entry_type;
+      TVector<NIP*DOF*DOF*NC,entry_type> QDD;
+      TVector<NIP*NIP*DOF*NC,entry_type> QQD;
 
       // QQD_{ii,j,k} = \sum_s B_1d_{s,j} qpt_data_{ii,s,k}
       Mult_1_2<false>(B_1d.layout, Dz ? G_1d : B_1d,
@@ -682,23 +694,23 @@ public:
                     dof_layout.template split_1<DOF,DOF*DOF>(), dof_data);
    }
 
-   // Multi-component shape evaluation transpose from quadrature points to DOFs.
-   // qpt_layout is (TNIP x NumComp) and dof_layout is (TDOF x NumComp).
+   /** @brief Multi-component shape evaluation transpose from quadrature points to DOFs.
+       qpt_layout is (TNIP x NumComp) and dof_layout is (TDOF x NumComp). */
    template <bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcT(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
               const dof_layout_t &dof_layout, dof_data_t &dof_data) const
    {
       CalcT<false,false,false,Add>(qpt_layout, qpt_data, dof_layout, dof_data);
    }
 
-   // Multi-component gradient evaluation from DOFs to quadrature points.
-   // dof_layout is (TDOF x NumComp) and grad_layout is (TNIP x DIM x NumComp).
+   /** @brief Multi-component gradient evaluation from DOFs to quadrature points.
+       dof_layout is (TDOF x NumComp) and grad_layout is (TNIP x DIM x NumComp). */
    template <typename dof_layout_t, typename dof_data_t,
              typename grad_layout_t, typename grad_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGrad(const dof_layout_t  &dof_layout,
                  const dof_data_t    &dof_data,
                  const grad_layout_t &grad_layout,
@@ -714,13 +726,13 @@ public:
       // y-derivatives and second time for the z-derivatives.
    }
 
-   // Multi-component gradient evaluation transpose from quadrature points to
-   // DOFs. grad_layout is (TNIP x DIM x NumComp), dof_layout is
-   // (TDOF x NumComp).
+   /** @brief Multi-component gradient evaluation transpose from quadrature points to
+       DOFs. grad_layout is (TNIP x DIM x NumComp), dof_layout is
+       (TDOF x NumComp). */
    template <bool Add,
              typename grad_layout_t, typename grad_data_t,
              typename dof_layout_t, typename dof_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void CalcGradT(const grad_layout_t &grad_layout,
                   const grad_data_t   &grad_data,
                   const dof_layout_t  &dof_layout,
@@ -734,17 +746,18 @@ public:
                                    dof_layout, dof_data);
    }
 
-   // Multi-component assemble.
-   // qpt_layout is (TNIP x NumComp), M_layout is (TDOF x TDOF x NumComp)
+   /** @brief Multi-component assemble.
+       qpt_layout is (TNIP x NumComp), M_layout is (TDOF x TDOF x NumComp) */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename M_layout_t, typename M_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout, const qpt_data_t &qpt_data,
                  const M_layout_t &M_layout, M_data_t &M_data) const
    {
       const int NC = qpt_layout_t::dim_2;
-      TTensor4<DOF,NIP*NIP,DOF,NC> A1;
-      TTensor4<DOF,DOF*NIP,DOF,DOF*NC> A2;
+      typedef typename qpt_data_t::data_type entry_type;
+      TTensor4<DOF,NIP*NIP,DOF,NC,entry_type> A1;
+      TTensor4<DOF,DOF*NIP,DOF,DOF*NC,entry_type> A2;
 
       // Using TensorAssemble: <I,NIP,J> --> <DOF,I,DOF,J>
 
@@ -788,15 +801,16 @@ public:
    template <int D1, int D2, bool Add,
              typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(const qpt_layout_t &qpt_layout,
                  const qpt_data_t   &qpt_data,
                  const D_layout_t   &D_layout,
                  D_data_t           &D_data) const
    {
       const int NC = qpt_layout_t::dim_2;
-      TTensor4<DOF,NIP*NIP,DOF,NC> A1;
-      TTensor4<DOF,DOF*NIP,DOF,DOF*NC> A2;
+      typedef typename qpt_data_t::data_type entry_type;
+      TTensor4<DOF,NIP*NIP,DOF,NC,entry_type> A1;
+      TTensor4<DOF,DOF*NIP,DOF,DOF*NC,entry_type> A2;
 
       // Using TensorAssemble: <I,NIP,J> --> <DOF,I,DOF,J>
 
@@ -824,7 +838,7 @@ public:
 #if 0
    template <typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void Assemble(int D1, int D2,
                  const qpt_layout_t &qpt_layout,
                  const qpt_data_t   &qpt_data,
@@ -859,12 +873,12 @@ public:
    }
 #endif
 
-   // Multi-component assemble of grad-grad element matrices.
-   // qpt_layout is (TNIP x DIM x DIM x NumComp), and
-   // D_layout is (TDOF x TDOF x NumComp).
+   /** @brief Multi-component assemble of grad-grad element matrices.
+       qpt_layout is (TNIP x DIM x DIM x NumComp), and
+       D_layout is (TDOF x TDOF x NumComp). */
    template <typename qpt_layout_t, typename qpt_data_t,
              typename D_layout_t, typename D_data_t>
-   MFEM_ALWAYS_INLINE
+   inline MFEM_ALWAYS_INLINE
    void AssembleGradGrad(const qpt_layout_t &qpt_layout,
                          const qpt_data_t   &qpt_data,
                          const D_layout_t   &D_layout,
@@ -895,7 +909,7 @@ public:
    }
 };
 
-// ShapeEvaluator with tensor-product structure in any dimension
+/// ShapeEvaluator with tensor-product structure in any dimension
 template <class FE, class IR, typename real_t>
 class ShapeEvaluator_base<FE, IR, true, real_t>
    : public TProductShapeEvaluator<FE::dim, FE::dofs_1d, IR::qpts_1d, real_t>
@@ -921,7 +935,7 @@ public:
    // default copy constructor
 };
 
-// General ShapeEvaluator for any scalar FE type (L2 or H1)
+/// General ShapeEvaluator for any scalar FE type (L2 or H1)
 template <class FE, class IR, typename real_t>
 class ShapeEvaluator
    : public ShapeEvaluator_base<FE,IR,FE::tensor_prod && IR::tensor_prod,real_t>
@@ -946,8 +960,9 @@ public:
 };
 
 
-// Field evaluators -- values of a given global FE grid function
-
+/** @brief Field evaluators -- values of a given global FE grid function
+    This is roughly speaking a templated version of GridFunction
+*/
 template <typename FESpace_t, typename VecLayout_t, typename IR,
           typename complex_t, typename real_t>
 class FieldEvaluator_base
@@ -960,7 +975,7 @@ protected:
    ShapeEval_type  shapeEval;
    VecLayout_t     vec_layout;
 
-   // With this constructor, fespace is a shallow copy.
+   /// With this constructor, fespace is a shallow copy.
    inline MFEM_ALWAYS_INLINE
    FieldEvaluator_base(const FESpace_t &tfes, const ShapeEval_type &shape_eval,
                        const VecLayout_t &vec_layout)
@@ -969,14 +984,14 @@ protected:
         vec_layout(vec_layout)
    { }
 
-   // This constructor creates new fespace, not a shallow copy.
+   /// This constructor creates new fespace, not a shallow copy.
    inline MFEM_ALWAYS_INLINE
    FieldEvaluator_base(const FE_type &fe, const FiniteElementSpace &fes)
       : fespace(fe, fes), shapeEval(fe), vec_layout(fes)
    { }
 };
 
-// complex_t - dof/qpt data type, real_t - ShapeEvaluator (FE basis) data type
+/// complex_t - dof/qpt data type, real_t - ShapeEvaluator (FE basis) data type
 template <typename FESpace_t, typename VecLayout_t, typename IR,
           typename complex_t = double, typename real_t = double>
 class FieldEvaluator
@@ -1009,7 +1024,7 @@ protected:
    complex_t       *data_out;
 
 public:
-   // With this constructor, fespace is a shallow copy of tfes.
+   /// With this constructor, fespace is a shallow copy of tfes.
    inline MFEM_ALWAYS_INLINE
    FieldEvaluator(const FESpace_t &tfes, const ShapeEval_type &shape_eval,
                   const VecLayout_type &vec_layout,
@@ -1019,7 +1034,7 @@ public:
         data_out(global_data_out)
    { }
 
-   // With this constructor, fespace is a shallow copy of f.fespace.
+   /// With this constructor, fespace is a shallow copy of f.fespace.
    inline MFEM_ALWAYS_INLINE
    FieldEvaluator(const FieldEvaluator &f,
                   const complex_t *global_data_in, complex_t *global_data_out)
@@ -1028,7 +1043,7 @@ public:
         data_out(global_data_out)
    { }
 
-   // This constructor creates a new fespace, not a shallow copy.
+   /// This constructor creates a new fespace, not a shallow copy.
    inline MFEM_ALWAYS_INLINE
    FieldEvaluator(const FiniteElementSpace &fes,
                   const complex_t *global_data_in, complex_t *global_data_out)
@@ -1049,25 +1064,25 @@ public:
       fespace.SetElement(el);
    }
 
-   // val_layout_t is (qpts x vdim x NE)
+   /// val_layout_t is (qpts x vdim x NE)
    template <typename val_layout_t, typename val_data_t>
    inline MFEM_ALWAYS_INLINE
    void GetValues(int el, const val_layout_t &l, val_data_t &vals)
    {
       const int ne = val_layout_t::dim_3;
-      TTensor3<dofs,vdim,ne,complex_type> val_dofs;
+      TTensor3<dofs,vdim,ne,typename val_data_t::data_type> val_dofs;
       SetElement(el);
       fespace.VectorExtract(vec_layout, data_in, val_dofs.layout, val_dofs);
       shapeEval.Calc(val_dofs.layout.merge_23(), val_dofs, l.merge_23(), vals);
    }
 
-   // grad_layout_t is (qpts x dim x vdim x NE)
+   /// grad_layout_t is (qpts x dim x vdim x NE)
    template <typename grad_layout_t, typename grad_data_t>
    inline MFEM_ALWAYS_INLINE
    void GetGradients(int el, const grad_layout_t &l, grad_data_t &grad)
    {
       const int ne = grad_layout_t::dim_4;
-      TTensor3<dofs,vdim,ne,complex_type> val_dofs;
+      TTensor3<dofs,vdim,ne,typename grad_data_t::data_type> val_dofs;
       SetElement(el);
       fespace.VectorExtract(vec_layout, data_in, val_dofs.layout, val_dofs);
       shapeEval.CalcGrad(val_dofs.layout.merge_23(), val_dofs,
@@ -1112,23 +1127,25 @@ public:
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
    template <typename DataType>
    inline MFEM_ALWAYS_INLINE
-   void EvalSerialized(const complex_t *loc_dofs, DataType &F)
+   void EvalSerialized(const typename DataType::vcomplex_t *loc_dofs,
+                       DataType &F)
    {
       Action<DataType::InData,true>::EvalSerialized(*this, loc_dofs, F);
    }
 
    template <bool Add, typename DataType>
    inline MFEM_ALWAYS_INLINE
-   void AssembleSerialized(const DataType &F, complex_t *loc_dofs)
+   void AssembleSerialized(const DataType &F,
+                           typename DataType::vcomplex_t *loc_dofs)
    {
       Action<DataType::OutData,true>::
       template AssembleSerialized<Add>(*this, F, loc_dofs);
    }
 #endif
 
-   // Enumeration for the data type used by the Eval() and Assemble() methods.
-   // The types can obtained by summing constants from this enumeration and used
-   // as a template parameter in struct Data.
+   /** @brief Enumeration for the data type used by the Eval() and Assemble() methods.
+       The types can be obtained by summing constants from this enumeration and used
+       as a template parameter in struct Data. */
    enum InOutData
    {
       None      = 0,
@@ -1136,65 +1153,72 @@ public:
       Gradients = 2
    };
 
-   // Auxiliary templated struct AData, used by the Eval() and Assemble()
-   // methods. The template parameter IOData is "bitwise or" of constants from
-   // the enum InOutData. The parameter NE is the number of elements to be
-   // processed in the Eval() and Assemble() methods.
-   template<int IOData, int NE> struct AData;
+   /** @brief  Auxiliary templated struct AData, used by the Eval() and Assemble()
+       methods.
 
-   template <int NE> struct AData<0,NE> // 0 = None
+       The template parameter IOData is "bitwise or" of constants from
+       the enum InOutData. The parameter NE is the number of elements to be
+       processed in the Eval() and Assemble() methods. */
+   template<int IOData, typename impl_traits_t> struct AData;
+
+   template <typename it_t> struct AData<0,it_t> // 0 = None
    {
       // Do we need this?
    };
 
-   template <int NE> struct AData<1,NE> // 1 = Values
+   template <typename it_t> struct AData<1,it_t> // 1 = Values
    {
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vcomplex_t vcomplex_t;
 #ifdef MFEM_TEMPLATE_FIELD_EVAL_DATA_HAS_DOFS
-      typedef TTensor3<dofs,vdim,NE,complex_t,true> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t,true> val_dofs_t;
       val_dofs_t val_dofs;
 #else
-      typedef TTensor3<dofs,vdim,NE,complex_t> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t> val_dofs_t;
 #endif
-      TTensor3<qpts,vdim,NE,complex_t>      val_qpts;
+      TTensor3<qpts,vdim,ne,vcomplex_t>      val_qpts;
    };
 
-   template <int NE> struct AData<2,NE> // 2 = Gradients
+   template <typename it_t> struct AData<2,it_t> // 2 = Gradients
    {
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vcomplex_t vcomplex_t;
 #ifdef MFEM_TEMPLATE_FIELD_EVAL_DATA_HAS_DOFS
-      typedef TTensor3<dofs,vdim,NE,complex_t,true> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t,true> val_dofs_t;
       val_dofs_t val_dofs;
 #else
-      typedef TTensor3<dofs,vdim,NE,complex_t> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t> val_dofs_t;
 #endif
-      TTensor4<qpts,dim,vdim,NE,complex_t>      grad_qpts;
+      TTensor4<qpts,dim,vdim,ne,vcomplex_t>      grad_qpts;
    };
 
-   template <int NE> struct AData<3,NE> // 3 = Values+Gradients
+   template <typename it_t> struct AData<3,it_t> // 3 = Values+Gradients
    {
+      static const int ne = it_t::batch_size;
+      typedef typename it_t::vcomplex_t vcomplex_t;
 #ifdef MFEM_TEMPLATE_FIELD_EVAL_DATA_HAS_DOFS
-      typedef TTensor3<dofs,vdim,NE,complex_t,true> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t,true> val_dofs_t;
       val_dofs_t val_dofs;
 #else
-      typedef TTensor3<dofs,vdim,NE,complex_t> val_dofs_t;
+      typedef TTensor3<dofs,vdim,ne,vcomplex_t> val_dofs_t;
 #endif
-      TTensor3<qpts,    vdim,NE,complex_t,true>  val_qpts;
-      TTensor4<qpts,dim,vdim,NE,complex_t>      grad_qpts;
+      TTensor3<qpts,    vdim,ne,vcomplex_t,true>  val_qpts;
+      TTensor4<qpts,dim,vdim,ne,vcomplex_t>      grad_qpts;
    };
 
-   // This struct is similar to struct AData, adding separate static data
-   // members for the input (InData) and output (OutData) data types.
-   template <int IData, int OData, int NE>
-   struct BData : public AData<IData|OData,NE>
+   /** @brief This struct is similar to struct AData, adding separate static data
+       members for the input (InData) and output (OutData) data types. */
+   template <int IData, int OData, typename it_t>
+   struct BData : public AData<IData|OData,it_t>
    {
       typedef T_type eval_type;
-      static const int ne = NE;
       static const int InData = IData;
       static const int OutData = OData;
    };
 
-   // This struct implements the input (Eval, EvalSerialized) and output
-   // (Assemble, AssembleSerialized) operations for the given Ops.
-   // Ops is "bitwise or" of constants from the enum InOutData.
+   /** @brief This struct implements the input (Eval, EvalSerialized) and output
+       (Assemble, AssembleSerialized) operations for the given Ops.
+       Ops is "bitwise or" of constants from the enum InOutData. */
    template <int Ops, bool dummy> struct Action;
 
    template <bool dummy> struct Action<0,dummy> // 0 = None
@@ -1238,7 +1262,9 @@ public:
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       template <typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(T_type &T, const complex_t *loc_dofs, AData_t &D)
+      void EvalSerialized(T_type &T,
+                          const typename AData_t::vcomplex_t *loc_dofs,
+                          AData_t &D)
       {
          T.shapeEval.Calc(AData_t::val_dofs_t::layout.merge_23(), loc_dofs,
                           D.val_qpts.layout.merge_23(), D.val_qpts);
@@ -1246,7 +1272,8 @@ public:
 
       template <bool Add, typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void AssembleSerialized(T_type &T, const AData_t &D, complex_t *loc_dofs)
+      void AssembleSerialized(T_type &T, const AData_t &D,
+                              typename AData_t::vcomplex_t *loc_dofs)
       {
          T.shapeEval.template CalcT<Add>(
             D.val_qpts.layout.merge_23(), D.val_qpts,
@@ -1291,7 +1318,9 @@ public:
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       template <typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(T_type &T, const complex_t *loc_dofs, AData_t &D)
+      void EvalSerialized(T_type &T,
+                          const typename AData_t::vcomplex_t *loc_dofs,
+                          AData_t &D)
       {
          T.shapeEval.CalcGrad(AData_t::val_dofs_t::layout.merge_23(), loc_dofs,
                               D.grad_qpts.layout.merge_34(), D.grad_qpts);
@@ -1299,7 +1328,8 @@ public:
 
       template <bool Add, typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void AssembleSerialized(T_type &T, const AData_t &D, complex_t *loc_dofs)
+      void AssembleSerialized(T_type &T, const AData_t &D,
+                              typename AData_t::vcomplex_t *loc_dofs)
       {
          T.shapeEval.template CalcGradT<Add>(
             D.grad_qpts.layout.merge_34(), D.grad_qpts,
@@ -1349,7 +1379,9 @@ public:
 #ifdef MFEM_TEMPLATE_ENABLE_SERIALIZE
       template <typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void EvalSerialized(T_type &T, const complex_t *loc_dofs, AData_t &D)
+      void EvalSerialized(T_type &T,
+                          const typename AData_t::vcomplex_t *loc_dofs,
+                          AData_t &D)
       {
          T.shapeEval.Calc(AData_t::val_dofs_t::layout.merge_23(), loc_dofs,
                           D.val_qpts.layout.merge_23(), D.val_qpts);
@@ -1359,7 +1391,8 @@ public:
 
       template <bool Add, typename AData_t>
       static inline MFEM_ALWAYS_INLINE
-      void AssembleSerialized(T_type &T, const AData_t &D, complex_t *loc_dofs)
+      void AssembleSerialized(T_type &T, const AData_t &D,
+                              typename AData_t::vcomplex_t *loc_dofs)
       {
          T.shapeEval.template CalcT<Add>(
             D.val_qpts.layout.merge_23(), D.val_qpts,
@@ -1371,14 +1404,15 @@ public:
 #endif
    };
 
-   // This struct implements element matrix computation for some combinations
-   // of input (InOps) and output (OutOps) operations.
-   template <int InOps, int OutOps, int NE> struct TElementMatrix;
+   /** @brief This struct implements element matrix computation for some combinations
+       of input (InOps) and output (OutOps) operations. */
+   template <int InOps, int OutOps, typename it_t> struct TElementMatrix;
 
-   template <int NE> struct TElementMatrix<1,1,NE> // 1,1 = Values,Values
+   // Case 1,1 = Values,Values
+   template <typename it_t> struct TElementMatrix<1,1,it_t>
    {
       // qpt_layout_t is (nip), M_layout_t is (dof x dof)
-      // NE = 1 is assumed
+      // it_t::batch_size = 1 is assumed
       template <typename qpt_layout_t, typename qpt_data_t,
                 typename M_layout_t, typename M_data_t>
       static inline MFEM_ALWAYS_INLINE
@@ -1390,10 +1424,18 @@ public:
       }
    };
 
-   template <int NE> struct TElementMatrix<2,2,NE> // 2,2 = Gradients,Gradients
+   // Case 2,2 = Gradients,Gradients
+   template <typename it_t> struct TElementMatrix<2,2,it_t>
    {
-      // qpt_layout_t is (nip x dim x dim), M_layout_t is (dof x dof)
-      // NE = 1 is assumed
+      /** @brief Assemble element mass matrix
+          @param a the layout for the quadrature point data
+          @param A given quadrature point data for element (incl. coefficient,
+                 geometry)
+          @param m the layout for the resulting element mass matrix
+          @param M the resulting element mass matrix
+          @param ev the shape evaluator
+          qpt_layout_t is (nip), M_layout_t is (dof x dof)
+          NE = 1 is assumed */
       template <typename qpt_layout_t, typename qpt_data_t,
                 typename M_layout_t, typename M_data_t>
       static inline MFEM_ALWAYS_INLINE
@@ -1405,15 +1447,15 @@ public:
       }
    };
 
-   template <typename kernel_t, int NE> struct Spec
+   template <typename kernel_t, typename impl_traits_t> struct Spec
    {
       static const int InData =
          Values*kernel_t::in_values + Gradients*kernel_t::in_gradients;
       static const int OutData =
          Values*kernel_t::out_values + Gradients*kernel_t::out_gradients;
 
-      typedef BData<InData,OutData,NE>          DataType;
-      typedef TElementMatrix<InData,OutData,NE> ElementMatrix;
+      typedef BData<InData,OutData,impl_traits_t>          DataType;
+      typedef TElementMatrix<InData,OutData,impl_traits_t> ElementMatrix;
    };
 };
 

fem/tfe.hpp

@@ -20,6 +20,18 @@ namespace mfem
 
 // Templated finite element classes, cf. fe.?pp
 
+/** @brief Store mass-like matrix B for each integration point on the reference
+    element.
+    For tensor product evaluation, this is only called on the 1D reference
+    element, and higher dimensions are put together from that.
+    The element mass matrix can be written \f$ M_E = B^T D_E B \f$ where the B
+    built here is the B, and is unchanging across the mesh. The diagonal matrix
+    \f$ D_E \f$ then contains all the element-specific geometry and physics data.
+    @param fe the element we are calculating on
+    @param ir the integration rule to calculate the shape matrix on
+    @param B must be (nip x dof) with column major storage
+    @param dof_map the inverse of dof_map is applied to reorder local dofs.
+*/
 template <typename real_t>
 void CalcShapeMatrix(const FiniteElement &fe, const IntegrationRule &ir,
                      real_t *B, const Array<int> *dof_map = NULL)
@@ -41,6 +53,23 @@ void CalcShapeMatrix(const FiniteElement &fe, const IntegrationRule &ir,
    }
 }
 
+/** @brief store gradient matrix G for each integration point on the reference
+    element.
+    For tensor product evaluation, this is only called on the 1D reference
+    element, and higher dimensions are put together from that.
+    The element stiffness matrix can be written
+    \f[
+       S_E = \sum_{k=1}^{nq} G_{k,i}^T (D_E^G)_{k,k} G_{k,j}
+    \f]
+    where \f$ nq \f$ is the number of quadrature points, \f$ D_E^G \f$ contains
+    all the information about the element geometry and coefficients (Jacobians
+    etc.), and \f$ G \f$ is the matrix built in this routine, which is the same
+    for all elements in a mesh.
+    @param fe the element we are calculating on
+    @param ir the integration rule to calculate the gradients on
+    @param[out] G must be (nip x dim x dof) with column major storage
+    @param[in] dof_map the inverse of dof_map is applied to reorder local dofs.
+*/
 template <typename real_t>
 void CalcGradTensor(const FiniteElement &fe, const IntegrationRule &ir,
                     real_t *G, const Array<int> *dof_map = NULL)

fem/tfespace.hpp

@@ -114,18 +114,23 @@ class TFiniteElementSpace_simple
 public:
    typedef FE        FE_type;
    typedef IndexType index_type;
+   static const int dofs = FE::dofs;
 
 protected:
    index_type ind;
+   int num_elems, remain_elems;
 
 public:
    TFiniteElementSpace_simple(const FE &fe, const FiniteElementSpace &fes)
-      : ind(fe, fes) { }
+      : ind(fe, fes), num_elems(fes.GetNE()), remain_elems(num_elems) { }
 
    // default copy constructor
 
-   void SetElement(int el) { ind.SetElement(el); }
+   int GetNE() const { return num_elems; }
 
+   void SetElement(int el) { ind.SetElement(el); remain_elems = num_elems-el; }
+
+#if 0
    // Multi-element Extract:
    // Extract dofs for multiple elements starting with the current element.
    // The number of elements to extract is given by the second dimension of
@@ -137,6 +142,7 @@ public:
                 const dof_layout_t    &dof_layout,
                 dof_data_t            &dof_data) const
    {
+      const int SS = sizeof(dof_data[0])/sizeof(dof_data[0][0]);
       const int NE = dof_layout_t::dim_2;
       MFEM_STATIC_ASSERT(FE::dofs == dof_layout_t::dim_1,
                          "invalid number of dofs");
@@ -144,8 +150,11 @@ public:
       {
          for (int i = 0; i < FE::dofs; i++)
          {
-            Assign<Op>(dof_data[dof_layout.ind(i,j)],
-                       glob_dof_data[ind.map(i,j)]);
+            for (int s = 0; s < SS; s++)
+            {
+               Assign<Op>(dof_data[dof_layout.ind(i,j)][s],
+                          glob_dof_data[ind.map(i,s+SS*j)]);
+            }
          }
       }
    }
@@ -169,6 +178,7 @@ public:
                  const dof_data_t   &dof_data,
                  glob_dof_data_t    &glob_dof_data) const
    {
+      const int SS = sizeof(dof_data[0])/sizeof(dof_data[0][0]);
       const int NE = dof_layout_t::dim_2;
       MFEM_STATIC_ASSERT(FE::dofs == dof_layout_t::dim_1,
                          "invalid number of dofs");
@@ -176,8 +186,11 @@ public:
       {
          for (int i = 0; i < FE::dofs; i++)
          {
-            Assign<Op>(glob_dof_data[ind.map(i,j)],
-                       dof_data[dof_layout.ind(i,j)]);
+            for (int s = 0; s < SS; s++)
+            {
+               Assign<Op>(glob_dof_data[ind.map(i,s+SS*j)],
+                          dof_data[dof_layout.ind(i,j)][s]);
+            }
          }
       }
    }
@@ -191,6 +204,7 @@ public:
    {
       Assemble<AssignOp::Add>(dof_layout, dof_data, glob_dof_data);
    }
+#endif
 
    // Multi-element VectorExtract: vdof_layout is (DOFS x NumComp x NumElems).
    template <AssignOp::Type Op,
@@ -202,21 +216,39 @@ public:
                       const vdof_layout_t    &vdof_layout,
                       vdof_data_t            &vdof_data) const
    {
+      const int SS = sizeof(vdof_data[0])/sizeof(vdof_data[0][0]);
       const int NC = vdof_layout_t::dim_2;
       const int NE = vdof_layout_t::dim_3;
       MFEM_STATIC_ASSERT(FE::dofs == vdof_layout_t::dim_1,
                          "invalid number of dofs");
       MFEM_ASSERT(NC == vl.NumComponents(), "invalid number of components");
+      const int TE = std::min(SS*NE, remain_elems);
+      // const int TE = SS*NE;
       for (int k = 0; k < NC; k++)
       {
+#if 0
          for (int j = 0; j < NE; j++)
          {
             for (int i = 0; i < FE::dofs; i++)
             {
-               Assign<Op>(vdof_data[vdof_layout.ind(i,k,j)],
-                          glob_vdof_data[vl.ind(ind.map(i,j), k)]);
+               for (int s = 0; s < SS; s++)
+               {
+                  Assign<Op>(vdof_data[vdof_layout.ind(i,k,j)][s],
+                             glob_vdof_data[vl.ind(ind.map(i,s+SS*j), k)]);
+               }
             }
          }
+#else
+         for (int js = 0; js < TE; js++)
+         {
+            for (int i = 0; i < FE::dofs; i++)
+            {
+               const int s = js % SS, j = js / SS;
+               Assign<Op>(vdof_data[vdof_layout.ind(i,k,j)][s],
+                          glob_vdof_data[vl.ind(ind.map(i,js), k)]);
+            }
+         }
+#endif
       }
    }
 
@@ -241,21 +273,39 @@ public:
                        const vec_layout_t  &vl,
                        glob_vdof_data_t    &glob_vdof_data) const
    {
+      const int SS = sizeof(vdof_data[0])/sizeof(vdof_data[0][0]);
       const int NC = vdof_layout_t::dim_2;
       const int NE = vdof_layout_t::dim_3;
       MFEM_STATIC_ASSERT(FE::dofs == vdof_layout_t::dim_1,
                          "invalid number of dofs");
       MFEM_ASSERT(NC == vl.NumComponents(), "invalid number of components");
+      const int TE = std::min(SS*NE, remain_elems);
+      // const int TE = SS*NE;
       for (int k = 0; k < NC; k++)
       {
+#if 0
          for (int j = 0; j < NE; j++)
          {
             for (int i = 0; i < FE::dofs; i++)
             {
-               Assign<Op>(glob_vdof_data[vl.ind(ind.map(i,j), k)],
-                          vdof_data[vdof_layout.ind(i,k,j)]);
+               for (int s = 0; s < SS; s++)
+               {
+                  Assign<Op>(glob_vdof_data[vl.ind(ind.map(i,s+SS*j), k)],
+                             vdof_data[vdof_layout.ind(i,k,j)][s]);
+               }
             }
          }
+#else
+         for (int js = 0; js < TE; js++)
+         {
+            for (int i = 0; i < FE::dofs; i++)
+            {
+               const int s = js % SS, j = js / SS;
+               Assign<Op>(glob_vdof_data[vl.ind(ind.map(i,js), k)],
+                          vdof_data[vdof_layout.ind(i,k,j)][s]);
+            }
+         }
+#endif
       }
    }
 
@@ -282,21 +332,24 @@ public:
                           const vdof_layout_t    &vdof_layout,
                           vdof_data_t            &vdof_data) const
    {
+      const int SS = sizeof(vdof_data[0])/sizeof(vdof_data[0][0]);
       const int NC = vdof_layout_t::dim_2;
       const int NE = vdof_layout_t::dim_3;
+      const int TE = std::min(SS*NE, remain_elems);
       MFEM_STATIC_ASSERT(FE::dofs == vdof_layout_t::dim_1,
                          "invalid number of dofs");
       MFEM_ASSERT(first_comp + NC <= vl.NumComponents(),
                   "invalid number of components");
       for (int k = 0; k < NC; k++)
       {
-         for (int j = 0; j < NE; j++)
+         for (int js = 0; js < TE; js++)
          {
             for (int i = 0; i < FE::dofs; i++)
             {
+               const int s = js % SS, j = js / SS;
                Assign<AssignOp::Set>(
-                  vdof_data[vdof_layout.ind(i,k,j)],
-                  glob_vdof_data[vl.ind(ind.map(i,j), first_comp+k)]);
+                  vdof_data[vdof_layout.ind(i,k,j)][s],
+                  glob_vdof_data[vl.ind(ind.map(i,js), first_comp+k)]);
             }
          }
       }
@@ -314,55 +367,69 @@ public:
                            const vec_layout_t  &vl,
                            glob_vdof_data_t    &glob_vdof_data) const
    {
+      const int SS = sizeof(vdof_data[0])/sizeof(vdof_data[0][0]);
       const int NC = vdof_layout_t::dim_2;
       const int NE = vdof_layout_t::dim_3;
+      const int TE = std::min(SS*NE, remain_elems);
       MFEM_STATIC_ASSERT(FE::dofs == vdof_layout_t::dim_1,
                          "invalid number of dofs");
       MFEM_ASSERT(first_comp + NC <= vl.NumComponents(),
                   "invalid number of components");
       for (int k = 0; k < NC; k++)
       {
-         for (int j = 0; j < NE; j++)
+         for (int js = 0; js < TE; js++)
          {
             for (int i = 0; i < FE::dofs; i++)
             {
+               const int s = js % SS, j = js / SS;
                Assign<AssignOp::Add>(
-                  glob_vdof_data[vl.ind(ind.map(i,j), first_comp+k)],
-                  vdof_data[vdof_layout.ind(i,k,j)]);
+                  glob_vdof_data[vl.ind(ind.map(i,js), first_comp+k)],
+                  vdof_data[vdof_layout.ind(i,k,j)][s]);
             }
          }
       }
    }
 
-   void Assemble(const TMatrix<FE::dofs,FE::dofs,double> &m,
+   template <typename vcomplex_t>
+   void Assemble(const TMatrix<FE::dofs,FE::dofs,vcomplex_t> &m,
                  SparseMatrix &M) const
    {
+      const int SS = sizeof(m[0])/sizeof(m[0][0]);
+      const int TE = std::min(SS, remain_elems);
       MFEM_FLOPS_ADD(FE::dofs*FE::dofs);
-      for (int i = 0; i < FE::dofs; i++)
+      for (int s = 0; s < TE; s++)
       {
-         M.SetColPtr(ind.map(i,0));
-         for (int j = 0; j < FE::dofs; j++)
+         for (int i = 0; i < FE::dofs; i++)
          {
-            M._Add_(ind.map(j,0), m(i,j));
+            M.SetColPtr(ind.map(i,s));
+            for (int j = 0; j < FE::dofs; j++)
+            {
+               M._Add_(ind.map(j,s), m(i,j)[s]);
+            }
+            M.ClearColPtr();
          }
-         M.ClearColPtr();
       }
    }
 
-   template <typename vec_layout_t>
+   template <typename vec_layout_t, typename vcomplex_t>
    void AssembleBlock(int block_i, int block_j, const vec_layout_t &vl,
-                      const TMatrix<FE::dofs,FE::dofs,double> &m,
+                      const TMatrix<FE::dofs,FE::dofs,vcomplex_t> &m,
                       SparseMatrix &M) const
    {
+      const int SS = sizeof(m[0])/sizeof(m[0][0]);
+      const int TE = std::min(SS, remain_elems);
       MFEM_FLOPS_ADD(FE::dofs*FE::dofs);
-      for (int i = 0; i < FE::dofs; i++)
+      for (int s = 0; s < TE; s++)
       {
-         M.SetColPtr(vl.ind(ind.map(i,0), block_i));
-         for (int j = 0; j < FE::dofs; j++)
+         for (int i = 0; i < FE::dofs; i++)
          {
-            M._Add_(vl.ind(ind.map(j,0), block_j), m(i,j));
+            M.SetColPtr(vl.ind(ind.map(i,s), block_i));
+            for (int j = 0; j < FE::dofs; j++)
+            {
+               M._Add_(vl.ind(ind.map(j,s), block_j), m(i,j)[s]);
+            }
+            M.ClearColPtr();
          }
-         M.ClearColPtr();
       }
    }
 };