Suppress Doxygen warnings

Introduce some workarounds for MSVC:

- Need to expand variadic macros explicitly
- Adjacent parameter packs in function templates not supported; use nested
  structs instead
- Can't use default parameters in template definition if not present in
  declaration

Some improvements to the kernel dispatch:

- Run is now a static member function (don't need to call Get)
- DIM is not treated differently from the other parameters

.gitignore

@@ -15,6 +15,9 @@
 CMakeCache.txt
 CMakeFiles/
 
+# Clangd server cache
+*.cache*
+
 # Backup files
 *~
 
@@ -272,16 +275,27 @@ miniapps/navier/*_output
 
 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
+miniapps/nurbs/nurbs_ex3
+miniapps/nurbs/nurbs_ex5
 miniapps/nurbs/nurbs_ex11p
+miniapps/nurbs/nurbs_ex24
+miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
+miniapps/nurbs/sol_?.gf
 miniapps/nurbs/sol.*
 miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
+miniapps/nurbs/Example3*
+miniapps/nurbs/Example5*
+miniapps/nurbs/Solenoidal*
+miniapps/nurbs/ParaView
 miniapps/nurbs/sin-fit.mesh
+miniapps/nurbs/ex5.mesh
+miniapps/nurbs/exsol.mesh
 miniapps/nurbs/CurveInt
 miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh

CHANGELOG

@@ -11,6 +11,23 @@
 Version 4.7.1 (development)
 ===========================
 
+- Refactored the `ARKStepSolver` class (ARKODE interface) to use
+  `TimeDependentOperator::Mult` only when the associated ODE operator is
+  expressed in explicit form (i.e., `TimeDependentOperator::isExplicit()`),
+  otherwise `TimeDependentOperator::ExplicitMult` is used. A check has been
+  added to `ARKStepSolver` to verify that the associated ODE operator is not in
+  explicit form when a mass matrix solver is enabled via a call to either the
+  `UseMFEMMassLinearSolver` or `UseSundialsMassLinearSolver` methods. This is
+  because enabling a mass matrix solver assumes that F(u,k,t) = M k in the
+  associated ODE operator.
+
+- Added support for custom interpolation procedure in FindPointsGSLIB.
+
+- Added NURBS-based H(div) and H(curl) elements in 2D and 3D. Only on single
+  patch meshes. Only implemented for serial computations.
+
+- Added miniapps to demonstrate the H(div) and H(curl) NURBS elements.
+
 - Added an MFEM example for the eikonal equation. This new solver is based on
   the proximal Galerkin method introduced by Keith and Surowiec.
 
@@ -40,6 +57,9 @@ Meshing improvements
 
 - Added support for internal boundary elements in nonconforming meshes.
 
+- Added ExodusII output capability. The writer can handle first-order (Pyramid5,
+  Wedge6, Hex8, Tet4) and second-order FE types (Pyramid14, Wedge18, Hex27, Tet10).
+
 - The ReadCubit Genesis mesh importer has been rewritten to improve readability.
 
 Discretization improvements

config/sample-runs.sh

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

data/pipe-nurbs-2d.mesh

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

doc/CodeDocumentation.conf.in

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

doc/CodeDocumentation.dox

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

examples/hiop/ex9p.cpp

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

examples/sundials/CMakeLists.txt

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

examples/sundials/ex10.cpp

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

examples/sundials/ex10p.cpp

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

examples/sundials/ex16.cpp

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

examples/sundials/ex16p.cpp

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

examples/sundials/ex9.cpp

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

examples/sundials/ex9p.cpp

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

examples/sundials/makefile

@@ -100,6 +100,12 @@ ex10-test-seq: ex10
 	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX10_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX10P_ARGS))
+# Example 16: test ARKODE with implicit time stepping using mass form
+EX16_COMMON_ARGS := -s 15
+ex16-test-seq: ex16
+	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX16_COMMON_ARGS))
+ex16p-test-par: ex16p
+	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX16_COMMON_ARGS))
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

fem/CMakeLists.txt

@@ -112,8 +112,6 @@ set(SRCS
   qinterp/eval_by_vdim.cpp
   qinterp/grad_by_nodes.cpp
   qinterp/grad_by_vdim.cpp
-  qinterp/grad_phys_by_nodes.cpp
-  qinterp/grad_phys_by_vdim.cpp
   qspace.cpp
   quadinterpolator.cpp
   quadinterpolator_face.cpp
@@ -192,6 +190,9 @@ set(HDRS
   hybridization.hpp
   intrules.hpp
   intrules_cut.hpp
+  kernel_dispatch.hpp
+  kernel_reporter.hpp
+  kernels.hpp
   ceed/interface/basis.hpp
   ceed/interface/integrator.hpp
   ceed/interface/interface.hpp
@@ -223,7 +224,6 @@ set(HDRS
   nonlinearform_ext.hpp
   nonlininteg.hpp
   qfunction.hpp
-  qinterp/dispatch.hpp
   qinterp/eval.hpp
   qinterp/grad.hpp
   qspace.hpp

fem/bilininteg.hpp

@@ -19,6 +19,8 @@
 #include "qfunction.hpp"
 #include <memory>
 
+#include "kernel_dispatch.hpp"
+
 namespace mfem
 {
 
@@ -2127,6 +2129,22 @@ public:
     can be a scalar or a matrix coefficient. */
 class DiffusionIntegrator: public BilinearFormIntegrator
 {
+public:
+
+   using ApplyKernelType = void(*)(const int, const bool, const Array<real_t>&,
+                                   const Array<real_t>&, const Array<real_t>&,
+                                   const Array<real_t>&,
+                                   const Vector&, const Vector&,
+                                   Vector&, const int, const int);
+
+   using DiagonalKernelType = void(*)(const int, const bool, const Array<real_t>&,
+                                      const Array<real_t>&, const Vector&, Vector&,
+                                      const int, const int);
+
+   MFEM_REGISTER_KERNELS(ApplyPAKernels, ApplyKernelType, (int, int, int));
+   MFEM_REGISTER_KERNELS(DiagonalPAKernels, DiagonalKernelType, (int, int, int));
+   static struct Kernels { Kernels(); } kernels;
+
 protected:
    Coefficient *Q;
    VectorCoefficient *VQ;
@@ -2287,6 +2305,13 @@ public:
    bool SupportsCeed() const { return DeviceCanUseCeed(); }
 
    Coefficient *GetCoefficient() const { return Q; }
+
+   template <int DIM, int D1D, int Q1D>
+   static void AddSpecialization()
+   {
+      ApplyPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+      DiagonalPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+   }
 };
 
 /** Class for local mass matrix assembling $a(u,v) := (Q u, v)$ */
@@ -2306,6 +2331,20 @@ protected:
    const FaceGeometricFactors *face_geom; ///< Not owned
    int dim, ne, nq, dofs1D, quad1D;
 
+public:
+
+   using ApplyKernelType = void(*)(const int, const Array<real_t>&,
+                                   const Array<real_t>&, const Vector&,
+                                   const Vector&, Vector&, const int, const int);
+
+   using DiagonalKernelType =  void(*)(const int, const Array<real_t>&,
+                                       const Vector&, Vector&, const int,
+                                       const int);
+
+   MFEM_REGISTER_KERNELS(ApplyPAKernels, ApplyKernelType, (int, int, int));
+   MFEM_REGISTER_KERNELS(DiagonalPAKernels, DiagonalKernelType, (int, int, int));
+   static struct Kernels { Kernels(); } kernels;
+
 public:
    MassIntegrator(const IntegrationRule *ir = NULL)
       : BilinearFormIntegrator(ir), Q(NULL), maps(NULL), geom(NULL) { }
@@ -2351,6 +2390,13 @@ public:
    bool SupportsCeed() const { return DeviceCanUseCeed(); }
 
    const Coefficient *GetCoefficient() const { return Q; }
+
+   template <int DIM, int D1D, int Q1D>
+   static void AddSpecialization()
+   {
+      ApplyPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+      DiagonalPAKernels::Specialization<DIM,D1D,Q1D>::Add();
+   }
 };
 
 /** Mass integrator $(u, v)$ restricted to the boundary of a domain */

fem/eltrans.hpp

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

fem/fe/fe_base.hpp

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

fem/fe/fe_nurbs.cpp

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

fem/fe/fe_nurbs.hpp

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

fem/fe_coll.cpp

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

fem/fe_coll.hpp

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

fem/fespace.cpp

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

fem/fespace.hpp

@@ -268,6 +268,10 @@ protected:
    Array<int> dof_elem_array, dof_ldof_array;
 
    NURBSExtension *NURBSext;
+   /** array of NURBS extension for H(div) and H(curl) vector elements.
+       For each direction an extension is created from the base NURBSext,
+       with an increase in order in the appropriate direction. */
+   Array<NURBSExtension*> VNURBSext;
    int own_ext;
    mutable Array<int> face_to_be; // NURBS FE space only
 
@@ -469,6 +473,11 @@ protected:
                                        const Table *coarse_elem_fos,
                                        const DenseTensor localP[]) const;
 
+   /* This method returns the Refinement matrix (i.e., the embedding)
+      from a coarse variable-order fes to a fine fes (after a geometric refinement) */
+   SparseMatrix *VariableOrderRefinementMatrix(const int coarse_ndofs,
+                                               const Table &coarse_elem_dof) const;
+
    void GetLocalRefinementMatrices(Geometry::Type geom,
                                    DenseTensor &localP) const;
    void GetLocalDerefinementMatrices(Geometry::Type geom,
@@ -517,6 +526,8 @@ protected:
                                                const Array<int> *perm);
 
 public:
+
+
    /** @brief Default constructor: the object is invalid until initialized using
        the method Load(). */
    FiniteElementSpace();

fem/gridfunc.cpp

@@ -12,6 +12,8 @@
 // Implementation of GridFunction
 
 #include "gridfunc.hpp"
+#include "linearform.hpp"
+#include "bilinearform.hpp"
 #include "quadinterpolator.hpp"
 #include "../mesh/nurbs.hpp"
 #include "../general/text.hpp"
@@ -2372,19 +2374,48 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff)
 
    if (delta_c == NULL)
    {
-      Array<int> vdofs;
-      Vector vals;
-
-      for (int i = 0; i < fes->GetNE(); i++)
+      if (fes->GetNURBSext() == NULL)
       {
-         doftrans = fes->GetElementVDofs(i, vdofs);
-         vals.SetSize(vdofs.Size());
-         fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
-         if (doftrans)
+         Array<int> vdofs;
+         Vector vals;
+
+         for (int i = 0; i < fes->GetNE(); i++)
          {
-            doftrans->TransformPrimal(vals);
+            doftrans = fes->GetElementVDofs(i, vdofs);
+            vals.SetSize(vdofs.Size());
+            fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+            if (doftrans)
+            {
+               doftrans->TransformPrimal(vals);
+            }
+            SetSubVector(vdofs, vals);
          }
-         SetSubVector(vdofs, vals);
+      }
+      else
+      {
+         // Define and assemble linear form
+         LinearForm b(fes);
+         b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+         b.Assemble();
+
+         // Define and assemble bilinear form
+         BilinearForm a(fes);
+         a.AddDomainIntegrator(new MassIntegrator());
+         a.Assemble();
+
+         // Set solver and preconditioner
+         SparseMatrix A(a.SpMat());
+         GSSmoother  prec(A);
+         CGSolver cg;
+         cg.SetOperator(A);
+         cg.SetPreconditioner(prec);
+         cg.SetRelTol(1e-12);
+         cg.SetMaxIter(1000);
+         cg.SetPrintLevel(0);
+
+         // Solve and get solution
+         *this = 0.0;
+         cg.Mult(b,*this);
       }
    }
    else
@@ -2425,22 +2456,54 @@ void GridFunction::ProjectCoefficient(
 
 void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
 {
-   int i;
-   Array<int> vdofs;
-   Vector vals;
-
-   DofTransformation * doftrans = NULL;
-
-   for (i = 0; i < fes->GetNE(); i++)
+   if (fes->GetNURBSext() == NULL)
    {
-      doftrans = fes->GetElementVDofs(i, vdofs);
-      vals.SetSize(vdofs.Size());
-      fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-      if (doftrans)
+
+      int i;
+      Array<int> vdofs;
+      Vector vals;
+
+      DofTransformation * doftrans = NULL;
+
+      for (i = 0; i < fes->GetNE(); i++)
       {
-         doftrans->TransformPrimal(vals);
+         doftrans = fes->GetElementVDofs(i, vdofs);
+         vals.SetSize(vdofs.Size());
+         fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+         if (doftrans)
+         {
+            doftrans->TransformPrimal(vals);
+         }
+         SetSubVector(vdofs, vals);
       }
-      SetSubVector(vdofs, vals);
+
+   }
+
+   else
+   {
+      // Define and assemble linear form
+      LinearForm b(fes);
+      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
+      b.Assemble();
+
+      // Define and assemble bilinear form
+      BilinearForm a(fes);
+      a.AddDomainIntegrator(new VectorFEMassIntegrator());
+      a.Assemble();
+
+      // Set solver and preconditioner
+      SparseMatrix A(a.SpMat());
+      GSSmoother  prec(A);
+      CGSolver cg;
+      cg.SetOperator(A);
+      cg.SetPreconditioner(prec);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(1000);
+      cg.SetPrintLevel(0);
+
+      // Solve and get solution
+      *this = 0.0;
+      cg.Mult(b,*this);
    }
 }
 

fem/gridfunc.hpp

@@ -387,7 +387,8 @@ public:
    /** @brief Project @a coeff Coefficient to @a this GridFunction. The
        projection computation depends on the choice of the FiniteElementSpace
        #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection). */
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
    virtual void ProjectCoefficient(Coefficient &coeff);
 
    /** @brief Project @a coeff Coefficient to @a this GridFunction, using one
@@ -398,7 +399,8 @@ public:
    /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction. The
        projection computation depends on the choice of the FiniteElementSpace
        #fes. Note that this is usually interpolation at the degrees of freedom
-       in each element (not L2 projection).*/
+       in each element (not L2 projection). For NURBS spaces these degrees of
+       freedom are not available and L2 projection is resorted to as fallback. */
    void ProjectCoefficient(VectorCoefficient &vcoeff);
 
    /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction, using

fem/gslib.cpp

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

fem/gslib.hpp

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

fem/integ/bilininteg_diffusion_kernels.cpp

@@ -14,6 +14,33 @@
 namespace mfem
 {
 
+// PA Diffusion Integrator
+
+DiffusionIntegrator::Kernels DiffusionIntegrator::kernels;
+DiffusionIntegrator::Kernels::Kernels()
+{
+   // 2D
+   DiffusionIntegrator::AddSpecialization<2,2,2>();
+   DiffusionIntegrator::AddSpecialization<2,3,3>();
+   DiffusionIntegrator::AddSpecialization<2,4,4>();
+   DiffusionIntegrator::AddSpecialization<2,5,5>();
+   DiffusionIntegrator::AddSpecialization<2,6,6>();
+   DiffusionIntegrator::AddSpecialization<2,7,7>();
+   DiffusionIntegrator::AddSpecialization<2,8,8>();
+   DiffusionIntegrator::AddSpecialization<2,9,9>();
+   // 3D
+   DiffusionIntegrator::AddSpecialization<3,2,2>();
+   DiffusionIntegrator::AddSpecialization<3,2,3>();
+   DiffusionIntegrator::AddSpecialization<3,3,4>();
+   DiffusionIntegrator::AddSpecialization<3,4,5>();
+   DiffusionIntegrator::AddSpecialization<3,4,6>();
+   DiffusionIntegrator::AddSpecialization<3,5,6>();
+   DiffusionIntegrator::AddSpecialization<3,5,8>();
+   DiffusionIntegrator::AddSpecialization<3,6,7>();
+   DiffusionIntegrator::AddSpecialization<3,7,8>();
+   DiffusionIntegrator::AddSpecialization<3,8,9>();
+}
+
 namespace internal
 {
 
@@ -363,118 +390,6 @@ void OccaPADiffusionSetup3D(const int D1D,
 }
 #endif // MFEM_USE_OCCA
 
-void PADiffusionAssembleDiagonal(const int dim,
-                                 const int D1D,
-                                 const int Q1D,
-                                 const int NE,
-                                 const bool symm,
-                                 const Array<real_t> &B,
-                                 const Array<real_t> &G,
-                                 const Vector &D,
-                                 Vector &Y)
-{
-   if (dim == 2)
-   {
-      switch ((D1D << 4 ) | Q1D)
-      {
-         case 0x22: return SmemPADiffusionDiagonal2D<2,2,8>(NE,symm,B,G,D,Y);
-         case 0x33: return SmemPADiffusionDiagonal2D<3,3,8>(NE,symm,B,G,D,Y);
-         case 0x44: return SmemPADiffusionDiagonal2D<4,4,4>(NE,symm,B,G,D,Y);
-         case 0x55: return SmemPADiffusionDiagonal2D<5,5,4>(NE,symm,B,G,D,Y);
-         case 0x66: return SmemPADiffusionDiagonal2D<6,6,2>(NE,symm,B,G,D,Y);
-         case 0x77: return SmemPADiffusionDiagonal2D<7,7,2>(NE,symm,B,G,D,Y);
-         case 0x88: return SmemPADiffusionDiagonal2D<8,8,1>(NE,symm,B,G,D,Y);
-         case 0x99: return SmemPADiffusionDiagonal2D<9,9,1>(NE,symm,B,G,D,Y);
-         default: return PADiffusionDiagonal2D(NE,symm,B,G,D,Y,D1D,Q1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((D1D << 4 ) | Q1D)
-      {
-         case 0x22: return SmemPADiffusionDiagonal3D<2,2>(NE,symm,B,G,D,Y);
-         case 0x23: return SmemPADiffusionDiagonal3D<2,3>(NE,symm,B,G,D,Y);
-         case 0x34: return SmemPADiffusionDiagonal3D<3,4>(NE,symm,B,G,D,Y);
-         case 0x45: return SmemPADiffusionDiagonal3D<4,5>(NE,symm,B,G,D,Y);
-         case 0x46: return SmemPADiffusionDiagonal3D<4,6>(NE,symm,B,G,D,Y);
-         case 0x56: return SmemPADiffusionDiagonal3D<5,6>(NE,symm,B,G,D,Y);
-         case 0x67: return SmemPADiffusionDiagonal3D<6,7>(NE,symm,B,G,D,Y);
-         case 0x78: return SmemPADiffusionDiagonal3D<7,8>(NE,symm,B,G,D,Y);
-         case 0x89: return SmemPADiffusionDiagonal3D<8,9>(NE,symm,B,G,D,Y);
-         case 0x9A: return SmemPADiffusionDiagonal3D<9,10>(NE,symm,B,G,D,Y);
-         default: return PADiffusionDiagonal3D(NE,symm,B,G,D,Y,D1D,Q1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-void PADiffusionApply(const int dim,
-                      const int D1D,
-                      const int Q1D,
-                      const int NE,
-                      const bool symm,
-                      const Array<real_t> &B,
-                      const Array<real_t> &G,
-                      const Array<real_t> &Bt,
-                      const Array<real_t> &Gt,
-                      const Vector &D,
-                      const Vector &X,
-                      Vector &Y)
-{
-#ifdef MFEM_USE_OCCA
-   if (DeviceCanUseOcca())
-   {
-      if (dim == 2)
-      {
-         OccaPADiffusionApply2D(D1D,Q1D,NE,B,G,Bt,Gt,D,X,Y);
-         return;
-      }
-      if (dim == 3)
-      {
-         OccaPADiffusionApply3D(D1D,Q1D,NE,B,G,Bt,Gt,D,X,Y);
-         return;
-      }
-      MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
-   }
-#endif // MFEM_USE_OCCA
-   const int id = (D1D << 4) | Q1D;
-
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,symm,B,G,D,X,Y);
-         case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,symm,B,G,D,X,Y);
-         case 0x44: return SmemPADiffusionApply2D<4,4,8>(NE,symm,B,G,D,X,Y);
-         case 0x55: return SmemPADiffusionApply2D<5,5,8>(NE,symm,B,G,D,X,Y);
-         case 0x66: return SmemPADiffusionApply2D<6,6,4>(NE,symm,B,G,D,X,Y);
-         case 0x77: return SmemPADiffusionApply2D<7,7,4>(NE,symm,B,G,D,X,Y);
-         case 0x88: return SmemPADiffusionApply2D<8,8,2>(NE,symm,B,G,D,X,Y);
-         case 0x99: return SmemPADiffusionApply2D<9,9,2>(NE,symm,B,G,D,X,Y);
-         default:   return PADiffusionApply2D(NE,symm,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
-      }
-   }
-
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x22: return SmemPADiffusionApply3D<2,2>(NE,symm,B,G,D,X,Y);
-         case 0x23: return SmemPADiffusionApply3D<2,3>(NE,symm,B,G,D,X,Y);
-         case 0x34: return SmemPADiffusionApply3D<3,4>(NE,symm,B,G,D,X,Y);
-         case 0x45: return SmemPADiffusionApply3D<4,5>(NE,symm,B,G,D,X,Y);
-         case 0x46: return SmemPADiffusionApply3D<4,6>(NE,symm,B,G,D,X,Y);
-         case 0x56: return SmemPADiffusionApply3D<5,6>(NE,symm,B,G,D,X,Y);
-         case 0x58: return SmemPADiffusionApply3D<5,8>(NE,symm,B,G,D,X,Y);
-         case 0x67: return SmemPADiffusionApply3D<6,7>(NE,symm,B,G,D,X,Y);
-         case 0x78: return SmemPADiffusionApply3D<7,8>(NE,symm,B,G,D,X,Y);
-         case 0x89: return SmemPADiffusionApply3D<8,9>(NE,symm,B,G,D,X,Y);
-         default:   return PADiffusionApply3D(NE,symm,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel: 0x"<<std::hex << id << std::dec);
-}
-
 #ifdef MFEM_USE_OCCA
 void OccaPADiffusionApply2D(const int D1D,
                             const int Q1D,

fem/integ/bilininteg_diffusion_kernels.hpp

@@ -12,6 +12,7 @@
 #ifndef MFEM_BILININTEG_DIFFUSION_KERNELS_HPP
 #define MFEM_BILININTEG_DIFFUSION_KERNELS_HPP
 
+#include "../kernel_dispatch.hpp"
 #include "../../config/config.hpp"
 #include "../../general/array.hpp"
 #include "../../general/forall.hpp"
@@ -36,7 +37,7 @@ void PADiffusionSetup(const int dim,
                       const Vector &C,
                       Vector &D);
 
-// PA Diffusion Assemble 2D kernel
+// PA Diffusion Assemble 2D f
 template<int T_SDIM>
 void PADiffusionSetup2D(const int Q1D,
                         const int coeffDim,
@@ -151,8 +152,23 @@ inline void PADiffusionDiagonal2D(const int NE,
    });
 }
 
+namespace diffusion
+{
+constexpr int ipow(int x, int p) { return p == 0 ? 1 : x*ipow(x, p-1); }
+constexpr int D11(int x) { return (11 - x)/2; }
+constexpr int D10(int x) { return (10 - x)/2; }
+constexpr int NBZApply(int D1D)
+{
+   return ipow(2, D11(D1D) >= 0 ? D11(D1D) : 0);
+}
+constexpr int NBZDiagonal(int D1D)
+{
+   return ipow(2, D10(D1D) >= 0 ? D10(D1D) : 0);
+}
+}
+
 // Shared memory PA Diffusion Diagonal 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
+template<int T_D1D = 0, int T_Q1D = 0>
 inline void SmemPADiffusionDiagonal2D(const int NE,
                                       const bool symmetric,
                                       const Array<real_t> &b_,
@@ -162,9 +178,10 @@ inline void SmemPADiffusionDiagonal2D(const int NE,
                                       const int d1d = 0,
                                       const int q1d = 0)
 {
+   static constexpr int T_NBZ = diffusion::NBZDiagonal(T_D1D);
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int max_q1d = T_Q1D ? T_Q1D : DeviceDofQuadLimits::Get().MAX_Q1D;
    const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
    MFEM_VERIFY(D1D <= max_d1d, "");
@@ -178,7 +195,6 @@ inline void SmemPADiffusionDiagonal2D(const int NE,
       const int tidz = MFEM_THREAD_ID(z);
       const int D1D = T_D1D ? T_D1D : d1d;
       const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
       constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
       constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
       MFEM_SHARED real_t BG[2][MQ1*MD1];
@@ -628,20 +644,23 @@ inline void PADiffusionApply2D(const int NE,
 }
 
 // Shared memory PA Diffusion Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
+template<int T_D1D = 0, int T_Q1D = 0>
 inline void SmemPADiffusionApply2D(const int NE,
                                    const bool symmetric,
                                    const Array<real_t> &b_,
                                    const Array<real_t> &g_,
+                                   const Array<real_t> &bt_,
+                                   const Array<real_t> &gt_,
                                    const Vector &d_,
                                    const Vector &x_,
                                    Vector &y_,
                                    const int d1d = 0,
                                    const int q1d = 0)
 {
+   static constexpr int T_NBZ = diffusion::NBZApply(T_D1D);
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int max_q1d = T_Q1D ? T_Q1D : DeviceDofQuadLimits::Get().MAX_Q1D;
    const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
    MFEM_VERIFY(D1D <= max_d1d, "");
@@ -656,7 +675,6 @@ inline void SmemPADiffusionApply2D(const int NE,
       const int tidz = MFEM_THREAD_ID(z);
       const int D1D = T_D1D ? T_D1D : d1d;
       const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
       constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
       constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
       MFEM_SHARED real_t sBG[2][MQ1*MD1];
@@ -984,6 +1002,8 @@ inline void SmemPADiffusionApply3D(const int NE,
                                    const bool symmetric,
                                    const Array<real_t> &b_,
                                    const Array<real_t> &g_,
+                                   const Array<real_t> &,
+                                   const Array<real_t> &,
                                    const Vector &d_,
                                    const Vector &x_,
                                    Vector &y_,
@@ -1203,6 +1223,44 @@ inline void SmemPADiffusionApply3D(const int NE,
 
 } // namespace internal
 
+namespace
+{
+using ApplyKernelType = DiffusionIntegrator::ApplyKernelType;
+using DiagonalKernelType = DiffusionIntegrator::DiagonalKernelType;
+}
+
+template<int DIM, int T_D1D, int T_Q1D>
+ApplyKernelType DiffusionIntegrator::ApplyPAKernels::Kernel()
+{
+   if (DIM == 2) { return internal::SmemPADiffusionApply2D<T_D1D,T_Q1D>; }
+   else if (DIM == 3) { return internal::SmemPADiffusionApply3D<T_D1D, T_Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+inline
+ApplyKernelType DiffusionIntegrator::ApplyPAKernels::Fallback(int DIM, int, int)
+{
+   if (DIM == 2) { return internal::PADiffusionApply2D; }
+   else if (DIM == 3) { return internal::PADiffusionApply3D; }
+   else { MFEM_ABORT(""); }
+}
+
+template<int DIM, int D1D, int Q1D>
+DiagonalKernelType DiffusionIntegrator::DiagonalPAKernels::Kernel()
+{
+   if (DIM == 2) { return internal::SmemPADiffusionDiagonal2D<D1D,Q1D>; }
+   else if (DIM == 3) { return internal::SmemPADiffusionDiagonal3D<D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+inline DiagonalKernelType
+DiffusionIntegrator::DiagonalPAKernels::Fallback(int DIM, int, int)
+{
+   if (DIM == 2) { return internal::PADiffusionDiagonal2D; }
+   else if (DIM == 3) { return internal::PADiffusionDiagonal3D; }
+   else { MFEM_ABORT(""); }
+}
+
 } // namespace mfem
 
 #endif

fem/integ/bilininteg_diffusion_pa.cpp

@@ -19,6 +19,73 @@
 namespace mfem
 {
 
+void DiffusionIntegrator::AssembleDiagonalPA(Vector &diag)
+{
+   if (DeviceCanUseCeed())
+   {
+      ceedOp->GetDiagonal(diag);
+   }
+   else
+   {
+      if (pa_data.Size() == 0) { AssemblePA(*fespace); }
+      const Array<real_t> &B = maps->B;
+      const Array<real_t> &G = maps->G;
+      const Vector &Dv = pa_data;
+      DiagonalPAKernels::Run(dim, dofs1D, quad1D, ne, symmetric, B, G, Dv,
+                             diag, dofs1D, quad1D);
+   }
+}
+
+// PA Diffusion Apply kernel
+void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   if (DeviceCanUseCeed())
+   {
+      ceedOp->AddMult(x, y);
+   }
+   else
+   {
+      const Array<real_t> &B = maps->B;
+      const Array<real_t> &G = maps->G;
+      const Array<real_t> &Bt = maps->Bt;
+      const Array<real_t> &Gt = maps->Gt;
+      const Vector &Dv = pa_data;
+
+#ifdef MFEM_USE_OCCA
+      if (DeviceCanUseOcca())
+      {
+         if (dim == 2)
+         {
+            OccaPADiffusionApply2D(dofs1D,quad1D,ne,B,G,Bt,Gt,Dv,x,y);
+            return;
+         }
+         if (dim == 3)
+         {
+            OccaPADiffusionApply3D(dofs1D,quad1D,ne,B,G,Bt,Gt,Dv,x,y);
+            return;
+         }
+         MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
+      }
+#endif // MFEM_USE_OCCA
+
+      ApplyPAKernels::Run(dim, dofs1D, quad1D, ne, symmetric, B, G, Bt,
+                          Gt, Dv, x, y, dofs1D, quad1D);
+   }
+}
+
+void DiffusionIntegrator::AddMultTransposePA(const Vector &x, Vector &y) const
+{
+   if (symmetric)
+   {
+      AddMultPA(x, y);
+   }
+   else
+   {
+      MFEM_ABORT("DiffusionIntegrator::AddMultTransposePA only implemented in "
+                 "the symmetric case.")
+   }
+}
+
 void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
@@ -98,47 +165,6 @@ void DiffusionIntegrator::AssemblePatchPA(const int patch,
    SetupPatchPA(patch, mesh);  // For full quadrature, unitWeights = false
 }
 
-void DiffusionIntegrator::AssembleDiagonalPA(Vector &diag)
-{
-   if (DeviceCanUseCeed())
-   {
-      ceedOp->GetDiagonal(diag);
-   }
-   else
-   {
-      if (pa_data.Size()==0) { AssemblePA(*fespace); }
-      internal::PADiffusionAssembleDiagonal(dim, dofs1D, quad1D, ne, symmetric,
-                                            maps->B, maps->G, pa_data, diag);
-   }
-}
-
-void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (DeviceCanUseCeed())
-   {
-      ceedOp->AddMult(x, y);
-   }
-   else
-   {
-      internal::PADiffusionApply(dim, dofs1D, quad1D, ne, symmetric,
-                                 maps->B, maps->G, maps->Bt, maps->Gt,
-                                 pa_data, x, y);
-   }
-}
-
-void DiffusionIntegrator::AddMultTransposePA(const Vector &x, Vector &y) const
-{
-   if (symmetric)
-   {
-      AddMultPA(x, y);
-   }
-   else
-   {
-      MFEM_ABORT("DiffusionIntegrator::AddMultTransposePA only implemented in "
-                 "the symmetric case.")
-   }
-}
-
 // This version uses full 1D quadrature rules, taking into account the
 // minimum interaction between basis functions and integration points.
 void DiffusionIntegrator::AddMultPatchPA(const int patch, const Vector &x,

fem/integ/bilininteg_mass_kernels.cpp

@@ -14,78 +14,34 @@
 namespace mfem
 {
 
+MassIntegrator::Kernels MassIntegrator::kernels;
+MassIntegrator::Kernels::Kernels()
+{
+   // 2D
+   MassIntegrator::AddSpecialization<2,2,2>();
+   MassIntegrator::AddSpecialization<2,3,3>();
+   MassIntegrator::AddSpecialization<2,4,4>();
+   MassIntegrator::AddSpecialization<2,5,5>();
+   MassIntegrator::AddSpecialization<2,6,6>();
+   MassIntegrator::AddSpecialization<2,7,7>();
+   MassIntegrator::AddSpecialization<2,8,8>();
+   MassIntegrator::AddSpecialization<2,9,9>();
+   // 3D
+   MassIntegrator::AddSpecialization<3,2,2>();
+   MassIntegrator::AddSpecialization<3,2,3>();
+   MassIntegrator::AddSpecialization<3,3,4>();
+   MassIntegrator::AddSpecialization<3,4,5>();
+   MassIntegrator::AddSpecialization<3,4,6>();
+   MassIntegrator::AddSpecialization<3,5,6>();
+   MassIntegrator::AddSpecialization<3,5,8>();
+   MassIntegrator::AddSpecialization<3,6,7>();
+   MassIntegrator::AddSpecialization<3,7,8>();
+   MassIntegrator::AddSpecialization<3,8,9>();
+}
+
 namespace internal
 {
 
-// PA Mass Diagonal 1D kernel
-static void PAMassAssembleDiagonal1D(const int NE,
-                                     const Array<real_t> &b,
-                                     const Vector &d,
-                                     Vector &y,
-                                     const int D1D,
-                                     const int Q1D)
-{
-   auto B = Reshape(b.Read(), Q1D, D1D);
-   auto D = Reshape(d.Read(), Q1D, NE);
-   auto Y = Reshape(y.ReadWrite(), D1D, NE);
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      for (int dx = 0; dx < D1D; ++dx)
-      {
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            Y(dx, e) += B(qx, dx) * B(qx, dx) * D(qx, e);
-         }
-      }
-   });
-}
-
-void PAMassAssembleDiagonal(const int dim, const int D1D,
-                            const int Q1D, const int NE,
-                            const Array<real_t> &B,
-                            const Vector &D,
-                            Vector &Y)
-{
-   if (dim == 1)
-   {
-      return PAMassAssembleDiagonal1D(NE,B,D,Y,D1D,Q1D);
-   }
-   else if (dim == 2)
-   {
-      switch ((D1D << 4 ) | Q1D)
-      {
-         case 0x22: return SmemPAMassAssembleDiagonal2D<2,2,16>(NE,B,D,Y);
-         case 0x33: return SmemPAMassAssembleDiagonal2D<3,3,16>(NE,B,D,Y);
-         case 0x44: return SmemPAMassAssembleDiagonal2D<4,4,8>(NE,B,D,Y);
-         case 0x55: return SmemPAMassAssembleDiagonal2D<5,5,8>(NE,B,D,Y);
-         case 0x66: return SmemPAMassAssembleDiagonal2D<6,6,4>(NE,B,D,Y);
-         case 0x77: return SmemPAMassAssembleDiagonal2D<7,7,4>(NE,B,D,Y);
-         case 0x88: return SmemPAMassAssembleDiagonal2D<8,8,2>(NE,B,D,Y);
-         case 0x99: return SmemPAMassAssembleDiagonal2D<9,9,2>(NE,B,D,Y);
-         default:   return PAMassAssembleDiagonal2D(NE,B,D,Y,D1D,Q1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((D1D << 4 ) | Q1D)
-      {
-         case 0x23: return SmemPAMassAssembleDiagonal3D<2,3>(NE,B,D,Y);
-         case 0x24: return SmemPAMassAssembleDiagonal3D<2,4>(NE,B,D,Y);
-         case 0x26: return SmemPAMassAssembleDiagonal3D<2,6>(NE,B,D,Y);
-         case 0x34: return SmemPAMassAssembleDiagonal3D<3,4>(NE,B,D,Y);
-         case 0x35: return SmemPAMassAssembleDiagonal3D<3,5>(NE,B,D,Y);
-         case 0x45: return SmemPAMassAssembleDiagonal3D<4,5>(NE,B,D,Y);
-         case 0x48: return SmemPAMassAssembleDiagonal3D<4,8>(NE,B,D,Y);
-         case 0x56: return SmemPAMassAssembleDiagonal3D<5,6>(NE,B,D,Y);
-         case 0x67: return SmemPAMassAssembleDiagonal3D<6,7>(NE,B,D,Y);
-         case 0x78: return SmemPAMassAssembleDiagonal3D<7,8>(NE,B,D,Y);
-         case 0x89: return SmemPAMassAssembleDiagonal3D<8,9>(NE,B,D,Y);
-         default:   return PAMassAssembleDiagonal3D(NE,B,D,Y,D1D,Q1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
 #ifdef MFEM_USE_OCCA
 void OccaPAMassApply2D(const int D1D,
                        const int Q1D,
@@ -176,154 +132,6 @@ void OccaPAMassApply3D(const int D1D,
 }
 #endif // MFEM_USE_OCCA
 
-MFEM_HOST_DEVICE inline
-void PAMassApply1D_Element(const int e,
-                           const int NE,
-                           const real_t *b_,
-                           const real_t *bt_,
-                           const real_t *d_,
-                           const real_t *x_,
-                           real_t *y_,
-                           const int d1d = 0,
-                           const int q1d = 0)
-{
-   const int D1D = d1d;
-   const int Q1D = q1d;
-   auto B = ConstDeviceMatrix(b_, Q1D, D1D);
-   auto Bt = ConstDeviceMatrix(bt_, D1D, Q1D);
-   auto D = ConstDeviceMatrix(d_, Q1D, NE);
-   auto X = ConstDeviceMatrix(x_, D1D, NE);
-   auto Y = DeviceMatrix(y_, D1D, NE);
-
-   real_t XQ[DofQuadLimits::MAX_Q1D];
-   for (int qx = 0; qx < Q1D; ++qx)
-   {
-      XQ[qx] = 0.0;
-   }
-   for (int dx = 0; dx < D1D; ++dx)
-   {
-      const real_t s = X(dx,e);
-      for (int qx = 0; qx < Q1D; ++qx)
-      {
-         XQ[qx] += B(qx,dx)*s;
-      }
-   }
-   for (int qx = 0; qx < Q1D; ++qx)
-   {
-      const real_t q = XQ[qx]*D(qx,e);
-      for (int dx = 0; dx < D1D; ++dx)
-      {
-         Y(dx,e) += Bt(dx,qx) * q;
-      }
-   }
-}
-
-// PA Mass Apply 1D kernel
-static void PAMassApply1D(const int NE,
-                          const Array<real_t> &b_,
-                          const Array<real_t> &bt_,
-                          const Vector &d_,
-                          const Vector &x_,
-                          Vector &y_,
-                          const int d1d = 0,
-                          const int q1d = 0)
-{
-   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
-   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
-
-   const auto B = b_.Read();
-   const auto Bt = bt_.Read();
-   const auto D = d_.Read();
-   const auto X = x_.Read();
-   auto Y = y_.ReadWrite();
-
-   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
-   {
-      internal::PAMassApply1D_Element(e, NE, B, Bt, D, X, Y, d1d, q1d);
-   });
-}
-
-void PAMassApply(const int dim,
-                 const int D1D,
-                 const int Q1D,
-                 const int NE,
-                 const Array<real_t> &B,
-                 const Array<real_t> &Bt,
-                 const Vector &D,
-                 const Vector &X,
-                 Vector &Y)
-{
-#ifdef MFEM_USE_OCCA
-   if (DeviceCanUseOcca())
-   {
-      if (dim == 2)
-      {
-         return OccaPAMassApply2D(D1D,Q1D,NE,B,Bt,D,X,Y);
-      }
-      if (dim == 3)
-      {
-         return OccaPAMassApply3D(D1D,Q1D,NE,B,Bt,D,X,Y);
-      }
-      MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
-   }
-#endif // MFEM_USE_OCCA
-   const int id = (D1D << 4) | Q1D;
-
-   if (dim == 1)
-   {
-      return PAMassApply1D(NE,B,Bt,D,X,Y,D1D,Q1D);
-   }
-   else if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x22: return SmemPAMassApply2D<2,2,16>(NE,B,Bt,D,X,Y);
-         case 0x24: return SmemPAMassApply2D<2,4,16>(NE,B,Bt,D,X,Y);
-         case 0x33: return SmemPAMassApply2D<3,3,16>(NE,B,Bt,D,X,Y);
-         case 0x34: return SmemPAMassApply2D<3,4,16>(NE,B,Bt,D,X,Y);
-         case 0x35: return SmemPAMassApply2D<3,5,16>(NE,B,Bt,D,X,Y);
-         case 0x36: return SmemPAMassApply2D<3,6,16>(NE,B,Bt,D,X,Y);
-         case 0x44: return SmemPAMassApply2D<4,4,8>(NE,B,Bt,D,X,Y);
-         case 0x46: return SmemPAMassApply2D<4,6,8>(NE,B,Bt,D,X,Y);
-         case 0x48: return SmemPAMassApply2D<4,8,4>(NE,B,Bt,D,X,Y);
-         case 0x55: return SmemPAMassApply2D<5,5,8>(NE,B,Bt,D,X,Y);
-         case 0x57: return SmemPAMassApply2D<5,7,8>(NE,B,Bt,D,X,Y);
-         case 0x58: return SmemPAMassApply2D<5,8,2>(NE,B,Bt,D,X,Y);
-         case 0x66: return SmemPAMassApply2D<6,6,4>(NE,B,Bt,D,X,Y);
-         case 0x77: return SmemPAMassApply2D<7,7,4>(NE,B,Bt,D,X,Y);
-         case 0x88: return SmemPAMassApply2D<8,8,2>(NE,B,Bt,D,X,Y);
-         case 0x99: return SmemPAMassApply2D<9,9,2>(NE,B,Bt,D,X,Y);
-         default:   return PAMassApply2D(NE,B,Bt,D,X,Y,D1D,Q1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x22: return SmemPAMassApply3D<2,2>(NE,B,Bt,D,X,Y);
-         case 0x23: return SmemPAMassApply3D<2,3>(NE,B,Bt,D,X,Y);
-         case 0x24: return SmemPAMassApply3D<2,4>(NE,B,Bt,D,X,Y);
-         case 0x26: return SmemPAMassApply3D<2,6>(NE,B,Bt,D,X,Y);
-         case 0x34: return SmemPAMassApply3D<3,4>(NE,B,Bt,D,X,Y);
-         case 0x35: return SmemPAMassApply3D<3,5>(NE,B,Bt,D,X,Y);
-         case 0x36: return SmemPAMassApply3D<3,6>(NE,B,Bt,D,X,Y);
-         case 0x37: return SmemPAMassApply3D<3,7>(NE,B,Bt,D,X,Y);
-         case 0x45: return SmemPAMassApply3D<4,5>(NE,B,Bt,D,X,Y);
-         case 0x46: return SmemPAMassApply3D<4,6>(NE,B,Bt,D,X,Y);
-         case 0x48: return SmemPAMassApply3D<4,8>(NE,B,Bt,D,X,Y);
-         case 0x56: return SmemPAMassApply3D<5,6>(NE,B,Bt,D,X,Y);
-         case 0x58: return SmemPAMassApply3D<5,8>(NE,B,Bt,D,X,Y);
-         case 0x67: return SmemPAMassApply3D<6,7>(NE,B,Bt,D,X,Y);
-         case 0x78: return SmemPAMassApply3D<7,8>(NE,B,Bt,D,X,Y);
-         case 0x89: return SmemPAMassApply3D<8,9>(NE,B,Bt,D,X,Y);
-         case 0x9A: return SmemPAMassApply3D<9,10>(NE,B,Bt,D,X,Y);
-         default:   return PAMassApply3D(NE,B,Bt,D,X,Y,D1D,Q1D);
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Unknown kernel.");
-}
-
 } // namespace internal
 
 } // namespace mfem

fem/integ/bilininteg_mass_kernels.hpp

@@ -25,11 +25,95 @@ namespace mfem
 namespace internal
 {
 
-void PAMassAssembleDiagonal(const int dim, const int D1D,
-                            const int Q1D, const int NE,
-                            const Array<real_t> &B,
-                            const Vector &D,
-                            Vector &Y);
+// PA Mass Diagonal 1D kernel
+static void PAMassAssembleDiagonal1D(const int NE,
+                                     const Array<real_t> &b,
+                                     const Vector &d,
+                                     Vector &y,
+                                     const int D1D,
+                                     const int Q1D)
+{
+   auto B = Reshape(b.Read(), Q1D, D1D);
+   auto D = Reshape(d.Read(), Q1D, NE);
+   auto Y = Reshape(y.ReadWrite(), D1D, NE);
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int dx = 0; dx < D1D; ++dx)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            Y(dx, e) += B(qx, dx) * B(qx, dx) * D(qx, e);
+         }
+      }
+   });
+}
+
+MFEM_HOST_DEVICE inline
+void PAMassApply1D_Element(const int e,
+                           const int NE,
+                           const real_t *b_,
+                           const real_t *bt_,
+                           const real_t *d_,
+                           const real_t *x_,
+                           real_t *y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
+{
+   const int D1D = d1d;
+   const int Q1D = q1d;
+   auto B = ConstDeviceMatrix(b_, Q1D, D1D);
+   auto Bt = ConstDeviceMatrix(bt_, D1D, Q1D);
+   auto D = ConstDeviceMatrix(d_, Q1D, NE);
+   auto X = ConstDeviceMatrix(x_, D1D, NE);
+   auto Y = DeviceMatrix(y_, D1D, NE);
+
+   real_t XQ[DofQuadLimits::MAX_Q1D];
+   for (int qx = 0; qx < Q1D; ++qx)
+   {
+      XQ[qx] = 0.0;
+   }
+   for (int dx = 0; dx < D1D; ++dx)
+   {
+      const real_t s = X(dx,e);
+      for (int qx = 0; qx < Q1D; ++qx)
+      {
+         XQ[qx] += B(qx,dx)*s;
+      }
+   }
+   for (int qx = 0; qx < Q1D; ++qx)
+   {
+      const double q = XQ[qx]*D(qx,e);
+      for (int dx = 0; dx < D1D; ++dx)
+      {
+         Y(dx,e) += Bt(dx,qx) * q;
+      }
+   }
+}
+
+// PA Mass Apply 1D kernel
+static void PAMassApply1D(const int NE,
+                          const Array<real_t> &b_,
+                          const Array<real_t> &bt_,
+                          const Vector &d_,
+                          const Vector &x_,
+                          Vector &y_,
+                          const int d1d = 0,
+                          const int q1d = 0)
+{
+   MFEM_VERIFY(d1d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q1d <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto B = b_.Read();
+   const auto Bt = bt_.Read();
+   const auto D = d_.Read();
+   const auto X = x_.Read();
+   auto Y = y_.ReadWrite();
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      internal::PAMassApply1D_Element(e, NE, B, Bt, D, X, Y, d1d, q1d);
+   });
+}
 
 // PA Mass Diagonal 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
@@ -78,8 +162,18 @@ inline void PAMassAssembleDiagonal2D(const int NE,
    });
 }
 
+namespace mass
+{
+constexpr int ipow(int x, int p) { return p == 0 ? 1 : x*ipow(x, p-1); }
+constexpr int D(int D1D) { return (11 - D1D) / 2; }
+constexpr int NBZ(int D1D)
+{
+   return ipow(2, D(D1D) >= 0 ? D(D1D) : 0);
+}
+}
+
 // Shared memory PA Mass Diagonal 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
+template<int T_D1D = 0, int T_Q1D = 0>
 inline void SmemPAMassAssembleDiagonal2D(const int NE,
                                          const Array<real_t> &b_,
                                          const Vector &d_,
@@ -87,9 +181,10 @@ inline void SmemPAMassAssembleDiagonal2D(const int NE,
                                          const int d1d = 0,
                                          const int q1d = 0)
 {
+   static constexpr int T_NBZ = mass::NBZ(T_D1D);
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int max_q1d = T_Q1D ? T_Q1D : DeviceDofQuadLimits::Get().MAX_Q1D;
    const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
    MFEM_VERIFY(D1D <= max_d1d, "");
@@ -102,7 +197,6 @@ inline void SmemPAMassAssembleDiagonal2D(const int NE,
       const int tidz = MFEM_THREAD_ID(z);
       const int D1D = T_D1D ? T_D1D : d1d;
       const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
       constexpr int MQ1 = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
       constexpr int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
       MFEM_SHARED real_t B[MQ1][MD1];
@@ -302,16 +396,6 @@ inline void SmemPAMassAssembleDiagonal3D(const int NE,
    });
 }
 
-void PAMassApply(const int dim,
-                 const int D1D,
-                 const int Q1D,
-                 const int NE,
-                 const Array<real_t> &B,
-                 const Array<real_t> &Bt,
-                 const Vector &D,
-                 const Vector &X,
-                 Vector &Y);
-
 #ifdef MFEM_USE_OCCA
 // OCCA PA Mass Apply 2D kernel
 void OccaPAMassApply2D(const int D1D,
@@ -964,7 +1048,7 @@ inline void PAMassApply2D(const int NE,
 }
 
 // Shared memory PA Mass Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
+template<int T_D1D = 0, int T_Q1D = 0>
 inline void SmemPAMassApply2D(const int NE,
                               const Array<real_t> &b_,
                               const Array<real_t> &bt_,
@@ -975,9 +1059,10 @@ inline void SmemPAMassApply2D(const int NE,
                               const int q1d = 0)
 {
    MFEM_CONTRACT_VAR(bt_);
+   static constexpr int T_NBZ = mass::NBZ(T_D1D);
+   static constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
    const int max_q1d = T_Q1D ? T_Q1D : DeviceDofQuadLimits::Get().MAX_Q1D;
    const int max_d1d = T_D1D ? T_D1D : DeviceDofQuadLimits::Get().MAX_D1D;
    MFEM_VERIFY(D1D <= max_d1d, "");
@@ -988,8 +1073,8 @@ inline void SmemPAMassApply2D(const int NE,
    auto Y = y_.ReadWrite();
    mfem::forall_2D_batch(NE, Q1D, Q1D, NBZ, [=] MFEM_HOST_DEVICE (int e)
    {
-      internal::SmemPAMassApply2D_Element<T_D1D,T_Q1D,T_NBZ>(e, NE, b, D, x, Y, d1d,
-                                                             q1d);
+      internal::SmemPAMassApply2D_Element<T_D1D,T_Q1D,T_NBZ>(
+         e, NE, b, D, x, Y, d1d, q1d);
    });
 }
 
@@ -1049,6 +1134,48 @@ inline void SmemPAMassApply3D(const int NE,
 
 } // namespace internal
 
+namespace
+{
+using ApplyKernelType = MassIntegrator::ApplyKernelType;
+using DiagonalKernelType = MassIntegrator::DiagonalKernelType;
+}
+
+template<int DIM, int T_D1D, int T_Q1D>
+ApplyKernelType MassIntegrator::ApplyPAKernels::Kernel()
+{
+   if (DIM == 1) { return internal::PAMassApply1D; }
+   else if (DIM == 2) { return internal::SmemPAMassApply2D<T_D1D,T_Q1D>; }
+   else if (DIM == 3) { return internal::SmemPAMassApply3D<T_D1D, T_Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+inline ApplyKernelType MassIntegrator::ApplyPAKernels::Fallback(
+   int DIM, int, int)
+{
+   if (DIM == 1) { return internal::PAMassApply1D; }
+   else if (DIM == 2) { return internal::PAMassApply2D; }
+   else if (DIM == 3) { return internal::PAMassApply3D; }
+   else { MFEM_ABORT(""); }
+}
+
+template<int DIM, int T_D1D, int T_Q1D>
+DiagonalKernelType MassIntegrator::DiagonalPAKernels::Kernel()
+{
+   if (DIM == 1) { return internal::PAMassAssembleDiagonal1D; }
+   else if (DIM == 2) { return internal::SmemPAMassAssembleDiagonal2D<T_D1D,T_Q1D>; }
+   else if (DIM == 3) { return internal::SmemPAMassAssembleDiagonal3D<T_D1D, T_Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+inline DiagonalKernelType MassIntegrator::DiagonalPAKernels::Fallback(
+   int DIM, int, int)
+{
+   if (DIM == 1) { return internal::PAMassAssembleDiagonal1D; }
+   else if (DIM == 2) { return internal::PAMassAssembleDiagonal2D; }
+   else if (DIM == 3) { return internal::PAMassAssembleDiagonal3D; }
+   else { MFEM_ABORT(""); }
+}
+
 } // namespace mfem
 
 #endif

fem/integ/bilininteg_mass_pa.cpp

@@ -19,6 +19,8 @@
 namespace mfem
 {
 
+// PA Mass Integrator
+
 void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
@@ -195,8 +197,8 @@ void MassIntegrator::AssembleDiagonalPA(Vector &diag)
    }
    else
    {
-      internal::PAMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data,
-                                       diag);
+      DiagonalPAKernels::Run(dim, dofs1D, quad1D, ne, maps->B, pa_data,
+                             diag, dofs1D, quad1D);
    }
 }
 
@@ -208,8 +210,26 @@ void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
    }
    else
    {
-      internal::PAMassApply(dim, dofs1D, quad1D, ne, maps->B, maps->Bt, pa_data, x,
-                            y);
+      const int D1D = dofs1D;
+      const int Q1D = quad1D;
+      const Array<real_t> &B = maps->B;
+      const Array<real_t> &Bt = maps->Bt;
+      const Vector &D = pa_data;
+#ifdef MFEM_USE_OCCA
+      if (DeviceCanUseOcca())
+      {
+         if (dim == 2)
+         {
+            return OccaPAMassApply2D(D1D,Q1D,ne,B,Bt,D,x,y);
+         }
+         if (dim == 3)
+         {
+            return OccaPAMassApply3D(D1D,Q1D,ne,B,Bt,D,x,y);
+         }
+         MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
+      }
+#endif // MFEM_USE_OCCA
+      ApplyPAKernels::Run(dim, D1D, Q1D, ne, B, Bt, D, x, y, D1D, Q1D);
    }
 }
 

fem/intrules_cut.cpp

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

fem/intrules_cut.hpp

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

fem/kernel_dispatch.hpp

@@ -0,0 +1,183 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_KERNEL_DISPATCH_HPP
+#define MFEM_KERNEL_DISPATCH_HPP
+
+#include "../config/config.hpp"
+#include "kernel_reporter.hpp"
+#include <unordered_map>
+#include <tuple>
+#include <cstddef>
+
+namespace mfem
+{
+
+// The MFEM_REGISTER_KERNELS macro registers kernels for runtime dispatch using
+// a dispatch map.
+//
+// This creates a dispatch table (a static member variable) named @a KernelName
+// containing function points of type @a KernelType. These are followed by one
+// or two sets of parenthesized argument types.
+//
+// The first set of argument types contains the types that are used to dispatch
+// to either specialized or fallback kernels. The second set of argument types
+// can be used to further specialize the kernel without participating in
+// dispatch (a canonical example is NBZ, determining the size of the thread
+// blocks; this is required to specialize kernels for optimal performance, but
+// is not relevant for dispatch).
+//
+// After calling this macro, the user must implement the Kernel and Fallback
+// static member functions, which return pointers to the appropriate kernel
+// functions depending on the parameters.
+//
+// Specialized functions can be registered using the static AddSpecialization
+// member function.
+
+#define MFEM_EXPAND(X) X // Workaround needed for MSVC compiler
+
+#define MFEM_REGISTER_KERNELS(KernelName, KernelType, ...)                     \
+   MFEM_EXPAND(MFEM_EXPAND(MFEM_REGISTER_KERNELS_N(__VA_ARGS__,2,1,))          \
+      (KernelName,KernelType,__VA_ARGS__))
+
+#define MFEM_REGISTER_KERNELS_N(_1, _2, N, ...) MFEM_REGISTER_KERNELS_##N
+
+// Expands a variable length macro parameter so that multiple variable length
+// parameters can be passed to the same macro.
+#define MFEM_PARAM_LIST(...) __VA_ARGS__
+
+// Version of MFEM_REGISTER_KERNELS without any "optional" (non-dispatch)
+// parameters.
+#define MFEM_REGISTER_KERNELS_1(KernelName, KernelType, Params)                \
+   MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, (), Params)
+
+// Version of MFEM_REGISTER_KERNELS without any optional (non-dispatch)
+// parameters (e.g. NBZ).
+#define MFEM_REGISTER_KERNELS_2(KernelName, KernelType, Params, OptParams)     \
+   MFEM_REGISTER_KERNELS_(KernelName, KernelType, Params, OptParams,           \
+                          (MFEM_PARAM_LIST Params, MFEM_PARAM_LIST OptParams))
+
+// P1 are the parameters, P2 are the optional (non-dispatch parameters), and P3
+// is the concatenation of P1 and P2. We need to pass it as a separate argument
+// to avoid a trailing comma in the case that P2 is empty.
+#define MFEM_REGISTER_KERNELS_(KernelName, KernelType, P1, P2, P3)             \
+   class KernelName : public                                                   \
+   KernelDispatchTable<KernelName, KernelType,                                 \
+      internal::KernelTypeList<MFEM_PARAM_LIST P1>,                            \
+      internal::KernelTypeList<MFEM_PARAM_LIST P2>>                            \
+   {                                                                           \
+   public:                                                                     \
+      const char *kernel_name = MFEM_KERNEL_NAME(KernelName);                  \
+      using KernelSignature = KernelType;                                      \
+      template <MFEM_PARAM_LIST P3>                                            \
+      static KernelSignature Kernel();                                         \
+      static KernelSignature Fallback(MFEM_PARAM_LIST P1);                     \
+      static KernelName &Get()                                                 \
+      { static KernelName table; return table;}                                \
+   }
+
+/// @brief Hashes variadic packs for which each type contained in the variadic
+/// pack has a specialization of `std::hash` available.
+///
+/// For example, packs containing int, bool, enum values, etc.
+template<typename ...KernelParameters>
+struct KernelDispatchKeyHash
+{
+private:
+   template<int N>
+   size_t operator()(std::tuple<KernelParameters...> value) const { return 0; }
+
+   // The hashing formula here is taken directly from the Boost library, with
+   // the magic number 0x9e3779b9 chosen to minimize hashing collisions.
+   template<std::size_t N, typename THead, typename... TTail>
+   size_t operator()(std::tuple<KernelParameters...> value) const
+   {
+      constexpr int Index = N - sizeof...(TTail) - 1;
+      auto lhs_hash = std::hash<THead>()(std::get<Index>(value));
+      auto rhs_hash = operator()<N, TTail...>(value);
+      return lhs_hash^(rhs_hash + 0x9e3779b9 + (lhs_hash<<6) + (lhs_hash>>2));
+   }
+public:
+   /// Returns the hash of the given @a value.
+   size_t operator()(std::tuple<KernelParameters...> value) const
+   {
+      return operator()<sizeof...(KernelParameters),KernelParameters...>(value);
+   }
+};
+
+namespace internal { template<typename... Types> struct KernelTypeList { }; }
+
+template<typename... T> class KernelDispatchTable { };
+
+template <typename Kernels,
+          typename Signature,
+          typename... Params,
+          typename... OptParams>
+class KernelDispatchTable<Kernels,
+         Signature,
+         internal::KernelTypeList<Params...>,
+         internal::KernelTypeList<OptParams...>>
+{
+   std::unordered_map<std::tuple<Params...>,
+       Signature,
+       KernelDispatchKeyHash<Params...>> table;
+
+public:
+   /// @brief Run the kernel with the given dispatch parameters and arguments.
+   ///
+   /// If a compile-time specialized version of the kernel with the given
+   /// parameters has been registered, it will be called. Otherwise, the
+   /// fallback kernel will be called.
+   template<typename... Args>
+   static void Run(Params... params, Args&&... args)
+   {
+      const auto &table = Kernels::Get().table;
+      const std::tuple<Params...> key = std::make_tuple(params...);
+      const auto it = table.find(key);
+      if (it != table.end())
+      {
+         it->second(std::forward<Args>(args)...);
+      }
+      else
+      {
+         ReportFallback(Kernels::Get().kernel_name, params...);
+         Kernels::Fallback(params...)(std::forward<Args>(args)...);
+      }
+   }
+
+   /// Register a specialized kernel for dispatch.
+   template <Params... PARAMS>
+   struct Specialization
+   {
+      // Version without optional parameters
+      static void Add()
+      {
+         std::tuple<Params...> param_tuple(PARAMS...);
+         Kernels::Get().table[param_tuple] =
+            Kernels:: template Kernel<PARAMS...>();
+      };
+      // Version with optional parameters
+      template <OptParams... OPT_PARAMS>
+      struct Opt
+      {
+         static void Add()
+         {
+            std::tuple<Params...> param_tuple(PARAMS...);
+            Kernels::Get().table[param_tuple] =
+               Kernels:: template Kernel<PARAMS..., OPT_PARAMS...>();
+         }
+      };
+   };
+};
+
+}
+
+#endif

fem/kernel_reporter.hpp

@@ -0,0 +1,82 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_KERNEL_REPORTER_HPP
+#define MFEM_KERNEL_REPORTER_HPP
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_REPORT_KERNELS
+
+#include "../general/globals.hpp"
+#include <set>
+#include <sstream>
+#include <string>
+
+#define MFEM_STR_(X) #X
+#define MFEM_STR(X) MFEM_STR_(X)
+#define MFEM_KERNEL_NAME(KernelName)  \
+   __FILE__ ":" MFEM_STR(__LINE__) " : " #KernelName
+
+namespace mfem
+{
+
+namespace
+{
+
+template <typename Last>
+static void Stringify_(std::ostream &o, Last &&arg)
+{
+   o << arg;
+}
+
+template <typename T1, typename T2, typename... Rest>
+static void Stringify_(std::ostream &o, T1 &&a1, T2 &&a2, Rest&&... rest)
+{
+   o << int(a1) << ",";
+   Stringify_(o, a2, rest...);
+}
+
+template <typename... Args>
+static std::string Stringify(Args&&... args)
+{
+   std::stringstream o;
+   Stringify_(o, args...);
+   return o.str();
+}
+
+} // namespace
+
+template <typename... Params>
+void ReportFallback(const std::string &kernel_name, Params&&... params)
+{
+   static std::set<std::string> reported_fallbacks;
+   const std::string requested_kernel =
+      kernel_name + "<" + Stringify(params...) + ">";
+   if (reported_fallbacks.find(requested_kernel) == reported_fallbacks.end())
+   {
+      reported_fallbacks.insert(requested_kernel);
+      mfem::err << "Fallback kernel. Requested "
+                << requested_kernel << std::endl;
+   }
+}
+
+} // namespace mfem
+
+#else // #ifdef MFEM_REPORT_KERNELS
+
+// No-op
+#define MFEM_KERNEL_NAME(KernelName) ""
+template <typename... T> void ReportFallback(T&&...) { }
+
+#endif
+
+#endif

fem/qinterp/det.cpp

@@ -27,12 +27,16 @@ namespace quadrature_interpolator
 {
 
 static void Det1D(const int NE,
+                  const real_t *b,
                   const real_t *g,
                   const real_t *x,
                   real_t *y,
                   const int d1d,
-                  const int q1d)
+                  const int q1d,
+                  Vector *d_buff = nullptr)
 {
+   MFEM_CONTRACT_VAR(b);
+   MFEM_CONTRACT_VAR(d_buff);
    const auto G = Reshape(g, q1d, d1d);
    const auto X = Reshape(x, d1d, NE);
 
@@ -59,8 +63,10 @@ static void Det2D(const int NE,
                   const real_t *x,
                   real_t *y,
                   const int d1d = 0,
-                  const int q1d = 0)
+                  const int q1d = 0,
+                  Vector *d_buff = nullptr)
 {
+   MFEM_CONTRACT_VAR(d_buff);
    static constexpr int SDIM = 2;
    static constexpr int NBZ = 1;
 
@@ -109,8 +115,11 @@ static void Det2DSurface(const int NE,
                          const real_t *x,
                          real_t *y,
                          const int d1d = 0,
-                         const int q1d = 0)
+                         const int q1d = 0,
+                         Vector *d_buff = nullptr)
 {
+   MFEM_CONTRACT_VAR(d_buff);
+
    static constexpr int SDIM = 3;
    static constexpr int NBZ = 1;
 
@@ -272,91 +281,63 @@ static void Det3D(const int NE,
    });
 }
 
-// Tensor-product evaluation of quadrature point determinants: dispatch
-// function.
-void TensorDeterminants(const int NE,
-                        const int vdim,
-                        const DofToQuad &maps,
-                        const Vector &e_vec,
-                        Vector &q_det,
-                        Vector &d_buff)
+void InitDetKernels()
 {
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const real_t *B = maps.B.Read();
-   const real_t *G = maps.G.Read();
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_det.Write();
-
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
-
-   if (dim == 1)
-   {
-      MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D,
-                  "Orders higher than " << DeviceDofQuadLimits::Get().MAX_D1D-1
-                  << " are not supported!");
-      MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D,
-                  "Quadrature rules with more than "
-                  << DeviceDofQuadLimits::Get().MAX_Q1D << " 1D points are not supported!");
-      Det1D(NE, G, X, Y, D1D, Q1D);
-      return;
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x222: return Det2D<2,2>(NE,B,G,X,Y);
-         case 0x223: return Det2D<2,3>(NE,B,G,X,Y);
-         case 0x224: return Det2D<2,4>(NE,B,G,X,Y);
-         case 0x226: return Det2D<2,6>(NE,B,G,X,Y);
-         case 0x234: return Det2D<3,4>(NE,B,G,X,Y);
-         case 0x236: return Det2D<3,6>(NE,B,G,X,Y);
-         case 0x244: return Det2D<4,4>(NE,B,G,X,Y);
-         case 0x246: return Det2D<4,6>(NE,B,G,X,Y);
-         case 0x256: return Det2D<5,6>(NE,B,G,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            if (vdim == 2) { Det2D(NE,B,G,X,Y,D1D,Q1D); }
-            else if (vdim == 3) { Det2DSurface(NE,B,G,X,Y,D1D,Q1D); }
-            else { MFEM_ABORT("Invalid space dimension."); }
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x324: return Det3D<2,4>(NE,B,G,X,Y);
-         case 0x333: return Det3D<3,3>(NE,B,G,X,Y);
-         case 0x335: return Det3D<3,5>(NE,B,G,X,Y);
-         case 0x336: return Det3D<3,6>(NE,B,G,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_DET_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_DET_1D;
-            // Highest orders that fit in shared memory
-            if (D1D <= MD && Q1D <= MQ)
-            { return Det3D<0,0,true>(NE,B,G,X,Y,D1D,Q1D); }
-            // Last fall-back will use global memory
-            return Det3D<0,0,false>(
-                      NE,B,G,X,Y,D1D,Q1D,&d_buff);
-         }
-      }
-   }
-   MFEM_ABORT("Kernel " << std::hex << id << std::dec << " not supported yet");
+   using k = QuadratureInterpolator::DetKernels;
+   // 2D
+   k::Specialization<2,2,2,2>::Add();
+   k::Specialization<2,2,2,3>::Add();
+   k::Specialization<2,2,2,4>::Add();
+   k::Specialization<2,2,2,6>::Add();
+   k::Specialization<2,2,3,4>::Add();
+   k::Specialization<2,2,3,6>::Add();
+   k::Specialization<2,2,4,4>::Add();
+   k::Specialization<2,2,4,6>::Add();
+   k::Specialization<2,2,5,6>::Add();
+   // 3D
+   k::Specialization<3,3,2,4>::Add();
+   k::Specialization<3,3,3,3>::Add();
+   k::Specialization<3,3,3,5>::Add();
+   k::Specialization<3,3,3,6>::Add();
 }
 
 } // namespace quadrature_interpolator
 
 } // namespace internal
 
+/// @cond Suppress_Doxygen_warnings
+
+namespace
+{
+using DetKernel = QuadratureInterpolator::DetKernelType;
+}
+
+template<int DIM, int SDIM, int D1D, int Q1D>
+DetKernel QuadratureInterpolator::DetKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D<D1D, Q1D>; }
+   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface<D1D, Q1D>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Det3D<D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+DetKernel QuadratureInterpolator::DetKernels::Fallback(
+   int DIM, int SDIM, int D1D, int Q1D)
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   else if (DIM == 2 && SDIM == 2) { return internal::quadrature_interpolator::Det2D; }
+   else if (DIM == 2 && SDIM == 3) { return internal::quadrature_interpolator::Det2DSurface; }
+   else if (DIM == 3)
+   {
+      const int MD = DeviceDofQuadLimits::Get().MAX_DET_1D;
+      const int MQ = DeviceDofQuadLimits::Get().MAX_DET_1D;
+      if (D1D <= MD && Q1D <= MQ) { return internal::quadrature_interpolator::Det3D<0,0,true>; }
+      else { return internal::quadrature_interpolator::Det3D<0,0,false>; }
+   }
+   else { MFEM_ABORT(""); }
+}
+
+/// @endcond
+
 } // namespace mfem

fem/qinterp/dispatch.hpp

@@ -1,64 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-// Internal header, included only by .cpp files
-
-#include "../quadinterpolator.hpp"
-
-namespace mfem
-{
-
-namespace internal
-{
-
-namespace quadrature_interpolator
-{
-
-// Tensor-product evaluation of quadrature point values: dispatch function.
-template<QVectorLayout VL>
-void TensorValues(const int NE,
-                  const int vdim,
-                  const DofToQuad &maps,
-                  const Vector &e_vec,
-                  Vector &q_val);
-
-// Tensor-product evaluation of quadrature point derivatives: dispatch function.
-template<QVectorLayout VL>
-void TensorDerivatives(const int NE,
-                       const int vdim,
-                       const DofToQuad &maps,
-                       const Vector &e_vec,
-                       Vector &q_der);
-
-// Tensor-product evaluation of quadrature point physical derivatives: dispatch
-// function.
-template<QVectorLayout VL>
-void TensorPhysDerivatives(const int NE,
-                           const int vdim,
-                           const DofToQuad &maps,
-                           const GeometricFactors &geom,
-                           const Vector &e_vec,
-                           Vector &q_der);
-
-// Tensor-product evaluation of quadrature point determinants: dispatch
-// function.
-void TensorDeterminants(const int NE,
-                        const int vdim,
-                        const DofToQuad &maps,
-                        const Vector &e_vec,
-                        Vector &q_det,
-                        Vector &d_buff);
-
-} // namespace quadrature_interpolator
-
-} // namespace internal
-
-} // namespace mfem

fem/qinterp/eval.hpp

@@ -12,6 +12,9 @@
 // Internal header, included only by .cpp files.
 // Template function implementations.
 
+#ifndef MFEM_QUADINTERP_EVAL
+#define MFEM_QUADINTERP_EVAL
+
 #include "../quadinterpolator.hpp"
 #include "../../general/forall.hpp"
 #include "../../linalg/dtensor.hpp"
@@ -63,7 +66,7 @@ static void Values1D(const int NE,
 // Template compute kernel for Values in 2D: tensor product version.
 template<QVectorLayout Q_LAYOUT,
          int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
-         int T_NBZ = 1, int MAX_D1D = 0, int MAX_Q1D = 0>
+         int T_NBZ = 1>
 static void Values2D(const int NE,
                      const real_t *b_,
                      const real_t *x_,
@@ -193,4 +196,21 @@ static void Values3D(const int NE,
 
 } // namespace internal
 
+/// @cond Suppress_Doxygen_warnings
+
+template<int DIM, QVectorLayout Q_LAYOUT,
+         int VDIM, int D1D, int Q1D, int NBZ>
+QuadratureInterpolator::TensorEvalKernelType
+QuadratureInterpolator::TensorEvalKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Values1D<Q_LAYOUT>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::Values2D<Q_LAYOUT, VDIM, D1D, Q1D, NBZ>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Values3D<Q_LAYOUT, VDIM, D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+/// @endcond
+
 } // namespace mfem
+
+#endif

fem/qinterp/eval_by_nodes.cpp

@@ -10,143 +10,75 @@
 // CONTRIBUTING.md for details.
 
 #include "../quadinterpolator.hpp"
-#include "dispatch.hpp"
 #include "eval.hpp"
 
 namespace mfem
 {
-
 namespace internal
 {
-
 namespace quadrature_interpolator
 {
 
-// Tensor-product evaluation of quadrature point values: dispatch function.
-// Instantiation for the case QVectorLayout::byNODES.
-template<>
-void TensorValues<QVectorLayout::byNODES>(const int NE,
-                                          const int vdim,
-                                          const DofToQuad &maps,
-                                          const Vector &e_vec,
-                                          Vector &q_val)
+void InitEvalByNodesKernels()
 {
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const real_t *B = maps.B.Read();
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_val.Write();
+   using k = QuadratureInterpolator::TensorEvalKernels;
 
-   constexpr QVectorLayout L = QVectorLayout::byNODES;
+   // 2D
+   k::Specialization<2,QVectorLayout::byNODES,1,3,3>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,1,2,4>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,1,3,2>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,1,3,4>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,1,4,3>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,1,4,4>::Opt<1>::Add();
 
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
+   k::Specialization<2,QVectorLayout::byNODES,2,2,2>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,2,3>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,2,4>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,2,5>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,2,6>::Opt<1>::Add();
 
-   if (dim == 1)
-   {
-      MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D,
-                  "Orders higher than " << DeviceDofQuadLimits::Get().MAX_D1D-1
-                  << " are not supported!");
-      MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D,
-                  "Quadrature rules with more than "
-                  << DeviceDofQuadLimits::Get().MAX_Q1D << " 1D points are not supported!");
-      Values1D<L>(NE, B, X, Y, vdim, D1D, Q1D);
-      return;
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x133: return Values2D<L,1,3,3>(NE,B,X,Y);
-         case 0x124: return Values2D<L,1,2,4>(NE,B,X,Y);
-         case 0x132: return Values2D<L,1,3,2>(NE,B,X,Y);
-         case 0x134: return Values2D<L,1,3,4>(NE,B,X,Y);
-         case 0x143: return Values2D<L,1,4,3>(NE,B,X,Y);
-         case 0x144: return Values2D<L,1,4,4>(NE,B,X,Y);
+   k::Specialization<2,QVectorLayout::byNODES,2,3,3>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,3,4>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,3,6>::Opt<1>::Add();
 
-         case 0x222: return Values2D<L,2,2,2>(NE,B,X,Y);
-         case 0x223: return Values2D<L,2,2,3>(NE,B,X,Y);
-         case 0x224: return Values2D<L,2,2,4>(NE,B,X,Y);
-         case 0x225: return Values2D<L,2,2,5>(NE,B,X,Y);
-         case 0x226: return Values2D<L,2,2,6>(NE,B,X,Y);
+   k::Specialization<2,QVectorLayout::byNODES,2,4,3>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,4,4>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,4,5>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,4,6>::Opt<1>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,2,4,7>::Opt<1>::Add();
 
-         case 0x233: return Values2D<L,2,3,3>(NE,B,X,Y);
-         case 0x234: return Values2D<L,2,3,4>(NE,B,X,Y);
-         case 0x236: return Values2D<L,2,3,6>(NE,B,X,Y);
+   k::Specialization<2,QVectorLayout::byNODES,2,5,6>::Opt<1>::Add();
 
-         case 0x243: return Values2D<L,2,4,3>(NE,B,X,Y);
-         case 0x244: return Values2D<L,2,4,4>(NE,B,X,Y);
-         case 0x245: return Values2D<L,2,4,5>(NE,B,X,Y);
-         case 0x246: return Values2D<L,2,4,6>(NE,B,X,Y);
-         case 0x247: return Values2D<L,2,4,7>(NE,B,X,Y);
+   // 3D
+   k::Specialization<3,QVectorLayout::byNODES,1,2,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,3,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,3,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,3,6>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,4,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,4,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,1,4,8>::Opt<1>::Add();
 
-         case 0x256: return Values2D<L,2,5,6>(NE,B,X,Y);
+   k::Specialization<3,QVectorLayout::byNODES,2,2,2>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,2,2,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,2,3,4>::Opt<1>::Add();
 
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Values2D<L>(NE,B,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x124: return Values3D<L,1,2,4>(NE,B,X,Y);
-         case 0x133: return Values3D<L,1,3,3>(NE,B,X,Y);
-         case 0x134: return Values3D<L,1,3,4>(NE,B,X,Y);
-         case 0x136: return Values3D<L,1,3,6>(NE,B,X,Y);
-         case 0x143: return Values3D<L,1,4,3>(NE,B,X,Y);
-         case 0x144: return Values3D<L,1,4,4>(NE,B,X,Y);
-         case 0x148: return Values3D<L,1,4,8>(NE,B,X,Y);
+   k::Specialization<3,QVectorLayout::byNODES,3,2,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,2,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,2,5>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,2,6>::Opt<1>::Add();
 
-         case 0x222: return Values3D<L,2,2,2>(NE,B,X,Y);
-         case 0x223: return Values3D<L,2,2,3>(NE,B,X,Y);
-         case 0x234: return Values3D<L,2,3,4>(NE,B,X,Y);
+   k::Specialization<3,QVectorLayout::byNODES,3,3,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,3,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,3,5>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,3,6>::Opt<1>::Add();
 
-         case 0x323: return Values3D<L,3,2,3>(NE,B,X,Y);
-         case 0x324: return Values3D<L,3,2,4>(NE,B,X,Y);
-         case 0x325: return Values3D<L,3,2,5>(NE,B,X,Y);
-         case 0x326: return Values3D<L,3,2,6>(NE,B,X,Y);
-
-         case 0x333: return Values3D<L,3,3,3>(NE,B,X,Y);
-         case 0x334: return Values3D<L,3,3,4>(NE,B,X,Y);
-         case 0x335: return Values3D<L,3,3,5>(NE,B,X,Y);
-         case 0x336: return Values3D<L,3,3,6>(NE,B,X,Y);
-
-         case 0x343: return Values3D<L,3,4,3>(NE,B,X,Y);
-         case 0x344: return Values3D<L,3,4,4>(NE,B,X,Y);
-         case 0x346: return Values3D<L,3,4,6>(NE,B,X,Y);
-         case 0x347: return Values3D<L,3,4,7>(NE,B,X,Y);
-         case 0x348: return Values3D<L,3,4,8>(NE,B,X,Y);
-
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Values3D<L>(NE,B,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
+   k::Specialization<3,QVectorLayout::byNODES,3,4,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,4,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,4,6>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,4,7>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,3,4,8>::Opt<1>::Add();
 }
 
 } // namespace quadrature_interpolator
-
 } // namespace internal
-
 } // namespace mfem

fem/qinterp/eval_by_vdim.cpp

@@ -10,117 +10,45 @@
 // CONTRIBUTING.md for details.
 
 #include "../quadinterpolator.hpp"
-#include "dispatch.hpp"
 #include "eval.hpp"
 
 namespace mfem
 {
-
 namespace internal
 {
-
 namespace quadrature_interpolator
 {
 
-// Tensor-product evaluation of quadrature point values: dispatch function.
-// Instantiation for the case QVectorLayout::byVDIM.
-template<>
-void TensorValues<QVectorLayout::byVDIM>(const int NE,
-                                         const int vdim,
-                                         const DofToQuad &maps,
-                                         const Vector &e_vec,
-                                         Vector &q_val)
+void InitEvalByVDimKernels()
 {
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const real_t *B = maps.B.Read();
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_val.Write();
+   using k = QuadratureInterpolator::TensorEvalKernels;
+   // 2D
+   k::Specialization<2,QVectorLayout::byVDIM,1,2,4>::Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,1,3,6>::Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,1,4,8>::Opt<2>::Add();
 
-   constexpr QVectorLayout L = QVectorLayout::byVDIM;
+   k::Specialization<2,QVectorLayout::byVDIM,2,2,4>::Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,2,3,4>::Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,2,3,6>::Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,2,4,8>::Opt<2>::Add();
+   // 3D
+   k::Specialization<3,QVectorLayout::byVDIM,1,2,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,1,3,6>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,1,4,8>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,2,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,3,6>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,4,8>::Opt<1>::Add();
 
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
-
-   if (dim == 1)
-   {
-      MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D,
-                  "Orders higher than " << DeviceDofQuadLimits::Get().MAX_D1D-1
-                  << " are not supported!");
-      MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D,
-                  "Quadrature rules with more than "
-                  << DeviceDofQuadLimits::Get().MAX_Q1D << " 1D points are not supported!");
-      Values1D<L>(NE, B, X, Y, vdim, D1D, Q1D);
-      return;
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x124: return Values2D<L,1,2,4,8>(NE,B,X,Y);
-         case 0x136: return Values2D<L,1,3,6,4>(NE,B,X,Y);
-         case 0x148: return Values2D<L,1,4,8,2>(NE,B,X,Y);
-
-         case 0x224: return Values2D<L,2,2,4,8>(NE,B,X,Y);
-         case 0x234: return Values2D<L,2,3,4,8>(NE,B,X,Y);
-         case 0x236: return Values2D<L,2,3,6,4>(NE,B,X,Y);
-         case 0x248: return Values2D<L,2,4,8,2>(NE,B,X,Y);
-
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Values2D<L>(NE,B,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x124: return Values3D<L,1,2,4>(NE,B,X,Y);
-         case 0x136: return Values3D<L,1,3,6>(NE,B,X,Y);
-         case 0x148: return Values3D<L,1,4,8>(NE,B,X,Y);
-
-         case 0x324: return Values3D<L,3,2,4>(NE,B,X,Y);
-         case 0x336: return Values3D<L,3,3,6>(NE,B,X,Y);
-         case 0x348: return Values3D<L,3,4,8>(NE,B,X,Y);
-
-         // Used for LOR batched assembly
-         case 0x322: return Values3D<L,3,2,2>(NE,B,X,Y);
-         case 0x333: return Values3D<L,3,3,3>(NE,B,X,Y);
-         case 0x344: return Values3D<L,3,4,4>(NE,B,X,Y);
-         case 0x355: return Values3D<L,3,5,5>(NE,B,X,Y);
-         case 0x366: return Values3D<L,3,6,6>(NE,B,X,Y);
-         case 0x377: return Values3D<L,3,7,7>(NE,B,X,Y);
-         case 0x388: return Values3D<L,3,8,8>(NE,B,X,Y);
-         case 0x399: return Values3D<L,3,9,9>(NE,B,X,Y);
-
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Values3D<L>(NE,B,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
+   k::Specialization<3,QVectorLayout::byVDIM,3,2,2>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,3,3>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,4,4>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,5,5>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,6,6>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,7,7>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,8,8>::Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,3,9,9>::Opt<1>::Add();
 }
 
 } // namespace quadrature_interpolator
-
 } // namespace internal
-
 } // namespace mfem

fem/qinterp/grad.hpp

@@ -12,6 +12,9 @@
 // Internal header, included only by .cpp files.
 // Template function implementations.
 
+#ifndef MFEM_QUADINTERP_GRAD
+#define MFEM_QUADINTERP_GRAD
+
 #include "../quadinterpolator.hpp"
 #include "../../general/forall.hpp"
 #include "../../linalg/dtensor.hpp"
@@ -29,6 +32,7 @@ namespace quadrature_interpolator
 
 template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS>
 static void Derivatives1D(const int NE,
+                          const real_t *b_,
                           const real_t *g_,
                           const real_t *j_,
                           const real_t *x_,
@@ -38,6 +42,7 @@ static void Derivatives1D(const int NE,
                           const int d1d,
                           const int q1d)
 {
+   MFEM_CONTRACT_VAR(b_);
    const auto g = Reshape(g_, q1d, d1d);
    const auto j = Reshape(j_, q1d, sdim, NE);
    const auto x = Reshape(x_, d1d, vdim, NE);
@@ -232,6 +237,7 @@ static void Derivatives3D(const int NE,
                           const real_t *j_,
                           const real_t *x_,
                           real_t *y_,
+                          const int sdim = 3,
                           const int vdim = 0,
                           const int d1d = 0,
                           const int q1d = 0)
@@ -370,4 +376,21 @@ static void Derivatives3D(const int NE,
 
 } // namespace internal
 
+/// @cond Suppress_Doxygen_warnings
+
+template<int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS,
+         int VDIM, int D1D, int Q1D, int NBZ>
+QuadratureInterpolator::GradKernelType
+QuadratureInterpolator::GradKernels::Kernel()
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Derivatives1D<Q_LAYOUT, GRAD_PHYS>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::Derivatives2D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D, NBZ>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Derivatives3D<Q_LAYOUT, GRAD_PHYS, VDIM, D1D, Q1D>; }
+   else { MFEM_ABORT(""); }
+}
+
+/// @endcond
+
 } // namespace mfem
+
+#endif

fem/qinterp/grad_by_nodes.cpp

@@ -9,128 +9,69 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "dispatch.hpp"
+#include "../quadinterpolator.hpp"
 #include "grad.hpp"
 
 namespace mfem
 {
-
 namespace internal
 {
-
 namespace quadrature_interpolator
 {
 
-// Tensor-product evaluation of quadrature point derivatives: dispatch function.
-// Instantiation for the case QVectorLayout::byNODES.
-template<>
-void TensorDerivatives<QVectorLayout::byNODES>(const int NE,
-                                               const int vdim,
-                                               const DofToQuad &maps,
-                                               const Vector &e_vec,
-                                               Vector &q_der)
+template <bool P>
+void InitGradByNodesKernels()
 {
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const real_t *B = maps.B.Read();
-   const real_t *G = maps.G.Read();
-   const real_t *J = nullptr; // not used in DERIVATIVES (non-GRAD_PHYS) mode
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_der.Write();
+   using k = QuadratureInterpolator::GradKernels;
+   // 2D
+   k::Specialization<2,QVectorLayout::byNODES,P,1,3,3>::template Opt<16>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,1,3,4>::template Opt<16>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,1,4,3>::template Opt<16>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,1,4,4>::template Opt<16>::Add();
 
-   constexpr QVectorLayout L = QVectorLayout::byNODES;
-   constexpr bool P = false; // GRAD_PHYS
+   k::Specialization<2,QVectorLayout::byNODES,P,2,2,2>::template Opt<16>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,2,3>::template Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,2,4>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,2,5>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,2,6>::template Opt<2>::Add();
 
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
+   k::Specialization<2,QVectorLayout::byNODES,P,2,3,3>::template Opt<2>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,3,4>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,4,3>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,3,6>::template Opt<2>::Add();
 
-   if (dim == 1)
-   {
-      return Derivatives1D<L,P>(NE,G,J,X,Y,dim,vdim,D1D,Q1D);
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x133: return Derivatives2D<L,P,1,3,3,16>(NE,B,G,J,X,Y);
-         case 0x134: return Derivatives2D<L,P,1,3,4,16>(NE,B,G,J,X,Y);
-         case 0x143: return Derivatives2D<L,P,1,4,3,16>(NE,B,G,J,X,Y);
-         case 0x144: return Derivatives2D<L,P,1,4,4,16>(NE,B,G,J,X,Y);
+   k::Specialization<2,QVectorLayout::byNODES,P,2,4,4>::template Opt<2>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,4,5>::template Opt<2>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,4,6>::template Opt<2>::Add();
+   k::Specialization<2,QVectorLayout::byNODES,P,2,4,7>::template Opt<2>::Add();
 
-         case 0x222: return Derivatives2D<L,P,2,2,2,16>(NE,B,G,J,X,Y);
-         case 0x223: return Derivatives2D<L,P,2,2,3,8>(NE,B,G,J,X,Y);
-         case 0x224: return Derivatives2D<L,P,2,2,4,4>(NE,B,G,J,X,Y);
-         case 0x225: return Derivatives2D<L,P,2,2,5,4>(NE,B,G,J,X,Y);
-         case 0x226: return Derivatives2D<L,P,2,2,6,2>(NE,B,G,J,X,Y);
+   k::Specialization<2,QVectorLayout::byNODES,P,2,5,6>::template Opt<2>::Add();
+   // 3D
+   k::Specialization<3,QVectorLayout::byNODES,P,1,2,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,1,3,3>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,1,3,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,1,3,6>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,1,4,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,1,4,8>::template Opt<1>::Add();
 
-         case 0x233: return Derivatives2D<L,P,2,3,3,2>(NE,B,G,J,X,Y);
-         case 0x234: return Derivatives2D<L,P,2,3,4,4>(NE,B,G,J,X,Y);
-         case 0x243: return Derivatives2D<L,P,2,4,3,4>(NE,B,G,J,X,Y);
-         case 0x236: return Derivatives2D<L,P,2,3,6,2>(NE,B,G,J,X,Y);
+   k::Specialization<3,QVectorLayout::byNODES,P,3,2,3>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,2,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,2,5>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,2,6>::template Opt<1>::Add();
 
-         case 0x244: return Derivatives2D<L,P,2,4,4,2>(NE,B,G,J,X,Y);
-         case 0x245: return Derivatives2D<L,P,2,4,5,2>(NE,B,G,J,X,Y);
-         case 0x246: return Derivatives2D<L,P,2,4,6,2>(NE,B,G,J,X,Y);
-         case 0x247: return Derivatives2D<L,P,2,4,7,2>(NE,B,G,J,X,Y);
-
-         case 0x256: return Derivatives2D<L,P,2,5,6,2>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            if (D1D > MD || Q1D > MQ)
-            {
-               MFEM_ABORT("");
-            }
-            Derivatives2D<L,P>(NE,B,G,J,X,Y,dim,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x124: return Derivatives3D<L,P,1,2,4>(NE,B,G,J,X,Y);
-         case 0x133: return Derivatives3D<L,P,1,3,3>(NE,B,G,J,X,Y);
-         case 0x134: return Derivatives3D<L,P,1,3,4>(NE,B,G,J,X,Y);
-         case 0x136: return Derivatives3D<L,P,1,3,6>(NE,B,G,J,X,Y);
-         case 0x144: return Derivatives3D<L,P,1,4,4>(NE,B,G,J,X,Y);
-         case 0x148: return Derivatives3D<L,P,1,4,8>(NE,B,G,J,X,Y);
-
-         case 0x323: return Derivatives3D<L,P,3,2,3>(NE,B,G,J,X,Y);
-         case 0x324: return Derivatives3D<L,P,3,2,4>(NE,B,G,J,X,Y);
-         case 0x325: return Derivatives3D<L,P,3,2,5>(NE,B,G,J,X,Y);
-         case 0x326: return Derivatives3D<L,P,3,2,6>(NE,B,G,J,X,Y);
-
-         case 0x333: return Derivatives3D<L,P,3,3,3>(NE,B,G,J,X,Y);
-         case 0x334: return Derivatives3D<L,P,3,3,4>(NE,B,G,J,X,Y);
-         case 0x335: return Derivatives3D<L,P,3,3,5>(NE,B,G,J,X,Y);
-         case 0x336: return Derivatives3D<L,P,3,3,6>(NE,B,G,J,X,Y);
-         case 0x344: return Derivatives3D<L,P,3,4,4>(NE,B,G,J,X,Y);
-         case 0x346: return Derivatives3D<L,P,3,4,6>(NE,B,G,J,X,Y);
-         case 0x347: return Derivatives3D<L,P,3,4,7>(NE,B,G,J,X,Y);
-         case 0x348: return Derivatives3D<L,P,3,4,8>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives3D<L,P>(NE,B,G,J,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
+   k::Specialization<3,QVectorLayout::byNODES,P,3,3,3>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,3,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,3,5>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,3,6>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,4,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,4,6>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,4,7>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byNODES,P,3,4,8>::template Opt<1>::Add();
 }
 
+template void InitGradByNodesKernels<true>();
+template void InitGradByNodesKernels<false>();
+
 } // namespace quadrature_interpolator
-
 } // namespace internal
-
 } // namespace mfem

fem/qinterp/grad_by_vdim.cpp

@@ -9,100 +9,41 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "dispatch.hpp"
+#include "../quadinterpolator.hpp"
 #include "grad.hpp"
 
 namespace mfem
 {
-
 namespace internal
 {
-
 namespace quadrature_interpolator
 {
 
-// Tensor-product evaluation of quadrature point derivatives: dispatch function.
-// Instantiation for the case QVectorLayout::byVDIM.
-template<>
-void TensorDerivatives<QVectorLayout::byVDIM>(const int NE,
-                                              const int vdim,
-                                              const DofToQuad &maps,
-                                              const Vector &e_vec,
-                                              Vector &q_der)
+template <bool P>
+void InitGradByVDimKernels()
 {
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const real_t *B = maps.B.Read();
-   const real_t *G = maps.G.Read();
-   const real_t *J = nullptr; // not used in DERIVATIVES (non-GRAD_PHYS) mode
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_der.Write();
+   using k = QuadratureInterpolator::GradKernels;
+   // 2D
+   k::Specialization<2,QVectorLayout::byVDIM,P,1,3,4>::template Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,P,1,4,6>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,P,1,5,8>::template Opt<2>::Add();
 
-   constexpr QVectorLayout L = QVectorLayout::byVDIM;
-   constexpr bool P = false; // GRAD_PHYS
-
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
-
-   if (dim == 1)
-   {
-      return Derivatives1D<L,P>(NE,G,J,X,Y,dim,vdim,D1D,Q1D);
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x134: return Derivatives2D<L,P,1,3,4,8>(NE,B,G,J,X,Y);
-         case 0x146: return Derivatives2D<L,P,1,4,6,4>(NE,B,G,J,X,Y);
-         case 0x158: return Derivatives2D<L,P,1,5,8,2>(NE,B,G,J,X,Y);
-
-         case 0x234: return Derivatives2D<L,P,2,3,4,8>(NE,B,G,J,X,Y);
-         case 0x246: return Derivatives2D<L,P,2,4,6,4>(NE,B,G,J,X,Y);
-         case 0x258: return Derivatives2D<L,P,2,5,8,2>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives2D<L,P>(NE,B,G,J,X,Y,dim,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x134: return Derivatives3D<L,P,1,3,4>(NE,B,G,J,X,Y);
-         case 0x146: return Derivatives3D<L,P,1,4,6>(NE,B,G,J,X,Y);
-         case 0x158: return Derivatives3D<L,P,1,5,8>(NE,B,G,J,X,Y);
-
-         case 0x334: return Derivatives3D<L,P,3,3,4>(NE,B,G,J,X,Y);
-         case 0x346: return Derivatives3D<L,P,3,4,6>(NE,B,G,J,X,Y);
-         case 0x358: return Derivatives3D<L,P,3,5,8>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives3D<L,P>(NE,B,G,J,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
+   k::Specialization<2,QVectorLayout::byVDIM,P,2,3,3>::template Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,P,2,3,4>::template Opt<8>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,P,2,4,6>::template Opt<4>::Add();
+   k::Specialization<2,QVectorLayout::byVDIM,P,2,5,8>::template Opt<2>::Add();
+   // 3D
+   k::Specialization<3,QVectorLayout::byVDIM,P,1,3,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,P,1,4,6>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,P,1,5,8>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,P,3,3,4>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,P,3,4,6>::template Opt<1>::Add();
+   k::Specialization<3,QVectorLayout::byVDIM,P,3,5,8>::template Opt<1>::Add();
 }
 
+template void InitGradByVDimKernels<true>();
+template void InitGradByVDimKernels<false>();
+
 } // namespace quadrature_interpolator
-
 } // namespace internal
-
 } // namespace mfem

fem/qinterp/grad_phys_by_nodes.cpp

@@ -1,123 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "dispatch.hpp"
-#include "grad.hpp"
-
-namespace mfem
-{
-
-namespace internal
-{
-
-namespace quadrature_interpolator
-{
-
-// Tensor-product evaluation of quadrature point physical derivatives: dispatch
-// function.
-// Instantiation for the case QVectorLayout::byNODES.
-template<>
-void TensorPhysDerivatives<QVectorLayout::byNODES>(const int NE,
-                                                   const int vdim,
-                                                   const DofToQuad &maps,
-                                                   const GeometricFactors &geom,
-                                                   const Vector &e_vec,
-                                                   Vector &q_der)
-{
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-
-   const int sdim = geom.mesh->SpaceDimension();
-
-   const real_t *B = maps.B.Read();
-   const real_t *G = maps.G.Read();
-   const real_t *J = geom.J.Read();
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_der.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byNODES;
-   constexpr bool P = true; // GRAD_PHYS
-
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
-
-   if (dim == 1)
-   {
-      return Derivatives1D<L,P>(NE,G,J,X,Y,sdim,vdim,D1D,Q1D);
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x133: return Derivatives2D<L,P,1,3,3,8>(NE,B,G,J,X,Y,sdim);
-         case 0x134: return Derivatives2D<L,P,1,3,4,8>(NE,B,G,J,X,Y,sdim);
-         case 0x143: return Derivatives2D<L,P,1,4,3,4>(NE,B,G,J,X,Y,sdim);
-         case 0x144: return Derivatives2D<L,P,1,4,4,4>(NE,B,G,J,X,Y,sdim);
-         case 0x146: return Derivatives2D<L,P,1,4,6,4>(NE,B,G,J,X,Y,sdim);
-         case 0x158: return Derivatives2D<L,P,1,5,8,2>(NE,B,G,J,X,Y,sdim);
-
-         case 0x233: return Derivatives2D<L,P,2,3,3,8>(NE,B,G,J,X,Y,sdim);
-         case 0x234: return Derivatives2D<L,P,2,3,4,8>(NE,B,G,J,X,Y,sdim);
-         case 0x243: return Derivatives2D<L,P,2,4,3,4>(NE,B,G,J,X,Y,sdim);
-         case 0x244: return Derivatives2D<L,P,2,4,4,4>(NE,B,G,J,X,Y,sdim);
-         case 0x246: return Derivatives2D<L,P,2,4,6,4>(NE,B,G,J,X,Y,sdim);
-         case 0x258: return Derivatives2D<L,P,2,5,8,2>(NE,B,G,J,X,Y,sdim);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives2D<L,P>(NE,B,G,J,X,Y,sdim,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x133: return Derivatives3D<L,P,1,3,3>(NE,B,G,J,X,Y);
-         case 0x134: return Derivatives3D<L,P,1,3,4>(NE,B,G,J,X,Y);
-         case 0x144: return Derivatives3D<L,P,1,4,4>(NE,B,G,J,X,Y);
-         case 0x146: return Derivatives3D<L,P,1,4,6>(NE,B,G,J,X,Y);
-         case 0x158: return Derivatives3D<L,P,1,5,8>(NE,B,G,J,X,Y);
-
-         case 0x333: return Derivatives3D<L,P,3,3,3>(NE,B,G,J,X,Y);
-         case 0x334: return Derivatives3D<L,P,3,3,4>(NE,B,G,J,X,Y);
-         case 0x344: return Derivatives3D<L,P,3,4,4>(NE,B,G,J,X,Y);
-         case 0x346: return Derivatives3D<L,P,3,4,6>(NE,B,G,J,X,Y);
-         case 0x358: return Derivatives3D<L,P,3,5,8>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives3D<L,P>(NE,B,G,J,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Unknown kernel");
-}
-
-} // namespace quadrature_interpolator
-
-} // namespace internal
-
-} // namespace mfem

fem/qinterp/grad_phys_by_vdim.cpp

@@ -1,114 +0,0 @@
-// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "dispatch.hpp"
-#include "grad.hpp"
-
-namespace mfem
-{
-
-namespace internal
-{
-
-namespace quadrature_interpolator
-{
-
-// Tensor-product evaluation of quadrature point physical derivatives: dispatch
-// function.
-// Instantiation for the case QVectorLayout::byVDIM.
-template<>
-void TensorPhysDerivatives<QVectorLayout::byVDIM>(const int NE,
-                                                  const int vdim,
-                                                  const DofToQuad &maps,
-                                                  const GeometricFactors &geom,
-                                                  const Vector &e_vec,
-                                                  Vector &q_der)
-{
-   if (NE == 0) { return; }
-   const int dim = maps.FE->GetDim();
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-
-   const int sdim = geom.mesh->SpaceDimension();
-
-   const real_t *B = maps.B.Read();
-   const real_t *G = maps.G.Read();
-   const real_t *J = geom.J.Read();
-   const real_t *X = e_vec.Read();
-   real_t *Y = q_der.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byVDIM;
-   constexpr bool P = true; // GRAD_PHYS
-
-   const int id = (vdim<<8) | (D1D<<4) | Q1D;
-
-   if (dim == 1)
-   {
-      return Derivatives1D<L,P>(NE,G,J,X,Y,sdim,vdim,D1D,Q1D);
-   }
-   if (dim == 2)
-   {
-      switch (id)
-      {
-         case 0x134: return Derivatives2D<L,P,1,3,4,8>(NE,B,G,J,X,Y,sdim);
-         case 0x146: return Derivatives2D<L,P,1,4,6,4>(NE,B,G,J,X,Y,sdim);
-         case 0x158: return Derivatives2D<L,P,1,5,8,2>(NE,B,G,J,X,Y,sdim);
-
-         case 0x233: return Derivatives2D<L,P,2,3,3,8>(NE,B,G,J,X,Y,sdim);
-         case 0x234: return Derivatives2D<L,P,2,3,4,8>(NE,B,G,J,X,Y,sdim);
-         case 0x246: return Derivatives2D<L,P,2,4,6,4>(NE,B,G,J,X,Y,sdim);
-         case 0x258: return Derivatives2D<L,P,2,5,8,2>(NE,B,G,J,X,Y,sdim);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_D1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_Q1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives2D<L,P>(NE,B,G,J,X,Y,sdim,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   if (dim == 3)
-   {
-      switch (id)
-      {
-         case 0x134: return Derivatives3D<L,P,1,3,4>(NE,B,G,J,X,Y);
-         case 0x146: return Derivatives3D<L,P,1,4,6>(NE,B,G,J,X,Y);
-         case 0x158: return Derivatives3D<L,P,1,5,8>(NE,B,G,J,X,Y);
-
-         case 0x334: return Derivatives3D<L,P,3,3,4>(NE,B,G,J,X,Y);
-         case 0x346: return Derivatives3D<L,P,3,4,6>(NE,B,G,J,X,Y);
-         case 0x358: return Derivatives3D<L,P,3,5,8>(NE,B,G,J,X,Y);
-         default:
-         {
-            const int MD = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            const int MQ = DeviceDofQuadLimits::Get().MAX_INTERP_1D;
-            MFEM_VERIFY(D1D <= MD, "Orders higher than " << MD-1
-                        << " are not supported!");
-            MFEM_VERIFY(Q1D <= MQ, "Quadrature rules with more than "
-                        << MQ << " 1D points are not supported!");
-            Derivatives3D<L,P>(NE,B,G,J,X,Y,vdim,D1D,Q1D);
-            return;
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Unknown kernel");
-}
-
-} // namespace quadrature_interpolator
-
-} // namespace internal
-
-} // namespace mfem

fem/quadinterpolator.cpp

@@ -10,7 +10,8 @@
 // CONTRIBUTING.md for details.
 
 #include "quadinterpolator.hpp"
-#include "qinterp/dispatch.hpp"
+#include "qinterp/grad.hpp"
+#include "qinterp/eval.hpp"
 #include "qspace.hpp"
 #include "../general/forall.hpp"
 #include "../linalg/dtensor.hpp"
@@ -19,6 +20,38 @@
 namespace mfem
 {
 
+namespace internal
+{
+namespace quadrature_interpolator
+{
+void InitEvalByNodesKernels();
+void InitEvalByVDimKernels();
+void InitEvalKernels();
+void InitDetKernels();
+template <bool P> void InitGradByNodesKernels();
+template <bool P> void InitGradByVDimKernels();
+}
+}
+
+QuadratureInterpolator::Kernels QuadratureInterpolator::kernels;
+QuadratureInterpolator::Kernels::Kernels()
+{
+   using namespace internal::quadrature_interpolator;
+
+   InitEvalByNodesKernels();
+   InitEvalByVDimKernels();
+   // Non-phys grad kernels
+   InitGradByNodesKernels<false>();
+   InitGradByVDimKernels<false>();
+   // Phys grad kernels
+   InitGradByNodesKernels<true>();
+   InitGradByVDimKernels<true>();
+   // Determinants
+   InitDetKernels();
+   // Non-tensor
+   InitEvalKernels();
+}
+
 QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
                                                const IntegrationRule &ir):
 
@@ -467,6 +500,7 @@ void QuadratureInterpolator::Mult(const Vector &e_vec,
    const int ne = fespace->GetNE();
    if (ne == 0) { return; }
    const int vdim = fespace->GetVDim();
+   const int sdim = fespace->GetMesh()->SpaceDimension();
    const FiniteElement *fe = fespace->GetFE(0);
    const bool use_tensor_eval =
       use_tensor_products &&
@@ -477,6 +511,8 @@ void QuadratureInterpolator::Mult(const Vector &e_vec,
       use_tensor_eval ? DofToQuad::TENSOR : DofToQuad::FULL;
    const DofToQuad &maps = fe->GetDofToQuad(*ir, mode);
    const int dim = maps.FE->GetDim();
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
    const GeometricFactors *geom = nullptr;
    if (eval_flags & PHYSICAL_DERIVATIVES)
    {
@@ -492,202 +528,31 @@ void QuadratureInterpolator::Mult(const Vector &e_vec,
 
    if (use_tensor_eval)
    {
-      // TODO: use fused kernels
-      if (q_layout == QVectorLayout::byNODES)
+      if (eval_flags & VALUES)
       {
-         if (eval_flags & VALUES)
-         {
-            TensorValues<QVectorLayout::byNODES>(ne, vdim, maps, e_vec, q_val);
-         }
-         if (eval_flags & DERIVATIVES)
-         {
-            TensorDerivatives<QVectorLayout::byNODES>(
-               ne, vdim, maps, e_vec, q_der);
-         }
-         if (eval_flags & PHYSICAL_DERIVATIVES)
-         {
-            TensorPhysDerivatives<QVectorLayout::byNODES>(
-               ne, vdim, maps, *geom, e_vec, q_der);
-         }
+         TensorEvalKernels::Run(dim, q_layout, vdim, nd, nq, ne, maps.B.Read(),
+                                e_vec.Read(), q_val.Write(), vdim, nd, nq);
       }
-
-      if (q_layout == QVectorLayout::byVDIM)
+      if (eval_flags & (DERIVATIVES | PHYSICAL_DERIVATIVES))
       {
-         if (eval_flags & VALUES)
-         {
-            TensorValues<QVectorLayout::byVDIM>(ne, vdim, maps, e_vec, q_val);
-         }
-         if (eval_flags & DERIVATIVES)
-         {
-            TensorDerivatives<QVectorLayout::byVDIM>(
-               ne, vdim, maps, e_vec, q_der);
-         }
-         if (eval_flags & PHYSICAL_DERIVATIVES)
-         {
-            TensorPhysDerivatives<QVectorLayout::byVDIM>(
-               ne, vdim, maps, *geom, e_vec, q_der);
-         }
+         const bool phys = (eval_flags & PHYSICAL_DERIVATIVES);
+         const real_t *J = phys ? geom->J.Read() : nullptr;
+         const int s_dim = phys ? sdim : dim;
+         GradKernels::Run(dim, q_layout, phys, vdim, nd, nq, ne,
+                          maps.B.Read(), maps.G.Read(), J, e_vec.Read(),
+                          q_der.Write(), s_dim, vdim, nd, nq);
       }
       if (eval_flags & DETERMINANTS)
       {
-         TensorDeterminants(ne, vdim, maps, e_vec, q_det, d_buffer);
+         DetKernels::Run(dim, vdim, nd, nq, ne, maps.B.Read(),
+                         maps.G.Read(), e_vec.Read(), q_det.Write(), nd,
+                         nq, &d_buffer);
       }
    }
    else // use_tensor_eval == false
    {
-      const int nd = maps.ndof;
-      const int nq = maps.nqpt;
-
-      void (*mult)(const int NE,
-                   const int vdim,
-                   const QVectorLayout q_layout,
-                   const GeometricFactors *geom,
-                   const DofToQuad &maps,
-                   const Vector &e_vec,
-                   Vector &q_val,
-                   Vector &q_der,
-                   Vector &q_det,
-                   const int eval_flags) = NULL;
-
-      if (dim == 1)
-      {
-         mult = &Eval1D;
-      }
-      else if (vdim == 1) // dim == 2 || dim == 3
-      {
-         if (dim == 2)
-         {
-            switch (100*nd + nq)
-            {
-               // Q0
-               case 101: mult = &Eval2D<1,1,1>; break;
-               case 104: mult = &Eval2D<1,1,4>; break;
-               // Q1
-               case 404: mult = &Eval2D<1,4,4>; break;
-               case 409: mult = &Eval2D<1,4,9>; break;
-               // Q2
-               case 909: mult = &Eval2D<1,9,9>; break;
-               case 916: mult = &Eval2D<1,9,16>; break;
-               // Q3
-               case 1616: mult = &Eval2D<1,16,16>; break;
-               case 1625: mult = &Eval2D<1,16,25>; break;
-               case 1636: mult = &Eval2D<1,16,36>; break;
-               // Q4
-               case 2525: mult = &Eval2D<1,25,25>; break;
-               case 2536: mult = &Eval2D<1,25,36>; break;
-               case 2549: mult = &Eval2D<1,25,49>; break;
-               case 2564: mult = &Eval2D<1,25,64>; break;
-            }
-            if (nq >= 100 || !mult)
-            {
-               mult = &Eval2D<1,0,0>;
-            }
-         }
-         else if (dim == 3)
-         {
-            switch (1000*nd + nq)
-            {
-               // Q0
-               case 1001: mult = &Eval3D<1,1,1>; break;
-               case 1008: mult = &Eval3D<1,1,8>; break;
-               // Q1
-               case 8008: mult = &Eval3D<1,8,8>; break;
-               case 8027: mult = &Eval3D<1,8,27>; break;
-               // Q2
-               case 27027: mult = &Eval3D<1,27,27>; break;
-               case 27064: mult = &Eval3D<1,27,64>; break;
-               // Q3
-               case 64064: mult = &Eval3D<1,64,64>; break;
-               case 64125: mult = &Eval3D<1,64,125>; break;
-               case 64216: mult = &Eval3D<1,64,216>; break;
-               // Q4
-               case 125125: mult = &Eval3D<1,125,125>; break;
-               case 125216: mult = &Eval3D<1,125,216>; break;
-            }
-            if (nq >= 1000 || !mult)
-            {
-               mult = &Eval3D<1,0,0>;
-            }
-         }
-      }
-      else if (vdim == 3 && dim == 2)
-      {
-         switch (100*nd + nq)
-         {
-            // Q0
-            case 101: mult = &Eval2D<3,1,1>; break;
-            case 104: mult = &Eval2D<3,1,4>; break;
-            // Q1
-            case 404: mult = &Eval2D<3,4,4>; break;
-            case 409: mult = &Eval2D<3,4,9>; break;
-            // Q2
-            case 904: mult = &Eval2D<3,9,4>; break;
-            case 909: mult = &Eval2D<3,9,9>; break;
-            case 916: mult = &Eval2D<3,9,16>; break;
-            case 925: mult = &Eval2D<3,9,25>; break;
-            // Q3
-            case 1616: mult = &Eval2D<3,16,16>; break;
-            case 1625: mult = &Eval2D<3,16,25>; break;
-            case 1636: mult = &Eval2D<3,16,36>; break;
-            // Q4
-            case 2525: mult = &Eval2D<3,25,25>; break;
-            case 2536: mult = &Eval2D<3,25,36>; break;
-            case 2549: mult = &Eval2D<3,25,49>; break;
-            case 2564: mult = &Eval2D<3,25,64>; break;
-            default:   mult = &Eval2D<3,0,0>;
-         }
-      }
-      else if (vdim == dim)
-      {
-         if (dim == 2)
-         {
-            switch (100*nd + nq)
-            {
-               // Q1
-               case 404: mult = &Eval2D<2,4,4>; break;
-               case 409: mult = &Eval2D<2,4,9>; break;
-               // Q2
-               case 909: mult = &Eval2D<2,9,9>; break;
-               case 916: mult = &Eval2D<2,9,16>; break;
-               // Q3
-               case 1616: mult = &Eval2D<2,16,16>; break;
-               case 1625: mult = &Eval2D<2,16,25>; break;
-               case 1636: mult = &Eval2D<2,16,36>; break;
-               // Q4
-               case 2525: mult = &Eval2D<2,25,25>; break;
-               case 2536: mult = &Eval2D<2,25,36>; break;
-               case 2549: mult = &Eval2D<2,25,49>; break;
-               case 2564: mult = &Eval2D<2,25,64>; break;
-            }
-            if (nq >= 100 || !mult) { mult = &Eval2D<2,0,0>; }
-         }
-         else if (dim == 3)
-         {
-            switch (1000*nd + nq)
-            {
-               // Q1
-               case 8008: mult = &Eval3D<3,8,8>; break;
-               case 8027: mult = &Eval3D<3,8,27>; break;
-               // Q2
-               case 27027: mult = &Eval3D<3,27,27>; break;
-               case 27064: mult = &Eval3D<3,27,64>; break;
-               case 27125: mult = &Eval3D<3,27,125>; break;
-               // Q3
-               case 64064: mult = &Eval3D<3,64,64>; break;
-               case 64125: mult = &Eval3D<3,64,125>; break;
-               case 64216: mult = &Eval3D<3,64,216>; break;
-               // Q4
-               case 125125: mult = &Eval3D<3,125,125>; break;
-               case 125216: mult = &Eval3D<3,125,216>; break;
-            }
-            if (nq >= 1000 || !mult) {  mult = &Eval3D<3,0,0>; }
-         }
-      }
-      if (mult)
-      {
-         mult(ne,vdim,q_layout,geom,maps,e_vec,q_val,q_der,q_det,eval_flags);
-      }
-      else { MFEM_ABORT("case not supported yet"); }
+      EvalKernels::Run(dim, vdim, maps.ndof, maps.nqpt, ne,vdim,q_layout,
+                       geom, maps,e_vec, q_val,q_der,q_det,eval_flags);
    }
 }
 
@@ -731,4 +596,186 @@ void QuadratureInterpolator::Determinants(const Vector &e_vec,
    Mult(e_vec, DETERMINANTS, empty, empty, q_det);
 }
 
+/// @cond Suppress_Doxygen_warnings
+
+namespace
+{
+using EvalKernel = QuadratureInterpolator::EvalKernelType;
+using TensorEvalKernel = QuadratureInterpolator::TensorEvalKernelType;
+using GradKernel = QuadratureInterpolator::GradKernelType;
+
+template <QVectorLayout Q_LAYOUT>
+TensorEvalKernel FallbackTensorEvalKernel(int DIM)
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Values1D<Q_LAYOUT>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::Values2D<Q_LAYOUT>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Values3D<Q_LAYOUT>; }
+   else { MFEM_ABORT(""); }
+}
+
+template<QVectorLayout Q_LAYOUT, bool GRAD_PHYS>
+GradKernel GetGradKernel(int DIM)
+{
+   if (DIM == 1) { return internal::quadrature_interpolator::Derivatives1D<Q_LAYOUT, GRAD_PHYS>; }
+   else if (DIM == 2) { return internal::quadrature_interpolator::Derivatives2D<Q_LAYOUT, GRAD_PHYS>; }
+   else if (DIM == 3) { return internal::quadrature_interpolator::Derivatives3D<Q_LAYOUT, GRAD_PHYS>; }
+   else { MFEM_ABORT(""); }
+}
+
+template<QVectorLayout Q_LAYOUT>
+GradKernel GetGradKernel(int DIM, bool GRAD_PHYS)
+{
+   if (GRAD_PHYS) { return GetGradKernel<Q_LAYOUT, true>(DIM); }
+   else { return GetGradKernel<Q_LAYOUT, false>(DIM); }
+}
+} // namespace
+
+template <int DIM, int VDIM, int ND, int NQ>
+EvalKernel QuadratureInterpolator::EvalKernels::Kernel()
+{
+   using namespace internal::quadrature_interpolator;
+   if (DIM == 1) { return Eval1D; }
+   else if (DIM == 2) { return Eval2D<VDIM,ND,NQ>; }
+   else if (DIM == 3) { return Eval3D<VDIM,ND,NQ>; }
+   else { MFEM_ABORT(""); }
+}
+
+template <int DIM>
+EvalKernel GetEvalKernelVDimFallback(int VDIM)
+{
+   using EvalKernels = QuadratureInterpolator::EvalKernels;
+   if (VDIM == 1) { return EvalKernels::Kernel<DIM,1,0,0>(); }
+   else if (VDIM == 2) { return EvalKernels::Kernel<DIM,2,0,0>(); }
+   else if (VDIM == 3) { return EvalKernels::Kernel<DIM,3,0,0>(); }
+   else { MFEM_ABORT(""); }
+}
+
+EvalKernel QuadratureInterpolator::EvalKernels::Fallback(
+   int DIM, int VDIM, int ND, int NQ)
+{
+   if (DIM == 1) { return GetEvalKernelVDimFallback<1>(VDIM); }
+   else if (DIM == 2) { return GetEvalKernelVDimFallback<2>(VDIM); }
+   else if (DIM == 3) { return GetEvalKernelVDimFallback<3>(VDIM); }
+   else { MFEM_ABORT(""); }
+}
+
+TensorEvalKernel QuadratureInterpolator::TensorEvalKernels::Fallback(
+   int DIM, QVectorLayout Q_LAYOUT, int, int, int)
+{
+   if (Q_LAYOUT == QVectorLayout::byNODES) { return FallbackTensorEvalKernel<QVectorLayout::byNODES>(DIM); }
+   else { return FallbackTensorEvalKernel<QVectorLayout::byVDIM>(DIM); }
+}
+
+GradKernel QuadratureInterpolator::GradKernels::Fallback(
+   int DIM, QVectorLayout Q_LAYOUT, bool GRAD_PHYS, int, int, int)
+{
+   if (Q_LAYOUT == QVectorLayout::byNODES) { return GetGradKernel<QVectorLayout::byNODES>(DIM, GRAD_PHYS); }
+   else { return GetGradKernel<QVectorLayout::byVDIM>(DIM, GRAD_PHYS); }
+}
+
+/// @endcond
+
+namespace internal
+{
+namespace quadrature_interpolator
+{
+void InitEvalKernels()
+{
+   using k = QuadratureInterpolator::EvalKernels;
+   // 2D, VDIM = 1
+   k::Specialization<2,1,1,1>::Add();
+   k::Specialization<2,1,1,4>::Add();
+   // Q1
+   k::Specialization<2,1,4,4>::Add();
+   k::Specialization<2,1,4,9>::Add();
+   // Q2
+   k::Specialization<2,1,9,9>::Add();
+   k::Specialization<2,1,9,16>::Add();
+   // Q3
+   k::Specialization<2,1,16,16>::Add();
+   k::Specialization<2,1,16,25>::Add();
+   k::Specialization<2,1,16,36>::Add();
+   // Q4
+   k::Specialization<2,1,25,25>::Add();
+   k::Specialization<2,1,25,36>::Add();
+   k::Specialization<2,1,25,49>::Add();
+   k::Specialization<2,1,25,64>::Add();
+
+   // 3D, VDIM = 1
+   // Q0
+   k::Specialization<3,1,1,1>::Add();
+   k::Specialization<3,1,1,8>::Add();
+   // Q1
+   k::Specialization<3,1,8,8>::Add();
+   k::Specialization<3,1,8,27>::Add();
+   // Q2
+   k::Specialization<3,1,27,27>::Add();
+   k::Specialization<3,1,27,64>::Add();
+   // Q3
+   k::Specialization<3,1,64,64>::Add();
+   k::Specialization<3,1,64,125>::Add();
+   k::Specialization<3,1,64,216>::Add();
+   // Q4
+   k::Specialization<3,1,125,125>::Add();
+   k::Specialization<3,1,125,216>::Add();
+
+   // 2D, VDIM = 3
+   // Q0
+   k::Specialization<2,3,1,1>::Add();
+   k::Specialization<2,3,1,4>::Add();
+   // Q1
+   k::Specialization<2,3,4,4>::Add();
+   k::Specialization<2,3,4,9>::Add();
+   // Q2
+   k::Specialization<2,3,9,4>::Add();
+   k::Specialization<2,3,9,9>::Add();
+   k::Specialization<2,3,9,16>::Add();
+   k::Specialization<2,3,9,25>::Add();
+   // Q3
+   k::Specialization<2,3,16,16>::Add();
+   k::Specialization<2,3,16,25>::Add();
+   k::Specialization<2,3,16,36>::Add();
+   // Q4
+   k::Specialization<2,3,25,25>::Add();
+   k::Specialization<2,3,25,36>::Add();
+   k::Specialization<2,3,25,49>::Add();
+   k::Specialization<2,3,25,64>::Add();
+
+   // 2D, VDIM = 2
+   // Q1
+   k::Specialization<2,2,4,4>::Add();
+   k::Specialization<2,2,4,9>::Add();
+   // Q2
+   k::Specialization<2,2,9,9>::Add();
+   k::Specialization<2,2,9,16>::Add();
+   // Q3
+   k::Specialization<2,2,16,16>::Add();
+   k::Specialization<2,2,16,25>::Add();
+   k::Specialization<2,2,16,36>::Add();
+   // Q4
+   k::Specialization<2,2,25,25>::Add();
+   k::Specialization<2,2,25,36>::Add();
+   k::Specialization<2,2,25,49>::Add();
+   k::Specialization<2,2,25,64>::Add();
+
+   // 3D, VDIM = 3
+   // Q1
+   k::Specialization<3,3,8,8>::Add();
+   k::Specialization<3,3,8,27>::Add();
+   // Q2
+   k::Specialization<3,3,27,27>::Add();
+   k::Specialization<3,3,27,64>::Add();
+   k::Specialization<3,3,27,125>::Add();
+   // Q3
+   k::Specialization<3,3,64,64>::Add();
+   k::Specialization<3,3,64,125>::Add();
+   k::Specialization<3,3,64,216>::Add();
+   // Q4
+   k::Specialization<3,3,125,125>::Add();
+   k::Specialization<3,3,125,216>::Add();
+}
+
+} // namespace quadrature_Interpolator
+} // namespace internal
+
 } // namespace mfem

fem/quadinterpolator.hpp

@@ -13,6 +13,7 @@
 #define MFEM_QUADINTERP
 
 #include "fespace.hpp"
+#include "kernel_dispatch.hpp"
 
 namespace mfem
 {
@@ -130,6 +131,29 @@ public:
    /// Perform the transpose operation of Mult(). (TODO)
    void MultTranspose(unsigned eval_flags, const Vector &q_val,
                       const Vector &q_der, Vector &e_vec) const;
+
+
+   using TensorEvalKernelType = void(*)(const int, const real_t *, const real_t *,
+                                        real_t *, const int, const int, const int);
+   using GradKernelType = void(*)(const int, const real_t *, const real_t *,
+                                  const real_t *, const real_t *, real_t *,
+                                  const int, const int, const int, const int);
+   using DetKernelType = void(*)(const int NE, const real_t *, const real_t *,
+                                 const real_t *, real_t *, const int, const int,
+                                 Vector *);
+   using EvalKernelType = void(*)(const int, const int, const QVectorLayout,
+                                  const GeometricFactors *, const DofToQuad &,
+                                  const Vector &, Vector &, Vector &, Vector &,
+                                  const int);
+
+   MFEM_REGISTER_KERNELS(TensorEvalKernels, TensorEvalKernelType,
+                         (int, QVectorLayout, int, int, int), (int));
+   MFEM_REGISTER_KERNELS(GradKernels, GradKernelType,
+                         (int, QVectorLayout, bool, int, int, int), (int));
+   MFEM_REGISTER_KERNELS(DetKernels, DetKernelType, (int, int, int, int));
+   MFEM_REGISTER_KERNELS(EvalKernels, EvalKernelType, (int, int, int, int));
+
+   static struct Kernels { Kernels(); } kernels;
 };
 
 }

fem/restriction.cpp

@@ -855,7 +855,8 @@ void ConformingFaceRestriction::SetFaceDofsScatterIndices(
                "This method should not be used on nonconforming coarse faces.");
    MFEM_ASSERT(face.element[0].orientation==0,
                "FaceRestriction used on degenerated mesh.");
-   MFEM_CONTRACT_VAR(f_ordering); // not supported yet
+   MFEM_VERIFY(f_ordering == ElementDofOrdering::LEXICOGRAPHIC,
+               "NATIVE ordering is not supported yet");
 
    fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
 
@@ -883,7 +884,8 @@ void ConformingFaceRestriction::SetFaceDofsGatherIndices(
 {
    MFEM_ASSERT(!(face.IsNonconformingCoarse()),
                "This method should not be used on nonconforming coarse faces.");
-   MFEM_CONTRACT_VAR(f_ordering); // not supported yet
+   MFEM_VERIFY(f_ordering == ElementDofOrdering::LEXICOGRAPHIC,
+               "NATIVE ordering is not supported yet");
 
    fes.GetFE(0)->GetFaceMap(face.element[0].local_face_id, face_map);
 

fem/transfer.cpp

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

general/backends.hpp

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

general/table.cpp

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

general/table.hpp

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

linalg/CMakeLists.txt

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

linalg/complex_densemat.cpp

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

linalg/densemat.cpp

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

linalg/lapack.hpp

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

linalg/operator.hpp

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

linalg/solvers.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "linalg.hpp"
+#include "lapack.hpp"
 #include "../general/annotation.hpp"
 #include "../general/forall.hpp"
 #include "../general/globals.hpp"
@@ -3543,38 +3544,6 @@ void AuxSpaceSmoother::Mult(const Vector &x, Vector &y, bool transpose) const
 #endif // MFEM_USE_MPI
 
 #ifdef MFEM_USE_LAPACK
-// LAPACK routines for NNLSSolver
-#ifdef MFEM_USE_SINGLE
-extern "C" void
-sormqr_(char *, char *, int *, int *, int *, float *, int*, float *,
-        float *, int *, float *, int*, int*);
-
-extern "C" void
-sgeqrf_(int *, int *, float *, int *, float *, float *, int *, int *);
-
-extern "C" void
-sgemv_(char *, int *, int *, float *, float *, int *, float *, int *,
-       float *, float *, int *);
-
-extern "C" void
-strsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       float *alpha, float *a, int *lda, float *b, int *ldb);
-#elif defined MFEM_USE_DOUBLE
-extern "C" void
-dormqr_(char *, char *, int *, int *, int *, double *, int*, double *,
-        double *, int *, double *, int*, int*);
-
-extern "C" void
-dgeqrf_(int *, int *, double *, int *, double *, double *, int *, int *);
-
-extern "C" void
-dgemv_(char *, int *, int *, double *, double *, int *, double *, int *,
-       double *, double *, int *);
-
-extern "C" void
-dtrsm_(char *side, char *uplo, char *transa, char *diag, int *m, int *n,
-       double *alpha, double *a, int *lda, double *b, int *ldb);
-#endif
 
 NNLSSolver::NNLSSolver()
    : Solver(0), mat(nullptr), const_tol_(1.0e-14), min_nnz_(0),
@@ -3938,25 +3907,19 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             lwork = -1;
             work.resize(10);
 
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    mat_qr_data.GetData() + (i_qr_start * m), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &n_update,
+                                       &i_qr_start, mat_qr_data.GetData(), &m,
+                                       tau.GetData(),
+                                       mat_qr_data.GetData() + (i_qr_start * m),
+                                       &m, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T A update work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &n_update, &i_qr_start,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    mat_qr_data.GetData() + (i_qr_start * m), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &n_update,
+                                       &i_qr_start, mat_qr_data.GetData(), &m,
+                                       tau.GetData(),
+                                       mat_qr_data.GetData() + (i_qr_start * m),
+                                       &m, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T A update failed
             // Compute QR factorization of the submatrix
             lwork = -1;
@@ -3977,24 +3940,16 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
                sub_tau[j] = tau[i_qr_start + j];
             }
 
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m_update, &n_update,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m_update, &n_update,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m_update, &n_update, submat_data.GetData(),
+                                       &m_update, sub_tau.GetData(), work.data(),
+                                       &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR update factorization work calc
             lwork = static_cast<int>(work[0]);
             if (lwork == 0) { lwork = 1; }
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m_update, &n_update,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m_update, &n_update,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m_update, &n_update, submat_data.GetData(),
+                                       &m_update, sub_tau.GetData(), work.data(),
+                                       &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR update factorization failed
 
             // Copy result back
@@ -4023,23 +3978,13 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             // perform qr)
             lwork = -1;
             work.resize(10);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m, &n_glob, mat_qr_data.GetData(), &m,
+                                       tau.GetData(), work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR factorization work calculation
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sgeqrf_(&m, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dgeqrf_(&m, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(geqrf_)(&m, &n_glob, mat_qr_data.GetData(), &m,
+                                       tau.GetData(), work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // QR factorization failed
          }
 
@@ -4067,25 +4012,17 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
 
             sub_tau[0] = tau[i_qr_start];
 
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m_update, &ione, &ione,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m_update, &ione, &ione,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    sub_qt.GetData(), &m_update,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m_update, &ione, &ione,
+                                       submat_data.GetData(), &m_update,
+                                       sub_tau.GetData(), sub_qt.GetData(),
+                                       &m_update, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // H_last y work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m_update, &ione, &ione,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m_update, &ione, &ione,
-#endif
-                    submat_data.GetData(), &m_update, sub_tau.GetData(),
-                    sub_qt.GetData(), &m_update,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m_update, &ione, &ione,
+                                       submat_data.GetData(), &m_update,
+                                       sub_tau.GetData(), sub_qt.GetData(),
+                                       &m_update, work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // H_last y failed
             // Copy result back
             for (int i=0; i<m_update; ++i)
@@ -4099,25 +4036,17 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             qt_rhs_glob = rhs_avg_glob;
             lwork = -1;
             work.resize(10);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &ione, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &ione, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    qt_rhs_glob.GetData(), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &ione, &n_glob,
+                                       mat_qr_data.GetData(), &m, tau.GetData(),
+                                       qt_rhs_glob.GetData(), &m,
+                                       work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T b work calculation failed
             lwork = static_cast<int>(work[0]);
             work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-            sormqr_(&lside, &trans, &m, &ione, &n_glob,
-#elif defined MFEM_USE_DOUBLE
-            dormqr_(&lside, &trans, &m, &ione, &n_glob,
-#endif
-                    mat_qr_data.GetData(), &m, tau.GetData(),
-                    qt_rhs_glob.GetData(), &m,
-                    work.data(), &lwork, &info);
+            MFEM_LAPACK_PREFIX(ormqr_)(&lside, &trans, &m, &ione, &n_glob,
+                                       mat_qr_data.GetData(), &m, tau.GetData(),
+                                       qt_rhs_glob.GetData(), &m,
+                                       work.data(), &lwork, &info);
             MFEM_VERIFY(info == 0, ""); // Q^T b failed
          }
 
@@ -4130,14 +4059,10 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
          char upper = 'U';
          char nounit = 'N';
          vec1 = qt_rhs_glob;
-#ifdef MFEM_USE_SINGLE
-         strsm_(&lside, &upper, &notrans, &nounit,
-#elif defined MFEM_USE_DOUBLE
-         dtrsm_(&lside, &upper, &notrans, &nounit,
-#endif
-                &n_glob, &ione, &fone,
-                mat_qr_data.GetData(), &m,
-                vec1.GetData(), &n_glob);
+         MFEM_LAPACK_PREFIX(trsm_)(&lside, &upper, &notrans, &nounit,
+                                   &n_glob, &ione, &fone,
+                                   mat_qr_data.GetData(), &m,
+                                   vec1.GetData(), &n_glob);
 
          if (verbosity_ > 2)
          {
@@ -4360,14 +4285,10 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
       {
          res_glob = rhs_avg_glob;
          real_t fmone = -1.0;
-#ifdef MFEM_USE_SINGLE
-         sgemv_(&notrans, &m, &n_glob, &fmone,
-#elif defined MFEM_USE_DOUBLE
-         dgemv_(&notrans, &m, &n_glob, &fmone,
-#endif
-                mat_0_data.GetData(), &m,
-                soln_nz_glob.GetData(), &ione, &fone,
-                res_glob.GetData(), &ione);
+         MFEM_LAPACK_PREFIX(gemv_)(&notrans, &m, &n_glob, &fmone,
+                                   mat_0_data.GetData(), &m,
+                                   soln_nz_glob.GetData(), &ione, &fone,
+                                   res_glob.GetData(), &ione);
       }
       else
       {
@@ -4381,24 +4302,18 @@ void NNLSSolver::Solve(const Vector& rhs_lb, const Vector& rhs_ub,
             qqt_rhs_glob(i) = qt_rhs_glob(i);
          }
 
-#ifdef MFEM_USE_SINGLE
-         sormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#elif defined MFEM_USE_DOUBLE
-         dormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#endif
-                 tau.GetData(), qqt_rhs_glob.GetData(), &m,
-                 work.data(), &lwork, &info);
+         MFEM_LAPACK_PREFIX(ormqr_)(&lside, &notrans, &m, &ione, &n_glob,
+                                    mat_qr_data.GetData(), &m,
+                                    tau.GetData(), qqt_rhs_glob.GetData(), &m,
+                                    work.data(), &lwork, &info);
 
          MFEM_VERIFY(info == 0, ""); // Q Q^T b work calculation failed.
          lwork = static_cast<int>(work[0]);
          work.resize(lwork);
-#ifdef MFEM_USE_SINGLE
-         sormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#elif defined MFEM_USE_DOUBLE
-         dormqr_(&lside, &notrans, &m, &ione, &n_glob, mat_qr_data.GetData(), &m,
-#endif
-                 tau.GetData(), qqt_rhs_glob.GetData(), &m,
-                 work.data(), &lwork, &info);
+         MFEM_LAPACK_PREFIX(ormqr_)(&lside, &notrans, &m, &ione, &n_glob,
+                                    mat_qr_data.GetData(), &m,
+                                    tau.GetData(), qqt_rhs_glob.GetData(), &m,
+                                    work.data(), &lwork, &info);
          MFEM_VERIFY(info == 0, ""); // Q Q^T b calculation failed.
          res_glob = rhs_avg_glob;
          res_glob -= qqt_rhs_glob;

linalg/sparsemat.cpp

@@ -1267,24 +1267,32 @@ real_t SparseMatrix::InnerProduct(const Vector &x, const Vector &y) const
 
 void SparseMatrix::GetRowSums(Vector &x) const
 {
-   for (int i = 0; i < height; i++)
+   if (Finalized())
    {
-      real_t a = 0.0;
-      if (A)
+      auto d_I = ReadI();
+      auto d_A = ReadData();
+      auto d_x = x.Write();
+      mfem::forall(height, [=] MFEM_HOST_DEVICE (int i)
       {
-         for (int j = I[i], end = I[i+1]; j < end; j++)
+         real_t sum = 0.0;
+         for (int j = d_I[i], end = d_I[i+1]; j < end; j++)
          {
-            a += A[j];
+            sum += d_A[j];
          }
-      }
-      else
+         d_x[i] = sum;
+      });
+   }
+   else
+   {
+      for (int i = 0; i < height; i++)
       {
+         real_t a = 0.0;
          for (RowNode *np = Rows[i]; np != NULL; np = np->Prev)
          {
             a += np->Value;
          }
+         x(i) = a;
       }
-      x(i) = a;
    }
 }
 
@@ -3300,7 +3308,7 @@ void SparseMatrix::Print(std::ostream & os, int width_) const
 {
    int i, j;
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)
@@ -3354,7 +3362,7 @@ void SparseMatrix::PrintMatlab(std::ostream & os) const
    os.setf(ios::scientific);
    std::streamsize old_prec = os.precision(14);
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)
@@ -3397,7 +3405,7 @@ void SparseMatrix::PrintMM(std::ostream & os) const
 
    os << height << " " << width << " " << NumNonZeroElems() << '\n';
 
-   if (A == NULL)
+   if (A.Empty())
    {
       RowNode *nd;
       for (i = 0; i < height; i++)

linalg/sparsemat.hpp

@@ -216,7 +216,7 @@ public:
    void ClearCuSparse() { ClearGPUSparse(); }
 
    /// Check if the SparseMatrix is empty.
-   bool Empty() const { return (A == NULL) && (Rows == NULL); }
+   bool Empty() const { return A.Empty() && (Rows == NULL); }
 
    /// Return the array #I.
    inline int *GetI() { return I; }

linalg/sundials.cpp

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

linalg/sundials.hpp

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

mesh/CMakeLists.txt

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

mesh/mesh.cpp

@@ -466,7 +466,8 @@ void Mesh::GetBdrElementTransformation(int i,
          {
             for (int j = 0; j < n; j++)
             {
-               pm(k,j) = nodes(vdofs[n*k+j]);
+               int idx = vdofs[n*k+j];
+               pm(k,j) = nodes((idx<0)? -1-idx:idx);
             }
          }
          ElTr->SetFE(bdr_el);
@@ -7131,17 +7132,15 @@ Table *Mesh::GetEdgeVertexTable() const
 
 Table *Mesh::GetVertexToElementTable()
 {
-   int i, j, nv, *v;
-
    Table *vert_elem = new Table;
 
    vert_elem->MakeI(NumOfVertices);
 
-   for (i = 0; i < NumOfElements; i++)
+   for (int i = 0; i < NumOfElements; i++)
    {
-      nv = elements[i]->GetNVertices();
-      v  = elements[i]->GetVertices();
-      for (j = 0; j < nv; j++)
+      const int nv = elements[i]->GetNVertices();
+      const int *v = elements[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
       {
          vert_elem->AddAColumnInRow(v[j]);
       }
@@ -7149,11 +7148,11 @@ Table *Mesh::GetVertexToElementTable()
 
    vert_elem->MakeJ();
 
-   for (i = 0; i < NumOfElements; i++)
+   for (int i = 0; i < NumOfElements; i++)
    {
-      nv = elements[i]->GetNVertices();
-      v  = elements[i]->GetVertices();
-      for (j = 0; j < nv; j++)
+      const int nv = elements[i]->GetNVertices();
+      const int *v = elements[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
       {
          vert_elem->AddConnection(v[j], i);
       }
@@ -7164,6 +7163,39 @@ Table *Mesh::GetVertexToElementTable()
    return vert_elem;
 }
 
+Table *Mesh::GetVertexToBdrElementTable()
+{
+   Table *vert_bdr_elem = new Table;
+
+   vert_bdr_elem->MakeI(NumOfVertices);
+
+   for (int i = 0; i < NumOfBdrElements; i++)
+   {
+      const int nv = boundary[i]->GetNVertices();
+      const int *v = boundary[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
+      {
+         vert_bdr_elem->AddAColumnInRow(v[j]);
+      }
+   }
+
+   vert_bdr_elem->MakeJ();
+
+   for (int i = 0; i < NumOfBdrElements; i++)
+   {
+      const int nv = boundary[i]->GetNVertices();
+      const int *v = boundary[i]->GetVertices();
+      for (int j = 0; j < nv; j++)
+      {
+         vert_bdr_elem->AddConnection(v[j], i);
+      }
+   }
+
+   vert_bdr_elem->ShiftUpI();
+
+   return vert_bdr_elem;
+}
+
 Table *Mesh::GetFaceToElementTable() const
 {
    Table *face_elem = new Table;

mesh/mesh.hpp

@@ -1537,6 +1537,9 @@ public:
    /// @note The returned Table should be deleted by the caller
    Table *GetVertexToElementTable();
 
+   /// @note The returned Table should be deleted by the caller
+   Table *GetVertexToBdrElementTable();
+
    /// Return the "face"-element Table. Here "face" refers to face (3D),
    /// edge (2D), or vertex (1D).
    ///
@@ -2331,6 +2334,11 @@ public:
                     bool high_order_output=false,
                     int compression_level=0);
 
+#ifdef MFEM_USE_NETCDF
+   /// @brief Export a mesh to an Exodus II file.
+   void PrintExodusII(const std::string fpath);
+#endif
+
    /** @brief Prints the mesh with boundary elements given by the boundary of
        the subdomains, so that the boundary of subdomain i has boundary
        attribute i+1. */

mesh/nurbs.cpp

@@ -1857,7 +1857,7 @@ NURBSPatch *Revolve3D(NURBSPatch &patch, real_t n[], real_t ang, int times)
 {
    if (patch.Dim != 4)
    {
-      mfem_error("Revolve3D(NURBSPatch &, double [], double)");
+      mfem_error("Revolve3D(NURBSPatch &, real_t [], real_t)");
    }
 
    int size = 1, ns;
@@ -2008,23 +2008,23 @@ NURBSExtension::NURBSExtension(std::istream &input, bool spacing)
          input >> numSpacing;
          for (int j = 0; j < numSpacing; j++)
          {
-            int ki, spacingType, numIntParam, numDoubleParam;
-            input >> ki >> spacingType >> numIntParam >> numDoubleParam;
+            int ki, spacingType, numIntParam, numRealParam;
+            input >> ki >> spacingType >> numIntParam >> numRealParam;
 
             MFEM_VERIFY(0 <= ki && ki < NumOfKnotVectors,
                         "Invalid knotvector index");
-            MFEM_VERIFY(numIntParam >= 0 && numDoubleParam >= 0,
+            MFEM_VERIFY(numIntParam >= 0 && numRealParam >= 0,
                         "Invalid number of parameters in KnotVector");
 
             Array<int> ipar(numIntParam);
-            Vector dpar(numDoubleParam);
+            Vector dpar(numRealParam);
 
             for (int i=0; i<numIntParam; ++i)
             {
                input >> ipar[i];
             }
 
-            for (int i=0; i<numDoubleParam; ++i)
+            for (int i=0; i<numRealParam; ++i)
             {
                input >> dpar[i];
             }
@@ -2064,7 +2064,7 @@ NURBSExtension::NURBSExtension(std::istream &input, bool spacing)
                   new KnotVector(*patches[p]->GetKV(0));
             }
          }
-         if (Dimension() == 2)
+         else if (Dimension() == 2)
          {
             patchTopo->GetElementEdges(p, edges, oedge);
             if (knotVectors[KnotInd(edges[0])] == NULL)
@@ -2230,7 +2230,8 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent, int newOrder)
 }
 
 NURBSExtension::NURBSExtension(NURBSExtension *parent,
-                               const Array<int> &newOrders)
+                               const Array<int> &newOrders, Mode mode)
+   : mode(mode)
 {
    newOrders.Copy(mOrders);
    SetOrderFromOrders();
@@ -3891,7 +3892,16 @@ void NURBSExtension::GenerateBdrElementDofTable()
    int ndof = bel_dof->Size_of_connections();
    for (int i = 0; i < ndof; i++)
    {
-      dof[i] = activeDof[dof[i]] - 1;
+      int idx = dof[i];
+      if (idx < 0)
+      {
+         dof[i] = -1 - (activeDof[-1-idx] - 1);
+         dof[i] = -activeDof[-1-idx];
+      }
+      else
+      {
+         dof[i] = activeDof[idx] - 1;
+      }
    }
 }
 
@@ -3943,6 +3953,22 @@ void NURBSExtension::Generate2DBdrElementDofTable()
       // Load dofs
       const int nks0 = kv[0]->GetNKS();
       const int ord0 = kv[0]->GetOrder();
+
+      bool add_dofs = true;
+      int  s = 1;
+
+      if (mode == Mode::H_DIV)
+      {
+         int fn = patchTopo->GetBdrElementFaceIndex(b);
+         if (ord0 == mOrders.Max()) { add_dofs = false; }
+         if (fn == 0) { s = -1; }
+         if (fn == 2) { s = -1; }
+      }
+      else if (mode == Mode::H_CURL)
+      {
+         if (ord0 == mOrders.Max()) { add_dofs = false; }
+      }
+
       for (int i = 0; i < nks0; i++)
       {
          if (kv[0]->isElement(i))
@@ -3950,10 +3976,14 @@ void NURBSExtension::Generate2DBdrElementDofTable()
             if (activeBdrElem[gbe])
             {
                Connection conn(lbe,0);
-               for (int ii = 0; ii <= ord0; ii++)
+               if (add_dofs)
                {
-                  conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
-                  bel_dof_list.Append(conn);
+                  for (int ii = 0; ii <= ord0; ii++)
+                  {
+                     conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
+                     if (s == -1) { conn.to = -1 -conn.to; }
+                     bel_dof_list.Append(conn);
+                  }
                }
                bel_to_patch[lbe] = b;
                bel_to_IJK(lbe,0) = (okv[0] >= 0) ? i : (-1-i);
@@ -3990,6 +4020,25 @@ void NURBSExtension::Generate3DBdrElementDofTable()
       const int ord0 = kv[0]->GetOrder();
       const int nks1 = kv[1]->GetNKS();
       const int ord1 = kv[1]->GetOrder();
+
+      // Check if dofs are actually defined on boundary
+      bool add_dofs = true;
+      int  s = 1;
+
+      if (mode == Mode::H_DIV)
+      {
+         int fn = patchTopo->GetBdrElementFaceIndex(b);
+         if (ord0 != ord1) { add_dofs = false; }
+         if (fn == 4) { s = -1; }
+         if (fn == 1) { s = -1; }
+         if (fn == 0) { s = -1; }
+      }
+      else if (mode == Mode::H_CURL)
+      {
+         if (ord0 == ord1) { add_dofs = false; }
+      }
+
+
       for (int j = 0; j < nks1; j++)
       {
          if (kv[1]->isElement(j))
@@ -4001,14 +4050,18 @@ void NURBSExtension::Generate3DBdrElementDofTable()
                   if (activeBdrElem[gbe])
                   {
                      Connection conn(lbe,0);
-                     for (int jj = 0; jj <= ord1; jj++)
+                     if (add_dofs)
                      {
-                        const int jj_ = (okv[1] >= 0) ? (j+jj) : (ny-j-jj);
-                        for (int ii = 0; ii <= ord0; ii++)
+                        for (int jj = 0; jj <= ord1; jj++)
                         {
-                           const int ii_ = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
-                           conn.to = DofMap(p2g(ii_, jj_));
-                           bel_dof_list.Append(conn);
+                           const int jj_ = (okv[1] >= 0) ? (j+jj) : (ny-j-jj);
+                           for (int ii = 0; ii <= ord0; ii++)
+                           {
+                              const int ii_ = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
+                              conn.to = DofMap(p2g(ii_, jj_));
+                              if (s == -1) { conn.to = -1 -conn.to; }
+                              bel_dof_list.Append(conn);
+                           }
                         }
                      }
                      bel_to_patch[lbe] = b;
@@ -4241,6 +4294,38 @@ void NURBSExtension::DegreeElevate(int rel_degree, int degree)
    }
 }
 
+NURBSExtension* NURBSExtension::GetDivExtension(int component)
+{
+   // Smarter routine
+   if (GetNP() > 1)
+   {
+      mfem_error("NURBSExtension::GetDivExtension currently "
+                 "only works for single patch NURBS meshes ");
+   }
+
+   Array<int> newOrders  = GetOrders();
+   newOrders[component] += 1;
+
+   return new NURBSExtension(this, newOrders, Mode::H_DIV);
+}
+
+NURBSExtension* NURBSExtension::GetCurlExtension(int component)
+{
+   // Smarter routine
+   if (GetNP() > 1)
+   {
+      mfem_error("NURBSExtension::GetCurlExtension currently "
+                 "only works for single patch NURBS meshes ");
+   }
+
+   Array<int> newOrders  = GetOrders();
+   for (int c = 0; c < newOrders.Size(); c++) { newOrders[c]++; }
+   newOrders[component] -= 1;
+
+   return new NURBSExtension(this, newOrders, Mode::H_CURL);
+}
+
+
 void NURBSExtension::UniformRefinement(Array<int> const& rf)
 {
    for (int p = 0; p < patches.Size(); p++)

mesh/nurbs.hpp

@@ -426,6 +426,16 @@ class NURBSExtension
    friend class NURBSPatchMap;
 
 protected:
+
+   /// Flag for indicating what type of NURBS fespace this extension is used for.
+   enum class Mode
+   {
+      H_1,    ///> Extension for a standard scalar-valued space
+      H_DIV,  ///> Extension for a divergence conforming vector-valued space
+      H_CURL, ///> Extension for a curl conforming vector-valued space
+   };
+   Mode mode = Mode::H_1;
+
    /// Order of KnotVectors, see GetOrder() for description.
    int mOrder;
 
@@ -655,8 +665,10 @@ public:
    /** @a note If a KnotVector in @a parent already has order greater than or
        equal to the corresponding entry in @a newOrder, it will be used
        unmodified. */
-   NURBSExtension(NURBSExtension *parent, const Array<int> &newOrders);
+   NURBSExtension(NURBSExtension *parent, const Array<int> &newOrders,
+                  Mode mode = Mode::H_1);
    /// Construct a NURBSExtension by merging a partitioned NURBS mesh.
+
    NURBSExtension(Mesh *mesh_array[], int num_pieces);
 
    /// Copy assignment not supported.
@@ -841,6 +853,16 @@ public:
    void KnotInsert(Array<KnotVector *> &kv);
    void KnotInsert(Array<Vector *> &kv);
 
+   /** Returns the NURBSExtension to be used for @a component of
+       an H(div) conforming NURBS space. Caller gets ownership of
+       the returned object, and is responsible for deletion.*/
+   NURBSExtension* GetDivExtension(int component);
+
+   /** Returns the NURBSExtension to be used for @a component of
+       an H(curl) conforming NURBS space. Caller gets ownership of
+       the returned object, and is responsible for deletion.*/
+   NURBSExtension* GetCurlExtension(int component);
+
    void KnotRemove(Array<Vector *> &kv, real_t tol = 1.0e-12);
 
    /** Calls GetCoarseningFactors for each patch and finds the minimum factor
@@ -848,6 +870,7 @@ public:
        non-nested spacing functions. */
    void GetCoarseningFactors(Array<int> & f) const;
 
+
    /// Returns the index of the patch containing element @a elem.
    int GetElementPatch(int elem) const { return el_to_patch[elem]; }
 

miniapps/dpg/acoustics.cpp

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

miniapps/dpg/convection-diffusion.cpp

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

miniapps/dpg/maxwell.cpp

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

miniapps/dpg/pacoustics.cpp

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

miniapps/dpg/pconvection-diffusion.cpp

@@ -11,17 +11,17 @@
 //
 //             MFEM Ultraweak DPG parallel example for convection-diffusion
 //
-// Compile with: make  pconvection-diffusion
+// Compile with: make pconvection-diffusion
 //
 // sample runs
-// mpirun -np 4 pconvection-diffusion  -o 2 -ref 3 -prob 0 -eps 1e-1 -beta '4 2' -theta 0.0
-// mpirun -np 4 pconvection-diffusion  -o 3 -ref 3 -prob 0 -eps 1e-2 -beta '2 3' -theta 0.0
-// mpirun -np 4 pconvection-diffusion -m ../../data/inline-hex.mesh -o 2 -ref 1 -prob 0 -sc -eps 1e-1 -theta 0.0
+//  mpirun -np 4 pconvection-diffusion -o 2 -ref 3 -prob 0 -eps 1e-1 -beta '4 2' -theta 0.0
+//  mpirun -np 4 pconvection-diffusion -o 3 -ref 3 -prob 0 -eps 1e-2 -beta '2 3' -theta 0.0
+//  mpirun -np 4 pconvection-diffusion -m ../../data/inline-hex.mesh -o 2 -ref 1 -prob 0 -sc -eps 1e-1 -theta 0.0
 
 // AMR runs
-// mpirun -np 4 pconvection-diffusion  -o 3 -ref 10 -prob 1 -eps 1e-3 -beta '1 0' -theta 0.7 -sc
-// mpirun -np 4 pconvection-diffusion  -o 3 -ref 15 -prob 2 -eps 5e-3 -theta 0.7 -sc
-// mpirun -np 4 pconvection-diffusion  -o 2 -ref 12 -prob 3 -eps 1e-2 -beta '1 2' -theta 0.7 -sc
+//  mpirun -np 4 pconvection-diffusion -o 3 -ref 10 -prob 1 -eps 1e-3 -beta '1 0' -theta 0.7 -sc
+//  mpirun -np 4 pconvection-diffusion -o 3 -ref 15 -prob 2 -eps 5e-3 -theta 0.7 -sc
+//  mpirun -np 4 pconvection-diffusion -o 2 -ref 12 -prob 3 -eps 1e-2 -beta '1 2' -theta 0.7 -sc
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve a parallel

miniapps/dpg/pdiffusion.cpp

@@ -14,18 +14,18 @@
 // Compile with: make pdiffusion
 //
 // Sample runs
-// mpirun -np 4 pdiffusion -m ../../data/inline-quad.mesh -o 3 -sref 1 -pref 2 -theta 0.0 -prob 0
-// mpirun -np 4 pdiffusion -m ../../data/inline-hex.mesh -o 2 -sref 0 -pref 1 -theta 0.0 -prob 0 -sc
-// mpirun -np 4 pdiffusion -m ../../data/beam-tet.mesh -o 3 -sref 0 -pref 2 -theta 0.0 -prob 0 -sc
+//  mpirun -np 4 pdiffusion -m ../../data/inline-quad.mesh -o 3 -sref 1 -pref 2 -theta 0.0 -prob 0
+//  mpirun -np 4 pdiffusion -m ../../data/inline-hex.mesh -o 2 -sref 0 -pref 1 -theta 0.0 -prob 0 -sc
+//  mpirun -np 4 pdiffusion -m ../../data/beam-tet.mesh -o 3 -sref 0 -pref 2 -theta 0.0 -prob 0 -sc
 
 // L-shape runs
 // Note: uniform ref are expected to give sub-optimal rate for the L-shape problem (rate = 2/3)
-// mpirun -np 4 pdiffusion -o 2 -sref 1 -pref 5 -theta 0.0 -prob 1
+//  mpirun -np 4 pdiffusion -o 2 -sref 1 -pref 5 -theta 0.0 -prob 1
 
 // L-shape AMR runs
-// mpirun -np 4 pdiffusion -o 1 -sref 1 -pref 10 -theta 0.8 -prob 1
-// mpirun -np 4 pdiffusion -o 2 -sref 1 -pref 8 -theta 0.75 -prob 1 -sc
-// mpirun -np 4 pdiffusion -o 3 -sref 1 -pref 6 -theta 0.75 -prob 1 -sc -do 2
+//  mpirun -np 4 pdiffusion -o 1 -sref 1 -pref 10 -theta 0.8 -prob 1
+//  mpirun -np 4 pdiffusion -o 2 -sref 1 -pref 8 -theta 0.75 -prob 1 -sc
+//  mpirun -np 4 pdiffusion -o 3 -sref 1 -pref 6 -theta 0.75 -prob 1 -sc -do 2
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve

miniapps/dpg/pmaxwell.cpp

@@ -14,16 +14,16 @@
 // Compile with: make pmaxwell
 //
 // sample run
-// mpirun -np 4 pmaxwell -m ../../data/star.mesh -o 2 -sref 0 -pref 3 -rnum 0.5 -prob 0
-// mpirun -np 4 pmaxwell -m ../../data/inline-quad.mesh -o 3 -sref 0 -pref 3 -rnum 4.8 -sc -prob 0
-// mpirun -np 4 pmaxwell -m ../../data/inline-hex.mesh -o 2 -sref 0 -pref 1 -rnum 0.8 -sc -prob 0
-// mpirun -np 4 pmaxwell -m ../../data/inline-quad.mesh -o 3 -sref 1 -pref 3 -rnum 4.8 -sc -prob 2
-// mpirun -np 4 pmaxwell -o 3 -sref 1 -pref 2 -rnum 11.8 -sc -prob 3
-// mpirun -np 4 pmaxwell -o 3 -sref 1 -pref 2 -rnum 9.8 -sc -prob 4
+//  mpirun -np 4 pmaxwell -m ../../data/star.mesh -o 2 -sref 0 -pref 3 -rnum 0.5 -prob 0
+//  mpirun -np 4 pmaxwell -m ../../data/inline-quad.mesh -o 3 -sref 0 -pref 3 -rnum 4.8 -sc -prob 0
+//  mpirun -np 4 pmaxwell -m ../../data/inline-hex.mesh -o 2 -sref 0 -pref 1 -rnum 0.8 -sc -prob 0
+//  mpirun -np 4 pmaxwell -m ../../data/inline-quad.mesh -o 3 -sref 1 -pref 3 -rnum 4.8 -sc -prob 2
+//  mpirun -np 4 pmaxwell -o 3 -sref 1 -pref 2 -rnum 11.8 -sc -prob 3
+//  mpirun -np 4 pmaxwell -o 3 -sref 1 -pref 2 -rnum 9.8 -sc -prob 4
 
 // AMR run. Note that this is a computationally intensive sample run.
 // We recommend trying it on a large machine with more mpi ranks
-// mpirun -np 4 pmaxwell -o 3 -sref 0 -pref 15 -prob 1 -theta 0.7 -sc
+//  mpirun -np 4 pmaxwell -o 3 -sref 0 -pref 15 -prob 1 -theta 0.7 -sc
 
 // Description:
 // This example code demonstrates the use of MFEM to define and solve

miniapps/hdiv-linear-solver/change_basis.cpp

@@ -10,7 +10,6 @@
 // CONTRIBUTING.md for details.
 
 #include "change_basis.hpp"
-#include "../../fem/qinterp/dispatch.hpp"
 #include "../../general/forall.hpp"
 #include "../../linalg/dtensor.hpp"
 
@@ -105,17 +104,25 @@ ChangeOfBasis_L2::ChangeOfBasis_L2(FiniteElementSpace &fes)
 void ChangeOfBasis_L2::Mult(const Vector &x, Vector &y) const
 {
    if (no_op) { y = x; return; }
-   using namespace internal::quadrature_interpolator;
    dof2quad.B.MakeRef(B_1d);
-   TensorValues<QVectorLayout::byVDIM>(ne, 1, dof2quad, x, y);
+   const int dim = dof2quad.FE->GetDim();
+   const int nd = dof2quad.ndof;
+   const int nq = dof2quad.nqpt;
+   QuadratureInterpolator::TensorEvalKernels::Run(
+      dim, QVectorLayout::byVDIM, 1, nd, nq, ne, dof2quad.B.Read(), x.Read(),
+      y.Write(), 1, nd, nq);
 }
 
 void ChangeOfBasis_L2::MultTranspose(const Vector &x, Vector &y) const
 {
    if (no_op) { y = x; return; }
-   using namespace internal::quadrature_interpolator;
    dof2quad.B.MakeRef(Bt_1d);
-   TensorValues<QVectorLayout::byVDIM>(ne, 1, dof2quad, x, y);
+   const int dim = dof2quad.FE->GetDim();
+   const int nd = dof2quad.ndof;
+   const int nq = dof2quad.nqpt;
+   QuadratureInterpolator::TensorEvalKernels::Run(
+      dim, QVectorLayout::byVDIM, 1, nd, nq, ne, dof2quad.B.Read(), x.Read(),
+      y.Write(), 1, nd, nq);
 }
 
 ChangeOfBasis_RT::ChangeOfBasis_RT(FiniteElementSpace &fes)

miniapps/meshing/mesh-explorer.cpp

@@ -386,6 +386,9 @@ int main (int argc, char *argv[])
            "S) Save in MFEM serial format\n"
            "T) Save in MFEM parallel format using the current partitioning\n"
            "V) Save in VTK format (only linear and quadratic meshes)\n"
+#ifdef MFEM_USE_NETCDF
+           "X) Save in Exodus II format (only linear and quadratic meshes)\n"
+#endif
            "D) Save as a DataCollection\n"
            "q) Quit\n"
 #ifdef MFEM_USE_ZLIB
@@ -1288,6 +1291,15 @@ int main (int argc, char *argv[])
          cout << "New VTK mesh file: " << omesh_file << endl;
       }
 
+#ifdef MFEM_USE_NETCDF
+      if (mk == 'X')
+      {
+         const char omesh_file[] = "mesh-explorer.e";
+         mesh->PrintExodusII(omesh_file);
+         cout << "New Exodus II mesh file: " << omesh_file << endl;
+      }
+#endif
+
       if (mk == 'D')
       {
          cout << "What type of DataCollection?\n"

miniapps/nurbs/CMakeLists.txt

@@ -13,6 +13,18 @@ add_mfem_miniapp(nurbs_ex1
   MAIN nurbs_ex1.cpp
   LIBRARIES mfem)
 
+add_mfem_miniapp(nurbs_ex3
+  MAIN nurbs_ex3.cpp
+  LIBRARIES mfem)
+
+add_mfem_miniapp(nurbs_ex5
+  MAIN nurbs_ex5.cpp
+  LIBRARIES mfem)
+
+add_mfem_miniapp(nurbs_ex24
+  MAIN nurbs_ex24.cpp
+  LIBRARIES mfem)
+
 add_mfem_miniapp(nurbs_curveint
   MAIN nurbs_curveint.cpp
   LIBRARIES mfem)
@@ -29,6 +41,10 @@ add_mfem_miniapp(nurbs_patch_ex1
   MAIN nurbs_patch_ex1.cpp
   LIBRARIES mfem)
 
+add_mfem_miniapp(nurbs_solenoidal
+  MAIN nurbs_solenoidal.cpp
+  LIBRARIES mfem)
+
 if (MFEM_ENABLE_TESTING)
   add_test(NAME nurbs_ex1_1d_r1_o2_ser
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
@@ -64,6 +80,10 @@ if (MFEM_ENABLE_TESTING)
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
     -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -o 2 --weak-bc -r 2)
 
+  add_test(NAME nurbs_ex1_neu_r2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
+    -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -o 2 -r 2 --neu "3")
+
   add_test(NAME nurbs_ex1_weak_mp_ser
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
     -m ${PROJECT_SOURCE_DIR}/data/ball-nurbs.mesh -o 2 --weak-bc -r 0)
@@ -125,9 +145,60 @@ if (MFEM_ENABLE_TESTING)
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
     -m ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/two-cubes-nurbs-autoedge.mesh -o 1 -r 3 -rf ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/two-cubes.ref)
 
+  add_test(NAME nurbs_ex1_periodic_2d
+    COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
+    -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -o 2 -r 2 --master "3" --slave "4")
+
   add_test(NAME nurbs_ex1_periodic_3d
     COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
-    -m ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/cube-nurbs.mesh -pm "1" -ps "2" -rf ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/cube.ref)
+    -m ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/cube-nurbs.mesh
+    -rf ${PROJECT_SOURCE_DIR}/miniapps/nurbs/meshes/cube.ref
+    --master "1" --slave "2")
+
+  add_test(NAME nurbs_ex3_2d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex3> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/square-nurbs.mesh -r 1 -o 2)
+
+  add_test(NAME nurbs_ex3_3d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex3> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2)
+
+  add_test(NAME nurbs_ex5_2d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex5> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/square-nurbs.mesh -r 1 -o 2)
+
+  add_test(NAME nurbs_ex5_3d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex5> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2)
+
+  add_test(NAME nurbs_ex24_2d_r1_o2_p0_ser
+    COMMAND $<TARGET_FILE:nurbs_ex24> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -r 1 -o 2 -p 0)
+
+  add_test(NAME nurbs_ex24_2d_r1_o2_p2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex24> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -r 1 -o 2 -p 2)
+
+  add_test(NAME nurbs_ex24_3d_r1_o2_p0_ser
+    COMMAND $<TARGET_FILE:nurbs_ex24> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2 -p 0)
+
+  add_test(NAME nurbs_ex24_3d_r1_o2_p1_ser
+    COMMAND $<TARGET_FILE:nurbs_ex24> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2 -p 1)
+
+  add_test(NAME nurbs_ex24_3d_r1_o2_p2_ser
+    COMMAND $<TARGET_FILE:nurbs_ex24> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2 -p 2)
+
+  add_test(NAME nurbs_solenoidal_2d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_solenoidal> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/pipe-nurbs-2d.mesh -r 1 -o 2)
+
+  add_test(NAME nurbs_solenoidal_3d_r1_o2_ser
+    COMMAND $<TARGET_FILE:nurbs_solenoidal> -no-vis
+        -m ${PROJECT_SOURCE_DIR}/data/cube-nurbs.mesh -r 1 -o 2)
+
 endif()
 
 if (MFEM_USE_MPI)
@@ -135,6 +206,10 @@ if (MFEM_USE_MPI)
     MAIN nurbs_ex1p.cpp
     LIBRARIES mfem)
 
+  add_mfem_miniapp(nurbs_ex11p
+    MAIN nurbs_ex11p.cpp
+    LIBRARIES mfem)
+
   if (MFEM_ENABLE_TESTING)
     add_test(NAME nurbs_ex1p_np=4
       COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
@@ -169,13 +244,7 @@ if (MFEM_USE_MPI)
         COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
         ${MPIEXEC_PREFLAGS}  $<TARGET_FILE:nurbs_ex1p> -no-vis
         -m ${PROJECT_SOURCE_DIR}/data/square-disc-nurbs-patch.mesh -o 2 --weak-bc -r 1)
-  endif()
 
-  add_mfem_miniapp(nurbs_ex11p
-    MAIN nurbs_ex11p.cpp
-    LIBRARIES mfem)
-
-  if (MFEM_ENABLE_TESTING)
     add_test(NAME nurbs_ex11p_np=4
       COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS} $<TARGET_FILE:nurbs_ex11p> -no-vis

miniapps/nurbs/makefile

@@ -21,8 +21,7 @@ CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
-SEQ_MINIAPPS = nurbs_ex1 nurbs_patch_ex1 nurbs_curveint nurbs_printfunc nurbs_naca_cmesh
-
+SEQ_MINIAPPS = nurbs_ex1 nurbs_patch_ex1 nurbs_ex3 nurbs_ex5 nurbs_ex24 nurbs_curveint nurbs_printfunc nurbs_solenoidal nurbs_naca_cmesh
 PAR_MINIAPPS = nurbs_ex1p nurbs_ex11p
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -103,6 +102,36 @@ endif
 	@$(call mfem-test,$<,, NURBS miniapp,$(EX1PATCH_ARGS_2))
 	@$(call mfem-test,$<,, NURBS miniapp,$(EX1PATCH_ARGS_3))
 
+EX3_ARGS_1 := -m $(MFEM_DIR)/data/square-nurbs.mesh -r 1 -o 2
+EX3_ARGS_2 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2
+nurbs_ex3-test-seq: nurbs_ex3
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX3_ARGS_1))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX3_ARGS_2))
+
+EX5_ARGS_1 := -m $(MFEM_DIR)/data/square-nurbs.mesh -r 1 -o 2
+EX5_ARGS_2 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2
+nurbs_ex5-test-seq: nurbs_ex5
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX5_ARGS_1))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX5_ARGS_2))
+
+EX24_ARGS_1 := -m $(MFEM_DIR)/data/pipe-nurbs-2d.mesh -r 1 -o 2 -p 0
+EX24_ARGS_2 := -m $(MFEM_DIR)/data/pipe-nurbs-2d.mesh -r 1 -o 2 -p 2
+EX24_ARGS_3 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2 -p 0
+EX24_ARGS_4 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2 -p 1
+EX24_ARGS_5 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2 -p 2
+nurbs_ex24-test-seq: nurbs_ex24
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX24_ARGS_1))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX24_ARGS_2))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX24_ARGS_3))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX24_ARGS_4))
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX24_ARGS_5))
+
+SOL_ARGS_1 := -m $(MFEM_DIR)/data/pipe-nurbs-2d.mesh -r 1 -o 2
+SOL_ARGS_1 := -m $(MFEM_DIR)/data/cube-nurbs.mesh -r 1 -o 2
+nurbs_sol-test-seq: nurbs_solenoidal
+	@$(call mfem-test,$<,, NURBS miniapp,$(SOL_ARGS_1))
+	@$(call mfem-test,$<,, NURBS miniapp,$(SOl_ARGS_2))
+
 CI_ARGS_1 := -uw -n 9 -no-visit
 CI_ARGS_2 := -nw -n 9 -no-visit
 
@@ -151,6 +180,6 @@ clean-build:
 	rm -rf *.dSYM *.TVD.*breakpoints
 
 clean-exec:
-	@rm -f refined.mesh sin-fit.mesh mesh.* sol.* mode_* naca-cmesh.mesh
-	@rm -rf Example1*
+	@rm -f refined.mesh sin-fit.mesh ex5.mesh exsol.mesh mesh.* sol.* mode_* naca-cmesh.mesh sol_?.gf
+	@rm -rf Example1* Example3* Example5* Solenoidal_* ParaView
 	@rm -rf CurveInt Naca_cmesh glvis_naca-cmesh.mesh

miniapps/nurbs/nurbs_ex1.cpp

@@ -6,6 +6,7 @@
 //               nurbs_ex1 -m ../../data/square-nurbs.mesh -o 2 --weak-bc
 //               nurbs_ex1 -m ../../data/cube-nurbs.mesh -o 2 -no-ibp
 //               nurbs_ex1 -m ../../data/pipe-nurbs-2d.mesh -o 2 -no-ibp
+//               nurbs_ex1 -m ../../data/pipe-nurbs-2d.mesh -o 2 -r 2 --neu "3"
 //               nurbs_ex1 -m ../../data/square-disc-nurbs.mesh -o -1
 //               nurbs_ex1 -m ../../data/disc-nurbs.mesh -o -1
 //               nurbs_ex1 -m ../../data/pipe-nurbs.mesh -o -1
@@ -147,6 +148,7 @@ int main(int argc, char *argv[])
    int ref_levels = -1;
    Array<int> master(0);
    Array<int> slave(0);
+   Array<int> neu(0);
    bool static_cond = false;
    bool visualization = 1;
    int lod = 0;
@@ -169,6 +171,8 @@ int main(int argc, char *argv[])
                   "Master boundaries for periodic BCs");
    args.AddOption(&slave, "-ps", "--slave",
                   "Slave boundaries for periodic BCs");
+   args.AddOption(&neu, "-n", "--neu",
+                  "Boundaries with Neumann BCs");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree) or -1 for"
                   " isoparametric space.");
@@ -266,8 +270,6 @@ int main(int argc, char *argv[])
          slave.Load(in, psize);
          in.close();
       }
-      master.Print();
-      slave.Print();
       NURBSext->ConnectBoundaries(master,slave);
    }
    else if (order[0] == -1) // Isoparametric
@@ -323,39 +325,84 @@ int main(int argc, char *argv[])
    //    In this example, the boundary conditions are defined by marking all
    //    the boundary attributes from the mesh as essential (Dirichlet) and
    //    converting them to a list of true dofs.
-   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(0);
+   Array<int> neu_bdr(0);
+   Array<int> per_bdr(0);
    if (mesh->bdr_attributes.Size())
    {
-      Array<int> ess_bdr(mesh->bdr_attributes.Max());
-      if (strongBC)
+      ess_bdr.SetSize(mesh->bdr_attributes.Max());
+      neu_bdr.SetSize(mesh->bdr_attributes.Max());
+      per_bdr.SetSize(mesh->bdr_attributes.Max());
+
+      ess_bdr = 1;
+      neu_bdr = 0;
+      per_bdr = 0;
+
+      // Apply Neumann BCs
+      for (int i = 0; i < neu.Size(); i++)
       {
-         ess_bdr = 1;
-      }
-      else
-      {
-         ess_bdr = 0;
+         if ( neu[i]-1 >= 0 &&
+              neu[i]-1 < mesh->bdr_attributes.Max())
+         {
+            ess_bdr[neu[i]-1] = 0;
+            neu_bdr[neu[i]-1] = 1;
+         }
+         else
+         {
+            cout <<"Neumann boundary "<<neu[i]<<" out of range -- discarded"<< endl;
+         }
       }
 
-      // Remove periodic BCs
+      // Correct for periodic BCs
       for (int i = 0; i < master.Size(); i++)
       {
-         ess_bdr[master[i]-1] = 0;
-         ess_bdr[slave[i]-1] = 0;
+         if ( master[i]-1 >= 0 &&
+              master[i]-1 < mesh->bdr_attributes.Max())
+         {
+            ess_bdr[master[i]-1] = 0;
+            neu_bdr[master[i]-1] = 0;
+            per_bdr[master[i]-1] = 1;
+         }
+         else
+         {
+            cout <<"Master boundary "<<master[i]<<" out of range -- discarded"<< endl;
+         }
+      }
+      for (int i = 0; i < slave.Size(); i++)
+      {
+         if ( slave[i]-1 >= 0 &&
+              slave[i]-1 < mesh->bdr_attributes.Max())
+         {
+            ess_bdr[slave[i]-1] = 0;
+            neu_bdr[slave[i]-1] = 0;
+            per_bdr[slave[i]-1] = 1;
+         }
+         else
+         {
+            cout <<"Slave boundary "<<slave[i]<<" out of range -- discarded"<< endl;
+         }
       }
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
+   cout <<"Boundary conditions:"<< endl;
+   cout <<" - Periodic  : "; per_bdr.Print();
+   cout <<" - Essential : "; ess_bdr.Print();
+   cout <<" - Neumann   : "; neu_bdr.Print();
+
 
    // 6. Set up the linear form b(.) which corresponds to the right-hand side of
    //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
    //    the basis functions in the finite element fespace.
    ConstantCoefficient one(1.0);
+   ConstantCoefficient mone(-1.0);
    ConstantCoefficient zero(0.0);
 
    LinearForm *b = new LinearForm(fespace);
    b->AddDomainIntegrator(new DomainLFIntegrator(one));
+   b->AddBoundaryIntegrator( new BoundaryLFIntegrator(one),neu_bdr);
    if (!strongBC)
       b->AddBdrFaceIntegrator(
-         new DGDirichletLFIntegrator(zero, one, -1.0, kappa));
+         new DGDirichletLFIntegrator(zero, one, -1.0, kappa), ess_bdr);
+
    b->Assemble();
 
    // 7. Define the solution vector x as a finite element grid function
@@ -375,11 +422,12 @@ int main(int argc, char *argv[])
    else
    {
       a->AddDomainIntegrator(new Diffusion2Integrator(one));
+      a->AddBdrFaceIntegrator(new DGDiffusionIntegrator(mone, 0.0, 0.0), neu_bdr);
    }
 
    if (!strongBC)
    {
-      a->AddBdrFaceIntegrator(new DGDiffusionIntegrator(one, -1.0, kappa));
+      a->AddBdrFaceIntegrator(new DGDiffusionIntegrator(one, -1.0, kappa), ess_bdr);
    }
 
    // 9. Assemble the bilinear form and the corresponding linear system,
@@ -391,6 +439,11 @@ int main(int argc, char *argv[])
 
    SparseMatrix A;
    Vector B, X;
+   Array<int> ess_tdof_list(0);
+   if (strongBC)
+   {
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
 
    cout << "Size of linear system: " << A.Height() << endl;

miniapps/nurbs/nurbs_ex24.cpp

@@ -0,0 +1,459 @@
+//                                MFEM Example 24 -- modified for NURBS FE
+//
+// Compile with: make nurbs_ex24
+//
+// Sample runs:  nurbs_ex24 -m ../../data/pipe-nurbs-2d.mesh -o 2
+//               nurbs_ex24 -m ../../data/pipe-nurbs-2d.mesh -p 2
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2 -p 1
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2 -p 2
+//               nurbs_ex24 -m ../../data/escher.mesh
+//               nurbs_ex24 -m ../../data/escher.mesh -o 2
+//               nurbs_ex24 -m ../../data/fichera.mesh
+//               nurbs_ex24 -m ../../data/fichera-q2.vtk
+//               nurbs_ex24 -m ../../data/fichera-q3.mesh
+//               nurbs_ex24 -m ../../data/amr-quad.mesh -o 2
+//               nurbs_ex24 -m ../../data/amr-hex.mesh
+//
+// Device sample runs -- do not work for NURBS:
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d cuda
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d raja-cuda
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d raja-omp
+//
+// Description:  This example code illustrates usage of mixed finite element
+//               spaces, with three variants:
+//
+//               0) (grad p, u) for p in H^1 tested against u in H(curl)
+//               1) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               2) (div v, q) for v in H(div) tested against q in L_2
+//
+//               Using different approaches, we project the gradient, curl, or
+//               divergence to the appropriate space.
+//
+//               NURBS-based H(curl) and H(div) spaces only implemented
+//               for meshes consisting of a single patch.
+//
+//               We recommend viewing examples 1, 3, and 5 before viewing this
+//               example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+real_t p_exact(const Vector &x);
+void gradp_exact(const Vector &, Vector &);
+real_t div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);
+
+int dim;
+real_t freq = 1.0, kappa;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/cube-nurbs.mesh";
+   int ref_levels = -1;
+   int order = 1;
+   bool NURBS = true;
+   int prob = 0;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   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, -1 for auto.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&NURBS, "-n", "--nurbs", "-nn","--no-nurbs",
+                  "NURBS.");
+   args.AddOption(&prob, "-p", "--problem-type",
+                  "Choose between 0: grad, 1: curl, 2: div");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--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.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   if ((prob == 1) &&(dim != 3))
+   {
+      MFEM_ABORT("The curl problem is only defined in 3D.");
+   }
+   int sdim = mesh->SpaceDimension();
+
+   // 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 50,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels = (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 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 = nullptr;
+   FiniteElementCollection *test_fec = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+   if (mesh->NURBSext && NURBS)
+   {
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      if (prob == 0)
+      {
+         trial_fec  = new NURBSFECollection(order);
+         test_fec = new NURBS_HCurlFECollection(order, dim);
+      }
+      else if (prob == 1)
+      {
+         trial_fec = new NURBS_HCurlFECollection(order, dim);
+         test_fec = new NURBS_HDivFECollection(order, dim);
+      }
+      else
+      {
+         trial_fec = new NURBS_HDivFECollection(order, dim);
+         test_fec  = new NURBSFECollection(order);
+      }
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      if (prob == 0)
+      {
+         trial_fec = new H1_FECollection(order, dim);
+         test_fec = new ND_FECollection(order, dim);
+      }
+      else if (prob == 1)
+      {
+         trial_fec = new ND_FECollection(order, dim);
+         test_fec = new RT_FECollection(order-1, dim);
+      }
+      else
+      {
+         trial_fec = new RT_FECollection(order-1, dim);
+         test_fec = new L2_FECollection(order-1, dim);
+      }
+   }
+
+   FiniteElementSpace trial_fes(mesh, NURBSext, trial_fec);
+   FiniteElementSpace test_fes(mesh,trial_fes.StealNURBSext(), 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 if (prob == 1)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+      cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+           endl;
+   }
+   else
+   {
+      cout << "Number of Raviart-Thomas finite element unknowns: "
+           << 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);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
+   FunctionCoefficient divgradp_coef(div_gradp_exact);
+
+   if (prob == 0)
+   {
+      gftrial.ProjectCoefficient(p_coef);
+   }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
+   else
+   {
+      gftrial.ProjectCoefficient(gradp_coef);
+   }
+
+   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 if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(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(&test_fes);
+      rhs = x;
+      x = 0.0;
+
+      CGSolver cg;
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(1000);
+      cg.SetPrintLevel(1);
+      if (pa)
+      {
+         Array<int> ess_tdof_list; // empty
+         OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
+
+         cg.SetOperator(a);
+         cg.SetPreconditioner(Jacobi);
+         cg.Mult(rhs, x);
+      }
+      else
+      {
+         SparseMatrix& Amat = a.SpMat();
+         DSmoother Jacobi(Amat);
+
+         cg.SetOperator(Amat);
+         cg.SetPreconditioner(Jacobi);
+         cg.Mult(rhs, x);
+      }
+   }
+
+   // 10. Compute the projection of the exact field.
+   GridFunction exact_proj(&test_fes);
+   if (prob == 0)
+   {
+      exact_proj.ProjectCoefficient(gradp_coef);
+   }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
+   else
+   {
+      exact_proj.ProjectCoefficient(divgradp_coef);
+   }
+
+   exact_proj.SetTrueVector();
+   exact_proj.SetFromTrueVector();
+
+   // 11. Compute and print the L_2 norm of the error.
+   if (prob == 0)
+   {
+      real_t errSol = x.ComputeL2Error(gradp_coef);
+      real_t 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;
+      cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+   else if (prob == 1)
+   {
+      real_t errSol = x.ComputeL2Error(curlv_coef);
+      real_t errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
+           "|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+      cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+   else
+   {
+      int order_quad = max(3, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      real_t errSol = x.ComputeL2Error(divgradp_coef, irs);
+      real_t 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 << " Projection f_h of exact div v in L_2: || f_h - div v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+
+   // 12. Save the refined mesh and the solution. This output can be viewed
+   //     later using GLVis: "glvis -m refined.mesh -g sol.gf".
+   ofstream mesh_ofs("refined.mesh");
+   mesh_ofs.precision(8);
+   mesh->Print(mesh_ofs);
+   ofstream sol_ofs("sol.gf");
+   sol_ofs.precision(8);
+   x.Save(sol_ofs);
+
+   // 13. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *mesh << x << flush;
+   }
+
+   // 14. Free the used memory.
+   delete trial_fec;
+   delete test_fec;
+   delete mesh;
+
+   return 0;
+}
+
+real_t p_exact(const Vector &x)
+{
+   if (dim == 3)
+   {
+      return sin(x(0)) * sin(x(1)) * sin(x(2));
+   }
+   else if (dim == 2)
+   {
+      return sin(x(0)) * sin(x(1));
+   }
+
+   return 0.0;
+}
+
+void gradp_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+      f(0) = cos(x(0)) * sin(x(1)) * sin(x(2));
+      f(1) = sin(x(0)) * cos(x(1)) * sin(x(2));
+      f(2) = sin(x(0)) * sin(x(1)) * cos(x(2));
+   }
+   else
+   {
+      f(0) = cos(x(0)) * sin(x(1));
+      f(1) = sin(x(0)) * cos(x(1));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}
+
+real_t 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;
+}
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}

miniapps/nurbs/nurbs_ex3.cpp

@@ -0,0 +1,284 @@
+//                                MFEM Example 3 -- modified for NURBS FE
+//
+// Compile with: make nurbs_ex3
+//
+// Sample runs:  nurbs_ex3 -m ../../data/square-nurbs.mesh
+//               nurbs_ex3 -m ../../data/square-nurbs.mesh -o 2
+//               nurbs_ex3 -m ../../data/cube-nurbs.mesh
+//
+// Description:  This example code solves a simple electromagnetic diffusion
+//               problem corresponding to the second order definite Maxwell
+//               equation curl curl E + E = f with boundary condition
+//               E x n = <given tangential field>. Here, we use a given exact
+//               solution E and compute the corresponding r.h.s. f.
+//               We discretize with Nedelec finite elements in 2D or 3D.
+//
+//               The example demonstrates the use of H(curl) finite element
+//               spaces with the curl-curl and the (vector finite element) mass
+//               bilinear form, as well as the computation of discretization
+//               error when the exact solution is known. Static condensation is
+//               also illustrated.
+//
+//               NURBS-based H(curl) spaces only implemented for meshes
+//               consisting of a single patch.
+//
+//               We recommend viewing examples 1-2 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Exact solution, E, and r.h.s., f. See below for implementation.
+void E_exact(const Vector &, Vector &);
+void f_exact(const Vector &, Vector &);
+real_t freq = 1.0, kappa;
+int dim;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/square-nurbs.mesh";
+   int ref_levels = -1;
+   bool NURBS = true;
+   int order = 1;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   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, -1 for auto.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&NURBS, "-n", "--nurbs", "-nn","--no-nurbs",
+                  "NURBS.");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   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.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 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 50,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels =
+            (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *fec = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+
+   if (mesh->NURBSext && NURBS)
+   {
+      fec = new NURBS_HCurlFECollection(order,dim);
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      NURBS = false;
+      fec = new ND_FECollection(order, dim);
+      mfem::out<<"Create Normal fec"<<std::endl;
+   }
+
+   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, NURBSext, fec);
+   cout << "Number of finite element unknowns: "
+        << fespace->GetTrueVSize() << endl;
+
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
+   //    In this example, the boundary conditions are defined by marking all
+   //    the boundary attributes from the mesh as essential (Dirichlet) and
+   //    converting them to a list of true dofs.
+   Array<int> ess_tdof_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+   cout << "Number of knowns in essential BCs: "
+        << ess_tdof_list.Size() << endl;
+
+   // 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.
+   VectorFunctionCoefficient f(sdim, f_exact);
+   LinearForm *b = new LinearForm(fespace);
+   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+   b->Assemble();
+
+   // 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 edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   GridFunction x(fespace);
+   VectorFunctionCoefficient E(sdim, E_exact);
+   x.ProjectCoefficient(E);
+
+   // 9. Set up the bilinear form corresponding to the EM diffusion operator
+   //    curl muinv curl + sigma I, by adding the curl-curl and the mass domain
+   //    integrators.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(1.0);
+   BilinearForm *a = new BilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+
+   // 10. Assemble the bilinear form and the corresponding linear system,
+   //     applying any necessary transformations such as: eliminating boundary
+   //     conditions, applying conforming constraints for non-conforming AMR,
+   //     static condensation, etc.
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   OperatorPtr A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+   cout << "Size of linear system: " << A->Height() << endl;
+
+   // 11. Solve the linear system A X = B.
+   if (pa) // Jacobi preconditioning in partial assembly mode
+   {
+      OperatorJacobiSmoother M(*a, ess_tdof_list);
+      PCG(*A, M, B, X, 1, 1000, 1e-12, 0.0);
+   }
+   else
+   {
+#ifndef MFEM_USE_SUITESPARSE
+      // 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
+      //     solve the system Ax=b with PCG.
+      GSSmoother M((SparseMatrix&)(*A));
+      PCG(*A, M, B, X, 1, 500, 1e-12, 0.0);
+#else
+      // 11. 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
+   }
+
+   // 12. Recover the solution as a finite element grid function.
+   a->RecoverFEMSolution(X, *b, x);
+
+   // 13. Compute and print the L^2 norm of the error.
+   cout << "\n|| E_h - E ||_{L^2} = " << x.ComputeL2Error(E) << '\n' << endl;
+
+   // 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");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+      ofstream sol_ofs("sol.gf");
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 15. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *mesh << x << flush;
+   }
+
+   // 16. Create output in visit format
+   VisItDataCollection visit_dc("Example3", mesh);
+   visit_dc.RegisterField("x", &x);
+   visit_dc.Save();
+
+   // 17. Free the used memory.
+   delete a;
+   delete sigma;
+   delete muinv;
+   delete b;
+   delete fespace;
+   delete fec;
+   delete mesh;
+
+   return 0;
+}
+
+
+void E_exact(const Vector &x, Vector &E)
+{
+   if (dim == 3)
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+void f_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (1. + kappa * kappa) * sin(kappa * x(0));
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}

miniapps/nurbs/nurbs_ex5.cpp

@@ -0,0 +1,498 @@
+//                                MFEM Example 5 -- modified for NURBS FE
+//
+// Compile with: make nurbs_ex5
+//
+// Sample runs:  nurbs_ex5 -m ../../data/square-nurbs.mesh -o 3
+//               nurbs_ex5 -m ../../data/cube-nurbs.mesh -r 3
+//               nurbs_ex5 -m ../../data/pipe-nurbs-2d.mesh
+//               nurbs_ex5 -m ../../data/beam-tet.mesh
+//               nurbs_ex5 -m ../../data/beam-hex.mesh
+//               nurbs_ex5 -m ../../data/escher.mesh
+//               nurbs_ex5 -m ../../data/fichera.mesh
+//
+// Device sample runs -- do not work for NURBS:
+//               nurbs_ex5 -m ../../data/escher.mesh -pa -d cuda
+//               nurbs_ex5 -m ../../data/escher.mesh -pa -d raja-cuda
+//               nurbs_ex5 -m ../../data/escher.mesh -pa -d raja-omp
+//
+// Description:  This example code solves a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system
+//
+//                                 k*u + grad p = f
+//                                 - div u      = g
+//
+//               with natural boundary condition -p = <given pressure>.
+//               Here, we use a given exact solution (u,p) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Raviart-Thomas
+//               finite elements (velocity u) and piecewise discontinuous
+//               polynomials (pressure p).
+//
+//               NURBS-based H(div) spaces only implemented for meshes
+//               consisting of a single patch.
+//
+//               The example demonstrates the use of the BlockOperator class, as
+//               well as the collective saving of several grid functions in
+//               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+// Sample runs:  nurbs_ex3 -m ../../data/square-nurbs.mesh
+//               nurbs_ex3 -m ../../data/square-nurbs.mesh -o 2
+//               nurbs_ex3 -m ../../data/cube-nurbs.mesh
+
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void uFun_ex(const Vector & x, Vector & u);
+real_t pFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/square-nurbs.mesh";
+   int ref_levels = -1;
+   int order = 1;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   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, -1 for auto.");
+   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(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels =
+            (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *hdiv_coll = nullptr;
+   FiniteElementCollection *l2_coll = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+
+   if (mesh->NURBSext && !pa)
+   {
+      hdiv_coll = new NURBS_HDivFECollection(order,dim);
+      l2_coll   = new NURBSFECollection(order);
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      hdiv_coll = new RT_FECollection(order, dim);
+      l2_coll   = new L2_FECollection(order, dim);
+      mfem::out<<"Create Normal fec"<<std::endl;
+   }
+   pa = false;
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, NURBSext, l2_coll);
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh,
+                                                        W_space->StealNURBSext(),
+                                                        hdiv_coll);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   Array<int> block_offsets(3); // number of variables + 1
+   block_offsets[0] = 0;
+   block_offsets[1] = R_space->GetVSize();
+   block_offsets[2] = W_space->GetVSize();
+   block_offsets.PartialSum();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+   {
+      Array<int> ess_tdof_list;
+      if (mesh->bdr_attributes.Size())
+      {
+         Array<int> ess_bdr(mesh->bdr_attributes.Max());
+         ess_bdr = 1;
+         R_space->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      }
+      cout << "Number boundary dofs in H(div): "
+           << ess_tdof_list.Size() << endl;
+   }
+
+   {
+      Array<int> ess_tdof_list;
+      if (mesh->bdr_attributes.Size())
+      {
+         Array<int> ess_bdr(mesh->bdr_attributes.Max());
+         ess_bdr = 1;
+         W_space->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      }
+      cout << "Number boundary dofs in H1: "
+           << ess_tdof_list.Size() << endl;
+   }
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   ConstantCoefficient k(1.0);
+
+   VectorFunctionCoefficient fcoeff(dim, fFun);
+   FunctionCoefficient fnatcoeff(f_natural);
+   FunctionCoefficient gcoeff(gFun);
+
+   VectorFunctionCoefficient ucoeff(dim, uFun_ex);
+   FunctionCoefficient pcoeff(pFun_ex);
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction u,p for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (u,p) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+   fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   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();
+   if (!pa) { mVarf->Finalize(); }
+
+   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+   bVarf->Assemble();
+   if (!pa) { bVarf->Finalize(); }
+
+   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);
+   }
+
+   // 10. Construct the operators for preconditioner
+   //
+   //                 P = [ diag(M)         0         ]
+   //                     [  0       B diag(M)^-1 B^T ]
+   //
+   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+   //     pressure Schur Complement
+   SparseMatrix *MinvBt = NULL;
+   Vector Md(mVarf->Height());
+
+   BlockDiagonalPreconditioner darcyPrec(block_offsets);
+   Solver *invM, *invS;
+   SparseMatrix *S = NULL;
+
+   if (pa)
+   {
+      mVarf->AssembleDiagonal(Md);
+      auto Md_host = Md.HostRead();
+      Vector invMd(mVarf->Height());
+      for (int i=0; i<mVarf->Height(); ++i)
+      {
+         invMd(i) = 1.0 / Md_host[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);
+      Md.HostReadWrite();
+
+      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);
+#else
+      invS = new UMFPackSolver(*S);
+#endif
+   }
+
+   invM->iterative_mode = false;
+   invS->iterative_mode = false;
+
+   darcyPrec.SetDiagonalBlock(0, invM);
+   darcyPrec.SetDiagonalBlock(1, invS);
+
+   // 11. Solve the linear system with MINRES.
+   //     Check the norm of the unpreconditioned residual.
+   int maxIter(10000);
+   real_t rtol(1.e-10);
+   real_t atol(1.e-10);
+
+   chrono.Clear();
+   chrono.Start();
+   MINRESSolver solver;
+   solver.SetAbsTol(atol);
+   solver.SetRelTol(rtol);
+   solver.SetMaxIter(maxIter);
+   solver.SetOperator(darcyOp);
+   solver.SetPreconditioner(darcyPrec);
+   solver.SetPrintLevel(1);
+   x = 0.0;
+   solver.Mult(rhs, x);
+   if (device.IsEnabled()) { x.HostRead(); }
+   chrono.Stop();
+
+   if (solver.GetConverged())
+   {
+      std::cout << "MINRES converged in " << solver.GetNumIterations()
+                << " iterations with a residual norm of "
+                << solver.GetFinalNorm() << ".\n";
+   }
+   else
+   {
+      std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                << " iterations. Residual norm is " << solver.GetFinalNorm()
+                << ".\n";
+   }
+   std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+   // 12. Create the grid functions u and p. Compute the L2 error norms.
+   GridFunction u, p;
+   u.MakeRef(R_space, x.GetBlock(0), 0);
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   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));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeLpNorm(2., pcoeff, *mesh, irs);
+
+   std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+   std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream u_ofs("sol_u.gf");
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs("sol_p.gf");
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock.precision(8);
+      u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      socketstream p_sock(vishost, visport);
+      p_sock.precision(8);
+      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   delete invM;
+   delete invS;
+   delete S;
+   delete Bt;
+   delete MinvBt;
+   delete mVarf;
+   delete bVarf;
+   delete W_space;
+   delete R_space;
+   delete l2_coll;
+   delete hdiv_coll;
+   delete mesh;
+
+   return 0;
+}
+
+
+void uFun_ex(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   u(0) = - exp(xi)*sin(yi)*cos(zi);
+   u(1) = - exp(xi)*cos(yi)*cos(zi);
+
+   if (x.Size() == 3)
+   {
+      u(2) = exp(xi)*sin(yi)*sin(zi);
+   }
+}
+
+// Change if needed
+real_t pFun_ex(const Vector & x)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return exp(xi)*sin(yi)*cos(zi);
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   f = 0.0;
+}
+
+real_t gFun(const Vector & x)
+{
+   if (x.Size() == 3)
+   {
+      return -pFun_ex(x);
+   }
+   else
+   {
+      return 0;
+   }
+}
+
+real_t f_natural(const Vector & x)
+{
+   return (-pFun_ex(x));
+}

miniapps/nurbs/nurbs_patch_ex1.cpp

@@ -153,7 +153,8 @@ int main(int argc, char *argv[])
    if (patchAssembly && reducedIntegration && !pa)
    {
 #ifdef MFEM_USE_SINGLE
-      MFEM_ABORT("Reduced integration is not supported in single precision.");
+      cout << "Reduced integration is not supported in single precision.\n";
+      return MFEM_SKIP_RETURN_VALUE;
 #endif
 
       di->SetIntegrationMode(NonlinearFormIntegrator::Mode::PATCHWISE_REDUCED);

miniapps/nurbs/nurbs_solenoidal.cpp

@@ -0,0 +1,401 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+//
+//        ------------------------------------------------------------
+//        NURBS Solenoidal Miniapp: Project solenoidal velocity
+//        ------------------------------------------------------------
+//
+//
+// Compile with: make nurbs_solenoidal
+//
+// Sample runs:  nurbs_solenoidal -m ../../data/square-nurbs.mesh -o 2
+//               nurbs_solenoidal -m ../../data/cube-nurbs.mesh -o 2
+//
+// Description:  This code projects a velocity field, and forces this field
+//               to be solenoidal, viz. the divergence is zero. If the correct
+//               discrete spaces are chosen the divergence is pointwise zero.
+//
+//               This is achieved by solving a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system   (similar to ex5)
+//
+//                                 u + grad p = u_ex
+//                                    - div u = 0
+//
+//               NURBS-based H(div) spaces only implemented for meshes
+//               consisting of a single patch.
+//
+//               Here, u_ex is the specified velocity field. If u_ex is
+//               divergence free, we expect the pressure to converge to zero.
+//               We discretize with H(div) and L2/H1 conforming elements.
+
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+
+void u_2d(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+
+   int p = 4;
+
+   u(0) =  pow(xi,p + 1)*pow(yi,p    );
+   u(1) = -pow(xi,p    )*pow(yi,p + 1);
+}
+
+void u_3d(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(x(2));
+
+   int p = 4;
+
+   real_t cx = 3.0/4.0;
+   real_t cy = 2.0/3.0;
+   real_t cz = -cx - cy;
+
+   u(0) = cx*pow(xi,p + 1)*pow(yi,p    )*pow(zi,p    );
+   u(1) = cy*pow(xi,p    )*pow(yi,p + 1)*pow(zi,p    );
+   u(2) = cz*pow(xi,p    )*pow(yi,p    )*pow(zi,p + 1);
+}
+
+// Define the analytical solution and forcing terms / boundary conditions
+void u_ex(const Vector & x, Vector & u)
+{
+   if (x.Size() == 2)
+   {
+      u_2d(x, u);
+   }
+   else if (x.Size() == 3)
+   {
+      u_3d(x, u);
+   }
+}
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/square-nurbs.mesh";
+   int ref_levels = -1;
+   int order = 1;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+   bool NURBS = true;
+   bool div_free = true;
+
+   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, -1 for auto.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&div_free, "-df", "--div-free", "-p","--proj",
+                  "Div-free or standard projection.");
+   args.AddOption(&NURBS, "-n", "--nurbs", "-nn","--no-nurbs",
+                  "NURBS.");
+   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.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(mfem::out);
+      return 1;
+   }
+   args.PrintOptions(mfem::out);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels =
+            (int)floor(log(5000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *hdiv_coll = nullptr;
+   FiniteElementCollection *l2_coll = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+
+   if (mesh->NURBSext&& NURBS)
+   {
+      hdiv_coll = new NURBS_HDivFECollection(order, dim);
+      l2_coll   = new NURBSFECollection(order);
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      NURBS = false;
+      hdiv_coll = new RT_FECollection(order, dim);
+      l2_coll   = new L2_FECollection(order, dim);
+      mfem::out<<"Create Normal fec"<<std::endl;
+   }
+
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, NURBSext, l2_coll);
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh,
+                                                        W_space->StealNURBSext(),
+                                                        hdiv_coll);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   Array<int> block_offsets(3); // number of variables + 1
+   block_offsets[0] = 0;
+   block_offsets[1] = R_space->GetVSize();
+   block_offsets[2] = W_space->GetVSize();
+   block_offsets.PartialSum();
+
+   mfem::out << "***********************************************************\n";
+   mfem::out << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   mfem::out << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   mfem::out << "dim(R+W) = " << block_offsets.Last() << "\n";
+   mfem::out << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient zero(0.0);
+   VectorFunctionCoefficient ucoeff(dim, u_ex);
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction u,p for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (u,p) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+   rhs = 0.0;
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(ucoeff));
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   BilinearForm *mVarf(new BilinearForm(R_space));
+   MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
+
+   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(one));
+   mVarf->Assemble();
+   mVarf->Finalize();
+
+   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+   bVarf->Assemble();
+   bVarf->Finalize();
+
+   SparseMatrix &M(mVarf->SpMat());
+   SparseMatrix &B(bVarf->SpMat());
+   B *= -1.;
+   TransposeOperator *Bt = new TransposeOperator(&B);
+
+   BlockOperator darcyOp(block_offsets);
+   darcyOp.SetBlock(0,0, &M);
+   if (div_free) { darcyOp.SetBlock(0,1, Bt); }
+   if (div_free) { darcyOp.SetBlock(1,0, &B); }
+
+   // 10. Construct the operators for preconditioner
+   //
+   //                 P = [ diag(M)         0         ]
+   //                     [  0       B diag(M)^-1 B^T ]
+   //
+   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+   //     pressure Schur Complement
+   Vector Md(mVarf->Height());
+   M.GetDiag(Md);
+   Md.HostReadWrite();
+   SparseMatrix *MinvBt = Transpose(B);
+   for (int i = 0; i < Md.Size(); i++)
+   {
+      MinvBt->ScaleRow(i, 1./Md(i));
+   }
+   SparseMatrix *S = Mult(B, *MinvBt);
+   Solver *invS;
+#ifndef MFEM_USE_SUITESPARSE
+   invS = new GSSmoother(*S);
+#else
+   invS = new UMFPackSolver(*S);
+#endif
+   invS->iterative_mode = false;
+
+   Solver *invM = new GSSmoother(M);
+   invM->iterative_mode = false;
+
+   BlockDiagonalPreconditioner darcyPrec(block_offsets);
+   darcyPrec.SetDiagonalBlock(0, invM);
+   darcyPrec.SetDiagonalBlock(1, invS);
+
+   // 11. Solve the linear system with MINRES.
+   //     Check the norm of the unpreconditioned residual.
+   int maxIter(10000);
+   real_t rtol(10*std::numeric_limits<real_t>::epsilon());
+   real_t atol(10*std::numeric_limits<real_t>::epsilon());
+
+   chrono.Clear();
+   chrono.Start();
+   MINRESSolver solver;
+   solver.SetAbsTol(atol);
+   solver.SetRelTol(rtol);
+   solver.SetMaxIter(maxIter);
+   solver.SetOperator(darcyOp);
+   solver.SetPreconditioner(darcyPrec);
+   solver.SetPrintLevel(2);
+   x = 0.0;
+   solver.Mult(rhs, x);
+   if (device.IsEnabled()) { x.HostRead(); }
+   chrono.Stop();
+
+   if (solver.GetConverged())
+   {
+      mfem::out << "MINRES converged in " << solver.GetNumIterations()
+                << " iterations with a residual norm of "
+                << solver.GetFinalNorm() << ".\n";
+   }
+   else
+   {
+      mfem::out << "MINRES did not converge in " << solver.GetNumIterations()
+                << " iterations. Residual norm is " << solver.GetFinalNorm()
+                << ".\n";
+   }
+   mfem::out << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+   // 12. Create the grid functions u and p
+   GridFunction u, p, uu, vv, ww;
+   u.MakeRef(R_space, x.GetBlock(0), 0);
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m exsol.mesh -g sol_u.gf" or "glvis -m exsol.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("exsol.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream u_ofs("sol_u.gf");
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs("sol_p.gf");
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Solenoidal", mesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Solenoidal", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock.precision(8);
+      u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      socketstream p_sock(vishost, visport);
+      p_sock.precision(8);
+      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+   }
+
+   // 17. Compute errors
+   int order_quad = 2*order+2;
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t err_p  = p.ComputeL2Error(zero, irs);
+   real_t err_div  = u.ComputeDivError(&zero, irs);
+
+   mfem::out << "|| u_h - u_ex ||  = " << err_u  << "\n";
+   mfem::out << "|| div u_h - div u_ex ||  = " << err_div  << "\n";
+   mfem::out << "|| p_h - p_ex ||  = " << err_p  << "\n";
+
+   // 18. Free the used memory.
+   delete fform;
+   delete invM;
+   delete invS;
+   delete S;
+   delete Bt;
+   delete MinvBt;
+   delete mVarf;
+   delete bVarf;
+   delete W_space;
+   delete R_space;
+   delete l2_coll;
+   delete hdiv_coll;
+   delete mesh;
+
+   if (err_div > 1e4*std::numeric_limits<real_t>::epsilon() )
+   {
+      mfem::out << "std::numeric_limits<real_t>::epsilon() = "
+                << std::numeric_limits<real_t>::epsilon()  << "\n";
+      mfem_error("Divergence error larger than expected");
+   }
+
+   return 0;
+}

tests/unit/CMakeLists.txt

@@ -56,6 +56,7 @@ set(UNIT_TESTS_SRCS
   mesh/test_submesh.cpp
   mesh/test_vtu.cpp
   mesh/test_nurbs.cpp
+  mesh/test_exodus_writer.cpp
   fem/test_1d_bilininteg.cpp
   fem/test_2d_bilininteg.cpp
   fem/test_3d_bilininteg.cpp
@@ -85,6 +86,7 @@ set(UNIT_TESTS_SRCS
   fem/test_get_value.cpp
   fem/test_getderivative.cpp
   fem/test_getgradient.cpp
+  fem/test_gslib.cpp
   fem/test_intrules.cpp
   fem/test_intruletypes.cpp
   fem/test_inversetransform.cpp

tests/unit/fem/test_gslib.cpp

@@ -369,6 +369,124 @@ TEST_CASE("GSLIBInterpolateL2ElementBoundary",
 }
 
 #ifdef MFEM_USE_MPI
+// Custom interpolation procedure with gslib
+TEST_CASE("GSLIBCustomInterpolation",
+          "[GSLIBCustomInterpolation][Parallel][GSLIB]")
+{
+   int myid;
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+   int dim      = GENERATE(2, 3);
+   bool simplex = GENERATE(true, false);
+
+   CAPTURE(dim, simplex);
+
+   int nex = 4;
+   int mesh_order = 2;
+   Mesh mesh;
+   if (dim == 2)
+   {
+      Element::Type type = simplex ? Element::TRIANGLE : Element::QUADRILATERAL;
+      mesh = Mesh::MakeCartesian2D(nex, nex, type);
+   }
+   else
+   {
+      Element::Type type = simplex ? Element::TETRAHEDRON : Element::HEXAHEDRON;
+      mesh = Mesh::MakeCartesian3D(nex, nex, nex, type);
+   }
+
+   mesh.SetCurvature(mesh_order);
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+
+   // f(x,y,z) = x^2 + y^2 + z^2
+   auto func = [](const Vector &x)
+   {
+      const int dim = x.Size();
+      double res = 0.0;
+      for (int d = 0; d < dim; d++) { res += std::pow(x(d), 2); }
+      return res;
+   };
+
+   // \nabla f(x,y,z) = [2*x,2*y,2*z]
+   auto func_grad = [](const Vector &x, Vector &p)
+   {
+      const int dim = x.Size();
+      p.SetSize(dim);
+      for (int d = 0; d < dim; d++) { p(d) = 2.0*x(d); }
+   };
+
+   // Set GridFunction to be interpolated
+   int func_order = 3;
+   H1_FECollection c_fec(func_order, dim);
+   FiniteElementSpace c_fespace(&pmesh, &c_fec, 1);
+   GridFunction field_vals(&c_fespace);
+
+   FunctionCoefficient f(func);
+   field_vals.ProjectCoefficient(f);
+
+   // Generate randomized points in [0, 1]^D. Assume ordering by VDIM.
+   int npt = 101;
+   Vector xyz(npt*dim);
+   xyz.Randomize(myid + 1);
+
+   // Find points on the ParMesh
+   Vector interp_vals(npt);
+   FindPointsGSLIB finder;
+   finder.Setup(pmesh);
+   finder.FindPoints(xyz, Ordering::byVDIM);
+
+   /** Interpolate gradient using custom interpolation procedure. */
+   // We first send information to MPI ranks that own the element corresponding
+   // to each point.
+   Array<unsigned int> recv_elem, recv_code;
+   Vector recv_rst;
+   finder.DistributePointInfoToOwningMPIRanks(recv_elem, recv_rst, recv_code);
+   int npt_recv = recv_elem.Size();
+   // Compute gradient locally
+   Vector grad(npt_recv*dim);
+   for (int i = 0; i < npt_recv; i++)
+   {
+      const int e = recv_elem[i];
+
+      IntegrationPoint ip;
+      if (dim == 2)
+      {
+         ip.Set2(recv_rst(dim*i + 0),recv_rst(dim*i + 1));
+      }
+      else
+      {
+         ip.Set3(recv_rst(dim*i + 0),recv_rst(dim*i + 1),
+                 recv_rst(dim*i + 2));
+      }
+      ElementTransformation *Tr = c_fespace.GetElementTransformation(e);
+      Tr->SetIntPoint(&ip);
+
+      Vector gradloc(grad.GetData()+i*dim,dim);
+      field_vals.GetGradient(*Tr, gradloc);
+   }
+
+   // Send the computed gradient back to the ranks that requested it.
+   Vector recv_grad;
+   finder.DistributeInterpolatedValues(grad, dim, Ordering::byVDIM, recv_grad);
+
+   // Check if the received gradient matched analytic gradient.
+   for (int i = 0; i < npt && myid == 0; i++)
+   {
+      Vector x(xyz.GetData()+i*dim,dim);
+      Vector grad_exact(dim);
+      func_grad(x, grad_exact);
+
+      Vector recv_grad_i(recv_grad.GetData()+i*dim,dim);
+
+      for (int d = 0; d < dim; d++)
+      {
+         REQUIRE(grad_exact(d) == Approx(recv_grad(i*dim + d)));
+      }
+   }
+
+   finder.FreeData();
+}
+
 TEST_CASE("GSLIBGSOP", "[GSLIBGSOP][Parallel][GSLIB]")
 {
    int myid;
@@ -434,7 +552,7 @@ TEST_CASE("GSLIBGSOP", "[GSLIBGSOP][Parallel][GSLIB]")
       REQUIRE(vals(i) < 0);
    }
 }
-#endif
+#endif // MFEM_USE_MPI
 
 } //namespace_gslib
 #endif

tests/unit/fem/test_hp_transfer.cpp

@@ -0,0 +1,298 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "unit_tests.hpp"
+#include "mfem.hpp"
+
+using namespace mfem;
+namespace hptransfer_test
+{
+
+int order=1;
+
+double u(const Vector & x)
+{
+   return pow(x.Sum(),order);
+}
+
+void vecu(const Vector & x, Vector & U)
+{
+   for (int i = 0; i<x.Size(); i++)
+   {
+      U[i] = pow(x[i], order);
+   }
+}
+
+void RandomPRefinement(FiniteElementSpace & fes)
+{
+   Mesh *mesh = fes.GetMesh();
+   for (int i = 0; i < mesh->GetNE(); i++)
+   {
+      if ((double) rand() / RAND_MAX < 0.5)
+      {
+         const int eorder = fes.GetElementOrder(i);
+         fes.SetElementOrder(i,eorder+1);
+      }
+   }
+   fes.Update(false);
+}
+
+/* This function randomly selects elements to be de-refined and sets the
+   order of the elements that share the same parent to their minimum */
+void PreprocessRandomDerefinement(FiniteElementSpace & fes, Array<int> &drefs,
+                                  double prob=0.5)
+{
+   Mesh * mesh = fes.GetMesh();
+   const Table & dereftable = mesh->ncmesh->GetDerefinementTable();
+   int dref = dereftable.Size();
+   for (int i = 0; i < dref; i++)
+   {
+      if ((double) rand() / RAND_MAX < prob)
+      {
+         drefs.Append(i);
+      }
+   }
+
+   // Go through the possible derefinements and set the orders to minimum
+   Array<int> row;
+   for (int i = 0; i<drefs.Size(); i++)
+   {
+      dereftable.GetRow(drefs[i], row);
+      int minorder = 100;
+      for (int j = 0; j<row.Size(); j++)
+      {
+         minorder = std::min(minorder, fes.GetElementOrder(row[j]));
+      }
+      // set the min order
+      for (int j = 0; j<row.Size(); j++)
+      {
+         fes.SetElementOrder(row[j],minorder);
+      }
+   }
+   fes.Update(false);
+}
+
+void Derefine(Mesh &mesh, const Array<int> &drefs)
+{
+   const Table & dereftable = mesh.ncmesh->GetDerefinementTable();
+
+   Array<int> row;
+   Vector errors(mesh.GetNE()); errors = infinity();
+   for (int i = 0; i<drefs.Size(); i++)
+   {
+      dereftable.GetRow(drefs[i], row);
+      for (int j = 0; j<row.Size(); j++)
+      {
+         errors[row[j]] = 0.0;
+      }
+   }
+   mesh.DerefineByError(errors,1.0);
+}
+
+enum class Space {H1, L2, VectorH1, VectorL2};
+
+TEST_CASE("hpTransfer", "[hpTransfer]")
+{
+   auto space   = GENERATE(Space::H1, Space::L2, Space::VectorH1, Space::VectorL2);
+   int dim      = GENERATE(2,3);
+   auto simplex = GENERATE(false, true);
+   order        = GENERATE(1,2);
+   auto relax_conformity = GENERATE(false, true);
+
+   /* No need to distinguish between relaxed and full conformity in the DG case*/
+   if ((space == Space::L2 || space == Space::VectorL2) && relax_conformity) { return; }
+
+   constexpr int ne = 3;
+
+   CAPTURE(space, dim, simplex, order, relax_conformity);
+
+   Mesh mesh;
+   if (dim == 2)
+   {
+      Element::Type type = simplex ? Element::TRIANGLE : Element::QUADRILATERAL;
+      mesh = Mesh::MakeCartesian2D(ne, ne, type, 1, 1.0, 1.0);
+   }
+   else
+   {
+      Element::Type type = simplex ? Element::TETRAHEDRON : Element::HEXAHEDRON;
+      mesh = Mesh::MakeCartesian3D(ne, ne, ne, type, 1.0, 1.0, 1.0);
+   }
+   mesh.EnsureNCMesh(true);
+
+   // 1. Set up initial state by randomly h- and p- refinement
+   mesh.RandomRefinement(0.5);
+
+   FiniteElementCollection * fec = nullptr;
+   if (space == Space::H1 || space == Space::VectorH1)
+   {
+      fec = new H1_FECollection(order, dim);
+   }
+   else
+   {
+      fec = new L2_FECollection(order, dim);
+   }
+
+   int dimc = (space<=Space::L2) ? 1 : dim;
+   FiniteElementSpace fes(&mesh, fec, dimc);
+   fes.SetRelaxedHpConformity(relax_conformity);
+   RandomPRefinement(fes);
+
+   // 2. Set up a GridFunction on the initial hp-mesh
+   FunctionCoefficient f(u);
+   VectorFunctionCoefficient vf(dim,vecu);
+   GridFunction gf(&fes); gf = 0.0;
+   if (space<=Space::L2)
+   {
+      gf.ProjectCoefficient(f);
+   }
+   else
+   {
+      gf.ProjectCoefficient(vf);
+   }
+
+   // 3. Randomly h-refine the mesh and transfer the GridFunction
+   mesh.RandomRefinement(0.5);
+   fes.Update();
+   gf.Update();
+
+   GridFunction err_gf(&fes);
+   if (space<=Space::L2)
+   {
+      err_gf.ProjectCoefficient(f);
+   }
+   else
+   {
+      err_gf.ProjectCoefficient(vf);
+   }
+   err_gf-= gf;
+
+   if (fes.GetHpRestrictionMatrix())
+   {
+      Vector tmp0(fes.GetHpRestrictionMatrix()->Height());
+      fes.GetHpRestrictionMatrix()->Mult(err_gf,tmp0);
+      fes.GetProlongationMatrix()->Mult(tmp0,err_gf);
+   }
+
+   // 3a. Check if the prolonged GridFunction to the h-refined
+   //     mesh exactly reproduces the polynomial GridFunction
+   REQUIRE(err_gf.Norml2() < 1e-11);
+
+   // 4. Randomly p-refine the mesh and transfer the GridFunction
+   Mesh cmesh(mesh);
+   FiniteElementSpace cfes(&cmesh, fec, dimc);
+   cfes.SetRelaxedHpConformity(relax_conformity);
+   for (int i = 0; i<cmesh.GetNE(); i++)
+   {
+      cfes.SetElementOrder(i,fes.GetElementOrder(i));
+   }
+   cfes.Update(false);
+
+   RandomPRefinement(fes);
+   PRefinementTransferOperator T(cfes, fes);
+
+   GridFunction hpgf(&fes);
+   T.Mult(gf,hpgf);
+
+   err_gf.SetSpace(&fes);
+   if (space<=Space::L2)
+   {
+      err_gf.ProjectCoefficient(f);
+   }
+   else
+   {
+      err_gf.ProjectCoefficient(vf);
+   }
+   err_gf-= hpgf;
+
+   if (fes.GetHpRestrictionMatrix())
+   {
+      Vector tmp(fes.GetHpRestrictionMatrix()->Height());
+      fes.GetHpRestrictionMatrix()->Mult(err_gf,tmp);
+      fes.GetProlongationMatrix()->Mult(tmp,err_gf);
+   }
+
+   // 4a. Check if the prolonged GridFunction to the p-refined
+   //     mesh exactly reproduces the polynomial GridFunction
+   REQUIRE(err_gf.Norml2() < 1e-11);
+
+   // 5. Before randomly de-refining the mesh ensure that the elements
+   //    (of the same parent) that are going to be de-refined
+   //    have the same order
+   Mesh fmesh(mesh);
+   FiniteElementSpace ffes(&fmesh, fec, dimc);
+   ffes.SetRelaxedHpConformity(relax_conformity);
+   for (int i = 0; i<fmesh.GetNE(); i++)
+   {
+      ffes.SetElementOrder(i,fes.GetElementOrder(i));
+   }
+   ffes.Update(false);
+
+   Array<int> drefs;
+   // lower the order of the children to their minimum
+   PreprocessRandomDerefinement(fes, drefs);
+   PRefinementTransferOperator T2(ffes, fes);
+   gf.SetSpace(&fes);
+   T2.Mult(hpgf, gf);
+
+   err_gf.SetSpace(&fes);
+   if (space<=Space::L2)
+   {
+      err_gf.ProjectCoefficient(f);
+   }
+   else
+   {
+      err_gf.ProjectCoefficient(vf);
+   }
+   err_gf-= gf;
+
+   if (fes.GetHpRestrictionMatrix())
+   {
+      Vector temp(fes.GetHpRestrictionMatrix()->Height());
+      fes.GetHpRestrictionMatrix()->Mult(err_gf,temp);
+      fes.GetProlongationMatrix()->Mult(temp,err_gf);
+   }
+
+   // 5a. Check if the restricted GridFunction to the p-derefined
+   //     mesh exactly reproduces the polynomial GridFunction
+   REQUIRE(err_gf.Norml2() < 1e-11);
+
+   // 6. De-refine the mesh and transfer the GridFunction
+   Derefine(mesh,drefs);
+
+   fes.Update();
+   gf.Update();
+
+   err_gf.SetSpace(&fes); err_gf = 0.0;
+   if (space<=Space::L2)
+   {
+      err_gf.ProjectCoefficient(f);
+   }
+   else
+   {
+      err_gf.ProjectCoefficient(vf);
+   }
+
+   err_gf-= gf;
+
+   if (fes.GetHpRestrictionMatrix())
+   {
+      Vector temp(fes.GetHpRestrictionMatrix()->Height());
+      fes.GetHpRestrictionMatrix()->Mult(err_gf,temp);
+      fes.GetProlongationMatrix()->Mult(temp,err_gf);
+   }
+
+   // 6a. Check if the restricted GridFunction to the de-refined
+   //     mesh exactly reproduces the polynomial GridFunction
+   REQUIRE(err_gf.Norml2() < 1e-11);
+   delete fec;
+}
+
+}

tests/unit/general/test_umpire_mem.cpp

@@ -18,12 +18,13 @@
 #include <unistd.h>
 #include <stdio.h>
 #include "umpire/Umpire.hpp"
+#include <umpire/strategy/QuickPool.hpp>
 
 #ifdef MFEM_USE_CUDA
 #include <cuda.h>
 constexpr const char * device_name = "cuda";
 #elif defined(MFEM_USE_HIP)
-constexpr const char * device_name = "raja-hip";
+constexpr const char * device_name = "hip";
 #endif
 
 using namespace mfem;
@@ -45,10 +46,12 @@ static bool is_pinned_host(void * h_p)
    unsigned flags;
 #ifdef MFEM_USE_CUDA
    auto err = cudaHostGetFlags(&flags, h_p);
+   cudaGetLastError(); // also resets last error
    if (err == cudaSuccess) { return true; }
    else if (err == cudaErrorInvalidValue) { return false; }
 #elif defined(MFEM_USE_HIP)
    auto err = hipHostGetFlags(&flags, h_p);
+   hipGetLastError(); // also resets last error
    if (err == hipSuccess) { return true; }
    else if (err == hipErrorInvalidValue) { return false; }
 #endif

tests/unit/mesh/test_exodus_writer.cpp

@@ -0,0 +1,129 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "mfem.hpp"
+#include "unit_tests.hpp"
+
+using namespace mfem;
+
+#ifdef MFEM_USE_NETCDF
+static void CompareMeshes(Mesh &mesh1, Mesh &mesh2)
+{
+   REQUIRE(mesh1.GetNE() == mesh2.GetNE());
+   REQUIRE(mesh1.GetNV() == mesh2.GetNV());
+   REQUIRE(mesh1.GetNBE() == mesh2.GetNBE());
+   REQUIRE(mesh1.GetNFaces() == mesh2.GetNFaces());
+
+   const FiniteElementSpace *fespace1 = mesh1.GetNodalFESpace();
+   const FiniteElementSpace *fespace2 = mesh2.GetNodalFESpace();
+
+   // Check elements.
+   Array<int> element_faces1, element_faces2;
+   Array<int> element_orient1, element_orient2;
+   Array<int> dofs1, dofs2;
+
+   for (int ielement = 0; ielement < mesh1.GetNE(); ielement++)
+   {
+      int attr1 = mesh1.GetAttribute(ielement);
+      int attr2 = mesh2.GetAttribute(ielement);
+
+      REQUIRE(attr1 == attr2);
+
+      Element::Type type1 = mesh1.GetElementType(ielement);
+      Element::Type type2 = mesh2.GetElementType(ielement);
+
+      REQUIRE(type1 == type2);
+
+      mesh1.GetElementFaces(ielement, element_faces1, element_orient1);
+      mesh2.GetElementFaces(ielement, element_faces2, element_orient2);
+
+      REQUIRE(element_faces1 == element_faces2);
+      REQUIRE(element_orient1 == element_orient2);
+
+      if (fespace1 && fespace2)
+      {
+         fespace1->GetElementDofs(ielement, dofs1);
+         fespace2->GetElementDofs(ielement, dofs2);
+      }
+      else
+      {
+         mesh1.GetElementVertices(ielement, dofs1);
+         mesh2.GetElementVertices(ielement, dofs2);
+      }
+
+      REQUIRE(dofs1 == dofs2);
+   }
+
+   // Check bdr elements.
+   for (int ibdr_element = 0; ibdr_element < mesh1.GetNBE(); ibdr_element++)
+   {
+      int attr1 = mesh1.GetBdrAttribute(ibdr_element);
+      int attr2 = mesh2.GetBdrAttribute(ibdr_element);
+
+      REQUIRE(attr1 == attr2);
+
+      Element::Type type1 = mesh1.GetBdrElementType(ibdr_element);
+      Element::Type type2 = mesh2.GetBdrElementType(ibdr_element);
+
+      REQUIRE(type1 == type2);
+
+      int face_index1 = mesh1.GetBdrElementFaceIndex(ibdr_element);
+      int face_index2 = mesh2.GetBdrElementFaceIndex(ibdr_element);
+
+      REQUIRE(face_index1 == face_index2);
+   }
+
+   // Check face vertices.
+   Array<int> face_vertices1, face_vertices2;
+   for (int iface_index = 0; iface_index < mesh1.GetNFaces(); iface_index++)
+   {
+      mesh1.GetFaceVertices(iface_index, face_vertices1);
+      mesh2.GetFaceVertices(iface_index, face_vertices2);
+
+      REQUIRE(face_vertices1 == face_vertices2);
+   }
+}
+#endif
+
+TEST_CASE("ExodusII Writer", "[Mesh][ExodusII][MFEMData]")
+{
+#ifdef MFEM_USE_NETCDF
+   // NB: wedge, pyramid and mixed mesh tests require the ExodusII reader PR
+   // to be merged. Pyramid14 tests require the pyramid-dev branch to be merged.
+   auto filename = GENERATE("simple-cube-hex8.e",
+                            "simple-cube-hex27.e",
+                            "simple-cube-tet4.e",
+                            "simple-cube-tet10.e"//,
+                            //  "simple-cube-wedge6.e",
+                            //  "simple-cube-wedge18.e",
+                            //  "simple-cube-pyramid5.e",
+                            //  "simple-cube-pyramid14.e",
+                            //  "simple-cube-multi-element-order1.e",
+                            //  "simple-cube-multi-element-order2.e"
+                           );
+
+   // Load Exodus II mesh from file. NB: do NOT refine as this changes vertex ordering!
+   Mesh original_mesh = Mesh::LoadFromFile(mfem_data_dir + "/exodusii/" + filename,
+                                           0, 0, true);
+
+   // Write generated Exodus II mesh to file.
+   std::string filename_generated = "generated-mesh.e";
+   original_mesh.PrintExodusII(filename_generated);
+
+   // Load generated Exodus II mesh.
+   Mesh generated_mesh = Mesh::LoadFromFile(filename_generated, 0, 0, true);
+
+   CompareMeshes(original_mesh, generated_mesh);
+
+   // Remove temporary file.
+   REQUIRE(remove(filename_generated.c_str()) == 0);
+#endif
+}