add a test

Improve HYPRE solver documentation

.gitignore

@@ -313,6 +313,8 @@ miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
 miniapps/nurbs/nurbs_ex3
 miniapps/nurbs/nurbs_ex5
+miniapps/nurbs/nurbs_ex10
+miniapps/nurbs/nurbs_ex10p
 miniapps/nurbs/nurbs_ex11p
 miniapps/nurbs/nurbs_ex24
 miniapps/nurbs/nurbs_solenoidal
@@ -338,7 +340,14 @@ miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
 miniapps/nurbs/glvis_naca-cmesh.mesh
 miniapps/nurbs/Naca_cmesh
+miniapps/nurbs/nurbs_mesh_info
+miniapps/nurbs/k*_*.dat
 miniapps/nurbs/*-Surface.mesh
+miniapps/nurbs/*.mesh
+miniapps/nurbs/*.sol
+miniapps/nurbs/deformed.*
+miniapps/nurbs/elastic_energy.*
+miniapps/nurbs/velocity.*
 
 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -360,6 +369,7 @@ miniapps/shifted/lsf_integral
 miniapps/tools/display-basis
 miniapps/tools/load-dc
 miniapps/tools/convert-dc
+miniapps/tools/compare-dc
 miniapps/tools/gridfunction-bounds
 miniapps/tools/lor-transfer
 miniapps/tools/plor-transfer

CHANGELOG

@@ -11,6 +11,22 @@
 Version 4.9.1 (development)
 ===========================
 
+Discretization improvements
+---------------------------
+- Improved the gridfunction projection routines. Projections work for Scalar,
+  Vector and VectorFE, also NURBS versions. Optionally different types of
+  projections can be selected, default behaviour has not changed.
+
+Meshing improvements
+--------------------
+- Improved support for 1D NURBS meshes with variable order, including using
+  the patches construct for 1D NURBS meshes.
+
+New and updated examples and miniapps
+-------------------------------------
+- Electromagnetics/lorentz miniapp has been updated to leverage the ParticleSet
+  capability.
+
 
 Version 4.9, released on Dec 11, 2025
 =====================================
@@ -95,6 +111,23 @@ Linear and nonlinear solvers
   Filtering (AMGF), providing robust preconditioning for linear systems arising
   in constrained optimization problems such as frictionless contact.
 
+  Added 'GetResiduals' and 'GetFinalAbsResidualNorm' to 'HyprePCG',
+  'HypreGMRES', and 'HypreFGMRES' to get 'r' and '|r|_p'. Note that the latter
+  computes '|r|_p' from 'r' instead of returning a cached value like the
+  relative 'GetFinalResidualNorm'. These require Hypre >= 2.15.0.
+
+  Changed the default solver parameters for 'HyprePCG' to 'tol=1e-6' and
+  'max_iter=1000'. This matches the default parameters in Hypre 3.0.
+
+  Added various helper functions for querying/modifying Hypre solvers:
+  'HypreSmoother::GetType', 'HypreSmoother::GetSOROptions',
+  'HypreSmoother::GetPolyOptions', 'HypreSmoother::GetWindowParameters',
+  'HypreSmoother::IsOperatorSymmetric', 'HyprePCG::GetTol',
+  'HyprePCG::GetAbsTol', 'HyprePCG::GetMaxIter', 'HyprePCG::SetUseTwoNorm',
+  'HypreGMRES::GetTol', 'HypreGMRES::GetAbsTol', 'HypreGMRES::GetMaxIter',
+  'HypreGMRES::GetKDim', 'HypreFGMRES::GetTol', 'HypreFGMRES::GetMaxIter',
+  'HypreFGMRES::GetKDim', and 'HypreBoomerAMG::GetMaxIter'.
+
 GPU computing
 -------------
 - Added the 'gpu', 'raja-gpu', and 'ceed-gpu' backend aliases/shortcuts which

CMakeLists.txt

@@ -723,6 +723,7 @@ set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX})
 
 # Declaring the library
 mfem_add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
+target_compile_features(mfem PUBLIC cxx_std_${CMAKE_CXX_STANDARD})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
 target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES} ${TPL_TARGETS})
 if (TPL_TARGETS)
@@ -869,11 +870,12 @@ add_dependencies(exec
 #  - https://cmake.org/Bug/view.php?id=8438
 
 # Add a target to copy the mfem data directory to the build directory
-add_custom_command(OUTPUT data_is_copied
-  COMMAND ${CMAKE_COMMAND} -E copy_directory ${PROJECT_SOURCE_DIR}/data data
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying the data directory ...")
-add_custom_target(copy_data DEPENDS data_is_copied)
+# Implementable as a single copy_directory_if_different command w/ CMake >= 3.26
+file(GLOB DATA_FILES CONFIGURE_DEPENDS ${PROJECT_SOURCE_DIR}/data/*)
+add_custom_target(copy_data
+  COMMAND ${CMAKE_COMMAND} -E make_directory data
+  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${DATA_FILES} data
+  COMMENT "Syncing the data directory ...")
 # Add 'copy_data' as a prerequisite for all executables, if the source and the
 # build directories are not the same.
 if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
@@ -1005,6 +1007,10 @@ install(FILES
 install(EXPORT ${PROJECT_NAME_UC}Targets
     DESTINATION ${INSTALL_CMAKE_DIR})
 
+# Install the data directory if present, i.e. if the copy_data target is built
+install(DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/data
+  DESTINATION ${MFEM_INSTALL_DIR} OPTIONAL)
+
 #-------------------------------------------------------------------------------
 # Create 'config.mk' from 'config.mk.in' for the build and install locations and
 # define install rules for 'config.mk' and 'test.mk'

INSTALL

@@ -725,7 +725,9 @@ The specific libraries and their options are:
   URL: https://ginkgo-project.github.io
   Options: GINKGO_OPT, GINKGO_LIB, GINKGO_DIR, GINKGO_BUILD_TYPE (Release or
            Debug).
-  Versions: Ginkgo >= 1.9.0.
+  Versions: Ginkgo >= 1.9.0. When building Ginkgo with distributed support, a
+            recent version of the "develop" branch is required (1.11 as defined
+            in include/ginkgo/config.hpp).
 
 - AmgX (optional), used when MFEM_USE_AMGX = YES.
   URL: https://github.com/NVIDIA/AMGX

config/defaults.mk

@@ -18,6 +18,7 @@
 # Some choices below are based on the OS type:
 NOTMAC := $(subst Darwin,,$(shell uname -s))
 
+ASTYLE_BIN = astyle
 ETAGS_BIN = $(shell command -v etags 2> /dev/null)
 EGREP_BIN = $(shell command -v egrep 2> /dev/null)
 
@@ -407,7 +408,7 @@ AMGX_LIB = -L$(AMGX_DIR)/lib -lamgx -lcusparse -lcusolver -lcublas -lnvToolsExt
 # MAGMA library configuration
 MAGMA_DIR = @MFEM_DIR@/../magma
 MAGMA_OPT = -I$(MAGMA_DIR)/include
-MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a -lcublas -lcusparse $(LAPACK_LIB)
+MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a $(LAPACK_LIB)
 
 # GnuTLS library configuration
 GNUTLS_OPT =

data/nurbs-segments2d-patches-multispan.mesh

@@ -0,0 +1,86 @@
+MFEM NURBS mesh v1.0
+
+dimension
+1
+
+# Four segments with different NURBS orders, described via patches.
+elements
+4
+1 1 0 1
+2 1 2 3
+3 1 4 5
+4 1 6 7
+
+boundary
+0
+
+edges
+4
+0 0 1
+1 2 3
+2 4 5
+3 6 7
+
+vertices
+8
+
+patches
+
+# Patch 0: linear (order 1, 3 spans)
+knotvectors
+1
+1 4  0 0  .4 .6 1 1
+
+dimension
+2
+
+controlpoints
+0.0  0.0  1.0
+0.6  0.4  1.0
+0.4  0.6  1.0
+1.0  1.0  1.0
+
+# Patch 1: quadratic (order 2, 2 spans)
+knotvectors
+1
+2 4  0 0 0  .5 1 1 1
+
+dimension
+2
+
+controlpoints
+1.0  0.0  1.0
+1.9  0.0  1.21
+2.0  0.9  1.22
+2.0  1.0  1.0
+
+# Patch 2: cubic (order 3, 3 spans)
+knotvectors
+1
+3 6  0 0 0 0 .33 .66 1 1 1 1
+
+dimension
+2
+
+controlpoints
+2.0   0.0  1.0
+2.1   0.2  1.31
+3.5   0.4  1.32
+2.5   0.6  1.33
+2.9   1.0  1.34
+3.0   1.0  1.0
+
+# Patch 3: quartic (order 4, 1 span)
+knotvectors
+1
+4 5  0 0 0 0 0 1 1 1 1 1
+
+dimension
+2
+
+controlpoints
+3.0    0.0  1.0
+3.45   0.5  1.41
+3.50   1.0  1.42
+3.75   0.8  1.43
+4.0    0.0  1.0

data/nurbs-segments2d-patches.mesh

@@ -0,0 +1,79 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+# Three segments with different NURBS orders, described via patches.
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+patches
+
+# Patch 0: linear (order 1, 2 control points)
+knotvectors
+1
+1 2  0 0  1 1
+
+dimension
+2
+
+controlpoints
+0.0  0.0  1.0
+1.0  1.0  1.0
+
+# Patch 1: quadratic (order 2, 3 control points)
+knotvectors
+1
+2 3  0 0 0  1 1 1
+
+dimension
+2
+
+controlpoints
+1.0  0.0   1.0
+1.02 1.02  1.2
+2.0  1.0   1.0
+
+# Patch 2: cubic (order 3, 4 control points)
+knotvectors
+1
+3 4  0 0 0 0  1 1 1 1
+
+dimension
+2
+
+controlpoints
+2.0   0.0   1.0
+2.03  0.83  1.31
+2.33  1.03  1.32
+3.0   1.0   1.0
+

data/nurbs-segments2d.mesh

@@ -0,0 +1,72 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+# Edge 0: linear (order 1, 2 control points)
+# Edge 1: quadratic (order 2, 3 control points)
+# Edge 2: cubic (order 3, 4 control points)
+knotvectors
+3
+1 2  0 0  1 1
+2 3  0 0 0  1 1 1
+3 4  0 0 0 0  1 1 1 1
+
+# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
+weights
+1
+1
+1
+1
+1
+1
+1.2
+1.31
+1.32
+
+FiniteElementSpace
+FiniteElementCollection: NURBS
+VDim: 2
+Ordering: 1
+
+0.0  0.0
+1.0  1.0
+1.0  0.0
+2.0  1.0
+2.0  0.0
+3.0  1.0
+1.02 1.02
+2.03 0.83
+2.33 1.03

data/nurbs-segments3d-patches.mesh

@@ -0,0 +1,79 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+# Three segments with different NURBS orders, described via patches.
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+patches
+
+# Patch 0: linear (order 1, 2 control points)
+knotvectors
+1
+1 2  0 0  1 1
+
+dimension
+3
+
+controlpoints
+0.0  0.0  0.01 1.0
+1.0  1.0  1.01 1.0
+
+# Patch 1: quadratic (order 2, 3 control points)
+knotvectors
+1
+2 3  0 0 0  1 1 1
+
+dimension
+3
+
+controlpoints
+1.0  0.0   0.02 1.0
+1.02 1.02  0.52 1.2
+2.0  1.0   1.02 1.0
+
+# Patch 2: cubic (order 3, 4 control points)
+knotvectors
+1
+3 4  0 0 0 0  1 1 1 1
+
+dimension
+3
+
+controlpoints
+2.0   0.0   0.03 1.0
+2.03  0.83  0.33 1.31
+2.33  1.03  0.63 1.32
+3.0   1.0   1.03 1.0
+

data/nurbs-segments3d.mesh

@@ -0,0 +1,72 @@
+MFEM NURBS mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# SEGMENT     = 1
+# SQUARE      = 3
+# CUBE        = 5
+#
+
+dimension
+1
+
+elements
+3
+1 1 0 1
+2 1 2 3
+3 1 4 5
+
+boundary
+6
+1 0 0
+1 0 1
+1 0 2
+1 0 3
+1 0 4
+1 0 5
+
+edges
+3
+0 0 1
+1 2 3
+2 4 5
+
+vertices
+6
+
+# Edge 0: linear (order 1, 2 control points)
+# Edge 1: quadratic (order 2, 3 control points)
+# Edge 2: cubic (order 3, 4 control points)
+knotvectors
+3
+1 2  0 0  1 1
+2 3  0 0 0  1 1 1
+3 4  0 0 0 0  1 1 1 1
+
+# One weight per control point, in the same order as the control points; (2 + 3 + 4) = 9 weights total
+weights
+1
+1
+1
+1
+1
+1
+1.2
+1.31
+1.32
+
+FiniteElementSpace
+FiniteElementCollection: NURBS
+VDim: 3
+Ordering: 1
+
+0.0  0.0   0.01
+1.0  1.0   1.01
+1.0  0.0   0.02
+2.0  1.0   1.02
+2.0  0.0   0.03
+3.0  1.0   1.03
+1.02 1.02  0.52
+2.03 0.83  0.33
+2.33 1.03  0.63

doc/CodeDocumentation.dox

@@ -117,6 +117,8 @@ namespace mfem {
  * - <a class="el" href="ex39p_8cpp_source.html">Example 39p</a>: parallel named mesh attributes
  * - <a class="el" href="ex40_8cpp_source.html">Example 40</a>: eikonal equation
  * - <a class="el" href="ex40p_8cpp_source.html">Example 40p</a>: parallel eikonal equation
+ * - <a class="el" href="ex41_8cpp_source.html">Example 41</a>: DG/CG IMEX time-dependent advection-diffusion
+ * - <a class="el" href="ex41p_8cpp_source.html">Example 41p</a>: parallel DG/CG IMEX time-dependent advection-diffusion
  *
  * <H4>AmgX Examples</H4>
  * - Variants of Examples
@@ -188,6 +190,8 @@ namespace mfem {
  *  <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__ex10_8cpp_source.html">10</a>,
+ *  <a class="el" href="nurbs__ex10p_8cpp_source.html">10p</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.
@@ -196,6 +200,7 @@ namespace mfem {
  * - <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
+ * - <a class="el" href="nurbs__mesh_info_8cpp_source.html">NURBS Mesh info</a>: print the info of a NURBS mesh
  *
  * <H3>Miniapps</H3>
  * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
@@ -234,7 +239,8 @@ namespace mfem {
  * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Poisson problem
  * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Poisson problem
  * - <a class="el" href="generate__random__field_8cpp_source.html">SPDE Solvers</a>: SPDE solver random field generation
- * - <a class="el" href="contact-patch-test_8cpp_source.html">Contact</a>: mortar contact patch test for elasticity
+ * - <a class="el" href="contact-patch-test_8cpp_source.html">Tribol</a>: mortar contact patch test for elasticity
+ * - <a class="el" href="contact_8cpp_source.html">Contact</a>: Frictionless contact examples using <a class="el" href="classmfem_1_1IPSolver.html#details">IP optimization</a> and the <a class="el" href="classmfem_1_1AMGFSolver.html#details">AMGF solver</a>
  * - <a class="el" href="multidomain_8cpp_source.html">Multidomain miniapp</a>: Multidomain and Submesh demonstration miniapp
  * - <a class="el" href="pdiffusion_8cpp_source.html">DPG Diffusion example</a>: DPG formulation for the diffusion problem
  * - <a class="el" href="pmaxwell_8cpp_source.html">DPG Maxwell example</a>: DPG formulation for the indefinite Maxwell problem

examples/ex16.cpp

@@ -105,6 +105,7 @@ int main(int argc, char *argv[])
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
+   bool solve_implicit_state = false;
 
    int precision = 8;
    cout.precision(precision);
@@ -126,6 +127,9 @@ int main(int argc, char *argv[])
                   "Alpha coefficient.");
    args.AddOption(&kappa, "-k", "--kappa",
                   "Kappa coefficient offset.");
+   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
+                  "-imp-slope", "--implicit-slope",
+                  "Implicitly solve for stage state or slope.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -179,6 +183,11 @@ int main(int argc, char *argv[])
 
    // 7. Initialize the conduction operator and the visualization.
    ConductionOperator oper(fespace, alpha, kappa, u);
+   using ImplicitVariableType = ConductionOperator::ImplicitVariableType;
+   ImplicitVariableType imp_var = solve_implicit_state ?
+                                  ImplicitVariableType::STATE
+                                  : ImplicitVariableType::SLOPE;
+   oper.SetImplicitVariableType(imp_var);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -316,11 +325,14 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 }
 
 void ConductionOperator::ImplicitSolve(const real_t dt,
-                                       const Vector &u, Vector &du_dt)
+                                       const Vector &u, Vector &k)
 {
    // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt, where K is linearized by using u from the previous timestep
+   //    M*k = -K(u + dt*k) for k = du/dt, if solving for stage-slope
+   // or
+   //    M*k = -dt*K(k) + M*u for k = u_s, if solving for stage-state
+   // where K is linearized by using u from the previous timestep, and
+   // the stage-state and slope relation: du/dt = (u_s - u)/dt.
    if (!T)
    {
       T = Add(1.0, Mmat, dt, Kmat);
@@ -328,9 +340,20 @@ void ConductionOperator::ImplicitSolve(const real_t dt,
       T_solver.SetOperator(*T);
    }
    MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
+
+   // Construct current right-hand side for stage state vs. slope solve
+   if (ImplicitVarTypeIsState())
+   {
+      // k, on return, is the stage value u_s
+      Mmat.Mult(u, z);
+   }
+   else
+   {
+      // k, on return, is the stage slope du/dt
+      Kmat.Mult(u, z);
+      z.Neg();
+   }
+   T_solver.Mult(z, k);
 }
 
 void ConductionOperator::SetParameters(const Vector &u)

examples/ex16p.cpp

@@ -115,6 +115,7 @@ int main(int argc, char *argv[])
    bool visit = false;
    int vis_steps = 5;
    bool adios2 = false;
+   bool solve_implicit_state = false;
 
    int precision = 8;
    cout.precision(precision);
@@ -138,6 +139,9 @@ int main(int argc, char *argv[])
                   "Alpha coefficient.");
    args.AddOption(&kappa, "-k", "--kappa",
                   "Kappa coefficient offset.");
+   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
+                  "-imp-slope", "--implicit-slope",
+                  "Implicitly solve for stage state or slope.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -212,6 +216,11 @@ int main(int argc, char *argv[])
 
    // 9. Initialize the conduction operator and the VisIt visualization.
    ConductionOperator oper(fespace, alpha, kappa, u);
+   using ImplicitVariableType = ConductionOperator::ImplicitVariableType;
+   ImplicitVariableType imp_var = solve_implicit_state ?
+                                  ImplicitVariableType::STATE
+                                  : ImplicitVariableType::SLOPE;
+   oper.SetImplicitVariableType(imp_var);
 
    u_gf.SetFromTrueDofs(u);
    {
@@ -407,11 +416,14 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 }
 
 void ConductionOperator::ImplicitSolve(const real_t dt,
-                                       const Vector &u, Vector &du_dt)
+                                       const Vector &u, Vector &k)
 {
    // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt, where K is linearized by using u from the previous timestep
+   //    M*k = -K(u + dt*k) for k = du/dt, if solving for stage-slope
+   // or
+   //    M*k = -dt*K(k) + M*u for k = u_s, if solving for stage-state
+   // where K is linearized by using u from the previous timestep, and
+   // the stage-state and slope relation: du/dt = (u_s - u)/dt.
    if (!T)
    {
       T = Add(1.0, Mmat, dt, Kmat);
@@ -419,9 +431,20 @@ void ConductionOperator::ImplicitSolve(const real_t dt,
       T_solver.SetOperator(*T);
    }
    MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
+
+   // Construct current right-hand side for stage state vs. slope solve
+   if (ImplicitVarTypeIsState())
+   {
+      // k, on return, is the stage value u
+      Mmat.Mult(u, z);
+   }
+   else
+   {
+      // k, on return, is the stage slope du/dt
+      Kmat.Mult(u, z);
+      z.Neg();
+   }
+   T_solver.Mult(z, k);
 }
 
 void ConductionOperator::SetParameters(const Vector &u)

examples/ex21.cpp

@@ -119,7 +119,7 @@ int main(int argc, char *argv[])
    }
 
    LinearForm b(&fespace);
-   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
 
    // 6. Set up the bilinear form a(.,.) on the finite element space
    //    corresponding to the linear elasticity integrator with piece-wise

examples/ex21p.cpp

@@ -140,7 +140,7 @@ int main(int argc, char *argv[])
    }
 
    ParLinearForm b(&fespace);
-   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+   b.AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
 
    // 6. Set up the bilinear form a(.,.) on the finite element space
    //    corresponding to the linear elasticity integrator with piece-wise

examples/ex4.cpp

@@ -9,6 +9,7 @@
 //               ex4 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex4 -m ../data/escher.mesh
 //               ex4 -m ../data/fichera.mesh -o 2 -hb
+//               ex4 -m ../data/fichera.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-q2.vtk
 //               ex4 -m ../data/fichera-q3.mesh -o 2 -sc
 //               ex4 -m ../data/square-disc-nurbs.mesh
@@ -18,6 +19,7 @@
 //               ex4 -m ../data/amr-quad.mesh
 //               ex4 -m ../data/amr-hex.mesh
 //               ex4 -m ../data/amr-hex.mesh -o 2 -hb
+//               ex4 -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
 //               ex4 -m ../data/ref-prism.mesh -o 1
 //               ex4 -m ../data/octahedron.mesh -o 1
@@ -25,6 +27,8 @@
 //
 // Device sample runs:
 //               ex4 -m ../data/star.mesh -pa -d cuda
+//               ex4 -m ../data/star.mesh -hb -ea -d cuda
+//               ex4 -m ../data/amr-quad.mesh -hb -ea -d cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-cuda
 //               ex4 -m ../data/star.mesh -pa -d raja-omp
 //               ex4 -m ../data/beam-hex.mesh -pa -d cuda
@@ -193,7 +197,7 @@ int main(int argc, char *argv[])
    cout << "Size of linear system: " << A->Height() << endl;
 
    // 11. Solve the linear system A X = B.
-   if (!pa)
+   if (!pa && (!ea || hybridization))
    {
 #ifndef MFEM_USE_SUITESPARSE
       // Use a simple symmetric Gauss-Seidel preconditioner with PCG.

examples/ex4p.cpp

@@ -9,6 +9,7 @@
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex4p -m ../data/escher.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb
+//               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/fichera-q2.vtk
 //               mpirun -np 4 ex4p -m ../data/fichera-q3.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/square-disc-nurbs.mesh -o 3
@@ -17,14 +18,18 @@
 //               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
 //               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
+//               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
+//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb -ea
 //               mpirun -np 4 ex4p -m ../data/ref-prism.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
 // Device sample runs:
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d cuda
+//               mpirun -np 4 ex4p -m ../data/star.mesh -ea -hb -d cuda
+//               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -ea -hb -d cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-cuda
 //               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-omp
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -pa -d cuda
@@ -230,7 +235,7 @@ int main(int argc, char *argv[])
    pcg->SetMaxIter(2000);
    pcg->SetPrintLevel(1);
    if (hybridization) { prec = new HypreBoomerAMG(*A.As<HypreParMatrix>()); }
-   else if (pa) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
+   else if (pa || ea) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
    else
    {
       ParFiniteElementSpace *prec_fespace =

examples/ex9.cpp

@@ -160,6 +160,7 @@ int main(int argc, char *argv[])
    bool paraview = false;
    bool binary = false;
    int vis_steps = 5;
+   bool solve_implicit_state = false;
 
    int precision = 8;
    cout.precision(precision);
@@ -187,6 +188,9 @@ int main(int argc, char *argv[])
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
                   "Time step.");
+   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
+                  "-imp-slope", "--implicit-slope",
+                  "Implicitly solve for stage state or slope.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -366,6 +370,11 @@ int main(int argc, char *argv[])
    //    right-hand side, and perform time-integration (looping over the time
    //    iterations, ti, with a time-step dt).
    FE_Evolution adv(m, k, b);
+   using ImplicitVariableType = FE_Evolution::ImplicitVariableType;
+   ImplicitVariableType imp_var = solve_implicit_state ?
+                                  ImplicitVariableType::STATE
+                                  : ImplicitVariableType::SLOPE;
+   adv.SetImplicitVariableType(imp_var);
 
    real_t t = 0.0;
    adv.SetTime(t);
@@ -459,7 +468,17 @@ void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
    MFEM_VERIFY(dg_solver != NULL,
                "Implicit time integration is not supported with partial assembly");
-   K.Mult(x, z);
+   // Construct current right-hand side for stage state vs. slope solve
+   if (ImplicitVarTypeIsState())
+   {
+      // k, on return, is the stage value u
+      M.Mult(x, z);
+   }
+   else
+   {
+      // k, on return, is the stage slope du/dt
+      K.Mult(x, z);
+   }
    z += b;
    dg_solver->SetTimeStep(dt);
    dg_solver->Mult(z, k);

examples/ex9p.cpp

@@ -257,6 +257,7 @@ int main(int argc, char *argv[])
    bool adios2 = false;
    bool binary = false;
    int vis_steps = 5;
+   bool solve_implicit_state = false;
 #if MFEM_HYPRE_VERSION >= 21800
    PrecType prec_type = PrecType::AIR;
 #else
@@ -290,6 +291,9 @@ int main(int argc, char *argv[])
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
                   "Time step.");
+   args.AddOption(&solve_implicit_state, "-imp-state", "--implicit-state",
+                  "-imp-slope", "--implicit-slope",
+                  "Implicitly solve for stage state or slope.");
    args.AddOption((int *)&prec_type, "-pt", "--prec-type", "Preconditioner for "
                   "implicit solves. 0 for ILU, 1 for pAIR-AMG.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -536,6 +540,11 @@ int main(int argc, char *argv[])
    //     right-hand side, and perform time-integration (looping over the time
    //     iterations, ti, with a time-step dt).
    FE_Evolution adv(*m, *k, *B, prec_type);
+   using ImplicitVariableType = FE_Evolution::ImplicitVariableType;
+   ImplicitVariableType imp_var = solve_implicit_state ?
+                                  ImplicitVariableType::STATE
+                                  : ImplicitVariableType::SLOPE;
+   adv.SetImplicitVariableType(imp_var);
 
    real_t t = 0.0;
    adv.SetTime(t);
@@ -676,7 +685,17 @@ FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
 //    (M - dt*K) d = K*u + b
 void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
-   K->Mult(x, z);
+   // Construct current right-hand side for stage state vs. slope solve
+   if (ImplicitVarTypeIsState())
+   {
+      // k, on return, is the stage value u
+      M->Mult(x, z);
+   }
+   else
+   {
+      // k, on return, is the stage slope du/dt
+      K->Mult(x, z);
+   }
    z += b;
    dg_solver->SetTimeStep(dt);
    dg_solver->Mult(z, k);

examples/ginkgo/CMakeLists.txt

@@ -14,6 +14,12 @@ list(APPEND GINKGO_EXAMPLES_SRCS
   ex1.cpp
 )
 
+if (MFEM_USE_MPI AND GINKGO_BUILD_MPI)
+    list(APPEND GINKGO_EXAMPLES_SRCS
+    ex1p.cpp
+)
+endif()
+
 # Include the source directory where mfem.hpp and mfem-performance.hpp are.
 include_directories(BEFORE ${PROJECT_BINARY_DIR})
 

examples/ginkgo/ex1.cpp

@@ -207,7 +207,7 @@ int main(int argc, char *argv[])
             Ginkgo::IcPreconditioner ginkgo_precond(exec, "paric", 30);
             Ginkgo::CGSolver ginkgo_solver(exec, ginkgo_precond);
             ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(1e-12);
+            ginkgo_solver.SetRelTol(sqrt(1e-12));
             ginkgo_solver.SetAbsTol(0.0);
             ginkgo_solver.SetMaxIter(400);
             ginkgo_solver.SetOperator(*(A.Ptr()));
@@ -225,7 +225,7 @@ int main(int argc, char *argv[])
             Ginkgo::MFEMPreconditioner gko_M(exec, M);
             Ginkgo::CGSolver ginkgo_solver(exec, gko_M);
             ginkgo_solver.SetPrintLevel(print_lvl);
-            ginkgo_solver.SetRelTol(1e-12);
+            ginkgo_solver.SetRelTol(sqrt(1e-12));
             ginkgo_solver.SetAbsTol(0.0);
             ginkgo_solver.SetMaxIter(400);
             ginkgo_solver.SetOperator(*(A.Ptr()));
@@ -283,7 +283,7 @@ int main(int argc, char *argv[])
                Ginkgo::MFEMPreconditioner gko_M(exec, M);
                Ginkgo::CGSolver ginkgo_solver(exec, gko_M);
                ginkgo_solver.SetPrintLevel(print_lvl);
-               ginkgo_solver.SetRelTol(1e-12);
+               ginkgo_solver.SetRelTol(sqrt(1e-12));
                ginkgo_solver.SetAbsTol(0.0);
                ginkgo_solver.SetMaxIter(400);
                ginkgo_solver.SetOperator(*(A.Ptr()));

examples/ginkgo/ex1p.cpp

@@ -0,0 +1,436 @@
+//                       MFEM Example 1 - Parallel Version
+//                             GINKGO Modification
+//
+// Compile with: make ex1p
+//
+// Sample runs:  mpirun -np 4 ex1p -m ../data/square-disc.mesh
+//               mpirun -np 4 ex1p -m ../data/star.mesh
+//               mpirun -np 4 ex1p -m ../data/star-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/escher.mesh
+//               mpirun -np 4 ex1p -m ../data/fichera.mesh
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../data/octahedron.mesh -o 1
+//               mpirun -np 4 ex1p -m ../data/periodic-annulus-sector.msh
+//               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
+//               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
+//               mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
+//               mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/star-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/pipe-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/ball-nurbs.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/star-surf.mesh
+//               mpirun -np 4 ex1p -m ../data/square-disc-surf.mesh
+//               mpirun -np 4 ex1p -m ../data/inline-segment.mesh
+//               mpirun -np 4 ex1p -m ../data/amr-quad.mesh
+//               mpirun -np 4 ex1p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh
+//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh -o -1 -sc
+//
+// Device sample runs:
+//               mpirun -np 4 ex1p -pa -d cuda
+//               mpirun -np 4 ex1p -fa -d cuda
+//               mpirun -np 4 ex1p -pa -d occa-cuda
+//               mpirun -np 4 ex1p -pa -d raja-omp
+//               mpirun -np 4 ex1p -pa -d ceed-cpu
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -o 4 -a
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/square-mixed.mesh
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/fichera-mixed.mesh
+//             * mpirun -np 4 ex1p -pa -d ceed-cuda
+//             * mpirun -np 4 ex1p -pa -d ceed-hip
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/beam-tet.mesh -pa -d ceed-cpu
+//
+// Description:  This example code demonstrates the use of MFEM to define a
+//               simple finite element discretization of the Laplace problem
+//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
+//               Specifically, we discretize using a FE space of the specified
+//               order, or if order < 1 using an isoparametric/isogeometric
+//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
+//               NURBS mesh, etc.)
+//
+//               The example highlights the use of mesh refinement, finite
+//               element grid functions, as well as linear and bilinear forms
+//               corresponding to the left-hand side and right-hand side of the
+//               discrete linear system. We also cover the explicit elimination
+//               of essential boundary conditions, static condensation, and the
+//               optional connection to the GLVis tool for visualization.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+#ifndef MFEM_USE_GINKGO
+#error This example requires that MFEM is built with MFEM_USE_GINKGO=YES
+#endif
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI and HYPRE.
+   Mpi::Init();
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+
+   // 2. Parse command-line options.
+   const char *mesh_file = "../../data/star.mesh";
+   int order = 1;
+   bool static_cond = false;
+   bool pa = false;
+   bool fa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
+   int solver_config = 0;
+   int print_lvl = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree) or -1 for"
+                  " isoparametric space.");
+   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(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&solver_config, "-s", "--solver-config",
+                  "Solver and preconditioner combination: \n\t"
+                  "   0 - Ginkgo solver and Ginkgo preconditioner, \n\t"
+                  "   1 - Ginkgo solver and MFEM preconditioner, \n\t"
+                  "   2 - MFEM solver and Ginkgo preconditioner, \n\t"
+                  "   3 - MFEM solver and MFEM preconditioner.");
+   args.AddOption(&print_lvl, "-pl", "--print-level",
+                  "Print level for iterative solver (1 prints every iteration).");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.SetGPUAwareMPI(true);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 10,000 elements.
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh.UniformRefinement();
+      }
+   }
+
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted.
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
+   {
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh.UniformRefinement();
+      }
+   }
+
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
+   //    use continuous Lagrange finite elements of the specified order. If
+   //    order < 1, we instead use an isoparametric/isogeometric space.
+   FiniteElementCollection *fec;
+   bool delete_fec;
+   if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+      delete_fec = true;
+   }
+   else if (pmesh.GetNodes())
+   {
+      fec = pmesh.GetNodes()->OwnFEC();
+      delete_fec = false;
+      if (myid == 0)
+      {
+         cout << "Using isoparametric FEs: " << fec->Name() << endl;
+      }
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
+   }
+   ParFiniteElementSpace fespace(&pmesh, fec);
+   HYPRE_BigInt size = fespace.GlobalTrueVSize();
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+   }
+
+   // 8. Determine the list of true (i.e. parallel conforming) essential
+   //    boundary dofs. In this example, the boundary conditions are defined
+   //    by marking all the boundary attributes from the mesh as essential
+   //    (Dirichlet) and converting them to a list of true dofs.
+   Array<int> ess_tdof_list;
+   if (pmesh.bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(pmesh.bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   // 9. Set up the parallel linear form b(.) which corresponds to the
+   //    right-hand side of the FEM linear system, which in this case is
+   //    (1,phi_i) where phi_i are the basis functions in fespace.
+   ParLinearForm b(&fespace);
+   ConstantCoefficient one(1.0);
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
+
+   // 10. Define the solution vector x as a parallel finite element grid
+   //     function corresponding to fespace. Initialize x with initial guess of
+   //     zero, which satisfies the boundary conditions.
+   ParGridFunction x(&fespace);
+   x = 0.0;
+
+   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
+   //     corresponding to the Laplacian operator -Delta, by adding the
+   //     Diffusion domain integrator.
+   ParBilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   if (fa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::FULL);
+      // Sort the matrix column indices when running on GPU or with OpenMP (i.e.
+      // when Device::IsEnabled() returns true). This makes the results
+      // bit-for-bit deterministic at the cost of somewhat longer run time.
+      a.EnableSparseMatrixSorting(Device::IsEnabled());
+   }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));
+
+   // 12. Assemble the parallel bilinear form and the corresponding linear
+   //     system, applying any necessary transformations such as: parallel
+   //     assembly, eliminating boundary conditions, applying conforming
+   //     constraints for non-conforming AMR, static condensation, etc.
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
+
+   OperatorPtr A;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   // 13. Solve the linear system A X = B.
+   if (!pa)
+   {
+      switch (solver_config)
+      {
+         // Solve the linear system with CG + Schwarz (with IC) from Ginkgo
+         case 0:
+         {
+            if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
+            Ginkgo::GinkgoExecutor exec(device);
+            Ginkgo::IcPreconditioner local_solver(exec, "exact");
+            Ginkgo::SchwarzPreconditioner gko_M(exec, MPI_COMM_WORLD, local_solver);
+            Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
+            ginkgo_solver.SetPrintLevel(print_lvl);
+            ginkgo_solver.SetRelTol(sqrt(1e-12));
+            ginkgo_solver.SetAbsTol(0.0);
+            ginkgo_solver.SetMaxIter(400);
+            ginkgo_solver.SetOperator(*(A.Ptr()));
+            ginkgo_solver.Mult(B, X);
+            break;
+         }
+
+         // Solve the linear system with CG from Ginkgo + MFEM preconditioner
+         case 1:
+         {
+            if (myid == 0) { cout << "Using Ginkgo solver + MFEM preconditioner...\n"; }
+            Ginkgo::GinkgoExecutor exec(device);
+            //Create MFEM preconditioner and wrap it for Ginkgo's use.
+            HypreBoomerAMG M((HypreParMatrix&)(*A));
+            Ginkgo::MFEMPreconditioner gko_M(exec, M, MPI_COMM_WORLD);
+            Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
+            ginkgo_solver.SetPrintLevel(print_lvl);
+            ginkgo_solver.SetRelTol(sqrt(1e-12));
+            ginkgo_solver.SetAbsTol(0.0);
+            ginkgo_solver.SetMaxIter(400);
+            ginkgo_solver.SetOperator(*(A.Ptr()));
+            ginkgo_solver.Mult(B, X);
+            break;
+         }
+
+         // Ginkgo Schwarz preconditioner (local ParIC) +  MFEM CG solver
+         case 2:
+         {
+            if (myid == 0) { cout << "Using MFEM solver + Ginkgo preconditioner...\n"; }
+            Ginkgo::GinkgoExecutor exec(device);
+            Ginkgo::IcPreconditioner local_M(exec, "exact");
+            Ginkgo::SchwarzPreconditioner M(exec, MPI_COMM_WORLD, local_M);
+            M.SetOperator(*(A.Ptr()));  // Generate the preconditioner for the matrix A.
+            CGSolver cg(MPI_COMM_WORLD);
+            cg.SetRelTol(sqrt(1e-12));
+            cg.SetMaxIter(400);
+            cg.SetPrintLevel(1);
+            cg.SetPreconditioner(M);
+            cg.SetOperator(*A);
+            cg.Mult(B, X);
+            break;
+         }
+
+         // MFEM solver + MFEM preconditioner
+         case 3:
+         {
+            if (myid == 0) { cout << "Using MFEM solver + MFEM preconditioner...\n"; }
+            HypreBoomerAMG M((HypreParMatrix&)(*A));
+            CGSolver cg(MPI_COMM_WORLD);
+            cg.SetRelTol(sqrt(1e-12));
+            cg.SetMaxIter(400);
+            cg.SetPrintLevel(1);
+            cg.SetPreconditioner(M);
+            cg.SetOperator(*A);
+            cg.Mult(B, X);
+            break;
+         }
+      } // End switch on solver_config
+   }
+   // Partial assembly mode.  Cannot use Ginkgo preconditioners, but can use Ginkgo
+   // solvers.
+   else
+   {
+      if (UsesTensorBasis(fespace))
+      {
+         // Use Jacobi preconditioning in partial assembly mode.
+         OperatorJacobiSmoother M(a, ess_tdof_list);
+         switch (solver_config)
+         {
+            case 0:
+            {
+               if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
+               MFEM_ABORT("Cannot use Ginkgo preconditioner in partial assembly mode.\n"
+                          "            Try -s 1 to test Ginkgo solver with an MFEM preconditioner.");
+               break;
+            }
+
+            // Use Ginkgo solver with MFEM preconditioner
+            case 1:
+            {
+               if (myid == 0) { cout << "Using Ginkgo solver + MFEM preconditioner...\n"; }
+               Ginkgo::GinkgoExecutor exec(device);
+               // Wrap MFEM preconditioner for Ginkgo's use.
+               Ginkgo::MFEMPreconditioner gko_M(exec, M, MPI_COMM_WORLD);
+               Ginkgo::CGSolver ginkgo_solver(exec, MPI_COMM_WORLD, gko_M);
+               ginkgo_solver.SetPrintLevel(print_lvl);
+               ginkgo_solver.SetRelTol(sqrt(1e-12));
+               ginkgo_solver.SetAbsTol(0.0);
+               ginkgo_solver.SetMaxIter(400);
+               ginkgo_solver.SetOperator(*(A.Ptr()));
+               ginkgo_solver.Mult(B, X);
+               break;
+            }
+
+            // No Ginkgo preconditioners work with matrix-free; error
+            case 2:
+            {
+               if (myid == 0) { cout << "Using Ginkgo solver + preconditioner...\n"; }
+               MFEM_ABORT("Cannot use Ginkgo preconditioner in partial assembly mode.\n"
+                          "            Try -s 1 to test Ginkgo solver with an MFEM preconditioner.");
+               break;
+            }
+
+            // Use MFEM solver and preconditioner
+            case 3:
+            {
+               if (myid == 0) { cout << "Using MFEM solver + MFEM preconditioner...\n"; }
+               CGSolver cg(MPI_COMM_WORLD);
+               cg.SetRelTol(sqrt(1e-12));
+               cg.SetMaxIter(400);
+               cg.SetPrintLevel(1);
+               cg.SetPreconditioner(M);
+               cg.SetOperator(*A);
+               cg.Mult(B, X);
+               break;
+            }
+         } // End switch on solver_config
+      }
+      else // CG with no preconditioning
+      {
+         if (myid == 0) { cout << "Using MFEM solver + no preconditioner...\n"; }
+         CGSolver cg(MPI_COMM_WORLD);
+         cg.SetRelTol(sqrt(1e-12));
+         cg.SetMaxIter(400);
+         cg.SetPrintLevel(1);
+         cg.SetOperator(*A);
+         cg.Mult(B, X);
+      }
+   }
+
+   // 14. Recover the parallel grid function corresponding to X. This is the
+   //     local finite element solution on each processor.
+   a.RecoverFEMSolution(X, b, x);
+
+   // 15. Save the refined mesh and the solution in parallel. This output can
+   //     be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
+   {
+      ostringstream mesh_name, sol_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh.Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << pmesh << x << flush;
+   }
+
+   // 17. Free the used memory.
+   if (delete_fec)
+   {
+      delete fec;
+   }
+
+   return 0;
+}

examples/ginkgo/makefile

@@ -20,9 +20,8 @@ CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
-# Currently there are only serial Ginkgo examples
 SEQ_EXAMPLES = ex1
-PAR_EXAMPLES =
+PAR_EXAMPLES = ex1p
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
 else

fem/bilinearform.cpp

@@ -825,14 +825,46 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
                                     Vector &b, OperatorHandle &A, Vector &X,
                                     Vector &B, int copy_interior)
 {
+   const SparseMatrix *P = fes->GetConformingProlongation();
+   const SparseMatrix *R = fes->GetConformingRestriction();
    if (ext)
    {
       if (hybridization)
       {
          FormSystemMatrix(ess_tdof_list, A);
-         ConstrainedOperator A_constrained(this, ess_tdof_list);
-         A_constrained.EliminateRHS(x, b);
-         hybridization->ReduceRHS(b, B);
+
+         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
+         {
+            Operator *op;
+            Operator::FormSystemOperator(ess_tdof_list, op);
+            return dynamic_cast<ConstrainedOperator*>(op);
+         }());
+         MFEM_ASSERT(A_constrained != nullptr, "");
+
+         Vector conf_b, conf_x;
+         if (P)
+         {
+            // Nonconforming
+            conf_b.SetSize(P->Width());
+            conf_x.SetSize(P->Width());
+            P->MultTranspose(b, conf_b);
+            R->Mult(x, conf_x);
+         }
+         else
+         {
+            // Conforming
+            conf_b.MakeRef(b, 0, b.Size());
+            conf_x.MakeRef(x, 0, x.Size());
+         }
+
+         A_constrained->EliminateRHS(conf_x, conf_b);
+
+         if (P)
+         {
+            R->MultTranspose(conf_b, b); // store eliminated rhs in b
+         }
+
+         hybridization->ReduceRHS(conf_b, B);
          X.SetSize(B.Size());
          X = 0.0;
       }
@@ -842,7 +874,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
       }
       return;
    }
-   const SparseMatrix *P = fes->GetConformingProlongation();
    FormSystemMatrix(ess_tdof_list, A);
 
    // Transform the system and perform the elimination in B, based on the
@@ -878,7 +909,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
       if (hybridization)
       {
          // Reduction to the Lagrange multipliers system
-         const SparseMatrix *R = fes->GetConformingRestriction();
          Vector conf_b(P->Width()), conf_x(P->Width());
          P->MultTranspose(b, conf_b);
          R->Mult(x, conf_x);
@@ -891,7 +921,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
       else
       {
          // Variational restriction with P
-         const SparseMatrix *R = fes->GetConformingRestriction();
          B.SetSize(P->Width());
          P->MultTranspose(b, B);
          X.SetSize(R->Height());

fem/coefficient.cpp

@@ -1302,6 +1302,73 @@ real_t TraceCoefficient::Eval(ElementTransformation &T,
    return ma.Trace();
 }
 
+VectorComponentCoefficient::VectorComponentCoefficient(VectorCoefficient &A,
+                                                       int c)
+   : a(&A), va(A.GetVDim())
+{
+   SetComponent(c);
+}
+
+void VectorComponentCoefficient::SetComponent(int c)
+{
+   MFEM_ASSERT(c < a->GetVDim() && c >= 0,
+               "VectorComponentCoefficient:  "
+               "Index not in range.");
+
+   component = c;
+}
+
+void VectorComponentCoefficient::SetTime(real_t t)
+{
+   if (a) { a->SetTime(t); }
+   this->Coefficient::SetTime(t);
+}
+
+real_t VectorComponentCoefficient::Eval(ElementTransformation &T,
+                                        const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   return va[component];
+}
+
+MatrixComponentCoefficient::MatrixComponentCoefficient(MatrixCoefficient &A,
+                                                       int ri, int ci)
+   : a(&A), ma(A.GetHeight(), A.GetWidth())
+{
+   SetRowIndex(ri);
+   SetColumnIndex(ci);
+}
+
+void MatrixComponentCoefficient::SetRowIndex(int ri)
+{
+   MFEM_ASSERT(ri < a->GetHeight() && ri >= 0,
+               "MatrixComponentCoefficient:  "
+               "Row index not in range.");
+
+   row_idx = ri;
+}
+
+void MatrixComponentCoefficient::SetColumnIndex(int ci)
+{
+   MFEM_ASSERT(ci < a->GetWidth() && ci >= 0,
+               "MatrixComponentCoefficient:  "
+               "Column index not in range.");
+   col_idx = ci;
+}
+
+void MatrixComponentCoefficient::SetTime(real_t t)
+{
+   if (a) { a->SetTime(t); }
+   this->Coefficient::SetTime(t);
+}
+
+real_t MatrixComponentCoefficient::Eval(ElementTransformation &T,
+                                        const IntegrationPoint &ip)
+{
+   a->Eval(ma, T, ip);
+   return ma(row_idx,col_idx);
+}
+
 VectorSumCoefficient::VectorSumCoefficient(int dim)
    : VectorCoefficient(dim),
      ACoef(NULL), BCoef(NULL),

fem/coefficient.hpp

@@ -114,11 +114,10 @@ public:
    /// Construct the constant coefficient using a vector of constants.
    /** @a c should be a vector defined by attributes, so for region with
        attribute @a i @a c[i-1] is the coefficient in that region */
-   PWConstCoefficient(Vector &c)
-   { constants.SetSize(c.Size()); constants=c; }
+   PWConstCoefficient(const Vector &c) { UpdateConstants(c); }
 
    /// Update the constants with vector @a c.
-   void UpdateConstants(Vector &c) { constants.SetSize(c.Size()); constants=c; }
+   void UpdateConstants(const Vector &c) { constants = c; }
 
    /// Return a reference to the i-th constant
    real_t &operator()(int i) { return constants(i-1); }
@@ -1332,8 +1331,8 @@ public:
    /// Get the coefficient located at (i,j) in the matrix.
    Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }
 
-   /** @brief Set the coefficient located at (i,j) in the matrix.  By default by
-       default this will take ownership of the Coefficient passed in, but this
+   /** @brief Set the coefficient located at (i,j) in the matrix.  By default
+       this will take ownership of the Coefficient passed in, but this
        can be overridden with the @a own parameter. */
    void Set(int i, int j, Coefficient * c, bool own=true);
 
@@ -1873,6 +1872,85 @@ public:
                const IntegrationPoint &ip) override;
 };
 
+/// Scalar coefficient defined as component of a vector coefficient
+class VectorComponentCoefficient : public Coefficient
+{
+private:
+   VectorCoefficient *a = nullptr;
+
+   mutable Vector va;
+   int component;
+
+public:
+   /// Construct with a vector coefficient.
+   VectorComponentCoefficient(VectorCoefficient &A)
+      : a(&A), va(A.GetVDim()), component(0) {};
+
+   VectorComponentCoefficient(VectorCoefficient &A, int c);
+
+   /// Set the time for internally stored coefficients
+   void SetTime(real_t t) override;
+
+   /// Reset the vector coefficient
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+
+   /// Return the vector coefficient
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Set the component
+   void SetComponent(int c);
+
+   /// Return the component
+   int GetComponent() const { return component; }
+
+   /// Evaluate the trace coefficient at @a ip.
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
+};
+
+/// Scalar coefficient defined as component of a matrix coefficient
+class MatrixComponentCoefficient : public Coefficient
+{
+private:
+   MatrixCoefficient *a = nullptr;
+
+   mutable DenseMatrix ma;
+   int row_idx,col_idx;
+
+public:
+   MatrixComponentCoefficient(MatrixCoefficient &A)
+      : a(&A), ma(A.GetHeight(), A.GetWidth()), row_idx(0), col_idx(0) {};
+
+   /// Construct with the matrix coefficient.
+   MatrixComponentCoefficient(MatrixCoefficient &A, int ri, int ci);
+
+   /// Set the time for internally stored coefficients
+   void SetTime(real_t t) override;
+
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
+   /// Reset the index
+   void SetRowIndex(int ri);
+
+   /// Return the index
+   int GetRowIndex() const { return row_idx; }
+
+   /// Reset the index
+   void SetColumnIndex(int ci);
+
+   /// Return the index
+   int GetColumnIndex() const { return col_idx; }
+
+
+   /// Evaluate the trace coefficient at @a ip.
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
+};
+
 /// Vector coefficient defined as the linear combination of two vectors
 class VectorSumCoefficient : public VectorCoefficient
 {

fem/dfem/tuple.hpp

@@ -10,7 +10,7 @@
 // CONTRIBUTING.md for details.
 #pragma once
 
-// This is serac's tuple implementation
+// This is smith's tuple implementation
 
 #include <ostream>
 #include "../../config/config.hpp"

fem/dgmassinv.cpp

@@ -12,7 +12,6 @@
 #include "dgmassinv.hpp"
 #include "bilinearform.hpp"
 #include "dgmassinv_kernels.hpp"
-#include "../general/forall.hpp"
 
 namespace mfem
 {
@@ -119,151 +118,6 @@ void DGMassInverse::Update()
 
 DGMassInverse::~DGMassInverse() = default;
 
-template<int DIM, int D1D, int Q1D>
-void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
-{
-   using namespace internal; // host/device kernel functions
-
-   const int NE = fes.GetNE();
-   const int d1d = m->dofs1D;
-   const int q1d = m->quad1D;
-
-   const int ND = static_cast<int>(pow(d1d, DIM));
-
-   const auto B = m->maps->B.Read();
-   const auto Bt = m->maps->Bt.Read();
-   const auto pa_data = m->pa_data.Read();
-   const auto dinv = diag_inv.Read();
-   auto r = r_.Write();
-   auto d = d_.Write();
-   auto z = z_.Write();
-   auto u = u_.ReadWrite();
-
-   const real_t RELTOL = rel_tol;
-   const real_t ABSTOL = abs_tol;
-   const int MAXIT = max_iter;
-   const bool IT_MODE = iterative_mode;
-   const bool CHANGE_BASIS = (d2q != nullptr);
-
-   // b is the right-hand side (if no change of basis, this just points to the
-   // incoming RHS vector, if we have to change basis, this points to the
-   // internal b2 vector where we put the transformed RHS)
-   const real_t *b;
-   // the following are non-null if we have to change basis
-   real_t *b2 = nullptr; // non-const access to b2
-   const real_t *b_orig = nullptr; // RHS vector in "original" basis
-   const real_t *d2q_B = nullptr; // matrix to transform initial guess
-   const real_t *q2d_B = nullptr; // matrix to transform solution
-   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
-   if (CHANGE_BASIS)
-   {
-      d2q_B = d2q->B.Read();
-      q2d_B = B_.Read();
-      q2d_Bt = Bt_.Read();
-
-      b2 = b2_.Write();
-      b_orig = b_.Read();
-      b = b2;
-   }
-   else
-   {
-      b = b_.Read();
-   }
-
-   static constexpr int NB = Q1D ? Q1D : 1; // block size
-
-   mfem::forall_2D(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
-   {
-      // Perform change of basis if needed
-      if (CHANGE_BASIS)
-      {
-         // Transform RHS
-         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
-         if (IT_MODE)
-         {
-            // Transform initial guess
-            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
-         }
-      }
-
-      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
-
-      // Compute first residual
-      if (IT_MODE)
-      {
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
-         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
-      }
-      else
-      {
-         // if not in iterative mode, use zero initial guess
-         const int BX = MFEM_THREAD_SIZE(x);
-         const int BY = MFEM_THREAD_SIZE(y);
-         const int bxy = BX*BY;
-         const auto B = ConstDeviceMatrix(b, ND, NE);
-         auto U = DeviceMatrix(u, ND, NE);
-         auto R = DeviceMatrix(r, ND, NE);
-         for (int i = tid; i < ND; i += bxy)
-         {
-            U(i, e) = 0.0;
-            R(i, e) = B(i, e);
-         }
-         MFEM_SYNC_THREAD;
-      }
-
-      DGMassPreconditioner(e, NE, ND, dinv, r, z);
-      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
-
-      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
-      if (nom < 0.0) { return; /* Not positive definite */ }
-      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
-      if (nom <= r0) { return; /* Converged */ }
-
-      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
-      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
-      if (den <= 0.0)
-      {
-         DGMassDot<NB>(e, NE, ND, d, d);
-         // d2 > 0 => not positive definite
-         if (den == 0.0) { return; }
-      }
-
-      // start iteration
-      int i = 1;
-      while (true)
-      {
-         const real_t alpha = nom/den;
-         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
-         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
-
-         DGMassPreconditioner(e, NE, ND, dinv, r, z);
-
-         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
-         if (betanom < 0.0) { return; /* Not positive definite */ }
-         if (betanom <= r0) { break; /* Converged */ }
-
-         if (++i > MAXIT) { break; }
-
-         const real_t beta = betanom/nom;
-         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
-         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
-         den = DGMassDot<NB>(e, NE, ND, d, z);
-         if (den <= 0.0)
-         {
-            DGMassDot<NB>(e, NE, ND, d, d);
-            // d2 > 0 => not positive definite
-            if (den == 0.0) { break; }
-         }
-         nom = betanom;
-      }
-
-      if (CHANGE_BASIS)
-      {
-         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
-      }
-   });
-}
-
 void DGMassInverse::Mult(const Vector &Mu, Vector &u) const
 {
    // Dispatch to templated version based on dim, d1d, and q1d.
@@ -306,23 +160,4 @@ DGMassInvKernels::DGMassInvKernels()
    k::Specialization<3,6,7>::Add();
 }
 
-/// @cond Suppress_Doxygen_warnings
-
-template <int DIM, int D1D, int Q1D>
-DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
-{
-   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
-}
-
-DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
-   int dim, int, int)
-{
-   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
-   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
-   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
-   else { MFEM_ABORT("Unsupported dimension."); }
-}
-
-/// @endcond
-
 } // namespace mfem

fem/dgmassinv_kernels.hpp

@@ -15,6 +15,7 @@
 #include "../linalg/kernels.hpp"
 #include "kernels.hpp"
 #include "integ/bilininteg_mass_kernels.hpp"
+#include "dgmassinv.hpp"
 
 namespace mfem
 {
@@ -333,6 +334,170 @@ void DGMassBasis(const int e,
 
 } // namespace internal
 
+template<int DIM, int D1D, int Q1D>
+void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
+{
+   using namespace internal; // host/device kernel functions
+
+   const int NE = fes.GetNE();
+   const int d1d = m->dofs1D;
+   const int q1d = m->quad1D;
+
+   const int ND = static_cast<int>(pow(d1d, DIM));
+
+   const auto B = m->maps->B.Read();
+   const auto Bt = m->maps->Bt.Read();
+   const auto pa_data = m->pa_data.Read();
+   const auto dinv = diag_inv.Read();
+   auto r = r_.Write();
+   auto d = d_.Write();
+   auto z = z_.Write();
+   auto u = u_.ReadWrite();
+
+   const real_t RELTOL = rel_tol;
+   const real_t ABSTOL = abs_tol;
+   const int MAXIT = max_iter;
+   const bool IT_MODE = iterative_mode;
+   const bool CHANGE_BASIS = (d2q != nullptr);
+
+   // b is the right-hand side (if no change of basis, this just points to the
+   // incoming RHS vector, if we have to change basis, this points to the
+   // internal b2 vector where we put the transformed RHS)
+   const real_t *b;
+   // the following are non-null if we have to change basis
+   real_t *b2 = nullptr; // non-const access to b2
+   const real_t *b_orig = nullptr; // RHS vector in "original" basis
+   const real_t *d2q_B = nullptr; // matrix to transform initial guess
+   const real_t *q2d_B = nullptr; // matrix to transform solution
+   const real_t *q2d_Bt = nullptr; // matrix to transform RHS
+   if (CHANGE_BASIS)
+   {
+      d2q_B = d2q->B.Read();
+      q2d_B = B_.Read();
+      q2d_Bt = Bt_.Read();
+
+      b2 = b2_.Write();
+      b_orig = b_.Read();
+      b = b2;
+   }
+   else
+   {
+      b = b_.Read();
+   }
+
+   static constexpr int NB = Q1D ? Q1D : 1; // block size
+
+   mfem::forall_2D(NE, NB, NB, [=] MFEM_HOST_DEVICE (int e)
+   {
+      // Perform change of basis if needed
+      if (CHANGE_BASIS)
+      {
+         // Transform RHS
+         DGMassBasis<DIM,D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
+         if (IT_MODE)
+         {
+            // Transform initial guess
+            DGMassBasis<DIM,D1D>(e, NE, d2q_B, u, u, d1d);
+         }
+      }
+
+      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
+
+      // Compute first residual
+      if (IT_MODE)
+      {
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
+         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
+      }
+      else
+      {
+         // if not in iterative mode, use zero initial guess
+         const int BX = MFEM_THREAD_SIZE(x);
+         const int BY = MFEM_THREAD_SIZE(y);
+         const int bxy = BX*BY;
+         const auto B = ConstDeviceMatrix(b, ND, NE);
+         auto U = DeviceMatrix(u, ND, NE);
+         auto R = DeviceMatrix(r, ND, NE);
+         for (int i = tid; i < ND; i += bxy)
+         {
+            U(i, e) = 0.0;
+            R(i, e) = B(i, e);
+         }
+         MFEM_SYNC_THREAD;
+      }
+
+      DGMassPreconditioner(e, NE, ND, dinv, r, z);
+      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
+
+      real_t nom = DGMassDot<NB>(e, NE, ND, d, r);
+      if (nom < 0.0) { return; /* Not positive definite */ }
+      real_t r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
+      if (nom <= r0) { return; /* Converged */ }
+
+      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
+      real_t den = DGMassDot<NB>(e, NE, ND, z, d);
+      if (den <= 0.0)
+      {
+         DGMassDot<NB>(e, NE, ND, d, d);
+         // d2 > 0 => not positive definite
+         if (den == 0.0) { return; }
+      }
+
+      // start iteration
+      int i = 1;
+      while (true)
+      {
+         const real_t alpha = nom/den;
+         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
+         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
+
+         DGMassPreconditioner(e, NE, ND, dinv, r, z);
+
+         real_t betanom = DGMassDot<NB>(e, NE, ND, r, z);
+         if (betanom < 0.0) { return; /* Not positive definite */ }
+         if (betanom <= r0) { break; /* Converged */ }
+
+         if (++i > MAXIT) { break; }
+
+         const real_t beta = betanom/nom;
+         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
+         den = DGMassDot<NB>(e, NE, ND, d, z);
+         if (den <= 0.0)
+         {
+            DGMassDot<NB>(e, NE, ND, d, d);
+            // d2 > 0 => not positive definite
+            if (den == 0.0) { break; }
+         }
+         nom = betanom;
+      }
+
+      if (CHANGE_BASIS)
+      {
+         DGMassBasis<DIM,D1D>(e, NE, q2d_B, u, u, d1d);
+      }
+   });
+}
+
+/// @cond Suppress_Doxygen_warnings
+
+template <int DIM, int D1D, int Q1D>
+inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Kernel()
+{
+   return &DGMassInverse::DGMassCGIteration<DIM,D1D,Q1D>;
+}
+
+inline DGMassInverse::CGKernelType DGMassInverse::CGKernels::Fallback(
+   int dim, int, int)
+{
+   if (dim == 1) { return &DGMassInverse::DGMassCGIteration<1>; }
+   else if (dim == 2) { return &DGMassInverse::DGMassCGIteration<2>; }
+   else if (dim == 3) { return &DGMassInverse::DGMassCGIteration<3>; }
+   else { MFEM_ABORT("Unsupported dimension."); }
+}
+
+/// @endcond
+
 } // namespace mfem
 
 #endif

fem/fe/face_map_utils.hpp

@@ -69,9 +69,9 @@ inline int ToLexOrdering2D(const int face_id, const int size1d, const int i)
 }
 
 /// @brief Given a face DOF index on a shared face, ordered lexicographically
-/// relative to element the element (where the local face is face_id), and
-/// return the corresponding face DOF index ordered lexicographically relative
-/// to the face itself.
+/// relative to the element (where the local face is face_id), return the
+/// corresponding face DOF index ordered lexicographically relative to the face
+/// itself.
 MFEM_HOST_DEVICE
 inline int PermuteFace2D(const int face_id, const int orientation,
                          const int size1d, const int index)

fem/fe/fe_base.cpp

@@ -231,7 +231,7 @@ void FiniteElement::CalcPhysLaplacian(ElementTransformation &Trans,
    {
       for (int nd = 0; nd < dof; nd++)
       {
-         Laplacian[nd] = hess(nd,0) + hess(nd,4) + hess(nd,5);
+         Laplacian[nd] = hess(nd,0) + hess(nd,3) + hess(nd,5);
       }
    }
    else if (dim == 2)
@@ -268,11 +268,9 @@ void FiniteElement::CalcPhysLinLaplacian(ElementTransformation &Trans,
       scale[0] =   Gij(0,0);
       scale[1] = 2*Gij(0,1);
       scale[2] = 2*Gij(0,2);
-
-      scale[3] = 2*Gij(1,2);
-      scale[4] =   Gij(2,2);
-
-      scale[5] =   Gij(1,1);
+      scale[3] =   Gij(1,1);
+      scale[4] = 2*Gij(1,2);
+      scale[5] =   Gij(2,2);
    }
    else if (dim == 2)
    {
@@ -309,12 +307,12 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
       map[2] = 2;
 
       map[3] = 1;
-      map[4] = 5;
-      map[5] = 3;
+      map[4] = 3;
+      map[5] = 4;
 
       map[6] = 2;
-      map[7] = 3;
-      map[8] = 4;
+      map[7] = 4;
+      map[8] = 5;
    }
    else if (dim == 2)
    {
@@ -382,11 +380,7 @@ const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &ir,
    #pragma omp critical (DofToQuad)
 #endif
    {
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         d2q = dof2quad_array[i];
-         if (d2q->IntRule != &ir || d2q->mode != mode) { d2q = nullptr; }
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
       if (!d2q)
       {
 #ifdef MFEM_THREAD_SAFE
@@ -661,14 +655,22 @@ void ScalarFiniteElement::ScalarLocalL2Restriction(
 void NodalFiniteElement::CreateLexicographicFullMap(const IntegrationRule &ir)
 const
 {
+   // Get the FULL version of the map. This call contains omp critical region,
+   // so it is done before the critical region below.
+   auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);
 
 #if defined(MFEM_THREAD_SAFE) && defined(MFEM_USE_OPENMP)
    #pragma omp critical (DofToQuad)
 #endif
    {
-      // Get the FULL version of the map.
-      auto &d2q = GetDofToQuad(ir, DofToQuad::FULL);
-      //Undo the native ordering which is what FiniteElement::GetDofToQuad returns.
+      // If the new Dof2Quad is already present, e.g. added in a previous call
+      // or added by another omp thread, return.
+      if (DofToQuad::SearchArray(dof2quad_array, ir,
+                                 DofToQuad::LEXICOGRAPHIC_FULL))
+      { return; }
+
+      // Undo the native ordering which is what FiniteElement::GetDofToQuad
+      // returns.
       auto *d2q_new = new DofToQuad(d2q);
       d2q_new->mode = DofToQuad::LEXICOGRAPHIC_FULL;
       const int nqpt = ir.GetNPoints();
@@ -724,13 +726,7 @@ const DofToQuad &NodalFiniteElement::GetDofToQuad(const IntegrationRule &ir,
    #pragma omp critical (DofToQuad)
 #endif
    {
-      //Should make this loop a function of FiniteElement
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         d2q = dof2quad_array[i];
-         if (d2q->IntRule == &ir && d2q->mode == mode) { break; }
-         d2q = nullptr;
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
    }
    if (d2q) { return *d2q; }
    if (mode != DofToQuad::LEXICOGRAPHIC_FULL)
@@ -2631,15 +2627,7 @@ const DofToQuad &TensorBasisElement::GetTensorDofToQuad(
    #pragma omp critical (DofToQuad)
 #endif
    {
-      for (int i = 0; i < dof2quad_array.Size(); i++)
-      {
-         auto* d2q_ = dof2quad_array[i];
-         if (d2q_->IntRule == &ir && d2q_->mode == mode)
-         {
-            d2q = d2q_;
-            break;
-         }
-      }
+      d2q = DofToQuad::SearchArray(dof2quad_array, ir, mode);
       if (!d2q)
       {
          d2q = new DofToQuad;

fem/fe/fe_base.hpp

@@ -44,7 +44,7 @@ public:
       NumBasisTypes   = 9   /**< Keep track of maximum types to prevent
                                  hard-coding */
    };
-   /** @brief If the input does not represents a valid BasisType, abort with an
+   /** @brief If the input does not represent a valid BasisType, abort with an
        error; otherwise return the input. */
    static int Check(int b_type)
    {
@@ -52,7 +52,7 @@ public:
                   "unknown BasisType: " << b_type);
       return b_type;
    }
-   /** @brief If the input does not represents a valid nodal BasisType, abort
+   /** @brief If the input does not represent a valid nodal BasisType, abort
        with an error; otherwise return the input. */
    static int CheckNodal(int b_type)
    {
@@ -222,6 +222,12 @@ public:
 
    /// Returns absolute value of the maps
    DofToQuad Abs() const;
+
+   /// Auxiliary function for searching DofToQuad arrays.
+   static inline DofToQuad *SearchArray(
+      const Array<DofToQuad*> &dof2quad_array,
+      const IntegrationRule &ir,
+      DofToQuad::Mode mode);
 };
 
 /// Describes the function space on each element
@@ -407,6 +413,7 @@ public:
    /** 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 order in 3D is {u_xx, u_xy, u_xz, u_yy, u_yz, u_zz}.
        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;
@@ -1120,7 +1127,7 @@ public:
       return GetPoints(p, btype, on_device);
    }
 
-   /// Get coordinates of a closed (GaussLegendre) set of points if degree @a p
+   /// Get coordinates of a closed (GaussLobatto) set of points if degree @a p
    const real_t *ClosedPoints(const int p,
                               const int btype = BasisType::GaussLobatto,
                               bool on_device = false)
@@ -1376,6 +1383,21 @@ public:
 void InvertLinearTrans(ElementTransformation &trans,
                        const IntegrationPoint &pt, Vector &x);
 
+
+// static inline method
+inline DofToQuad *DofToQuad::SearchArray(
+   const Array<DofToQuad*> &dof2quad_array,
+   const IntegrationRule &ir,
+   DofToQuad::Mode mode)
+{
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      DofToQuad *d2q = dof2quad_array[i];
+      if (d2q->IntRule == &ir && d2q->mode == mode) { return d2q; }
+   }
+   return nullptr;
+}
+
 } // namespace mfem
 
 #endif

fem/fe/fe_fixed_order.cpp

@@ -60,6 +60,12 @@ void Linear1DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    dshape(1,0) =  1.;
 }
 
+void Linear1DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}
+
 Linear2DFiniteElement::Linear2DFiniteElement()
    : NodalFiniteElement(2, Geometry::TRIANGLE, 3, 1)
 {
@@ -87,6 +93,11 @@ void Linear2DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    dshape(2,0) =  0.; dshape(2,1) =  1.;
 }
 
+void Linear2DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}
 
 BiLinear2DFiniteElement::BiLinear2DFiniteElement()
    : NodalFiniteElement(2, Geometry::SQUARE, 4, 1, FunctionSpace::Qk)
@@ -1256,6 +1267,12 @@ void Linear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    }
 }
 
+void Linear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                        DenseMatrix &h) const
+{
+   h = 0.0;
+}
+
 void Linear3DFiniteElement::GetFaceDofs (int face, int **dofs, int *ndofs)
 const
 {
@@ -1632,6 +1649,37 @@ void TriLinear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    dshape(7,2) =   ox *  y;
 }
 
+void TriLinear3DFiniteElement::CalcHessian(const IntegrationPoint &ip,
+                                           DenseMatrix &h) const
+{
+   real_t x = ip.x, y = ip.y, z = ip.z;
+   real_t ox = 1.-x, oy = 1.-y, oz = 1.-z;
+
+   h(0,0) = 0.;   h(0,1) =  oz;   h(0,2) = oy;
+   h(0,3) = 0.;   h(0,4) =  ox;   h(0,5) = 0.;
+
+   h(1,0) = 0.;   h(1,1) = -oz;   h(1,2) = -oy;
+   h(1,3) = 0.;   h(1,4) =  x;    h(1,5) = 0.;
+
+   h(2,0) = 0.;   h(2,1) =  oz;   h(2,2) = -y;
+   h(2,3) = 0.;   h(2,4) =  -x;   h(2,5) = 0.;
+
+   h(3,0) = 0.;   h(3,1) = -oz;   h(3,2) = y;
+   h(3,3) = 0.;   h(3,4) = -ox;   h(3,5) = 0.;
+
+   h(4,0) = 0.;   h(4,1) =  z;    h(4,2) = -oy;
+   h(4,3) = 0.;   h(4,4) = -ox;   h(4,5) = 0.;
+
+   h(5,0) = 0.;   h(5,1) = -z;    h(5,2) = oy;
+   h(5,3) = 0.;   h(5,4) = -x;    h(5,5) = 0.;
+
+   h(6,0) = 0.;   h(6,1) =  z;    h(6,2) = y;
+   h(6,3) = 0.;   h(6,4) =  x;    h(6,5) = 0.;
+
+   h(7,0) = 0.;   h(7,1) = -z;    h(7,2) = -y;
+   h(7,3) = 0.;   h(7,4) = ox;    h(7,5) = 0.;
+}
+
 
 P0SegmentFiniteElement::P0SegmentFiniteElement(int Ord)
    : NodalFiniteElement(1, Geometry::SEGMENT, 1, Ord)   // default Ord = 0

fem/fe/fe_fixed_order.hpp

@@ -50,6 +50,8 @@ public:
        contains the derivative of one shape function */
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
 };
 
 /// A 2D linear element on triangle with nodes at the vertices of the triangle
@@ -70,6 +72,8 @@ public:
        so that each row contains the derivatives of one shape function */
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
    void ProjectDelta(int vertex, Vector &dofs) const override
    { dofs = 0.0; dofs(vertex) = 1.0; }
 };
@@ -404,6 +408,9 @@ public:
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;
 
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
+
    void ProjectDelta(int vertex, Vector &dofs) const override
    { dofs = 0.0; dofs(vertex) = 1.0; }
 
@@ -445,7 +452,8 @@ public:
        so that each row contains the derivatives of one shape function */
    void CalcDShape(const IntegrationPoint &ip,
                    DenseMatrix &dshape) const override;
-
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &h) const override;
    void ProjectDelta(int vertex, Vector &dofs) const override
    { dofs = 0.0; dofs(vertex) = 1.0; }
 };

fem/fe/fe_nurbs.cpp

@@ -84,6 +84,46 @@ void NURBS1DFiniteElement::CalcHessian (const IntegrationPoint &ip,
    add(1.0, hess, (-d2sum + 2*dsum*dsum*sum)*sum*sum, shape_x, hess);
 }
 
+void NURBS1DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+
+   for (int i = 0; i <= order; i++)
+   {
+      real_t kx = kv[0]->GetBotella(ijk[0] + i);
+      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
+      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
+
+      Trans.SetIntPoint(&ip);
+      dofs(i) = coeff.Eval(Trans, ip);
+   }
+}
+
+void NURBS1DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+
+   for (int i = 0; i <= order; i++)
+   {
+      real_t kx = kv[0]->GetBotella(ijk[0] + i);
+      if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
+      ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
+
+      Trans.SetIntPoint(&ip);
+      vc.Eval(x, Trans, ip);
+      for (int j = 0; j < x.Size(); j++)
+      {
+         dofs(dof*j+i) = x(j);
+      }
+   }
+}
+
 
 void NURBS2DFiniteElement::SetOrder() const
 {
@@ -215,6 +255,63 @@ void NURBS2DFiniteElement::CalcHessian (const IntegrationPoint &ip,
    }
 }
 
+void NURBS2DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+   for (int o = 0, j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         dofs(o) = coeff.Eval(Trans, ip);
+      }
+   }
+}
+
+void NURBS2DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+   for (int o = 0, j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+         for (int v = 0; v < x.Size(); v++)
+         {
+            dofs(dof*v+o) = x(v);
+         }
+      }
+   }
+}
 
 void NURBS3DFiniteElement::SetOrder() const
 {
@@ -348,11 +445,10 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
             d2sum[0] += ( hessian(o,0) = d2sx*sy*sz*weights(o) );
             d2sum[1] += ( hessian(o,1) = dsx*dsy*sz*weights(o) );
             d2sum[2] += ( hessian(o,2) = dsx*sy*dsz*weights(o) );
+            d2sum[3] += ( hessian(o,3) = sx*d2sy*sz*weights(o) );
+            d2sum[4] += ( hessian(o,4) = sx*dsy*dsz*weights(o) );
+            d2sum[5] += ( hessian(o,5) = sx*sy*d2sz*weights(o) );
 
-            d2sum[3] += ( hessian(o,3) = sx*dsy*dsz*weights(o) );
-
-            d2sum[4] += ( hessian(o,4) = sx*sy*d2sz*weights(o) );
-            d2sum[5] += ( hessian(o,5) = sx*d2sy*sz*weights(o) );
          }
       }
    }
@@ -401,6 +497,85 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
    }
 }
 
+void NURBS3DFiniteElement::Project(Coefficient &coeff,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   IntegrationPoint ip;
+
+   for (int o = 0, k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            dofs(o) = coeff.Eval(Trans, ip);
+         }
+      }
+   }
+}
+
+void NURBS3DFiniteElement::Project(VectorCoefficient &vc,
+                                   ElementTransformation &Trans,
+                                   Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
+   Vector x(vc.GetVDim());
+   IntegrationPoint ip;
+
+   for (int o = 0, k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+            for (int v = 0; v < x.Size(); v++)
+            {
+               dofs(dof*v+o) = x(v);
+            }
+         }
+      }
+   }
+}
 
 void NURBS_HDiv2DFiniteElement::SetOrder() const
 {
@@ -517,6 +692,63 @@ void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
    }
 }
 
+void NURBS_HDiv2DFiniteElement::Project(VectorCoefficient &vc,
+                                        ElementTransformation &Trans,
+                                        Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 2, "");
+   Vector x(2), mx(2);
+   IntegrationPoint ip;
+   int o = 0;
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 2;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.AdjugateJacobian().Mult(x,mx);
+         dofs(o) = mx(0);
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.AdjugateJacobian().Mult(x,mx);
+         dofs(o) = mx(1);
+      }
+   }
+}
+
 NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
 {
    if (kv1[0]) { delete kv1[0]; }
@@ -696,6 +928,120 @@ void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
    }
 }
 
+
+void NURBS_HDiv3DFiniteElement::Project(VectorCoefficient &vc,
+                                        ElementTransformation &Trans,
+                                        Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 3, "");
+   Vector x(2), mx(3);
+   IntegrationPoint ip;
+
+   int o = 0;
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 2)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(0);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 1)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(1);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 1)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.AdjugateJacobian().Mult(x,mx);
+            dofs(o) = mx(2);
+         }
+      }
+   }
+
+}
+
+
 NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
 {
    if (kv1[0]) { delete kv1[0]; }
@@ -817,13 +1163,68 @@ void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
    }
 }
 
+void NURBS_HCurl2DFiniteElement::Project(VectorCoefficient &vc,
+                                         ElementTransformation &Trans,
+                                         Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 2, "");
+   Vector x(2), xm(2);
+   IntegrationPoint ip;
+   int i, j, o;
+   for (o = 0, j = 0; j <= orders[1]+1; j++)
+   {
+      real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+      if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+      {
+         o += orders[0] + 1;
+         continue;
+      }
+      ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+      for (i = 0; i <= orders[0]; i++, o++)
+      {
+         real_t kx = kv[0]->GetBotella(ijk[0] + i);
+         if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+         ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.Jacobian().MultTranspose(x,xm);
+         dofs(o) = xm(0);
+      }
+   }
+
+   for (j = 0; j <= orders[1]; j++)
+   {
+      real_t ky = kv[1]->GetBotella(ijk[1] + j);
+      if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+      {
+         o += orders[0] + 2;
+         continue;
+      }
+      ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+      for (i = 0; i <= orders[0]+1; i++, o++)
+      {
+         real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+         if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+         ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+         Trans.SetIntPoint(&ip);
+         vc.Eval(x, Trans, ip);
+
+         Trans.Jacobian().MultTranspose(x,xm);
+         dofs(o) = xm(1);
+      }
+   }
+}
+
 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();
@@ -1003,11 +1404,124 @@ void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
             curl_shape(o,0) = shape1_x(i)*dsy1_sz;
             curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
             curl_shape(o,2) = 0.0;
+
          }
       }
    }
 }
 
+void NURBS_HCurl3DFiniteElement::Project(VectorCoefficient &vc,
+                                         ElementTransformation &Trans,
+                                         Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == dof, "");
+   MFEM_ASSERT(vc.GetVDim() == 3, "");
+   Vector x(3), xm(3);
+   IntegrationPoint ip;
+
+   int o = 0;
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 1)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 1;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            real_t kx = kv[0]->GetBotella(ijk[0] + i);
+            if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
+            ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(0);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]+1; k++)
+   {
+      real_t kz = kv1[2]->GetBotella(ijk[2] + k);
+      if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
+      {
+         o += (orders[0] + 2)*(orders[1] + 1);
+         continue;
+      }
+      ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         real_t ky = kv[1]->GetBotella(ijk[1] + j);
+         if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(1);
+         }
+      }
+   }
+
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      real_t kz = kv[2]->GetBotella(ijk[2] + k);
+      if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
+      {
+         o += (orders[0] + 2)*(orders[1] + 2);
+         continue;
+      }
+      ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         real_t ky = kv1[1]->GetBotella(ijk[1] + j);
+         if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
+         {
+            o += orders[0] + 2;
+            continue;
+         }
+         ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            real_t kx = kv1[0]->GetBotella(ijk[0] + i);
+            if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
+            ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
+
+            Trans.SetIntPoint(&ip);
+            vc.Eval(x, Trans, ip);
+
+            Trans.Jacobian().MultTranspose(x,xm);
+            dofs(o) = xm(2);
+         }
+      }
+   }
+
+}
+
+
 NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
 {
    if (kv1[0]) { delete kv1[0]; }

fem/fe/fe_nurbs.hpp

@@ -86,6 +86,18 @@ public:
                    DenseMatrix &dshape) const override;
    void CalcHessian (const IntegrationPoint &ip,
                      DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };
 
 /// An arbitrary order 2D NURBS element on a square
@@ -121,6 +133,18 @@ public:
                    DenseMatrix &dshape) const override;
    void CalcHessian (const IntegrationPoint &ip,
                      DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };
 
 /// An arbitrary order 3D NURBS element on a cube
@@ -161,6 +185,18 @@ public:
                    DenseMatrix &dshape) const override;
    void CalcHessian (const IntegrationPoint &ip,
                      DenseMatrix &hessian) const override;
+
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };
 
 
@@ -242,6 +278,13 @@ public:
    void CalcDivShape(const IntegrationPoint &ip,
                      Vector &divshape) const override;
 
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
    ~NURBS_HDiv2DFiniteElement();
 };
 
@@ -336,6 +379,13 @@ public:
    void CalcDivShape(const IntegrationPoint &ip,
                      Vector &divshape) const override;
 
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
    ~NURBS_HDiv3DFiniteElement();
 };
 
@@ -415,6 +465,13 @@ public:
    void CalcCurlShape(const IntegrationPoint &ip,
                       DenseMatrix &curl_shape) const override;
 
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
    ~NURBS_HCurl2DFiniteElement();
 };
 
@@ -506,6 +563,13 @@ public:
    void CalcCurlShape(const IntegrationPoint &ip,
                       DenseMatrix &curl_shape) const override;
 
+   using FiniteElement::Project;
+
+   /** Evaluate the dofs that are defined on this element.
+       Dofs that can not be evaluated will remain unmodified. */
+   void Project(VectorCoefficient &vcoeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
+
    ~NURBS_HCurl3DFiniteElement();
 };
 

fem/fe_coll.hpp

@@ -111,36 +111,36 @@ public:
    | :------: | :---: | :---: | :-------: | :-----: | :---: |
    | H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
    | H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
-   | H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
+   | H1Pos_[DIM]_[ORDER] | H1 | * | 2 | VALUE | H1 nodal elements |
    | H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
    | H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
+   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
    | ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
    | ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
-   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
-   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
+   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
+   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * / * | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces,edges) |
    | ND_R1D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
    | ND_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 1D. |
    | ND_R2D_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
    | ND_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | 3D H(curl)-conforming Nedelec vector elements in 2D. |
    | RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
    | RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
-   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | * | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
+   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | * | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
    | RT_R1D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
    | RT_R1D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 1D. |
    | RT_R2D_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
    | RT_R2D@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | 3D H(div)-conforming Raviart-Thomas vector elements in 2D. |
    | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
-   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
+   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | VALUE | Discontinuous L2 elements |
    | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
-   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
+   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | * | INTEGRAL | Discontinuous L2 elements |
    | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | * | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
    | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
+   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | * | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
    | NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
    | LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
    | CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
@@ -172,7 +172,7 @@ public:
    | :------: | :--------: |
    | [DIM]    | Dimension of the elements (1D, 2D, 3D) |
    | [ORDER]  | Approximation order of the elements (P0, P1, P2, ...) |
-   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
+   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1-GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform 6-Serendipity 7-ClosedGL 8-IntegratedGLL) |
    | [OBTYPE] | Open BasisType of the element for elements which have both types |
    | [CBTYPE] | Closed BasisType of the element for elements which have both types |
 

fem/fespace.cpp

@@ -1516,36 +1516,76 @@ const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
    const bool is_dg_space = IsDGSpace();
    const L2FaceValues m = (is_dg_space && mul==L2FaceValues::DoubleValued) ?
                           L2FaceValues::DoubleValued : L2FaceValues::SingleValued;
-   key_face key = std::make_tuple(is_dg_space, f_ordering, type, m);
+   auto key = std::make_tuple(is_dg_space, f_ordering, type, m);
    auto itr = L2F.find(key);
    if (itr != L2F.end())
    {
-      return itr->second;
+      return itr->second.get();
    }
    else
    {
-      FaceRestriction *res;
+      std::unique_ptr<FaceRestriction> res;
       if (is_dg_space)
       {
          if (Conforming())
          {
-            res = new L2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new L2FaceRestriction(*this, f_ordering, type, m));
          }
          else
          {
-            res = new NCL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new NCL2FaceRestriction(*this, f_ordering, type, m));
          }
       }
       else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
       {
-         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
+         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
       }
       else
       {
-         res = new ConformingFaceRestriction(*this, f_ordering, type);
+         res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
       }
-      L2F[key] = res;
-      return res;
+      return L2F.emplace(key, std::move(res)).first->second.get();
+   }
+}
+
+const InterpolationManager &FiniteElementSpace::GetInterpolationManager(
+   ElementDofOrdering f_ordering, FaceType type) const
+{
+   const auto key = make_tuple(f_ordering, type);
+
+   auto it = interpolations.find(key);
+   if (it != interpolations.end())
+   {
+      return *it->second;
+   }
+   else
+   {
+      auto interp = make_unique<InterpolationManager>(*this, f_ordering, type);
+
+      int face_idx = 0;
+      for (int f = 0; f < mesh->GetNumFacesWithGhost(); ++f)
+      {
+         Mesh::FaceInformation face = mesh->GetFaceInformation(f);
+         if (!face.IsOfFaceType(type) || face.IsNonconformingCoarse())
+         {
+            continue;
+         }
+         if (face.IsConforming() || face.IsBoundary())
+         {
+            interp->RegisterFaceConformingInterpolation(face, face_idx);
+         }
+         else
+         {
+            interp->RegisterFaceCoarseToFineInterpolation(face, face_idx);
+         }
+         ++face_idx;
+      }
+
+      // Transform the interpolation matrix map into contiguous memory.
+      interp->LinearizeInterpolatorMapIntoVector();
+      interp->InitializeNCInterpConfig();
+
+      return *interpolations.emplace(key, std::move(interp)).first->second;
    }
 }
 
@@ -3969,11 +4009,8 @@ void FiniteElementSpace::Destroy()
       delete E2Q_array[i];
    }
    E2Q_array.SetSize(0);
-   for (auto &x : L2F)
-   {
-      delete x.second;
-   }
    L2F.clear();
+   interpolations.clear();
    for (int i = 0; i < E2IFQ_array.Size(); i++)
    {
       delete E2IFQ_array[i];

fem/fespace.hpp

@@ -13,6 +13,7 @@
 #define MFEM_FESPACE
 
 #include "../config/config.hpp"
+#include "../general/hash_util.hpp"
 #include "../linalg/ordering.hpp"
 #include "../linalg/sparsemat.hpp"
 #include "../mesh/mesh.hpp"
@@ -320,18 +321,11 @@ protected:
    mutable OperatorHandle L2E_nat, L2E_lex;
    /// The face restriction operators, see GetFaceRestriction().
    using key_face = std::tuple<bool, ElementDofOrdering, FaceType, L2FaceValues>;
-   struct key_hash
-   {
-      std::size_t operator()(const key_face& k) const
-      {
-         return std::get<0>(k)
-                + 2 * (int)std::get<1>(k)
-                + 4 * (int)std::get<2>(k)
-                + 8 * (int)std::get<3>(k);
-      }
-   };
-   using map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>;
-   mutable map_L2F L2F;
+   mutable std::unordered_map<key_face,std::unique_ptr<FaceRestriction>,
+           TupleHasher> L2F;
+
+   mutable std::unordered_map<std::tuple<ElementDofOrdering,FaceType>,
+           std::unique_ptr<InterpolationManager>, TupleHasher> interpolations;
 
    mutable Array<QuadratureInterpolator*> E2Q_array;
    mutable Array<FaceQuadratureInterpolator*> E2IFQ_array;
@@ -751,6 +745,9 @@ public:
       ElementDofOrdering f_ordering, FaceType,
       L2FaceValues mul = L2FaceValues::DoubleValued) const;
 
+   const InterpolationManager &GetInterpolationManager(
+      ElementDofOrdering f_ordering, FaceType type) const;
+
    /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
        quadrature point values and/or derivatives (Q-vectors). */
    /** An E-vector represents the element-wise discontinuous version of the FE

fem/gridfunc.cpp

@@ -2352,52 +2352,83 @@ void GridFunction::ProjectDeltaCoefficient(DeltaCoefficient &delta_coeff,
    }
 }
 
-void GridFunction::ProjectCoefficient(Coefficient &coeff)
+void GridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
    DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector vals;
 
    if (delta_c == NULL)
    {
       if (fes->GetNURBSext() == NULL)
       {
-         Array<int> vdofs;
-         Vector vals;
-
-         for (int i = 0; i < fes->GetNE(); i++)
+         switch (type)
          {
-            fes->GetElementVDofs(i, vdofs, doftrans);
-            vals.SetSize(vdofs.Size());
-            fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
-            doftrans.TransformPrimal(vals);
-            SetSubVector(vdofs, vals);
+            case ProjectType::ELEMENT_L2:
+               ProjectCoefficientElementL2(coeff);
+               return;
+            case ProjectType::GLOBAL_L2:
+               ProjectCoefficientGlobalL2(coeff);
+               return;
+            default:
+               for (int i = 0; i < fes->GetNE(); i++)
+               {
+                  fes->GetElementVDofs(i, vdofs, doftrans);
+                  vals.SetSize(vdofs.Size());
+                  fes->GetFE(i)->Project(coeff, *fes->GetElementTransformation(i), vals);
+                  doftrans.TransformPrimal(vals);
+                  SetSubVector(vdofs, vals);
+               }
          }
       }
       else
       {
-         // Define and assemble linear form
-         LinearForm b(fes);
-         b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
-         b.Assemble();
+         switch (type)
+         {
+            case ProjectType::DEFAULT:
+            case ProjectType::ELEMENT_L2:
+               ProjectCoefficientElementL2(coeff);
+               return;
+            case ProjectType::GLOBAL_L2:
+               ProjectCoefficientGlobalL2(coeff);
+               return;
+            case ProjectType::ELEMENT:
+               constexpr real_t signal = std::numeric_limits<real_t>::min();
 
-         // Define and assemble bilinear form
-         BilinearForm a(fes);
-         a.AddDomainIntegrator(new MassIntegrator());
-         a.Assemble();
+               for (int i = 0; i < fes->GetNE(); i++)
+               {
+                  fes->GetElementVDofs(i, vdofs, doftrans);
+                  vals.SetSize(vdofs.Size());
+                  vals = signal;
 
-         // 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);
+                  fes->GetFE(i)->Project(coeff,
+                                         *fes->GetElementTransformation(i),
+                                         vals);
+                  doftrans.TransformPrimal(vals);
 
-         // Solve and get solution
-         *this = 0.0;
-         cg.Mult(b,*this);
+                  // Remove undefined dofs
+                  // The knot location (either Botella, Demko or Greville point)
+                  // where the NURBS dof are evaluated might fall outside of the
+                  // domain of the element. In that case the value is not set, and
+                  // the value remains the signal value.
+                  int s = 0;
+                  for (int ii = 0; ii < vals.Size(); ii++)
+                  {
+                     if (vals[ii] != signal)
+                     {
+                        vdofs[s] = vdofs[ii];
+                        vals(s) = vals(ii);
+                        s++;
+                     }
+                  }
+                  vdofs.SetSize(s);
+                  vals.SetSize(s);
+
+                  // Add reduced dofs to global vector
+                  SetSubVector(vdofs, vals);
+               }
+         }
       }
    }
    else
@@ -2410,6 +2441,167 @@ void GridFunction::ProjectCoefficient(Coefficient &coeff)
    }
 }
 
+void GridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff, real_t rtol,
+                                              int iter)
+{
+   // 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(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+
+   // Solve and get solution
+   *this = 0.0;
+   cg.Mult(b,*this);
+}
+
+void GridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
+{
+   Vector Va;
+   ProjectCoefficientElementL2_(coeff, *this, Va);
+   (*this) /= Va;
+}
+
+void GridFunction::ProjectCoefficientElementL2_(Coefficient &coeff,
+                                                Vector &x, Vector &Va)
+{
+   DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector shape,shape2, elvect, elwght;
+   DenseMatrix elmat;
+   Va.SetSize(fes->GetNDofs() );
+   x.SetSize(fes->GetNDofs() );
+   Va = 0.0;
+   x = 0.0;
+
+   if (fes->GetNURBSext() == NULL)
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         shape.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            real_t val = coeff.Eval(tr, ip);
+
+            el.CalcPhysShape(tr, shape);
+
+            elvect.Add(wght * val, shape);
+            elwght.Add(wght, shape);
+            AddMult_a_VVt(wght, shape, elmat);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add reduced dofs to global vector
+         x.AddElementVector(vdofs, elvect);
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+   else
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetDim();
+         int p = el.GetOrder();
+         L2_FECollection fe_coll(p,  dim);
+         //H1_FECollection fe_coll(p,  dim, BasisType::Positive);
+         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
+         MFEM_ASSERT(el2.GetDof() == dof, "Element dofs do not match.");
+
+         shape.SetSize(dof);
+         shape2.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            real_t val = coeff.Eval(tr, ip);
+            el.CalcPhysShape(tr, shape);
+            el2.CalcPhysShape(tr, shape2);
+
+            elvect.Add(wght * val, shape2);
+            elwght.Add(wght, shape);
+            AddMult_a_VVt(wght, shape2, elmat);
+         }
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix 2");
+         }
+         // Map to NURBS
+         DenseMatrix I;
+         el2.Project(el,tr,I);
+         if (!LinearSolve(I, elvect.GetData(),1e-32))
+         {
+            MFEM_WARNING("Error in inverting element local matrix 3");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add reduced dofs to global vector
+         x.AddElementVector(vdofs, elvect);
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+}
+
 void GridFunction::ProjectCoefficient(
    Coefficient &coeff, Array<int> &dofs, int vd)
 {
@@ -2434,49 +2626,318 @@ void GridFunction::ProjectCoefficient(
    }
 }
 
-void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff)
+void GridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
+                                      ProjectType type)
 {
+   Array<int> vdofs;
+   Vector vals;
    DofTransformation doftrans;
+
    if (fes->GetNURBSext() == NULL)
    {
-      int i;
-      Array<int> vdofs;
-      Vector vals;
-
-      for (i = 0; i < fes->GetNE(); i++)
+      switch (type)
       {
-         fes->GetElementVDofs(i, vdofs, doftrans);
-         vals.SetSize(vdofs.Size());
-         fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
-         doftrans.TransformPrimal(vals);
-         SetSubVector(vdofs, vals);
+         case ProjectType::ELEMENT_L2:
+            ProjectCoefficientElementL2(vcoeff);
+            return;
+         case ProjectType::GLOBAL_L2:
+            ProjectCoefficientGlobalL2(vcoeff);
+            return;
+         default:
+            for (int i = 0; i < fes->GetNE(); i++)
+            {
+               fes->GetElementVDofs(i, vdofs, doftrans);
+               vals.SetSize(vdofs.Size());
+               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+               doftrans.TransformPrimal(vals);
+               SetSubVector(vdofs, vals);
+            }
       }
    }
    else
    {
-      // Define and assemble linear form
-      LinearForm b(fes);
+      switch (type)
+      {
+         case ProjectType::DEFAULT:
+         case ProjectType::ELEMENT_L2:
+            ProjectCoefficientElementL2(vcoeff);
+            return;
+         case ProjectType::GLOBAL_L2:
+            ProjectCoefficientGlobalL2(vcoeff);
+            return;
+         case ProjectType::ELEMENT:
+            constexpr real_t signal = std::numeric_limits<real_t>::min();
+            for (int i = 0; i < fes->GetNE(); i++)
+            {
+               fes->GetElementVDofs(i, vdofs, doftrans);
+               vals.SetSize(vdofs.Size());
+               vals = signal;
+               fes->GetFE(i)->Project(vcoeff, *fes->GetElementTransformation(i), vals);
+               doftrans.TransformPrimal(vals);
+               // Remove undefined dofs
+               // The knot location (either Botella, Demko or Greville point)
+               // where the NURBS dof are evaluated might fall outside of the
+               // domain of the element. In that case the value is not set, and
+               // the value remains the signal value.
+               int s = 0;
+               for (int ii = 0; ii < vals.Size(); ii++)
+               {
+                  if (vals[ii] != signal)
+                  {
+                     vdofs[s] = vdofs[ii];
+                     vals(s) = vals(ii);
+                     s++;
+                  }
+               }
+               vdofs.SetSize(s);
+               vals.SetSize(s);
+
+               // Add reduced dofs to global vector
+               SetSubVector(vdofs, vals);
+            }
+      }
+   }
+}
+
+void GridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                              real_t rtol, int iter)
+{
+   // Define and assemble linear form
+   LinearForm b(fes);
+   BilinearForm a(fes);
+
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
       b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
-      b.Assemble();
-
-      // Define and assemble bilinear form
-      BilinearForm a(fes);
       a.AddDomainIntegrator(new VectorFEMassIntegrator());
-      a.Assemble();
+   }
+   else
+   {
+      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorMassIntegrator());
+   }
+   a.Assemble();
+   b.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);
+   // Set solver and preconditioner
+   SparseMatrix A(a.SpMat());
+   GSSmoother  prec(A);
+   CGSolver cg;
+   cg.SetOperator(A);
+   cg.SetPreconditioner(prec);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
 
-      // Solve and get solution
-      *this = 0.0;
-      cg.Mult(b,*this);
+   // Solve and get solution
+   *this = 0.0;
+   cg.Mult(b,*this);
+}
+
+void GridFunction::ProjectCoefficientElementL2_(VectorCoefficient &vcoeff,
+                                                Vector &x, Vector &Va)
+{
+   DofTransformation doftrans;
+   Array<int> vdofs;
+   Vector shapel2, elvect, elwght, val;
+   DenseMatrix  shape, elmat;
+   Va.SetSize(Size());
+   x.SetSize(Size());
+   Va = 0.0;
+   x = 0.0;
+
+   if (fes->GetNURBSext() == NULL)
+   {
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementVDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetRangeDim();
+         shape.SetSize(dof,dim);
+         shapel2.SetSize(dof);
+         elvect.SetSize(dof);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof,dof);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            vcoeff.Eval(val, tr, ip);
+            val *= wght;
+
+            el.CalcPhysVShape(tr, shape);
+
+            shape.AddMult (val, elvect);
+            AddMult_a_AAt(wght, shape, elmat);
+
+            shape.GetRowl2(shapel2);
+            elwght.Add(wght, shapel2);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData(),1e-12))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Scale
+         elvect *= elwght;
+
+         // Add to global vector
+         x.AddElementVector(vdofs, elvect);
+
+         // Add to weight vector -- no need for an orientation
+         for (int i = 0; i < vdofs.Size(); i++)
+         {
+            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
+         }
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+   else
+   {
+      DenseMatrix partelmat;
+      Vector shape2;
+
+      if (fes->GetTypicalFE()->GetOrder() >= 6 )
+      {
+         MFEM_WARNING("This project is not stable for"
+                      "NURBS VectorFE with order >= 5");
+      }
+      for (int e = 0; e < fes->GetNE(); e++)
+      {
+         fes->GetElementVDofs (e, vdofs, doftrans);
+         ElementTransformation &tr = *fes -> GetElementTransformation (e);
+         const FiniteElement &el = *fes->GetFE(e);
+         int dof = el.GetDof();
+         int dim = el.GetRangeDim();
+         int p = el.GetOrder();
+         L2_FECollection fe_coll(p,  dim);
+         const FiniteElement &el2 = *fe_coll.FiniteElementForGeometry(el.GetGeomType());
+         int dof2 = el2.GetDof();
+         MFEM_ASSERT(dof2*dim >= dof, "Element dofs do not match.");
+         shape2.SetSize(dof2);
+         shape.SetSize(dof,dim);
+         shapel2.SetSize(dof);
+         elvect.SetSize(dof2*dim);
+         elwght.SetSize(dof);
+         elmat.SetSize(dof2*dim,dof2*dim);
+         partelmat.SetSize(dof2,dof2);
+         elvect = 0.0;
+         elwght = 0.0;
+         elmat = 0.0;
+
+         const IntegrationRule &ir = IntRules.Get(el.GetGeomType(),
+                                                  2 * el.GetOrder() + 1);
+
+         // Element vector & weight
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+
+            tr.SetIntPoint (&ip);
+            real_t wght = ip.weight*tr.Weight();
+            vcoeff.Eval(val, tr, ip);
+            val *= wght;
+
+            el2.CalcPhysShape(tr, shape2);
+            el.CalcPhysVShape(tr, shape);
+
+            for (int k = 0; k < dim; k++)
+            {
+               for (int s = 0; s < dof2; s++)
+               {
+                  elvect(dof2*k+s) += val(k) * shape2(s);
+               }
+            }
+
+            MultVVt(shape2, partelmat);
+            partelmat *= wght;
+            for (int k = 0; k < dim; k++)
+            {
+               elmat.AddMatrix(partelmat, dof2*k, dof2*k);
+            }
+
+            shape.GetRowl2(shapel2);
+            elwght.Add(wght, shapel2);
+         }
+
+         // Solve
+         if (!LinearSolve(elmat, elvect.GetData()))
+         {
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+
+         // Map to NURBS
+         DenseMatrix I;
+         el2.Project(el,tr,I);
+
+         // LSQ solve
+         // For higher order NURBS solving this non-square matrix causes issues.
+         // For Order <=4 the routine seems to work fine.
+         Vector vec(dof);
+         DenseMatrix mat(dof, dof);
+         I.Transpose();
+         I.Mult(elvect, vec);
+         MultAAt(I, mat);
+         if (!LinearSolve(mat, vec.GetData(), 1e-24))
+         {
+            mat.TestInversion();
+            MFEM_WARNING("Error in inverting element local matrix");
+         }
+         elvect = vec;
+
+         // Scale
+         elvect *= elwght;
+
+         // Add to global vector
+         x.AddElementVector(vdofs, elvect);
+
+         // Add to weight vector -- no need for an orientation
+         for (int i = 0; i < vdofs.Size(); i++)
+         {
+            vdofs[i] = FiniteElementSpace::DecodeDof(vdofs[i]);
+         }
+         Va.AddElementVector(vdofs, elwght);
+      }
+   }
+}
+
+void GridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
+{
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
+      Vector Va;
+      ProjectCoefficientElementL2_(vcoeff, *this, Va);
+      (*this) /= Va;
+   }
+   else
+   {
+      Array<int> vdofs(fes->GetNDofs());
+      Vector x, Va;
+      VectorComponentCoefficient coeff(vcoeff,
+                                       0);  // 0  to ensure we have a valid object
+
+      for (int v = 0; v < VectorDim(); v++)
+      {
+         coeff.SetComponent(v);
+         ProjectCoefficientElementL2_(coeff, x, Va);
+         x /= Va;
+         fes->GetVDofs(v, vdofs);
+         SetSubVector(vdofs, x);
+      }
    }
 }
 

fem/gridfunc.hpp

@@ -27,6 +27,24 @@
 namespace mfem
 {
 
+/** This enumerated type describes the three main projection types:
+    - ELEMENT, assigns the degree of freedom per element, as specified in the
+      specific element
+    - GLOBAL_L2, solves a global L2 projection
+    - ELEMENT_L2, solves a element level L2 projection. Inter element
+      connectivity is dealt with similar as in:
+      Bezier-Projection : A unified approach for local projection and
+      quadrature-free refinement and coarsening of NURBS and T-splines with
+      particular application to isogeometric design and analysis
+      [CMAME (284) 2015 pg 55-105]
+    - DEFAULT, for NURBS spaces this is ELEMENT_L2, while for all other spaces
+      this ELEMENT.
+   Note 1: ELEMENT_L2 also works for non NURBS elements
+   Note 2: For NURBS elements the ELEMENT projection gives results without
+   over and undershoots. However, the gradient near the boundary does not
+   converge.*/
+enum class ProjectType { DEFAULT, ELEMENT, GLOBAL_L2, ELEMENT_L2 };
+
 /// Class for grid function - Vector with associated FE space.
 class GridFunction : public Vector
 {
@@ -66,13 +84,17 @@ protected:
        degree of freedom. */
    void ProjectDiscCoefficient(VectorCoefficient &coeff, Array<int> &dof_attr);
 
+   /** Helper function for ProjectCoefficientElementL2 */
+   void ProjectCoefficientElementL2_(Coefficient &coeff, Vector &sol, Vector &Va);
+   void ProjectCoefficientElementL2_(VectorCoefficient &vcoeff, Vector &sol,
+                                     Vector &Va);
+
    /// Loading helper.
    void LegacyNCReorder();
 
    void Destroy();
 
 public:
-
    GridFunction() { fes = NULL; fec_owned = NULL; fes_sequence = 0; UseDevice(true); }
 
    /// Copy constructor. The internal true-dof vector #t_vec is not copied.
@@ -84,6 +106,10 @@ public:
    GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
    { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
 
+   /// Same as above but specify the memory type
+   GridFunction(FiniteElementSpace *f, MemoryType mt) : Vector(f->GetVSize(), mt)
+   { fes = f; fec_owned = NULL; fes_sequence = f->GetSequence(); UseDevice(true); }
+
    /// Construct a GridFunction using previously allocated array @a data.
    /** The GridFunction does not assume ownership of @a data which is assumed to
        be of size at least `f->GetVSize()`. Similar to the Vector constructor
@@ -420,9 +446,30 @@ 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). For NURBS spaces these degrees of
-       freedom are not available and L2 projection is resorted to as fallback. */
-   virtual void ProjectCoefficient(Coefficient &coeff);
+       in each element (not L2 projection). For elements without a projection
+       member function one could use ProjectCoefficientGlobalL2 instead.
+       NOTE: For parallel simulations with NURBS elements some dofs might
+       not be defined, if the evaluation point does not reside on this rank.
+       If that is the case it is defined on another rank, and the issue is
+       rectified with the appropriate communication, see in ParGridFunction.
+       */
+   virtual void ProjectCoefficient(Coefficient &coeff,
+                                   ProjectType type = ProjectType::DEFAULT);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                           real_t rtol = 1e-12,
+                                           int iter = 1000);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is an element local L2 projection, with an appropriate
+       weighting for Dofs that are shared between elements. Inspired on
+       Bezier-Projection [CMAME (284) 2015 pg 55-105]
+       This routine can be used a fallback for elements without a projection
+       member function.*/
+   virtual void ProjectCoefficientElementL2(Coefficient &coeff);
 
    /** @brief Project @a coeff Coefficient to @a this GridFunction, using one
        element for each degree of freedom in @a dofs and nodal interpolation on
@@ -432,9 +479,26 @@ 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). For NURBS spaces these degrees of
-       freedom are not available and L2 projection is resorted to as fallback. */
-   void ProjectCoefficient(VectorCoefficient &vcoeff);
+       in each element (not L2 projection). For elements without a projection
+       member function one could use ProjectCoefficientGlobalL2 instead.
+       NOTE: For parallel simulations with NURBS elements some dofs might
+       not be defined, if the evaluation point does not reside on this rank.
+       If that is the case it is defined on another rank, and the issue is
+       rectified with the appropriate communication, see in ParGridFunction.*/
+   virtual void ProjectCoefficient(VectorCoefficient &vcoeff,
+                                   ProjectType type = ProjectType::DEFAULT);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                           real_t rtol = 1e-12,
+                                           int iter = 1000);
+
+   /** @brief Project @a coeff Coefficient to @a this GridFunction. The
+       projection is a global L2 projection. This routine can be used a
+       fallback for elements without a projection member function.*/
+   virtual void ProjectCoefficientElementL2(VectorCoefficient &vcoeff);
 
    /** @brief Project @a vcoeff VectorCoefficient to @a this GridFunction, using
        one element for each degree of freedom in @a dofs and nodal interpolation

fem/gslib.cpp

@@ -234,7 +234,7 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
 }
 
 void FindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                 int point_pos_ordering)
+                                 const int point_pos_ordering)
 {
    MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
    bool dev_mode = (point_pos.UseDevice() && Device::IsEnabled());
@@ -482,7 +482,7 @@ void FindPointsGSLIB::SetupDevice()
 }
 
 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         int point_pos_ordering)
+                                         const int point_pos_ordering)
 {
    if (!DEV.setup_device)
    {
@@ -505,13 +505,13 @@ void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
 
    if (dim == 2)
    {
-      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
-                       gsl_dist, points_cnt);
+      FindPointsLocal2(point_pos, point_pos_ordering, gsl_code, gsl_elem,
+                       gsl_ref, gsl_dist, points_cnt);
    }
    else
    {
-      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem, gsl_ref,
-                       gsl_dist, points_cnt);
+      FindPointsLocal3(point_pos, point_pos_ordering, gsl_code, gsl_elem,
+                       gsl_ref, gsl_dist, points_cnt);
    }
 
    // Sync from device to host
@@ -1085,7 +1085,7 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #else
 void FindPointsGSLIB::SetupDevice() {};
 void FindPointsGSLIB::FindPointsOnDevice(const Vector &point_pos,
-                                         int point_pos_ordering) {};
+                                         const int point_pos_ordering) {};
 void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
                                           Vector &field_out,
                                           const int nel, const int ncomp,
@@ -1094,7 +1094,8 @@ void FindPointsGSLIB::InterpolateOnDevice(const Vector &field_in_evec,
 #endif
 
 void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
-                                 int point_pos_ordering, const double bb_t,
+                                 const int point_pos_ordering,
+                                 const double bb_t,
                                  const double newt_tol, const int npt_max)
 {
    if (!setupflag || (mesh != &m) )
@@ -1105,16 +1106,28 @@ void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
 }
 
 void FindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out,
-                                  int point_pos_ordering)
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering)
 {
    FindPoints(point_pos, point_pos_ordering);
    Interpolate(field_in, field_out);
 }
 
+void FindPointsGSLIB::Interpolate(const Vector &point_pos,
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering,
+                                  const int field_out_ordering)
+{
+   FindPoints(point_pos, point_pos_ordering);
+   Interpolate(field_in, field_out, field_out_ordering);
+}
+
 void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out,
-                                  int point_pos_ordering)
+                                  const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int point_pos_ordering)
 {
    FindPoints(m, point_pos, point_pos_ordering);
    Interpolate(field_in, field_out);
@@ -1470,7 +1483,7 @@ void FindPointsGSLIB::SetupSplitMeshesAndIntegrationRules(const int order)
 }
 
 void FindPointsGSLIB::GetNodalValues(const GridFunction *gf_in,
-                                     Vector &node_vals)
+                                     Vector &node_vals) const
 {
    const GridFunction *nodes     = gf_in;
    const FiniteElementSpace *fes = nodes->FESpace();
@@ -1758,6 +1771,13 @@ void FindPointsGSLIB::MapRefPosAndElemIndices()
 
 void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
                                   Vector &field_out)
+{
+   Interpolate(field_in, field_out, field_in.FESpace()->GetOrdering());
+}
+
+void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
+                                  Vector &field_out,
+                                  const int field_out_ordering)
 {
    const int  gf_order   = field_in.FESpace()->GetMaxElementOrder(),
               mesh_order = mesh->GetNodalFESpace()->GetMaxElementOrder();
@@ -1800,7 +1820,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
       const int maxOrder = field_in.FESpace()->GetMaxElementOrder();
 
       InterpolateOnDevice(node_vals, field_out, NE_split_total, ncomp,
-                          maxOrder+1, field_in.FESpace()->GetOrdering());
+                          maxOrder+1, field_out_ordering);
       return;
 #endif
    }
@@ -1812,12 +1832,13 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
        field_in.FESpace()->IsVariableOrder() ==
        mesh->GetNodalFESpace()->IsVariableOrder())
    {
-      InterpolateH1(field_in, field_out);
+      InterpolateH1(field_in, field_out, field_out_ordering);
       return;
    }
    else
    {
-      InterpolateGeneral(field_in, field_out);
+      InterpolateGeneral(field_in, field_out,
+                         field_out_ordering);
       if (!fec_l2 || avgtype == AvgType::NONE) { return; }
    }
 
@@ -1861,11 +1882,11 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
 
       if (gf_order_h1 == mesh_order) // basis is GaussLobatto by default
       {
-         InterpolateH1(field_in_h1, field_out_l2);
+         InterpolateH1(field_in_h1, field_out_l2, field_out_ordering);
       }
       else
       {
-         InterpolateGeneral(field_in_h1, field_out_l2);
+         InterpolateGeneral(field_in_h1, field_out_l2, field_out_ordering);
       }
 
       // Copy interpolated values for the points on element border
@@ -1873,7 +1894,7 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
       {
          for (int i = 0; i < indl2.Size(); i++)
          {
-            int idx = field_in_h1.FESpace()->GetOrdering() == Ordering::byNODES?
+            int idx = field_out_ordering == Ordering::byNODES?
                       indl2[i] + j*points_cnt:
                       indl2[i]*ncomp + j;
             field_out(idx) = field_out_l2(idx);
@@ -1883,7 +1904,8 @@ void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
 }
 
 void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
-                                    Vector &field_out)
+                                    Vector &field_out,
+                                    const int field_out_ordering)
 {
    FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
    if (field_in.FESpace()->IsVariableOrder())
@@ -1913,7 +1935,8 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                 dataptrout = i*points_cnt;
       if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
       {
-         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
+         field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin,
+                                        points_fld);
       }
       else
       {
@@ -1945,7 +1968,7 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
                         (gslib::findpts_data_3 *)this->fdataD);
       }
    }
-   if (field_in.FESpace()->GetOrdering() == Ordering::byVDIM)
+   if (field_out_ordering == Ordering::byVDIM)
    {
       Vector field_out_temp = field_out;
       for (int i = 0; i < ncomp; i++)
@@ -1959,7 +1982,8 @@ void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
 }
 
 void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
-                                         Vector &field_out)
+                                         Vector &field_out,
+                                         const int field_out_ordering)
 {
    int ncomp   = field_in.VectorDim(),
        nptorig = points_cnt,
@@ -1979,7 +2003,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
          if (dim == 3) { ip.z = gsl_mfem_ref(index*dim + 2); }
          Vector localval(ncomp);
          field_in.GetVectorValue(gsl_mfem_elem[index], ip, localval);
-         if (field_in.FESpace()->GetOrdering() == Ordering::byNODES)
+         if (field_out_ordering == Ordering::byNODES)
          {
             for (int i = 0; i < ncomp; i++)
             {
@@ -2014,7 +2038,10 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
       for (int index = 0; index < npt; index++)
       {
          if (gsl_code[index] == 2) { continue; }
-         for (int d = 0; d < dim; ++d) { pt->r[d]= gsl_mfem_ref(index*dim + d); }
+         for (int d = 0; d < dim; ++d)
+         {
+            pt->r[d]= gsl_mfem_ref(index*dim + d);
+         }
          pt->index = index;
          pt->proc  = gsl_proc[index];
          pt->el    = gsl_mfem_elem[index];
@@ -2104,7 +2131,7 @@ void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
             sdpt = (struct send_pt *)sendpt->ptr;
             for (int index = 0; index < static_cast<int>(sendpt->n); index++)
             {
-               int idx = field_in.FESpace()->GetOrdering() == Ordering::byNODES ?
+               int idx = field_out_ordering == Ordering::byNODES ?
                          sdpt->index + j*nptorig :
                          sdpt->index*ncomp + j;
                field_out(idx) = sdpt->ival;
@@ -2246,7 +2273,7 @@ void FindPointsGSLIB::DistributeInterpolatedValues(const Vector &int_vals,
    }
 }
 
-void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb)
+void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb) const
 {
    MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
    auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2317,7 +2344,7 @@ void FindPointsGSLIB::GetAxisAlignedBoundingBoxes(Vector &aabb)
 }
 
 void FindPointsGSLIB::GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
-                                               Vector &obbV)
+                                               Vector &obbV) const
 {
    MFEM_VERIFY(setupflag, "Call FindPointsGSLIB::Setup method first");
    auto *findptsData3 = (gslib::findpts_data_3 *)this->fdataD;
@@ -2502,8 +2529,8 @@ void OversetFindPointsGSLIB::Setup(Mesh &m, const int meshid,
 }
 
 void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                        Array<unsigned int> &point_id,
-                                        int point_pos_ordering)
+                                        const Array<unsigned int> &point_id,
+                                        const int point_pos_ordering)
 {
    MFEM_VERIFY(setupflag, "Use OversetFindPointsGSLIB::Setup before "
                "finding points.");
@@ -2582,10 +2609,10 @@ void OversetFindPointsGSLIB::FindPoints(const Vector &point_pos,
 }
 
 void OversetFindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                         Array<unsigned int> &point_id,
+                                         const Array<unsigned int> &point_id,
                                          const GridFunction &field_in,
                                          Vector &field_out,
-                                         int point_pos_ordering)
+                                         const int point_pos_ordering)
 {
    FindPoints(point_pos, point_id, point_pos_ordering);
    Interpolate(field_in, field_out);

fem/gslib.hpp

@@ -119,11 +119,13 @@ protected:
    } DEV;
 
    /// Use GSLIB for communication and interpolation
-   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out);
+   virtual void InterpolateH1(const GridFunction &field_in, Vector &field_out,
+                              const int field_out_ordering);
    /// Uses GSLIB Crystal Router for communication followed by MFEM's
    /// interpolation functions
    virtual void InterpolateGeneral(const GridFunction &field_in,
-                                   Vector &field_out);
+                                   Vector &field_out,
+                                   const int field_out_ordering);
 
    /// Since GSLIB is designed to work with quads/hexes, we split every
    /// triangle/tet/prism/pyramid element into quads/hexes.
@@ -140,7 +142,7 @@ protected:
    virtual void SetupSplitMeshesAndIntegrationRules(const int order);
 
    /// Get GridFunction value at the points expected by GSLIB.
-   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals);
+   virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals) const;
 
    /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices,
    /// find the original element number (that was split into micro quads/hexes)
@@ -182,7 +184,7 @@ protected:
        These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
        byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering. */
    void FindPointsOnDevice(const Vector &point_pos,
-                           int point_pos_ordering = Ordering::byNODES);
+                           const int point_pos_ordering = Ordering::byNODES);
 
    /** Interpolation of field values at prescribed reference space positions.
        @param[in] field_in_evec E-vector of grid function to be interpolated.
@@ -253,10 +255,15 @@ public:
        #gsl_dist        Distance between the sought and the found point
                         in physical space. */
    void FindPoints(const Vector &point_pos,
-                   int point_pos_ordering = Ordering::byNODES);
+                   const int point_pos_ordering = Ordering::byNODES);
+   /// Convenience function when point positions are in a ParticleVector
+   void FindPoints(const ParticleVector &point_pos)
+   {
+      FindPoints(point_pos, point_pos.GetOrdering());
+   }
    /// Setup FindPoints and search positions
    void FindPoints(Mesh &m, const Vector &point_pos,
-                   int point_pos_ordering = Ordering::byNODES,
+                   const int point_pos_ordering = Ordering::byNODES,
                    const double bb_t = 0.1, const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
@@ -266,20 +273,28 @@ public:
                               \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. */
+                              the value is set to #default_interp_value.
+                              The output ordering is determined from field_in.*/
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
+   /// Interpolation of field values, with output ordering specification.
+   virtual void Interpolate(const GridFunction &field_in, Vector &field_out,
+                            const int field_out_ordering);
    /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
        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);
+                    const int point_pos_ordering = Ordering::byNODES);
+   /// Search positions and interpolate with given point and output ordering.
+   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
+                    Vector &field_out, const int point_pos_ordering,
+                    const int field_out_ordering);
    /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
        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);
+                    const int point_pos_ordering = Ordering::byNODES);
 
    /// Average type to be used for L2 functions in-case a point is located at
    /// an element boundary where the function might be multi-valued.
@@ -376,7 +391,7 @@ public:
    /// The size of the returned vector is (nel x nverts x dim), where nel is the
    /// number of elements (after splitting for simplcies), nverts is number of
    /// vertices (4 in 2D, 8 in 3D), and dim is the spatial dimension.
-   void GetAxisAlignedBoundingBoxes(Vector &aabb);
+   void GetAxisAlignedBoundingBoxes(Vector &aabb) const;
 
    /// Return the oriented bounding boxes (OBB) computed during \ref Setup.
    /// Each OBB is represented using the inverse transformation (A^{-1}) and
@@ -386,7 +401,8 @@ public:
    /// size (dim x dim x nel), and the OBB centers are returned in \p obbC,
    /// a vector of size (nel x dim). The vertices of the OBBs are returned in
    /// \p obbV, a vector of size (nel x nverts x dim) .
-   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC, Vector &obbV);
+   void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
+                                 Vector &obbV) const;
 };
 
 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -446,13 +462,14 @@ public:
                                        byNodes: (XXX...,YYY...,ZZZ) or
                                        byVDim: (XYZ,XYZ,....XYZ) */
    void FindPoints(const Vector &point_pos,
-                   Array<unsigned int> &point_id,
-                   int point_pos_ordering = Ordering::byNODES);
+                   const Array<unsigned int> &point_id,
+                   const int point_pos_ordering = Ordering::byNODES);
 
    /** Search positions and interpolate */
-   void Interpolate(const Vector &point_pos, Array<unsigned int> &point_id,
+   void Interpolate(const Vector &point_pos,
+                    const Array<unsigned int> &point_id,
                     const GridFunction &field_in, Vector &field_out,
-                    int point_pos_ordering = Ordering::byNODES);
+                    const int point_pos_ordering = Ordering::byNODES);
    using FindPointsGSLIB::Interpolate;
 };
 

fem/hybridization.cpp

@@ -789,7 +789,6 @@ void Hybridization::ComputeH()
    }
    else
    {
-      // TODO: add ones on the diagonal of zero rows
       V->Finalize();
       Array<HYPRE_BigInt> V_J(V->NumNonZeroElems());
       MFEM_ASSERT(c_pfes, "");
@@ -823,6 +822,13 @@ void Hybridization::ComputeH()
       MFEM_VERIFY(pH.Type() != Operator::PETSC_MATIS, "To be implemented");
       pH.MakePtAP(plpH, pP);
       delete lpH;
+
+      HypreParMatrix *hH = pH.As<HypreParMatrix>();
+      MFEM_ASSERT(hH, "");
+
+      SparseMatrix H_diag;
+      hH->GetDiag(H_diag);
+      H_diag.SetDiagIdentity();
    }
 #endif
 }

fem/hybridization_ext.hpp

@@ -14,8 +14,11 @@
 
 #include "../config/config.hpp"
 #include "../general/array.hpp"
+#include "../linalg/operator.hpp"
 #include "../linalg/vector.hpp"
 
+#include <memory>
+
 namespace mfem
 {
 
@@ -45,15 +48,30 @@ protected:
    Array<int> hat_dof_gather_map;
    Array<DofType> hat_dof_marker;
 
-   Array<int> el_to_face;
-   Array<int> face_to_el;
+   Array<int> el_to_face; ///< Element to face connectivity.
+   Array<int> el_face_offsets; ///< Per-element offsets into @a el_to_face.
+   Array<int> face_to_el; ///< Face-to-element connectivity.
+   Array<int> face_face_offsets; ///< Face-to-face offsets.
+
+   int n_el_face; ///< Total number of element-to-face connections.
+   int n_face_face; ///< Total number of face-to-face connections.
+
    Vector Ct_mat; ///< Constraint matrix (transposed) stored element-wise.
 
+   /// @name For parallel non-conforming meshes
+   ///@{
+   std::unique_ptr<Operator> P_pc; ///< Partially conforming prolongation.
+   std::unique_ptr<Operator> P_nbr; ///< Face-neighbor prolongation.
+   ///@}
+
    Array<int> idofs, bdofs;
 
    Vector Ahat, Ahat_ii, Ahat_ib, Ahat_bi, Ahat_bb;
    Array<int> Ahat_ii_piv, Ahat_bb_piv;
 
+   /// Return the (partially) conforming prolongation on the constraint space.
+   const Operator &GetProlongation() const;
+
 public:
    /// Construct the constraint matrix.
    void ConstructC();

fem/integ/bilininteg_trace_jump_ea.cpp

@@ -28,7 +28,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
    const FaceType ftype = FaceType::Interior;
    const int nf = mesh.GetNFbyType(ftype);
 
-   const Geometry::Type geom = mesh.GetFaceGeometry(0);
+   const Geometry::Type geom = mesh.GetTypicalFaceGeometry();
    const int trial_order = trial_fes.GetMaxElementOrder();
    const int test_order = test_fes.GetMaxElementOrder();
    const int qorder = test_order + trial_order - 1;
@@ -47,7 +47,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
       });
    }
 
-   const FiniteElement &trial_face_el = *trial_fes.GetFaceElement(0);
+   const FiniteElement &trial_face_el = *trial_fes.GetTypicalTraceElement();
    const auto maps = &trial_face_el.GetDofToQuad(ir, DofToQuad::TENSOR);
    const int ndof_face = trial_face_el.GetDof();
 
@@ -72,7 +72,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
       MFEM_ABORT("Unknown kernel.");
    }
 
-   const FiniteElement &test_el = *test_fes.GetFE(0);
+   const FiniteElement &test_el = *test_fes.GetTypicalFE();
    const int n_faces_per_el = 2*dim; // assuming tensor product
    // Get all the local face maps (mapping from lexicographic face index to
    // lexicographic volume index, depending on the local face index).
@@ -90,10 +90,10 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
    Array<int> face_info(nf * 4);
    {
       int fidx = 0;
-      for (int f = 0; f < mesh.GetNumFaces(); ++f)
+      for (int f = 0; f < mesh.GetNumFacesWithGhost(); ++f)
       {
          Mesh::FaceInformation finfo = mesh.GetFaceInformation(f);
-         if (!finfo.IsInterior()) { continue; }
+         if (!finfo.IsInterior() || finfo.IsNonconformingCoarse()) { continue; }
          face_info[0 + fidx*4] = finfo.element[0].local_face_id;
          face_info[1 + fidx*4] = finfo.element[0].orientation;
          face_info[2 + fidx*4] = finfo.element[1].local_face_id;
@@ -114,7 +114,7 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
    else
    {
       d_emat = emat.Write();
-      mfem::forall(emat.Size(), [=] MFEM_HOST_DEVICE (int i) { d_emat[i] = 0.0; });
+      emat = 0.0; // Will execute on device, since Write() sets the device flag
    }
 
    const auto face_mats = Reshape(mass_emat.Read(), ndof_face, ndof_face, nf);
@@ -133,26 +133,104 @@ void NormalTraceJumpIntegrator::AssembleEAInteriorFaces(
       }
    };
 
-   mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
+   auto permute_face_2 = [=] MFEM_HOST_DEVICE(int local_face_1, int local_face_2,
+                                              int orient, int size1d, int index)
    {
-      MFEM_FOREACH_THREAD(el_i, z, 2)
+      if (dim == 2)
       {
-         const int lf_i = d_face_info(0, el_i, f);
-         const int orient = d_face_info(1, el_i, f);
-         // Loop over face indices in "native ordering"
-         MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
+         return internal::PermuteFace2D(local_face_1, local_face_2, orient,
+                                        size1d, index);
+      }
+      else // dim == 3
+      {
+         return internal::PermuteFace3D(local_face_1, local_face_2, orient,
+                                        size1d, index);
+      }
+   };
+
+   if (mesh.Conforming())
+   {
+      mfem::forall_3D(nf, ndof_face, ndof_face, 2, [=] MFEM_HOST_DEVICE (int f)
+      {
+         MFEM_FOREACH_THREAD(el_i, z, 2)
          {
-            // Convert to lexicographic relative to the face itself
-            const int i_face = permute_face(lf_i, orient, d1d, i_lex);
-            // Convert from lexicographic face DOF to volume DOF
-            const int i = d_face_maps(i_lex, lf_i);
-            MFEM_FOREACH_THREAD(j, y, ndof_face)
+            const int lf_i = d_face_info(0, el_i, f);
+            const int orient = d_face_info(1, el_i, f);
+            // Loop over face indices in "native ordering"
+            MFEM_FOREACH_THREAD(i_lex, x, ndof_face)
             {
-               el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
+               // Convert to lexicographic relative to the face itself
+               const int i_face = permute_face(lf_i, orient, d1d, i_lex);
+               // Convert from lexicographic face DOF to volume DOF
+               const int i = d_face_maps(i_lex, lf_i);
+               MFEM_FOREACH_THREAD(j, y, ndof_face)
+               {
+                  el_mats(i, j, el_i, f) += face_mats(i_face, j, f);
+               }
             }
          }
-      }
-   });
+      });
+   }
+   else
+   {
+      const InterpolationManager &interp =
+         test_fes.GetInterpolationManager(ElementDofOrdering::LEXICOGRAPHIC, ftype);
+
+      auto interp_configs = interp.GetFaceInterpConfig().Read();
+      const int nc_size = interp.GetNumInterpolators();
+      auto d_interp = Reshape(interp.GetInterpolators().Read(),
+                              ndof_face, ndof_face, nc_size);
+
+      mfem::forall(nf, [=] MFEM_HOST_DEVICE (int f)
+      {
+         const InterpConfig conf = interp_configs[f];
+         const int master_side = conf.master_side;
+         const int interp_index = conf.index;
+
+         const int lf_0 = d_face_info(0, 0, f);
+
+         for (int el_i = 0; el_i < 2; ++el_i)
+         {
+            const int lf_i = d_face_info(0, el_i, f);
+            const int orient = d_face_info(1, el_i, f);
+
+            for (int j = 0; j < ndof_face; j++)
+            {
+               for (int i_lex = 0; i_lex < ndof_face; i_lex++)
+               {
+                  real_t val = 0.0;
+                  if (conf.is_non_conforming && el_i == master_side)
+                  {
+                     // Interpolate from el_i (coarse element) to the fine face.
+                     // The mapping is given by d_interp, which uses indices
+                     // relative to element 0.
+
+                     // i0 is lexicographic relative to element 0
+                     const int i0 = permute_face_2(lf_i, lf_0, orient, d1d, i_lex);
+
+                     // k0 is lexicographic relative to element 0
+                     for (int k0 = 0; k0 < ndof_face; k0++)
+                     {
+                        // k is relative to the face itself
+                        const int k = permute_face(lf_0, orient, d1d, k0);
+                        val += d_interp(k0, i0, interp_index)
+                               * face_mats(k, j, f);
+                     }
+                  }
+                  else
+                  {
+                     // Convert to lexicographic relative to the face itself
+                     const int i_face = permute_face(lf_i, orient, d1d, i_lex);
+                     val = face_mats(i_face, j, f);
+                  }
+                  // Convert from lexicographic face DOF to volume DOF
+                  const int i = d_face_maps(i_lex, lf_i);
+                  el_mats(i, j, el_i, f) += val;
+               }
+            }
+         }
+      });
+   }
 }
 
 }

fem/kernel_dispatch.hpp

@@ -14,6 +14,7 @@
 
 #include "../config/config.hpp"
 #include "kernel_reporter.hpp"
+#include "../general/hash_util.hpp"
 #include <unordered_map>
 #include <tuple>
 #include <type_traits>
@@ -86,35 +87,6 @@ namespace mfem
     }                                                                          \
   }
 
-/// @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 { };
@@ -128,8 +100,8 @@ class KernelDispatchTable<Kernels,
          internal::KernelTypeList<Params...>,
          internal::KernelTypeList<OptParams...>>
 {
-   using TableType = std::unordered_map<std::tuple<Params...>,
-         Signature, KernelDispatchKeyHash<Params...>>;
+   using TableType =
+      std::unordered_map<std::tuple<Params...>, Signature, TupleHasher>;
    TableType table;
 
    /// @brief Call function @a f with arguments @a args (perfect forwaring).

fem/lor/lor_dg.hpp

@@ -23,6 +23,8 @@ class BatchedLOR_DG : BatchedLORKernel
 {
    IntegrationRule ir_face; ///< Collocated Gauss-Lobatto face quadrature rule.
    real_t kappa; ///< DG penalty parameter.
+   bool has_bdr_integ; ///< Is there a boundary integrator?
+   const Array<int> *bdr_markers; ///< Boundary integrator markers.
 public:
    template <int ORDER, int SDIM> void Assemble2D();
    template <int ORDER> void Assemble3D();
@@ -38,8 +40,7 @@ public:
       ProjectLORCoefficient<MassIntegrator>(a, c1);
       ProjectLORCoefficient<DiffusionIntegrator>(a, c2);
 
-      auto *integ = GetInteriorFaceIntegrator<DGDiffusionIntegrator>(a);
-      if (integ)
+      if (auto *integ = GetInteriorFaceIntegrator<DGDiffusionIntegrator>(a))
       {
          kappa = integ->GetPenaltyParameter();
       }
@@ -47,6 +48,19 @@ public:
       {
          kappa = 0.0;
       }
+
+      has_bdr_integ = false;
+      auto *bdr_face_integs = a.GetBFBFI();
+      for (int i = 0; i < bdr_face_integs->Size(); ++i)
+      {
+         if (auto *integ = dynamic_cast<DGDiffusionIntegrator*>((*bdr_face_integs)[i]))
+         {
+            kappa = integ->GetPenaltyParameter();
+            bdr_markers = (*a.GetBFBFI_Marker())[i];
+            has_bdr_integ = true;
+            break;
+         }
+      }
    }
 
    /// @brief Compute and return the face info array.

fem/lor/lor_dg_impl.hpp

@@ -22,9 +22,13 @@ namespace mfem
 Array<int> BatchedLOR_DG::GetFaceInfo() const
 {
    Mesh &mesh = *fes_ho.GetMesh();
+   const Array<int> &bdr_face_attrs = mesh.GetBdrFaceAttributes();
    const int nf = mesh.GetNumFaces();
    Array<int> face_info(nf * 6); // (e0, f0, o0, e1, f1, o1)
    auto h_face_info = Reshape(face_info.HostWrite(), 6, nf);
+
+   int bdr_face_counter = 0;
+
    for (int f = 0; f < nf; ++f)
    {
       auto finfo = mesh.GetFaceInformation(f);
@@ -43,6 +47,19 @@ Array<int> BatchedLOR_DG::GetFaceInfo() const
          h_face_info(4, f) = -1;
          h_face_info(5, f) = -1;
       }
+
+      if (finfo.IsBoundary())
+      {
+         // Check if Neumann boundary; skip these when adding boundary penalties
+         const int bdr_attr = bdr_face_attrs[bdr_face_counter];
+         if (!has_bdr_integ || (bdr_markers && !(*bdr_markers)[bdr_attr - 1]))
+         {
+            h_face_info(0, f) = -1;
+            h_face_info(1, f) = -1;
+            h_face_info(2, f) = -1;
+         }
+         bdr_face_counter += 1;
+      }
    }
    return face_info;
 }
@@ -144,6 +161,7 @@ void BatchedLOR_DG::AssembleFaceTerms()
    {
       const int f_0 = d_face_info(1, f);
       const int f_1 = d_face_info(4, f);
+      if (f_0 < 0) { return; } // Skip Neumann boundary faces
       const int nsides = (f_1 >= 0) ? 2 : 1;
       for (int el_i = 0; el_i < nsides; ++el_i)
       {

fem/moonolith/mortarassembler.cpp

@@ -78,10 +78,7 @@ template <int Dim>
 void BuildBoxes(const Mesh &mesh,
                 std::vector<::moonolith::AABB<Dim, double>> &element_boxes)
 {
-#ifndef NDEBUG
-   const int dim = mesh.Dimension();
-   assert(dim == Dim);
-#endif
+   MFEM_ASSERT(mesh.Dimension() == Dim, "Mesh and box dimensions mismatched");
    element_boxes.resize(mesh.GetNE());
 
    DenseMatrix pts;

fem/pbilinearform.cpp

@@ -488,10 +488,16 @@ void ParBilinearForm::FormLinearSystem(
          R.Mult(x, true_X);
 
          FormSystemMatrix(ess_tdof_list, A);
-         ConstrainedOperator *A_constrained;
-         Operator::FormConstrainedSystemOperator(ess_tdof_list, A_constrained);
+
+         std::unique_ptr<ConstrainedOperator> A_constrained([&]()
+         {
+            Operator *op;
+            Operator::FormSystemOperator(ess_tdof_list, op);
+            return dynamic_cast<ConstrainedOperator*>(op);
+         }());
+         MFEM_ASSERT(A_constrained != nullptr, "");
+
          A_constrained->EliminateRHS(true_X, true_B);
-         delete A_constrained;
          R.MultTranspose(true_B, b);
          hybridization->ReduceRHS(true_B, B);
          X.SetSize(B.Size());

fem/pfespace.cpp

@@ -646,39 +646,38 @@ const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
    auto itr = L2F.find(key);
    if (itr != L2F.end())
    {
-      return itr->second;
+      return itr->second.get();
    }
    else
    {
-      FaceRestriction *res;
+      std::unique_ptr<FaceRestriction> res;
       if (is_dg_space)
       {
          if (Conforming())
          {
-            res = new ParL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new ParL2FaceRestriction(*this, f_ordering, type, m));
          }
          else
          {
-            res = new ParNCL2FaceRestriction(*this, f_ordering, type, m);
+            res.reset(new ParNCL2FaceRestriction(*this, f_ordering, type, m));
          }
       }
       else if (dynamic_cast<const DG_Interface_FECollection*>(fec))
       {
-         res = new L2InterfaceFaceRestriction(*this, f_ordering, type);
+         res.reset(new L2InterfaceFaceRestriction(*this, f_ordering, type));
       }
       else
       {
          if (Conforming())
          {
-            res = new ConformingFaceRestriction(*this, f_ordering, type);
+            res.reset(new ConformingFaceRestriction(*this, f_ordering, type));
          }
          else
          {
-            res = new ParNCH1FaceRestriction(*this, f_ordering, type);
+            res.reset(new ParNCH1FaceRestriction(*this, f_ordering, type));
          }
       }
-      L2F[key] = res;
-      return res;
+      return L2F.emplace(key, std::move(res)).first->second.get();
    }
 }
 

fem/pfespace.hpp

@@ -483,6 +483,8 @@ public:
    const FiniteElement *GetFaceNbrFaceFE(int i) const;
    const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() { return face_nbr_glob_dof_map; }
    const HYPRE_BigInt *GetFaceNbrGlobalDofMap() { return face_nbr_glob_dof_map; }
+   const Array<HYPRE_BigInt> &GetFaceNbrGlobalDofMapArray() const
+   { return face_nbr_glob_dof_map; }
    ElementTransformation *GetFaceNbrElementTransformation(int i) const
    { return pmesh->GetFaceNbrElementTransformation(i); }
 

fem/pgridfunc.cpp

@@ -543,13 +543,22 @@ void ParGridFunction::GetElementDofValues(int el, Vector &dof_vals) const
    }
 }
 
-void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
+void ParGridFunction::ProjectCoefficient(Coefficient &coeff, ProjectType type)
 {
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
 
    if (delta_c == NULL)
    {
-      GridFunction::ProjectCoefficient(coeff);
+      (*this) = std::numeric_limits<real_t>::min();
+      GridFunction::ProjectCoefficient(coeff,type);
+
+      // Accumulate for all vdofs.
+      if (pfes->GetNURBSext())
+      {
+         GroupCommunicator &gcomm = pfes->GroupComm();
+         gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
+         gcomm.Bcast<real_t>(data);
+      }
    }
    else
    {
@@ -565,6 +574,147 @@ void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
    }
 }
 
+void ParGridFunction::ProjectCoefficient(VectorCoefficient &vcoeff,
+                                         ProjectType type)
+{
+   GridFunction::ProjectCoefficient(vcoeff, type);
+
+   // Accumulate for all vdofs.
+   if (pfes->GetNURBSext())
+   {
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(data, GroupCommunicator::Max);
+      gcomm.Bcast<real_t>(data);
+   }
+}
+
+void ParGridFunction::ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                                 real_t rtol,
+                                                 int iter)
+{
+   // Define and assemble linear form
+   ParLinearForm b(pfes);
+   b.AddDomainIntegrator(new DomainLFIntegrator(coeff));
+   b.Assemble();
+
+   // Define and assemble bilinear form
+   ParBilinearForm a(pfes);
+   a.AddDomainIntegrator(new MassIntegrator());
+   a.Assemble();
+
+   // Configure solver
+   OperatorPtr A;
+   Vector B, X, x(*this);
+   Array<int> ess_tdof_list;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+   Solver *prec = new HypreBoomerAMG;
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+   cg.SetPreconditioner(*prec);
+   cg.SetOperator(*A);
+   cg.Mult(B, X);
+   a.RecoverFEMSolution(X, b, x);
+   delete prec;
+}
+
+void ParGridFunction::ProjectCoefficientElementL2(Coefficient &coeff)
+{
+   Vector Va;
+   ProjectCoefficientElementL2_(coeff, *this, Va);
+
+   GroupCommunicator &gcomm = pfes->GroupComm();
+   gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+   gcomm.Bcast<real_t>(GetData());
+
+   gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
+   gcomm.Bcast<real_t>(Va.GetData());
+   (*this)/=Va;
+}
+
+void ParGridFunction::ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                                 real_t rtol, int iter)
+{
+   // Define and assemble linear form
+   ParLinearForm b(pfes);
+   ParBilinearForm a(pfes);
+
+   // Dimension argument to GetRangeType is arbitrary to be 3, could also be 2.
+   if (fes->FEColl()->GetRangeType(3)  == mfem::FiniteElement::VECTOR)
+   {
+      b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorFEMassIntegrator());
+   }
+   else
+   {
+      b.AddDomainIntegrator(new VectorDomainLFIntegrator(vcoeff));
+      a.AddDomainIntegrator(new VectorMassIntegrator());
+   }
+   b.Assemble();
+   a.Assemble();
+
+   // Configure solver
+   OperatorPtr A;
+   Vector B, X, x(*this);
+   x = 0.0;
+   Array<int> ess_tdof_list;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+   Solver *prec = new HypreBoomerAMG;
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(rtol);
+   cg.SetMaxIter(iter);
+   cg.SetPrintLevel(0);
+   cg.SetPreconditioner(*prec);
+   cg.SetOperator(*A);
+   cg.Mult(B, X);
+   a.RecoverFEMSolution(X, b, x);
+   x.Print();
+   delete prec;
+}
+
+void ParGridFunction::ProjectCoefficientElementL2(VectorCoefficient &vcoeff)
+{
+   if (fes->GetTypicalFE()->GetRangeType() == mfem::FiniteElement::VECTOR)
+   {
+      Vector Va;
+      ProjectCoefficientElementL2_(vcoeff, *this, Va);
+
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(GetData());
+
+      gcomm.Reduce<real_t>(Va.GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(Va.GetData());
+      (*this)/=Va;
+   }
+   else
+   {
+      Array<int> vdofs(fes->GetNDofs());
+      Vector x, Va, gVa(Size());
+      VectorComponentCoefficient coeff(vcoeff,0);
+      *this = 0.0;
+      gVa = 0.0;
+      for (int v = 0; v < VectorDim(); v++)
+      {
+         coeff.SetComponent(v);
+         ProjectCoefficientElementL2_(coeff, x, Va);
+         fes->GetVDofs(v, vdofs);
+         SetSubVector(vdofs, x);
+         gVa.SetSubVector(vdofs, Va);
+      }
+
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<real_t>(GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(GetData());
+
+      gcomm.Reduce<real_t>(gVa.GetData(), GroupCommunicator::Sum);
+      gcomm.Bcast<real_t>(gVa.GetData());
+      *this /= gVa;
+   }
+}
+
+
 void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff)
 {
    // local maximal element attribute for each dof

fem/pgridfunc.hpp

@@ -72,6 +72,10 @@ public:
 
    ParGridFunction(ParFiniteElementSpace *pf) : GridFunction(pf), pfes(pf) { }
 
+   /// Same as above but specify the device memory type
+   ParGridFunction(ParFiniteElementSpace *pf, MemoryType mt) :
+      GridFunction(pf, mt), pfes(pf) { }
+
    /// Construct a ParGridFunction using previously allocated array @a data.
    /** The ParGridFunction does not assume ownership of @a data which is assumed
        to be of size at least `pf->GetVSize()`. Similar to the GridFunction and
@@ -257,7 +261,11 @@ public:
    void GetElementDofValues(int el, Vector &dof_vals) const override;
 
    using GridFunction::ProjectCoefficient;
-   void ProjectCoefficient(Coefficient &coeff) override;
+   void ProjectCoefficient(Coefficient &coeff,
+                           ProjectType type = ProjectType::DEFAULT) override;
+
+   void ProjectCoefficient(VectorCoefficient &vcoeff,
+                           ProjectType type = ProjectType::DEFAULT) override;
 
    using GridFunction::ProjectDiscCoefficient;
    /** @brief Project a discontinuous vector coefficient as a grid function on
@@ -282,6 +290,18 @@ public:
    void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                      const Array<int> &bdr_attr) override;
 
+   void ProjectCoefficientGlobalL2(Coefficient &coeff,
+                                   real_t rtol = 1e-12,
+                                   int iter = 1000) override;
+
+   void ProjectCoefficientElementL2(Coefficient &coeff) override;
+
+   void ProjectCoefficientGlobalL2(VectorCoefficient &vcoeff,
+                                   real_t rtol = 1e-12,
+                                   int iter = 1000) override;
+
+   void ProjectCoefficientElementL2(VectorCoefficient &vcoeff) override;
+
    /// @brief Returns ||u_ex - u_h||_L1 in parallel for H1 or L2 elements
    ///
    /// @see GridFunction::ComputeL1Error(Coefficient *exsol[],

fem/prestriction.cpp

@@ -994,7 +994,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
       {
          if ( face.IsConforming() )
          {
-            interpolations.RegisterFaceConformingInterpolation(face,f_ind);
             SetFaceDofsScatterIndices1(face,f_ind);
             if ( m==L2FaceValues::DoubleValued )
             {
@@ -1010,7 +1009,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
          }
          else // Non-conforming face
          {
-            interpolations.RegisterFaceCoarseToFineInterpolation(face,f_ind);
             SetFaceDofsScatterIndices1(face,f_ind);
             if ( m==L2FaceValues::DoubleValued )
             {
@@ -1028,7 +1026,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
       }
       else if (type==FaceType::Boundary && face.IsBoundary())
       {
-         interpolations.RegisterFaceConformingInterpolation(face,f_ind);
          SetFaceDofsScatterIndices1(face,f_ind);
          if ( m==L2FaceValues::DoubleValued )
          {
@@ -1046,10 +1043,6 @@ void ParNCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
    {
       gather_offsets[i] += gather_offsets[i - 1];
    }
-
-   // Transform the interpolation matrix map into a contiguous memory structure.
-   interpolations.LinearizeInterpolatorMapIntoVector();
-   interpolations.InitializeNCInterpConfig();
 }
 
 void ParNCL2FaceRestriction::ComputeGatherIndices()

fem/prestriction.hpp

@@ -326,9 +326,7 @@ public:
        @param[in] keep_nbr_block When set to true the SparseMatrix will
                                  include the rows (in addition to the columns)
                                  corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
    void FillI(SparseMatrix &mat,
               const bool keep_nbr_block = false) const override;
 
@@ -364,9 +362,7 @@ public:
        @param[in] keep_nbr_block When set to true the SparseMatrix will
                                  include the rows (in addition to the columns)
                                  corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
    void FillJAndData(const Vector &fea_data,
                      SparseMatrix &mat,
                      const bool keep_nbr_block = false) const override;

fem/qinterp/det.cpp

@@ -50,7 +50,13 @@ QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Fallback(
    int DIM, int SDIM, int D1D, int Q1D)
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   if (DIM == 1)
+   {
+      if (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
+      else if (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<0,0,2>; }
+      else if (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<0,0,3>; }
+      else { MFEM_ABORT(""); }
+   }
    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)

fem/qinterp/det.hpp

@@ -56,6 +56,50 @@ inline void Det1D(const int NE,
    });
 }
 
+template<int T_D1D = 0, int T_Q1D = 0, int T_SDIM = 3>
+inline void Det1DSurface(const int NE,
+                         const real_t *b,
+                         const real_t *g,
+                         const real_t *x,
+                         real_t *y,
+                         const int d1d = 0,
+                         const int q1d = 0,
+                         Vector *d_buff = nullptr)
+{
+   MFEM_CONTRACT_VAR(b);
+   MFEM_CONTRACT_VAR(d_buff);
+
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto G = Reshape(g, Q1D, D1D);
+   const auto X = Reshape(x, D1D, T_SDIM, NE);
+   auto Y = Reshape(y, Q1D, NE);
+
+   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
+   {
+      for (int q = 0; q < Q1D; q++)
+      {
+         real_t grad[T_SDIM];
+         for (int s = 0; s < T_SDIM; s++) { grad[s] = 0.0; }
+         for (int d = 0; d < D1D; d++)
+         {
+            const real_t gval = G(q, d);
+            for (int s = 0; s < T_SDIM; s++)
+            {
+               grad[s] += gval * X(d, s, e);
+            }
+         }
+         real_t norm2 = 0.0;
+         for (int s = 0; s < T_SDIM; s++)
+         {
+            norm2 += grad[s] * grad[s];
+         }
+         Y(q, e) = std::sqrt(norm2);
+      }
+   });
+}
+
 template<int T_D1D = 0, int T_Q1D = 0>
 inline void Det2D(const int NE,
                   const real_t *b,
@@ -290,7 +334,13 @@ template<int DIM, int SDIM, int D1D, int Q1D>
 QuadratureInterpolator::DetKernelType
 QuadratureInterpolator::DetKernels::Kernel()
 {
-   if (DIM == 1) { return internal::quadrature_interpolator::Det1D; }
+   if (DIM == 1)
+   {
+      if (SDIM == 1) { return internal::quadrature_interpolator::Det1D; }
+      else if (SDIM == 2) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 2>; }
+      else if (SDIM == 3) { return internal::quadrature_interpolator::Det1DSurface<D1D, Q1D, 3>; }
+      else { MFEM_ABORT(""); }
+   }
    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>; }

fem/quadinterpolator.cpp

@@ -542,7 +542,8 @@ void QuadratureInterpolator::Mult(const Vector &e_vec,
    }
 
    MFEM_ASSERT(!(eval_flags & DETERMINANTS) || dim == vdim ||
-               (dim == 2 && vdim == 3), "Invalid dimensions for determinants.");
+               (dim == 2 && vdim == 3) || (dim == 1 && vdim == 2) ||
+               (dim == 1 && vdim == 3), "Invalid dimensions for determinants.");
    MFEM_ASSERT(fespace->GetMesh()->GetNumGeometries(
                   fespace->GetMesh()->Dimension()) == 1,
                "mixed meshes are not supported");

fem/restriction.cpp

@@ -1506,12 +1506,12 @@ void L2FaceRestriction::EnsureNormalDerivativeRestriction() const
    }
 }
 
-InterpolationManager::InterpolationManager(const FiniteElementSpace &fes,
-                                           ElementDofOrdering ordering,
+InterpolationManager::InterpolationManager(const FiniteElementSpace &fes_,
+                                           ElementDofOrdering ordering_,
                                            FaceType type)
-   : fes(fes),
-     ordering(ordering),
-     interp_config( fes.GetNFbyType(type) ),
+   : fes(fes_),
+     ordering(ordering_),
+     interp_config(fes.GetNFbyType(type)),
      nc_cpt(0)
 { }
 
@@ -1536,7 +1536,8 @@ void InterpolationManager::RegisterFaceCoarseToFineInterpolation(
                         face.element[0].local_face_id +
                         6*face.element[1].local_face_id +
                         36*face.element[1].orientation ;
-   // Unfortunately we can't trust unicity of the ptMat to identify the transformation.
+   // Unfortunately we can't trust uniqueness of the ptMat to identify the
+   // transformation.
    Key key(ptMat, face_key);
    auto itr = interp_map.find(key);
    if ( itr == interp_map.end() )
@@ -1583,17 +1584,27 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
    IsoparametricTransformation isotr;
    isotr.SetIdentityTransformation(trace_fe->GetGeomType());
    isotr.SetPointMat(*ptMat);
-   DenseMatrix& trans_pt_mat = isotr.GetPointMat();
-   // PointMatrix needs to be flipped in 2D
-   if ( trace_fe->GetGeomType()==Geometry::SEGMENT && !is_ghost_slave )
-   {
-      std::swap(trans_pt_mat(0,0),trans_pt_mat(0,1));
-   }
    DenseMatrix native_interpolator(face_dofs,face_dofs);
    trace_fe->GetLocalInterpolation(isotr, native_interpolator);
+
+   if (trace_fe->GetMapType() == FiniteElement::INTEGRAL)
+   {
+      // Handle potentially inverted Jacobian matrix
+      isotr.SetIntPoint(&Geometries.GetCenter(trace_fe->GetGeomType()));
+      native_interpolator *= (isotr.Weight() >= 0) ? 1.0 : -1.0;
+   }
+
    const int dim = trace_fe->GetDim()+1;
    const int dof1d = trace_fe->GetOrder()+1;
-   const int orientation = face.element[1].orientation;
+   int orientation_i = face.element[1].orientation;
+   const int orientation_j = face.element[1].orientation;
+
+   // In 2D, need to flip orientation of the segments`
+   if (trace_fe->GetGeomType() == Geometry::SEGMENT && !is_ghost_slave)
+   {
+      orientation_i = 1;
+   }
+
    for (int i = 0; i < face_dofs; i++)
    {
       const int ni = (dof_map.Size()==0) ? i : dof_map[i];
@@ -1602,7 +1613,7 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
       {
          // master side is elem 2, so we permute to order dofs as elem 1.
          li = PermuteFaceL2(dim, face_id2, face_id1,
-                            orientation, dof1d, li);
+                            orientation_i, dof1d, li);
       }
       for (int j = 0; j < face_dofs; j++)
       {
@@ -1611,7 +1622,7 @@ const DenseMatrix* InterpolationManager::GetCoarseToFineInterpolation(
          {
             // master side is elem 2, so we permute to order dofs as elem 1.
             lj = PermuteFaceL2(dim, face_id2, face_id1,
-                               orientation, dof1d, lj);
+                               orientation_j, dof1d, lj);
          }
          const int nj = (dof_map.Size()==0) ? j : dof_map[j];
          (*interpolator)(li,lj) = native_interpolator(ni,nj);
@@ -1676,7 +1687,7 @@ NCL2FaceRestriction::NCL2FaceRestriction(const FiniteElementSpace &fes,
                                          const L2FaceValues m,
                                          bool build)
    : L2FaceRestriction(fes, f_ordering, type, m, false),
-     interpolations(fes, f_ordering, type)
+     interpolations(fes.GetInterpolationManager(ordering, type))
 {
    if (!build) { return; }
    x_interp.UseDevice(true);
@@ -2202,14 +2213,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
          {
             PermuteAndSetFaceDofsScatterIndices2(face,f_ind);
          }
-         if ( face.IsConforming() )
-         {
-            interpolations.RegisterFaceConformingInterpolation(face,f_ind);
-         }
-         else // Non-conforming face
-         {
-            interpolations.RegisterFaceCoarseToFineInterpolation(face,f_ind);
-         }
          f_ind++;
       }
       else if ( type==FaceType::Boundary && face.IsBoundary() )
@@ -2219,7 +2222,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
          {
             SetBoundaryDofsScatterIndices2(face,f_ind);
          }
-         interpolations.RegisterFaceConformingInterpolation(face,f_ind);
          f_ind++;
       }
    }
@@ -2232,10 +2234,6 @@ void NCL2FaceRestriction::ComputeScatterIndicesAndOffsets()
    {
       gather_offsets[i] += gather_offsets[i - 1];
    }
-
-   // Transform the interpolation matrix map into a contiguous memory structure.
-   interpolations.LinearizeInterpolatorMapIntoVector();
-   interpolations.InitializeNCInterpConfig();
 }
 
 void NCL2FaceRestriction::ComputeGatherIndices()
@@ -2278,6 +2276,18 @@ void NCL2FaceRestriction::ComputeGatherIndices()
    gather_offsets[0] = 0;
 }
 
+static int GetSharedVSize(const FiniteElementSpace &fes)
+{
+#ifdef MFEM_USE_MPI
+   if (auto pfes = dynamic_cast<const ParFiniteElementSpace*>(&fes))
+   {
+      const_cast<ParFiniteElementSpace*>(pfes)->ExchangeFaceNbrData();
+      return pfes->GetFaceNbrVSize();
+   }
+#endif
+   return 0;
+}
+
 L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(
    const FiniteElementSpace& fes_,
    const ElementDofOrdering ordering_,
@@ -2288,25 +2298,54 @@ L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(
      nfaces(fes.GetNFbyType(type)),
      vdim(fes.GetVDim()),
      byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     face_dofs(nfaces > 0 ? fes.GetFaceElement(0)->GetDof() : 0),
+     face_dofs(fes.GetTypicalTraceElement()->GetDof()),
      nfdofs(face_dofs*nfaces),
-     ndofs(fes.GetNDofs())
+     ndofs(fes.GetNDofs()),
+     nsdofs(GetSharedVSize(fes))
 {
    height = nfdofs;
    width = ndofs;
 
+#ifdef MFEM_USE_MPI
+   auto pfes = dynamic_cast<const ParFiniteElementSpace*>(&fes);
+#endif
+
    const Table &face2dof = fes.GetFaceToDofTable();
 
    const Mesh &mesh = *fes.GetMesh();
    int face_idx = 0;
-   gather_map.SetSize(nfdofs);
-   for (int f = 0; f < mesh.GetNumFaces(); ++f)
+   scatter_map.SetSize(nfdofs);
+   gather_map.SetSize(ndofs + nsdofs);
+   gather_map = -1;
+
+   Array<int> dofs;
+   for (int f = 0; f < mesh.GetNumFacesWithGhost(); ++f)
    {
       Mesh::FaceInformation face = mesh.GetFaceInformation(f);
-      if (!face.IsOfFaceType(type)) { continue; }
-      for (int i = 0; i < face_dofs; ++i)
+      if (!face.IsOfFaceType(type) || face.IsNonconformingCoarse()) { continue; }
+
+      if (f < mesh.GetNumFaces())
       {
-         gather_map[i + face_idx*face_dofs] = face2dof.GetJ()[i + f*face_dofs];
+         // Local face
+         face2dof.GetRow(f, dofs);
+         for (int i = 0; i < face_dofs; ++i)
+         {
+            scatter_map[i + face_idx*face_dofs] = dofs[i];
+            gather_map[dofs[i]] = i + face_idx*face_dofs;
+         }
+      }
+      else
+      {
+         // Shared (non-conforming) ghost face
+#ifdef MFEM_USE_MPI
+         MFEM_ASSERT(pfes != nullptr, "");
+         pfes->GetFaceNbrFaceVDofs(f, dofs);
+         for (int i = 0; i < face_dofs; ++i)
+         {
+            scatter_map[i + face_idx*face_dofs] = ndofs + dofs[i];
+            gather_map[ndofs + dofs[i]] = i + face_idx*face_dofs;
+         }
+#endif
       }
       ++face_idx;
    }
@@ -2314,13 +2353,19 @@ L2InterfaceFaceRestriction::L2InterfaceFaceRestriction(
 
 void L2InterfaceFaceRestriction::Mult(const Vector &x, Vector &y) const
 {
+   const int NDOFS = ndofs;
    const int nd = face_dofs;
    const int nf = nfaces;
    const int vd = vdim;
    const bool t = byvdim;
-   const int *map = gather_map.Read();
+   const int *map = scatter_map.Read();
+
+   Vector face_nbr_data = GetLVectorFaceNbrData(fes, x, type);
+   MFEM_ASSERT(face_nbr_data.Size() / vd == nsdofs, "");
 
    const auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   const auto d_x_shared = Reshape(face_nbr_data.Read(),
+                                   t?vd:nsdofs, t?nsdofs:vd);
    auto d_y = Reshape(y.Write(), nd, vd, nf);
 
    mfem::forall(nd*nf, [=] MFEM_HOST_DEVICE (int i)
@@ -2328,7 +2373,8 @@ void L2InterfaceFaceRestriction::Mult(const Vector &x, Vector &y) const
       const int j = map[i];
       for (int c = 0; c < vd; ++c)
       {
-         d_y(i % nd, c, i / nd) = d_x(t?c:j, t?j:c);
+         if (j < NDOFS) { d_y(i % nd, c, i / nd) = d_x(t?c:j, t?j:c); }
+         else { d_y(i % nd, c, i / nd) = d_x_shared(t?c:(j-NDOFS), t?(j-NDOFS):c); }
       }
    });
 }
@@ -2343,15 +2389,39 @@ void L2InterfaceFaceRestriction::AddMultTranspose(
    const int *map = gather_map.Read();
 
    const auto d_x = Reshape(x.Read(), nd, vd, nf);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.ReadWrite(), t?vd:ndofs, t?ndofs:vd);
 
-   mfem::forall(ndofs, [=] MFEM_HOST_DEVICE (int i) { d_y[i] = 0.0; });
-   mfem::forall(nd*nf, [=] MFEM_HOST_DEVICE (int i)
+   mfem::forall(ndofs, [=] MFEM_HOST_DEVICE (int i)
    {
       const int j = map[i];
+      if (j < 0) { return; }
       for (int c = 0; c < vd; ++c)
       {
-         d_y(t?c:j, t?j:c) = d_x(i % nd, c, i / nd);
+         d_y(t?c:i, t?i:c) += a*d_x(j % nd, c, j / nd);
+      }
+   });
+}
+
+void L2InterfaceFaceRestriction::MultTransposeShared(
+   const Vector &x, Vector &y) const
+{
+   const int nd = face_dofs;
+   const int nf = nfaces;
+   const int vd = vdim;
+   const bool t = byvdim;
+   const int *map = gather_map.Read();
+
+   const auto d_x = Reshape(x.Read(), nd, vd, nf);
+   auto d_y = Reshape(y.Write(), t?vd:(ndofs+nsdofs), t?(ndofs+nsdofs):vd);
+   y = 0.0;
+
+   mfem::forall(ndofs + nsdofs, [=] MFEM_HOST_DEVICE (int i)
+   {
+      const int j = map[i];
+      if (j < 0) { return; }
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(t?c:i, t?i:c) = d_x(j % nd, c, j / nd);
       }
    });
 }
@@ -2361,6 +2431,11 @@ const Array<int> &L2InterfaceFaceRestriction::GatherMap() const
    return gather_map;
 }
 
+const Array<int> &L2InterfaceFaceRestriction::ScatterMap() const
+{
+   return scatter_map;
+}
+
 Vector GetLVectorFaceNbrData(
    const FiniteElementSpace &fes, const Vector &x, FaceType ftype)
 {
@@ -2382,6 +2457,7 @@ Vector GetLVectorFaceNbrData(
          {
             ParGridFunction gf(pfes, const_cast<Vector&>(x));
             gf.ExchangeFaceNbrData();
+            x.SyncMemory(gf);
             return std::move(gf.FaceNbrData());
          }
       }

fem/restriction.hpp

@@ -812,13 +812,12 @@ protected:
        PointMatrix and a local face identifier. */
    using Key = std::pair<const DenseMatrix*,int>;
    /// The temporary map used to store the different interpolators.
-   using Map = std::map<Key, std::pair<int,const DenseMatrix*>>;
+   using Map =
+      std::unordered_map<Key, std::pair<int,const DenseMatrix*>, PairHasher>;
    Map interp_map; // The temporary map that stores the interpolators.
 
 public:
-   InterpolationManager() = delete;
-
-   /** @brief main constructor.
+   /** @brief Constructor.
 
        @param[in] fes      The FiniteElementSpace on which this operates
        @param[in] ordering Request a specific element ordering.
@@ -909,7 +908,7 @@ private:
 class NCL2FaceRestriction : virtual public L2FaceRestriction
 {
 protected:
-   InterpolationManager interpolations;
+   const InterpolationManager &interpolations;
    mutable Vector x_interp;
 
    /** @brief Constructs an NCL2FaceRestriction, this is a specialization of a
@@ -996,9 +995,7 @@ public:
        @param[in] keep_nbr_block When set to true the SparseMatrix will
                                  include the rows (in addition to the columns)
                                  corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
    void FillI(SparseMatrix &mat,
               const bool keep_nbr_block = false) const override;
 
@@ -1016,9 +1013,7 @@ public:
        @param[in] keep_nbr_block When set to true the SparseMatrix will
                                  include the rows (in addition to the columns)
                                  corresponding to face-neighbor dofs. The
-                                 default behavior is to disregard those rows.
-
-       @warning This method is not implemented yet. */
+                                 default behavior is to disregard those rows. */
    void FillJAndData(const Vector &fea_data,
                      SparseMatrix &mat,
                      const bool keep_nbr_block = false) const override;
@@ -1036,9 +1031,7 @@ public:
                               added the face contributions.
                               The format is: dofs x dofs x ne, where dofs is the
                               number of dofs per element and ne the number of
-                              elements.
-
-       @warning This method is not implemented yet. */
+                              elements. */
    void AddFaceMatricesToElementMatrices(const Vector &fea_data,
                                          Vector &ea_data) const override;
 
@@ -1130,7 +1123,9 @@ protected:
    const int face_dofs; ///< Number of dofs on each face
    const int nfdofs; ///< Total number of dofs on the faces (E-vector size)
    const int ndofs; ///< Number of dofs in the space (L-vector size)
+   const int nsdofs; ///< Number of shared face neighbor (ghost) dofs
    Array<int> gather_map; ///< Gather map
+   Array<int> scatter_map; ///< Scatter map
 
 public:
    /** @brief Constructs an L2InterfaceFaceRestriction.
@@ -1168,7 +1163,24 @@ public:
    void AddMultTranspose(const Vector &x, Vector &y,
                          const real_t a = 1.0) const override;
 
+   /// @brief Gather degrees of freedom, from face E-vector to L-vector and
+   /// shared (ghost) DOFs.
+   ///
+   /// @param[in]     x The face E-Vector degrees of freedom with size
+   ///                  (face_dofs, vdim, nf), where nf is the number of
+   ///                  interior or boundary faces requested by @a type in the
+   ///                  constructor. The face_dofs should be ordered according
+   ///                  to the given ElementDofOrdering
+   /// @param[out]    y Vector of length vsize + face neighbor vsize
+   void MultTransposeShared(const Vector &x, Vector &y) const;
+
    const Array<int> &GatherMap() const override;
+
+   /// @brief Return the low-level mapping from L-dofs to E-dofs.
+   ///
+   /// L-dofs that do not correspond to an E-dof (e.g. that lie on a face of a
+   /// different type) are given index -1.
+   const Array<int> &ScatterMap() const;
 };
 
 /** @brief Convert a dof face index from Native ordering to lexicographic

fem/transfer.cpp

@@ -333,6 +333,12 @@ void L2ProjectionGridTransfer::L2Projection::MixedMassEA(
    int nel_ho = mesh_ho->GetNE();
    int nel_lor = mesh_lor->GetNE();
 
+   if (nel_ho == 0)
+   {
+      M_LH.SetSize(0);
+      return;
+   }
+
    const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();
 
    int nref_max = 0;
@@ -831,11 +837,17 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::Mult(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMult(
    const Vector &x, Vector &y) const
 {
+   const int nel_ho = fes_ho.GetMesh()->GetNE();
+
+   if (nel_ho == 0)
+   {
+      return;
+   }
+
    const int iho = 0;
    const int nref = ho2lor.RowSize(iho);
    const int ndof_ho = fes_ho.GetFE(iho)->GetDof();
    const int ndof_lor = fes_lor.GetFE(ho2lor.GetRow(iho)[0])->GetDof();
-   const int nel_ho = fes_ho.GetMesh()->GetNE();
 
    DenseTensor R_dt;
    R_dt.NewMemoryAndSize(R.GetMemory(), ndof_lor*nref, ndof_ho, nel_ho, false);
@@ -887,11 +899,17 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::MultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMultTranspose(
    const Vector &x, Vector &y) const
 {
+   const int nel_ho = fes_ho.GetMesh()->GetNE();
+
+   if (nel_ho == 0)
+   {
+      return;
+   }
+
    const int iho = 0;
    const int nref = ho2lor.RowSize(iho);
    const int ndof_ho = fes_ho.GetFE(iho)->GetDof();
    const int ndof_lor = fes_lor.GetFE(ho2lor.GetRow(iho)[0])->GetDof();
-   const int nel_ho = fes_ho.GetMesh()->GetNE();
 
    DenseTensor R_dt;
    R_dt.NewMemoryAndSize(R.GetMemory(), ndof_lor*nref, ndof_ho, nel_ho, false);
@@ -901,7 +919,6 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAMultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::Prolongate(
    const Vector &x, Vector &y) const
 {
-
    if (fes_ho.GetNE() == 0) { return; }
 
    if (use_ea)
@@ -960,14 +977,13 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAProlongate(
 void L2ProjectionGridTransfer::L2ProjectionL2Space::ProlongateTranspose(
    const Vector &x, Vector &y) const
 {
+   if (fes_ho.GetNE() == 0) { return; }
 
    if (use_ea)
    {
       return EAProlongateTranspose(x,y);
    }
 
-
-   if (fes_ho.GetNE() == 0) { return; }
    MFEM_VERIFY(P.Size() > 0, "Prolongation not supported for these spaces.")
    int vdim = fes_ho.GetVDim();
    Array<int> vdofs;
@@ -1014,12 +1030,52 @@ void L2ProjectionGridTransfer::L2ProjectionL2Space::EAProlongateTranspose(
    BatchedLinAlg::MultTranspose(P_dt, x, y);
 }
 
+namespace
+{
+
+class H1ConsistentMassOperator : public Operator
+{
+private:
+   const Operator &M_LH;
+   const Solver &M_L_solver;
+
+public:
+   H1ConsistentMassOperator(const Operator &M_LH_, const Solver &M_L_solver_)
+      : Operator(M_LH_.Height(), M_LH_.Width()),
+        M_LH(M_LH_),
+        M_L_solver(M_L_solver_)
+   {
+      MFEM_VERIFY(M_LH.Height() == M_L_solver.Height() &&
+                  M_LH.Height() == M_L_solver.Width(),
+                  "incompatible consistent mass operator dimensions");
+   }
+
+   void Mult(const Vector &x, Vector &y) const override
+   {
+      Vector tmp(M_LH.Height());
+      M_LH.Mult(x, tmp);
+      M_L_solver.Mult(tmp, y);
+   }
+
+   void MultTranspose(const Vector &x, Vector &y) const override
+   {
+      Vector tmp(M_LH.Height());
+      M_L_solver.Mult(x, tmp);
+      M_LH.MultTranspose(tmp, y);
+   }
+};
+
+}
+
 L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
    const FiniteElementSpace& fes_ho_, const FiniteElementSpace& fes_lor_,
-   const bool use_ea_, MemoryType d_mt_)
+   const bool use_ea_, const bool use_consistent_mass_, MemoryType d_mt_)
    : L2Projection(fes_ho_, fes_lor_, d_mt_),
-     use_ea(use_ea_)
+     use_ea(use_ea_),
+     use_consistent_mass(use_consistent_mass_)
 {
+   MFEM_VERIFY(!(use_ea && use_consistent_mass),
+               "consistent mass is not supported with element assembly");
 
    // need scalar to keep dimensions matching (operators are built to apply
    // individually on each vdim)
@@ -1037,7 +1093,7 @@ L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
 
    std::unique_ptr<SparseMatrix> R_mat, M_LH_mat;
 
-   std::tie(R_mat, M_LH_mat) = ComputeSparseRAndM_LH();
+   std::tie(R_mat, M_LH_mat) = ComputeSparseRAndM_LH(!use_consistent_mass);
 
    const SparseMatrix *P_ho = fes_ho_scalar->GetConformingProlongation();
    const SparseMatrix *P_lor = fes_lor_scalar->GetConformingProlongation();
@@ -1046,40 +1102,68 @@ L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
    {
       if (P_ho && P_lor)
       {
-         R_mat.reset(RAP(*P_lor, *R_mat, *P_ho));
+         if (R_mat) { R_mat.reset(RAP(*P_lor, *R_mat, *P_ho)); }
          M_LH_mat.reset(RAP(*P_lor, *M_LH_mat, *P_ho));
       }
       else if (P_ho)
       {
-         R_mat.reset(mfem::Mult(*R_mat, *P_ho));
+         if (R_mat) { R_mat.reset(mfem::Mult(*R_mat, *P_ho)); }
          M_LH_mat.reset(mfem::Mult(*M_LH_mat, *P_ho));
       }
       else // P_lor != nullptr
       {
-         R_mat.reset(mfem::Mult(*P_lor, *R_mat));
+         if (R_mat) { R_mat.reset(mfem::Mult(*P_lor, *R_mat)); }
          M_LH_mat.reset(mfem::Mult(*P_lor, *M_LH_mat));
       }
    }
 
-   SparseMatrix *RTxM_LH_mat = TransposeMult(*R_mat, *M_LH_mat);
-   precon.reset(new DSmoother(*RTxM_LH_mat));
+   if (use_consistent_mass)
+   {
+      BilinearForm M_lor(fes_lor_scalar.get());
+      M_lor.AddDomainIntegrator(new MassIntegrator);
+      M_lor.Assemble();
+      M_lor.Finalize(0);
+      SparseMatrix *M_L_mat = new SparseMatrix(M_lor.SpMat());
 
-   // Set ownership
-   RTxM_LH.reset(RTxM_LH_mat);
-   R = std::move(R_mat);
-   M_LH = std::move(M_LH_mat);
+      ML_precon.reset(new DSmoother(*M_L_mat));
+      ML_pcg.SetPrintLevel(0);
+      ML_pcg.SetMaxIter(1000);
+      ML_pcg.SetRelTol(1e-13);
+      ML_pcg.SetAbsTol(1e-13);
+      ML_pcg.SetPreconditioner(*ML_precon);
+      ML_pcg.SetOperator(*M_L_mat);
 
-   SetupPCG();
+      M_L.reset(M_L_mat);
+      M_LH = std::move(M_LH_mat);
+      R.reset(new H1ConsistentMassOperator(*M_LH, ML_pcg));
+   }
+   else
+   {
+      SparseMatrix *RTxM_LH_mat = TransposeMult(*R_mat, *M_LH_mat);
+      precon.reset(new DSmoother(*RTxM_LH_mat));
+
+      // Set ownership
+      RTxM_LH.reset(RTxM_LH_mat);
+      R = std::move(R_mat);
+      M_LH = std::move(M_LH_mat);
+
+      SetupPCG();
+   }
 }
 
 #ifdef MFEM_USE_MPI
 
 L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
    const ParFiniteElementSpace& pfes_ho, const ParFiniteElementSpace& pfes_lor,
-   const bool use_ea_, MemoryType d_mt_)
+   const bool use_ea_, const bool use_consistent_mass_, MemoryType d_mt_)
    : L2Projection(pfes_ho, pfes_lor, d_mt_),
-     use_ea(use_ea_), pcg(pfes_ho.GetComm())
+     use_ea(use_ea_),
+     use_consistent_mass(use_consistent_mass_),
+     pcg(pfes_ho.GetComm()),
+     ML_pcg(pfes_ho.GetComm())
 {
+   MFEM_VERIFY(!(use_ea && use_consistent_mass),
+               "consistent mass is not supported with element assembly");
 
    // need scalar to keep dimensions matching (operators are built to apply
    // individually on each vdim)
@@ -1095,26 +1179,58 @@ L2ProjectionGridTransfer::L2ProjectionH1Space::L2ProjectionH1Space(
       return;
    }
 
-   std::tie(R, M_LH) = ComputeSparseRAndM_LH();
+   std::unique_ptr<SparseMatrix> R_local_sp, M_LH_local_sp;
+   std::tie(R_local_sp, M_LH_local_sp) =
+      ComputeSparseRAndM_LH(!use_consistent_mass);
 
+   M_LH_local_sp->Finalize(0);
+   if (R_local_sp) { R_local_sp->Finalize(0); }
+
+   HypreParMatrix M_LH_local = HypreParMatrix(pfes_ho.GetComm(),
+                                              pfes_lor_scalar->GlobalVSize(),
+                                              pfes_ho_scalar->GlobalVSize(),
+                                              pfes_lor_scalar->GetDofOffsets(),
+                                              pfes_ho_scalar->GetDofOffsets(),
+                                              M_LH_local_sp.get());
+   HypreParMatrix *M_LH_mat = RAP(pfes_lor_scalar->Dof_TrueDof_Matrix(),
+                                  &M_LH_local, pfes_ho_scalar->Dof_TrueDof_Matrix());
+
+   if (use_consistent_mass)
+   {
+      ParBilinearForm M_lor(pfes_lor_scalar.get());
+      M_lor.AddDomainIntegrator(new MassIntegrator);
+      M_lor.Assemble();
+      M_lor.Finalize(0);
+      HypreParMatrix *M_L_mat = M_lor.ParallelAssemble();
+
+      ML_pcg.SetPrintLevel(0);
+      ML_pcg.SetMaxIter(1000);
+      ML_pcg.SetRelTol(1e-13);
+      ML_pcg.SetAbsTol(1e-13);
+      ML_pcg.SetOperator(*M_L_mat);
+
+      M_L.reset(M_L_mat);
+      M_LH.reset(M_LH_mat);
+      HyprePCG *ML_hypre_pcg = new HyprePCG(*M_L_mat);
+      ML_hypre_pcg->SetPrintLevel(0);
+      ML_hypre_pcg->SetMaxIter(1000);
+      ML_hypre_pcg->SetTol(1e-13);
+      ML_hypre_pcg->SetAbsTol(1e-13);
+      ML_hypre_pcg->SetZeroInitialIterate();
+      ML_solver.reset(ML_hypre_pcg);
+      R.reset(new H1ConsistentMassOperator(*M_LH, *ML_solver));
+      return;
+   }
 
    HypreParMatrix R_local = HypreParMatrix(pfes_ho.GetComm(),
                                            pfes_lor_scalar->GlobalVSize(),
                                            pfes_ho_scalar->GlobalVSize(),
                                            pfes_lor_scalar->GetDofOffsets(),
                                            pfes_ho_scalar->GetDofOffsets(),
-                                           static_cast<SparseMatrix*>(R.get()));
-   HypreParMatrix M_LH_local = HypreParMatrix(pfes_ho.GetComm(),
-                                              pfes_lor_scalar->GlobalVSize(),
-                                              pfes_ho_scalar->GlobalVSize(),
-                                              pfes_lor_scalar->GetDofOffsets(),
-                                              pfes_ho_scalar->GetDofOffsets(),
-                                              static_cast<SparseMatrix*>(M_LH.get()));
+                                           R_local_sp.get());
 
    HypreParMatrix *R_mat = RAP(pfes_lor_scalar->Dof_TrueDof_Matrix(),
                                &R_local, pfes_ho_scalar->Dof_TrueDof_Matrix());
-   HypreParMatrix *M_LH_mat = RAP(pfes_lor_scalar->Dof_TrueDof_Matrix(),
-                                  &M_LH_local, pfes_ho_scalar->Dof_TrueDof_Matrix());
 
    std::unique_ptr<HypreParMatrix> R_T(R_mat->Transpose());
    HypreParMatrix *RTxM_LH_mat = ParMult(R_T.get(), M_LH_mat, true);
@@ -1244,13 +1360,6 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::EAL2ProjectionH1Space
    int ndof_ho = pfes_ho.GetNDofs();
    int ndof_lor = pfes_lor.GetNDofs();
 
-
-   // If the local mesh is empty, skip all computations
-   if (nel_ho == 0)
-   {
-      return;
-   }
-
    const CoarseFineTransformations& cf_tr = mesh_lor->GetRefinementTransforms();
 
    int nref_max = 0;
@@ -1429,6 +1538,8 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::MultTranspose(
 void L2ProjectionGridTransfer::L2ProjectionH1Space::Prolongate(
    const Vector& x, Vector& y) const
 {
+   MFEM_VERIFY(!use_consistent_mass,
+               "BackwardOperator is not supported with consistent mass");
 
    Vector X(fes_lor.GetTrueVSize());
    Vector X_dim(M_LH->Height());
@@ -1460,6 +1571,9 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::Prolongate(
 void L2ProjectionGridTransfer::L2ProjectionH1Space::ProlongateTranspose(
    const Vector& x, Vector& y) const
 {
+   MFEM_VERIFY(!use_consistent_mass,
+               "BackwardOperator is not supported with consistent mass");
+
    Vector X(fes_ho.GetTrueVSize());
    Vector X_dim(pcg.Width());
    Vector Xbar(pcg.Height());
@@ -1490,17 +1604,34 @@ void L2ProjectionGridTransfer::L2ProjectionH1Space::ProlongateTranspose(
 void L2ProjectionGridTransfer::L2ProjectionH1Space::SetRelTol(real_t p_rtol_)
 {
    pcg.SetRelTol(p_rtol_);
+   ML_pcg.SetRelTol(p_rtol_);
+#ifdef MFEM_USE_MPI
+   if (ML_solver)
+   {
+      HyprePCG *hypre_pcg = dynamic_cast<HyprePCG*>(ML_solver.get());
+      if (hypre_pcg) { hypre_pcg->SetTol(p_rtol_); }
+   }
+#endif
 }
 
 void L2ProjectionGridTransfer::L2ProjectionH1Space::SetAbsTol(real_t p_atol_)
 {
    pcg.SetAbsTol(p_atol_);
+   ML_pcg.SetAbsTol(p_atol_);
+#ifdef MFEM_USE_MPI
+   if (ML_solver)
+   {
+      HyprePCG *hypre_pcg = dynamic_cast<HyprePCG*>(ML_solver.get());
+      if (hypre_pcg) { hypre_pcg->SetAbsTol(p_atol_); }
+   }
+#endif
 }
 
 std::pair<
 std::unique_ptr<SparseMatrix>,
 std::unique_ptr<SparseMatrix>>
-                            L2ProjectionGridTransfer::L2ProjectionH1Space::ComputeSparseRAndM_LH()
+L2ProjectionGridTransfer::L2ProjectionH1Space::ComputeSparseRAndM_LH(
+   bool build_R)
 {
    std::pair<std::unique_ptr<SparseMatrix>,
        std::unique_ptr<SparseMatrix>> r_and_mlh;
@@ -1533,69 +1664,76 @@ std::unique_ptr<SparseMatrix>>
 
    BuildHo2Lor(nel_ho, nel_lor, cf_tr);
 
-   // ML_inv contains the inverse lumped (row sum) mass matrix. Note that the
-   // method will also work with a full (consistent) mass matrix, though this is
-   // not implemented here. L refers to the low-order refined mesh
    Vector ML_inv(ndof_lor);
-   ML_inv = 0.0;
-
-   // Compute ML_inv
-   for (int iho = 0; iho < nel_ho; ++iho)
+   if (build_R)
    {
-      Array<int> lor_els;
-      ho2lor.GetRow(iho, lor_els);
-      int nref = ho2lor.RowSize(iho);
+      // ML_inv contains the inverse lumped (row sum) mass matrix. L refers to
+      // the low-order refined mesh.
+      ML_inv = 0.0;
 
-      Geometry::Type geom = mesh_ho->GetElementBaseGeometry(iho);
-      const FiniteElement& fe_lor = *fes_lor.GetFE(lor_els[0]);
-      int nedof_lor = fe_lor.GetDof();
-
-      // Instead of using a MassIntegrator, manually loop over integration
-      // points so we can row sum and store the diagonal as a Vector.
-      Vector ML_el(nedof_lor);
-      Vector shape_lor(nedof_lor);
-      Array<int> dofs_lor(nedof_lor);
-
-      for (int iref = 0; iref < nref; ++iref)
+      // Compute ML_inv
+      for (int iho = 0; iho < nel_ho; ++iho)
       {
-         int ilor = lor_els[iref];
-         ElementTransformation* el_tr = fes_lor.GetElementTransformation(ilor);
+         Array<int> lor_els;
+         ho2lor.GetRow(iho, lor_els);
+         int nref = ho2lor.RowSize(iho);
 
-         int order = 2 * fe_lor.GetOrder() + el_tr->OrderW();
-         const IntegrationRule* ir = &IntRules.Get(geom, order);
-         ML_el = 0.0;
-         for (int i = 0; i < ir->GetNPoints(); ++i)
+         Geometry::Type geom = mesh_ho->GetElementBaseGeometry(iho);
+         const FiniteElement& fe_lor = *fes_lor.GetFE(lor_els[0]);
+         int nedof_lor = fe_lor.GetDof();
+
+         // Instead of using a MassIntegrator, manually loop over integration
+         // points so we can row sum and store the diagonal as a Vector.
+         Vector ML_el(nedof_lor);
+         Vector shape_lor(nedof_lor);
+         Array<int> dofs_lor(nedof_lor);
+
+         for (int iref = 0; iref < nref; ++iref)
          {
-            const IntegrationPoint& ip_lor = ir->IntPoint(i);
-            fe_lor.CalcShape(ip_lor, shape_lor);
-            el_tr->SetIntPoint(&ip_lor);
-            ML_el += (shape_lor *= (el_tr->Weight() * ip_lor.weight));
+            int ilor = lor_els[iref];
+            ElementTransformation* el_tr = fes_lor.GetElementTransformation(ilor);
+
+            int order = 2 * fe_lor.GetOrder() + el_tr->OrderW();
+            const IntegrationRule* ir = &IntRules.Get(geom, order);
+            ML_el = 0.0;
+            for (int i = 0; i < ir->GetNPoints(); ++i)
+            {
+               const IntegrationPoint& ip_lor = ir->IntPoint(i);
+               fe_lor.CalcShape(ip_lor, shape_lor);
+               el_tr->SetIntPoint(&ip_lor);
+               ML_el += (shape_lor *= (el_tr->Weight() * ip_lor.weight));
+            }
+            fes_lor.GetElementDofs(ilor, dofs_lor);
+            ML_inv.AddElementVector(dofs_lor, ML_el);
          }
-         fes_lor.GetElementDofs(ilor, dofs_lor);
-         ML_inv.AddElementVector(dofs_lor, ML_el);
       }
+      // DOF by DOF inverse of non-zero entries
+      LumpedMassInverse(ML_inv);
    }
-   // DOF by DOF inverse of non-zero entries
-   LumpedMassInverse(ML_inv);
 
    // Compute sparsity pattern for R = M_L^(-1) M_LH and allocate
-   r_and_mlh.first = AllocR();
+   std::unique_ptr<SparseMatrix> pattern = AllocR();
+   if (build_R)
+   {
+      r_and_mlh.first = std::move(pattern);
+   }
    // Allocate M_LH (same sparsity pattern as R)
    // L refers to the low-order refined mesh (DOFs correspond to rows)
    // H refers to the higher-order mesh (DOFs correspond to columns)
-   Memory<int> I(r_and_mlh.first->Height() + 1);
-   for (int icol = 0; icol < r_and_mlh.first->Height() + 1; ++icol)
+   SparseMatrix &pattern_mat = build_R ? *r_and_mlh.first : *pattern;
+   Memory<int> I(pattern_mat.Height() + 1);
+   for (int icol = 0; icol < pattern_mat.Height() + 1; ++icol)
    {
-      I[icol] = r_and_mlh.first->GetI()[icol];
+      I[icol] = pattern_mat.GetI()[icol];
    }
-   Memory<int> J(r_and_mlh.first->NumNonZeroElems());
-   for (int jcol = 0; jcol < r_and_mlh.first->NumNonZeroElems(); ++jcol)
+   Memory<int> J(pattern_mat.NumNonZeroElems());
+   for (int jcol = 0; jcol < pattern_mat.NumNonZeroElems(); ++jcol)
    {
-      J[jcol] = r_and_mlh.first->GetJ()[jcol];
+      J[jcol] = pattern_mat.GetJ()[jcol];
    }
    r_and_mlh.second = std::unique_ptr<SparseMatrix>(
-                         new SparseMatrix(I, J, NULL, r_and_mlh.first->Height(),
-                                          r_and_mlh.first->Width(), true, true, true));
+                         new SparseMatrix(I, J, NULL, pattern_mat.Height(),
+                                          pattern_mat.Width(), true, true, true));
 
    IntegrationPointTransformation ip_tr;
    IsoparametricTransformation& emb_tr = ip_tr.Transf;
@@ -1638,15 +1776,21 @@ std::unique_ptr<SparseMatrix>>
          Array<int> dofs_lor(nedof_lor);
          fes_lor.GetElementDofs(ilor, dofs_lor);
          Vector R_row;
-         for (int i = 0; i < nedof_lor; ++i)
+         if (build_R)
          {
-            M_LH_el.GetRow(i, R_row);
-            R_el.SetRow(i, R_row.Set(ML_inv[dofs_lor[i]], R_row));
+            for (int i = 0; i < nedof_lor; ++i)
+            {
+               M_LH_el.GetRow(i, R_row);
+               R_el.SetRow(i, R_row.Set(ML_inv[dofs_lor[i]], R_row));
+            }
          }
          Array<int> dofs_ho(nedof_ho);
          fes_ho.GetElementDofs(iho, dofs_ho);
          r_and_mlh.second->AddSubMatrix(dofs_lor, dofs_ho, M_LH_el);
-         r_and_mlh.first->AddSubMatrix(dofs_lor, dofs_ho, R_el);
+         if (build_R)
+         {
+            r_and_mlh.first->AddSubMatrix(dofs_lor, dofs_ho, R_el);
+         }
 
       }
    }
@@ -1860,6 +2004,11 @@ L2ProjectionGridTransfer::H1SpaceMixedMassOperator::H1SpaceMixedMassOperator(
 void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::Mult(const Vector &x,
                                                               Vector &y) const
 {
+   if (fes_ho->GetNE() == 0)
+   {
+      return;
+   }
+
    const Operator* elem_restrict_ho = fes_ho->GetElementRestriction(
                                          ElementDofOrdering::NATIVE);
    const Operator* elem_restrict_lor = fes_lor->GetElementRestriction(
@@ -1906,6 +2055,11 @@ void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::Mult(const Vector &x,
 void L2ProjectionGridTransfer::H1SpaceMixedMassOperator::MultTranspose(
    const Vector &x, Vector &y) const
 {
+   if (fes_ho->GetNE() == 0)
+   {
+      return;
+   }
+
    const Operator* elem_restrict_ho = fes_ho->GetElementRestriction(
                                          ElementDofOrdering::NATIVE);
    const Operator* elem_restrict_lor = fes_lor->GetElementRestriction(
@@ -1990,6 +2144,10 @@ const Operator &L2ProjectionGridTransfer::ForwardOperator()
 
 const Operator &L2ProjectionGridTransfer::BackwardOperator()
 {
+   MFEM_VERIFY(!(use_consistent_mass && !force_l2_space &&
+                 dom_fes.FEColl()->GetContType() ==
+                 FiniteElementCollection::CONTINUOUS),
+               "BackwardOperator is not supported with consistent mass");
    if (!B)
    {
       if (!F) { BuildF(); }
@@ -1998,15 +2156,24 @@ const Operator &L2ProjectionGridTransfer::BackwardOperator()
    return *B;
 }
 
+void L2ProjectionGridTransfer::UseConsistentMass(bool use_consistent_mass_)
+{
+   MFEM_VERIFY(!F && !B,
+               "UseConsistentMass must be called before constructing operators");
+   use_consistent_mass = use_consistent_mass_;
+}
+
 void L2ProjectionGridTransfer::BuildF()
 {
+   MFEM_VERIFY(!(use_ea && use_consistent_mass),
+               "consistent mass is not supported with element assembly");
    if (!force_l2_space &&
        dom_fes.FEColl()->GetContType() == FiniteElementCollection::CONTINUOUS)
    {
       if (!Parallel())
       {
          F = new L2ProjectionH1Space(dom_fes, ran_fes,
-                                     use_ea, d_mt);
+                                     use_ea, use_consistent_mass, d_mt);
       }
       else
       {
@@ -2016,7 +2183,7 @@ void L2ProjectionGridTransfer::BuildF()
          const mfem::ParFiniteElementSpace& ran_pfes =
             static_cast<mfem::ParFiniteElementSpace&>(ran_fes);
          F = new L2ProjectionH1Space(dom_pfes, ran_pfes,
-                                     use_ea, d_mt);
+                                     use_ea, use_consistent_mass, d_mt);
 #endif
       }
    }
@@ -2029,6 +2196,11 @@ void L2ProjectionGridTransfer::BuildF()
 
 bool L2ProjectionGridTransfer::SupportsBackwardsOperator() const
 {
+   if (use_consistent_mass && !force_l2_space &&
+       dom_fes.FEColl()->GetContType() == FiniteElementCollection::CONTINUOUS)
+   {
+      return false;
+   }
    return ran_fes.GetTrueVSize() >= dom_fes.GetTrueVSize();
 }
 

fem/transfer.hpp

@@ -169,8 +169,10 @@ public:
     is the forward transfer matrix, and M_f is the mass matrix on the coarse
     element. For L2 spaces, M_f is the mass matrix on the union of all fine
     elements comprising the coarse element. For H1 spaces, M_f is a diagonal
-    (lumped) mass matrix computed through row-summation. Note that the backward
-    transfer operator, B, is a left inverse of the forward transfer operator, F,
+    (lumped) mass matrix computed through row-summation, unless
+    UseConsistentMass() is enabled for the forward H1 operator. Note that the
+    backward transfer operator, B, is a left inverse of the forward transfer
+    operator, F,
     i.e. B F = I. Both F and B are defined in physical space and, generally for
     L2 spaces, vary between different mesh elements.
 
@@ -352,16 +354,19 @@ public:
    class L2ProjectionH1Space : public L2Projection
    {
       const bool use_ea;
+      const bool use_consistent_mass;
 
    public:
       L2ProjectionH1Space(const FiniteElementSpace &fes_ho_,
                           const FiniteElementSpace &fes_lor_,
                           const bool use_ea_,
+                          const bool use_consistent_mass_,
                           MemoryType d_mt_ = Device::GetHostMemoryType());
 #ifdef MFEM_USE_MPI
       L2ProjectionH1Space(const ParFiniteElementSpace &pfes_ho_,
                           const ParFiniteElementSpace &pfes_lor_,
                           const bool use_ea_,
+                          const bool use_consistent_mass_,
                           MemoryType d_mt_ = Device::GetHostMemoryType());
 #endif
       /// Same as above but assembles action of R through 4 parts:
@@ -423,7 +428,8 @@ public:
       /// @brief Computes on-rank R and M_LH matrices. If true, computes mixed mass and/or
       /// inverse lumped mass matrix error when compared to device implementation.
       std::pair<std::unique_ptr<SparseMatrix>,
-          std::unique_ptr<SparseMatrix>> ComputeSparseRAndM_LH();
+          std::unique_ptr<SparseMatrix>> ComputeSparseRAndM_LH(
+             bool build_R = true);
 
       /// @brief Recovers vector of tdofs given a vector of dofs and a finite
       /// element space
@@ -454,7 +460,11 @@ public:
       std::unique_ptr<SparseMatrix> AllocR();
 
       CGSolver pcg;
+      CGSolver ML_pcg;
       std::unique_ptr<Solver> precon;
+      std::unique_ptr<Solver> ML_precon;
+      std::unique_ptr<Solver> ML_solver;
+      std::unique_ptr<Operator> M_L;
       // The restriction operator is represented as an Operator R. The
       // prolongation operator is a dense matrix computed as the inverse of (R^T
       // M_L R), and hence, is not stored.
@@ -478,7 +488,6 @@ public:
       Vector M_LH_ea;
       // Element Assembled lumped M_L inverse built via EA. Stores diagonal as a Ldof vector.
       Vector ML_inv_ea;
-
 #ifdef MFEM_USE_MPI
       std::unique_ptr<ParFiniteElementSpace> pfes_ho_scalar;
       std::unique_ptr<ParFiniteElementSpace> pfes_lor_scalar;
@@ -511,6 +520,7 @@ public:
    L2Projection   *F; ///< Forward, coarse-to-fine, operator
    L2Prolongation *B; ///< Backward, fine-to-coarse, operator
    bool force_l2_space;
+   bool use_consistent_mass;
 
 public:
    L2ProjectionGridTransfer(FiniteElementSpace &coarse_fes_,
@@ -518,10 +528,15 @@ public:
                             bool force_l2_space_ = false,
                             MemoryType d_mt_ = Device::GetHostMemoryType()) // move to method
       : GridTransfer(coarse_fes_, fine_fes_),
-        F(NULL), B(NULL), force_l2_space(force_l2_space_)
+        F(NULL), B(NULL), force_l2_space(force_l2_space_),
+        use_consistent_mass(false)
    { }
    virtual ~L2ProjectionGridTransfer();
 
+   /** Use the consistent low-order mass matrix in H1 non-EA Mult() and
+       MultTranspose(). This option does not support BackwardOperator(). */
+   void UseConsistentMass(bool use_consistent_mass_ = true);
+
    const Operator &ForwardOperator() override;
 
    const Operator &BackwardOperator() override;

general/CMakeLists.txt

@@ -18,6 +18,7 @@ list(APPEND SRCS
   gecko.cpp
   globals.cpp
   hash.cpp
+  hash_util.cpp
   isockstream.cpp
   mem_manager.cpp
   occa.cpp
@@ -46,6 +47,7 @@ list(APPEND HDRS
   globals.hpp
   zstr.hpp
   hash.hpp
+  hash_util.hpp
   isockstream.hpp
   kdtree.hpp
   mem_alloc.hpp

general/device.cpp

@@ -22,6 +22,8 @@
 
 #include <unordered_map>
 #include <map>
+#include <sstream>
+#include <iomanip>
 
 namespace mfem
 {
@@ -716,6 +718,29 @@ void Device::DeviceMem(size_t *free, size_t *total)
 #endif
 }
 
+std::string Device::GetUUID(const int device_id)
+{
+   std::stringstream res;
+#if defined(MFEM_USE_CUDA)
+   cudaDeviceProp prop;
+   MFEM_GPU_CHECK(cudaGetDeviceProperties(&prop, device_id));
+   for (int i = 0; i < 16; ++i)
+   {
+      res << std::setfill('0') << std::setw(2) << std::hex
+          << static_cast<unsigned>(prop.uuid.bytes[i]);
+   }
+#elif defined(MFEM_USE_HIP)
+   hipUUID uuid;
+   MFEM_GPU_CHECK(hipDeviceGetUuid(&uuid, device_id));
+   for (int i = 0; i < 16; ++i)
+   {
+      res << std::setfill('0') << std::setw(2) << std::hex
+          << static_cast<unsigned>(uuid.bytes[i]);
+   }
+#endif
+   return res.str();
+}
+
 int Device::NumMultiprocessors(int dev)
 {
 #if defined(MFEM_USE_CUDA)

general/device.hpp

@@ -255,6 +255,10 @@ public:
    /// Get the number of available devices (may be called before configuration).
    static int GetDeviceCount();
 
+   /// Gets a string representation of the GPU UUID.
+   /// 0 <= @a device_id < GetDeviceCount()
+   static std::string GetUUID(const int device_id = 0);
+
    /** @brief Return true if any of the backends in the backend mask, @a b_mask,
        are allowed. */
    /** This method can be used with any of the Backend::Id constants, the

general/hash.cpp

@@ -80,159 +80,4 @@ std::string HashFunction::GetHash() const
    return hash;
 }
 
-constexpr static uint64_t rotl64(uint64_t x, int r)
-{
-   return (x << r) | (x >> (64 - r));
-}
-
-void Hasher::init(uint64_t seed)
-{
-   data[0] = seed;
-   data[1] = seed;
-   nbytes = 0;
-}
-
-void Hasher::add_block(uint64_t k1, uint64_t k2)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] = rotl64(data[0], 27);
-   data[0] += data[1];
-   data[0] = data[0] * 5 + 0x52dce729ull;
-
-   k2 *= c2;
-   k2 = rotl64(k2, 33);
-   k2 *= c1;
-   data[1] ^= k2;
-
-   data[1] = rotl64(data[1], 31);
-   data[1] += data[0];
-   data[1] = data[1] * 5 + 0x38495ab5ull;
-}
-
-static uint64_t fmix64(uint64_t k)
-{
-   // http://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html
-   // mix13
-   k ^= k >> 30;
-   k *= 0xbf58476d1ce4e5b9ull;
-   k ^= k >> 27;
-   k *= 0x94d049bb133111ebull;
-   k ^= k >> 31;
-   return k;
-}
-
-void Hasher::append(const uint8_t *vs, uint64_t bytes)
-{
-   if (bytes == 0)
-   {
-      return;
-   }
-   auto rem = nbytes % 16;
-   nbytes += bytes;
-   uint8_t *tmp = reinterpret_cast<uint8_t *>(buf_);
-   while (true)
-   {
-      if (bytes + rem >= 16)
-      {
-         std::copy(vs, vs + 16 - rem, tmp + rem);
-         add_block(buf_[0], buf_[1]);
-         vs += (16 - rem);
-         bytes -= (16 - rem);
-         rem = 0;
-      }
-      else
-      {
-         std::copy(vs, vs + bytes, tmp + rem);
-         return;
-      }
-   }
-}
-
-void Hasher::finalize()
-{
-   auto rem = nbytes % 16;
-   if (rem > 0)
-   {
-      nbytes -= rem;
-      if (rem <= 8)
-      {
-         finalize(buf_[0], rem);
-      }
-      else
-      {
-         finalize(buf_[0], buf_[1], rem);
-      }
-      return;
-   }
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
-void Hasher::finalize(uint64_t k1, int num)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-   nbytes += num;
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
-void Hasher::finalize(uint64_t k1, uint64_t k2, int num)
-{
-   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
-   constexpr uint64_t c2 = 0x4cf5ad432745937full;
-   nbytes += num;
-   k2 *= c2;
-   k2 = rotl64(k2, 33);
-   k2 *= c1;
-   data[1] ^= k2;
-
-   k1 *= c1;
-   k1 = rotl64(k1, 31);
-   k1 *= c2;
-   data[0] ^= k1;
-
-   data[0] ^= nbytes;
-   data[1] ^= nbytes;
-
-   data[0] += data[1];
-   data[1] += data[0];
-
-   data[0] = fmix64(data[0]);
-   data[1] = fmix64(data[1]);
-
-   data[0] += data[1];
-   data[1] += data[0];
-}
-
 } // namespace mfem

general/hash.hpp

@@ -15,8 +15,8 @@
 #include "../config/config.hpp"
 #include "array.hpp"
 #include "globals.hpp"
+#include "hash_util.hpp"
 
-#include <array>
 #include <cstdint>
 #include <type_traits>
 #include <utility>
@@ -457,75 +457,6 @@ protected:
    int BinSize(int idx) const;
 };
 
-///
-/// @brief streaming implementation for murmurhash3 128 (x64).
-/// Constructs the hash in 3 stages: init, append, finalize.
-///
-struct Hasher
-{
-   /// where the final hash result is stored after finalize. Use data[1] when
-   /// only 64 bits are required.
-   uint64_t data[2] = {0, 0};
-
-private:
-   uint64_t nbytes = 0;
-
-   uint64_t buf_[2] = {0, 0};
-
-public:
-
-   /// resets this hasher back to an initial seed
-   void init(uint64_t seed = 0);
-   void append(const uint8_t *vs, uint64_t bytes);
-
-   void finalize();
-
-private:
-   // add 16 bytes
-   void add_block(uint64_t k1, uint64_t k2);
-
-   // add [1-8] more bytes, then finalize
-   void finalize(uint64_t k1, int num);
-
-   // add [1-15] more bytes, then finalize
-   // 0 < num < 16
-   void finalize(uint64_t k1, uint64_t k2, int num);
-};
-
-/// Helper class for hashing std::pair. Usable in place of std::hash<std::pair<T,U>>
-struct PairHasher
-{
-   template <class T, class V>
-   size_t operator()(const std::pair<T, V> &v) const noexcept
-   {
-      Hasher hash;
-      // chosen randomly with a 2^64-sided dice
-      hash.init(0xfebd1fe69813c14full);
-      hash.append(reinterpret_cast<const uint8_t *>(&v.first), sizeof(T));
-      hash.append(reinterpret_cast<const uint8_t *>(&v.second), sizeof(V));
-      hash.finalize();
-      return hash.data[1];
-   }
-};
-
-/// Helper class for hashing std::array. Usable in place of std::hash<std::array<T,N>>
-struct ArrayHasher
-{
-   template <class T, size_t N>
-   size_t operator()(const std::array<T, N> &v) const noexcept
-   {
-      Hasher hash;
-      // chosen randomly with a 2^64-sided dice
-      hash.init(0xfebd1fe69813c14full);
-      for (size_t i = 0; i < N; ++i)
-      {
-         hash.append(reinterpret_cast<const uint8_t *>(&v[i]), sizeof(T));
-      }
-      hash.finalize();
-      return hash.data[1];
-   }
-};
-
 /// Hash function for data sequences.
 /** Depends on GnuTLS for SHA-256 hashing. */
 class HashFunction

general/hash_util.cpp

@@ -0,0 +1,172 @@
+// Copyright (c) 2010-2025, 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 "hash_util.hpp"
+
+namespace mfem
+{
+
+constexpr static uint64_t rotl64(uint64_t x, int r)
+{
+   return (x << r) | (x >> (64 - r));
+}
+
+void Hasher::init(uint64_t seed)
+{
+   data[0] = seed;
+   data[1] = seed;
+   nbytes = 0;
+}
+
+void Hasher::add_block(uint64_t k1, uint64_t k2)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] = rotl64(data[0], 27);
+   data[0] += data[1];
+   data[0] = data[0] * 5 + 0x52dce729ull;
+
+   k2 *= c2;
+   k2 = rotl64(k2, 33);
+   k2 *= c1;
+   data[1] ^= k2;
+
+   data[1] = rotl64(data[1], 31);
+   data[1] += data[0];
+   data[1] = data[1] * 5 + 0x38495ab5ull;
+}
+
+static uint64_t fmix64(uint64_t k)
+{
+   // http://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html
+   // mix13
+   k ^= k >> 30;
+   k *= 0xbf58476d1ce4e5b9ull;
+   k ^= k >> 27;
+   k *= 0x94d049bb133111ebull;
+   k ^= k >> 31;
+   return k;
+}
+
+void Hasher::append(const std::byte *vs, uint64_t bytes)
+{
+   if (bytes == 0)
+   {
+      return;
+   }
+   auto rem = nbytes % 16;
+   nbytes += bytes;
+   std::byte *tmp = reinterpret_cast<std::byte *>(buf_);
+   while (true)
+   {
+      if (bytes + rem >= 16)
+      {
+         std::copy(vs, vs + 16 - rem, tmp + rem);
+         add_block(buf_[0], buf_[1]);
+         vs += (16 - rem);
+         bytes -= (16 - rem);
+         rem = 0;
+      }
+      else
+      {
+         std::copy(vs, vs + bytes, tmp + rem);
+         return;
+      }
+   }
+}
+
+void Hasher::finalize()
+{
+   auto rem = nbytes % 16;
+   if (rem > 0)
+   {
+      nbytes -= rem;
+      if (rem <= 8)
+      {
+         finalize(buf_[0], rem);
+      }
+      else
+      {
+         finalize(buf_[0], buf_[1], rem);
+      }
+      return;
+   }
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+void Hasher::finalize(uint64_t k1, int num)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+   nbytes += num;
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+void Hasher::finalize(uint64_t k1, uint64_t k2, int num)
+{
+   constexpr uint64_t c1 = 0x87c37b91114253d5ull;
+   constexpr uint64_t c2 = 0x4cf5ad432745937full;
+   nbytes += num;
+   k2 *= c2;
+   k2 = rotl64(k2, 33);
+   k2 *= c1;
+   data[1] ^= k2;
+
+   k1 *= c1;
+   k1 = rotl64(k1, 31);
+   k1 *= c2;
+   data[0] ^= k1;
+
+   data[0] ^= nbytes;
+   data[1] ^= nbytes;
+
+   data[0] += data[1];
+   data[1] += data[0];
+
+   data[0] = fmix64(data[0]);
+   data[1] = fmix64(data[1]);
+
+   data[0] += data[1];
+   data[1] += data[0];
+}
+
+}

general/hash_util.hpp

@@ -0,0 +1,172 @@
+// Copyright (c) 2010-2025, 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_HASH_UTIL_HPP
+#define MFEM_HASH_UTIL_HPP
+
+#include <array>
+#include <cstddef>
+#include <tuple>
+#include <functional>
+#include <utility>
+#include <cstdint>
+
+namespace mfem
+{
+
+/// @brief streaming implementation for murmurhash3 128 (x64).
+///
+/// Constructs the hash in 3 stages: init, append, finalize.
+struct Hasher
+{
+   /// @brief Storage for the final hash result after finalize() is called.
+   ///
+   /// Use data[1] when only 64 bits are required.
+   uint64_t data[2] = {0, 0};
+
+private:
+   uint64_t nbytes = 0;
+   uint64_t buf_[2] = {0, 0};
+
+public:
+
+   /// Resets the Hasher back to an initial seed
+   void init(uint64_t seed = 0);
+
+   /// Append data @a vs of size @a bytes.
+   void append(const std::byte *vs, uint64_t bytes);
+
+   void finalize();
+
+private:
+   /// Add a block of 16 bytes.
+   void add_block(uint64_t k1, uint64_t k2);
+
+   /// @brief Add [1-8] more bytes, then finalize.
+   ///
+   /// @a num must satisfy 0 < num < 9.
+   void finalize(uint64_t k1, int num);
+
+   /// @brief Add [1-15] more bytes, then finalize.
+   ///
+   /// @a num must satisfy 0 < num < 16.
+   void finalize(uint64_t k1, uint64_t k2, int num);
+};
+
+template <class T> struct ChainedHasher
+{
+   static void Append(Hasher &hasher, const T &value)
+   {
+      if constexpr (std::is_fundamental_v<T> || std::is_pointer_v<T>)
+      {
+         hasher.append(reinterpret_cast<const std::byte *>(&value), sizeof(T));
+      }
+      else
+      {
+         std::hash<T> h;
+         auto v = h(value);
+         hasher.append(reinterpret_cast<std::byte *>(&v), sizeof(v));
+      }
+   }
+};
+
+template <class T, class V> struct ChainedHasher<std::pair<T, V>>
+{
+   static void Append(Hasher &hasher, const std::pair<T, V> &value)
+   {
+      ChainedHasher<T>::Append(hasher, value.first);
+      ChainedHasher<V>::Append(hasher, value.second);
+   }
+};
+
+template <class T, size_t N> struct ChainedHasher<std::array<T, N>>
+{
+   static void Append(Hasher &hasher, const std::array<T, N> &value)
+   {
+      for (size_t i = 0; i < N; ++i)
+      {
+         ChainedHasher<T>::Append(hasher, value[i]);
+      }
+   }
+};
+
+template<class... Ts> struct ChainedHasher<std::tuple<Ts...>>
+{
+private:
+   template <size_t N>
+   static void AppendImpl(Hasher &hasher, const std::tuple<Ts...> &value)
+   {
+      ChainedHasher<std::decay_t<decltype(std::get<N>(value))>>::Append(
+                                                                hasher, std::get<N>(value));
+      if constexpr (N + 1 < sizeof...(Ts))
+      {
+         AppendImpl<N + 1>(hasher, value);
+      }
+   }
+
+public:
+   static void Append(Hasher &hasher, const std::tuple<Ts...> &value)
+   {
+      if constexpr (sizeof...(Ts))
+      {
+         AppendImpl<0>(hasher, value);
+      }
+   }
+};
+
+/// Helper class for hashing std::pair of hashable types.
+struct PairHasher
+{
+   template <class T, class V>
+   size_t operator()(const std::pair<T, V> &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<std::pair<T, V>>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+/// Helper class for hashing std::array of a hashable type.
+struct ArrayHasher
+{
+   template <class T, size_t N>
+   size_t operator()(const std::array<T, N> &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<std::array<T, N>>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+/// Helper class for hashing std::tuple of hashable types.
+struct TupleHasher
+{
+   template <class T>
+   size_t operator()(const T &v) const noexcept
+   {
+      Hasher hash;
+      // chosen randomly with a 2^64-sided dice
+      hash.init(0xfebd1fe69813c14full);
+      ChainedHasher<T>::Append(hash, v);
+      hash.finalize();
+      return hash.data[1];
+   }
+};
+
+} // namespace mfem
+
+#endif

general/table.hpp

@@ -146,7 +146,7 @@ public:
    int *ReadWriteJ(bool on_dev = true) { return J.ReadWrite(on_dev); }
    const int *HostReadJ() const { return J.HostRead(); }
    int *HostWriteJ() { return J.HostWrite(); }
-   int *ReadWriteJ() { return J.HostReadWrite(); }
+   int *HostReadWriteJ() { return J.HostReadWrite(); }
 
    /// Sort the column (TYPE II) indices in each row.
    void SortRows();

linalg/densemat.cpp

@@ -1370,6 +1370,35 @@ void DenseMatrix::Getl1Diag(Vector &l) const
       }
 }
 
+void DenseMatrix::GetRowl1(Vector &l) const
+{
+   l.SetSize(height);
+   l = 0.0;
+
+   for (int j = 0; j < width; ++j)
+      for (int i = 0; i < height; ++i)
+      {
+         l(i) += fabs((*this)(i,j));
+      }
+}
+
+void DenseMatrix::GetRowl2(Vector &l) const
+{
+   l.SetSize(height);
+   l = 0.0;
+
+   for (int j = 0; j < width; ++j)
+      for (int i = 0; i < height; ++i)
+      {
+         l[i] += operator()(i,j)*operator()(i,j);
+      }
+
+   for (int i = 0; i < height; ++i)
+   {
+      l[i] = sqrt(l[i]);
+   }
+}
+
 void DenseMatrix::GetRowSums(Vector &l) const
 {
    l.SetSize(height);

linalg/densemat.hpp

@@ -346,8 +346,12 @@ public:
    /// Returns the diagonal of the matrix
    void GetDiag(Vector &d) const;
    /// Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|
-   void Getl1Diag(Vector &l) const;
-   /// Compute the row sums of the DenseMatrix
+   MFEM_DEPRECATED void Getl1Diag(Vector &l) const;
+   /// Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|
+   void GetRowl1(Vector &l) const;
+   /// Returns the l2norm of the rows of the DenseMatrix
+   void GetRowl2(Vector &l) const;
+   /// Returns the row sums of the DenseMatrix
    void GetRowSums(Vector &l) const;
 
    /// Creates n x n diagonal matrix with diagonal elements c

linalg/hypre.cpp

@@ -1681,6 +1681,13 @@ void HypreParMatrix::GetOffd(SparseMatrix &offd, HYPRE_BigInt* &cmap) const
    cmap = A->col_map_offd;
 }
 
+void HypreParMatrix::GetOffdColMap(HYPRE_BigInt* &cmap,
+                                   HYPRE_Int &num_cols) const
+{
+   cmap = A->col_map_offd;
+   num_cols = hypre_CSRMatrixNumCols(A->offd);
+}
+
 void HypreParMatrix::MergeDiagAndOffd(SparseMatrix &merged)
 {
    HostRead();
@@ -3627,12 +3634,25 @@ void HypreSmoother::SetType(HypreSmoother::Type type_, int relax_times_)
    relax_times = relax_times_;
 }
 
+void HypreSmoother::GetType(HypreSmoother::Type &type_, int &relax_times_) const
+{
+   type_ = static_cast<HypreSmoother::Type>(type);
+   relax_times_ = relax_times;
+}
+
 void HypreSmoother::SetSOROptions(real_t relax_weight_, real_t omega_)
 {
    relax_weight = relax_weight_;
    omega = omega_;
 }
 
+void HypreSmoother::GetSOROptions(real_t &relax_weight_, real_t &omega_) const
+{
+   // TODO: are these used for all smoother types?
+   relax_weight_ = relax_weight;
+   omega_ = omega;
+}
+
 void HypreSmoother::SetPolyOptions(int poly_order_, real_t poly_fraction_,
                                    int eig_est_cg_iter_)
 {
@@ -3641,6 +3661,15 @@ void HypreSmoother::SetPolyOptions(int poly_order_, real_t poly_fraction_,
    eig_est_cg_iter = eig_est_cg_iter_;
 }
 
+void HypreSmoother::GetPolyOptions(int &poly_order_, real_t &poly_fraction_,
+                                   int &eig_est_cg_iter_) const
+{
+   // TODO: are these used for all smoother types?
+   poly_order_ = poly_order;
+   poly_fraction_ = poly_fraction;
+   eig_est_cg_iter_ = eig_est_cg_iter;
+}
+
 void HypreSmoother::SetTaubinOptions(real_t lambda_, real_t mu_,
                                      int taubin_iter_)
 {
@@ -3649,6 +3678,14 @@ void HypreSmoother::SetTaubinOptions(real_t lambda_, real_t mu_,
    taubin_iter = taubin_iter_;
 }
 
+void HypreSmoother::GetTaubinOptions(real_t &lambda_, real_t &mu_,
+                                     int &taubin_iter_) const
+{
+   lambda_ = lambda;
+   mu_ = mu;
+   taubin_iter_ = taubin_iter;
+}
+
 void HypreSmoother::SetWindowByName(const char* name)
 {
    real_t a = -1, b, c;
@@ -3671,6 +3708,13 @@ void HypreSmoother::SetWindowParameters(real_t a, real_t b, real_t c)
    window_params[2] = c;
 }
 
+void HypreSmoother::GetWindowParameters(real_t &a, real_t &b, real_t &c) const
+{
+   a = window_params[0];
+   b = window_params[1];
+   c = window_params[2];
+}
+
 void HypreSmoother::SetOperator(const Operator &op)
 {
    A = const_cast<HypreParMatrix *>(dynamic_cast<const HypreParMatrix *>(&op));
@@ -4166,12 +4210,20 @@ HypreSolver::~HypreSolver()
    auxX.Delete();
 }
 
+void HyprePCG::SetDefaultOptions()
+{
+   // Explicitly set just in case past/future versions of hypre change the
+   // defaults
+   SetTol(1e-6);
+   SetMaxIter(1000);
+}
 
 HyprePCG::HyprePCG(MPI_Comm comm) : precond(NULL)
 {
    iterative_mode = true;
 
    HYPRE_ParCSRPCGCreate(comm, &pcg_solver);
+   SetDefaultOptions();
 }
 
 HyprePCG::HyprePCG(const HypreParMatrix &A_) : HypreSolver(&A_), precond(NULL)
@@ -4183,6 +4235,7 @@ HyprePCG::HyprePCG(const HypreParMatrix &A_) : HypreSolver(&A_), precond(NULL)
    HYPRE_ParCSRMatrixGetComm(*A, &comm);
 
    HYPRE_ParCSRPCGCreate(comm, &pcg_solver);
+   SetDefaultOptions();
 }
 
 void HyprePCG::SetOperator(const Operator &op)
@@ -4207,21 +4260,54 @@ void HyprePCG::SetOperator(const Operator &op)
    auxX.Delete(); auxX.Reset();
 }
 
+void HyprePCG::SetUseTwoNorm(bool val)
+{
+   HYPRE_PCGSetTwoNorm(pcg_solver, val);
+}
+
+bool HyprePCG::GetUseTwoNorm() const
+{
+   HYPRE_Int val;
+   HYPRE_PCGGetTwoNorm(pcg_solver, &val);
+   return val != 0;
+}
+
 void HyprePCG::SetTol(real_t tol)
 {
    HYPRE_PCGSetTol(pcg_solver, tol);
 }
 
+real_t HyprePCG::GetTol() const
+{
+   HYPRE_Real tol;
+   HYPRE_PCGGetTol(pcg_solver, &tol);
+   return tol;
+}
+
 void HyprePCG::SetAbsTol(real_t atol)
 {
    HYPRE_PCGSetAbsoluteTol(pcg_solver, atol);
 }
 
+real_t HyprePCG::GetAbsTol() const
+{
+   HYPRE_Real atol;
+   hypre_PCGGetAbsoluteTol(pcg_solver, &atol);
+   return atol;
+}
+
 void HyprePCG::SetMaxIter(int max_iter)
 {
    HYPRE_PCGSetMaxIter(pcg_solver, max_iter);
 }
 
+int HyprePCG::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_PCGGetMaxIter(pcg_solver, &max_iter);
+   return max_iter;
+}
+
 void HyprePCG::SetLogging(int logging)
 {
    HYPRE_PCGSetLogging(pcg_solver, logging);
@@ -4337,6 +4423,20 @@ HyprePCG::~HyprePCG()
    HYPRE_ParCSRPCGDestroy(pcg_solver);
 }
 
+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HyprePCG::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRPCGGetResidual(pcg_solver, &r);
+   return HypreParVector(r);
+}
+
+void HyprePCG::GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif
 
 HypreGMRES::HypreGMRES(MPI_Comm comm) : precond(NULL)
 {
@@ -4392,26 +4492,69 @@ void HypreGMRES::SetOperator(const Operator &op)
    auxX.Delete(); auxX.Reset();
 }
 
+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HypreGMRES::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRGMRESGetResidual(gmres_solver, &r);
+   return HypreParVector(r);
+}
+
+void HypreGMRES::GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif
+
 void HypreGMRES::SetTol(real_t tol)
 {
    HYPRE_GMRESSetTol(gmres_solver, tol);
 }
 
+real_t HypreGMRES::GetTol()const
+{
+   HYPRE_Real tol;
+   HYPRE_GMRESGetTol(gmres_solver, &tol);
+   return tol;
+}
+
 void HypreGMRES::SetAbsTol(real_t tol)
 {
    HYPRE_GMRESSetAbsoluteTol(gmres_solver, tol);
 }
 
+real_t HypreGMRES::GetAbsTol() const
+{
+   HYPRE_Real atol;
+   HYPRE_GMRESGetAbsoluteTol(gmres_solver, &atol);
+   return atol;
+}
+
 void HypreGMRES::SetMaxIter(int max_iter)
 {
    HYPRE_GMRESSetMaxIter(gmres_solver, max_iter);
 }
 
+int HypreGMRES::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_GMRESGetMaxIter(gmres_solver, &max_iter);
+   return max_iter;
+}
+
 void HypreGMRES::SetKDim(int k_dim)
 {
    HYPRE_GMRESSetKDim(gmres_solver, k_dim);
 }
 
+int HypreGMRES::GetKDim() const
+{
+   HYPRE_Int k_dim;
+   HYPRE_GMRESGetKDim(gmres_solver, &k_dim);
+   return k_dim;
+}
+
 void HypreGMRES::SetLogging(int logging)
 {
    HYPRE_GMRESSetLogging(gmres_solver, logging);
@@ -4569,16 +4712,37 @@ void HypreFGMRES::SetTol(real_t tol)
    HYPRE_ParCSRFlexGMRESSetTol(fgmres_solver, tol);
 }
 
+real_t HypreFGMRES::GetTol() const
+{
+   HYPRE_Real tol;
+   HYPRE_FlexGMRESGetTol(fgmres_solver, &tol);
+   return tol;
+}
+
 void HypreFGMRES::SetMaxIter(int max_iter)
 {
    HYPRE_ParCSRFlexGMRESSetMaxIter(fgmres_solver, max_iter);
 }
 
+int HypreFGMRES::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_FlexGMRESGetMaxIter(fgmres_solver, &max_iter);
+   return max_iter;
+}
+
 void HypreFGMRES::SetKDim(int k_dim)
 {
    HYPRE_ParCSRFlexGMRESSetKDim(fgmres_solver, k_dim);
 }
 
+int HypreFGMRES::GetKDim() const
+{
+   HYPRE_Int k_dim;
+   HYPRE_FlexGMRESGetKDim(fgmres_solver, &k_dim);
+   return k_dim;
+}
+
 void HypreFGMRES::SetLogging(int logging)
 {
    HYPRE_ParCSRFlexGMRESSetLogging(fgmres_solver, logging);
@@ -4675,6 +4839,21 @@ HypreFGMRES::~HypreFGMRES()
    HYPRE_ParCSRFlexGMRESDestroy(fgmres_solver);
 }
 
+#if MFEM_HYPRE_VERSION >= 21500
+HypreParVector HypreFGMRES::GetResiduals() const
+{
+   HYPRE_ParVector r;
+   HYPRE_ParCSRFlexGMRESGetResidual(fgmres_solver, &r);
+   return HypreParVector(r);
+}
+
+void HypreFGMRES::GetFinalAbsResidualNorm(real_t &final_res_norm,
+                                          real_t p) const
+{
+   auto r = GetResiduals();
+   ParNormlp(r, p, r.GetComm());
+}
+#endif
 
 void HypreDiagScale::SetOperator(const Operator &op)
 {
@@ -5163,6 +5342,13 @@ void HypreBoomerAMG::ResetAMGPrecond()
    }
 }
 
+int HypreBoomerAMG::GetMaxIter() const
+{
+   HYPRE_Int max_iter;
+   HYPRE_BoomerAMGGetMaxIter(amg_precond, &max_iter);
+   return max_iter;
+}
+
 void HypreBoomerAMG::SetOperator(const Operator &op)
 {
    const HypreParMatrix *new_A = dynamic_cast<const HypreParMatrix *>(&op);

linalg/hypre.hpp

@@ -665,6 +665,8 @@ public:
    void GetDiag(SparseMatrix &diag) const;
    /// Get the local off-diagonal block. NOTE: 'offd' will not own any data.
    void GetOffd(SparseMatrix &offd, HYPRE_BigInt* &cmap) const;
+   /// Get the global column mapping for the local off-diagonal block.
+   void GetOffdColMap(HYPRE_BigInt* &cmap, HYPRE_Int &num_cols) const;
    /** @brief Get a single SparseMatrix containing all rows from this processor,
        merged from the diagonal and off-diagonal blocks stored by the
        HypreParMatrix. */
@@ -959,6 +961,14 @@ public:
    const Memory<HYPRE_Int> &GetDiagMemoryJ() const { return mem_diag.J; }
    const Memory<real_t> &GetDiagMemoryData() const { return mem_diag.data; }
 
+   Memory<HYPRE_Int> &GetOffdMemoryI() { return mem_offd.I; }
+   Memory<HYPRE_Int> &GetOffdMemoryJ() { return mem_offd.J; }
+   Memory<real_t> &GetOffdMemoryData() { return mem_offd.data; }
+
+   const Memory<HYPRE_Int> &GetOffdMemoryI() const { return mem_offd.I; }
+   const Memory<HYPRE_Int> &GetOffdMemoryJ() const { return mem_offd.J; }
+   const Memory<real_t> &GetOffdMemoryData() const { return mem_offd.data; }
+
    /// @brief Prints the locally owned rows in parallel. The resulting files can
    /// be read with Read_IJMatrix().
    void Print(const std::string &fname, HYPRE_Int offi = 0,
@@ -1150,6 +1160,15 @@ public:
       return HypreUsingGPU() ? l1Jacobi : l1GS;
    }
 
+   /// Default solver settings:
+   /// type = DefaultType()
+   /// relax_times = 1
+   /// omega = 1.0
+   /// poly_order = 2
+   /// poly_fraction = 0.3
+   /// lambda = 0.5
+   /// mu = -0.5
+   /// taubin_iter = 40
    HypreSmoother();
 
    HypreSmoother(const HypreParMatrix &A_, int type = DefaultType(),
@@ -1159,20 +1178,28 @@ public:
 
    /// Set the relaxation type and number of sweeps
    void SetType(HypreSmoother::Type type, int relax_times = 1);
+   using Operator::GetType;
+   void GetType(HypreSmoother::Type &type, int &relax_times) const;
    /// Set SOR-related parameters
    void SetSOROptions(real_t relax_weight, real_t omega);
+   void GetSOROptions(real_t &relax_weight, real_t &omega) const;
+
    /// Set parameters for polynomial smoothing
    /** By default, 10 iterations of CG are used to estimate the eigenvalues.
        Setting eig_est_cg_iter = 0 uses hypre's hypre_ParCSRMaxEigEstimate() instead. */
    void SetPolyOptions(int poly_order, real_t poly_fraction,
                        int eig_est_cg_iter = 10);
+   void GetPolyOptions(int &poly_order, real_t &poly_fraction,
+                       int &eig_est_cg_iter) const;
    /// Set parameters for Taubin's lambda-mu method
    void SetTaubinOptions(real_t lambda, real_t mu, int iter);
+   void GetTaubinOptions(real_t &lambda, real_t &mu, int &iter) const;
 
    /// Convenience function for setting canonical windowing parameters
    void SetWindowByName(const char* window_name);
    /// Set parameters for windowing function for FIR smoother.
    void SetWindowParameters(real_t a, real_t b, real_t c);
+   void GetWindowParameters(real_t &a, real_t &b, real_t &c) const;
    /// Compute window and Chebyshev coefficients for given polynomial order.
    void SetFIRCoefficients(real_t max_eig);
 
@@ -1180,12 +1207,15 @@ public:
    /** By default, the l1-norms take their sign from the corresponding diagonal
        entries in the associated matrix. */
    void SetPositiveDiagonal(bool pos = true) { pos_l1_norms = pos; }
+   bool IsPositiveDiagonal() const { return pos_l1_norms; };
 
    /** Explicitly indicate whether the linear system matrix A is symmetric. If A
        is symmetric, the smoother will also be symmetric. In this case, calling
        MultTranspose will be redirected to Mult. (This is also done if the
        smoother is diagonal.) By default, A is assumed to be nonsymmetric. */
    void SetOperatorSymmetry(bool is_sym) { A_is_symmetric = is_sym; }
+   /// @return true if the smoother assumes A is symmetric, false otherwise
+   bool IsOperatorSymmetric() const { return A_is_symmetric; }
 
    /** Set/update the associated operator. Must be called after setting the
        HypreSmoother type and options. */
@@ -1317,6 +1347,7 @@ public:
 #endif
 
 /// PCG solver in hypre
+/// Defaults to (relative) tol=1e-6, atol=0, max_iter=1000
 class HyprePCG : public HypreSolver
 {
 private:
@@ -1324,6 +1355,9 @@ private:
 
    HypreSolver * precond;
 
+   /// Default PCG options
+   void SetDefaultOptions();
+
 public:
    HyprePCG(MPI_Comm comm);
 
@@ -1332,8 +1366,11 @@ public:
    void SetOperator(const Operator &op) override;
 
    void SetTol(real_t tol);
+   real_t GetTol() const;
    void SetAbsTol(real_t atol);
+   real_t GetAbsTol() const;
    void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
    void SetLogging(int logging);
    void SetPrintLevel(int print_lvl);
 
@@ -1358,12 +1395,32 @@ public:
       num_iterations = internal::to_int(num_it);
    }
 
+   /// Gets the relative residual norm
    void GetFinalResidualNorm(real_t &final_res_norm) const
    {
       HYPRE_ParCSRPCGGetFinalRelativeResidualNorm(pcg_solver,
                                                   &final_res_norm);
    }
 
+   /// @param[in] use
+   ///   Convergence criterion:
+   ///   - when true: (r, r) < max(r_tol^2 (b, b), a_tol^2)
+   ///   - when false: (r, A r) < max(r_tol^2 (b, A b), a_tol^2)
+   /// @sa HYPRE_PCGSetTwoNorm
+   void SetUseTwoNorm(bool use);
+
+   /// @sa HYPRE_PCGGetTwoNorm
+   bool GetUseTwoNorm() const;
+
+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRPCGGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
    /// The typecast to HYPRE_Solver returns the internal pcg_solver
    operator HYPRE_Solver() const override { return pcg_solver; }
 
@@ -1381,7 +1438,8 @@ public:
    virtual ~HyprePCG();
 };
 
-/// GMRES solver in hypre
+/// GMRES solver in hypre.
+/// Defaults to k=50, (relative) tol=1e-6, atol=0, max_iter=100.
 class HypreGMRES : public HypreSolver
 {
 private:
@@ -1400,9 +1458,13 @@ public:
    void SetOperator(const Operator &op) override;
 
    void SetTol(real_t tol);
+   real_t GetTol() const;
    void SetAbsTol(real_t tol);
+   real_t GetAbsTol() const;
    void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
    void SetKDim(int dim);
+   int GetKDim() const;
    void SetLogging(int logging);
    void SetPrintLevel(int print_lvl);
 
@@ -1422,12 +1484,22 @@ public:
       num_iterations = internal::to_int(num_it);
    }
 
+   /// Gets the relative residual norm
    void GetFinalResidualNorm(real_t &final_res_norm) const
    {
       HYPRE_ParCSRGMRESGetFinalRelativeResidualNorm(gmres_solver,
                                                     &final_res_norm);
    }
 
+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRGMRESGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
    /// The typecast to HYPRE_Solver returns the internal gmres_solver
    operator HYPRE_Solver() const override { return gmres_solver; }
 
@@ -1445,7 +1517,8 @@ public:
    virtual ~HypreGMRES();
 };
 
-/// Flexible GMRES solver in hypre
+/// Flexible GMRES solver in hypre.
+/// Defaults to k=50, (relative) tol=1e-6, max_iter=100.
 class HypreFGMRES : public HypreSolver
 {
 private:
@@ -1464,8 +1537,11 @@ public:
    void SetOperator(const Operator &op) override;
 
    void SetTol(real_t tol);
+   real_t GetTol() const;
    void SetMaxIter(int max_iter);
+   int GetMaxIter() const;
    void SetKDim(int dim);
+   int GetKDim() const;
    void SetLogging(int logging);
    void SetPrintLevel(int print_lvl);
 
@@ -1485,12 +1561,22 @@ public:
       num_iterations = internal::to_int(num_it);
    }
 
+   /// Gets the relative residual norm
    void GetFinalResidualNorm(real_t &final_res_norm) const
    {
       HYPRE_ParCSRFlexGMRESGetFinalRelativeResidualNorm(fgmres_solver,
                                                         &final_res_norm);
    }
 
+#if MFEM_HYPRE_VERSION >= 21500
+   /// Gets the internal Hypre solver residual vector.
+   /// @sa HYPRE_ParCSRFlexGMRESGetResidual
+   HypreParVector GetResiduals() const;
+
+   /// Computes the absolute residual p-norm.
+   void GetFinalAbsResidualNorm(real_t &final_res_norm, real_t p = 2) const;
+#endif
+
    /// The typecast to HYPRE_Solver returns the internal fgmres_solver
    operator HYPRE_Solver() const override { return fgmres_solver; }
 
@@ -1546,7 +1632,8 @@ public:
    virtual ~HypreDiagScale() { }
 };
 
-/// The ParaSails preconditioner in hypre
+/// The ParaSails preconditioner in hypre.
+/// See SetDefaultOptions() for default solver options.
 class HypreParaSails : public HypreSolver
 {
 private:
@@ -1675,10 +1762,14 @@ public:
 /**
 @brief Wrapper for Hypre's native parallel ILU preconditioner.
 
-The default ILU factorization type is ILU(k).  If you need to change this, or
-any other option, you can use the HYPRE_Solver method to cast the object for use
-with Hypre's native functions. For example, if want to use natural ordering
-rather than RCM reordering, you can use the following approach:
+Default parameters: ILU(k) factorization type, tol=0.0 (for use as a
+preconditioner), fill level = 1 (for ILU(k)), reverse Cuthill-McKee (RCM)
+re-ordering.
+
+If you need to change this, or any other option, you can use the HYPRE_Solver
+method to cast the object for use with Hypre's native functions. For example, if
+want to use natural ordering rather than RCM reordering, you can use the
+following approach:
 
 @code
 mfem::HypreILU ilu();
@@ -1819,6 +1910,7 @@ public:
 
    void SetMaxIter(int max_iter)
    { HYPRE_BoomerAMGSetMaxIter(amg_precond, max_iter); }
+   int GetMaxIter() const;
 
    /// Expert option - consult hypre documentation/team
    void SetMaxLevels(int max_levels)
@@ -1843,6 +1935,8 @@ public:
    /// Expert option - consult hypre documentation/team
    void SetRelaxType(int relax_type)
    { HYPRE_BoomerAMGSetRelaxType(amg_precond, relax_type); }
+   // not implemented in hypre
+   // int GetRelaxType() const;
 
    /// Expert option - consult hypre documentation/team
    void SetCycleType(int cycle_type)
@@ -2143,8 +2237,14 @@ public:
    ~HypreLOBPCG();
 
    void SetTol(real_t tol);
+   // not implemented in HYPRE
+   // real_t GetTol() const;
    void SetRelTol(real_t rel_tol);
+   // not implemented in HYPRE
+   // real_t GetRelTol() const;
    void SetMaxIter(int max_iter);
+   // not implemented in HYPRE
+   // int GetMaxIter() const;
    void SetPrintLevel(int logging);
    void SetNumModes(int num_eigs) { nev = num_eigs; }
    void SetPrecondUsageMode(int pcg_mode);

linalg/ode.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "../general/communication.hpp"
+#include "../general/forall.hpp"
 #include "operator.hpp"
 #include "ode.hpp"
 
@@ -184,6 +185,23 @@ void ODESolver::Init(TimeDependentOperator &f_)
    mem_type = GetMemoryType(f_.GetMemoryClass());
 }
 
+void ODESolver::ComputeSlopeFromState(const real_t dt, const Vector &u,
+                                      Vector &k)
+{
+   // k currently holds state u(t+dt),
+   // convert to slope k = du/dt ~= (u(t+dt)-u(t))/dt
+   const int usz = u.Size();
+   real_t fac = 1.0/dt;
+   auto d_u = u.Read();
+   auto d_k = k.ReadWrite();
+
+   mfem::forall(usz, [=] MFEM_HOST_DEVICE (int i)
+   {
+      d_k[i] -= d_u[i];
+      d_k[i] *= fac;
+   });
+}
+
 void ForwardEulerSolver::Init(TimeDependentOperator &f_)
 {
    ODESolver::Init(f_);
@@ -629,6 +647,10 @@ void AdamsMoultonSolver::Step(Vector &x, real_t &t, real_t &dt)
       }
       state.ShiftStages();
       f->ImplicitSolve(a[0]*dt, x, state[0]);
+      if (f->ImplicitVarTypeIsState())
+      {
+         ComputeSlopeFromState(a[0]*dt, x, state[0]);
+      }
       x.Add(a[0]*dt, state[0]);
       t += dt;
    }
@@ -661,7 +683,15 @@ void BackwardEulerSolver::Step(Vector &x, real_t &t, real_t &dt)
 {
    f->SetTime(t + dt);
    f->ImplicitSolve(dt, x, k); // solve for k: k = f(x + dt*k, t + dt)
-   x.Add(dt, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      x = k; // x = u_{i+1}
+   }
+   else
+   {
+      x.Add(dt, k);
+   }
+
    t += dt;
 }
 
@@ -676,7 +706,16 @@ void ImplicitMidpointSolver::Step(Vector &x, real_t &t, real_t &dt)
 {
    f->SetTime(t + dt/2);
    f->ImplicitSolve(dt/2, x, k);
-   x.Add(dt, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      x.Neg();
+      x.Add(2.0, k);
+   }
+   else
+   {
+      x.Add(dt, k);
+   }
+
    t += dt;
 }
 
@@ -718,11 +757,19 @@ void SDIRK23Solver::Step(Vector &x, real_t &t, real_t &dt)
    // note: with gamma_opt=3, both solve are outside [t,t+dt] since a>1
    f->SetTime(t + gamma*dt);
    f->ImplicitSolve(gamma*dt, x, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(gamma*dt, x, k);
+   }
    add(x, (1.-2.*gamma)*dt, k, y); // y = x + (1-2*gamma)*dt*k
    x.Add(dt/2, k);
 
    f->SetTime(t + (1.-gamma)*dt);
    f->ImplicitSolve(gamma*dt, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(gamma*dt, y, k);
+   }
    x.Add(dt/2, k);
    t += dt;
 }
@@ -749,17 +796,29 @@ void SDIRK34Solver::Step(Vector &x, real_t &t, real_t &dt)
 
    f->SetTime(t + a*dt);
    f->ImplicitSolve(a*dt, x, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, x, k);
+   }
    add(x, (0.5-a)*dt, k, y);
    add(x,  (2.*a)*dt, k, z);
    x.Add(b*dt, k);
 
    f->SetTime(t + dt/2);
    f->ImplicitSolve(a*dt, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, y, k);
+   }
    z.Add((1.-4.*a)*dt, k);
    x.Add((1.-2.*b)*dt, k);
 
    f->SetTime(t + (1.-a)*dt);
    f->ImplicitSolve(a*dt, z, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, z, k);
+   }
    x.Add(b*dt, k);
    t += dt;
 }
@@ -785,15 +844,27 @@ void SDIRK33Solver::Step(Vector &x, real_t &t, real_t &dt)
 
    f->SetTime(t + a*dt);
    f->ImplicitSolve(a*dt, x, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, x, k);
+   }
    add(x, (c-a)*dt, k, y);
    x.Add(b*dt, k);
 
    f->SetTime(t + c*dt);
    f->ImplicitSolve(a*dt, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, y, k);
+   }
    x.Add((1.0-a-b)*dt, k);
 
    f->SetTime(t + dt);
    f->ImplicitSolve(a*dt, x, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, x, k);
+   }
    x.Add(a*dt, k);
    t += dt;
 }
@@ -818,6 +889,10 @@ void TrapezoidalRuleSolver::Step(Vector &x, real_t &t, real_t &dt)
 
    f->SetTime(t + dt);
    f->ImplicitSolve(dt/2.0, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(0.5*dt, y, k);
+   }
    x.Add(dt/2.0, k);
    t += dt;
 }
@@ -848,11 +923,19 @@ void ESDIRK32Solver::Step(Vector &x, real_t &t, real_t &dt)
 
    f->SetTime(t + (2.0*a)*dt);
    f->ImplicitSolve(a*dt, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, y, k);
+   }
    z.Add(b*dt, k);
    x.Add(b*dt, k);
 
    f->SetTime(t + dt);
    f->ImplicitSolve(a*dt, z, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, z, k);
+   }
    x.Add(a*dt, k);
    t += dt;
 }
@@ -885,11 +968,19 @@ void ESDIRK33Solver::Step(Vector &x, real_t &t, real_t &dt)
 
    f->SetTime(t + (2.0*a)*dt);
    f->ImplicitSolve(a*dt, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, y, k);
+   }
    z.Add(b*dt, k);
    x.Add(b_2*dt, k);
 
    f->SetTime(t + dt);
    f->ImplicitSolve(a*dt, z, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(a*dt, z, k);
+   }
    x.Add(b_3*dt, k);
    t += dt;
 }
@@ -955,6 +1046,10 @@ void GeneralizedAlphaSolver::Step(Vector &x, real_t &t, real_t &dt)
    real_t dt_eff = (gamma*alpha_f/alpha_m)*dt;
    f->SetTime(t + alpha_f*dt);
    f->ImplicitSolve(dt_eff, y, k);
+   if (f->ImplicitVarTypeIsState())
+   {
+      ComputeSlopeFromState(dt_eff, y, k);
+   }
 
    // Update x and xdot
    x.Add((1.0 - (gamma/alpha_m))*dt, state[0]);
@@ -1116,8 +1211,8 @@ void SecondOrderODESolver::EulerStep(Vector &x, Vector &dxdt, real_t &t,
    f->SetTime(t + dt);
    f->ImplicitSolve(0.5*dt*dt, dt, x, dxdt, state[0]);
 
-   x   .Add(0.5*dt*dt, state[0]);
-   dxdt.Add(dt,    state[0]);
+   x.Add(0.5*dt*dt, state[0]);
+   dxdt.Add(dt, state[0]);
    t += dt;
 }
 
@@ -1203,8 +1298,8 @@ void NewmarkSolver::Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt)
    f->SetTime(t + dt);
    f->ImplicitSolve(fac3*dt*dt, fac4*dt, x, dxdt, state[0]);
 
-   x   .Add(fac3*dt*dt, state[0]);
-   dxdt.Add(fac4*dt,    state[0]);
+   x.Add(fac3*dt*dt, state[0]);
+   dxdt.Add(fac4*dt, state[0]);
    t += dt;
 }
 

linalg/ode.hpp

@@ -120,6 +120,7 @@ public:
 class ODESolver
 {
 protected:
+   using ImplicitVariableType = TimeDependentOperator::ImplicitVariableType;
    /// Pointer to the associated TimeDependentOperator.
    TimeDependentOperator *f;  // f(.,t) : R^n --> R^n
    MemoryType mem_type;
@@ -192,6 +193,22 @@ public:
    /// Returns how many State vectors the ODE requires
    virtual int GetStateSize() { return 0; };
 
+   ///@brief Returns @a true if the ODESolver supports the given
+   /// #ImplicitVariableType, @a var, and returns @a false otherwise.
+   ///@note Should be overriden in ODESolver that calls TimeDependentOperator::ImplicitSolve().
+   virtual bool SupportsImplicitVariableType(ImplicitVariableType var) const
+   { return false; };
+
+   /** @brief Compute the finite-difference slope, @a $\frac{du}{dt} \approx \frac{u(t+dt)-u(t)}{dt}$,
+    * and store it in @a k.
+    * @param [in] dt Finite difference step size.
+    * @param [in] u  state vector, @a u(t).
+    * @param [in,out] k   On input, @a k contains the state vector, @a u( @a t+ @a dt).
+    * On output, @a k contains the computed slope, @a du/dt.
+    * */
+   virtual void ComputeSlopeFromState(const real_t dt, const Vector &u,
+                                      Vector &k);
+
    // Help info for ODESolver options
    static MFEM_EXPORT std::string ExplicitTypes;
    static MFEM_EXPORT std::string ImplicitTypes;
@@ -361,6 +378,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -374,6 +397,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -395,6 +424,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -409,6 +444,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -423,6 +464,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -437,6 +484,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -451,6 +504,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -465,6 +524,12 @@ public:
    void Init(TimeDependentOperator &f_) override;
 
    void Step(Vector &x, real_t &t, real_t &dt) override;
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -490,6 +555,12 @@ public:
 
    ODEStateData& GetState() override { return state; }
    const ODEStateData& GetState() const override { return state; }
+
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 
@@ -606,6 +677,11 @@ public:
 
    ODEStateData& GetState() override { return state; }
    const ODEStateData& GetState() const override { return state; }
+   bool SupportsImplicitVariableType(ImplicitVariableType var) const override
+   {
+      return (var == ImplicitVariableType::STATE ||
+              var == ImplicitVariableType::SLOPE);
+   }
 };
 
 /** A 1-stage, 2nd order AM method. */

linalg/operator.hpp

@@ -381,11 +381,24 @@ public:
       ADDITIVE_TERM_2
    };
 
+   /** Used to specify the variable being returned by ImplicitSolve(). This can
+    * be queried by ODESolver to identify the variable being solved for.
+    * @warning Not all ODESolver may support all options. See ODESolver::SupportsImplicitVariableType() */
+   enum ImplicitVariableType
+   {
+      SLOPE, ///< stage slope, $k = \frac{du}{dt}$.
+      STATE  ///< stage state, $k = u$.
+   };
+
 protected:
    real_t t;  ///< Current time.
    Type type; /**< @brief Describes the form of the TimeDependentOperator, see
                    the documentation of #Type. */
    EvalMode eval_mode; ///< Current evaluation mode.
+   ImplicitVariableType implicit_variable_type =
+      ImplicitVariableType::SLOPE; /**< @brief
+                                                        Return variable for
+                                                        ImplicitSolve()*/
 
 public:
    /** @brief Construct a "square" TimeDependentOperator (u,t) -> k(u,t), where
@@ -429,6 +442,24 @@ public:
    virtual void SetEvalMode(const EvalMode new_eval_mode)
    { eval_mode = new_eval_mode; }
 
+   /** @brief Sets the #ImplicitVariableType for ImplicitSolve()*/
+   virtual void SetImplicitVariableType(const ImplicitVariableType variable_type)
+   { implicit_variable_type = variable_type; }
+
+   /** @brief Returns the #ImplicitVariableType for ImplicitSolve(). */
+   virtual ImplicitVariableType GetImplicitVariableType() const
+   { return implicit_variable_type; }
+
+   /** @brief Returns @a true if implicit variable is #STATE and @a false otherwise.
+    * Used by ODESolver to identify the stage variable returned by ImplicitSolve() */
+   virtual bool ImplicitVarTypeIsState() const
+   { return (implicit_variable_type == ImplicitVariableType::STATE); }
+
+   /** @brief Returns @a true if implicit variable is #SLOPE and @a false otherwise.
+    * Used by ODESolver to identify the stage variable returned by ImplicitSolve() */
+   virtual bool ImplicitVarTypeIsSlope() const
+   { return (implicit_variable_type == ImplicitVariableType::SLOPE); }
+
    /** @brief Perform the action of the explicit part of the operator, G:
        @a v = G(@a u, t) where t is the current time.
 
@@ -462,7 +493,8 @@ public:
 
    /** @brief Solve for the unknown @a k, at the current time t, the following
        equation:
-       F(@a u + @a gamma @a k, @a k, t) = G(@a u + @a gamma @a k, t).
+        1. $F( u + \gamma k, k, t) = G( u +  \gamma k, t)$, if solving for stage-slope (default)
+        2. $F( u , \frac{k-u}{\gamma}, t) = G(k, t)$, if solving for stage-state
 
        For solving an ordinary differential equation of the form
        $ M \frac{dy}{dt} = g(y,t) $, recall that F and G can be defined in
@@ -472,8 +504,9 @@ 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
 
-       Regardless of the choice of F and G, this function should solve for @a k
-       in M @a k = g(@a u + @a gamma @a k, t).
+        Regardless of the choice of F and G, this function should solve for @a k:
+        - $~Mk = g( u + \gamma k, t)~$, if solving for stage-slope.
+        - $~Mk  = \gamma g(k, t) + Mu~$, if solving for stage-state
 
        To see how @a k can be useful, consider the backward Euler method defined
        by $ y(t + \Delta t) = y(t) + \Delta t k_0 $ where
@@ -491,6 +524,7 @@ public:
        $ y(t) + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j $ and @a gamma set to
        $ a_{ii} \Delta t $, for $ k_i $. For example, see class SDIRK33Solver.
 
+       See SetImplicitVariableType() to switch between different variable modes.
        If not re-implemented, this method simply generates an error. */
    virtual void ImplicitSolve(const real_t gamma, const Vector &u, Vector &k);
 

linalg/petsc.cpp

@@ -3639,12 +3639,20 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
       // make sure ess/nat_dof have been collectively set
       PetscBool lpr = PETSC_FALSE,pr;
       if (opts.ess_dof) { lpr = PETSC_TRUE; }
+#if PETSC_VERSION_LT(3,24,0)
       mpiierr = MPI_Allreduce(&lpr,&pr,1,MPIU_BOOL,MPI_LOR,comm);
+#else
+      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPI_C_BOOL,MPI_LOR,comm);
+#endif
       CCHKERRQ(comm,mpiierr);
       MFEM_VERIFY(lpr == pr,"ess_dof should be collectively set");
       lpr = PETSC_FALSE;
       if (opts.nat_dof) { lpr = PETSC_TRUE; }
+#if PETSC_VERSION_LT(3,24,0)
       mpiierr = MPI_Allreduce(&lpr,&pr,1,MPIU_BOOL,MPI_LOR,comm);
+#else
+      mpiierr = MPI_Allreduce(&lpr,&pr,1,MPI_C_BOOL,MPI_LOR,comm);
+#endif
       CCHKERRQ(comm,mpiierr);
       MFEM_VERIFY(lpr == pr,"nat_dof should be collectively set");
       // make sure fields have been collectively set
@@ -4058,8 +4066,13 @@ void PetscNonlinearSolver::SetOperator(const Operator &op)
       ls = (PetscBool)(height == op.Height() && width  == op.Width() &&
                        (void*)&op == fctx &&
                        (void*)&op == jctx);
+#if PETSC_VERSION_LT(3,24,0)
       mpiierr = MPI_Allreduce(&ls,&gs,1,MPIU_BOOL,MPI_LAND,
                               PetscObjectComm((PetscObject)snes));
+#else
+      mpiierr = MPI_Allreduce(&ls,&gs,1,MPI_C_BOOL,MPI_LAND,
+                              PetscObjectComm((PetscObject)snes));
+#endif
       CCHKERRQ(PetscObjectComm((PetscObject)snes),mpiierr);
       if (!gs)
       {

linalg/sparsemat.cpp

@@ -1066,6 +1066,11 @@ void SparseMatrix::BooleanMultTranspose(const Array<int> &x,
    y.SetSize(Width());
    y = 0;
 
+   HostReadI();
+   HostReadJ();
+   x.HostRead();
+   y.HostReadWrite();
+
    for (int i = 0; i < Height(); i++)
    {
       if (x[i])

linalg/sparsesmoothers.cpp

@@ -23,15 +23,31 @@ namespace mfem
 void SparseSmoother::SetOperator(const Operator &a)
 {
    oper = dynamic_cast<const SparseMatrix*>(&a);
-   if (oper == NULL)
-   {
-      mfem_error("SparseSmoother::SetOperator : not a SparseMatrix!");
-   }
+   MFEM_VERIFY(oper != nullptr, "Operator must be a SparseMatrix");
    height = oper->Height();
    width = oper->Width();
+
+   At.reset();
+   oper_T = nullptr;
+}
+
+void SparseSmoother::EnsureTranspose() const
+{
+   if (oper_T) { return; }
+
+   const real_t tol = 1e-14;
+   if (oper->IsSymmetric() > tol * oper->MaxNorm())
+   {
+      At.reset(Transpose(*oper));
+      oper_T = At.get();
+   }
+   else
+   {
+      At.reset();
+      oper_T = oper;
+   }
 }
 
-/// Matrix vector multiplication with GS Smoother.
 void GSSmoother::Mult(const Vector &x, Vector &y) const
 {
    if (!iterative_mode)
@@ -51,21 +67,33 @@ void GSSmoother::Mult(const Vector &x, Vector &y) const
    }
 }
 
-/// Create the Jacobi smoother.
-DSmoother::DSmoother(const SparseMatrix &a, int t, real_t s, int it)
-   : SparseSmoother(a)
+void GSSmoother::MultTranspose(const Vector &x, Vector &y) const
 {
-   type = t;
-   scale = s;
-   iterations = it;
+   EnsureTranspose();
+
+   if (!iterative_mode)
+   {
+      y = 0.0;
+   }
+
+   for (int i = 0; i < iterations; i++)
+   {
+      if (type != 1)
+      {
+         oper_T->Gauss_Seidel_forw(x, y);
+      }
+      if (type != 2)
+      {
+         oper_T->Gauss_Seidel_back(x, y);
+      }
+   }
 }
 
-/// Matrix vector multiplication with Jacobi smoother.
-void DSmoother::Mult(const Vector &x, Vector &y) const
+void DSmoother::Mult_(const SparseMatrix &A, const Vector &x, Vector &y) const
 {
    if (!iterative_mode && type == 0 && iterations == 1)
    {
-      oper->DiagScale(x, y, scale, use_abs_diag);
+      A.DiagScale(x, y, scale, use_abs_diag);
       return;
    }
 
@@ -90,22 +118,41 @@ void DSmoother::Mult(const Vector &x, Vector &y) const
    {
       if (type == 0)
       {
-         oper->Jacobi(x, *p, *r, scale, use_abs_diag);
+         A.Jacobi(x, *p, *r, scale, use_abs_diag);
       }
       else if (type == 1)
       {
-         oper->Jacobi2(x, *p, *r, scale);
+         A.Jacobi2(x, *p, *r, scale);
       }
       else if (type == 2)
       {
-         oper->Jacobi3(x, *p, *r, scale);
+         A.Jacobi3(x, *p, *r, scale);
       }
       else
       {
-         mfem_error("DSmoother::Mult wrong type");
+         MFEM_ABORT("Invalid type.");
       }
       Swap<Vector*>(r, p);
    }
 }
 
+void DSmoother::Mult(const Vector &x, Vector &y) const
+{
+   Mult_(*oper, x, y);
+}
+
+void DSmoother::MultTranspose(const Vector &x, Vector &y) const
+{
+   if (iterations == 1 && !iterative_mode)
+   {
+      Mult_(*oper, x, y);
+      return;
+   }
+
+   EnsureTranspose();
+   MFEM_VERIFY(type == 0 || !At, "l1 or lumped Jacobi transpose not implemented"
+               " for non-symmetric matrices");
+   Mult_(*oper_T, x, y);
+}
+
 }

linalg/sparsesmoothers.hpp

@@ -15,67 +15,159 @@
 #include "../config/config.hpp"
 #include "sparsemat.hpp"
 
+#include <memory>
+
 namespace mfem
 {
 
+/// Abstract base class for smoothers created from a SparseMatrix.
 class SparseSmoother : public MatrixInverse
 {
 protected:
-   const SparseMatrix *oper;
+   const SparseMatrix *oper = nullptr; ///< The underlying matrix.
+
+   /// Pointer to the transpose of the underlying matrix. If the matrix is
+   /// symmetric, this will be the same as @a oper. If the matrix is not
+   /// symmetric, the transpose will be formed and stored in @a At. The
+   /// transpose will only be formed if MultTranspose() is called.
+   mutable const SparseMatrix *oper_T = nullptr;
+
+   mutable std::unique_ptr<SparseMatrix> At; ///< Transpose of A, if needed.
+
+   void EnsureTranspose() const; ///< Ensure that the transpose is set.
 
 public:
-   SparseSmoother() { oper = NULL; }
+   SparseSmoother() = default;
 
-   SparseSmoother(const SparseMatrix &a)
-      : MatrixInverse(a) { oper = &a; }
+   SparseSmoother(const SparseMatrix &a) { SetOperator(a); }
 
+   /// Sets the underlying matrix. @a a must be a SparseMatrix.
    void SetOperator(const Operator &a) override;
 };
 
-/// Data type for Gauss-Seidel smoother of sparse matrix
+/// Gauss-Seidel smoother of a sparse matrix.
 class GSSmoother : public SparseSmoother
 {
+public:
+   enum GSType
+   {
+      SYMMETRIC, ///< Forward Gauss-Seidel, then backward.
+      FORWARD, ///< Forward Gauss-Seidel ($L^{-1}$).
+      BACKWARD ///< Backward Gauss-Seidel ($U^{-1}$).
+   };
 protected:
-   int type; // 0, 1, 2 - symmetric, forward, backward
-   int iterations;
+   GSType type; ///< Type of Gauss-Seidel, see GSSmoother::GSType.
+   int iterations; ///< Number of stationary iterations.
 
 public:
-   /// Create GSSmoother.
-   GSSmoother(int t = 0, int it = 1) { type = t; iterations = it; }
+   /// @brief Create a Gauss-Seidel smoother. SetOperator() will need to be
+   /// called with a SparseMatrix before first use.
+   ///
+   /// @param[in]  t        Type of GS smoother (see GSSmoother::GSType)
+   /// @param[in]  it       Number of stationary iterations to perform
+   GSSmoother(GSType t = SYMMETRIC, int it = 1) { type = t; iterations = it; }
 
-   /// Create GSSmoother.
-   GSSmoother(const SparseMatrix &a, int t = 0, int it = 1)
-      : SparseSmoother(a) { type = t; iterations = it; }
+   /// @brief Create a Jacobi smoother using the SparseMatrix @a a.
+   ///
+   /// @param[in]  a        The underlying SparseMatrix
+   /// @param[in]  t        Type of GS smoother (see GSSmoother::GSType)
+   /// @param[in]  it       Number of stationary iterations to perform
+   GSSmoother(const SparseMatrix &a, GSType t = SYMMETRIC, int it = 1)
+      : GSSmoother(t, it) { SetOperator(a); }
 
-   /// Matrix vector multiplication with GS Smoother.
+   /// Same as GSSmoother(GSType,int), for backwards compatibility.
+   GSSmoother(int t, int it = 1) : GSSmoother(GSType(t), it) { }
+
+   /// @brief Same as GSSmoother(const SparseMatrix&,GSType,int), for
+   /// backwards compatibility.
+   GSSmoother(const SparseMatrix &a, int t, int it = 1)
+      : GSSmoother(a, GSType(t), it) { }
+
+   /// @brief Application of the Gauss-Seidel smoother.
+   ///
+   /// Applies a stationary Gauss-Seidel iteration. If Solver::iterative_mode is
+   /// true, then @a y is used as the initial guess, and Gauss-Seidel is applied
+   /// to the residual $x - Ay$.
    void Mult(const Vector &x, Vector &y) const override;
+
+   /// Application of the transpose of the Gauss-Seidel smoother.
+   void MultTranspose(const Vector &x, Vector &y) const override;
 };
 
-/// Data type for scaled Jacobi-type smoother of sparse matrix
+/// Jacobi-type diagonal smoother of a sparse matrix.
 class DSmoother : public SparseSmoother
 {
+public:
+   enum JacobiType
+   {
+      JACOBI,       ///< Scale by the diagonal of the matrix.
+      L1_JACOBI,    ///< Scale by the l1-norm of the rows.
+      LUMPED_JACOBI ///< Scale by the sum of the rows.
+   };
 protected:
-   int type; // 0, 1, 2 - scaled Jacobi, scaled l1-Jacobi, scaled lumped-Jacobi
-   real_t scale;
-   int iterations;
-   /// Uses abs values of the diagonal entries. Relevant only when type = 0.
+   JacobiType type; ///< Type of diagonal scaling, see DSmoother::JacobiType.
+   real_t scale; ///< Scaling (damping) factor.
+   int iterations; ///< Number of stationary iterations to perform.
+
+   /// @brief Uses abs values of the diagonal entries. Relevant only with type
+   /// JacobiType::JACOBI.
    bool use_abs_diag = false;
 
-   mutable Vector z;
+   mutable Vector z; ///< Temporary work vector.
+
+   /// Apply the Jacobi smoother (used internally by Mult() and MultTranspose())
+   void Mult_(const SparseMatrix &A, const Vector &x, Vector &y) const;
 
 public:
-   /// Create Jacobi smoother.
-   DSmoother(int t = 0, real_t s = 1., int it = 1)
+   /// @brief Create a Jacobi smoother. SetOperator() will need to be called
+   /// with a SparseMatrix before first use.
+   ///
+   /// @param[in]  t        Type of Jacobi smoother (see DSmoother::JacobiType)
+   /// @param[in]  s        Scaling factor
+   /// @param[in]  it       Number of stationary iterations to perform
+   DSmoother(JacobiType t = JACOBI, real_t s = 1., int it = 1)
    { type = t; scale = s; iterations = it; }
 
-   /// Create Jacobi smoother.
-   DSmoother(const SparseMatrix &a, int t = 0, real_t s = 1., int it = 1);
+   /// @brief Create a Jacobi smoother using the SparseMatrix @a a.
+   ///
+   /// @param[in]  a        The underlying SparseMatrix
+   /// @param[in]  t        Type of Jacobi smoother (see DSmoother::JacobiType)
+   /// @param[in]  s        Scaling factor
+   /// @param[in]  it       Number of stationary iterations to perform
+   DSmoother(const SparseMatrix &a, JacobiType t = JACOBI, real_t s = 1.,
+             int it = 1) : DSmoother(t, s, it) { SetOperator(a); }
 
-   /// Replace diag entries with their abs values. Relevant only when type = 0.
+   /// @brief Same as DSmoother(JacobiType,real_t,int), for backwards compatbility.
+   DSmoother(int t, real_t s = 1., int it = 1)
+      : DSmoother(JacobiType(t), s, it) { }
+
+   /// @brief Same as DSmoother(const SparseMatrix&,JacobiType,real_t,int), for
+   /// backwards compatbility.
+   DSmoother(const SparseMatrix &a, int t, real_t s = 1., int it = 1)
+      : DSmoother(a, JacobiType(t), s, it) { }
+
+   /// @brief Replace diagonal entries with their absolute values. Relevant only
+   /// with JacobiType::JACOBI.
    void SetPositiveDiagonal(bool pos_diag = true) { use_abs_diag = pos_diag; }
 
-   /// Matrix vector multiplication with Jacobi smoother.
+   /// @brief Apply the Jacobi smoother.
+   ///
+   /// Applies a stationary iteration with diagonal scaling. If
+   /// Solver::iterative_mode is true, then @a y is used as the initial guess
+   /// (and the diagonal scaling is applied to the residual $x - Ay$, giving
+   /// $D^{-1}(x - Ay)$).
+   ///
+   /// By default, Solver::iterative_mode is false and only one iteration is
+   /// performed, corresponding to $y = D^{-1}x$.
    void Mult(const Vector &x, Vector &y) const override;
+
+   /// @brief Apply the transpose of the Jacobi smoother.
+   ///
+   /// If the underlying matrix is symmetric, or if only one iteration is
+   /// performed with zero initial guess (Solver::iterative_mode is false), then
+   /// this is the same as Mult(). For non-symmetric matrices with iteration
+   /// count greater than one, only JacobiType::JACOBI is supported.
+   void MultTranspose(const Vector &x, Vector &y) const override;
 };
 
 }

makefile

@@ -794,7 +794,6 @@ status info:
 	$(info MFEM_MPI_NP            = $(MFEM_MPI_NP))
 	@true
 
-ASTYLE_BIN = astyle
 ASTYLE = $(ASTYLE_BIN) --options=$(SRC)config/mfem.astylerc
 ASTYLE_VER = "Artistic Style Version 3.1"
 FORMAT_FILES = $(foreach dir,$(DIRS) $(EM_DIRS) config,$(dir)/*.?pp)

mesh/attribute_sets.cpp

@@ -113,13 +113,13 @@ AttributeSets::GetAttributeSetMarker(const std::string & set_name) const
 
 Array<int> AttributeSets::AttrToMarker(int max_attr, const Array<int> &attrs)
 {
-   MFEM_ASSERT(attrs.Max() <= max_attr, "Invalid attribute number present.");
+   MFEM_VERIFY(attrs.Min() >= 1, "Found attribute less than one")
+   MFEM_ASSERT(attrs.Max() <= max_attr, "Found attribute greater than max_attr")
 
    Array<int> marker(max_attr);
    marker = 0;
    for (auto const &attr : attrs)
    {
-      MFEM_VERIFY(attr > 0, "Attribute number less than one!");
       marker[attr-1] = 1;
    }
    return marker;

mesh/mesh.cpp

@@ -36,6 +36,7 @@
 #include <numeric>
 #include <unordered_map>
 #include <unordered_set>
+#include <list>
 
 // Include the METIS header, if using version 5. If using METIS 4, the needed
 // declarations are inlined below, i.e. no header is needed.
@@ -4772,12 +4773,12 @@ Mesh::Mesh(real_t *vertices_, int num_vertices,
    FinalizeTopology();
 }
 
-Mesh::Mesh( const NURBSExtension& ext )
+Mesh::Mesh(const NURBSExtension& ext)
    : attribute_sets(attributes), bdr_attribute_sets(bdr_attributes)
 {
    SetEmpty();
    /// make an internal copy of the NURBSExtension
-   NURBSext = new NURBSExtension( ext );
+   NURBSext = new NURBSExtension(ext);
 
    Dim              = NURBSext->Dimension();
    NumOfVertices    = NURBSext->GetNV();
@@ -4791,11 +4792,12 @@ Mesh::Mesh( const NURBSExtension& ext )
    if (NURBSext->HavePatches())
    {
       NURBSFECollection  *fec = new NURBSFECollection(NURBSext->GetOrder());
-      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, Dim,
+      const int vdim = NURBSext->GetPatchSpaceDimension();
+      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, vdim,
                                                        Ordering::byVDIM);
       Nodes = new GridFunction(fes);
       Nodes->MakeOwner(fec);
-      NURBSext->SetCoordsFromPatches(*Nodes);
+      NURBSext->SetCoordsFromPatches(*Nodes, vdim);
       own_nodes = 1;
       spaceDim = Nodes->VectorDim();
       for (int i = 0; i < spaceDim; i++)
@@ -6409,7 +6411,7 @@ void Mesh::UpdateNURBS()
    NURBSext->SetKnotsFromPatches();
 
    Dim = NURBSext->Dimension();
-   spaceDim = Dim;
+   spaceDim = Nodes->FESpace()->GetVDim();
 
    if (NumOfElements != NURBSext->GetNE())
    {
@@ -6434,7 +6436,8 @@ void Mesh::UpdateNURBS()
    Nodes->FESpace()->Update();
    Nodes->Update();
    NodesUpdated();
-   NURBSext->SetCoordsFromPatches(*Nodes);
+   const int vdim = Nodes->FESpace()->GetVDim();
+   NURBSext->SetCoordsFromPatches(*Nodes, vdim);
 
    if (NumOfVertices != NURBSext->GetNV())
    {
@@ -6537,6 +6540,8 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_ukv)
       Array<int> ukv_to_rpkv;
       GetEdgeToUniqueKnotvector(edge_to_ukv, ukv_to_rpkv);
    }
+
+   CorrectPatchTopoOrientations(edge_to_ukv);
 }
 
 void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
@@ -6547,9 +6552,9 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
    const int NPKV = NP * dim;    // number of patch knotvectors
    constexpr int notset = -9999999;
    // Sign convention
-   auto sign = [](int i) { return -1 - i; };
-   auto unsign = [](int i) { return (i < 0) ? -1 - i : i; };
-   // Edge index -> dimension convention
+   auto flipSign = [](int i) { return -1 - i; };
+   auto unSign = [](int i) { return (i < 0) ? -1 - i : i; };
+   // Local edge index -> dimension convention
    auto edge_to_dim = [](int i) { return (i < 8) ? ((i & 1) ? 1 : 0) : 2; };
 
    Array<int> v(2); // vertices of an edge
@@ -6564,7 +6569,7 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
       {
          GetElementVertices(i, v);
          // Sign is based on the edge's vertex indices
-         edge_to_ukv[i] = (v[1] > v[0]) ? i : sign(i);
+         edge_to_ukv[i] = (v[1] > v[0]) ? i : flipSign(i);
          ukv_to_rpkv[i] = i;
       }
       return;
@@ -6614,14 +6619,14 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
          // We've set this edge already - link this index to it
          if (edge_to_pkv[edge] != notset)
          {
-            const int pkv_other = unsign(edge_to_pkv[edge]);
+            const int pkv_other = unSign(edge_to_pkv[edge]);
             unite(pkv, pkv_other);
          }
          else
          {
             GetEdgeVertices(edge, v);
             // Sign is based on the edge's vertex indices
-            edge_to_pkv[edge] = (v[1] > v[0]) ? pkv : sign(pkv);
+            edge_to_pkv[edge] = (v[1] > v[0]) ? pkv : flipSign(pkv);
          }
       }
    }
@@ -6648,11 +6653,255 @@ void Mesh::GetEdgeToUniqueKnotvector(Array<int> &edge_to_ukv,
    edge_to_ukv.SetSize(NumOfEdges);
    for (int i = 0; i < NumOfEdges; i++)
    {
-      const int pkv = unsign(edge_to_pkv[i]);
+      const int pkv = unSign(edge_to_pkv[i]);
       const int rpkv = pkv_to_rpkv[pkv];
       const int ukv = rpkv_to_ukv[rpkv];
-      edge_to_ukv[i] = (edge_to_pkv[i] < 0) ? sign(ukv) : ukv;
+      edge_to_ukv[i] = (edge_to_pkv[i] < 0) ? flipSign(ukv) : ukv;
    }
+
+   CorrectPatchTopoOrientations(edge_to_ukv);
+}
+
+void Mesh::CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const
+{
+   const int dim = Dimension(); // Topological (not physical) dimension
+   if (dim == 1) { return; }
+
+   // Sign convention
+   auto flipSign = [](int i) { return -1 - i; };
+
+   const Table *face2elem = GetFaceToElementTable();
+   Array<int> pfaces, orient;
+   Array<int> fe, feo;
+
+   // Finds elements sharing a face containing knotvector kv.
+   auto faceNeighbors = [&](int p, int kv, std::unordered_set<int> &nghb)
+   {
+      if (dim == 2) { GetElementEdges(p, pfaces, orient); }
+      else { GetElementFaces(p, pfaces, orient); }
+
+      for (auto face : pfaces)
+      {
+         // Check whether this face contains kv.
+         GetFaceEdges(face, fe, feo);
+         bool hasKV = false;
+         for (auto e : fe)
+         {
+            const int skv = edge_to_ukv[e];
+            if (skv == kv || flipSign(skv) == kv) { hasKV = true; }
+         }
+         if (hasKV)
+         {
+            Array<int> row;
+            face2elem->GetRow(face, row);
+            for (auto elem : row) { nghb.insert(elem); }
+         }
+      }
+   };
+
+   std::vector<std::vector<int>> dir_edges;
+   if (dim == 2)
+   {
+      dir_edges =
+      {
+         {0,2},
+         {1,3}
+      };
+   }
+   else
+   {
+      dir_edges =
+      {
+         {0,2,4,6},
+         {1,3,5,7},
+         {8,9,10,11}
+      };
+   }
+
+   Array<int> ukvs((dim==2) ? 4 : 12);
+   Array<int> pe, oe;
+   bool initKV = false;
+
+   auto setPatchDirections = [&](int p, int kv, Array<bool> &edgeSet,
+                                 std::unordered_set<int> &visited)
+   {
+      // Edges and orientations for this patch
+      GetElementEdges(p, pe, oe);
+
+      // Get the signed unique knot vector indices
+      for (int i = 0; i < pe.Size(); i++)
+      {
+         ukvs[i] = edge_to_ukv[pe[i]];
+         ukvs[i] = (oe[i] < 0) ? flipSign(ukvs[i]) : ukvs[i];
+      }
+
+      // Find the direction with this kv.
+      int thisDir = -1;
+      for (int d=0; d<dim; ++d) // Loop over directions.
+      {
+         const int skv = edge_to_ukv[pe[dir_edges[d][0]]];
+         if (skv == kv || flipSign(skv) == kv)
+         {
+            thisDir = d;
+         }
+      }
+      MFEM_VERIFY(thisDir >= 0, "");
+
+      // For this direction, find any edge already set. If no edge is set, we
+      // arbitrarily take the first.
+      int ref_edge0 = dir_edges[thisDir][0];
+      for (auto ref_edge : dir_edges[thisDir])
+      {
+         const int edge = pe[ref_edge];
+         if (edgeSet[edge])
+         {
+            ref_edge0 = ref_edge;
+         }
+      }
+
+      if (initKV && !edgeSet[pe[ref_edge0]])
+      {
+         visited.erase(p);
+         return false; // There is no set edge in this direction on this patch.
+      }
+
+      initKV = true;
+
+      // Use ref_edge0 to set other edges in this direction.
+      edgeSet[pe[ref_edge0]] = true;
+      for (auto i : dir_edges[thisDir])
+      {
+         if (i == ref_edge0)
+         {
+            continue;
+         }
+
+         const int edge = pe[i];
+         if ((dim == 2 && ukvs[i] != flipSign(ukvs[ref_edge0])) ||
+             (dim == 3 && ukvs[i] == flipSign(ukvs[ref_edge0])))
+         {
+            // Flip the sign of this edge
+            MFEM_VERIFY(!edgeSet[edge], "");
+            edge_to_ukv[edge] = flipSign(edge_to_ukv[edge]);
+         }
+
+         edgeSet[edge] = true;
+      }
+
+      return true;
+   };
+
+   Array<bool> edgeSet(NumOfEdges); // Whether edge has orientation set
+   edgeSet = false;
+
+   std::unordered_set<int> unset; // Patches with an unset edge
+   for (int i=0; i<NumOfElements; ++i) { unset.insert(i); }
+
+   const int max_iter = 3 * NumOfElements;
+   for (int iter=0; iter<max_iter; ++iter)
+   {
+      // Iteratively choose an unset patch (meaning not all edges have
+      // orientation set), choose a knotvector index for which the corresponding
+      // edges on this patch are not set, and sweep over all patches containing
+      // this knotvector. The patch sweep is ordered, by maintaining an ordered
+      // list `nextPatches` set by finding face-neighbor patches of visited
+      // patches, where the common face contains the knotvector. When each patch
+      // is visited, the edge orientations are set consistently. This iteration
+      // terminates when all edges have been set on all patches.
+
+      std::list<int> nextPatches; // Next patches to visit, ordered
+      std::unordered_set<int> nextSet; // nextPatches as a set
+      std::unordered_set<int> visited; // Visit each patch only once
+
+      if (unset.size() == 0)
+      {
+         break;
+      }
+
+      const int p0 = *unset.begin();
+      nextPatches.push_back(p0); // Start from arbitrary unset patch
+      nextSet.insert(p0);
+
+      // Choose an arbitrary unset direction for the first patch.
+      GetElementEdges(p0, pe, oe);
+      int unsetDim = -1;
+      for (int d=0; d<dim; ++d) // Loop over dimensions.
+      {
+         if (!edgeSet[pe[dir_edges[d][0]]])
+         {
+            unsetDim = d;
+         }
+      }
+
+      if (unsetDim == -1)
+      {
+         unset.erase(p0);
+         continue;
+      }
+
+      const int kv_signed = edge_to_ukv[pe[dir_edges[unsetDim][0]]];
+      const int kv = kv_signed < 0 ? flipSign(kv_signed) : kv_signed;
+      MFEM_VERIFY(!edgeSet[pe[dir_edges[unsetDim][0]]], "");
+
+      initKV = false;
+
+      while (nextPatches.size() > 0)
+      {
+         const int p = nextPatches.front();
+         nextPatches.pop_front();
+         nextSet.erase(p);
+         visited.insert(p);
+
+         const bool somethingSet = setPatchDirections(p, kv, edgeSet, visited);
+         if (!somethingSet)
+         {
+            continue;
+         }
+
+         // Find neighbors of patch p sharing a conforming face, via face2elem.
+         std::unordered_set<int> neighbors;
+         faceNeighbors(p, kv, neighbors);
+
+         bool allSet = true;
+         GetElementEdges(p, pe, oe);
+         for (auto edge : pe)
+         {
+            if (!edgeSet[edge])
+            {
+               allSet = false;
+            }
+         }
+         if (allSet)
+         {
+            unset.erase(p);
+         }
+
+         // Add neighbors not done to nextPatches.
+         for (auto n : neighbors)
+         {
+            if (n != p && visited.count(n) == 0 && unset.count(n) > 0)
+            {
+               if (nextSet.count(n) == 0)
+               {
+                  nextPatches.push_back(n);
+                  nextSet.insert(n);
+               }
+            }
+         }
+      }
+   }
+
+   bool allSet = true;
+   for (auto eset : edgeSet)
+   {
+      if (!eset)
+      {
+         allSet = false;
+      }
+   }
+   MFEM_VERIFY(allSet && unset.size() == 0, "Some edge is not set");
+
+   delete face2elem;
 }
 
 void Mesh::LoadNonconformingPatchTopo(std::istream &input,
@@ -7587,6 +7836,17 @@ bool Mesh::IsMixedMesh() const
 
 void Mesh::GetElementEdges(int i, Array<int> &edges, Array<int> &cor) const
 {
+   if (Dim == 1)
+   {
+      // In 1D, elements are segments and can be treated as edges.
+      edges.SetSize(1);
+      cor.SetSize(1);
+      edges[0] = i;
+      const int *v = elements[i]->GetVertices();
+      cor[0] = (v[0] < v[1]) ? (1) : (-1);
+      return;
+   }
+
    if (el_to_edge)
    {
       el_to_edge->GetRow(i, edges);
@@ -9563,6 +9823,8 @@ void Mesh::GetVertices(Vector &vert_coord) const
 
 void Mesh::SetVertices(const Vector &vert_coord)
 {
+   MFEM_VERIFY(vert_coord.Size() == spaceDim * NumOfVertices, "");
+   vertices.SetSize(NumOfVertices);
    for (int i = 0, nv = vertices.Size(); i < nv; i++)
       for (int j = 0; j < spaceDim; j++)
       {
@@ -12140,6 +12402,38 @@ void Mesh::PrintTopoEdges(std::ostream &os, const Array<int> &e_to_k,
 {
    Array<int> vert;
 
+   // In 1D patch-topology NURBS meshes, knotvector orientation is stored in the
+   // file's `edges` section, but the topological 1D mesh has NumOfEdges == 0
+   // (its "faces" are vertices). When a valid edge->knotvector map is provided,
+   // print a pseudo-edge list derived from the 1D elements so external tools
+   // (e.g. VisIt) can consume the mapping.
+   if (Dim == 1 && NumOfEdges == 0 && e_to_k.Size() == NumOfElements)
+   {
+      const int ne = NumOfElements;
+      os << "\nedges\n" << ne << '\n';
+      for (int i = 0; i < ne; i++)
+      {
+         const int *v = elements[i]->GetVertices();
+         int v0 = v[0], v1 = v[1];
+
+         int ki = e_to_k[i];
+         const bool flip = (ki < 0); // desired output vertex order: descending
+         if (flip) { ki = -1 - ki; } // print the unsigned knotvector index
+
+         // Encode the sign of e_to_k in the vertex ordering, consistent with
+         // Mesh::LoadPatchTopo(): v0 > v1 => negative sign.
+         if ((v0 > v1) != flip) { std::swap(v0, v1); }
+
+         os << ki << ' ' << v0 << ' ' << v1 << '\n';
+      }
+
+      if (!vmap)
+      {
+         os << "\nvertices\n" << NumOfVertices << '\n';
+      }
+      return;
+   }
+
    os << "\nedges\n" << NumOfEdges << '\n';
    for (int i = 0; i < NumOfEdges; i++)
    {
@@ -15452,6 +15746,128 @@ Mesh *Extrude2D(Mesh *mesh, const int nz, const real_t sz)
    return mesh3d;
 }
 
+Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
+                  int &par_ref, Array<int> &partitioning)
+{
+   MFEM_VERIFY(dim > 1, "Not implemented for 1D meshes.");
+
+   auto factor = [&](int N)
+   {
+      for (int i = static_cast<int>(sqrt(N)); i > 0; i--)
+      { if (N % i == 0) { return i; } }
+      return 1;
+   };
+
+   par_ref = 0;
+   const int ref_factor = (dim == 2) ? 4 : 8;
+
+   // Elements per task before performing parallel refinements.
+   // This will be used to form the serial mesh.
+   int el0 = elem_per_mpi;
+   while (el0 % ref_factor == 0)
+   {
+      el0 /= ref_factor;
+      par_ref++;
+   }
+
+   // In the serial mesh we have:
+   // The number of MPI blocks is mpi_cnt = mp_x.mpy_y.mpy_z.
+   // The size of each MPI block is el0 = el0_x.el0_y.el0_z.
+   int mpi_x, mpi_y, mpi_z;
+   int el0_x, el0_y, el0_z;
+   if (dim == 2)
+   {
+      mpi_x = factor(mpi_cnt);
+      mpi_y = mpi_cnt / mpi_x;
+
+      // Switch order for better balance.
+      el0_y = factor(el0);
+      el0_x = el0 / el0_y;
+   }
+   else
+   {
+      mpi_x = factor(mpi_cnt);
+      mpi_y = factor(mpi_cnt / mpi_x);
+      mpi_z = mpi_cnt / mpi_x / mpi_y;
+
+      // Switch order for better balance.
+      el0_z = factor(el0);
+      el0_y = factor(el0 / el0_z);
+      el0_x = el0 / el0_y / el0_z;
+   }
+
+   if (print && dim == 2)
+   {
+      int elem_par_x = mpi_x * el0_x * pow(2, par_ref),
+          elem_par_y = mpi_y * el0_y * pow(2, par_ref);
+
+      mfem::out << "--- Mesh generation: \n";
+      mfem::out << "Par mesh:    " << elem_par_x << " x " << elem_par_y
+                << " (" << elem_par_x * elem_par_y << " elements)\n"
+                << "Elem / task: "
+                << el0_x * pow(2, par_ref) << " x "
+                << el0_y * pow(2, par_ref)
+                << " (" << el0_x * pow(2, 2*par_ref) * el0_y << " elements)\n"
+                << "MPI blocks:  " << mpi_x << " x " << mpi_y
+                << " (" << mpi_x * mpi_y << " mpi tasks)\n" << "-\n"
+                << "Serial mesh: "
+                << mpi_x * el0_x << " x " << mpi_y * el0_y
+                << " (" << mpi_x * el0_x * mpi_y * el0_y << " elements)\n"
+                << "Elem / task: " << el0_x << " x " << el0_y << std::endl
+                << "Par refine:  " << par_ref << std::endl;
+      mfem::out << "--- \n";
+   }
+
+   if (print && dim == 3)
+   {
+      int elem_par_x = mpi_x * el0_x * pow(2, par_ref),
+          elem_par_y = mpi_y * el0_y * pow(2, par_ref),
+          elem_par_z = mpi_z * el0_z * pow(2, par_ref);
+
+      mfem::out << "--- Mesh generation: \n";
+      mfem::out << "Par mesh:    "
+                << elem_par_x << " x " << elem_par_y << " x " << elem_par_z
+                << " (" << elem_par_x*elem_par_y*elem_par_z << " elements)\n"
+                << "Elem / task: "
+                << el0_x * pow(2, par_ref) << " x "
+                << el0_y * pow(2, par_ref) << " x "
+                << el0_z * pow(2, par_ref)
+                << " (" << el0_x*pow(2, 3*par_ref)*el0_y*el0_z << " elements)\n"
+                << "MPI blocks:  " << mpi_x << " x " << mpi_y << " x " << mpi_z
+                << " (" << mpi_x * mpi_y * mpi_z << " mpi tasks)\n" << "-\n"
+                << "Serial mesh: "
+                << mpi_x*el0_x << " x " << mpi_y*el0_y << " x " << mpi_z*el0_z
+                << " (" << mpi_x*el0_x*mpi_y*el0_y*mpi_z*el0_z << " elements)\n"
+                << "Elem / task: "
+                << el0_x << " x " << el0_y << " x " << el0_z  << std::endl
+                << "Par refine:  " << par_ref << std::endl;
+      mfem::out << "--- \n";
+   }
+
+   Mesh mesh;
+   int nxyz[3];
+   if (dim == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(mpi_x * el0_x,
+                                   mpi_y * el0_y, Element::QUADRILATERAL, true);
+      nxyz[0] = mpi_x; nxyz[1] = mpi_y;
+   }
+   else
+   {
+      mesh = Mesh::MakeCartesian3D(mpi_x * el0_x,
+                                   mpi_y * el0_y,
+                                   mpi_z * el0_z, Element::HEXAHEDRON, true);
+      nxyz[0] = mpi_x; nxyz[1] = mpi_y; nxyz[2] = mpi_z;
+   }
+
+   const int NE = mesh.GetNE();
+   partitioning.SetSize(NE);
+   std::unique_ptr<int[]> p_raw(mesh.CartesianPartitioning(nxyz));
+   std::copy(p_raw.get(), p_raw.get() + NE, partitioning.GetData());
+
+   return mesh;
+}
+
 bool Mesh::Conforming() const
 {
    if (NURBSext)

mesh/mesh.hpp

@@ -527,6 +527,9 @@ protected:
    void PrintTopoEdges(std::ostream &out, const Array<int> &e_to_k,
                        bool vmap = false) const;
 
+   /// Set signs to ensure knotvectors are pointed in the same direction.
+   void CorrectPatchTopoOrientations(Array<int> &edge_to_ukv) const;
+
    /// Used in GetFaceElementTransformations (...)
    void GetLocalPtToSegTransformation(IsoparametricTransformation &,
                                       int i) const;
@@ -984,8 +987,8 @@ public:
 
    ///@}
 
-   /// Construct a Mesh from a NURBSExtension
-   explicit Mesh( const NURBSExtension& ext );
+   /// Construct a Mesh from a NURBSExtension, which is deep-copied.
+   explicit Mesh(const NURBSExtension& ext);
 
    /** @anchor mfem_Mesh_construction
        @name Methods for piecewise Mesh construction.
@@ -2075,12 +2078,13 @@ public:
        contrary to the ones obtained through Mesh::GetFacesElements and can
        directly be used, e.g., Elem1 and Elem2 indices.
        Likewise the orientations for Elem1 and Elem2 already take into account
-       special cases and can be used as is.
-   */
+       special cases and can be used as is. */
    struct FaceInformation
    {
+      /// The face topology (boundary, conforming, or nonconforming).
       FaceTopology topology;
 
+      /// Information about the adjacent elements.
       struct
       {
          ElementLocation location;
@@ -2090,8 +2094,13 @@ public:
          int orientation;
       } element[2];
 
+      /// Detailed face information (see FaceInfoTag).
       FaceInfoTag tag;
+
+      /// If the face is nonconforming, the index of the NC face. -1 otherwise.
       int ncface;
+
+      /// The point matrix for nonconforming faces.
       const DenseMatrix* point_matrix;
 
       /** @brief Return true if the face is a local interior face which is NOT
@@ -2110,21 +2119,20 @@ public:
 
       /** @brief return true if the face is an interior face to the computation
           domain, either a local or shared interior face (not a boundary face)
-          which is NOT a master nonconforming face.
-       */
+          which is NOT a master nonconforming face. */
       bool IsInterior() const
       {
          return topology == FaceTopology::Conforming ||
                 topology == FaceTopology::Nonconforming;
       }
 
-      /** @brief Return true if the face is a boundary face. */
+      /// Return true if the face is a boundary face.
       bool IsBoundary() const
       {
          return topology == FaceTopology::Boundary;
       }
 
-      /// @brief Return true if the face is of the same type as @a type.
+      /// Return true if the face is of the same type as @a type.
       bool IsOfFaceType(FaceType type) const
       {
          switch (type)
@@ -2138,13 +2146,13 @@ public:
          }
       }
 
-      /// @brief Return true if the face is a conforming face.
+      /// Return true if the face is a conforming face.
       bool IsConforming() const
       {
          return topology == FaceTopology::Conforming;
       }
 
-      /// @brief Return true if the face is a nonconforming fine face.
+      /// Return true if the face is a nonconforming fine face.
       bool IsNonconformingFine() const
       {
          return topology == FaceTopology::Nonconforming &&
@@ -2152,7 +2160,7 @@ public:
                  element[1].conformity == ElementConformity::Superset);
       }
 
-      /// @brief Return true if the face is a nonconforming coarse face.
+      /// Return true if the face is a nonconforming coarse face.
       /** Note that ghost nonconforming master faces cannot be clearly
           identified as such with the currently available information, so this
           method will return false for such faces. */
@@ -2162,7 +2170,7 @@ public:
                 element[1].conformity == ElementConformity::Subset;
       }
 
-      /// @brief cast operator from FaceInformation to FaceInfo.
+      /// cast operator from FaceInformation to FaceInfo.
       operator Mesh::FaceInfo() const;
    };
 
@@ -2538,13 +2546,16 @@ public:
        changing the mesh file itself. Examples in miniapps/nurbs/meshes. */
    void RefineNURBSFromFile(std::string ref_file);
 
-   /// For NURBS meshes, insert the new knots in @a kv, for each direction.
+   /// For NURBS meshes, insert the new knots in @a kv, for each KnotVector.
+   /// The size of @a kv should be the number of KnotVectors in NURBSExtension.
    void KnotInsert(Array<KnotVector*> &kv);
 
-   /// For NURBS meshes, insert the knots in @a kv, for each direction.
+   /// For NURBS meshes, insert the knots in @a kv, for each KnotVector.
+   /// The size of @a kv should be the number of KnotVectors in NURBSExtension.
    void KnotInsert(Array<Vector*> &kv);
 
-   /// For NURBS meshes, remove the knots in @a kv, for each direction.
+   /// For NURBS meshes, remove the knots in @a kv, for each KnotVector.
+   /// The size of @a kv should be the number of KnotVectors in NURBSExtension.
    void KnotRemove(Array<Vector*> &kv);
 
    /* For each knot vector:
@@ -3201,6 +3212,28 @@ Mesh *Extrude1D(Mesh *mesh, const int ny, const real_t sy,
 /// Extrude a 2D mesh
 Mesh *Extrude2D(Mesh *mesh, const int nz, const real_t sz);
 
+/** @brief Constructs the smallest possible [0,1]^dim serial mesh that can be
+    used later to obtain a ParMesh with @a elem_per_mpi elements, with the same
+    topology, for each of the @a mpi_cnt MPI tasks. For quads and hexes.
+
+    The serial mesh has the smallest possible number of elements. The parallel
+    mesh will be obtained by parallel refinements. Each MPI task will have
+    elements with the same topology (same number, same connectivity).
+
+    @param[in]  dim          dimension (2 or 3).
+    @param[in]  mpi_cnt      number of MPI tasks.
+    @param[in]  elem_per_mpi number of elements per MPI task.
+    @param[in]  print        shows meshing info in the terminal.
+    @param[out] par_ref      number of parallel refinement needed afterwards.
+    @param[out] partitioning partitioning to create the desired ParMesh.
+
+    Usual use case:
+    Mesh mesh = PartitionMPI(dim, mpi_cnt, elem_per_mpi, print, par_ref, par);
+    ParMesh pmesh(MPI_COMM_WORLD, mesh, par.GetData());
+    for (int lev = 0; lev < par_ref; lev++) { pmesh.UniformRefinement(); }   */
+Mesh PartitionMPI(int dim, int mpi_cnt, int elem_per_mpi, bool print,
+                  int &par_ref, Array<int> &partitioning);
+
 // shift cyclically 3 integers left-to-right
 inline void ShiftRight(int &a, int &b, int &c)
 {

mesh/mesh_readers.cpp

@@ -1328,11 +1328,12 @@ void Mesh::ReadNURBSMesh(std::istream &input, int &curved, int &read_gf,
    if (NURBSext->HavePatches())
    {
       NURBSFECollection  *fec = new NURBSFECollection(NURBSext->GetOrder());
-      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, Dim,
+      const int vdim = NURBSext->GetPatchSpaceDimension();
+      FiniteElementSpace *fes = new FiniteElementSpace(this, fec, vdim,
                                                        Ordering::byVDIM);
       Nodes = new GridFunction(fes);
       Nodes->MakeOwner(fec);
-      NURBSext->SetCoordsFromPatches(*Nodes);
+      NURBSext->SetCoordsFromPatches(*Nodes, vdim);
       own_nodes = 1;
       read_gf = 0;
       spaceDim = Nodes->VectorDim();

mesh/ncnurbs.cpp

@@ -2827,6 +2827,8 @@ void NCNURBSExtension::PropagateFactorsForKV(int rf_default)
       }
    }
 
+   delete face2elem;
+
    // For any unset entries of kvf, set to default refinement factor rf_default.
    for (size_t i=0; i<kvf.size(); ++i)
    {

mesh/nurbs.hpp

@@ -51,6 +51,21 @@ protected:
    /// Number of elements, defined by distinct knots.
    int NumOfElements;
 
+   // Stores the demko points
+   mutable Vector demko;
+
+   /// Compute all the Demko points
+   void ComputeDemko() const;
+
+#ifdef MFEM_USE_LAPACK
+   // Data for reusing banded matrix factorization in FindInterpolant().
+   mutable DenseMatrix fact_AB; /// Banded matrix factorization
+   mutable Array<int> fact_ipiv; /// Row pivot indices
+#else
+   mutable DenseMatrix A_coll_inv; /// Collocation matrix inverse
+#endif
+
+
 public:
    /// Create an empty KnotVector.
    KnotVector() = default;
@@ -59,18 +74,28 @@ public:
        integers are read, for order and number of control points. */
    KnotVector(std::istream &input);
 
-   /** @brief Create a KnotVector with undefined knots (initialized to -1) of
-       order @a order and number of control points @a NCP. */
-   KnotVector(int order, int NCP);
+   /** @brief Create a KnotVector with order @a order.
+       When @a NCP is not provided  the number of control points is set to
+       @a order + 1, and the first @a order + 1 knots are set to 0 and last
+       @a order + 1 knots are set to 1.
+       When @a NCP is given number of control points is @a NCP and
+       the knots are initialized to -1) */
+   KnotVector(int order, int NCP = -1);
+
+   /** @brief Create a KnotVector with order @a order and knots @a knot.
+       If @a k has the correct number of repeated knots at the begin and end,
+       then this constructor will copy the knots as provided.
+       Otherwise, the knot vector will be extended by repeating the end knots
+       (order + 1) times. Internal knots will retain the multiplicity as given
+       in the input. */
+   KnotVector(int order, const Vector &k);
 
    /** @brief Create a KnotVector by passing in a degree, a Vector of interval
        lengths of length n, and a list of continuity of length n + 1.
-
        The intervals refer to spans between unique knot values (not counting
        zero-size intervals at repeated knots), and the continuity values should
        be >= -1 (discontinuous) and <= order-1 (maximally-smooth for the given
-       polynomial degree). Periodicity is not supported.
-   */
+       polynomial degree). Periodicity is not supported.*/
    KnotVector(int order, const Vector& intervals,
               const Array<int>& continuity);
 
@@ -103,13 +128,69 @@ public:
        with @a isElement for non-empty knot spans (elements). */
    int GetNKS() const { return NumOfControlPoints - Order; }
 
-   /** @brief Return the parameter for element reference coordinate @a xi
-       in [0,1], for the element beginning at knot @a ni. */
-   real_t getKnotLocation(real_t xi, int ni) const
-   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); }
+   /// Return whether knot location @a u is in a given span @a ni.
+   bool inSpan(real_t u, int ni) const
+   {
+      if ((u < knot(ni)) || (u > knot(ni+1))) { return false; }
+      return true;
+   }
 
    /// Return the index of the knot span containing parameter @a u.
-   int findKnotSpan(real_t u) const;
+   int GetSpan(real_t u) const;
+
+   /** @brief Return the reference coordinate in [0,1] for parameter @a u
+       in the element beginning at knot @a ni. */
+   real_t GetRefPoint(real_t u, int ni) const
+   { return (u-knot(ni))/(knot(ni+1)-knot(ni)); };
+
+   /** @brief Return the knot location for element reference coordinate @a xi
+       in [0,1], for the element beginning at knot @a ni. */
+   real_t GetKnotLocation(real_t xi, int ni) const
+   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); }
+
+   /** @brief Return the parameter for element reference coordinate @a xi
+       in [0,1], for the element beginning at knot @a ni. */
+   MFEM_DEPRECATED real_t getKnotLocation(real_t xi, int ni) const
+   { return (xi*knot(ni+1) + (1. - xi)*knot(ni)); } // Use GetKnotLocation instead
+
+   /// Return the index of the knot span containing parameter @a u.
+   MFEM_DEPRECATED int findKnotSpan(real_t u) const;  // Use GetSpan instead
+
+   /** Gives the @a i average knot location. Average is taken over @a Order
+       number of knots.*/
+   real_t GetGreville(int i) const;
+
+   void GetGreville(Vector &xi) const;
+
+   /** Gives the knot location where the @a i shape function is maximum.
+       Reverts to the Greville point if knot is repeated @a Order +1 times.
+       For background see:
+
+       Olivier Botella and Karim Shariff.
+       "B-spline methods in fluid dynamics."
+       International Journal of Computational Fluid Dynamics 17.2 (2003): 133-149.
+
+       Points are found using Newton iteration, with the Greville point as the
+       starting value. */
+   real_t GetBotella(int i) const;
+
+   void GetBotella(Vector &xi) const;
+
+   /** Gives the knot location of the @a i extremum of the Chebyshev spline.
+       For background see:
+
+       Stephen Demko
+       "On the existence of interpolating projections onto spline spaces."
+       Journal of approximation theory 43.2 (1985): 151-156.
+
+       Points are found using Remez iteration:
+        - Find interpolant, given by a, through given points, given by Demko
+        - Find extrema of this polynomial and update Demko points
+        - Repeat until converged
+        - Use the Greville point as starting point */
+   real_t GetDemko(int i) const;
+
+   void GetDemko(Vector &xi) const;
 
    // The following functions evaluate shape functions, which are B-spline basis
    // functions.
@@ -136,19 +217,32 @@ public:
    /** @brief Gives the locations of the maxima of the KnotVector in reference
        space. The function gives the knot span @a ks, the coordinate in the
        knot span @a xi, and the coordinate of the maximum in parameter space
-       @a u. */
-   void FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const;
+       @a u.
+       The main purpose of this function is its use in FindInterpolant.
+       Use GetBotella instead for each shape function separately, perhaps in
+       conjuction with GetSpan and GetRefPoint.*/
+   MFEM_DEPRECATED void FindMaxima(Array<int> &ks, Vector &xi, Vector &u) const;
 
    /** @brief Global curve interpolation through the points @a x (overwritten).
        @a x is an array with the length of the spatial dimension containing
        vectors with spatial coordinates. The control points of the interpolated
        curve are returned in @a x in the same form.
+       Use GetInterpolant instead. For the knot location one can use either
+       GetBotella, GetDemko or GetGreville. FindInterpolant uses the Botella
+       points, however, the Demko points might be more appropriate. */
+   MFEM_DEPRECATED void FindInterpolant(Array<Vector*> &x, bool reuse_inverse);
 
-       The inverse of the collocation matrix, used in the interpolation, is
-       stored for repeated calls and used if @a reuse_inverse is true. Reuse is
-       valid only if this KnotVector has not changed since the initial call with
-       @a reuse_inverse false. */
-   void FindInterpolant(Array<Vector*> &x, bool reuse_inverse = false);
+   /** @brief Global curve interpolation through the points @a x (overwritten)
+       at the knot location @a u. The control points of the
+       interpolated curve are returned in @a x in the same form.
+       For the knot location one can use  for instance GetBotella, GetDemko or
+       GetGreville. The Demko points might be most appropriate.*/
+   void GetInterpolant(Array<Vector*> &x, const Vector &u,
+                       bool reuse_inverse = false) const;
+
+   /// Different interface to same routine
+   void GetInterpolant(const Vector &x, const Vector &u,
+                       Vector &a, bool reuse_inverse = false) const;
 
    /** Set @a diff, comprised of knots in @a kv not contained in this KnotVector.
        @a kv must be of the same order as this KnotVector. The current
@@ -191,6 +285,18 @@ public:
        number of samples of the shape functions per element.*/
    void PrintFunctions(std::ostream &os, int samples=11) const;
 
+   /** Prints the function with basis function coefficient @a a, and its first
+       and second derivatives associated with the KnotVector per element.
+       Use GetElements() to count the elements before using this function.
+       @a samples is the number of samples of the shape functions per element.*/
+   void PrintFunction(std::ostream &os, const Vector &a, int samples=11) const;
+
+   /** Prints the @a i-th function and its first and second
+       derivatives associated with the KnotVector per element. Use GetElements()
+       to count the elements before using this function. @a samples is the
+       number of samples of the shape functions per element.*/
+   void PrintFunction(std::ostream &os, int i, int samples=11) const;
+
    /// Destroys KnotVector
    ~KnotVector() { }
 
@@ -209,14 +315,6 @@ public:
    /** @brief Flag to indicate whether the KnotVector has been coarsened, which
        means it is ready for non-nested refinement. */
    bool coarse;
-
-#ifdef MFEM_USE_LAPACK
-   // Data for reusing banded matrix factorization in FindInterpolant().
-   DenseMatrix fact_AB; /// Banded matrix factorization
-   Array<int> fact_ipiv; /// Row pivot indices
-#else
-   DenseMatrix A_coll_inv; /// Collocation matrix inverse
-#endif
 };
 
 
@@ -596,28 +694,29 @@ protected:
        if the KnotVector index associated with edge @a edge is negative. */
    inline const KnotVector *KnotVec(int edge, int oedge, int *okv) const;
 
-   /// Throw an error if any patch has an inconsistent edge_to_ukv mapping.
-   void CheckPatches();
-
    /// Throw an error if any boundary patch has invalid KnotVector orientation.
-   void CheckBdrPatches();
+   MFEM_DEPRECATED void CheckBdrPatches();
+
+   /// Return the patch-topology edge indices that define the KnotVectors for
+   /// patch @a p in each parametric direction.
+   void GetPatchDirectionEdges(int p, Array<int> &edges);
 
    /** @brief Return the directions in @a kvdir of the KnotVectors in patch @a p
        based on the patch edge orientations. Each entry of @a kvdir is -1 if the
        KnotVector direction is flipped, +1 otherwise. */
    void CheckKVDirection(int p, Array <int> &kvdir);
 
-   /**  @brief Create the comprehensive set of KnotVectors. In 1D, this set is
-    identical to the unique set of KnotVectors. */
+   /** @brief Create the comprehensive set of KnotVectors, one per patch and
+       parametric direction, accounting for the edge orientations. */
    void CreateComprehensiveKV();
 
-   /**  Update the unique set of KnotVectors. In 1D, this set is identical to
-    the comprehensive set of KnotVectors. */
+   /** @brief Update the unique set of KnotVectors from the comprehensive set
+       of KnotVectors. */
    void UpdateUniqueKV();
 
    /** @brief Check if the comprehensive array of KnotVectors agrees with the
        unique set of KnotVectors, on each patch. Return false if there is a
-       difference, true otherwise. This function throws an error in 1D. */
+       difference, true otherwise. */
    bool ConsistentKVSets();
 
    /// Return KnotVectors in @a kv in each dimension for patch @a p.
@@ -794,6 +893,9 @@ public:
    void MergeGridFunctions(GridFunction *gf_array[], int num_pieces,
                            GridFunction &merged);
 
+   /// Returns false if any patch has an inconsistent edge_to_ukv mapping.
+   bool CheckPatches();
+
    /// Destroy a NURBSExtension.
    virtual ~NURBSExtension();
 
@@ -820,6 +922,13 @@ public:
    /// Return the dimension of the reference space (not physical space).
    int Dimension() const { return patchTopo->Dimension(); }
 
+   /** @brief Return the physical dimension of the NURBS geometry
+
+       The physical dimension is inferred from the first patch,
+       i.e. number of coordinates per control point minus one (for the weight).
+       This method requires patch data to be present, i.e. HavePatches() == true */
+   int GetPatchSpaceDimension() const;
+
    /// Return the number of patches.
    int GetNP()     const { return patchTopo->GetNE(); }
 
@@ -933,9 +1042,9 @@ public:
    void ConvertToPatches(const Vector &Nodes);
    /// Set KnotVectors from @a patches and construct mesh and space data.
    void SetKnotsFromPatches();
-   /** @brief Set FE coordinates in @a Nodes, using data from @a patches, and
-       erase @a patches. */
-   void SetCoordsFromPatches(Vector &Nodes);
+   /** @brief Set FE coordinates in @a Nodes, using data from @a patches,
+       with physical vector dimension @a vdim, and erase @a patches. */
+   void SetCoordsFromPatches(Vector &Nodes, int vdim);
 
    /** @brief Read a GridFunction @a sol from stream @a input, written
        patch-by-patch, e.g. with PrintSolution(). */

mesh/pmesh.cpp

@@ -3041,7 +3041,7 @@ void ParMesh::GetSharedFaceTransformationsByLocalIndex(
    // for ghost faces we need a special version of GetFaceTransformation
    if (is_ghost)
    {
-      GetGhostFaceTransformation(FElTr, face_type, face_geom);
+      GetGhostFaceTransformation(FaceNo, FElTr);
       mask |= FaceElementTransformations::HAVE_FACE;
    }
 
@@ -3064,19 +3064,29 @@ void ParMesh::GetSharedFaceTransformationsByLocalIndex(
 }
 
 void ParMesh::GetGhostFaceTransformation(
-   FaceElementTransformations &FElTr, Element::Type face_type,
-   Geometry::Type face_geom) const
+   int FaceNo, FaceElementTransformations &FElTr) const
 {
+   MFEM_ASSERT(FaceNo >= GetNumFaces(), "Not a ghost face.");
+
+   // use the local face data
+   const int LocFaceNo = nc_faces_info[faces_info[FaceNo].NCFace].MasterFace;
+   FElTr.Attribute = (Dim == 1) ? 1 : faces[LocFaceNo]->GetAttribute();
+   FElTr.ElementNo = FaceNo;
+   FElTr.ElementType = ElementTransformation::FACE;
+   FElTr.mesh = this;
+
    // calculate composition of FElTr.Loc1 and FElTr.Elem1
    DenseMatrix &face_pm = FElTr.GetPointMat();
    FElTr.Reset();
    if (Nodes == NULL)
    {
+      const Element::Type face_type = GetFaceElementType(LocFaceNo);
       FElTr.Elem1->Transform(FElTr.Loc1.Transf.GetPointMat(), face_pm);
       FElTr.SetFE(GetTransformationFEforElementType(face_type));
    }
    else
    {
+      const Geometry::Type face_geom = GetFaceGeometry(LocFaceNo);
       const FiniteElement* face_el =
          Nodes->FESpace()->GetTraceElement(FElTr.Elem1No, face_geom);
       MFEM_VERIFY(dynamic_cast<const NodalFiniteElement*>(face_el),

mesh/pmesh.hpp

@@ -150,15 +150,7 @@ protected:
                     int elem, int start, int end, const int fverts[][N]);
 
    void GetGhostFaceTransformation(
-      FaceElementTransformations &FElTr, Element::Type face_type,
-      Geometry::Type face_geom) const;
-   void GetGhostFaceTransformation(
-      FaceElementTransformations *FElTr, Element::Type face_type,
-      Geometry::Type face_geom) const
-   {
-      MFEM_ASSERT(FElTr, "Missing FaceElementTransformations object!");
-      GetGhostFaceTransformation(*FElTr, face_type, face_geom);
-   }
+      int FaceNo, FaceElementTransformations &FElTr) const;
 
    /// Update the groups after triangle refinement
    void RefineGroups(const DSTable &v_to_v, int *middle);

mesh/pncmesh.cpp

@@ -1195,14 +1195,22 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
       }
    }
 
-   // If there are shared slaves, they will also need to be updated.
+   // If there are shared slaves, they will also need to be updated. First,
+   // check whether the update has already been done.
+   bool sharedUpdated = false;
    if (shared.slaves.Size())
+   {
+      int nfaces = NFaces, nghosts = NGhostFaces;
+      if (Dim <= 2) { nfaces = NEdges, nghosts = NGhostEdges; }
+      sharedUpdated = (pmesh.faces_info.Size() == nfaces + nghosts);
+   }
+
+   if (shared.slaves.Size() && !sharedUpdated)
    {
       int nfaces = NFaces, nghosts = NGhostFaces;
       if (Dim <= 2) { nfaces = NEdges, nghosts = NGhostEdges; }
 
       // enlarge Mesh::faces_info for ghost slaves
-      MFEM_ASSERT(pmesh.faces_info.Size() == nfaces, "");
       MFEM_ASSERT(pmesh.GetNumFaces() == nfaces, "");
       pmesh.faces_info.SetSize(nfaces + nghosts);
       for (int i = nfaces; i < pmesh.faces_info.Size(); i++)
@@ -1303,14 +1311,12 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
                // Mesh::ApplyLocalSlaveTransformation.
             }
 
-            MFEM_ASSERT(fi.NCFace < 0, "fi.NCFace = " << fi.NCFace);
             fi.NCFace = pmesh.nc_faces_info.Size();
             pmesh.nc_faces_info.Append(Mesh::NCFaceInfo(true, sf.master, pm));
          }
       }
    }
 
-
    // In 3D some extra orientation data structures can be needed.
    if (Dim == 3)
    {

mesh/submesh/psubmesh.hpp

@@ -34,14 +34,16 @@ class ParNCSubMesh;
  * subset of the parent Mesh and reuses the parallel distribution.
  *
  * The attributes are taken from the parent. That means if a volume is extracted
- * from a volume, it has the same domain attribute as the parent. Its boundary
- * attributes are generated (there will be one boundary attribute 1 for all of
- * the boundaries).
+ * from a volume, it has the same domain attribute as the parent. Its new
+ * boundary attributes are, for any boundary common to the parent and the new
+ * submesh, the boundary attribute of the parent; and, for all new boundaries,
+ * a single, generated, common attribute equal to one plus the largest boundary
+ * attribute of the parent.
  *
  * If a surface is extracted from a volume, the boundary attribute from the
- * parent is assigned to be the new domain attribute. Its boundary attributes
- * are generated (there will be one boundary attribute 1 for all of the
- * boundaries).
+ * parent is assigned to be the new domain attribute. Its new boundary attribute
+ * is a single, generated, common attribute equal to one plus the largest
+ * boundary attribute of the parent.
  *
  * For more customized boundary attributes, the resulting ParSubMesh has to be
  * postprocessed.

mesh/submesh/submesh.hpp

@@ -28,14 +28,16 @@ class NCSubMesh;
  * subset of the parents Mesh and reuses the parallel distribution.
  *
  * The attributes are taken from the parent. That means if a volume is extracted
- * from a volume, it has the same domain attribute as the parent. Its boundary
- * attributes are generated (there will be one boundary attribute 1 for all of
- * the boundaries).
+ * from a volume, it has the same domain attribute as the parent. Its new
+ * boundary attributes are, for any boundary common to the parent and the new
+ * submesh, the boundary attribute of the parent; and, for all new boundaries,
+ * a single, generated, common attribute equal to one plus the largest boundary
+ * attribute of the parent.
  *
  * If a surface is extracted from a volume, the boundary attribute from the
- * parent is assigned to be the new domain attribute. Its boundary attributes
- * are generated (there will be one boundary attribute 1 for all of the
- * boundaries).
+ * parent is assigned to be the new domain attribute. Its new boundary attribute
+ * is a single, generated, common attribute equal to one plus the largest
+ * boundary attribute of the parent.
  *
  * For more customized boundary attributes, the resulting SubMesh has to be
  * postprocessed.

miniapps/common/mesh_extras.cpp

@@ -232,27 +232,6 @@ MergeMeshNodes(Mesh * mesh, int logging)
    }
 }
 
-void AttrToMarker(int max_attr, const Array<int> &attrs, Array<int> &marker)
-{
-   MFEM_ASSERT(attrs.Max() <= max_attr, "Invalid attribute number present.");
-
-   marker.SetSize(max_attr);
-   if (attrs.Size() == 1 && attrs[0] == -1)
-   {
-      marker = 1;
-   }
-   else
-   {
-      marker = 0;
-      for (int j=0; j<attrs.Size(); j++)
-      {
-         int attr = attrs[j];
-         MFEM_VERIFY(attr > 0, "Attribute number less than one!");
-         marker[attr-1] = 1;
-      }
-   }
-}
-
 void AffineTransformation::Eval(Vector &V, ElementTransformation &T,
                                 const IntegrationPoint &ip)
 {