Merge branch 'moonolith_h1_bugfix' into moonolith_h1_vector_space

Adding H(div) and H(curl) conforming NURBS FiniteElements

.gitignore

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

CHANGELOG

@@ -11,9 +11,16 @@
 Version 4.7.1 (development)
 ===========================
 
+- Added NURBS-based H(div) and H(curl) elements in 2D and 3D. Only on single 
+  patch meshes. Only implemented for serial computations.
+
+- Added miniapps to demonstrate the H(div) and H(curl) NURBS elements.
+
 - Added an MFEM example for the eikonal equation. This new solver is based on
   the proximal Galerkin method introduced by Keith and Surowiec.
 
+- API change: in class GridFunction, 'fec' was renamed to 'fec_owned'.
+
 
 Version 4.7, released on May 7, 2024
 ====================================

config/sample-runs.sh

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

data/pipe-nurbs-2d.mesh

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

doc/CodeDocumentation.conf.in

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

doc/CodeDocumentation.dox

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

examples/moonolith/ex1p.cpp

@@ -5,7 +5,8 @@
 // Moonolith sample runs:
 //   mpirun -np 4 ex1p
 //   mpirun -np 4 ex1p --source_refinements 1 --dest_refinements 2
-//   mpirun -np 4 ex1p -s ../../data/inline-hex.mesh -d ../../data/inline-tet.mesh
+//   mpirun -np 4 ex1p -s ../../data/inline-hex.mesh -d
+//   ../../data/inline-tet.mesh
 //
 // Description:  This example code demonstrates the use of MFEM for transferring
 //               discrete fields from one finite element mesh to another. The
@@ -50,6 +51,8 @@ int main(int argc, char *argv[])
    int dest_fe_order = 1;
    bool visualization = true;
    bool use_vector_fe = false;
+   bool use_h1 = true;
+   bool use_vector_space = false;
    bool verbose = false;
    bool assemble_mass_and_coupling_together = true;
 
@@ -72,14 +75,27 @@ int main(int argc, char *argv[])
    args.AddOption(&verbose, "-verb", "--verbose", "--no-verb", "--no-verbose",
                   "Enable/Disable verbose output");
    args.AddOption(&use_vector_fe, "-vfe", "--use_vector_fe", "-no-vfe",
-                  "--no-vector_fe", "Use vector finite elements (Experimental)");
+                  "--no-vector_fe",
+                  "Use RT|ND vector finite elements (Experimental)");
+   args.AddOption(&use_vector_space, "-vfs", "--use_vector_space", "-no-vfs",
+                  "--no-vector_space",
+                  "Use Lagrange vector finite elements (Experimental)");
+   args.AddOption(&use_h1, "-h1", "--use-h1", "-nh1", "--no-h1",
+                  "Use H1 collection");
    args.AddOption(&assemble_mass_and_coupling_together, "-act",
                   "--assemble_mass_and_coupling_together", "-no-act",
                   "--no-assemble_mass_and_coupling_together",
-                  "Assemble mass and coupling operators together (better for non-affine elements)");
+                  "Assemble mass and coupling operators together (better for "
+                  "non-affine elements)");
    args.Parse();
    check_options(args);
 
+   if (use_vector_fe && use_vector_space)
+   {
+      mfem::err <<
+                "WARNING: use_vector_fe and use_vector_space options are both true, ignoring use_vector_fe\n";
+   }
+
    shared_ptr<Mesh> src_mesh, dest_mesh;
 
    ifstream imesh;
@@ -169,17 +185,30 @@ int main(int argc, char *argv[])
    }
    else
    {
-      src_fe_coll =
-         make_shared<L2_FECollection>(source_fe_order, src_mesh->Dimension());
-      dest_fe_coll =
-         make_shared<L2_FECollection>(dest_fe_order, dest_mesh->Dimension());
+
+      if (use_h1)
+      {
+         src_fe_coll =
+            make_shared<H1_FECollection>(source_fe_order, src_mesh->Dimension());
+         dest_fe_coll =
+            make_shared<H1_FECollection>(dest_fe_order, dest_mesh->Dimension());
+      }
+      else
+      {
+         src_fe_coll =
+            make_shared<L2_FECollection>(source_fe_order, src_mesh->Dimension());
+         dest_fe_coll =
+            make_shared<L2_FECollection>(dest_fe_order, dest_mesh->Dimension());
+      }
    }
 
-   auto src_fe =
-      make_shared<ParFiniteElementSpace>(p_src_mesh.get(), src_fe_coll.get());
+   auto src_fe = make_shared<ParFiniteElementSpace>(
+                    p_src_mesh.get(), src_fe_coll.get(),
+                    use_vector_space ? src_mesh->Dimension() : 1);
 
-   auto dest_fe =
-      make_shared<ParFiniteElementSpace>(p_dest_mesh.get(), dest_fe_coll.get());
+   auto dest_fe = make_shared<ParFiniteElementSpace>(
+                     p_dest_mesh.get(), dest_fe_coll.get(),
+                     use_vector_space ? dest_mesh->Dimension() : 1);
 
    ParGridFunction src_fun(src_fe.get());
 
@@ -189,7 +218,7 @@ int main(int argc, char *argv[])
    // To be used with vector fe
    VectorFunctionCoefficient vector_coeff(dim, &vector_fun);
 
-   if (use_vector_fe)
+   if (use_vector_fe || use_vector_space)
    {
       src_fun.ProjectCoefficient(vector_coeff);
       src_fun.Update();
@@ -209,7 +238,11 @@ int main(int argc, char *argv[])
       assemble_mass_and_coupling_together);
    assembler.SetVerbose(verbose);
 
-   if (use_vector_fe)
+   if (use_vector_space)
+   {
+      assembler.AddMortarIntegrator(make_shared<TPL2MortarIntegrator>());
+   }
+   else if (use_vector_fe)
    {
       assembler.AddMortarIntegrator(make_shared<VectorL2MortarIntegrator>());
    }

examples/pumi/ex1.cpp

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

examples/pumi/ex2.cpp

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

fem/eltrans.hpp

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

fem/fe/fe_base.hpp

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

fem/fe/fe_nurbs.cpp

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

fem/fe/fe_nurbs.hpp

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

fem/fe_coll.cpp

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

fem/fe_coll.hpp

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

fem/fespace.cpp

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

fem/fespace.hpp

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

fem/gridfunc.cpp

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

fem/gridfunc.hpp

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

fem/intrules_cut.cpp

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

fem/intrules_cut.hpp

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

fem/moonolith/mortarassembler.cpp

@@ -40,31 +40,10 @@ public:
    bool assemble_mass_and_coupling_together{true};
    int max_solver_iterations{400};
 
-   bool is_vector_fe() const
+   BilinearFormIntegrator * newBFormIntegrator() const
    {
-      bool is_vector_fe = false;
-      for (auto i_ptr : integrators)
-      {
-         if (i_ptr->is_vector_fe())
-         {
-            is_vector_fe = true;
-            break;
-         }
-      }
-
-      return is_vector_fe;
-   }
-
-   BilinearFormIntegrator * new_mass_integrator() const
-   {
-      if (is_vector_fe())
-      {
-         return new VectorFEMassIntegrator();
-      }
-      else
-      {
-         return new MassIntegrator();
-      }
+      assert(!integrators.empty());
+      return integrators[0]->newBFormIntegrator();
    }
 };
 
@@ -200,7 +179,7 @@ bool MortarAssembler::Assemble(std::shared_ptr<SparseMatrix> &B)
                                  impl_->source->GetNDofs());
 
 
-   std::unique_ptr<BilinearFormIntegrator> mass_integr(impl_->new_mass_integrator());
+   std::unique_ptr<BilinearFormIntegrator> mass_integr(impl_->newBFormIntegrator());
 
    if(impl_->assemble_mass_and_coupling_together) {
       impl_->mass_matrix = make_shared<SparseMatrix>(impl_->destination->GetNDofs(), impl_->destination->GetNDofs());
@@ -389,7 +368,7 @@ bool MortarAssembler::Update()
    if(!impl_->assemble_mass_and_coupling_together) {
       BilinearForm b_form(impl_->destination.get());
 
-      b_form.AddDomainIntegrator(impl_->new_mass_integrator());
+      b_form.AddDomainIntegrator(impl_->newBFormIntegrator());
 
       b_form.Assemble();
       b_form.Finalize();

fem/moonolith/mortarintegrator.cpp

@@ -47,6 +47,8 @@ void L2MortarIntegrator::AssembleElementMatrix(
    }
 }
 
+BilinearFormIntegrator * L2MortarIntegrator::newBFormIntegrator() const { return new MassIntegrator(); }
+
 void VectorL2MortarIntegrator::AssembleElementMatrix(
    const FiniteElement &trial, const IntegrationRule &trial_ir,
    ElementTransformation &trial_Trans, const FiniteElement &test,
@@ -212,4 +214,92 @@ void VectorL2MortarIntegrator::AssembleElementMatrix(
    }
 }
 
+BilinearFormIntegrator * VectorL2MortarIntegrator::newBFormIntegrator() const { return new VectorFEMassIntegrator(); }
+
+
+void TPL2MortarIntegrator::AssembleElementMatrix(const FiniteElement &trial,
+                              const IntegrationRule &trial_ir,
+                              ElementTransformation &trial_Trans,
+                              const FiniteElement &test,
+                              const IntegrationRule &test_ir,
+                              ElementTransformation &test_Trans,
+                              DenseMatrix &elmat)
+{
+   int tr_nd = trial.GetDof();
+   int te_nd = test.GetDof();
+
+   double norm;
+
+   // If vdim is not set, set it to the space dimension
+   vdim = (vdim == -1) ? test_Trans.GetSpaceDim() : vdim;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector D;
+   Vector vec;
+   DenseMatrix K;
+   Vector test_shape;
+   Vector trial_shape;
+   DenseMatrix partelmat;
+   DenseMatrix mcoeff;
+#endif
+
+   elmat.SetSize(te_nd*vdim, tr_nd*vdim);
+   trial_shape.SetSize(tr_nd);
+   test_shape.SetSize(te_nd);
+   partelmat.SetSize(te_nd, tr_nd);
+
+   if (VQ)
+   {
+      vec.SetSize(vdim);
+   }
+   else if (MQ)
+   {
+      mcoeff.SetSize(vdim);
+   }
+
+   elmat = 0.0;
+   for (int s = 0; s < test_ir.GetNPoints(); s++)
+   {
+      trial.CalcShape(trial_ir.IntPoint(s), trial_shape);
+      test.CalcShape(test_ir.IntPoint(s), test_shape);
+
+      test_Trans.SetIntPoint(&test_ir.IntPoint(s));
+      norm = test_ir.IntPoint(s).weight * test_Trans.Weight();
+
+      MultVWt(test_shape, trial_shape, partelmat);
+
+      if (VQ)
+      {
+         VQ->Eval(vec, test_Trans, test_ir.IntPoint(s));
+         for (int k = 0; k < vdim; k++)
+         {
+            elmat.AddMatrix(norm*vec(k), partelmat, te_nd*k, tr_nd*k);
+         }
+      }
+      else if (MQ)
+      {
+         MQ->Eval(mcoeff, test_Trans, test_ir.IntPoint(s));
+         for (int i = 0; i < vdim; i++)
+            for (int j = 0; j < vdim; j++)
+            {
+               elmat.AddMatrix(norm*mcoeff(i,j), partelmat, te_nd*i, tr_nd*j);
+            }
+      }
+      else
+      {
+         if (Q)
+         {
+            norm *= Q->Eval(test_Trans, test_ir.IntPoint(s));
+         }
+         partelmat *= norm;
+         for (int k = 0; k < vdim; k++)
+         {
+            elmat.AddMatrix(partelmat, te_nd*k, tr_nd*k);
+         }
+      }
+   }
+}
+
+BilinearFormIntegrator * TPL2MortarIntegrator::newBFormIntegrator() const { return new VectorMassIntegrator(); }
+
 } // namespace mfem

fem/moonolith/mortarintegrator.hpp

@@ -60,9 +60,9 @@ public:
    virtual ~MortarIntegrator() {}
 
    /*!
-    * @return true if it uses vector fe and false otherwise
+    * @return an equivalent BilinearFormIntegrator 
     */
-   virtual bool is_vector_fe() const = 0;
+   virtual BilinearFormIntegrator * newBFormIntegrator() const = 0;
 };
 
 /*!
@@ -81,7 +81,7 @@ public:
                               ElementTransformation &test_Trans,
                               DenseMatrix &elemmat) override;
 
-   inline bool is_vector_fe() const override { return false; }
+   BilinearFormIntegrator * newBFormIntegrator() const override;
 };
 
 /*!
@@ -101,6 +101,8 @@ public:
 #endif
 
 public:
+   BilinearFormIntegrator * newBFormIntegrator() const override;
+
    VectorL2MortarIntegrator() { Init(NULL, NULL, NULL); }
    VectorL2MortarIntegrator(Coefficient *_q) { Init(_q, NULL, NULL); }
    VectorL2MortarIntegrator(VectorCoefficient *_vq) { Init(NULL, _vq, NULL); }
@@ -114,9 +116,56 @@ public:
                               ElementTransformation &test_Trans,
                               DenseMatrix &elemmat) override;
 
-   inline bool is_vector_fe() const override { return true; }
+private:
+   Coefficient *Q;
+   VectorCoefficient *VQ;
+   MatrixCoefficient *MQ;
+
+   void Init(Coefficient *q, VectorCoefficient *vq, MatrixCoefficient *mq)
+   {
+      Q = q;
+      VQ = vq;
+      MQ = mq;
+   }
+};
+
+/*!
+ * @brief Integrator for Lagrange vector finite elements. Experimental.
+ * $$ (u, v)_{L^2(\mathcal{T}_m \cap \mathcal{T}_s)}, u \in U(\mathcal{T}_m )
+ * and v \in V(\mathcal{T}_s ) $$
+ */
+class TPL2MortarIntegrator : public MortarIntegrator
+{
+public:
+#ifndef MFEM_THREAD_SAFE
+   Vector D;
+   Vector vec;
+   DenseMatrix K;
+   Vector test_shape;
+   Vector trial_shape;
+   DenseMatrix partelmat;
+   DenseMatrix mcoeff;
+#endif
+
+public:
+   BilinearFormIntegrator * newBFormIntegrator() const override;
+
+   TPL2MortarIntegrator() : vdim(-1) { Init(NULL, NULL, NULL); }
+   TPL2MortarIntegrator(Coefficient *_q) : vdim(-1) { Init(_q, NULL, NULL); }
+   TPL2MortarIntegrator(VectorCoefficient *_vq) : vdim(-1) { Init(NULL, _vq, NULL); }
+   TPL2MortarIntegrator(MatrixCoefficient *_mq) : vdim(-1) { Init(NULL, NULL, _mq); }
+   inline void SetVDim(const int _vdim) { vdim = _vdim; }
+
+   void AssembleElementMatrix(const FiniteElement &trial,
+                              const IntegrationRule &trial_ir,
+                              ElementTransformation &trial_Trans,
+                              const FiniteElement &test,
+                              const IntegrationRule &test_ir,
+                              ElementTransformation &test_Trans,
+                              DenseMatrix &elemmat) override;
 
 private:
+   int vdim;
    Coefficient *Q;
    VectorCoefficient *VQ;
    MatrixCoefficient *MQ;

fem/pgridfunc.cpp

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

fem/transfer.cpp

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

general/backends.hpp

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

general/isockstream.cpp

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

general/table.cpp

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

general/table.hpp

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

linalg/CMakeLists.txt

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

linalg/complex_densemat.cpp

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

linalg/densemat.cpp

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

linalg/lapack.hpp

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

linalg/solvers.cpp

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

mesh/mesh.cpp

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

mesh/mesh.hpp

@@ -1537,6 +1537,9 @@ public:
    /// @note The returned Table should be deleted by the caller
    Table *GetVertexToElementTable();
 
+   /// @note The returned Table should be deleted by the caller
+   Table *GetVertexToBdrElementTable();
+
    /// Return the "face"-element Table. Here "face" refers to face (3D),
    /// edge (2D), or vertex (1D).
    ///

mesh/nurbs.cpp

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

mesh/nurbs.hpp

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

mesh/pumi.cpp

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

miniapps/dpg/acoustics.cpp

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

miniapps/dpg/convection-diffusion.cpp

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

miniapps/dpg/maxwell.cpp

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

miniapps/dpg/pacoustics.cpp

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

miniapps/dpg/pconvection-diffusion.cpp

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

miniapps/dpg/pdiffusion.cpp

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

miniapps/dpg/pmaxwell.cpp

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

miniapps/nurbs/CMakeLists.txt

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

miniapps/nurbs/makefile

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

miniapps/nurbs/nurbs_ex1.cpp

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

miniapps/nurbs/nurbs_ex24.cpp

@@ -0,0 +1,459 @@
+//                                MFEM Example 24 -- modified for NURBS FE
+//
+// Compile with: make nurbs_ex24
+//
+// Sample runs:  nurbs_ex24 -m ../../data/pipe-nurbs-2d.mesh -o 2
+//               nurbs_ex24 -m ../../data/pipe-nurbs-2d.mesh -p 2
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2 -p 1
+//               nurbs_ex24 -m ../../data/cube-nurbs.mesh -o 2 -p 2
+//               nurbs_ex24 -m ../../data/escher.mesh
+//               nurbs_ex24 -m ../../data/escher.mesh -o 2
+//               nurbs_ex24 -m ../../data/fichera.mesh
+//               nurbs_ex24 -m ../../data/fichera-q2.vtk
+//               nurbs_ex24 -m ../../data/fichera-q3.mesh
+//               nurbs_ex24 -m ../../data/amr-quad.mesh -o 2
+//               nurbs_ex24 -m ../../data/amr-hex.mesh
+//
+// Device sample runs -- do not work for NURBS:
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d cuda
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d raja-cuda
+//               nurbs_ex24 -m ../../data/escher.mesh -pa -d raja-omp
+//
+// Description:  This example code illustrates usage of mixed finite element
+//               spaces, with three variants:
+//
+//               0) (grad p, u) for p in H^1 tested against u in H(curl)
+//               1) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               2) (div v, q) for v in H(div) tested against q in L_2
+//
+//               Using different approaches, we project the gradient, curl, or
+//               divergence to the appropriate space.
+//
+//               NURBS-based H(curl) and H(div) spaces only implemented
+//               for meshes consisting of a single patch.
+//
+//               We recommend viewing examples 1, 3, and 5 before viewing this
+//               example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+real_t p_exact(const Vector &x);
+void gradp_exact(const Vector &, Vector &);
+real_t div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);
+
+int dim;
+real_t freq = 1.0, kappa;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/cube-nurbs.mesh";
+   int ref_levels = -1;
+   int order = 1;
+   bool NURBS = true;
+   int prob = 0;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of times to refine the mesh uniformly, -1 for auto.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&NURBS, "-n", "--nurbs", "-nn","--no-nurbs",
+                  "NURBS.");
+   args.AddOption(&prob, "-p", "--problem-type",
+                  "Choose between 0: grad, 1: curl, 2: div");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   if ((prob == 1) &&(dim != 3))
+   {
+      MFEM_ABORT("The curl problem is only defined in 3D.");
+   }
+   int sdim = mesh->SpaceDimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 50,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels = (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use Nedelec or
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *trial_fec = nullptr;
+   FiniteElementCollection *test_fec = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+   if (mesh->NURBSext && NURBS)
+   {
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      if (prob == 0)
+      {
+         trial_fec  = new NURBSFECollection(order);
+         test_fec = new NURBS_HCurlFECollection(order, dim);
+      }
+      else if (prob == 1)
+      {
+         trial_fec = new NURBS_HCurlFECollection(order, dim);
+         test_fec = new NURBS_HDivFECollection(order, dim);
+      }
+      else
+      {
+         trial_fec = new NURBS_HDivFECollection(order, dim);
+         test_fec  = new NURBSFECollection(order);
+      }
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      if (prob == 0)
+      {
+         trial_fec = new H1_FECollection(order, dim);
+         test_fec = new ND_FECollection(order, dim);
+      }
+      else if (prob == 1)
+      {
+         trial_fec = new ND_FECollection(order, dim);
+         test_fec = new RT_FECollection(order-1, dim);
+      }
+      else
+      {
+         trial_fec = new RT_FECollection(order-1, dim);
+         test_fec = new L2_FECollection(order-1, dim);
+      }
+   }
+
+   FiniteElementSpace trial_fes(mesh, NURBSext, trial_fec);
+   FiniteElementSpace test_fes(mesh,trial_fes.StealNURBSext(), test_fec);
+
+   int trial_size = trial_fes.GetTrueVSize();
+   int test_size = test_fes.GetTrueVSize();
+
+   if (prob == 0)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
+      cout << "Number of H1 finite element unknowns: " << trial_size << endl;
+   }
+   else if (prob == 1)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+      cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+           endl;
+   }
+   else
+   {
+      cout << "Number of Raviart-Thomas finite element unknowns: "
+           << trial_size << endl;
+      cout << "Number of L2 finite element unknowns: " << test_size << endl;
+   }
+
+   // 6. Define the solution vector as a finite element grid function
+   //    corresponding to the trial fespace.
+   GridFunction gftest(&test_fes);
+   GridFunction gftrial(&trial_fes);
+   GridFunction x(&test_fes);
+   FunctionCoefficient p_coef(p_exact);
+   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
+   FunctionCoefficient divgradp_coef(div_gradp_exact);
+
+   if (prob == 0)
+   {
+      gftrial.ProjectCoefficient(p_coef);
+   }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
+   else
+   {
+      gftrial.ProjectCoefficient(gradp_coef);
+   }
+
+   gftrial.SetTrueVector();
+   gftrial.SetFromTrueVector();
+
+   // 7. Set up the bilinear forms for L2 projection.
+   ConstantCoefficient one(1.0);
+   BilinearForm a(&test_fes);
+   MixedBilinearForm a_mixed(&trial_fes, &test_fes);
+   if (pa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+   }
+
+   if (prob == 0)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
+   }
+   else if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
+   }
+   else
+   {
+      a.AddDomainIntegrator(new MassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
+   }
+
+   // 8. Assemble the bilinear form and the corresponding linear system,
+   //    applying any necessary transformations such as: eliminating boundary
+   //    conditions, applying conforming constraints for non-conforming AMR,
+   //    static condensation, etc.
+   if (static_cond) { a.EnableStaticCondensation(); }
+
+   a.Assemble();
+   if (!pa) { a.Finalize(); }
+
+   a_mixed.Assemble();
+   if (!pa) { a_mixed.Finalize(); }
+
+   if (pa)
+   {
+      a_mixed.Mult(gftrial, x);
+   }
+   else
+   {
+      SparseMatrix& mixed = a_mixed.SpMat();
+      mixed.Mult(gftrial, x);
+   }
+
+   // 9. Define and apply a PCG solver for Ax = b with Jacobi preconditioner.
+   {
+      GridFunction rhs(&test_fes);
+      rhs = x;
+      x = 0.0;
+
+      CGSolver cg;
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(1000);
+      cg.SetPrintLevel(1);
+      if (pa)
+      {
+         Array<int> ess_tdof_list; // empty
+         OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
+
+         cg.SetOperator(a);
+         cg.SetPreconditioner(Jacobi);
+         cg.Mult(rhs, x);
+      }
+      else
+      {
+         SparseMatrix& Amat = a.SpMat();
+         DSmoother Jacobi(Amat);
+
+         cg.SetOperator(Amat);
+         cg.SetPreconditioner(Jacobi);
+         cg.Mult(rhs, x);
+      }
+   }
+
+   // 10. Compute the projection of the exact field.
+   GridFunction exact_proj(&test_fes);
+   if (prob == 0)
+   {
+      exact_proj.ProjectCoefficient(gradp_coef);
+   }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
+   else
+   {
+      exact_proj.ProjectCoefficient(divgradp_coef);
+   }
+
+   exact_proj.SetTrueVector();
+   exact_proj.SetFromTrueVector();
+
+   // 11. Compute and print the L_2 norm of the error.
+   if (prob == 0)
+   {
+      real_t errSol = x.ComputeL2Error(gradp_coef);
+      real_t errProj = exact_proj.ComputeL2Error(gradp_coef);
+
+      cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
+           "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
+      cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+   else if (prob == 1)
+   {
+      real_t errSol = x.ComputeL2Error(curlv_coef);
+      real_t errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
+           "|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+      cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+   else
+   {
+      int order_quad = max(3, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      real_t errSol = x.ComputeL2Error(divgradp_coef, irs);
+      real_t errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
+
+      cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
+           "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
+
+      cout << " Projection f_h of exact div v in L_2: || f_h - div v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
+
+   // 12. Save the refined mesh and the solution. This output can be viewed
+   //     later using GLVis: "glvis -m refined.mesh -g sol.gf".
+   ofstream mesh_ofs("refined.mesh");
+   mesh_ofs.precision(8);
+   mesh->Print(mesh_ofs);
+   ofstream sol_ofs("sol.gf");
+   sol_ofs.precision(8);
+   x.Save(sol_ofs);
+
+   // 13. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *mesh << x << flush;
+   }
+
+   // 14. Free the used memory.
+   delete trial_fec;
+   delete test_fec;
+   delete mesh;
+
+   return 0;
+}
+
+real_t p_exact(const Vector &x)
+{
+   if (dim == 3)
+   {
+      return sin(x(0)) * sin(x(1)) * sin(x(2));
+   }
+   else if (dim == 2)
+   {
+      return sin(x(0)) * sin(x(1));
+   }
+
+   return 0.0;
+}
+
+void gradp_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+      f(0) = cos(x(0)) * sin(x(1)) * sin(x(2));
+      f(1) = sin(x(0)) * cos(x(1)) * sin(x(2));
+      f(2) = sin(x(0)) * sin(x(1)) * cos(x(2));
+   }
+   else
+   {
+      f(0) = cos(x(0)) * sin(x(1));
+      f(1) = sin(x(0)) * cos(x(1));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}
+
+real_t div_gradp_exact(const Vector &x)
+{
+   if (dim == 3)
+   {
+      return -3.0 * sin(x(0)) * sin(x(1)) * sin(x(2));
+   }
+   else if (dim == 2)
+   {
+      return -2.0 * sin(x(0)) * sin(x(1));
+   }
+
+   return 0.0;
+}
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}

miniapps/nurbs/nurbs_ex3.cpp

@@ -0,0 +1,284 @@
+//                                MFEM Example 3 -- modified for NURBS FE
+//
+// Compile with: make nurbs_ex3
+//
+// Sample runs:  nurbs_ex3 -m ../../data/square-nurbs.mesh
+//               nurbs_ex3 -m ../../data/square-nurbs.mesh -o 2
+//               nurbs_ex3 -m ../../data/cube-nurbs.mesh
+//
+// Description:  This example code solves a simple electromagnetic diffusion
+//               problem corresponding to the second order definite Maxwell
+//               equation curl curl E + E = f with boundary condition
+//               E x n = <given tangential field>. Here, we use a given exact
+//               solution E and compute the corresponding r.h.s. f.
+//               We discretize with Nedelec finite elements in 2D or 3D.
+//
+//               The example demonstrates the use of H(curl) finite element
+//               spaces with the curl-curl and the (vector finite element) mass
+//               bilinear form, as well as the computation of discretization
+//               error when the exact solution is known. Static condensation is
+//               also illustrated.
+//
+//               NURBS-based H(curl) spaces only implemented for meshes
+//               consisting of a single patch.
+//
+//               We recommend viewing examples 1-2 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Exact solution, E, and r.h.s., f. See below for implementation.
+void E_exact(const Vector &, Vector &);
+void f_exact(const Vector &, Vector &);
+real_t freq = 1.0, kappa;
+int dim;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/square-nurbs.mesh";
+   int ref_levels = -1;
+   bool NURBS = true;
+   int order = 1;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of times to refine the mesh uniformly, -1 for auto.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&NURBS, "-n", "--nurbs", "-nn","--no-nurbs",
+                  "NURBS.");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 50,000
+   //    elements.
+   {
+      if (ref_levels < 0)
+      {
+         ref_levels =
+            (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *fec = nullptr;
+   NURBSExtension *NURBSext = nullptr;
+
+   if (mesh->NURBSext && NURBS)
+   {
+      fec = new NURBS_HCurlFECollection(order,dim);
+      NURBSext  = new NURBSExtension(mesh->NURBSext, order);
+      mfem::out<<"Create NURBS fec and ext"<<std::endl;
+   }
+   else
+   {
+      NURBS = false;
+      fec = new ND_FECollection(order, dim);
+      mfem::out<<"Create Normal fec"<<std::endl;
+   }
+
+   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, NURBSext, fec);
+   cout << "Number of finite element unknowns: "
+        << fespace->GetTrueVSize() << endl;
+
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
+   //    In this example, the boundary conditions are defined by marking all
+   //    the boundary attributes from the mesh as essential (Dirichlet) and
+   //    converting them to a list of true dofs.
+   Array<int> ess_tdof_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+   cout << "Number of knowns in essential BCs: "
+        << ess_tdof_list.Size() << endl;
+
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side
+   //    of the FEM linear system, which in this case is (f,phi_i) where f is
+   //    given by the function f_exact and phi_i are the basis functions in the
+   //    finite element fespace.
+   VectorFunctionCoefficient f(sdim, f_exact);
+   LinearForm *b = new LinearForm(fespace);
+   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+   b->Assemble();
+
+   // 8. Define the solution vector x as a finite element grid function
+   //    corresponding to fespace. Initialize x by projecting the exact
+   //    solution. Note that only values from the boundary edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   GridFunction x(fespace);
+   VectorFunctionCoefficient E(sdim, E_exact);
+   x.ProjectCoefficient(E);
+
+   // 9. Set up the bilinear form corresponding to the EM diffusion operator
+   //    curl muinv curl + sigma I, by adding the curl-curl and the mass domain
+   //    integrators.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(1.0);
+   BilinearForm *a = new BilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+
+   // 10. Assemble the bilinear form and the corresponding linear system,
+   //     applying any necessary transformations such as: eliminating boundary
+   //     conditions, applying conforming constraints for non-conforming AMR,
+   //     static condensation, etc.
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   OperatorPtr A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+   cout << "Size of linear system: " << A->Height() << endl;
+
+   // 11. Solve the linear system A X = B.
+   if (pa) // Jacobi preconditioning in partial assembly mode
+   {
+      OperatorJacobiSmoother M(*a, ess_tdof_list);
+      PCG(*A, M, B, X, 1, 1000, 1e-12, 0.0);
+   }
+   else
+   {
+#ifndef MFEM_USE_SUITESPARSE
+      // 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
+      //     solve the system Ax=b with PCG.
+      GSSmoother M((SparseMatrix&)(*A));
+      PCG(*A, M, B, X, 1, 500, 1e-12, 0.0);
+#else
+      // 11. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the
+      //     system.
+      UMFPackSolver umf_solver;
+      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver.SetOperator(*A);
+      umf_solver.Mult(B, X);
+#endif
+   }
+
+   // 12. Recover the solution as a finite element grid function.
+   a->RecoverFEMSolution(X, *b, x);
+
+   // 13. Compute and print the L^2 norm of the error.
+   cout << "\n|| E_h - E ||_{L^2} = " << x.ComputeL2Error(E) << '\n' << endl;
+
+   // 14. Save the refined mesh and the solution. This output can be viewed
+   //     later using GLVis: "glvis -m refined.mesh -g sol.gf".
+   {
+      ofstream mesh_ofs("refined.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+      ofstream sol_ofs("sol.gf");
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 15. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *mesh << x << flush;
+   }
+
+   // 16. Create output in visit format
+   VisItDataCollection visit_dc("Example3", mesh);
+   visit_dc.RegisterField("x", &x);
+   visit_dc.Save();
+
+   // 17. Free the used memory.
+   delete a;
+   delete sigma;
+   delete muinv;
+   delete b;
+   delete fespace;
+   delete fec;
+   delete mesh;
+
+   return 0;
+}
+
+
+void E_exact(const Vector &x, Vector &E)
+{
+   if (dim == 3)
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+void f_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (1. + kappa * kappa) * sin(kappa * x(0));
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}

miniapps/nurbs/nurbs_ex5.cpp

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

miniapps/nurbs/nurbs_patch_ex1.cpp

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

miniapps/nurbs/nurbs_solenoidal.cpp

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

tests/unit/fem/test_hp_transfer.cpp

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