Pyramid18 geometry + LAGRANGE support

include/Makefile.in

@@ -717,6 +717,7 @@ include_HEADERS = \
         geom/cell_pyramid.h \
         geom/cell_pyramid13.h \
         geom/cell_pyramid14.h \
+        geom/cell_pyramid18.h \
         geom/cell_pyramid5.h \
         geom/cell_tet.h \
         geom/cell_tet10.h \
@@ -1074,6 +1075,7 @@ include_HEADERS = \
         utils/tree_node.h \
         utils/utility.h \
         utils/vectormap.h \
+        utils/win_gettimeofday.h \
         utils/xdr_cxx.h 
 
 

include/fe/fe.h

@@ -1324,6 +1324,16 @@ OutputShape fe_fdm_deriv(const Elem * elem,
                             const unsigned int, const Point &,
                             const bool));
 
+template <typename OutputShape>
+OutputShape fe_fdm_deriv(const ElemType type,
+                         const Order order,
+                         const unsigned int i,
+                         const unsigned int j,
+                         const Point & p,
+                         OutputShape(*shape_func)
+                           (const ElemType, const Order,
+                            const unsigned int, const Point &));
+
 template <typename OutputShape>
 OutputShape
 fe_fdm_second_deriv(const Elem * elem,
@@ -1337,6 +1347,18 @@ fe_fdm_second_deriv(const Elem * elem,
                        const unsigned int, const unsigned int,
                        const Point &, const bool));
 
+template <typename OutputShape>
+OutputShape fe_fdm_second_deriv(const ElemType type,
+                                const Order order,
+                                const unsigned int i,
+                                const unsigned int j,
+                                const Point & p,
+                                OutputShape(*deriv_func)
+                                  (const ElemType, const Order,
+                                   const unsigned int,
+                                   const unsigned int,
+                                   const Point &));
+
 /**
  * Helper functions for Lagrange-based basis functions.
  */

include/geom/cell_prism20.h

@@ -211,7 +211,8 @@ class Prism20 final : public Prism
                             std::vector<dof_id_type> & conn) const override;
 
   /**
-   * \returns 2 for all edge nodes and 4 for face nodes.
+   * \returns 2 for all edge nodes, 4 for quad face nodes, 6 for tri
+   * face nodes.
    */
   virtual unsigned int n_second_order_adjacent_vertices (const unsigned int) const override;
 

include/geom/cell_prism21.h

@@ -214,7 +214,8 @@ class Prism21 final : public Prism
                             std::vector<dof_id_type> & conn) const override;
 
   /**
-   * \returns 2 for all edge nodes and 4 for face nodes.
+   * \returns 2 for all edge nodes, 4 for quad face nodes, 3 for tri
+   * face nodes, 6 for the interior node.
    */
   virtual unsigned int n_second_order_adjacent_vertices (const unsigned int) const override;
 

include/geom/cell_pyramid18.h

@@ -0,0 +1,287 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2022 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+
+
+#ifndef LIBMESH_CELL_PYRAMID18_H
+#define LIBMESH_CELL_PYRAMID18_H
+
+// Local includes
+#include "libmesh/cell_pyramid.h"
+
+namespace libMesh
+{
+
+/**
+ * The \p Pyramid18 is an element in 3D composed of 18 nodes, designed
+ * to interface with a QUAD9 element on the base and a TRI7 element on
+ * each of the triangular faces.  Cubit will generate hybrid meshes
+ * with linear pyramids, but as of version 18 will not export
+ * quadratic pyramids.  Paraview may support 13-node pyramids, but
+ * does not render 18-node pyramids correctly.  So even if this
+ * element works in libmesh, we are currently limited in what we can do
+ * with it outside the library...
+ *
+ * The node numbering for the pyramid18 is given below:
+ *
+ * \verbatim
+ *   PYRAMID18:
+ *                       o 4
+ *                     //|\
+ *                    // | \
+ *                   //  |  \
+ *                  //   |   \
+ *              12 o/    |    o 11
+ *                //     |     \
+ *               /o 9    o 10   \
+ *              //       |       \          zeta
+ *             //        |        \          ^   eta (into page)
+ *          3 o/.......o.|........o 2        | /
+ *           ./       7  |       /           |/
+ *          ./           |      /            o---> xi
+ *         ./            |     /
+ *        ./             |    /
+ *     8 o/       o      |   o 6
+ *      ./        13     |  /
+ *     ./                | /
+ *    ./                 |/
+ *    o--------o---------o
+ *    0        5         1
+ * \endverbatim
+ *
+ * And it also includes four triangle face nodes:
+ * Node 14, on side 0, equidistant from 0/1/4 or 5/9/10
+ * Node 15, on side 1, equidistant from 1/2/4 or 6/10/11
+ * Node 16, on side 2, equidistant from 2/3/4 or 7/11/12
+ * Node 17, on side 3, equidistant from 0/3/4 or 8/9/12
+ *
+ * (xi, eta, zeta): { zeta-1 <= xi   <= 1-zeta
+ *                  { zeta-1 <= eta  <= 1-zeta
+ *                  {      0 <= zeta <= 1
+ * are the reference element coordinates associated with the given
+ * numbering.
+ *
+ * \author Roy H. Stogner
+ * \date 2022
+ * \brief A 3D pyramid element with 18 nodes.
+ */
+class Pyramid18 final : public Pyramid
+{
+public:
+
+  /**
+   * Constructor.  By default this element has no parent.
+   */
+  explicit
+  Pyramid18 (Elem * p=nullptr) :
+    Pyramid(Pyramid18::n_nodes(), p, _nodelinks_data)
+  {}
+
+  Pyramid18 (Pyramid18 &&) = delete;
+  Pyramid18 (const Pyramid18 &) = delete;
+  Pyramid18 & operator= (const Pyramid18 &) = delete;
+  Pyramid18 & operator= (Pyramid18 &&) = delete;
+  virtual ~Pyramid18() = default;
+
+  /**
+   * \returns 18.
+   */
+  virtual unsigned int n_nodes() const override { return num_nodes; }
+
+  /**
+   * \returns \p PYRAMID18.
+   */
+  virtual ElemType type () const override { return PYRAMID18; }
+
+  /**
+   * FIXME: we don't yet have a refinement pattern for pyramids...
+   * \returns 1.
+   */
+  virtual unsigned int n_sub_elem() const override { return 1; }
+
+  /**
+   * \returns \p true if the specified (local) node number is a vertex.
+   */
+  virtual bool is_vertex(const unsigned int i) const override;
+
+  /**
+   * \returns \p true if the specified (local) node number is an edge.
+   */
+  virtual bool is_edge(const unsigned int i) const override;
+
+  /**
+   * \returns \p true if the specified (local) node number is a face.
+   */
+  virtual bool is_face(const unsigned int i) const override;
+
+  /**
+   * \returns \p true if the specified (local) node number is on the
+   * specified side.
+   */
+  virtual bool is_node_on_side(const unsigned int n,
+                               const unsigned int s) const override;
+
+  virtual std::vector<unsigned int> nodes_on_side(const unsigned int s) const override;
+
+  virtual std::vector<unsigned int> nodes_on_edge(const unsigned int e) const override;
+
+  /**
+   * \returns \p true if the specified (local) node number is on the
+   * specified edge.
+   */
+  virtual bool is_node_on_edge(const unsigned int n,
+                               const unsigned int e) const override;
+
+  /**
+   * \returns \p true if the element map is definitely affine within
+   * numerical tolerances.
+   */
+  virtual bool has_affine_map () const override;
+
+  /**
+   * \returns SECOND.
+   */
+  virtual Order default_order() const override;
+
+  /**
+   * Don't hide Pyramid::key() defined in the base class.
+   */
+  using Pyramid::key;
+
+  /**
+   * \returns An id associated with the \p s side of this element.
+   * The id is not necessarily unique, but should be close.  This is
+   * particularly useful in the \p MeshBase::find_neighbors() routine.
+   *
+   * We reimplement this method here for the \p Pyramid18 since we can
+   * use the center node of the base face to provide a perfect (unique)
+   * key.
+   */
+  virtual dof_id_type key (const unsigned int s) const override;
+
+  /**
+   * \returns \p Pyramid18::side_nodes_map[side][side_node] after doing some range checking.
+   */
+  virtual unsigned int local_side_node(unsigned int side,
+                                       unsigned int side_node) const override;
+
+  /**
+   * \returns \p Pyramid18::edge_nodes_map[edge][edge_node] after doing some range checking.
+   */
+  virtual unsigned int local_edge_node(unsigned int edge,
+                                       unsigned int edge_node) const override;
+
+  /**
+   * Builds a \p QUAD9 or \p TRI7 coincident with face i.
+   * The \p std::unique_ptr<Elem> handles the memory aspect.
+   */
+  virtual std::unique_ptr<Elem> build_side_ptr (const unsigned int i,
+                                                bool proxy=false) override;
+
+  /**
+   * Rebuilds a \p QUAD9 or \p TRI7 built coincident with face i.
+   */
+  virtual void build_side_ptr (std::unique_ptr<Elem> & elem,
+                               const unsigned int i) override;
+
+  /**
+   * Builds a \p EDGE3 coincident with edge i.
+   * The \p std::unique_ptr<Elem> handles the memory aspect.
+   */
+  virtual std::unique_ptr<Elem> build_edge_ptr (const unsigned int i) override;
+
+  /**
+   * Rebuilds a \p EDGE3 coincident with edge i.
+   */
+  virtual void build_edge_ptr (std::unique_ptr<Elem> & edge, const unsigned int i) override;
+
+  virtual void connectivity(const unsigned int sc,
+                            const IOPackage iop,
+                            std::vector<dof_id_type> & conn) const override;
+
+  /**
+   * \returns 2 for all edge nodes, 4 for quad face nodes, 3 for tri
+   * face nodes.
+   */
+  virtual unsigned int n_second_order_adjacent_vertices (const unsigned int n) const override;
+
+  /**
+   * \returns The element-local number of the \f$ v^{th} \f$ vertex
+   * that defines the \f$ n^{th} \f$ second-order node.
+   */
+  virtual unsigned short int second_order_adjacent_vertex (const unsigned int n,
+                                                           const unsigned int v) const override;
+
+  /**
+   * Geometric constants for Pyramid18.
+   */
+  static const int num_nodes = 18;
+  static const int num_sides = 5;
+  static const int num_edges = 8;
+  static const int num_children = 0; // not implemented
+  static const int nodes_per_side = 9;
+  static const int nodes_per_edge = 3;
+
+  /**
+   * This maps the \f$ j^{th} \f$ node of the \f$ i^{th} \f$ side to
+   * element node numbers.
+   */
+  static const unsigned int side_nodes_map[num_sides][nodes_per_side];
+
+  /**
+   * This maps the \f$ j^{th} \f$ node of the \f$ i^{th} \f$ edge to
+   * element node numbers.
+   */
+  static const unsigned int edge_nodes_map[num_edges][nodes_per_edge];
+
+  virtual void permute(unsigned int perm_num) override final;
+
+  virtual void flip(BoundaryInfo *) override final;
+
+  unsigned int center_node_on_side(const unsigned short side) const override final;
+
+  ElemType side_type (const unsigned int s) const override final;
+
+protected:
+
+  /**
+   * Data for links to nodes.
+   */
+  Node * _nodelinks_data[num_nodes];
+
+
+
+#ifdef LIBMESH_ENABLE_AMR
+
+  /**
+   * Matrix used to create the elements children.
+   */
+  virtual Real embedding_matrix (const unsigned int,
+                                 const unsigned int,
+                                 const unsigned int) const override
+  { libmesh_not_implemented(); return 0.; }
+
+  LIBMESH_ENABLE_TOPOLOGY_CACHES;
+
+#endif // LIBMESH_ENABLE_AMR
+
+};
+
+} // namespace libMesh
+
+
+#endif // LIBMESH_CELL_PYRAMID18_H

include/include_HEADERS

@@ -127,6 +127,7 @@ include_HEADERS =  \
         geom/cell_pyramid.h \
         geom/cell_pyramid13.h \
         geom/cell_pyramid14.h \
+        geom/cell_pyramid18.h \
         geom/cell_pyramid5.h \
         geom/cell_tet.h \
         geom/cell_tet10.h \
@@ -484,4 +485,5 @@ include_HEADERS =  \
         utils/tree_node.h \
         utils/utility.h \
         utils/vectormap.h \
+        utils/win_gettimeofday.h \
         utils/xdr_cxx.h 

include/libmesh/Makefile.am

@@ -117,6 +117,7 @@ BUILT_SOURCES = \
         cell_pyramid.h \
         cell_pyramid13.h \
         cell_pyramid14.h \
+        cell_pyramid18.h \
         cell_pyramid5.h \
         cell_tet.h \
         cell_tet10.h \
@@ -911,6 +912,9 @@ cell_pyramid13.h: $(top_srcdir)/include/geom/cell_pyramid13.h
 cell_pyramid14.h: $(top_srcdir)/include/geom/cell_pyramid14.h
 	$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
 
+cell_pyramid18.h: $(top_srcdir)/include/geom/cell_pyramid18.h
+	$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
+
 cell_pyramid5.h: $(top_srcdir)/include/geom/cell_pyramid5.h
 	$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@