cell_hex8.h

// 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_HEX8_H
#define LIBMESH_CELL_HEX8_H

// Local includes
#include "libmesh/cell_hex.h"

namespace libMesh
{

/**
 * The \p Hex8 is an element in 3D composed of 8 nodes.  It is
 * numbered like this:
 *
 * \verbatim
 *   HEX8: 7        6
 *         o--------z
 *        /:       /|         zeta
 *       / :      / |          ^   eta (into page)
 *    4 /  :   5 /  |          | /
 *     o--------o   |          |/
 *     |   o....|...o 2        o---> xi
 *     |  .3    |  /
 *     | .      | /
 *     |.       |/
 *     o--------o
 *     0        1
 * \endverbatim
 *
 * (xi, eta, zeta) in [-1,1]^3 are the reference element coordinates
 * associated with the given numbering.
 *
 * \author Benjamin S. Kirk
 * \date 2002
 * \brief A 3D hexahedral element with 8 nodes.
 */
class Hex8 final : public Hex
{
public:

  /**
   * Constructor.  By default this element has no parent.
   */
  explicit
  Hex8 (Elem * p=nullptr) :
    Hex(Hex8::n_nodes(), p, _nodelinks_data)
  {}

  Hex8 (Hex8 &&) = delete;
  Hex8 (const Hex8 &) = delete;
  Hex8 & operator= (const Hex8 &) = delete;
  Hex8 & operator= (Hex8 &&) = delete;
  virtual ~Hex8() = default;

  /**
   * \returns \p HEX8.
   */
  virtual ElemType type () const override { return HEX8; }

  /**
   * \returns 8.
   */
  virtual unsigned int n_nodes() const override { return num_nodes; }

  /**
   * \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 const unsigned int * nodes_on_side_ptr(const unsigned short s) const override final
  { return this->_nodes_on_side_ptr<Hex8>(s); }

  virtual std::vector<unsigned int> nodes_on_edge(const unsigned int e) const override;

  virtual const unsigned int * nodes_on_edge_ptr(const unsigned short e) const override final
  { return this->_nodes_on_edge_ptr<Hex8>(e); }

  /**
   * \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 FIRST.
   */
  virtual Order default_order() const override;

  /**
   * Builds a QUAD4 built 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 QUAD4 built coincident with face i.
   */
  virtual void build_side_ptr (std::unique_ptr<Elem> & elem,
                               const unsigned int i) override;

  /**
   * Builds a EDGE2 built 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 EDGE2 built 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;

  /**
   * Geometric constants for Hex8.
   */
  static const int num_nodes = 8;
  static const int num_sides = 6;
  static const int num_edges = 12;
  static const int num_children = 8;
  static const int nodes_per_side = 4;
  static const int nodes_per_edge = 2;

  /**
   * 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];

  /**
   * Class static helper function that computes the centroid of a
   * hexahedral region from a set of input points which are assumed to
   * be in the standard "Hex8" ordering, possibly with some duplicates
   * indicating a "degenerate" side. Hex8::true_centroid() and
   * Pyramid5::true_centroid() are implemented in terms of this
   * function.
   */
  static Point centroid_from_points(
    const Point & x0, const Point & x1, const Point & x2, const Point & x3,
    const Point & x4, const Point & x5, const Point & x6, const Point & x7);

  /**
   * We compute the centroid of the Hex using a customized numerical
   * quadrature approach that avoids unnecessary object creation/heap
   * allocations.
   */
  virtual Point true_centroid () const override;

  /**
   * A specialization for computing the area of a hexahedron
   * with flat sides.
   */
  virtual Real volume () const override;

  /**
   * Builds a bounding box out of the nodal positions
   */
  virtual BoundingBox loose_bounding_box () const override;

  virtual void permute(unsigned int perm_num) override final;

  virtual void flip(BoundaryInfo *) override final;

  ElemType side_type (const unsigned int s) const override final;

  /**
   * \returns 4. Every side has four nodes.
   */
  virtual unsigned int n_nodes_on_side(const unsigned short s) const override final
  { return this->_n_nodes_on_side_constant<Hex8>(s); }

  /**
   * \returns 2. Every edge has two nodes.
   */
  virtual unsigned int n_nodes_on_edge(const unsigned short e) const override final
  { return this->_n_nodes_on_edge_constant<Hex8>(e); }

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 i,
                                 const unsigned int j,
                                 const unsigned int k) const override
  { return _embedding_matrix[i][j][k]; }

  /**
   * Matrix that computes new nodal locations/solution values
   * from current nodes/solution.
   */
  static const Real _embedding_matrix[num_children][num_nodes][num_nodes];

  LIBMESH_ENABLE_TOPOLOGY_CACHES;

#endif // LIBMESH_ENABLE_AMR
};

} // namespace libMesh

#endif // LIBMESH_CELL_HEX8_H