cell_hex.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2014 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


// C++ includes
#include <algorithm> // for std::min, std::max

// Local includes
#include "libmesh/cell_hex.h"
#include "libmesh/cell_hex8.h"
#include "libmesh/face_quad4.h"

namespace libMesh
{




// ------------------------------------------------------------
// Hex class member functions
dof_id_type Hex::key (const unsigned int s) const
{
  libmesh_assert_less (s, this->n_sides());

  // Think of a unit cube: (-1,1) x (-1,1)x (-1,1)
  switch (s)
    {
    case 0:  // the face at z = -1

      return
        this->compute_key (this->node(0),
                           this->node(3),
                           this->node(2),
                           this->node(1));

    case 1:  // the face at y = -1

      return
        this->compute_key (this->node(0),
                           this->node(1),
                           this->node(5),
                           this->node(4));

    case 2:  // the face at x = 1

      return
        this->compute_key (this->node(1),
                           this->node(2),
                           this->node(6),
                           this->node(5));

    case 3: // the face at y = 1

      return
        this->compute_key (this->node(2),
                           this->node(3),
                           this->node(7),
                           this->node(6));

    case 4: // the face at x = -1

      return
        this->compute_key (this->node(3),
                           this->node(0),
                           this->node(4),
                           this->node(7));

    case 5: // the face at z = 1

      return
        this->compute_key (this->node(4),
                           this->node(5),
                           this->node(6),
                           this->node(7));

    default:
      libmesh_error_msg("Invalid s = " << s);
    }

  libmesh_error_msg("We'll never get here!");
  return 0;
}



UniquePtr<Elem> Hex::side (const unsigned int i) const
{
  libmesh_assert_less (i, this->n_sides());

  Elem* face = new Quad4;

  // Think of a unit cube: (-1,1) x (-1,1) x (-1,1)
  switch (i)
    {
    case 0:  // the face at z = -1
      {
        face->set_node(0) = this->get_node(0);
        face->set_node(1) = this->get_node(3);
        face->set_node(2) = this->get_node(2);
        face->set_node(3) = this->get_node(1);
        break;
      }
    case 1:  // the face at y = -1
      {
        face->set_node(0) = this->get_node(0);
        face->set_node(1) = this->get_node(1);
        face->set_node(2) = this->get_node(5);
        face->set_node(3) = this->get_node(4);
        break;
      }
    case 2:  // the face at x = 1
      {
        face->set_node(0) = this->get_node(1);
        face->set_node(1) = this->get_node(2);
        face->set_node(2) = this->get_node(6);
        face->set_node(3) = this->get_node(5);
        break;
      }
    case 3: // the face at y = 1
      {
        face->set_node(0) = this->get_node(2);
        face->set_node(1) = this->get_node(3);
        face->set_node(2) = this->get_node(7);
        face->set_node(3) = this->get_node(6);
        break;
      }
    case 4: // the face at x = -1
      {
        face->set_node(0) = this->get_node(3);
        face->set_node(1) = this->get_node(0);
        face->set_node(2) = this->get_node(4);
        face->set_node(3) = this->get_node(7);
        break;
      }
    case 5: // the face at z = 1
      {
        face->set_node(0) = this->get_node(4);
        face->set_node(1) = this->get_node(5);
        face->set_node(2) = this->get_node(6);
        face->set_node(3) = this->get_node(7);
        break;
      }
    default:
      libmesh_error_msg("Unsupported side i = " << i);
    }

  return UniquePtr<Elem>(face);
}



bool Hex::is_child_on_side(const unsigned int c,
                           const unsigned int s) const
{
  libmesh_assert_less (c, this->n_children());
  libmesh_assert_less (s, this->n_sides());

  // This array maps the Hex8 node numbering to the Hex8 child
  // numbering.  I.e.
  //   node 6 touches child 7, and
  //   node 7 touches child 6, etc.
  const unsigned int node_child_map[8] = { 0, 1, 3, 2, 4, 5, 7, 6 };

  for (unsigned int i = 0; i != 4; ++i)
    if (node_child_map[Hex8::side_nodes_map[s][i]] == c)
      return true;

  return false;
}



bool Hex::is_edge_on_side(const unsigned int e,
                          const unsigned int s) const
{
  libmesh_assert_less (e, this->n_edges());
  libmesh_assert_less (s, this->n_sides());

  return (is_node_on_side(Hex8::edge_nodes_map[e][0],s) &&
          is_node_on_side(Hex8::edge_nodes_map[e][1],s));
}



unsigned int Hex::opposite_side(const unsigned int side_in) const
{
  libmesh_assert_less (side_in, 6);
  static const unsigned char hex_opposites[6] = {5, 3, 4, 1, 2, 0};
  return hex_opposites[side_in];
}



unsigned int Hex::opposite_node(const unsigned int node_in,
                                const unsigned int side_in) const
{
  libmesh_assert_less (node_in, 26);
  libmesh_assert_less (node_in, this->n_nodes());
  libmesh_assert_less (side_in, this->n_sides());
  libmesh_assert(this->is_node_on_side(node_in, side_in));

  static const unsigned char side05_nodes_map[] =
    {4, 5, 6, 7, 0, 1, 2, 3, 16, 17, 18, 19, 255, 255, 255, 255, 8, 9, 10, 11, 25, 255, 255, 255, 255, 20};
  static const unsigned char side13_nodes_map[] =
    {3, 2, 1, 0, 7, 6, 5, 4, 10, 255, 8, 255, 15, 14, 13, 12, 18, 255, 16, 255, 255, 23, 255, 21, 255, 255};
  static const unsigned char side24_nodes_map[] =
    {1, 0, 3, 2, 5, 4, 7, 6, 255, 11, 255, 9, 13, 12, 15, 14, 255, 19, 255, 17, 255, 255, 24, 255, 22, 255};

  switch (side_in)
    {
    case 0:
    case 5:
      return side05_nodes_map[node_in];
    case 1:
    case 3:
      return side13_nodes_map[node_in];
    case 2:
    case 4:
      return side24_nodes_map[node_in];
    default:
      libmesh_error_msg("Unsupported side_in = " << side_in);
    }

  libmesh_error_msg("We'll never get here!");
  return 255;
}



Real Hex::quality (const ElemQuality q) const
{
  switch (q)
    {

    case DIAGONAL:
      {
        // Diagonal between node 0 and node 6
        const Real d06 = this->length(0,6);

        // Diagonal between node 3 and node 5
        const Real d35 = this->length(3,5);

        // Diagonal between node 1 and node 7
        const Real d17 = this->length(1,7);

        // Diagonal between node 2 and node 4
        const Real d24 = this->length(2,4);

        // Find the biggest and smallest diagonals
        const Real min = std::min(d06, std::min(d35, std::min(d17, d24)));
        const Real max = std::max(d06, std::max(d35, std::max(d17, d24)));

        libmesh_assert_not_equal_to (max, 0.0);

        return min / max;

        break;
      }

    case TAPER:
      {

        const Real d01 = this->length(0,1);
        const Real d12 = this->length(1,2);
        const Real d23 = this->length(2,3);
        const Real d03 = this->length(0,3);
        const Real d45 = this->length(4,5);
        const Real d56 = this->length(5,6);
        const Real d67 = this->length(6,7);
        const Real d47 = this->length(4,7);
        const Real d04 = this->length(0,4);
        const Real d15 = this->length(1,5);
        const Real d37 = this->length(3,7);
        const Real d26 = this->length(2,6);

        std::vector<Real> edge_ratios(12);
        // Front
        edge_ratios[0] = std::min(d01, d45) / std::max(d01, d45);
        edge_ratios[1] = std::min(d04, d15) / std::max(d04, d15);

        // Right
        edge_ratios[2] = std::min(d15, d26) / std::max(d15, d26);
        edge_ratios[3] = std::min(d12, d56) / std::max(d12, d56);

        // Back
        edge_ratios[4] = std::min(d67, d23) / std::max(d67, d23);
        edge_ratios[5] = std::min(d26, d37) / std::max(d26, d37);

        // Left
        edge_ratios[6] = std::min(d04, d37) / std::max(d04, d37);
        edge_ratios[7] = std::min(d03, d47) / std::max(d03, d47);

        // Bottom
        edge_ratios[8] = std::min(d01, d23) / std::max(d01, d23);
        edge_ratios[9] = std::min(d03, d12) / std::max(d03, d12);

        // Top
        edge_ratios[10] = std::min(d45, d67) / std::max(d45, d67);
        edge_ratios[11] = std::min(d56, d47) / std::max(d56, d47);

        return *(std::min_element(edge_ratios.begin(), edge_ratios.end())) ;

        break;
      }


    case STRETCH:
      {
        const Real sqrt3 = 1.73205080756888;

        const Real d06 = this->length(0,6);
        const Real d17 = this->length(1,7);
        const Real d35 = this->length(3,5);
        const Real d24 = this->length(2,4);
        const Real max_diag = std::max(d06, std::max(d17, std::max(d35, d24)));

        libmesh_assert_not_equal_to ( max_diag, 0.0 );

        std::vector<Real> edges(12);
        edges[0]  = this->length(0,1);
        edges[1]  = this->length(1,2);
        edges[2]  = this->length(2,3);
        edges[3]  = this->length(0,3);
        edges[4]  = this->length(4,5);
        edges[5]  = this->length(5,6);
        edges[6]  = this->length(6,7);
        edges[7]  = this->length(4,7);
        edges[8]  = this->length(0,4);
        edges[9]  = this->length(1,5);
        edges[10] = this->length(2,6);
        edges[11] = this->length(3,7);

        const Real min_edge = *(std::min_element(edges.begin(), edges.end()));
        return sqrt3 * min_edge / max_diag ;
      }


    default:
      return Elem::quality(q);
    }

  libmesh_error_msg("We'll never get here!");
  return 0.;
}



std::pair<Real, Real> Hex::qual_bounds (const ElemQuality q) const
{
  std::pair<Real, Real> bounds;

  switch (q)
    {

    case ASPECT_RATIO:
      bounds.first  = 1.;
      bounds.second = 4.;
      break;

    case SKEW:
      bounds.first  = 0.;
      bounds.second = 0.5;
      break;

    case SHEAR:
    case SHAPE:
      bounds.first  = 0.3;
      bounds.second = 1.;
      break;

    case CONDITION:
      bounds.first  = 1.;
      bounds.second = 8.;
      break;

    case JACOBIAN:
      bounds.first  = 0.5;
      bounds.second = 1.;
      break;

    case DISTORTION:
      bounds.first  = 0.6;
      bounds.second = 1.;
      break;

    case TAPER:
      bounds.first  = 0.;
      bounds.second = 0.4;
      break;

    case STRETCH:
      bounds.first  = 0.25;
      bounds.second = 1.;
      break;

    case DIAGONAL:
      bounds.first  = 0.65;
      bounds.second = 1.;
      break;

    case SIZE:
      bounds.first  = 0.5;
      bounds.second = 1.;
      break;

    default:
      libMesh::out << "Warning: Invalid quality measure chosen." << std::endl;
      bounds.first  = -1;
      bounds.second = -1;
    }

  return bounds;
}



const unsigned short int Hex::_second_order_vertex_child_number[27] =
  {
    99,99,99,99,99,99,99,99, // Vertices
    0,1,2,0,0,1,2,3,4,5,6,5, // Edges
    0,0,1,2,0,4,             // Faces
    0                        // Interior
  };



const unsigned short int Hex::_second_order_vertex_child_index[27] =
  {
    99,99,99,99,99,99,99,99, // Vertices
    1,2,3,3,4,5,6,7,5,6,7,7, // Edges
    2,5,6,7,7,6,             // Faces
    6                        // Interior
  };


const unsigned short int Hex::_second_order_adjacent_vertices[12][2] =
  {
    { 0,  1}, // vertices adjacent to node 8
    { 1,  2}, // vertices adjacent to node 9
    { 2,  3}, // vertices adjacent to node 10
    { 0,  3}, // vertices adjacent to node 11

    { 0,  4}, // vertices adjacent to node 12
    { 1,  5}, // vertices adjacent to node 13
    { 2,  6}, // vertices adjacent to node 14
    { 3,  7}, // vertices adjacent to node 15

    { 4,  5}, // vertices adjacent to node 16
    { 5,  6}, // vertices adjacent to node 17
    { 6,  7}, // vertices adjacent to node 18
    { 4,  7}  // vertices adjacent to node 19
  };

} // namespace libMesh