face_tri6.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 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
 
// Local includes
#include "libmesh/edge_edge3.h"
#include "libmesh/face_tri6.h"
#include "libmesh/enum_io_package.h"
#include "libmesh/enum_order.h"
 
namespace libMesh
{
 
 
 
 
// ------------------------------------------------------------
// Tri6 class static member initializations
const int Tri6::num_nodes;
const int Tri6::nodes_per_side;
 
const unsigned int Tri6::side_nodes_map[Tri6::num_sides][Tri6::nodes_per_side] =
  {
    {0, 1, 3}, // Side 0
    {1, 2, 4}, // Side 1
    {2, 0, 5}  // Side 2
  };
 
 
#ifdef LIBMESH_ENABLE_AMR
 
const Real Tri6::_embedding_matrix[Tri6::num_children][Tri6::num_nodes][Tri6::num_nodes] =
  {
    // embedding matrix for child 0
    {
      //  0      1      2    3    4    5
      { 1.0,   0.0,   0.0, 0.0, 0.0, 0.0}, // 0
      { 0.0,   0.0,   0.0, 1.0, 0.0, 0.0}, // 1
      { 0.0,   0.0,   0.0, 0.0, 0.0, 1.0}, // 2
      {.375, -.125,   0.0, .75, 0.0, 0.0}, // 3
      { 0.0, -.125, -.125, 0.5, .25, 0.5}, // 4
      {.375,   0.0, -.125, 0.0, 0.0, .75}  // 5
    },
 
    // embedding matrix for child 1
    {
      //  0      1      2    3    4    5
      {  0.0,  0.0,   0.0, 1.0, 0.0, 0.0}, // 0
      {  0.0,  1.0,   0.0, 0.0, 0.0, 0.0}, // 1
      {  0.0,  0.0,   0.0, 0.0, 1.0, 0.0}, // 2
      {-.125, .375,   0.0, .75, 0.0, 0.0}, // 3
      {  0.0, .375, -.125, 0.0, .75, 0.0}, // 4
      {-.125,  0.0, -.125, 0.5, 0.5, .25}  // 5
    },
 
    // embedding matrix for child 2
    {
      //  0       1     2    3    4    5
      {  0.0,   0.0,  0.0, 0.0, 0.0, 1.0}, // 0
      {  0.0,   0.0,  0.0, 0.0, 1.0, 0.0}, // 1
      {  0.0,   0.0,  1.0, 0.0, 0.0, 0.0}, // 2
      {-.125, -.125,  0.0, .25, 0.5, 0.5}, // 3
      {  0.0, -.125, .375, 0.0, .75, 0.0}, // 4
      {-.125,   0.0, .375, 0.0, 0.0, .75}  // 5
    },
 
    // embedding matrix for child 3
    {
      //  0       1      2    3    4    5
      {  0.0,   0.0,   0.0, 1.0, 0.0, 0.0}, // 0
      {  0.0,   0.0,   0.0, 0.0, 1.0, 0.0}, // 1
      {  0.0,   0.0,   0.0, 0.0, 0.0, 1.0}, // 2
      {-.125,   0.0, -.125, 0.5, 0.5, .25}, // 3
      {-.125, -.125,   0.0, .25, 0.5, 0.5}, // 4
      {  0.0, -.125, -.125, 0.5, .25, 0.5}  // 5
    }
  };
 
#endif
 
 
 
// ------------------------------------------------------------
// Tri6 class member functions
 
bool Tri6::is_vertex(const unsigned int i) const
{
  if (i < 3)
    return true;
  return false;
}
 
bool Tri6::is_edge(const unsigned int i) const
{
  if (i < 3)
    return false;
  return true;
}
 
bool Tri6::is_face(const unsigned int) const
{
  return false;
}
 
bool Tri6::is_node_on_side(const unsigned int n,
                           const unsigned int s) const
{
  libmesh_assert_less (s, n_sides());
  return std::find(std::begin(side_nodes_map[s]),
                   std::end(side_nodes_map[s]),
                   n) != std::end(side_nodes_map[s]);
}
 
std::vector<unsigned>
Tri6::nodes_on_side(const unsigned int s) const
{
  libmesh_assert_less(s, n_sides());
  return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
}
 
std::vector<unsigned>
Tri6::nodes_on_edge(const unsigned int e) const
{
  return nodes_on_side(e);
}
 
bool Tri6::has_affine_map() const
{
  // Make sure edges are straight
  Point v = this->point(1) - this->point(0);
  if (!v.relative_fuzzy_equals
      ((this->point(3) - this->point(0))*2, affine_tol))
    return false;
  v = this->point(2) - this->point(1);
  if (!v.relative_fuzzy_equals
      ((this->point(4) - this->point(1))*2, affine_tol))
    return false;
  v = this->point(2) - this->point(0);
  if (!v.relative_fuzzy_equals
      ((this->point(5) - this->point(0))*2, affine_tol))
    return false;
 
  return true;
}
 
 
 
Order Tri6::default_order() const
{
  return SECOND;
}
 
 
 
dof_id_type Tri6::key (const unsigned int s) const
{
  libmesh_assert_less (s, this->n_sides());
 
  switch (s)
    {
    case 0:
 
      return
        this->compute_key (this->node_id(3));
 
    case 1:
 
      return
        this->compute_key (this->node_id(4));
 
    case 2:
 
      return
        this->compute_key (this->node_id(5));
 
    default:
      libmesh_error_msg("Invalid side s = " << s);
    }
}
 
 
 
unsigned int Tri6::local_side_node(unsigned int side,
                                   unsigned int side_node) const
{
  libmesh_assert_less (side, this->n_sides());
  libmesh_assert_less (side_node, Tri6::nodes_per_side);
 
  return Tri6::side_nodes_map[side][side_node];
}
 
 
 
std::unique_ptr<Elem> Tri6::build_side_ptr (const unsigned int i)
{
  return this->simple_build_side_ptr<Edge3, Tri6>(i);
}
 
 
 
void Tri6::build_side_ptr (std::unique_ptr<Elem> & side,
                           const unsigned int i)
{
  this->simple_build_side_ptr<Tri6>(side, i, EDGE3);
}
 
 
 
void Tri6::connectivity(const unsigned int sf,
                        const IOPackage iop,
                        std::vector<dof_id_type> & conn) const
{
  libmesh_assert_less (sf, this->n_sub_elem());
  libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
 
  switch (iop)
    {
    case TECPLOT:
      {
        conn.resize(4);
        switch(sf)
          {
          case 0:
            // linear sub-triangle 0
            conn[0] = this->node_id(0)+1;
            conn[1] = this->node_id(3)+1;
            conn[2] = this->node_id(5)+1;
            conn[3] = this->node_id(5)+1;
 
            return;
 
          case 1:
            // linear sub-triangle 1
            conn[0] = this->node_id(3)+1;
            conn[1] = this->node_id(1)+1;
            conn[2] = this->node_id(4)+1;
            conn[3] = this->node_id(4)+1;
 
            return;
 
          case 2:
            // linear sub-triangle 2
            conn[0] = this->node_id(5)+1;
            conn[1] = this->node_id(4)+1;
            conn[2] = this->node_id(2)+1;
            conn[3] = this->node_id(2)+1;
 
            return;
 
          case 3:
            // linear sub-triangle 3
            conn[0] = this->node_id(3)+1;
            conn[1] = this->node_id(4)+1;
            conn[2] = this->node_id(5)+1;
            conn[3] = this->node_id(5)+1;
 
            return;
 
          default:
            libmesh_error_msg("Invalid sf = " << sf);
          }
      }
 
    case VTK:
      {
        // VTK_QUADRATIC_TRIANGLE has same numbering as libmesh TRI6
        conn.resize(Tri6::num_nodes);
        for (auto i : index_range(conn))
          conn[i] = this->node_id(i);
        return;
      }
 
    default:
      libmesh_error_msg("Unsupported IO package " << iop);
    }
}
 
 
 
BoundingBox Tri6::loose_bounding_box () const
{
  // This might have curved edges, or might be a curved surface in
  // 3-space, in which case the full bounding box can be larger than
  // the bounding box of just the nodes.
  //
  //
  // FIXME - I haven't yet proven the formula below to be correct for
  // quadratics in 2D - RHS
  Point pmin, pmax;
 
  for (unsigned d=0; d<LIBMESH_DIM; ++d)
    {
      Real center = this->point(0)(d);
      for (unsigned int p=1; p != 6; ++p)
        center += this->point(p)(d);
      center /= 6;
 
      Real hd = std::abs(center - this->point(0)(d));
      for (unsigned int p=1; p != 6; ++p)
        hd = std::max(hd, std::abs(center - this->point(p)(d)));
 
      pmin(d) = center - hd;
      pmax(d) = center + hd;
    }
 
  return BoundingBox(pmin, pmax);
}
 
 
 
Real Tri6::volume () const
{
  // This specialization is good for Lagrange mappings only in general
  if (this->mapping_type() != LAGRANGE_MAP)
    return this->Elem::volume();
 
  Real vol=0.;
 
#if LIBMESH_DIM > 1
  // Make copies of our points.  It makes the subsequent calculations a bit
  // shorter and avoids dereferencing the same pointer multiple times.
  Point
    x0 = point(0), x1 = point(1), x2 = point(2),
    x3 = point(3), x4 = point(4), x5 = point(5);
 
  // Construct constant data vectors.
  // \vec{x}_{\xi}  = \vec{a1}*xi + \vec{b1}*eta + \vec{c1}
  // \vec{x}_{\eta} = \vec{a2}*xi + \vec{b2}*eta + \vec{c2}
  Point
    a1 =  4*x0 + 4*x1 - 8*x3,
    b1 =  4*x0 - 4*x3 + 4*x4 - 4*x5, /*=a2*/
    c1 = -3*x0 - 1*x1 + 4*x3,
    b2 =  4*x0 + 4*x2 - 8*x5,
    c2 = -3*x0 - 1*x2 + 4*x5;
 
  // If a1 == b1 == a2 == b2 == 0, this is a TRI6 with straight sides,
  // and we can use the TRI3 formula to compute the volume.
  if (a1.relative_fuzzy_equals(Point(0,0,0)) &&
      b1.relative_fuzzy_equals(Point(0,0,0)) &&
      b2.relative_fuzzy_equals(Point(0,0,0)))
    return 0.5 * cross_norm(c1, c2);
 
  // 7-point rule, exact for quintics.
  const unsigned int N = 7;
 
  // Parameters of the quadrature rule
  static const Real
    w1 = Real(31)/480 + std::sqrt(Real(15))/2400,
    w2 = Real(31)/480 - std::sqrt(Real(15))/2400,
    q1 = Real(2)/7 + std::sqrt(Real(15))/21,
    q2 = Real(2)/7 - std::sqrt(Real(15))/21;
 
  static const Real xi[N]  = {Real(1)/3,  q1, q1,     1-2*q1, q2, q2,     1-2*q2};
  static const Real eta[N] = {Real(1)/3,  q1, 1-2*q1, q1,     q2, 1-2*q2, q2};
  static const Real wts[N] = {Real(9)/80, w1, w1,     w1,     w2, w2,     w2};
 
  // Approximate the area with quadrature
  for (unsigned int q=0; q<N; ++q)
    vol += wts[q] * cross_norm(xi[q]*a1 + eta[q]*b1 + c1,
                               xi[q]*b1 + eta[q]*b2 + c2);
#endif // LIBMESH_DIM > 1
 
  return vol;
}
 
 
 
unsigned short int Tri6::second_order_adjacent_vertex (const unsigned int n,
                                                       const unsigned int v) const
{
  libmesh_assert_greater_equal (n, this->n_vertices());
  libmesh_assert_less (n, this->n_nodes());
  libmesh_assert_less (v, 2);
  return _second_order_adjacent_vertices[n-this->n_vertices()][v];
}
 
 
 
const unsigned short int Tri6::_second_order_adjacent_vertices[Tri6::num_sides][2] =
  {
    {0, 1}, // vertices adjacent to node 3
    {1, 2}, // vertices adjacent to node 4
    {0, 2}  // vertices adjacent to node 5
  };
 
 
 
std::pair<unsigned short int, unsigned short int>
Tri6::second_order_child_vertex (const unsigned int n) const
{
  libmesh_assert_greater_equal (n, this->n_vertices());
  libmesh_assert_less (n, this->n_nodes());
  return std::pair<unsigned short int, unsigned short int>
    (_second_order_vertex_child_number[n],
     _second_order_vertex_child_index[n]);
}
 
 
 
const unsigned short int Tri6::_second_order_vertex_child_number[Tri6::num_nodes] =
  {
    99,99,99, // Vertices
    0,1,0     // Edges
  };
 
 
 
const unsigned short int Tri6::_second_order_vertex_child_index[Tri6::num_nodes] =
  {
    99,99,99, // Vertices
    1,2,2     // Edges
  };
 
 
void Tri6::permute(unsigned int perm_num)
{
  libmesh_assert_less (perm_num, 3);
 
  for (unsigned int i = 0; i != perm_num; ++i)
    {
      swap3nodes(0,1,2);
      swap3nodes(3,4,5);
      swap3neighbors(0,1,2);
    }
}
 
 
void Tri6::flip(BoundaryInfo * boundary_info)
{
  libmesh_assert(boundary_info);
 
  swap2nodes(0,1);
  swap2nodes(4,5);
  swap2neighbors(1,2);
  swap2boundarysides(1,2,boundary_info);
  swap2boundaryedges(1,2,boundary_info);
}
 
 
unsigned int Tri6::center_node_on_side(const unsigned short side) const
{
  libmesh_assert_less (side, Tri6::num_sides);
  return side + 3;
}
 
 
ElemType
Tri6::side_type (const unsigned int libmesh_dbg_var(s)) const
{
  libmesh_assert_less (s, 3);
  return EDGE3;
}
 
 
} // namespace libMesh