libMesh
cell_hex20.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2019 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3 
4 // This library is free software; you can redistribute it and/or
5 // modify it under the terms of the GNU Lesser General Public
6 // License as published by the Free Software Foundation; either
7 // version 2.1 of the License, or (at your option) any later version.
8 
9 // This library is distributed in the hope that it will be useful,
10 // but WITHOUT ANY WARRANTY; without even the implied warranty of
11 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 // Lesser General Public License for more details.
13 
14 // You should have received a copy of the GNU Lesser General Public
15 // License along with this library; if not, write to the Free Software
16 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 
18 
19 // Local includes
20 #include "libmesh/side.h"
21 #include "libmesh/cell_hex20.h"
22 #include "libmesh/edge_edge3.h"
23 #include "libmesh/face_quad8.h"
24 #include "libmesh/enum_io_package.h"
25 #include "libmesh/enum_order.h"
26 
27 namespace libMesh
28 {
29 
30 
31 
32 // ------------------------------------------------------------
33 // Hex20 class static member initializations
34 const int Hex20::num_nodes;
35 const int Hex20::num_sides;
36 const int Hex20::num_edges;
37 const int Hex20::num_children;
38 const int Hex20::nodes_per_side;
39 const int Hex20::nodes_per_edge;
40 
41 const unsigned int Hex20::side_nodes_map[Hex20::num_sides][Hex20::nodes_per_side] =
42  {
43  {0, 3, 2, 1, 11, 10, 9, 8}, // Side 0
44  {0, 1, 5, 4, 8, 13, 16, 12}, // Side 1
45  {1, 2, 6, 5, 9, 14, 17, 13}, // Side 2
46  {2, 3, 7, 6, 10, 15, 18, 14}, // Side 3
47  {3, 0, 4, 7, 11, 12, 19, 15}, // Side 4
48  {4, 5, 6, 7, 16, 17, 18, 19} // Side 5
49  };
50 
51 const unsigned int Hex20::edge_nodes_map[Hex20::num_edges][Hex20::nodes_per_edge] =
52  {
53  {0, 1, 8}, // Edge 0
54  {1, 2, 9}, // Edge 1
55  {2, 3, 10}, // Edge 2
56  {0, 3, 11}, // Edge 3
57  {0, 4, 12}, // Edge 4
58  {1, 5, 13}, // Edge 5
59  {2, 6, 14}, // Edge 6
60  {3, 7, 15}, // Edge 7
61  {4, 5, 16}, // Edge 8
62  {5, 6, 17}, // Edge 9
63  {6, 7, 18}, // Edge 10
64  {4, 7, 19} // Edge 11
65  };
66 
67 
68 
69 // ------------------------------------------------------------
70 // Hex20 class member functions
71 
72 bool Hex20::is_vertex(const unsigned int i) const
73 {
74  if (i < 8)
75  return true;
76  return false;
77 }
78 
79 bool Hex20::is_edge(const unsigned int i) const
80 {
81  if (i > 7)
82  return true;
83  return false;
84 }
85 
86 bool Hex20::is_face(const unsigned int) const
87 {
88  return false;
89 }
90 
91 bool Hex20::is_node_on_side(const unsigned int n,
92  const unsigned int s) const
93 {
94  libmesh_assert_less (s, n_sides());
95  return std::find(std::begin(side_nodes_map[s]),
96  std::end(side_nodes_map[s]),
97  n) != std::end(side_nodes_map[s]);
98 }
99 
100 std::vector<unsigned>
101 Hex20::nodes_on_side(const unsigned int s) const
102 {
103  libmesh_assert_less(s, n_sides());
104  return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
105 }
106 
107 bool Hex20::is_node_on_edge(const unsigned int n,
108  const unsigned int e) const
109 {
110  libmesh_assert_less (e, n_edges());
111  return std::find(std::begin(edge_nodes_map[e]),
112  std::end(edge_nodes_map[e]),
113  n) != std::end(edge_nodes_map[e]);
114 }
115 
116 
117 
118 bool Hex20::has_affine_map() const
119 {
120  // Make sure x-edge endpoints are affine
121  Point v = this->point(1) - this->point(0);
122  if (!v.relative_fuzzy_equals(this->point(2) - this->point(3)) ||
123  !v.relative_fuzzy_equals(this->point(5) - this->point(4)) ||
124  !v.relative_fuzzy_equals(this->point(6) - this->point(7)))
125  return false;
126  // Make sure x-edges are straight
127  v /= 2;
128  if (!v.relative_fuzzy_equals(this->point(8) - this->point(0)) ||
129  !v.relative_fuzzy_equals(this->point(10) - this->point(3)) ||
130  !v.relative_fuzzy_equals(this->point(16) - this->point(4)) ||
131  !v.relative_fuzzy_equals(this->point(18) - this->point(7)))
132  return false;
133  // Make sure xz-faces are identical parallelograms
134  v = this->point(4) - this->point(0);
135  if (!v.relative_fuzzy_equals(this->point(7) - this->point(3)))
136  return false;
137  v /= 2;
138  if (!v.relative_fuzzy_equals(this->point(12) - this->point(0)) ||
139  !v.relative_fuzzy_equals(this->point(13) - this->point(1)) ||
140  !v.relative_fuzzy_equals(this->point(14) - this->point(2)) ||
141  !v.relative_fuzzy_equals(this->point(15) - this->point(3)))
142  return false;
143  // Make sure y-edges are straight
144  v = (this->point(3) - this->point(0))/2;
145  if (!v.relative_fuzzy_equals(this->point(11) - this->point(0)) ||
146  !v.relative_fuzzy_equals(this->point(9) - this->point(1)) ||
147  !v.relative_fuzzy_equals(this->point(17) - this->point(5)) ||
148  !v.relative_fuzzy_equals(this->point(19) - this->point(4)))
149  return false;
150  // If all the above checks out, the map is affine
151  return true;
152 }
153 
154 
155 
156 Order Hex20::default_order() const
157 {
158  return SECOND;
159 }
160 
161 
162 
163 std::unique_ptr<Elem> Hex20::build_side_ptr (const unsigned int i,
164  bool proxy )
165 {
166  libmesh_assert_less (i, this->n_sides());
167 
168  if (proxy)
169  return libmesh_make_unique<Side<Quad8,Hex20>>(this,i);
170 
171  else
172  {
173  std::unique_ptr<Elem> face = libmesh_make_unique<Quad8>();
174  face->subdomain_id() = this->subdomain_id();
175 
176  for (auto n : face->node_index_range())
177  face->set_node(n) = this->node_ptr(Hex20::side_nodes_map[i][n]);
178 
179  return face;
180  }
181 }
182 
183 
184 
185 void Hex20::build_side_ptr (std::unique_ptr<Elem> & side,
186  const unsigned int i)
187 {
188  this->simple_build_side_ptr<Hex20>(side, i, QUAD8);
189 }
190 
191 
192 
193 unsigned int Hex20::which_node_am_i(unsigned int side,
194  unsigned int side_node) const
195 {
196  libmesh_assert_less (side, this->n_sides());
197  libmesh_assert_less (side_node, Hex20::nodes_per_side);
198 
199  return Hex20::side_nodes_map[side][side_node];
200 }
201 
202 
203 
204 std::unique_ptr<Elem> Hex20::build_edge_ptr (const unsigned int i)
205 {
206  libmesh_assert_less (i, this->n_edges());
207 
208  return libmesh_make_unique<SideEdge<Edge3,Hex20>>(this,i);
209 }
210 
211 
212 
213 void Hex20::connectivity(const unsigned int sc,
214  const IOPackage iop,
215  std::vector<dof_id_type> & conn) const
216 {
217  libmesh_assert(_nodes);
218  libmesh_assert_less (sc, this->n_sub_elem());
219  libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
220 
221 
222  switch (iop)
223  {
224  case TECPLOT:
225  {
226  switch (sc)
227  {
228  case 0:
229  conn.resize(8);
230  conn[0] = this->node_id(0)+1;
231  conn[1] = this->node_id(1)+1;
232  conn[2] = this->node_id(2)+1;
233  conn[3] = this->node_id(3)+1;
234  conn[4] = this->node_id(4)+1;
235  conn[5] = this->node_id(5)+1;
236  conn[6] = this->node_id(6)+1;
237  conn[7] = this->node_id(7)+1;
238 
239  return;
240 
241  default:
242  libmesh_error_msg("Unknown sc = " << sc);
243  }
244  }
245 
246  case VTK:
247  {
248  switch (sc)
249  {
250  case 0:
251  conn.resize(20);
252  conn[0] = this->node_id(0);
253  conn[1] = this->node_id(1);
254  conn[2] = this->node_id(2);
255  conn[3] = this->node_id(3);
256  conn[4] = this->node_id(4);
257  conn[5] = this->node_id(5);
258  conn[6] = this->node_id(6);
259  conn[7] = this->node_id(7);
260  conn[8] = this->node_id(8);
261  conn[9] = this->node_id(9);
262  conn[10] = this->node_id(10);
263  conn[11] = this->node_id(11);
264  conn[12] = this->node_id(16);
265  conn[13] = this->node_id(17);
266  conn[14] = this->node_id(18);
267  conn[15] = this->node_id(19);
268  conn[16] = this->node_id(12);
269  conn[17] = this->node_id(13);
270  conn[18] = this->node_id(14);
271  conn[19] = this->node_id(15);
272  return;
273 
274  default:
275  libmesh_error_msg("Unknown sc = " << sc);
276  }
277  }
278 
279  default:
280  libmesh_error_msg("Unsupported IO package " << iop);
281  }
282 }
283 
284 
285 
286 
287 unsigned short int Hex20::second_order_adjacent_vertex (const unsigned int n,
288  const unsigned int v) const
289 {
290  libmesh_assert_greater_equal (n, this->n_vertices());
291  libmesh_assert_less (n, this->n_nodes());
292  libmesh_assert_less (v, 2);
293  /*
294  * the _second_order_adjacent_vertices matrix is
295  * stored in cell_hex.C, since this matrix is identical
296  * for Hex20 and Hex27 (for the first 12 higher-order nodes)
297  */
298  return _second_order_adjacent_vertices[n-this->n_vertices()][v];
299 }
300 
301 
302 
303 std::pair<unsigned short int, unsigned short int>
304 Hex20::second_order_child_vertex (const unsigned int n) const
305 {
306  libmesh_assert_greater_equal (n, this->n_vertices());
307  libmesh_assert_less (n, this->n_nodes());
308  /*
309  * the _second_order_vertex_child_* vectors are
310  * stored in cell_hex.C, since they are identical
311  * for Hex20 and Hex27 (for the first 12 higher-order nodes)
312  */
313  return std::pair<unsigned short int, unsigned short int>
314  (_second_order_vertex_child_number[n],
315  _second_order_vertex_child_index[n]);
316 }
317 
318 
319 
320 Real Hex20::volume () const
321 {
322  // This specialization is good for Lagrange mappings only
323  if (this->mapping_type() != LAGRANGE_MAP)
324  return this->Elem::volume();
325 
326  // Make copies of our points. It makes the subsequent calculations a bit
327  // shorter and avoids dereferencing the same pointer multiple times.
328  Point
329  x0 = point(0), x1 = point(1), x2 = point(2), x3 = point(3), x4 = point(4),
330  x5 = point(5), x6 = point(6), x7 = point(7), x8 = point(8), x9 = point(9),
331  x10 = point(10), x11 = point(11), x12 = point(12), x13 = point(13), x14 = point(14),
332  x15 = point(15), x16 = point(16), x17 = point(17), x18 = point(18), x19 = point(19);
333 
334  // The constant components of the dx/dxi vector,
335  // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
336  // These were copied directly from the output of a Python script.
337  // There are at most 17 terms with total degree <=3, but only 12
338  // of them are non-zero for each direction.
339  Point dx_dxi[17] =
340  {
341  x0/8 - x1/8 - x11/4 - x12/4 + x13/4 + x14/4 - x15/4 + x17/4 - x19/4 - x2/8 + x3/8 + x4/8 - x5/8 - x6/8 + x7/8 + x9/4,
342  x11/4 + x17/4 - x19/4 - x9/4,
343  -x0/8 + x1/8 + x12/4 - x13/4 - x14/4 + x15/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8,
344  x12/4 - x13/4 + x14/4 - x15/4,
345  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
346  x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
347  -x0/8 + x1/8 + x11/4 - x17/4 + x19/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8 - x9/4,
348  x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
349  x0/4 + x1/4 - x10/2 - x16/2 - x18/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2,
350  -x0/4 - x1/4 + x10/2 - x16/2 - x18/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2,
351  Point(0,0,0),
352  -x0/4 - x1/4 - x10/2 + x16/2 - x18/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2,
353  x0/4 + x1/4 + x10/2 + x16/2 - x18/2 - x2/4 - x3/4 - x4/4 - x5/4 + x6/4 + x7/4 - x8/2,
354  Point(0,0,0),
355  Point(0,0,0),
356  Point(0,0,0),
357  Point(0,0,0)
358  };
359 
360  // The constant components of the dx/deta vector. These were copied
361  // directly from the output of a Python script. There are at most
362  // 17 terms with total degree <=3, but only 12 of them are non-zero
363  // for each direction.
364  Point dx_deta[17] =
365  {
366  x0/8 + x1/8 + x10/4 - x12/4 - x13/4 + x14/4 + x15/4 - x16/4 + x18/4 - x2/8 - x3/8 + x4/8 + x5/8 - x6/8 - x7/8 - x8/4,
367  -x10/4 - x16/4 + x18/4 + x8/4,
368  -x0/8 - x1/8 + x12/4 + x13/4 - x14/4 - x15/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8,
369  x0/4 + x1/4 - x11/2 - x17/2 - x19/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x9/2,
370  -x0/4 - x1/4 + x11/2 - x17/2 - x19/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x9/2,
371  Point(0,0,0),
372  Point(0,0,0),
373  Point(0,0,0),
374  x12/4 - x13/4 + x14/4 - x15/4,
375  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
376  x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
377  -x0/4 + x1/4 + x11/2 - x17/2 + x19/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2,
378  x0/4 - x1/4 - x11/2 - x17/2 + x19/2 - x2/4 + x3/4 - x4/4 + x5/4 + x6/4 - x7/4 + x9/2,
379  Point(0,0,0),
380  -x0/8 - x1/8 - x10/4 + x16/4 - x18/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8 + x8/4,
381  x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
382  Point(0,0,0)
383  };
384 
385  // The constant components of the dx/dzeta vector. These were copied
386  // directly from the output of a Python script. There are at most
387  // 17 terms with total degree <=3, but only 12 of them are non-zero
388  // for each direction.
389  Point dx_dzeta[17] =
390  {
391  x0/8 + x1/8 - x10/4 - x11/4 + x16/4 + x17/4 + x18/4 + x19/4 + x2/8 + x3/8 - x4/8 - x5/8 - x6/8 - x7/8 - x8/4 - x9/4,
392  x0/4 + x1/4 - x12/2 - x13/2 - x14/2 - x15/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4,
393  Point(0,0,0),
394  -x10/4 - x16/4 + x18/4 + x8/4,
395  -x0/4 - x1/4 + x12/2 + x13/2 - x14/2 - x15/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4,
396  Point(0,0,0),
397  -x0/8 - x1/8 + x11/4 - x17/4 - x19/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x9/4,
398  Point(0,0,0),
399  x11/4 + x17/4 - x19/4 - x9/4,
400  -x0/4 + x1/4 + x12/2 - x13/2 - x14/2 + x15/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4,
401  Point(0,0,0),
402  -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
403  x0/4 - x1/4 - x12/2 + x13/2 - x14/2 + x15/2 + x2/4 - x3/4 + x4/4 - x5/4 + x6/4 - x7/4,
404  x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
405  -x0/8 - x1/8 + x10/4 - x16/4 - x18/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x8/4,
406  Point(0,0,0),
407  x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
408  };
409 
410  // The integer exponents for each term.
411  static const int exponents[17][3] =
412  {
413  {0, 0, 0},
414  {0, 0, 1},
415  {0, 0, 2},
416  {0, 1, 0},
417  {0, 1, 1},
418  {0, 1, 2},
419  {0, 2, 0},
420  {0, 2, 1},
421  {1, 0, 0},
422  {1, 0, 1},
423  {1, 0, 2},
424  {1, 1, 0},
425  {1, 1, 1},
426  {1, 2, 0},
427  {2, 0, 0},
428  {2, 0, 1},
429  {2, 1, 0}
430  };
431 
432 
433  // 3x3 quadrature, exact for bi-quintics
434  const int N = 3;
435  const Real w[N] = {5./9, 8./9, 5./9};
436 
437  // Quadrature point locations raised to powers. q[0][2] is
438  // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
439  // first power, etc.
440  const Real q[N][N] =
441  {
442  //^0 ^1 ^2
443  { 1., -std::sqrt(15)/5., 15./25},
444  { 1., 0., 0.},
445  { 1., std::sqrt(15)/5., 15./25}
446  };
447 
448 
449  Real vol = 0.;
450  for (int i=0; i<N; ++i)
451  for (int j=0; j<N; ++j)
452  for (int k=0; k<N; ++k)
453  {
454  // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
455  Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
456  for (int c=0; c<17; ++c)
457  {
458  Real coeff =
459  q[i][exponents[c][0]] *
460  q[j][exponents[c][1]] *
461  q[k][exponents[c][2]];
462 
463  dx_dxi_q += coeff * dx_dxi[c];
464  dx_deta_q += coeff * dx_deta[c];
465  dx_dzeta_q += coeff * dx_dzeta[c];
466  }
467 
468  // Compute scalar triple product, multiply by weight, and accumulate volume.
469  vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
470  }
471 
472  return vol;
473 }
474 
475 
476 
477 
478 #ifdef LIBMESH_ENABLE_AMR
479 
480 const float Hex20::_embedding_matrix[Hex20::num_children][Hex20::num_nodes][Hex20::num_nodes] =
481  {
482  // embedding matrix for child 0
483  {
484  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
485  { 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
486  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
487  { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
488  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
489  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
490  { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 5
491  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 6
492  { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 7
493  { 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
494  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
495  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
496  { 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
497  { 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
498  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000 }, // 13
499  { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 14
500  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000 }, // 15
501  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 16
502  { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 17
503  { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 18
504  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000 } // 19
505  },
506 
507  // embedding matrix for child 1
508  {
509  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
510  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
511  { 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
512  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
513  { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
514  { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 4
515  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
516  { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 6
517  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 7
518  { -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
519  { 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
520  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
521  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
522  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000 }, // 12
523  { 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
524  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000 }, // 14
525  { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 15
526  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 16
527  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 17
528  { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 18
529  { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 } // 19
530  },
531 
532  // embedding matrix for child 2
533  {
534  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
535  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
536  { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
537  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
538  { 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
539  { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 4
540  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 5
541  { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 6
542  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
543  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
544  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
545  { 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
546  { -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
547  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000 }, // 12
548  { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 13
549  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000 }, // 14
550  { 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
551  { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 16
552  { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 17
553  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 18
554  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000 } // 19
555  },
556 
557  // embedding matrix for child 3
558  {
559  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
560  { -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
561  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
562  { 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
563  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
564  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 4
565  { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 5
566  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
567  { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 7
568  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 8
569  { 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 9
570  { 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 10
571  { -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 11
572  { -0.281250, -0.281250, -0.281250, -0.281250, -0.156250, -0.156250, -0.156250, -0.156250, 0.375000, 0.375000, 0.375000, 0.375000, 0.187500, 0.187500, 0.187500, 0.187500, 0.125000, 0.125000, 0.125000, 0.125000 }, // 12
573  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000 }, // 13
574  { 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
575  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.250000, 0.00000 }, // 15
576  { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 16
577  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 17
578  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 18
579  { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 } // 19
580  },
581 
582  // embedding matrix for child 4
583  {
584  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
585  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 0
586  { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 1
587  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 2
588  { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 3
589  { 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 4
590  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 5
591  { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 6
592  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 7
593  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 8
594  { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 9
595  { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 10
596  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000 }, // 11
597  { -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 12
598  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 13
599  { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 14
600  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000 }, // 15
601  { 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 16
602  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000 }, // 17
603  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000 }, // 18
604  { 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000 } // 19
605  },
606 
607  // embedding matrix for child 5
608  {
609  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
610  { -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000 }, // 0
611  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 1
612  { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 2
613  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 3
614  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 4
615  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 5
616  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 6
617  { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 7
618  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000 }, // 8
619  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 9
620  { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 10
621  { -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500 }, // 11
622  { -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 12
623  { 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 13
624  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 14
625  { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 15
626  { 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000 }, // 16
627  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 17
628  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000 }, // 18
629  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.375000, 0.250000, 0.375000 } // 19
630  },
631 
632  // embedding matrix for child 6
633  {
634  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
635  { -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000 }, // 0
636  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 1
637  { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 2
638  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
639  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000 }, // 4
640  { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 5
641  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 6
642  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 7
643  { -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, 0.187500, 0.125000, 0.187500, 0.375000, 0.375000, 0.125000, 0.125000, 0.375000, 0.187500, 0.125000, 0.187500, 0.375000 }, // 8
644  { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 9
645  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 10
646  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.375000 }, // 11
647  { -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000 }, // 12
648  { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 13
649  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 14
650  { 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 15
651  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.250000, 0.375000, 0.750000 }, // 16
652  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000 }, // 17
653  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
654  { 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000 } // 19
655  },
656 
657  // embedding matrix for child 7
658  {
659  // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
660  { -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, -0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000, 0.250000 }, // 0
661  { 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000 }, // 1
662  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
663  { 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, -0.250000, -0.250000, 0.00000, 0.00000, 0.500000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.00000, 0.00000, 0.500000, 0.00000 }, // 3
664  { 0.00000, 0.00000, 0.00000, 0.00000, -0.250000, -0.250000, -0.250000, -0.250000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.500000, 0.500000, 0.500000, 0.500000 }, // 4
665  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000 }, // 5
666  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
667  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000, 0.00000 }, // 7
668  { -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000 }, // 8
669  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.250000, 0.750000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000 }, // 9
670  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.750000, 0.250000, 0.00000, 0.00000, 0.375000, 0.00000 }, // 10
671  { -0.156250, -0.156250, -0.281250, -0.281250, -0.156250, -0.156250, -0.281250, -0.281250, 0.125000, 0.187500, 0.375000, 0.187500, 0.125000, 0.125000, 0.375000, 0.375000, 0.125000, 0.187500, 0.375000, 0.187500 }, // 11
672  { -0.156250, -0.156250, -0.156250, -0.156250, -0.281250, -0.281250, -0.281250, -0.281250, 0.125000, 0.125000, 0.125000, 0.125000, 0.187500, 0.187500, 0.187500, 0.187500, 0.375000, 0.375000, 0.375000, 0.375000 }, // 12
673  { 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 13
674  { 0.00000, 0.00000, -0.125000, 0.00000, 0.00000, 0.00000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 14
675  { 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, -0.187500, -0.187500, 0.00000, 0.00000, 0.250000, 0.00000, 0.00000, 0.00000, 0.375000, 0.375000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 15
676  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, 0.750000, 0.375000, 0.250000 }, // 16
677  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.125000, 0.375000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000, 0.00000 }, // 17
678  { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.375000, -0.125000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.750000, 0.00000 }, // 18
679  { 0.00000, 0.00000, 0.00000, 0.00000, -0.187500, -0.187500, -0.187500, -0.187500, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.250000, 0.375000, 0.750000, 0.375000 } // 19
680  }
681  };
682 
683 #endif
684 
685 } // namespace libMesh
libMesh::Hex20::volume
virtual Real volume() const override
A specialization for computing the volume of a Hex20.
Definition: cell_hex20.C:320
libMesh::Hex::_second_order_vertex_child_number
static const unsigned short int _second_order_vertex_child_number[27]
Vector that names a child sharing each second order node.
Definition: cell_hex.h:182
libMesh::Hex20::build_edge_ptr
virtual std::unique_ptr< Elem > build_edge_ptr(const unsigned int i) override
Builds a EDGE3 built coincident with edge i.
Definition: cell_hex20.C:204
libMesh::IOPackage
IOPackage
libMesh interfaces with several different software packages for the purposes of creating,...
Definition: enum_io_package.h:37
libMesh::Hex::_second_order_vertex_child_index
static const unsigned short int _second_order_vertex_child_index[27]
Vector that names the child vertex index for each second order node.
Definition: cell_hex.h:187
libMesh::Hex20::nodes_on_side
virtual std::vector< unsigned int > nodes_on_side(const unsigned int s) const override
Definition: cell_hex20.C:101
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
Definition: factoryfunction.C:55
libMesh::Hex20::_embedding_matrix
static const float _embedding_matrix[num_children][num_nodes][num_nodes]
Matrix that computes new nodal locations/solution values from current nodes/solution.
Definition: cell_hex20.h:245
libMesh::Order
Order
Definition: enum_order.h:40
libMesh::INVALID_IO_PACKAGE
Definition: enum_io_package.h:48
libMesh::Hex20::which_node_am_i
virtual unsigned int which_node_am_i(unsigned int side, unsigned int side_node) const override
Definition: cell_hex20.C:193
end
IterBase * end
Also have a polymorphic pointer to the end object, this prevents iterating past the end.
Definition: variant_filter_iterator.h:343
std::sqrt
MetaPhysicL::DualNumber< T, D > sqrt(const MetaPhysicL::DualNumber< T, D > &in)
libMesh::Hex20::connectivity
virtual void connectivity(const unsigned int sc, const IOPackage iop, std::vector< dof_id_type > &conn) const override
Definition: cell_hex20.C:213
libMesh::Hex20::num_edges
static const int num_edges
Definition: cell_hex20.h:200
libMesh::triple_product
T triple_product(const TypeVector< T > &a, const TypeVector< T > &b, const TypeVector< T > &c)
Definition: type_vector.h:1106
libMesh::Hex20::is_node_on_edge
virtual bool is_node_on_edge(const unsigned int n, const unsigned int e) const override
Definition: cell_hex20.C:107
libMesh::SECOND
Definition: enum_order.h:43
libMesh::Elem::_nodes
Node ** _nodes
Pointers to the nodes we are connected to.
Definition: elem.h:1743
libMesh::Hex20::second_order_child_vertex
virtual std::pair< unsigned short int, unsigned short int > second_order_child_vertex(const unsigned int n) const override
Definition: cell_hex20.C:304
libMesh::Elem::point
const Point & point(const unsigned int i) const
Definition: elem.h:1955
libMesh::Hex20::num_children
static const int num_children
Definition: cell_hex20.h:201
libMesh::libmesh_assert
libmesh_assert(ctx)
libMesh::Hex20::default_order
virtual Order default_order() const override
Definition: cell_hex20.C:156
libMesh::Hex20::is_face
virtual bool is_face(const unsigned int i) const override
Definition: cell_hex20.C:86
libMesh::Elem::volume
virtual Real volume() const
Definition: elem.C:2617
libMesh::Hex20::is_node_on_side
virtual bool is_node_on_side(const unsigned int n, const unsigned int s) const override
Definition: cell_hex20.C:91
libMesh::Hex20::build_side_ptr
virtual std::unique_ptr< Elem > build_side_ptr(const unsigned int i, bool proxy=true) override
Builds a QUAD8 built coincident with face i.
Definition: cell_hex20.C:163
libMesh::Point
A Point defines a location in LIBMESH_DIM dimensional Real space.
Definition: point.h:38
libMesh::Hex20::has_affine_map
virtual bool has_affine_map() const override
Definition: cell_hex20.C:118
libMesh::Elem::mapping_type
ElemMappingType mapping_type() const
Definition: elem.h:2524
libMesh::Hex20::is_vertex
virtual bool is_vertex(const unsigned int i) const override
Definition: cell_hex20.C:72
libMesh::Hex20::second_order_adjacent_vertex
virtual unsigned short int second_order_adjacent_vertex(const unsigned int n, const unsigned int v) const override
Definition: cell_hex20.C:287
libMesh::Hex20::n_nodes
virtual unsigned int n_nodes() const override
Definition: cell_hex20.h:94
libMesh::Hex20::side_nodes_map
static const unsigned int side_nodes_map[num_sides][nodes_per_side]
This maps the node of the side to element node numbers.
Definition: cell_hex20.h:209
libMesh::LAGRANGE_MAP
Definition: enum_elem_type.h:83
libMesh::Hex20::is_edge
virtual bool is_edge(const unsigned int i) const override
Definition: cell_hex20.C:79
libMesh::Hex20::n_sub_elem
virtual unsigned int n_sub_elem() const override
Definition: cell_hex20.h:99
libMesh::Hex::n_vertices
virtual unsigned int n_vertices() const override final
Definition: cell_hex.h:78
libMesh::Elem::subdomain_id
subdomain_id_type subdomain_id() const
Definition: elem.h:2069
libMesh::Hex::n_sides
virtual unsigned int n_sides() const override final
Definition: cell_hex.h:73
libMesh::VTK
Definition: enum_io_package.h:42
libMesh::Elem::node_id
dof_id_type node_id(const unsigned int i) const
Definition: elem.h:1977
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:121
libMesh::Hex::_second_order_adjacent_vertices
static const unsigned short int _second_order_adjacent_vertices[12][2]
Matrix that tells which vertices define the location of mid-side (or second-order) nodes.
Definition: cell_hex.h:177
libMesh::Hex::n_edges
virtual unsigned int n_edges() const override final
Definition: cell_hex.h:83
libMesh::Hex20::edge_nodes_map
static const unsigned int edge_nodes_map[num_edges][nodes_per_edge]
This maps the node of the edge to element node numbers.
Definition: cell_hex20.h:215
libMesh::Hex20::num_nodes
static const int num_nodes
Geometric constants for Hex20.
Definition: cell_hex20.h:198
libMesh::Elem::node_ptr
const Node * node_ptr(const unsigned int i) const
Definition: elem.h:2009
libMesh::Hex20::num_sides
static const int num_sides
Definition: cell_hex20.h:199
libMesh::Hex20::nodes_per_side
static const int nodes_per_side
Definition: cell_hex20.h:202
libMesh::TypeVector::relative_fuzzy_equals
bool relative_fuzzy_equals(const TypeVector< T > &rhs, Real tol=TOLERANCE) const
Definition: type_vector.h:1042
libMesh::TECPLOT
Definition: enum_io_package.h:39
libMesh::QUAD8
Definition: enum_elem_type.h:42
libMesh::Hex20::nodes_per_edge
static const int nodes_per_edge
Definition: cell_hex20.h:203
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