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cell_hex20.C
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1// The libMesh Finite Element Library.
2// Copyright (C) 2002-2026 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/cell_hex20.h"
21#include "libmesh/edge_edge3.h"
22#include "libmesh/face_quad8.h"
23#include "libmesh/enum_io_package.h"
24#include "libmesh/enum_order.h"
25
26namespace libMesh
27{
28
29
30
31// ------------------------------------------------------------
32// Hex20 class static member initializations
33const int Hex20::num_nodes;
34const int Hex20::nodes_per_side;
35const int Hex20::nodes_per_edge;
36
37// ------------------------------------------------------------
38// Hex20 class member functions
39
40bool Hex20::is_vertex(const unsigned int i) const
41{
42 if (i < 8)
43 return true;
44 return false;
45}
46
47bool Hex20::is_edge(const unsigned int i) const
48{
49 if (i > 7)
50 return true;
51 return false;
52}
53
54bool Hex20::is_face(const unsigned int) const
55{
56 return false;
57}
58
59bool Hex20::is_node_on_side(const unsigned int n,
60 const unsigned int s) const
61{
62 libmesh_assert_less (s, n_sides());
63 return std::find(std::begin(side_nodes_map[s]),
64 std::end(side_nodes_map[s]),
65 n) != std::end(side_nodes_map[s]);
66}
67
68std::vector<unsigned>
69Hex20::nodes_on_side(const unsigned int s) const
70{
71 libmesh_assert_less(s, n_sides());
72 return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s])};
73}
74
75std::vector<unsigned>
76Hex20::nodes_on_edge(const unsigned int e) const
77{
78 libmesh_assert_less(e, n_edges());
79 return {std::begin(edge_nodes_map[e]), std::end(edge_nodes_map[e])};
80}
81
82bool Hex20::is_node_on_edge(const unsigned int n,
83 const unsigned int e) const
84{
85 libmesh_assert_less (e, n_edges());
86 return std::find(std::begin(edge_nodes_map[e]),
87 std::end(edge_nodes_map[e]),
88 n) != std::end(edge_nodes_map[e]);
89}
90
91
92
93bool Hex20::has_affine_map() const
94{
95 // Make sure x-edge endpoints are affine
96 Point v = this->point(1) - this->point(0);
97 if (!v.relative_fuzzy_equals(this->point(2) - this->point(3), affine_tol) ||
98 !v.relative_fuzzy_equals(this->point(5) - this->point(4), affine_tol) ||
99 !v.relative_fuzzy_equals(this->point(6) - this->point(7), affine_tol))
100 return false;
101 // Make sure x-edges are straight
102 v /= 2;
103 if (!v.relative_fuzzy_equals(this->point(8) - this->point(0), affine_tol) ||
104 !v.relative_fuzzy_equals(this->point(10) - this->point(3), affine_tol) ||
105 !v.relative_fuzzy_equals(this->point(16) - this->point(4), affine_tol) ||
106 !v.relative_fuzzy_equals(this->point(18) - this->point(7), affine_tol))
107 return false;
108 // Make sure xz-faces are identical parallelograms
109 v = this->point(4) - this->point(0);
110 if (!v.relative_fuzzy_equals(this->point(7) - this->point(3), affine_tol))
111 return false;
112 v /= 2;
113 if (!v.relative_fuzzy_equals(this->point(12) - this->point(0), affine_tol) ||
114 !v.relative_fuzzy_equals(this->point(13) - this->point(1), affine_tol) ||
115 !v.relative_fuzzy_equals(this->point(14) - this->point(2), affine_tol) ||
116 !v.relative_fuzzy_equals(this->point(15) - this->point(3), affine_tol))
117 return false;
118 // Make sure y-edges are straight
119 v = (this->point(3) - this->point(0))/2;
120 if (!v.relative_fuzzy_equals(this->point(11) - this->point(0), affine_tol) ||
121 !v.relative_fuzzy_equals(this->point(9) - this->point(1), affine_tol) ||
122 !v.relative_fuzzy_equals(this->point(17) - this->point(5), affine_tol) ||
123 !v.relative_fuzzy_equals(this->point(19) - this->point(4), affine_tol))
124 return false;
125 // If all the above checks out, the map is affine
126 return true;
127}
128
129
130
131Order Hex20::default_order() const
132{
133 return SECOND;
134}
135
136
137
138std::unique_ptr<Elem> Hex20::build_side_ptr (const unsigned int i)
139{
140 return this->simple_build_side_ptr<Quad8, Hex20>(i);
141}
142
143
144
145void Hex20::build_side_ptr (std::unique_ptr<Elem> & side,
146 const unsigned int i)
147{
148 this->simple_build_side_ptr<Hex20>(side, i, QUAD8);
149}
150
151
152
153unsigned int Hex20::local_side_node(unsigned int side,
154 unsigned int side_node) const
155{
156 libmesh_assert_less (side, this->n_sides());
157 libmesh_assert_less (side_node, Hex20::nodes_per_side);
158
159 return Hex20::side_nodes_map[side][side_node];
160}
161
162
163
164unsigned int Hex20::local_edge_node(unsigned int edge,
165 unsigned int edge_node) const
166{
167 libmesh_assert_less (edge, this->n_edges());
168 libmesh_assert_less (edge_node, Hex20::nodes_per_edge);
169
170 return Hex20::edge_nodes_map[edge][edge_node];
171}
172
173
174
175std::unique_ptr<Elem> Hex20::build_edge_ptr (const unsigned int i)
176{
177 return this->simple_build_edge_ptr<Edge3,Hex20>(i);
178}
179
180
181
182void Hex20::build_edge_ptr (std::unique_ptr<Elem> & edge, const unsigned int i)
183{
184 this->simple_build_edge_ptr<Hex20>(edge, i, EDGE3);
185}
186
187
188
189void Hex20::connectivity(const unsigned int sc,
190 const IOPackage iop,
191 std::vector<dof_id_type> & conn) const
192{
193 libmesh_assert(_nodes);
194 libmesh_assert_less (sc, this->n_sub_elem());
195 libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
196
197
198 switch (iop)
199 {
200 case TECPLOT:
201 {
202 switch (sc)
203 {
204 case 0:
205 conn.resize(8);
206 conn[0] = this->node_id(0)+1;
207 conn[1] = this->node_id(1)+1;
208 conn[2] = this->node_id(2)+1;
209 conn[3] = this->node_id(3)+1;
210 conn[4] = this->node_id(4)+1;
211 conn[5] = this->node_id(5)+1;
212 conn[6] = this->node_id(6)+1;
213 conn[7] = this->node_id(7)+1;
214
215 return;
216
217 default:
218 libmesh_error_msg("Unknown sc = " << sc);
219 }
220 }
221
222 case VTK:
223 {
224 switch (sc)
225 {
226 case 0:
227 conn.resize(20);
228 conn[0] = this->node_id(0);
229 conn[1] = this->node_id(1);
230 conn[2] = this->node_id(2);
231 conn[3] = this->node_id(3);
232 conn[4] = this->node_id(4);
233 conn[5] = this->node_id(5);
234 conn[6] = this->node_id(6);
235 conn[7] = this->node_id(7);
236 conn[8] = this->node_id(8);
237 conn[9] = this->node_id(9);
238 conn[10] = this->node_id(10);
239 conn[11] = this->node_id(11);
240 conn[12] = this->node_id(16);
241 conn[13] = this->node_id(17);
242 conn[14] = this->node_id(18);
243 conn[15] = this->node_id(19);
244 conn[16] = this->node_id(12);
245 conn[17] = this->node_id(13);
246 conn[18] = this->node_id(14);
247 conn[19] = this->node_id(15);
248 return;
249
250 default:
251 libmesh_error_msg("Unknown sc = " << sc);
252 }
253 }
254
255 default:
256 libmesh_error_msg("Unsupported IO package " << iop);
257 }
258}
259
260
261
262
263unsigned short int Hex20::second_order_adjacent_vertex (const unsigned int n,
264 const unsigned int v) const
265{
266 libmesh_assert_greater_equal (n, this->n_vertices());
267 libmesh_assert_less (n, this->n_nodes());
268 libmesh_assert_less (v, 2);
269 /*
270 * the _second_order_adjacent_vertices matrix is
271 * stored in cell_hex.C, since this matrix is identical
272 * for Hex20 and Hex27 (for the first 12 higher-order nodes)
273 */
274 return _second_order_adjacent_vertices[n-this->n_vertices()][v];
275}
276
277
278
279std::pair<unsigned short int, unsigned short int>
280Hex20::second_order_child_vertex (const unsigned int n) const
281{
282 libmesh_assert_greater_equal (n, this->n_vertices());
283 libmesh_assert_less (n, this->n_nodes());
284 /*
285 * the _second_order_vertex_child_* vectors are
286 * stored in cell_hex.C, since they are identical
287 * for Hex20 and Hex27 (for the first 12 higher-order nodes)
288 */
289 return std::pair<unsigned short int, unsigned short int>
290 (_second_order_vertex_child_number[n],
291 _second_order_vertex_child_index[n]);
292}
293
294
295
296Real Hex20::volume () const
297{
298 // This specialization is good for Lagrange mappings only in general
299 if (this->mapping_type() != LAGRANGE_MAP)
300 return this->Elem::volume();
301
302 // Make copies of our points. It makes the subsequent calculations a bit
303 // shorter and avoids dereferencing the same pointer multiple times.
304 Point
305 x0 = point(0), x1 = point(1), x2 = point(2), x3 = point(3), x4 = point(4),
306 x5 = point(5), x6 = point(6), x7 = point(7), x8 = point(8), x9 = point(9),
307 x10 = point(10), x11 = point(11), x12 = point(12), x13 = point(13), x14 = point(14),
308 x15 = point(15), x16 = point(16), x17 = point(17), x18 = point(18), x19 = point(19);
309
310 // The constant components of the dx/dxi vector,
311 // dx/dxi = \vec{a000} + \vec{a001}*zeta + \vec{a002}*zeta^2 + ...
312 // These were copied directly from the output of a Python script.
313 // There are at most 17 terms with total degree <=3, but only 12
314 // of them are non-zero for each direction.
315 Point dx_dxi[17] =
316 {
317 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,
318 x11/4 + x17/4 - x19/4 - x9/4,
319 -x0/8 + x1/8 + x12/4 - x13/4 - x14/4 + x15/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8,
320 x12/4 - x13/4 + x14/4 - x15/4,
321 -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
322 x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
323 -x0/8 + x1/8 + x11/4 - x17/4 + x19/4 + x2/8 - x3/8 - x4/8 + x5/8 + x6/8 - x7/8 - x9/4,
324 x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
325 x0/4 + x1/4 - x10/2 - x16/2 - x18/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x8/2,
326 -x0/4 - x1/4 + x10/2 - x16/2 - x18/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x8/2,
327 Point(0,0,0),
328 -x0/4 - x1/4 - x10/2 + x16/2 - x18/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4 + x8/2,
329 x0/4 + x1/4 + x10/2 + x16/2 - x18/2 - x2/4 - x3/4 - x4/4 - x5/4 + x6/4 + x7/4 - x8/2,
330 Point(0,0,0),
331 Point(0,0,0),
332 Point(0,0,0),
333 Point(0,0,0)
334 };
335
336 // The constant components of the dx/deta vector. These were copied
337 // directly from the output of a Python script. There are at most
338 // 17 terms with total degree <=3, but only 12 of them are non-zero
339 // for each direction.
340 Point dx_deta[17] =
341 {
342 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,
343 -x10/4 - x16/4 + x18/4 + x8/4,
344 -x0/8 - x1/8 + x12/4 + x13/4 - x14/4 - x15/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8,
345 x0/4 + x1/4 - x11/2 - x17/2 - x19/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4 - x9/2,
346 -x0/4 - x1/4 + x11/2 - x17/2 - x19/2 - x2/4 - x3/4 + x4/4 + x5/4 + x6/4 + x7/4 + x9/2,
347 Point(0,0,0),
348 Point(0,0,0),
349 Point(0,0,0),
350 x12/4 - x13/4 + x14/4 - x15/4,
351 -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
352 x0/8 - x1/8 - x12/4 + x13/4 - x14/4 + x15/4 + x2/8 - x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
353 -x0/4 + x1/4 + x11/2 - x17/2 + x19/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4 - x9/2,
354 x0/4 - x1/4 - x11/2 - x17/2 + x19/2 - x2/4 + x3/4 - x4/4 + x5/4 + x6/4 - x7/4 + x9/2,
355 Point(0,0,0),
356 -x0/8 - x1/8 - x10/4 + x16/4 - x18/4 + x2/8 + x3/8 - x4/8 - x5/8 + x6/8 + x7/8 + x8/4,
357 x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
358 Point(0,0,0)
359 };
360
361 // The constant components of the dx/dzeta vector. These were copied
362 // directly from the output of a Python script. There are at most
363 // 17 terms with total degree <=3, but only 12 of them are non-zero
364 // for each direction.
365 Point dx_dzeta[17] =
366 {
367 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,
368 x0/4 + x1/4 - x12/2 - x13/2 - x14/2 - x15/2 + x2/4 + x3/4 + x4/4 + x5/4 + x6/4 + x7/4,
369 Point(0,0,0),
370 -x10/4 - x16/4 + x18/4 + x8/4,
371 -x0/4 - x1/4 + x12/2 + x13/2 - x14/2 - x15/2 + x2/4 + x3/4 - x4/4 - x5/4 + x6/4 + x7/4,
372 Point(0,0,0),
373 -x0/8 - x1/8 + x11/4 - x17/4 - x19/4 - x2/8 - x3/8 + x4/8 + x5/8 + x6/8 + x7/8 + x9/4,
374 Point(0,0,0),
375 x11/4 + x17/4 - x19/4 - x9/4,
376 -x0/4 + x1/4 + x12/2 - x13/2 - x14/2 + x15/2 + x2/4 - x3/4 - x4/4 + x5/4 + x6/4 - x7/4,
377 Point(0,0,0),
378 -x0/8 + x1/8 - x2/8 + x3/8 + x4/8 - x5/8 + x6/8 - x7/8,
379 x0/4 - x1/4 - x12/2 + x13/2 - x14/2 + x15/2 + x2/4 - x3/4 + x4/4 - x5/4 + x6/4 - x7/4,
380 x0/8 - x1/8 - x11/4 - x17/4 + x19/4 - x2/8 + x3/8 - x4/8 + x5/8 + x6/8 - x7/8 + x9/4,
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 x0/8 + x1/8 + x10/4 + x16/4 - x18/4 - x2/8 - x3/8 - x4/8 - x5/8 + x6/8 + x7/8 - x8/4,
384 };
385
386 // The integer exponents for each term.
387 static const int exponents[17][3] =
388 {
389 {0, 0, 0},
390 {0, 0, 1},
391 {0, 0, 2},
392 {0, 1, 0},
393 {0, 1, 1},
394 {0, 1, 2},
395 {0, 2, 0},
396 {0, 2, 1},
397 {1, 0, 0},
398 {1, 0, 1},
399 {1, 0, 2},
400 {1, 1, 0},
401 {1, 1, 1},
402 {1, 2, 0},
403 {2, 0, 0},
404 {2, 0, 1},
405 {2, 1, 0}
406 };
407
408
409 // 3x3 quadrature, exact for bi-quintics
410 const int N = 3;
411 const Real w[N] = {5./9, 8./9, 5./9};
412
413 // Quadrature point locations raised to powers. q[0][2] is
414 // quadrature point 0, squared, q[1][1] is quadrature point 1 to the
415 // first power, etc.
416 const Real q[N][N] =
417 {
418 //^0 ^1 ^2
419 { 1., -std::sqrt(15)/5., 15./25},
420 { 1., 0., 0.},
421 { 1., std::sqrt(15)/5., 15./25}
422 };
423
424
425 Real vol = 0.;
426 for (int i=0; i<N; ++i)
427 for (int j=0; j<N; ++j)
428 for (int k=0; k<N; ++k)
429 {
430 // Compute dx_dxi, dx_deta, dx_dzeta at the current quadrature point.
431 Point dx_dxi_q, dx_deta_q, dx_dzeta_q;
432 for (int c=0; c<17; ++c)
433 {
434 Real coeff =
435 q[i][exponents[c][0]] *
436 q[j][exponents[c][1]] *
437 q[k][exponents[c][2]];
438
439 dx_dxi_q += coeff * dx_dxi[c];
440 dx_deta_q += coeff * dx_deta[c];
441 dx_dzeta_q += coeff * dx_dzeta[c];
442 }
443
444 // Compute scalar triple product, multiply by weight, and accumulate volume.
445 vol += w[i] * w[j] * w[k] * triple_product(dx_dxi_q, dx_deta_q, dx_dzeta_q);
446 }
447
448 return vol;
449}
450
451
452
453
454#ifdef LIBMESH_ENABLE_AMR
455
456const Real Hex20::_embedding_matrix[Hex20::num_children][Hex20::num_nodes][Hex20::num_nodes] =
457 {
458 // embedding matrix for child 0
459 {
460 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
461 { 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
462 { 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
463 { -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
464 { 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
465 { 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
466 { -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
467 { -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
468 { -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
469 { 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
470 { -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
471 { -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
472 { 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
473 { 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
474 { -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
475 { -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
476 { -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
477 { -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
478 { -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
479 { -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
480 { -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
481 },
482
483 // embedding matrix for child 1
484 {
485 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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 }, // 0
487 { 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
488 { 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
489 { -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
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 }, // 4
491 { 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
492 { 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
493 { -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
494 { -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
495 { 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
496 { -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
497 { -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
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 }, // 12
499 { 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
500 { 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
501 { -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
502 { -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
503 { 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
504 { -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
505 { -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
506 },
507
508 // embedding matrix for child 2
509 {
510 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
511 { 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
512 { -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
513 { 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
514 { 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
515 { -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
516 { -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
517 { 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
518 { 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
519 { -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
520 { -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
521 { 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
522 { -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
523 { -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
524 { -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
525 { 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
526 { 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
527 { -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
528 { -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
529 { 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
530 { -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
531 },
532
533 // embedding matrix for child 3
534 {
535 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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 }, // 0
537 { 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
538 { 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
539 { 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
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 }, // 4
541 { 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
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, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 6
543 { 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
544 { -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
545 { 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
546 { 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
547 { -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
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 }, // 12
549 { 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
550 { 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
551 { 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
552 { -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
553 { 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
554 { 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
555 { -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
556 },
557
558 // embedding matrix for child 4
559 {
560 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
561 { 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
562 { -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
563 { -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
564 { -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
565 { 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
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, 0.00000, 0.00000, 1.00000, 0.00000, 0.00000, 0.00000 }, // 5
567 { 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
568 { 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
569 { -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
570 { -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
571 { -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
572 { -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
573 { -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
574 { -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
575 { -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
576 { -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
577 { 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
578 { 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
579 { 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
580 { 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
581 },
582
583 // embedding matrix for child 5
584 {
585 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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 }, // 0
587 { 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
588 { 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
589 { -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
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 }, // 4
591 { 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
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, 1.00000, 0.00000, 0.00000 }, // 6
593 { 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
594 { -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
595 { 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
596 { -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
597 { -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
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 }, // 12
599 { 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
600 { 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
601 { -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
602 { 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
603 { 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
604 { 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
605 { 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
606 },
607
608 // embedding matrix for child 6
609 {
610 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
611 { -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
612 { -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
613 { 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
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, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 3
615 { 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
616 { 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
617 { 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
618 { 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
619 { -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
620 { -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
621 { 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
622 { -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
623 { -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
624 { -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
625 { 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
626 { 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
627 { 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
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, 0.250000, 0.375000, 0.750000, 0.375000 }, // 17
629 { 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
630 { 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
631 },
632
633 // embedding matrix for child 7
634 {
635 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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 }, // 0
637 { 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
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, 1.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000 }, // 2
639 { 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
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 }, // 4
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, 1.00000, 0.00000, 0.00000 }, // 5
642 { 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
643 { 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
644 { -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
645 { 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
646 { 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
647 { -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
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 }, // 12
649 { 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
650 { 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
651 { 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
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, 0.375000, 0.750000, 0.375000, 0.250000 }, // 16
653 { 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
654 { 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
655 { 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
656 }
657 };
658
659#endif
660
661void
662Hex20::permute(unsigned int perm_num)
663{
664 libmesh_assert_less (perm_num, 24);
665 const unsigned int side = perm_num % 6;
666 const unsigned int rotate = perm_num / 6;
667
668 for (unsigned int i = 0; i != rotate; ++i)
669 {
670 swap4nodes(0,1,2,3);
671 swap4nodes(4,5,6,7);
672 swap4nodes(8,9,10,11);
673 swap4nodes(12,13,14,15);
674 swap4nodes(16,17,18,19);
675 swap4neighbors(1,2,3,4);
676 }
677
678 switch (side) {
679 case 0:
680 break;
681 case 1:
682 swap4nodes(3,7,4,0);
683 swap4nodes(11,15,19,12);
684 swap4nodes(10,18,16,8);
685 swap4nodes(2,6,5,1);
686 swap4nodes(9,14,17,13);
687 swap4neighbors(0,3,5,1);
688 break;
689 case 2:
690 swap4nodes(0,4,5,1);
691 swap4nodes(8,12,16,13);
692 swap4nodes(3,7,6,2);
693 swap4nodes(10,15,18,14);
694 swap4nodes(11,19,17,9);
695 swap4neighbors(0,4,5,2);
696 break;
697 case 3:
698 swap4nodes(0,4,7,3);
699 swap4nodes(12,19,15,11);
700 swap4nodes(8,16,18,10);
701 swap4nodes(1,5,6,2);
702 swap4nodes(13,17,14,9);
703 swap4neighbors(0,1,5,3);
704 break;
705 case 4:
706 swap4nodes(1,5,4,0);
707 swap4nodes(8,13,16,12);
708 swap4nodes(9,17,19,11);
709 swap4nodes(2,6,7,3);
710 swap4nodes(10,14,18,15);
711 swap4neighbors(0,2,5,4);
712 break;
713 case 5:
714 swap2nodes(0,7);
715 swap2nodes(8,18);
716 swap2nodes(1,6);
717 swap2nodes(2,5);
718 swap2nodes(10,16);
719 swap2nodes(3,4);
720 swap2nodes(11,19);
721 swap2nodes(12,15);
722 swap2nodes(9,17);
723 swap2nodes(13,14);
724 swap2neighbors(0,5);
725 swap2neighbors(1,3);
726 break;
727 default:
728 libmesh_error();
729 }
730}
731
732
733void
734Hex20::flip(BoundaryInfo * boundary_info)
735{
736 libmesh_assert(boundary_info);
737
738 swap2nodes(0,1);
739 swap2nodes(2,3);
740 swap2nodes(4,5);
741 swap2nodes(6,7);
742 swap2nodes(9,11);
743 swap2nodes(12,13);
744 swap2nodes(14,15);
745 swap2nodes(17,19);
746 swap2neighbors(2,4);
747 swap2boundarysides(2,4,boundary_info);
748 swap2boundaryedges(1,3,boundary_info);
749 swap2boundaryedges(4,5,boundary_info);
750 swap2boundaryedges(6,7,boundary_info);
751 swap2boundaryedges(9,11,boundary_info);
752}
753
754
755ElemType
756Hex20::side_type (const unsigned int libmesh_dbg_var(s)) const
757{
758 libmesh_assert_less (s, 6);
759 return QUAD8;
760}
761
762
763} // namespace libMesh
libMesh::BoundaryInfo
The BoundaryInfo class contains information relevant to boundary conditions including storing faces,...
Definition boundary_info.h:58
libMesh::Elem::swap4nodes
void swap4nodes(unsigned int n1, unsigned int n2, unsigned int n3, unsigned int n4)
Swaps four node_ptrs, "rotating" them.
Definition elem.h:2273
libMesh::Elem::affine_tol
static constexpr Real affine_tol
Default tolerance to use in has_affine_map().
Definition elem.h:2191
libMesh::Elem::point
const Point & point(const unsigned int i) const
Definition elem.h:2583
libMesh::Elem::swap2nodes
void swap2nodes(unsigned int n1, unsigned int n2)
Swaps two node_ptrs.
Definition elem.h:2222
libMesh::Elem::_nodes
Node ** _nodes
Pointers to the nodes we are connected to.
Definition elem.h:2375
libMesh::Elem::swap2neighbors
void swap2neighbors(unsigned int n1, unsigned int n2)
Swaps two neighbor_ptrs.
Definition elem.h:2232
libMesh::Elem::swap2boundarysides
void swap2boundarysides(unsigned short s1, unsigned short s2, BoundaryInfo *boundary_info) const
Swaps two sides in boundary_info, if it is non-null.
Definition elem.C:3982
libMesh::Elem::mapping_type
ElemMappingType mapping_type() const
Definition elem.h:3258
libMesh::Elem::volume
virtual Real volume() const
Definition elem.C:3865
libMesh::Elem::swap2boundaryedges
void swap2boundaryedges(unsigned short e1, unsigned short e2, BoundaryInfo *boundary_info) const
Swaps two edges in boundary_info, if it is non-null.
Definition elem.C:3998
libMesh::Elem::node_id
dof_id_type node_id(const unsigned int i) const
Definition elem.h:2605
libMesh::Elem::swap4neighbors
void swap4neighbors(unsigned int n1, unsigned int n2, unsigned int n3, unsigned int n4)
Swaps four neighbor_ptrs, "rotating" them.
Definition elem.h:2283
libMesh::Hex20::is_face
virtual bool is_face(const unsigned int i) const override
Definition cell_hex20.C:54
libMesh::Hex20::nodes_per_side
static const int nodes_per_side
Definition cell_hex20.h:218
libMesh::Hex20::side_nodes_map
static constexpr const unsigned int(& side_nodes_map)[num_sides][nodes_per_side]
Definition cell_hex20.h:233
libMesh::Hex20::n_sub_elem
virtual unsigned int n_sub_elem() const override
Definition cell_hex20.h:103
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:189
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:263
libMesh::Hex20::edge_nodes_map
static constexpr const unsigned int(& edge_nodes_map)[num_edges][nodes_per_edge]
Definition cell_hex20.h:228
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:175
libMesh::Hex20::build_side_ptr
virtual std::unique_ptr< Elem > build_side_ptr(const unsigned int i) override
Builds a QUAD8 built coincident with face i.
Definition cell_hex20.C:138
libMesh::Hex20::is_edge
virtual bool is_edge(const unsigned int i) const override
Definition cell_hex20.C:47
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:280
libMesh::Hex20::side_type
ElemType side_type(const unsigned int s) const override final
Definition cell_hex20.C:756
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:59
libMesh::Hex20::nodes_per_edge
static const int nodes_per_edge
Definition cell_hex20.h:219
libMesh::Hex20::n_nodes
virtual unsigned int n_nodes() const override
Definition cell_hex20.h:98
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:82
libMesh::Hex20::flip
virtual void flip(BoundaryInfo *) override final
Flips the element (by swapping node and neighbor pointers) to have a mapping Jacobian of opposite sig...
Definition cell_hex20.C:734
libMesh::Hex20::_embedding_matrix
static const Real _embedding_matrix[num_children][num_nodes][num_nodes]
Matrix that computes new nodal locations/solution values from current nodes/solution.
Definition cell_hex20.h:269
libMesh::Hex20::nodes_on_side
virtual std::vector< unsigned int > nodes_on_side(const unsigned int s) const override
Definition cell_hex20.C:69
libMesh::Hex20::is_vertex
virtual bool is_vertex(const unsigned int i) const override
Definition cell_hex20.C:40
libMesh::Hex20::local_edge_node
virtual unsigned int local_edge_node(unsigned int edge, unsigned int edge_node) const override
Definition cell_hex20.C:164
libMesh::Hex20::permute
virtual void permute(unsigned int perm_num) override final
Permutes the element (by swapping node and neighbor pointers) according to the specified index.
Definition cell_hex20.C:662
libMesh::Hex20::volume
virtual Real volume() const override
A specialization for computing the volume of a Hex20.
Definition cell_hex20.C:296
libMesh::Hex20::default_order
virtual Order default_order() const override
Definition cell_hex20.C:131
libMesh::Hex20::has_affine_map
virtual bool has_affine_map() const override
Definition cell_hex20.C:93
libMesh::Hex20::local_side_node
virtual unsigned int local_side_node(unsigned int side, unsigned int side_node) const override
Definition cell_hex20.C:153
libMesh::Hex20::nodes_on_edge
virtual std::vector< unsigned int > nodes_on_edge(const unsigned int e) const override
Definition cell_hex20.C:76
libMesh::Hex20::num_nodes
static const int num_nodes
Geometric constants for Hex20.
Definition cell_hex20.h:217
libMesh::Hex::n_edges
virtual unsigned int n_edges() const override final
Definition cell_hex.h:90
libMesh::Hex::n_vertices
virtual unsigned int n_vertices() const override final
Definition cell_hex.h:85
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:224
libMesh::Hex::n_sides
virtual unsigned int n_sides() const override final
Definition cell_hex.h:80
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:219
libMesh::Hex::num_children
static const int num_children
Definition cell_hex.h:75
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:214
libMesh::Point
A Point defines a location in LIBMESH_DIM dimensional Real space.
Definition point.h:41
libMesh::TypeVector::relative_fuzzy_equals
bool relative_fuzzy_equals(const TypeVector< T > &rhs, Real tol=TOLERANCE) const
Definition type_vector.h:1052
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::IOPackage
IOPackage
libMesh interfaces with several different software packages for the purposes of creating,...
Definition enum_io_package.h:38
libMesh::triple_product
LIBMESH_DEVICE_INLINE T triple_product(const TypeVector< T > &a, const TypeVector< T > &b, const TypeVector< T > &c)
Definition type_vector.h:1100
libMesh::ElemType
ElemType
Defines an enum for geometric element types.
Definition enum_elem_type.h:33
libMesh::libmesh_assert
libmesh_assert(ctx)
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition libmesh_common.h:148
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