1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2020 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 // Local includes
19 #include "libmesh/libmesh_config.h"
20
21 #ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
22
23 // Local includes cont'd
24 #include "libmesh/cell_inf_hex16.h"
25 #include "libmesh/edge_edge3.h"
26 #include "libmesh/edge_inf_edge2.h"
27 #include "libmesh/face_quad8.h"
28 #include "libmesh/face_inf_quad6.h"
29 #include "libmesh/side.h"
30 #include "libmesh/enum_io_package.h"
31 #include "libmesh/enum_order.h"
32
33 namespace libMesh
34 {
35
36
37 // ------------------------------------------------------------
38 // InfHex16 class static member initializations
39 const int InfHex16::num_nodes;
40 const int InfHex16::num_sides;
41 const int InfHex16::num_edges;
42 const int InfHex16::num_children;
43 const int InfHex16::nodes_per_side;
44 const int InfHex16::nodes_per_edge;
45
46 const unsigned int InfHex16::side_nodes_map[InfHex16::num_sides][InfHex16::nodes_per_side] =
47 {
48 { 0, 1, 2, 3, 8, 9, 10, 11}, // Side 0
49 { 0, 1, 4, 5, 8, 12, 99, 99}, // Side 1
50 { 1, 2, 5, 6, 9, 13, 99, 99}, // Side 2
51 { 2, 3, 6, 7, 10, 14, 99, 99}, // Side 3
52 { 3, 0, 7, 4, 11, 15, 99, 99} // Side 4
53 };
54
55 const unsigned int InfHex16::edge_nodes_map[InfHex16::num_edges][InfHex16::nodes_per_edge] =
56 {
57 {0, 1, 8}, // Edge 0
58 {1, 2, 9}, // Edge 1
59 {2, 3, 10}, // Edge 2
60 {0, 3, 11}, // Edge 3
61 {0, 4, 99}, // Edge 4
62 {1, 5, 99}, // Edge 5
63 {2, 6, 99}, // Edge 6
64 {3, 7, 99} // Edge 7
65 };
66
67 const unsigned int InfHex16::edge_sides_map[InfHex16::num_edges][2] =
68 {
69 {0, 1}, // Edge 0
70 {1, 2}, // Edge 1
71 {0, 3}, // Edge 2
72 {0, 4}, // Edge 3
73 {1, 4}, // Edge 4
74 {1, 2}, // Edge 5
75 {2, 3}, // Edge 6
76 {3, 4} // Edge 7
77 };
78
79 // ------------------------------------------------------------
80 // InfHex16 class member functions
81
is_vertex(const unsigned int i)82 bool InfHex16::is_vertex(const unsigned int i) const
83 {
84 if (i < 4)
85 return true;
86 return false;
87 }
88
is_edge(const unsigned int i)89 bool InfHex16::is_edge(const unsigned int i) const
90 {
91 if (i < 4)
92 return false;
93 if (i > 11)
94 return false;
95 return true;
96 }
97
is_face(const unsigned int i)98 bool InfHex16::is_face(const unsigned int i) const
99 {
100 if (i > 11)
101 return true;
102 return false;
103 }
104
is_node_on_side(const unsigned int n,const unsigned int s)105 bool InfHex16::is_node_on_side(const unsigned int n,
106 const unsigned int s) const
107 {
108 libmesh_assert_less (s, n_sides());
109 return std::find(std::begin(side_nodes_map[s]),
110 std::end(side_nodes_map[s]),
111 n) != std::end(side_nodes_map[s]);
112 }
113
114 std::vector<unsigned>
nodes_on_side(const unsigned int s)115 InfHex16::nodes_on_side(const unsigned int s) const
116 {
117 libmesh_assert_less(s, n_sides());
118 auto trim = (s == 0) ? 0 : 2;
119 return {std::begin(side_nodes_map[s]), std::end(side_nodes_map[s]) - trim};
120 }
121
122 std::vector<unsigned>
nodes_on_edge(const unsigned int e)123 InfHex16::nodes_on_edge(const unsigned int e) const
124 {
125 libmesh_assert_less(e, n_edges());
126 auto trim = (e < 4) ? 0 : 1;
127 return {std::begin(edge_nodes_map[e]), std::end(edge_nodes_map[e]) - trim};
128 }
129
is_node_on_edge(const unsigned int n,const unsigned int e)130 bool InfHex16::is_node_on_edge(const unsigned int n,
131 const unsigned int e) const
132 {
133 libmesh_assert_less (e, n_edges());
134 return std::find(std::begin(edge_nodes_map[e]),
135 std::end(edge_nodes_map[e]),
136 n) != std::end(edge_nodes_map[e]);
137 }
138
139
140
default_order()141 Order InfHex16::default_order() const
142 {
143 return SECOND;
144 }
145
146
147
local_side_node(unsigned int side,unsigned int side_node)148 unsigned int InfHex16::local_side_node(unsigned int side,
149 unsigned int side_node) const
150 {
151 libmesh_assert_less (side, this->n_sides());
152
153 // Never more than 8 nodes per side.
154 libmesh_assert_less (side_node, InfHex16::nodes_per_side);
155
156 // Some sides have 6 nodes.
157 libmesh_assert(side == 0 || side_node < 6);
158
159 return InfHex16::side_nodes_map[side][side_node];
160 }
161
162
163
local_edge_node(unsigned int edge,unsigned int edge_node)164 unsigned int InfHex16::local_edge_node(unsigned int edge,
165 unsigned int edge_node) const
166 {
167 libmesh_assert_less (edge, this->n_edges());
168
169 // Never more than 3 nodes per edge.
170 libmesh_assert_less (edge_node, InfHex16::nodes_per_edge);
171
172 // Some edges only have 2 nodes.
173 libmesh_assert(edge < 4 || edge_node < 2);
174
175 return InfHex16::edge_nodes_map[edge][edge_node];
176 }
177
178
179
build_side_ptr(const unsigned int i,bool proxy)180 std::unique_ptr<Elem> InfHex16::build_side_ptr (const unsigned int i,
181 bool proxy)
182 {
183 libmesh_assert_less (i, this->n_sides());
184
185 std::unique_ptr<Elem> face;
186 if (proxy)
187 {
188 switch (i)
189 {
190 // base
191 case 0:
192 {
193 face = libmesh_make_unique<Side<Quad8,InfHex16>>(this,i);
194 break;
195 }
196
197 // ifem sides
198 case 1:
199 case 2:
200 case 3:
201 case 4:
202 {
203 face = libmesh_make_unique<Side<InfQuad6,InfHex16>>(this,i);
204 break;
205 }
206
207 default:
208 libmesh_error_msg("Invalid side i = " << i);
209 }
210 }
211
212 else
213 {
214 // Think of a unit cube: (-1,1) x (-1,1) x (1,1)
215 switch (i)
216 {
217 // the base face
218 case 0:
219 {
220 face = libmesh_make_unique<Quad8>(this);
221 break;
222 }
223
224 // connecting to another infinite element
225 case 1:
226 case 2:
227 case 3:
228 case 4:
229 {
230 face = libmesh_make_unique<InfQuad6>(this);
231 break;
232 }
233
234 default:
235 libmesh_error_msg("Invalid side i = " << i);
236 }
237
238 // Set the nodes
239 for (auto n : face->node_index_range())
240 face->set_node(n) = this->node_ptr(InfHex16::side_nodes_map[i][n]);
241 }
242
243 #ifdef LIBMESH_ENABLE_DEPRECATED
244 if (!proxy) // proxy sides used to leave parent() set
245 #endif
246 face->set_parent(nullptr);
247 face->set_interior_parent(this);
248
249 return face;
250 }
251
252
253
build_side_ptr(std::unique_ptr<Elem> & side,const unsigned int i)254 void InfHex16::build_side_ptr (std::unique_ptr<Elem> & side,
255 const unsigned int i)
256 {
257 libmesh_assert_less (i, this->n_sides());
258
259 // Think of a unit cube: (-1,1) x (-1,1) x (1,1)
260 switch (i)
261 {
262 // the base face
263 case 0:
264 {
265 if (!side.get() || side->type() != QUAD8)
266 {
267 side = this->build_side_ptr(i, false);
268 return;
269 }
270 break;
271 }
272
273 // connecting to another infinite element
274 case 1:
275 case 2:
276 case 3:
277 case 4:
278 {
279 if (!side.get() || side->type() != INFQUAD6)
280 {
281 side = this->build_side_ptr(i, false);
282 return;
283 }
284 break;
285 }
286
287 default:
288 libmesh_error_msg("Invalid side i = " << i);
289 }
290
291 side->subdomain_id() = this->subdomain_id();
292
293 // Set the nodes
294 for (auto n : side->node_index_range())
295 side->set_node(n) = this->node_ptr(InfHex16::side_nodes_map[i][n]);
296 }
297
298
299
build_edge_ptr(const unsigned int i)300 std::unique_ptr<Elem> InfHex16::build_edge_ptr (const unsigned int i)
301 {
302 libmesh_assert_less (i, this->n_edges());
303
304 if (i < 4) // base edges
305 return libmesh_make_unique<SideEdge<Edge3,InfHex16>>(this,i);
306
307 // infinite edges
308 return libmesh_make_unique<SideEdge<InfEdge2,InfHex16>>(this,i);
309 }
310
311
connectivity(const unsigned int sc,const IOPackage iop,std::vector<dof_id_type> & conn)312 void InfHex16::connectivity(const unsigned int sc,
313 const IOPackage iop,
314 std::vector<dof_id_type> & conn) const
315 {
316 libmesh_assert(_nodes);
317 libmesh_assert_less (sc, this->n_sub_elem());
318 libmesh_assert_not_equal_to (iop, INVALID_IO_PACKAGE);
319
320 switch (iop)
321 {
322 case TECPLOT:
323 {
324 switch (sc)
325 {
326 case 0:
327
328 conn[0] = this->node_id(0)+1;
329 conn[1] = this->node_id(1)+1;
330 conn[2] = this->node_id(2)+1;
331 conn[3] = this->node_id(3)+1;
332 conn[4] = this->node_id(4)+1;
333 conn[5] = this->node_id(5)+1;
334 conn[6] = this->node_id(6)+1;
335 conn[7] = this->node_id(7)+1;
336 return;
337
338 default:
339 libmesh_error_msg("Invalid sc = " << sc);
340 }
341 }
342
343 default:
344 libmesh_error_msg("Unsupported IO package " << iop);
345 }
346 }
347
348
349
350
second_order_adjacent_vertex(const unsigned int n,const unsigned int v)351 unsigned short int InfHex16::second_order_adjacent_vertex (const unsigned int n,
352 const unsigned int v) const
353 {
354 libmesh_assert_greater_equal (n, this->n_vertices());
355 libmesh_assert_less (n, this->n_nodes());
356 libmesh_assert_less (v, 2);
357 // note that the _second_order_adjacent_vertices matrix is
358 // stored in \p InfHex
359 return _second_order_adjacent_vertices[n-this->n_vertices()][v];
360 }
361
362
363
364 std::pair<unsigned short int, unsigned short int>
second_order_child_vertex(const unsigned int n)365 InfHex16::second_order_child_vertex (const unsigned int n) const
366 {
367 libmesh_assert_greater_equal (n, this->n_vertices());
368 libmesh_assert_less (n, this->n_nodes());
369 /*
370 * the _second_order_vertex_child_* vectors are
371 * stored in cell_inf_hex.C, since they are identical
372 * for InfHex16 and InfHex18
373 */
374 return std::pair<unsigned short int, unsigned short int>
375 (_second_order_vertex_child_number[n],
376 _second_order_vertex_child_index[n]);
377 }
378
379
380
381
382
383 #ifdef LIBMESH_ENABLE_AMR
384
385 const float InfHex16::_embedding_matrix[InfHex16::num_children][InfHex16::num_nodes][InfHex16::num_nodes] =
386 {
387 // embedding matrix for child 0
388 {
389 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 th parent Node
390 { 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 0th child N.
391 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 1
392 { -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0}, // 2
393 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0}, // 3
394 { 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 4
395 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0}, // 5
396 { 0.0, 0.0, 0.0, 0.0, -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5}, // 6
397 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0}, // 7
398 { 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 8
399 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.75, 0.375, 0.25, 0.375, 0.0, 0.0, 0.0, 0.0}, // 9
400 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.25, 0.375, 0.75, 0.0, 0.0, 0.0, 0.0}, // 10
401 { 0.375, 0.0, 0.0, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0}, // 11
402 { 0.0, 0.0, 0.0, 0.0, 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0}, // 12
403 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.75, 0.375, 0.25, 0.375}, // 13
404 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.25, 0.375, 0.75}, // 14
405 { 0.0, 0.0, 0.0, 0.0, 0.375, 0.0, 0.0, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75} // 15
406 },
407
408 // embedding matrix for child 1
409 {
410 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 th parent Node
411 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 0th child N.
412 { 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 1
413 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 2
414 { -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0}, // 3
415 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0}, // 4
416 { 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 5
417 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0}, // 6
418 { 0.0, 0.0, 0.0, 0.0, -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5}, // 7
419 { -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 8
420 { 0.0, 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 9
421 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.75, 0.375, 0.25, 0.0, 0.0, 0.0, 0.0}, // 10
422 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.75, 0.375, 0.25, 0.375, 0.0, 0.0, 0.0, 0.0}, // 11
423 { 0.0, 0.0, 0.0, 0.0, -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0}, // 12
424 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0}, // 13
425 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.75, 0.375, 0.25}, // 14
426 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.75, 0.375, 0.25, 0.375} // 15
427 },
428
429 // embedding matrix for child 2
430 {
431 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 th parent Node
432 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0}, // 0th child N.
433 { -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0}, // 1
434 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 2
435 { 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 3
436 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0}, // 4
437 { 0.0, 0.0, 0.0, 0.0, -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5}, // 5
438 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0}, // 6
439 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 7
440 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.25, 0.375, 0.75, 0.0, 0.0, 0.0, 0.0}, // 8
441 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.25, 0.375, 0.75, 0.375, 0.0, 0.0, 0.0, 0.0}, // 9
442 { 0.0, 0.0, -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0}, // 10
443 { -0.125, 0.0, 0.0, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0}, // 11
444 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.25, 0.375, 0.75}, // 12
445 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.25, 0.375, 0.75, 0.375}, // 13
446 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0}, // 14
447 { 0.0, 0.0, 0.0, 0.0, -0.125, 0.0, 0.0, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75} // 15
448 },
449
450 // embedding matrix for child 3
451 {
452 // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 th parent Node
453 { -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0}, // 0th child N.
454 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 1
455 { 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 2
456 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 3
457 { 0.0, 0.0, 0.0, 0.0, -0.25, -0.25, -0.25, -0.25, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 0.5}, // 4
458 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0}, // 5
459 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 6
460 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0}, // 7
461 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.75, 0.375, 0.25, 0.0, 0.0, 0.0, 0.0}, // 8
462 { 0.0, -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, // 9
463 { 0.0, 0.0, 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 0.0}, // 10
464 { -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.25, 0.375, 0.75, 0.375, 0.0, 0.0, 0.0, 0.0}, // 11
465 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.375, 0.75, 0.375, 0.25}, // 12
466 { 0.0, 0.0, 0.0, 0.0, 0.0, -0.125, 0.375, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0, 0.0}, // 13
467 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.375, -0.125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75, 0.0}, // 14
468 { 0.0, 0.0, 0.0, 0.0, -0.1875, -0.1875, -0.1875, -0.1875, 0.0, 0.0, 0.0, 0.0, 0.25, 0.375, 0.75, 0.375} // 15
469 }
470 };
471
472
473
474 #endif
475
476 } // namespace libMesh
477
478 #endif // ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
479