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