BELFEM 0.9.3
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_pyra64.hpp
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1/*
2 * BELFEM -- The Berkeley Lab Finite Element Framework
3 * Copyright (c) 2026, The Regents of the University of California,
4 * through Lawrence Berkeley National Laboratory (subject to receipt of any required
5 * approvals from the U.S. Dept. of Energy). All rights reserved.
6 *
7 * Developers: Christian Messe, Gregory Giard
8 *
9 * See the top-level LICENSE file for the complete license and disclaimer.
10 */
11
12#ifndef BELFEM_FN_INTPOINTS_GAUSS_PYRA64_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_PYRA64_HPP
14
15
16#include "typedefs.hpp"
17#include "cl_Vector.hpp"
18#include "cl_Matrix.hpp"
19
20
21namespace belfem
22{
23 namespace integration
24 {
25// ----------------------------------------------------------------------------
26
35 inline void
36 gauss_pyra64(
37 Vector <real> & aWeights,
38 Matrix <real> & aPoints )
39 {
40 aPoints.set_size( 3, 64 );
41 aWeights.set_size( 64 );
42
43 aPoints( 0, 0 ) = -0.81937072733298044 ;
44 aPoints( 1, 0 ) = -0.81937072733298044 ;
45 aPoints( 2, 0 ) = 0.048500549446997276 ;
46 aWeights( 0 ) = 0.01341783020966248 ;
47
48 aPoints( 0, 1 ) = -0.32349177616942726 ;
49 aPoints( 1, 1 ) = -0.81937072733298044 ;
50 aPoints( 2, 1 ) = 0.048500549446997276 ;
51 aWeights( 1 ) = 0.025155242430336153 ;
52
53 aPoints( 0, 2 ) = 0.32349177616942726 ;
54 aPoints( 1, 2 ) = -0.81937072733298044 ;
55 aPoints( 2, 2 ) = 0.048500549446997276 ;
56 aWeights( 2 ) = 0.025155242430336153 ;
57
58 aPoints( 0, 3 ) = 0.81937072733298044 ;
59 aPoints( 1, 3 ) = -0.81937072733298044 ;
60 aPoints( 2, 3 ) = 0.048500549446997276 ;
61 aWeights( 3 ) = 0.01341783020966248 ;
62
63 aPoints( 0, 4 ) = -0.81937072733298044 ;
64 aPoints( 1, 4 ) = -0.32349177616942726 ;
65 aPoints( 2, 4 ) = 0.048500549446997276 ;
66 aWeights( 4 ) = 0.025155242430336153 ;
67
68 aPoints( 0, 5 ) = -0.32349177616942726 ;
69 aPoints( 1, 5 ) = -0.32349177616942726 ;
70 aPoints( 2, 5 ) = 0.048500549446997276 ;
71 aWeights( 5 ) = 0.047160100540942954 ;
72
73 aPoints( 0, 6 ) = 0.32349177616942726 ;
74 aPoints( 1, 6 ) = -0.32349177616942726 ;
75 aPoints( 2, 6 ) = 0.048500549446997276 ;
76 aWeights( 6 ) = 0.047160100540942954 ;
77
78 aPoints( 0, 7 ) = 0.81937072733298044 ;
79 aPoints( 1, 7 ) = -0.32349177616942726 ;
80 aPoints( 2, 7 ) = 0.048500549446997276 ;
81 aWeights( 7 ) = 0.025155242430336153 ;
82
83 aPoints( 0, 8 ) = -0.81937072733298044 ;
84 aPoints( 1, 8 ) = 0.32349177616942726 ;
85 aPoints( 2, 8 ) = 0.048500549446997276 ;
86 aWeights( 8 ) = 0.025155242430336153 ;
87
88 aPoints( 0, 9 ) = -0.32349177616942726 ;
89 aPoints( 1, 9 ) = 0.32349177616942726 ;
90 aPoints( 2, 9 ) = 0.048500549446997276 ;
91 aWeights( 9 ) = 0.047160100540942954 ;
92
93 aPoints( 0, 10 ) = 0.32349177616942726 ;
94 aPoints( 1, 10 ) = 0.32349177616942726 ;
95 aPoints( 2, 10 ) = 0.048500549446997276 ;
96 aWeights( 10 ) = 0.047160100540942954 ;
97
98 aPoints( 0, 11 ) = 0.81937072733298044 ;
99 aPoints( 1, 11 ) = 0.32349177616942726 ;
100 aPoints( 2, 11 ) = 0.048500549446997276 ;
101 aWeights( 11 ) = 0.025155242430336153 ;
102
103 aPoints( 0, 12 ) = -0.81937072733298044 ;
104 aPoints( 1, 12 ) = 0.81937072733298044 ;
105 aPoints( 2, 12 ) = 0.048500549446997276 ;
106 aWeights( 12 ) = 0.01341783020966248 ;
107
108 aPoints( 0, 13 ) = -0.32349177616942726 ;
109 aPoints( 1, 13 ) = 0.81937072733298044 ;
110 aPoints( 2, 13 ) = 0.048500549446997276 ;
111 aWeights( 13 ) = 0.025155242430336153 ;
112
113 aPoints( 0, 14 ) = 0.32349177616942726 ;
114 aPoints( 1, 14 ) = 0.81937072733298044 ;
115 aPoints( 2, 14 ) = 0.048500549446997276 ;
116 aWeights( 14 ) = 0.025155242430336153 ;
117
118 aPoints( 0, 15 ) = 0.81937072733298044 ;
119 aPoints( 1, 15 ) = 0.81937072733298044 ;
120 aPoints( 2, 15 ) = 0.048500549446997276 ;
121 aWeights( 15 ) = 0.01341783020966248 ;
122
123 aPoints( 0, 16 ) = -0.65566855251502121 ;
124 aPoints( 1, 16 ) = -0.65566855251502121 ;
125 aPoints( 2, 16 ) = 0.23860073755186234 ;
126 aWeights( 16 ) = 0.017358942978834929 ;
127
128 aPoints( 0, 17 ) = -0.25886131583185773 ;
129 aPoints( 1, 17 ) = -0.65566855251502121 ;
130 aPoints( 2, 17 ) = 0.23860073755186234 ;
131 aWeights( 17 ) = 0.032543892130377346 ;
132
133 aPoints( 0, 18 ) = 0.25886131583185773 ;
134 aPoints( 1, 18 ) = -0.65566855251502121 ;
135 aPoints( 2, 18 ) = 0.23860073755186234 ;
136 aWeights( 18 ) = 0.032543892130377346 ;
137
138 aPoints( 0, 19 ) = 0.65566855251502121 ;
139 aPoints( 1, 19 ) = -0.65566855251502121 ;
140 aPoints( 2, 19 ) = 0.23860073755186234 ;
141 aWeights( 19 ) = 0.017358942978834929 ;
142
143 aPoints( 0, 20 ) = -0.65566855251502121 ;
144 aPoints( 1, 20 ) = -0.25886131583185773 ;
145 aPoints( 2, 20 ) = 0.23860073755186234 ;
146 aWeights( 20 ) = 0.032543892130377346 ;
147
148 aPoints( 0, 21 ) = -0.25886131583185773 ;
149 aPoints( 1, 21 ) = -0.25886131583185773 ;
150 aPoints( 2, 21 ) = 0.23860073755186234 ;
151 aWeights( 21 ) = 0.061012062559624818 ;
152
153 aPoints( 0, 22 ) = 0.25886131583185773 ;
154 aPoints( 1, 22 ) = -0.25886131583185773 ;
155 aPoints( 2, 22 ) = 0.23860073755186234 ;
156 aWeights( 22 ) = 0.061012062559624818 ;
157
158 aPoints( 0, 23 ) = 0.65566855251502121 ;
159 aPoints( 1, 23 ) = -0.25886131583185773 ;
160 aPoints( 2, 23 ) = 0.23860073755186234 ;
161 aWeights( 23 ) = 0.032543892130377346 ;
162
163 aPoints( 0, 24 ) = -0.65566855251502121 ;
164 aPoints( 1, 24 ) = 0.25886131583185773 ;
165 aPoints( 2, 24 ) = 0.23860073755186234 ;
166 aWeights( 24 ) = 0.032543892130377346 ;
167
168 aPoints( 0, 25 ) = -0.25886131583185773 ;
169 aPoints( 1, 25 ) = 0.25886131583185773 ;
170 aPoints( 2, 25 ) = 0.23860073755186234 ;
171 aWeights( 25 ) = 0.061012062559624818 ;
172
173 aPoints( 0, 26 ) = 0.25886131583185773 ;
174 aPoints( 1, 26 ) = 0.25886131583185773 ;
175 aPoints( 2, 26 ) = 0.23860073755186234 ;
176 aWeights( 26 ) = 0.061012062559624818 ;
177
178 aPoints( 0, 27 ) = 0.65566855251502121 ;
179 aPoints( 1, 27 ) = 0.25886131583185773 ;
180 aPoints( 2, 27 ) = 0.23860073755186234 ;
181 aWeights( 27 ) = 0.032543892130377346 ;
182
183 aPoints( 0, 28 ) = -0.65566855251502121 ;
184 aPoints( 1, 28 ) = 0.65566855251502121 ;
185 aPoints( 2, 28 ) = 0.23860073755186234 ;
186 aWeights( 28 ) = 0.017358942978834929 ;
187
188 aPoints( 0, 29 ) = -0.25886131583185773 ;
189 aPoints( 1, 29 ) = 0.65566855251502121 ;
190 aPoints( 2, 29 ) = 0.23860073755186234 ;
191 aWeights( 29 ) = 0.032543892130377346 ;
192
193 aPoints( 0, 30 ) = 0.25886131583185773 ;
194 aPoints( 1, 30 ) = 0.65566855251502121 ;
195 aPoints( 2, 30 ) = 0.23860073755186234 ;
196 aWeights( 30 ) = 0.032543892130377346 ;
197
198 aPoints( 0, 31 ) = 0.65566855251502121 ;
199 aPoints( 1, 31 ) = 0.65566855251502121 ;
200 aPoints( 2, 31 ) = 0.23860073755186234 ;
201 aWeights( 31 ) = 0.017358942978834929 ;
202
203 aPoints( 0, 32 ) = -0.415888110968196 ;
204 aPoints( 1, 32 ) = -0.415888110968196 ;
205 aPoints( 2, 32 ) = 0.51704729510436742 ;
206 aWeights( 32 ) = 0.0083049057887499764 ;
207
208 aPoints( 0, 33 ) = -0.16419476461254631 ;
209 aPoints( 1, 33 ) = -0.415888110968196 ;
210 aPoints( 2, 33 ) = 0.51704729510436742 ;
211 aWeights( 33 ) = 0.015569724404968665 ;
212
213 aPoints( 0, 34 ) = 0.16419476461254631 ;
214 aPoints( 1, 34 ) = -0.415888110968196 ;
215 aPoints( 2, 34 ) = 0.51704729510436742 ;
216 aWeights( 34 ) = 0.015569724404968665 ;
217
218 aPoints( 0, 35 ) = 0.415888110968196 ;
219 aPoints( 1, 35 ) = -0.415888110968196 ;
220 aPoints( 2, 35 ) = 0.51704729510436742 ;
221 aWeights( 35 ) = 0.0083049057887499764 ;
222
223 aPoints( 0, 36 ) = -0.415888110968196 ;
224 aPoints( 1, 36 ) = -0.16419476461254631 ;
225 aPoints( 2, 36 ) = 0.51704729510436742 ;
226 aWeights( 36 ) = 0.015569724404968665 ;
227
228 aPoints( 0, 37 ) = -0.16419476461254631 ;
229 aPoints( 1, 37 ) = -0.16419476461254631 ;
230 aPoints( 2, 37 ) = 0.51704729510436742 ;
231 aWeights( 37 ) = 0.029189532574235792 ;
232
233 aPoints( 0, 38 ) = 0.16419476461254631 ;
234 aPoints( 1, 38 ) = -0.16419476461254631 ;
235 aPoints( 2, 38 ) = 0.51704729510436742 ;
236 aWeights( 38 ) = 0.029189532574235792 ;
237
238 aPoints( 0, 39 ) = 0.415888110968196 ;
239 aPoints( 1, 39 ) = -0.16419476461254631 ;
240 aPoints( 2, 39 ) = 0.51704729510436742 ;
241 aWeights( 39 ) = 0.015569724404968665 ;
242
243 aPoints( 0, 40 ) = -0.415888110968196 ;
244 aPoints( 1, 40 ) = 0.16419476461254631 ;
245 aPoints( 2, 40 ) = 0.51704729510436742 ;
246 aWeights( 40 ) = 0.015569724404968665 ;
247
248 aPoints( 0, 41 ) = -0.16419476461254631 ;
249 aPoints( 1, 41 ) = 0.16419476461254631 ;
250 aPoints( 2, 41 ) = 0.51704729510436742 ;
251 aWeights( 41 ) = 0.029189532574235792 ;
252
253 aPoints( 0, 42 ) = 0.16419476461254631 ;
254 aPoints( 1, 42 ) = 0.16419476461254631 ;
255 aPoints( 2, 42 ) = 0.51704729510436742 ;
256 aWeights( 42 ) = 0.029189532574235792 ;
257
258 aPoints( 0, 43 ) = 0.415888110968196 ;
259 aPoints( 1, 43 ) = 0.16419476461254631 ;
260 aPoints( 2, 43 ) = 0.51704729510436742 ;
261 aWeights( 43 ) = 0.015569724404968665 ;
262
263 aPoints( 0, 44 ) = -0.415888110968196 ;
264 aPoints( 1, 44 ) = 0.415888110968196 ;
265 aPoints( 2, 44 ) = 0.51704729510436742 ;
266 aWeights( 44 ) = 0.0083049057887499764 ;
267
268 aPoints( 0, 45 ) = -0.16419476461254631 ;
269 aPoints( 1, 45 ) = 0.415888110968196 ;
270 aPoints( 2, 45 ) = 0.51704729510436742 ;
271 aWeights( 45 ) = 0.015569724404968665 ;
272
273 aPoints( 0, 46 ) = 0.16419476461254631 ;
274 aPoints( 1, 46 ) = 0.415888110968196 ;
275 aPoints( 2, 46 ) = 0.51704729510436742 ;
276 aWeights( 46 ) = 0.015569724404968665 ;
277
278 aPoints( 0, 47 ) = 0.415888110968196 ;
279 aPoints( 1, 47 ) = 0.415888110968196 ;
280 aPoints( 2, 47 ) = 0.51704729510436742 ;
281 aWeights( 47 ) = 0.0083049057887499764 ;
282
283 aPoints( 0, 48 ) = -0.17579975700952866 ;
284 aPoints( 1, 48 ) = -0.17579975700952866 ;
285 aPoints( 2, 48 ) = 0.79585141789677283 ;
286 aWeights( 48 ) = 0.0012526521179532725 ;
287
288 aPoints( 0, 49 ) = -0.069406647989823891 ;
289 aPoints( 1, 49 ) = -0.17579975700952866 ;
290 aPoints( 2, 49 ) = 0.79585141789677283 ;
291 aWeights( 49 ) = 0.00234842498493512 ;
292
293 aPoints( 0, 50 ) = 0.069406647989823891 ;
294 aPoints( 1, 50 ) = -0.17579975700952866 ;
295 aPoints( 2, 50 ) = 0.79585141789677283 ;
296 aWeights( 50 ) = 0.00234842498493512 ;
297
298 aPoints( 0, 51 ) = 0.17579975700952866 ;
299 aPoints( 1, 51 ) = -0.17579975700952866 ;
300 aPoints( 2, 51 ) = 0.79585141789677283 ;
301 aWeights( 51 ) = 0.0012526521179532725 ;
302
303 aPoints( 0, 52 ) = -0.17579975700952866 ;
304 aPoints( 1, 52 ) = -0.069406647989823891 ;
305 aPoints( 2, 52 ) = 0.79585141789677283 ;
306 aWeights( 52 ) = 0.00234842498493512 ;
307
308 aPoints( 0, 53 ) = -0.069406647989823891 ;
309 aPoints( 1, 53 ) = -0.069406647989823891 ;
310 aPoints( 2, 53 ) = 0.79585141789677283 ;
311 aWeights( 53 ) = 0.0044027386620945682 ;
312
313 aPoints( 0, 54 ) = 0.069406647989823891 ;
314 aPoints( 1, 54 ) = -0.069406647989823891 ;
315 aPoints( 2, 54 ) = 0.79585141789677283 ;
316 aWeights( 54 ) = 0.0044027386620945682 ;
317
318 aPoints( 0, 55 ) = 0.17579975700952866 ;
319 aPoints( 1, 55 ) = -0.069406647989823891 ;
320 aPoints( 2, 55 ) = 0.79585141789677283 ;
321 aWeights( 55 ) = 0.00234842498493512 ;
322
323 aPoints( 0, 56 ) = -0.17579975700952866 ;
324 aPoints( 1, 56 ) = 0.069406647989823891 ;
325 aPoints( 2, 56 ) = 0.79585141789677283 ;
326 aWeights( 56 ) = 0.00234842498493512 ;
327
328 aPoints( 0, 57 ) = -0.069406647989823891 ;
329 aPoints( 1, 57 ) = 0.069406647989823891 ;
330 aPoints( 2, 57 ) = 0.79585141789677283 ;
331 aWeights( 57 ) = 0.0044027386620945682 ;
332
333 aPoints( 0, 58 ) = 0.069406647989823891 ;
334 aPoints( 1, 58 ) = 0.069406647989823891 ;
335 aPoints( 2, 58 ) = 0.79585141789677283 ;
336 aWeights( 58 ) = 0.0044027386620945682 ;
337
338 aPoints( 0, 59 ) = 0.17579975700952866 ;
339 aPoints( 1, 59 ) = 0.069406647989823891 ;
340 aPoints( 2, 59 ) = 0.79585141789677283 ;
341 aWeights( 59 ) = 0.00234842498493512 ;
342
343 aPoints( 0, 60 ) = -0.17579975700952866 ;
344 aPoints( 1, 60 ) = 0.17579975700952866 ;
345 aPoints( 2, 60 ) = 0.79585141789677283 ;
346 aWeights( 60 ) = 0.0012526521179532725 ;
347
348 aPoints( 0, 61 ) = -0.069406647989823891 ;
349 aPoints( 1, 61 ) = 0.17579975700952866 ;
350 aPoints( 2, 61 ) = 0.79585141789677283 ;
351 aWeights( 61 ) = 0.00234842498493512 ;
352
353 aPoints( 0, 62 ) = 0.069406647989823891 ;
354 aPoints( 1, 62 ) = 0.17579975700952866 ;
355 aPoints( 2, 62 ) = 0.79585141789677283 ;
356 aWeights( 62 ) = 0.00234842498493512 ;
357
358 aPoints( 0, 63 ) = 0.17579975700952866 ;
359 aPoints( 1, 63 ) = 0.17579975700952866 ;
360 aPoints( 2, 63 ) = 0.79585141789677283 ;
361 aWeights( 63 ) = 0.0012526521179532725 ;
362 }
363
364// ----------------------------------------------------------------------------
365 } /* namespace integration */
366} /* namespace belfem */
367
368#endif //BELFEM_FN_INTPOINTS_GAUSS_PYRA64_HPP
cl_Matrix.hpp
cl_Vector.hpp
belfem::Matrix::set_size
void set_size(const size_t aNumRows, const size_t aNumCols)
Definition cl_AR_Matrix.hpp:164
belfem::Vector::set_size
void set_size(const size_t aNumRows)
change the size of the vector
Definition cl_AR_Vector.hpp:215
belfem::integration
Definition fn_intpoints.cpp:576
belfem::integration::gauss_pyra64
void gauss_pyra64(Vector< real > &aWeights, Matrix< real > &aPoints)
Conical-product Gauss rule on the reference pyramid ( base [-1,1]^2 at zeta = 0, apex ( 0,...
Definition fn_intpoints_gauss_pyra64.hpp:36
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16