BELFEM 0.9.0
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
36 inline void
37 gauss_pyra64(
38 Vector <real> & aWeights,
39 Matrix <real> & aPoints )
40 {
41 aPoints.set_size( 3, 64 );
42 aWeights.set_size( 64 );
43
44 aPoints( 0, 0 ) = -0.81937072733298044 ;
45 aPoints( 1, 0 ) = -0.81937072733298044 ;
46 aPoints( 2, 0 ) = 0.048500549446997276 ;
47 aWeights( 0 ) = 0.01341783020966248 ;
48
49 aPoints( 0, 1 ) = -0.32349177616942726 ;
50 aPoints( 1, 1 ) = -0.81937072733298044 ;
51 aPoints( 2, 1 ) = 0.048500549446997276 ;
52 aWeights( 1 ) = 0.025155242430336153 ;
53
54 aPoints( 0, 2 ) = 0.32349177616942726 ;
55 aPoints( 1, 2 ) = -0.81937072733298044 ;
56 aPoints( 2, 2 ) = 0.048500549446997276 ;
57 aWeights( 2 ) = 0.025155242430336153 ;
58
59 aPoints( 0, 3 ) = 0.81937072733298044 ;
60 aPoints( 1, 3 ) = -0.81937072733298044 ;
61 aPoints( 2, 3 ) = 0.048500549446997276 ;
62 aWeights( 3 ) = 0.01341783020966248 ;
63
64 aPoints( 0, 4 ) = -0.81937072733298044 ;
65 aPoints( 1, 4 ) = -0.32349177616942726 ;
66 aPoints( 2, 4 ) = 0.048500549446997276 ;
67 aWeights( 4 ) = 0.025155242430336153 ;
68
69 aPoints( 0, 5 ) = -0.32349177616942726 ;
70 aPoints( 1, 5 ) = -0.32349177616942726 ;
71 aPoints( 2, 5 ) = 0.048500549446997276 ;
72 aWeights( 5 ) = 0.047160100540942954 ;
73
74 aPoints( 0, 6 ) = 0.32349177616942726 ;
75 aPoints( 1, 6 ) = -0.32349177616942726 ;
76 aPoints( 2, 6 ) = 0.048500549446997276 ;
77 aWeights( 6 ) = 0.047160100540942954 ;
78
79 aPoints( 0, 7 ) = 0.81937072733298044 ;
80 aPoints( 1, 7 ) = -0.32349177616942726 ;
81 aPoints( 2, 7 ) = 0.048500549446997276 ;
82 aWeights( 7 ) = 0.025155242430336153 ;
83
84 aPoints( 0, 8 ) = -0.81937072733298044 ;
85 aPoints( 1, 8 ) = 0.32349177616942726 ;
86 aPoints( 2, 8 ) = 0.048500549446997276 ;
87 aWeights( 8 ) = 0.025155242430336153 ;
88
89 aPoints( 0, 9 ) = -0.32349177616942726 ;
90 aPoints( 1, 9 ) = 0.32349177616942726 ;
91 aPoints( 2, 9 ) = 0.048500549446997276 ;
92 aWeights( 9 ) = 0.047160100540942954 ;
93
94 aPoints( 0, 10 ) = 0.32349177616942726 ;
95 aPoints( 1, 10 ) = 0.32349177616942726 ;
96 aPoints( 2, 10 ) = 0.048500549446997276 ;
97 aWeights( 10 ) = 0.047160100540942954 ;
98
99 aPoints( 0, 11 ) = 0.81937072733298044 ;
100 aPoints( 1, 11 ) = 0.32349177616942726 ;
101 aPoints( 2, 11 ) = 0.048500549446997276 ;
102 aWeights( 11 ) = 0.025155242430336153 ;
103
104 aPoints( 0, 12 ) = -0.81937072733298044 ;
105 aPoints( 1, 12 ) = 0.81937072733298044 ;
106 aPoints( 2, 12 ) = 0.048500549446997276 ;
107 aWeights( 12 ) = 0.01341783020966248 ;
108
109 aPoints( 0, 13 ) = -0.32349177616942726 ;
110 aPoints( 1, 13 ) = 0.81937072733298044 ;
111 aPoints( 2, 13 ) = 0.048500549446997276 ;
112 aWeights( 13 ) = 0.025155242430336153 ;
113
114 aPoints( 0, 14 ) = 0.32349177616942726 ;
115 aPoints( 1, 14 ) = 0.81937072733298044 ;
116 aPoints( 2, 14 ) = 0.048500549446997276 ;
117 aWeights( 14 ) = 0.025155242430336153 ;
118
119 aPoints( 0, 15 ) = 0.81937072733298044 ;
120 aPoints( 1, 15 ) = 0.81937072733298044 ;
121 aPoints( 2, 15 ) = 0.048500549446997276 ;
122 aWeights( 15 ) = 0.01341783020966248 ;
123
124 aPoints( 0, 16 ) = -0.65566855251502121 ;
125 aPoints( 1, 16 ) = -0.65566855251502121 ;
126 aPoints( 2, 16 ) = 0.23860073755186234 ;
127 aWeights( 16 ) = 0.017358942978834929 ;
128
129 aPoints( 0, 17 ) = -0.25886131583185773 ;
130 aPoints( 1, 17 ) = -0.65566855251502121 ;
131 aPoints( 2, 17 ) = 0.23860073755186234 ;
132 aWeights( 17 ) = 0.032543892130377346 ;
133
134 aPoints( 0, 18 ) = 0.25886131583185773 ;
135 aPoints( 1, 18 ) = -0.65566855251502121 ;
136 aPoints( 2, 18 ) = 0.23860073755186234 ;
137 aWeights( 18 ) = 0.032543892130377346 ;
138
139 aPoints( 0, 19 ) = 0.65566855251502121 ;
140 aPoints( 1, 19 ) = -0.65566855251502121 ;
141 aPoints( 2, 19 ) = 0.23860073755186234 ;
142 aWeights( 19 ) = 0.017358942978834929 ;
143
144 aPoints( 0, 20 ) = -0.65566855251502121 ;
145 aPoints( 1, 20 ) = -0.25886131583185773 ;
146 aPoints( 2, 20 ) = 0.23860073755186234 ;
147 aWeights( 20 ) = 0.032543892130377346 ;
148
149 aPoints( 0, 21 ) = -0.25886131583185773 ;
150 aPoints( 1, 21 ) = -0.25886131583185773 ;
151 aPoints( 2, 21 ) = 0.23860073755186234 ;
152 aWeights( 21 ) = 0.061012062559624818 ;
153
154 aPoints( 0, 22 ) = 0.25886131583185773 ;
155 aPoints( 1, 22 ) = -0.25886131583185773 ;
156 aPoints( 2, 22 ) = 0.23860073755186234 ;
157 aWeights( 22 ) = 0.061012062559624818 ;
158
159 aPoints( 0, 23 ) = 0.65566855251502121 ;
160 aPoints( 1, 23 ) = -0.25886131583185773 ;
161 aPoints( 2, 23 ) = 0.23860073755186234 ;
162 aWeights( 23 ) = 0.032543892130377346 ;
163
164 aPoints( 0, 24 ) = -0.65566855251502121 ;
165 aPoints( 1, 24 ) = 0.25886131583185773 ;
166 aPoints( 2, 24 ) = 0.23860073755186234 ;
167 aWeights( 24 ) = 0.032543892130377346 ;
168
169 aPoints( 0, 25 ) = -0.25886131583185773 ;
170 aPoints( 1, 25 ) = 0.25886131583185773 ;
171 aPoints( 2, 25 ) = 0.23860073755186234 ;
172 aWeights( 25 ) = 0.061012062559624818 ;
173
174 aPoints( 0, 26 ) = 0.25886131583185773 ;
175 aPoints( 1, 26 ) = 0.25886131583185773 ;
176 aPoints( 2, 26 ) = 0.23860073755186234 ;
177 aWeights( 26 ) = 0.061012062559624818 ;
178
179 aPoints( 0, 27 ) = 0.65566855251502121 ;
180 aPoints( 1, 27 ) = 0.25886131583185773 ;
181 aPoints( 2, 27 ) = 0.23860073755186234 ;
182 aWeights( 27 ) = 0.032543892130377346 ;
183
184 aPoints( 0, 28 ) = -0.65566855251502121 ;
185 aPoints( 1, 28 ) = 0.65566855251502121 ;
186 aPoints( 2, 28 ) = 0.23860073755186234 ;
187 aWeights( 28 ) = 0.017358942978834929 ;
188
189 aPoints( 0, 29 ) = -0.25886131583185773 ;
190 aPoints( 1, 29 ) = 0.65566855251502121 ;
191 aPoints( 2, 29 ) = 0.23860073755186234 ;
192 aWeights( 29 ) = 0.032543892130377346 ;
193
194 aPoints( 0, 30 ) = 0.25886131583185773 ;
195 aPoints( 1, 30 ) = 0.65566855251502121 ;
196 aPoints( 2, 30 ) = 0.23860073755186234 ;
197 aWeights( 30 ) = 0.032543892130377346 ;
198
199 aPoints( 0, 31 ) = 0.65566855251502121 ;
200 aPoints( 1, 31 ) = 0.65566855251502121 ;
201 aPoints( 2, 31 ) = 0.23860073755186234 ;
202 aWeights( 31 ) = 0.017358942978834929 ;
203
204 aPoints( 0, 32 ) = -0.415888110968196 ;
205 aPoints( 1, 32 ) = -0.415888110968196 ;
206 aPoints( 2, 32 ) = 0.51704729510436742 ;
207 aWeights( 32 ) = 0.0083049057887499764 ;
208
209 aPoints( 0, 33 ) = -0.16419476461254631 ;
210 aPoints( 1, 33 ) = -0.415888110968196 ;
211 aPoints( 2, 33 ) = 0.51704729510436742 ;
212 aWeights( 33 ) = 0.015569724404968665 ;
213
214 aPoints( 0, 34 ) = 0.16419476461254631 ;
215 aPoints( 1, 34 ) = -0.415888110968196 ;
216 aPoints( 2, 34 ) = 0.51704729510436742 ;
217 aWeights( 34 ) = 0.015569724404968665 ;
218
219 aPoints( 0, 35 ) = 0.415888110968196 ;
220 aPoints( 1, 35 ) = -0.415888110968196 ;
221 aPoints( 2, 35 ) = 0.51704729510436742 ;
222 aWeights( 35 ) = 0.0083049057887499764 ;
223
224 aPoints( 0, 36 ) = -0.415888110968196 ;
225 aPoints( 1, 36 ) = -0.16419476461254631 ;
226 aPoints( 2, 36 ) = 0.51704729510436742 ;
227 aWeights( 36 ) = 0.015569724404968665 ;
228
229 aPoints( 0, 37 ) = -0.16419476461254631 ;
230 aPoints( 1, 37 ) = -0.16419476461254631 ;
231 aPoints( 2, 37 ) = 0.51704729510436742 ;
232 aWeights( 37 ) = 0.029189532574235792 ;
233
234 aPoints( 0, 38 ) = 0.16419476461254631 ;
235 aPoints( 1, 38 ) = -0.16419476461254631 ;
236 aPoints( 2, 38 ) = 0.51704729510436742 ;
237 aWeights( 38 ) = 0.029189532574235792 ;
238
239 aPoints( 0, 39 ) = 0.415888110968196 ;
240 aPoints( 1, 39 ) = -0.16419476461254631 ;
241 aPoints( 2, 39 ) = 0.51704729510436742 ;
242 aWeights( 39 ) = 0.015569724404968665 ;
243
244 aPoints( 0, 40 ) = -0.415888110968196 ;
245 aPoints( 1, 40 ) = 0.16419476461254631 ;
246 aPoints( 2, 40 ) = 0.51704729510436742 ;
247 aWeights( 40 ) = 0.015569724404968665 ;
248
249 aPoints( 0, 41 ) = -0.16419476461254631 ;
250 aPoints( 1, 41 ) = 0.16419476461254631 ;
251 aPoints( 2, 41 ) = 0.51704729510436742 ;
252 aWeights( 41 ) = 0.029189532574235792 ;
253
254 aPoints( 0, 42 ) = 0.16419476461254631 ;
255 aPoints( 1, 42 ) = 0.16419476461254631 ;
256 aPoints( 2, 42 ) = 0.51704729510436742 ;
257 aWeights( 42 ) = 0.029189532574235792 ;
258
259 aPoints( 0, 43 ) = 0.415888110968196 ;
260 aPoints( 1, 43 ) = 0.16419476461254631 ;
261 aPoints( 2, 43 ) = 0.51704729510436742 ;
262 aWeights( 43 ) = 0.015569724404968665 ;
263
264 aPoints( 0, 44 ) = -0.415888110968196 ;
265 aPoints( 1, 44 ) = 0.415888110968196 ;
266 aPoints( 2, 44 ) = 0.51704729510436742 ;
267 aWeights( 44 ) = 0.0083049057887499764 ;
268
269 aPoints( 0, 45 ) = -0.16419476461254631 ;
270 aPoints( 1, 45 ) = 0.415888110968196 ;
271 aPoints( 2, 45 ) = 0.51704729510436742 ;
272 aWeights( 45 ) = 0.015569724404968665 ;
273
274 aPoints( 0, 46 ) = 0.16419476461254631 ;
275 aPoints( 1, 46 ) = 0.415888110968196 ;
276 aPoints( 2, 46 ) = 0.51704729510436742 ;
277 aWeights( 46 ) = 0.015569724404968665 ;
278
279 aPoints( 0, 47 ) = 0.415888110968196 ;
280 aPoints( 1, 47 ) = 0.415888110968196 ;
281 aPoints( 2, 47 ) = 0.51704729510436742 ;
282 aWeights( 47 ) = 0.0083049057887499764 ;
283
284 aPoints( 0, 48 ) = -0.17579975700952866 ;
285 aPoints( 1, 48 ) = -0.17579975700952866 ;
286 aPoints( 2, 48 ) = 0.79585141789677283 ;
287 aWeights( 48 ) = 0.0012526521179532725 ;
288
289 aPoints( 0, 49 ) = -0.069406647989823891 ;
290 aPoints( 1, 49 ) = -0.17579975700952866 ;
291 aPoints( 2, 49 ) = 0.79585141789677283 ;
292 aWeights( 49 ) = 0.00234842498493512 ;
293
294 aPoints( 0, 50 ) = 0.069406647989823891 ;
295 aPoints( 1, 50 ) = -0.17579975700952866 ;
296 aPoints( 2, 50 ) = 0.79585141789677283 ;
297 aWeights( 50 ) = 0.00234842498493512 ;
298
299 aPoints( 0, 51 ) = 0.17579975700952866 ;
300 aPoints( 1, 51 ) = -0.17579975700952866 ;
301 aPoints( 2, 51 ) = 0.79585141789677283 ;
302 aWeights( 51 ) = 0.0012526521179532725 ;
303
304 aPoints( 0, 52 ) = -0.17579975700952866 ;
305 aPoints( 1, 52 ) = -0.069406647989823891 ;
306 aPoints( 2, 52 ) = 0.79585141789677283 ;
307 aWeights( 52 ) = 0.00234842498493512 ;
308
309 aPoints( 0, 53 ) = -0.069406647989823891 ;
310 aPoints( 1, 53 ) = -0.069406647989823891 ;
311 aPoints( 2, 53 ) = 0.79585141789677283 ;
312 aWeights( 53 ) = 0.0044027386620945682 ;
313
314 aPoints( 0, 54 ) = 0.069406647989823891 ;
315 aPoints( 1, 54 ) = -0.069406647989823891 ;
316 aPoints( 2, 54 ) = 0.79585141789677283 ;
317 aWeights( 54 ) = 0.0044027386620945682 ;
318
319 aPoints( 0, 55 ) = 0.17579975700952866 ;
320 aPoints( 1, 55 ) = -0.069406647989823891 ;
321 aPoints( 2, 55 ) = 0.79585141789677283 ;
322 aWeights( 55 ) = 0.00234842498493512 ;
323
324 aPoints( 0, 56 ) = -0.17579975700952866 ;
325 aPoints( 1, 56 ) = 0.069406647989823891 ;
326 aPoints( 2, 56 ) = 0.79585141789677283 ;
327 aWeights( 56 ) = 0.00234842498493512 ;
328
329 aPoints( 0, 57 ) = -0.069406647989823891 ;
330 aPoints( 1, 57 ) = 0.069406647989823891 ;
331 aPoints( 2, 57 ) = 0.79585141789677283 ;
332 aWeights( 57 ) = 0.0044027386620945682 ;
333
334 aPoints( 0, 58 ) = 0.069406647989823891 ;
335 aPoints( 1, 58 ) = 0.069406647989823891 ;
336 aPoints( 2, 58 ) = 0.79585141789677283 ;
337 aWeights( 58 ) = 0.0044027386620945682 ;
338
339 aPoints( 0, 59 ) = 0.17579975700952866 ;
340 aPoints( 1, 59 ) = 0.069406647989823891 ;
341 aPoints( 2, 59 ) = 0.79585141789677283 ;
342 aWeights( 59 ) = 0.00234842498493512 ;
343
344 aPoints( 0, 60 ) = -0.17579975700952866 ;
345 aPoints( 1, 60 ) = 0.17579975700952866 ;
346 aPoints( 2, 60 ) = 0.79585141789677283 ;
347 aWeights( 60 ) = 0.0012526521179532725 ;
348
349 aPoints( 0, 61 ) = -0.069406647989823891 ;
350 aPoints( 1, 61 ) = 0.17579975700952866 ;
351 aPoints( 2, 61 ) = 0.79585141789677283 ;
352 aWeights( 61 ) = 0.00234842498493512 ;
353
354 aPoints( 0, 62 ) = 0.069406647989823891 ;
355 aPoints( 1, 62 ) = 0.17579975700952866 ;
356 aPoints( 2, 62 ) = 0.79585141789677283 ;
357 aWeights( 62 ) = 0.00234842498493512 ;
358
359 aPoints( 0, 63 ) = 0.17579975700952866 ;
360 aPoints( 1, 63 ) = 0.17579975700952866 ;
361 aPoints( 2, 63 ) = 0.79585141789677283 ;
362 aWeights( 63 ) = 0.0012526521179532725 ;
363 }
364
365// ----------------------------------------------------------------------------
366 } /* namespace integration */
367} /* namespace belfem */
368
369#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:186
belfem::Vector::set_size
void set_size(const size_t aNumRows)
change the size of the vector
Definition cl_AR_Vector.hpp:237
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:37
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16