BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_penta71.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_PENTA71_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_PENTA71_HPP
14
15#include "typedefs.hpp"
16#include "cl_Vector.hpp"
17#include "cl_Matrix.hpp"
18
19namespace belfem
20{
21 namespace integration
22 {
23// ----------------------------------------------------------------------------
24
25 // source: 10.1016/j.compfluid.2013.01.002
26 inline void
27 gauss_penta71(
28 Vector< real > & aWeights,
29 Matrix< real > & aPoints )
30 {
31 aPoints.set_size( 3, 71 );
32
33 aPoints( 0, 0 ) = 0.16489443883634;
34 aPoints( 1, 0 ) = 0.67021112232731;
35 aPoints( 2, 0 ) = 0.00000000000000;
36
37 aPoints( 0, 1 ) = 0.16489443883634;
38 aPoints( 1, 1 ) = 0.16489443883634;
39 aPoints( 2, 1 ) = 0.00000000000000;
40
41 aPoints( 0, 2 ) = 0.67021112232731;
42 aPoints( 1, 2 ) = 0.16489443883634;
43 aPoints( 2, 2 ) = 0.00000000000000;
44
45 aPoints( 0, 3 ) = 0.81358044305765;
46 aPoints( 1, 3 ) = 0.00615649368998;
47 aPoints( 2, 3 ) = 0.00000000000000;
48
49 aPoints( 0, 4 ) = 0.18026306325238;
50 aPoints( 1, 4 ) = 0.00615649368998;
51 aPoints( 2, 4 ) = 0.00000000000000;
52
53 aPoints( 0, 5 ) = 0.00615649368998;
54 aPoints( 1, 5 ) = 0.18026306325238;
55 aPoints( 2, 5 ) = 0.00000000000000;
56
57 aPoints( 0, 6 ) = 0.00615649368998;
58 aPoints( 1, 6 ) = 0.81358044305765;
59 aPoints( 2, 6 ) = 0.00000000000000;
60
61 aPoints( 0, 7 ) = 0.18026306325238;
62 aPoints( 1, 7 ) = 0.81358044305765;
63 aPoints( 2, 7 ) = 0.00000000000000;
64
65 aPoints( 0, 8 ) = 0.81358044305765;
66 aPoints( 1, 8 ) = 0.18026306325238;
67 aPoints( 2, 8 ) = 0.00000000000000;
68
69 aPoints( 0, 9 ) = 0.33333333333333;
70 aPoints( 1, 9 ) = 0.33333333333333;
71 aPoints( 2, 9 ) = 0.13056559997756;
72
73 aPoints( 0, 10 ) = 0.33333333333333;
74 aPoints( 1, 10 ) = 0.33333333333333;
75 aPoints( 2, 10 ) = -0.13056559997756;
76
77 aPoints( 0, 11 ) = 0.23385471435193;
78 aPoints( 1, 11 ) = 0.53229057129614;
79 aPoints( 2, 11 ) = 0.89617446257078;
80
81 aPoints( 0, 12 ) = 0.23385471435193;
82 aPoints( 1, 12 ) = 0.53229057129614;
83 aPoints( 2, 12 ) = -0.89617446257078;
84
85 aPoints( 0, 13 ) = 0.23385471435193;
86 aPoints( 1, 13 ) = 0.23385471435193;
87 aPoints( 2, 13 ) = 0.89617446257078;
88
89 aPoints( 0, 14 ) = 0.23385471435193;
90 aPoints( 1, 14 ) = 0.23385471435193;
91 aPoints( 2, 14 ) = -0.89617446257078;
92
93 aPoints( 0, 15 ) = 0.53229057129614;
94 aPoints( 1, 15 ) = 0.23385471435193;
95 aPoints( 2, 15 ) = 0.89617446257078;
96
97 aPoints( 0, 16 ) = 0.53229057129614;
98 aPoints( 1, 16 ) = 0.23385471435193;
99 aPoints( 2, 16 ) = -0.89617446257078;
100
101 aPoints( 0, 17 ) = 0.42311429990533;
102 aPoints( 1, 17 ) = 0.15377140018934;
103 aPoints( 2, 17 ) = 0.49688610195670;
104
105 aPoints( 0, 18 ) = 0.42311429990533;
106 aPoints( 1, 18 ) = 0.15377140018934;
107 aPoints( 2, 18 ) = -0.49688610195670;
108
109 aPoints( 0, 19 ) = 0.42311429990533;
110 aPoints( 1, 19 ) = 0.42311429990533;
111 aPoints( 2, 19 ) = 0.49688610195670;
112
113 aPoints( 0, 20 ) = 0.42311429990533;
114 aPoints( 1, 20 ) = 0.42311429990533;
115 aPoints( 2, 20 ) = -0.49688610195670;
116
117 aPoints( 0, 21 ) = 0.15377140018934;
118 aPoints( 1, 21 ) = 0.42311429990533;
119 aPoints( 2, 21 ) = 0.49688610195670;
120
121 aPoints( 0, 22 ) = 0.15377140018934;
122 aPoints( 1, 22 ) = 0.42311429990533;
123 aPoints( 2, 22 ) = -0.49688610195670;
124
125 aPoints( 0, 23 ) = 0.03794159128322;
126 aPoints( 1, 23 ) = 0.92411681743356;
127 aPoints( 2, 23 ) = 0.44172010057187;
128
129 aPoints( 0, 24 ) = 0.03794159128322;
130 aPoints( 1, 24 ) = 0.92411681743356;
131 aPoints( 2, 24 ) = -0.44172010057187;
132
133 aPoints( 0, 25 ) = 0.03794159128322;
134 aPoints( 1, 25 ) = 0.03794159128322;
135 aPoints( 2, 25 ) = 0.44172010057187;
136
137 aPoints( 0, 26 ) = 0.03794159128322;
138 aPoints( 1, 26 ) = 0.03794159128322;
139 aPoints( 2, 26 ) = -0.44172010057187;
140
141 aPoints( 0, 27 ) = 0.92411681743356;
142 aPoints( 1, 27 ) = 0.03794159128322;
143 aPoints( 2, 27 ) = 0.44172010057187;
144
145 aPoints( 0, 28 ) = 0.92411681743356;
146 aPoints( 1, 28 ) = 0.03794159128322;
147 aPoints( 2, 28 ) = -0.44172010057187;
148
149 aPoints( 0, 29 ) = 0.06293072777203;
150 aPoints( 1, 29 ) = 0.87413854445593;
151 aPoints( 2, 29 ) = 0.93872429591872;
152
153 aPoints( 0, 30 ) = 0.06293072777203;
154 aPoints( 1, 30 ) = 0.87413854445593;
155 aPoints( 2, 30 ) = -0.93872429591872;
156
157 aPoints( 0, 31 ) = 0.06293072777203;
158 aPoints( 1, 31 ) = 0.06293072777203;
159 aPoints( 2, 31 ) = 0.93872429591872;
160
161 aPoints( 0, 32 ) = 0.06293072777203;
162 aPoints( 1, 32 ) = 0.06293072777203;
163 aPoints( 2, 32 ) = -0.93872429591872;
164
165 aPoints( 0, 33 ) = 0.87413854445593;
166 aPoints( 1, 33 ) = 0.06293072777203;
167 aPoints( 2, 33 ) = 0.93872429591872;
168
169 aPoints( 0, 34 ) = 0.87413854445593;
170 aPoints( 1, 34 ) = 0.06293072777203;
171 aPoints( 2, 34 ) = -0.93872429591872;
172
173 aPoints( 0, 35 ) = 0.59545222074592;
174 aPoints( 1, 35 ) = 0.03243941631799;
175 aPoints( 2, 35 ) = 0.93233631474388;
176
177 aPoints( 0, 36 ) = 0.59545222074592;
178 aPoints( 1, 36 ) = 0.03243941631799;
179 aPoints( 2, 36 ) = -0.93233631474388;
180
181 aPoints( 0, 37 ) = 0.37210836293609;
182 aPoints( 1, 37 ) = 0.03243941631799;
183 aPoints( 2, 37 ) = 0.93233631474388;
184
185 aPoints( 0, 38 ) = 0.37210836293609;
186 aPoints( 1, 38 ) = 0.03243941631799;
187 aPoints( 2, 38 ) = -0.93233631474388;
188
189 aPoints( 0, 39 ) = 0.03243941631799;
190 aPoints( 1, 39 ) = 0.37210836293609;
191 aPoints( 2, 39 ) = 0.93233631474388;
192
193 aPoints( 0, 40 ) = 0.03243941631799;
194 aPoints( 1, 40 ) = 0.37210836293609;
195 aPoints( 2, 40 ) = -0.93233631474388;
196
197 aPoints( 0, 41 ) = 0.03243941631799;
198 aPoints( 1, 41 ) = 0.59545222074592;
199 aPoints( 2, 41 ) = 0.93233631474388;
200
201 aPoints( 0, 42 ) = 0.03243941631799;
202 aPoints( 1, 42 ) = 0.59545222074592;
203 aPoints( 2, 42 ) = -0.93233631474388;
204
205 aPoints( 0, 43 ) = 0.37210836293609;
206 aPoints( 1, 43 ) = 0.59545222074592;
207 aPoints( 2, 43 ) = 0.93233631474388;
208
209 aPoints( 0, 44 ) = 0.37210836293609;
210 aPoints( 1, 44 ) = 0.59545222074592;
211 aPoints( 2, 44 ) = -0.93233631474388;
212
213 aPoints( 0, 45 ) = 0.59545222074592;
214 aPoints( 1, 45 ) = 0.37210836293609;
215 aPoints( 2, 45 ) = 0.93233631474388;
216
217 aPoints( 0, 46 ) = 0.59545222074592;
218 aPoints( 1, 46 ) = 0.37210836293609;
219 aPoints( 2, 46 ) = -0.93233631474388;
220
221 aPoints( 0, 47 ) = 0.51715834884211;
222 aPoints( 1, 47 ) = 0.03019436479121;
223 aPoints( 2, 47 ) = 0.25140731824727;
224
225 aPoints( 0, 48 ) = 0.51715834884211;
226 aPoints( 1, 48 ) = 0.03019436479121;
227 aPoints( 2, 48 ) = -0.25140731824727;
228
229 aPoints( 0, 49 ) = 0.45264728636668;
230 aPoints( 1, 49 ) = 0.03019436479121;
231 aPoints( 2, 49 ) = 0.25140731824727;
232
233 aPoints( 0, 50 ) = 0.45264728636668;
234 aPoints( 1, 50 ) = 0.03019436479121;
235 aPoints( 2, 50 ) = -0.25140731824727;
236
237 aPoints( 0, 51 ) = 0.03019436479121;
238 aPoints( 1, 51 ) = 0.45264728636668;
239 aPoints( 2, 51 ) = 0.25140731824727;
240
241 aPoints( 0, 52 ) = 0.03019436479121;
242 aPoints( 1, 52 ) = 0.45264728636668;
243 aPoints( 2, 52 ) = -0.25140731824727;
244
245 aPoints( 0, 53 ) = 0.03019436479121;
246 aPoints( 1, 53 ) = 0.51715834884211;
247 aPoints( 2, 53 ) = 0.25140731824727;
248
249 aPoints( 0, 54 ) = 0.03019436479121;
250 aPoints( 1, 54 ) = 0.51715834884211;
251 aPoints( 2, 54 ) = -0.25140731824727;
252
253 aPoints( 0, 55 ) = 0.45264728636668;
254 aPoints( 1, 55 ) = 0.51715834884211;
255 aPoints( 2, 55 ) = 0.25140731824727;
256
257 aPoints( 0, 56 ) = 0.45264728636668;
258 aPoints( 1, 56 ) = 0.51715834884211;
259 aPoints( 2, 56 ) = -0.25140731824727;
260
261 aPoints( 0, 57 ) = 0.51715834884211;
262 aPoints( 1, 57 ) = 0.45264728636668;
263 aPoints( 2, 57 ) = 0.25140731824727;
264
265 aPoints( 0, 58 ) = 0.51715834884211;
266 aPoints( 1, 58 ) = 0.45264728636668;
267 aPoints( 2, 58 ) = -0.25140731824727;
268
269 aPoints( 0, 59 ) = 0.71885570514069;
270 aPoints( 1, 59 ) = 0.05098994407996;
271 aPoints( 2, 59 ) = 0.64977396874569;
272
273 aPoints( 0, 60 ) = 0.71885570514069;
274 aPoints( 1, 60 ) = 0.05098994407996;
275 aPoints( 2, 60 ) = -0.64977396874569;
276
277 aPoints( 0, 61 ) = 0.23015435077935;
278 aPoints( 1, 61 ) = 0.05098994407996;
279 aPoints( 2, 61 ) = 0.64977396874569;
280
281 aPoints( 0, 62 ) = 0.23015435077935;
282 aPoints( 1, 62 ) = 0.05098994407996;
283 aPoints( 2, 62 ) = -0.64977396874569;
284
285 aPoints( 0, 63 ) = 0.05098994407996;
286 aPoints( 1, 63 ) = 0.23015435077935;
287 aPoints( 2, 63 ) = 0.64977396874569;
288
289 aPoints( 0, 64 ) = 0.05098994407996;
290 aPoints( 1, 64 ) = 0.23015435077935;
291 aPoints( 2, 64 ) = -0.64977396874569;
292
293 aPoints( 0, 65 ) = 0.05098994407996;
294 aPoints( 1, 65 ) = 0.71885570514069;
295 aPoints( 2, 65 ) = 0.64977396874569;
296
297 aPoints( 0, 66 ) = 0.05098994407996;
298 aPoints( 1, 66 ) = 0.71885570514069;
299 aPoints( 2, 66 ) = -0.64977396874569;
300
301 aPoints( 0, 67 ) = 0.23015435077935;
302 aPoints( 1, 67 ) = 0.71885570514069;
303 aPoints( 2, 67 ) = 0.64977396874569;
304
305 aPoints( 0, 68 ) = 0.23015435077935;
306 aPoints( 1, 68 ) = 0.71885570514069;
307 aPoints( 2, 68 ) = -0.64977396874569;
308
309 aPoints( 0, 69 ) = 0.71885570514069;
310 aPoints( 1, 69 ) = 0.23015435077935;
311 aPoints( 2, 69 ) = 0.64977396874569;
312
313 aPoints( 0, 70 ) = 0.71885570514069;
314 aPoints( 1, 70 ) = 0.23015435077935;
315 aPoints( 2, 70 ) = -0.64977396874569;
316
317 aWeights.set_size( 71 );
318 aWeights( 0 ) = 0.04492449998351;
319 aWeights( 1 ) = 0.04492449998351;
320 aWeights( 2 ) = 0.04492449998351;
321 aWeights( 3 ) = 0.00744494250520;
322 aWeights( 4 ) = 0.00744494250520;
323 aWeights( 5 ) = 0.00744494250520;
324 aWeights( 6 ) = 0.00744494250520;
325 aWeights( 7 ) = 0.00744494250520;
326 aWeights( 8 ) = 0.00744494250520;
327 aWeights( 9 ) = 0.02331298637932;
328 aWeights( 10 ) = 0.02331298637932;
329 aWeights( 11 ) = 0.01984746470312;
330 aWeights( 12 ) = 0.01984746470312;
331 aWeights( 13 ) = 0.01984746470312;
332 aWeights( 14 ) = 0.01984746470312;
333 aWeights( 15 ) = 0.01984746470312;
334 aWeights( 16 ) = 0.01984746470312;
335 aWeights( 17 ) = 0.03610279159418;
336 aWeights( 18 ) = 0.03610279159418;
337 aWeights( 19 ) = 0.03610279159418;
338 aWeights( 20 ) = 0.03610279159418;
339 aWeights( 21 ) = 0.03610279159418;
340 aWeights( 22 ) = 0.03610279159418;
341 aWeights( 23 ) = 0.00751493659997;
342 aWeights( 24 ) = 0.00751493659997;
343 aWeights( 25 ) = 0.00751493659997;
344 aWeights( 26 ) = 0.00751493659997;
345 aWeights( 27 ) = 0.00751493659997;
346 aWeights( 28 ) = 0.00751493659997;
347 aWeights( 29 ) = 0.00536566758380;
348 aWeights( 30 ) = 0.00536566758380;
349 aWeights( 31 ) = 0.00536566758380;
350 aWeights( 32 ) = 0.00536566758380;
351 aWeights( 33 ) = 0.00536566758380;
352 aWeights( 34 ) = 0.00536566758380;
353 aWeights( 35 ) = 0.00506368997469;
354 aWeights( 36 ) = 0.00506368997469;
355 aWeights( 37 ) = 0.00506368997469;
356 aWeights( 38 ) = 0.00506368997469;
357 aWeights( 39 ) = 0.00506368997469;
358 aWeights( 40 ) = 0.00506368997469;
359 aWeights( 41 ) = 0.00506368997469;
360 aWeights( 42 ) = 0.00506368997469;
361 aWeights( 43 ) = 0.00506368997469;
362 aWeights( 44 ) = 0.00506368997469;
363 aWeights( 45 ) = 0.00506368997469;
364 aWeights( 46 ) = 0.00506368997469;
365 aWeights( 47 ) = 0.00773182710698;
366 aWeights( 48 ) = 0.00773182710698;
367 aWeights( 49 ) = 0.00773182710698;
368 aWeights( 50 ) = 0.00773182710698;
369 aWeights( 51 ) = 0.00773182710698;
370 aWeights( 52 ) = 0.00773182710698;
371 aWeights( 53 ) = 0.00773182710698;
372 aWeights( 54 ) = 0.00773182710698;
373 aWeights( 55 ) = 0.00773182710698;
374 aWeights( 56 ) = 0.00773182710698;
375 aWeights( 57 ) = 0.00773182710698;
376 aWeights( 58 ) = 0.00773182710698;
377 aWeights( 59 ) = 0.01728329203277;
378 aWeights( 60 ) = 0.01728329203277;
379 aWeights( 61 ) = 0.01728329203277;
380 aWeights( 62 ) = 0.01728329203277;
381 aWeights( 63 ) = 0.01728329203277;
382 aWeights( 64 ) = 0.01728329203277;
383 aWeights( 65 ) = 0.01728329203277;
384 aWeights( 66 ) = 0.01728329203277;
385 aWeights( 67 ) = 0.01728329203277;
386 aWeights( 68 ) = 0.01728329203277;
387 aWeights( 69 ) = 0.01728329203277;
388 aWeights( 70 ) = 0.01728329203277;
389 }
390
391// ----------------------------------------------------------------------------
392 } /* namespace integration */
393} /* namespace belfem */
394
395#endif //BELFEM_FN_INTPOINTS_GAUSS_PENTA71_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_penta71
void gauss_penta71(Vector< real > &aWeights, Matrix< real > &aPoints)
Definition fn_intpoints_gauss_penta71.hpp:27
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16