BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tri73.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_TRI73_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TRI73_HPP
14
15#include "typedefs.hpp"
16#include "cl_Vector.hpp"
17#include "cl_Matrix.hpp"
18#include "fn_sum.hpp"
19
20namespace belfem
21{
22 namespace integration
23 {
24// ----------------------------------------------------------------------------
25
34 inline void
35 gauss_tri73(
36 Vector< real > & aWeights,
37 Matrix< real > & aPoints )
38 {
39 aPoints.set_size( 3, 73 );
40
41 aPoints( 0, 0 ) = 1./3.;
42 aPoints( 1, 0 ) = 1./3.;
43
44 aPoints( 0, 1 ) = 0.48960998707300485;
45 aPoints( 1, 1 ) = 0.48960998707300485;
46
47 aPoints( 0, 2 ) = 0.4545368926978903;
48 aPoints( 1, 2 ) = 0.4545368926978903;
49
50 aPoints( 0, 3 ) = 0.40141668064942987;
51 aPoints( 1, 3 ) = 0.40141668064942987;
52
53 aPoints( 0, 4 ) = 0.25555165440309735;
54 aPoints( 1, 4 ) = 0.25555165440309735;
55
56 aPoints( 0, 5 ) = 0.1770779421521279;
57 aPoints( 1, 5 ) = 0.1770779421521279;
58
59 aPoints( 0, 6 ) = 0.11006105322795084;
60 aPoints( 1, 6 ) = 0.11006105322795084;
61
62 aPoints( 0, 7 ) = 0.05552862425183902;
63 aPoints( 1, 7 ) = 0.05552862425183902;
64
65 aPoints( 0, 8 ) = 0.012621863777228966;
66 aPoints( 1, 8 ) = 0.012621863777228966;
67
68 aPoints( 0, 9 ) = 0.48960998707300485;
69 aPoints( 1, 9 ) = 0.020780025853990303;
70
71 aPoints( 0, 10 ) = 0.4545368926978903;
72 aPoints( 1, 10 ) = 0.09092621460421935;
73
74 aPoints( 0, 11 ) = 0.40141668064942987;
75 aPoints( 1, 11 ) = 0.19716663870114026;
76
77 aPoints( 0, 12 ) = 0.25555165440309735;
78 aPoints( 1, 12 ) = 0.4888966911938053;
79
80 aPoints( 0, 13 ) = 0.1770779421521279;
81 aPoints( 1, 13 ) = 0.6458441156957442;
82
83 aPoints( 0, 14 ) = 0.11006105322795084;
84 aPoints( 1, 14 ) = 0.7798778935440983;
85
86 aPoints( 0, 15 ) = 0.05552862425183902;
87 aPoints( 1, 15 ) = 0.888942751496322;
88
89 aPoints( 0, 16 ) = 0.012621863777228966;
90 aPoints( 1, 16 ) = 0.9747562724455421;
91
92 aPoints( 0, 17 ) = 0.020780025853990303;
93 aPoints( 1, 17 ) = 0.48960998707300485;
94
95 aPoints( 0, 18 ) = 0.09092621460421935;
96 aPoints( 1, 18 ) = 0.4545368926978903;
97
98 aPoints( 0, 19 ) = 0.19716663870114026;
99 aPoints( 1, 19 ) = 0.40141668064942987;
100
101 aPoints( 0, 20 ) = 0.4888966911938053;
102 aPoints( 1, 20 ) = 0.25555165440309735;
103
104 aPoints( 0, 21 ) = 0.6458441156957442;
105 aPoints( 1, 21 ) = 0.1770779421521279;
106
107 aPoints( 0, 22 ) = 0.7798778935440983;
108 aPoints( 1, 22 ) = 0.11006105322795084;
109
110 aPoints( 0, 23 ) = 0.888942751496322;
111 aPoints( 1, 23 ) = 0.05552862425183902;
112
113 aPoints( 0, 24 ) = 0.9747562724455421;
114 aPoints( 1, 24 ) = 0.012621863777228966;
115
116 aPoints( 0, 25 ) = 0.3957547873569518;
117 aPoints( 1, 25 ) = 0.6006337947946352;
118
119 aPoints( 0, 26 ) = 0.3079299838804336;
120 aPoints( 1, 26 ) = 0.5576032615887845;
121
122 aPoints( 0, 27 ) = 0.26456694840652617;
123 aPoints( 1, 27 ) = 0.720987025817359;
124
125 aPoints( 0, 28 ) = 0.3585393522059518;
126 aPoints( 1, 28 ) = 0.594527068955867;
127
128 aPoints( 0, 29 ) = 0.15780740596860005;
129 aPoints( 1, 29 ) = 0.839331473680833;
130
131 aPoints( 0, 30 ) = 0.07505059697591038;
132 aPoints( 1, 30 ) = 0.7010879789261739;
133
134 aPoints( 0, 31 ) = 0.14242160111338437;
135 aPoints( 1, 31 ) = 0.8229313240698561;
136
137 aPoints( 0, 32 ) = 0.06549462808293982;
138 aPoints( 1, 32 ) = 0.9243442526207822;
139
140 aPoints( 0, 33 ) = 0.003611417848413012;
141 aPoints( 1, 33 ) = 0.3957547873569518;
142
143 aPoints( 0, 34 ) = 0.13446675453078194;
144 aPoints( 1, 34 ) = 0.3079299838804336;
145
146 aPoints( 0, 35 ) = 0.014446025776114868;
147 aPoints( 1, 35 ) = 0.26456694840652617;
148
149 aPoints( 0, 36 ) = 0.04693357883818117;
150 aPoints( 1, 36 ) = 0.3585393522059518;
151
152 aPoints( 0, 37 ) = 0.002861120350566848;
153 aPoints( 1, 37 ) = 0.15780740596860005;
154
155 aPoints( 0, 38 ) = 0.22386142409791576;
156 aPoints( 1, 38 ) = 0.07505059697591038;
157
158 aPoints( 0, 39 ) = 0.03464707481675955;
159 aPoints( 1, 39 ) = 0.14242160111338437;
160
161 aPoints( 0, 40 ) = 0.010161119296277943;
162 aPoints( 1, 40 ) = 0.06549462808293982;
163
164 aPoints( 0, 41 ) = 0.6006337947946352;
165 aPoints( 1, 41 ) = 0.003611417848413012;
166
167 aPoints( 0, 42 ) = 0.5576032615887845;
168 aPoints( 1, 42 ) = 0.13446675453078194;
169
170 aPoints( 0, 43 ) = 0.720987025817359;
171 aPoints( 1, 43 ) = 0.014446025776114868;
172
173 aPoints( 0, 44 ) = 0.594527068955867;
174 aPoints( 1, 44 ) = 0.04693357883818117;
175
176 aPoints( 0, 45 ) = 0.839331473680833;
177 aPoints( 1, 45 ) = 0.002861120350566848;
178
179 aPoints( 0, 46 ) = 0.7010879789261739;
180 aPoints( 1, 46 ) = 0.22386142409791576;
181
182 aPoints( 0, 47 ) = 0.8229313240698561;
183 aPoints( 1, 47 ) = 0.03464707481675955;
184
185 aPoints( 0, 48 ) = 0.9243442526207822;
186 aPoints( 1, 48 ) = 0.010161119296277943;
187
188 aPoints( 0, 49 ) = 0.6006337947946352;
189 aPoints( 1, 49 ) = 0.3957547873569518;
190
191 aPoints( 0, 50 ) = 0.5576032615887845;
192 aPoints( 1, 50 ) = 0.3079299838804336;
193
194 aPoints( 0, 51 ) = 0.720987025817359;
195 aPoints( 1, 51 ) = 0.26456694840652617;
196
197 aPoints( 0, 52 ) = 0.594527068955867;
198 aPoints( 1, 52 ) = 0.3585393522059518;
199
200 aPoints( 0, 53 ) = 0.839331473680833;
201 aPoints( 1, 53 ) = 0.15780740596860005;
202
203 aPoints( 0, 54 ) = 0.7010879789261739;
204 aPoints( 1, 54 ) = 0.07505059697591038;
205
206 aPoints( 0, 55 ) = 0.8229313240698561;
207 aPoints( 1, 55 ) = 0.14242160111338437;
208
209 aPoints( 0, 56 ) = 0.9243442526207822;
210 aPoints( 1, 56 ) = 0.06549462808293982;
211
212 aPoints( 0, 57 ) = 0.003611417848413012;
213 aPoints( 1, 57 ) = 0.6006337947946352;
214
215 aPoints( 0, 58 ) = 0.13446675453078194;
216 aPoints( 1, 58 ) = 0.5576032615887845;
217
218 aPoints( 0, 59 ) = 0.014446025776114868;
219 aPoints( 1, 59 ) = 0.720987025817359;
220
221 aPoints( 0, 60 ) = 0.04693357883818117;
222 aPoints( 1, 60 ) = 0.594527068955867;
223
224 aPoints( 0, 61 ) = 0.002861120350566848;
225 aPoints( 1, 61 ) = 0.839331473680833;
226
227 aPoints( 0, 62 ) = 0.22386142409791576;
228 aPoints( 1, 62 ) = 0.7010879789261739;
229
230 aPoints( 0, 63 ) = 0.03464707481675955;
231 aPoints( 1, 63 ) = 0.8229313240698561;
232
233 aPoints( 0, 64 ) = 0.010161119296277943;
234 aPoints( 1, 64 ) = 0.9243442526207822;
235
236 aPoints( 0, 65 ) = 0.3957547873569518;
237 aPoints( 1, 65 ) = 0.003611417848413012;
238
239 aPoints( 0, 66 ) = 0.3079299838804336;
240 aPoints( 1, 66 ) = 0.13446675453078194;
241
242 aPoints( 0, 67 ) = 0.26456694840652617;
243 aPoints( 1, 67 ) = 0.014446025776114868;
244
245 aPoints( 0, 68 ) = 0.3585393522059518;
246 aPoints( 1, 68 ) = 0.04693357883818117;
247
248 aPoints( 0, 69 ) = 0.15780740596860005;
249 aPoints( 1, 69 ) = 0.002861120350566848;
250
251 aPoints( 0, 70 ) = 0.07505059697591038;
252 aPoints( 1, 70 ) = 0.22386142409791576;
253
254 aPoints( 0, 71 ) = 0.14242160111338437;
255 aPoints( 1, 71 ) = 0.03464707481675955;
256
257 aPoints( 0, 72 ) = 0.06549462808293982;
258 aPoints( 1, 72 ) = 0.010161119296277943;
259
260 for( uint k=0; k<73; ++k )
261 {
262 aPoints( 2, k ) = 1.0
263 - aPoints( 0, k )
264 - aPoints( 1, k );
265 }
266
267 aWeights.set_size( 73 );
268
269 aWeights( 0 ) = 0.016453165694459072;
270 aWeights( 1 ) = 0.005165365945636057;
271 aWeights( 2 ) = 0.011193623631508172;
272 aWeights( 3 ) = 0.01513306293473382;
273 aWeights( 4 ) = 0.015245483901098674;
274 aWeights( 5 ) = 0.012079606370820341;
275 aWeights( 6 ) = 0.008025401793400435;
276 aWeights( 7 ) = 0.004042290130892056;
277 aWeights( 8 ) = 0.0010396810137424325;
278 aWeights( 9 ) = 0.005165365945636057;
279 aWeights( 10 ) = 0.011193623631508172;
280 aWeights( 11 ) = 0.01513306293473382;
281 aWeights( 12 ) = 0.015245483901098674;
282 aWeights( 13 ) = 0.012079606370820341;
283 aWeights( 14 ) = 0.008025401793400435;
284 aWeights( 15 ) = 0.004042290130892056;
285 aWeights( 16 ) = 0.0010396810137424325;
286 aWeights( 17 ) = 0.005165365945636057;
287 aWeights( 18 ) = 0.011193623631508172;
288 aWeights( 19 ) = 0.01513306293473382;
289 aWeights( 20 ) = 0.015245483901098674;
290 aWeights( 21 ) = 0.012079606370820341;
291 aWeights( 22 ) = 0.008025401793400435;
292 aWeights( 23 ) = 0.004042290130892056;
293 aWeights( 24 ) = 0.0010396810137424325;
294 aWeights( 25 ) = 0.001942438452490906;
295 aWeights( 26 ) = 0.012787080306010813;
296 aWeights( 27 ) = 0.004440451786669143;
297 aWeights( 28 ) = 0.008062273380865757;
298 aWeights( 29 ) = 0.0012459709087453818;
299 aWeights( 30 ) = 0.009121420059475261;
300 aWeights( 31 ) = 0.0051292818680992785;
301 aWeights( 32 ) = 0.0018999644276509542;
302 aWeights( 33 ) = 0.001942438452490906;
303 aWeights( 34 ) = 0.012787080306010813;
304 aWeights( 35 ) = 0.004440451786669143;
305 aWeights( 36 ) = 0.008062273380865757;
306 aWeights( 37 ) = 0.0012459709087453818;
307 aWeights( 38 ) = 0.009121420059475261;
308 aWeights( 39 ) = 0.0051292818680992785;
309 aWeights( 40 ) = 0.0018999644276509542;
310 aWeights( 41 ) = 0.001942438452490906;
311 aWeights( 42 ) = 0.012787080306010813;
312 aWeights( 43 ) = 0.004440451786669143;
313 aWeights( 44 ) = 0.008062273380865757;
314 aWeights( 45 ) = 0.0012459709087453818;
315 aWeights( 46 ) = 0.009121420059475261;
316 aWeights( 47 ) = 0.0051292818680992785;
317 aWeights( 48 ) = 0.0018999644276509542;
318 aWeights( 49 ) = 0.001942438452490906;
319 aWeights( 50 ) = 0.012787080306010813;
320 aWeights( 51 ) = 0.004440451786669143;
321 aWeights( 52 ) = 0.008062273380865757;
322 aWeights( 53 ) = 0.0012459709087453818;
323 aWeights( 54 ) = 0.009121420059475261;
324 aWeights( 55 ) = 0.0051292818680992785;
325 aWeights( 56 ) = 0.0018999644276509542;
326 aWeights( 57 ) = 0.001942438452490906;
327 aWeights( 58 ) = 0.012787080306010813;
328 aWeights( 59 ) = 0.004440451786669143;
329 aWeights( 60 ) = 0.008062273380865757;
330 aWeights( 61 ) = 0.0012459709087453818;
331 aWeights( 62 ) = 0.009121420059475261;
332 aWeights( 63 ) = 0.0051292818680992785;
333 aWeights( 64 ) = 0.0018999644276509542;
334 aWeights( 65 ) = 0.001942438452490906;
335 aWeights( 66 ) = 0.012787080306010813;
336 aWeights( 67 ) = 0.004440451786669143;
337 aWeights( 68 ) = 0.008062273380865757;
338 aWeights( 69 ) = 0.0012459709087453818;
339 aWeights( 70 ) = 0.009121420059475261;
340 aWeights( 71 ) = 0.0051292818680992785;
341 aWeights( 72 ) = 0.0018999644276509542;
342
343 aWeights( 0 ) = 0.0;
344 aWeights( 0 ) = 0.5 - sum( aWeights );
345 }
346
347// ----------------------------------------------------------------------------
348 } /* namespace integration */
349} /* end namespace belfem */
350
351#endif // BELFEM_FN_INTPOINTS_GAUSS_TRI73_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
fn_sum.hpp
Sum of the entries of a vector.
belfem::integration
Definition fn_intpoints.cpp:576
belfem::integration::gauss_tri73
void gauss_tri73(Vector< real > &aWeights, Matrix< real > &aPoints)
19th order interpolation
Definition fn_intpoints_gauss_tri73.hpp:35
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16
belfem::uint
unsigned int uint
Definition typedefs.hpp:30
belfem::sum
auto sum(const Vector< T > &aA) -> decltype(sum(aA.vector_data()))
Definition fn_sum.hpp:49