BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tri67.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_TRI67_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TRI67_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_tri67(
36 Vector< real > & aWeights,
37 Matrix< real > & aPoints )
38 {
39 aPoints.set_size( 3, 67 );
40
41 aPoints( 0, 0 ) = 1./3. ;
42 aPoints( 1, 0 ) = 1./3. ;
43
44 aPoints( 0, 1 ) = 0.03883025608868562;
45 aPoints( 1, 1 ) = 0.03883025608868562;
46
47 aPoints( 0, 2 ) = 0.48758030157486953;
48 aPoints( 1, 2 ) = 0.48758030157486953;
49
50 aPoints( 0, 3 ) = 0.0919477421216432;
51 aPoints( 1, 3 ) = 0.0919477421216432;
52
53 aPoints( 0, 4 ) = 0.46180950640644924;
54 aPoints( 1, 4 ) = 0.46180950640644924;
55
56 aPoints( 0, 5 ) = 0.39995562806757623;
57 aPoints( 1, 5 ) = 0.39995562806757623;
58
59 aPoints( 0, 6 ) = 0.24226470251427196;
60 aPoints( 1, 6 ) = 0.24226470251427196;
61
62 aPoints( 0, 7 ) = 0.03883025608868562;
63 aPoints( 1, 7 ) = 0.9223394878226288;
64
65 aPoints( 0, 8 ) = 0.48758030157486953;
66 aPoints( 1, 8 ) = 0.02483939685026093;
67
68 aPoints( 0, 9 ) = 0.0919477421216432;
69 aPoints( 1, 9 ) = 0.8161045157567136;
70
71 aPoints( 0, 10 ) = 0.46180950640644924;
72 aPoints( 1, 10 ) = 0.07638098718710151;
73
74 aPoints( 0, 11 ) = 0.39995562806757623;
75 aPoints( 1, 11 ) = 0.20008874386484754;
76
77 aPoints( 0, 12 ) = 0.24226470251427196;
78 aPoints( 1, 12 ) = 0.5154705949714561;
79
80 aPoints( 0, 13 ) = 0.9223394878226288;
81 aPoints( 1, 13 ) = 0.03883025608868562;
82
83 aPoints( 0, 14 ) = 0.02483939685026093;
84 aPoints( 1, 14 ) = 0.48758030157486953;
85
86 aPoints( 0, 15 ) = 0.8161045157567136;
87 aPoints( 1, 15 ) = 0.0919477421216432;
88
89 aPoints( 0, 16 ) = 0.07638098718710151;
90 aPoints( 1, 16 ) = 0.46180950640644924;
91
92 aPoints( 0, 17 ) = 0.20008874386484754;
93 aPoints( 1, 17 ) = 0.39995562806757623;
94
95 aPoints( 0, 18 ) = 0.5154705949714561;
96 aPoints( 1, 18 ) = 0.24226470251427196;
97
98 aPoints( 0, 19 ) = 0.0005483600420422841;
99 aPoints( 1, 19 ) = 0.027090910995162032;
100
101 aPoints( 0, 20 ) = 0.0038976110334733582;
102 aPoints( 1, 20 ) = 0.3956834343322697;
103
104 aPoints( 0, 21 ) = 0.005298335186609826;
105 aPoints( 1, 21 ) = 0.23577218495819174;
106
107 aPoints( 0, 22 ) = 0.013462016741444982;
108 aPoints( 1, 22 ) = 0.10819579379103328;
109
110 aPoints( 0, 23 ) = 0.045804915859860795;
111 aPoints( 1, 23 ) = 0.183822707925464;
112
113 aPoints( 0, 24 ) = 0.040260283469908065;
114 aPoints( 1, 24 ) = 0.3197516245253773;
115
116 aPoints( 0, 25 ) = 0.12269675737192753;
117 aPoints( 1, 25 ) = 0.20634925743383792;
118
119 aPoints( 0, 26 ) = 0.12058769516392465;
120 aPoints( 1, 26 ) = 0.33349352944988075;
121
122 aPoints( 0, 27 ) = 0.9723607289627957;
123 aPoints( 1, 27 ) = 0.0005483600420422841;
124
125 aPoints( 0, 28 ) = 0.6004189546342569;
126 aPoints( 1, 28 ) = 0.0038976110334733582;
127
128 aPoints( 0, 29 ) = 0.7589294798551984;
129 aPoints( 1, 29 ) = 0.005298335186609826;
130
131 aPoints( 0, 30 ) = 0.8783421894675217;
132 aPoints( 1, 30 ) = 0.013462016741444982;
133
134 aPoints( 0, 31 ) = 0.7703723762146752;
135 aPoints( 1, 31 ) = 0.045804915859860795;
136
137 aPoints( 0, 32 ) = 0.6399880920047146;
138 aPoints( 1, 32 ) = 0.040260283469908065;
139
140 aPoints( 0, 33 ) = 0.6709539851942345;
141 aPoints( 1, 33 ) = 0.12269675737192753;
142
143 aPoints( 0, 34 ) = 0.5459187753861946;
144 aPoints( 1, 34 ) = 0.12058769516392465;
145
146 aPoints( 0, 35 ) = 0.027090910995162032;
147 aPoints( 1, 35 ) = 0.9723607289627957;
148
149 aPoints( 0, 36 ) = 0.3956834343322697;
150 aPoints( 1, 36 ) = 0.6004189546342569;
151
152 aPoints( 0, 37 ) = 0.23577218495819174;
153 aPoints( 1, 37 ) = 0.7589294798551984;
154
155 aPoints( 0, 38 ) = 0.10819579379103328;
156 aPoints( 1, 38 ) = 0.8783421894675217;
157
158 aPoints( 0, 39 ) = 0.183822707925464;
159 aPoints( 1, 39 ) = 0.7703723762146752;
160
161 aPoints( 0, 40 ) = 0.3197516245253773;
162 aPoints( 1, 40 ) = 0.6399880920047146;
163
164 aPoints( 0, 41 ) = 0.20634925743383792;
165 aPoints( 1, 41 ) = 0.6709539851942345;
166
167 aPoints( 0, 42 ) = 0.33349352944988075;
168 aPoints( 1, 42 ) = 0.5459187753861946;
169
170 aPoints( 0, 43 ) = 0.027090910995162032;
171 aPoints( 1, 43 ) = 0.0005483600420422841;
172
173 aPoints( 0, 44 ) = 0.3956834343322697;
174 aPoints( 1, 44 ) = 0.0038976110334733582;
175
176 aPoints( 0, 45 ) = 0.23577218495819174;
177 aPoints( 1, 45 ) = 0.005298335186609826;
178
179 aPoints( 0, 46 ) = 0.10819579379103328;
180 aPoints( 1, 46 ) = 0.013462016741444982;
181
182 aPoints( 0, 47 ) = 0.183822707925464;
183 aPoints( 1, 47 ) = 0.045804915859860795;
184
185 aPoints( 0, 48 ) = 0.3197516245253773;
186 aPoints( 1, 48 ) = 0.040260283469908065;
187
188 aPoints( 0, 49 ) = 0.20634925743383792;
189 aPoints( 1, 49 ) = 0.12269675737192753;
190
191 aPoints( 0, 50 ) = 0.33349352944988075;
192 aPoints( 1, 50 ) = 0.12058769516392465;
193
194 aPoints( 0, 51 ) = 0.9723607289627957;
195 aPoints( 1, 51 ) = 0.027090910995162032;
196
197 aPoints( 0, 52 ) = 0.6004189546342569;
198 aPoints( 1, 52 ) = 0.3956834343322697;
199
200 aPoints( 0, 53 ) = 0.7589294798551984;
201 aPoints( 1, 53 ) = 0.23577218495819174;
202
203 aPoints( 0, 54 ) = 0.8783421894675217;
204 aPoints( 1, 54 ) = 0.10819579379103328;
205
206 aPoints( 0, 55 ) = 0.7703723762146752;
207 aPoints( 1, 55 ) = 0.183822707925464;
208
209 aPoints( 0, 56 ) = 0.6399880920047146;
210 aPoints( 1, 56 ) = 0.3197516245253773;
211
212 aPoints( 0, 57 ) = 0.6709539851942345;
213 aPoints( 1, 57 ) = 0.20634925743383792;
214
215 aPoints( 0, 58 ) = 0.5459187753861946;
216 aPoints( 1, 58 ) = 0.33349352944988075;
217
218 aPoints( 0, 59 ) = 0.0005483600420422841;
219 aPoints( 1, 59 ) = 0.9723607289627957;
220
221 aPoints( 0, 60 ) = 0.0038976110334733582;
222 aPoints( 1, 60 ) = 0.6004189546342569;
223
224 aPoints( 0, 61 ) = 0.005298335186609826;
225 aPoints( 1, 61 ) = 0.7589294798551984;
226
227 aPoints( 0, 62 ) = 0.013462016741444982;
228 aPoints( 1, 62 ) = 0.8783421894675217;
229
230 aPoints( 0, 63 ) = 0.045804915859860795;
231 aPoints( 1, 63 ) = 0.7703723762146752;
232
233 aPoints( 0, 64 ) = 0.040260283469908065;
234 aPoints( 1, 64 ) = 0.6399880920047146;
235
236 aPoints( 0, 65 ) = 0.12269675737192753;
237 aPoints( 1, 65 ) = 0.6709539851942345;
238
239 aPoints( 0, 66 ) = 0.12058769516392465;
240 aPoints( 1, 66 ) = 0.5459187753861946;
241
242 for( uint k=0; k<67; ++k )
243 {
244 aPoints( 2, k ) = 1.0
245 - aPoints( 0, k )
246 - aPoints( 1, k );
247 }
248
249 aWeights.set_size( 67 );
250
251 aWeights( 0 ) = 0.018177867650713334;
252 aWeights( 1 ) = 0.0035646630098594852;
253 aWeights( 2 ) = 0.0060233238169998555;
254 aWeights( 3 ) = 0.008279579976001624;
255 aWeights( 4 ) = 0.009474585753389433;
256 aWeights( 5 ) = 0.016652235016695067;
257 aWeights( 6 ) = 0.01823754470447182;
258 aWeights( 7 ) = 0.0035646630098594852;
259 aWeights( 8 ) = 0.0060233238169998555;
260 aWeights( 9 ) = 0.008279579976001624;
261 aWeights( 10 ) = 0.009474585753389433;
262 aWeights( 11 ) = 0.016652235016695067;
263 aWeights( 12 ) = 0.01823754470447182;
264 aWeights( 13 ) = 0.0035646630098594852;
265 aWeights( 14 ) = 0.0060233238169998555;
266 aWeights( 15 ) = 0.008279579976001624;
267 aWeights( 16 ) = 0.009474585753389433;
268 aWeights( 17 ) = 0.016652235016695067;
269 aWeights( 18 ) = 0.01823754470447182;
270 aWeights( 19 ) = 0.0006114740634805449;
271 aWeights( 20 ) = 0.0022652672511285325;
272 aWeights( 21 ) = 0.002505330437289861;
273 aWeights( 22 ) = 0.003420055059803591;
274 aWeights( 23 ) = 0.006879808117471103;
275 aWeights( 24 ) = 0.008873744551010202;
276 aWeights( 25 ) = 0.011890955450076415;
277 aWeights( 26 ) = 0.01274108765591222;
278 aWeights( 27 ) = 0.0006114740634805449;
279 aWeights( 28 ) = 0.0022652672511285325;
280 aWeights( 29 ) = 0.002505330437289861;
281 aWeights( 30 ) = 0.003420055059803591;
282 aWeights( 31 ) = 0.006879808117471103;
283 aWeights( 32 ) = 0.008873744551010202;
284 aWeights( 33 ) = 0.011890955450076415;
285 aWeights( 34 ) = 0.01274108765591222;
286 aWeights( 35 ) = 0.0006114740634805449;
287 aWeights( 36 ) = 0.0022652672511285325;
288 aWeights( 37 ) = 0.002505330437289861;
289 aWeights( 38 ) = 0.003420055059803591;
290 aWeights( 39 ) = 0.006879808117471103;
291 aWeights( 40 ) = 0.008873744551010202;
292 aWeights( 41 ) = 0.011890955450076415;
293 aWeights( 42 ) = 0.01274108765591222;
294 aWeights( 43 ) = 0.0006114740634805449;
295 aWeights( 44 ) = 0.0022652672511285325;
296 aWeights( 45 ) = 0.002505330437289861;
297 aWeights( 46 ) = 0.003420055059803591;
298 aWeights( 47 ) = 0.006879808117471103;
299 aWeights( 48 ) = 0.008873744551010202;
300 aWeights( 49 ) = 0.011890955450076415;
301 aWeights( 50 ) = 0.01274108765591222;
302 aWeights( 51 ) = 0.0006114740634805449;
303 aWeights( 52 ) = 0.0022652672511285325;
304 aWeights( 53 ) = 0.002505330437289861;
305 aWeights( 54 ) = 0.003420055059803591;
306 aWeights( 55 ) = 0.006879808117471103;
307 aWeights( 56 ) = 0.008873744551010202;
308 aWeights( 57 ) = 0.011890955450076415;
309 aWeights( 58 ) = 0.01274108765591222;
310 aWeights( 59 ) = 0.0006114740634805449;
311 aWeights( 60 ) = 0.0022652672511285325;
312 aWeights( 61 ) = 0.002505330437289861;
313 aWeights( 62 ) = 0.003420055059803591;
314 aWeights( 63 ) = 0.006879808117471103;
315 aWeights( 64 ) = 0.008873744551010202;
316 aWeights( 65 ) = 0.011890955450076415;
317 aWeights( 66 ) = 0.01274108765591222;
318
319 aWeights( 0 ) = 0.0;
320 aWeights( 0 ) = 0.5 - sum( aWeights );
321 }
322
323// ----------------------------------------------------------------------------
324 } /* namespace integration */
325} /* end namespace belfem */
326
327#endif // BELFEM_FN_INTPOINTS_GAUSS_TRI67_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_tri67
void gauss_tri67(Vector< real > &aWeights, Matrix< real > &aPoints)
18th order interpolation
Definition fn_intpoints_gauss_tri67.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