BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tri60.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_TRI60_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TRI60_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
33 inline void
34 gauss_tri60(
35 Vector< real > & aWeights,
36 Matrix< real > & aPoints )
37 {
38 aPoints.set_size( 3, 60 );
39
40 aPoints( 0, 0 ) = 0.4171034443615992;
41 aPoints( 1, 0 ) = 0.4171034443615992;
42
43 aPoints( 0, 1 ) = 0.18035811626637066;
44 aPoints( 1, 1 ) = 0.18035811626637066;
45
46 aPoints( 0, 2 ) = 0.2857065024365867;
47 aPoints( 1, 2 ) = 0.2857065024365867;
48
49 aPoints( 0, 3 ) = 0.06665406347959701;
50 aPoints( 1, 3 ) = 0.06665406347959701;
51
52 aPoints( 0, 4 ) = 0.014755491660754072;
53 aPoints( 1, 4 ) = 0.014755491660754072;
54
55 aPoints( 0, 5 ) = 0.46559787161889027;
56 aPoints( 1, 5 ) = 0.46559787161889027;
57
58 aPoints( 0, 6 ) = 0.4171034443615992;
59 aPoints( 1, 6 ) = 0.16579311127680163;
60
61 aPoints( 0, 7 ) = 0.18035811626637066;
62 aPoints( 1, 7 ) = 0.6392837674672587;
63
64 aPoints( 0, 8 ) = 0.2857065024365867;
65 aPoints( 1, 8 ) = 0.42858699512682663;
66
67 aPoints( 0, 9 ) = 0.06665406347959701;
68 aPoints( 1, 9 ) = 0.866691873040806;
69
70 aPoints( 0, 10 ) = 0.014755491660754072;
71 aPoints( 1, 10 ) = 0.9704890166784919;
72
73 aPoints( 0, 11 ) = 0.46559787161889027;
74 aPoints( 1, 11 ) = 0.06880425676221946;
75
76 aPoints( 0, 12 ) = 0.16579311127680163;
77 aPoints( 1, 12 ) = 0.4171034443615992;
78
79 aPoints( 0, 13 ) = 0.6392837674672587;
80 aPoints( 1, 13 ) = 0.18035811626637066;
81
82 aPoints( 0, 14 ) = 0.42858699512682663;
83 aPoints( 1, 14 ) = 0.2857065024365867;
84
85 aPoints( 0, 15 ) = 0.866691873040806;
86 aPoints( 1, 15 ) = 0.06665406347959701;
87
88 aPoints( 0, 16 ) = 0.9704890166784919;
89 aPoints( 1, 16 ) = 0.014755491660754072;
90
91 aPoints( 0, 17 ) = 0.06880425676221946;
92 aPoints( 1, 17 ) = 0.46559787161889027;
93
94 aPoints( 0, 18 ) = 0.011575175903180683;
95 aPoints( 1, 18 ) = 0.07250547079900238;
96
97 aPoints( 0, 19 ) = 0.013229672760086951;
98 aPoints( 1, 19 ) = 0.41547545929522905;
99
100 aPoints( 0, 20 ) = 0.013135870834002753;
101 aPoints( 1, 20 ) = 0.27179187005535477;
102
103 aPoints( 0, 21 ) = 0.15750547792686992;
104 aPoints( 1, 21 ) = 0.29921894247697034;
105
106 aPoints( 0, 22 ) = 0.06734937786736123;
107 aPoints( 1, 22 ) = 0.3062815917461865;
108
109 aPoints( 0, 23 ) = 0.07804234056828245;
110 aPoints( 1, 23 ) = 0.16872251349525944;
111
112 aPoints( 0, 24 ) = 0.016017642362119337;
113 aPoints( 1, 24 ) = 0.15919228747279268;
114
115 aPoints( 0, 25 ) = 0.9159193532978169;
116 aPoints( 1, 25 ) = 0.011575175903180683;
117
118 aPoints( 0, 26 ) = 0.5712948679446841;
119 aPoints( 1, 26 ) = 0.013229672760086951;
120
121 aPoints( 0, 27 ) = 0.7150722591106424;
122 aPoints( 1, 27 ) = 0.013135870834002753;
123
124 aPoints( 0, 28 ) = 0.5432755795961598;
125 aPoints( 1, 28 ) = 0.15750547792686992;
126
127 aPoints( 0, 29 ) = 0.6263690303864522;
128 aPoints( 1, 29 ) = 0.06734937786736123;
129
130 aPoints( 0, 30 ) = 0.7532351459364581;
131 aPoints( 1, 30 ) = 0.07804234056828245;
132
133 aPoints( 0, 31 ) = 0.824790070165088;
134 aPoints( 1, 31 ) = 0.016017642362119337;
135
136 aPoints( 0, 32 ) = 0.07250547079900238;
137 aPoints( 1, 32 ) = 0.9159193532978169;
138
139 aPoints( 0, 33 ) = 0.41547545929522905;
140 aPoints( 1, 33 ) = 0.5712948679446841;
141
142 aPoints( 0, 34 ) = 0.27179187005535477;
143 aPoints( 1, 34 ) = 0.7150722591106424;
144
145 aPoints( 0, 35 ) = 0.29921894247697034;
146 aPoints( 1, 35 ) = 0.5432755795961598;
147
148 aPoints( 0, 36 ) = 0.3062815917461865;
149 aPoints( 1, 36 ) = 0.6263690303864522;
150
151 aPoints( 0, 37 ) = 0.16872251349525944;
152 aPoints( 1, 37 ) = 0.7532351459364581;
153
154 aPoints( 0, 38 ) = 0.15919228747279268;
155 aPoints( 1, 38 ) = 0.824790070165088;
156
157 aPoints( 0, 39 ) = 0.07250547079900238;
158 aPoints( 1, 39 ) = 0.011575175903180683;
159
160 aPoints( 0, 40 ) = 0.41547545929522905;
161 aPoints( 1, 40 ) = 0.013229672760086951;
162
163 aPoints( 0, 41 ) = 0.27179187005535477;
164 aPoints( 1, 41 ) = 0.013135870834002753;
165
166 aPoints( 0, 42 ) = 0.29921894247697034;
167 aPoints( 1, 42 ) = 0.15750547792686992;
168
169 aPoints( 0, 43 ) = 0.3062815917461865;
170 aPoints( 1, 43 ) = 0.06734937786736123;
171
172 aPoints( 0, 44 ) = 0.16872251349525944;
173 aPoints( 1, 44 ) = 0.07804234056828245;
174
175 aPoints( 0, 45 ) = 0.15919228747279268;
176 aPoints( 1, 45 ) = 0.016017642362119337;
177
178 aPoints( 0, 46 ) = 0.9159193532978169;
179 aPoints( 1, 46 ) = 0.07250547079900238;
180
181 aPoints( 0, 47 ) = 0.5712948679446841;
182 aPoints( 1, 47 ) = 0.41547545929522905;
183
184 aPoints( 0, 48 ) = 0.7150722591106424;
185 aPoints( 1, 48 ) = 0.27179187005535477;
186
187 aPoints( 0, 49 ) = 0.5432755795961598;
188 aPoints( 1, 49 ) = 0.29921894247697034;
189
190 aPoints( 0, 50 ) = 0.6263690303864522;
191 aPoints( 1, 50 ) = 0.3062815917461865;
192
193 aPoints( 0, 51 ) = 0.7532351459364581;
194 aPoints( 1, 51 ) = 0.16872251349525944;
195
196 aPoints( 0, 52 ) = 0.824790070165088;
197 aPoints( 1, 52 ) = 0.15919228747279268;
198
199 aPoints( 0, 53 ) = 0.011575175903180683;
200 aPoints( 1, 53 ) = 0.9159193532978169;
201
202 aPoints( 0, 54 ) = 0.013229672760086951;
203 aPoints( 1, 54 ) = 0.5712948679446841;
204
205 aPoints( 0, 55 ) = 0.013135870834002753;
206 aPoints( 1, 55 ) = 0.7150722591106424;
207
208 aPoints( 0, 56 ) = 0.15750547792686992;
209 aPoints( 1, 56 ) = 0.5432755795961598;
210
211 aPoints( 0, 57 ) = 0.06734937786736123;
212 aPoints( 1, 57 ) = 0.6263690303864522;
213
214 aPoints( 0, 58 ) = 0.07804234056828245;
215 aPoints( 1, 58 ) = 0.7532351459364581;
216
217 aPoints( 0, 59 ) = 0.016017642362119337;
218 aPoints( 1, 59 ) = 0.824790070165088;
219
220 for( uint k=0; k<60; ++k )
221 {
222 aPoints( 2, k ) = 1.0
223 - aPoints( 0, k )
224 - aPoints( 1, k );
225 }
226
227 aWeights.set_size( 60 );
228
229 aWeights( 0 ) = 0.013655463264051053;
230 aWeights( 1 ) = 0.013156315294008993;
231 aWeights( 2 ) = 0.01885811857639764;
232 aWeights( 3 ) = 0.006229500401152722;
233 aWeights( 4 ) = 0.001386943788818821;
234 aWeights( 5 ) = 0.01250972547524868;
235 aWeights( 6 ) = 0.013655463264051053;
236 aWeights( 7 ) = 0.013156315294008993;
237 aWeights( 8 ) = 0.01885811857639764;
238 aWeights( 9 ) = 0.006229500401152722;
239 aWeights( 10 ) = 0.001386943788818821;
240 aWeights( 11 ) = 0.01250972547524868;
241 aWeights( 12 ) = 0.013655463264051053;
242 aWeights( 13 ) = 0.013156315294008993;
243 aWeights( 14 ) = 0.01885811857639764;
244 aWeights( 15 ) = 0.006229500401152722;
245 aWeights( 16 ) = 0.001386943788818821;
246 aWeights( 17 ) = 0.01250972547524868;
247 aWeights( 18 ) = 0.002292174200867934;
248 aWeights( 19 ) = 0.005199219977919768;
249 aWeights( 20 ) = 0.004346107250500596;
250 aWeights( 21 ) = 0.013085812967668494;
251 aWeights( 22 ) = 0.011243886273345534;
252 aWeights( 23 ) = 0.01027894916022726;
253 aWeights( 24 ) = 0.003989150102964797;
254 aWeights( 25 ) = 0.002292174200867934;
255 aWeights( 26 ) = 0.005199219977919768;
256 aWeights( 27 ) = 0.004346107250500596;
257 aWeights( 28 ) = 0.013085812967668494;
258 aWeights( 29 ) = 0.011243886273345534;
259 aWeights( 30 ) = 0.01027894916022726;
260 aWeights( 31 ) = 0.003989150102964797;
261 aWeights( 32 ) = 0.002292174200867934;
262 aWeights( 33 ) = 0.005199219977919768;
263 aWeights( 34 ) = 0.004346107250500596;
264 aWeights( 35 ) = 0.013085812967668494;
265 aWeights( 36 ) = 0.011243886273345534;
266 aWeights( 37 ) = 0.01027894916022726;
267 aWeights( 38 ) = 0.003989150102964797;
268 aWeights( 39 ) = 0.002292174200867934;
269 aWeights( 40 ) = 0.005199219977919768;
270 aWeights( 41 ) = 0.004346107250500596;
271 aWeights( 42 ) = 0.013085812967668494;
272 aWeights( 43 ) = 0.011243886273345534;
273 aWeights( 44 ) = 0.01027894916022726;
274 aWeights( 45 ) = 0.003989150102964797;
275 aWeights( 46 ) = 0.002292174200867934;
276 aWeights( 47 ) = 0.005199219977919768;
277 aWeights( 48 ) = 0.004346107250500596;
278 aWeights( 49 ) = 0.013085812967668494;
279 aWeights( 50 ) = 0.011243886273345534;
280 aWeights( 51 ) = 0.01027894916022726;
281 aWeights( 52 ) = 0.003989150102964797;
282 aWeights( 53 ) = 0.002292174200867934;
283 aWeights( 54 ) = 0.005199219977919768;
284 aWeights( 55 ) = 0.004346107250500596;
285 aWeights( 56 ) = 0.013085812967668494;
286 aWeights( 57 ) = 0.011243886273345534;
287 aWeights( 58 ) = 0.01027894916022726;
288 aWeights( 59 ) = 0.003989150102964797;
289 }
290
291// ----------------------------------------------------------------------------
292 } /* namespace integration */
293} /* end namespace belfem */
294
295#endif // BELFEM_FN_INTPOINTS_GAUSS_TRI60_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_tri60
void gauss_tri60(Vector< real > &aWeights, Matrix< real > &aPoints)
17th order interpolation
Definition fn_intpoints_gauss_tri60.hpp:34
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16
belfem::uint
unsigned int uint
Definition typedefs.hpp:30