BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tri42.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_TRI42_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TRI42_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_tri42(
35 Vector< real > & aWeights,
36 Matrix< real > & aPoints )
37 {
38 aPoints.set_size( 3, 42 );
39
40 aPoints( 0, 0 ) = 0.41764471934045394;
41 aPoints( 1, 0 ) = 0.41764471934045394;
42
43 aPoints( 0, 1 ) = 0.0617998830908727;
44 aPoints( 1, 1 ) = 0.0617998830908727;
45
46 aPoints( 0, 2 ) = 0.2734775283088387;
47 aPoints( 1, 2 ) = 0.2734775283088387;
48
49 aPoints( 0, 3 ) = 0.1772055324125435;
50 aPoints( 1, 3 ) = 0.1772055324125435;
51
52 aPoints( 0, 4 ) = 0.0193909612487011;
53 aPoints( 1, 4 ) = 0.0193909612487011;
54
55 aPoints( 0, 5 ) = 0.4889639103621786;
56 aPoints( 1, 5 ) = 0.4889639103621786;
57
58 aPoints( 0, 6 ) = 0.41764471934045394;
59 aPoints( 1, 6 ) = 0.16471056131909212;
60
61 aPoints( 0, 7 ) = 0.0617998830908727;
62 aPoints( 1, 7 ) = 0.8764002338182546;
63
64 aPoints( 0, 8 ) = 0.2734775283088387;
65 aPoints( 1, 8 ) = 0.4530449433823226;
66
67 aPoints( 0, 9 ) = 0.1772055324125435;
68 aPoints( 1, 9 ) = 0.645588935174913;
69
70 aPoints( 0, 10 ) = 0.0193909612487011;
71 aPoints( 1, 10 ) = 0.9612180775025978;
72
73 aPoints( 0, 11 ) = 0.4889639103621786;
74 aPoints( 1, 11 ) = 0.022072179275642756;
75
76 aPoints( 0, 12 ) = 0.16471056131909212;
77 aPoints( 1, 12 ) = 0.41764471934045394;
78
79 aPoints( 0, 13 ) = 0.8764002338182546;
80 aPoints( 1, 13 ) = 0.0617998830908727;
81
82 aPoints( 0, 14 ) = 0.4530449433823226;
83 aPoints( 1, 14 ) = 0.2734775283088387;
84
85 aPoints( 0, 15 ) = 0.645588935174913;
86 aPoints( 1, 15 ) = 0.1772055324125435;
87
88 aPoints( 0, 16 ) = 0.9612180775025978;
89 aPoints( 1, 16 ) = 0.0193909612487011;
90
91 aPoints( 0, 17 ) = 0.022072179275642756;
92 aPoints( 1, 17 ) = 0.4889639103621786;
93
94 aPoints( 0, 18 ) = 0.014646950055654471;
95 aPoints( 1, 18 ) = 0.29837288213625773;
96
97 aPoints( 0, 19 ) = 0.09291624935697185;
98 aPoints( 1, 19 ) = 0.336861459796345;
99
100 aPoints( 0, 20 ) = 0.05712475740364799;
101 aPoints( 1, 20 ) = 0.17226668782135557;
102
103 aPoints( 0, 21 ) = 0.001268330932872076;
104 aPoints( 1, 21 ) = 0.11897449769695682;
105
106 aPoints( 0, 22 ) = 0.6869801678080878;
107 aPoints( 1, 22 ) = 0.014646950055654471;
108
109 aPoints( 0, 23 ) = 0.5702222908466832;
110 aPoints( 1, 23 ) = 0.09291624935697185;
111
112 aPoints( 0, 24 ) = 0.7706085547749965;
113 aPoints( 1, 24 ) = 0.05712475740364799;
114
115 aPoints( 0, 25 ) = 0.8797571713701712;
116 aPoints( 1, 25 ) = 0.001268330932872076;
117
118 aPoints( 0, 26 ) = 0.29837288213625773;
119 aPoints( 1, 26 ) = 0.6869801678080878;
120
121 aPoints( 0, 27 ) = 0.336861459796345;
122 aPoints( 1, 27 ) = 0.5702222908466832;
123
124 aPoints( 0, 28 ) = 0.17226668782135557;
125 aPoints( 1, 28 ) = 0.7706085547749965;
126
127 aPoints( 0, 29 ) = 0.11897449769695682;
128 aPoints( 1, 29 ) = 0.8797571713701712;
129
130 aPoints( 0, 30 ) = 0.29837288213625773;
131 aPoints( 1, 30 ) = 0.014646950055654471;
132
133 aPoints( 0, 31 ) = 0.336861459796345;
134 aPoints( 1, 31 ) = 0.09291624935697185;
135
136 aPoints( 0, 32 ) = 0.17226668782135557;
137 aPoints( 1, 32 ) = 0.05712475740364799;
138
139 aPoints( 0, 33 ) = 0.11897449769695682;
140 aPoints( 1, 33 ) = 0.001268330932872076;
141
142 aPoints( 0, 34 ) = 0.6869801678080878;
143 aPoints( 1, 34 ) = 0.29837288213625773;
144
145 aPoints( 0, 35 ) = 0.5702222908466832;
146 aPoints( 1, 35 ) = 0.336861459796345;
147
148 aPoints( 0, 36 ) = 0.7706085547749965;
149 aPoints( 1, 36 ) = 0.17226668782135557;
150
151 aPoints( 0, 37 ) = 0.8797571713701712;
152 aPoints( 1, 37 ) = 0.11897449769695682;
153
154 aPoints( 0, 38 ) = 0.014646950055654471;
155 aPoints( 1, 38 ) = 0.6869801678080878;
156
157 aPoints( 0, 39 ) = 0.09291624935697185;
158 aPoints( 1, 39 ) = 0.5702222908466832;
159
160 aPoints( 0, 40 ) = 0.05712475740364799;
161 aPoints( 1, 40 ) = 0.7706085547749965;
162
163 aPoints( 0, 41 ) = 0.001268330932872076;
164 aPoints( 1, 41 ) = 0.8797571713701712;
165
166 for( uint k=0; k<42; ++k )
167 {
168 aPoints( 2, k ) = 1.0
169 - aPoints( 0, k )
170 - aPoints( 1, k );
171 }
172
173 aWeights.set_size( 42 );
174
175 aWeights( 0 ) = 0.016394176772062678;
176 aWeights( 1 ) = 0.007216849834888334;
177 aWeights( 2 ) = 0.025887052253645793;
178 aWeights( 3 ) = 0.02108129436849651;
179 aWeights( 4 ) = 0.002461701801200041;
180 aWeights( 5 ) = 0.010941790684714446;
181 aWeights( 6 ) = 0.016394176772062678;
182 aWeights( 7 ) = 0.007216849834888334;
183 aWeights( 8 ) = 0.025887052253645793;
184 aWeights( 9 ) = 0.02108129436849651;
185 aWeights( 10 ) = 0.002461701801200041;
186 aWeights( 11 ) = 0.010941790684714446;
187 aWeights( 12 ) = 0.016394176772062678;
188 aWeights( 13 ) = 0.007216849834888334;
189 aWeights( 14 ) = 0.025887052253645793;
190 aWeights( 15 ) = 0.02108129436849651;
191 aWeights( 16 ) = 0.002461701801200041;
192 aWeights( 17 ) = 0.010941790684714446;
193 aWeights( 18 ) = 0.007218154056766921;
194 aWeights( 19 ) = 0.019285755393530342;
195 aWeights( 20 ) = 0.012332876606281839;
196 aWeights( 21 ) = 0.002505114419250336;
197 aWeights( 22 ) = 0.007218154056766921;
198 aWeights( 23 ) = 0.019285755393530342;
199 aWeights( 24 ) = 0.012332876606281839;
200 aWeights( 25 ) = 0.002505114419250336;
201 aWeights( 26 ) = 0.007218154056766921;
202 aWeights( 27 ) = 0.019285755393530342;
203 aWeights( 28 ) = 0.012332876606281839;
204 aWeights( 29 ) = 0.002505114419250336;
205 aWeights( 30 ) = 0.007218154056766921;
206 aWeights( 31 ) = 0.019285755393530342;
207 aWeights( 32 ) = 0.012332876606281839;
208 aWeights( 33 ) = 0.002505114419250336;
209 aWeights( 34 ) = 0.007218154056766921;
210 aWeights( 35 ) = 0.019285755393530342;
211 aWeights( 36 ) = 0.012332876606281839;
212 aWeights( 37 ) = 0.002505114419250336;
213 aWeights( 38 ) = 0.007218154056766921;
214 aWeights( 39 ) = 0.019285755393530342;
215 aWeights( 40 ) = 0.012332876606281839;
216 aWeights( 41 ) = 0.002505114419250336;
217 }
218
219// ----------------------------------------------------------------------------
220 } /* namespace integration */
221} /* end namespace belfem */
222
223#endif // BELFEM_FN_INTPOINTS_GAUSS_TRI42_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_tri42
void gauss_tri42(Vector< real > &aWeights, Matrix< real > &aPoints)
14th order interpolation
Definition fn_intpoints_gauss_tri42.hpp:34
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16
belfem::uint
unsigned int uint
Definition typedefs.hpp:30