BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tri33.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_TRI33_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TRI33_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_tri33(
35 Vector< real > & aWeights,
36 Matrix< real > & aPoints )
37 {
38 aPoints.set_size( 3, 33 );
39
40 aPoints( 0, 0 ) = 0.27146250701492614;
41 aPoints( 1, 0 ) = 0.27146250701492614;
42
43 aPoints( 0, 1 ) = 0.10925782765935432;
44 aPoints( 1, 1 ) = 0.10925782765935432;
45
46 aPoints( 0, 2 ) = 0.4401116486585931;
47 aPoints( 1, 2 ) = 0.4401116486585931;
48
49 aPoints( 0, 3 ) = 0.4882037509455415;
50 aPoints( 1, 3 ) = 0.4882037509455415;
51
52 aPoints( 0, 4 ) = 0.02464636343633564;
53 aPoints( 1, 4 ) = 0.02464636343633564;
54
55 aPoints( 0, 5 ) = 0.27146250701492614;
56 aPoints( 1, 5 ) = 0.45707498597014773;
57
58 aPoints( 0, 6 ) = 0.10925782765935432;
59 aPoints( 1, 6 ) = 0.7814843446812914;
60
61 aPoints( 0, 7 ) = 0.4401116486585931;
62 aPoints( 1, 7 ) = 0.11977670268281382;
63
64 aPoints( 0, 8 ) = 0.4882037509455415;
65 aPoints( 1, 8 ) = 0.02359249810891695;
66
67 aPoints( 0, 9 ) = 0.02464636343633564;
68 aPoints( 1, 9 ) = 0.9507072731273287;
69
70 aPoints( 0, 10 ) = 0.45707498597014773;
71 aPoints( 1, 10 ) = 0.27146250701492614;
72
73 aPoints( 0, 11 ) = 0.7814843446812914;
74 aPoints( 1, 11 ) = 0.10925782765935432;
75
76 aPoints( 0, 12 ) = 0.11977670268281382;
77 aPoints( 1, 12 ) = 0.4401116486585931;
78
79 aPoints( 0, 13 ) = 0.02359249810891695;
80 aPoints( 1, 13 ) = 0.4882037509455415;
81
82 aPoints( 0, 14 ) = 0.9507072731273287;
83 aPoints( 1, 14 ) = 0.02464636343633564;
84
85 aPoints( 0, 15 ) = 0.1162960196779266;
86 aPoints( 1, 15 ) = 0.25545422863851736;
87
88 aPoints( 0, 16 ) = 0.021382490256170623;
89 aPoints( 1, 16 ) = 0.12727971723358936;
90
91 aPoints( 0, 17 ) = 0.023034156355267166;
92 aPoints( 1, 17 ) = 0.29165567973834094;
93
94 aPoints( 0, 18 ) = 0.6282497516835561;
95 aPoints( 1, 18 ) = 0.1162960196779266;
96
97 aPoints( 0, 19 ) = 0.85133779251024;
98 aPoints( 1, 19 ) = 0.021382490256170623;
99
100 aPoints( 0, 20 ) = 0.6853101639063919;
101 aPoints( 1, 20 ) = 0.023034156355267166;
102
103 aPoints( 0, 21 ) = 0.25545422863851736;
104 aPoints( 1, 21 ) = 0.6282497516835561;
105
106 aPoints( 0, 22 ) = 0.12727971723358936;
107 aPoints( 1, 22 ) = 0.85133779251024;
108
109 aPoints( 0, 23 ) = 0.29165567973834094;
110 aPoints( 1, 23 ) = 0.6853101639063919;
111
112 aPoints( 0, 24 ) = 0.25545422863851736;
113 aPoints( 1, 24 ) = 0.1162960196779266;
114
115 aPoints( 0, 25 ) = 0.12727971723358936;
116 aPoints( 1, 25 ) = 0.021382490256170623;
117
118 aPoints( 0, 26 ) = 0.29165567973834094;
119 aPoints( 1, 26 ) = 0.023034156355267166;
120
121 aPoints( 0, 27 ) = 0.6282497516835561;
122 aPoints( 1, 27 ) = 0.25545422863851736;
123
124 aPoints( 0, 28 ) = 0.85133779251024;
125 aPoints( 1, 28 ) = 0.12727971723358936;
126
127 aPoints( 0, 29 ) = 0.6853101639063919;
128 aPoints( 1, 29 ) = 0.29165567973834094;
129
130 aPoints( 0, 30 ) = 0.1162960196779266;
131 aPoints( 1, 30 ) = 0.6282497516835561;
132
133 aPoints( 0, 31 ) = 0.021382490256170623;
134 aPoints( 1, 31 ) = 0.85133779251024;
135
136 aPoints( 0, 32 ) = 0.023034156355267166;
137 aPoints( 1, 32 ) = 0.6853101639063919;
138
139 for( uint k=0; k<33; ++k )
140 {
141 aPoints( 2, k ) = 1.0
142 - aPoints( 0, k )
143 - aPoints( 1, k );
144 }
145
146 aWeights.set_size( 33 );
147
148 aWeights( 0 ) = 0.03127060659795138;
149 aWeights( 1 ) = 0.014243026034438775;
150 aWeights( 2 ) = 0.024959167464030475;
151 aWeights( 3 ) = 0.012133419040726017;
152 aWeights( 4 ) = 0.0039658212549868194;
153 aWeights( 5 ) = 0.03127060659795138;
154 aWeights( 6 ) = 0.014243026034438775;
155 aWeights( 7 ) = 0.024959167464030475;
156 aWeights( 8 ) = 0.012133419040726017;
157 aWeights( 9 ) = 0.0039658212549868194;
158 aWeights( 10 ) = 0.03127060659795138;
159 aWeights( 11 ) = 0.014243026034438775;
160 aWeights( 12 ) = 0.024959167464030475;
161 aWeights( 13 ) = 0.012133419040726017;
162 aWeights( 14 ) = 0.0039658212549868194;
163 aWeights( 15 ) = 0.021613681829707104;
164 aWeights( 16 ) = 0.007541838788255721;
165 aWeights( 17 ) = 0.01089179251930378;
166 aWeights( 18 ) = 0.021613681829707104;
167 aWeights( 19 ) = 0.007541838788255721;
168 aWeights( 20 ) = 0.01089179251930378;
169 aWeights( 21 ) = 0.021613681829707104;
170 aWeights( 22 ) = 0.007541838788255721;
171 aWeights( 23 ) = 0.01089179251930378;
172 aWeights( 24 ) = 0.021613681829707104;
173 aWeights( 25 ) = 0.007541838788255721;
174 aWeights( 26 ) = 0.01089179251930378;
175 aWeights( 27 ) = 0.021613681829707104;
176 aWeights( 28 ) = 0.007541838788255721;
177 aWeights( 29 ) = 0.01089179251930378;
178 aWeights( 30 ) = 0.021613681829707104;
179 aWeights( 31 ) = 0.007541838788255721;
180 aWeights( 32 ) = 0.01089179251930378;
181 }
182
183// ----------------------------------------------------------------------------
184 } /* namespace integration */
185} /* end namespace belfem */
186
187#endif // BELFEM_FN_INTPOINTS_GAUSS_TRI33_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_tri33
void gauss_tri33(Vector< real > &aWeights, Matrix< real > &aPoints)
12th order interpolation
Definition fn_intpoints_gauss_tri33.hpp:34
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16
belfem::uint
unsigned int uint
Definition typedefs.hpp:30