BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_tet11.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_TET11_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_TET11_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 inline void
26 gauss_tet11(
27 Vector <real> & aWeights,
28 Matrix <real> & aPoints )
29 {
30 // source Keast: 10.1016/0045-7825(86)90059-9
31
32 aPoints.set_size( 4, 11 );
33
34 real tAlpha1 = 1.0/14.0;
35 real tBeta1 = 1.0 - 3.0*tAlpha1;
36
37 real tAlpha2 = 0.25*( 1.0 - std::sqrt( 5.0/14.0 ) );
38 real tBeta2 = 0.5 - tAlpha2;
39
40 aPoints( 0, 0 ) = 0.25;
41 aPoints( 1, 0 ) = 0.25;
42 aPoints( 2, 0 ) = 0.25;
43
44 aPoints( 0, 1 ) = tAlpha1;
45 aPoints( 1, 1 ) = tAlpha1;
46 aPoints( 2, 1 ) = tAlpha1;
47
48 aPoints( 0, 2 ) = tAlpha1;
49 aPoints( 1, 2 ) = tAlpha1;
50 aPoints( 2, 2 ) = tBeta1;
51
52 aPoints( 0, 3 ) = tAlpha1;
53 aPoints( 1, 3 ) = tBeta1;
54 aPoints( 2, 3 ) = tAlpha1;
55
56
57 aPoints( 0, 4 ) = tBeta1;
58 aPoints( 1, 4 ) = tAlpha1;
59 aPoints( 2, 4 ) = tAlpha1;
60
61 aPoints( 0, 5 ) = tAlpha2;
62 aPoints( 1, 5 ) = tAlpha2;
63 aPoints( 2, 5 ) = tBeta2;
64
65 aPoints( 0, 6 ) = tAlpha2;
66 aPoints( 1, 6 ) = tBeta2;
67 aPoints( 2, 6 ) = tAlpha2;
68
69 aPoints( 0, 7 ) = tAlpha2;
70 aPoints( 1, 7 ) = tBeta2;
71 aPoints( 2, 7 ) = tBeta2;
72
73 aPoints( 0, 8 ) = tBeta2;
74 aPoints( 1, 8 ) = tAlpha2;
75 aPoints( 2, 8 ) = tAlpha2;
76
77 aPoints( 0, 9 ) = tBeta2;
78 aPoints( 1, 9 ) = tAlpha2;
79 aPoints( 2, 9 ) = tBeta2;
80
81 aPoints( 0, 10 ) = tBeta2;
82 aPoints( 1, 10 ) = tBeta2;
83 aPoints( 2, 10 ) = tAlpha2;
84
85 for( uint k=0; k<11; ++k )
86 {
87 aPoints( 3, k ) = 1.0
88 - aPoints( 0, k )
89 - aPoints( 1, k )
90 - aPoints( 2, k );
91 }
92
93
94 aWeights.set_size( 11 );
95
96 aWeights( 0 ) = -74.0/5625.0;
97 aWeights( 1 ) = 343.0/45000.0;
98 aWeights( 2 ) = aWeights( 1 );
99 aWeights( 3 ) = aWeights( 1 );
100 aWeights( 4 ) = aWeights( 1 );
101 aWeights( 5 ) = 56.0/2250.0;
102 aWeights( 6 ) = aWeights( 5 );
103 aWeights( 7 ) = aWeights( 5 );
104 aWeights( 8 ) = aWeights( 5 );
105 aWeights( 9 ) = aWeights( 5 );
106 aWeights( 10 ) = aWeights( 5 );
107
108 aWeights( 0 ) = 0.0 ;
109 aWeights( 0 ) = 1./6. - sum( aWeights );
110 }
111
112// ----------------------------------------------------------------------------
113 } /* namespace integration */
114} /* namespace belfem */
115
116#endif //BELFEM_FN_INTPOINTS_GAUSS_TET11_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_tet11
void gauss_tet11(Vector< real > &aWeights, Matrix< real > &aPoints)
Definition fn_intpoints_gauss_tet11.hpp:26
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
belfem::real
double real
Definition typedefs.hpp:36