libMesh
quadrature_gm_3D.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3 
4 // This library is free software; you can redistribute it and/or
5 // modify it under the terms of the GNU Lesser General Public
6 // License as published by the Free Software Foundation; either
7 // version 2.1 of the License, or (at your option) any later version.
8 
9 // This library is distributed in the hope that it will be useful,
10 // but WITHOUT ANY WARRANTY; without even the implied warranty of
11 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 // Lesser General Public License for more details.
13 
14 // You should have received a copy of the GNU Lesser General Public
15 // License along with this library; if not, write to the Free Software
16 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 
18 
19 
20 // Local includes
21 #include "libmesh/quadrature_gm.h"
22 #include "libmesh/enum_to_string.h"
23 
24 namespace libMesh
25 {
26 
27 void QGrundmann_Moller::init_3D()
28 {
29  // Nearly all GM rules contain negative weights, so if you are not
30  // allowing rules with negative weights, we cannot continue!
31  libmesh_error_msg_if(!allow_rules_with_negative_weights,
32  "You requested a Grundmann-Moller rule but\n"
33  "are not allowing rules with negative weights!\n"
34  "Either select a different quadrature class or\n"
35  "set allow_rules_with_negative_weights==true.");
36 
37  switch (_type)
38  {
39  case TET4:
40  case TET10:
41  case TET14:
42  {
43  switch(get_order())
44  {
45  // We hard-code the first few orders based on output from
46  // the mp-quadrature library:
47  //
48  // https://code.google.com/p/mp-quadrature
49  //
50  // The points are ordered in such a way that the amount of
51  // round-off error in the quadrature calculations is
52  // (hopefully) minimized. These orderings were obtained
53  // via a simple permutation optimization strategy designed
54  // to produce the smallest overall average error while
55  // integrating all polynomials of degree <= d.
56  case CONSTANT:
57  case FIRST:
58  {
59  _points.resize(1);
60  _weights.resize(1);
61 
62  _points[0](0) = Real(1)/4;
63  _points[0](1) = Real(1)/4;
64  _points[0](2) = Real(1)/4;
65 
66  _weights[0] = Real(1)/6;
67  return;
68  }
69 
70  case SECOND:
71  case THIRD:
72  {
73  _points.resize(5);
74  _weights.resize(5);
75 
76  _points[0](0) = Real(1)/6; _points[0](1) = Real(1)/6; _points[0](2) = Real(1)/2; _weights[0] = Real(3)/40;
77  _points[1](0) = Real(1)/6; _points[1](1) = Real(1)/6; _points[1](2) = Real(1)/6; _weights[1] = Real(3)/40;
78  _points[2](0) = Real(1)/4; _points[2](1) = Real(1)/4; _points[2](2) = Real(1)/4; _weights[2] = -Real(2)/15;
79  _points[3](0) = Real(1)/2; _points[3](1) = Real(1)/6; _points[3](2) = Real(1)/6; _weights[3] = Real(3)/40;
80  _points[4](0) = Real(1)/6; _points[4](1) = Real(1)/2; _points[4](2) = Real(1)/6; _weights[4] = Real(3)/40;
81  return;
82  }
83 
84  case FOURTH:
85  case FIFTH:
86  {
87  _points.resize(15);
88  _weights.resize(15);
89 
90  _points[ 0](0) = Real(1)/8; _points[ 0](1) = Real(3)/8; _points[ 0](2) = Real(1)/8; _weights[ 0] = Real(16)/315;
91  _points[ 1](0) = Real(1)/8; _points[ 1](1) = Real(1)/8; _points[ 1](2) = Real(5)/8; _weights[ 1] = Real(16)/315;
92  _points[ 2](0) = Real(3)/8; _points[ 2](1) = Real(1)/8; _points[ 2](2) = Real(1)/8; _weights[ 2] = Real(16)/315;
93  _points[ 3](0) = Real(1)/6; _points[ 3](1) = Real(1)/2; _points[ 3](2) = Real(1)/6; _weights[ 3] = -Real(27)/280;
94  _points[ 4](0) = Real(3)/8; _points[ 4](1) = Real(1)/8; _points[ 4](2) = Real(3)/8; _weights[ 4] = Real(16)/315;
95  _points[ 5](0) = Real(1)/8; _points[ 5](1) = Real(3)/8; _points[ 5](2) = Real(3)/8; _weights[ 5] = Real(16)/315;
96  _points[ 6](0) = Real(1)/6; _points[ 6](1) = Real(1)/6; _points[ 6](2) = Real(1)/6; _weights[ 6] = -Real(27)/280;
97  _points[ 7](0) = Real(1)/6; _points[ 7](1) = Real(1)/6; _points[ 7](2) = Real(1)/2; _weights[ 7] = -Real(27)/280;
98  _points[ 8](0) = Real(1)/8; _points[ 8](1) = Real(1)/8; _points[ 8](2) = Real(1)/8; _weights[ 8] = Real(16)/315;
99  _points[ 9](0) = Real(1)/4; _points[ 9](1) = Real(1)/4; _points[ 9](2) = Real(1)/4; _weights[ 9] = Real(2)/45;
100  _points[10](0) = Real(1)/8; _points[10](1) = Real(5)/8; _points[10](2) = Real(1)/8; _weights[10] = Real(16)/315;
101  _points[11](0) = Real(1)/2; _points[11](1) = Real(1)/6; _points[11](2) = Real(1)/6; _weights[11] = -Real(27)/280;
102  _points[12](0) = Real(1)/8; _points[12](1) = Real(1)/8; _points[12](2) = Real(3)/8; _weights[12] = Real(16)/315;
103  _points[13](0) = Real(5)/8; _points[13](1) = Real(1)/8; _points[13](2) = Real(1)/8; _weights[13] = Real(16)/315;
104  _points[14](0) = Real(3)/8; _points[14](1) = Real(3)/8; _points[14](2) = Real(1)/8; _weights[14] = Real(16)/315;
105  return;
106  }
107 
108  case SIXTH:
109  case SEVENTH:
110  {
111  _points.resize(35);
112  _weights.resize(35);
113 
114  _points[ 0](0) = Real(3)/10; _points[ 0](1) = Real(1)/10; _points[ 0](2) = Real(3)/10; _weights[ 0] = Real(3125)/72576;
115  _points[ 1](0) = Real(1)/6; _points[ 1](1) = Real(1)/2; _points[ 1](2) = Real(1)/6; _weights[ 1] = Real(243)/4480;
116  _points[ 2](0) = Real(1)/6; _points[ 2](1) = Real(1)/6; _points[ 2](2) = Real(1)/2; _weights[ 2] = Real(243)/4480;
117  _points[ 3](0) = Real(1)/2; _points[ 3](1) = Real(1)/10; _points[ 3](2) = Real(1)/10; _weights[ 3] = Real(3125)/72576;
118  _points[ 4](0) = Real(3)/10; _points[ 4](1) = Real(1)/10; _points[ 4](2) = Real(1)/10; _weights[ 4] = Real(3125)/72576;
119  _points[ 5](0) = Real(3)/10; _points[ 5](1) = Real(3)/10; _points[ 5](2) = Real(1)/10; _weights[ 5] = Real(3125)/72576;
120  _points[ 6](0) = Real(1)/2; _points[ 6](1) = Real(1)/6; _points[ 6](2) = Real(1)/6; _weights[ 6] = Real(243)/4480;
121  _points[ 7](0) = Real(3)/10; _points[ 7](1) = Real(1)/10; _points[ 7](2) = Real(1)/2; _weights[ 7] = Real(3125)/72576;
122  _points[ 8](0) = Real(7)/10; _points[ 8](1) = Real(1)/10; _points[ 8](2) = Real(1)/10; _weights[ 8] = Real(3125)/72576;
123  _points[ 9](0) = Real(3)/8; _points[ 9](1) = Real(1)/8; _points[ 9](2) = Real(1)/8; _weights[ 9] = -Real(256)/2835;
124  _points[10](0) = Real(3)/10; _points[10](1) = Real(3)/10; _points[10](2) = Real(3)/10; _weights[10] = Real(3125)/72576;
125  _points[11](0) = Real(1)/10; _points[11](1) = Real(1)/2; _points[11](2) = Real(3)/10; _weights[11] = Real(3125)/72576;
126  _points[12](0) = Real(1)/10; _points[12](1) = Real(1)/10; _points[12](2) = Real(7)/10; _weights[12] = Real(3125)/72576;
127  _points[13](0) = Real(1)/2; _points[13](1) = Real(1)/10; _points[13](2) = Real(3)/10; _weights[13] = Real(3125)/72576;
128  _points[14](0) = Real(1)/10; _points[14](1) = Real(7)/10; _points[14](2) = Real(1)/10; _weights[14] = Real(3125)/72576;
129  _points[15](0) = Real(1)/10; _points[15](1) = Real(1)/2; _points[15](2) = Real(1)/10; _weights[15] = Real(3125)/72576;
130  _points[16](0) = Real(1)/6; _points[16](1) = Real(1)/6; _points[16](2) = Real(1)/6; _weights[16] = Real(243)/4480;
131  _points[17](0) = Real(3)/8; _points[17](1) = Real(1)/8; _points[17](2) = Real(3)/8; _weights[17] = -Real(256)/2835;
132  _points[18](0) = Real(1)/8; _points[18](1) = Real(1)/8; _points[18](2) = Real(5)/8; _weights[18] = -Real(256)/2835;
133  _points[19](0) = Real(1)/10; _points[19](1) = Real(1)/10; _points[19](2) = Real(3)/10; _weights[19] = Real(3125)/72576;
134  _points[20](0) = Real(1)/8; _points[20](1) = Real(3)/8; _points[20](2) = Real(3)/8; _weights[20] = -Real(256)/2835;
135  _points[21](0) = Real(5)/8; _points[21](1) = Real(1)/8; _points[21](2) = Real(1)/8; _weights[21] = -Real(256)/2835;
136  _points[22](0) = Real(1)/8; _points[22](1) = Real(5)/8; _points[22](2) = Real(1)/8; _weights[22] = -Real(256)/2835;
137  _points[23](0) = Real(1)/10; _points[23](1) = Real(3)/10; _points[23](2) = Real(1)/10; _weights[23] = Real(3125)/72576;
138  _points[24](0) = Real(1)/4; _points[24](1) = Real(1)/4; _points[24](2) = Real(1)/4; _weights[24] = -Real(8)/945;
139  _points[25](0) = Real(1)/8; _points[25](1) = Real(1)/8; _points[25](2) = Real(3)/8; _weights[25] = -Real(256)/2835;
140  _points[26](0) = Real(3)/8; _points[26](1) = Real(3)/8; _points[26](2) = Real(1)/8; _weights[26] = -Real(256)/2835;
141  _points[27](0) = Real(1)/8; _points[27](1) = Real(3)/8; _points[27](2) = Real(1)/8; _weights[27] = -Real(256)/2835;
142  _points[28](0) = Real(1)/10; _points[28](1) = Real(3)/10; _points[28](2) = Real(1)/2; _weights[28] = Real(3125)/72576;
143  _points[29](0) = Real(3)/10; _points[29](1) = Real(1)/2; _points[29](2) = Real(1)/10; _weights[29] = Real(3125)/72576;
144  _points[30](0) = Real(1)/10; _points[30](1) = Real(1)/10; _points[30](2) = Real(1)/2; _weights[30] = Real(3125)/72576;
145  _points[31](0) = Real(1)/2; _points[31](1) = Real(3)/10; _points[31](2) = Real(1)/10; _weights[31] = Real(3125)/72576;
146  _points[32](0) = Real(1)/8; _points[32](1) = Real(1)/8; _points[32](2) = Real(1)/8; _weights[32] = -Real(256)/2835;
147  _points[33](0) = Real(1)/10; _points[33](1) = Real(3)/10; _points[33](2) = Real(3)/10; _weights[33] = Real(3125)/72576;
148  _points[34](0) = Real(1)/10; _points[34](1) = Real(1)/10; _points[34](2) = Real(1)/10; _weights[34] = Real(3125)/72576;
149  return;
150  }
151 
152  default:
153  {
154  // Untested above _order=23 but should work...
155  gm_rule(get_order()/2, /*dim=*/3);
156  return;
157  }
158  } // end switch (order)
159  } // end case TET
160 
161  default:
162  libmesh_error_msg("ERROR: Unsupported element type: " << Utility::enum_to_string(_type));
163  } // end switch (_type)
164 }
165 
166 } // namespace libMesh
libMesh::QBase::allow_rules_with_negative_weights
bool allow_rules_with_negative_weights
Flag (default true) controlling the use of quadrature rules with negative weights.
Definition: quadrature.h:301
libMesh::QBase::_type
ElemType _type
The type of element for which the current values have been computed.
Definition: quadrature.h:391
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::QBase::_points
std::vector< Point > _points
The locations of the quadrature points in reference element space.
Definition: quadrature.h:409
libMesh::QBase::_weights
std::vector< Real > _weights
The quadrature weights.
Definition: quadrature.h:415
libMesh::QGrundmann_Moller::gm_rule
void gm_rule(unsigned int s, unsigned int dim)
This routine is called from init_2D() and init_3D().
Definition: quadrature_gm.C:57
libMesh::QGrundmann_Moller::init_3D
virtual void init_3D() override
Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate val...
Definition: quadrature_gm_3D.C:27
libMesh::QBase::get_order
Order get_order() const
Definition: quadrature.h:249
libMesh::Utility::enum_to_string
std::string enum_to_string(const T e)
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
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