BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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cl_IF_TET10.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_CL_IF_TET10_HPP
13#define BELFEM_CL_IF_TET10_HPP
14
15namespace belfem
16{
17 namespace fem
18 {
19//------------------------------------------------------------------------------
20
21 template<>
22 InterpolationOrder
23 InterpolationFunctionTemplate<
24 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >
29
30//------------------------------------------------------------------------------
31
32 template<>
33 ElementType
34 InterpolationFunctionTemplate<
35 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >
36 ::element_type() const
37 {
38 return ElementType::TET10;
39 }
40
41//------------------------------------------------------------------------------
42
43 template<>
44 void
45 InterpolationFunctionTemplate<
46 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >
47 ::param_coords( Matrix< real > & aXiHat ) const
48 {
49 aXiHat.set_size( 3, 10 );
50
51 aXiHat(0, 0) = 1.0;
52 aXiHat(1, 0) = 0.0;
53 aXiHat(2, 0) = 0.0;
54
55 aXiHat(0, 1) = 0.0;
56 aXiHat(1, 1) = 0.0;
57 aXiHat(2, 1) = 1.0;
58
59 aXiHat(0, 2) = 0.0;
60 aXiHat(1, 2) = 1.0;
61 aXiHat(2, 2) = 0.0;
62
63 aXiHat(0, 3) = 0.0;
64 aXiHat(1, 3) = 0.0;
65 aXiHat(2, 3) = 0.0;
66
67 aXiHat(0, 4) = 0.5;
68 aXiHat(1, 4) = 0.0;
69 aXiHat(2, 4) = 0.5;
70
71 aXiHat(0, 5) = 0.0;
72 aXiHat(1, 5) = 0.5;
73 aXiHat(2, 5) = 0.5;
74
75 aXiHat(0, 6) = 0.5;
76 aXiHat(1, 6) = 0.5;
77 aXiHat(2, 6) = 0.0;
78
79 aXiHat(0, 7) = 0.5;
80 aXiHat(1, 7) = 0.0;
81 aXiHat(2, 7) = 0.0;
82
83 aXiHat(0, 8) = 0.0;
84 aXiHat(1, 8) = 0.0;
85 aXiHat(2, 8) = 0.5;
86
87 aXiHat(0, 9) = 0.0;
88 aXiHat(1, 9) = 0.5;
89 aXiHat(2, 9) = 0.0;
90 }
91
92//------------------------------------------------------------------------------
93
94 template<>
95 void
96 InterpolationFunctionTemplate<
97 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::N(
98 const Vector< real > & aXi,
99 Matrix< real > & aN ) const
100 {
101 const real xi = aXi( 0 );
102 const real eta = aXi( 1 );
103 const real zeta = aXi( 2 );
104 const real tau = 1.0 - xi - eta - zeta;
105
106 const real xi2 = xi + xi ;
107 const real eta2 = eta + eta ;
108 const real zeta2 = zeta + zeta ;
109 const real tau2 = tau + tau ;
110
111 aN.set_size( 1, 10 );
112
113 aN( 0, 0 ) = xi*(xi2-1.0);
114 aN( 0, 1 ) = zeta*(zeta2-1.0);
115 aN( 0, 2 ) = eta*(eta2-1.0);
116 aN( 0, 3 ) = tau*(tau2-1.0);
117 aN( 0, 4 ) = xi2*zeta2;
118 aN( 0, 5 ) = eta2*zeta2;
119 aN( 0, 6 ) = xi2*eta2;
120 aN( 0, 7 ) = xi2*tau2;
121 aN( 0, 8 ) = zeta2*tau2;
122 aN( 0, 9 ) = eta2*tau2;
123 }
124
125//------------------------------------------------------------------------------
126
127 template<>
128 void
129 InterpolationFunctionTemplate<
130 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::dNdXi(
131 const Vector< real > & aXi,
132 Matrix< real > & adNdXi ) const
133 {
134 const real xi = aXi( 0 );
135 const real eta = aXi( 1 );
136 const real zeta = aXi( 2 );
137
138 const real xi4 = xi+xi+xi+xi ;
139 const real eta4 = eta+eta+eta+eta ;
140 const real zeta4 = zeta+zeta+zeta+zeta ;
141
142 adNdXi.set_size( 3, 10 );
143
144 adNdXi( 0, 0 ) = xi4-1.0;
145 adNdXi( 1, 0 ) = 0.0;
146 adNdXi( 2, 0 ) = 0.0;
147
148 adNdXi( 0, 1 ) = 0.0;
149 adNdXi( 1, 1 ) = 0.0 ;
150 adNdXi( 2, 1 ) = zeta4-1.0;
151
152 adNdXi( 0, 2 ) = 0.0;
153 adNdXi( 1, 2 ) = eta4-1.0;
154 adNdXi( 2, 2 ) = 0.0 ;
155
156 adNdXi( 0, 3 ) = (xi4+eta4+zeta4)-3.0;
157 adNdXi( 1, 3 ) = (xi4+eta4+zeta4)-3.0;
158 adNdXi( 2, 3 ) = (xi4+eta4+zeta4)-3.0;
159
160 adNdXi( 0, 4 ) = zeta4 ;
161 adNdXi( 1, 4 ) = 0.0 ;
162 adNdXi( 2, 4 ) = xi4 ;
163
164 adNdXi( 0, 5 ) = 0.0;
165 adNdXi( 1, 5 ) = zeta4 ;
166 adNdXi( 2, 5 ) = eta4 ;
167
168 adNdXi( 0, 6 ) = eta4 ;
169 adNdXi( 1, 6 ) = xi4 ;
170 adNdXi( 2, 6 ) = 0.0 ;
171
172 adNdXi( 0, 7 ) = 4. - xi4 - xi4 - eta4 - zeta4 ;
173 adNdXi( 1, 7 ) = -xi4 ;
174 adNdXi( 2, 7 ) = -xi4 ;
175
176 adNdXi( 0, 8 ) = -zeta4 ;
177 adNdXi( 1, 8 ) = -zeta4 ;
178 adNdXi( 2, 8 ) = 4. - xi4 - eta4 - zeta4- zeta4 ;
179
180 adNdXi( 0, 9 ) = -eta4 ;
181 adNdXi( 1, 9 ) = 4. - xi4 - eta4 - eta4- zeta4 ;
182 adNdXi( 2, 9 ) = -eta4 ;
183 }
184
185//------------------------------------------------------------------------------
186
187 template<>
188 void
189 InterpolationFunctionTemplate<
190 GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::d2NdXi2(
191 const Vector< real > & aXi,
192 Matrix< real > & ad2NdXi2 ) const
193 {
194 ad2NdXi2.set_size( 6, 10 );
195
196 ad2NdXi2( 0, 0 ) = 4.0;
197 ad2NdXi2( 1, 0 ) = 0.0;
198 ad2NdXi2( 2, 0 ) = 0.0;
199 ad2NdXi2( 3, 0 ) = 0.0;
200 ad2NdXi2( 4, 0 ) = 0.0;
201 ad2NdXi2( 5, 0 ) = 0.0;
202
203 ad2NdXi2( 0, 1 ) = 0.0;
204 ad2NdXi2( 1, 1 ) = 0.0;
205 ad2NdXi2( 2, 1 ) = 4.0;
206 ad2NdXi2( 3, 1 ) = 0.0;
207 ad2NdXi2( 4, 1 ) = 0.0;
208 ad2NdXi2( 5, 1 ) = 0.0;
209
210 ad2NdXi2( 0, 2 ) = 0.0;
211 ad2NdXi2( 1, 2 ) = 4.0;
212 ad2NdXi2( 2, 2 ) = 0.0;
213 ad2NdXi2( 3, 2 ) = 0.0;
214 ad2NdXi2( 4, 2 ) = 0.0;
215 ad2NdXi2( 5, 2 ) = 0.0;
216
217 ad2NdXi2( 0, 3 ) = 4.0;
218 ad2NdXi2( 1, 3 ) = 4.0;
219 ad2NdXi2( 2, 3 ) = 4.0;
220 ad2NdXi2( 3, 3 ) = 4.0;
221 ad2NdXi2( 4, 3 ) = 4.0;
222 ad2NdXi2( 5, 3 ) = 4.0;
223
224 ad2NdXi2( 0, 4 ) = 0.0;
225 ad2NdXi2( 1, 4 ) = 0.0;
226 ad2NdXi2( 2, 4 ) = 0.0;
227 ad2NdXi2( 3, 4 ) = 0.0;
228 ad2NdXi2( 4, 4 ) = 4.0;
229 ad2NdXi2( 5, 4 ) = 0.0;
230
231 ad2NdXi2( 0, 5 ) = 0.0;
232 ad2NdXi2( 1, 5 ) = 0.0;
233 ad2NdXi2( 2, 5 ) = 0.0;
234 ad2NdXi2( 3, 5 ) = 4.0;
235 ad2NdXi2( 4, 5 ) = 0.0;
236 ad2NdXi2( 5, 5 ) = 0.0;
237
238 ad2NdXi2( 0, 6 ) = 0.0;
239 ad2NdXi2( 1, 6 ) = 0.0;
240 ad2NdXi2( 2, 6 ) = 0.0;
241 ad2NdXi2( 3, 6 ) = 0.0;
242 ad2NdXi2( 4, 6 ) = 0.0;
243 ad2NdXi2( 5, 6 ) = 4.0;
244
245 ad2NdXi2( 0, 7 ) = -8.0;
246 ad2NdXi2( 1, 7 ) = 0.0;
247 ad2NdXi2( 2, 7 ) = 0.0;
248 ad2NdXi2( 3, 7 ) = 0.0;
249 ad2NdXi2( 4, 7 ) = -4.0;
250 ad2NdXi2( 5, 7 ) = -4.0;
251
252 ad2NdXi2( 0, 8 ) = 0.0;
253 ad2NdXi2( 1, 8 ) = 0.0;
254 ad2NdXi2( 2, 8 ) = -8.0;
255 ad2NdXi2( 3, 8 ) = -4.0;
256 ad2NdXi2( 4, 8 ) = -4.0;
257 ad2NdXi2( 5, 8 ) = 0.0;
258
259 ad2NdXi2( 0, 9 ) = 0.0;
260 ad2NdXi2( 1, 9 ) = -8.0;
261 ad2NdXi2( 2, 9 ) = 0.0;
262 ad2NdXi2( 3, 9 ) = -4.0;
263 ad2NdXi2( 4, 9 ) = 0.0;
264 ad2NdXi2( 5, 9 ) = -4.0;
265 }
266
267//------------------------------------------------------------------------------
268 }
269}
270
271#endif //BELFEM_CL_IF_TET10_HPP
belfem::Matrix::set_size
void set_size(const size_t aNumRows, const size_t aNumCols)
Definition cl_AR_Matrix.hpp:186
belfem::fem::InterpolationFunctionTemplate
shape function templated class G : Geometry T : Type D : Dimension B : Number of Basis
Definition cl_IF_InterpolationFunctionTemplate.hpp:25
belfem::fem::InterpolationFunctionTemplate::param_coords
void param_coords(Matrix< real > &aXiHat) const override
returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of...
Definition cl_IF_InterpolationFunctionTemplate.hpp:49
belfem::fem::InterpolationFunctionTemplate::interpolation_order
InterpolationOrder interpolation_order() const override
returns the interpolation order
Definition cl_IF_InterpolationFunctionTemplate.hpp:145
belfem::fem::InterpolationFunctionTemplate::d2NdXi2
void d2NdXi2(const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const override
calculates the second derivative of the shape function in parameter space
Definition cl_IF_InterpolationFunctionTemplate.hpp:110
belfem::fem::InterpolationFunctionTemplate::dNdXi
void dNdXi(const Vector< real > &aXi, Matrix< real > &adNdXi) const override
calculates the first derivative of the shape function in parameter space
Definition cl_IF_InterpolationFunctionTemplate.hpp:89
belfem::fem::InterpolationFunctionTemplate::N
void N(const Vector< real > &aXi, Matrix< real > &aN) const override
evaluates the shape function at a given point
Definition cl_IF_InterpolationFunctionTemplate.hpp:68
belfem::fem
Definition cl_IFB_LINE3.hpp:21
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16
belfem::InterpolationType::LAGRANGE
@ LAGRANGE
Definition Mesh_Enums.hpp:100
belfem::element_type
ElementType element_type(const std::string &aStr)
Definition Mesh_Enums.hpp:370
belfem::ElementType
ElementType
Element types.
Definition Mesh_Enums.hpp:27
belfem::ElementType::TET10
@ TET10
Definition Mesh_Enums.hpp:39
belfem::InterpolationOrder
InterpolationOrder
Definition Mesh_Enums.hpp:85
belfem::InterpolationOrder::QUADRATIC
@ QUADRATIC
Definition Mesh_Enums.hpp:88
belfem::real
double real
Definition typedefs.hpp:36
belfem::GeometryType::TET
@ TET
Definition Mesh_Enums.hpp:75