BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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cl_IF_PENTA15.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_PENTA15_HPP
13#define BELFEM_CL_IF_PENTA15_HPP
14
15
16#include "cl_IF_InterpolationFunctionTemplate.hpp"
17
18namespace belfem
19{
20 namespace fem
21 {
22//------------------------------------------------------------------------------
23
24 template<>
25 InterpolationOrder
26 InterpolationFunctionTemplate<
27 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >
32
33//------------------------------------------------------------------------------
34
35 template<>
36 ElementType
37 InterpolationFunctionTemplate<
38 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >
39 ::element_type() const
40 {
41 return ElementType::PENTA15;
42 }
43
44//------------------------------------------------------------------------------
45
46 template<>
47 void
48 InterpolationFunctionTemplate<
49 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >
50 ::param_coords( Matrix< real > & aXiHat ) const
51 {
52 aXiHat.set_size( 3, 15 );
53
54 aXiHat( 0, 0 ) = 1.0;
55 aXiHat( 1, 0 ) = 0.0;
56 aXiHat( 2, 0 ) = -1.0;
57
58 aXiHat( 0, 1 ) = 0.0;
59 aXiHat( 1, 1 ) = 1.0;
60 aXiHat( 2, 1 ) = -1.0;
61
62 aXiHat( 0, 2 ) = 0.0;
63 aXiHat( 1, 2 ) = 0.0;
64 aXiHat( 2, 2 ) = -1.0;
65
66 aXiHat( 0, 3 ) = 1.0;
67 aXiHat( 1, 3 ) = 0.0;
68 aXiHat( 2, 3 ) = 1.0;
69
70 aXiHat( 0, 4 ) = 0.0;
71 aXiHat( 1, 4 ) = 1.0;
72 aXiHat( 2, 4 ) = 1.0;
73
74 aXiHat( 0, 5 ) = 0.0;
75 aXiHat( 1, 5 ) = 0.0;
76 aXiHat( 2, 5 ) = 1.0;
77
78 aXiHat( 0, 6 ) = 0.5;
79 aXiHat( 1, 6 ) = 0.5;
80 aXiHat( 2, 6 ) = -1.0;
81
82 aXiHat( 0, 7 ) = 0.0;
83 aXiHat( 1, 7 ) = 0.5;
84 aXiHat( 2, 7 ) = -1.0;
85
86 aXiHat( 0, 8 ) = 0.5;
87 aXiHat( 1, 8 ) = 0.0;
88 aXiHat( 2, 8 ) = -1.0;
89
90 aXiHat( 0, 9 ) = 1.0;
91 aXiHat( 1, 9 ) = 0.0;
92 aXiHat( 2, 9 ) = 0.0;
93
94 aXiHat( 0, 10 ) = 0.0;
95 aXiHat( 1, 10 ) = 1.0;
96 aXiHat( 2, 10 ) = 0.0;
97
98 aXiHat( 0, 11 ) = 0.0;
99 aXiHat( 1, 11 ) = 0.0;
100 aXiHat( 2, 11 ) = 0.0;
101
102 aXiHat( 0, 12 ) = 0.5;
103 aXiHat( 1, 12 ) = 0.5;
104 aXiHat( 2, 12 ) = 1.0;
105
106 aXiHat( 0, 13 ) = 0.0;
107 aXiHat( 1, 13 ) = 0.5;
108 aXiHat( 2, 13 ) = 1.0;
109
110 aXiHat( 0, 14 ) = 0.5;
111 aXiHat( 1, 14 ) = 0.0;
112 aXiHat( 2, 14 ) = 1.0;
113 }
114
115//------------------------------------------------------------------------------
116
117 template<>
118 void
119 InterpolationFunctionTemplate<
120 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >::N(
121 const Vector< real > & aXi,
122 Matrix< real > & aN ) const
123 {
124 const real xi = aXi( 0 );
125 const real eta = aXi( 1 );
126 const real zeta = aXi( 2 );
127
128 const real zeta2 = zeta*zeta;
129
130 aN.set_size( 1, 15 );
131
132 aN( 0, 0 ) = (xi*(zeta-1.0)*(xi*(-2.0)+zeta+2.0))*0.5;
133 aN( 0, 1 ) = (eta*(zeta-1.0)*(eta*(-2.0)+zeta+2.0))*0.5;
134 aN( 0, 2 ) = (1.0-zeta)*(eta+xi-1.0)*(eta*2.0+xi*2.0+zeta)*0.5;
135 aN( 0, 3 ) = (xi*(zeta+1.0)*(xi*2.0+zeta-2.0))*0.5;
136 aN( 0, 4 ) = (eta*(zeta+1.0)*(eta*2.0+zeta-2.0))*0.5;
137 aN( 0, 5 ) = ((zeta+1.0)*(eta+xi-1.0)*(eta*2.0+xi*2.0-zeta))*0.5;
138 aN( 0, 6 ) = eta*xi*(1.0-zeta)*2.0;
139 aN( 0, 7 ) = eta*(zeta-1.0)*(eta+xi-1.0)*2.0;
140 aN( 0, 8 ) = xi*(zeta-1.0)*(eta+xi-1.0)*2.0;
141 aN( 0, 9 ) = xi*(1.0-zeta2);
142 aN( 0, 10 ) = eta*(1.0-zeta2);
143 aN( 0, 11 ) = (zeta2-1.0)*(eta+xi-1.0);
144 aN( 0, 12 ) = eta*xi*(zeta+1.0)*2.0;
145 aN( 0, 13 ) = eta*(zeta+1.0)*(1.0-eta-xi)*2.0;
146 aN( 0, 14 ) = xi*(zeta+1.0)*(1.0-eta-xi)*2.0;
147
148 }
149
150//------------------------------------------------------------------------------
151
152 template<>
153 void
154 InterpolationFunctionTemplate<
155 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >::dNdXi(
156 const Vector< real > & aXi,
157 Matrix< real > & adNdXi ) const
158 {
159 const real xi = aXi( 0 );
160 const real eta = aXi( 1 );
161 const real zeta = aXi( 2 );
162
163 adNdXi.set_size( 3, 15 );
164
165 adNdXi( 0, 0 ) = 0.5*((zeta - 1.0)*(zeta - 4.0*xi + 2.0));
166 adNdXi( 1, 0 ) = 0.0;
167 adNdXi( 2, 0 ) = 0.5*xi*(1.0+2.0*(zeta-xi));
168
169 adNdXi( 0, 1 ) = 0.0;
170 adNdXi( 1, 1 ) = 0.5*(zeta-1.0)*(zeta-4.0*eta+2.0);
171 adNdXi( 2, 1 ) = 0.5*eta*(1.0+2.0*(zeta-eta));
172
173 adNdXi( 0, 2 ) = 0.5*(1.0-zeta)*(zeta+4.0*(xi+eta)-2.0);
174 adNdXi( 1, 2 ) = 0.5*(1.0-zeta)*(zeta+4.0*(xi+eta)-2.0);
175 adNdXi( 2, 2 ) = 0.5*(1-xi-eta)*(2.0*(xi+eta+zeta)-1.0);
176
177 adNdXi( 0, 3 ) = 0.5*(1.0+zeta)*(4.0*xi+zeta-2.0);
178 adNdXi( 1, 3 ) = 0.0;
179 adNdXi( 2, 3 ) = xi*(xi+zeta-0.5);
180
181 adNdXi( 0, 4 ) = 0.0;
182 adNdXi( 1, 4 ) = 0.5*(1.0+zeta)*(4.0*eta+zeta-2.0);
183 adNdXi( 2, 4 ) = eta*(eta+zeta-0.5);
184
185 adNdXi( 0, 5 ) = 0.5*(1.0+zeta)*(4.0*(xi+eta)-zeta-2.0);
186 adNdXi( 1, 5 ) = 0.5*(1.0+zeta)*(4.0*(xi+eta)-zeta-2.0);
187 adNdXi( 2, 5 ) = 0.5*(xi+eta-1.0)*(2.0*(xi+eta-zeta)-1.0);
188
189 adNdXi( 0, 6 ) = 2.0*eta*(1.0-zeta);
190 adNdXi( 1, 6 ) = 2.0*xi*(1.0-zeta);
191 adNdXi( 2, 6 ) = -2.0*xi*eta;
192
193 adNdXi( 0, 7 ) = 2.0*eta*(zeta-1.0);
194 adNdXi( 1, 7 ) = 2.0*(zeta-1.0)*(xi+2.0*eta-1.0);
195 adNdXi( 2, 7 ) = 2.0*eta*(xi+eta-1.0);
196
197 adNdXi( 0, 8 ) = 2.0*(zeta-1.0)*(2.0*xi+eta-1.0);
198 adNdXi( 1, 8 ) = 2.0*xi*(zeta-1.0);
199 adNdXi( 2, 8 ) = 2.0*xi*(xi+eta-1.0);
200
201 adNdXi( 0, 9 ) = 1.0-zeta*zeta;
202 adNdXi( 1, 9 ) = 0.0;
203 adNdXi( 2, 9 ) = -2.0*xi*zeta;
204
205 adNdXi( 0, 10 ) = 0.0;
206 adNdXi( 1, 10 ) = 1.0-zeta*zeta;
207 adNdXi( 2, 10 ) = -2.0*eta*zeta;
208
209 adNdXi( 0, 11 ) = zeta*zeta-1.0;
210 adNdXi( 1, 11 ) = zeta*zeta-1.0;
211 adNdXi( 2, 11 ) = 2.0*zeta*(xi+eta-1.0);
212
213 adNdXi( 0, 12 ) = 2.0*eta*(1.0+zeta);
214 adNdXi( 1, 12 ) = 2.0*xi*(1.0+zeta);
215 adNdXi( 2, 12 ) = 2.0*xi*eta;
216
217 adNdXi( 0, 13 ) = -2.0*eta*(1.0+zeta);
218 adNdXi( 1, 13 ) = 2.0*(1.0-xi-2.0*eta)*(1.0+zeta);
219 adNdXi( 2, 13 ) = 2.0*eta*(1.0-xi-eta);
220
221 adNdXi( 0, 14 ) = 2.0*(1.0-2.0*xi-eta)*(1.0+zeta);
222 adNdXi( 1, 14 ) = -2.0*xi*(1.0+zeta);
223 adNdXi( 2, 14 ) = 2.0*xi*(1.0-xi-eta);
224 }
225
226//------------------------------------------------------------------------------
227
228 template<>
229 void
230 InterpolationFunctionTemplate<
231 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >::d2NdXi2(
232 const Vector< real > & aXi,
233 Matrix< real > & ad2NdXi2 ) const
234 {
235 const real xi = aXi( 0 );
236 const real eta = aXi( 1 );
237 const real zeta = aXi( 2 );
238
239 ad2NdXi2.set_size( 6, 15 );
240
241 ad2NdXi2( 0, 0 ) = 2.0-2.0*zeta;
242 ad2NdXi2( 1, 0 ) = 0.0;
243 ad2NdXi2( 2, 0 ) = xi;
244 ad2NdXi2( 3, 0 ) = 0.0;
245 ad2NdXi2( 4, 0 ) = zeta-2.0*xi+0.5;
246 ad2NdXi2( 5, 0 ) = 0.0;
247
248 ad2NdXi2( 0, 1 ) = 0.0;
249 ad2NdXi2( 1, 1 ) = 2.0-2.0*zeta;
250 ad2NdXi2( 2, 1 ) = eta;
251 ad2NdXi2( 3, 1 ) = zeta-2.0*eta+0.5;
252 ad2NdXi2( 4, 1 ) = 0.0;
253 ad2NdXi2( 5, 1 ) = 0.0;
254
255 ad2NdXi2( 0, 2 ) = 2.0-2.0*zeta;
256 ad2NdXi2( 1, 2 ) = 2.0-2.0*zeta;
257 ad2NdXi2( 2, 2 ) = 1.0-xi-eta;
258 ad2NdXi2( 3, 2 ) = 1.5-2.0*(xi+eta)-zeta;
259 ad2NdXi2( 4, 2 ) = 1.5-2.0*(xi+eta)-zeta;
260 ad2NdXi2( 5, 2 ) = 2.0-2.0*zeta;
261
262 ad2NdXi2( 0, 3 ) = 2.0*zeta+2.0;
263 ad2NdXi2( 1, 3 ) = 0.0;
264 ad2NdXi2( 2, 3 ) = xi;
265 ad2NdXi2( 3, 3 ) = 0.0;
266 ad2NdXi2( 4, 3 ) = 2.0*xi+zeta-0.5;
267 ad2NdXi2( 5, 3 ) = 0.0;
268
269 ad2NdXi2( 0, 4 ) = 0.0;
270 ad2NdXi2( 1, 4 ) = 2.0*zeta+2.0;
271 ad2NdXi2( 2, 4 ) = eta;
272 ad2NdXi2( 3, 4 ) = 2.0*eta+zeta-0.5;
273 ad2NdXi2( 4, 4 ) = 0.0;
274 ad2NdXi2( 5, 4 ) = 0.0;
275
276 ad2NdXi2( 0, 5 ) = 2.0*zeta+2.0;
277 ad2NdXi2( 1, 5 ) = 2.0*zeta+2.0;
278 ad2NdXi2( 2, 5 ) = 1.0-eta-xi;
279 ad2NdXi2( 3, 5 ) = 2.0*eta+2.0*xi-zeta-1.5;
280 ad2NdXi2( 4, 5 ) = 2.0*eta+2.0*xi-zeta-1.5;
281 ad2NdXi2( 5, 5 ) = 2.0*zeta+2.0;
282
283 ad2NdXi2( 0, 6 ) = 0.0;
284 ad2NdXi2( 1, 6 ) = 0.0;
285 ad2NdXi2( 2, 6 ) = 0.0;
286 ad2NdXi2( 3, 6 ) = -2.0*xi;
287 ad2NdXi2( 4, 6 ) = -2.0*eta;
288 ad2NdXi2( 5, 6 ) = 2.0-2.0*zeta;
289
290 ad2NdXi2( 0, 7 ) = 0.0;
291 ad2NdXi2( 1, 7 ) = zeta*4.0-4.0;
292 ad2NdXi2( 2, 7 ) = 0.0;
293 ad2NdXi2( 3, 7 ) = eta*4.0+2.0*xi-2.0;
294 ad2NdXi2( 4, 7 ) = 2.0*eta;
295 ad2NdXi2( 5, 7 ) = 2.0*zeta-2.0;
296
297 ad2NdXi2( 0, 8 ) = zeta*4.0-4.0;
298 ad2NdXi2( 1, 8 ) = 0.0;
299 ad2NdXi2( 2, 8 ) = 0.0;
300 ad2NdXi2( 3, 8 ) = 2.0*xi;
301 ad2NdXi2( 4, 8 ) = 4.0*xi+2.0*eta-2.0;
302 ad2NdXi2( 5, 8 ) = 2.0*zeta-2.0;
303
304 ad2NdXi2( 0, 9 ) = 0.0;
305 ad2NdXi2( 1, 9 ) = 0.0;
306 ad2NdXi2( 2, 9 ) = -2.0*xi;
307 ad2NdXi2( 3, 9 ) = 0.0;
308 ad2NdXi2( 4, 9 ) = -2.0*zeta;
309 ad2NdXi2( 5, 9 ) = 0.0;
310
311 ad2NdXi2( 0, 10 ) = 0.0;
312 ad2NdXi2( 1, 10 ) = 0.0;
313 ad2NdXi2( 2, 10 ) = -2.0*eta;
314 ad2NdXi2( 3, 10 ) = -2.0*zeta;
315 ad2NdXi2( 4, 10 ) = 0.0;
316 ad2NdXi2( 5, 10 ) = 0.0;
317
318 ad2NdXi2( 0, 11 ) = 0.0;
319 ad2NdXi2( 1, 11 ) = 0.0;
320 ad2NdXi2( 2, 11 ) = 2.0*xi+2.0*eta-2.0;
321 ad2NdXi2( 3, 11 ) = 2.0*zeta;
322 ad2NdXi2( 4, 11 ) = 2.0*zeta;
323 ad2NdXi2( 5, 11 ) = 0.0;
324
325 ad2NdXi2( 0, 12 ) = 0.0;
326 ad2NdXi2( 1, 12 ) = 0.0;
327 ad2NdXi2( 2, 12 ) = 0.0;
328 ad2NdXi2( 3, 12 ) = 2.0*xi;
329 ad2NdXi2( 4, 12 ) = 2.0*eta;
330 ad2NdXi2( 5, 12 ) = 2.0*zeta+2.0;
331
332 ad2NdXi2( 0, 13 ) = 0.0;
333 ad2NdXi2( 1, 13 ) = -4.0*zeta-4.0;
334 ad2NdXi2( 2, 13 ) = 0.0;
335 ad2NdXi2( 3, 13 ) = 2.0-2.0*xi-4.0*eta;
336 ad2NdXi2( 4, 13 ) = -2.0*eta;
337 ad2NdXi2( 5, 13 ) = -2.0*zeta-2.0;
338
339 ad2NdXi2( 0, 14 ) = -4.0*zeta-4.0;
340 ad2NdXi2( 1, 14 ) = 0.0;
341 ad2NdXi2( 2, 14 ) = 0.0;
342 ad2NdXi2( 3, 14 ) = -2.0*xi;
343 ad2NdXi2( 4, 14 ) = 2.0-4.0*xi-2.0*eta;
344 ad2NdXi2( 5, 14 ) = -2.0*zeta-2.0;
345
346 }
347
348//------------------------------------------------------------------------------
349 }
350}
351
352#endif //BELFEM_CL_IF_PENTA15_HPP
cl_IF_InterpolationFunctionTemplate.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::PENTA15
@ PENTA15
Definition Mesh_Enums.hpp:46
belfem::InterpolationOrder
InterpolationOrder
Definition Mesh_Enums.hpp:85
belfem::InterpolationOrder::SERENDIPITY
@ SERENDIPITY
Definition Mesh_Enums.hpp:89
belfem::real
double real
Definition typedefs.hpp:36
belfem::GeometryType::PENTA
@ PENTA
Definition Mesh_Enums.hpp:77