BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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cl_IF_PENTA18.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_PENTA18_HPP
13#define BELFEM_CL_IF_PENTA18_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, 18 >
32
33//------------------------------------------------------------------------------
34
35 template<>
36 ElementType
37 InterpolationFunctionTemplate<
38 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >
39 ::element_type() const
40 {
41 return ElementType::PENTA18;
42 }
43
44//------------------------------------------------------------------------------
45
46 template<>
47 void
48 InterpolationFunctionTemplate<
49 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >
50 ::param_coords( Matrix< real > & aXiHat ) const
51 {
52 aXiHat.set_size( 3, 18 );
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 aXiHat( 0, 15 ) = 0.5;
115 aXiHat( 1, 15 ) = 0.5;
116 aXiHat( 2, 15 ) = 0.0;
117
118 aXiHat( 0, 16 ) = 0.0;
119 aXiHat( 1, 16 ) = 0.5;
120 aXiHat( 2, 16 ) = 0.0;
121
122 aXiHat( 0, 17 ) = 0.5;
123 aXiHat( 1, 17 ) = 0.0;
124 aXiHat( 2, 17 ) = 0.0;
125
126 }
127
128//------------------------------------------------------------------------------
129
130 template<>
131 void
132 InterpolationFunctionTemplate<
133 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >::N(
134 const Vector< real > & aXi,
135 Matrix< real > & aN ) const
136 {
137 const real xi = aXi( 0 );
138 const real eta = aXi( 1 );
139 const real zeta = aXi( 2 );
140
141 const real zeta2 = zeta*zeta;
142
143 aN.set_size( 1, 18 );
144
145 aN( 0, 0 ) = 0.5*(xi*zeta*(xi*2.0-1.0)*(zeta-1.0));
146 aN( 0, 1 ) = 0.5*(eta*zeta*(eta*2.0-1.0)*(zeta-1.0));
147 aN( 0, 2 ) = 0.5*((1.0-xi-eta)*(2*(xi+eta)-1.0)*(1.0-zeta)*zeta);
148 aN( 0, 3 ) = 0.5*(xi*zeta*(xi*2.0-1.0)*(zeta+1.0));
149 aN( 0, 4 ) = 0.5*(eta*zeta*(eta*2.0-1.0)*(zeta+1.0));
150 aN( 0, 5 ) = 0.5*((1.0-xi-eta)*(1.0-2.0*(xi+eta))*zeta*(1.0+zeta));
151 aN( 0, 6 ) = xi*eta*zeta*(zeta-1.0)*2.0;
152 aN( 0, 7 ) = 2.0*eta*zeta*(1.0-zeta)*(eta+xi-1.0);
153 aN( 0, 8 ) = 2.0*xi*zeta*(1.0-zeta)*(eta+xi-1.0);
154 aN( 0, 9 ) = xi*(1.0-2.0*xi)*(zeta2-1.0);
155 aN( 0, 10 ) = eta*(1.0-2.0*eta)*(zeta2-1.0);
156 aN( 0, 11 ) = (1-xi-eta)*(2.0*(xi+eta)-1)*(zeta2-1.0);
157 aN( 0, 12 ) = xi*eta*zeta*(1.0+zeta)*2.0;
158 aN( 0, 13 ) = 2.0*eta*zeta*(1.0+zeta)*(1.0-xi-eta);
159 aN( 0, 14 ) = 2.0*xi*zeta*(1.0+zeta)*(1.0-xi-eta);
160 aN( 0, 15 ) = 4.0*eta*xi*(1.0-zeta2);
161 aN( 0, 16 ) = 4.0*eta*(1.0-zeta2)*(1.0-xi-eta);
162 aN( 0, 17 ) = 4.0*xi*(1.0-zeta2)*(1.0-xi-eta);
163
164 }
165
166//------------------------------------------------------------------------------
167
168 template<>
169 void
170 InterpolationFunctionTemplate<
171 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >::dNdXi(
172 const Vector< real > & aXi,
173 Matrix< real > & adNdXi ) const
174 {
175 const real xi = aXi( 0 );
176 const real eta = aXi( 1 );
177 const real zeta = aXi( 2 );
178
179 const real zeta2 = zeta * zeta ;
180
181 adNdXi.set_size( 3, 18 );
182
183 adNdXi( 0, 0 ) = zeta*(0.5-0.5*zeta+xi*2.0*(zeta-1.0));
184 adNdXi( 1, 0 ) = 0.0;
185 adNdXi( 2, 0 ) = xi*(0.5-zeta+xi*(2.0*zeta-1.0));
186
187 adNdXi( 0, 1 ) = 0.0;
188 adNdXi( 1, 1 ) = zeta*(0.5-0.5*zeta+2.0*eta*(zeta-1.0));
189 adNdXi( 2, 1 ) = eta*(0.5-zeta+eta*(2.0*zeta-1.0));
190
191 adNdXi( 0, 2 ) = zeta*(1.5-1.5*zeta+2.0*(xi+eta)*(zeta-1.0));
192 adNdXi( 1, 2 ) = zeta*(1.5-1.5*zeta+2.0*(xi+eta)*(zeta-1.0));
193 adNdXi( 2, 2 ) = 0.5*(1.0-xi-eta)*(1.0-2.0*(xi+eta))*(2.0*zeta-1.0);
194
195 adNdXi( 0, 3 ) = zeta*(xi*(2.0+2.0*zeta)-0.5-0.5*zeta);
196 adNdXi( 1, 3 ) = 0.0;
197 adNdXi( 2, 3 ) = xi*(xi*(1.+2.0*zeta)-0.5-zeta);
198
199 adNdXi( 0, 4 ) = 0.0;
200 adNdXi( 1, 4 ) = zeta*(eta*(2.0+2.0*zeta)-0.5-0.5*zeta);
201 adNdXi( 2, 4 ) = eta*(eta*(1.+2.0*zeta)-0.5-zeta);
202
203 adNdXi( 0, 5 ) = zeta*(2.0*(xi+eta)*(1.0+zeta)-1.5-1.5*zeta);
204 adNdXi( 1, 5 ) = 0.5*(zeta*(zeta + 1.0)*(4.0*(xi+eta)-3.0));
205 adNdXi( 2, 5 ) = 2.0*(1.0-xi-eta)*(0.5-xi-eta)*(0.5+zeta);
206
207 adNdXi( 0, 6 ) = 2.0*eta*zeta*(zeta-1.0);
208 adNdXi( 1, 6 ) = 2.0*xi*zeta*(zeta-1.0);
209 adNdXi( 2, 6 ) = 2.0*eta*xi*(2.0*zeta-1.0);
210
211 adNdXi( 0, 7 ) = 2.0*eta*zeta*(1.0-zeta);
212 adNdXi( 1, 7 ) = 4.0*zeta*(eta+0.5*xi-0.5)*(1.0-zeta);
213 adNdXi( 2, 7 ) = 4.0*eta*(1.0-xi-eta)*(zeta-0.5);
214
215 adNdXi( 0, 8 ) = 2.0*(1.0-2.0*xi-eta)*(zeta-1.0)*zeta;
216 adNdXi( 1, 8 ) = 2.0*xi*zeta*(1.0-zeta);
217 adNdXi( 2, 8 ) = 2.0*xi*(1.0-xi-eta)*(2.0*zeta-1.0);
218
219 adNdXi( 0, 9 ) = xi*(4.-4.0*zeta2)+zeta2-1.0;
220 adNdXi( 1, 9 ) = 0.0;
221 adNdXi( 2, 9 ) = 2.0*xi*zeta*(1.0-2.0*xi);
222
223 adNdXi( 0, 10 ) = 0.0;
224 adNdXi( 1, 10 ) = zeta2-1.0+eta*(4.-4.0*zeta2);
225 adNdXi( 2, 10 ) = 2.0*eta*zeta*(1.0-2.0*eta);
226
227 adNdXi( 0, 11 ) = (1.0-zeta2)*(4.0*(xi+eta)-3.0);
228 adNdXi( 1, 11 ) = (1.0-zeta2)*(4.0*(xi+eta)-3.0);
229 adNdXi( 2, 11 ) = 4.0*(1.0-xi-eta)*(xi+eta-0.5)*zeta;
230
231 adNdXi( 0, 12 ) = 2.0*eta*zeta*(1.0+zeta);
232 adNdXi( 1, 12 ) = 2.0*xi*zeta*(1.0+zeta);
233 adNdXi( 2, 12 ) = 2.0*xi*eta*(1.0+2.0*zeta);
234
235 adNdXi( 0, 13 ) = -2.0*eta*zeta*(1.0+zeta);
236 adNdXi( 1, 13 ) = 2.0*zeta*(1.0-2.0*eta-xi)*(1.0+zeta);
237 adNdXi( 2, 13 ) = 2.0*eta*(1.0+2.0*zeta-(xi+eta)*(1.0+2.0*zeta));
238
239 adNdXi( 0, 14 ) = 2.0*(1.0-eta-2.0*xi)*zeta*(1.0+zeta);
240 adNdXi( 1, 14 ) = -2.0*xi*zeta*(1.0+zeta);
241 adNdXi( 2, 14 ) = 2.0*xi*(1.0-(xi+eta)*(1.0+2.0*zeta)+2.0*zeta);
242
243 adNdXi( 0, 15 ) = 4.0*eta*(1.0-zeta2);
244 adNdXi( 1, 15 ) = 4.0*xi*(1.0-zeta2);
245 adNdXi( 2, 15 ) = -8.0*xi*eta*zeta;
246
247 adNdXi( 0, 16 ) = 4.0*eta*(zeta2-1.0);
248 adNdXi( 1, 16 ) = 4.0*(1.0-zeta2+(xi+2.0*eta)*(zeta2-1.0));
249 adNdXi( 2, 16 ) = 8.0*eta*zeta*(eta+xi-1.0);
250
251 adNdXi( 0, 17 ) = 4.0*(1.0-2.0*xi-eta)*(1.0-zeta2);
252 adNdXi( 1, 17 ) = 4.0*xi*(zeta2-1.0);
253 adNdXi( 2, 17 ) = 8.0*xi*zeta*(xi+eta-1.0);
254 }
255
256//------------------------------------------------------------------------------
257
258 template<>
259 void
260 InterpolationFunctionTemplate<
261 GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >::d2NdXi2(
262 const Vector< real > & aXi,
263 Matrix< real > & ad2NdXi2 ) const
264 {
265 const real xi = aXi( 0 );
266 const real eta = aXi( 1 );
267 const real zeta = aXi( 2 );
268
269 const real zeta2 = zeta*zeta ;
270
271 ad2NdXi2.set_size( 6, 18 );
272
273 ad2NdXi2( 0, 0 ) = 2.0*(zeta-1.0)*zeta;
274 ad2NdXi2( 1, 0 ) = 0.0;
275 ad2NdXi2( 2, 0 ) = xi*(2.0*xi-1.0);
276 ad2NdXi2( 3, 0 ) = 0.0;
277 ad2NdXi2( 4, 0 ) = 0.5-zeta+2.0*xi*(2.0*zeta-1.0);
278 ad2NdXi2( 5, 0 ) = 0.0;
279
280 ad2NdXi2( 0, 1 ) = 0.0;
281 ad2NdXi2( 1, 1 ) = 2.0*(zeta-1.0)*zeta;
282 ad2NdXi2( 2, 1 ) = eta*(2.0*eta-1.0);
283 ad2NdXi2( 3, 1 ) = 0.5-zeta+2.0*eta*(2.0*zeta-1.0);
284 ad2NdXi2( 4, 1 ) = 0.0;
285 ad2NdXi2( 5, 1 ) = 0.0;
286
287 ad2NdXi2( 0, 2 ) = 2.0*zeta*(zeta-1.0);
288 ad2NdXi2( 1, 2 ) = 2.0*zeta*(zeta-1.0);
289 ad2NdXi2( 2, 2 ) = 2.0*(1.0-xi-eta)*(0.5-eta-xi);
290 ad2NdXi2( 3, 2 ) = 1.5-3.0*zeta+2.0*(xi+eta)*(2.0*zeta-1.0);
291 ad2NdXi2( 4, 2 ) = 1.5-3.0*zeta+2.0*(xi+eta)*(2.0*zeta-1.0);
292 ad2NdXi2( 5, 2 ) = 2.0*zeta*(zeta-1.0);
293
294 ad2NdXi2( 0, 3 ) = 2.0*zeta*(1.0+zeta);
295 ad2NdXi2( 1, 3 ) = 0.0;
296 ad2NdXi2( 2, 3 ) = xi*(2.0*xi-1.0);
297 ad2NdXi2( 3, 3 ) = 0.0;
298 ad2NdXi2( 4, 3 ) = 2.0*xi*(1.0+2.0*zeta)-zeta-0.5;
299 ad2NdXi2( 5, 3 ) = 0.0;
300
301 ad2NdXi2( 0, 4 ) = 0.0;
302 ad2NdXi2( 1, 4 ) = 2.0*zeta*(1.0+zeta);
303 ad2NdXi2( 2, 4 ) = eta*(2.0*eta-1.0);
304 ad2NdXi2( 3, 4 ) = 2.0*eta*(1.0+2.0*zeta)-0.5-zeta;
305 ad2NdXi2( 4, 4 ) = 0.0;
306 ad2NdXi2( 5, 4 ) = 0.0;
307
308 ad2NdXi2( 0, 5 ) = 2.0*zeta*(1.0+zeta);
309 ad2NdXi2( 1, 5 ) = 2.0*zeta*(1.0+zeta);
310 ad2NdXi2( 2, 5 ) = 2.0*(1.0-xi-eta)*(0.5-xi-eta);
311 ad2NdXi2( 3, 5 ) = 2.0*(xi+eta)*(1.0+2.0*zeta)-3.0*zeta-1.5;
312 ad2NdXi2( 4, 5 ) = 2.0*(xi+eta)*(1.0+2.0*zeta)-3.0*zeta-1.5;
313 ad2NdXi2( 5, 5 ) = 2.0*zeta*(1.0+zeta);
314
315 ad2NdXi2( 0, 6 ) = 0.0;
316 ad2NdXi2( 1, 6 ) = 0.0;
317 ad2NdXi2( 2, 6 ) = 4.0*xi*eta;
318 ad2NdXi2( 3, 6 ) = 2.0*xi*(2.0*zeta-1.0);
319 ad2NdXi2( 4, 6 ) = 2.0*eta*(2.0*zeta-1.0);
320 ad2NdXi2( 5, 6 ) = 2.0*zeta*(zeta-1.0);
321
322 ad2NdXi2( 0, 7 ) = 0.0;
323 ad2NdXi2( 1, 7 ) = 4.0*(1.0-zeta)*zeta;
324 ad2NdXi2( 2, 7 ) = 4.0*eta*(1.0-xi-eta);
325 ad2NdXi2( 3, 7 ) = 2.0*(xi+2.0*eta)*(1.0-2.0*zeta)+4.0*zeta-2.0;
326 ad2NdXi2( 4, 7 ) = eta*(2.0-4.0*zeta);
327 ad2NdXi2( 5, 7 ) = 2.0*(1.0-zeta)*zeta;
328
329 ad2NdXi2( 0, 8 ) = 4.0*(1.0-zeta)*zeta;
330 ad2NdXi2( 1, 8 ) = 0.0;
331 ad2NdXi2( 2, 8 ) = 4.0*xi*(1.0-xi-eta);
332 ad2NdXi2( 3, 8 ) = 2.0*xi*(1.0-2.0*zeta);
333 ad2NdXi2( 4, 8 ) = 4.0*zeta+2.0*(1.0-2.0*zeta)*(2.0*xi+eta)-2.0;
334 ad2NdXi2( 5, 8 ) = 2.0*(1.0-zeta)*zeta;
335
336 ad2NdXi2( 0, 9 ) = 4.0*(1.0-zeta2);
337 ad2NdXi2( 1, 9 ) = 0.0;
338 ad2NdXi2( 2, 9 ) = (2.0-4.0*xi)*xi;
339 ad2NdXi2( 3, 9 ) = 0.0;
340 ad2NdXi2( 4, 9 ) = (2.0-8.0*xi)*zeta;
341 ad2NdXi2( 5, 9 ) = 0.0;
342
343 ad2NdXi2( 0, 10 ) = 0.0;
344 ad2NdXi2( 1, 10 ) = 4.0*(1.0-zeta2);
345 ad2NdXi2( 2, 10 ) = (2.0-4.0*eta)*eta;
346 ad2NdXi2( 3, 10 ) = (2.0-8.0*eta)*zeta;
347 ad2NdXi2( 4, 10 ) = 0.0;
348 ad2NdXi2( 5, 10 ) = 0.0;
349
350 ad2NdXi2( 0, 11 ) = 4.0*(1.0-zeta2);
351 ad2NdXi2( 1, 11 ) = 4.0*(1.0-zeta2);
352 ad2NdXi2( 2, 11 ) = 4.0*(1.0-xi-eta)*(xi+eta-0.5);
353 ad2NdXi2( 3, 11 ) = (6.0-8.0*(xi+eta))*zeta;
354 ad2NdXi2( 4, 11 ) = (6.0-8.0*(xi+eta))*zeta;
355 ad2NdXi2( 5, 11 ) = 4.0*(1.0-zeta2);
356
357 ad2NdXi2( 0, 12 ) = 0.0;
358 ad2NdXi2( 1, 12 ) = 0.0;
359 ad2NdXi2( 2, 12 ) = 4.0*xi*eta;
360 ad2NdXi2( 3, 12 ) = xi*(2.0+4.0*zeta);
361 ad2NdXi2( 4, 12 ) = eta*(2.0+4.0*zeta);
362 ad2NdXi2( 5, 12 ) = 2.0*zeta*(1.0+zeta);
363
364 ad2NdXi2( 0, 13 ) = 0.0;
365 ad2NdXi2( 1, 13 ) = -4.0*zeta*(1.0+zeta);
366 ad2NdXi2( 2, 13 ) = 4.0*eta*(1.0-xi-eta);
367 ad2NdXi2( 3, 13 ) =2.0*(1.0+2.0*zeta)*(1.0-xi-2.0*eta);
368 ad2NdXi2( 4, 13 ) = -2.0*eta*(1.0+2.0*zeta);
369 ad2NdXi2( 5, 13 ) = -2.0*zeta*(1.0+zeta);
370
371 ad2NdXi2( 0, 14 ) = -4.0*zeta*(1.0+zeta);
372 ad2NdXi2( 1, 14 ) = 0.0;
373 ad2NdXi2( 2, 14 ) = 4.0*xi*(1.0-xi-eta);
374 ad2NdXi2( 3, 14 ) = -xi*(2.0+4.0*zeta);
375 ad2NdXi2( 4, 14 ) = 2.0*(1.0+2.0*zeta)*(1.0-2.0*xi-eta);
376 ad2NdXi2( 5, 14 ) = -2.0*zeta*(1.0+zeta);
377
378 ad2NdXi2( 0, 15 ) = 0.0;
379 ad2NdXi2( 1, 15 ) = 0.0;
380 ad2NdXi2( 2, 15 ) = -8.0*xi*eta;
381 ad2NdXi2( 3, 15 ) = -8.0*xi*zeta;
382 ad2NdXi2( 4, 15 ) = -8.0*eta*zeta;
383 ad2NdXi2( 5, 15 ) = 4.0-4.0*zeta2;
384
385 ad2NdXi2( 0, 16 ) = 0.0;
386 ad2NdXi2( 1, 16 ) = 8.0*zeta2-8.0;
387 ad2NdXi2( 2, 16 ) = 8.0*eta*(xi+eta-1.0);
388 ad2NdXi2( 3, 16 ) = (8.0*xi+16.0*eta-8.0)*zeta;
389 ad2NdXi2( 4, 16 ) = 8.0*eta*zeta;
390 ad2NdXi2( 5, 16 ) = 4.0*zeta2-4.0;
391
392 ad2NdXi2( 0, 17 ) = 8.0*zeta2-8.0;
393 ad2NdXi2( 1, 17 ) = 0.0;
394 ad2NdXi2( 2, 17 ) = 8.0*xi*(xi+eta-1.0);
395 ad2NdXi2( 3, 17 ) = 8.0*xi*zeta;
396 ad2NdXi2( 4, 17 ) = (16.0*xi+8.0*eta-8.0)*zeta;
397 ad2NdXi2( 5, 17 ) = 4.0*zeta2-4.0;
398 }
399
400//------------------------------------------------------------------------------
401 }
402}
403
404#endif //BELFEM_CL_IF_PENTA18_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::PENTA18
@ PENTA18
Definition Mesh_Enums.hpp:41
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::PENTA
@ PENTA
Definition Mesh_Enums.hpp:77