Dune Core Modules (2.6.0)

brezzidouglasmarini1cube3dlocalbasis.hh
1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_CUBE3D_LOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_CUBE3D_LOCALBASIS_HH
5 
6 #include <array>
7 #include <bitset>
8 #include <numeric>
9 #include <vector>
10 
11 #include <dune/common/fmatrix.hh>
12 
13 #include "../../common/localbasis.hh"
14 
15 namespace Dune
16 {
27  template<class D, class R>
28  class BDM1Cube3DLocalBasis
29  {
30 
31  public:
32  typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,
33  R,3,Dune::FieldVector<R,3>,
34  Dune::FieldMatrix<R,3,3> > Traits;
35 
37  BDM1Cube3DLocalBasis()
38  {
39  for (size_t i=0; i<6; i++)
40  sign_[i] = 1.0;
41  }
42 
48  BDM1Cube3DLocalBasis(std::bitset<6> s)
49  {
50  for (size_t i=0; i<6; i++)
51  sign_[i] = s[i] ? -1.0 : 1.0;
52  }
53 
55  unsigned int size() const
56  {
57  return 18;
58  }
59 
66  inline void evaluateFunction(const typename Traits::DomainType& in,
67  std::vector<typename Traits::RangeType>& out) const
68  {
69  out.resize(size());
70 
71  out[0][0] = sign_[0] * (in[0] - 1.0);
72  out[0][1] = 0.0;
73  out[0][2] = 0.0;
74  out[1][0] = sign_[1] * in[0];
75  out[1][1] = 0.0;
76  out[1][2] = 0.0;
77  out[2][0] = 0.0;
78  out[2][1] = sign_[2] * (in[1] - 1.0);
79  out[2][2] = 0.0;
80  out[3][0] = 0.0;
81  out[3][1] = sign_[3] * in[1];
82  out[3][2] = 0.0;
83  out[4][0] = 0.0;
84  out[4][1] = 0.0;
85  out[4][2] = sign_[4] * (in[2] - 1.0);
86  out[5][0] = 0.0;
87  out[5][1] = 0.0;
88  out[5][2] = sign_[5] * in[2];
89  out[6][0] = 6.0 * in[0] * in[1] - 3 * in[0]-6 * in[1] + 3.0;
90  out[6][1] = -3.0 * in[1] * in[1] + 3 * in[1];
91  out[6][2] = 0.0;
92  out[7][0] = -6.0 * in[0] * in[1] + 3 * in[0];
93  out[7][1] = 3.0 * in[1] * in[1] - 3 * in[1];
94  out[7][2] = 0.0;
95  out[8][0] = 3.0 * in[0] * in[0] - 3 * in[0];
96  out[8][1] = -6.0 * in[0] * in[1] + 3 * in[1]+6 * in[0]-3.0;
97  out[8][2] = 0.0;
98  out[9][0] = -3.0 * in[0] * in[0] + 3 * in[0];
99  out[9][1] = 6.0 * in[0] * in[1] - 3 * in[1];
100  out[9][2] = 0.0;
101  out[10][0] = -3.0 * in[0] * in[0] + 3 * in[0];
102  out[10][1] = 0.0;
103  out[10][2] = 6.0 * in[0] * in[2]-6 * in[0]-3 * in[2] + 3.0;
104  out[11][0] = 3.0 * in[0] * in[0]-3 * in[0];
105  out[11][1] = 0.0;
106  out[11][2] = -6.0 * in[0] * in[2] + 3 * in[2];
107  out[12][0] = -6.0 * in[0] * in[2]+6 * in[2] + 3 * in[0]-3.0;
108  out[12][1] = 0.0;
109  out[12][2] = 3.0 * in[2] * in[2]-3 * in[2];
110  out[13][0] = -3 * in[0]+6 * in[0] * in[2];
111  out[13][1] = 0.0;
112  out[13][2] = -3.0 * in[2] * in[2] + 3 * in[2];
113  out[14][0] = 0.0;
114  out[14][1] = 6.0 * in[1] * in[2]-3 * in[1]-6 * in[2] + 3.0;
115  out[14][2] = -3 * in[2] * in[2] + 3 * in[2];
116  out[15][0] = 0.0;
117  out[15][1] = -6.0 * in[1] * in[2] + 3 * in[1];
118  out[15][2] = 3.0 * in[2] * in[2]-3 * in[2];
119  out[16][0] = 0.0;
120  out[16][1] = 3.0 * in[1] * in[1]-3 * in[1];
121  out[16][2] = -6.0 * in[1] * in[2] + 3 * in[2]+6 * in[1]-3.0;
122  out[17][0] = 0.0;
123  out[17][1] = -3.0 * in[1] * in[1] + 3 * in[1];
124  out[17][2] = 6.0 * in[1] * in[2] - 3.0 * in[2];
125  }
126 
133  inline void evaluateJacobian(const typename Traits::DomainType& in,
134  std::vector<typename Traits::JacobianType>& out) const
135  {
136  out.resize(size());
137 
138  out[0][0][0] = sign_[0]; out[0][0][1] = 0; out[0][0][2] = 0;
139  out[0][1][0] = 0; out[0][1][1] = 0; out[0][1][2] = 0;
140  out[0][2][0] = 0; out[0][2][1] = 0; out[0][2][2] = 0;
141 
142  out[1][0][0] = sign_[1]; out[1][0][1] = 0; out[1][0][2] = 0;
143  out[1][1][0] = 0; out[1][1][1] = 0; out[1][1][2] = 0;
144  out[1][2][0] = 0; out[1][2][1] = 0; out[1][2][2] = 0;
145 
146  out[2][0][0] = 0; out[2][0][1] = 0; out[2][0][2] = 0;
147  out[2][1][0] = 0; out[2][1][1] = sign_[2]; out[2][1][2] = 0;
148  out[2][2][0] = 0; out[2][2][1] = 0; out[2][2][2] = 0;
149 
150  out[3][0][0] = 0; out[3][0][1] = 0; out[3][0][2] = 0;
151  out[3][1][0] = 0; out[3][1][1] = sign_[3]; out[3][1][2] = 0;
152  out[3][2][0] = 0; out[3][2][1] = 0; out[3][2][2] = 0;
153 
154  out[4][0][0] = 0; out[4][0][1] = 0; out[4][0][2] = 0;
155  out[4][1][0] = 0; out[4][1][1] = 0; out[4][1][2] = 0;
156  out[4][2][0] = 0; out[4][2][1] = 0; out[4][2][2] = sign_[4];
157 
158  out[5][0][0] = 0; out[5][0][1] = 0; out[5][0][2] = 0;
159  out[5][1][0] = 0; out[5][1][1] = 0; out[5][1][2] = 0;
160  out[5][2][0] = 0; out[5][2][1] = 0; out[5][2][2] = sign_[5];
161 
162 
163 
164  out[6][0][0] = 6*in[1]-3; out[6][0][1] = 6*in[0]-6; out[6][0][2] = 0.0;
165  out[6][1][0] = 0.0; out[6][1][1] =-6*in[1]+3; out[6][1][2] = 0.0;
166  out[6][2][0] = 0.0; out[6][2][1] = 0.0; out[6][2][2] = 0.0;
167 
168  out[7][0][0] = -6*in[1]+3; out[7][0][1] =-6*in[0]; out[7][0][2] = 0.0;
169  out[7][1][0] = 0.0; out[7][1][1] = 6*in[1]-3; out[7][1][2] = 0.0;
170  out[7][2][0] = 0.0; out[7][2][1] = 0.0; out[7][2][2] = 0.0;
171 
172 
173  out[8][0][0] = 6*in[0]-3; out[8][0][1] = 0.0; out[8][0][2] = 0.0;
174  out[8][1][0] =-6*in[1]+6; out[8][1][1] =-6*in[0]+3; out[8][1][2] = 0.0;
175  out[8][2][0] = 0.0; out[8][2][1] = 0.0; out[8][2][2] = 0.0;
176 
177  out[9][0][0] = -6*in[0]+3; out[9][0][1] = 0.0; out[9][0][2] = 0.0;
178  out[9][1][0] = 6*in[1]; out[9][1][1] = 6*in[0]-3; out[9][1][2] = 0.0;
179  out[9][2][0] = 0.0; out[9][2][1] = 0.0; out[9][2][2] = 0.0;
180 
181  out[10][0][0] = -6*in[0]+3; out[10][0][1] = 0.0; out[10][0][2] = 0.0;
182  out[10][1][0] = 0.0; out[10][1][1] = 0.0; out[10][1][2] = 0.0;
183  out[10][2][0] =6*in[2]-6; out[10][2][1] = 0.0; out[10][2][2] =6*in[0]-3;
184 
185  out[11][0][0] =6*in[0]-3; out[11][0][1] = 0.0; out[11][0][2] = 0.0;
186  out[11][1][0] = 0.0; out[11][1][1] = 0.0; out[11][1][2] = 0.0;
187  out[11][2][0] = -6*in[2]; out[11][2][1] = 0.0; out[11][2][2] = -6*in[0]+3;
188 
189 
190  out[12][0][0] = -6*in[2]+3; out[12][0][1] =0.0; out[12][0][2] = -6*in[0]+6;
191  out[12][1][0] = 0.0; out[12][1][1] = 0.0; out[12][1][2] = 0.0;
192  out[12][2][0] = 0.0; out[12][2][1] = 0.0; out[12][2][2] =6*in[2]-3;
193 
194 
195  out[13][0][0] =6*in[2]-3; out[13][0][1] = 0.0; out[13][0][2] = 6*in[0];
196  out[13][1][0] = 0.0; out[13][1][1] = 0.0; out[13][1][2] = 0.0;
197  out[13][2][0] = 0.0; out[13][2][1] = 0.0; out[13][2][2] =-6*in[2]+3;
198 
199  out[14][0][0] = 0.0; out[14][0][1] = 0.0; out[14][0][2] = 0.0;
200  out[14][1][0] = 0.0; out[14][1][1] = 6*in[2]-3; out[14][1][2] = 6*in[1]-6;
201  out[14][2][0] = 0.0; out[14][2][1] = 0.0; out[14][2][2] =-6*in[2]+3;
202 
203  out[15][0][0] = 0.0; out[15][0][1] = 0.0; out[15][0][2] = 0.0;
204  out[15][1][0] = 0.0; out[15][1][1] =-6*in[2]+3; out[15][1][2] =-6*in[1];
205  out[15][2][0] = 0.0; out[15][2][1] = 0.0; out[15][2][2] = 6*in[2]-3;
206 
207  out[16][0][0] = 0.0; out[16][0][1] = 0.0; out[16][0][2] = 0.0;
208  out[16][1][0] = 0.0; out[16][1][1] = 6*in[1]-3; out[16][1][2] = 0.0;
209  out[16][2][0] = 0.0; out[16][2][1] =-6*in[2]+6; out[16][2][2] =-6*in[1]+3;
210 
211  out[17][0][0] = 0.0; out[17][0][1] = 0.0; out[17][0][2] = 0.0;
212  out[17][1][0] = 0.0; out[17][1][1] =-6*in[1]+3; out[17][1][2] = 0.0;
213  out[17][2][0] = 0.0; out[17][2][1] = 6*in[2]; out[17][2][2] = 6*in[1]-3;
214  }
215 
217  void partial (const std::array<unsigned int, 3>& order,
218  const typename Traits::DomainType& in, // position
219  std::vector<typename Traits::RangeType>& out) const // return value
220  {
221  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
222  if (totalOrder == 0) {
223  evaluateFunction(in, out);
224  } else if (totalOrder == 1) {
225  out.resize(size());
226  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
227 
228  switch (direction) {
229  case 0:
230  out[0][0] = sign_[0];
231  out[0][1] = 0;
232  out[0][2] = 0;
233 
234  out[1][0] = sign_[1];
235  out[1][1] = 0;
236  out[1][2] = 0;
237 
238  out[2][0] = 0;
239  out[2][1] = 0;
240  out[2][2] = 0;
241 
242  out[3][0] = 0;
243  out[3][1] = 0;
244  out[3][2] = 0;
245 
246  out[4][0] = 0;
247  out[4][1] = 0;
248  out[4][2] = 0;
249 
250  out[5][0] = 0;
251  out[5][1] = 0;
252  out[5][2] = 0;
253 
254  out[6][0] = 6*in[1]-3;
255  out[6][1] = 0.0;
256  out[6][2] = 0.0;
257 
258  out[7][0] = -6*in[1]+3;
259  out[7][1] = 0.0;
260  out[7][2] = 0.0;
261 
262  out[8][0] = 6*in[0]-3;
263  out[8][1] =-6*in[1]+6;
264  out[8][2] = 0.0;
265 
266  out[9][0] = -6*in[0]+3;
267  out[9][1] = 6*in[1];
268  out[9][2] = 0.0;
269 
270  out[10][0] = -6*in[0]+3;
271  out[10][1] = 0.0;
272  out[10][2] =6*in[2]-6;
273 
274  out[11][0] =6*in[0]-3;
275  out[11][1] = 0.0;
276  out[11][2] = -6*in[2];
277 
278  out[12][0] = -6*in[2]+3;
279  out[12][1] = 0.0;
280  out[12][2] = 0.0;
281 
282  out[13][0] =6*in[2]-3;
283  out[13][1] = 0.0;
284  out[13][2] = 0.0;
285 
286  out[14][0] = 0.0;
287  out[14][1] = 0.0;
288  out[14][2] = 0.0;
289 
290  out[15][0] = 0.0;
291  out[15][1] = 0.0;
292  out[15][2] = 0.0;
293 
294  out[16][0] = 0.0;
295  out[16][1] = 0.0;
296  out[16][2] = 0.0;
297 
298  out[17][0] = 0.0;
299  out[17][1] = 0.0;
300  out[17][2] = 0.0;
301  break;
302  case 1:
303  out[0][0] = 0;
304  out[0][1] = 0;
305  out[0][2] = 0;
306 
307  out[1][0] = 0;
308  out[1][1] = 0;
309  out[1][2] = 0;
310 
311  out[2][0] = 0;
312  out[2][1] = sign_[2];
313  out[2][2] = 0;
314 
315  out[3][0] = 0;
316  out[3][1] = sign_[3];
317  out[3][2] = 0;
318 
319  out[4][0] = 0;
320  out[4][1] = 0;
321  out[4][2] = 0;
322 
323  out[5][0] = 0;
324  out[5][1] = 0;
325  out[5][2] = 0;
326 
327  out[6][0] = 6*in[0]-6;
328  out[6][1] =-6*in[1]+3;
329  out[6][2] = 0.0;
330 
331  out[7][0] =-6*in[0];
332  out[7][1] = 6*in[1]-3;
333  out[7][2] = 0.0;
334 
335  out[8][0] = 0.0;
336  out[8][1] =-6*in[0]+3;
337  out[8][2] = 0.0;
338 
339  out[9][0] = 0.0;
340  out[9][1] = 6*in[0]-3;
341  out[9][2] = 0.0;
342 
343  out[10][0] = 0.0;
344  out[10][1] = 0.0;
345  out[10][2] = 0.0;
346 
347  out[11][0] = 0.0;
348  out[11][1] = 0.0;
349  out[11][2] = 0.0;
350 
351  out[12][0] =0.0;
352  out[12][1] = 0.0;
353  out[12][2] = 0.0;
354 
355  out[13][0] = 0.0;
356  out[13][1] = 0.0;
357  out[13][2] = 0.0;
358 
359  out[14][0] = 0.0;
360  out[14][1] = 6*in[2]-3;
361  out[14][2] = 0.0;
362 
363  out[15][0] = 0.0;
364  out[15][1] =-6*in[2]+3;
365  out[15][2] = 0.0;
366 
367  out[16][0] = 0.0;
368  out[16][1] = 6*in[1]-3;
369  out[16][2] =-6*in[2]+6;
370 
371  out[17][0] = 0.0;
372  out[17][1] =-6*in[1]+3;
373  out[17][2] = 6*in[2];
374  break;
375  case 2:
376  out[0][0] = 0;
377  out[0][1] = 0;
378  out[0][2] = 0;
379 
380  out[1][0] = 0;
381  out[1][1] = 0;
382  out[1][2] = 0;
383 
384  out[2][0] = 0;
385  out[2][1] = 0;
386  out[2][2] = 0;
387 
388  out[3][0] = 0;
389  out[3][1] = 0;
390  out[3][2] = 0;
391 
392  out[4][0] = 0;
393  out[4][1] = 0;
394  out[4][2] = sign_[4];
395 
396  out[5][0] = 0;
397  out[5][1] = 0;
398  out[5][2] = sign_[5];
399 
400  out[6][0] = 0.0;
401  out[6][1] = 0.0;
402  out[6][2] = 0.0;
403 
404  out[7][0] = 0.0;
405  out[7][1] = 0.0;
406  out[7][2] = 0.0;
407 
408  out[8][0] = 0.0;
409  out[8][1] = 0.0;
410  out[8][2] = 0.0;
411 
412  out[9][0] = 0.0;
413  out[9][1] = 0.0;
414  out[9][2] = 0.0;
415 
416  out[10][0] = 0.0;
417  out[10][1] = 0.0;
418  out[10][2] =6*in[0]-3;
419 
420  out[11][0] = 0.0;
421  out[11][1] = 0.0;
422  out[11][2] = -6*in[0]+3;
423 
424  out[12][0] = -6*in[0]+6;
425  out[12][1] = 0.0;
426  out[12][2] =6*in[2]-3;
427 
428  out[13][0] = 6*in[0];
429  out[13][1] = 0.0;
430  out[13][2] =-6*in[2]+3;
431 
432  out[14][0] = 0.0;
433  out[14][1] = 6*in[1]-6;
434  out[14][2] =-6*in[2]+3;
435 
436  out[15][0] = 0.0;
437  out[15][1] =-6*in[1];
438  out[15][2] = 6*in[2]-3;
439 
440  out[16][0] = 0.0;
441  out[16][1] = 0.0;
442  out[16][2] =-6*in[1]+3;
443 
444  out[17][0] = 0.0;
445  out[17][1] = 0.0;
446  out[17][2] = 6*in[1]-3;
447  break;
448  default:
449  DUNE_THROW(RangeError, "Component out of range.");
450  }
451  } else {
452  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
453  }
454  }
455 
457  unsigned int order() const
458  {
459  return 2;
460  }
461 
462  private:
463  std::array<R,6> sign_;
464  };
465 } // end namespace Dune
466 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_CUBE3D_LOCALBASIS_HH
Dune::BDM1Cube3DLocalBasis
First order Brezzi-Douglas-Marini shape functions on the reference hexahedron.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:29
Dune::BDM1Cube3DLocalBasis::evaluateJacobian
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:133
Dune::BDM1Cube3DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:66
Dune::BDM1Cube3DLocalBasis::partial
void partial(const std::array< unsigned int, 3 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:217
Dune::BDM1Cube3DLocalBasis::BDM1Cube3DLocalBasis
BDM1Cube3DLocalBasis(std::bitset< 6 > s)
Make set number s, where 0 <= s < 64.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:48
Dune::BDM1Cube3DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:457
Dune::BDM1Cube3DLocalBasis::BDM1Cube3DLocalBasis
BDM1Cube3DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:37
Dune::BDM1Cube3DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:55
Dune::FieldMatrix
A dense n x m matrix.
Definition: fmatrix.hh:68
Dune::FieldVector
vector space out of a tensor product of fields.
Definition: fvector.hh:93
Dune::NotImplemented
Default exception for dummy implementations.
Definition: exceptions.hh:261
Dune::RangeError
Default exception class for range errors.
Definition: exceptions.hh:252
fmatrix.hh
Implements a matrix constructed from a given type representing a field and compile-time given number ...
DUNE_THROW
#define DUNE_THROW(E, m)
Definition: exceptions.hh:216
Dune::Hybrid::accumulate
T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:331
Dune
Dune namespace.
Definition: alignedallocator.hh:10
Dune::LocalBasisTraits
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:32
Dune::LocalBasisTraits::DomainType
D DomainType
domain type
Definition: localbasis.hh:43
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