Dune Core Modules (2.7.1)

raviartthomas4cube2dlocalbasis.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_RAVIARTTHOMAS4_CUBE2D_LOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS4_CUBE2D_LOCALBASIS_HH
5 
6 #include <bitset>
7 #include <numeric>
8 #include <vector>
9 
10 #include <dune/common/fmatrix.hh>
11 
12 #include "../../common/localbasis.hh"
13 
14 namespace Dune
15 {
25  template<class D, class R>
26  class RT4Cube2DLocalBasis
27  {
28 
29  public:
30  typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
31  Dune::FieldMatrix<R,2,2> > Traits;
32 
38  RT4Cube2DLocalBasis (std::bitset<4> s = 0)
39  {
40  sign0 = (s[0]) ? -1.0 : 1.0;
41  sign1 = (s[1]) ? -1.0 : 1.0;
42  sign2 = (s[2]) ? -1.0 : 1.0;
43  sign3 = (s[3]) ? -1.0 : 1.0;
44  }
45 
47  unsigned int size () const
48  {
49  return 60;
50  }
51 
58  inline void evaluateFunction (const typename Traits::DomainType& in,
59  std::vector<typename Traits::RangeType>& out) const
60  {
61  out.resize(60);
62 
63  auto const& x = in[0], y = in[1];
64 
65  const auto l1_x = 2*x - 1;
66  const auto l2_x = x*(6*x - 6) + 1;
67  const auto l3_x = x*(x*(20*x - 30) + 12) - 1;
68  const auto l4_x = x*(x*(x*(70*x - 140) + 90) - 20) + 1;
69  const auto l5_x = x*(x*(x*(x*(252*x - 630) + 560) - 210) + 30) - 1;
70  const auto l1_y = 2*y - 1;
71  const auto l2_y = y*(6*y - 6) + 1;
72  const auto l3_y = y*(y*(20*y - 30) + 12) - 1;
73  const auto l4_y = y*(y*(y*(70*y - 140) + 90) - 20) + 1;
74  const auto l5_y = y*(y*(y*(y*(252*y - 630) + 560) - 210) + 30) - 1;
75 
76  out[0][0]=sign0*(0.5*(-l4_x)+0.5*l5_x);
77  out[0][1]=0.0;
78  out[1][0]=-(1.5)*l4_x*l1_y+1.5*l5_x*l1_y;
79  out[1][1]=0.0;
80  out[2][0]=sign0*(-(2.5)*l4_x*l2_y+2.5*l5_x*l2_y);
81  out[2][1]=0.0;
82  out[3][0]=-(3.5)*l4_x*l3_y+3.5*l5_x*l3_y;
83  out[3][1]=0.0;
84  out[4][0]=sign0*(-(4.5)*l4_x*l4_y+4.5*l5_x*l4_y);
85  out[4][1]=0.0;
86 
87  out[5][0]=sign1*(0.5*l4_x+0.5*l5_x);
88  out[5][1]=0.0;
89  out[6][0]=-(1.5)*l4_x*l1_y-1.5*l5_x*l1_y;
90  out[6][1]=0.0;
91  out[7][0]=sign1*(2.5*l4_x*l2_y+2.5*l5_x*l2_y);
92  out[7][1]=0.0;
93  out[8][0]=-(3.5)*l4_x*l3_y-3.5*l5_x*l3_y;
94  out[8][1]=0.0;
95  out[9][0]=sign1*(4.5*l4_x*l4_y+4.5*l5_x*l4_y);
96  out[9][1]=0.0;
97 
98  out[10][0]=0.0;
99  out[10][1]=sign2*(0.5*(-l4_y)+0.5*l5_y);
100  out[11][0]=0.0;
101  out[11][1]=1.5*l1_x*l4_y-1.5*l1_x*l5_y;
102  out[12][0]=0.0;
103  out[12][1]=sign2*(-(2.5)*l2_x*l4_y+2.5*l2_x*l5_y);
104  out[13][0]=0.0;
105  out[13][1]=3.5*l3_x*l4_y-3.5*l3_x*l5_y;
106  out[14][0]=0.0;
107  out[14][1]=sign2*(-(4.5)*l4_x*l4_y+4.5*l4_x*l5_y);
108 
109  out[15][0]=0.0;
110  out[15][1]=sign3*(0.5*l4_y+0.5*l5_y);
111  out[16][0]=0.0;
112  out[16][1]=1.5*l1_x*l4_y+1.5*l1_x*l5_y;
113  out[17][0]=0.0;
114  out[17][1]=sign3*(2.5*l2_x*l4_y+2.5*l2_x*l5_y);
115  out[18][0]=0.0;
116  out[18][1]=3.5*l3_x*l4_y+3.5*l3_x*l5_y;
117  out[19][0]=0.0;
118  out[19][1]=sign3*(4.5*l4_x*l4_y+4.5*l4_x*l5_y);
119 
120  out[20][0]=1.0-l4_x;
121  out[20][1]=0.0;
122  out[21][0]=3.0*l1_y-3.0*l4_x*l1_y;
123  out[21][1]=0.0;
124  out[22][0]=5.0*l2_y-5.0*l4_x*l2_y;
125  out[22][1]=0.0;
126  out[23][0]=7.0*l3_y-7.0*l4_x*l3_y;
127  out[23][1]=0.0;
128  out[24][0]=9.0*l4_y-9.0*l4_x*l4_y;
129  out[24][1]=0.0;
130  out[25][0]=3.0*l1_x-3.0*l5_x;
131  out[25][1]=0.0;
132  out[26][0]=9.0*l1_x*l1_y-9.0*l5_x*l1_y;
133  out[26][1]=0.0;
134  out[27][0]=15.0*l1_x*l2_y-15.0*l5_x*l2_y;
135  out[27][1]=0.0;
136  out[28][0]=21.0*l1_x*l3_y-21.0*l5_x*l3_y;
137  out[28][1]=0.0;
138  out[29][0]=27.0*l1_x*l4_y-27.0*l5_x*l4_y;
139  out[29][1]=0.0;
140  out[30][0]=5.0*l2_x-5.0*l4_x;
141  out[30][1]=0.0;
142  out[31][0]=15.0*l2_x*l1_y-15.0*l4_x*l1_y;
143  out[31][1]=0.0;
144  out[32][0]=25.0*l2_x*l2_y-25.0*l4_x*l2_y;
145  out[32][1]=0.0;
146  out[33][0]=35.0*l2_x*l3_y-35.0*l4_x*l3_y;
147  out[33][1]=0.0;
148  out[34][0]=45.0*l2_x*l4_y-45.0*l4_x*l4_y;
149  out[34][1]=0.0;
150  out[35][0]=7.0*l3_x-7.0*l5_x;
151  out[35][1]=0.0;
152  out[36][0]=21.0*l3_x*l1_y-21.0*l5_x*l1_y;
153  out[36][1]=0.0;
154  out[37][0]=35.0*l3_x*l2_y-35.0*l5_x*l2_y;
155  out[37][1]=0.0;
156  out[38][0]=49.0*l3_x*l3_y-49.0*l5_x*l3_y;
157  out[38][1]=0.0;
158  out[39][0]=63.0*l3_x*l4_y-63.0*l5_x*l4_y;
159  out[39][1]=0.0;
160  out[40][0]=0.0;
161  out[40][1]=1.0-l4_y;
162  out[41][0]=0.0;
163  out[41][1]=3.0*l1_y-3.0*l5_y;
164  out[42][0]=0.0;
165  out[42][1]=5.0*l2_y-5.0*l4_y;
166  out[43][0]=0.0;
167  out[43][1]=7.0*l3_y-7.0*l5_y;
168  out[44][0]=0.0;
169  out[44][1]=3.0*l1_x-3.0*l1_x*l4_y;
170  out[45][0]=0.0;
171  out[45][1]=9.0*l1_x*l1_y-9.0*l1_x*l5_y;
172  out[46][0]=0.0;
173  out[46][1]=15.0*l1_x*l2_y-15.0*l1_x*l4_y;
174  out[47][0]=0.0;
175  out[47][1]=21.0*l1_x*l3_y-21.0*l1_x*l5_y;
176  out[48][0]=0.0;
177  out[48][1]=5.0*l2_x-5.0*l2_x*l4_y;
178  out[49][0]=0.0;
179  out[49][1]=15.0*l2_x*l1_y-15.0*l2_x*l5_y;
180  out[50][0]=0.0;
181  out[50][1]=25.0*l2_x*l2_y-25.0*l2_x*l4_y;
182  out[51][0]=0.0;
183  out[51][1]=35.0*l2_x*l3_y-35.0*l2_x*l5_y;
184  out[52][0]=0.0;
185  out[52][1]=7.0*l3_x-7.0*l3_x*l4_y;
186  out[53][0]=0.0;
187  out[53][1]=21.0*l3_x*l1_y-21.0*l3_x*l5_y;
188  out[54][0]=0.0;
189  out[54][1]=35.0*l3_x*l2_y-35.0*l3_x*l4_y;
190  out[55][0]=0.0;
191  out[55][1]=49.0*l3_x*l3_y-49.0*l3_x*l5_y;
192  out[56][0]=0.0;
193  out[56][1]=9.0*l4_x-9.0*l4_x*l4_y;
194  out[57][0]=0.0;
195  out[57][1]=27.0*l4_x*l1_y-27.0*l4_x*l5_y;
196  out[58][0]=0.0;
197  out[58][1]=45.0*l4_x*l2_y-45.0*l4_x*l4_y;
198  out[59][0]=0.0;
199  out[59][1]=63.0*l4_x*l3_y-63.0*l4_x*l5_y;
200  }
201 
208  inline void evaluateJacobian (const typename Traits::DomainType& in,
209  std::vector<typename Traits::JacobianType>& out) const
210  {
211  out.resize(60);
212  auto const& x = in[0], y = in[1];
213 
214  const auto l1_x = 2*x - 1;
215  const auto l2_x = x*(6*x - 6) + 1;
216  const auto l3_x = x*(x*(20*x - 30) + 12) - 1;
217  const auto l4_x = x*(x*(x*(70*x - 140) + 90) - 20) + 1;
218  const auto l5_x = x*(x*(x*(x*(252*x - 630) + 560) - 210) + 30) - 1;
219  const auto l1_y = 2*y - 1;
220  const auto l2_y = y*(6*y - 6) + 1;
221  const auto l3_y = y*(y*(20*y - 30) + 12) - 1;
222  const auto l4_y = y*(y*(y*(70*y - 140) + 90) - 20) + 1;
223  const auto l5_y = y*(y*(y*(y*(252*y - 630) + 560) - 210) + 30) - 1;
224 
225  const auto dxl1_x = 2.0;
226  const auto dxl2_x = 12*x - 6;
227  const auto dxl3_x = x*(60*x - 60) + 12;
228  const auto dxl4_x = x*(x*(280*x - 420) + 180) - 20;
229  const auto dxl5_x = x*(x*(x*(1260*x - 2520) + 1680) - 420) + 30;
230  const auto dyl1_y = 2.0;
231  const auto dyl2_y = 12*y - 6;
232  const auto dyl3_y = y*(60*y - 60) + 12;
233  const auto dyl4_y = y*(y*(280*y - 420) + 180) - 20;
234  const auto dyl5_y = y*(y*(y*(1260*y - 2520) + 1680) - 420) + 30;
235 
236  // x-component
237  out[0][0][0]=sign0*(0.5*(-dxl4_x)+0.5*dxl5_x);
238  out[0][1][0]=0.0;
239  out[1][0][0]=-(1.5)*dxl4_x*l1_y+1.5*dxl5_x*l1_y;
240  out[1][1][0]=0.0;
241  out[2][0][0]=sign0*(-(2.5)*dxl4_x*l2_y+2.5*dxl5_x*l2_y);
242  out[2][1][0]=0.0;
243  out[3][0][0]=-(3.5)*dxl4_x*l3_y+3.5*dxl5_x*l3_y;
244  out[3][1][0]=0.0;
245  out[4][0][0]=sign0*(-(4.5)*dxl4_x*l4_y+4.5*dxl5_x*l4_y);
246  out[4][1][0]=0.0;
247 
248  out[5][0][0]=sign1*(0.5*dxl4_x+0.5*dxl5_x);
249  out[5][1][0]=0.0;
250  out[6][0][0]=-(1.5)*dxl4_x*l1_y-1.5*dxl5_x*l1_y;
251  out[6][1][0]=0.0;
252  out[7][0][0]=sign1*(2.5*dxl4_x*l2_y+2.5*dxl5_x*l2_y);
253  out[7][1][0]=0.0;
254  out[8][0][0]=-(3.5)*dxl4_x*l3_y-3.5*dxl5_x*l3_y;
255  out[8][1][0]=0.0;
256  out[9][0][0]=sign1*(4.5*dxl4_x*l4_y+4.5*dxl5_x*l4_y);
257  out[9][1][0]=0.0;
258 
259  out[10][0][0]=0.0;
260  out[10][1][0]=0.0;
261  out[11][0][0]=0.0;
262  out[11][1][0]=1.5*dxl1_x*l4_y-1.5*dxl1_x*l5_y;
263  out[12][0][0]=0.0;
264  out[12][1][0]=sign2*(-(2.5)*dxl2_x*l4_y+2.5*dxl2_x*l5_y);
265  out[13][0][0]=0.0;
266  out[13][1][0]=3.5*dxl3_x*l4_y-3.5*dxl3_x*l5_y;
267  out[14][0][0]=0.0;
268  out[14][1][0]=sign2*(-(4.5)*dxl4_x*l4_y+4.5*dxl4_x*l5_y);
269 
270  out[15][0][0]=0.0;
271  out[15][1][0]=0.0;
272  out[16][0][0]=0.0;
273  out[16][1][0]=1.5*dxl1_x*l4_y+1.5*dxl1_x*l5_y;
274  out[17][0][0]=0.0;
275  out[17][1][0]=sign3*(2.5*dxl2_x*l4_y+2.5*dxl2_x*l5_y);
276  out[18][0][0]=0.0;
277  out[18][1][0]=3.5*dxl3_x*l4_y+3.5*dxl3_x*l5_y;
278  out[19][0][0]=0.0;
279  out[19][1][0]=sign3*(4.5*dxl4_x*l4_y+4.5*dxl4_x*l5_y);
280 
281  out[20][0][0]=-dxl4_x;
282  out[20][1][0]=0.0;
283  out[21][0][0]=-3.0*dxl4_x*l1_y;
284  out[21][1][0]=0.0;
285  out[22][0][0]=-5.0*dxl4_x*l2_y;
286  out[22][1][0]=0.0;
287  out[23][0][0]=-7.0*dxl4_x*l3_y;
288  out[23][1][0]=0.0;
289  out[24][0][0]=-9.0*dxl4_x*l4_y;
290  out[24][1][0]=0.0;
291  out[25][0][0]=3.0*dxl1_x-3.0*dxl5_x;
292  out[25][1][0]=0.0;
293  out[26][0][0]=9.0*dxl1_x*l1_y-9.0*dxl5_x*l1_y;
294  out[26][1][0]=0.0;
295  out[27][0][0]=15.0*dxl1_x*l2_y-15.0*dxl5_x*l2_y;
296  out[27][1][0]=0.0;
297  out[28][0][0]=21.0*dxl1_x*l3_y-21.0*dxl5_x*l3_y;
298  out[28][1][0]=0.0;
299  out[29][0][0]=27.0*dxl1_x*l4_y-27.0*dxl5_x*l4_y;
300  out[29][1][0]=0.0;
301  out[30][0][0]=5.0*dxl2_x-5.0*dxl4_x;
302  out[30][1][0]=0.0;
303  out[31][0][0]=15.0*dxl2_x*l1_y-15.0*dxl4_x*l1_y;
304  out[31][1][0]=0.0;
305  out[32][0][0]=25.0*dxl2_x*l2_y-25.0*dxl4_x*l2_y;
306  out[32][1][0]=0.0;
307  out[33][0][0]=35.0*dxl2_x*l3_y-35.0*dxl4_x*l3_y;
308  out[33][1][0]=0.0;
309  out[34][0][0]=45.0*dxl2_x*l4_y-45.0*dxl4_x*l4_y;
310  out[34][1][0]=0.0;
311  out[35][0][0]=7.0*dxl3_x-7.0*dxl5_x;
312  out[35][1][0]=0.0;
313  out[36][0][0]=21.0*dxl3_x*l1_y-21.0*dxl5_x*l1_y;
314  out[36][1][0]=0.0;
315  out[37][0][0]=35.0*dxl3_x*l2_y-35.0*dxl5_x*l2_y;
316  out[37][1][0]=0.0;
317  out[38][0][0]=49.0*dxl3_x*l3_y-49.0*dxl5_x*l3_y;
318  out[38][1][0]=0.0;
319  out[39][0][0]=63.0*dxl3_x*l4_y-63.0*dxl5_x*l4_y;
320  out[39][1][0]=0.0;
321  out[40][0][0]=0.0;
322  out[40][1][0]=0.0;
323  out[41][0][0]=0.0;
324  out[41][1][0]=0.0;
325  out[42][0][0]=0.0;
326  out[42][1][0]=0.0;
327  out[43][0][0]=0.0;
328  out[43][1][0]=0.0;
329  out[44][0][0]=0.0;
330  out[44][1][0]=3.0*dxl1_x-3.0*dxl1_x*l4_y;
331  out[45][0][0]=0.0;
332  out[45][1][0]=9.0*dxl1_x*l1_y-9.0*dxl1_x*l5_y;
333  out[46][0][0]=0.0;
334  out[46][1][0]=15.0*dxl1_x*l2_y-15.0*dxl1_x*l4_y;
335  out[47][0][0]=0.0;
336  out[47][1][0]=21.0*dxl1_x*l3_y-21.0*dxl1_x*l5_y;
337  out[48][0][0]=0.0;
338  out[48][1][0]=5.0*dxl2_x-5.0*dxl2_x*l4_y;
339  out[49][0][0]=0.0;
340  out[49][1][0]=15.0*dxl2_x*l1_y-15.0*dxl2_x*l5_y;
341  out[50][0][0]=0.0;
342  out[50][1][0]=25.0*dxl2_x*l2_y-25.0*dxl2_x*l4_y;
343  out[51][0][0]=0.0;
344  out[51][1][0]=35.0*dxl2_x*l3_y-35.0*dxl2_x*l5_y;
345  out[52][0][0]=0.0;
346  out[52][1][0]=7.0*dxl3_x-7.0*dxl3_x*l4_y;
347  out[53][0][0]=0.0;
348  out[53][1][0]=21.0*dxl3_x*l1_y-21.0*dxl3_x*l5_y;
349  out[54][0][0]=0.0;
350  out[54][1][0]=35.0*dxl3_x*l2_y-35.0*dxl3_x*l4_y;
351  out[55][0][0]=0.0;
352  out[55][1][0]=49.0*dxl3_x*l3_y-49.0*dxl3_x*l5_y;
353  out[56][0][0]=0.0;
354  out[56][1][0]=9.0*dxl4_x-9.0*dxl4_x*l4_y;
355  out[57][0][0]=0.0;
356  out[57][1][0]=27.0*dxl4_x*l1_y-27.0*dxl4_x*l5_y;
357  out[58][0][0]=0.0;
358  out[58][1][0]=45.0*dxl4_x*l2_y-45.0*dxl4_x*l4_y;
359  out[59][0][0]=0.0;
360  out[59][1][0]=63.0*dxl4_x*l3_y-63.0*dxl4_x*l5_y;
361 
362  // y-component
363  out[0][0][1]=0.0;
364  out[0][1][1]=0.0;
365  out[1][0][1]=-(1.5)*l4_x*dyl1_y+1.5*l5_x*dyl1_y;
366  out[1][1][1]=0.0;
367  out[2][0][1]=sign0*(-(2.5)*l4_x*dyl2_y+2.5*l5_x*dyl2_y);
368  out[2][1][1]=0.0;
369  out[3][0][1]=-(3.5)*l4_x*dyl3_y+3.5*l5_x*dyl3_y;
370  out[3][1][1]=0.0;
371  out[4][0][1]=sign0*(-(4.5)*l4_x*dyl4_y+4.5*l5_x*dyl4_y);
372  out[4][1][1]=0.0;
373 
374  out[5][0][1]=0.0;
375  out[5][1][1]=0.0;
376  out[6][0][1]=-(1.5)*l4_x*dyl1_y-1.5*l5_x*dyl1_y;
377  out[6][1][1]=0.0;
378  out[7][0][1]=sign1*(2.5*l4_x*dyl2_y+2.5*l5_x*dyl2_y);
379  out[7][1][1]=0.0;
380  out[8][0][1]=-(3.5)*l4_x*dyl3_y-3.5*l5_x*dyl3_y;
381  out[8][1][1]=0.0;
382  out[9][0][1]=sign1*(4.5*l4_x*dyl4_y+4.5*l5_x*dyl4_y);
383  out[9][1][1]=0.0;
384 
385  out[10][0][1]=0.0;
386  out[10][1][1]=sign2*(0.5*(-dyl4_y)+0.5*dyl5_y);
387  out[11][0][1]=0.0;
388  out[11][1][1]=1.5*l1_x*dyl4_y-1.5*l1_x*dyl5_y;
389  out[12][0][1]=0.0;
390  out[12][1][1]=sign2*(-(2.5)*l2_x*dyl4_y+2.5*l2_x*dyl5_y);
391  out[13][0][1]=0.0;
392  out[13][1][1]=3.5*l3_x*dyl4_y-3.5*l3_x*dyl5_y;
393  out[14][0][1]=0.0;
394  out[14][1][1]=sign2*(-(4.5)*l4_x*dyl4_y+4.5*l4_x*dyl5_y);
395 
396  out[15][0][1]=0.0;
397  out[15][1][1]=sign3*(0.5*dyl4_y+0.5*dyl5_y);
398  out[16][0][1]=0.0;
399  out[16][1][1]=1.5*l1_x*dyl4_y+1.5*l1_x*dyl5_y;
400  out[17][0][1]=0.0;
401  out[17][1][1]=sign3*(2.5*l2_x*dyl4_y+2.5*l2_x*dyl5_y);
402  out[18][0][1]=0.0;
403  out[18][1][1]=3.5*l3_x*dyl4_y+3.5*l3_x*dyl5_y;
404  out[19][0][1]=0.0;
405  out[19][1][1]=sign3*(4.5*l4_x*dyl4_y+4.5*l4_x*dyl5_y);
406 
407  out[20][0][1]=0.0;
408  out[20][1][1]=0.0;
409  out[21][0][1]=3.0*dyl1_y-3.0*l4_x*dyl1_y;
410  out[21][1][1]=0.0;
411  out[22][0][1]=5.0*dyl2_y-5.0*l4_x*dyl2_y;
412  out[22][1][1]=0.0;
413  out[23][0][1]=7.0*dyl3_y-7.0*l4_x*dyl3_y;
414  out[23][1][1]=0.0;
415  out[24][0][1]=9.0*dyl4_y-9.0*l4_x*dyl4_y;
416  out[24][1][1]=0.0;
417  out[25][0][1]=0.0;
418  out[25][1][1]=0.0;
419  out[26][0][1]=9.0*l1_x*dyl1_y-9.0*l5_x*dyl1_y;
420  out[26][1][1]=0.0;
421  out[27][0][1]=15.0*l1_x*dyl2_y-15.0*l5_x*dyl2_y;
422  out[27][1][1]=0.0;
423  out[28][0][1]=21.0*l1_x*dyl3_y-21.0*l5_x*dyl3_y;
424  out[28][1][1]=0.0;
425  out[29][0][1]=27.0*l1_x*dyl4_y-27.0*l5_x*dyl4_y;
426  out[29][1][1]=0.0;
427  out[30][0][1]=0.0;
428  out[30][1][1]=0.0;
429  out[31][0][1]=15.0*l2_x*dyl1_y-15.0*l4_x*dyl1_y;
430  out[31][1][1]=0.0;
431  out[32][0][1]=25.0*l2_x*dyl2_y-25.0*l4_x*dyl2_y;
432  out[32][1][1]=0.0;
433  out[33][0][1]=35.0*l2_x*dyl3_y-35.0*l4_x*dyl3_y;
434  out[33][1][1]=0.0;
435  out[34][0][1]=45.0*l2_x*dyl4_y-45.0*l4_x*dyl4_y;
436  out[34][1][1]=0.0;
437  out[35][0][1]=0.0;
438  out[35][1][1]=0.0;
439  out[36][0][1]=21.0*l3_x*dyl1_y-21.0*l5_x*dyl1_y;
440  out[36][1][1]=0.0;
441  out[37][0][1]=35.0*l3_x*dyl2_y-35.0*l5_x*dyl2_y;
442  out[37][1][1]=0.0;
443  out[38][0][1]=49.0*l3_x*dyl3_y-49.0*l5_x*dyl3_y;
444  out[38][1][1]=0.0;
445  out[39][0][1]=63.0*l3_x*dyl4_y-63.0*l5_x*dyl4_y;
446  out[39][1][1]=0.0;
447  out[40][0][1]=0.0;
448  out[40][1][1]=-dyl4_y;
449  out[41][0][1]=0.0;
450  out[41][1][1]=3.0*dyl1_y-3.0*dyl5_y;
451  out[42][0][1]=0.0;
452  out[42][1][1]=5.0*dyl2_y-5.0*dyl4_y;
453  out[43][0][1]=0.0;
454  out[43][1][1]=7.0*dyl3_y-7.0*dyl5_y;
455  out[44][0][1]=0.0;
456  out[44][1][1]=-3.0*l1_x*dyl4_y;
457  out[45][0][1]=0.0;
458  out[45][1][1]=9.0*l1_x*dyl1_y-9.0*l1_x*dyl5_y;
459  out[46][0][1]=0.0;
460  out[46][1][1]=15.0*l1_x*dyl2_y-15.0*l1_x*dyl4_y;
461  out[47][0][1]=0.0;
462  out[47][1][1]=21.0*l1_x*dyl3_y-21.0*l1_x*dyl5_y;
463  out[48][0][1]=0.0;
464  out[48][1][1]=-5.0*l2_x*dyl4_y;
465  out[49][0][1]=0.0;
466  out[49][1][1]=15.0*l2_x*dyl1_y-15.0*l2_x*dyl5_y;
467  out[50][0][1]=0.0;
468  out[50][1][1]=25.0*l2_x*dyl2_y-25.0*l2_x*dyl4_y;
469  out[51][0][1]=0.0;
470  out[51][1][1]=35.0*l2_x*dyl3_y-35.0*l2_x*dyl5_y;
471  out[52][0][1]=0.0;
472  out[52][1][1]=-7.0*l3_x*dyl4_y;
473  out[53][0][1]=0.0;
474  out[53][1][1]=21.0*l3_x*dyl1_y-21.0*l3_x*dyl5_y;
475  out[54][0][1]=0.0;
476  out[54][1][1]=35.0*l3_x*dyl2_y-35.0*l3_x*dyl4_y;
477  out[55][0][1]=0.0;
478  out[55][1][1]=49.0*l3_x*dyl3_y-49.0*l3_x*dyl5_y;
479  out[56][0][1]=0.0;
480  out[56][1][1]=-9.0*l4_x*dyl4_y;
481  out[57][0][1]=0.0;
482  out[57][1][1]=27.0*l4_x*dyl1_y-27.0*l4_x*dyl5_y;
483  out[58][0][1]=0.0;
484  out[58][1][1]=45.0*l4_x*dyl2_y-45.0*l4_x*dyl4_y;
485  out[59][0][1]=0.0;
486  out[59][1][1]=63.0*l4_x*dyl3_y-63.0*l4_x*dyl5_y;
487  }
488 
490  void partial (const std::array<unsigned int, 2>& order,
491  const typename Traits::DomainType& in, // position
492  std::vector<typename Traits::RangeType>& out) const // return value
493  {
494  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
495  if (totalOrder == 0) {
496  evaluateFunction(in, out);
497  } else if (totalOrder == 1) {
498  out.resize(size());
499  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
500  auto const& x = in[0], y = in[1];
501 
502  auto l1_x = 2*x - 1;
503  auto l2_x = x*(6*x - 6) + 1;
504  auto l3_x = x*(x*(20*x - 30) + 12) - 1;
505  auto l4_x = x*(x*(x*(70*x - 140) + 90) - 20) + 1;
506  auto l5_x = x*(x*(x*(x*(252*x - 630) + 560) - 210) + 30) - 1;
507  auto l1_y = 2*y - 1;
508  auto l2_y = y*(6*y - 6) + 1;
509  auto l3_y = y*(y*(20*y - 30) + 12) - 1;
510  auto l4_y = y*(y*(y*(70*y - 140) + 90) - 20) + 1;
511  auto l5_y = y*(y*(y*(y*(252*y - 630) + 560) - 210) + 30) - 1;
512 
513  if (direction == 0) {
514  auto dxl1_x = 2.0;
515  auto dxl2_x = 12*x - 6;
516  auto dxl3_x = x*(60*x - 60) + 12;
517  auto dxl4_x = x*(x*(280*x - 420) + 180) - 20;
518  auto dxl5_x = x*(x*(x*(1260*x - 2520) + 1680) - 420) + 30;
519 
520  out[0][0]=sign0*(0.5*(-dxl4_x)+0.5*dxl5_x);
521  out[0][1]=0.0;
522  out[1][0]=-(1.5)*dxl4_x*l1_y+1.5*dxl5_x*l1_y;
523  out[1][1]=0.0;
524  out[2][0]=sign0*(-(2.5)*dxl4_x*l2_y+2.5*dxl5_x*l2_y);
525  out[2][1]=0.0;
526  out[3][0]=-(3.5)*dxl4_x*l3_y+3.5*dxl5_x*l3_y;
527  out[3][1]=0.0;
528  out[4][0]=sign0*(-(4.5)*dxl4_x*l4_y+4.5*dxl5_x*l4_y);
529  out[4][1]=0.0;
530 
531  out[5][0]=sign1*(0.5*dxl4_x+0.5*dxl5_x);
532  out[5][1]=0.0;
533  out[6][0]=-(1.5)*dxl4_x*l1_y-1.5*dxl5_x*l1_y;
534  out[6][1]=0.0;
535  out[7][0]=sign1*(2.5*dxl4_x*l2_y+2.5*dxl5_x*l2_y);
536  out[7][1]=0.0;
537  out[8][0]=-(3.5)*dxl4_x*l3_y-3.5*dxl5_x*l3_y;
538  out[8][1]=0.0;
539  out[9][0]=sign1*(4.5*dxl4_x*l4_y+4.5*dxl5_x*l4_y);
540  out[9][1]=0.0;
541 
542  out[10][0]=0.0;
543  out[10][1]=0.0;
544  out[11][0]=0.0;
545  out[11][1]=1.5*dxl1_x*l4_y-1.5*dxl1_x*l5_y;
546  out[12][0]=0.0;
547  out[12][1]=sign2*(-(2.5)*dxl2_x*l4_y+2.5*dxl2_x*l5_y);
548  out[13][0]=0.0;
549  out[13][1]=3.5*dxl3_x*l4_y-3.5*dxl3_x*l5_y;
550  out[14][0]=0.0;
551  out[14][1]=sign2*(-(4.5)*dxl4_x*l4_y+4.5*dxl4_x*l5_y);
552 
553  out[15][0]=0.0;
554  out[15][1]=0.0;
555  out[16][0]=0.0;
556  out[16][1]=1.5*dxl1_x*l4_y+1.5*dxl1_x*l5_y;
557  out[17][0]=0.0;
558  out[17][1]=sign3*(2.5*dxl2_x*l4_y+2.5*dxl2_x*l5_y);
559  out[18][0]=0.0;
560  out[18][1]=3.5*dxl3_x*l4_y+3.5*dxl3_x*l5_y;
561  out[19][0]=0.0;
562  out[19][1]=sign3*(4.5*dxl4_x*l4_y+4.5*dxl4_x*l5_y);
563 
564  out[20][0]=-dxl4_x;
565  out[20][1]=0.0;
566  out[21][0]=-3.0*dxl4_x*l1_y;
567  out[21][1]=0.0;
568  out[22][0]=-5.0*dxl4_x*l2_y;
569  out[22][1]=0.0;
570  out[23][0]=-7.0*dxl4_x*l3_y;
571  out[23][1]=0.0;
572  out[24][0]=-9.0*dxl4_x*l4_y;
573  out[24][1]=0.0;
574  out[25][0]=3.0*dxl1_x-3.0*dxl5_x;
575  out[25][1]=0.0;
576  out[26][0]=9.0*dxl1_x*l1_y-9.0*dxl5_x*l1_y;
577  out[26][1]=0.0;
578  out[27][0]=15.0*dxl1_x*l2_y-15.0*dxl5_x*l2_y;
579  out[27][1]=0.0;
580  out[28][0]=21.0*dxl1_x*l3_y-21.0*dxl5_x*l3_y;
581  out[28][1]=0.0;
582  out[29][0]=27.0*dxl1_x*l4_y-27.0*dxl5_x*l4_y;
583  out[29][1]=0.0;
584  out[30][0]=5.0*dxl2_x-5.0*dxl4_x;
585  out[30][1]=0.0;
586  out[31][0]=15.0*dxl2_x*l1_y-15.0*dxl4_x*l1_y;
587  out[31][1]=0.0;
588  out[32][0]=25.0*dxl2_x*l2_y-25.0*dxl4_x*l2_y;
589  out[32][1]=0.0;
590  out[33][0]=35.0*dxl2_x*l3_y-35.0*dxl4_x*l3_y;
591  out[33][1]=0.0;
592  out[34][0]=45.0*dxl2_x*l4_y-45.0*dxl4_x*l4_y;
593  out[34][1]=0.0;
594  out[35][0]=7.0*dxl3_x-7.0*dxl5_x;
595  out[35][1]=0.0;
596  out[36][0]=21.0*dxl3_x*l1_y-21.0*dxl5_x*l1_y;
597  out[36][1]=0.0;
598  out[37][0]=35.0*dxl3_x*l2_y-35.0*dxl5_x*l2_y;
599  out[37][1]=0.0;
600  out[38][0]=49.0*dxl3_x*l3_y-49.0*dxl5_x*l3_y;
601  out[38][1]=0.0;
602  out[39][0]=63.0*dxl3_x*l4_y-63.0*dxl5_x*l4_y;
603  out[39][1]=0.0;
604  out[40][0]=0.0;
605  out[40][1]=0.0;
606  out[41][0]=0.0;
607  out[41][1]=0.0;
608  out[42][0]=0.0;
609  out[42][1]=0.0;
610  out[43][0]=0.0;
611  out[43][1]=0.0;
612  out[44][0]=0.0;
613  out[44][1]=3.0*dxl1_x-3.0*dxl1_x*l4_y;
614  out[45][0]=0.0;
615  out[45][1]=9.0*dxl1_x*l1_y-9.0*dxl1_x*l5_y;
616  out[46][0]=0.0;
617  out[46][1]=15.0*dxl1_x*l2_y-15.0*dxl1_x*l4_y;
618  out[47][0]=0.0;
619  out[47][1]=21.0*dxl1_x*l3_y-21.0*dxl1_x*l5_y;
620  out[48][0]=0.0;
621  out[48][1]=5.0*dxl2_x-5.0*dxl2_x*l4_y;
622  out[49][0]=0.0;
623  out[49][1]=15.0*dxl2_x*l1_y-15.0*dxl2_x*l5_y;
624  out[50][0]=0.0;
625  out[50][1]=25.0*dxl2_x*l2_y-25.0*dxl2_x*l4_y;
626  out[51][0]=0.0;
627  out[51][1]=35.0*dxl2_x*l3_y-35.0*dxl2_x*l5_y;
628  out[52][0]=0.0;
629  out[52][1]=7.0*dxl3_x-7.0*dxl3_x*l4_y;
630  out[53][0]=0.0;
631  out[53][1]=21.0*dxl3_x*l1_y-21.0*dxl3_x*l5_y;
632  out[54][0]=0.0;
633  out[54][1]=35.0*dxl3_x*l2_y-35.0*dxl3_x*l4_y;
634  out[55][0]=0.0;
635  out[55][1]=49.0*dxl3_x*l3_y-49.0*dxl3_x*l5_y;
636  out[56][0]=0.0;
637  out[56][1]=9.0*dxl4_x-9.0*dxl4_x*l4_y;
638  out[57][0]=0.0;
639  out[57][1]=27.0*dxl4_x*l1_y-27.0*dxl4_x*l5_y;
640  out[58][0]=0.0;
641  out[58][1]=45.0*dxl4_x*l2_y-45.0*dxl4_x*l4_y;
642  out[59][0]=0.0;
643  out[59][1]=63.0*dxl4_x*l3_y-63.0*dxl4_x*l5_y;
644 
645  } else if (direction == 1) {
646  auto dyl1_y = 2.0;
647  auto dyl2_y = 12*y - 6;
648  auto dyl3_y = y*(60*y - 60) + 12;
649  auto dyl4_y = y*(y*(280*y - 420) + 180) - 20;
650  auto dyl5_y = y*(y*(y*(1260*y - 2520) + 1680) - 420) + 30;
651 
652  out[0][0]=0.0;
653  out[0][1]=0.0;
654  out[1][0]=-(1.5)*l4_x*dyl1_y+1.5*l5_x*dyl1_y;
655  out[1][1]=0.0;
656  out[2][0]=sign0*(-(2.5)*l4_x*dyl2_y+2.5*l5_x*dyl2_y);
657  out[2][1]=0.0;
658  out[3][0]=-(3.5)*l4_x*dyl3_y+3.5*l5_x*dyl3_y;
659  out[3][1]=0.0;
660  out[4][0]=sign0*(-(4.5)*l4_x*dyl4_y+4.5*l5_x*dyl4_y);
661  out[4][1]=0.0;
662 
663  out[5][0]=0.0;
664  out[5][1]=0.0;
665  out[6][0]=-(1.5)*l4_x*dyl1_y-1.5*l5_x*dyl1_y;
666  out[6][1]=0.0;
667  out[7][0]=sign1*(2.5*l4_x*dyl2_y+2.5*l5_x*dyl2_y);
668  out[7][1]=0.0;
669  out[8][0]=-(3.5)*l4_x*dyl3_y-3.5*l5_x*dyl3_y;
670  out[8][1]=0.0;
671  out[9][0]=sign1*(4.5*l4_x*dyl4_y+4.5*l5_x*dyl4_y);
672  out[9][1]=0.0;
673 
674  out[10][0]=0.0;
675  out[10][1]=sign2*(0.5*(-dyl4_y)+0.5*dyl5_y);
676  out[11][0]=0.0;
677  out[11][1]=1.5*l1_x*dyl4_y-1.5*l1_x*dyl5_y;
678  out[12][0]=0.0;
679  out[12][1]=sign2*(-(2.5)*l2_x*dyl4_y+2.5*l2_x*dyl5_y);
680  out[13][0]=0.0;
681  out[13][1]=3.5*l3_x*dyl4_y-3.5*l3_x*dyl5_y;
682  out[14][0]=0.0;
683  out[14][1]=sign2*(-(4.5)*l4_x*dyl4_y+4.5*l4_x*dyl5_y);
684 
685  out[15][0]=0.0;
686  out[15][1]=sign3*(0.5*dyl4_y+0.5*dyl5_y);
687  out[16][0]=0.0;
688  out[16][1]=1.5*l1_x*dyl4_y+1.5*l1_x*dyl5_y;
689  out[17][0]=0.0;
690  out[17][1]=sign3*(2.5*l2_x*dyl4_y+2.5*l2_x*dyl5_y);
691  out[18][0]=0.0;
692  out[18][1]=3.5*l3_x*dyl4_y+3.5*l3_x*dyl5_y;
693  out[19][0]=0.0;
694  out[19][1]=sign3*(4.5*l4_x*dyl4_y+4.5*l4_x*dyl5_y);
695 
696  out[20][0]=0.0;
697  out[20][1]=0.0;
698  out[21][0]=3.0*dyl1_y-3.0*l4_x*dyl1_y;
699  out[21][1]=0.0;
700  out[22][0]=5.0*dyl2_y-5.0*l4_x*dyl2_y;
701  out[22][1]=0.0;
702  out[23][0]=7.0*dyl3_y-7.0*l4_x*dyl3_y;
703  out[23][1]=0.0;
704  out[24][0]=9.0*dyl4_y-9.0*l4_x*dyl4_y;
705  out[24][1]=0.0;
706  out[25][0]=0.0;
707  out[25][1]=0.0;
708  out[26][0]=9.0*l1_x*dyl1_y-9.0*l5_x*dyl1_y;
709  out[26][1]=0.0;
710  out[27][0]=15.0*l1_x*dyl2_y-15.0*l5_x*dyl2_y;
711  out[27][1]=0.0;
712  out[28][0]=21.0*l1_x*dyl3_y-21.0*l5_x*dyl3_y;
713  out[28][1]=0.0;
714  out[29][0]=27.0*l1_x*dyl4_y-27.0*l5_x*dyl4_y;
715  out[29][1]=0.0;
716  out[30][0]=0.0;
717  out[30][1]=0.0;
718  out[31][0]=15.0*l2_x*dyl1_y-15.0*l4_x*dyl1_y;
719  out[31][1]=0.0;
720  out[32][0]=25.0*l2_x*dyl2_y-25.0*l4_x*dyl2_y;
721  out[32][1]=0.0;
722  out[33][0]=35.0*l2_x*dyl3_y-35.0*l4_x*dyl3_y;
723  out[33][1]=0.0;
724  out[34][0]=45.0*l2_x*dyl4_y-45.0*l4_x*dyl4_y;
725  out[34][1]=0.0;
726  out[35][0]=0.0;
727  out[35][1]=0.0;
728  out[36][0]=21.0*l3_x*dyl1_y-21.0*l5_x*dyl1_y;
729  out[36][1]=0.0;
730  out[37][0]=35.0*l3_x*dyl2_y-35.0*l5_x*dyl2_y;
731  out[37][1]=0.0;
732  out[38][0]=49.0*l3_x*dyl3_y-49.0*l5_x*dyl3_y;
733  out[38][1]=0.0;
734  out[39][0]=63.0*l3_x*dyl4_y-63.0*l5_x*dyl4_y;
735  out[39][1]=0.0;
736  out[40][0]=0.0;
737  out[40][1]=-dyl4_y;
738  out[41][0]=0.0;
739  out[41][1]=3.0*dyl1_y-3.0*dyl5_y;
740  out[42][0]=0.0;
741  out[42][1]=5.0*dyl2_y-5.0*dyl4_y;
742  out[43][0]=0.0;
743  out[43][1]=7.0*dyl3_y-7.0*dyl5_y;
744  out[44][0]=0.0;
745  out[44][1]=-3.0*l1_x*dyl4_y;
746  out[45][0]=0.0;
747  out[45][1]=9.0*l1_x*dyl1_y-9.0*l1_x*dyl5_y;
748  out[46][0]=0.0;
749  out[46][1]=15.0*l1_x*dyl2_y-15.0*l1_x*dyl4_y;
750  out[47][0]=0.0;
751  out[47][1]=21.0*l1_x*dyl3_y-21.0*l1_x*dyl5_y;
752  out[48][0]=0.0;
753  out[48][1]=-5.0*l2_x*dyl4_y;
754  out[49][0]=0.0;
755  out[49][1]=15.0*l2_x*dyl1_y-15.0*l2_x*dyl5_y;
756  out[50][0]=0.0;
757  out[50][1]=25.0*l2_x*dyl2_y-25.0*l2_x*dyl4_y;
758  out[51][0]=0.0;
759  out[51][1]=35.0*l2_x*dyl3_y-35.0*l2_x*dyl5_y;
760  out[52][0]=0.0;
761  out[52][1]=-7.0*l3_x*dyl4_y;
762  out[53][0]=0.0;
763  out[53][1]=21.0*l3_x*dyl1_y-21.0*l3_x*dyl5_y;
764  out[54][0]=0.0;
765  out[54][1]=35.0*l3_x*dyl2_y-35.0*l3_x*dyl4_y;
766  out[55][0]=0.0;
767  out[55][1]=49.0*l3_x*dyl3_y-49.0*l3_x*dyl5_y;
768  out[56][0]=0.0;
769  out[56][1]=-9.0*l4_x*dyl4_y;
770  out[57][0]=0.0;
771  out[57][1]=27.0*l4_x*dyl1_y-27.0*l4_x*dyl5_y;
772  out[58][0]=0.0;
773  out[58][1]=45.0*l4_x*dyl2_y-45.0*l4_x*dyl4_y;
774  out[59][0]=0.0;
775  out[59][1]=63.0*l4_x*dyl3_y-63.0*l4_x*dyl5_y;
776  } else {
777  DUNE_THROW(RangeError, "Component out of range.");
778  }
779  } else {
780  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
781  }
782  }
783 
785  unsigned int order () const
786  {
787  return 9;
788  }
789 
790  private:
791  R sign0, sign1, sign2, sign3;
792  };
793 }
794 
795 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALBASIS_HH
Dune::FieldMatrix
A dense n x m matrix.
Definition: fmatrix.hh:69
Dune::FieldVector
vector space out of a tensor product of fields.
Definition: fvector.hh:96
Dune::NotImplemented
Default exception for dummy implementations.
Definition: exceptions.hh:261
Dune::RT4Cube2DLocalBasis
Second order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas4cube2dlocalbasis.hh:27
Dune::RT4Cube2DLocalBasis::partial
void partial(const std::array< unsigned int, 2 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: raviartthomas4cube2dlocalbasis.hh:490
Dune::RT4Cube2DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas4cube2dlocalbasis.hh:58
Dune::RT4Cube2DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: raviartthomas4cube2dlocalbasis.hh:47
Dune::RT4Cube2DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas4cube2dlocalbasis.hh:785
Dune::RT4Cube2DLocalBasis::evaluateJacobian
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas4cube2dlocalbasis.hh:208
Dune::RT4Cube2DLocalBasis::RT4Cube2DLocalBasis
RT4Cube2DLocalBasis(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas4cube2dlocalbasis.hh:38
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:290
Dune
Dune namespace.
Definition: alignedallocator.hh:14
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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