Dune Core Modules (2.9.0)

brezzidouglasmarini2simplex2dlocalbasis.hh
1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3 // SPDX-FileCopyrightInfo: Copyright (C) DUNE Project contributors, see file LICENSE.md in module root
4 // SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
6 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
7 
8 #include <array>
9 #include <bitset>
10 #include <numeric>
11 #include <vector>
12 
13 #include <dune/common/fmatrix.hh>
14 
15 #include "../../common/localbasis.hh"
16 
17 namespace Dune
18 {
28  template<class D, class R>
29  class BDM2Simplex2DLocalBasis
30  {
31 
32  public:
33  typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
34  R,2,Dune::FieldVector<R,2>,
35  Dune::FieldMatrix<R,2,2> > Traits;
36 
38  BDM2Simplex2DLocalBasis()
39  {
40  for (size_t i=0; i<3; i++)
41  sign_[i] = 1.0;
42  }
43 
49  BDM2Simplex2DLocalBasis(std::bitset<3> s)
50  {
51  for (size_t i=0; i<3; i++)
52  sign_[i] = s[i] ? -1.0 : 1.0;
53  }
54 
56  unsigned int size() const
57  {
58  return 12;
59  }
60 
67  inline void evaluateFunction(const typename Traits::DomainType& in,
68  std::vector<typename Traits::RangeType>& out) const
69  {
70  out.resize(size());
71 
72  out[0][0] = sign_[0]*(-2*in[0]*in[1] + in[0]*in[0]);
73  out[0][1] = sign_[0]*(-1 + 6*in[1] -2*in[0]*in[1] - 5*in[1]*in[1]);
74 
75  out[1][0] = 1.5*in[0] + 3*in[0]*in[1] - 4.5*in[0]*in[0];
76  out[1][1] = -3 + 6*in[0] + 10.5*in[1] - 15*in[0]*in[1] - 7.5*in[1]*in[1];
77 
78  out[2][0] = sign_[0]*(-7.5*in[0] + 5*in[0]*in[1] + 12.5*in[0]*in[0]);
79  out[2][1] = sign_[0]*(-5 + 30*in[0] + 7.5*in[1] - 25*in[0]*in[1] - 30*in[0]*in[0] - 2.5*in[1]*in[1]);
80 
81 
82 
83  out[3][0] = sign_[1]*(-1 + 6*in[0] - 2*in[0]*in[1] - 5*in[0]*in[0]);
84  out[3][1] = sign_[1]*(-2*in[0]*in[1] + in[1]*in[1]);
85 
86  out[4][0] = 3 - 10.5*in[0] - 6*in[1] + 15*in[0]*in[1] + 7.5*in[0]*in[0];
87  out[4][1] = -1.5*in[1] - 3*in[0]*in[1] + 4.5*in[1]*in[1];
88 
89  out[5][0] = sign_[1]*(-5 + 7.5*in[0] + 30*in[1] - 25*in[0]*in[1] - 2.5*in[0]*in[0] - 30*in[1]*in[1]);
90  out[5][1] = sign_[1]*(-7.5*in[1] + 5*in[0]*in[1] + 12.5*in[1]*in[1]);
91 
92 
93 
94  out[6][0] = sign_[2]*(-3*in[0] + 4*in[0]*in[1] + 4*in[0]*in[0]);
95  out[6][1] = sign_[2]*(-3*in[1] + 4*in[0]*in[1] + 4*in[1]*in[1]);
96 
97  out[7][0] = -3*in[0] + 6*in[0]*in[0];
98  out[7][1] = 3*in[1] - 6*in[1]*in[1];
99 
100  out[8][0] = sign_[2]*(-10*in[0]*in[1] + 5*in[0]*in[0]);
101  out[8][1] = sign_[2]*(-10*in[0]*in[1] + 5*in[1]*in[1]);
102 
103 
104 
105  out[9][0] = 18*in[0] - 12*in[0]*in[1] - 18*in[0]*in[0];
106  out[9][1] = 6*in[1] - 12*in[0]*in[1] - 6*in[1]*in[1];
107 
108  out[10][0] = 6*in[0] - 12*in[0]*in[1] - 6*in[0]*in[0];
109  out[10][1] = 18*in[1] - 12*in[0]*in[1] - 18*in[1]*in[1];
110 
111  out[11][0] = 90*in[0] - 180*in[0]*in[1] - 90*in[0]*in[0];
112  out[11][1] = -90*in[1] + 180*in[0]*in[1] + 90*in[1]*in[1];
113  }
114 
121  inline void evaluateJacobian(const typename Traits::DomainType& in,
122  std::vector<typename Traits::JacobianType>& out) const
123  {
124  out.resize(size());
125 
126  out[0][0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
127  out[0][0][1] = sign_[0]*(-2*in[0]);
128 
129  out[0][1][0] = sign_[0]*(-2*in[1]);
130  out[0][1][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
131 
132 
133  out[1][0][0] = 1.5 + 3*in[1] - 9*in[0];
134  out[1][0][1] = 3*in[0];
135 
136  out[1][1][0] = 6 - 15*in[1];
137  out[1][1][1] = 10.5 - 15*in[0] - 15*in[1];
138 
139 
140  out[2][0][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
141  out[2][0][1] = sign_[0]*(5*in[0]);
142 
143  out[2][1][0] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
144  out[2][1][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
145 
146 
147 
148  out[3][0][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
149  out[3][0][1] = sign_[1]*(-2*in[0]);
150 
151  out[3][1][0] = sign_[1]*(-2*in[1]);
152  out[3][1][1] = sign_[1]*(-2*in[0] + 2*in[1]);
153 
154 
155  out[4][0][0] = -10.5 + 15*in[1] + 15*in[0];
156  out[4][0][1] = -6 + 15*in[0];
157 
158  out[4][1][0] = -3*in[1];
159  out[4][1][1] = -1.5 - 3*in[0] + 9*in[1];
160 
161 
162  out[5][0][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
163  out[5][0][1] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
164 
165  out[5][1][0] = sign_[1]*(5*in[1]);
166  out[5][1][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
167 
168 
169 
170  out[6][0][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
171  out[6][0][1] = sign_[2]*(4*in[0]);
172 
173  out[6][1][0] = sign_[2]*(4*in[1]);
174  out[6][1][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
175 
176 
177  out[7][0][0] = -3 + 12*in[0];
178  out[7][0][1] = 0;
179 
180  out[7][1][0] = 0;
181  out[7][1][1] = 3 - 12*in[1];
182 
183 
184  out[8][0][0] = sign_[2]*(-10*in[1] + 10*in[0]);
185  out[8][0][1] = sign_[2]*(-10*in[0]);
186 
187  out[8][1][0] = sign_[2]*(-10*in[1]);
188  out[8][1][1] = sign_[2]*(-10*in[0] + 10*in[1]);
189 
190 
191  out[9][0][0] = 18 - 12*in[1] - 36*in[0];
192  out[9][0][1] = -12*in[0];
193 
194  out[9][1][0] = -12*in[1];
195  out[9][1][1] = 6 - 12*in[0] - 12*in[1];
196 
197  out[10][0][0] = 6 - 12*in[1] - 12*in[0];
198  out[10][0][1] = -12*in[0];
199 
200  out[10][1][0] = -12*in[1];
201  out[10][1][1] = 18 - 12*in[0] - 36*in[1];
202 
203  out[11][0][0] = 90 - 180*in[1] - 180*in[0];
204  out[11][0][1] = -180*in[0];
205 
206  out[11][1][0] = 180*in[1];
207  out[11][1][1] = -90 + 180*in[0] + 180*in[1];
208  }
209 
211  void partial (const std::array<unsigned int, 2>& order,
212  const typename Traits::DomainType& in, // position
213  std::vector<typename Traits::RangeType>& out) const // return value
214  {
215  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
216  if (totalOrder == 0) {
217  evaluateFunction(in, out);
218  } else if (totalOrder == 1) {
219  out.resize(size());
220  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
221 
222  switch (direction) {
223  case 0:
224  out[0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
225  out[0][1] = sign_[0]*(-2*in[1]);
226 
227  out[1][0] = 1.5 + 3*in[1] - 9*in[0];
228  out[1][1] = 6 - 15*in[1];
229 
230  out[2][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
231  out[2][1] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
232 
233  out[3][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
234  out[3][1] = sign_[1]*(-2*in[1]);
235 
236  out[4][0] = -10.5 + 15*in[1] + 15*in[0];
237  out[4][1] = -3*in[1];
238 
239  out[5][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
240  out[5][1] = sign_[1]*(5*in[1]);
241 
242  out[6][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
243  out[6][1] = sign_[2]*(4*in[1]);
244 
245  out[7][0] = -3 + 12*in[0];
246  out[7][1] = 0;
247 
248  out[8][0] = sign_[2]*(-10*in[1] + 10*in[0]);
249  out[8][1] = sign_[2]*(-10*in[1]);
250 
251  out[9][0] = 18 - 12*in[1] - 36*in[0];
252  out[9][1] = -12*in[1];
253 
254  out[10][0] = 6 - 12*in[1] - 12*in[0];
255  out[10][1] = -12*in[1];
256 
257  out[11][0] = 90 - 180*in[1] - 180*in[0];
258  out[11][1] = 180*in[1];
259  break;
260  case 1:
261  out[0][0] = sign_[0]*(-2*in[0]);
262  out[0][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
263 
264  out[1][0] = 3*in[0];
265  out[1][1] = 10.5 - 15*in[0] - 15*in[1];
266 
267  out[2][0] = sign_[0]*(5*in[0]);
268  out[2][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
269 
270  out[3][0] = sign_[1]*(-2*in[0]);
271  out[3][1] = sign_[1]*(-2*in[0] + 2*in[1]);
272 
273  out[4][0] = -6 + 15*in[0];
274  out[4][1] = -1.5 - 3*in[0] + 9*in[1];
275 
276  out[5][0] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
277  out[5][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
278 
279  out[6][0] = sign_[2]*(4*in[0]);
280  out[6][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
281 
282  out[7][0] = 0;
283  out[7][1] = 3 - 12*in[1];
284 
285  out[8][0] = sign_[2]*(-10*in[0]);
286  out[8][1] = sign_[2]*(-10*in[0] + 10*in[1]);
287 
288  out[9][0] = -12*in[0];
289  out[9][1] = 6 - 12*in[0] - 12*in[1];
290 
291  out[10][0] = -12*in[0];
292  out[10][1] = 18 - 12*in[0] - 36*in[1];
293 
294  out[11][0] = -180*in[0];
295  out[11][1] = -90 + 180*in[0] + 180*in[1];
296  break;
297  default:
298  DUNE_THROW(RangeError, "Component out of range.");
299  }
300  } else {
301  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
302  }
303  }
304 
306  unsigned int order() const
307  {
308  return 2; // TODO: check whether this is not order 3
309  }
310 
311  private:
312  std::array<R,3> sign_;
313  };
314 } // end namespace Dune
315 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
Dune::BDM2Simplex2DLocalBasis
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:30
Dune::BDM2Simplex2DLocalBasis::evaluateJacobian
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:121
Dune::BDM2Simplex2DLocalBasis::BDM2Simplex2DLocalBasis
BDM2Simplex2DLocalBasis(std::bitset< 3 > s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:49
Dune::BDM2Simplex2DLocalBasis::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: brezzidouglasmarini2simplex2dlocalbasis.hh:211
Dune::BDM2Simplex2DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:56
Dune::BDM2Simplex2DLocalBasis::BDM2Simplex2DLocalBasis
BDM2Simplex2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:38
Dune::BDM2Simplex2DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:67
Dune::BDM2Simplex2DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:306
Dune::FieldMatrix
A dense n x m matrix.
Definition: fmatrix.hh:117
Dune::FieldVector
vector space out of a tensor product of fields.
Definition: fvector.hh:95
Dune::NotImplemented
Default exception for dummy implementations.
Definition: exceptions.hh:263
Dune::RangeError
Default exception class for range errors.
Definition: exceptions.hh:254
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:218
Dune::Hybrid::accumulate
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:291
Dune
Dune namespace.
Definition: alignedallocator.hh:13
Dune::LocalBasisTraits
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:34
Dune::LocalBasisTraits::DomainType
D DomainType
domain type
Definition: localbasis.hh:42
Creative Commons License   |  Legal Statements / Impressum  |  Hosted by TU Dresden  |  generated with Hugo v0.80.0 (Apr 27, 22:29, 2024)