Dune Core Modules (2.6.0)

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 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_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 {
26  template<class D, class R>
27  class BDM2Simplex2DLocalBasis
28  {
29 
30  public:
31  typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
32  R,2,Dune::FieldVector<R,2>,
33  Dune::FieldMatrix<R,2,2> > Traits;
34 
36  BDM2Simplex2DLocalBasis()
37  {
38  for (size_t i=0; i<3; i++)
39  sign_[i] = 1.0;
40  }
41 
47  BDM2Simplex2DLocalBasis(std::bitset<3> s)
48  {
49  for (size_t i=0; i<3; i++)
50  sign_[i] = s[i] ? -1.0 : 1.0;
51  }
52 
54  unsigned int size() const
55  {
56  return 12;
57  }
58 
65  inline void evaluateFunction(const typename Traits::DomainType& in,
66  std::vector<typename Traits::RangeType>& out) const
67  {
68  out.resize(size());
69 
70  out[0][0] = sign_[0]*(-2*in[0]*in[1] + in[0]*in[0]);
71  out[0][1] = sign_[0]*(-1 + 6*in[1] -2*in[0]*in[1] - 5*in[1]*in[1]);
72 
73  out[1][0] = 1.5*in[0] + 3*in[0]*in[1] - 4.5*in[0]*in[0];
74  out[1][1] = -3 + 6*in[0] + 10.5*in[1] - 15*in[0]*in[1] - 7.5*in[1]*in[1];
75 
76  out[2][0] = sign_[0]*(-7.5*in[0] + 5*in[0]*in[1] + 12.5*in[0]*in[0]);
77  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]);
78 
79 
80 
81  out[3][0] = sign_[1]*(-1 + 6*in[0] - 2*in[0]*in[1] - 5*in[0]*in[0]);
82  out[3][1] = sign_[1]*(-2*in[0]*in[1] + in[1]*in[1]);
83 
84  out[4][0] = 3 - 10.5*in[0] - 6*in[1] + 15*in[0]*in[1] + 7.5*in[0]*in[0];
85  out[4][1] = -1.5*in[1] - 3*in[0]*in[1] + 4.5*in[1]*in[1];
86 
87  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]);
88  out[5][1] = sign_[1]*(-7.5*in[1] + 5*in[0]*in[1] + 12.5*in[1]*in[1]);
89 
90 
91 
92  out[6][0] = sign_[2]*(-3*in[0] + 4*in[0]*in[1] + 4*in[0]*in[0]);
93  out[6][1] = sign_[2]*(-3*in[1] + 4*in[0]*in[1] + 4*in[1]*in[1]);
94 
95  out[7][0] = -3*in[0] + 6*in[0]*in[0];
96  out[7][1] = 3*in[1] - 6*in[1]*in[1];
97 
98  out[8][0] = sign_[2]*(-10*in[0]*in[1] + 5*in[0]*in[0]);
99  out[8][1] = sign_[2]*(-10*in[0]*in[1] + 5*in[1]*in[1]);
100 
101 
102 
103  out[9][0] = 18*in[0] - 12*in[0]*in[1] - 18*in[0]*in[0];
104  out[9][1] = 6*in[1] - 12*in[0]*in[1] - 6*in[1]*in[1];
105 
106  out[10][0] = 6*in[0] - 12*in[0]*in[1] - 6*in[0]*in[0];
107  out[10][1] = 18*in[1] - 12*in[0]*in[1] - 18*in[1]*in[1];
108 
109  out[11][0] = 90*in[0] - 180*in[0]*in[1] - 90*in[0]*in[0];
110  out[11][1] = -90*in[1] + 180*in[0]*in[1] + 90*in[1]*in[1];
111  }
112 
119  inline void evaluateJacobian(const typename Traits::DomainType& in,
120  std::vector<typename Traits::JacobianType>& out) const
121  {
122  out.resize(size());
123 
124  out[0][0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
125  out[0][0][1] = sign_[0]*(-2*in[0]);
126 
127  out[0][1][0] = sign_[0]*(-2*in[1]);
128  out[0][1][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
129 
130 
131  out[1][0][0] = 1.5 + 3*in[1] - 9*in[0];
132  out[1][0][1] = 3*in[0];
133 
134  out[1][1][0] = 6 - 15*in[1];
135  out[1][1][1] = 10.5 - 15*in[0] - 15*in[1];
136 
137 
138  out[2][0][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
139  out[2][0][1] = sign_[0]*(5*in[0]);
140 
141  out[2][1][0] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
142  out[2][1][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
143 
144 
145 
146  out[3][0][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
147  out[3][0][1] = sign_[1]*(-2*in[0]);
148 
149  out[3][1][0] = sign_[1]*(-2*in[1]);
150  out[3][1][1] = sign_[1]*(-2*in[0] + 2*in[1]);
151 
152 
153  out[4][0][0] = -10.5 + 15*in[1] + 15*in[0];
154  out[4][0][1] = -6 + 15*in[0];
155 
156  out[4][1][0] = -3*in[1];
157  out[4][1][1] = -1.5 - 3*in[0] + 9*in[1];
158 
159 
160  out[5][0][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
161  out[5][0][1] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
162 
163  out[5][1][0] = sign_[1]*(5*in[1]);
164  out[5][1][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
165 
166 
167 
168  out[6][0][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
169  out[6][0][1] = sign_[2]*(4*in[0]);
170 
171  out[6][1][0] = sign_[2]*(4*in[1]);
172  out[6][1][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
173 
174 
175  out[7][0][0] = -3 + 12*in[0];
176  out[7][0][1] = 0;
177 
178  out[7][1][0] = 0;
179  out[7][1][1] = 3 - 12*in[1];
180 
181 
182  out[8][0][0] = sign_[2]*(-10*in[1] + 10*in[0]);
183  out[8][0][1] = sign_[2]*(-10*in[0]);
184 
185  out[8][1][0] = sign_[2]*(-10*in[1]);
186  out[8][1][1] = sign_[2]*(-10*in[0] + 10*in[1]);
187 
188 
189  out[9][0][0] = 18 - 12*in[1] - 36*in[0];
190  out[9][0][1] = -12*in[0];
191 
192  out[9][1][0] = -12*in[1];
193  out[9][1][1] = 6 - 12*in[0] - 12*in[1];
194 
195  out[10][0][0] = 6 - 12*in[1] - 12*in[0];
196  out[10][0][1] = -12*in[0];
197 
198  out[10][1][0] = -12*in[1];
199  out[10][1][1] = 18 - 12*in[0] - 36*in[1];
200 
201  out[11][0][0] = 90 - 180*in[1] - 180*in[0];
202  out[11][0][1] = -180*in[0];
203 
204  out[11][1][0] = 180*in[1];
205  out[11][1][1] = -90 + 180*in[0] + 180*in[1];
206  }
207 
209  void partial (const std::array<unsigned int, 2>& order,
210  const typename Traits::DomainType& in, // position
211  std::vector<typename Traits::RangeType>& out) const // return value
212  {
213  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
214  if (totalOrder == 0) {
215  evaluateFunction(in, out);
216  } else if (totalOrder == 1) {
217  out.resize(size());
218  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
219 
220  switch (direction) {
221  case 0:
222  out[0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
223  out[0][1] = sign_[0]*(-2*in[1]);
224 
225  out[1][0] = 1.5 + 3*in[1] - 9*in[0];
226  out[1][1] = 6 - 15*in[1];
227 
228  out[2][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
229  out[2][1] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
230 
231  out[3][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
232  out[3][1] = sign_[1]*(-2*in[1]);
233 
234  out[4][0] = -10.5 + 15*in[1] + 15*in[0];
235  out[4][1] = -3*in[1];
236 
237  out[5][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
238  out[5][1] = sign_[1]*(5*in[1]);
239 
240  out[6][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
241  out[6][1] = sign_[2]*(4*in[1]);
242 
243  out[7][0] = -3 + 12*in[0];
244  out[7][1] = 0;
245 
246  out[8][0] = sign_[2]*(-10*in[1] + 10*in[0]);
247  out[8][1] = sign_[2]*(-10*in[1]);
248 
249  out[9][0] = 18 - 12*in[1] - 36*in[0];
250  out[9][1] = -12*in[1];
251 
252  out[10][0] = 6 - 12*in[1] - 12*in[0];
253  out[10][1] = -12*in[1];
254 
255  out[11][0] = 90 - 180*in[1] - 180*in[0];
256  out[11][1] = 180*in[1];
257  break;
258  case 1:
259  out[0][0] = sign_[0]*(-2*in[0]);
260  out[0][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
261 
262  out[1][0] = 3*in[0];
263  out[1][1] = 10.5 - 15*in[0] - 15*in[1];
264 
265  out[2][0] = sign_[0]*(5*in[0]);
266  out[2][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
267 
268  out[3][0] = sign_[1]*(-2*in[0]);
269  out[3][1] = sign_[1]*(-2*in[0] + 2*in[1]);
270 
271  out[4][0] = -6 + 15*in[0];
272  out[4][1] = -1.5 - 3*in[0] + 9*in[1];
273 
274  out[5][0] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
275  out[5][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
276 
277  out[6][0] = sign_[2]*(4*in[0]);
278  out[6][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
279 
280  out[7][0] = 0;
281  out[7][1] = 3 - 12*in[1];
282 
283  out[8][0] = sign_[2]*(-10*in[0]);
284  out[8][1] = sign_[2]*(-10*in[0] + 10*in[1]);
285 
286  out[9][0] = -12*in[0];
287  out[9][1] = 6 - 12*in[0] - 12*in[1];
288 
289  out[10][0] = -12*in[0];
290  out[10][1] = 18 - 12*in[0] - 36*in[1];
291 
292  out[11][0] = -180*in[0];
293  out[11][1] = -90 + 180*in[0] + 180*in[1];
294  break;
295  default:
296  DUNE_THROW(RangeError, "Component out of range.");
297  }
298  } else {
299  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
300  }
301  }
302 
304  unsigned int order() const
305  {
306  return 2; // TODO: check whether this is not order 3
307  }
308 
309  private:
310  std::array<R,3> sign_;
311  };
312 } // end namespace Dune
313 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
Dune::BDM2Simplex2DLocalBasis
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:28
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:119
Dune::BDM2Simplex2DLocalBasis::BDM2Simplex2DLocalBasis
BDM2Simplex2DLocalBasis(std::bitset< 3 > s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:47
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:209
Dune::BDM2Simplex2DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:54
Dune::BDM2Simplex2DLocalBasis::BDM2Simplex2DLocalBasis
BDM2Simplex2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:36
Dune::BDM2Simplex2DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:65
Dune::BDM2Simplex2DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:304
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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