Dune Core Modules (2.7.1)

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;
73  out[0][2] = 0;
74  out[1][0] = sign_[1] * in[0];
75  out[1][1] = 0;
76  out[1][2] = 0;
77  out[2][0] = 0;
78  out[2][1] = sign_[2] * (in[1] - 1.0);
79  out[2][2] = 0;
80  out[3][0] = 0;
81  out[3][1] = sign_[3] * in[1];
82  out[3][2] = 0;
83  out[4][0] = 0;
84  out[4][1] = 0;
85  out[4][2] = sign_[4] * (in[2] - 1.0);
86  out[5][0] = 0;
87  out[5][1] = 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;
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;
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;
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;
101  out[10][0] = -3.0 * in[0] * in[0] + 3 * in[0];
102  out[10][1] = 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;
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;
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;
112  out[13][2] = -3.0 * in[2] * in[2] + 3 * in[2];
113  out[14][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;
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;
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;
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] = { sign_[0], 0, 0};
139  out[0][1] = { 0, 0, 0};
140  out[0][2] = { 0, 0, 0};
141 
142  out[1][0] = { sign_[1], 0, 0};
143  out[1][1] = { 0, 0, 0};
144  out[1][2] = { 0, 0, 0};
145 
146  out[2][0] = { 0, 0, 0};
147  out[2][1] = { 0, sign_[2], 0};
148  out[2][2] = { 0, 0, 0};
149 
150  out[3][0] = { 0, 0, 0};
151  out[3][1] = { 0, sign_[3], 0};
152  out[3][2] = { 0, 0, 0};
153 
154  out[4][0] = { 0, 0, 0};
155  out[4][1] = { 0, 0, 0};
156  out[4][2] = { 0, 0, sign_[4]};
157 
158  out[5][0] = { 0, 0, 0};
159  out[5][1] = { 0, 0, 0};
160  out[5][2] = { 0, 0, sign_[5]};
161 
162  out[6][0] = { 6*in[1]-3, 6*in[0]-6, 0};
163  out[6][1] = { 0, -6*in[1]+3, 0};
164  out[6][2] = { 0, 0, 0};
165 
166  out[7][0] = {-6*in[1]+3, -6*in[0], 0};
167  out[7][1] = { 0, 6*in[1]-3, 0};
168  out[7][2] = { 0, 0, 0};
169 
170  out[8][0] = { 6*in[0]-3, 0, 0};
171  out[8][1] = {-6*in[1]+6, -6*in[0]+3, 0};
172  out[8][2] = { 0, 0, 0};
173 
174  out[9][0] = {-6*in[0]+3, 0, 0};
175  out[9][1] = { 6*in[1], 6*in[0]-3, 0};
176  out[9][2] = { 0, 0, 0};
177 
178  out[10][0] = {-6*in[0]+3, 0, 0};
179  out[10][1] = { 0, 0, 0};
180  out[10][2] = { 6*in[2]-6, 0, 6*in[0]-3};
181 
182  out[11][0] = { 6*in[0]-3, 0, 0};
183  out[11][1] = { 0, 0, 0};
184  out[11][2] = { -6*in[2], 0, -6*in[0]+3};
185 
186  out[12][0] = {-6*in[2]+3, 0, -6*in[0]+6};
187  out[12][1] = { 0, 0, 0};
188  out[12][2] = { 0, 0, 6*in[2]-3};
189 
190  out[13][0] = { 6*in[2]-3, 0, 6*in[0]};
191  out[13][1] = { 0, 0, 0};
192  out[13][2] = { 0, 0, -6*in[2]+3};
193 
194  out[14][0] = { 0, 0, 0};
195  out[14][1] = { 0, 6*in[2]-3, 6*in[1]-6};
196  out[14][2] = { 0, 0, -6*in[2]+3};
197 
198  out[15][0] = { 0, 0, 0};
199  out[15][1] = { 0, -6*in[2]+3, -6*in[1]};
200  out[15][2] = { 0, 0, 6*in[2]-3};
201 
202  out[16][0] = { 0, 0, 0};
203  out[16][1] = { 0, 6*in[1]-3, 0};
204  out[16][2] = { 0, -6*in[2]+6, -6*in[1]+3};
205 
206  out[17][0] = { 0, 0, 0};
207  out[17][1] = { 0, -6*in[1]+3, 0};
208  out[17][2] = { 0, 6*in[2], 6*in[1]-3};
209  }
210 
212  void partial (const std::array<unsigned int, 3>& order,
213  const typename Traits::DomainType& in, // position
214  std::vector<typename Traits::RangeType>& out) const // return value
215  {
216  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
217  if (totalOrder == 0) {
218  evaluateFunction(in, out);
219  } else if (totalOrder == 1) {
220  out.resize(size());
221  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
222 
223  switch (direction) {
224  case 0:
225  out[0] = { sign_[0], 0, 0};
226  out[1] = { sign_[1], 0, 0};
227  out[2] = { 0, 0, 0};
228  out[3] = { 0, 0, 0};
229  out[4] = { 0, 0, 0};
230  out[5] = { 0, 0, 0};
231  out[6] = { 6*in[1]-3, 0, 0};
232  out[7] = {-6*in[1]+3, 0, 0};
233  out[8] = { 6*in[0]-3, -6*in[1]+6, 0};
234  out[9] = {-6*in[0]+3, 6*in[1], 0};
235  out[10] = {-6*in[0]+3, 0, 6*in[2]-6};
236  out[11] = { 6*in[0]-3, 0, -6*in[2]};
237  out[12] = {-6*in[2]+3, 0, 0};
238  out[13] = { 6*in[2]-3, 0, 0};
239  out[14] = { 0, 0, 0};
240  out[15] = { 0, 0, 0};
241  out[16] = { 0, 0, 0};
242  out[17] = { 0, 0, 0};
243  break;
244  case 1:
245  out[0] = { 0, 0, 0};
246  out[1] = { 0, 0, 0};
247  out[2] = { 0, sign_[2], 0};
248  out[3] = { 0, sign_[3], 0};
249  out[4] = { 0, 0, 0};
250  out[5] = { 0, 0, 0};
251  out[6] = { 6*in[0]-6, -6*in[1]+3, 0};
252  out[7] = { -6*in[0], 6*in[1]-3, 0};
253  out[8] = { 0, -6*in[0]+3, 0};
254  out[9] = { 0, 6*in[0]-3, 0};
255  out[10] = { 0, 0, 0};
256  out[11] = { 0, 0, 0};
257  out[12] = { 0, 0, 0};
258  out[13] = { 0, 0, 0};
259  out[14] = { 0, 6*in[2]-3, 0};
260  out[15] = { 0, -6*in[2]+3, 0};
261  out[16] = { 0, 6*in[1]-3, -6*in[2]+6};
262  out[17] = { 0, -6*in[1]+3, 6*in[2]};
263  break;
264  case 2:
265  out[0] = { 0, 0, 0};
266  out[1] = { 0, 0, 0};
267  out[2] = { 0, 0, 0};
268  out[3] = { 0, 0, 0};
269  out[4] = { 0, 0, sign_[4]};
270  out[5] = { 0, 0, sign_[5]};
271  out[6] = { 0, 0, 0};
272  out[7] = { 0, 0, 0};
273  out[8] = { 0, 0, 0};
274  out[9] = { 0, 0, 0};
275  out[10] = { 0, 0, 6*in[0]-3};
276  out[11] = { 0, 0, -6*in[0]+3};
277  out[12] = {-6*in[0]+6, 0, 6*in[2]-3};
278  out[13] = { 6*in[0], 0, -6*in[2]+3};
279  out[14] = { 0, 6*in[1]-6, -6*in[2]+3};
280  out[15] = { 0, -6*in[1], 6*in[2]-3};
281  out[16] = { 0, 0, -6*in[1]+3};
282  out[17] = { 0, 0, 6*in[1]-3};
283  break;
284  default:
285  DUNE_THROW(RangeError, "Component out of range.");
286  }
287  } else {
288  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
289  }
290  }
291 
293  unsigned int order() const
294  {
295  return 2;
296  }
297 
298  private:
299  std::array<R,6> sign_;
300  };
301 } // end namespace Dune
302 #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:212
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:293
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: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::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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