dune-localfunctions  2.4.1-rc2
brezzidouglasmarini1cube3dlocalbasis.hh
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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 <vector>
8 #include <bitset>
9 
10 #include <dune/common/fmatrix.hh>
11 
12 #include "../../common/localbasis.hh"
13 
14 namespace Dune
15 {
26  template<class D, class R>
28  {
29 
30  public:
32  R,3,Dune::FieldVector<R,3>,
33  Dune::FieldMatrix<R,3,3> > Traits;
34 
37  {
38  for (size_t i=0; i<6; i++)
39  sign_[i] = 1.0;
40  }
41 
47  BDM1Cube3DLocalBasis(std::bitset<6> s)
48  {
49  for (size_t i=0; i<6; i++)
50  sign_[i] = s[i] ? -1.0 : 1.0;
51  }
52 
54  unsigned int size() const
55  {
56  return 18;
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] * (in[0] - 1.0);
71  out[0][1] = 0.0;
72  out[0][2] = 0.0;
73  out[1][0] = sign_[1] * in[0];
74  out[1][1] = 0.0;
75  out[1][2] = 0.0;
76  out[2][0] = 0.0;
77  out[2][1] = sign_[2] * (in[1] - 1.0);
78  out[2][2] = 0.0;
79  out[3][0] = 0.0;
80  out[3][1] = sign_[3] * in[1];
81  out[3][2] = 0.0;
82  out[4][0] = 0.0;
83  out[4][1] = 0.0;
84  out[4][2] = sign_[4] * (in[2] - 1.0);
85  out[5][0] = 0.0;
86  out[5][1] = 0.0;
87  out[5][2] = sign_[5] * in[2];
88  out[6][0] = 6.0 * in[0] * in[1] - 3 * in[0]-6 * in[1] + 3.0;
89  out[6][1] = -3.0 * in[1] * in[1] + 3 * in[1];
90  out[6][2] = 0.0;
91  out[7][0] = -6.0 * in[0] * in[1] + 3 * in[0];
92  out[7][1] = 3.0 * in[1] * in[1] - 3 * in[1];
93  out[7][2] = 0.0;
94  out[8][0] = 3.0 * in[0] * in[0] - 3 * in[0];
95  out[8][1] = -6.0 * in[0] * in[1] + 3 * in[1]+6 * in[0]-3.0;
96  out[8][2] = 0.0;
97  out[9][0] = -3.0 * in[0] * in[0] + 3 * in[0];
98  out[9][1] = 6.0 * in[0] * in[1] - 3 * in[1];
99  out[9][2] = 0.0;
100  out[10][0] = -3.0 * in[0] * in[0] + 3 * in[0];
101  out[10][1] = 0.0;
102  out[10][2] = 6.0 * in[0] * in[2]-6 * in[0]-3 * in[2] + 3.0;
103  out[11][0] = 3.0 * in[0] * in[0]-3 * in[0];
104  out[11][1] = 0.0;
105  out[11][2] = -6.0 * in[0] * in[2] + 3 * in[2];
106  out[12][0] = -6.0 * in[0] * in[2]+6 * in[2] + 3 * in[0]-3.0;
107  out[12][1] = 0.0;
108  out[12][2] = 3.0 * in[2] * in[2]-3 * in[2];
109  out[13][0] = -3 * in[0]+6 * in[0] * in[2];
110  out[13][1] = 0.0;
111  out[13][2] = -3.0 * in[2] * in[2] + 3 * in[2];
112  out[14][0] = 0.0;
113  out[14][1] = 6.0 * in[1] * in[2]-3 * in[1]-6 * in[2] + 3.0;
114  out[14][2] = -3 * in[2] * in[2] + 3 * in[2];
115  out[15][0] = 0.0;
116  out[15][1] = -6.0 * in[1] * in[2] + 3 * in[1];
117  out[15][2] = 3.0 * in[2] * in[2]-3 * in[2];
118  out[16][0] = 0.0;
119  out[16][1] = 3.0 * in[1] * in[1]-3 * in[1];
120  out[16][2] = -6.0 * in[1] * in[2] + 3 * in[2]+6 * in[1]-3.0;
121  out[17][0] = 0.0;
122  out[17][1] = -3.0 * in[1] * in[1] + 3 * in[1];
123  out[17][2] = 6.0 * in[1] * in[2] - 3.0 * in[2];
124  }
125 
132  inline void evaluateJacobian(const typename Traits::DomainType& in,
133  std::vector<typename Traits::JacobianType>& out) const
134  {
135  out.resize(size());
136 
137  out[0][0][0] = sign_[0]; out[0][0][1] = 0; out[0][0][2] = 0;
138  out[0][1][0] = 0; out[0][1][1] = 0; out[0][1][2] = 0;
139  out[0][2][0] = 0; out[0][2][1] = 0; out[0][2][2] = 0;
140 
141  out[1][0][0] = sign_[1]; out[1][0][1] = 0; out[1][0][2] = 0;
142  out[1][1][0] = 0; out[1][1][1] = 0; out[1][1][2] = 0;
143  out[1][2][0] = 0; out[1][2][1] = 0; out[1][2][2] = 0;
144 
145  out[2][0][0] = 0; out[2][0][1] = 0; out[2][0][2] = 0;
146  out[2][1][0] = 0; out[2][1][1] = sign_[2]; out[2][1][2] = 0;
147  out[2][2][0] = 0; out[2][2][1] = 0; out[2][2][2] = 0;
148 
149  out[3][0][0] = 0; out[3][0][1] = 0; out[3][0][2] = 0;
150  out[3][1][0] = 0; out[3][1][1] = sign_[3]; out[3][1][2] = 0;
151  out[3][2][0] = 0; out[3][2][1] = 0; out[3][2][2] = 0;
152 
153  out[4][0][0] = 0; out[4][0][1] = 0; out[4][0][2] = 0;
154  out[4][1][0] = 0; out[4][1][1] = 0; out[4][1][2] = 0;
155  out[4][2][0] = 0; out[4][2][1] = 0; out[4][2][2] = sign_[4];
156 
157  out[5][0][0] = 0; out[5][0][1] = 0; out[5][0][2] = 0;
158  out[5][1][0] = 0; out[5][1][1] = 0; out[5][1][2] = 0;
159  out[5][2][0] = 0; out[5][2][1] = 0; out[5][2][2] = sign_[5];
160 
161 
162 
163  out[6][0][0] = 6*in[1]-3; out[6][0][1] = 6*in[0]-6; out[6][0][2] = 0.0;
164  out[6][1][0] = 0.0; out[6][1][1] =-6*in[1]+3; out[6][1][2] = 0.0;
165  out[6][2][0] = 0.0; out[6][2][1] = 0.0; out[6][2][2] = 0.0;
166 
167  out[7][0][0] = -6*in[1]+3; out[7][0][1] =-6*in[0]; out[7][0][2] = 0.0;
168  out[7][1][0] = 0.0; out[7][1][1] = 6*in[1]-3; out[7][1][2] = 0.0;
169  out[7][2][0] = 0.0; out[7][2][1] = 0.0; out[7][2][2] = 0.0;
170 
171 
172  out[8][0][0] = 6*in[0]-3; out[8][0][1] = 0.0; out[8][0][2] = 0.0;
173  out[8][1][0] =-6*in[1]+6; out[8][1][1] =-6*in[0]+3; out[8][1][2] = 0.0;
174  out[8][2][0] = 0.0; out[8][2][1] = 0.0; out[8][2][2] = 0.0;
175 
176  out[9][0][0] = -6*in[0]+3; out[9][0][1] = 0.0; out[9][0][2] = 0.0;
177  out[9][1][0] = 6*in[1]; out[9][1][1] = 6*in[0]-3; out[9][1][2] = 0.0;
178  out[9][2][0] = 0.0; out[9][2][1] = 0.0; out[9][2][2] = 0.0;
179 
180  out[10][0][0] = -6*in[0]+3; out[10][0][1] = 0.0; out[10][0][2] = 0.0;
181  out[10][1][0] = 0.0; out[10][1][1] = 0.0; out[10][1][2] = 0.0;
182  out[10][2][0] =6*in[2]-6; out[10][2][1] = 0.0; out[10][2][2] =6*in[0]-3;
183 
184  out[11][0][0] =6*in[0]-3; out[11][0][1] = 0.0; out[11][0][2] = 0.0;
185  out[11][1][0] = 0.0; out[11][1][1] = 0.0; out[11][1][2] = 0.0;
186  out[11][2][0] = -6*in[2]; out[11][2][1] = 0.0; out[11][2][2] = -6*in[0]+3;
187 
188 
189  out[12][0][0] = -6*in[2]+3; out[12][0][1] =0.0; out[12][0][2] = -6*in[0]+6;
190  out[12][1][0] = 0.0; out[12][1][1] = 0.0; out[12][1][2] = 0.0;
191  out[12][2][0] = 0.0; out[12][2][1] = 0.0; out[12][2][2] =6*in[2]-3;
192 
193 
194  out[13][0][0] =6*in[2]-3; out[13][0][1] = 0.0; out[13][0][2] = 6*in[0];
195  out[13][1][0] = 0.0; out[13][1][1] = 0.0; out[13][1][2] = 0.0;
196  out[13][2][0] = 0.0; out[13][2][1] = 0.0; out[13][2][2] =-6*in[2]+3;
197 
198  out[14][0][0] = 0.0; out[14][0][1] = 0.0; out[14][0][2] = 0.0;
199  out[14][1][0] = 0.0; out[14][1][1] = 6*in[2]-3; out[14][1][2] = 6*in[1]-6;
200  out[14][2][0] = 0.0; out[14][2][1] = 0.0; out[14][2][2] =-6*in[2]+3;
201 
202  out[15][0][0] = 0.0; out[15][0][1] = 0.0; out[15][0][2] = 0.0;
203  out[15][1][0] = 0.0; out[15][1][1] =-6*in[2]+3; out[15][1][2] =-6*in[1];
204  out[15][2][0] = 0.0; out[15][2][1] = 0.0; out[15][2][2] = 6*in[2]-3;
205 
206  out[16][0][0] = 0.0; out[16][0][1] = 0.0; out[16][0][2] = 0.0;
207  out[16][1][0] = 0.0; out[16][1][1] = 6*in[1]-3; out[16][1][2] = 0.0;
208  out[16][2][0] = 0.0; out[16][2][1] =-6*in[2]+6; out[16][2][2] =-6*in[1]+3;
209 
210  out[17][0][0] = 0.0; out[17][0][1] = 0.0; out[17][0][2] = 0.0;
211  out[17][1][0] = 0.0; out[17][1][1] =-6*in[1]+3; out[17][1][2] = 0.0;
212  out[17][2][0] = 0.0; out[17][2][1] = 6*in[2]; out[17][2][2] = 6*in[1]-3;
213  }
214 
216  unsigned int order() const
217  {
218  return 2;
219  }
220 
221  private:
222  std::array<R,6> sign_;
223  };
224 } // end namespace Dune
225 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_CUBE3D_LOCALBASIS_HH
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:216
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
BDM1Cube3DLocalBasis(std::bitset< 6 > s)
Make set number s, where 0 <= s < 64.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:47
First order Brezzi-Douglas-Marini shape functions on the reference hexahedron.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:27
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:14
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:65
BDM1Cube3DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:36
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:132
D DomainType
domain type
Definition: localbasis.hh:49
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 3, Dune::FieldVector< R, 3 >, Dune::FieldMatrix< R, 3, 3 > > Traits
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:33
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:54