dune-localfunctions  2.3.1-rc1
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 <vector>
7 #include <bitset>
8 
9 #include <dune/common/fmatrix.hh>
10 
11 #include "../../common/localbasis.hh"
12 
13 namespace Dune
14 {
25  template<class D, class R>
27  {
28 
29  public:
31  R,3,Dune::FieldVector<R,3>,
32  Dune::FieldMatrix<R,3,3> > Traits;
33 
36  {
37  for (size_t i=0; i<6; i++)
38  sign_[i] = 1.0;
39  }
40 
46  BDM1Cube3DLocalBasis(std::bitset<6> s)
47  {
48  for (size_t i=0; i<6; i++)
49  sign_[i] = s[i] ? -1.0 : 1.0;
50  }
51 
53  unsigned int size() const
54  {
55  return 18;
56  }
57 
64  inline void evaluateFunction(const typename Traits::DomainType& in,
65  std::vector<typename Traits::RangeType>& out) const
66  {
67  out.resize(size());
68 
69  out[0][0] = sign_[0] * (in[0] - 1.0);
70  out[0][1] = 0.0;
71  out[0][2] = 0.0;
72  out[1][0] = sign_[1] * in[0];
73  out[1][1] = 0.0;
74  out[1][2] = 0.0;
75  out[2][0] = 0.0;
76  out[2][1] = sign_[2] * (in[1] - 1.0);
77  out[2][2] = 0.0;
78  out[3][0] = 0.0;
79  out[3][1] = sign_[3] * in[1];
80  out[3][2] = 0.0;
81  out[4][0] = 0.0;
82  out[4][1] = 0.0;
83  out[4][2] = sign_[4] * (in[2] - 1.0);
84  out[5][0] = 0.0;
85  out[5][1] = 0.0;
86  out[5][2] = sign_[5] * in[2];
87  out[6][0] = 6.0 * in[0] * in[1] - 3 * in[0]-6 * in[1] + 3.0;
88  out[6][1] = -3.0 * in[1] * in[1] + 3 * in[1];
89  out[6][2] = 0.0;
90  out[7][0] = -6.0 * in[0] * in[1] + 3 * in[0];
91  out[7][1] = 3.0 * in[1] * in[1] - 3 * in[1];
92  out[7][2] = 0.0;
93  out[8][0] = 3.0 * in[0] * in[0] - 3 * in[0];
94  out[8][1] = -6.0 * in[0] * in[1] + 3 * in[1]+6 * in[0]-3.0;
95  out[8][2] = 0.0;
96  out[9][0] = -3.0 * in[0] * in[0] + 3 * in[0];
97  out[9][1] = 6.0 * in[0] * in[1] - 3 * in[1];
98  out[9][2] = 0.0;
99  out[10][0] = -3.0 * in[0] * in[0] + 3 * in[0];
100  out[10][1] = 0.0;
101  out[10][2] = 6.0 * in[0] * in[2]-6 * in[0]-3 * in[2] + 3.0;
102  out[11][0] = 3.0 * in[0] * in[0]-3 * in[0];
103  out[11][1] = 0.0;
104  out[11][2] = -6.0 * in[0] * in[2] + 3 * in[2];
105  out[12][0] = -6.0 * in[0] * in[2]+6 * in[2] + 3 * in[0]-3.0;
106  out[12][1] = 0.0;
107  out[12][2] = 3.0 * in[2] * in[2]-3 * in[2];
108  out[13][0] = -3 * in[0]+6 * in[0] * in[2];
109  out[13][1] = 0.0;
110  out[13][2] = -3.0 * in[2] * in[2] + 3 * in[2];
111  out[14][0] = 0.0;
112  out[14][1] = 6.0 * in[1] * in[2]-3 * in[1]-6 * in[2] + 3.0;
113  out[14][2] = -3 * in[2] * in[2] + 3 * in[2];
114  out[15][0] = 0.0;
115  out[15][1] = -6.0 * in[1] * in[2] + 3 * in[1];
116  out[15][2] = 3.0 * in[2] * in[2]-3 * in[2];
117  out[16][0] = 0.0;
118  out[16][1] = 3.0 * in[1] * in[1]-3 * in[1];
119  out[16][2] = -6.0 * in[1] * in[2] + 3 * in[2]+6 * in[1]-3.0;
120  out[17][0] = 0.0;
121  out[17][1] = -3.0 * in[1] * in[1] + 3 * in[1];
122  out[17][2] = 6.0 * in[1] * in[2] - 3.0 * in[2];
123  }
124 
131  inline void evaluateJacobian(const typename Traits::DomainType& in,
132  std::vector<typename Traits::JacobianType>& out) const
133  {
134  out.resize(size());
135 
136  out[0][0][0] = sign_[0]; out[0][0][1] = 0; out[0][0][2] = 0;
137  out[0][1][0] = 0; out[0][1][1] = 0; out[0][1][2] = 0;
138  out[0][2][0] = 0; out[0][2][1] = 0; out[0][2][2] = 0;
139 
140  out[1][0][0] = sign_[1]; out[1][0][1] = 0; out[1][0][2] = 0;
141  out[1][1][0] = 0; out[1][1][1] = 0; out[1][1][2] = 0;
142  out[1][2][0] = 0; out[1][2][1] = 0; out[1][2][2] = 0;
143 
144  out[2][0][0] = 0; out[2][0][1] = 0; out[2][0][2] = 0;
145  out[2][1][0] = 0; out[2][1][1] = sign_[2]; out[2][1][2] = 0;
146  out[2][2][0] = 0; out[2][2][1] = 0; out[2][2][2] = 0;
147 
148  out[3][0][0] = 0; out[3][0][1] = 0; out[3][0][2] = 0;
149  out[3][1][0] = 0; out[3][1][1] = sign_[3]; out[3][1][2] = 0;
150  out[3][2][0] = 0; out[3][2][1] = 0; out[3][2][2] = 0;
151 
152  out[4][0][0] = 0; out[4][0][1] = 0; out[4][0][2] = 0;
153  out[4][1][0] = 0; out[4][1][1] = 0; out[4][1][2] = 0;
154  out[4][2][0] = 0; out[4][2][1] = 0; out[4][2][2] = sign_[4];
155 
156  out[5][0][0] = 0; out[5][0][1] = 0; out[5][0][2] = 0;
157  out[5][1][0] = 0; out[5][1][1] = 0; out[5][1][2] = 0;
158  out[5][2][0] = 0; out[5][2][1] = 0; out[5][2][2] = sign_[5];
159 
160 
161 
162  out[6][0][0] = 6*in[1]-3; out[6][0][1] = 6*in[0]-6; out[6][0][2] = 0.0;
163  out[6][1][0] = 0.0; out[6][1][1] =-6*in[1]+3; out[6][1][2] = 0.0;
164  out[6][2][0] = 0.0; out[6][2][1] = 0.0; out[6][2][2] = 0.0;
165 
166  out[7][0][0] = -6*in[1]+3; out[7][0][1] =-6*in[0]; out[7][0][2] = 0.0;
167  out[7][1][0] = 0.0; out[7][1][1] = 6*in[1]-3; out[7][1][2] = 0.0;
168  out[7][2][0] = 0.0; out[7][2][1] = 0.0; out[7][2][2] = 0.0;
169 
170 
171  out[8][0][0] = 6*in[0]-3; out[8][0][1] = 0.0; out[8][0][2] = 0.0;
172  out[8][1][0] =-6*in[1]+6; out[8][1][1] =-6*in[0]+3; out[8][1][2] = 0.0;
173  out[8][2][0] = 0.0; out[8][2][1] = 0.0; out[8][2][2] = 0.0;
174 
175  out[9][0][0] = -6*in[0]+3; out[9][0][1] = 0.0; out[9][0][2] = 0.0;
176  out[9][1][0] = 6*in[1]; out[9][1][1] = 6*in[0]-3; out[9][1][2] = 0.0;
177  out[9][2][0] = 0.0; out[9][2][1] = 0.0; out[9][2][2] = 0.0;
178 
179  out[10][0][0] = -6*in[0]+3; out[10][0][1] = 0.0; out[10][0][2] = 0.0;
180  out[10][1][0] = 0.0; out[10][1][1] = 0.0; out[10][1][2] = 0.0;
181  out[10][2][0] =6*in[2]-6; out[10][2][1] = 0.0; out[10][2][2] =6*in[0]-3;
182 
183  out[11][0][0] =6*in[0]-3; out[11][0][1] = 0.0; out[11][0][2] = 0.0;
184  out[11][1][0] = 0.0; out[11][1][1] = 0.0; out[11][1][2] = 0.0;
185  out[11][2][0] = -6*in[2]; out[11][2][1] = 0.0; out[11][2][2] = -6*in[0]+3;
186 
187 
188  out[12][0][0] = -6*in[2]+3; out[12][0][1] =0.0; out[12][0][2] = -6*in[0]+6;
189  out[12][1][0] = 0.0; out[12][1][1] = 0.0; out[12][1][2] = 0.0;
190  out[12][2][0] = 0.0; out[12][2][1] = 0.0; out[12][2][2] =6*in[2]-3;
191 
192 
193  out[13][0][0] =6*in[2]-3; out[13][0][1] = 0.0; out[13][0][2] = 6*in[0];
194  out[13][1][0] = 0.0; out[13][1][1] = 0.0; out[13][1][2] = 0.0;
195  out[13][2][0] = 0.0; out[13][2][1] = 0.0; out[13][2][2] =-6*in[2]+3;
196 
197  out[14][0][0] = 0.0; out[14][0][1] = 0.0; out[14][0][2] = 0.0;
198  out[14][1][0] = 0.0; out[14][1][1] = 6*in[2]-3; out[14][1][2] = 6*in[1]-6;
199  out[14][2][0] = 0.0; out[14][2][1] = 0.0; out[14][2][2] =-6*in[2]+3;
200 
201  out[15][0][0] = 0.0; out[15][0][1] = 0.0; out[15][0][2] = 0.0;
202  out[15][1][0] = 0.0; out[15][1][1] =-6*in[2]+3; out[15][1][2] =-6*in[1];
203  out[15][2][0] = 0.0; out[15][2][1] = 0.0; out[15][2][2] = 6*in[2]-3;
204 
205  out[16][0][0] = 0.0; out[16][0][1] = 0.0; out[16][0][2] = 0.0;
206  out[16][1][0] = 0.0; out[16][1][1] = 6*in[1]-3; out[16][1][2] = 0.0;
207  out[16][2][0] = 0.0; out[16][2][1] =-6*in[2]+6; out[16][2][2] =-6*in[1]+3;
208 
209  out[17][0][0] = 0.0; out[17][0][1] = 0.0; out[17][0][2] = 0.0;
210  out[17][1][0] = 0.0; out[17][1][1] =-6*in[1]+3; out[17][1][2] = 0.0;
211  out[17][2][0] = 0.0; out[17][2][1] = 6*in[2]; out[17][2][2] = 6*in[1]-3;
212  }
213 
215  unsigned int order() const
216  {
217  return 2;
218  }
219 
220  private:
221  array<R,6> sign_;
222  };
223 } // end namespace Dune
224 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_CUBE3D_LOCALBASIS_HH
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:39
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:64
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:131
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:53
BDM1Cube3DLocalBasis(std::bitset< 6 > s)
Make set number s, where 0 <= s < 64.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:46
BDM1Cube3DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:35
First order Brezzi-Douglas-Marini shape functions on the reference hexahedron.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:26
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 3, Dune::FieldVector< R, 3 >, Dune::FieldMatrix< R, 3, 3 > > Traits
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:32
D DomainType
domain type
Definition: localbasis.hh:51
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini1cube3dlocalbasis.hh:215