dune-localfunctions  2.4.1-rc2
brezzidouglasmarini2cube2dlocalbasis.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_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_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 {
25  template<class D, class R>
27  {
28 
29  public:
31  R,2,Dune::FieldVector<R,2>,
32  Dune::FieldMatrix<R,2,2> > Traits;
33 
36  {
37  for (size_t i=0; i<4; i++)
38  sign_[i] = 1.0;
39  }
40 
46  BDM2Cube2DLocalBasis(std::bitset<4> s)
47  {
48  for (size_t i=0; i<4; i++)
49  sign_[i] = s[i] ? -1.0 : 1.0;
50  }
51 
53  unsigned int size() const
54  {
55  return 14;
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]*(-2.25 + 5.25*in[0] + 7.5*in[1] - 7.5*in[0]*in[1] - 3.0*in[0]*in[0] - 7.5*in[1]*in[1] + 7.5*in[0]*in[1]*in[1]);
70  out[0][1] = sign_[0]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
71  out[1][0] = 3.0 - 3.0*in[0]-6.0*in[1] + 6.0*in[0]*in[1];
72  out[1][1] = 0.0;
73  out[2][0] = sign_[0]*(-3.75 + 3.75*in[0] + 22.5*in[1] - 22.5*in[0]*in[1] - 22.5*in[1]*in[1] + 22.5*in[0]*in[1]*in[1]);
74  out[2][1] = sign_[0]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
75  out[3][0] = sign_[1]*(-0.75*in[0] - 7.5*in[0]*in[1] + 3.0*in[0]*in[0] + 7.5*in[0]*in[1]*in[1]);
76  out[3][1] = sign_[1]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
77  out[4][0] = 3.0*in[0] - 6.0*in[0]*in[1];
78  out[4][1] = 0.0;
79  out[5][0] = sign_[1]*(+3.75*in[0] - 22.5*in[0]*in[1] + 22.5*in[0]*in[1]*in[1]);
80  out[5][1] = sign_[1]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
81  out[6][0] = sign_[2]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
82  out[6][1] = sign_[2]*(-2.25 + 7.5*in[0] + 5.25*in[1] - 7.5*in[0]*in[1] - 7.5*in[0]*in[0] - 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
83  out[7][0] = 0.0;
84  out[7][1] = -3.0 + 6.0*in[0] + 3.0*in[1] - 6.0*in[0]*in[1];
85  out[8][0] = sign_[2]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
86  out[8][1] = sign_[2]*(-3.75 + 22.5*in[0] + 3.75*in[1] - 22.5*in[0]*in[1] - 22.5*in[0]*in[0] + 22.5*in[0]*in[0]*in[1]);
87  out[9][0] = sign_[3]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
88  out[9][1] = sign_[3]*(-0.75*in[1] - 7.5*in[0]*in[1] + 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
89  out[10][0] = 0.0;
90  out[10][1] = -3.0*in[1] + 6.0*in[0]*in[1];
91  out[11][0] = sign_[3]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
92  out[11][1] = sign_[3]*(3.75*in[1] - 22.5*in[0]*in[1] + 22.5*in[0]*in[0]*in[1]);
93  out[12][0] = 6.0*in[0] - 6.0*in[0]*in[0];
94  out[12][1] = 0.0;
95  out[13][0] = 0.0;
96  out[13][1] = 6.0*in[1] - 6.0*in[1]*in[1];
97  }
98 
105  inline void evaluateJacobian(const typename Traits::DomainType& in,
106  std::vector<typename Traits::JacobianType>& out) const
107  {
108  out.resize(size());
109 
110  out[0][0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
111  out[0][0][1] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
112  out[0][1][0] = 0.0;
113  out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
114 
115  out[1][0][0] = -3.0 + 6.0*in[1];
116  out[1][0][1] = -6.0 + 6.0*in[0];
117  out[1][1][0] = 0.0;
118  out[1][1][1] = 0.0;
119 
120  out[2][0][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
121  out[2][0][1] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
122  out[2][1][0] = 0.0;
123  out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
124 
125  out[3][0][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
126  out[3][0][1] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
127  out[3][1][0] = 0.0;
128  out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
129 
130  out[4][0][0] = 3.0 - 6.0*in[1];
131  out[4][0][1] = -6.0*in[0];
132  out[4][1][0] = 0.0;
133  out[4][1][1] = 0.0;
134 
135  out[5][0][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
136  out[5][0][1] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
137  out[5][1][0] = 0.0;
138  out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
139 
140  out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
141  out[6][0][1] = 0.0;
142  out[6][1][0] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
143  out[6][1][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
144 
145  out[7][0][0] = 0.0;
146  out[7][0][1] = 0.0;
147  out[7][1][0] = 6.0 - 6.0*in[1];
148  out[7][1][1] = 3.0 - 6.0*in[0];
149 
150  out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
151  out[8][0][1] = 0.0;
152  out[8][1][0] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
153  out[8][1][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
154 
155  out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
156  out[9][0][1] = 0.0;
157  out[9][1][0] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
158  out[9][1][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
159 
160  out[10][0][0] = 0.0;
161  out[10][0][1] = 0.0;
162  out[10][1][0] = 6.0*in[1];
163  out[10][1][1] = -3.0 + 6.0*in[0];
164 
165  out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
166  out[11][0][1] = 0.0;
167  out[11][1][0] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
168  out[11][1][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
169 
170  out[12][0][0] = 6.0 - 12.0*in[0];
171  out[12][0][1] = 0.0;
172  out[12][1][0] = 0.0;
173  out[12][1][1] = 0.0;
174 
175  out[13][0][0] = 0.0;
176  out[13][0][1] = 0.0;
177  out[13][1][0] = 0.0;
178  out[13][1][1] = 6.0 - 12.0*in[1];
179  }
180 
182  unsigned int order() const
183  {
184  return 3;
185  }
186 
187  private:
188  std::array<R,4> sign_;
189  };
190 } // end namespace Dune
191 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:26
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:182
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 2, Dune::FieldVector< R, 2 >, Dune::FieldMatrix< R, 2, 2 > > Traits
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:32
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:53
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:64
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
BDM2Cube2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:35
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:105
D DomainType
domain type
Definition: localbasis.hh:49
BDM2Cube2DLocalBasis(std::bitset< 4 > s)
Make set number s, where 0 <= s < 16.
Definition: brezzidouglasmarini2cube2dlocalbasis.hh:46