dune-localfunctions  2.4.1
raviartthomas0cube3dall.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_RAVIARTTHOMAS0_CUBE3D_ALL_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE3D_ALL_HH
5 
6 #include <cstddef>
7 #include <vector>
8 
9 #include <dune/common/fmatrix.hh>
10 
13 
14 namespace Dune
15 {
24  template<class D, class R>
26  {
27  public:
28  typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,3,Dune::FieldVector<R,3>,
29  Dune::FieldMatrix<R,3,3> > Traits;
30 
33  {
34  sign0 = sign1 = sign2 = sign3 = sign4 = sign5 = 1.0;
35  }
36 
38  RT0Cube3DLocalBasis (unsigned int s)
39  {
40  sign0 = sign1 = sign2 = sign3 = sign4 = sign5 = 1.0;
41  if (s&1) sign0 = -1.0;
42  if (s&2) sign1 = -1.0;
43  if (s&4) sign2 = -1.0;
44  if (s&8) sign3 = -1.0;
45  if (s&16) sign4 = -1.0;
46  if (s&32) sign5 = -1.0;
47  }
48 
50  unsigned int size () const
51  {
52  return 6;
53  }
54 
56  inline void evaluateFunction (const typename Traits::DomainType& in,
57  std::vector<typename Traits::RangeType>& out) const
58  {
59  out.resize(6);
60  out[0][0] = sign0*(in[0]-1.0); out[0][1]=0.0; out[0][2]=0.0;
61  out[1][0] = sign1*(in[0]); out[1][1]=0.0; out[1][2]=0.0;
62  out[2][0] = 0.0; out[2][1]=sign2*(in[1]-1.0); out[2][2]=0.0;
63  out[3][0] = 0.0; out[3][1]=sign3*(in[1]); out[3][2]=0.0;
64  out[4][0] = 0.0; out[4][1]=0.0; out[4][2]=sign4*(in[2]-1.0);
65  out[5][0] = 0.0; out[5][1]=0.0; out[5][2]=sign5*(in[2]);
66  }
67 
69  inline void
70  evaluateJacobian (const typename Traits::DomainType& in, // position
71  std::vector<typename Traits::JacobianType>& out) const // return value
72  {
73  out.resize(6);
74  out[0][0][0] = sign0; out[0][0][1] = 0; out[0][0][2] = 0;
75  out[0][1][0] = 0; out[0][1][1] = 0; out[0][1][2] = 0;
76  out[0][2][0] = 0; out[0][2][1] = 0; out[0][2][2] = 0;
77 
78  out[1][0][0] = sign1; out[1][0][1] = 0; out[1][0][2] = 0;
79  out[1][1][0] = 0; out[1][1][1] = 0; out[1][1][2] = 0;
80  out[1][2][0] = 0; out[1][2][1] = 0; out[1][2][2] = 0;
81 
82  out[2][0][0] = 0; out[2][0][1] = 0; out[2][0][2] = 0;
83  out[2][1][0] = 0; out[2][1][1] = sign2; out[2][1][2] = 0;
84  out[2][2][0] = 0; out[2][2][1] = 0; out[2][2][2] = 0;
85 
86  out[3][0][0] = 0; out[3][0][1] = 0; out[3][0][2] = 0;
87  out[3][1][0] = 0; out[3][1][1] = sign3; out[3][1][2] = 0;
88  out[3][2][0] = 0; out[3][2][1] = 0; out[3][2][2] = 0;
89 
90  out[4][0][0] = 0; out[4][0][1] = 0; out[4][0][2] = 0;
91  out[4][1][0] = 0; out[4][1][1] = 0; out[4][1][2] = 0;
92  out[4][2][0] = 0; out[4][2][1] = 0; out[4][2][2] = sign4;
93 
94  out[5][0][0] = 0; out[5][0][1] = 0; out[5][0][2] = 0;
95  out[5][1][0] = 0; out[5][1][1] = 0; out[5][1][2] = 0;
96  out[5][2][0] = 0; out[5][2][1] = 0; out[5][2][2] = sign5;
97  }
98 
100  unsigned int order () const
101  {
102  return 1;
103  }
104 
105  private:
106  R sign0, sign1, sign2, sign3, sign4, sign5;
107  };
108 
109 
117  template<class LB>
119  {
120  public:
121 
124  {
125  sign0 = sign1 = sign2 = sign3 = sign4 = sign5 = 1.0;
126  }
127 
130  {
131  sign0 = sign1 = sign2 = sign3 = sign4 = sign5 = 1.0;
132  if (s&1) sign0 *= -1.0;
133  if (s&2) sign1 *= -1.0;
134  if (s&4) sign2 *= -1.0;
135  if (s&8) sign3 *= -1.0;
136  if (s&16) sign4 *= -1.0;
137  if (s&32) sign5 *= -1.0;
138 
139  m0[0] = 0.0; m0[1] = 0.5; m0[2] = 0.5;
140  m1[0] = 1.0; m1[1] = 0.5; m1[2] = 0.5;
141  m2[0] = 0.5; m2[1] = 0.0; m2[2] = 0.5;
142  m3[0] = 0.5; m3[1] = 1.0; m3[2] = 0.5;
143  m4[0] = 0.5; m4[1] = 0.5; m4[2] = 0.0;
144  m5[0] = 0.5; m5[1] = 0.5; m5[2] = 1.0;
145 
146  n0[0] = -1.0; n0[1] = 0.0; n0[2] = 0.0;
147  n1[0] = 1.0; n1[1] = 0.0; n1[2] = 0.0;
148  n2[0] = 0.0; n2[1] = -1.0; n2[2] = 0.0;
149  n3[0] = 0.0; n3[1] = 1.0; n3[2] = 0.0;
150  n4[0] = 0.0; n4[1] = 0.0; n4[2] =-1.0;
151  n5[0] = 0.0; n5[1] = 0.0; n5[2] = 1.0;
152  }
153 
154  template<typename F, typename C>
155  void interpolate (const F& f, std::vector<C>& out) const
156  {
157  // f gives v*outer normal at a point on the edge!
158  typename F::Traits::RangeType y;
159 
160  out.resize(6);
161 
162  f.evaluate(m0,y); out[0] = (y[0]*n0[0]+y[1]*n0[1]+y[2]*n0[2])*sign0;
163  f.evaluate(m1,y); out[1] = (y[0]*n1[0]+y[1]*n1[1]+y[2]*n1[2])*sign1;
164  f.evaluate(m2,y); out[2] = (y[0]*n2[0]+y[1]*n2[1]+y[2]*n2[2])*sign2;
165  f.evaluate(m3,y); out[3] = (y[0]*n3[0]+y[1]*n3[1]+y[2]*n3[2])*sign3;
166  f.evaluate(m4,y); out[4] = (y[0]*n4[0]+y[1]*n4[1]+y[2]*n4[2])*sign4;
167  f.evaluate(m5,y); out[5] = (y[0]*n5[0]+y[1]*n5[1]+y[2]*n5[2])*sign5;
168  }
169 
170  private:
171  typename LB::Traits::RangeFieldType sign0,sign1,sign2,sign3,sign4,sign5;
172  typename LB::Traits::DomainType m0,m1,m2,m3,m4,m5;
173  typename LB::Traits::DomainType n0,n1,n2,n3,n4,n5;
174  };
175 
183  {
184  public:
187  {
188  for (std::size_t i=0; i<6; i++)
189  li[i] = LocalKey(i,1,0);
190  }
191 
193  std::size_t size () const
194  {
195  return 6;
196  }
197 
199  const LocalKey& localKey (std::size_t i) const
200  {
201  return li[i];
202  }
203 
204  private:
205  std::vector<LocalKey> li;
206  };
207 
208 }
209 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE3D_ALL_HH
std::size_t size() const
number of coefficients
Definition: raviartthomas0cube3dall.hh:193
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas0cube3dall.hh:56
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas0cube3dall.hh:70
RT0Cube3DLocalInterpolation()
Standard constructor.
Definition: raviartthomas0cube3dall.hh:123
const LocalKey & localKey(std::size_t i) const
get i&#39;th index
Definition: raviartthomas0cube3dall.hh:199
RT0Cube3DLocalBasis()
Standard constructor.
Definition: raviartthomas0cube3dall.hh:32
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 3, Dune::FieldVector< R, 3 >, Dune::FieldMatrix< R, 3, 3 > > Traits
Definition: raviartthomas0cube3dall.hh:29
RT0Cube3DLocalCoefficients()
Standard constructor.
Definition: raviartthomas0cube3dall.hh:186
Describe position of one degree of freedom.
Definition: localkey.hh:21
void interpolate(const F &f, std::vector< C > &out) const
Definition: raviartthomas0cube3dall.hh:155
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:14
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas0cube3dall.hh:100
RT0Cube3DLocalBasis(unsigned int s)
Make set numer s, where 0<=s<64.
Definition: raviartthomas0cube3dall.hh:38
Layout map for RT0 elements on quadrilaterals.
Definition: raviartthomas0cube3dall.hh:182
unsigned int size() const
number of shape functions
Definition: raviartthomas0cube3dall.hh:50
RT0Cube3DLocalInterpolation(unsigned int s)
Make set numer s, where 0<=s<64.
Definition: raviartthomas0cube3dall.hh:129
D DomainType
domain type
Definition: localbasis.hh:49
Lowest order Raviart-Thomas shape functions on the reference hexahedron.
Definition: raviartthomas0cube3dall.hh:118
Lowest order Raviart-Thomas shape functions on the reference hexahedron.
Definition: raviartthomas0cube3dall.hh:25