dune-localfunctions  2.3.1
hierarchicalprismp2localbasis.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_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
4 #define DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
5 
10 #include <dune/common/fvector.hh>
11 #include <dune/common/fmatrix.hh>
12 
14 
15 namespace Dune
16 {
17  template<class D, class R>
19  {
20  public:
22  typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,3> > Traits;
23 
25  unsigned int size () const
26  {
27  return 18;
28  }
29 
31  void evaluateFunction (const typename Traits::DomainType& in,
32  std::vector<typename Traits::RangeType> & out) const
33  {
34  out.resize(18);
35 
36  out[0]=(1.0-in[0]-in[1])*(1.0-in[2]);
37  out[1]= in[0]*(1-in[2]);
38  out[2]=in[1]*(1-in[2]);
39  out[3]=in[2]*(1.0-in[0]-in[1]);
40  out[4]=in[0]*in[2];
41  out[5]=in[1]*in[2];
42 
43  //edges
44  out[6]=2*(1.0-in[0]-in[1])*(0.5-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
45  out[7]=2*in[0]*(-0.5+in[0])*(4*in[2]-4*in[2]*in[2]);
46  out[8]=2*in[1]*(-0.5+in[1])*(4*in[2]-4*in[2]*in[2]);
47  out[9]=4*in[0]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
48  out[10]=4*in[1]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
49  out[11]=4*in[0]*in[1]*(1-3*in[2]+2*in[2]*in[2]);
50  out[12]=4*in[0]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
51  out[13]=4*in[1]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
52  out[14]=4*in[0]*in[1]*(-in[2]+2*in[2]*in[2]);
53 
54  //faces
55  out[15]=4*in[0]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
56  out[16]=4*in[1]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
57  out[17]=4*in[0]*in[1]*(4*in[2]-4*in[2]*in[2]);
58  }
59 
60 
61 
63  void evaluateJacobian (const typename Traits::DomainType& in, //position
64  std::vector<typename Traits::JacobianType>& out) const //return value
65  {
66  out.resize(18);
67 
68  //vertices
69  out[0][0][0] = in[2]-1;
70  out[0][0][1] = in[2]-1;
71  out[0][0][2] = in[0]+in[1]-1;
72 
73  out[1][0][0] = 1-in[2];
74  out[1][0][1] = 0;
75  out[1][0][2] =-in[0];
76 
77  out[2][0][0] = 0;
78  out[2][0][1] = 1-in[2];
79  out[2][0][2] = -in[1];
80 
81  out[3][0][0] = -in[2];
82  out[3][0][1] = -in[2];
83  out[3][0][2] = 1-in[0]-in[1];
84 
85  out[4][0][0] = in[2];
86  out[4][0][1] = 0;
87  out[4][0][2] = in[0];
88 
89  out[5][0][0] = 0;
90  out[5][0][1] = in[2];
91  out[5][0][2] = in[1];
92 
93  //edges
94  out[6][0][0] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
95  out[6][0][1] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
96  out[6][0][2] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
97 
98  out[7][0][0] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
99  out[7][0][1] = 0;
100  out[7][0][2] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
101 
102  out[8][0][0] = 0;
103  out[8][0][1] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
104  out[8][0][2] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
105 
106  out[9][0][0] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
107  out[9][0][1] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
108  out[9][0][2] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
109 
110  out[10][0][0] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
111  out[10][0][1] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
112  out[10][0][2] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
113 
114  out[11][0][0] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
115  out[11][0][1] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
116  out[11][0][2] = 4*in[0]*in[1]*(-3+4*in[2]);
117 
118  out[12][0][0] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
119  out[12][0][1] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
120  out[12][0][2] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
121 
122  out[13][0][0] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
123  out[13][0][1] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
124  out[13][0][2] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
125 
126  out[14][0][0] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
127  out[14][0][1] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
128  out[14][0][2] = 4*in[0]*in[1]*(-1+4*in[2]);
129 
130  //faces
131  out[15][0][0] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
132  out[15][0][1] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
133  out[15][0][2] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
134 
135  out[16][0][0] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
136  out[16][0][1] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
137  out[16][0][2] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
138 
139  out[17][0][0] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
140  out[17][0][1] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
141  out[17][0][2] = 4*in[0]*in[1]*(4-8*in[2]);
142 
143  }
146  unsigned int order() const
147  {
148  return 2;
149  }
150 
151  };
152 }
153 #endif
unsigned int size() const
number of shape functions
Definition: hierarchicalprismp2localbasis.hh:25
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 3 > > Traits
export type traits for function signature
Definition: hierarchicalprismp2localbasis.hh:22
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:39
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalprismp2localbasis.hh:63
unsigned int order() const
Polynomial order of the shape functions.
Definition: hierarchicalprismp2localbasis.hh:146
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalprismp2localbasis.hh:31
Definition: hierarchicalprismp2localbasis.hh:18
D DomainType
domain type
Definition: localbasis.hh:51