3 #ifndef DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
4 #define DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
10 #include <dune/common/fvector.hh>
11 #include <dune/common/fmatrix.hh>
17 template<
class D,
class R>
22 typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,3> >
Traits;
32 std::vector<typename Traits::RangeType> & out)
const
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]);
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]);
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]);
64 std::vector<typename Traits::JacobianType>& out)
const
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;
73 out[1][0][0] = 1-in[2];
78 out[2][0][1] = 1-in[2];
79 out[2][0][2] = -in[1];
81 out[3][0][0] = -in[2];
82 out[3][0][1] = -in[2];
83 out[3][0][2] = 1-in[0]-in[1];
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]);
98 out[7][0][0] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
100 out[7][0][2] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
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]);
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]);
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]);
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]);
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]);
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]);
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]);
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]);
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]);
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]);
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
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalprismp2localbasis.hh:31
unsigned int order() const
Polynomial order of the shape functions.
Definition: hierarchicalprismp2localbasis.hh:146
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
Definition: hierarchicalprismp2localbasis.hh:18
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:14
D DomainType
domain type
Definition: localbasis.hh:49
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalprismp2localbasis.hh:63