dune-localfunctions 3.0-git
raviartthomas02dlocalbasis.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_RT0TRIANGLELOCALBASIS_HH
4#define DUNE_RT0TRIANGLELOCALBASIS_HH
5
6#include <numeric>
7
8#include <dune/common/fmatrix.hh>
9
11
12namespace Dune
13{
22 template<class D, class R>
24 {
25 public:
26 typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
27 Dune::FieldMatrix<R,2,2> > Traits;
28
31 {
32 sign0 = sign1 = sign2 = 1.0;
33 }
34
36 RT02DLocalBasis (unsigned int s)
37 {
38 sign0 = sign1 = sign2 = 1.0;
39 if (s&1) sign0 = -1.0;
40 if (s&2) sign1 = -1.0;
41 if (s&4) sign2 = -1.0;
42 }
43
45 unsigned int size () const
46 {
47 return 3;
48 }
49
51 inline void evaluateFunction (const typename Traits::DomainType& in,
52 std::vector<typename Traits::RangeType>& out) const
53 {
54 out.resize(3);
55 out[0][0] = sign0*in[0]; out[0][1]=sign0*(in[1]-D(1));
56 out[1][0] = sign1*(in[0]-D(1)); out[1][1]=sign1*in[1];
57 out[2][0] = sign2*in[0]; out[2][1]=sign2*in[1];
58 }
59
61 inline void
62 evaluateJacobian (const typename Traits::DomainType& in, // position
63 std::vector<typename Traits::JacobianType>& out) const // return value
64 {
65 out.resize(3);
66 out[0][0][0] = sign0; out[0][0][1] = 0;
67 out[0][1][0] = 0; out[0][1][1] = sign0;
68 out[1][0][0] = sign1; out[1][0][1] = 0;
69 out[1][1][0] = 0; out[1][1][1] = sign1;
70 out[2][0][0] = sign2; out[2][0][1] = 0;
71 out[2][1][0] = 0; out[2][1][1] = sign2;
72 }
73
75 void partial (const std::array<unsigned int, 2>& order,
76 const typename Traits::DomainType& in, // position
77 std::vector<typename Traits::RangeType>& out) const // return value
78 {
79 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
80 if (totalOrder == 0) {
81 evaluateFunction(in, out);
82 } else if (totalOrder == 1) {
83 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
84 out.resize(size());
85
86 out[0][direction] = sign0;
87 out[0][1-direction] = 0;
88 out[1][direction] = sign1;
89 out[1][1-direction] = 0;
90 out[2][direction] = sign2;
91 out[2][1-direction] = 0;
92 } else {
93 out.resize(size());
94 for (std::size_t i = 0; i < size(); ++i)
95 for (std::size_t j = 0; j < 2; ++j)
96 out[i][j] = 0;
97 }
98
99 }
100
102 unsigned int order () const
103 {
104 return 1;
105 }
106
107 private:
108 R sign0, sign1, sign2;
109 };
110}
111#endif
Definition brezzidouglasmarini1cube2d.hh:14
Type traits for LocalBasisVirtualInterface.
Definition localbasis.hh:38
D DomainType
domain type
Definition localbasis.hh:49
Lowest order Raviart-Thomas shape functions on the reference triangle.
Definition raviartthomas02dlocalbasis.hh:24
unsigned int order() const
Polynomial order of the shape functions.
Definition raviartthomas02dlocalbasis.hh:102
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition raviartthomas02dlocalbasis.hh:62
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 2, Dune::FieldVector< R, 2 >, Dune::FieldMatrix< R, 2, 2 > > Traits
Definition raviartthomas02dlocalbasis.hh:27
RT02DLocalBasis(unsigned int s)
Make set numer s, where 0<=s<8.
Definition raviartthomas02dlocalbasis.hh:36
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition raviartthomas02dlocalbasis.hh:51
unsigned int size() const
number of shape functions
Definition raviartthomas02dlocalbasis.hh:45
RT02DLocalBasis()
Standard constructor.
Definition raviartthomas02dlocalbasis.hh:30
void partial(const std::array< unsigned int, 2 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition raviartthomas02dlocalbasis.hh:75